Low-Angle Radar Land Clutter

Low-Angle Radar Land Clutter Measurements and Empirical Models J. Barrie Billingsley Lincoln Laboratory Massachusetts Institute of Technology

William Andrew Publishing

Published in the United States of America by William Andrew Publishing / Noyes Publishing 13 Eaton Avenue Norwich, NY 13815 www.williamandrew.com President and CEO: William Woishnis Sponsoring Editor: Dudley R. Kay – SciTech Publishing, Inc. Production Manager: Kathy Breed Production services provided by TIPS Technical Publishing, Carrboro, North Carolina Copyeditor: Howard Jones Book Design: Robert Kern Compositor: Lynanne Fowle Proofreaders: Maria Mauriello, Jeff Eckert Printed in the United States

10 9 8 7 6 5 4 3 2 1 Copyright © 2002 by William Andrew Publishing, Inc. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without permission in writing from the Publisher.

SciTech is a partner with William Andrew for high-quality radar and aerospace books. See www.scitechpub.com for information. Library of Congress Cataloging-in-Publication Data Billingsley, J. Barrie. Low angle radar land clutter : measurements and empirical models / J. Barrie Billingsley. p. cm. Includes index. ISBN 1-891121-16-2 (alk. paper) 1. Radar—Interference. I. Title TK6580 .B45 2001 621.3848—dc21 2001034284 This book is co-published and distributed in the UK and Europe by: The Institution of Electrical Engineers Michael Faraday House Six Hills Way, Stevenage, SGI 2AY, UK Phone: +44 (0) 1438 313311 Fax: +44 (0) 1438 313465 Email: [email protected] www.iee.org.uk/publish IEE ISBN: 0-85296-230-4

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To my wife Mary, and to our children Jennifer, Michael, and Thomas, and grandchildren Andrew and Sylvia

Foreword MIT Lincoln Laboratory was founded in 1951 to develop a strategic air-defense system for the United States. The Laboratory engineers of that era quickly found that ground clutter greatly limited the performance of their radars. Consequently, they pioneered the development of Doppler processing techniques and later digital processing techniques to mitigate the effects of ground clutter. The Laboratory returned to the problem of air defense in the late 1970s with a major program to assess and ensure the survivability of U.S. cruise missiles. Once again ground clutter proved an important issue because a lowflying, low-observable cruise missile could hide in ground clutter and escape radar detection. The new challenge was to confidently predict low-grazing angle ground clutter for any number of specific sites with widely varying topographies. But the understanding of clutter phenomena at this time certainly did not permit these predictions. Therefore, with the early support of the Defense Advanced Research Projects Agency and later with the support of the United States Air Force, the Laboratory set out to make a major improvement in our understanding of ground clutter as seen by ground radars. Barrie Billingsley was the principal researcher at the start and I was the director of the overall Laboratory program. I recall telling Barrie to archive his data, document his experiments, calibrate his radars, and collect ground truth on his many test sites so that he could write the definitive textbook on low grazing angle ground clutter when our program was finished. I would say that Barrie has delivered magnificently on this challenge. I am delighted to see over 300 directly applicable charts characterizing ground clutter backscatter in this book. I confess that I had expected this book to appear about 10 years after the start, not 20 years. The long gestation period reflects the enormous technical problem of capturing what really happens at low grazing angles and the fact that Barrie Billingsley is an extremely meticulous and persistent researcher. He did stretch the patience of successive Lincoln Laboratory program managers, but he pulled it off by teasing us each year with additional insights into these complex clutter phenomena. We greatly admired his research abilities and his dedication to the task of unfolding the mystery of low grazing angle ground clutter. We had heard the violins and the horns and the woodwinds before, but now we could understand the whole orchestration—how frequency, terrain, propagation, resolution, and polarization all operated together to produce the complex result we had witnessed but did not understand. My congratulations to Barrie for this grand accomplishment—a book that will serve engineers and scientists for many years to come. My congratulations also to his collaborators and the long sequence of Lincoln Laboratory program managers who supported Barrie in this most important endeavor. My thanks to the Defense Advanced Research Projects Agency and United States Air Force for their enlightened support and management of this program. It is not very often in the defense research business that we get to complete and beautifully wrap a wonderful piece of scientific research. Enjoy! — William P. Delaney Pine Island, Meredith, New Hampshire November 2001

Preface Radar land clutter constitutes the unwanted radar echoes returned from the earth’s surface that compete against and interfere with the desired echoes returned from targets of interest, such as aircraft or other moving or stationary objects. To be able to knowledgeably design and predict the performance of radars operating to provide surveillance of airspace, detection and tracking of targets, and other functions in land clutter backgrounds out to the radar horizon, radar engineers require accurate descriptions of the strengths of the land clutter returns and their statistical attributes as they vary from pulse to pulse and cell to cell. The problem of bringing statistical order and predictability to land clutter is particularly onerous at the low angles (at or near grazing incidence) at which surface-sited radars illuminate the clutter-producing terrain, where the fundamental difficulty arising from the essentially infinite variability of composite terrain is exacerbated by such effects as specularity against discrete clutter sources and intermittent shadowing. Thus, predicting the effects of low-angle land clutter in surface radar was for many years a major unsolved problem in radar technology. Based on the results of a 20-year program of measuring and investigating low-angle land clutter carried out at Lincoln Laboratory, Massachusetts Institute of Technology, this book advances the state of understanding so as to “solve the low-angle clutter problem” in many important respects. The book thoroughly documents all important results of the Lincoln Laboratory clutter program. These results enable the user to predict land clutter effects in surface radar. This book is comprehensive in addressing the specific topic of low-angle land clutter phenomenology. It contains many interrelated results, each important in its own right, and unifies and integrates them so as to add up to a work of significant technological innovation and consequence. Mean clutter strength is specified for most important terrain types (e.g., forest, farmland, mountains, desert, urban, etc.). Information is also provided specifying the statistical distributions of clutter strength, necessary for determining probabilities of detection and false alarm against targets in clutter backgrounds. The totality of clutter modeling information so presented is parameterized, not only by the type of terrain giving rise to the clutter returns, but also (and importantly) by the angle at which the radar illuminates the ground and by such important radar parameters as carrier frequency, spatial resolution, and polarization. This information is put forward in terms of empirical clutter models. These include a Weibull statistical model for prediction of clutter strength and an exponential model for the prediction of clutter Doppler spreading due to wind-induced intrinsic clutter motion. Also included are analyses and results indicating, given the strength and spreading of clutter, to what extent various techniques of clutter cancellation can reduce the effects of clutter on target detection performance. The empirically-derived clutter modeling information thus provided in this book utilizes easy-to-understand formats and easy-to-implement models. Each of the six chapters is essentially self-contained, although reading them consecutively provides an iterative pedagogical approach that allows the ideas underlying the finalized modeling information of Chapters 5 and 6 to be fully explored. No difficult mathematics exist to prevent easy

xvi Preface

assimilation of the subject matter of each chapter by the reader. The technical writing style is formal and dedicated to maximizing clarity and conciseness of presentation. Meticulous attention is paid to accuracy, consistency, and correctness of results. No further prerequisite requirements are necessary beyond the normal knowledge base of the working radar engineer (or student) to access the information of this book. A fortuitous combination of national political, technological, and economic circumstances occurring in the late 1970s and early 1980s allowed the Lincoln Laboratory land clutter measurement project to be implemented and thereafter continued in studies and analysis over a 20-year period. It is highly unlikely that another program of the scope of the Lincoln Laboratory clutter program will take place in the foreseeable future. Future clutter measurement programs are expected to build on or extend the information of this book in defined specific directions, rather than supersede this information. Thus this book is expected to be of long-lasting significance and to be a definitive work and standard reference on the subject of land clutter phenomenology. A number of individuals and organizations provided significant contributions to the Phase Zero/Phase One land clutter measurements and modeling program at Lincoln Laboratory and consequently towards bringing this book into existence and affecting its final form and contents. This program commenced at Lincoln Laboratory in 1978 under sponsorship from the Defense Advanced Research Projects Agency. The United States Air Force began joint sponsorship several years into the program and subsequently assumed full sponsorship over the longer period of its complete duration. The program was originally conceived by Mr. William P. Delaney of Lincoln Laboratory, and largely came into focus in a short 1977 DARPA/USAF-sponsored summer study requested by the Department of Defense and directed by Mr. Delaney. The Phase Zero/Phase One program was first managed at Lincoln Laboratory by Mr. Carl E. Nielsen Jr. and by Dr. David L. Briggs, and subsequently by Dr. Lewis A. Thurman and Dr. Curtis W. Davis III. Early site selection studies for the Phase Zero/Phase One program indicated the desirability of focusing measurements in terrain of relatively low relief and at northern latitudes such as generally occurs in the prairie provinces of western Canada. As a result, a Memorandum of Understanding (MOU) was established between the United States and Canada implementing a joint clutter measurements program in which Canada, through Defence Research Establishment Ottawa, was to provide logistics support and share in the measured data and results. Dr. Hing C. Chan was the principal investigator of the clutter data at DREO. Dr. Chan became a close and valued member of the Phase One community; many useful discussions and interactions concerning the measured clutter data and its analysis occurred between Dr. Chan and the author down to the time of present writing. Substantial contracted data analysis support activity was provided to Dr. Chan by AIT Corporation, Ottawa. Information descriptive of the terrain at the clutter measurement sites was provided in a succession of contracted studies at Intera Information Technologies Ltd., Calgary. The government of the United Kingdom through its Defence Evaluation Research Agency became interested in the Lincoln Laboratory clutter program shortly after its commencement. DERA subsequently became involved in the analysis of Phase One clutter data under the aegis of The Technical Cooperation Program (TTCP), an international defense science technical information exchange program. The U.S./Canada MOU was terminated at the completion of measurements, and the sharing of the measurement data and its analysis was thereafter continued between all three countries under TTCP.

Preface xvii

Significant analyses of selected subsets of the Phase One measurement data occurred with DERA sponsorship in the U.K. at Smith Associates Limited and at GEC Marconi Research Centre. The principal coordinator of these interactions at DERA was Mr. Robert A. Blinston. Mr. John N. Entzminger Jr., former Director of the Tactical Technology Office at DARPA, provided much encouragement to these joint U.S./Canada/U.K. clutter study interactions in his role as head of the U.S. delegation to Subgroup K (radar) in TTCP. In its early years, the Lincoln Laboratory clutter program was followed by Mr. David K. Barton, then of Raytheon Company, now of ANRO Engineering, who stimulated our thinking with his insights on the interrelationships of clutter and propagation and discussions on approaches to clutter modeling. Also in the early years of the clutter program, several interactions with Mr. William L. Simkins of the Air Force Research Laboratory, Rome, N.Y., influenced methodology to develop correctly at Lincoln Laboratory in such matters as clutter data reduction and intrinsic-motion clutter spectral modeling. In the latter years of the Phase One program, Professor Alfonso Farina of Alenia Marconi Systems, Italy, became interested in the clutter data. An informal collaboration was organized by Professor Farina in which some particular Phase One clutter data sets were provided to and studied by him and his colleagues at the University of Pisa and University of Rome. These studies were from the point of view of signal processing and target detectability in ground clutter backgrounds. A number of jointly-authored technical journal papers in the scientific literature resulted. The five-frequency Phase One clutter measurement equipment was fabricated by the General Electric Co., Syracuse, N.Y. (now part of Lockheed Martin Corporation). Key members of the Phase One measurements crew were Harry Dence and Joe Miller of GE, Captain Ken Lockhart of the Canadian Forces, and Jerry Anderson of Intera. At Lincoln Laboratory, the principal people involved in the management and technical interface with GE were David Kettner and John Hartt. The project engineer of the precursor X-band Phase Zero clutter program was Ovide Fortier. People who had significant involvement in data reduction and computer programming activities include Gerry McCaffrey, Paul Crochetiere, Ken Gregson, Peter Briggs, Bill Dustin, Bob Graham-Munn, Carol Bernhard, Kim Jones, Charlotte Schell, Louise Moss, and Sharon Kelsey. Dr. Seichoong Chang served in an important consultant role in overseeing the accurate calibration of the clutter data. Many informative discussions with Dr. Serpil Ayasli helped provide understanding of the significant effects of electromagnetic propagation in the clutter data. Application of the resultant clutter models in radar system studies took place under the jurisdiction of Dr. John Eidson. The original idea that the results of the Lincoln Laboratory clutter program could be the basis of a clutter reference book valuable to the radar community at large came from Mr. Delaney. Dr. Merrill I. Skolnik, former Superintendent of the Radar Division at the Naval Research Laboratory in Washington, D.C., lent his support to this book idea and provided encouragement to the author in his efforts to follow through with it. When a first rough draft of Chapter 1 of the proposed book became available, Dr. Skolnik kindly read it and provided a number of constructive suggestions. Throughout the duration of the clutter book project, Dr. Thurman was a never-failing source of positive managerial support and insightful counsel to the author on how best to carry the book project forward. Mr. C.E. Muehe provided a thorough critical review of the original report material upon which much of Chapter 6 is based. Dr. William E. Keicher followed the book project in its later stages and provided a technical review of the entire book manuscript. Skillful typing of the

xviii Preface

original manuscript of this book was patiently and cheerfully performed through its many iterations by Gail Kirkwood. Pat DeCuir typed many of the original technical reports upon which the book is largely based. Members of the Lincoln Laboratory Publications group maintained an always positive and most helpful approach in transforming the original rough manuscript into highly finished form. These people in particular include Deborah Goodwin, Jennifer Weis, Dorothy Ryan, and Katherine Shackelford. Dudley R. Kay, president of SciTech Publishing and vice-president at William Andrew Publishing, and the book’s compositors, Lynanne Fowle and Robert Kern at TIPS Technical Publishing, ably and proficiently met the many challenges in successfully seeing the book to press. It is a particular pleasure for the author to acknowledge the dedicated and invaluable assistance provided by Mr. John F. Larrabee (Lockheed Martin Corporation) in the day-today management, reduction, and analyses of the clutter data at Lincoln Laboratory over the full duration of the project. In the latter days of the clutter project involving the production of this book, Mr. Larrabee managed the interface to the Lincoln Laboratory Publications group and provided meticulous attention to detail in the many necessary iterations required in preparing all the figures and tables of the book. Mr. Larrabee recently retired after a long professional career in contracted employment at Lincoln Laboratory, at about the time the book manuscript was being delivered to the publisher. Many others contributed to the land clutter project at Lincoln Laboratory. Lack of explicit mention here does not mean that the author is not fully aware of the value of each contribution or lessen the debt of gratitude owed to everyone involved in acquiring, reducing, and analyzing the clutter data. Although this book was written at Lincoln Laboratory, Massachusetts Institute of Technology, under the sponsorship of DARPA and the USAF, the opinions, recommendations, and conclusions of the book are those of the author and are not necessarily endorsed by the sponsoring agencies. Permissions received from the Institute of Electrical and Electronics Engineers, Inc., the Institution of Electrical Engineers (U.K.), and The McGraw-Hill Companies to make use of copyrighted materials are gratefully acknowledged. Any errors or shortcomings that remain in the material of the book are entirely the responsibility of the author. The author sincerely hopes that every reader of this book is able to find helpful information within its pages. — J. Barrie Billingsley Lexington, Massachusetts October 2001

Contents Foreword Preface

xiii xv

Chapter 1 Overview 1.1 Introduction 1.2 Historical Review 1.2.1 Constant σ ° 1.2.2 Wide Clutter Amplitude Distributions 1.2.3 Spatial Inhomogeneity/Resolution Dependence 1.2.4 Discrete Clutter Sources 1.2.5 Illumination Angle 1.2.6 Range Dependence 1.2.7 Status 1.3 Clutter Measurements at Lincoln Laboratory 1.4 Clutter Prediction at Lincoln Laboratory 1.4.1 Empirical Approach 1.4.2 Deterministic Patchiness 1.4.3 Statistical Clutter 1.4.4 One-Component σ ° Model 1.4.5 Depression Angle 1.4.6 Decoupling of Radar Frequency and Resolution 1.4.7 Radar Noise Corruption 1.5 Scope of Book 1.5.1 Overview 1.5.2 Two Basic Trends 1.5.3 Measurement-System-Independent Clutter Strength 1.5.4 Propagation 1.5.5 Statistical Issues 1.5.6 Simpler Models 1.5.7 Parameter Ranges 1.6 Organization of Book References

1 1 3 4 5 6 8 9 11 13 13 16 17 18 18 18 19 20 21 23 23 24 24 24 25 26 26 27 30

Chapter 2 Preliminary X-Band Clutter Measurements 35 2.1 Introduction 2.1.1 Outline 2.2 Phase Zero Clutter Measurements 2.2.1 Radar Instrumentation 2.2.2 Measurement Sites 2.2.3 Terrain Description

35 35 36 36 37 37

viii Contents

2.3 The Nature of Low-Angle Clutter 2.3.1 Clutter Physics I 2.3.2 Measured Land Clutter Maps 2.3.3 Clutter Patches 2.3.4 Depression Angle 2.3.5 Terrain Slope/Grazing Angle 2.3.6 Clutter Modeling 2.4 X-Band Clutter Spatial Amplitude Statistics 2.4.1 Amplitude Distributions by Depression Angle for Three General Terrain Types 2.4.2 Clutter Results for More Specific Terrain Types 2.4.3 Combining Strategies 2.4.4 Depression Angle Characteristics 2.4.5 Effect of Radar Spatial Resolution 2.4.6 Seasonal Effects 2.5 Summary References Appendix 2.A Phase Zero Radar Appendix 2.B Formulation of Clutter Statistics Reference Appendix 2.C Depression Angle Computation Reference

42 42 44 46 55 62 65 68 68 77 96 101 110 111 115 116 118 126 138 139 141

Chapter 3 Repeat Sector Clutter Measurements

143

3.1 Introduction 3.1.1 Outline 3.2 Multifrequency Clutter Measurements 3.2.1 Equipment and Schedule 3.2.2 Data Collection 3.2.3 Terrain Description 3.3 Fundamental Effects in Low-Angle Clutter 3.3.1 Clutter Physics II 3.3.2 Trends with Radar Frequency 3.3.3 Depression Angle and Terrain Slope 3.4 Mean Land Clutter Strength vs Frequency by Terrain Type 3.4.1 Detailed Discussion of Measurements 3.4.2 Twelve Multifrequency Clutter Strength Characteristics 3.5 Dependencies of Mean Land Clutter Strength with Radar Parameters 3.5.1 Frequency Dependence 3.5.2 Polarization Dependence 3.5.3 Resolution Dependence 3.6 Higher Moments and Percentiles in Measured Land

143 144 145 146 146 156 160 160 162 165 168 169 204 209 209 212 216

Contents

ix

Clutter Spatial Amplitude Distributions 3.6.1 Ratio of Standard Deviation-to-Mean 3.6.2 Skewness and Kurtosis 3.6.3 Fifty-, 70-, and 90-Percentile Levels 3.7 Effects of Weather and Season 3.7.1 Diurnal Variability 3.7.2 Six Repeated Visits 3.7.3 Temporal and Spatial Variation 3.8 Summary References Appendix 3.A Phase One Radar Appendix 3.B Multipath Propagation References Appendix 3.C Clutter Computations

222 222 227 228 231 234 235 237 242 246 247 259 272 274

Chapter 4 Approaches to Clutter Modeling

285

4.1 Introduction 4.1.1 Modeling Objective 4.1.2 Modeling Rationale 4.1.3 Modeling Scope 4.2 An Interim Angle-Specific Clutter Model 4.2.1 Model Basis 4.2.2 Interim Model 4.2.3 Error Bounds 4.3 Non-Angle-Specific Modeling Considerations 4.3.1 Phase Zero Results 4.3.2 Simple Clutter Model 4.3.3 Further Considerations 4.3.4 Summary 4.4 Terrain Visibility and Clutter Occurrence 4.4.1 Effects of Trees on Visibility at Cold Lake 4.4.2 Decreasing Shadowing with Increasing Site Height 4.4.3 Vertical Objects on Level Terrain at Altona 4.4.4 Summary 4.5 Discrete vs Distributed Clutter 4.5.1 Introduction 4.5.2 Discrete Clutter Sources at Cochrane 4.5.3 Separation of Discrete Source at Suffield 4.5.4 σ vs σ ° Normalization 4.5.5 Conclusions 4.6 Temporal Statistics, Spectra, and Correlation 4.6.1 Temporal Statistics 4.6.2 Spectral Characteristics 4.6.3 Correlative Properties

285 287 288 291 292 292 294 297 299 299 302 305 309 312 312 315 317 319 320 320 324 325 330 333 334 335 335 338

x

Contents

4.7 Summary References Appendix 4.A Clutter Strength vs Range Appendix 4.B Terrain Visibility as a Function of Site Height and Antenna Mast Height Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity Appendix 4.D Separation of Discretes in Clutter Modeling

Chapter 5 Multifrequency Land Clutter Modeling Information 5.1 Introduction 5.1.1 Review 5.2 Derivation of Clutter Modeling Information 5.2.1 Weibull Statistics 5.2.2 Clutter Model Framework 5.2.3 Derivation of Results 5.3 Land Clutter Coefficients for General Terrain 5.3.1 General Mixed Rural Terrain 5.3.2 Further Reduction 5.3.3 Validation of Clutter Model Framework 5.3.4 Simplified Clutter Prediction 5.4 Land Clutter Coefficients for Specific Terrain Types 5.4.1 Urban or Built-Up Terrain 5.4.2 Agricultural Terrain 5.4.3 Forest Terrain 5.4.4 Shrubland Terrain 5.4.5 Grassland Terrain 5.4.6 Wetland Terrain 5.4.7 Desert Terrain 5.4.8 Mountainous Terrain 5.5 PPI Clutter Map Prediction 5.5.1 Model Validation 5.5.2 Model Improvement 5.6 Summary References Appendix 5.A Weibull Statistics References

Chapter 6 Windblown Clutter Spectral Measurements 6.1 Introduction 6.2 Exponential Windblown Clutter Spectral Model 6.2.1 ac Spectral Shape

343 347 350 359 371 396

407 407 408 416 416 418 420 429 429 437 439 440 440 443 492 506 518 521 526 529 537 542 543 543 544 546 548 573

575 575 576 577

Contents

6.2.2 dc/ac Ratio 6.2.3 Model Scope 6.3 Measurement Basis for Clutter Spectral Model 6.3.1 Radar Instrumentation and Data Reduction 6.3.2 Measurements Illustrating ac Spectral Shape 6.3.3 Measured Ratios of dc/ac Spectral Power 6.4 Use of Clutter Spectral Model 6.4.1 Spreading of σ ° in Doppler 6.4.2 Two Regions of Spectral Approximation 6.4.3 Cells in Partially Open or Open Terrain 6.4.4 MTI Improvement Factor 6.5 Impact on MTI and STAP 6.5.1 Introduction 6.5.2 Impact on Performance of Optimum MTI 6.5.3 Impact on STAP Performance 6.5.4 Validation of Exponential Clutter Spectral Model 6.6 Historical Review 6.6.1 Three Analytic Spectral Shapes 6.6.2 Reconciliation of Exponential Shape with Historical Results 6.6.3 Reports of Unusually Long Spectral Tails 6.7 Summary References Index

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579 581 582 582 589 600 604 604 606 609 616 620 620 621 625 635 639 639 659 664 674 677 683

1 Overview 1.1 Introduction The performance of surface-sited radar against low-flying targets has been limited by land clutter since the earliest days of radar. Consider the beam of such a radar scanning over the surrounding terrain and illuminating it at grazing incidence. The amplitudes of the clutter returns received from all the spatially distributed resolution cells within the scan coverage on the ground vary randomly over extremely wide dynamic ranges, as the interrogating pulse encounters the complex variety of surface features and discrete reflecting objects comprising or associated with the terrain. The resultant clutter signal varies in a complex manner with time and space to interfere with and mask the much weaker target signal in the radar receiver. Early ground-based radars of necessity were restricted to operations at relatively long ranges beyond the clutter horizon where terrain was not directly illuminated. The development of Doppler signal processing techniques allowed radars to have capability within clutter regions against larger targets by exploiting the differences in frequency of the signal returned from the rapidly moving target compared to that from the relatively stationary clutter. However, because the clutter signal is often overwhelmingly stronger than the target signal and because of the lack of perfect waveform stability, modern pulsed radars often remain severely limited by land clutter residues against small targets even after clutter cancellation. The need of designers and analysts to accurately predict clutter-limited radar system performance led to many attempts to measure and model land clutter over the decades following World War II [1–13]. The problem was highly challenging, not just because of the variability and wide dynamic range of the clutter at a given site, but also because the overall severity of the clutter and resulting system performance varied dramatically from site to site. Early clutter measurements, although numerous, tended to be low-budget piecepart efforts overly influenced by terrain specificity in each measurement scene. In aggregate these efforts led to inconsistent, contradictory, and incomplete results. Early clutter models tended to be overly general, modeling clutter simply as a constant reflectivity level, or on a spherical but featureless earth, or as a simple function of grazing angle. As a result, they did not incorporate features of terrain specificity that dominated clutter effects at real sites. Thus there was a logical disconnection between models (overly general) and measurements (overly specific), and clutter-limited radar performance remained unpredictable into the decade of the 1970s. By that time it had become widely acknowledged that “there was no generally accepted clutter model available for calculation,” and there was “no accepted approach by which a model could be built up” [8].

2

Overview

The middle and late 1970s also saw an emerging era of low-observable technology in aircraft design and consequent new demands on air defense capabilities in which liabilities imposed by the lack of predictability of clutter-limited surface radar performance were much heightened. As a result, a significant new activity was established at Lincoln Laboratory in 1978 to advance the scientific understandings of air defense. An important initial element of this activity was the requirement to develop an accurate full-scale clutter simulation capability that would breach the previous impasse. The goal was to make clutter modeling a proper engineering endeavor typified by quantitative comparison of theory with measurement, and so allow confident prediction of clutter-limited performance of groundsited radar. It was believed on the basis of the historical evidence that a successful approach would have to be strongly empirical. To this end, a major new program of land clutter measurements was initiated at Lincoln Laboratory [14–18]. To solve the land clutter modeling problem, it was understood that the new measurements program would have to substantially raise the ante in terms of level of effort and new approaches compared with those undertaken in the past. Underlying the key aspect of variability in the low-angle clutter phenomenon was the obvious fact that landscape itself was essentially infinitely variable—every clutter measurement scenario was different. Rather than seek the general in any individual measurement, underlying trends among aggregates of similar measurements would be sought. In ensuing years, a large volume of coherent multifrequency land clutter measurement data was acquired (using dedicated new measurement instrumentation) from many sites widely distributed geographically over the North American continent [14]. A new site-specific approach was adopted in model development, based on the use of digitized terrain elevation data (DTED) to distinguish between visible and masked regions to the radar, which represented an important advance over earlier featureless or sandpaper-earth (i.e., statistically rough) constructs [15]. Extensive analysis of the new clutter measurements database led to a progression of increasingly accurate statistical clutter models for specifying the clutter in visible regions of clutter occurrence. A key requirement in the development of the statistical models was that only parametric trends directly observable in the measurement data would be employed; any postulated dependencies that could not be demonstrated to be statistically significant were discarded. As a result, a number of earlier insights into low-angle clutter phenomenology were often understood in a new light and employed in a different manner or at a different scale so as to reconcile with what was actually observed in the data. In addition, significant new advances in understanding lowangle clutter occurred that, when incorporated properly with the modified earlier insights, led to a unified statistical approach for modeling low-angle clutter in which all important trends observable in the data were reproducible. An empirically-based statistical clutter modeling capability now exists at Lincoln Laboratory. Clutter-limited performance of surface-sited radar in benign or difficult environments is routinely and accurately predicted. Time histories of the signal-to-clutter ratios existing in particular radars as they work against particular targets at particular sites are computed and closely compared to measurements. Systems computations involving tens or hundreds of netted radars are performed in which the ground clutter1 at each site is predicted separately and specifically. Little incentive remains at Lincoln Laboratory to develop generic non-site-specific approaches to clutter modeling for the benefit of saving

Overview

3

computer time, because the results of generic models lack specific realism and, as a result, are difficult to validate. This book provides a thorough summary and review of the results obtained in the clutter measurements and modeling program at Lincoln Laboratory over a 20-year period. The book covers (1) prediction of clutter strength (Weibull statistical model2), (2) clutter spreading in Doppler (exponential model), and (3) given the strength and spreading of clutter, the extent to which various techniques of clutter cancellation (e.g., simple delayline cancellation vs coherent signal processing) can reduce the effects of clutter on target detection performance.

1.2 Historical Review Although most surface-sited radars partially suppress land clutter interference from surrounding terrain to provide some capability in cluttered spatial regions, the design of clutter cancellers requires knowledge of the statistical properties of the clutter, and the clutter residues remaining after cancellation can still strongly limit radar performance (see Chapter 6, Sections 6.4.4 and 6.5). Because of this importance of land clutter to the operations of surface radar, there were very many early attempts [1–9] to measure and characterize the phenomenon and bring it into analytic predictability. A literature review of the subject of low-angle land clutter as the Lincoln Laboratory clutter measurement program commenced found over 100 different preceding measurement programs and over 300 different reports and journal articles on the subject. There exist many excellent sources of review [19–25] of these early efforts and preceding literature. These reviews without exception agree on the difficulty of generally characterizing low-angle land clutter. The difficulty arises largely because of the complexity and variability of land-surface form and the elements of land cover that exist at a scale of radar wavelength (typically, from a few meters to a few centimeters or less) over the hundreds or thousands of square kilometers of composite terrain that are usually under radar coverage at a typical radar site. As a result, the earlier efforts [1–9] to understand low-angle land clutter revealed that it was a highly non-Gaussian (i.e., non-noise-like), multifaceted, relatively intractable, statistical random process of which the most salient attribute was variability. The variability existed at whatever level the phenomenon was observed—pulse-to-pulse, cellto-cell, or site-to-site. Other important attributes of the low-angle clutter phenomenon included: patchiness in spatial occurrence [3–5]; lack of homogeneity and domination by point-like or spatially discrete sources within spatial patches [6–8]; and extremely widely-skewed distributions of clutter amplitudes over spatial patches often covering six orders of magnitude or more [1, 2, 4, 9]. Early efforts to capture these attributes and dependencies in simple clutter models 1.

2.

This book uses the terms “land clutter” and “ground clutter” interchangeably to refer to the same phenomenon. The adjective “land” is more global in reach and distinguishes land clutter from other, generically different types of clutter such as sea clutter or weather clutter. The adjective “ground” is often used when the subject focus is only on ground clutter, and more localized circumstances need to be distinguished, for example, the differences in ground clutter from one site to another, or from one area or type of ground to another. Weibull statistics are used as approximations only—not rigorous fits—to measured clutter spatial amplitude distributions. See Chapter 2, Section 2.4.1.1; Chapter 5, Section 5.2.1 and Appendix 5.A.

4

Overview

based only on range or illumination angle to the clutter cell were largely unsuccessful in being able to predict radar system performance. Figure 1.1 shows a measured planposition-indicator (PPI) clutter map that illustrates to 24-km range at a western prairie site the spatial complexity and variability of low-angle land clutter. The fact that the clutter does not occur uniformly but is spatially patchy over the region of surveillance is evident in this measurement, as is the granularity or discrete-like nature of the clutter such that it often occurs in spatially isolated cells over regions where it does occur. N

E

W

S

Figure 1.1 Measured X-band ground clutter map; Orion, Alberta. Maximum range = 24 km. Cells with discernible clutter are shown white. A large clutter patch (i.e., macroregion) to the SSW is also shown outlined in white.

Although the earlier efforts and preceding literature did not lead to a satisfactory clutter model, they did in total gradually develop a number of useful insights into the complexity of the land clutter phenomenon. Section 1.2 provides a summary of what these insights were, and the general approaches extant for attempting to bring the important observables of low-angle clutter under predictive constructs, as the Lincoln Laboratory program commenced.

1.2.1 Constant σ ° Initially, land clutter was conceptualized (unlike Figure 1.1) as arising from a spatially homogeneous surface surrounding the radar site, of uniform roughness (like sandpaper) at a

Overview

5

scale of radar wavelength to account for clutter backscatter. The backscatter reflectivity of this surface was characterized as being a surface-area density function, that is, by a clutter coefficient σ ° defined [20] to be the radar cross section (RCS) of the clutter signal returned per unit terrain surface-area within the radar spatial resolution cell (see Section 2.3.1.1). This characterization implies a power-additive random process, in which each resolution cell contains many elemental clutter scatterers of random amplitude and uniformly distributed phase, such that the central limit theorem applies and the resultant clutter signal is Rayleigh-distributed in amplitude (like thermal noise). As conceptualized in this simple manner, land clutter merely acts to uniformly raise the noise level in the receiver, the higher noise level being directly determined by σ °. A selected set of careful measurements of σ ° compiled in tables or handbooks for various combinations of terrain type (forest, farmland, etc.) and radar parameter (frequency, polarization) would allow radar system engineers to straightforwardly calculate signal-toclutter ratios and estimate target detection statistics and other performance measures on the basis of clutter statistics being like those of thermal noise, but stronger. Early radar system engineering textbooks promoted this view. However, this approach led to frustration in practice. Tabularization of σ ° into generally accepted, universal values proved elusive. Every measurement scenario seemed overly specific. Resulting matrices of σ ° numbers compiled from different investigators using different measurement instrumentation operating at different landscape scales (e.g., long-range scanning surveillance radar vs short-range small-spot-size experiments) and employing different data reduction procedures were erratic and incomplete, with little evidence of consistency, general trend, or connective tissue.

1.2.2 Wide Clutter Amplitude Distributions Clutter measurements that involved accumulating σ ° returns by scanning over a spatially continuous neighborhood of generally similar terrain (i.e., clutter patch) found that the resulting clutter spatial amplitude distributions were of extreme, highly skewed shapes very much wider than Rayleigh [2, 4, 9]. Unlike the narrow fixed-shape Rayleigh distribution with its tight mean-to-median ratio of only 1.6 dB, the measured broad distributions were of highly variable shapes with mean-to-median ratios as high as 15 or even 30 dB. Figure 1.2 shows five measured clutter histograms from typical clutter patches such as that shown in Figure 1.1, illustrating the wide variability in shape and broad spread that occurs in such data. Thus in the important aspect of its amplitude distribution, low-angle land clutter was decidedly non-noise-like. This fact was at best only awkwardly reconcilable with the constant-σ ° clutter model. The accompanying shapes of clutter distributions as well as their mean σ ° levels required specification against radar and environmental parameters, compounding the difficulties of compilation. As a result of both sea and land clutter measured distributions being wider than Rayleigh, an extensive literature came into being that addressed radar detection statistics in non-Rayleigh clutter backgrounds of wide spread typically characterizable as lognormal, Weibull, or K-distributed [26–31]. However, the need continued for a single-point constant-σ ° clutter model to provide an average indication of signal-to-clutter ratio which left the user with the nebulous question of what single value of σ ° (e.g., mean, median, mode, etc.) to use to best characterize the wide underlying distributions. Some investigators used the mean, others used the median, and it was not always clear what was being used since it did not make much difference under Rayleigh statistics and the question of underlying distribution was not always raised.

6

Overview

5070 90 99

Percent

10

Percentiles (dotted)

Mean (dashed)

(a) Mountains L-Band

5

0 −90 −80

−70 −60 −50 −40 −30 −20

−10 0

Percent

5

(b) Forest UHF

Percent

0 −90 −80

−70 −60 −50 −40 −30 −20 −10

0

3

(c) Farmland X-Band 0 −90 −80

−70 −60 −50 −40 −30 −20 −10

0

Percent

5

0 −90 −80

(d) Shrubland and Grassland VHF −70 −60 −50 −40 −30 −20 −10

0

Percent

4

(e) Wetland S-Band 0 −90 −80

−70 −60 −50 −40 −30 −20 −10

0

σ°F4(dB)

Figure 1.2 Histograms of measured clutter strength σ °F4 from five different clutter patches showing wide variability in shape and broad spread. σ ° = clutter coefficient (see Section 2.3.1.1); F = pattern propagation factor (see Section 1.5.4). Black values are receiver noise.

1.2.3 Spatial Inhomogeneity/Resolution Dependence The definition of σ ° as an area-density function implies spatial homogeneity of land clutter. The underlying necessary condition for the area-density concept to be valid is that

Overview

7

the mean value of σ ° be independent of the particular cell size or resolution utilized in a given clutter spatial field.3 As mentioned, it was additionally presumed that much the same invariant value of σ ° (tight Rayleigh variations) would exist among the individual spatial samples of σ ° independent of cell size. Early low-resolution radars showed land clutter generally surrounding the site and extending in range to the clutter horizon in an approximately area-extensive manner. Measurements at higher resolution with narrower beams and shorter pulses showed that clutter was not present everywhere as from a featureless sandpaper surface, but that resolved clutter typically occurred in patches or spatial regions of strong returns separated by regions of low returns near or at the radar noise floor [4]—see Figure 1.1. Thus, clutter was highly non-noise-like not only in its non-Rayleigh amplitude statistics, but also in its lack of spatial homogeneity. Highresolution radars took advantage of the spatial non-homogeneity of clutter by providing some operational capability known as interclutter visibility in relatively clear regions between clutter patches [23]. Within clutter patches, clutter is not uniformly distributed. The individual spatial samples of σ °, as opposed to their mean, depend strongly upon resolution cell size. Thus the shapes of the broad amplitude distributions of σ ° are highly dependent on resolution—increasing resolution results in less averaging within cells, more cell-to-cell variability, and increasing spread in values of σ °. In contrast, the fixed shape of a Rayleigh distribution describing simple homogeneous clutter is invariant with resolution. Significant early work was conducted into establishing necessary and sufficient conditions (e.g., number of scatterers and their relative amplitudes) in order for Rayleigh/Ricean statistics to prevail in temporal variations from individual cells, but the associated idea of how cell size affects shapes of spatial amplitude distributions from many individual cells was less a subject of investigation. One early study got so far as to document an observed trend of increasing spread in clutter spatial amplitude distributions with increasing radar resolution [8], but this fundamentally important observation into the nature of low-angle clutter4 was not generally followed up on or worked into empirical clutter models. Figure 1.3 shows how the Weibull shape parameter aw (see Section 2.4.1.1), which controls the extent of spread in histograms such as those of Figure 1.2, varies strongly with radar spatial resolution in low-relief farmland viewed at low depression angle. These and many other such results for various terrain types and viewing angles are presented and explained in Chapter 5. These two key attributes of low-angle clutter—patchiness and lack of uniformity in spatial extent (Figure 1.1), and extreme resolution-dependent cell-to-cell variability in clutter amplitudes within spatial patches of occurrence (Figures 1.2 and 1.3)—do not constitute extraneous complexity to be avoided in formulating simple clutter models aimed at

3.

4.

By “clutter spatial field” is meant a region of [land surface] space characterized by a physical property [clutter strength] having a determinable value at every point [resolution cell] in the region; see American Heritage Dictionary of the English Language, 3rd ed. This book uses the phrase “clutter spatial field” or “clutter field” as so defined to bring to mind when it is a spatially-distributed ensemble of backscattering clutter resolution cells that is of primary interest. The word “clutter” by itself can be vague (e.g., clutter signal vs clutter source; spatial vs temporal vs Doppler distribution), so that its use alone can bring different images to mind for different readers. Use of the phrase “clutter field” in this book does not refer to the strength of the propagating electromagnetic wave constituting the clutter return signal. That is, the effect of resolution on the spatial as opposed to the temporal statistics of clutter.

8

Overview

6 Low-Relief Farmland 0° ≤ Dep Ang < 0.25°

Weibull Shape Parameter aw

5

4

3

2

VHF UHF L-Band S-Band X-Band Regression Line

1

2

10

3

10

4

10

5

10

6

10

7

10

Resolution Cell Area A (m2)

Figure 1.3 Weibull shape parameter aw vs resolution cell area A for low-relief farmland viewed at low depression angle. Plot symbols are defined in Chapter 5. These data show a rapid decrease in the spread of measured clutter spatial amplitude statistics with increasing cell size (each plot symbol is a median over many patch measurements). aw = 1 represents a tight Rayleigh (voltage) distribution with little spread (mean/median ratio = 1.6 dB). aw = 5 represents a broadly spread Weibull distribution (mean/median ratio = 28.8 dB).

generality, but in fact are the important aspects of the phenomenon that determine system performance and that therefore must be captured in a realistic clutter model.

1.2.4 Discrete Clutter Sources The increasing awareness of the capability of higher resolution radars to resolve spatial feature and structure in ground clutter and see between clutter patches led to investigations using high resolution radars to determine the statistics of resolved patch size and patch separation as a function of thresholded strength of the received clutter signal. It was found that the spatial extents of clutter patches diminished with increasing signal-strength threshold such that in the limit the dominant land clutter signals came from spatially isolated or discrete point sources on the landscape (e.g., individual trees or localized stands of trees; individual or clustered groups of buildings or other man-made structures;

Overview

9

utility poles and towers; local heights of land, hilltops, hummocks, river bluffs, and rock faces) [6, 7]. This discrete or granular nature of the strongest clutter sources in low-angle clutter became relatively widely recognized—this granularity is quite evident in Figure 1.1. It became typical for clutter models to consist of two components: a spatiallyextensive background component modeled in terms of an area-density clutter coefficient σ °, and a discrete component modeled in terms of radar cross section (RCS) as being the appropriate measure for a point source of clutter isolated in its resolution cell and for which the strength of the RCS return is independent of the size of the cell encompassing it. The RCS levels of the discretes were specified by spatial incidence or density (so many per square km), with the incidence diminishing as the specified level of discrete RCS increased. Note that in such a representation for the discrete clutter component, although the strength of the RCS return from a single discrete source is independent of the spatial resolution of the observing radar, the probability of a cell capturing zero vs one vs more than one discrete does depend on resolution (i.e., discrete clutter is also affected by cell size). It was usual in such two-component clutter models for the extended background σ ° component to be developed more elaborately than the discrete RCS component, the latter usually being added in as an adjunct overlay to what was regarded as the main areaextensive phenomenon. Although the two-component clutter model seemed conceptually simple and satisfactory as an idealized concept to deal with first-level observations, attempting to sort out measured data following this approach was not so simple. The wide measured spatial amplitude distributions of clutter were continuous in clutter strength over many (typically, as many as six or eight) orders of magnitude and did not separate nicely into what could be recognized as a high-end cluster of strong discretes and a weaker bell-curve background. That is, in measured clutter data, there is no way of telling whether any given return is from a spatially discrete or distributed clutter source [25]. Additional complication arises due to radar spatial resolution diminishing linearly with range (i.e., cross-range resolution is determined by azimuth beamwidth) so that discretes of a given spatial density might be isolated at short range but not at longer ranges. The reality is that, at lower signal-strength thresholds, spatial cells capture more than one discrete and cell area affects returned clutter strength. This difficulty in the two-component model of how to transition in measured data and hence in modeling specification between extended σ ° and discrete RCS has been discussed very little in the literature. These matters are discussed more extensively in Chapter 4, Section 4.5.

1.2.5 Illumination Angle To many investigators, a land clutter model is basically just a characteristic of σ ° vs illumination angle in the vertical plane of incidence. The empirical relationship σ ° = γ sin ψ where ψ is grazing angle (i.e., the angle between the terrain surface and the radar line-ofsight; see Figure 2.15 in Chapter 2) and γ is a constant dependent on terrain type and radar frequency has come to be accepted as generally representative over a wide range of higher, airborne-like angles [24]. However, at the low angles of ground-based radar, typically with ψ < 1° or 2°, it was not clear how to proceed. One relatively widely-held school of thought5 was that at such low angles in typically-occurring low-relief terrain, grazing 5.

The phrase “school of thought” rather than “opinion” is used here to indicate a point-of-view held by a group [more than one investigator] and to which some effort [as opposed to a preliminary idea] along the line indicated took place.

10

Overview

angle was a rather nebulous concept, neither readily definable [e.g., at what scale should such a definition be attempted, that of radar wavelength (cm) or that of landform variation (km)?] nor necessarily very directly related to the clutter strengths arising from discontinuous or discrete sources of vertical discontinuity dominating the low-angle backscatter and principally associated with land cover. From this point-of-view, the radar wave was more like a horizontally-propagating surface wave than one impinging at an angle from above, and it made more sense to separate the clutter by gross terrain type (mountains vs plains, forest vs farmland) than by fine distinctions in what were all very oblique angles of incidence. Another widely held school-of-thought was to extend the constant-γ model to the lowangle regime by adding a low-angle correction term to prevent σ ° from becoming vanishingly small at grazing incidence (as ψ → 0°). Little appropriate measurement data (for example, from in situ surveillance radars) was available upon which to base such a corrective term. Moreover, the idea of a corrective term tends to oversimplify the low-angle regime. At higher angles, the assumption behind a constant-γ model is of Rayleigh statistics; at low angles, it was known that the shapes of clutter amplitude distributions were broader and modelable as Weibull or lognormal, but following through with information specifying shape parameters continuously with angle for corrected constant-γ models at low angles was generally not attempted. The gradually increasing availability of digitized terrain elevation data (DTED) in the 1970s and 1980s, typically at about 100 m horizontal sampling interval and 1 m quantization in elevation, quickly led to its use by the low-angle clutter modeling community. The hope was that the DTED would carry the burden of terrain representation by allowing the earth’s surface to be modeled as a grid of small interconnected triangular DTED planes or facets joining the points of terrain elevation. Then clutter modeling could proceed relatively straightforwardly in the low-angle regime, as a function of grazing angle (e.g., constant-γ or extended constant-γ) on inclined DTED facets. This approach to modeling low-angle clutter won a wide following and continues to receive much attention. Note that it is usually advocated as a seemingly sensible but unproven postulate, and not on the basis of successful reduction of actual measurement data via grazing angle on DTED facets. As applied on a cell-by-cell (or facet-by-facet) basis, such a model is usually thought of as returning deterministic samples of σ °, thus avoiding the difficult problem of specifying statistical clutter spreads at low angles (although such a model can return random draws from statistical distributions if the distributions are specified). Indeed, when applied deterministically, the cell-to-cell scintillations in the simulated clutter signal caused by variations in DTED facet inclinations appear to mimic scintillation in measured clutter signals. However, this simple deterministic approach to modeling generally does not result in predicted low-angle clutter amplitude distributions matching measurement data. Predicted signal-to-clutter ratios and track errors recorded in radar tracking of low-altitude targets across particular clutter spatial fields using such a model show little correlation with measured data. The root cause of this failure is that the bare-earth DTED-facet representation of terrain does not carry sufficient information to alone account for radar backscatter; it lacks precision and accuracy to define terrain slope at a scale of radar wavelength and provides no information on the discrete elements of land cover which dominate and cause scintillation in the measurement data. This is illustrated by the results of Figure 1.4. At the

Overview

11

top, Figure 1.4(a) shows X-band measurements of clutter strength vs grazing angle in two short-range canonical situations where the clutter-producing surface was very level—on a frozen snow-covered lake and on an artificially level, mown-grass, ground-reflecting antenna range. In such situations, the computation of grazing angle is straightforward—it is simply equal to the depression angle below the horizontal at which the clutter cell is observed at the radar antenna. In these two canonical or laboratory-like measurement situations, a strong dependence of increasing clutter strength with increasing grazing angle is indicated. Such results illustrate the thinking that lies behind the desire of many investigators to want to establish a grazing-angle dependent clutter model. However, as shown in Figure 1.4(b), when grazing angle is computed to DTED facets used to model real terrain surfaces, little correlation between clutter strength and grazing angle is seen in the results. Specifically, Figure 1.4(b) shows a scatter plot in which measured X-band clutter strength in each cell at the undulating western prairie site of Beiseker, Alberta is paired with an estimate of grazing angle to the cell derived from a DTED model of the terrain at the site. As mentioned, the reasons that little or no correlation is seen in the results have to do with lack of accuracy in the DTED and in the fact that the bare-earth DTED representation of the terrain surface contains no information on the spatially discrete land cover elements that usually dominate low-angle clutter. Results such as those shown in Figure 1.4(b) are discussed at greater length in Chapter 2 (see Section 2.3.5). Such results illustrate why attempting deterministic prediction of low-angle clutter strength via grazing angle to DTED facets has been an oversimplified micro-approach that fails.

1.2.6 Range Dependence Return now to the first school of thought mentioned in the preceding discussion concerning illumination angle, namely, that at grazing incidence in low-relief terrain, terrain slope and grazing angle are neither very definable nor of basic consequence in low angle clutter. Within this school of thought, the central observable fact concerning clutter in a groundbased radar is its obvious dissipation with increasing range. Thus some early clutter models for surface-sited radars were formulated from this point of view. Rather than model the clutter at microscale, such models treated the earth as a large featureless sphere, uniformly microrough to provide backscattering, but without specific large-scale terrain feature. Such an earth does not provide spatial patchiness; rather it is uniformly illuminated everywhere to the horizon, and clutter strength is diminished with increasing range via propagation losses over the spherical earth. This appears to be a simple general macroscale approach for providing a range-dependent clutter model for surface-sited radar. However, like the microscale grazing angle model, the macroscale range-dependent model does not conform to the measurement data. These data show that what actually diminishes with increasing range at real sites is the occurrence of the clutter—with increasing range, visible clutter-producing terrain regions become smaller, fewer, and farther between, until, beyond some maximum range, no more terrain is visible (see Chapter 4, Figure 4.10). Further, the measurement data show that clutter strength does not generally diminish with increasing range, either within visible patches or from patch to patch. To illustrate this, Figure 1.5 shows mean clutter strength vs range in a 20o azimuth sector at Katahdin Hill, Massachusetts, looking out 30 km over hilly forested terrain. The data in this figure scintillate from gate to gate and occasionally drop to the noise floor where visibility to terrain is lost, but the average level stays at ~ –30 dB over the full extent in range with no

12

Overview

–20 Snow

σ°F4 (dB)

–40

–60 Grass

–80 0.001

0.01

0.1

1

10

100

10

100

Grazing Angle (deg) (a)

0

σ°F4 (dB)

–20

–40

–60

0.001

0.01

0.1

1

Grazing Angle (deg) (b)

Figure 1.4 Measurements of clutter strength σ °F4 vs grazing angle. (a) Canonically level, discrete-free surfaces; (b) undulating open prairie landscape.

significant general trend exhibited of, for example, decreasing clutter strength with increasing range. Many similar results from Katahdin Hill and other sites are discussed in detail in what follows (see Chapter 2, Section 2.3 and Chapter 4, Appendix 4.A).

Overview

13

σ°F4 (dB)

-10

-30 Noise Floor -50

0

5

10

15

20

25

30

Range (km) 4

Figure 1.5 Mean clutter strength σ °F vs range at Katahdin Hill. X-band data, averaged range gate by range gate within a 20°-azimuth sector, 80 samples per gate. Range gate sampling interval = 148.4 m. Such results indicate little general trend of clutter strength with range.

Another way of examining the measurement data for range dependence of clutter strength is in PPI clutter maps such as is shown in Figure 1.1. If a gradually increasing threshold on clutter strength is applied to a measured long-range PPI clutter map, the clutter does not disappear at long ranges first, but tends to uniformly dissipate within patches of occurrence over much of the PPI independent of range (see Chapter 4, Figure 4.19). Thus patchiness is necessary in a clutter model, not only to realistically represent the spatial nature of the clutter in local areas, but also to provide the important global feature of diminishing clutter occurrence (not strength) with increasing range.

1.2.7 Status The preceding discussions give some sense as to the state of understanding of low-angle land clutter and different points of view regarding its modeling when the Lincoln Laboratory clutter program commenced. As has been indicated, various elements of this complex phenomenon were individually understood to greater or lesser degrees, but a useful overall prediction capability was not available. Next, Section 1.3 briefly describes the Lincoln Laboratory measurement equipment for obtaining an extensive new land clutter database of clutter for the development of new empirical clutter models. Then Section 1.4 takes up again the various facets of the clutter phenomenon introduced in the foregoing and shows how the successful predictive approaches developed in this book build on the thinking that went before but extend it in improved ways of analyzing the data and formulating the models.

1.3 Clutter Measurements at Lincoln Laboratory The Lincoln Laboratory program of radar ground clutter measurements went forward in two main phases, Phase Zero [18], a pilot phase that was noncoherent and at X-band only, followed by Phase One [14], the full-scale coherent program at five frequencies, VHF,

14

Overview

UHF, L-, S-, and X-bands. Photographs of the Phase Zero and Phase One measurement instruments are shown in Figures 1.6 and 1.7, respectively. The basis of the Phase Zero radar was a commercial marine navigation radar, in the receiver of which was installed a precision intermediate frequency (IF) attenuator to measure clutter strength. Phase Zero measurements were conducted at 106 different sites. The Phase One five-frequency radar was a one-of-a-kind special-purpose instrumentation radar specifically designed to measure ground clutter. It was computer-controlled with high data rate recording capability. It utilized a linear receiver with 13-bit analog-to-digital (A/D) converters in inphase (I) and quadrature (Q) channels, and maintained coherence and stability sufficient for 60-dB clutter attenuation in postprocessing. Phase One five-frequency measurements were conducted at 42 different sites.

Figure 1.6 Phase Zero equipment at a western prairie site.

Important system parameters associated with the Phase Zero and Phase One radars are shown in Table 1.1. Both instruments were self-contained and mobile on truck platforms. Antennas were mounted on erectable towers and had relatively wide elevation beams that were fixed horizontally at 0° depression angle. That is, no control was provided on the position of the elevation beam. For most sites and landscapes, the terrain at all ranges from one to many kilometers was usually illuminated within the 3-dB points of the fixed elevation beamwidth. At each site, terrain backscatter was measured by steering the azimuth beam through 360° and selecting a maximum range setting such that all discernible clutter within the field of view, typically from 1 km to about 25 or 50 km in

Overview

15

Figure 1.7 Phase One equipment at a northern forested site.

range, was recorded. The Phase Zero and Phase One radars had uncoded, pulsed waveforms. The Phase Zero and Phase One clutter measurement radars were internally calibrated for every clutter measurement. The Phase One instrument was externally calibrated at many sites, using standard gain antennas and corner reflectors mounted on portable towers. The Phase Zero instrument utilized balloon-borne spheres to provide several external calibrations. More detailed information describing the Phase Zero and Phase One clutter measurement radars is provided in Chapters 2 and 3, respectively. Several years after the Phase One measurement program was completed, the L-band component of the Phase One radar was upgraded to provide an improved LCE (L-band Clutter Experiment) instrument for the measurement of low-Doppler windblown clutter spectra to low levels of clutter spectral power. The LCE radar is described in Chapter 6.

16

Overview

Table 1.1 Clutter Measurement Parameters Phase Zero

Phase One

Frequency Band

X-Band

VHF

UHF

MHz

9375

165

435

Polarization

HH

L-Band

S-Band

X-Band

1230 3240 VV or HH

9200

Resolution Range Azimuth

9, 75, 150 m 0.9°

15, 36, 150 m 13°

5°

3°

1°

1°

50 kW

10 kW (50 kW at X-Band)

10 km Sensitivity

␴°F4 = –45 dB

␴°F4 = –60 dB

Antenna Control

Continuous Azimuth Scan

Step or Scan through Azimuth Sector (<185°)

50'

60' or 100'

2 Tapes/Site (800 bpi)

~ ~ 25 Tapes/Site (6250 bpi)

1/2 Day/Site

2 Weeks/Site

Peak Power

Tower Height Data Volume Acquisition Time

Figure 1.8 shows results of five-frequency measurements of ground clutter conducted by the Phase One instrument at 35 general rural sites. Each plotted point indicates the mean value of clutter strength σ °F4—F is the pattern propagation factor (see Section 1.5.4)— obtained from a particular clutter patch for given settings of radar frequency, polarization, and range resolution, one clutter patch per site from each of the 35 sites (Figure 1.1 shows the outline of a typical clutter patch). These results illustrate the variability in mean strength from measured clutter histograms (e.g., see the vertical dashed lines in Figure 1.2); the cell-to-cell variability within the clutter patches is usually much greater (indicated by the overall extent in σ °F4 of the histograms in Figure 1.2). Such variability in mean clutter strength as is indicated in Figure 1.8 occurs both due to variations in the intrinsic clutter coefficient σ ° as well as variations in the propagation factor F (e.g., as discussed in Section 3.3.2). The five-frequency results of Figure 1.8 show broad site-to-site variability and increasing variability with decreasing radar frequency (i.e., 20 dB of variability at X-band increasing to 65 dB of variability at VHF); but otherwise indicate little general trend of mean clutter strength with radar frequency when averaged over all rural terrain types. In contrast and as will be demonstrated, significant trends of mean clutter strength with frequency do occur in specific rural terrain types (e.g., farmland vs forest). The results of Figure 1.8 are discussed in much greater detail in Chapter 3 (see Section 3.5.1).

1.4 Clutter Prediction at Lincoln Laboratory Section 1.4 describes the basic tenets underpinning ground clutter modeling efforts at Lincoln Laboratory and upon which the success of the models fundamentally depends. These tenets are further developed in subsequent sections of this book. Much of the discussion follows from the preceding historical review (Section 1.2) of important ideas

Overview

17

0 General Rural (35 Sites) –10

Mean of σ°F4 (dB)

–20

–30

–40

–50

Key –60

100

1,000

10,000

–70

Range Res. (m)

Pol.

150 150 15/36

H V H

15/36

V

–80 VHF

UHF

L-

S-

X-Band

Frequency (MHz)

Figure 1.8 Mean clutter strength vs radar frequency in general rural terrain, as measured at 35 sites. These data show broad site-to-site variability, and increasing variability with decreasing frequency; but otherwise indicate little overall (e.g., medianized) trend of mean clutter strength with frequency.

that had emerged earlier concerning low-angle ground clutter and previous approaches to its modeling.

1.4.1 Empirical Approach The approach to solving the problem of bringing order and predictability to low-angle clutter, as carried forward in this book, is based on trend analysis in measurement data. Averaging over large amounts of high-quality, internally self-consistent measurement data allows fundamental underlying trends to emerge which are often obscured by specific effects in individual measurements. No attempts are made to hypothesize and validate theoretical solutions, and any notional dependencies that cannot be demonstrated in the data are also not utilized. Empirical predictive constructs for low-angle clutter in surface radar are developed based on replicating all important general trends observed in the measurement data.

18

Overview

1.4.2 Deterministic Patchiness As stated previously, the most salient characteristic of ground clutter in a surface radar is variability. One important way that this variability manifests itself is patchiness in spatial occurrence (see Figure 1.1). Clutter does not exist everywhere, and its on-again, off-again behavior is what fundamentally determines system performance at any given site. The main approach of this book presumes the use of DTED to deterministically approximate the site-specific spatial patterns of terrain visibility and hence clutter occurrence at each site of interest. Following this approach, answers about the degree to which clutter limits system performance are obtainable one site at a time. Clutter varies dramatically from site to site, and the extent to which clutter limits radar performance only has deterministic meaning on a site-specific basis. Some effort (coordinated with studies at Lincoln Laboratory) has been made elsewhere [32] to include mathematically-derived stochastic patchiness within a general non-site-specific clutter modeling framework, but in such efforts the statistics of patchiness, dependent upon terrain type, are themselves obtained from processing in DTED for the terrain type of interest. A site-specific deterministicallypatchy model allows quantitative comparison between prediction and measurement of given clutter patches at given sites; more general stochastically-patchy or non-patchy models cannot be validated in this direct manner.

1.4.3 Statistical Clutter Although the visible regions of occurrences of ground clutter (i.e., the macroscale clutter spatial occupancy map—see Figure 1.1) are predicted deterministically using DTED, the clutter amplitudes that occur distributed over such regions are a statistical phenomenon. The information content in DTED is suitable for defining kilometer-sized macroregions of terrain visibility, but this information content—in currently available or any foreseeable database of digitized terrain elevations and/or terrain descriptive information—is insufficient to deterministically predict clutter amplitudes in individual spatial cells. Thus this book characterizes land clutter strength (as opposed to its spatial occupancy map) as a statistical random process and determines predictive parametric trends in the parameters characterizing the statistical clutter amplitude distributions.

1.4.4 One-Component σ ° Model The difficulty in two-component clutter models6 of how to transition in measured data and modeling specification between extended σ ° and discrete RCS was previously brought into consideration in Section 1.2.4. Consider again the key role that spatial resolution plays in low-angle ground clutter (see Section 1.2.3). The shapes of clutter spatial amplitude distributions are highly dependent on resolution over their whole extents (not just their strong-side tails). This results from the fact that at grazing incidence much of the discernible clutter (not just the strongest returns) is discrete-like. This key fact has been relatively unrecognized in the clutter literature, although occasional past remarks may be found that begin to approach the idea. For example, Krason and Randig [3] based the interpretation of their measurements of forest clutter on what appeared to them to be a fundamental “transition from diffuse scattering at large angles to specular scattering at the very shallow angles.” Recall that surface clutter as originally conceptualized—wherein all cells, whether large or small, contain large numbers of small scatterers—provides amplitude distributions with unvarying tight Rayleigh shapes and no dependence of shape 6.

“Two-component clutter model” is defined in Section 1.2.4.

Overview

19

on resolution. In contrast, what the radar is actually collecting at low angles is a broad continuum of spiky returns from discretes over a wide range of amplitudes, such that there are usually a number of discretes in each cell. This number is small enough that changing cell size strongly affects the statistics of the results. Recognition of this fact allows the complete spatial field of low-angle land clutter from weakest to strongest cells to be understood and predicted in a unified manner using an areaextensive σ ° formulation. The approach properly deals with cells containing a number of relatively weak, randomly-phased discretes as a power-additive density function in the statistical aggregate of many such cells. However, the approach also properly treats occasional cells containing strong isolated discretes, despite the fact that representing isolated discretes with a density function may at first seem inappropriate. For such a cell, a high-resolution radar will contribute a strong σ ° into a wide amplitude distribution, and a low-resolution radar will contribute a weaker σ ° into a narrower amplitude distribution. Prediction of clutter RCS from these distributions will result in the same RCS for the large discrete in both cells (large σ ° times small cell area equals smaller σ ° times larger cell area). Thus a statistical σ ° model implementing the fundamental property of spread in amplitude distribution vs resolution can capture and recreate the observed spatial granularity and point-like nature of clutter fields at low angles of observation, without recourse to an additional RCS component that is difficult to implement realistically. The reasoning behind why the density function σ ° is the proper way to model clutter even when dominated by discrete sources is considerably expanded upon in Chapter 4, Section 4.5. The clutter modeling statistics provided in this book follow this approach (but see Appendix 4.D).

1.4.5 Depression Angle Return now to the preceding discussion (Section 1.2.5) of historical perceptions on whether illumination angle might be important in affecting low-angle clutter strength, and if so, how to implement it in a model. Another position on how to use illumination angle to help characterize low-angle clutter, intermediate between that of not using angle at all (following the first approach described in Section 1.2.5) and that based on fine-scale specification of local terrain slopes in DTED (following the subsequent approach described in Section 1.2.5), exists and was utilized in the early literature by Linell [1] to successfully reduce measurement data from a ground-sited radar working over ranges up to 12 km.7 Although terrain slopes may not be very definable or directly relatable to clutter strengths at grazing incidence (as under the first approach described in Section 1.2.5), this intermediate approach brings a more macroscopic measure of angle to bear on the problem, namely the depression angle at which larger patches of relatively uniform terrain are viewed below the local horizontal at the radar antenna. The use of DTED to define depression angle as a macroparameter in this manner is appropriate to the information content and accuracy of the DTED, in contrast to the use of DTED to define grazing angle as a microparameter associated with individual cells. That is, depression angle depends only on terrain elevations and not their rates of change and hence is a slowly varying 7.

That is, at more realistic ranges for surface radar than the several tens or hundreds of meters of many measurements of σ ° vs grazing angle reported in the literature and performed, for example, with radars mounted on portable “cherry-pickers” for the purpose of measuring backscatter from small areas of homogeneous ground and for the most part at higher angles [40].

20

Overview

quantity over clutter patches; whereas grazing angle depends also on rates of change of elevation (i.e., the derivative) and hence is a rapidly varying quantity much more susceptible to inaccuracies and error tolerances in DTED. Linell’s results [1] showed that levels and shapes of clutter amplitude distributions measured from such macropatches were extremely sensitive to the differences in depression angle (e.g., 0.7°, 1.25°, 5°) at which they were obtained. These data became widely referenced [21, 24, 26], but did not directly lead to clutter models. An important distinction is that such data did not directly provide a simple continuous angle characteristic (like constant-γ), but instead showed how complete clutter amplitude distributions vary in steps or intervals of depression angle regime. Similar effects with depression angle, as first seen much earlier by Linell, both on the mean levels and shapes of clutter amplitude distributions over large spatial macroregions of low-angle clutter occurrence, constitute a highly pervasive and important parametric influence observed throughout the Phase Zero and Phase One measurements. Figure 1.9 shows these strong effects of depression angle on levels and shapes of clutter amplitude distributions. The curves of Figure 1.9 are plotted from the Phase Zero X-band data in Table 2.4 of Chapter 2; they were first presented in this manner by Skolnik [19]. It is evident in these results that mean and median clutter strengths rise rapidly with increasing depression angle, and that spreads in clutter amplitude distributions as given by either the mean/median ratio (as shown in the lower part of Figure 1.9) or by the Weibull shape parameter aw rapidly decrease with increasing angle (the upper part of Figure 1.9 plots the inverse of aw against depression angle). The results shown in Figure 1.9 are described in greater detail in Chapter 2. Although Linell’s results reporting the sensitivity of shape parameter to angle were relatively widely referenced, the corresponding similar sensitivity of shape parameter to radar spatial resolution was less widely recognized, as of course were the consequent interdependent effects of angle and resolution together on shape. These important interdependent effects of both depression angle (Figure 1.9) and radar resolution (Figure 1.3) on the shapes of low-angle clutter amplitude distributions are key elements in the clutter modeling information provided in this book.

1.4.6 Decoupling of Radar Frequency and Resolution Statistical low-angle clutter amplitude distributions are fundamentally characterized by a mean absolute level, and by the shape or degree of spread (broad or narrow) about the mean level. Results in this book show that the mean level of the distribution depends strongly on radar frequency, depending on terrain type (see Figure 3.38);8 and that the shape of the distribution depends strongly on radar spatial resolution (as has been discussed, see Figure 1.3). In addition, both the mean level and the shape depend upon depression angle (see Figure 1.9). However, analyses of the clutter measurement data have uncovered an important further fact, fundamental to the development of the modeling information in this book. This further fact is the decoupling of the effects of radar frequency and resolution on 8.

To be clear what is meant, this book shows that there exists little or no general dependence of land clutter strength with radar carrier frequency, VHF to X-band, where by “general” is meant averaging across all specific terrain types; but that for specific terrain types the frequency dependence of clutter can be strong, ranging from varying directly with carrier frequency (i.e., strongly increasing with frequency) in open low-relief terrain to varying inversely with carrier frequency (i.e., strongly decreasing with frequency) in forested highrelief terrain (see Chapters 3 and 5).

Inverse of Weibull Shape Parameter, aw-1

Overview

21

0.8 0.7 0.6 0.5 aw-1, High-Relief

0.4 0.3

aw-1, Low-Relief

0.2 −20

Mean and Median Clutter Strength ␴°F4(dB)

Mean, High-Relief −30

Mean, Low-Relief Median, High-Relief

−40

−50

Median, Low-Relief

−60 0.1

0.2

0.4

0.6 0.8 1.0

2.0

4.0

6.0 8.0

Depression Angle (deg)

Figure 1.9 General variation of ground clutter strength (mean and median) and spread (aw) in measured ground clutter spatial amplitude statistics vs depression angle, for rural terrain of low and high relief. Clutter strengths increase and spreads decrease with increasing depression angle. X-band data, plotted from Table 2.4 in Chapter 2. (After Skolnik [19]; by permission, © 2001 The McGrawHill Companies, Inc.)

the clutter amplitude distributions. Thus, although radar frequency affects mean level, it does not significantly affect shape; and although radar resolution affects shape, it does not affect mean level. The mean level is the only statistical attribute of the distribution unaffected by resolution; for example, the median and other percentile levels are strongly affected by resolution. This decoupling of effects of radar frequency and resolution on clutter amplitude distributions greatly decreases the parametric dimensionality of the consequent clutter modeling construct, such that this construct constitutes a proper empirical model incorporating trends over many measurements, and does not simply degenerate to a table look-up procedure of specific measurements.

1.4.7 Radar Noise Corruption At the very low angles at which surface radar illuminates the surrounding terrain, typically < 1° or 2°, even within spatial macroregions (i.e., clutter patches comprising many resolution cells) that are under general illumination and not deep in shadow, there usually occurs a subset of randomly occurring radar return samples from low-lying or shadowed terrain cells interspersed within the patch that are at the noise level of the radar (see Figure

22

Overview

1.2; samples at radar noise level shown black). This phenomenon is henceforth referred to as the occurrence of microshadow within macropatches of clutter. Microshadow is inescapable in low-angle clutter statistics. The correct way of dealing with microshadow is as follows: once the boundaries of a spatial clutter patch are defined (for example, by terrain visibility in DTED), all of the samples returned from within the patch boundaries must be included in the clutter statistics, including those at radar noise level. Frequently, in the clutter literature, only the shadowless or noise-free set of samples above radar noise level (shown white in Figure 1.2) is retained to characterize the clutter in the region. Shadowless statistics are dependent on the sensitivity of the measurement radar; that is, radars of differing sensitivity obtain different numbers of noise samples and hence obtain different measures of shadowless clutter strength. The key requirement for determining correct absolute measures of clutter strength over a given spatial patch of clutter (as opposed to relative, sensitivity-dependent measures) is to include all samples from the patch in the computation, including those at radar noise level. Clutter amplitude distributions from spatial patches inclusive of all the returns from the patch (including those at radar noise level) will henceforth be referred to as all-sample distributions. The necessary existence of noise-level samples in all-sample clutter amplitude distributions is a source of corruption in clutter computation. This corruption is dealt with as follows. All statistical quantities including moments and percentile levels are computed and shown two ways: 1) as an upper bound in which samples at noise level keep their noise power values (for noise samples, the actual clutter power ≤ noise power); and 2) as a lower bound in which the samples at noise level are assigned zero or a very low value of power (for noise samples, the actual clutter power ≥ zero). The correct value of the statistical quantity, that is, the value that would be measured by a theoretically infinitely sensitive radar for which the upper and lower bounds would coalesce, must lie between the upper bound and lower bound values. Even when the amount of noise corruption is severe, upper and lower bounds to statistical moments are usually close to one another because these calculations are dominated by the strong returns from the discrete clutter sources within the patch. In contrast, moments and percentile levels in the less correct, noise-free or shadowless distributions can be significantly higher than upper and lower bounds to these quantities in the corresponding, more correct noise-corrupted all-sample distributions. Separation of upper and lower bound values by large amounts in all-sample distributions indicates a measurement too corrupted by noise to provide useful information. The modeling information provided in this book is based on noise-corrupted all-sample clutter amplitude distributions from measured clutter patches with tight upper and lower bounds. As a consequence, the Weibull distributions specified herein for predicting clutter amplitude distributions cover all the cells and samples in a given patch including those at noise level for a radar of given sensitivity. That is, the Weibull distributions specify the clutter as appropriate for an infinitely sensitive radar; a subsequent system-dependent calculation is required to determine the subset of weak Weibull clutter values that are predicted below system noise level for the particular radar and clutter patch being modeled. In this manner, the modeling approach of this book correctly provides absolute measures of clutter strength not dependent on Phase Zero or Phase One radar measurement sensitivities and correctly includes microshadow in predicted low-angle clutter amplitude distributions for a modeled radar depending on its specific sensitivity, which can be different from that of the Phase Zero and Phase One clutter measurement radars.

Overview

23

1.5 Scope of Book The subject matter of this book is the phenomenology of low-angle land clutter in surfacesited radar. Trend analyses are conducted of the measured ground clutter data, and empirical modeling of clutter based on the trends revealed is performed. Section 1.5 describes the overall scope of the material to follow, including the ranges in important radar and environmental parameters over which clutter modeling information is subsequently presented and to which this information is limited.

1.5.1 Overview A surface-sited radar often experiences ground clutter interference to ranges of many tens of kilometers. Most of the relatively significant clutter comes from directly visible terrain. From most places on the surface of the earth, terrain visibility is spatially patchy; to an observer looking out from a site, high regions of terrain are visible and intervening low regions of terrain are masked. Thus clutter occurs within kilometer-sized macroregions or patches under direct illumination, each containing hundreds or thousands of spatial resolution cells. The spatial patterns of occurrence of ground clutter can be predicted geometrically9 with reasonable accuracy using available DTED. Having predicted in this deterministic manner the existence of some patch of ground clutter, it is subsequently necessary to be able to predict the amplitude statistics of the clutter as they exist within that region to estimate signal-to-clutter ratios for the radar operating in that clutter. Thus an important objective of this book is the prediction of ground clutter amplitude statistics for distribution over spatial regions of visible terrain. This approach to modeling low-angle clutter as developed at Lincoln Laboratory has come to be known as “site specific.” What is actually specific to the site is the spatial pattern of occurrence of the clutter—or the clutter occupancy map—at the site, as determined by DTED. The statistical clutter amplitude distributions that are subsequently drawn upon to determine clutter strengths in visible patches of occurrence can be used to specify land clutter strength for various applications or end-purposes in surface radar studies, whether to replicate site-specific PPI clutter maps and subsequent radar performance (as is under discussion here) or in quite different contexts involving clutter-limited radar operations (e.g., development of general target detection statistics, design of clutter-cancellation processors, etc.). This book provides models for the prediction of clutter strength and its intrinsic Doppler spreading. In addition, Chapter 6 provides some theoretical examples concerning target detection in clutter utilizing moving target indicator (MTI) and space-time adaptive processing (STAP) clutter cancellation schemes. This system-related information illustrates the utility of the phenomenological clutter models in determining to what extent clutter can be rejected.

9.

The word “geometrically” here implies propagation along perfectly straight lines. As used in this book, “geometrically visible terrain” means that a clear, straight, line-of-sight exists from the radar antenna to the terrain point in question unobscured by any intervening terrain features, as would be computed geometrically using DTED to represent the surface of the earth. This also assumes the earth to have a radius of 4/3 times its actual value to account for standard refraction of the radar waves in the atmosphere.

24

Overview

1.5.2 Two Basic Trends Two fundamental parametric dependencies exist in low-angle clutter amplitude statistics. The first dependency is that of depression angle as it affects microshadowing in a sea10 of discrete clutter sources such that mean strengths increase and cell-to-cell fluctuations decrease with increasing angle. The second dependency in low-angle clutter amplitude statistics is that of spatial resolution. In the discrete-dominated heterogeneous spatial field of low-angle clutter, increasing resolution results in increased spread in amplitude distributions. This effect of resolution on shapes of clutter amplitude distributions is key to the understanding and realistic replication of the fundamental texture and graininess of clutter spatial fields.

1.5.3 Measurement-System-Independent Clutter Strength The measures of clutter amplitude statistics provided in this book are absolute measures not dependent on radar sensitivity. For this to be true, noise-level samples within visible regions are included in the clutter statistics. The Phase Zero and Phase One measurement radars were sensitive enough to measure discernible returns from the dominant discrete clutter sources that occurred within visible regions, regardless of range to the region. For clutter distributions that properly include the noise-level samples, increasing sensitivity merely acts to reduce the relative proportions of cells at radar noise level within such regions, but otherwise is of little consequence in its effect on cumulatives, moments, etc.

1.5.4 Propagation In land clutter, the intervening terrain can strongly influence the radiation between the clutter cell and the radar. These terrain effects are caused by multipath reflections and diffraction from the terrain. All such effects are included in the pattern propagation factor F, defined (see, for example, [20]) to be the ratio of the incident field strength11 that actually exists at the clutter cell being measured to the incident field strength that would exist there if the clutter cell existed by itself in free space and on the axis of the antenna beam. The measures of clutter strength provided throughout this book, both in reduction of measurement data and in predictive modeling information, do not separate the effects of propagation over the terrain between the radar and the clutter cell from those of intrinsic terrain backscatter from the clutter cell itself. Thus, the term “clutter strength” as used in this book is defined as the product of the intrinsic clutter coefficient σ ° (see Section 2.3.1.1) and the fourth power of the pattern propagation factor F, where F includes all propagation effects, including multipath and diffraction, between the radar and the clutter cell. Using currently available DTED, it is not generally possible to deterministically compute the propagation factor F at clutter source heights sufficiently accurately to allow cell-bycell separation of intrinsic σ ° in measured clutter data. Difficulties are encountered in attempting to accurately separate propagation effects using any of the currently available 10. This book uses the phrase “sea of discretes” to suggest “a widely extended, copious, or overwhelming quantity,” or “a vast expanse,” or “a large extended tract of some aggregate of objects;” see Oxford English Dictionary, or Random House Dictionary of the English Language, etc. In other words, at the low illumination angles of surface radar, the number of spatially localized or discrete scattering sources is extremely large and of extremely wide variation in strengths, so as to completely dominate the low-angle ground clutter phenomenon. This is in contrast to the much less frequent occurrence of discrete clutter sources at higher airbornelike angles of illumination, where the nature of the ground clutter phenomenon is generally diffuse. 11. The strength of the electromagnetic field constituting the incident radar wave.

Overview

25

propagation prediction computer codes, such as those based on SEKE [33, 34], Parabolic Equation [35–37], or Method of Moments [38]. For example, since at low angles F varies as the fourth power of clutter source height [10], the illumination of vertical sources increases rapidly with source height, and differences of several meters in source height can cause tens of dB differences in observed clutter strength σ °F4. Further, reflect that most clutter cells contain a variety of unspecified vertical scatterers of various unknown heights. Theoretical work by Barrick [39] on scattering from rough surfaces is based on the premise that at low angles scattering and propagation influences are intimately interwoven and phenomenologically inseparable. Thus all of the coefficients of clutter strength σ °F4 tabulated as modeling information in this book include propagation effects. Further illustrating the importance of propagation effects on low-angle clutter, Barton [10] has provided insightful work in modeling clutter in ground-sited radars as a largely propagation-dependent phenomenon over nominally level or nominally hilly terrain. Although propagation is generally not separable from clutter strength, mentioned here but not further developed in this book are two particular circumstances in which propagation effects can be dominant and to some extent predictable in low-angle clutter. These two circumstances are: 1) at low (VHF) radar frequencies over open low-relief terrain where dominant multipath effects affect clutter strengths by large amounts; and 2) from shipboard radars operating in littoral environments where ground clutter from inland cells is strongly affected by anomalous propagation and ducting. This book investigates low-angle land clutter from directly illuminated, visible terrain regions. Land clutter from regions well beyond the horizon is usually much weaker than that from directly illuminated regions. Although weak, such interference is not necessarily inconsequential to radars operating against targets beyond the horizon. Long-range diffraction-illuminated land clutter is understood fundamentally as clutter reduced by large propagation losses due to the indirect illumination and is not further considered in this book. Thus all measures of clutter strength provided herein apply to directly—i.e., geometrically—visible terrain and include propagation effects.

1.5.5 Statistical Issues This book determines fundamental parametric trends in the distributions of clutter amplitudes over kilometer-sized macroregions or patches of directly visible terrain. Lowangle ground clutter is a complex phenomenon, primarily because of the essentially infinite variety of terrain. As a result, there are many influences at work in any specific measurement. Thus the discernment of fundamental trends in clutter amplitude distributions must occur through a fog of obscuring detail. A science is winnowed out, through statistical combination of many similar measurements (i.e., measurements from like-classified patches of terrain at similar illumination angles). This brings the discussion to technical statistical issues concerning combination of measured data. Simply put, an individual resolution cell (from which a single spatial sample of clutter strength is obtained) may be regarded as the elemental spatial statistical quantity; or the complete terrain patch (from which an amplitude distribution is formed from the clutter returns from the many resolution cells comprising the patch) may be regarded as the elemental spatial statistical quantity. The former approach leads to ensemble amplitude distributions in which measured data from many similar patches are aggregated, sample by sample. The word “ensemble” distinguishes such results obtained by

26

Overview

combining individual cell values—many values per patch—from many patches. The latter approach leads to the generation of many statistical attributes for the amplitude distribution of a given patch, the subsequent combination of a given attribute (e.g., mean strength) into a distribution of that attribute from many similar patches, and the final determination of a best expected value of the attribute from its distribution. The words “expected value” distinguish such results obtained by combining patch values—one value per patch—from many patches. The advantage of the cell-by-cell ensemble approach is that it not only allows quick determination of trends in amplitude distributions, but also allows simple and straightforward actual specification of resultant general distributions. This is the major approach followed in Chapter 2. However, reduction of data via expected values is the more rigorously correct way to provide clutter modeling information. Thus the finalized results in Chapters 3, 4, and 5, largely based on Phase One data, are presented in terms of expected values. Trends seen in ensemble distributions also occur in expected values; fine adjustment of ensemble numbers to best expected values appropriate to a patch is a higherorder technical issue considered in Chapter 2.

1.5.6 Simpler Models A considerable amount of clutter modeling information is provided in this book within the context of approximating Weibull coefficients, reflecting the web of basic parametric trends that exist in clutter amplitude distributions. Simpler approaches to ground clutter modeling are often suggested. This book provides a comprehensive base of information upon which alternative clutter modeling constructs may be developed and verified. Realistic and useful models of the low-angle clutter phenomenon need to include the sorts of complex parametric variation discussed in what follows. The empirical modeling information presented herein for describing low-angle clutter amplitude distributions captures the fundamental characteristics of these variations and allows the understanding and quantitative prediction of the limiting effects of ground clutter on the system performance of surface-sited radar.

1.5.7 Parameter Ranges The ranges in important radar and environmental parameters over which clutter was measured with the Lincoln Laboratory measurement equipment, and to which the clutter modeling information presented in this book is limited, are discussed in this section. Radar frequency in the results of this book ranges from VHF (170 MHz) to X-band (9200 MHz). The behavior of ground clutter at higher or lower frequencies is not addressed. One particular result of the Phase One five-frequency analyses is that clutter strength at the Phase One VHF measurement frequency of 170 MHz for forested terrain illuminated at relatively high depression angles of 1° or 2°12 is as much as 10 dB stronger than at microwave frequencies. On the basis of recent synthetic aperture radar (SAR) measurement programs at Lincoln Laboratory and elsewhere, it is known that at lower VHF frequencies (e.g., ~50 MHz), the clutter strength from forests drops by ~10 dB as frequency decreases below the resonance range and enters the Rayleigh region of scattering. That is, clutter strength from trees decreases as frequency decreases below 12. Depression angles of 1° or 2°, although small in absolute terms, are relatively high angles [e.g., are at the 84 and 93 percentile positions, respectively, in the overall distribution of depression angles shown in Chapter 2, Figure 2.27(a)] for a surface radar to illuminate the ground.

Overview

27

~100 MHz. However, effects like this outside the Phase Zero/Phase One ranges of parameters are not addressed in this book. Radar spatial resolution in the results of this book ranges from ~103 to ~106 m2. A strong trend in shapes of clutter amplitude distributions with spatial resolution over this range is shown to exist. To what extent this trend can be extrapolated to lower or higher (i.e., SARlike) resolutions is not addressed. It may be expected that with increasing cell size a limit of Rayleigh statistics is eventually approached, beyond which little additional effect with increasing cell size would be expected. Also, perhaps with decreasing cell size (e.g., appropriate to high resolution SAR radars) a limit in the other direction might be approached wherein most cells resolve individual scatterers so that further effects with resolution diminish. Such speculative limits do not appear within the ranges of spatial resolution available in the Phase Zero/Phase One data. Radar polarization13 in the results of this book is largely limited to co-polarized linear transmit/receive states. The Phase One five-frequency radar acquired clutter data only at VV- or HH-polarizations. Some cross-polarized data at VH- and HV-polarization were acquired with the subsequent LCE-upgrade to the Phase One radar and are briefly discussed in Chapter 6. Phase Zero X-band clutter data are limited to HH-polarization. The clutter data in the results of this book are limited in the depression angle at which the terrain is illuminated to the relatively small angles associated with ground-based radars. Most of the results apply to depression angles less than 1° or 2°. With decreasing rates of occurrences, some results are applicable at somewhat higher angles. Although constrained by narrow elevation beamwidths, some Phase One five-frequency results were obtained up to ~4° (X-, S-bands) or up to ~6° (lower bands). Some Phase Zero X-band results reach up to ~8°. A small amount of X-band SAR clutter data is discussed that shows continuity in the transition with angle that occurs between the Phase Zero ground-based data of depression angles up to ~6° or 8° and airborne clutter data of depression angles ranging from ~4° to 16°. Land clutter results in this book are based on measurements from many sites widely dispersed over the North American continent and hence covering a variety of terrain types and terrain relief. Modeling information is provided for general rural terrain and various specific terrain types. Ranges at which clutter was measured are relatively long; that is, they begin at 1 or 2 km and extend in some cases to more than 50 km. Patch sizes are relatively large—typically, several kms on a side. Thus the scale at which the clutter results in this book apply is appropriate to surface-sited surveillance and tracking radar typically operating in composite, discrete-dominated, heterogeneous terrain over long ranges and low angles. In contrast, much of the existing ground clutter literature is not relevant to this situation, but rather is concerned with measurements at shorter ranges (< 1 km), higher angles, and homogeneous conditions over small areas of ground [40].

1.6 Organization of Book This book is organized into six chapters, in which for the most part each chapter is based upon data analysis in a particular subset from the overall database of Phase Zero and Phase 13. VH means transmit vertical polarization, receive horizontal polarization, etc.

28

Overview

One measurements. This section briefly describes the subset of data upon which each chapter is based. Also briefly indicated is how a comprehensive understanding of lowangle land clutter is sequentially built up chapter by chapter to provide a capability for predicting clutter effects in surface-sited radar. In each chapter, technical discussions of subject matter ancillary to the development of the main clutter modeling information of the chapter are included in appendices.

Chapter 2. Chapter 2 is based on the X-band data obtained in the Phase Zero ground clutter measurements program. Many of the Phase Zero results in Chapter 2 are obtained from a basic file of 2,177 clutter patch amplitude distributions obtained from the 12-km maximum range Phase Zero experiment as measured at 106 different sites [18]. Analyses of these data as described in Chapter 2 lead to the first of two major results. This first result is the dependence of low-angle ground clutter spatial amplitude distributions on depression angle, such that the mean strengths of these distributions increase and their spreads decrease with increasing depression angle. These depression angle effects are largely the result of shadowing at low angles in a sea of patchy visibility and discrete or localized scattering sources. This result and its ramifications are developed in Chapter 2. Chapter 3. Phase One five-frequency clutter measurement data were collected within three different types of experiments, namely, repeat sector measurements, survey experiments, and long-time-dwell experiments. Chapter 3 is based upon repeat sector measurements [14]. The repeat sector at each site was a narrow azimuth sector in which clutter measurements were repeated a number of times during the two or three week timeon-site of the measurement equipment, to increase the depth of understanding and the reliability of the results. The repeat sector database altogether comprises 4,465 measured clutter spatial amplitude distributions. This database—comparable in size to the Phase Zero database but much smaller than the spatially comprehensive 360° survey database to be taken up in Chapter 5—is utilized in Chapter 3 for in-depth investigations of multifrequency parametric effects in low-angle clutter beyond the preliminary X-band effects discussed in Chapter 2. Thus Chapter 3 leads to a second major result, which is the dependence of mean clutter strength on radar frequency, VHF to X-band, in various specific types of terrain. In addition, general trends of variation with frequency,14 polarization, and resolution are determined, not only for mean clutter strength, but also for the higher order moments and percentile levels in clutter spatial amplitude distributions. Also determined in Chapter 3 are the statistical effects of changing weather and season on clutter strength, the latter based on six seasonally-repeated data collection visits of the Phase One equipment to selected sites. Chapter 4. The two major results obtained in Chapters 2 and 3 provide an approach for modeling low-angle ground clutter spatial amplitude distributions. In this approach, the mean strengths of clutter amplitude distributions vary with frequency, and the spreads of these distributions vary with spatial resolution, depending on terrain type. For a given terrain type, mean strengths increase and spreads decrease with increasing depression angle. This main approach to clutter modeling as taken in the Lincoln Laboratory Phase Zero/Phase One clutter project is introduced and developed in Chapter 4. A preliminary site-specific model, following this approach and based on Phase Zero X-band and repeatsector Phase One five-frequency data, is provided. Also included in Chapter 4 are discussions of other, simpler approaches to clutter modeling. Phase Zero clutter data are 14. See footnote, Section 1.4.6.

Overview

29

reduced in various ways to aid in quantifying simple model constructs. Chapter 4 also discusses the interrelationship between geometrically visible terrain and clutter occurrence, and what is involved in separating discrete from distributed clutter in measured data and subsequent empirical models. Illustrative results are provided of the temporal statistics, spectral characteristics, and correlative properties of low-angle clutter.

Chapter 5. Chapter 5 obtains the statistical benefit of analyzing and subsuming within

the clutter model the much more voluminous 360° spatially comprehensive survey data at each site. This modeling information is presented in Chapter 5 following the same modeling construct as developed in Chapter 4, but based on 59,804 stored spatial clutter amplitude distributions measured from 3,361 clutter patches at 42 Phase One sites. This large set of stored clutter patch statistics together with associated terrain descriptions and ground truth are reduced to generalized land clutter coefficients in Chapter 5 for general rural terrain and for eight specific terrain types. An example is provided of how this modeling information is used to predict PPI clutter maps in surface-sited radar. Clutter model validation at Lincoln Laboratory is discussed. The modeling information in Chapter 5 is presented within a context of Weibull clutter coefficients.

Chapter 6. Most radar signal processing of target returns embedded in clutter is based on Doppler discrimination and hence is highly dependent not only on the relative strength of the clutter power to that of the target, but also on the spectral spreading of the clutter power away from zero Doppler. Clutter spectral spreading in surface-sited radar of fixed position and stable phase is due to the phenomenologically intrinsic motion of the clutter sources themselves, most commonly that of windblown vegetation. Chapter 6 characterizes intrinsic-motion windblown clutter spectral spreading by means of long-time-dwell clutter experiments, in which long sequences of pulses at low pulse repetition frequency (PRF) were recorded over a contiguous set of range gates with a stationary antenna beam. Longtime-dwell data were obtained both with the Phase One five-frequency radar and with its subsequent, L-band only, LCE upgrade with reduced phase noise levels. On the basis of Phase One and LCE long-time-dwell data, Chapter 6 develops an empirical model [41–43] for the intrinsic spectral spreading of windblown ground clutter. The model proportions total clutter power between dc and ac terms. The ac term is invested with exponential decay characteristics. The resultant modeling construct is parameterized by wind speed, radar frequency, and terrain type. Chapter 6 includes a discussion of the effect of clutter spectral shape on MTI delay line improvement factor and goes on to show how the exponentially shaped Doppler spectrum of windblown clutter affects coherent radar detection performance compared with corresponding performance under more commonly assumed Gaussian or power-law spectral shapes. These latter results are the work of Professor Alfonso Farina of Alenia Marconi Systems, Italy and his colleagues at the University of Rome and the University of Pisa, who became highly interested in the consequences to radar signal processors of the Lincoln Laboratory clutter spectral findings and model [44–46]. These Italian results include validation of the exponential spectral model by comparison of modeled clutter-cancellation system performance with the system performance obtained using measured clutter data as input to the clutter canceller [47, 48]. Chapter 6 also reviews the historical literature on intrinsic-motion ground clutter spectral spreading and brings it into accord with the Phase One and LCE results.

30

Overview

References 1.

T. Linell, “An experimental investigation of the amplitude distribution of radar terrain return,” 6th Conf. Swedish Natl. Comm. Sci. Radio, Research Institute of National Defence, Stockholm, March 1963.

2.

E. M. Holliday, E. W. Wood, D. E. Powell, and C. E. Basham, “L-Band Clutter Measurements,” U. S. Army Missile Command Report RE-TR-65-1, Redstone Arsenal, AL, November 1964; DTIC AD-461590.

3.

H. Krason and G. Randig, “Terrain backscattering characteristics at low grazing angles for X and S band,” Proc. IEEE (Letters) (special issue on computers), vol. 54, no. 12, December 1966.

4.

F. E. Nathanson and J. P. Reilly, “Clutter statistics that affect radar performance analysis,” EASCON Proc. (supplement to IEEE Trans.), vol. AES-3, no. 6, pp. 386– 398, November 1967.

5.

M. P. Warden and B. A. Wyndham, “A Study of Ground Clutter Using a 10-cm Surveillance Radar,” Royal Radar Establishment Technical Note No. 745, Malvern, U.K., September 1969; DTIC AD-704874.

6.

H. R. Ward, “A model environment for search radar evaluation,” IEEE EASCON Rec, pp. 164–171, 1971.

7.

C. J. Rigden, “High Resolution Land Clutter Characteristics,” Admiralty Surface Weapons Establishment Technical Report TR-73-6, Portsmouth, U.K., January 1973; DTIC AD-768412.

8.

M. P. Warden and E. J. Dodsworth, “A Review of Clutter, 1974,” Royal Radar Establishment Technical Note No. 783, Malvern, U.K., September 1974; DTIC AD A014421.

9.

W. L. Simkins, V. C. Vannicola, and J. P. Ryan, “Seek Igloo Radar Clutter Study,” Rome Air Development Center, Technical Rep. RADC-TR-77-338, October 1977. Updated in FAA-E-2763b Specification, Appendix A, May 1988. See also FAA-E2763a, September 1987; FAA-E-27263, January 1986, July 1985.

10. D. K. Barton, “Land clutter models for radar design and analysis,” Proc. IEEE, vol. 73, no. 2, 198–204 (February 1985). 11. K. Rajalakshmi Menon, N. Balakrishnan, M. Janakiraman, and K. Ramchand, “Characterization of fluctuating statistics of radar clutter for Indian terrain,” IEEE Transactions on Geoscience and Remote Sensing, vol. 33, no. 2 (March 1995), 317–323. 12. K. S. Chen and A. K. Fung, “Frequency dependence of backscattered signals from forest components,” IEE Proceedings, Pt. F, 142, 6 (December 1995), pp. 310–315. 13. V. Anastassopoulos and G. A. Lampropoulos, “High resolution radar clutter classification,” in Proceedings of IEEE International RADAR Conference, Washington, DC, May 1995, 662–66. 14. J. B. Billingsley and J. F. Larrabee, “Multifrequency Measurements of Radar Ground Clutter at 42 Sites,” Lexington, MA: MIT Lincoln Laboratory, Technical Rep. 916, Volumes 1, 2, 3; 15 November 1991; DTIC AD-A246710.

Overview

31

15. J. B. Billingsley, “Ground Clutter Measurements for Surface-Sited Radar,” Lexington, MA: MIT Lincoln Laboratory, Technical Rep. 786, Rev. 1, 1 February 1993; DTIC AD-A262472. 16. J. B. Billingsley, “Radar ground clutter measurements and models, part 1: Spatial amplitude statistics,” AGARD Conf. Proc. Target and Clutter Scattering and Their Effects on Military Radar Performance, Ottawa, AGARD-CP-501, 1991; DTIC ADP006 373. 17. J. B. Billingsley, A. Farina, F. Gini, M. V. Greco, and L. Verrazzani, “Statistical analyses of measured radar ground clutter data,” IEEE Trans. AES, vol. 35, no. 2 (April 1999). 18. J. B. Billingsley, “Low-Angle X-Band Radar Ground Clutter Spatial Amplitude Statistics,” Lexington, MA: MIT Lincoln Laboratory, Technical Report 958, 2002. 19. M. I. Skolnik, Introduction to Radar Systems (3rd ed)., New York: McGraw-Hill, 2001. 20. L. V. Blake, Radar Range-Performance Analysis (2nd ed.), Silver Spring, MD: Monroe Publishing, 1991. 21. M. W. Long, Radar Reflectivity of Land and Sea (3rd ed.), Boston: Artech House, Inc., 2001. 22. C. Currie, “Clutter Characteristics and Effects,” in Principles of Modern Radar, J. L. Eaves and E. K. Reedy (Eds.), New York: Chapman & Hall, 1987. 23. D. K. Barton, Modern Radar System Analysis, Norwood, MA: Artech House, 1988. 24. F. E. Nathanson (with J. P. Reilly and M. N. Cohen), Radar Design Principles (2nd ed.), New York: McGraw-Hill, 1991.Reprinted, SciTech Publishing, Inc., 1999. 25. D. C. Schleher, MTI and Pulsed Doppler Radar, Norwood, MA: Artech House, 1991. 26. R. R. Boothe, “The Weibull Distribution Applied to the Ground Clutter Backscatter Coefficient,” U. S. Army Missile Command Rept. No. RE-TR-69-15, Redstone Arsenal, AL, June 1969; DTIC AD-691109. 27. M. Sekine and Y. Mao, Weibull Radar Clutter, London, U. K.: Peter Peregrinus Ltd., 1990. 28. E. Jakeman, “On the statistics of K-distributed noise,” J. Physics A; Math. Gen., vol. 13, 31–48 (1980). 29. J. K. Jao, “Amplitude distribution of composite terrain radar clutter and the Kdistribution,” IEEE Trans. Ant. Prop., vol. AP-32, no. 10, 1049–1062 (October 1984). 30. K. D. Ward, “Application of the K-distribution to radar clutter—A review,” Proc. Internat. Symp. on Noise and Clutter Rejection in Radars and Imaging Sensors, pp. 15–21, IEICE, Tokyo (1989). 31. T. J. Nohara and S. Haykin, “Canadian East Coast radar trials and the Kdistribution,” IEE Proceedings, Pt. F, 138, 2 (Apr. 1991), 80–88. 32. S. P. Tonkin and M. A. Wood, “Stochastic model of terrain effects upon the performance of land-based radars,” AGARD Conference Proceedings on Target and Clutter Scattering and Their Effects on Military Radar Performance, AGARD-CP501, (1991).

32

Overview

33. S. Ayasli, “A computer model for low altitude radar propagation over irregular terrain,” IEEE Trans. Ant. Prop., vol. AP-34, no. 8, pp. 1013–1023 (August 1986). 34. M. P. Shatz and G. H. Polychronopoulos, “An algorithm for the evaluation of radar propagation in the spherical earth diffraction region,” The Lincoln Laboratory Journal, vol. 1, no. 2, 145–152 (Fall 1988). 35. G. D. Dockery and J. R. Kuttler, “An improved impedance boundary algorithm for Fourier split-step solutions of the parabolic wave equation,” IEEE Trans. Ant. Prop., 44 (12), 1592–1599 (1996). 36. A. E. Barrios, “A terrain parabolic equation model for propagation in the troposphere,” IEEE Trans. Ant. Prop., 42 (1), 90–98 (January 1994). 37. D. J. Donohue and J. R. Kuttler, “Modeling radar propagation over terrain,” Johns Hopkins APL Technical Digest, vol. 18, no. 2, 279–287, (April–June 1997). 38. J. T. Johnson, R. T. Shin, J. C. Eidson, L. Tsang, and J. A. Kong, “A method of moments model for VHF propagation,” IEEE Trans. Ant. Prop., 45 (1), 115–125 (January 1997). 39. D.E. Barrick, “Grazing behavior of scatter and propagation above any rough surface,” IEEE Trans. Ant. Prop., vol. 46, no. 1, pp. 73–83 (January 1998). 40. F. T. Ulaby and M. C. Dobson, Handbook of Radar Scattering Statistics for Terrain, Norwood, MA: Artech House, 1989. 41. J. B. Billingsley and J. F. Larrabee, “Measured Spectral Extent of L- and X-Band Radar Reflections from Windblown Trees,” Lexington, MA: MIT Lincoln Laboratory, Project Rep. CMT-57, 6 February 1987; DTIC AD-A179942. 42. J. B. Billingsley, “Exponential Decay in Windblown Radar Ground Clutter Doppler Spectra: Multifrequency Measurements and Model,” Lexington, MA: MIT Lincoln Laboratory, Technical Report 997, 29 July 1996; DTIC AD-A312399. 43. J. B. Billingsley, “Windblown radar ground clutter Doppler spectra: measurements and model,” submitted to IEEE Trans. AES, accepted subject to minor revision, October 2000. 44. J. B. Billingsley, A. Farina, F. Gini, M. V. Greco, P. Lombardo, “Impact of experimentally measured Doppler spectrum of ground clutter on MTI and STAP,” in Proceedings of IEE International Radar Conference (Radar ‘97), IEE Conf. Pub. No. 449, pp. 290–294, Edinburgh, 14–16 October 1997. 45. P. Lombardo, M. V. Greco, F. Gini, A. Farina, and J. B. Billingsley, “Impact of clutter spectra on radar performance prediction,”IEEE Trans. AES, Vol. 37, no. 3, July 2001. 46. P. Lombardo and J. B. Billingsley, “A new model for the Doppler spectrum of windblown radar ground clutter,” in Proceedings of IEEE 1999 Radar Conference, Boston, MA: 20–22 April 1999. 47. M. V. Greco, F. Gini, A. Farina, and J. B. Billingsley, “Analysis of clutter cancellation in the presence of measured L-band radar ground clutter data,” in Proceedings of IEEE International Radar Conference (Radar 2000), Alexandria, VA, May 8–12, 2000.

Overview

33

48. M. V. Greco, F. Gini, A. Farina, and J. B. Billingsley, “Validation of windblown radar ground clutter spectral shape,” IEEE Trans. AES, vol. 37, no. 2, April 2001.

2 Preliminary X-Band Clutter Measurements 2.1 Introduction Chapter 2 provides general information describing the amplitude distributions of X-band land clutter returns received from regions of visible ground, based on Phase Zero measurements at 106 sites. Subsequent chapters provide similar information at other frequencies. In presenting land clutter data and results, Chapter 2 attempts both to do justice to describing a very complex phenomenon, and also to efficiently provide useful and easily accessible modeling information. The result is a chapter that provides increasing insight into the clutter phenomenon by cyclically building up an understanding of the many interacting influences affecting clutter amplitude statistics. As insights are developed, they are accompanied with the presentation of modeling information that generalizes such influences at various levels of fidelity.

2.1.1 Outline The major results of Chapter 2 are summarized within this section.

Basic Clutter Modeling Information. Chapter 2 provides basic ensemble modeling information describing X-band clutter amplitude distributions over macropatches of visible terrain as a function of depression angle for three comprehensive terrain types—rural/lowrelief, rural/high-relief, and urban. Chapter 2 goes on to explain, enlarge upon, and extend the nature of low-angle clutter amplitude statistics as encoded within the basic modeling information.

Angle Characteristic. There traditionally has existed within the body of ground clutter literature the idea that a clutter model could be a simple characteristic of clutter strength vs illumination angle. Such a model is provided in Chapter 2 as an expected-value generalization of all the Phase Zero measurements. However, ground clutter is inherently a statistical phenomenon in which large statistical variation occurs. Thus this simple anglecharacteristic model shows two characteristics of clutter strength, mean and median, vs angle. Together these characteristics demonstrate the important fact that clutter is statistical and show not only clutter strength vs angle, but also specify the variability (i.e., mean-tomedian ratio) of clutter strength at any given angle.

Worst-Case Situations. The basic X-band modeling information of Chapter 2 provides general information. Chapter 2 also provides upper bounds on how strong ground clutter can become in exceptional circumstances by comparing the amplitude distributions from

36

Preliminary X-Band Clutter Measurements

the strongest Phase Zero clutter patches (urban clutter, mountain clutter) with those of the basic information.

Fine-Scaled Variations with Terrain. The basic modeling information separates terrain into just three categories, which, simply interpreted, implies that, in general, only “mountains” (rural/high-relief terrain) and “cities” (urban terrain) warrant separation from all other terrain types (rural/low-relief terrain). However, with decreasing significance finer trends occur in the Phase Zero data with more specific description of terrain type. Within rural low-relief terrain, fine-scaled differences in clutter amplitude statistics among wetland, forest, and agricultural land are shown to exist. Within urban terrain, fine-scaled differences between terrain of residential (i.e., low-rise) and commercial (i.e., high-rise) character are illustrated. The effect of trees as discrete scattering sources is discussed. Modeling information in which, on low-relief open terrain, trees are the predominant Xband discrete scattering source, and such that clutter amplitude distributions vary with the relative incidence of occurrence of trees (i.e., percent tree cover), is provided. Negative Depression Angle. Negative depression angles occur when terrain is observed by the radar at elevations above the antenna. Such terrain is usually rough and steep. Information is provided describing clutter amplitude distributions occurring at negative depression angles.

Non-Angle-Specific Modeling Information. Chapter 2 principally provides generalized X-band modeling information for clutter amplitude statistics as a function of depression angle. However, the chapter also provides some non-angle-specific modeling information. For example, the overall distribution that results from combining all of the Phase Zero measured clutter samples is specified, irrespective of terrain type and depression angle, into one allencompassing ensemble distribution. Much information concerning frequency of occurrence of various levels of low-angle clutter strength is contained in this overall distribution, as measured from 2,177 clutter macropatches at 96 different sites. Chapter 2 also provides non-anglespecific expected value information by showing distributions of mean patch clutter strength by landform and land cover, respectively. To the extent that the overall terrain at a given radar site may be classified as being of one terrain class, such information can characterize mean clutter strength over the whole site, not only in terms of most likely values, but also in terms of worstcase (strong clutter) and best-case (weak clutter) values.

Appendices. The appendices of Chapter 2 provide discussions of the following subjects: (a) Phase Zero measurement equipment and calibration, (b) formulation of clutter statistics, and (c) numerical computation of depression angle.

2.2 Phase Zero Clutter Measurements 2.2.1 Radar Instrumentation The pilot phase clutter measurements and modeling program was designated as Phase Zero. The Phase Zero radar was a pulsed system (0.5 µs pulse width for many of the Chapter 2 results) that operated at X-band (9375 MHz) with horizontal polarization. The primary display of this radar was a 16-inch diameter, digitally generated, PPI unit. A precision IF attenuator was installed in the radar receiver as a means of measuring clutter strength. The radar was put under control of a minicomputer, by means of which a raw digital record of clutter strength could be obtained by digitally recording the contents of the PPI display in stepped levels of attenuation (1-dB steps over a 50-dB dynamic range).

Preliminary X-Band Clutter Measurements

37

For many of the results of Chapter 2, the maximum PPI range was set at 12 km, and the clutter data sampling interval size in the polar PPI display was 37 m in range extent and ~0.25° in azimuth extent. The radar and digital recording equipment were installed in an all-wheel drive one-ton truck that was equipped with a 50-ft pneumatically extendable antenna mast and selfcontained prime power. With this mobile Phase Zero clutter measurement instrument, clutter data were recorded in surveillance mode from all clutter sources within the field-ofview by azimuthally scanning the beam which was narrow (0.9°) in azimuth, wide (23°) in elevation, and fixed horizontally at zero degrees depression angle, through 360° in azimuth. Azimuthally scanned data were acquired at each site for each of seven experiments of increasing maximum range from 1.5 to 94 km. Clutter strength calibration was based on the elevation beam gain applicable at the depression angle at which each clutter patch was measured, not just the boresight gain, even though most patches were measured within the 3-dB elevation beamwidth. Each Phase Zero clutter measurement included internal calibration based on accurate measurement of the minimum detectable signal of the receiver. Occasional external calibrations were performed using balloon-borne spheres as test targets. The Phase Zero radar is more fully described in Appendix 2.A.

2.2.2 Measurement Sites Figure 2.1 shows the location of all 106 sites at which Phase Zero ground clutter measurements were obtained. Photographs of the terrain at two of the measurement sites are shown in Figure 2.2. Figure 2.2(a) shows low-relief undulating prairie farmland at the Beiseker site located 75 km northeast of Calgary. Figure 2.2(b) shows high-relief mountainous terrain at the Plateau Mountain site located 120 km southwest of Calgary in the Canadian Rocky Mountains. Significantly different backscatter characteristics would be expected, and indeed were measured, from the terrain in Figure 2.2(a) compared with that of Figure 2.2(b). However, later in Chapter 2 it will be shown that a useful first step in clutter prediction is to simply distinguish terrain type by whether it is of low relief, as pictured in Figure 2.2(a), or of high relief, as pictured in Figure 2.2(b). The Phase Zero radar served in a pilot role in site selection activities for Phase One measurements. It is apparent in Figure 2.1 that many of the measurement sites were in Canada. The Phase Zero and Phase One clutter measurement programs were jointly conducted by the United States and Canada within an intergovernmental Memorandum of Understanding. Coordinated analyses of the measurement data took place in both countries [1, 2].

2.2.3 Terrain Description Procedures were developed to systematically describe and classify the clutter-producing terrain at each measurement site. It was necessary that these procedures cause the clutter data, as measured from many sites, to usefully cluster within the same terrain class, and separate between different terrain classes. The terrain within each clutter patch at each site was classified both in terms of the characteristics of its land cover [3] and of its landform or surface relief [4]. The land cover and landform categories utilized in this classification are shown in Tables 2.1 and 2.2, respectively. The classification was performed principally through use of topographic maps and stereo aerial photos, usually at 1:50,000 scale. Since clutter producing terrain is often heterogeneous in its character, even within spatial macropatches, terrain classification often proceeded at two or even three levels to adequately capture the terrain characteristics important in the clutter data.

38

Preliminary X-Band Clutter Measurements

Region of Interest

Figure 2.1 Map of 106 Phase Zero sites.

In addition to land cover and landform, the height of each site is also important in its effect on the ground clutter measured at that site. High sites see clutter to greater ranges and result in higher depression angles and stronger clutter, compared to low sites. Effective site height is the difference between the terrain elevation of the radar position and the mean of the elevations of all the discernible clutter cells (most of the visible terrain) that occurred at that site. Effective radar height is equal to effective site height plus antenna mast height. By such definition, effective site height and effective radar height are with respect to illuminated terrain only and indicate how high the site or antenna is above the terrain causing clutter backscatter; they are not influenced by masked or shadowed terrain. The question may be asked as to whether the Phase Zero set of site heights is extensive enough to cover the sorts of height variations that occur in actual radar siting. Figure 2.3 compares site heights for a set of 93 actual radar sites [in Figure 2.3(a)] with Phase Zero site heights [in Figure 2.3(b)], the latter over a set of 93 Phase Zero sites for which effective site height was quantized. In Figure 2.3(a), the 93 actual radar sites were known locations occurring worldwide—of these, 27 occurred around relatively low-relief urban areas, 43 were hilltop sites, and 27 were other sites geographically dispersed (see Appendix 4.B for the definition of “site advantage”). It is seen in Figure 2.3 that this set of other sites provides significantly less extreme siting situations than do the Phase Zero sites. The median Phase Zero site height is 20 m, compared to 10 m for the actual site set. The Phase Zero site set not only encompasses the regime of actual site heights but extends to

Preliminary X-Band Clutter Measurements

39

(a)

(b) Figure 2.2 Two clutter measurement sites in Alberta, Canada. (a) Low-relief farmland at Beiseker. (b) High-relief mountainous terrain at Plateau Mt.

significantly higher and lower sites. This broad expanse of Phase Zero site heights indicates that the database of clutter measurements that results is not constrained in any unrealistic way—for example, in terms of the range of depression angles available, or the range

40

Preliminary X-Band Clutter Measurements

Table 2.1 Land Cover Classes 1

Urban or Built-up Land 11 Residential 12 Commercial

2

Agricultural Land 21 Cropland

3

Rangeland 31 Herbaceous

22 Pasture

32 Shrub 33 Mixed 4

Forest 41 Deciduous 42 Coniferous

5

43 Mixed Water 51 Rivers, Streams, Canals

6

52 Lakes, Ponds, Sloughs Wetland

7

61 Forested 62 Non-Forested Barren Land

Table 2.2 Landform Classes and Descriptions

Landform Class

Terrain Relief (ft)

Terrain Slope (deg)

Comments

1

Level

< 25

< 1°

2

Inclined

> 50

1° – 2 °

3

Undulating

25 — 100

< 1°

4*

Rolling

> 150

2° – 5°

5

Hummocky

25 — 100

< 2°

6*

Ridged

50 — 500

2° – 10°

Sharp breaks in slope at tops and bottoms of terrain features

7*

Moderately Steep

> 100

2° – 10°

Unidirectional

8*

Steep

> 100

10° – 35°

Frequently unidirectional

9

Broken

> 50

1° – 5°

Unidirectional Regular sequences of gentle slopes; wavelike Regular to irregular sequences of moderate slopes Complex sequences of slopes

Short dissected slopes

* Classes so indicated are “high-relief;” classes not so indicated are “low-relief.”

Preliminary X-Band Clutter Measurements

41

22 20

Site Height a (m) Mean 32.5 Median 9.8 St. Dev. 48.6

18

Number of Sites

16 14 12 10 8 6 4 2 0

Site Heighta (m) (a)

14

Number of Sites

12

Site b Height (m) Mean 42.6 Median 19.8 St. Dev. 81.5

10 8 6 4 2 0 –200

–100

0

100

200

300

400

Site Heightb (m) (b) Notes: a. Site Height = Effective Site Height or Site Advantage b. Site Height = Effective Site Height

Figure 2.3 Comparison of Phase Zero site heights with site heights of radar positions from other geographical regions. (a) 93 radar sites from other regions; (b) 93 Phase Zero measurement sites.

42

Preliminary X-Band Clutter Measurements

extents at which clutter occurs, or any other important height-dependent parameter that might affect the clutter results.

2.3 The Nature of Low-Angle Clutter 2.3.1 Clutter Physics I 2.3.1.1 Clutter Coefficient σ °

Wa vef fr ron ant om t enn a

Radar land clutter is characterized herein in terms of the intrinsic clutter backscattering coefficient σ °, defined to be the radar cross section (RCS) per unit of intercepted surface area A within the spatial resolution cell of the radar on the ground. As shown in Figure 2.4, at the relatively low depression angles α of ground-based radar, the range dimension of A is given by ∆ r = (c τ/2) sec α, where c is the velocity of propagation (c ≅ 3 × 108 m/s in free space) and τ is the pulse length. The factor of 1/2 in this expression for ∆ r is necessitated by the two-way round trip travel of the radar pulse. See Section 2.3.4 and Appendix 2.C for definition of depression angle α. The cross-range dimension of A [see Figure 2.4(b)] is given by r•∆θ, where r is slant range to the cell and ∆θ is the one-way 3-dB azimuth beamwidth of the radar. Thus, A is given by A = r•∆r •∆θ; and σ ° is given by σ ° = σc/A, where σc is the RCS of the clutter cell under consideration. Appendix 2.A and Appendix 3.C, Eqs. (3.C.1) and (3.C.2), specify how σc is computed in the measurement data.

cτ/2

α ∆r =

1 2

cτ sec α

(a)

∆r ∆⍜

A

r∆⍜

(b)

Figure 2.4 Geometry of land clutter for surface radar showing the area A within the radar spatial resolution cell on the ground. (a) Elevation view—range extent ∆r is determined primarily by radar pulse length τ. (b) Plan view—cross-range extent is r∆θ, where r is range and ∆θ is azimuth beamwidth.

Preliminary X-Band Clutter Measurements

43

Formulas for A at higher angles where the elevation beamwidth starts to take effect instead of the radar pulse length are available elsewhere (e.g., see [5]). In the ground-based radar results of this book for which α is generally < 2° and at most < ~8°, not only is A given by A = r•∆r •∆θ, but in addition the sec α factor in ∆r differs insignificantly from unity. In characterizing A some authors have specified ∆θ to be the two-way 3-dB azimuth beamwidth rather than the one-way beamwidth (e.g., [6]; see discussion in [7]). The specification of which point on a tapered beam to take as its width in this matter is somewhat arbitrary. The σ° results of this book are based on the more traditional approach of specifying ∆θ as the one-way 3-dB beamwidth. If the σ° results of this book had been based on the two-way 3-dB beamwidth, they would have been ~1 to 2 dB stronger depending upon the actual beam shapes involved. This book uses the prefix micro to refer to resolution-cell-sized areas on the ground, as shown in Figure 2.4, where ∆r in the measured data ranges from 9 to 150 m and ∆θ is usually from one to several degrees. Each resolution cell area A contributes a value of σ ° into a histogram collected over a much larger region called a clutter patch (see Figure 2.5) consisting of many resolution cells. The prefix macro refers to such large clutter patches. Thus a clutter patch is a spatial macroregion typically several kilometers on a side, usually containing hundreds or thousands of resolution cells.

Lobing

Free Space

Depression Angle Clutter Patch Microshadowing

Propagation Factor F Clutter Strength =

Clutter Coefficient F

4

Figure 2.5 Clutter physics (X-band).

2.3.1.2 Major Elements The major elements that are involved in low-angle clutter are shown in Figure 2.5. Attention is focused on directly illuminated clutter from large kilometer-sized spatial macroregions or patches of visible terrain. Within such clutter patches, at the low angles of ground-based radars, the dominant clutter sources tend to be all of the vertical features on the landscape, either objects associated with the land cover such as trees or buildings, or just the high points of the terrain itself. Such sources are usually spatially localized or discrete in nature, with regions of microshadow occurring between them where the receiver is at its noise floor. As the angle of illumination increases, the amount of microshadowing decreases. As a result, mean strengths in clutter amplitude distributions increase, and spreads (i.e., statistical dispersions) in clutter amplitude distributions

44

Preliminary X-Band Clutter Measurements

decrease with increasing angle. These effects with angle constitute a highly significant parametric dependency in low-angle clutter data, and are emphasized in the modeling information presented in Chapter 2 and throughout the book. The terrain between the radar and the clutter patch influences the illumination of the clutter patch. For example, multipath reflections can interfere with the direct illumination and cause lobing on the free-space antenna pattern. All such propagation effects (including multipath reflection from intervening low-relief open surfaces; diffraction into shadowed regions over intervening high-relief terrain features; and non-standard refraction through the atmosphere) are included within the pattern propagation factor F, which is defined to be the ratio of the incident field that actually exists at the clutter cell being measured to the incident field that would exist there if the clutter cell existed by itself in free space and on the axis of the antenna beam (see Section 1.5.4). What is measured as clutter strength is the product of the clutter coefficient σ° and the fourth power of the propagation factor. The propagation factor F is a ratio of field strengths (voltages); it appears to the fourth power in clutter strength σ °F4, first because it is squared in going from voltage to power (σ ° is a power-like quantity), and second because F2 is squared again to account for the two-way round trip travel of the radar pulse. Clutter strength σ °F4 is the quantity in the radar range equation that requires characterization in dealing with clutter (and propagation to clutter) phenomenology. At X-band, terrain reflection coefficients are often lower, and hence multipath effects are diminished, from those that can exist at lower radar carrier frequencies. When they exist at X-band, propagation lobes are usually relatively narrow such that typical clutter sources such as trees and buildings over most visible terrain often subtend a number of lobes (see Figure 2.5). As a result, the effects of propagation are diminished and tend to average out at X-band, compared with lower radar frequencies (e.g., VHF) where they can dominate. Throughout this book, clutter strength is given by σ °F4, in units of m2/m2, and is usually expressed in decibels as 10log10(σ °F4). See Appendix 3.B for further discussion of propagation effects in ground clutter.

2.3.2 Measured Land Clutter Maps Low Range Resolution (150 m). Figure 2.6 shows Phase Zero X-band measurements of ground clutter in PPI format at six Canadian sites. In each case, the range resolution is 150 m, and the maximum range is 47 km. These data are shown at full Phase Zero sensitivity; cells with discernible clutter return from the ground are shown as white, and cells where the receiver is at its noise floor are shown as black. The terrain at Altona, Manitoba is level cropland. Clutter is measured there only from discrete vertical objects (such as barns, silos, telephone poles, isolated trees, etc.) to a spherical earth horizon (nominally given by 16 km for the 50-ft Phase Zero antenna mast) except for the terrain feature (Pembina Hills) that rises to the far southwest. Only on such level sites is a smooth spherical earth model of terrain applicable in characterizing low-angle microwave clutter. At such level sites, dominant clutter sources are often high cultural or natural discrete objects distributed over the spherical surface. At most other sites, even relatively low-relief sites, specific terrain features dominate in low-angle clutter measurements over what would be measured on a spherical earth. Thus, in moving across Saskatchewan (Dana) and into Alberta (Penhold and Beiseker), the terrain becomes more undulating and rolling, and the influence of specific large-scale terrain

Preliminary X-Band Clutter Measurements

45

features dominates over spherical earth effects in the clutter maps for these sites. For example, even in the relatively low-relief terrain at Beiseker, it is the terrain surfaces inclined toward the radar (e.g., to the north and south) from which clutter is received; these surfaces are shadowed (i.e., black) on their far sides. Moving on in Figure 2.6, Burnstick is a forested site in the foothills of the Rocky Mountains, and Plateau Mountain is a site high in the Rockies. To the west at Plateau Mountain, clutter is measured from barren rock faces of high mountain peaks, and to the east clutter is measured looking down at the prairie. Figure 2.2 shows photographs of the terrain at Beiseker and Plateau Mountain.

Altona

Dana

Pe n h o l d

Beiseker

B u r n s t i ck

Plateau Mt.

Figure 2.6 Ground clutter maps at six sites. Phase Zero X-band data, 150-m range resolution, horizontal polarization. In each map, maximum range = 47 km, north is zenith, clutter is white, clutter threshold is 8 dB from full sensitivity. PPI scope photos.

In all cases in Figure 2.6, the patterns of spatial occurrence of clutter are patchy and granular. The nature of the clutter is on-again, off-again as it arises from discrete sources distributed over surfaces within line-of-sight visibility. The details of each pattern are specific to the terrain features at that site. Digitized terrain elevation data (DTED) are useful for geometrically predicting and modeling the specific nature of the spatial patterns of occurrence of clutter such as are shown in Figure 2.6. Two general observations may be made about all such patterns. First, the amount of clutter that occurs gradually diminishes

46

Preliminary X-Band Clutter Measurements

with increasing range from the site. Second, where clutter occurs (i.e., white patches), its strength is relatively independent of range. Subsequently, Chapter 4 bases the development of non-site-specific modeling information on these two observations. Here attention is focused on the following question: Where clutter occurs (i.e., over spatial regions largely within geometric line-of-sight visibility in which a relatively high percentage of resolution cells contain discernible clutter), what are its spatial amplitude statistics?

High Range Resolution (9 m). Figure 2.7 shows measurements at six sites similar to those of Figure 2.6, but at higher range resolution, namely, 9 m. At this increased resolution (and shorter maximum range, 6 km), the discrete or localized nature of the clutter sources within regions of general terrain visibility is evident. The pattern of vertical cultural objects on the level cropland at Altona is obvious. On the undulating terrain at Beiseker, terrain features are evident in the clutter map, but a rectangular pattern of cultural discretes overlays them. At ranges within 6 km, Dundurn is a military wasteland area of shrub and brush-covered sand dunes, typically 20 to 30 ft high, but without a road grid or cultural overlay. The clutter pattern there is seen to be of granular texture, where the top of each sand dune gives rise to a discrete or localized clutter return. In totality, the high-resolution plots of Figure 2.7 amply illustrate that within directly illuminated clutter regions, the lowangle clutter sources are all of the discrete vertical objects that rise above the surface. These discrete sources are densely distributed within illuminated regions. Clutter returns from the area-extensive terrain surfaces themselves, as opposed to discrete objects rising above these surfaces, are much weaker and, in fact, are often below the sensitivity of the receiver. In viewing the clutter maps of Figure 2.7, a sea of discretes is envisaged as the appropriate physical model for low-angle ground clutter, in contrast to the historical tendency in clutter modeling to associate the phenomenon primarily with area-extensive σ° backscatter from the terrain surfaces themselves (with a relatively few strong discretes such as water towers sometimes added in subsequently as an RCS adjunct; see the preceding discussions of twocomponent clutter models in Sections 1.2.4 and 1.4.4). The discrete clutter sources that high resolution reveals in Figure 2.7 are also the dominant clutter sources at lower resolution.

2.3.3 Clutter Patches The approach taken to modeling clutter amplitude statistics in this book is as follows. Within the clutter map measured at each site, clutter patches were selected as spatial macroregions generally within line-of-sight illumination in which a relatively high percentage of resolution cells contained discernible clutter. The meaning of “relatively high” depends on the terrain type and corresponding nature of microshadow in the clutter map. Typically, relatively high meant about 50%, but for high sites and/or steep terrain in which relatively full illumination existed it could approach 100%, and in level terrain in which only isolated discretes were illuminated it could be as low as ~25%. Overlaying and registering clutter maps onto stereo aerial photographs and topographic maps ensured in patch specification that the terrain within each patch was, in large measure, uniform. Interpretation of the air photos and topographic maps provided descriptive information of the terrain within the patch. For each clutter patch, the distribution of clutter strengths occurring within the patch was obtained and stored in a computer file together with the applicable terrain descriptors of the patch. Altogether, 2,177 clutter patches were selected from the Phase Zero 12-km maximum range experiment at 96 different sites. The modeling task then became one of establishing general correlative properties between the 2,177 stored distributions of measured clutter strength and the corresponding terrain descriptions.

Preliminary X-Band Clutter Measurements

Altona

Wolseley

Rouleau

Dana

Dundurn

Beiseker

47

Figure 2.7 High resolution ground clutter maps at six sites. Phase Zero X-band data, 9-m range resolution, horizontal polarization. In each map, maximum range is 5.9 km, north is zenith, clutter is white, and clutter threshold is reduced by 6 dB to 18 dB from full sensitivity to show strong clutter cells. PPI scope photos.

2.3.3.1 Clutter Patches at Gull Lake West Some typical clutter patches and measured clutter patch spatial amplitude distribution from the Gull Lake West site in Manitoba are now shown. Figure 2.8(a) shows a measured clutter map of 12-km radius for Gull Lake West; selected clutter patches within the region are shown in Figure 2.8(b). Figure 2.9 shows the measured amplitude distributions for six of the Gull Lake West patches shown in Figure 2.8. The terrain from which clutter was measured at Gull Lake West lies in the valley of the Red River and as a result is extremely level. The site itself at Gull Lake West lies on the western brow of a north-south situated ridge about 100 ft above the level terrain to the west, which the site overlooks. The effect of the ridge is to extend the Phase Zero mast height from its nominal 50-ft value to a higher elevation of about 150 ft. Otherwise, the very level terrain at Gull Lake West in some respects represents a canonical situation in which complicating effects of terrain relief are absent. The specific effects observed in the clutter distributions at Gull Lake West are largely caused by variation and complexity in land cover.

48

Preliminary X-Band Clutter Measurements

a) Phase Zero X-Band Clutter Map, Maximum Range = 11.8 km

b) Clutter Patch Selection

Figure 2.8 (a) Measured ground clutter map and (b) patches at Gull Lake West, Manitoba.

Consideration of these effects provides a deeper understanding of the general low-angle clutter amplitude distributions presented subsequently.

Patches 19/1 and 19/2. First consider patches 19/1 and 19/2. These patches are level forested wetland, relatively uncomplicated by the presence of roads, clearings, cultural discretes, and shadowing caused by variations in terrain elevation. Many of the taller trees making up this forested wetland are larch or tamarack. The other major component of the forested wetland is spruce. Also present is an understory of willow. The radar overlooks these patches from its nearby ridge location at a depression angle of ~1°. At first consideration, 1° may not seem to be a very large illumination angle, but it is large enough to make all the difference in causing these patches to be fully illuminated obliquely from above, rather than from the side at grazing incidence as they would have been if the radar position had not had its 100-ft terrain elevation advantage. As a result, the clutter histograms for patches 19/1 and 19/2 in Figure 2.9 are uncontaminated by cells at radar noise level (σ °F4 bins containing one or more cells at radar noise level are doubly underlined; these bins appear to the left side of the histograms for the other four patches in Figure 2.9, and indicate the sensitivity limit of the radar in these histograms). That is, every cell in patches 19/1 and 19/2 provides a discernible clutter return, which is not the case for most low-angle clutter patches. In addition, patches 19/1 and 19/2 provide well-behaved histograms of traditional bell shape. In fact, and as expected for full illumination of relatively homogeneous tree foliage, the amplitude distributions for patches 19/1 and 19/2 are very nearly Rayleigh, as is evident from their close match to the Rayleigh slope in the Weibull cumulative plot in Figure 2.9, as well as from the relative values of σ °F4 moments and percentiles listed (in a Rayleigh distribution, mean = standard deviation, skewness = 3 dB, kurtosis = 9.5 dB, mean/median = 1.6 dB, 90 percentile/median = 5.2 dB, 99 percentile/median = 8.2 dB). Note the following matter of terminology—in this book, the adjective “Rayleigh” is often used to specify the situation in which σ ° is Rayleigh-

7176

Samples

Percent

18

19/2

0.999

23 0.99

2.0

Lognormal Scale

1.6

0.97 0

19/1

20

26

0 –50 –40 –30 –20 –10 0

10

–50 –40 –30 –20 –10

0

10

–50 –40 –30 –20 –10

0

10

Terrain Classification Patch Number 18 19/1 19/2 20 23 26

Land Cover

Landform

43-21 61 61 52-61 43-21 43-21

1 1 1 1 3-1 3

Depression Angle (deg)

Tree Cover (%)

0.45 1.07 1.11 0.68 0.38 0.11

>50 >50 >50 4-10 >50 >50

Supplementary Terrain Descriptors ........ Continuous forested wetland Continuous forested wetland Backwater area, shrubs on sandy bars Dense tree cover, lakeshore road, minor cottages Road, cleared fields

F (dB)* Percentiles

Y=m•

Patch Number

Mean

Standard Deviation

Skewness

Kurtosis

50

90

99

Slope (m)

18 19/1 19/2 20 23 26

-35.7 (-43.6) -30.9 (-34.2) -31.4 (-35.6) -34.9 (-50.1) -34.1 (-43.4) -34.9 (-41.2)

-30.6 (8.3) -29.9 (6.7) -29.9 (8.3) -27.0 (9.7) -26.3 (9.2) -30.7 (6.9)

10.9 (0.52) 5.4 (-1.30) 7.1 (-1.50) 13.4 (1.36) 16.6 (0.29) 9.3 (0.73)

23.6 (2.09) 14.2 (5.52) 17.8 (5.49) 28.8 (3.89) 34.6 (2.03) 20.7 (2.41)

-45 -33 -34 †† -54 -43 -44

-32 -27 -27 -34 -31 -31

-25 -23 -23 -22 -23 -24

0.040 (0.084) 0.087 (0.149) 0.077 (0.125) 0.022 (0.051) 0.038 (0.077) 0.043 (0.093)

† Weibull (Lognormal)

F4 (dB)+b

Coefficient of Sum of Squared Intercept (b) Determination Deviations 1.65 (3.73) 2.75 (5.13) 2.50 (4.50) 1.16 (2.77) 1.54 (3.43) 1.71 (3.94)

0.997 (0.979) 0.998 (0.975) 0.997 (0.967) 0.988 (0.958) 0.995 (0.998) 0.997 (0.979)

0.013 (0.377) 0.012 (0.507) 0.026 (0.777) 0.022 (0.405) 0.027 (0.287) 0.007 (0.244)

0.4

18

0.5 0.3

23 19/2

0

26 Linear Scale

19/1

0.1 –50 –40 –30 –20 –10

0

0.99 0.97

0.6 0.4

20 0.7

0.3

–0.8 0.8

Weibull Scale

0.9

0.5

–0.4

10

0.999

18 26

Regression Coefficients†

4

* Of Linear Values (of dB Values)

Probability That

F4 (dB)

0.7

lope

Percent

10

0.8

20

23 19/2

0.2

igh S

–50 –40 –30 –20 –10 0 10 5070 Samples

0

Rayle

–50 –40 –30 –20 –10 0 10 14440 Samples

F4 (dB) Abscissa

–50 –40 –30 –20 –10 0 10 6666 Samples

1.2

0.9

F4 (dB) + b

Samples

Y=m•

8651

–0.2 –0.4

Linear Scale

19/1

0.1

–0.6 –0.8

–50 –40 –30 –20 –10

†† Upper Bound

Figure 2.9 Phase Zero clutter statistics and terrain classification for selected patches at Gull Lake West site, February visit.

F4 (dB)

0

10

F4 (dB) + b

Samples

Y=m•

4708 10

50

Preliminary X-Band Clutter Measurements

distributed and thus σ ° is exponentially distributed (hence the values of moments and percentile ratios just specified apply to the σ ° distribution for which σ ° is Rayleigh).

Other Patches. Few low-angle clutter patches provide such well-behaved, nearly Rayleigh statistics as do patches 19/1 and 19/2. Over large extents of composite landscape such as typically produce low-angle clutter in surface radars, most sites provide very little in the way of homogeneous terrain. For example, consider patch 18 at Gull Lake West. Although the terrain is level, the land cover is mixed between forest and cropland. At a depression angle of ~0.5°, the clutter return from the agricultural field surfaces is either masked by the surrounding trees or is below sensitivity at this low angle. As a result, a considerable number of samples in the distribution are at noise level (spike at left side of histogram). To the right of the noise samples, the histogram is less bell-shaped and more spread out than those of patches 19/1 and 19/2 (dotted vertical lines indicating 50, 90, and 99 percentiles are more separated). The cumulative distribution for patch 18 plotted on the Weibull scale in Figure 2.9 is of much lower slope than Rayleigh. Patches 23 and 26 are relatively similar to patch 18. These three patch distributions as a set (bottom graph, Figure 2.9) characterize much of the clutter-producing terrain at Gull Lake West. Note that these cumulative distributions are shown only above (i.e., to the right of) their regions of noise contamination. Thus, over the regions shown in Figure 2.9, these distributions are not affected by the sensitivity limit of the radar and are what would be measured there by an infinitely sensitive radar. Even on canonically level terrain with an artificially high antenna mast, complexity and heterogeneity in land cover has introduced a considerable extra degree of spread in these three distributions (patches 18, 23, 26) compared with homogeneous land cover (patches 19/1 and 19/2), all evident in comparing their cumulative amplitude distributions on the Weibull scale.

2.3.3.2 Pure vs Mixed Terrain Figure 2.10 shows clutter strength vs range looking west at Gull Lake West. Between 2 and 3 km in range, a relatively constant level of return is received from the level forested wetland. In this region, only small-scale fluctuation is observed from range gate to range gate. However, beyond 3.3 km in Figure 2.10 the nature of the clutter phenomenon changes dramatically. This region is characterized by extreme and rapid fluctuations in clutter strength as the various vertical features, many of which are tree lines, are encountered. Knowing how homogeneous tree cells or homogeneous cropland cells backscatter does not provide much information on how important boundary cells backscatter in transition zones, where forest meets cropland. Clearly, even for this canonically level terrain, a cell-specific predictive approach would require an enormous amount of land cover information to be able to accurately predict the deterministic clutter strength profile shown across patches 17 and 18. Such an approach would be easier to apply if more terrain were, like patch 19/1, relatively homogeneous. Referring back to Figure 2.7, to a large extent most of the dominant backscatter sources in low-angle ground clutter are the myriad features of verticality that exist on landscape. A correct empirical approach in dealing with all these edges of features is to collect meaningful numbers of them together within macropatches, like patches 17 and 18 in Figure 2.10, and let the terrain classification system carry the burden of statistically describing the attributes of the discontinuous clutter sources within the patch at a general overall level of description. Study of heterogeneous patches like patches 17 and 18 at Gull

Preliminary X-Band Clutter Measurements

Patch 19/1 level forested wetland (Near Rayleigh Statistics)

10

0

51

Patch 18 like patch 17 but greater proportion of trees

Patch 17 level ; mixed woodland and cropland in equal proportion; many linear edges of forest

Saturation Ceiling

σ°F4 (dB)

–10 –20 –30 –40 –50 Mean 99.00 Percentile 50.00 Percentile

–60 –70

Noise Floor 60

80

100

120

140

160

180

200

Range Gate Number 2

3

4

5

6

7

8

Range in Kilometers

• Data shown for individual range gate positions, averaged

over a 2° sector, 271.5° to 273.5° (10 azimuth samples/gate).

• Measurement date, 23 February; leafless deciduous trees, snow-covered field surfaces.

Figure 2.10 Clutter strength vs range looking west at Gull Lake West, Manitoba, Phase Zero Xband data, 75-m range resolution. Compare with Figure 2.8.

Lake West help lead to a general understanding of the clutter spatial amplitude distributions occurring in radar receivers as their beams sweep over large extents of composite landscape. In Figure 2.9, the cumulative distributions plotted on the Weibull scale appear more linear than those plotted on the lognormal scale. This is often (but not always) the case. To the extent that this is the case, Weibull formulations represent better engineering approximations to clutter spatial amplitude distributions than do lognormal formulations. Lognormal formulations of clutter amplitude statistics tend to provide somewhat too much spread (see Appendix 5.A). The measured clutter amplitude distributions almost never pass rigorous statistical hypothesis tests for belonging to Weibull, lognormal, K-, or any other theoretical distributions that were routinely tried over the full extents of the measured distributions (see Appendix 5.A).

Microshadowing. Consider again the noise-level cells that occur in many of the Gull Lake West clutter patches. The random occurrence of noise-level cells in low-angle clutter within general regions of geometric visibility is referred to as microshadowing. Microshadowing is further illustrated by the results shown in Figure 2.11. Figure 2.11(a) shows measured clutter (white) in the northwest quadrant at Katahdin Hill, Massachusetts to 12-km maximum range over hilly forested terrain. For comparison, Figure 2.11(b) shows predicted terrain visibility (white) in the same quadrant. It is evident that there is a

52

Preliminary X-Band Clutter Measurements

considerable degree of general correspondence between predicted terrain visibility and discernible clutter in these results. This relatively good correspondence between predicted terrain visibility and clutter occurrence at Katahdin Hill is further illustrated by the results shown in Chapter 4, Figure 4.2. However, careful observation reveals that significant (black) microshadowing occurs within visible regions in Figure 2.11 where the radar is at its noise floor. That is, at low illumination angles (~0.5° in Figure 2.11) over hilly forested terrain it is not possible to predict every microshadowed cell. The theoretical probability distributions as developed herein for prediction of clutter statistics within visible regions include weak clutter values in the correct proportions by terrain type and illumination angle to correctly account for the microshadowing that occurs in the measurements. This matter is taken up again in Section 2.4.4.1 (see Figure 2.46), and in Chapter 4, Section 4.4 (see also the relevant discussion on phenomenology concluding Section 2.4.2.1).

(a) MEASURED. Phase Zero, 75-m range resolution, full sensitivity, clutter is white.

~ 100-m resolution DTED, (b) PREDICTED. ~ 10-m tree cover, visible terrain is white.

Figure 2.11 Measured and predicted clutter visibility in the northwest quadrant at Katahdin Hill. Maximum range is 12 km, north is zenith.

Tree Lines. Tree lines constitute dominant clutter sources on much composite landscape. Figure 2.12 shows backscatter from one particular tree line measured at relatively long range, 14.7 km, over intervening farmland at Gull Lake East. The data in Figure 2.12 show that, in the transition region between farmland and forest, a very strong specular-like return is received from the leading edge of the tree zone, which rapidly decays in the next few range gates as the wavefront penetrates further into the forest. The trees of this forest are predominantly aspen. The backscatter from the edge of the forest is from the beginning of a tree foliage zone (largely leaves and branches) rather than a line of trunks. Figure 2.13 shows Phase Zero backscatter from another tree line measured at much closer range at the Lincoln Laboratory outdoor antenna range at Bedford, Massachusetts. Here again a strong return is evident from the leading edge of the trees in the transition zone between the level grass (of the antenna range) and the forest, which rapidly decays with increasing penetration of the wavefront into the forest.

Preliminary X-Band Clutter Measurements

53

Saturation Ceiling 20 10 202 Range 204 Gate 206 Numbers

σ°F4 (dB)

0 –10 –20 –30 –40 –50

Farmland

–60

Noise Floor

Trees

Mean 99.00 Percentile 50.00 Percentile

Tree line at 14.7 km

200

210

220

230

240

250

260

270

Range Gate Number 14

15

16

17

18

19

20

Range in Kilometers

• Data shown for individual range gate positions, averaged over a 5° sector, 85° to 90° (22 azimuth samples/gate).

• Measurement date, 24 February; leafless

deciduous trees, snow-covered field surfaces.

Range Gate Number

σ°F4 (dB) Mean Median Maximum

202

–16

–16

–13

204

–21

–24

–15

206

–26

–27

–23

Figure 2.12 Backscatter from a tree line at 15-km range at Gull Lake East, Manitoba. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 23.5-km maximum range, 74.2-m sampling interval.

Step Discontinuity. A theoretical problem directly relatable to low-angle clutter is backscattering from a dielectric step discontinuity at grazing incidence [8], as is illustrated in Figure 2.14(a). A solution to this problem consisting of a strong impulse-like leading edge return followed by a subsequent decay is of more direct applicability to low-angle clutter than one attempting to deal with low-angle clutter as an extended continuous surface. A Poisson distribution of many such discrete landscape elements leads to a K-distribution of clutter amplitudes [9] similar to the empirical Weibull distributions of this book.

Generality vs Specificity. Patch 20 at Gull Lake West occurs at the edge of Lake Winnipeg and largely comprises open water in which the ground clutter sources are shrubcovered sandy bars illuminated at a depression angle of ≈0.7°. The clutter amplitude distributions for patch 20 shown in Figure 2.9 are characterized by extreme spread. These distributions are very similar to distributions measured at much lower depression angles, typically at 0.1° or 0.2°, from cropland. The reason that patch 20 at higher angle looks like cropland at lower angle is that, in both cases, there exists a relatively low incidence of discrete clutter sources of widely varying strength rising above a low-backscattering medium. Patch 20 illustrates a general point in ground clutter modeling. With ever

54

Preliminary X-Band Clutter Measurements

Range Gate Number 120

10

160

200

Level Grass Deciduous Forest

0 –10

σ°F4 (dB)

–20 –30 –40 –50 –60 –70

Noise Floor

–80 99 Pecentile 90 Percentile 50 Percentile

–90

0.6

0.8

Range (km)

• Data shown for individual range gate positions, averaged

over a 2° azimuth sector (9 azimuth samples/range gate).

• Measurement date, 13 April; leafless deciduous trees. Figure 2.13 Backscatter from a tree line at Bedford, Massachusetts. Phase Zero X-band data, 9-m range resolution, horizontal polarization, 1.47-km maximum range setting, 4.6-m sampling interval.

increasing detail and specificity in terrain description (e.g., the key to the unusualness of patch 20 is its land cover classification), prediction accuracy can be improved, but at the same time generality and simplicity—essential features of any model—are lost. Taken to the extreme, every measured patch is different (terrain is essentially infinitely variable) and an archival file of many specific measurements does not constitute a model. An objective of Chapter 2 is to develop simple general clutter modeling information that is not too demanding in terms of terrain representation but correctly presents fundamental trends in clutter statistics. Such a model will of necessity lack specificity in terrain representation— it will not predict every clutter patch exactly correctly, but over many patches and many sites it will exhibit correct general trends.

Preliminary X-Band Clutter Measurements

55

Wavefront

Step Discontinuity

(a) Wavefront

Step Discontinuity

(b)

Figure 2.14 Diagram illustrating backscatter from a dielectric step discontinuity.

2.3.4 Depression Angle Figure 2.15 shows depression angle α to be the angle below the horizontal at which a clutter patch is observed at the radar (see also Figure 2.5). More specifically, depression angle is defined herein to be the complement of incidence angle at the terrain point under consideration. Incidence angle equals the angle between the projection of the earth’s radius at the terrain point and the direction of illumination at that point, assuming a 4/3 earth radius to account for nominal atmospheric refraction. Thus the rigorous definition of depression angle is in a reference frame centered at the terrain point, not at the antenna. This definition of depression angle includes the effect of earth curvature on the angle of illumination, but does not include any effect of the local terrain slope. What is thusly referred to herein as “depression angle” has occasionally in the past been referred to as “grazing angle,” especially with airborne radar looking at long ranges over the spherical earth such that earth curvature effects are large (e.g., see [5], p.36). However, as shown in Figure 2.15, grazing angle as used herein refers to the angle between the tangent to the local terrain surface at the backscattering terrain point and the direction of illumination. Thus grazing angle as used herein does take into account the local terrain slope. The effects of grazing angle on clutter strength are discussed more fully in Section 2.3.5.

56

Preliminary X-Band Clutter Measurements

α = Depression Angle

Grazing Angle = ψ

α

ξ

ξ

ξ = Terrain Slope

Grazing angle ψ = Depression angle α + terrain slope ξ

Figure 2.15 Relationship of grazing angle to depression angle and terrain slope.

The formula used for rigorous computation of depression angle α is derived in Appendix 2.C to be

h r

r 2a

α ≅ --- – ------

(2.1)

where h = effective radar height, r = slant range from radar to terrain point, and a = effective earth’s radius (actual earth’s radius times 4/3 to account for standard atmospheric refraction). At short enough ranges that earth curvature is insignificant, which is the case for much of the data in Chapter 2, Eq. (2.1) for depression angle simplifies to be α ≅ h/r; i.e., to be the angle below the horizontal at which the terrain point is viewed from the antenna. Figure 2.16 shows three clutter histograms which together illustrate the major effect of depression angle on histogram shape, such that variations with depression angle— i.e., as it ranges from 2.8° [Figure 2.16(a)] to 0.8° [Figure 2.16(b)] to 0.2° [Figure 2.16(c)]—tend to wash out other variations such as those that occur with changing landform and land cover. Note that the mean strengths (dashed vertical lines) in these three histograms vary by only several dB; it is the shapes and resultant spreads (e.g., ratios of 99to 50-percentile) in these results that vary more dramatically with small changes in depression angle. In what follows, effects with depression angle on both mean strength and spread are discussed in low and high angle regimes.

2.3.4.1 Low-Angle Clutter To illustrate the effect of depression angle on low-angle clutter, results are shown from two sites. First, results are shown from Shilo, Manitoba at a very low depression angle, 0.1° or 0.2°. Then results are shown from Cazenovia, New York at a much higher depression angle of ~9°. In contrast to Gull Lake West, which was wooded terrain with occasional agricultural fields, the terrain at Shilo was open prairie farmland. Terrain relief at Shilo was low, less than 50 m over 10- to 20-km extents. The site position itself provided little elevation advantage over surrounding terrain. A terrain elevation profile to the southwest at Shilo is shown in Figure 2.17, incorporating the curvature of a 4/3 radius spherical earth. Geometrical masking is also shown in this figure. In this southwest terrain profile, the depressional dip at about 4.5-km range is a river valley. From 5.2 to 13.4 km, the terrain gradually rises out of the river valley at an average terrain slope of 0.26°. Although this is a

Preliminary X-Band Clutter Measurements

57

Radar Noise Contamination 14 Percent

Percent

6

50

Mean

8 90

99

Percentiles Depression Angle = 2.8°

4

Land Form 4 Landcover 43-52

2 Max = –5 dB 0

–50

–40

–30

–20

–10

(a)

0

10

8 50

99

Percentiles

Mean

6

Percent

90

Noise, 30 Percent

Depression Angle = 0.8°

4

LF 3 LC 21-31

2 Max = –4 dB 0

–50

–40

–30

–20

–10

(b)

0

10

50

90

Mean

8 99

Percentiles

Percent

6

Depression Angle = 0.2°

Noise, 75 Percent

4

LF 1-3 LC 21 2 Max = –3 dB 0

–50

–40

–30

–20

σ°F4 (dB)

–10

0

(c) 10

Figure 2.16 Histograms of Phase Zero clutter amplitude statistics for three clutter patches at different depression angles. (a) High Knob, dep. ang. = 2.8°; (b) Orion, dep. ang. = 0.8°; (c) Coaldale, dep. ang. = 0.2°.

small angle, it is more than sufficient to bring this terrain into full visibility from the radar position. Small changes in terrain slope to the southwest at Shilo, for example, in the regions from 13.4 to 15.1 km and beyond 17.3 km, are enough to cause these regions to be masked, which leads to an important point that is often misconstrued at first consideration. Terrain slope and changes in terrain slope, even when quite small, are very important in how they directly and deterministically affect the spatial patterns of occurrence of the

58

Preliminary X-Band Clutter Measurements

Elevation (m)

clutter. The effect of terrain slope on clutter strength, however, is an entirely different matter, which is discussed in Section 2.1.5.

Terrain Profile

Shilo

50-Ft Antenna

394 Unmasked Masked

SW 302 0

2

4

6

8

10

12

14

16

18

20

Range (km)

Figure 2.17 Terrain elevations and masking to the southwest at Shilo, Manitoba.

σ ° vs Range. Figure 2.18 shows clutter strength vs range in a narrow azimuth sector to the southwest at Shilo. The available dynamic range between the noise floor and the saturation ceiling of the Phase Zero receiver is shown in the figure. Only in the first 2 km on the relatively discrete-free prairie grassland that exists in this near-in region is seen anything approaching a traditional deterministic effect between area-extensive σ ° from the terrain surface itself and grazing angle. This close to the radar, the antenna mast height is sufficient to provide grazing angles greater than 0.5°. Thus as range decreases from 2 km, grazing angle increases from 0.5 degrees, and clutter strengths rise. Even in this near-in region, the nature of the increase of σ ° with grazing angle is not smooth and monotonic but shows wide fluctuations. Beyond 2 km, the clutter strengths in Figure 2.18 are dominated by discrete clutter sources. This is evident in Figure 2.19, which shows a sector of a measured 12-km Phase Zero ground clutter map looking to the southwest at Shilo, overlaid and registered on an aerial photograph of the site. The agricultural fields within this sector are within geometric lineof-sight of the radar and are thus under direct illumination. Yet it is evident in Figure 2.19 that the radar is not sensitive to the backscatter from the field surfaces themselves. Rather, the clutter sources in these fields are all vertical discrete objects, including individual farmsteads (usually surrounded by trees) and other vertical features such as fence lines, telephone poles, bushes, and buildings. The overall nature of the low-angle clutter amplitude phenomenon shown in Figure 2.18 shows extreme and rapid variation of clutter strength from range gate to range gate. These variations easily encompass 30 dB or more at a given percentile level of strength. The overall picture is not one of well-behaved or easy-to-describe statistics. Rather, it is one of patchiness and heterogeneity. The effects shown are not capturable in a traditional grazing angle model based on terrain slope. This, however, is the phenomenon, highly terrainprofile-specific and discrete-dominated, that requires characterization.

2.3.4.2 Higher-Angle Clutter Consider now clutter strength vs range data from a much higher site, Cazenovia, New York. At Cazenovia the radar was set up high on the side of a steep valley, as shown in the top sketch in Figure 2.20. The radar looked down into the valley at high airborne-like depression angles. Beneath the terrain profile in Figure 2.20 are σ °F4 data vs range shown

Preliminary X-Band Clutter Measurements

Trees 0.5° Increasing Irrigation Grazing River Equipment Valley Angle

σ°F4 (dB)

–3

59

Treed Farmstead Scrub Belt

Treeless Cropland

–23 –43 –63 99 Percentile 90 Percentile 50 Percentile

0

1

2

3

4

5

6

7

8

9

10

11

12

Range (km)

• Data shown for individual range gate positions, averaged

over a 7° sector, 232° to 239° (31 azimuth samples/gate).

• Measurement date, 3 March; leafless deciduous trees, snow-covered field surfaces.

Figure 2.18 Clutter strength vs range to the southwest at Shilo, Manitoba. Phase Zero X-band data, 11.8-km maximum range experiment, 75-m range resolution.

in the same manner as in Figure 2.18 for Shilo, averaged azimuthally over an azimuth sector in individual range gate positions. The dashed lines between the upper terrain profile and the lower clutter data trace are included merely to aid the eye in associating particular points within the data window on the terrain profile with corresponding points in the clutter data. The data in Figure 2.20 seem to belong to a completely different phenomenological regime than the data in Figure 2.18. At the higher depression angle, the fluctuations of clutter strength with range are much less, more on the order of 6 dB than the 30-dB swings shown in Figure 2.18. The variation of clutter strength with range at high depression angle in Figure 2.20 is much less patchy, more homogeneous, and gives much more indication of being of a continuous process rather than being like the discrete-dominated process of Figure 2.18. The amount of shadowing (i.e., noise level cells) is dramatically reduced (essentially to zero) from Figure 2.18 to Figure 2.20. Thus, the most remarkable feature in the high-angle data of Figure 2.20 is the reduction of spread in clutter amplitudes exhibited at the higher illumination angle. Besides reduction in spread, the mean clutter strength has increased with depression angle also, from about σ °F4 ~ –33 dB in Figure 2.18 to about σ °F4 ~ –24 dB in Figure 2.20. These two major effects of decreasing spread and increasing mean strength in clutter amplitude distributions as depression angle increases and shadowing decreases are basic effects around which is formulated the preliminary X-band clutter modeling information of Chapter 2. Next consider more closely the clutter data in Figure 2.20. The terrain on the valley floor is agricultural, with some scattered trees in wood lots, around farmsteads, and along roads. As

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Preliminary X-Band Clutter Measurements

A Sector of Ground Clutter at Shilo, Manitoba

Figure 2.19 A sector of ground clutter at Shilo, Manitoba. Within the sector, microregions of terrain generating discernible Phase Zero clutter are circumscribed with a heavy black line. Within each such microregion, some vertical feature can be identified in the air photo. Much of the area within the sector, including most open field surfaces, is at the Phase Zero noise floor (i.e., not circumscribed). The radial extent of the sector shown is 12 km.

the terrain slopes increase on the valley walls, however, the terrain becomes more completely forest covered. The effects of these variations in land cover are seen in the clutter data of Figure 2.20. There is more fluctuation in clutter strength from the farmland on the valley floor between 1.0 and 1.5 km in range. From the forested surfaces, between 0.75 and 1.0 km and between 1.75 km and 2.25 km, there is less fluctuation, and the amplitude distributions become close to Rayleigh.

Grazing Angle. Also shown in Figure 2.20 is an approximate indication of grazing angle. A traditional way to model higher angle ground clutter is by means of a constant-γ model, where clutter strength varies directly with the sine of the grazing angle, the constant of proportionality being γ (see Section 1.2.5). The mean clutter strength data in Figure 2.20 show rises and drops with changing grazing angle, with each of the changes being of about the expected 2- or 3-dB order of magnitude. Thus the data of Figure 2.20 support a constant-γ grazing angle model for mean clutter strength at high angle as being quite realistic. The value of γ suggested by the data of Figure 2.20 is 0.023 (i.e., –16.4 dB), with γ being somewhat independent of terrain type, a conclusion supported by the airborne SAR clutter measurements discussed in Section 2.4.4.2. However, the grazing angles of Figure 2.20 are so high as to be much more typical of airborne radar than general groundbased radar. Certainly a constant-γ model has no applicability to the lower angle regimes

Preliminary X-Band Clutter Measurements

61

Data Window 2.7 km

0.5 km 9°

st

–7°

re Fo

Fo re

st

500 ft

7°

Farmland

σ°F4 (dB)

90 Percentile Mean 50 Percentile –14 –24 –34 0.5

1.0

1.5

2.0

2.5

Range (km) 7.5

10.1

6.5

11.3

7.3

Grazing Angle (deg)

• Data shown for individual range gate positions, averaged over a 58° azimuth sector (9248 azimuth samples/gate).

Figure 2.20 Clutter strength vs range at a high depression angle at Cazenovia, NY. Phase Zero X-band data, 3-km maximum range experiment, 9-m range resolution.

of ground-based radar exemplified by the Shilo data and which constitute the major subject of this book. The data of Figure 2.20 indicate what kind of an unusual terrain geometry is required in a ground-based measurement for grazing angle and constant-γ to be useful. It is only because of its closeness (< ~2 km) that visibility exists into the deep Cazenovia valley at all. Similar valleys at longer ranges are typically screened to ground-based radar. Still, consideration of the Cazenovia data of Figure 2.20 within the context of the preliminary clutter modeling information presented later in Chapter 2 provides a better indication of how the model works and the terrain scale at which it is meant to work. Although the very local close-in data of Figure 2.20 can be analyzed through grazing angle, the subsequent model works more globally and to much longer ranges, utilizing large terrain patches characterized in terms of terrain relief (i.e., terrain slope) and depression angle. Only in special circumstances, such as looking down into and across a single deep linear valley at close range such as occurs at Cazenovia, are direct and specific causative influences of grazing angle on clutter strength in surface radar able to be shown. Consider again backscatter from a step discontinuity as shown in Figure 2.14. At very low angles of illumination [i.e., Figure 2.14(a)], vertical surfaces are illuminated at normal incidence and give rise to strong returns, whereas horizontal surfaces are illuminated at grazing incidence and give rise to weak returns. This is the situation prevailing in the Shilo data. However, at

62

Preliminary X-Band Clutter Measurements

higher angles of illumination [i.e., Figure 2.14(b)], both vertical and horizontal surfaces are illuminated at angles in between normal and grazing and give rise to returns of more nearly equivalent strength. This is the situation prevailing in the Cazenovia data. That is, at the higher angles of the constant-γ regime, vertical features are less obtrusive and tend to “melt into” the horizontal background.

2.3.5 Terrain Slope/Grazing Angle Depression angle does not depend on the local terrain slope at the backscattering terrain point, whereas grazing angle, defined to be the angle between the tangent to the local terrain surface at the backscattering terrain point and the direction of illumination, does depend on the local terrain slope (see Figure 2.15). If depression angle is a useful modeling parameter of low-angle clutter, should not grazing angle be a better parameter? Intuition strongly suggests that the best measure of illumination angle in considering backscattering from a rough surface is the angle between the direction of illumination and the plane of the surface. Discrete vertical land cover features often dominate as clutter sources in low-angle clutter. For example, if a tree exists in a spatial resolution cell, the slope of the ground under the tree is not very significant in affecting the backscatter from the cell. Trees and other vertical landscape features are vertical irrespective of the underlying terrain slope. Thus discrete land cover features, which are the dominant low-angle clutter sources, act to emphasize depression angle and de-emphasize grazing angle as the fundamental measure of illumination angle.

2.3.5.1 Digitized Terrain Elevation Data Set aside for the moment the issue of discrete vertical features in land cover—assume that terrain slope will act as a dominant parameter strong enough to overcome such dispersive effects in low-angle clutter. How should these important terrain slopes be computed or measured? At this point, consider the availability of digitized terrain elevation data (DTED) from various sources. Such DTED are provided as points of terrain elevation of specified vertical precision (e.g., ~ 1 m) on a horizontal latitude/longitude grid of specified sampling interval (e.g., ~100 m). In clutter modeling, can grazing angle be usefully brought to bear to predict clutter strength, cell by cell in the DTED, based on the elemental terrain slopes provided by these data? If such an approach were successful, the DTED could carry the burden of describing terrain, which is a root cause of difficulty in clutter modeling. A clutter model could then be a simple relationship between cell-level grazing angle and clutter strength.

σ ° vs Grazing Angle. An example of cell-level correlation between measured clutter strength and DTED-predicted grazing angle is shown in Figure 2.21. The site for which the data of Figure 2.21 apply is Brazeau, a forested site of significant relief in Alberta, Canada. Selection of a forested site provides a more spatially continuous scattering medium and minimizes the effects of strong discretes such as occur on more open landscapes, thus potentially giving grazing angle a better chance to work.15 For each resolution cell within 20-km maximum range at Brazeau, terrain slope and grazing angle were computed from DTED and registered with the measured Phase Zero clutter strength for the cell. Then, for each cell that was within geometric visibility and for which the Phase Zero radar measured 15. Figure 2.21 and its discussion here may be compared with Figure 1.4 and its discussion in Section 1.2.5.

Preliminary X-Band Clutter Measurements

63

a discernible clutter return, a single point was plotted in Figure 2.21. Doing so for all such points resulted in the scatter plot shown.

20 10 0

σ°F4 (dB)

–10 –20 –30 –40 –50 –60

0.001

0.01

0.10

1.0

10.0

Grazing Angle (deg)

Figure 2.21 Cell level scatter diagram of measured σ °F4 vs grazing angle at Brazeau, Alta. Range interval = 1 to 20 km. Azimuth interval = 1.0° to 360°. Phase Zero X-band clutter data, horizontal polarization, 75-m range resolution. Terrain slope at each cell computed from digitized terrain elevation data (DTED).

Very little useful correlation is seen between clutter strength and grazing angle in Figure 2.21. The actual correlation coefficient computed for these data is 0.21. Scatter plots similar to Figure 2.21 were generated for six different sites of widely varying terrain type. The largest correlation coefficient obtained was 0.23. Negative correlation between grazing angle and clutter strength was equally likely to positive correlation. For one site, additional DTED of five-fold improvement in scale, precision, and accuracy were utilized with little improvement in the results. These investigations have shown the idea of a simple clutter model based on statistically significant direct correlation between cell-level estimates of grazing angle from DTED and measured clutter strength to be inefficacious. Such a simple model does not resolve the complexities of real terrain. Any usefulness in such correlative associations requires more sophisticated analyses looking for more subtle effects (see Appendix 4.D).

DTED Accuracy. Why is so little correlation seen between clutter strength and grazing angle predicted from DTED? First recall that DTED describes only a bare earth and contains no information describing land cover, the edges of land cover features, or other discrete land cover objects that dominate low-angle clutter. Beyond this, however, the results shown in Figure 2.22 provide more insight. These results apply to forested terrain in eastern Massachusetts. In Figure 2.22, terrain elevations are shown based on two sources,

64

Preliminary X-Band Clutter Measurements

(1) DTED and (2) quadrangle topographic maps. The quadrangle maps from which information was plotted directly in Figure 2.22 were of much higher precision and accuracy (by a factor of ~10) than the DTED. The two terrain profiles in Figure 2.22, DTED and quadrangle, show general similarity. Consequently, use of DTED to predict macroscale regions of terrain visibility and shadow provides useful information. However, it is another matter to consider correlating local terrain slopes with clutter strength, cell by cell, in the data of Figure 2.22. Since the quadrangle data are more accurate, it is evident that many DTED cells provide markedly inaccurate estimates of terrain slope. Clearly such DTED do not contain precise and accurate enough information to provide terrain slope detail at the scale of radar transmission wavelength, which is the scale at which the mechanisms of electromagnetic backscattering take place. Nor, in fact, do the quadrangle data provide such necessary precision and accuracy, since any map is a simplification of reality. As has been observed elsewhere, “ . . . in typical agricultural and rolling terrain . . . the grazing angle is not readily definable”[10]; and “it [is] difficult to define grazing angle over a non-flat surface such as natural terrain” [6].

Dolbier Hill (42° 32' 45" N; 72° 03' 32" W)

Height (m)

400

DTED Quadrangle Data 300

200 0

2.5

5.0

7.5

10.0

12.5

15.0

Distance (km) East Ware River to Dolbier Hill (a)

Dolbier Hill

Height (m)

400

DTED Quadrangle Data

300

200 0

2.5

5.0

7.5

10.0

12.5

Distance (km) Natty Pond to Dolbier Hill (b)

Figure 2.22 Terrain elevation profile along two paths in Massachusetts, comparing digitized terrain elevation data (DTED) and data derived from quadrangle topographic maps. The quadranglemap-derived data are ~10 times more accurate than the DTED.

Preliminary X-Band Clutter Measurements

65

2.3.5.2 Patch Classification By Terrain Slope The discussion now returns to the implicit idea that, at some level or some scale, terrain slope must strongly affect clutter strength. In contrast to DTED cells, consider the Phase Zero clutter patches, typically sized to be several kilometers on a side. Such patches are macroscale in comparison with microscale DTED cells. Recall that the landform within each patch is classified through interpretation of stereo aerial photographs and topographic maps. In this classification, terrain slope is a principal criterion. Of course, any patch several kilometers on a side presents various slopes to the radar, so it is the distribution of slopes over each patch that must be considered. This distribution of slopes over a patch depends on the measurement scale employed—increasing magnification always reveals increasing detail and new structure in the surface (i.e., fractal phenomenon). Thus the actual distribution of slopes over a patch is regarded as an indeterminate quantity.

Mean Clutter Strength By Landform. Through subjective interpretation of air photos and maps, bounds or limits may be set to the slopes existing within each patch, and subsequent binning of patches can occur within classes defined by these slope limits. Figure 2.23 specifies six categories of landform in increasing order of terrain slope. Within the category of level terrain, there exist Phase Zero measurements from 524 different patches. For each level patch, there exists a corresponding measured mean clutter strength. Figure 2.23 shows the cumulative distribution of mean clutter strength from all 524 patches of level terrain. Wide spread exists in this distribution of mean clutter strength measured from level patches. From maximum to minimum measured mean values, there is over 30 dB of variation. The cumulative distributions of mean clutter strength from the five remaining terrain types are also shown. If, as a measure of centrality, the median level (indicated by the horizontal dashed line) is selected in each distribution of mean clutter strength in Figure 2.23, a statistically significant monotonic increase in mean clutter strength with terrain slope is observed. That is, at the median level the distributions are displaced increasingly to the right with increasing terrain slope over a range of 11 dB from minimum to maximum. Hence intuition is justified. These data unequivocally illustrate that clutter strength depends on terrain slope. The effect is strong enough to be observed through dispersive influences of land cover, terrain heterogeneity, and depression angle. Two other important facts are also observed: (1) there is much spread within the distribution of mean clutter strength for any given class of landform, and (2) although significant, there is relatively little separation between adjacent classes. Mean Clutter Strength By Land Cover. Similar to the way in which Figure 2.23 shows how Phase Zero mean clutter strengths separate in six classes of landform, Figure 2.24 shows how Phase Zero mean clutter strengths separate in six classes of land cover. As might be intuitively expected, the data of Figure 2.24 indicate that, in terms of mean clutter strength, urban terrain is stronger and wetland weaker than most other land cover types. The expected-value results in Figures 2.23 and 2.24 are derived from the same set of 2,177 Phase Zero clutter patch measurements described earlier. 2.3.6 Clutter Modeling Assume that DTED are available for the site to be modeled. The DTED can be used to define kilometer-sized clutter patches as regions of general geometric visibility. This is an appropriate use of DTED, well matched to the information content of the database. Within these macroregions of visibility, clutter strength cannot be accurately predicted cell by cell simply by association with the local terrain slope and grazing angle at the cell. This is an

66

Preliminary X-Band Clutter Measurements

Normal Scale 0.999

Probability That σ°F4 ≤ Abscissa

0.99

Terrain Slope (deg)

0.9

0.7

Level Undulating Inclined

High Relief

2–5 Rolling Moderately 2–10 Steep 10–35 Steep

0.5 0.3

<1 <1 1–2

Low Relief

0.1

0.01

0.001 –50

–40

–30

–20

–10

σ°F4 (dB) Figure 2.23 Cumulative distributions of mean ground clutter strength by landform in rural terrain. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 2- to 12-km range, 1809 patches, 96 sites. Each curve shows the cumulative distribution of mean clutter strengths from all patches of a given terrain type, one value of mean strength per patch.

inappropriate use of DTED because the sought-after information is at a scale, accuracy, and precision not contained within the data. Still, illumination angle is of major importance in its effects on low-angle clutter strength. Rather than grazing angle, results in this book are based on depression angle. Depression angle is a quantity that can be computed relatively rigorously and unambiguously from available information. For example, within a macropatch of visible terrain in DTED, depression angle—which depends only on the cell-level elevations over the patch and not the detailed rates of change of these elevations—is a quantity that varies relatively slowly over the patch. If the mean depression angle over the patch is computed, this mean value is relatively insensitive to the questions of accuracy, precision, and scale that plague grazing angle. But in using depression angle, how are the important effects of terrain slope incorporated? Reconsider the data in Figure 2.23 that statistically show how mean clutter strength increases with terrain slope. As shown there, terrain is simply separated into two categories, low and high relief. Low-relief terrain provides slopes of < 2°; high-relief terrain provides

Preliminary X-Band Clutter Measurements

67

Normal Scale 0.999

0.99

W

A

Abscissa

0.9

F4

0.5

Probability That

R

0.3

F B U

0.7

Wetland Rangeland Agriculture Forest Barren Urban

0.1

0.01

0.001

–50

–40

–30

–20

–10

F4 (dB)

Figure 2.24 Cumulative distributions of mean ground clutter strength by land cover. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 2- to 12-km range, 2,172 patches, 96 sites. Each curve shows the cumulative distribution of mean clutter strengths from all patches of a given terrain type, one value of mean strength per patch.

slopes of > 2°. Thus in Figure 2.23, level, inclined, and undulating terrain categories are all low relief; whereas rolling, moderately steep, and steep terrain categories are all high relief. This simple landform-descriptive scheme consisting of two relatively general classes captures much of the statistical significance in the dependency of clutter strength on terrain slope, given the large spread within and little separation between more specific classes. In addition, this simple twofold scheme has the attendant advantage of liberating the user of these results from providing highly detailed descriptions of terrain. Superficially, it may appear that terrain slope enters the current results only through specification of terrain relief as low or high. However, the further quantitative dependence of these results on depression angle also carries with it an implicit dependence on terrain slope, wherein higher terrain slopes generally occur at higher depression angles (i.e., high sites usually occur in hilly terrain). Thus, results in this book take into account terrain slope, not in simplistic or idealized ways, but in practicable ways that have stood the test of trial in the empirical data.

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Preliminary X-Band Clutter Measurements

2.4 X-Band Clutter Spatial Amplitude Statistics Section 2.4 provides modeling information for predicting ground clutter amplitude statistics applicable to spatial distribution over patches of visible terrain as seen by a surface-sited X-band radar. This information is arrived at by combining measurements from many similar Phase Zero patches into ensemble distributions of clutter amplitude statistics. By the word “similar” is meant patches of like-classified terrain that are viewed at closely similar depression angles. Section 2.4 provides clutter strength modeling information for both general and various specific levels of terrain classification. Modeling information is presented in Section 2.4 within a standard tabular format involving (1) terrain type, (2) depression angle, (3) Weibull coefficients of the approximating Weibull amplitude distribution, (4) measured mean strength of the ensemble amplitude distribution, (5) the percent of microshadowed cells (i.e., percent of cells at radar noise level)16 within the ensemble distribution, and (6) the number of clutter patches included in the ensemble. The three Weibull coefficients presented are the Weibull shape parameter aw , the Weibull median clutter strength σ 50 ° , and the Weibull mean clutter strength σ w° . The important characteristic of spread in the approximating Weibull distribution is observable, either directly in the aw parameter, or in the mean-to-median ratio. The modeling information in Section 2.4 illustrates the first important trends discovered in the Phase Zero data—namely, the dependencies of σ w° and aw on depression angle. The information provided for aw is limited to Phase Zero spatial resolution (i.e., 1° azimuth beamwidth and, generally, 0.5 µs pulse length; but see also Section 2.4.5). More general effects of resolution on aw are developed in following chapters. The important trends of σ w° and aw with depression angle observed to occur in the preliminary X-band modeling information of Section 2.4 also occur at other spatial resolutions, but the precise numbers specifying aw vary with the resolution of the radar under consideration.

2.4.1 Amplitude Distributions by Depression Angle for Three General Terrain Types Specified here are spatial amplitude distributions of low-angle X-band ground clutter for three general terrain types: (1) rural/low-relief, (2) rural/high-relief, and (3) urban. These three terrain types are summarily described in Table 2.3. These terrain types are allinclusive—any patch of terrain must be classified as one and only one of these three types. Thus rural terrain includes such diverse specific terrain types as agricultural, forest, rangeland, wetland, and barren. Urban terrain includes any kind of built-up land such as commercial, industrial, and residential. In terms of degrees of roughness of terrain surface, the classification system utilized (see Table 2.2) incorporates the following specific categories: level, undulating, hummocky, inclined, broken, rolling, ridged, moderately steep, and steep. Low relief encompasses the first five categories, and high relief encompasses the last four. Note that the actual distribution of slopes that exists within a macroscale clutter patch is specified, not the overall slope of the best-fit plane through the patch.

16. The quantity actually provided is the percent of samples above radar noise level, which is the complement of the percent of microshadowed cells.

Preliminary X-Band Clutter Measurements

69

Table 2.3 Three General Terrain Types 1

Rural/Low-Relief

2

(Slopes < 2°; Relief < 100 ft) Rural/High-Relief

3

(Slopes > 2°; Relief > 100 ft) Urban

In data reduction and analysis, X-band clutter amplitude distributions were formed from 2,177 Phase Zero clutter patches, each generally several kilometers on a side. For each patch, detailed terrain descriptions at the specific level just described were determined. It was found that in the separation of clutter amplitude data into such specific terraindescriptive classes, spread within class was broad and separation between similar or neighboring classes was narrow. Thus the three general terrain classes of Table 2.3 are utilized, which do provide significant and useful separation of X-band clutter data. A simple way of interpreting these three general terrain types is that only “mountains” (rural/ high-relief) and “cities” (urban) grossly warrant separation from all other terrain types (rural/low-relief). Empirical ground clutter spatial amplitude distributions are presented in Figure 2.25 by depression angle for rural/low- and rural/high-relief terrain. Similar results are presented in Figure 2.26 for urban terrain (in which the regime of the rural distributions is shown lightly shaded for comparison). These distributions include all spatial samples within patches including cells at radar noise level, but are shown only over σ °F4 regimes to the right of the highest noise-contaminated bin. Thus, where shown, these distributions are independent of Phase Zero sensitivity and represent what a theoretically infinitely sensitive radar would measure. It is seen that, within each of these three terrain types, the shape of the spatial amplitude distribution is strongly dependent on depression angle, such that there is a continuous rapid decrease in the spread of the distribution with increasing depression angle, even over the very small depression angles (usually < 1.5° in low-relief terrain) associated with surfacesited radar. The distributions in Figures 2.25 and 2.26 are formed by combining likeclassified clutter data from a large data set altogether comprising 2,177 clutter patch amplitude distributions obtained from measurements at 96 sites at ranges from 2- to 12-km from the radar. It is only by means of such extensive averaging that the smooth monotonic dependence of both strength (the distributions gradually move to the right with increasing angle) and spread (the slopes of the distributions gradually increase with increasing angle) emerge in these empirical distributions to provide a general predictive capability. These underlying fundamental trends are often obscured by specific effects in individual measurements. Most (66%) of these measured data are contained in the rural/low-relief distributions of Figure 2.25. It is this parametric regime that is applicable to most surface radar situations and has traditionally been least well understood. The set of rural/low-relief distributions is extended in the rural/high-relief distributions (the latter accounting for 18% of the data), where higher depression angles are realized in high-relief terrain through higher site

70

Preliminary X-Band Clutter Measurements

Weibull Scale

Rural Terrain Low-Relief High-Relief

0.97 0.95

h Slo

pe

0.9 0.8

4 2 to

0.25 to 0.50

0.6

Rayle ig

0.00 to 0.25 0.7

0t o2

1.00 to 1.50

Depression Angle (deg)

0.4

6 to

0.75 to 1.00

0.5

8

6

0.50 to 0.75

4 to

Probability That σ°F4 ≤ Abscissa

0.995 0.99

0.3

–60

–50

–40

–30

σ°F4

–20

–10

0

(dB)

Figure 2.25 Cumulative ground clutter amplitude distributions by depression angle for rural terrain of low- and high-relief. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 2- to 12-km range, 1,743 patches, 87 sites.

locations. Across the rural data set as a whole, the effect of continuously decreasing spread in the distributions with increasing angle is at the heart of understanding low-angle clutter as a physical phenomenon dominated by microshadowing. The highest angle distribution (6° to 8° depression angle) almost achieves the Rayleigh slope, reflecting the fact that the amount of microshadowing is relatively small at such high airborne-like angles. The resultant nearly full illumination, as expected, provides approximately Rayleigh statistics. The urban distributions of Figure 2.26 (which contain 6% of the measured data) also show monotonically decreasing spread with increasing angle, but contain significantly stronger clutter than the corresponding rural/low-relief distributions. Ten percent of clutter patches were measured at negative depression angles; these data are discussed in Section 2.4.2.6.

Depression Angle Distributions. The distributions of depression angle at which Phase Zero clutter patches were measured are shown in Figure 2.27, both as an overall distribution and separated into rural/low-relief, rural/high-relief, and urban components. Depression angle is a fundamental parameter in low-angle clutter. It is the distributions shown in Figure 2.27, partitioned into appropriate contiguous intervals, that exert controlling influence on the distributions in Figures 2.25 and 2.26. In each part of Figure 2.27, cumulative probability is given by the s-shaped curve and read on the left ordinate; percentage of patches is given by the underlying histogram and read on the right ordinate. The data in Figure 2.27 indicate that depression angles to visible terrain for surface-sited radars are usually quite low, but the data also show that depression angles in high-relief terrain range over significantly higher values than those in low-relief terrain. The single highest depression angle at which a Phase Zero clutter patch was measured was 13.8° at

Preliminary X-Band Clutter Measurements

Probability That σ°F4 Abscissa

0.995 0.99

71

Weibull Scale Urban Terrain

0.97 0.95 0.9

0.8 0.7

o

0t

Rural, Fig. 2.25 (for comparison)

5 0.2

0.0

70

0.6

25

to

0.

0.5

70

to

0.

00

4.

Depression Angle (deg)

0.

0.4 0.3 –60

–50

–40

–30

–20

–10

0

σ°F4 (dB)

Figure 2.26 Cumulative ground clutter amplitude distributions by depression angle for urban terrain. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 2- to 12-km range, 109 patches, 33 sites.

the Equinox Mountain site in Vermont. The largest negative depression angle at which a Phase Zero clutter patch was measured was –4.4° at the Waterton site in Alberta.

2.4.1.1 Weibull Parameters The cumulative clutter amplitude distributions shown in Figures 2.25 and 2.26 are relatively linear as plotted on the Weibull probability scale of these figures, and thus can be usefully approximated with Weibull statistics (a theoretical Weibull distribution plots as a straight line in these figures). The Weibull distribution is discussed in Appendix 2.B, including the methodology utilized for obtaining Weibull approximations to measured distributions. Weibull distributions provide the wide degree of spread appropriate to lowangle ground clutter amplitude distributions. The Weibull cumulative distribution function may be written [11, 12]:    ln2 ⋅x b  P ( x ) = 1 – exp  – -------------------   ( σ ° )b  50   where σ °50 = median value of x

(2.2)

72

Preliminary X-Band Clutter Measurements

b = 1/aw aw = Weibull shape parameter. The mean-to-median ratio for Weibull statistics is Γ ( 1 + aw ) σw ° ---------= ----------------------aw σ 50 °

(2.3)

( ln2 )

Depression Angle (deg) Maximum 13.8 90-Percentile 1.7 Median 0.4 Minimum –4.4

a) Overall 2148 Patches

0.5

Depression Angle (deg) Maximum 6.8 90-Percentile 1.2 Median 0.4 Minimum –1.4

b)Rural/ Low Relief 1559 Patches

100 10 1 0.1

Percentage of Patches

1.0

0.01

0 1.0

Depression Angle (deg) Maximum 13.8 90-Percentile 3.6 Median 0.9 Minimum –4.4

c) Rural/High Relief 468 Patches

0.5

Depression Angle (deg) Maximum 3.8 90-Percentile 2.4 Median 0.6 Minimum –0.5

d) Urban 121 Patches

100 10 1

Percentage of Patches

Probability That Depression Angle ≤ Abscissa

where σ w° is the mean value of x and Γ is the gamma function. Here the random variable x represents clutter strength σ °F4 including propagation effects.

0.1

0 –5

0

5

10

Depression Angle

15 –5

0

5

10

Depression Angle

Figure 2.27 Distributions of depression angle at which clutter patches were measured. Phase Zero measurements, 96 sites, 2- to 12-km range.

Section 2.4 characterizes measured Phase Zero empirical clutter amplitude distributions by means of the two Weibull coefficients, the Weibull shape parameter aw, and the decibel value of Weibull median clutter strength σ 50 ° (dB). These two coefficients entirely characterize the modeled distribution; from them the distribution can be easily visualized or sketched, and Weibull random numbers belonging to the modeled distribution can be generated. The Weibull shape parameter aw is a dimensionless quantity indicative of the spread of the distribution. For aw = 1, the Weibull distribution degenerates to a Rayleigh17 distribution, which represents a lower bound on spread in clutter spatial amplitude statistics. Most of the Phase Zero empirical spatial amplitude distributions are approximated by values of shape parameter such that aw > 1.

17. Rayleigh for

σ ° ; exponential for σ °.

Preliminary X-Band Clutter Measurements

73

In addition, Section 2.4 provides σ w° (dB), the decibel value of Weibull mean strength in the modeled distribution. The Weibull mean strength σ w° (dB) is provided to compare with the mean strength in the actual measured ensemble distribution as a first measure of goodness-of-fit of the Weibull model to the measured data. The spread in the approximating distribution may also be assessed by the mean-to-median ratio, σ w° (dB) minus σ 50 ° (dB). Median levels of the actual measured ensemble distributions may be read or estimated from their graphed cumulative distributions. As mentioned in Section 2.3.3.2, almost none of the measured distributions pass rigorous statistical hypothesis tests for Weibull on any other analytically representable statistical distribution that was tried (but see Appendix 5.A, Section 5.A.4). Figure 2.28 shows five theoretical Weibull distributions plotted in the same manner as the empirical Phase Zero ensemble clutter amplitude distributions in Figures 2.25 and 2.26. All five of these theoretical distributions have the same median clutter strength, σ 50 ° (dB) = –40, but have values of shape parameter aw ranging from aw = 1 to aw = 5. Comparison of similar percentile levels over these five distributions indicates their extreme differences. For example, for the distribution with aw = 5, one in a thousand samples is 50 dB stronger than σ 50 ° (dB), whereas for the distribution with aw = 1 (the Rayleigh degenerative case), ° (dB). Clearly the shape one in a thousand samples is only 10 dB stronger than σ 50 parameter aw of a ground clutter spatial amplitude distribution strongly affects the false alarm statistics of a radar operating in that clutter. Use of Eq. (2.3) shows that the distribution for aw = 5 has mean strength σ w° = –11.3 dB whereas the distribution for aw = 1 has σ w° = –38.4 dB, which is 27 dB weaker. Weibull Scale 0.999 1

aw

σ°w(dB)

–38

–34

3 –27

4

–20

–11

Rayle

0.9

0.7

P(σ°)

5

igh

0.99

2

P(σ°) = 1 – exp –

In 2 • (σ°)

1/aw

(σ°50) 1/aw

0.5 σ°50 = –40 dB 0.3

0.1 –60

aw 1 2 3 4 5 –50

–40

–30

–20

° σw° / σ50 (dB) 1.6 Rayleigh 6.2 12.6 20.2 28.8 –10

0

10

σ°(dB)

Figure 2.28 Five theoretical Weibull cumulative distributions; σ °50 = –40 dB; aw = 1, . . . 5.

74

Preliminary X-Band Clutter Measurements

Specific Weibull approximations for the ground clutter amplitude distributions shown in Figures 2.25 and 2.26 are presented in Table 2.4 by depression angle for each of the three general terrain types. The table shows that large shape parameters at low angles rapidly diminish with increasing angle, approaching the Rayleigh value of unity at the highest angles. At the same time, median clutter strengths rapidly increase with increasing angle. Mean clutter strengths increase more gradually with increasing angle, so spread in terms of mean-to-median ratio is also observed to rapidly decrease with increasing angle. This behavior mirrors that of K-distributions (which also decrease in spread and degenerate to Rayleigh) which arise out of theoretical investigations of low-angle clutter amplitude distributions [13, 14]. To just describe these amplitude distributions, which is the intent here, Weibull distributions serve the purpose as well as K-distributions (see Appendix 5.A) and are simpler to use. The depression angle regimes are narrower and more numerous in Table 2.4 than in Figures 2.25 and 2.26, indicating that the parametric trend with depression angle is significant even for small steps of depression angle. The measured mean clutter strength for each ensemble distribution in the table is observed to closely match the mean strength of the approximating Weibull distribution, a first indication that laying a bestfitting Weibull straight line over central parts of each measured distribution of Figures 2.25 and 2.26 produces approximating distributions of reasonable mean strength. Table 2.4 strongly indicates that shadowing is a major cause of the variations that are observed with depression angle—the incidence of microshadowed cells varies from as much as 64% at grazing incidence in low-relief terrain to as little as 14% at high angle in high-relief terrain. The condensation and codification of properties of low-angle ground clutter within Weibull coefficients as presented in Table 2.4 fulfills much of what was initially sought to be understood about low-angle X-band ground clutter.

2.4.1.2 Overall Distribution Figure 2.29 shows the overall cumulative clutter amplitude ensemble distribution resulting from combining individual measurements from all 2,177 Phase Zero clutter patches into one distribution. This overall distribution is plotted cumulatively in Figure 2.29 on a Weibull probability axis that shows much more of the high (i.e., strong-side) tail of the distribution, up to 0.999999 on the probability axis, compared to the upper limit defined by 0.995 on the probability axis for the distributions shown in Figures 2.25 and 2.26. For cumulative probabilities below 0.995, the overall distribution is reasonably well fit by a linear Weibull approximation with shape parameter aw ≅ 3.9. However, this overall distribution has an upper tail at higher probabilities greater than 0.995, approximated by a much larger value of shape parameter. This upper tail of strong clutter values of increased spread compared with the central part of the distribution is due to occasional strong localized discrete scattering sources on the landscape such as water towers and grain storage elevators. Such objects are larger and of less frequent occurrence than the myriad smaller discrete objects acting as sources for the central part of the distribution. This high tail is relatively linear on the Weibull scale. The distribution of these relatively infrequent, widely ranging, strong clutter values, is thus well approximated for cumulative probability > 0.999 with Weibull shape parameter aw ≅ 7. A Weibull fit to the central part of the overall distribution of Figure 2.29 represents the general spatial amplitude distribution of low-angle X-band land clutter, irrespective of depression angle and terrain type. The Weibull parameters of this general distribution are

Preliminary X-Band Clutter Measurements

75

Table 2.4 Statistical Attributes of X-Band Ground Clutter Amplitude Distributions for Rural/LowRelief Terrain, Rural/High-Relief Terrain, and Urban Terrain, by Depression Angle

Terrain Type

Depression Angle (deg)

Rural/ Low-Relief

Rural/ High-Relief

Urban

Weibull Parameters

Ensemble Mean Clutter Strength σ°F 4 (dB)

Percent of Samples above Radar Noise Floor

Number of Patches

aw

σ°50 (dB)

σ°w (dB)

0.00–0.25 0.25–0.50 0.50–0.75 0.75–1.00 1.00–1.25 1.25–1.50 1.50–4.00

4.8 4.1 3.7 3.4 3.2 2.8 2.2

–60 –53 –50 –46 –44 –40 –34

–33 –32 –32 –31 –30 –29 –27

–32.0 –30.7 –29.9 –28.5 –28.5 –27.0 –25.6

36 46 55 62 66 69 75

413 448 223 128 92 48 75

0–1 1–2 2–3 3–4 4–5 5–6 6–8

2.7 2.4 2.2 1.9 1.7 1.4 1.3

–39 –35 –32 –29 –26 –25 –22

–28 –26 –25 –23 –21 –21 –19

–26.7 –25.9 –24.1 –23.3 –22.2 –21.5 –19.1

58 61 70 66 74 78 86

176 107 44 31 16 9 8

0.00–0.25 0.25–0.70 0.70–4.00

5.6 4.3 3.3

–54 –42 –37

–20 –19 –22

–18.7 –17.0 –24.0

57 69 73

25 31 53

given in Table 2.5. The degree of linearity of the central part of the overall distribution in Figure 2.29 indicates that it is relatively well-fit by its Weibull approximation—this is borne out by the close comparison between the Weibull and actual ensemble mean clutter strengths in Table 2.5. In actuality, the central part of the overall distribution in Figure 2.29 is slightly concave upward, indicating that the exact shape of the distribution lies between that of a Weibull distribution and that of a K-distribution (see Appendix 5.A).

Rural/Low-Relief, Rural/High-Relief, Urban. Also shown in Figure 2.29 are the component ensemble distributions of the overall amplitude distribution corresponding to each of the three general terrain types: rural/low-relief, rural/high-relief, and urban. Statistical attributes for these three component distributions are also shown in Table 2.5. These three distributions may be used in non-site-specific ground clutter modeling to simply characterize the overall terrain at a site as one of these three general types. The increased spread in the high tail of the overall distribution caused by large discrete objects is mirrored in both the rural/low-relief and high-relief distributions in Figure 2.29. At higher probabilities (> 0.9999) in the high tails, there is no distinction between the rural/ low-relief and rural/high-relief distributions because large discrete objects cause these tails. The urban distribution also has a high tail with increased spread that extends to lower probability levels than do the high tails in rural terrain. The incidence of receiver saturation in the Phase Zero measurements is also shown in Figure 2.29. It is evident that the highside tails in the distributions of Figure 2.29 are significantly affected by saturation, increasingly so with increasing clutter strength. These effects of saturation are to slightly

76

Preliminary X-Band Clutter Measurements

Weibull Scale 0.999999 0.99999

0.999

Ur ba n

0.99

ra l/L ow -R er eli all ef

0.95 0.9

100 80

ef eli

Ov

0.8

-R

60

igh

0.7

l/H

40

Ru

ra

0.6

20

0.5

0 –50

–40

–30

–20

–10

0

10

Percent of Saturated Samples

0.97

Ru

Probability That σ°F4 ≤ Abscissa

0.9999

20

σ°F4 (dB)

Figure 2.29 Cumulative ground clutter amplitude distributions for rural/low-relief terrain, rural/ high-relief terrain, urban terrain, and the overall combination of all three terrain types. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 2- to 12-km range, 2,177 clutter patches. See also Table 2.5. Table 2.5 Statistical Attributes of Rural/Low-Relief, Rural/High-Relief, Urban, and Overall Ground Clutter Amplitude Distributionsa

aw

σ°50

σ°w

(dB)

(dB)

Ensemble Mean Clutter Strength σ°F 4 (dB)

Overall

3.9

–48

–28.4

–27.6

53

2177

Rural/ Low-Relief

3.9

–51

–31.4

–29.7

52

1584

Rural/ High-Relief

2.3

–34

–26.1

–25.3

64

471

Urban

3.8

–41

–22.4

–19.7

68

122

Weibull Parametersb Terrain Type

Percent of Samples above Radar Noise Floor

Number of Patches

a Phase Zero X-band data, 75 m range res., hor. pol., 2 to 12 km range, 2177 patches. See also Figure 2.29. b For cumulative probability < 0.999

under-estimate the high-side tails, which must extend to slightly higher strengths and be of slightly greater spread than indicated by the data of Figure 2.29. The effects of saturation

Preliminary X-Band Clutter Measurements

77

are somewhat greater in the urban distribution in Figure 2.29—they cause an obvious break in slope in the urban high tail.

2.4.1.3 High Distribution Tails Having discussed the high tails in the overall ensemble clutter amplitude distributions, the discussion now turns to the high tails in the measured ensemble clutter amplitude distributions partitioned by depression angle. The high tails of the rural terrain clutter ensemble amplitude distributions of Figure 2.25 partitioned by depression angle are shown in Figure 2.30—the distributions by depression angle for low-relief terrain are shown in Figure 2.30(a), and those for high-relief terrain are shown in Figure 2.30(b). Linear extrapolation of the distributions in Figure 2.25 to higher levels suggests a region of coalescence and possible crossover at higher probability levels. For low-relief terrain, Figure 2.30(a) shows that these distributions actually all roll to the right to assume the increased spread seen in the overall results of Figure 2.29, with little or no cross-over. For high-relief terrain, Figure 2.30(b) shows that the distributions for 0° to 2° and 2° to 4° also roll to the right with a crossover, but the distributions for 4° to 6° and 6° to 8° do not roll to the right but stay relatively linear on the Weibull scale to the highest probability levels shown. These results indicate that at low angles in high-relief terrain large discrete objects are still evident, but that at high enough angles large discretes become much less evident. That is, at high angles in high-relief terrain, large discrete objects tend to “melt into” the background (as previously discussed, see Figure 2.14) so that it is much less probable to receive specular-like broadside flashes from discrete vertical objects at high angles in high-relief terrain than is the case at lower angles in high-relief terrain or in low-relief terrain in general. The high tails shown in Figures 2.29 and 2.30 are of interest because of their potential to cause false alarms in surface-sited radar operating in ground clutter.

2.4.2 Clutter Results for More Specific Terrain Types The basic Phase Zero ground clutter modeling information of Section 2.4.1 is based on three general terrain types. Although Weibull statistics and three terrain types are enough to show fundamental trends in low-angle clutter, the resultant basic construct cannot contain all the complex higher-order attributes of the actual phenomenon. Section 2.4.2 illustrates that increasing fidelity in terrain descriptive information can reveal higher-order trends in clutter statistics.

2.4.2.1 Mountain Clutter Besides needing information describing general clutter strengths, an analyst may also need to know something about worst-case situations. Provided here is additional specific information on how strong mountain clutter can become.

Clutter Patches at Plateau Mountain. The steepest roughest terrain from which ground clutter was measured was that of the Canadian Rocky Mountains. One site, Plateau Mountain, was a flat-topped mountain site high in the Rockies that provided road access for the truck-borne clutter measurement equipment. From Plateau Mountain, the view to the west was of steep barren rock faces from high peaks in the Rockies. The lower slopes of these mountains were tree-covered with the trees gradually thinning out at the higher elevations. A photograph looking west from Plateau Mountain is shown in Figure 2.2(b). The measured Phase Zero clutter map for 12-km maximum range at Plateau Mountain is

78

Preliminary X-Band Clutter Measurements

0.9999 Rural/Low Relief Terrain

0.9997

1.5

1.0

75

0.999 50

to

0.

0.

25

to

0.995

0.

0.

50

00

to

0. 25

0.997

0. 75

to

1. 00

Depression Angle (deg)

(a)

0.

Probability That σ°F4 ≤ Abscissa

0

o 0t

0.9995

0.99 –20

–15

–10

–5

0

σ°F4 (dB)

to

4

8

0

2

6 to

4 to 6

Rural/High Relief Terrain

0.9997

to

2

0.9995

0.999

8

(b)

6 to

2t

4 to 6

o2

0.995

o4

0.997

0t

Probability That σ°F4 ≤ Abscissa

0.9999

0.99 –20

–15

–10

–5

0

4

σ°F (dB)

Figure 2.30 High tails of cumulative ground clutter amplitude distributions by depression angle for rural terrain of low- and high-relief. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 2- to 12-km range, 1,743 patches, 87 sites. See also Figure 2.25.

Preliminary X-Band Clutter Measurements

79

shown in Figure 2.31. The clutter patches selected within 12-km range at Plateau Mountain are also shown in Figure 2.31. Measured clutter amplitude distributions from the five strongest of these Plateau Mountain clutter patches are shown in Figure 2.32. Descriptive information and mean clutter strengths for these five patches are provided in Table 2.6. In Figure 2.32 the regime of the rural distributions of the basic Phase Zero clutter modeling information is shown lightly shaded for comparison. Also shown for comparison in Figure 2.32 is the strongest Phase Zero urban clutter patch amplitude distribution. Table 2.6 Descriptions and Statistical Attributes of the Five Strongest X-Band Clutter Patches at Plateau Mt. Mean Clutter Strength of Patch σ°F 4 (dB)

Percent Number of of Percent Samples Depression Land Patch Spatial Tree Landform Cover Angle Number* Including Excluding Samples above Cover (deg) Radar Samples Samples in η Noise at Radar at Radar Patch Floor Noise Floor Noise Floor 4/4

–9.6

–9.0

264

86

1.6

8

7

30 < η ≤ 50

4/5

–10.8

–9.5

336

74

0.6

8

7

30 < η ≤ 50

5/1

–10.8

–8.7

216

62

1.2

8

7

3 < η ≤ 10

5/2

–9.8

–9.0

264

84

0.8

8

7

1<η≤3

15/3

–16.2

–16.1

784

99.5

2.2

8

41

η > 50

* Except for patch 15/3, these patches all include exposed rock and near vertical rock faces at mountain summits; in patch 15/3, the terrain constitutes forested slopes (still steep) at lower elevations.

(a) Phase Zero X-Band Clutter Map

(b) Clutter Patch Selection

Figure 2.31 Measured ground clutter map and patches at Plateau Mountain. Maximum range = 11.8 km, north is zenith, clutter threshold is 3 dB from full sensitivity. See Figure 2.2(b), Figure 2.32, Table 2.6.

80

Preliminary X-Band Clutter Measurements

First consider patches 4/4, 4/5, 5/1, and 5/2. These four mountain patches represent very strong ground clutter. In terms of mean clutter strength, the strongest patch measured at Plateau Mountain was patch 4/4, at –9.6 dB, approximately 10 dB stronger than the strongest mean clutter from general rural terrain in Table 2.4. In perusing Table 2.6, it is seen that all four of these patches are of steep barren mountain peaks with various incidences of trees on their lower slopes and observed at various depression angles. Mean clutter strengths from these four patches range from –9.6 to –10.8 dB. Taken together, these four patches may be thought of as representing a worst-case (i.e., strongest clutter) for rural terrain. Altogether at Plateau Mountain there were 43 patches carrying the primary landform classification of “steep.” The average strength of these patches was –21.2 dB. Their average depression angle was +2.7°. The basic Phase Zero clutter modeling information of Table 2.4 predicts mean clutter strength σ w° of –24 or –25 dB for depression angle of 2.7° in high-relief terrain. Of course steep terrain is the extreme case of high-relief. A 3-dB increase in this predicted value of –24 or –25 dB comes very close to the average Plateau Mountain mean strength.

Waterton. The other Rocky Mountain site was at Waterton, Alberta. At Waterton the radar was set up on the high prairie in southern Alberta just a few kilometers east of steep mountain terrain. The area around Waterton is characterized by an abrupt transition from prairie to mountains without an intermediate forested foothills region. From the Waterton site, the first range of mountains screened from view other peaks at longer ranges. As a result, only four patches carrying primary landform classification of steep existed at Waterton. Their average strength is –22.0 dB. The average depression angle to these four Waterton patches was –2.8° (i.e., the radar looked up to this steep terrain). If more precise patch specification could completely avoid all shadowed cells in high-relief terrain, the worst-case clutter strengths that an analyst should assign to mountain terrain would be the “shadowless” mean strengths given in the third column of Table 2.6. The shadowless mean clutter strength is computed as the mean strength from the subset of cells within the patch above radar noise level. It is seen that avoidance of shadowing raises mean strengths by less than 1 or 2 dB for the patches shown in Table 2.6. Use of shadowless statistics must be approached cautiously since they are dependent on the particular sensitivity of the measurement radar.

Bi-Modal Distributions. The clutter amplitude distributions from the four Plateau Mountain patches, patches 4/4, 4/5, 5/1, and 5/2, in Figure 2.32 are bi-modal, meaning that each distribution is widely spread out over relatively weaker clutter strengths, but is much tighter over the strongest clutter strengths. In the cumulative plots of Figure 2.32, each of these four distributions consists of two parts, a shallowly sloped part to the left and a steeply sloped part to the right. The reasons for this bi-modality are as follows. Strong returns from relatively uniform rock faces oriented toward the radar are close to Rayleigh distributed. However, many other possibilities exist for the physical contents of visible resolution cells in mountain terrain, accounting for a large number of returns of widely spread out strength, all non-shadowed and well above radar noise level. These returns from physically complex cells account for the shallow parts of the distributions to the left in Figure 2.32. Physically complex high-relief cells cannot easily be distinguished a priori from uniformly steep high-relief cells. The interpretation of high-relief bi-modal distributions was validated

Preliminary X-Band Clutter Measurements

81

at one site, Blue Knob, Pennsylvania. At Blue Knob, a steep linear ridge existed across the field-of-view from the site at ~10-km range. An original patch was specified in the region where the line-of-sight of the radar was normal to the line of the ridge and to the contour lines rising up the ridge. The bi-modal amplitude distribution from this original patch specified on the steep side of the ridge at Blue Knob was separated under smaller, more precise, multiple patch specification into a Rayleigh distribution from a central area of uniform steep planar surface, and several highly spread out distributions from more complex surrounding areas on the side of the ridge.

Weibull Scale 0.995 0.99 0.97 0.95

Rural, Fig. 2.25 (for comparison)

0.9 0.8

0.5 0.4

lope

0.6

Strongest Urban, Rosetown, Fig. 2.33 (for comparison)

igh S

0.7

Plateau Mt. Patch No. 5/1

Rayle

Probability That σ°F4 (dB) ≤ Abscissa

n

tow

se Ro

0.3 4/5 0.2 5/2 4/4

15/3

0.1 –60

–50

–40

–30

–20

–10

0

10

σ°F4 (dB)

Figure 2.32 Ground clutter cumulative amplitude distributions for five patches containing strong clutter from the Rocky Mts. Phase Zero X-band data, Plateau Mt. site, 12-km maximum range experiment, 75-m range resolution, horizontal polarization. See Table 2.6.

Consider next the distribution for patch 15/3 in Figure 2.32. Patch 15/3 also has a small left-side shallow portion in its distribution, but it appears at cumulative probability < 0.1. Table 2.6 indicates that patch 15/3 is a steep forested patch rather than a steep barren patch, and that it was observed at a relatively high depression angle of 2.2 degrees. The mean strength of the clutter in patch 15/3 is –16.2 dB. The distribution for patch 15/3 in Figure 2.32 is seen to have a slope very close to the Rayleigh slope. Other indications that patch

82

Preliminary X-Band Clutter Measurements

15/3 provides close to Rayleigh statistics are that it has the following statistical attributes: ratio of standard deviation-to-mean = 0.15 dB; ratio of mean-to-median = 0.85 dB; ratio of 90 percentile-to-median = 4 dB; ratio of 99 percentile-to-median = 8 dB. Corresponding Rayleigh values are, respectively: 0 dB, 1.6 dB, 5.2 dB, and 8.2 dB. Most high-relief patches have bi-modal amplitude distributions like patches 4/4, 4/5, 5/l, and 5/2 in Figure 2.32. As a result, the high-relief cumulative ensemble clutter amplitude distributions in the basic clutter modeling information of Figure 2.25 are also bi-modal. The high-relief ensemble distributions of Figure 2.25 only show the right-side steep part of each distribution and are truncated at the left, at the point of onset of the left-side shallow part of the distribution. In Table 2.4, the Weibull distributions approximating the right-side steep parts of the distributions in Figure 2.25 closely match the measured ensemble mean strengths inclusive of their shallow-sloped parts, indicating that mean clutter strength in high-relief terrain is controlled by the right-side steep parts of the amplitude distributions.

Phenomenology. The distinction between low- and high-relief terrain in low-angle clutter is not an arbitrary separation by terrain roughness and steepness as first encountered in Figure 2.23, but more basically relates to shadowing. Low-relief terrain is characterized by large nearly-level regions of general geometric visibility, as predicted by DTED, in which cells containing discrete vertical sources causing strong returns are interspersed with weak cells—either microshadowed, or visible but discrete-free (e.g., see Figure 4.17 and its discussion). In such circumstances, it is not practicable to adjust patch boundaries to avoid interspersed geometrically microshadowed cells and to predict only individual discretes. High-relief terrain is characterized by highly-sloped regions of general geometric visibility in which the majority of cells return discernible clutter. In high-relief terrain, the distinction between cells with and without discretes is less apparent, and it is possible to set patch boundaries so as to contain only visible cells. The differences between these two kinds of terrain are those separating the low-angle specular phenomenon traditionally associated with ground-based radar and the high-angle diffuse phenomenon traditionally associated with airborne radar. Transition from the low-angle to the high-angle regime occurs gradually with increasing depression angle, as illustrated by the data in Figure 2.25 and Table 2.4.

2.4.2.2 Urban Clutter The basic Phase Zero clutter modeling information of Section 2.4.1 includes general clutter amplitude distributions for urban terrain. Besides such general information, an analyst may wish to know how severe urban clutter can become in worst-case situations. This section provides information on this subject by showing clutter patch amplitude distributions for several of the strongest urban patches measured by the Phase Zero radar. These strong urban patches are compared with the strong mountain patches discussed in Section 2.4.2.1. Figure 2.33 shows measured cumulative amplitude distributions for three urban clutter patches. The regime of the general urban ensemble distributions from Figure 2.26 is shown lightly shaded in Figure 2.33 for comparison. Table 2.7 shows terrain descriptions, depression angles, and mean clutter strengths for these three patches, which constitute backscatter measurements made from the town of Rosetown, Saskatchewan (population 2,500); the city of Lethbridge, Alberta (population 55,000); and the city of Calgary, Alberta (population 600,000), respectively. All three urban areas exist on the relatively low-relief

Preliminary X-Band Clutter Measurements

83

Canadian prairies. In each case, the patch was selected to include only relatively high commercial buildings within the urban complex in contrast to lower outlying residential areas. Differences in clutter strength between commercial and residential urban clutter are discussed subsequently. Table 2.7 Descriptions and Statistical Attributes of Three Urban Clutter Patches at X-Band

Site

Rosetown Northa Lethbridge West Strathcona a b c

b

c

Patch Number

City or Town

13/2

Rosetown

Percent of Mean Number Samples Percent Clutter Depression above Land Tree Strength of Spatial Landform Cover Angle Radar Cover of Patch Samples (Deg) Noise in Patch η σ°F 4 (dB) Floor –4.6

384

77

0.18

12

Lethbridge

–5.1

3066

74

0.29

7

Calgary

–13.4

6328

70

1.21

12

1<η≤3

1

12

1<η≤3

1–3

12-11-51

1<η≤3

1

Commercial sector of Rosetown. Industrial section, some open development land, TV tower. Downtown Calgary, high rise buildings, Bow River and parks near river, railroad, some residential (minor)

Weibull Scale

Probability That σ°F4 ≤ Abscissa

0.995 0.99 0.97 0.95 0.9

0.8 Urban Fig. 2.26 (for Comparison)

0.7 0.6

Rosetown Lethbridge Calgary

0.5 0.4 0.3 –50

–40

–30

–20

–10

0

10

20

σ°F (dB) 4

Figure 2.33 Ground clutter cumulative amplitude distributions for three patches containing strong urban clutter. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 12-km maximum range experiment. See Table 2.7.

Although the data in Figure 2.33 are from three commercial patches, their physical differences are great. Rosetown is a small prairie town providing services to the local agricultural community. Its commercial sector is physically very small but includes grain

84

Preliminary X-Band Clutter Measurements

elevators illuminated at low depression angle. The mean clutter strength of –4.6 dB for the Rosetown patch is the single strongest mean clutter strength that exists within the database of 2,177 Phase Zero patch measurements. However, this Rosetown patch is not particularly exceptional—there are many other relatively small, relatively strong clutter patches from small towns. It may be preferable to base the worst-case urban clutter strength estimate on larger urban patches than Rosetown, allowing for much more extensive statistical averaging to take place within the distributions. Lethbridge is a moderate-sized regional city in southern Alberta. The industrial area constituting its urban clutter patch is approximately ten times larger than Rosetown but, as was the Rosetown patch, is illuminated at quite low depression angle. Notwithstanding the substantial physical differences in these two patches, their clutter amplitude distributions and mean clutter strengths are very similar. The Calgary patch in Figure 2.33 is approximately twice as large as the Lethbridge patch. Calgary is a major city, and the Calgary patch was selected to include, for the most part, just the highrise central urban core. Thus the Calgary patch is quite different, physically, from both the Lethbridge and the Rosetown patches. At Calgary, the radar position was on a hill in the outskirts of the city, 490 ft higher than the average terrain height at the city center. Thus the depression angle at which the radar viewed the ground at the city center was substantial, 1.2°, although the highest buildings in the city core were more than 500 ft high. The hilltop location may have resulted in less multipath augmentation and in many surfaces being illuminated at more oblique angle than the near-grazing-incidence illumination at Rosetown and Lethbridge and may be the cause of the somewhat weaker mean clutter strength for Calgary (in Table 2.7) compared with Rosetown and Lethbridge. Taken together, these three distributions provide a reasonable indication of how strong Xband urban clutter can become. Compared with the general urban distributions of Table 2.4, the data in Table 2.7 indicate that worst-case urban clutter can be 10 dB stronger in mean strength than more general urban levels. This is approximately the same conclusion reached about severe mountain clutter compared with more general high-relief clutter. In terms of mean clutter strength, severe urban clutter can be 5 dB stronger than severe mountain clutter. The Rosetown urban clutter amplitude distribution is included in Figure 2.32 to compare with mountain distributions.

Residential vs Commercial. In considering urban clutter, attention has been restricted to relatively strong urban clutter from commercial sectors. Considered now are the differences in urban clutter strength between residential sectors (expected to be weaker) and commercial sectors (expected to be stronger). Table 2.1 indicates that within the general land cover class of urban, the more specific subclasses of residential and commercial are employed. All the measured clutter amplitude distributions from patches classified by land cover as residential were combined into one ensemble amplitude distribution, and all measured distributions from patches classified by land cover as commercial were combined into another ensemble amplitude distribution. These two clutter amplitude distributions for urban terrain of residential and commercial character, respectively, are shown in Figure 2.34. The regime of the rural amplitude distributions of the basic Phase Zero model is also shown lightly shaded in Figure 2.34 for comparison. Statistical attributes for the residential and commercial ensemble distributions are shown in Table 2.8. These two distributions are quite similar in shape but are horizontally displaced from one another, indicating that clutter from commercial urban sectors is several dB stronger than clutter from residential urban sectors at most percentile levels. In terms of

Preliminary X-Band Clutter Measurements

85

mean clutter strength, Table 2.8 indicates that clutter from commercial sectors is 3.4 dB stronger than clutter from residential sectors. This is regarded as a general result based on measurements from many clutter patches. Table 2.8 Statistical Attributes of Urban Residential and Commercial Ground Clutter Amplitude Distributions*

Weibull Parameters Terrain Type

Ensemble Mean Clutter Strength

Percent of Samples above Radar Noise Floor

Number of Patches

aw

σ°50 (dB)

σ°w (dB)

Urban/ Residential

3.9

–42

–23

–21.1

67

85

Urban/ Commercial

3.6

–36

–19

–17.7

74

28

σ° F 4(dB)

* Phase Zero X-band data, 75 m range res., hor. pol., 2 to 12 km range. Also see Figure 2.34.

Weibull Scale 0.995 0.99

Probability That σ°F4 ≤ Abscissa

0.97 0.95 0.9

Rural, Fig. 2.25 (for comparison)

0.8 0.7

Residential

0.6 Commercial

0.5 0.4 0.3 –60

–50

–40

–30

σ°F4

–20

–10

0

(dB)

Figure 2.34 Comparison of cumulative ground clutter amplitude distributions for urban terrain of residential character and urban terrain of commercial character. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 2- to 12-km range, 113 patches, 33 sites. See also Table 2.8.

2.4.2.3 Wetland Clutter Figure 2.35 shows cumulative expected value distributions of mean clutter strength from measured Phase Zero patches for four distinctive terrain types—wetland, rural/low-relief, mountains, and urban. The data of Figure 2.35 strongly reinforce the earlier finding that

86

Preliminary X-Band Clutter Measurements

mountain clutter and urban clutter are significantly stronger than most other clutter (i.e., rural/low-relief clutter). At the median position in Figure 2.35, mountain clutter and urban clutter are both about l0 dB stronger in clutter patch mean strength than rural/low-relief clutter. The distribution of mean clutter strength from wetland patches is included in Figure 2.35 with the expectation that wetland might be a terrain type for which clutter might be significantly weaker than most other clutter. Indeed, Figure 2.35 shows that, at the median level, wetland clutter patches are about 5 dB weaker in mean clutter strength than rural/low-relief patches.

s)

es tch pa 22

sit 3 (3 n

ba

Ur

Mo

)

pat

es ,1

0s ain

f (9 lie Re

Lo w

Ru

ral /

0.5

s (1

ite 6s

16 d( an We tl

0.7

ites , 90

58 s, 1

es ,9 sit

0.9

0.3

Urb

0.01

0.001

–50

–40

Mts

0.1

an

Probability That σ°F4 ≤ Abscissa

2p

4p

atc

atc

he

he

s)

0.99

che

s)

Normal Scale

unt

0.999

–30

–20

–10

σ°F (dB) 4

Figure 2.35 Cumulative distributions of mean ground clutter strength for four distinctive terrain types. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 2- to 12-km range, 1,796 patches, 96 sites. Each curve shows the cumulative distribution of mean clutter strengths from all patches of a given terrain type, one value of mean strength per patch.

Patches of trees often occur on wetland terrain—in thinking about backscatter from general wetland, it is necessary to think as much in terms of clumps of trees and tree lines as in terms of level reed- or sedge-covered marshland or open water conditions. Thus Table 2.1 separates wetland into forested wetland (class 61) and non-forested wetland (class 62) in land cover classification. About half of Phase Zero wetland patches are mixtures of various proportions of forested and non-forested wetland.

Preliminary X-Band Clutter Measurements

87

All of the Phase Zero wetland clutter patch amplitude distributions were combined into ensemble amplitude distributions in four regimes of depression angle, as shown in Figure 2.36. The regime of the rural amplitude distributions of the basic Phase Zero clutter modeling information is shown lightly shaded in Figure 2.36 for comparison. Statistical attributes for these four wetland ensemble distributions are shown in Table 2.9. These four wetland ensemble distributions are now compared with the rural/low-relief distributions of the basic Phase Zero model (see Figure 2.25 and Table 2.4) at similar depression angles. There is considerable overlap of the wetland ensemble distributions with the rural/lowrelief ensemble distributions, compared with the separation of the patch mean clutter strengths of these terrain types in Figure 2.35. In Figure 2.36, the wetland ensemble distributions only separate out as being substantially weaker than the rural/low-relief ensemble distributions at the higher percentile levels—it is the higher percentile levels that control the mean. Comparing ensemble mean clutter strengths (Tables 2.4 and 2.9), rural/ low-relief terrain is about 5 dB stronger than wetland in the first three depression angle regimes; in the fourth depression angle regime, 0.75° to 1°, the ensemble mean clutter strength from wetland terrain is approximately equal to that from rural/low-relief terrain. Table 2.9 Statistical Attributes of Wetland Ground Clutter Amplitude Distributions, by Depression Angle* Weibull Parameters

Depression Angle (deg)

Ensemble Mean Clutter Strength σ°F4 (dB)

Percent of Samples above Radar Noise Floor

Number of Patches

aw

σ °50 (dB)

0.00 – 0.25

3.6

–56

–38

–37.0

49

35

0.25 – 0.50 0.50 – 0.75 0.75 – 1.00

3.1 3.0 2.3

–50 –47 –38.5

–37 –34 –31

–35.6 –34.7 –29.6

52 63 75

29 6 5

σ°w (dB)

* Phase Zero X-band data, 75 m range res., hor. pol.,. 2 to 12 km range. Also see Figure 2.36.

In comparing the data of Figures 2.25 and 2.36, it is seen that the spreads in the wetland ensemble distributions are much less than those in rural/low-relief ensemble distributions at corresponding depression angles (significantly lower values of aw in wetland). Less spread in clutter amplitude statistics from wetland terrain indicates that wetland is more homogeneous than general rural/low-relief terrain. This is partly due to the fact that wetland is predominantly level, and also partly due to less heterogeneity of land cover in wetland. Because of the general overlap of wetland ensemble amplitude distributions with the corresponding rural/low-relief distributions, they were not separated out as a specific weak-clutter terrain category in the basic Phase Zero clutter modeling information in Section 2.4.1.

2.4.2.4 Level Terrain Level terrain is a canonically simple landform in which only variation in land cover and not variations in surface topology exist to introduce spread in clutter statistics. Thus level terrain provides the opportunity to isolate and understand better the parametric dependencies generally at work in low-angle clutter in which generality can be reached with fewer measurement samples. Twenty-six percent of Phase Zero patches have primary

88

Preliminary X-Band Clutter Measurements

Weibull Scale

Probability That σ°F4 (dB) ≤ Abscissa

0.995 0.99 0.97 0.95 0.9

0.8 0.7 0.6

Depression Angle (deg)

Rural, Fig. 2.25 (for comparison)

0.00 to 0.25 0.25 to 0.50 0.50 to 0.75

0.5 0.4 0.75 to 1.00 0.3 –60

–50

–40

–30

σ°F4

–20

–10

(dB)

Figure 2.36 Cumulative ground clutter amplitude distributions by depression angle for wetland terrain. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 2- to 12-km range, 75 patches, 16 sites. See also Table 2.9.

landform classification of level. In what follows, ensemble clutter amplitude distributions for level terrain formed from these level patches are shown for two quite different commonly occurring land cover classes, forest and agricultural, each as a function of depression angle.

Level Forest. All of the Phase Zero clutter measurements from patches of level forest were combined into ensemble amplitude distributions in three regimes of depression angle. The results are shown in Figure 2.37. Statistical attributes for these three level forest ensemble distributions are shown in Table 2.10. The regime of the rural ensemble distributions from Figure 2.25 is shown lightly shaded in Figure 2.37 for comparison. In the data of Figure 2.37 and Table 2.10, a strong trend with depression angle is observed—with increasing depression angle, spreads in clutter amplitude statistics from level forest rapidly decrease and mean strengths rapidly increase. Compared with clutter amplitude statistics from rural/low-relief terrain at similar depression angles, clutter statistics from level forested terrain have significantly less spread (i.e., much smaller values of aw). This results from the fact that level forested terrain represents a much more homogeneous backscattering medium than rural/low-relief terrain in general, in spite of the fact that, within level forest patches, there exists considerable heterogeneity introduced by higher-order classifiers. For example, 71% of level forested patches carry some category of open terrain (agriculture, rangeland, etc.) as secondary land cover classification.

Level Farmland. Ensemble amplitude distributions in four regimes of depression angle for level agricultural terrain are shown in Figure 2.38. Statistical attributes of these

Preliminary X-Band Clutter Measurements

89

Table 2.10 Statistical Attributes of Ground Clutter Amplitude Distributions for Level Forested Terrain, by Depression Angle* Weibull Parameters

Depression Angle (deg)

Ensemble Mean Clutter Strength σ°F4 (dB)

Percent of Samples above Radar Noise Floor

Number of Patches

aw

σ °50 (dB)

0.00 – 0.25

3.6

–54

–37

–36.0

48

39

0.25 – 0.75 0.75 – 1.50

3.0 2.3

–46 –36

–33 –28

–31.8 –26.9

63 70

36 13

σ°w (dB)

* Phase Zero X-band data, 75 m range res., hor. pol.,. 2 to 12 km range. Also see Figure 2.37.

Weibull Scale 0.995 0.99

Probability That σ°F4 (dB) ≤ Abscissa

0.97 0.95 0.9

Depression Angle (deg)

0.8

Rural, Fig. 2.25 (for comparison)

0.7

0.00 to 0.25 0.6

0.25 to 0.75

0.5

0.75 to 1.50 0.4

0.3 –60

–50

–40

–30

–20

–10

σ°F4 (dB)

Figure 2.37 Cumulative ground clutter amplitude distributions by depression angle for level forested terrain. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 2- to 12-km range, 88 patches. See also Table 2.10.

distributions are shown in Table 2.11. The regime of the rural ensemble distributions from Figure 2.25 is shown lightly shaded in Figure 2.38 for comparison. As with level forest, these level agricultural distributions show a strong dependence on depression angle. In other aspects, however, these level agricultural distributions are very different from level forest. The level agricultural distributions show a strong tendency to merge at the higher cumulative probability levels shown (around cumulative probability = 0.97), whereas at such levels the level forest distributions stay well separated. This indicates a dominating

90

Preliminary X-Band Clutter Measurements

influence from discrete clutter sources at these probability levels on level agricultural terrain, from which backscatter would be expected to be less sensitive to depression angle. The spreads in the level agricultural distributions are extreme (much larger values of aw) not only compared with level forest, but also, at very low depression angles (0° to 0.5°), with rural/low-relief terrain in general. At higher angles (0.75° to 1°), the spread in the level agricultural distribution becomes equal to that of the rural/low-relief distribution. Mean clutter strengths in level agricultural Table 2.11 Statistical Attributes of Ground Clutter Amplitude Distributions for Level Agricultural Terrain, by Depression Angle*

Weibull Parameters

Depression Angle (deg)

0.00 – 0.25 0.25 – 0.50 0.50 – 0.75 0.75 – 1.00

Ensemble Mean Clutter Strength σ°F4 (dB)

Percent of Samples above Radar Noise Floor

Number of Patches

aw

σ °50 (dB)

σ°w (dB)

5.9

–69

–32

–31.8

25

94

5.0 4.0 3.4

–60 –52 –47

–32 –32 –32

–30.7 –31.2 –31.3

38 54 60

101 36 14

* Phase Zero X-band data, 75 m range res., hor. pol.,. 2 to 12 km range. Also see Figure 2.38.

Weibull Scale

Probability That σ°F4 (dB) ≤ Abscissa

0.995 0.99 0.97 0.95

Depression Angle (deg)

0.9

0.00 to 0.25

0.8

Rural, Fig. 2.25 (for comparison)

0.25 to 0.50

0.7

0.50 to 0.75

0.6 0.75 to 1.00

0.5 0.4 0.3 –60

–50

–40

–30

–20

–10

σ°F4 (dB)

Figure 2.38 Cumulative ground clutter amplitude distributions by depression angle for level agricultural terrain. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 2- to 12-km range, 245 patches. See also Table 2.11.

Preliminary X-Band Clutter Measurements

91

terrain show very little variation with depression angle (although median strengths rise quickly as the spread decreases with increasing depression angle), in contrast to the significantly increasing mean strength with depression angle of level forest. Of the level agricultural patches, 34% carry secondary land cover classification of forest. That is, similarly to level forest containing openings of non-forested terrain, so also does open level agricultural terrain contain patches of trees. Level agricultural terrain is highly heterogeneous because of strong localized discrete scattering sources (including patches of trees) existing in a weakly backscattering medium (the field surfaces themselves).

Comparison with Wetland. Next the characteristics of wetland clutter (Figure 2.36, Table 2.9) are compared with those of level forest (Figure 2.37, Table 2.10). The wetland clutter patches were almost all level. Considered simplistically, both level forest and level wetland might be considered to constitute level vegetative backscattering mediums relatively free of discrete scattering objects. Hence level forest and level wetland might be expected to backscatter relatively similarly, with perhaps wetland causing somewhat weaker clutter because of a possibly enhanced tendency for forward scatter as a result of increased reflection coefficient. Consider next some of the complicating characteristics of real forest and wetland that have been previously discussed. It was indicated in previous discussions of terrain heterogeneity that the majority of wetland patches contained clumps of trees, and that many forested patches contained open areas of, for example, farmland or other open land cover types brought in through second- and third-order classifiers. Thus, from this point of view also, the backscattering characteristics of wetland and level forest might still be expected to be similar. It turns out that the clutter characteristics of wetland and level forest are, indeed, surprisingly similar. The distributions of Figure 2.36 and Figure 2.37 almost exactly overlay one another in similar regimes of depression angle. (Since the level forest and level wetland depression angle regimes do not exactly coincide, some minor angular interpolation is required to see the match.) This almost exact overlay of the resultant two sets of three curves requires, however, a horizontal displacement of approximately 2 to 3 dB between the two sets of curves, such that the wetland curves are shifted to the right. Thus these data suggest that wetland backscatters very similarly to level forest, except that wetland clutter is about 2 or 3 dB weaker. Thus the initial simplistic speculation that wetland clutter might be like forest clutter, but weaker, is borne out. It is quite remarkable that such similarities should exist between two entirely different data sets, with the approximately 2 or 3 dB offset maintained throughout, depression angle regime by depression angle regime and percentile level by percentile level. The similarity in shapes (Weibull shape parameter aw) and approximately 2 to 3 dB difference in strength between these two data sets is also evident in comparing Tables 2.9 and 2.10.

2.4.2.5 Effects of Trees Trees are a dominant component of landscape. In examining any particular low-angle clutter measurement involving trees, the influence of the trees on the backscatter data is often paramount. When large numbers of trees exist as a forest, they cover many other potential sources of clutter on the ground, including discrete cultural objects, so that a relatively homogeneous vegetative medium is presented to the radar. In partially cleared forested regions, the edges of forest can dominate the backscatter. On open agricultural land containing only small incidences of trees, either in isolated occurrence, in shelter belts around farmsteads, in tree lots, or around ponds and along streams, even a small

92

Preliminary X-Band Clutter Measurements

incidence of trees can dominate the landscape in terms of large vertical discrete objects and hence dominate the backscatter. Because of the importance of trees in low-angle ground clutter, a procedure was implemented within the terrain classification system utilized whereby every clutter patch was classified by percent tree cover. This was done by moving a fine uniform dot pattern over the region of the patch on the air photo and counting the number of dots within the area of the patch containing trees. Clutter statistics were separated into six categories of percent tree cover. For assigning “forest” as the primary land cover classifier of any patch, the percent tree cover within the patch had to be greater than 50%. In what follows, in separating clutter statistics by percent tree cover, all forest patch data were combined to represent greater than 50% tree cover and, for the five remaining categories of percent tree cover less than 50%, patch data were combined from all patches specified to have percent tree cover within each category, irrespective of land cover class. Ensemble amplitude distributions by percent tree cover η are shown in Figure 2.39 for patches of “level” primary landform classification (similar percent tree cover results were obtained for other landform classes). Statistical attributes of the ensemble distributions of Figure 2.39 are shown in Table 2.12. A significant trend is observed in these distributions, whereby the spread in the distributions as given by the Weibull shape parameter aw strongly decreases with increasing percent tree cover, for percent tree cover between zero and 50%. The “no trees” distribution is a special case. Median clutter strengths gradually increase with increasing percent tree cover, also over the same range for percent tree cover between zero and 50% , but not enough to compensate for the decreasing spread, so to a lesser extent mean clutter strengths tend to decrease with increasing percent tree cover. Spreads in these statistics decrease with increasing percent tree cover between zero and 50% because, with increasing percent tree cover, the sizes of individual stands of trees grow, resulting in fewer isolated trees, tree lines, and edges of stands (with their inherent wide variability in clutter strength) and larger areas covered more or less homogeneously with trees (within each of which the inherent variability in clutter strength is less). For the same reason, the percent of samples above noise level in these ensemble distributions increases with increasing percent tree cover as shown in Table 2.12. In transitioning from the category with percent tree cover between 30% and 50% to the forest category (percent tree cover > 50% ), the spread in the amplitude distributions remains about the same (aw = 3.4) but the strengths at most percentile levels increase by about 2 dB. Table 2.12 Statistical Attributes of Ground Clutter Amplitude Distributions by Percent Tree Cover on Level Terrain*

Weibull Parameters

Depression Angle (deg)

η

aw

σ °50 (dB)

0<η≤3 3 < η ≤ 10 10 < η ≤ 30 30 < η ≤ 50 No Trees (η = 0) Forest (η > 50)

5.3 4.9 4.4 3.4 3.5 3.4

–59 –58 –55 –50 –51 –48

σ°w (dB) –28 –31 –31 –34 –34 –32

Ensemble Mean Clutter Strength σ°F4 (dB)

Percent of Samples above Radar Noise Floor

–27.7 –28.9 –30.8 –31.8 –32.4 –31.4

35 40 46 54 57 57

* Phase Zero X-band data, 75 m range res., hor. pol.,. 2 to 12 km range. Also see Figure 2.39.

Number of Patches 190 88 61 12 88 91

Preliminary X-Band Clutter Measurements

93

Weibull Scale 0.999

Forest

0.995

30 < η ≤ 50

No trees

0.99

10 < η ≤ 30

0.97 0.95

0 10

0.8

<

η

≤

3

0.9

0)

3

(η

<

=

η

Forest (η > 50)

50

η

≤

η = Percent Tree Cover

0.6

30

<

No

tre

es

10

0.7

≤

<

30

η

≤

Probability That σ°F4 ≤ Abscissa

0<η≤3 3 < η ≤ 10

–40

–30

–20

–10

σ°F4 (dB)

Figure 2.39 Ground clutter amplitude statistics by percent tree cover η on level terrain. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 2- to 12-km maximum range, 530 clutter patches. See also Table 2.12.

The “no tree” distribution is a special case, standing outside the general trend of variation in the other distributions with percent tree cover. Simplistically interpreted, “no trees” means, to some extent, “no discretes” (or at least a de-emphasis of discretes). That is, treeless terrain brings out more of the characteristics of area-extensive backscatter from a continuous medium. Forest terrain also begins to show more of the characteristics of a continuous medium, with a de-emphasis on discretes. Hence, simplistically, treeless terrain might be expected to backscatter somewhat like forested terrain. In fact, in Figure 2.39, the “no trees” distribution has abruptly departed from the general trend of increasing spread aw with decreasing percent tree cover and has suddenly assumed much reduced spread characteristics nearly identical to the forest distribution at the other extreme of percent tree cover. In terms of strength, the “no trees” distribution is 2 or 3 dB weaker than the forest distribution. The data of Figure 2.39 and Table 2.12 clearly show a considerable difference in low-angle clutter characteristics between terrain with absolutely no trees and terrain with “few trees” (where “few” means tree cover between zero and three percent). This emphasizes the importance of isolated trees as the dominant type of discrete clutter source causing the wide spreads seen in low-angle clutter from agricultural land and other open terrain types.

94

Preliminary X-Band Clutter Measurements

2.4.2.6 Negative Depression Angle A small portion of the Phase Zero clutter measurement sites are of negative effective site height. This is the result of terrain features in some directions rising abruptly to elevations higher than the site elevation. Terrain higher than the antenna is observed by the radar at negative depression angle. Ten percent of the 2,177 Phase Zero clutter patches were observed at negative depression angle. To see terrain at negative depression angle from antennas of positive mast height implies a positive terrain slope greater than the absolute value of the particular depression angle involved. Indeed, the terrain occurring above a radar position was often observed to be inaccessibly rough and steep—otherwise, the radar would have been sited at the higher position. Patches observed at negative depression angle are now separated into three regions of negative depression angle, namely, 0° to –0.25°, –0.25° to –0.75°, and –0.75° to –1.75°, irrespective of terrain type. The clutter data from each of these three sets of patches are combined into an ensemble amplitude distribution. The resultant cumulative ensemble amplitude distributions for three regimes of negative depression angle are shown in Figure 2.40. Statistical attributes for these ensembles are given in Table 2.13. The regime of the rural terrain distributions of Figure 2.25 is shown lightly shaded in Figure 2.40 for comparison. Table 2.13 Statistical Attributes of Ground Clutter Amplitude Distributions in Three Regimes of Negative Depression Angle*

Weibull Parameters Depression Angle (deg) aw

σ °50 (dB)

σ°w (dB)

Ensemble Mean Clutter Strength

Number of Patches

σ°F (dB)

Percent of Samples above Radar Noise Floor

4

0.00 to –0.25

3.9

–50

–31

–29.8

48

119

–0.25 to –0.75

3.8

–45

–27

–24.9

54

48

–0.75 to –1.75

2.6

–35

–26

–24.2

74

27

* Phase Zero X-band data, 75 m range res., hor. pol.,. 2 to 12 km range. See also Figure 2.40.

First, consider the data in the 0° to –0.25° regime. The clutter data within this low negative depression angle regime are dominated by terrain in the undulating and inclined classes presenting slight positive slopes that are visible. In contrast, the clutter data at low positive depression angle from 0° to +0.25° in Figure 2.25 and Table 2.4 are much more influenced by level terrain. As a result, the 0° to –0.25° amplitude distribution is about 2 dB stronger in mean strength than the 0° to +0.25° amplitude distribution and is of less significantly spread (aw = 3.9 compared with 4.8). Next, consider the data in the –0.25° to –0.75° depression angle regime. Within this regime, many of the patches have moderately steep or steep landform components. As a result, the clutter amplitude distribution in the –0.25° to –0.75° depression angle regime is about 5 dB stronger in mean strength than the corresponding distribution at positive depression angle. In terms of spread, however, the shape parameter aw at –0.25° to –0.75° is very similar to that for terrain at corresponding positive depression angles.

Preliminary X-Band Clutter Measurements

95

Weibull Scale 0.995 0.99

Probability That σ°F4 ≤ Abscissa

0.97 0.95 0.9

0.8 0.7

Depression Angle (deg)

Rural, Fig 2.25 (for comparison)

–0.25 to 0.00 0.6 –0.75 to –0.25 0.5

0.4 –1.75 to –0.75 0.3 –60

–50

–40

–30

σ°F4

–20

–10

(dB)

Figure 2.40 Cumulative ground clutter amplitude distributions in three regimes of negative depression angle. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 2- to 12-km range, 194 patches. See also Table 2.13.

For depression angles from –0.75° to –1.75°, these trends continue but with increasing domination by high-relief terrain. The clutter amplitude distribution in this regime is similar to corresponding distributions in the 0° to 1° and 1° to 2° regimes in high-relief terrain. In moving from the –0.25° to –0.75° depression angle regime to the –0.75° to –1.75° regime, the increased incidence of steep terrain has increased mean strength very little but has substantially reduced the spread aw. Thus, it is evident that clutter amplitude statistics at negative depression angles are, on the whole, relatively dissimilar to amplitude statistics at corresponding positive depression angles. At low negative angles (i.e., 0° to –0.25°), strengths are somewhat higher and spreads are somewhat lower than corresponding positive angles because the generally lowrelief terrain surfaces under observation at low negative angles have to be slightly more inclined towards the radar to be seen. At slightly higher negative angles (i.e., above –0.25°), the only terrain usually seen is for the most part quite rough and steep, with attendant increases in clutter strength. Once the terrain is high enough and steep enough to be observed at significant negative depression angles (i.e., depression angle < –0.25°), further increases in negative depression angle (i.e., depression angle < –0.75°) do not significantly increase mean clutter strengths but do continue to significantly decrease clutter spreads.

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Preliminary X-Band Clutter Measurements

2.4.3 Combining Strategies 2.4.3.1 Ensemble Distributions vs Expected Values Throughout Section 2.4, general understandings and descriptions of the low-angle clutter phenomenon have been sought for the most part by combining measurement data from many individual, like-classified, clutter patches into ensemble amplitude distributions generally representative of that class. In combining clutter data, individual spatial cells or samples can represent the elemental spatial quantity being combined, or clutter macropatches—each patch containing many cells—can represent the elemental quantity. First consider combination at the cell level. Imagine from a set of like-classified patches, a set of clutter amplitude histograms—one histogram per patch—that all have identical bell shapes but that have widely varying means so that there exists little overlap from histogram to histogram. Aggregation of the data in all of these elemental histograms, cell by cell, into one overall ensemble histogram, yields an ensemble histogram of quite different characteristics from any of the individual histograms. In particular, in these circumstances the ensemble histogram contains much more spread in its data than any of the individual histograms. The failure of the above set of histograms as a proper ensemble is the failure of the classification system that grouped the patches together in the first place. Now, from a set of like-classified patches, imagine a set of histograms of similar but not identical shape, with similar means and standard deviations, but with each histogram containing different specific higher-order attributes. Combining these histograms cell-by-cell into an ensemble histogram yields a useful general distribution in which individual differences are averaged out. The resultant ensemble distribution is generally representative of any of the individual histograms. This situation is the result of a classification system which successfully finds and groups together patches with similar amplitude statistics in the first place. In the actual world of clutter patches, neither of the above positions is entirely true. The classification system utilized works usefully but not perfectly. As a result, aggregation of amplitude statistics from a set of patches sample by sample at the spatial cell level does provide much useful information, but it also introduces some extra spread into the resultant ensemble distributions. The above discussion is now quantified around a specific example; namely, the ensemble of rural/low-relief terrain with depression angle from 0.25° to 0.5°. This ensemble contains 448 individual clutter patches giving rise to 448 individual clutter amplitude histograms. For each patch, the mean strength of its histogram is computed, and the distribution of 448 mean strengths is plotted cumulatively in Figure 2.41. Given this set of data, the task of modeling is to select an appropriate general value for representing mean clutter strength in rural/low-relief terrain at depression angles from 0.25° to 0.5°. Observe that the cumulative distribution in Figure 2.41 is quite linear as plotted against the normal probability scale there. To the extent that it is linear, the distribution can be represented by a normal or Gaussian distribution. That is, the distribution of dB values of mean patch clutter strength (each mean computed in units of m2/m2 and subsequently converted to dB, as per Eqs. (2.B.3) and (2.B.8), in Figure 2.41 is closely approximated by a well-behaved normal distribution. This being the case, a reasonable value to select from this distribution as being generally representative of rural/low-relief, 0.25° to 0.5° depression angle, mean patch clutter strength is the median value in the distribution, –33.6 dB. If the distribution were exactly symmetrical, its mean, median, and modal measures of

Preliminary X-Band Clutter Measurements

97

Normal Scale 0.999

0.99 Mean of the m2/m2 means = –28.5 dB

Probability That σ°F4 ≤ Abscissa

0.9 Ensemble mean = –30.7 dB 0.7

0.5 0.3

Mean of the dB means = –33.0 dB

Median of the means = –33.6 dB

0.1

0.01

0.001 –60

–40

σ°F4

–20

0

(dB)

Figure 2.41 Cumulative distribution of mean ground clutter strength for rural/low-relief terrain with depression angle from 0.25° to 0.5°. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 2- to 12-km range, 448 patches, 70 sites. The curve shows the distribution of mean strengths, one value of mean strength (Eq. 2.B.8) per patch. See text for definitions of indicated central measures of the distribution.

dB values would be identical. The mean value of the dB values of mean clutter strength [calculated similarly to Eq. (2.B.12), although with yi representing mean clutter strength of the i-th patch in dB as computed by Eq. (2.B.8)] in Figure 2.41 is –33.0 dB. If the distribution of dB values of mean clutter strength in Figure 2.41 is normal, then the distribution of the values of mean clutter strength in units of m2/m2 is lognormal. All of the percentile values in this fundamental m2/m2 distribution simply transform logarithmically to corresponding values in the dB distribution (e.g., the median position in the m2/m2 distribution is also the median position in the dB distribution). But mean and modal values in the m2/m2 distribution are not simply related to corresponding values in the dB distribution, and do not occur at the same percentile positions in the m2/m2 distribution as they do in the dB distribution. The mean value of the m2/m2 values of mean patch clutter strength in the distribution of Figure 2.41 is –28.5 dB, 4.5 dB stronger than the mean value

98

Preliminary X-Band Clutter Measurements

of the dB values of mean patch clutter strength in the same distribution. Note that this value of –28.5 dB occurs at the 82-percentile level in the distribution. Finally, consider the overall ensemble histogram of individual cell-by-cell spatial samples assembled aggregatively from the 448 patches corresponding to the data of Figure 2.41. The mean value of this ensemble histogram computed in m2/m2 and converted to dB [by Eqs. (2.B.3) and (2.B.8)] is –30.7 dB. This value of –30.7 dB occurs at the 72-percentile level in the distribution. Let this value, –30.7 dB, be called the cell-level ensemble mean. Comparing it to the mean of the m2/m2 means = –28.5 dB, the mean of the dB means = –33.0 dB, and the median of the means = –33.6 dB, the ensemble mean lies between the mean of the m2/m2 means and the mean of the dB means, 1.2 dB below the former and 2.3 dB above the latter. The ensemble mean is not equal to the mean of the m2/m2 means because the clutter patches are not all of equal size; if they were, these two quantities would be identically equal. At this point in the discussion, three reasonable definitions of mean clutter strength exist to represent a patch of rural/low-relief terrain observed at 0.25° to 0.5° depression angle. There is no single correct definition. The clutter modeler wants to select a reasonable definition appropriate to the application of the model. The modeler wants to look for parametric trends in this defined quantity and wants to stay aware of the extent to which the characteristics of such trends might be dependent on the quantity selected. There is nothing in Figure 2.41 to discourage use of the ensemble aggregation of cell-level statistics to model clutter. The ensemble mean occupies middle ground between the mean of the dB means and the mean of the m2/m2 means at the 72-percentile level in the distribution. Thus a model based on ensemble aggregations of cell-level statistics is biased somewhat towards more severe clutter leading to conservative estimates of radar capability. This is not necessarily undesirable. In overview, there are many patches with both stronger and weaker clutter strength than the ensemble mean value. At the beginning of Section 2.4, the question was raised of whether cell values or patch values should be regarded as elemental spatial statistical quantities to be combined in clutter modeling. The data in Figure 2.41 show the combination of all patch mean clutter strengths for a given ensemble of patches. Thus within the distribution of Figure 2.41, the patch is the elemental quantity. The particular statistical attribute of the patch amplitude histogram that is quantified in Figure 2.41 is patch mean strength. Other statistical attributes of patch amplitude may be similarly plotted (see Figure 2.42). The advantage of regarding patches as elemental statistical quantities is that it avoids cell-level aggregation of data from non-similar histograms. However, once the distribution of a particular patch attribute is plotted such as in Figure 2.41, the modeler still has to face up to selecting one value from a range of values. In the end, it still is an act of reasoned judgment to select the modeling quantity. If it is argued that a cell-level aggregative approach to ensemble statistics is too demanding of a terrain classification system, it is certainly true that a failed classification system also fails at the patch level. Under a failed system, collections of patch attributes will contain much spread and show no parametric variation. The advantage of forming cell-level aggregative ensemble distributions is that it is a convenient way to show resultant averaged or generalized amplitude distributions. That is, the general histogram is just the sample-by-sample sum of the data in the individual histograms. It is less easy to provide an actual general histogram or

Preliminary X-Band Clutter Measurements

99

cumulative distribution in a patch-oriented approach in which only various attributes of individual patch histograms are collected, as opposed to the histograms themselves.

Normal Scale 0.999

Cumulative Probability

0.99

Ensemble aw parameter = 4.1

0.9

Median of the σ°50 = –48.0 dB

Mean aw parameter = 3.3

0.7

Mean of the dB values of σ°50 = –48.9 dB

0.5 0.3 Median aw parameter = 3.0

0.1

Ensemble value of σ°50 = –52.5 dB

0.01 0.001 0

2

4

6

8

–100

–80

–60

–40

–20

aw Parameter

σ°50 (dB)

(a) Distribution of aw

(b) Distribution of σ°50 (dB)

Figure 2.42 Cumulative distributions of approximating Weibull coefficients aw and σ °50 (dB) for clutter patch amplitude distributions for rural/low-relief terrain with depression angle from 0.25° to 0.5°. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 2- to 12-km range, 448 patches, 70 sites. The curves show distributions of Weibull shape parameter aw and mean clutter strength σ °50, one value of each per patch.

One thing that can be done in this regard is to approximate the shape of each individual patch amplitude distribution with a Weibull shape parameter aw. The distribution of all such values of aw can then be formed for a particular ensemble of patches. Such a result is shown in Figure 2.42(a), for the same rural/low-relief, 0.25° to 0.5° depression angle ensemble for which data are shown in Figure 2.41. Three representative values for aw are also indicated in Figure 2.42(a), the median value of aw equal to 3.0, the mean value of aw equal to 3.3, and the value of approximating shape parameter aw for the cell-level aggregate distribution previously obtained (see Table 2.4) equal to 4.1. This last quantity is denoted as the celllevel ensemble value of aw. The data shown in Figure 2.42(a) quantify the concern discussed at the beginning of Section 2.4; that cell-level aggregation can cause too much spread in resultant average distributions. The ensemble value of aw is, indeed, greater than the mean or median values of aw in Figure 2.42(a). The ensemble value of aw is at the 80-percentile level in the distribution. Consider that the median level does not necessarily constitute a better modeling value than the 80-percentile level. There are many individual patches with both significantly greater spread and significantly less spread than that specified by the ensemble value of aw in the data of Figure 2.42(a). However, use of the cell-level aggregation does provide a slight bias towards increased spread in clutter amplitude statistics in the modeling

100 Preliminary X-Band Clutter Measurements

information of Chapter 2, as well as increased strength. Again, such a conservative bias from the point-of-view of radar capability is not necessarily undesirable. It does, however, require quantification. In the data of Figure 2.42(a), this bias is not extreme. The bias is most extreme at the lowest depression angles, as in the depression angle regime of 0.25° to 0.5° for which data are shown in Figures 2.41 and 2.42. The bias decreases with increasing depression angle. Comprehensive modeling information of clutter amplitude statistics based on patch-level expected-value characterization is the main approach taken in subsequent chapters in this book. This is a more challenging empirical task than that based on simple cell-level sample-to-sample ensemble aggregation. Besides the shape parameter aw , a Weibull model requires specification of the σ 50 ° parameter. In approximating the clutter amplitude distribution of each of the 448 rural/lowrelief patches observed at 0.25° to 0.5° depression angle with a Weibull distribution, besides collecting all of the patch values of aw as shown in Figure 2.42(a), all of the patch σ 50 ° (dB) values were also collected as shown in Figure 2.42(b). It is observed that the ensemble value of σ 50 ° is 4.5 dB weaker than the median value. This also reflects the increased spread of cell-level aggregate models compared with aggregates of patch attributes. The increased spread of the cell-level distribution has driven σ 50 ° in the approximating Weibull distribution to somewhat lower levels (i.e., 33 percentile) in the distribution of patch-level σ 50 ° values. Again, compared to the overall range of this distribution, this value of –52.5 dB appears reasonable for a general model. In the end, the relative goodness or badness of the cell-level ensemble aggregate approach is the fidelity with which the ensemble distribution represents a typical patch distribution. As indicated by the comparisons with constituent patch data shown in Figures 2.41 and 2.42, the rural/low-relief, 0.25° to 0.5° depression angle, ensemble aggregate distribution on the whole satisfactorily represents a clutter amplitude distribution from a typical clutter patch.

2.4.3.2 Statistical Convergence Consideration now is given to whether a given ensemble of like-classified patches contains enough patches to provide generality. A simple empirical test for whether a trial set of patches is sufficient to provide converged results18 characteristic of the general set is to simply randomly partition the trial set any number of ways into two equal and independent subsets, each containing half as many patches as the original set, and to subsequently determine if the results obtained from the subsets agree with those of the original set [15]. Continuing with the rural/low-relief, 0.25° to 0.5° depression angle ensemble of 448 patches selected for previous discussion in Section 2.4.3.1, these patches are now randomly divided into two subsets, each containing 224 patches. This is done in three different ways. For each of these six subsets, the cell-level ensemble clutter amplitude distribution is formed and plotted cumulatively in Figure 2.43. It is apparent in Figure 2.43 that, within each partition generating two independent subsets, each independent pair of distributions are closely converged to one another. On the basis of 18. Also, consider the distribution of Figure 2.41 from the point-of-view of statistical estimation theory. Thus, sample size N = 448, sample mean x = –33.0 dB, and sample variance σ 2 = 25 dB. The rms error of x is 12 ⁄  σ2   ------  N  

= 0.24 dB. Hence the quantity

x = –33.0 dB is statistically “good” to –33.0 ± 0.24 dB.

Preliminary X-Band Clutter Measurements 101

these results, it is expected that, if a new clutter measurement program were to be initiated, in which clutter was measured from 448 newly selected patches of similar classification, the new measurements would lead to a new cell-level ensemble clutter amplitude distribution well within the interval of uncertainty indicated in Figure 2.43. Normal Scale 0.999 Rural/Low-Relief Terrain 0.25° to 0.5° Depression Angle

Probability That σ°F4 ≤ Abscissa

0.99

Three Ensemble Halvings

0.98

0.95

0.9 Method of Separation in File of 448 Patches 0.8

Half-Ensemble Mean Clutter Strength (dB) First Second Half Half

First Half, Second Half

–30.80

–30.64

Every Odd Pair, Every Even Pair

–30.94

–30.49

Every Odd One, Every Even One –31.07

–30.34

0.7

0.6 –45

–40

–35

–30

σ°F4

–25

–20

–15

–10

(dB)

Figure 2.43 Three halvings of the 0.25° to 0.5° depression angle, rural/low-relief ensemble clutter amplitude distribution. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 2- to 12-km range. Full ensemble mean clutter strength = –30.72 dB.

2.4.4 Depression Angle Characteristics 2.4.4.1 General Characteristics A traditional approach to ground clutter modeling is to specify clutter strength as a simple characteristic of illumination angle. Following this approach, Figure 2.44 shows generalized mean and median clutter strengths as a function of depression angle, inclusive of all terrain types. The results of Figure 2.44 are based on Phase Zero measurements of 1,926 macropatches from 86 sites. Figures 2.45 and 2.46 show the ratio of standard

102 Preliminary X-Band Clutter Measurements

deviation-to-mean vs depression angle and the incidence of occurrence of microshadowing within clutter patches vs depression angle, respectively, for the same set of Phase Zero data upon which the results in Figure 2.44 are based. At very low angles, clutter is caused to a very great extent by discrete sources distributed over a weakly backscattering surface. Hence, at very low angles, less than half (38%) of cells within visible patches contain clutter discernible to the Phase Zero radar. As angle rises through the low-angle regime (depression angle < 2°), the percent of cells containing discernible clutter rises very quickly as the shadowed terrain between discrete sources rapidly comes into view. As a result, the median clutter strength, which was driven down by the large number of shadowed cells at very low angles, also rises relatively quickly with increasing depression angle. Median clutter strength does not rise quite as abruptly as the shadowing function, because even when terrain comes into visibility at very low angle, the areaextensive backscatter from the terrain surfaces themselves, as opposed to the discrete objects on them, is very weak. With increasing angle, however, as the shadowing function levels off, the median clutter strength continues to rise as area-extensive backscatter rises with increasing angle. Mean clutter strengths rise less rapidly than median clutter strengths, because the means are dominated more by the discrete vertical sources and less by the statistics of shadowing. The ratio of mean-to-median in Figure 2.44 and the ratio of standard deviation-to-mean in Figure 2.45, which are measures of spread in clutter amplitude distributions, both decrease strongly with increasing angle as the shadowed and weak samples at the low end of the distributions rise towards the stronger values that are dominating the mean. In the high angle limit of 8o for the data in Figures 2.44 and 2.45, both these measures of spread begin to approach their limiting values associated with Rayleigh statistics. This reflects the relatively low incidence of microshadowing (14%) and relatively full illumination prevailing at high angles. In modeling ground clutter at the high depression angles associated with airborne platforms, clutter strength is often approximated as being directly dependent on the sine of the depression angle. Such a model is referred to as “constant γ,” where σ ° = γ sin α (see Sections 1.2.5 and 2.3.4.2). Typical decibel values of γ (i.e., 10 log10γ) in use for rural terrain are –10 and –15 dB [5, 10, 16]. The mean clutter strength curve above 1° in Figure 2.44 is very accurately represented by σ ° = γ (sin α)1.2 with a decibel value of γ equal to –8.9 dB. Note that the exponent to which sin α is raised in this latter expression is 1.2; that is, the sin α dependence of the Phase Zero data in Figure 2.44 above 1° (457 macropatches) is somewhat stronger than the linear dependence often assumed [5, 10, 16]. Fitting the constant-γ model with linear sin α dependence to the mean clutter strength data above 1° in Figure 2.44 leads to a decibel value of γ of approximately –11 dB, although doing so results in a poorer fit to the data. A summary of simple semi-empirical clutter models such as the constant-γ model and its variations that have been utilized historically to fit various experimental data sets is provided in Ruck [17]. At lower angles, however, where most land clutter occurs in surface-sited radar, mean clutter strength is much stronger than is predicted by the sine of the depression angle dependency, the latter becoming vanishingly small as depression angle approaches zero. Strong mean clutter at low angles is the consequence of domination of the low-angle phenomenon by discrete clutter sources. There has been occasional speculation in the clutter literature as to whether clutter strengths might “come back up” at very low angles because of possible specular incidence on discretes. The data of Figure 2.44 indicate that,

Preliminary X-Band Clutter Measurements 103

–10

Mean

Mean or Median of σ°F4 (dB)

–20

Median

–30

–40

X = Upper Bound Only Due to Radar Noise Contamination –50 0

2

4

6

8

Depression Angle (deg)

Figure 2.44 General variation of ground clutter strength with depression angle. Phase Zero Xband data, 75-m range resolution, horizontal polarization, 2- to 12-km range. All terrain types, 1,926 patches from 86 sites. Data shown are expected values, see text.

although mean clutter strength remains relatively high at low angles, its general characteristic is to always decrease with decreasing angle, with no reversal occurring in this characteristic at very low angle. Mean clutter strength is observed to vary over a range of 15 dB with depression angle in Figure 2.44, from –34.2 dB at grazing incidence in the 0° to 0.25° depression angle regime to –19.3 dB in the 7° to 8° regime. This mean strength variation of 15 dB with depression angle is the most significant general parametric variation observed of any single parameter in the Phase Zero X-band data. The effect of higher average terrain slopes at higher depression angles is implicit in this dependence. The dependence may be summarized by saying that it is depression angle as it influences shadowing on a sea of discretes that most directly affects strength in low-angle ground clutter. Most of the measured Phase Zero data occur at low depression angle. For example, 95% of Phase Zero patches were observed at depression angles of < 2.6°. Thus, in Figures 2.44, 2.45, and 2.46, in the 0° to 0.25° depression angle regime there are 456 patches contributing, but in the 7° to 8° depression angle regime there are only 3 patches

104 Preliminary X-Band Clutter Measurements

contributing. The major information content in these figures is at the low angles—available data are included at higher angles to show a more complete depression angle characteristic. The data in Figures 2.44 and 2.45 are expected-value results. The microshadowing data in Figure 2.46 are ensemble values. 8

Ratio of Standard Deviation-to-Mean (dB)

6

4

2

0 0

2

4

6

8

Depression Angle (deg)

Figure 2.45 General dependence of ratio of standard deviation-to-mean in ground clutter spatial amplitude statistics on depression angle. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 2- to 12-km range. All terrain types, 1,926 patches from 86 sites. Data shown are expected values, see text.

2.4.4.2 Farmland vs Forest Figure 2.47 shows how the depression angle characteristics of low-angle clutter strongly depend on terrain type. In this figure, σ w° and aw are shown as a function of depression angle for four rural terrain types. First, if rural terrain is separated into low relief (terrain slopes < 2°) and high relief (terrain slopes > 2°), in both categories of relief σ w° increases and aw decreases with increasing depression angle; and σ w° is significantly greater and aw significantly less in high-relief terrain than in low-relief terrain, for a given depression angle. The results of Figure 2.47 may be compared with those of Figure 1.9 in Chapter 1. Second, if within general rural/low-relief terrain specific subcategories of level farmland and level forest are separated out, Figure 2.47 shows that with increasing depression angle

80

20

60

40

40

60

0

2

4

6

Percent of Cells at Radar Noise Level

Percent of Cells in Discernible Clutter

Preliminary X-Band Clutter Measurements 105

8

Depression Angle (deg) Figure 2.46 General incidence of microshadowing within clutter patches as a function of depression angle. Phase Zero X-band data, 75-m range resolution, horizontal polarization, 2- to 12km range. All terrain types, 1926 patches from 86 sites. Each plotted point represents the overall percentage of all cells from all patches at a given depression angle.

6

–25

5 a)

–30

aw

σ°w (dB)

b)

c)

c)

4 d)

a)

3

–35 d)

b) 2

0

0.5

1.0

Depression Angle (deg)

1.5

0

0.5

1.0

1.5

Depression Angle (deg)

Figure 2.47 X-band ground clutter results for (a) rural/low-relief terrain, (b) rural/high-relief terrain, (c) level farmland, and (d) level forest.

in level farmland σ w° does not vary at all, but aw rapidly decreases, whereas in level forest σ w° gradually increases and aw gradually decreases. The reasons for this are as follows. In level farmland dominant clutter sources are large, discrete, vertical objects, which at low depression angles cause the clutter amplitude distributions to have very large spread. As depression angle increases, the weak returns from the intervening terrain between strong discrete sources rapidly increase, causing spreads in amplitude distributions to rapidly decrease, but the strong returns from the

106 Preliminary X-Band Clutter Measurements

discrete objects continue to dominate their mean strengths relatively independent of depression angle. In contrast, level forest is much more a homogenous scattering medium, not dominated by large discrete objects. Nevertheless, at low angles in level forest, there still occurs a large amount (e.g., 50%) of microshadowing. As angle increases, the shadowing gradually decreases. As a result the amplitude distributions gradually tighten up, and their mean strengths—not dominated here by large singular discrete sources— gradually rise. The depression angle characteristics of Figure 2.47 were obtained from ensemble clutter amplitude distributions previously discussed in Section 2.4—the rural/low-relief and rural/ high-relief data come from Section 2.4.1, and the level farmland and forest data come from Section 2.4.2.4.

2.4.4.3 Some Airborne Clutter Measurements As part of the ground clutter studies at Lincoln Laboratory, some airborne ground clutter data were collected with an X-band synthetic-aperture radar (SAR) contemporaneously with the ground-based Phase Zero program. Motivation existed to collect airborne data to validate the presumed better understanding of airborne clutter and to provide some connectivity to ground-based measurements at higher angles. Clutter statistics at the higher angles provided by an airborne platform were expected to be approximately Rayleigh distributed—if so, this would largely confirm that the airborne clutter phenomenon is properly represented in traditional manner as a simple constant-γ angle characteristic. The SAR was mounted on a Convair 580 aircraft. The SAR operated at both L- and X-bands but only X-band data are discussed in what follows. The resolution of the SAR at X-band was six meters. Calibrated X-band ground clutter measurement data were collected at six measurement sites of various terrain types in western Canada in side-looking ground swath or strip map mode. Depression angle ranged from 4° to 18°. Within each 5 km × 30 km ground swath, many clutter patches of uniform terrain were identified. The terrain within these clutter patches was characterized through use of maps and air photos. For each patch, the clutter distribution was formed and pertinent parameters such as mean, median, and standard deviation were calculated. Figure 2.48 shows clutter results from many patches selected from all six sites. These results show mean values of clutter strength from each patch as scatter plots vs depression angle, separated in four classes of terrain—agricultural, rangeland, forest, and wetland. Each scatter plot shows wide variability, although suggestions of trends of increasing mean strength with increasing depression angle are evident in each plot. Overall, mean clutter strength in agricultural terrain and forest is stronger, compared to rangeland and wetland where it is weaker. However, as in the Phase Zero low-angle data, wide variability exists within terrain class and little separation exists between classes in these airborne data. Figure 2.49 focuses on agricultural patches collected at five sites. The top two scatter plots show mean and median clutter strength vs depression angle. The bottom two scatter plots show patch values of standard deviation vs mean and mean vs median. A regression curve is shown through each of the top two scatter plots. These curves indicate that, as expected, both mean and median clutter strengths gradually increase with increasing depression angle. Furthermore, they indicate that the mean strength is slightly stronger than the

Preliminary X-Band Clutter Measurements 107

Agricultural

Rangeland

0 Number of Patches 44 229 182 212 99

Mean σ° (dB)

–5

–10

Number of Patches 44 8 13 96 147 2

–15

–20

–25

Forest

Wetland

0 Number of Patches 95 42 135 42 20 245

Mean σ° (dB)

–5

–10

Number of Patches 71 105 15 25 76

–15

–20

–25 2

4

6

8

10

12

14

Depression Angle (deg)

16

18

2

4

6

8

10

12

14

16

18

Depression Angle (deg)

Figure 2.48 X-band SAR airborne clutter measurements: clutter strength vs depression angle for four terrain types.

median. The bottom two plots indicate that the standard deviation is usually very nearly equal to the mean (in Rayleigh statistics, standard deviation = mean), and that the mean is usually 1 or 2 dB stronger than the median (in Rayleigh statistics, mean/median ratio = 1.6 dB). Hence these farmland data strongly suggest near-Rayleigh statistics, based on the first two moments and the median of clutter amplitude distributions measured over many (622) clutter patches. Early reduction of the SAR X-band clutter measurement data was based on optical processing in which cumulative distributions of clutter patch amplitude statistics appeared to be lognormal. Subsequent finalized reduction of the SAR clutter measurement data utilized digital processing. Comparison with the digitally processed data revealed that the lognormal distributions of the optically reduced data were caused by an averaging effect in the optical processor due to the finite sample aperture. The digitally processed data, as expected, showed near-Rayleigh distributions, as shown by the results of Figure 2.50 and

108 Preliminary X-Band Clutter Measurements

–5

Median (dB)

Mean (dB)

–5 –10 –15 –20 –25

–10 –15 –20 –25

6

8

10

12

14

16

6

8

10

12

14

16

Depression Angle (deg)

–5

–5

–10

–10

Mean (dB)

Standard Deviation (dB)

Depression Angle (deg)

–15 –20

–15 –20 –25

–25 –25 –20 –15 –10 –5

Mean (dB)

0

5

10

–25 –20 –15 –10 –5

0

5

10

Median (dB)

Figure 2.49 X-band SAR airborne clutter measurements: clutter patch statistics in agricultural terrain.

Table 2.14. Figure 2.50 shows plots of cumulative distributions of amplitude distributions from a number of clutter patches of agricultural terrain—top [(a) and (c)], and forest terrain—bottom [(b) and (d)]; plotted against a Rayleigh probability scale—left [(a) and (b)], and a lognormal probability scale—right [(c) and (d)]. It is evident that all of these measured patch cumulatives without exception are very linear on the Rayleigh scale and are very much upwards curved on the lognormal scale, strongly indicating that all these patch cumulatives are well approximated as Rayleigh distributions. Table 2.14 confirms this finding in terms of mean/median ratio (Rayleigh = 1.6 dB), and sd/mean ratio (Rayleigh = 0 dB). These results indicate that the agricultural data are indeed very nearly Rayleigh; whereas the forest data are on the whole of just slightly more spread than purely Rayleigh. Thus, with respect to spatial amplitude statistics, these airborne clutter data are indeed of simple behavior and well approximated as tight Rayleigh or quasi-Rayleigh distributions. Next, consider continuity with depression angle between the low-angle Phase Zero data and the higher-angle airborne data. Figure 2.51 shows global characteristics of mean clutter strength vs depression angle as measured across very many rural clutter patches for both ground-based Phase Zero data and the X-band SAR airborne data. Most of the groundbased data are at angles below 2° depression angle; most of the airborne data are at angles above 8°. General continuity of increasing mean clutter strength with increasing angle inclusive of both ground-based and airborne angle regimes and including the more lightly sampled crossover regime is evidenced in the data of Figure 2.51; a single overall characteristic of mean strength vs depression angle closely approximates these data. Thus ground-based and airborne land clutter, which at first observation appear to be completely different phenomena, can be viewed as a single continuous process connected by depression angle. At low angles clutter distributions are very broad and spread out

Preliminary X-Band Clutter Measurements 109

Table 2.14 X-Band Airborne SAR Sample Patch Clutter Statistics for Agricultural and Forest Terrain

Land Cover

Mean/ Median (dB)

SD/ Mean (dB)

9 10 11 12 13 14

Agricultural " " " " "

1.7 1.6 1.7 1.7 1.7 1.8

0.1 0.2 0.1 0.4 0.2 0.3

15 16 17 18 19

Forest " " " "

1.5 2.0 2.9 2.7 2.6

–0.3 0.4 1.0 1.1 1.7

Agricultural

0.999999 0.999 0.95 0.8 0.6 0.4 0.2

Rayleigh Scale

a)

0.01 Forest Rayleigh Scale

0.95 0.8 0.6 0.4 0.2 0.05

b)

0.01 0

20

Lognormal Scale

0.9999 0.999 0.99 0.95

0.05

0.999999 0.999

Agricultural

0.999999

Cumulative Probability

Cumulative Probability

Patch #

40

σ° (dB)

60

80

0.8 0.6 0.4 0.2 0.05 0.01

c) Forest

0.999999 0.9999 0.999 0.99 0.95 0.8 0.6 0.4 0.2 0.05 0.01

Lognormal Scale

d) 0

20

40

60

8

σ° (dB)

Figure 2.50 X-band SAR cumulative clutter distribution for sample patches in agricultural and forest terrain. Rayleigh (a),(b) vs lognormal (c),(d) probability scales.

because of effects of discrete sources and microshadow. With increasing angle, mean clutter strengths rise and spreads diminish. Eventually, at high enough angles, floodlit illumination occurs with no microshadowing and little effect from discretes. The spiky

110 Preliminary X-Band Clutter Measurements

0

X-Band

σ°F4 (dB)

–10

Airborne

–20

GroundBased

–30

–40

–50 0

2

4

6

8

10

12

14

16

Depression Angle (deg)

Figure 2.51 Continuity between ground-based and airborne clutter measurements.

discrete-dominated heterogeneous Weibull process at low angles gradually converts over, with increasing depression angle, to more diffuse clutter and the accompanying homogeneous Rayleigh process that exists in airborne radar.

2.4.5 Effect of Radar Spatial Resolution Ensemble amplitude distributions were formed from ground clutter measured at each of the three Phase Zero pulse lengths over common spatial regions between 2 and 6 km in range from the radar at 14 sites of various terrain types. The three pulse lengths available were 60 ns, 0.5 µs, and 1.0 µs; corresponding range resolutions were 9, 75, and 150 m. The ratio of standard deviation-to-mean was computed as a measure of spread for each of these three ensemble distributions and plotted vs range resolution in Figure 2.52. The results in Figure 2.52 indicate a strong trend of increasing spread in low-angle clutter amplitude distributions with increasing resolution, or in other words, with decreasing resolution cell size A. In the discrete-dominated, heterogeneous process of low-angle clutter, increasing resolution results in less averaging within cells, more cell-to-cell variability (i.e., more strong cells, more weak cells), and increasing spread in clutter amplitude distributions. A scale showing Weibull shape parameter aw as it varies with ratio of standard deviation-tomean in Weibull distributions is also shown in Figure 2.52. The characterization of low-angle clutter strength by σ °, an area density function, implies spatial homogeneity of land clutter. If each clutter resolution cell in a spatial field contained a large number of elemental scatterers with no single scatterer dominating, cell-to-cell variations in clutter amplitudes would be Rayleigh distributed. In these circumstances, neither the mean strength of the distribution of clutter amplitudes over the spatial field nor their spread would vary with resolution cell size. However, the conditions for Rayleigh statistics do not apply to low-angle clutter—strong discretes often dominate within low-

Preliminary X-Band Clutter Measurements 111

4.5

4.0 9

8 3.5

7

Weibull Shape Parameter aw

Standard Deviation-to-Mean of σ°F4

10

3.0 6 150

75

9

Range Resolution (m)

Figure 2.52 Spread in clutter amplitude statistics vs resolution. Phase Zero X-band data measured at each of the three Phase Zero pulse lengths over common spatial regions from 2 to 6 km in range at 14 sites of various terrain types.

angle cells. In these circumstances, Phase Zero results indicate that the mean strength over the spatial field or clutter patch is still largely insensitive to the resolution cell area, thus validating the basic characterization of low-angle clutter as properly being a density function σ °. However, as indicated in the results of Figure 2.52, the spreads in low-angle clutter amplitude distributions take on much greater values than Rayleigh (for Rayleigh voltage statistics and hence exponential σ ° statistics, aw = 1; ratio of standard deviation-tomean = 0 dB) and vary strongly with resolution cell size A. It is fundamentally important to accurately model the wide spreads that occur in low-angle land clutter. These spreads strongly affect radar performance in clutter through target detection and false alarm statistics. The results of Figure 2.52 provide a first indication of the effect of radar resolution cell size on spreads in low-angle clutter and a preliminary means to adjust the Phase Zero modeling information of Chapter 2—heretofore provided as clutter modeling information based on range resolution of 75 m—to apply to other resolutions. In subsequent chapters, the dependence of spread in low-angle clutter spatial amplitude distributions is developed as fundamentally dependent on radar spatial resolution from the outset within the basic parameterization of the modeling information provided.

2.4.6 Seasonal Effects Microwave backscatter from terrain depends upon the fine-scale structure of the landscape surfaces being illuminated. Dynamic processes of change associated with season, weather, human activity (i.e., land use), and even plant morphology (i.e., diurnal variability) cause these surfaces to be continuously varying. The effects of such variations on clutter statistics and the extent to which they need to be incorporated in clutter modeling require investigation.

112 Preliminary X-Band Clutter Measurements

The overall effects of season on land clutter are not obvious. If attention is focused on a single agricultural field, its constitutive characteristics and hence radar backscatter will be considerably different in the summer when it is covered with mature wheat than in the winter after the wheat has been harvested to stubble and the field is covered with snow. However, it has been shown that over large composite landscapes as viewed by groundbased radar, backscatter is often largely caused by macroscopic features of vertical discontinuity (e.g., treelines, woodlots, towns, ridge tops, vertical obstructions along roads and field boundaries, etc.). To the extent that the major physical characteristics of such vertical features do not change substantially with season, it may be that seasonal effects on clutter are not strong. This latter supposition is supported by the data of Figure 2.53. This figure compares summer and winter Phase Zero clutter measurements at Gull Lake West, Manitoba. The Gull Lake West site (as previously discussed at some length in Section 2.3.3) presented a mixed woodland and farmland scene with many composite features, including a railway, a high voltage power line, rivers and streams, the shoreline of a large lake, and considerable areas of wetland, all over relatively low-relief terrain and viewed from a local site elevation advantage of 100 ft. The winter measurements were performed in February with deep snow cover over the fields, plowed roads with high snowbanks, frozen streams and lake (with piled ice along the shoreline), and with all deciduous trees bare of leaves. The summer measurements were performed in June with crops up, leaves out, and the countryside generally verdant. In comparing summer and winter data for many clutter patches at Gull Lake West, very few significant differences were observed. Data from three such representative patches—patches (a), (b), and (c)—are shown in Figure 2.53. (This patch designation is from a different analysis period and does not correspond to that shown in Figure 2.8.) Patch (a) is an area largely cleared for crops but with some patches of trees remaining, and with some trees along roads and the edges of fields. The summer and winter σ° distributions largely overlap for this patch, except that the winter measurement shows an accumulation of strong σ° values as a high-side tail in the distribution, which is not evident in the summer data. Note that these relatively few strong values in the tail of this distribution cause the mean and ratio of standard deviationto-mean of the winter distribution to be significantly different from those of the summer distribution. Whatever the cause of this high-side winter tail, it is not acting in the patch (c) measurement, which is from a similar composite scene except that it is more forested and less cropland, and which indicates very little seasonal variation. Patch (b) consists of level forested wetland at close range where the 100 ft terrain advantage (plus 50 ft tower height) allows full illumination of the tree canopy at ~1° depression angle (cf. patch 19/2 in Figure 2.8). This patch of forested wetland, unlike patches (a) and (c), is highly homogeneous (i.e., no roads, no cultural discretes, no gaps in the tree cover). It consists largely of coniferous tree cover of two major intermixed components, 60 ft tamarack and 40 ft spruce. The resultant measurement is as close to a classical Rayleigh situation (level, uniform tree cover) as is ever encountered in viewing large patches of usually heterogeneous terrain, where by Rayleigh is meant (as elsewhere in this book) that σ ° (voltage) is Rayleigh distributed, so that σ ° (power) is exponentially distributed. The measured statistics indicate that the data are close to Rayleigh, both in the fact that the slope of the cumulative σ ° distribution in Figure 2.53(b) is, as indicated there, very nearly equivalent to that of a Rayleigh distribution; and as shown by the results of

Preliminary X-Band Clutter Measurements 113

Weibull Scale 0.999 Patch (a) 10,126 Samples

Patch (b) 12,846 Samples

Patch (c) 5,187 Samples

0.97 0.95 0.9 slope

0.8 0.7

Rayleigh

Probability That σ°F4 ≤ Abscissa

0.995 0.99

0.6 0.5 0.4

Summer Winter

0.3 0.2

σ °F 4 (dB) Mean SD/Mean Sum –31 6 Wint –28 10

σ °F 4 (dB) Mean SD/Mean Sum –31 0 Wint –32 1

σ °F 4 (dB) Mean SD/Mean Sum –36 5 Wint –35 4

0.1 –50 –40 –30 –20 –10 0

σ°F4 (dB) (a)

–50 –40 –30 –20 –10 0

σ°F4 (dB) (b)

–50 –40 –30 –20 –10 0

σ°F4 (dB) (c)

Figure 2.53 Seasonal variations in low-angle clutter amplitude statistics for three clutter patches. Phase Zero data, 75-m range resolution. Gull Lake West, Manitoba. (a) Composite cropland/mixed forest, dep. ang. = 0.7°; (b) level uniform forest, dep. ang. = 1.1°; (c) mixed forest/cropland (with river), dep. ang. = 0.5°.

Table 2.15 which compare moments and percentile ratios of the patch (b) distribution with those of a theoretical Rayleigh distribution (cf. Table 2.B.1). The patch (b) data show an almost complete absence of significant seasonal dependence. This might be largely expected of a coniferous forest but somewhat less expected upon considering that there was snow and ice in the branches as well as under them in February, and upon noting that tamarack is a deciduous conifer and its branches were bare of needles in February. The Phase Zero results of Figure 2.53 and other similar results from other seasonally revisited sites indicate that seasonal variations in composite low-angle clutter data are low. A more general Phase Zero result with respect to seasonal variation is shown in Figure 2.54, where many of the Phase Zero measurements on rural/low-relief terrain are separated by time of year. The February measurements were conducted on wintry snow-covered landscapes. The April measurements were conducted on wet muddy landscapes without crops and without deciduous foliage. The June, July, and August measurements were conducted on dry summer landscapes with leaves out and crops up. If there were any profound order-of-magnitude seasonal variation in ground clutter strengths, such mean strength data, averaged over many different kinds of sites, would show it. No strong general seasonal variation is seen in the X-band results of Figure 2.54. Similar conclusions on

114 Preliminary X-Band Clutter Measurements

Table 2.15 Little Seasonal Variability in Approximately Rayleigh Spatial Amplitude Statistics from Patch (b)* at Gull Lake West, Manitoba. Phase Zero X-Band Data, Range Resolution = 75 m.

σ°F4 (dB) Statistical Attribute Of Spatial Amplitude Distribution

Measured Values Winter Visit 23 February

Summer Visit 28 June

Theoretical Rayleigh Values

-31.9

-31.2

–

Standard Deviation-to-Mean

0.9

0.5

0

Skewness

6.6

4.4

3

Kurtosis

17.2

12.0

9.5

Mean-to-Median

2.1

1.8

1.6

90 Percentile-to-Median

6

5

5.2

99 Percentile-to-Median

10

9

8.2

Mean

*Patch (b) is level forested wetland. Landform = 1-3; land cover = 61; depression angle = 1.1°.

seasonal effects in low-angle ground clutter are reached when five-frequency Phase One measurement data are brought into consideration in Chapter 3 (e.g., see Figures 3.11 and 3.12 for additional Gull Lake West seasonal results; see also Figures 3.24 and 3.31 and Section 3.7).

Mean of σ°F4 (dB)

Rural/Low Relief -30 (9) (12) (7)

(11)

(30)

(18)

(5)

Jul

Aug

Number of Sites -40 Feb

Mar

Winter

Apr

May

Spring

Jun

Summer

Figure 2.54 Month-by-month seasonal variation in mean clutter strength. Phase Zero X-band data, 92 sites.

Preliminary X-Band Clutter Measurements 115

2.5 Summary The data available from the Phase Zero program comprise calibrated clutter files covering all of the clutter within the field-of-view from 106 different sites. Extensive analyses of these data lead to an understanding of a basic unifying mechanism underlying what appears at first consideration to be extreme variability and little predictability in low-angle clutter spatial amplitude distributions. This understanding is based on the fact that, at the very low angles of illumination of surface radar, ground clutter largely consists of backscatter from a sea of discrete clutter sources. That is, a wave is skimming over the landscape at grazing incidence, and backscatter is being measured from all the vertical sources that rise up from the landscape. Such discrete f0revertical sources may be natural or cultural and comprise such things as: roads and field boundaries (or, more specifically, the vertical objects clustered along them); buildings (usually in clusters or complexes, for example, at farmsteads and industrial facilities, along road and rail lines, in towns and villages); trees (isolated trees, or tree lines, as at the edge of forest cover, or as shelter belts, or along river valleys); or even high points in terrain or breaks in terrain slope (for example, that occur in hummocky, hilly, or mountainous regions, or at edges of river valleys). All such clutter sources are spatially localized and thus discrete. Numerous low reflectivity or shadowed cells occur between cells containing discrete clutter sources, even though the overall region from which the clutter amplitude distribution is being formed is under general illumination by the radar. In other words, at very low angles, small rises in terrain throw long ground shadows and even unshadowed terrain surfaces near grazing incidence backscatter very weakly. The combination of many shadowed or low-reflectivity weak cells together with many discrete-dominated strong cells causes extreme spread in the resultant low-angle amplitude distributions in which individual samples of clutter strength vary over orders of magnitude. As illumination angle increases, the low reflectivity areas between discrete vertical features become more strongly illuminated, resulting in less shadowing and a rapid decrease in the spread of the distributions. The upper tails of the clutter distributions, however, and the mean strengths that are largely determined by the upper tails are still primarily caused by discrete sources and increase more slowly with increasing illumination angle. Therefore, as a unifying mechanism, depression angle (i.e., the angle below the horizontal at which a clutter patch is observed at the radar) as it affects shadowing on a sea of discretes is the most important parameter at work in low-angle ground clutter data, even at the very low angles (typically, < 1°) and small (typically fractional) variations in angle that occur in surface-sited radar. This basic parametric dependence in ground clutter spatial amplitude distributions is such that strengths increase and spreads decrease as depression angle rises and percent shadowing falls. Attempts to refine this basic dependency through use of grazing angle (i.e., the angle between the tangent to the local terrain surface at the terrain point and the direction of illumination) have met with little additional success (but see Appendix 4.D). Reasons contributing to this lack of success include the extreme complexity that exists in terrain surfaces, the lack of detailed information defining these surfaces such that slopes (i.e., rates of change of elevation) are accurate, and difficulties in formulating a quantitative definition of terrain slope uniformly applicable across the various physical scales (centimeters to kilometers) at which slopes exist in landscape. Over and above such considerations of scale and accuracy in terrain elevation data is the fact that the backscatter is frequently dominated by vertical elements of land cover irrespective of the underlying terrain slope.

116 Preliminary X-Band Clutter Measurements

Chapter 2 presents preliminary low-angle X-band ground clutter modeling information for clutter amplitude statistics within a construct that requires relatively detailed specification of depression angle, but that requires specification of terrain type minimally as one of just three types— rural/low-relief, rural/high-relief, or urban. Terrain slope enters the model explicitly through the two categories of relief. This basic information is refined by providing additional results for more specific terrain types— e.g., farmland, forest, wetland, mountains. The modeling information is presented largely in terms of Weibull coefficients. The low-angle heterogeneous regime of widespread spiky Weibull statistics applicable to surface radar gradually transitions with increasing depression angle to the high-angle, more homogeneous regime of Rayleigh statistics applicable to airborne radar. Chapter 2 emphasizes the importance of spatially localized or discrete sources in low-angle clutter statistics. The dominant role of discrete sources is not, in itself, a new idea in the clutter literature. Clutter models, however, have traditionally been developed, first, on a basis of area-extensive scattering from the statistically rough surface itself, as opposed to localized scattering from just the high points of that surface or high objects on it. One of the more valuable results of the Phase Zero clutter program is that low-angle clutter is now imagined as arising, first, from a sea of discrete vertical features or edges, separated by microshadow, and distributed over complex surfaces. The role of illumination angle in this construct is more as depression angle influences clutter strength through its effect on shadowing statistics between discrete features of vertical discontinuity, and less in the influence of grazing angle on area-extensive backscatter from tilted, statistically rough, terrain facets, although both sorts of illumination angle effects are at work in the actual phenomenon. Chapter 2 provides information on how clutter amplitude distributions vary with percent tree cover, which indicates that the dominant sources causing much of the wide spread typically observed in these distributions in open terrain are trees. The problem of making radar ground clutter understandable and predictable is as much one of statistics as of physics. Given enough time and effort, the backscattering processes within and contributions from any particular clutter patch can be understood, but the heterogeneity of terrain often prevents useful generalization of such particular results. The ambiguous state of the historical clutter literature fundamentally reflects this problem. Hence the approach taken in this book is empirical, involving measurements from many patches and across many sites. This approach bounds the problem of clutter strengths for various terrain types by presenting generalized data with considerable averaging across sites and patches and not data specific to some particular clutter scene that is nonrepresentative of other scenes.

References 1.

J. B. Billingsley, “ Radar ground clutter measurements and models,” AGARD Conf. Proc. Target and Clutter Scattering and Their Effects on Military Radar Performance, Ottawa, AGARD-CP-501, 1991; DTIC AD-P006 373.

2.

H. C. Chan, “ Radar ground clutter measurements and models, part 2: Spectral characteristics and temporal statistics,” AGARD Conference Proceedings on Target and Clutter Scattering and Their Effects on Military Radar Performance, AGARDCP-501 (1991).

Preliminary X-Band Clutter Measurements 117

3.

J. R. Anderson, et al., “ A land use and land cover classification system for use with remote sensor data,” Professional Paper 964, Geological Survey, U.S. Department of the Interior (1975).

4.

J. A. McKeague, et al., The Canadian System of Soil Classification, Canadian Department of Agriculture Publ. 1646, Supply and Services, Ottawa, Canada (1978).

5.

F. E. Nathanson (with J. P. Reilly and M. N. Cohen), Radar Design Principles (2nd ed.), New York: McGraw-Hill, 1991.

6.

M. I. Skolnik, Introduction to Radar Systems (3rd ed.), New York: McGraw-Hill, 2001.

7.

M. W. Long, Radar Reflectivity of Land and Sea (3rd ed.), Boston, Mass.: Artech House, 2001.

8.

D. A. Hill and J. R. Wait, “ Ground wave propagation over a mixed path with an elevation change,” IEEE Trans. Ant. and Prop, Vol. AP-30, No. 1, pp. 139-141 (January 1982).

9.

J. K. Jao, “ Amplitude distribution of composite terrain radar clutter and the Kdistribution,” IEEE Trans. Ant. Prop., vol. AP-32, no. 10, 1049-1062 (October 1984).

10. D. K. Barton, “ Land clutter models for radar design and analysis,” Proc. IEEE, vol. 73, no. 2, pp. 198-204 (February 1985). 11. M. Sekine and Y. Mao, Weibull Radar Clutter, London, U.K.: Peter Peregrinus Ltd., 1990. 12. R. R. Boothe, “ The Weibull Distribution Applied to the Ground Clutter Backscatter Coefficient,” U.S. Army Missile Command Rept. No. RE-TR-69-15, Redstone Arsenal, AL June 1969; DTIC AD-691109. 13. E. Jakeman, “ On the statistics of K-distributed noise,” J. Physics A; Math. Gen., vol. 13, 31-48 (1980). 14. C. J. Oliver, “ A model for non-Rayleigh scattering statistics,” Opt. Acta. Vol. 31, pp. 701-722 (1984). 15. J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurement Procedures, (2nd ed.), New York: Wiley, 1986. 16. D. K. Barton, Modern Radar System Analysis, Norwood, MA: Artech House, 1988. 17. G. T. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, Radar Cross Section Handbook, New York: Plenum Press, 1970, pp. 676-679.

Preliminary X-Band Clutter Measurements 115

2.5 Summary The data available from the Phase Zero program comprise calibrated clutter files covering all of the clutter within the field-of-view from 106 different sites. Extensive analyses of these data lead to an understanding of a basic unifying mechanism underlying what appears at first consideration to be extreme variability and little predictability in low-angle clutter spatial amplitude distributions. This understanding is based on the fact that, at the very low angles of illumination of surface radar, ground clutter largely consists of backscatter from a sea of discrete clutter sources. That is, a wave is skimming over the landscape at grazing incidence, and backscatter is being measured from all the vertical sources that rise up from the landscape. Such discrete f0revertical sources may be natural or cultural and comprise such things as: roads and field boundaries (or, more specifically, the vertical objects clustered along them); buildings (usually in clusters or complexes, for example, at farmsteads and industrial facilities, along road and rail lines, in towns and villages); trees (isolated trees, or tree lines, as at the edge of forest cover, or as shelter belts, or along river valleys); or even high points in terrain or breaks in terrain slope (for example, that occur in hummocky, hilly, or mountainous regions, or at edges of river valleys). All such clutter sources are spatially localized and thus discrete. Numerous low reflectivity or shadowed cells occur between cells containing discrete clutter sources, even though the overall region from which the clutter amplitude distribution is being formed is under general illumination by the radar. In other words, at very low angles, small rises in terrain throw long ground shadows and even unshadowed terrain surfaces near grazing incidence backscatter very weakly. The combination of many shadowed or low-reflectivity weak cells together with many discrete-dominated strong cells causes extreme spread in the resultant low-angle amplitude distributions in which individual samples of clutter strength vary over orders of magnitude. As illumination angle increases, the low reflectivity areas between discrete vertical features become more strongly illuminated, resulting in less shadowing and a rapid decrease in the spread of the distributions. The upper tails of the clutter distributions, however, and the mean strengths that are largely determined by the upper tails are still primarily caused by discrete sources and increase more slowly with increasing illumination angle. Therefore, as a unifying mechanism, depression angle (i.e., the angle below the horizontal at which a clutter patch is observed at the radar) as it affects shadowing on a sea of discretes is the most important parameter at work in low-angle ground clutter data, even at the very low angles (typically, < 1°) and small (typically fractional) variations in angle that occur in surface-sited radar. This basic parametric dependence in ground clutter spatial amplitude distributions is such that strengths increase and spreads decrease as depression angle rises and percent shadowing falls. Attempts to refine this basic dependency through use of grazing angle (i.e., the angle between the tangent to the local terrain surface at the terrain point and the direction of illumination) have met with little additional success (but see Appendix 4.D). Reasons contributing to this lack of success include the extreme complexity that exists in terrain surfaces, the lack of detailed information defining these surfaces such that slopes (i.e., rates of change of elevation) are accurate, and difficulties in formulating a quantitative definition of terrain slope uniformly applicable across the various physical scales (centimeters to kilometers) at which slopes exist in landscape. Over and above such considerations of scale and accuracy in terrain elevation data is the fact that the backscatter is frequently dominated by vertical elements of land cover irrespective of the underlying terrain slope.

116 Preliminary X-Band Clutter Measurements

Chapter 2 presents preliminary low-angle X-band ground clutter modeling information for clutter amplitude statistics within a construct that requires relatively detailed specification of depression angle, but that requires specification of terrain type minimally as one of just three types—rural/low-relief, rural/high-relief, or urban. Terrain slope enters the model explicitly through the two categories of relief. This basic information is refined by providing additional results for more specific terrain types—e.g., farmland, forest, wetland, mountains. The modeling information is presented largely in terms of Weibull coefficients. The low-angle heterogeneous regime of widespread spiky Weibull statistics applicable to surface radar gradually transitions with increasing depression angle to the high-angle, more homogeneous regime of Rayleigh statistics applicable to airborne radar. Chapter 2 emphasizes the importance of spatially localized or discrete sources in low-angle clutter statistics. The dominant role of discrete sources is not, in itself, a new idea in the clutter literature. Clutter models, however, have traditionally been developed, first, on a basis of area-extensive scattering from the statistically rough surface itself, as opposed to localized scattering from just the high points of that surface or high objects on it. One of the more valuable results of the Phase Zero clutter program is that low-angle clutter is now imagined as arising, first, from a sea of discrete vertical features or edges, separated by microshadow, and distributed over complex surfaces. The role of illumination angle in this construct is more as depression angle influences clutter strength through its effect on shadowing statistics between discrete features of vertical discontinuity, and less in the influence of grazing angle on area-extensive backscatter from tilted, statistically rough, terrain facets, although both sorts of illumination angle effects are at work in the actual phenomenon. Chapter 2 provides information on how clutter amplitude distributions vary with percent tree cover, which indicates that the dominant sources causing much of the wide spread typically observed in these distributions in open terrain are trees. The problem of making radar ground clutter understandable and predictable is as much one of statistics as of physics. Given enough time and effort, the backscattering processes within and contributions from any particular clutter patch can be understood, but the heterogeneity of terrain often prevents useful generalization of such particular results. The ambiguous state of the historical clutter literature fundamentally reflects this problem. Hence the approach taken in this book is empirical, involving measurements from many patches and across many sites. This approach bounds the problem of clutter strengths for various terrain types by presenting generalized data with considerable averaging across sites and patches and not data specific to some particular clutter scene that is nonrepresentative of other scenes.

References 1.

J. B. Billingsley, “Radar ground clutter measurements and models,” AGARD Conf. Proc. Target and Clutter Scattering and Their Effects on Military Radar Performance, Ottawa, AGARD-CP-501, 1991; DTIC AD-P006 373.

2.

H. C. Chan, “Radar ground clutter measurements and models, part 2: Spectral characteristics and temporal statistics,” AGARD Conference Proceedings on Target and Clutter Scattering and Their Effects on Military Radar Performance, AGARDCP-501 (1991).

Preliminary X-Band Clutter Measurements 117

3.

J. R. Anderson, et al., “A land use and land cover classification system for use with remote sensor data,” Professional Paper 964, Geological Survey, U.S. Department of the Interior (1975).

4.

J. A. McKeague, et al., The Canadian System of Soil Classification, Canadian Department of Agriculture Publ. 1646, Supply and Services, Ottawa, Canada (1978).

5.

F. E. Nathanson (with J. P. Reilly and M. N. Cohen), Radar Design Principles (2nd ed.), New York: McGraw-Hill, 1991.

6.

M. I. Skolnik, Introduction to Radar Systems (3rd ed.), New York: McGraw-Hill, 2001.

7.

M. W. Long, Radar Reflectivity of Land and Sea (3rd ed.), Boston, Mass.: Artech House, 2001.

8.

D. A. Hill and J. R. Wait, “Ground wave propagation over a mixed path with an elevation change,” IEEE Trans. Ant. and Prop, Vol. AP-30, No. 1, pp. 139-141 (January 1982).

9.

J. K. Jao, “Amplitude distribution of composite terrain radar clutter and the Kdistribution,” IEEE Trans. Ant. Prop., vol. AP-32, no. 10, 1049-1062 (October 1984).

10. D. K. Barton, “Land clutter models for radar design and analysis,” Proc. IEEE, vol. 73, no. 2, pp. 198-204 (February 1985). 11. M. Sekine and Y. Mao, Weibull Radar Clutter, London, U.K.: Peter Peregrinus Ltd., 1990. 12. R. R. Boothe, “The Weibull Distribution Applied to the Ground Clutter Backscatter Coefficient,” U.S. Army Missile Command Rept. No. RE-TR-69-15, Redstone Arsenal, AL June 1969; DTIC AD-691109. 13. E. Jakeman, “On the statistics of K-distributed noise,” J. Physics A; Math. Gen., vol. 13, 31-48 (1980). 14. C. J. Oliver, “A model for non-Rayleigh scattering statistics,” Opt. Acta. Vol. 31, pp. 701-722 (1984). 15. J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurement Procedures, (2nd ed.), New York: Wiley, 1986. 16. D. K. Barton, Modern Radar System Analysis, Norwood, MA: Artech House, 1988. 17. G. T. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, Radar Cross Section Handbook, New York: Plenum Press, 1970, pp. 676-679.

3 Repeat Sector Clutter Measurements 3.1 Introduction Phase One multifrequency land clutter measurements were conducted during a three-year period at 42 different sites widely dispersed geographically across the North American continent. Many of the sites were in western Canada. The Phase One clutter measurement equipment was self-contained and mobile, principally housed within three, 18-wheel tractor-trailer combination trucks and manned by a five-man crew. The equipment included a transportable antenna tower expandable in six sections to a maximum height of 100 ft. A photograph of the Phase One equipment erected at the Lethbridge West site in Alberta, Canada, is shown in Figure 3.1. At each site, all discernible ground clutter within the field-of-view through 360° in azimuth and from 1 to 25 or 50 km or more in range was measured at each of five frequencies: VHF, UHF, L-, S-, and X-bands. The duration of time that the Phase One equipment spent at each site making these measurements was typically two to three weeks. The amount of raw, digitally recorded, pulse-by-pulse measurement data collected at each site usually filled about 25 to 30 high-density magnetic tapes. Within the measurement program, six repeated data collection visits to a few sites at different times of the year were included to provide seasonal variations in the clutter measurement database. The objective in conducting the Phase One measurements was to develop a capability for predicting multifrequency variations in ground clutter spatial amplitude distributions in surface-sited radar. Data from each site are analyzed in Chapter 3. From these data multifrequency clutter models are subsequently developed in Chapters 4 and 5. In particular, Chapter 3 shows how ground clutter strength varies with radar frequency, VHF to X-band, in various types of terrain. The clutter spatial amplitude distributions analyzed in Chapter 3 were measured in what is called the repeat sector at each site. That is, at each site a narrow azimuth sector was selected as a sector of concentration in which measurements were repeated a number of times during the time on site. Typically, the repeat sector is about 20° in azimuth extent and exists at ranges beginning a few kilometers from the radar and extending 5 or 10 km.

144 Repeat Sector Clutter Measurements

Figure 3.1 Phase One equipment at Lethbridge West, Alberta. Antenna tower erected to 60 ft.

3.1.1 Outline This section is a brief introduction to the contents of Chapter 3.

Land Clutter Strength vs Frequency. A major purpose of Chapter 3 is to show how land clutter strength varies with radar frequency, VHF to X-band, in various types of terrain. The best high-level way of showing such variation based on repeat sector measurements is given in Section 3.4 by mean clutter strength data vs frequency for 12 different terrain categories, generalized across a number of similar measurement sites in each category. The remainder of Chapter 3 explains, enlarges upon, and provides background about these generalized multifrequency characteristics, organized within broad terrain groups of urban, mountains, forest, farmland, and desert. Means and Medians. Each value of mean clutter strength provided in Chapter 3 comes from a clutter amplitude distribution measured over a repeat sector spatial macroregion. These distributions are brought under more complete statistical description by tabulation of their higher moments and several percentile levels, including the median. These additional statistical attributes are generalized within the same terrain categories as are the means. Polarization and Resolution. The mean clutter strength vs frequency results are combined across measurements of both vertical and horizontal polarization, using both 150-m and 15- or 36-m pulse lengths. Variations of mean clutter strength with polarization

Repeat Sector Clutter Measurements 145

and range resolution are generally small, typically on the order of 1 or 2 dB. Discussion of differences in clutter strength with polarization and resolution is presented in Section 3.5.

Weather and Season. Because low-angle land clutter is dominated by discrete scattering sources, effects with weather and season are also small, usually less than 1.5 dB and 3.0 dB, respectively. Discussion of variability of mean clutter strength with weather and season is given in Section 3.7. Multipath Propagation. At low angles in open terrain, clutter measurements are dominated by multipath propagation that causes lobing on the free-space antenna pattern and hence introduces strong variations in effective antenna gain to the measured clutter. These propagation-induced variations are generally not removable in assessments of clutter strength. In interpreting many of the measurement results in Chapter 3, it is necessary to estimate the effects of propagation, particularly multipath, in the data. How effects of multipath are estimated is discussed in Appendix 3.B.

Antenna Tower Height. Multifrequency Phase One clutter measurements were obtained with multiple antenna tower heights at four different sites. Results for different Phase One antenna heights are discussed in Section 3.4.1.4. In addition, Section 3.4.1.4 provides a comparison at X-band between Phase Zero and Phase One measurements across many sites in two regimes of antenna height—one where the Phase One radar had similar heights to the Phase Zero radar, and another where the Phase One antenna height was twice as high as that of Phase Zero.

Long-Range Mountain Clutter. A surface-sited radar can occasionally experience strong land clutter from visible terrain at very long ranges, such as 100 km or more. Such clutter comes from mountains because only mountains rise high enough to be within geometric line-of-sight at long ranges. Phase One measurements show that long-range mountain clutter at VHF is significantly stronger than in the microwave bands. In all Phase One bands, the long-range mountain clutter is substantially weaker than mountain clutter observed at shorter ranges due to diffraction over the intervening terrain. Discussion of this matter is included in Appendix 3.B. Coherency of Clutter Returns. The Phase One measurements were coherent; the phase (provided by in-phase and quadrature samples from 13-bit A/D converters at rates of 1 to 10 MHz) of the clutter return signal was recorded, as well as its amplitude. Clutter may be regarded as partially correlated noise in which the degree of correlation depends on the type of clutter. Pulse-by-pulse coherent integration can increase clutter-to-noise ratios; however, care must be taken not to integrate beyond a correlation period in the clutter, or the quasinoiselike clutter returns will also be unintentionally reduced. These matters concerning Phase One data reduction are discussed, and examples are given in Appendix 3.C.

3.2 Multifrequency Clutter Measurements Chapter 2 discusses how, at X-band, variations in clutter amplitude statistics with land cover (for example, between forest and farmland terrains of similar relief and observed at similar viewing angles) are not extreme, and how good modeling headway can be made by combining them as rural/low-relief terrain. Chapter 3 shows that as frequency decreases from X-band to VHF, mean clutter strengths of forested terrain viewed at high angle for surface-sited radar strongly increase; whereas mean clutter strengths of level farmland terrain viewed at grazing incidence strongly decrease. As a result, forested terrain provides

146 Repeat Sector Clutter Measurements

mean clutter strengths at VHF 10 or 15 dB stronger than in the microwave bands; whereas farmland terrain provides mean clutter strengths at VHF 20 or 30 dB weaker than in the microwave bands. Plots showing mean clutter strength vs frequency at seven different Phase One sites are shown in Figures 3.2 through 3.8. Each plot shows results across the 20-element Phase One parameter matrix (five frequencies, two polarizations, two pulse lengths) based on repeat sector measurements. It is evident in this set of site-specific plots that the frequency dependence of ground clutter is highly variable. Included among this set of plots are forest results (e.g., from Blue Knob, Figure 3.3) and farmland results (e.g., from Corinne, Figure 3.7), as well as results for mountains, rangeland, and wetland. Chapter 3 expands upon and explains these and other variations of mean clutter strength with frequency.

3.2.1 Equipment and Schedule The Phase One radar [1] was a computer-controlled five-frequency instrumentation radar (see Appendix 3.A). The instrument had uncoded, pulsed waveforms with two pulse lengths available in each band to provide high and low range resolution. Polarization was selectable as vertical or horizontal with transmit and receive antennas always copolarized (the cross-polarized component in the radar return signal could not be received). The Phase One system activated one combination of frequency, polarization, and pulse length at a time for any particular clutter experiment. These three major radar parameters as well as other parameters (e.g., spatial extent in range and azimuth, number of pulses, pulse repetition rate, etc.) were selectable at the onboard computer console for each clutter experiment recorded. The Phase One measurement program consisted of setting up and acquiring clutter measurement data 49 times at 42 different sites [1] (see Appendix 3.A).

3.2.2 Data Collection Phase One clutter measurement data were collected within three different kinds of experiments, namely, survey experiments, repeat sector experiments, and long-time-dwell experiments. The spatially comprehensive survey data are discussed in Section 3.2.2.1. The more in-depth repeat sector data are discussed in Section 3.2.2.2. Chapters 4 and 6 discuss temporal and spectral characteristics of ground clutter returns based on the longtime-dwell experiments [2]. See Appendix 3.A for more detailed information on all three major types of Phase One experiment.

3.2.2.1 360-Degree Survey Data One important aspect in Phase One data collection was to record in survey mode all of the discernible clutter within the field-of-view through 360° in azimuth and to 25 or 50 km or more in range. These survey data provide a comprehensive spatial database upon which to base accurate clutter modeling information (see Chapter 5). Figure 3.9 shows ground clutter maps measured in survey mode at all five Phase One frequencies at Gull Lake West in Manitoba. These maps are at high range resolution and horizontal polarization. They are thresholded such that cells in which clutter strength σ°F4 is greater than or equal to –35 dB are shown as black. Maximum range in these maps is 15 km. North is zenith. As discussed in Chapter 2 (Section 2.3.3.1), at Gull Lake West the Phase One site is on a 100-ft-high ridge running north-south. This ridge provides good visibility to the west and southwest down onto level composite terrain. The shoreline of Lake Winnipeg is observable in the northwest quadrant with some lake clutter evident at X-band. The X-band Phase One clutter map in

Repeat Sector Clutter Measurements 147

0

Mean of σ°F4(dB)

−20

−40

Pol.

150 150 15/36 15/36

H V H V

1,000

100

−80

Range Res. (m)

10,000

−60

VHF

UHF

L-Band

S-Band

X-Band

Frequency (MHz)

Figure 3.2 Mean clutter strength vs frequency at Waterton. For the Waterton repeat sector, depression angle = –1.8 deg, landform = 8-7, land cover = 42-7-41, range = 9 to 14.9 km, azimuth = 175 to 185 deg.

Figure 3.9 obtained with a 100-ft antenna mast may be compared with the Phase Zero Gull Lake West clutter map of Figure 2.7 which was obtained with a 50-ft antenna mast.

148 Repeat Sector Clutter Measurements

0

Mean of σ°F4(dB)

−20

−40

H V H V

1,000

100

−80

Pol.

150 150 15/36 15/36

10,000

−60

Range Res. (m)

VHF

UHF

L-Band

S-Band

X-Band

Frequency (MHz)

Figure 3.3 Mean clutter strength vs frequency at Blue Knob. For the Blue Knob repeat sector, depression angle = 1.6 deg, landform = 4, land cover = 21-43-11, range = 16 to 21.9 km, azimuth = 80 to 100 deg.

The first and most obvious thing to notice in the clutter maps of Figure 3.9 is that, as patterns of spatial occurrence of ground clutter, in overall measure they are quite similar. The reason for this similarity is that the relatively significant or strong clutter being shown comes from visible terrain. Such patterns of spatial occurrence of ground clutter can be

Repeat Sector Clutter Measurements 149

0

−40

100

−80

Pol.

150 150 15/36 15/36

H V H V

1,000

−60

Range Res. (m)

10,000

Mean of σ°F4 (dB)

−20

VHF

UHF

L-Band

S-Band

X-Band

Frequency (MHz)

Figure 3.4 Mean clutter strength vs frequency at Wachusett Mountain. For the Wachusett Mountain repeat sector, depression angle = 2.1 deg, landform = 5-4, land cover = 43-21-11, range = 8 to 13.9 km, azimuth = 156 to 176 deg.

approximately and deterministically predicted at a given site simply as geometric visibility using available digitized terrain elevation data (DTED).

150 Repeat Sector Clutter Measurements

0

−40

Range Res. (m)

Pol.

150 150 15/36 15/36

H V H V

100

1,000

−60

10,000

Mean of σ°F4 (dB)

−20

−80 VHF

UHF

L-Band

S-Band

X-Band

Frequency (MHz)

Figure 3.5 Mean clutter strength vs frequency at Wainwright. For the Wainwright repeat sector, depression angle = 0.6 deg, landform = 5-3, land cover = 41-32-31, range = 1 to 6.9 km, azimuth = 120 to 150 deg.

The second thing to notice in the clutter maps of Figure 3.9 is the patchy, granular, onagain, off-again nature of the clutter. That is, clutter comes from discrete sources distributed over geometrically visible surfaces and separated by microshadowed cells where the radar is often at its noise floor. As a result, depression angle is of fundamental

Repeat Sector Clutter Measurements 151

0

–40

Range Res. (m)

Pol.

150 150 15/36 15/36

H V H V

100

1,000

–60

10,000

Mean of σ°F4 (dB)

–20

–80 VHF

UHF

L-Band

S-Band

X-Band

Frequency (MHz)

Figure 3.6 Mean clutter strength vs frequency at Vananda East. For the Vananda East repeat sector, depression angle = 1.0 deg, landform = 3-5, land cover = 31-32, range = 3.6 to 9.5 km, azimuth = 40 to 60 deg.

parametric importance in clutter modeling investigations because of its influence on shadowing in a sea of patchy visibility and discrete scattering sources. First discussed in the Phase Zero data of Chapter 2, depression angle continues to be of principal influence in the multifrequency measurements of Chapter 3, where mean strengths of clutter amplitude

152 Repeat Sector Clutter Measurements

0

−40

100

−80

Range Res. (m)

Pol.

150 150 15/36 15/36

H V H V

1,000

−60

10,000

Mean of σ°F4 (dB)

−20

VHF

UHF

L-Band

S-Band

X-Band

Frequency (MHz)

Figure 3.7 Mean clutter strength vs frequency at Corinne. For the Corinne repeat sector, depression angle = 0.15 deg, landform = 1, land cover = 21, range = 1 to 8.9 km, azimuth = 330 to 30 deg.

distributions increase, and cell-to-cell variations in these distributions decrease with increasing angle. The final thing to notice in the clutter maps of Figure 3.9 is the effect of increasing azimuth beamwidth with decreasing frequency (see Table 3.A.2) to smear out the clutter. This illustrates that the role of spatial resolution of the radar is important as it influences spreads

Repeat Sector Clutter Measurements 153

0 Range Res. (m)

Pol.

150 150 15/36 15/36

H V H V

Mean of σ°F4 (dB)

−20

−40

1,000

100

−80

10,000

−60

VHF

UHF

L-Band

S-Band

X-Band

Frequency (MHz)

Figure 3.8 Mean clutter strength vs frequency at Big Grass Marsh. For the Big Grass Marsh repeat sector, depression angle = 0.2 deg, landform = 1, land cover = 62-22, range = 1 to 6.9 km, azimuth = 350 to 10 deg.

in clutter amplitude distributions. The multifrequency clutter models developed in Chapters 4 and 5 directly implement this important dependency. Chapter 3 documents spreads in measured repeat sector clutter spatial amplitude distributions as ratios of standard deviation-to-mean and ratios of various percentile levels in these distributions. Beyond this,

154 Repeat Sector Clutter Measurements

VHF

UHF

S-Band

L-Band

X-Band

Figure 3.9 Measured multifrequency ground clutter maps at Gull Lake West, Manitoba. Phase One data, 15-km maximum range, σ °F4 ≥ –35 dB.

however, the primary emphasis in Chapter 3 is to comprehensively discuss and document the important trends observed in mean strength vs frequency, not spreads vs resolution.

3.2.2.2 Repeat Sector Data One limitation in the Phase One survey data is that, due to limitations in acquisition time and data volume, a long time record could not be established for each spatial clutter cell that was measured in this mode. In much of the survey data, only about 125 pulses were recorded from each cell for each of the 20 data acquisition experiments in the 20-element radar parameter matrix (five frequencies, two polarizations, two pulse lengths). To help overcome this limitation, a second mode of data acquisition was established whereby, at each Phase One site, a series of ground clutter measurements was repeatedly conducted over a specially selected narrow azimuth sector. In total these measurements are referred to as repeat sector measurements. In each repeat sector measurement, many more pulses (e.g., 1,024) per spatial cell were recorded than were recorded in the survey data, and, in addition, each measurement in the repeat sector was repeated a number of times (often four) for each set of radar parameters during the Phase One stay at each site. The approximately 80 repeat sector measurements at each site (four repeated measurements for each combination of parameters in the 20-element Phase One radar parameter matrix) also encompassed variations of other underlying parameters, such as data rate of recording, pulse repetition frequency, number of pulses recorded, scan and step antenna modes, fixed and variable radio frequency (RF) attenuation schedules, and, occasionally, different antenna mast heights. The objectives in collecting the repeat sector

Repeat Sector Clutter Measurements 155

data were (1) to allow an assessment of quality of data to be made based on comparison of similar measurements, (2) to provide a database with substantially more depth in terms of parameter variations than the mainline survey measurements, and (3) to allow determination of day-to-day temporal clutter variations caused by weather and other natural and cultural processes of change occurring on the landscape. The analyses of Phase One measurements in Chapter 3 give special attention to the repeat sector measurements. These data provide a manageable subset of the overall data acquired at each site. Descriptions of the terrain within the various repeat sectors are subsequently provided in Table 3.3. Across all repeat sectors, the median azimuth extent is 20°, the median start range is 4 km, the median range extent is 6 km, and the median area is 12 km2 (compare with the 5.3-km2 median patch size of the 2,177 patches lying between 2- and 12km range that constitute the Phase Zero database of Chapter 2). Altogether, 4,465 measurements of pulse-by-pulse clutter backscatter from repeat sector spatial macroregions were obtained in the 49 setups of the Phase One equipment.

Gull Lake West. Repeat sector data are now shown in several formats at Gull Lake West. This discussion continues the Phase Zero Gull Lake West discussion in Chapter 2. Figure 3.10 shows an expanded X-band PPI clutter map at Gull Lake West at a reduced maximum range of 7 km in which the spatial nature of the clutter is apparent. This clutter map shows spatial correlation and texture, both man-made and natural (i.e., clutter does not occur as random salt and pepper). The boundaries of the repeat sector are shown overlaid in Figure 3.10 with heavy black lines. The Phase One antenna looked into this repeat sector from a 100-ft-high ridge, initially over level forested wetland to 3.5-km range, then across a swampy open pond area from 3.5 to 5 km, then to a higher sand dune area along the shoreline of Lake Winnipeg between 5 and 6 km, and then to the open water of Lake Winnipeg. Figure 3.11 shows mean clutter strength vs range through the Gull Lake West repeat sector at all five Phase One frequencies. These data are shown as range gate-by-range gate sector displays, averaged over the 20°-azimuth sector in each range gate. A comparable Phase Zero sector display at Gull Lake West is shown in Figure 2.10. These Gull Lake West sector displays in Figure 3.11 depict not only the varying spatial nature of the clutter, as does the PPI clutter map, but also the extreme variation in mean clutter strength (40 dB in Figure 3.11) that can occur in a given repeat sector. As is indicated in Figure 3.11, the Phase One radar visited Gull Lake West twice, in winter (February) and late spring (May), as one of six seasonally revisited sites. Discussions of diurnal and seasonal changes in clutter, begun in Chapter 2, Section 2.4.6, continue in Chapter 3, particularly in Section 3.7. Multifrequency mean clutter strengths over the Gull Lake West repeat sector are shown in Figure 3.12. Results from both winter and spring visits are included. At first consideration, these results seem relatively scattered and trendless. They do not show a strong, clear-cut dependence of mean strength with frequency, except that the S-band data are lower. In terms of seasonal variations in mean clutter strength between winter (snow and ice, deciduous foliage off trees) and spring (no snow or ice, deciduous foliage beginning to emerge), the spring results in Figure 3.12 tend to be a few decibels stronger than winter results, although with considerable overlap within bands except at X-band where a more clear-cut 5-dB seasonal difference is indicated.

156 Repeat Sector Clutter Measurements

N

E

W

S

Figure 3.10 PPI clutter map and repeat sector at Gull Lake West. Repeat sector is outlined in black. Max range = 7 km; X-band, 15-m pulse, horizontal polarization; cells with σ °F4 ≥ –40 dB are white. Second visit (May).

It is difficult to know how to generalize from the mean clutter strength results of Figure 3.12. Isolated single-point measurements or even multipoint measurements at a single site are not easily extrapolable to other sites. A solution to this dilemma and the main thrust of Chapter 3 is to obtain results like those of Figure 3.12 at many sites, to combine them within similar terrain categories, to separate them between different terrain categories, and by this means to provide the missing connecting tissue between dissimilar single-point results that leads to generality and predictability. Thus, Chapter 3 provides results like Figure 3.12 for repeat sectors at all the measurement sites and looks for important similarities among them and differences between them.

3.2.3 Terrain Description Any attempt to investigate and predict ground clutter can only be as successful as its terrain description methodology permits. As an indication of the variability of terrain, Figures 3.13(a) and (b) show terrain elevation profiles and masking in five Phase One repeat sectors [Figure 3.13(a) utilizes an adaptive ordinate that varies from site to site;

Repeat Sector Clutter Measurements 157

VHF

Winter (Feb.) Late Spring (May)

Mean Clutter Strength (dB)

UHF

L-Band

S-Band

X-Band

Range (km)

Figure 3.11 Seasonal variation in mean clutter strength vs range for five frequency bands at Gull Lake West, Manitoba. Repeat sector data; level forest and forested wetland with lake edges; winter visit in February (solid lines), spring visit in May (dotted lines); vertical polarization, high range resolution data, except VHF winter visit where low range resolution data are shown.

Figure 3.13(b) utilizes a common ordinate; the indicated elevations include the sphericity of a 4/3 radius spherical earth to account for standard atmospheric refraction]. These profiles indicate that terrain visibility and hence clutter is patchy at low angles. Visibility is shown at two antenna heights, 50 ft in Figure 3.13(a) and 100 ft in Figure 3.13(b); these results indicate that visibility is usually not very sensitive to antenna height (see Appendix 4.B). The terrain elevation data of Figures 3.13(a) and (b) were obtained manually from 1:50,000 scale topographic maps.

158 Repeat Sector Clutter Measurements

0

Range Res. (m) Pol. 150 150 15/36 15/36

Mean of σ°F4 (dB)

–10

2

–20

H V H V

2 2 2

2

2

2 2

2

2 22

2

2

2

2 2

–30

1,000

100

–40

VHF

UHF

2 2

10,000

2

L-

S-

X-Band

Frequency (MHz) Figure 3.12 Mean clutter strength vs frequency at Gull Lake West. Repeat sector data. Two seasonal visits, February (winter) and May (spring). Data from the May visit are indicated with superscript 2’s to the upper-right of the plot symbol.

Figures 3.13(a) and (b) illustrate that there is a large range of variation in Phase One site heights. Table 3.1 tabulates Phase One site height above repeat sector midpoint elevation for the 42 Phase One sites, in decreasing order by site height. It is observed that site height varies from 4,021 ft at Plateau Mountain to –1,250 ft at Waterton. Site height strongly affects clutter statistics in that high sites see clutter at higher depression angles and to longer ranges than low sites The terrain in each repeat sector is classified both in terms of its land cover characteristics and in terms of its land-surface form. The classes of land cover and landform are the same as used in Chapter 2 (see Tables 2.1 and 2.2). Although nine specific landform classes are employed, they are separated into two overview classes; namely, high-relief with terrain slopes > 2° and relief > 100 ft, and low-relief with slopes < 2° and relief < 100 ft (see Table 2.3). As in Chapter 2, repeat sector terrain classification was performed principally through use of stereo air photos and topographic maps. Preexisting available stereo air photos were at 1:50,000 scale. As part of coordinated Phase One studies that took place in Canada in which an emphasis was on a more fine-grained approach to analyzing the data, special aerial photography missions were commissioned and flown over many repeat sectors to provide more accurate color infrared stereo air photographs of repeat sector terrain at 1:10,000 scale. The repeat sectors are large, ranging in area from 4 km2 (Puskwaskau) to 105 km2 [Plateau Mountain (a)]. Over such areas, terrain is usually to some extent composite, heterogeneous, or nonuniform. Thus, a single classifier either for land cover or

Repeat Sector Clutter Measurements 159

Altona

Elevation (Meters, 20 Meter Increments)

Unmasked Masked

Westlock

Suffield

Beiseker Terrain Slope ≈ 0.97°

Cochrane

Range (km)

Figure 3.13(a) Terrain elevations and masking in five Phase One repeat sectors. Antenna mast height = 50 ft; adaptive ordinate. Data from 1:50,000 scale topographic maps.

landform is usually not sufficient to completely describe the terrain. Usually more than one classifier is used, arranged in order of decreasing percent area of occurrence within the repeat sector. See Table 3.3 for terrain classifications of all repeat sectors. Additional ground truth information was collected during Phase One data acquisition. To keep track of wind, weather, and seasonal conditions during the measurements, a ground truth file consisting of 60 parameters was written to the raw clutter data tapes in front of each clutter experiment recorded. Weather stations were maintained on site and in the repeat sector to provide information for this file. TV video was recorded in a 360° azimuth scan from an antenna-boresighted TV camera atop the tower. At each site many field photographs were taken of the terrain being measured, where the photography position and direction were keyed to points on maps. The photographs collected included a 360° pan from the top of the Phase One tower. Such terrain descriptive detail can be overwhelming. The approach in Chapter 3 is to funnel all such information down to key macroclassifiers that cause the clutter statistics to cluster within class and separate between classes.

160 Repeat Sector Clutter Measurements

165.0 W

Unmasked Masked

Elevation (Meters, 20 Meter Increments)

–165.0

Altona

165.0 NE Westlock

–165.0 165.0 SE

Suffield –165.0 165.0 S Beiseker –165.0 165.0 SW

Cochrane

–165.0 0

10

20

Range (km)

Figure 3.13(b) Terrain elevations and masking in five Phase One repeat sectors. Antenna mast height = 100 ft; common ordinate. Data from 1:50,000 scale topographic maps.

3.3 Fundamental Effects in Low-Angle Clutter Section 3.3 reviews the basic mechanisms at work in low-angle ground clutter. The causes of major parametric trends in the Phase One repeat sector results as radar frequency ranges from VHF to X-band are established. Multifrequency examples of measured clutter at forest and farmland sites are provided to illustrate the mechanisms under discussion.

3.3.1 Clutter Physics II The major elements that are involved in low-angle clutter were first discussed in Chapter 2. These are shown again in Figure 3.14. Attention here is focused on Phase One repeat sector patches as the large regions of visible terrain providing directly illuminated clutter. Within the repeat sector patches, as in the Phase Zero patches of Chapter 2, the clutter sources continue to be all the discrete vertical features on the landscape associated with either the land cover or the terrain itself. As a result, the Phase Zero X-band effects of angle of illumination continue to exist at all the Phase One frequencies such that mean clutter strengths measured over repeat sectors increase, and cell-to-cell fluctuations decrease, with increasing angle.

Repeat Sector Clutter Measurements 161

Table 3.1 Phase One Site Heights

Site

Site Height above Repeat Sector (ft)

Site

Site Height above Repeat Sector (ft)

Plateau Mt. (a)

4021

Lethbridge West

105

Blue Knob

1710

Wainwright

102

Booker Mt.

1570

Rosetown Hill

98

Wachusett Mt.

1259

Penhold II

68

Plateau Mt. (b)

921

Spruce Home

63

Polonia

576

Pakowki Lake

50

Scranton

555

Turtle Mountain

49

Cochrane

509

Headingley

38

Strathcona

425

Knolls

25

Brazeau

392

Woking

25

Puskwaskau

382

Shilo

20

Vananda East

342

Sandridge

10

Orion

335

Katahdin Hill

5

Magrath

300

Cold Lake

0

Beiseker

255

Big Grass Marsh

Beulah

214

Corinne

–10

Picture Butte II

210

Dundurn

–12

Wolseley

180

Altona II

Westlock

150

Peace River South II

–150

Gull Lake West

147

Neepawa

–340

Suffield

125

Waterton

–1250

–3

–22

Note: Site elevation minus repeat sector midpoint elevation, in feet. In order of decreasing site height.

Multipath reflections interfere with the direct illumination and cause lobing on the freespace antenna pattern. As shown in Figure 3.14, such lobing can act to significantly increase or decrease the effective gain at which the patch is measured, more so at the lower frequencies (particularly VHF for which the lobes are broad, see Figure 3.14) than at higher frequencies (e.g., X-band, narrow lobes, see Figure 2.5). All propagation effects including multipath are included within the pattern propagation factor F (previously defined—see Chapter 1, Section 1.5.4 and Chapter 2, Section 2.3.1.2). Throughout Chapter 3 clutter strength continues to be given by σ°F4, where σ° is the intrinsic clutter coefficient (see Chapter 2, Section 2.3.1.1). How clutter strength is computed in the Phase One data is defined in more detail in Appendix 3.C. Section 3.4 determines general variations of clutter strength σ°F4 over and above terrain-specific dispersive influences entering via the pattern propagation factor F. This often requires multiple independent measurements of similar terrain from different sites to find underlying parametric trends. The important, often poorly predictable role of propagation in low-angle clutter can be confusing at first consideration. Appendix 3.B provides further discussion of how to deal with propagation in clutter analysis and modeling.

162 Repeat Sector Clutter Measurements

Lobing

Free Space

r Depression Angle α

h Visible Terrain

Multipath

Microshadowing Propagation Factor F

Clutter Coefficient σ°

Clutter Strength = σ°F4

Figure 3.14 Clutter physics (VHF).

Within the low-angle clutter phenomenon thus characterized by granularity of sources and specific propagation influences, how are clutter strengths affected by the spatial resolution of the radar? Theoretically, the mean clutter strength from a spatial region such as a repeat sector is independent of the spatial resolution of the measurement radar in situations involving many randomly phased clutter returns per resolution cell (see Section 3.5.3 for details). The theoretical expectation of little dependence of mean strength on resolution is largely borne out in the Phase One results (< 1 dB average variation of mean strength with pulse length, see Section 3.5.3). Although spatial resolution does not usually affect mean clutter strength significantly, because of the heterogeneous nature of low-angle clutter the spatial resolution of the radar plays a fundamental role in the amount of spread in clutter amplitude distributions from large spatial regions (see Chapter 2, Section 2.4.5). Ratios of standard deviation-to-mean for the repeat sectors generally increase both with decreasing pulse length at each Phase One frequency and with decreasing azimuth beamwidth as Phase One radar frequency increases (Tables 3.12, 3.13). Polarization has very little effect on clutter amplitude statistics. In Section 3.5.2, the distribution of differences of vertically polarized mean clutter strength minus horizontally polarized mean clutter strength across the complete repeat sector database shows a median difference of only 1.5 dB. However, occasional specific measurements can show more significant variation with polarization. For example, repeat sector measurements from both of the steep mountainous sites, Plateau Mountain and Waterton, indicate that at VHF, vertically polarized backscatter can be 7 to 8 dB stronger than horizontally polarized backscatter.

3.3.2 Trends with Radar Frequency Two strong trends of ground clutter strength with radar carrier frequency occur in particular circumstances. One of these trends is directly the result of the intrinsic backscattering coefficient σ ° having an inherent frequency-dependent characteristic. Thus, at high illumination angles in forested terrain, propagation measurements conducted at selected Phase One sites indicate that forward reflections are minimal (F ≈1), and in such terrain σ ° is observed to decrease strongly with increasing frequency. This result is due to

Repeat Sector Clutter Measurements 163

the radio frequency (RF) absorption characteristic of forest increasing with frequency, and hence the diffusely radiative characteristic of forest (including the backscatter direction) decreasing with frequency. The other trend with frequency is the result of a general propagation effect entering clutter strength σ °F4 through the pattern propagation factor F. At low depression angles over level open terrain, strong forward reflections cause multipath lobing on the free-space antenna pattern. At low frequencies such as VHF, these lobes tend to be broad for typical antenna heights. As a result, at such low frequencies returns from most clutter sources are received well on the underside of the first multipath lobe, and effective clutter strengths are much reduced. As frequency increases for a given antenna height, from VHF to UHF to L-band, the multipath lobes become narrower, and the first lobe is increasingly squeezed closer to the ground. As a result, the effective gain on the underside of this lobe at which backscatter from clutter sources is received increases, and hence clutter strengths rise with increasing frequency. Eventually, as frequency increases further to S- and X-band, the multipath lobes become still narrower, and typical clutter sources such as buildings or trees tend to subtend multiple lobes. The result is that at higher frequencies the overall multipath effect on illumination tends to average out and have less dominating influence on the effective clutter strength. Thus, at low angles on level open terrain, a strongly increasing characteristic of mean clutter strength with frequency introduced through the propagation factor is observed. Because this characteristic is caused by the interference between the direct ray and the multipath ray, it depends on geometric factors such as antenna mast height and range to the clutter patch (see Appendix 3.B). In inclined or rolling open terrain of increased relief, multipath is as likely to reinforce as to cancel clutter returns even at low frequencies.

3.3.2.1 Measurement Examples The frequency dependencies of ground clutter in steep forest and level farmland are now illustrated by measurement example. Results are shown first based on forest data from Blue Knob, Pennsylvania, and on farmland data from Corinne, Saskatchewan. Figures 3.15 and 3.16 show measured ground clutter from Blue Knob and Corinne at X-band and VHF, respectively. First consider the X-band clutter in Figure 3.15. Although the shapes of the forest and farmland histograms are quite different, the mean strengths in these two histograms are nearly the same: –24 dB in forest and –23 dB in farmland. The differences in histogram shape in Figure 3.15 are accounted for in the clutter models of Chapters 4 and 5 by means of the Weibull shape parameter. Figure 3.15 indicates 8-dB mean-to-median ratio at X-band in steep forest vs 33-dB mean-to-median ratio at X-band in level farmland, this latter large value reflecting the extreme spread evident in the farmland histogram. Now consider the VHF clutter from Blue Knob and Corinne, as shown in Figure 3.16. In the steep forest histogram from Blue Knob, mean clutter strength at VHF has increased by 13 dB from its X-band value to –11 dB; whereas, in the level farmland histogram from Corinne, mean clutter strength at VHF has decreased by 32 dB from its X-band value to –55 dB. In both VHF histograms in Figure 3.16, the mean-to-median ratios indicating spread in the histograms have decreased considerably, from an X-band value of 8 dB to a VHF value of 4 dB in forest and from an X-band value of 33 dB to a VHF value of 15 dB in farmland. This decreased spread is the result of the decreased spatial resolution of the Phase One radar at VHF due to its increased azimuth beamwidth (13° at VHF vs 1° at X-band).

Blue Knob, PA RMAX = 22 km

Forest

50

Mean

164 Repeat Sector Clutter Measurements

90 99

10

σ°F4 = –24 dB 5

0 −70

−60

−50

−40

−30

−20

σ°F4 (dB)

X-Band; σ°F4 ≥ −50 dB

Corinne, Sask. RMAX = 10 km

Farmland

90

50

−10

Mean

Percent

X-Band

0

99

10 X-Band

Percent

σ°F4= –23 dB

5

0 −80 X-Band;

σ°F4

≥ −50 dB

−70

−60

−50

−40 −30

−20

−10

σ°F

4 (dB)

Figure 3.15 X-band ground clutter in steep forest and level farmland. Histograms show repeat sector data. In the PPI clutter maps, cells with σ °F4 ≥ –50 dB are shown as black.

Additional forest (Scranton) and farmland (Corinne) histograms are shown in Figure 3.17 for all five Phase One frequency bands. It is evident in these results that the effects of increasing frequency on mean clutter strength and spread for these two terrain types take place continuously across the frequency regime from VHF to X-band. Table 3.2 shows means and ratios of standard deviation-to-mean for the histograms of Figure 3.17. It is clear from Table 3.2 that in steep forest, mean clutter strengths decrease strongly with increasing frequency; whereas, in level farmland, mean clutter strengths increase strongly with increasing frequency. Table 3.2 also shows that spreads (i.e., ratios of standard deviation-tomean) in clutter amplitude statistics are much greater in level farmland terrain than in steep forest terrain, but that in both terrain types spreads decrease with decreasing spatial resolution as the azimuth beamwidth increases from 1° at X-band to 13° at VHF. Thus there are many influences at work in forested and farmland clutter. These influences include effects of (1) landform—steep vs level, (2) land cover—forest vs farmland, (3) depression angle—at Blue Knob, 1.6°; at Corinne, 0.15°, (4) radar frequency, and (5) spatial resolution. The set of plots of Figures 3.2–3.8 showing the frequency dependence of ground clutter from repeat sectors at seven different sites include results from Blue Knob (Figure 3.3) and

Blue Knob, PA RMAX = 22 km

50

Forest

Mean

Repeat Sector Clutter Measurements 165

90 99

10 VHF

Percent

σ°F 4 = −11 dB

5

0 −70

−60

−30 4 σ°F (dB)

−50

−40

50 90 Farmland

Mean

VHF; σ°F4 ≥ −25 dB

Corinne, Sask. RMAX = 10 km

−20

−10

0

99

10 VHF

Percent

σ°F4 = −55 dB 5

0 −80 VHF;

σ°F4

≥ −50 dB

−70

−60

−50

−40

−30

−20

−10

σ°F4(dB)

Figure 3.16 VHF ground clutter in steep forest and level farmland. Histograms show repeat sector data. In the PPI clutter maps, cells containing clutter stronger than the indicated threshold are shown as black.

Corinne (Figure 3.7). The data of Figures 3.3 and 3.7 dramatically illustrate that the frequency dependency of mean clutter strength at high angles in steep forest terrain is very different from that at grazing incidence in level farmland terrain. Following sections include dramatic variations in mean clutter strength such as those shown in Figures 3.2–3.8, but within an overall scheme involving finer gradations with terrain type and depression angle so as to provide a continuous matrix of information across all terrain types and measurement scenarios.

3.3.3 Depression Angle and Terrain Slope As in the X-band data of Chapter 2, depression angle continues to be of major importance in its effects on both strength and spread in the multifrequency low-angle ground clutter spatial amplitude statistics of Chapter 3. Recall that depression angle is rigorously defined to be the complement of incidence angle at the backscattering terrain point under consideration, but that at short ranges depression angle simplifies to be approximately the

166 Repeat Sector Clutter Measurements

Steep Forest (Scranton) 10

Level Farmland (Corinne)

VHF

VHF

UHF

UHF

L-Band

L-Band

S-Band

S-Band

X-Band Radar Noise Contamination

X-Band

Percent

8 6 4 2 0

Percent

6 4 2 0

Percent

6 4 2 0

Percent

6 4 2 0

4

90

50

Mean

Percent

6

2

99 Percentiles

0 –80

–60

–40

–20

σ°F4(dB)

0

20

–80

–60

–40

–20

0

σ°F4(dB)

Figure 3.17 Five-frequency histograms of clutter strength from steep forest at Scranton, Pennsylvania, and level farmland at Corinne, Saskatchewan. Repeat sector data; 15-m range resolution (36 m at VHF and UHF), vertical polarization at Scranton; 150-m range resolution, horizontal polarization at Corinne. See Table 3.2.

20

Repeat Sector Clutter Measurements 167

Table 3.2 Clutter Strengths for Steep Forest at Scranton and Level Farmland at Corinne

Mean (dB)

SD/Mean (dB)

Percent of Samples above Noise Floor

Scranton VHF

–10.6

1.2

99.8

UHF L-Band

–12.3

1.8

99.4

S-Band

–16.7 –18.5

2.0 4.6

92.9 89.7

X-Band

–17.9

5.2

86.2

Corinne VHF

–54.8

8.1

89.3

UHF

–45.8

11.0

60.8

L-Band

–33.6 –26.9

10.4 12.5

52.8 44.6

–22.4

13.0

80.9

S-Band X-Band

angle below the horizontal at which the terrain point is viewed from the antenna (see Appendix 2.C). Depression angle includes the effect of earth curvature on the angle of illumination but does not include any effect of the local terrain slope, whereas grazing angle, being the angle between the tangent to the local terrain surface at the backscattering terrain point and the direction of illumination, does take into account local terrain slope. As in Chapter 2, grazing angle is not used in what follows as the measure of angle at which terrain is illuminated because as computed from DTED it does not correlate significantly with clutter returns from terrain cells at the scale of radar resolution. Rather than attempting to assign a single numerical value of terrain slope to each resolution cell, the distribution of terrain slopes contained within each large repeat sector clutter patch is classified in terms of terrain relief (Table 2.2). As in the Phase Zero results, in most terrains much of the statistical significance in the dependency of clutter strength on terrain slope in the Phase One repeat sector results is captured by using just two classes of relief, namely, “highrelief” terrain (terrain slopes > 2°) and “low-relief” terrain (terrain slopes < 2°). However, the repeat sector results require an important modification to this basic two-class terrain relief descriptive scheme. In low-relief open agricultural terrain supportive of multipath, the general effect of increasing effective clutter strength with increasing frequency requires the terrain to be very level, so that low-frequency clutter returns are always received on the underside of the first multipath lobe. Even relatively low inclinations of terrain at between 1° and 2° of terrain slope are enough to prevent this general illumination effect by directing the multipath lobes more randomly with respect to the clutter sources in the repeat sector. In such terrain, even at low frequencies, clutter returns are received well up on the multipath lobing pattern, not just on the extreme underside of the first lobe, at increased or decreased gain over free space depending on the particular terrain involved. Therefore, in low-relief agricultural terrain, terrain relief is further classified into two subcategories, namely, “moderately low-relief” (terrain slopes that lie between 1° and

168 Repeat Sector Clutter Measurements

2°) and “very low-relief” (terrain slopes < 1°). This refinement in classification is sufficient to distinguish between terrain that is level enough so that multipath results in generally increasing strength of illumination of clutter sources with increasing frequency, and terrain in which multipath effects on illumination are more specific.

3.4 Mean Land Clutter Strength vs Frequency by Terrain Type Section 3.4 shows how mean land clutter strength varies with radar frequency as measured within Phase One repeat sectors. These results depend on three different categories of descriptive parameter. First, there are parameters descriptive of the radar; namely, frequency, resolution, and polarization. The basic format of data presentation shows mean strength vs frequency across the five Phase One frequency bands for each of four combinations of pulse length and polarization. Second, there are parameters descriptive of the geometry of illumination. Depression angle is the parameter used herein, a quantity relatively simple and unambiguous to determine, depending as it does simply on range and relative elevation difference (Table 3.1) between the radar antenna and the centroid of the repeat sector clutter patch. Third, there are parameters descriptive of the terrain within the repeat sector clutter patch. The terrain within each repeat sector is classified herein both in terms of its land cover (Table 2.1) and its landform (Table 2.2). The terrain classifications were obtained by overlaying and registering measured clutter maps onto stereo aerial photos and topographic maps. All of these parameters have been previously introduced. Table 3.3 describes the repeat sectors at 38 different Phase One measurement sites in terms of range and azimuth extent from the radar, depression angle, and terrain type by landform and land cover in decreasing order by percent area within the repeat sector clutter patch. It is apparent in Table 3.3 that every repeat sector is different (terrain is essentially infinitely variable). As a result of this variability, the set of 20 multifrequency repeat sector mean clutter strengths is different, at least in detail, for every site. The current objective is to move beyond this abundance of detail to determine useful simple generalizations in the measurement results. The approach taken here to achieve this objective requires the statistical combination of measurements that are reasonably similar within broad classes of terrain type and depression angle, such that the results satisfactorily cluster within each class and significantly separate between different classes. The repeat sectors in Table 3.3 are grouped within the best such broad classes that were developed in the repeat sector database. Five broadly different terrain classes are defined in Table 3.3, namely, (1) urban, (2) mountains, (3) forest, (4) agricultural, and (5) desert, marsh, or grassland. Except for mountains, these groups are basically distinguished by major land cover type; mountains are distinguished more by landform. Within each class, when terrain relief can vary enough within class to require further subclassification, two subcategories of terrain relief are usually enough, low-relief with terrain slopes < 2°, and high-relief with terrain slopes > 2°. An exception is agricultural terrain, which requires additional subclassification of low-relief terrain into categories of moderately low-relief with terrain slopes between 1° and 2°, and very low-relief with terrain slopes < 1°. For each terrain type/relief category, when depression angle can vary enough within class to be important, usually three categories of depression angle (low, intermediate, and high) are enough to separate effects.

168 Repeat Sector Clutter Measurements

2°) and “very low-relief” (terrain slopes < 1°). This refinement in classification is sufficient to distinguish between terrain that is level enough so that multipath results in generally increasing strength of illumination of clutter sources with increasing frequency, and terrain in which multipath effects on illumination are more specific.

3.4 Mean Land Clutter Strength vs Frequency by Terrain Type Section 3.4 shows how mean land clutter strength varies with radar frequency as measured within Phase One repeat sectors. These results depend on three different categories of descriptive parameter. First, there are parameters descriptive of the radar; namely, frequency, resolution, and polarization. The basic format of data presentation shows mean strength vs frequency across the five Phase One frequency bands for each of four combinations of pulse length and polarization. Second, there are parameters descriptive of the geometry of illumination. Depression angle is the parameter used herein, a quantity relatively simple and unambiguous to determine, depending as it does simply on range and relative elevation difference (Table 3.1) between the radar antenna and the centroid of the repeat sector clutter patch. Third, there are parameters descriptive of the terrain within the repeat sector clutter patch. The terrain within each repeat sector is classified herein both in terms of its land cover (Table 2.1) and its landform (Table 2.2). The terrain classifications were obtained by overlaying and registering measured clutter maps onto stereo aerial photos and topographic maps. All of these parameters have been previously introduced. Table 3.3 describes the repeat sectors at 38 different Phase One measurement sites in terms of range and azimuth extent from the radar, depression angle, and terrain type by landform and land cover in decreasing order by percent area within the repeat sector clutter patch. It is apparent in Table 3.3 that every repeat sector is different (terrain is essentially infinitely variable). As a result of this variability, the set of 20 multifrequency repeat sector mean clutter strengths is different, at least in detail, for every site. The current objective is to move beyond this abundance of detail to determine useful simple generalizations in the measurement results. The approach taken here to achieve this objective requires the statistical combination of measurements that are reasonably similar within broad classes of terrain type and depression angle, such that the results satisfactorily cluster within each class and significantly separate between different classes. The repeat sectors in Table 3.3 are grouped within the best such broad classes that were developed in the repeat sector database. Five broadly different terrain classes are defined in Table 3.3, namely, (1) urban, (2) mountains, (3) forest, (4) agricultural, and (5) desert, marsh, or grassland. Except for mountains, these groups are basically distinguished by major land cover type; mountains are distinguished more by landform. Within each class, when terrain relief can vary enough within class to require further subclassification, two subcategories of terrain relief are usually enough, low-relief with terrain slopes < 2°, and high-relief with terrain slopes > 2°. An exception is agricultural terrain, which requires additional subclassification of low-relief terrain into categories of moderately low-relief with terrain slopes between 1° and 2°, and very low-relief with terrain slopes < 1°. For each terrain type/relief category, when depression angle can vary enough within class to be important, usually three categories of depression angle (low, intermediate, and high) are enough to separate effects.

Repeat Sector Clutter Measurements 169

Table 3.3 Terrain Descriptions of 38 Repeat Sectors within 12 Groups by Terrain Type and Depression Angle

Dep LandAng (deg) form Urban Strathcona, Alta. Lethbridge West, Alta. Altona II, Man. Picture Butte II, Alta. Headingley, Man.

1.5 0.3 0.2 0.1 0.04

Land Cover

Range (km)

Azimuth (deg)

Setup Number

3–2 3–8 1 3–8 1

11–12–51 11–12–21 21–11–14 11–12 11–12–41

1–10 6–11.9 2.5–8.4 22–27.9 14–19.9

62–82 92–102 262–272 172–182 82–92

7 18 31 22 30

Mountains Plateau Mountain, Alta. Waterton, Alta.

1.2 -1.8

8 8–7

42–7 42–7–41

11–16.7 9–14.9

255–265 175–185

21(b) 20

Forest/High-Relief (Terrain Slopes > 2°) High Depression Angle Blue Knob, PA Scranton, PA

1.6 1.0

4 7–4–3

21–43–11 43–12–11

16–21.9 8–13.9

80–100 300–320

48 47

0.2 0.2 0.1 -0.1

3–7 2–7 4–2 2–7

43–21 43 21–41–11 21–41

5–10.9 4–9.9 15–24 12–17.9

120–130 118–136 54–74 348–358

11 27 8 26

2.1 1.2

2 3

43 42–62–41

1–6.9 4–9.9

230–240 170–180

25 17,24

Intermediate Depression Angle Gull Lake West, Man. Wainwright, Alta. Turtle Mountain, Man. Katahdin Hill, MA Westlock, Alta.

1.0 0.6 0.5 0.4 0.4

1 5–3 5 5–4 3

61–52–43 41–32–31 41–52 43–21–52 43–21–62

1–6.9 1–6.9 2–7.9 1–6.9 8–13.9

300–320 120–150 102–122 220–250 42–52

33,39 36 41 49 10

Low Depression Angle Sandridge, Man. Dundurn, Sask.

0.3 0.2

1 5

41–62–22 32–41–31

1–6.9 1–6.9

298–318 295–325

40 37

Low Depression Angle Cold Lake, Alta. Woking, Alta. Penhold II, Alta. Peace River South II, Alta. Forest/Low-Relief (Terrain Slopes < 2°) High Depression Angle Puskwaskau, Alta. Brazeau, Alta.

General effects of polarization and resolution on mean clutter strength are small. Nevertheless, polarization and range resolution are carried as explicit parameters in the Phase One results presented in the following subsections. Later, Section 3.4.2 provides general results for mean clutter strength vs radar frequency in each of the 12 terrain type/ relief/depression angle categories obtained as median averages within each category independent of polarization and resolution (see Table 3.6). Discussions throughout Section 3.4 often implicitly draw upon the medianized mean clutter strength data of Table 3.6 to quantify observed trends. See Section 3.5 for more extensive discussion of polarization and resolution effects.

3.4.1 Detailed Discussion of Measurements In total, Table 3.3 indicates that separating the five broadly different terrain types into subclasses by relief and depression angle leads to a manageable set of 12 categories. Following subsections discuss how measured mean clutter strength varies with radar

170 Repeat Sector Clutter Measurements

Table 3.3 (Cont’d) Terrain Descriptions of 38 Repeat Sectors within 12 Groups by Terrain Type and Depression Angle Dep Ang (deg)

Landform

Land Cover

Range (km)

Azimuth (deg)

Setup Number

2.3 2.0 -0.9

4 7–2 7–2

31–32–21 21–41 21–41

20–40 1–10 1–10

40–50 107–127 287–307

21(a) 4 3

1.2 0.7 0.4

2 3–2 3–2

21 21–33 21–31

1–6.9 5–10.9 8–17

50–70 125–135 150–170

42 19 9,15 23,28

Very Low-Relief (Terrain Slopes < 1°) Orion, Alta. Wolseley, Sask. Rosetown Hill, Sask. Pakowki Lake, Alta. Shilo, Man. Corinne, Sask.

1.2 0.5 0.4 0.3 0.2 0.15

3–1 3–1 1 1–3 1–3 1

21–31 21 21 21–31 21–31 21

1–10 6–10 4–9 1–10 1–10 1–8.9

186–196 301–311 45–65 6–16 228–258 330–30

14 29 35 13 2 38

Desert, Marsh, or Grassland (Few Discretes) High Depression Angle Booker Mountain, NV Vananda East, MT

1.8 1.0

3 3–5

7–33 31–32

12–17.9 3.6–9.5

125–145 40–60

44 45

0.3 0.2

1 1

7–33 62–22

3–6.5 1–6.9

290–307 350–10

43 32

Agricultural/High-Relief (Terrain Slopes > 2°) Plateau Mountain, Alta. Polonia, Man. Neepawa, Man. Agricultural/Low-Relief Moderately Low-Relief (1° < Terrain Slopes < 2°) Beulah, ND Magrath, Alta. Beiseker, Alta.

Low Depression Angle Knolls, UT Big Grass Marsh, Man.

frequency in each category. In each subsection, repeat sector results are provided for each measurement site across the 20-element Phase One parameter matrix. Each of the 20 measurements at each site is centrally selected from a group of identically repeated measurements, thereby improving the reliability of the results.

3.4.1.1 Urban Multifrequency measurements of mean ground clutter strength from the five urban repeat sector patches are shown in Figure 3.18. The setup numbers associated with these sites shown in the box to the lower-left in Figure 3.18 and in all similar following figures are listed in order in Table 3.A.1 of Appendix 3.A. All five sites with urban repeat sectors are located on open low-relief terrain supportive of multipath. At X-, S-, and L-band, the angle to the first maximum on the Phase One multipath lobing pattern is small enough (viz., 0.03°, 0.07°, and 0.20°) that typical urban clutter sources such as buildings at typical repeat sector ranges usually reach well up on the lobing pattern even on very level terrain. As a result, multipath effects on illumination, although still acting to introduce considerable statistical fluctuation from measurement to measurement in these bands, do not introduce any strong general dependence of mean clutter strength with frequency. Thus, in these

Repeat Sector Clutter Measurements 171

bands, Figure 3.18 shows very strong, relatively frequency-independent mean clutter strength to exist from the group of urban patches as a whole at the ≈–10-dB level.

0

Mean of σ°F4 (dB)

−10

−20 Range Res. (m) Pol. 150 150 15/36 15/36

−30

H V H V

−40 VHF

UHF

L-

S-

X-Band

Frequency (MHz) 7-Strathcona 18-Lethbridge West 22-Picture Butte ll 30-Headingley 31-Altona ll

Figure 3.18 Mean clutter strength vs frequency for urban terrain. See Table 3.3.

At VHF and UHF, multipath effects in the urban data of Figure 3.18 are more complex. At these lower frequencies, multipath lobes are broader and can significantly increase or decrease the effective gain of the measurement over the whole repeat sector. At both the Altona II and Headingley sites, mean clutter strengths decrease by more than 20 dB with decreasing frequency, from maximum mean levels of greater than –10 dB at X- or S-band to minimum mean levels of less than –30 dB at VHF. At both of these sites, the terrain is very level (i.e., landform = 1). Neither site has any terrain elevation advantage over its surroundings, resulting in low depression angles to the clutter patches. Therefore, at both sites the effect of decreasing mean clutter strength with decreasing frequency is due to strongly decreasing intensity of illumination caused by multipath. The city center of Calgary (population 600,000) is located in the Strathcona repeat sector (see related discussion, Section 2.4.2.2). The Strathcona measurement site was situated on a grassy hill in the city outskirts. The slope of the hill at Strathcona, 5°, was so situated as

172 Repeat Sector Clutter Measurements

to direct the peak of the second VHF multipath lobe at the city center clutter patch; as a result, the urban mean clutter strengths measured at Strathcona are 10 to 12 dB stronger at VHF than at UHF and L-band (see Figure 3.19). It is evident that multipath propagation augments rather than cancels VHF clutter at Strathcona.

Free Space

5°

12 dB 5°

1.7 ° Suburbs

UHF

L

S

X

170

430

1250

3250

9000

0 Mean of σ°F4 (dB)

Calgary City Center

VHF

–10 –20 –30

8 km

Frequency (MHz) VHF Lobing

Frequency Dependence

Figure 3.19 Strong VHF clutter induced by multipath at Strathcona.

At both Lethbridge West and Picture Butte II, urban clutter was measured from the city of Lethbridge (population 55,000) as viewed from across the Oldman River valley (see related discussion, Section 2.4.2.2). An aerial photo of Lethbridge is shown in Figure 3.20. From both sites, steep banks on the far side of the river were illuminated in the repeat sector just before the urban clutter was encountered. From the Lethbridge West site, the city was illuminated from the west over relatively low-relief terrain. As a result, from Lethbridge West a VHF multipath propagation loss of more than 20 dB occurred in the mean clutter strength measured from the city. However, from the Picture Butte II site, the city was illuminated at longer range from the north, over an initial long gradual downslope in terrain elevation of about 0.5°. This initial slight incline rotated the multipath lobing pattern downwards by about 0.5° with respect to the clutter sources distributed on the more level terrain further out (see Section 3.B.2) and substantially reduced the VHF propagation loss to less than 10 dB. Thus, VHF mean clutter strength measured from the city of Lethbridge was 12 dB stronger measured from the north than from the west over relatively similar agricultural terrain. Such specific propagation-induced variations occur in many repeat sector measurements.

3.4.1.2 Mountains Mountain clutter was measured by the Phase One radar from the same two sites in the Canadian Rocky Mountains in southern Alberta at which measurements were conducted by the Phase Zero radar (see Chapter 2, Section 2.4.2.1). One of the sites, Plateau Mountain, was located high in the Rockies. From Plateau Mountain, the view in repeat sector (b) to the west was of steep barren rock faces from high mountain peaks. [Repeat sector (a) at Plateau Mountain is discussed in Section 3.4.1.4.1.] A photograph of Plateau Mountain and the view looking west into repeat sector (b) is given in Figure 2.2(b). The other Rocky Mountain site was at Waterton, Alberta. At Waterton, the Phase One

Repeat Sector Clutter Measurements 173

Figure 3.20 Aerial photo of the City of Lethbridge showing the Picture Butte II repeat sector. Scale = 1:50,000. North is to the left.

equipment was set up on the high prairie a few kilometers from steep mountain terrain. From Waterton, the view in the repeat sector beyond the intervening rangeland also included regions of steep exposed bedrock. At both Plateau Mountain and Waterton, the lower slopes of the mountains visible at near ranges in the repeat sector patches were densely forested, with the trees gradually thinning out at higher elevations. At far ranges in both repeat sectors, but particularly at Plateau Mountain, there were substantial areas where the clutter originated only from rocky peaks.

174 Repeat Sector Clutter Measurements

Multifrequency measurements of mean ground clutter strength from the two mountain sites are shown in Figure 3.21. First, observe that mean clutter strength decreases strongly with increasing frequency band, VHF to X-band, by about 14 dB. Much of this observed effect (as much as 10 dB) is attributed to the increasing absorption of RF power from the incident radar wave by the forest vegetation within the repeat sector with increasing frequency. Second, observe in Figure 3.21 that Waterton mean strengths are greater than Plateau Mountain mean strengths in all bands and waveforms. This effect is attributed to multipath from the intervening rangeland in the Waterton measurements. Consider this effect in more detail. At Waterton, the highest peaks in the repeat sector subtend a positive elevation angle at the Phase One antenna of 3.8°. This is a large enough angle to include multiple multipath lobes, certainly at the higher Phase One frequencies. Even at VHF, depending on details in assumptions concerning terrain profiles and Fresnel zones, at least between one and two lobes and probably between two and three lobes are included within 3.8° (see Figure 3.B.5). For the theoretical situation of interference between a direct ray and a multipath ray reflected from a perfectly conducting infinite planar surface, the mean value of F4 averaged over one or more complete interference lobes is 7.8 dB. Thus, at Waterton, mountain values of σ° should be augmented by multipath by as much as 7.8 dB in the measurements of σ°F4. At Plateau Mountain, on the other hand, the terrain falls off from the site steeply enough to prevent any multipath. Thus, at Plateau Mountain essentially intrinsic values of σ° occurred from mountain terrain under freespace illumination (i.e., F = 1). Indeed, measured values of mean clutter strength σ°F4 at Waterton at VHF and S-band are observed in Figure 3.21 to be 6 or 7 dB stronger than at Plateau Mountain. This difference suggests similar values of intrinsic σ° from mountains at both sites at VHF and S-band with multipath augmentation at Waterton close to that theoretically expected from a flat plane with unity reflection coefficient. In contrast, at UHF and L-band, mean clutter strengths at Waterton are observed in Figure 3.21 to be only 2 or 3 dB stronger than at Plateau Mountain, although in each measurement the Waterton value remains greater than the Plateau Mountain value. This result indicates differing values of intrinsic σ° at the two sites in these two bands and more complicated propagation effects at Waterton. Third, observe in Figure 3.21 that at both mountain sites, mean clutter strengths at VHF are usually 7 to 8 dB stronger at vertical polarization than at horizontal polarization. At UHF the polarization differences have dropped to the 2- to 3-dB range, although vertical is still always stronger than horizontal, respectively, by pulse length at both sites. In the higher bands, the polarization differences are smaller, usually less than 1 dB. See corresponding discussions of X-band mountain clutter at Plateau Mountain and Waterton in Section 2.4.2.1.

Bare Rock Faces. The bare rock faces dominant in the far range portions of the Plateau Mountain (b) repeat sector were isolated to determine whether “pure rock” clutter returns are frequency independent. Measurement data from Plateau Mountain were reduced at vertical polarization and 15/36-m pulse length over a pure rock region in repeat sector (b) from 14.7 to 16.7 km. Resultant mean clutter strengths from these pure rocks at VHF, UHF, L-, and S-bands were –14.3 dB, –19.6 dB, –19.2 dB, and –20.1 dB, respectively. (No Xband data were collected at Plateau Mountain because of a high altitude transmitter failure.) These results indicate essential frequency invariance of mean clutter strength from pure rocks, UHF through S-band, at about the –19 or –20-dB level but a 5-dB increase of mean strength from this level at VHF.

Repeat Sector Clutter Measurements 175

0

Range Res. (m) Pol. 150 150 15/36 15/36

Mean of σ°F4 (dB)

−10

H V H V

−20

−30

−40 VHF

UHF

L-

Frequency (MHz)

S-

X-Band 20-Waterton 21B-Plateau Mtn

Figure 3.21 Mean clutter strength vs frequency for mountain terrain. See Table 3.3.

3.4.1.3 Forest The following subsections present multifrequency mean clutter strengths from forest in five regimes of relief and depression angle, as shown in Table 3.3. Because forest is poorly supportive of multipath, particularly at high illumination angles, many of these forest measurements are much more measurements of relatively pure intrinsic σ ° and are much less contaminated by dispersive propagation influences than are measurements in open terrain. To the extent that this is true, fewer measurements can establish trends in forest terrain than in farmland terrain. However, VHF multipath propagation loss can appear in these forest results at low angles of illumination.

3.4.1.3.1 Forest/High-Relief/High Depression Angle Two sites, Scranton and Blue Knob, fall into the category of forest/high-relief/high depression angle. Both sites are located in the steeply ridged, generally forested terrain of the Appalachian Mountains in Pennsylvania. Multifrequency mean clutter strengths measured over the repeat sectors at these two sites are shown in Figure 3.22. The results from these two sites, for which there is considerable commonality in classification by terrain type and depression angle (see Table 3.3), are quite similar. Figure 3.22 indicates a trend of decreasing mean strength with increasing frequency, extending from VHF to S-band. As in the mountain data, as much as 10 dB of this 12.8-dB effect in Figure 3.22 can be attributed to increasing vegetative absorption of the forest with increasing frequency. Observe in

176 Repeat Sector Clutter Measurements

0

Range Res. (m) Pol. 150 150 15/36 15/36

Mean of σ°F4 (dB)

−10

H V H V

−20

−30

−40 VHF

UHF

L-

Frequency (MHz)

S-

X-Band 47-Scranton 48-Blue Knob

Figure 3.22 Mean clutter strength vs frequency for forest/high-relief terrain at high depression angle. See Table 3.3.

Figure 3.22 that mean strengths measured from the steeper terrain at Scranton (i.e., landform = 7, moderately steep) are 3 or 4 dB stronger than those measured from the less steep terrain at Blue Knob (i.e., landform = 4, rolling) in most bands and waveforms. At both sites, the four measurements at each combination of polarization and pulse length in each of the lower three bands cluster remarkably tightly, indicating relatively little propagation influence. The Scranton site is located high on the east side of the Lackawanna River. The view into the repeat sector is west across the river valley and the city of Scranton, and up steeply rising forested slopes on the far side of the river valley. Blue Knob is located in high-relief forested terrain in the Allegheny Range south of Altoona. From Blue Knob, the view into the repeat sector is east across an intervening sharp forested ridge at 10-km range to a farmland valley beyond. The repeat sector patch is of geometrically visible terrain within this distant agricultural valley at ranges from 16 to 22 km. Most of the terrain within the patch is agricultural. However, there are many trees scattered throughout the patch, as woodlots, orchards, etc. A 20-m tree throws a 716-m geometrical shadow at a depression angle of 1.6°. Thus the percent of visual area occupied by trees in a plane normal to a 1.6° line-of-sight in the Blue Knob repeat sector is expected to be high. The multifrequency clutter characteristic from this patch in Figure 3.22 shows the clear trend of decreasing strength with increasing frequency associated with forest at high angles of illumination.

Repeat Sector Clutter Measurements 177

In contrast, clutter returns from treeless farmland or rangeland at similar high depression angles show a multifrequency characteristic that is essentially invariant with frequency at a mean level of about –30 dB. Hence, it is the secondary component of trees (i.e., land cover = 43) in the rolling agricultural valley at Blue Knob that dominates its clutter characteristics. Similar results were obtained at Cochrane and, at lower depression angle, at Penhold II. Chapter 2 provides results indicating how small percent incidences of trees on agricultural landscapes dominate low-angle terrain backscatter characteristics at X-band.

3.4.1.3.2 Forest/High-Relief/Low Depression Angle Table 3.3 shows that there are four sites that fall into the category of forest/high-relief/low depression angle. All four sites are located in Alberta. Multifrequency mean clutter strengths measured over the repeat sectors at these four sites are shown in Figure 3.23. Again, a general trend is observed of decreasing mean strength with increasing frequency in the data of Figure 3.23 due to increasing vegetative absorption with increasing frequency. In this low depression angle data, this trend extends monotonically from UHF to X-band and accounts for a decrease of 8.2 dB in mean strength over this range. However, there is a counter-trend at very low frequencies such that mean clutter strengths at VHF are 2.7 dB lower than at UHF. This drop in clutter strength at VHF is caused by multipath loss due to forward reflections from the intervening terrain between the radar and the repeat sector clutter patch at these very low depression angles, even though the intervening terrain is largely forested. Woking is a solidly forested site (i.e., land cover = 43). The repeat sector patch at 4- to 9.9-km range is illuminated at grazing incidence (i.e., depression angle = 0.2°). Terrain elevations rise with increasing range in the repeat sector patch, gradually at first over the near ranges in the patch (i.e., landform = 2, inclined) and then more rapidly at farther ranges in the patch (i.e., landform = 7, moderately steep). As a result, moderately steep terrain is viewed at the far end of the patch at grazing incidence over intervening lowrelief terrain. At Cold Lake an approximately similar situation exists as at Woking, where a moderately steep forested ridge is viewed in the distance over undulating largely wooded terrain that has been opened in places for agriculture (i.e., note the secondary component of agriculture in the land cover classification = 43–21 at Cold Lake). At Peace River South II, the Phase One radar was set up on one side of the river valley and looked across the relatively broad deep river valley to the repeat sector patch beginning on the far bank and extending beyond. On the far bank the terrain was moderately steep (landform = 7) and wooded but transitioned to gradually rising inclined (landform = 2) farmland beyond the bank. The low-relief terrain in the patch occurs at longer ranges beyond the high-relief terrain at the beginning of the patch, unlike Woking and Cold Lake. The situation at Penhold II is quite different from those at the other three sites in this terrain category; the Penhold terrain is rolling farmland with a substantial incidence of trees (10 to 30%) occurring in shelter belts and woodlots (not forest). The terrain within the repeat sector patch at Penhold is remarkably similar in land cover and landform classification to that at Blue Knob, although at Blue Knob the intervening terrain is forest and the depression angles are quite different for these two sites. These four sites involve four quite different terrain situations, yet as a group they exhibit the generally decreasing mean strength with increasing frequency characteristic indicating

178 Repeat Sector Clutter Measurements

Range Res. (m) Pol.

0

150 150 15/36 15/36

Mean of σ°F4 (dB)

−10

H V H V

−20

−30

−40 VHF

UHF

L-

S-

X-Band

Frequency (MHz) 8-Penhold ll 11-Cold Lake 26-Peace River So. ll 27-Woking

Figure 3.23 Mean clutter strength vs frequency for forest/high-relief terrain at low depression angle. See Table 3.3.

domination by trees at substantial illumination angle (where here the substantial illumination angles arise from high-relief terrain slopes rather than high depression angles). Also, all four sites exhibit a reduction or at least leveling off of VHF mean strengths compared to UHF, explainable by greater or lesser amounts of multipath loss at the low depression angles involved over intervening low-relief terrain.

3.4.1.3.3 Forest/Low-Relief/High Depression Angle Table 3.3 shows that two sites, Brazeau and Puskwaskau, fall into the category of forest/ low-relief/high depression angle. Both of these sites are located in the northern boreal wilderness on prominent heights of land with good 360° visibility of low-relief forested wilderness terrain to far horizons. Therefore, the repeat sectors at these two sites are canonically representative of general low-relief forest illuminated from above at high depression angle, and relatively uncontaminated by specific dominating terrain features. Multifrequency mean clutter strengths measured over the repeat sectors at Brazeau and Puskwaskau are shown in Figure 3.24. Results from both seasonal visits to Brazeau are included in Figure 3.24, Brazeau (1), a winter visit, and Brazeau (2), a summer visit. Again, a general trend of decreasing mean strength with increasing frequency occurs in

Repeat Sector Clutter Measurements 179

the data of Figure 3.24 due to increasing vegetative absorption with increasing frequency. This trend extends monotonically from VHF to S-band and accounts for a decrease of 15.1 dB over this range. A small reversal is observed in this trend such that mean strengths increase by 2.8 dB as frequency increases from S- to X-band.

0

Range Res. (m) Pol. 150 150 15/36 15/36

Mean of σ°F4 (dB)

–10

H V H V

–20

100

1,000

10,000

–30

–40 VHF

UHF

L-

S-

X-Band

Frequency (MHz) 17-Brazeau (1) 24-Brazeau (2) 25-Puskwaskau

Figure 3.24 Mean clutter strength vs frequency for forest/low-relief terrain at high depression angle. See Table 3.3. There were two seasonal visits to Brazeau; the second visit results are indicated by superscript 2’s to the upper-right of the plot symbol.

Within the Puskwaskau repeat sector the terrain gradually falls away (landform = 2, inclined) from the height of land upon which the radar is situated with increasing range over the repeat sector range from 1 to 6.9 km. The forest cover within the Puskwaskau repeat sector is largely deciduous aspen with some young spruce in the understory and occasional small clear patches of spruce. At the time the measurements were made, the deciduous leaves were mostly off the trees. The X-band transmitter was not operable at Puskwaskau. Brazeau was emphasized in the measurements with two Phase One data collection visits to establish summer/winter seasonal variations in forest, and also with helicopter propagation measurements. The repeat sector at Brazeau is at longer range (from 4 to 9.9 km) than at Puskwaskau and is beyond the falloff from the local hilltop on which the radar is situated. Hence, the terrain within the repeat sector is undulating (landform = 3)

180 Repeat Sector Clutter Measurements

rather than inclined. The Brazeau forest is of more composite nature or less homogeneous than at Puskwaskau, with more distinct separate patches of evergreen spruce and deciduous aspen, some openings of nonforested wetland, and a small lake. The second visit to Brazeau also provided no X-band data.

Seasonal Variations at Brazeau. Seasonal variations in mean clutter strength at Brazeau are indicated in Figure 3.24. During the first visit (March/April), there was moderate to deep snow on the ground, and new snow fell during the visit. There was some snow in the branches of the spruce, and the deciduous aspen was not yet leaved out. During the second visit (August/September), there was, of course, no snow, and the deciduous leaves were still mostly on the aspen, although beginning to fall. At first observation, the Brazeau seasonal variations in Figure 3.24 appear quite small. The tight clustering of data within groups by frequency band for measurements taken five months apart with independent setups is remarkable and provides a positive indication of long-term calibration consistency. Close examination reveals that the second visit mean strengths are generally 1 or 2 dB stronger than the first visit mean strengths. There is little significant dependence of mean clutter strength on polarization evident in the results of Figure 3.24.

3.4.1.3.4 Forest/Low-Relief/Intermediate Depression Angle Table 3.3 includes five sites that fall into the general category of forest/low-relief/ intermediate depression angle. As a group, the repeat sectors of these sites are more representative of composite landscape, in which forest predominates but in which the forest is broken by open areas of agricultural land, wetland, rangeland, or areas of open water, as is indicated by the composite nature of the land cover classification in Table 3.3, rather than unbroken homogeneous forest such as Woking or Puskwaskau. Multifrequency mean clutter strengths measured over the repeat sectors at these five sites are shown in Figure 3.25. The data of Figure 3.25 indicate that, by and large, these measurements at intermediate depression angle in composite forest terrain no longer show a trend of decreasing mean strength with increasing frequency due to increasing vegetative absorption that has been observed up until now at higher illumination angles (due to higher depression angles and/or higher terrain slopes) in forest terrain. Instead, the trend of mean strength with frequency in Figure 3.25 is largely one of frequency independence. As defined by the medians of these groups of measurements by frequency band, the characteristic of mean strength with frequency is within 0.6 dB of a constant value of –29.2 dB at all three bands of UHF, L-, and X-band. About this constant value, the mean strength rises by 3 dB at VHF and drops by 2.9 dB at S-band. Within ±3 dB, the mean strength in this terrain category is constant at all five frequency bands. There is no longer a significant trend of decreasing mean clutter strength with increasing frequency in the results for the five composite forest sites at intermediate depression angle, as shown in Figure 3.25, partly because, at the lower depression angles, the incident energy is less likely to penetrate the forest as a continuous absorbing medium but instead is more likely to be reflected back by individual high trees rising up as scattering objects. This transition in type of phenomenon from a continuously illuminated surface at high angles to a sea of discrete scatterers at lower angles is aided by the discontinuous nature of the land cover at these five sites. As an example of relatively frequency-independent results at one

Repeat Sector Clutter Measurements 181

0

Range Res. (m) Pol. 150 150 15/36 15/36

Mean of σ°F4 (dB)

–10

H V H V

–20

–30

–40 VHF

UHF

L-

S-

X-Band

Frequency (MHz) 10-Westlock 36-Wainwright 41-Turtle Mtn. 49-Katahdin Hill 33,39-GLW(1), GLW(2)

Figure 3.25 Mean clutter strength vs frequency for forest/low-relief terrain at intermediate depression angle. See Table 3.3.

particular site, Figure 3.5 shows mean clutter strengths for the Wainwright site in which the results in all five bands lie within 2 or 3 dB of their overall median level of –29.4 dB. Although in general terms these five sites all provide composite forest terrain observed at intermediate depression angle in their repeat sectors, in fact all five sites are quite different from each other in physical detail. At Gull Lake West, Manitoba, the Phase One antenna looked out from a 100-ft-high ridge initially onto very homogeneous level forested wetland (from 1.6 to 3.5 km). Beyond this forested wetland there occurred a nonforested shallow, swampy, open-pond area (from 4.3 to 5 km), then a distinct higher sand dune and beach area constituting the shoreline of Lake Winnipeg (between 5 and 6 km), and finally the open water of Lake Winnipeg itself. Gull Lake West results were previously discussed both here in Chapter 3, Section 3.2.2.2, and in Chapter 2. The Phase One radar visited Gull Lake West twice to establish seasonal dependencies, in February (winter) and in May (spring). The seasonal Gull Lake West data previously shown in Figure 3.12 and discussed in Section 3.2.2.2 are also included in Figure 3.25.

182 Repeat Sector Clutter Measurements

The Katahdin Hill, Massachusetts site is located adjacent to Lincoln Laboratory. The hilly wooded terrain in the repeat sector at Katahdin Hill contains a dozen or so significant hills, typically separated by 1 km or so, with the hilltops typically 100 to 150 ft higher than the low areas between them. This terrain is classified as primarily hummocky, the highest relief category included as low-relief (see Table 2.2). The first kilometer or so of this repeat sector is level, some of which is used as farmland. Most of the repeat sector is relatively intensely settled and is crisscrossed with roads and highways and a rail line. However, trees substantially cover much of the sector. These trees are typical of the eastern forest, being largely a mixed deciduous forest with occasional evergreen stands (e.g., hemlock). Many of the hilltops in the sector have cultural features, such as water towers or radio masts that are visible to the Phase One radar. Turtle Mountain is an unusual site, near the Manitoba/North Dakota border, where the setup area was on a large forested glacial deposit 20 or 30 km across and several hundred feet above the surrounding prairie. On top of this large glacial deposit, the terrain is hummocky knob-and-kettle topography, of approximately 50-ft relief about a relatively unvarying mean level. The area is covered with many small lakes in the depressional areas. Aside from the lakes, the land cover is a mixed deciduous forest of aspen, poplar, birch, and some burr oak, with very occasional stands of spruce. The site area was a clearing in the 50- to 60-ft trees with little inherent terrain elevation advantage. The repeat sector, at ranges from 2 to 7.9 km, lies entirely within this knob-and-kettle forested terrain. The Wainwright site was located within Camp Wainwright, a Canadian Forces base in Alberta, near the Saskatchewan border. The Wainwright setup area was located on a small hill about 100 ft higher than general elevations of the hummocky terrain in the repeat sector farther out to the southeast at ranges from 1 to 6.9 km. The terrain in the wasteland prairie Wainwright repeat sector is largely tree and/or shrub covered. Wainwright exists at a latitude of prairie rangeland, not in the dense boreal forest wilderness farther north. Within the repeat sector at Wainwright, 54% of the area is covered with deciduous aspen trees, and 32% of the area is covered with shrubby or scrubby mixed rangeland. These trees and scrub growth generally occur in patches or groves with openings between them of herbaceous or grassy rangeland. Other openings include wetland and a few small lakes. Thus, rather than continuous forest at Wainwright, patches of trees exist on a hummocky prairie landscape. Westlock occurs farther north in Alberta at the northern edge of the prairie farmland and in a transitional zone between the prairie and the northern boreal forest wilderness. The Westlock site was located on a local height of ground on undulating prairie farmland. Looking into the repeat sector, over the first 8 km the undulating prairie farmland (with scattered groves of aspen) gradually declined in elevation, then on the average leveled out (although the terrain was still locally undulating) in a lowland area and gradually transitioned to forest with scattered open areas of nonforested wetland at 8- to 12-km range, and gradually began to rise from 12- to 14-km range with some of this rising land again being under agriculture. This forested area which begins at 8 km in the repeat sector is the beginning of the northern forest. The prairie-to-forest transitional region of the Westlock repeat sector at ranges from 8 to 13.9 km was selected as the repeat sector clutter patch. Within this area, the land cover is 58% mixed forest, 25% agricultural land (partly cropland, partly pasture), and 14% wetland.

Repeat Sector Clutter Measurements 183

3.4.1.3.5 Forest/Low-Relief/Low Depression Angle Table 3.3 indicates that there are two sites, Sandridge and Dundurn, both on the central Canadian prairies, which fall into the terrain category of forest/low-relief/low depression angle. In general terms, these two sites have a very constant mean elevation (i.e., no long rolls or undulations in the terrain at either site), with a sparse, stunted tree, or scrub brush vegetation cover. At Sandridge, the terrain is very level over many square miles around the site and covered with a sparse stunted deciduous forest. At Dundurn, many small hillocks rise 25 or 35 ft above a very level substrate. This hummocky terrain has a vegetation cover consisting of patches of deciduous aspen trees, other patches of shrub and brush, with some open areas of native grassland between the patches of trees and brush. Therefore, at both of these sites, the Phase One antenna looked out from a setup area with no local terrain elevation advantage into repeat sectors of constant mean elevation containing scrubby vegetation. At both sites, the repeat sectors extend from 1 to 6.9 km in range. Multifrequency mean clutter strengths measured over the repeat sectors at Sandridge and Dundurn are shown in Figure 3.26. In contrast to other forested sites, which at high illumination angles (due to high terrain slopes and/or high depression angles) showed a strong trend of decreasing mean clutter strength with increasing frequency and which at intermediate illumination angles showed either very slightly decreasing or no variation of mean clutter strength with increasing frequency, the results of Figure 3.26 show a moderate but significant trend of increasing mean clutter strength with increasing frequency. In terms of the median positions of the set of measurements of different waveforms in each band, mean clutter strength rises monotonically in this terrain category from –43.6 dB at VHF to –35.4 dB at X-band, an increase of 8.2 dB. This variation is largely due to multipath propagation loss at the lower frequencies caused by ground reflections from the level open terrain around the Phase One setup areas at these two sites. VHF mean clutter strengths over the Dundurn repeat sector in Figure 3.26 closely match those at Sandridge. X-band mean clutter strengths are also very similar at both sites at a level of –35.4 dB, significantly weaker than forest/low-relief terrain at higher depression angles. This low X-band value of mean clutter strength for the forest/low-relief/low depression angle terrain category is very closely corroborated by Phase Zero results (where, over all 43 Phase Zero patches of forest/low-relief terrain measured at depression angles below 0.3°, the median value of mean clutter strength is –35.5 dB) and the Phase One survey data in Chapter 5. So not only are the X-band repeat sector results valid for this forest/low-relief/low depression angle terrain category, significantly weaker than other forest terrain categories, but also clutter strengths at VHF may be expected to be generally lower than this X-band level, partially due to multipath loss if the terrain and site area are somewhat open. Based on Sandridge and Dundurn results, how much clutter strengths fall off from X-band as frequency decreases depends on the details of how the multipath sets up. Based on Sandridge alone, which is the best repeat sector example of a very level forested site, one might expect that, in a similarly level but denser forest with less opportunity for terrain multipath, multifrequency mean clutter strengths might be relatively invariant with frequency, VHF to X-band, in the –35- to –40-dB range. This expectation is largely borne out in the Phase One survey results of Chapter 5.

184 Repeat Sector Clutter Measurements

–20

Range Res. (m) Pol. 150 150 15/36 15/36

Mean of σ°F4 (dB)

–30

H V H V

–40

–50

–60 VHF

UHF

L-

Frequency (MHz)

S-

X-Band 37-Dundurn 40-Sandridge

Figure 3.26 Mean clutter strength vs frequency for forest/low-relief terrain at low depression angle. See Table 3.3.

3.4.1.4 Agricultural Terrain Following subsections present multifrequency mean clutter strengths from agricultural terrain in three regimes of relief as shown in Table 3.3. Multipath exists in many of these results to cause specific variations in mean clutter strength through the pattern propagation factor, depending on the particular variations of terrain elevation involved. Furthermore, unlike forest, the dominant clutter sources in agricultural terrain are often discrete vertical objects associated with man’s use of the land, and clutter strengths can depend quite specifically on what particular discretes exist and how they are distributed over any given repeat sector. In fact, one may argue that farmland clutter is quite a different, more heterogeneous statistical random process than forest clutter. Or one may argue that it is not properly a statistical process at all, but deterministic, in that farmland clutter is so dominated by occasional strong isolated discrete cells in a weakly scattering background and that many of the strong cells occur in definite, culturally determined, spatial patterns. As a result of this multifold specificity affecting mean clutter strengths in agricultural terrain, there are fewer general trends of mean clutter strength to discuss in agricultural terrain than in forest terrain. The trends that are found depend on the approach taken here of reaching beyond specificity toward generality by combining measurements from a number of nominally similar repeat sectors in the Phase One multisite measurement program,

Repeat Sector Clutter Measurements 185

thereby averaging out specific effects of propagation and/or discrete sources in individual measurements. By this means, two basic trends of variation of mean clutter strength will be observed in agricultural terrain. First, in agricultural terrain that is of high-relief or moderately low-relief (i.e., terrain slopes > 1°), mean clutter strengths tend to be largely frequency independent, VHF through X-band, at about the –30-dB level. Second, in agricultural terrain that is either level or of very low-relief (i.e., terrain slopes < 1°), it will be observed that as frequency decreases below L-band through UHF to VHF, effective mean clutter strengths drop off dramatically. This latter effect is due to the generally decreasing intensity of illumination of such open level surfaces due to increasing multipath propagation loss with decreasing frequency. That is, clutter sources are being illuminated, and clutter returns are being received, well down into the horizon plane null on the multipath lobing elevation pattern, and the width of this null and hence the amount of multipath propagation loss increases as the effective height of the antenna in wavelengths decreases with decreasing frequency. In addition to the above two observations, it will also be observed that, in major contrast with forested terrain, mean clutter strengths in agricultural terrain, whatever its relief, are independent of depression angle at all five Phase One frequencies. Independence of mean clutter strength with depression angle in agricultural terrain agrees with the X-band Phase Zero findings discussed in Chapter 2. These Chapter 2 findings made a major point of the fact, however, that spreads in clutter amplitude distributions from large spatial regions (particularly in low-relief agricultural terrain, but in other terrain types as well) decrease rapidly with increasing depression angle. The current emphasis in this chapter is on determining multifrequency trends of the means, not the spreads, of clutter amplitude distributions from 42 repeat sectors. However, the ground clutter models developed subsequently specify both means and spreads of clutter amplitude distributions, tying each to their major dependencies as observed in the measurements. Thus, the models divide open farmland into a closely graduated set of depression angle regimes to provide the important dependency of spread on depression angle.

3.4.1.4.1 High-Relief Agricultural Terrain Table 3.3 includes three sites within the category of agricultural/high-relief terrain. Recall that in high-relief terrain, terrain slopes are > 2° (see Table 2.2). Table 3.3 indicates that the high-relief landform classes that cause these three sites to group together as high-relief are rolling (LF = 4) and moderately steep (LF = 7). Multifrequency mean clutter strengths measured over the repeat sectors at these three sites are shown in Figure 3.27. No clear trend emerges in the data of Figure 3.27. Mean strengths are observed to rise from VHF to UHF and L-band and then to drop again at S-band and X-band. However, such particular variations are caused by specific terrain and propagation characteristics. The mean clutter strength data in Figure 3.27 generally represents agricultural/high-relief terrain as largely lying in the range from –20 to –40 dB (–29 dB is the median of all the points plotted in Figure 3.27). Each of the three agricultural/high-relief sites are now discussed in turn. Plateau Mountain [see Figure 2.2(b)] was the only site with two repeat sectors. Repeat sector (b), looking to the west at steep rocky mountain peaks, was discussed in Section 3.4.1.2. Here, repeat sector (a) is discussed. In repeat sector (a), the Phase One antenna looked down at long ranges to the northeast from the top of Plateau Mountain to rolling prairie rangeland

186 Repeat Sector Clutter Measurements

−10

Range Res. (m) Pol. 150 150 15/36 15/36

Mean of σ°F4 (dB)

−20

H V H V

−30

−40

−50 VHF

UHF

L-

S-

X-Band

Frequency (MHz) 3-Neepawa 4-Polonia 21A-Plateau Mtn.

Figure 3.27 Mean clutter strength vs frequency for agricultural/high-relief terrain. See Table 3.3.

beyond at ranges from 20 to 40 km and at depression angle of 2.3°. Over the first 20 km, the terrain in repeat sector (a) was almost entirely masked to the radar as the terrain elevation rapidly falls off down the side of the mountain and over the forested foothills below. No significant multipath occurred over the rough, masked terrain between the radar and the repeat sector clutter patch. Beyond these forested foothills, the rolling rangeland of the high prairie comes into view at about 20 km range. The rangeland terrain in repeat sector (a) has substantial relief. Several roads and a creek bottom traverse the sector, and various scattered ranch buildings exist within the sector. Thus, although predominantly rangeland, the sector is by no means discrete-free. The sector is tree-free. Mean clutter strengths for repeat sector (a) at Plateau Mountain are largely frequency invariant at about the –32-dB level overall. Repeat sector (a) at Plateau Mountain (with site height = 4,021 ft; see Table 3.1) is the most airborne-like measurement situation that exists among the 42 Phase One repeat sectors. Neepawa and Polonia constitute a pair of sites in Manitoba that are separated by 8 km and where the repeat sectors face each other. That is, the Neepawa repeat sector is centered in azimuth on the Polonia setup position and vice versa. Both repeat sectors cover 1 to 10 km in range. The consequence is that the same terrain is observed from two different directions. Dominating the low-relief prairie in the general area where Neepawa and

Repeat Sector Clutter Measurements 187

Polonia are situated is Riding Mountain escarpment, a major terrain feature rising 1000 ft off the prairie floor. Polonia is situated near the top of the escarpment. The repeat sector at Polonia looks southeast down the side of the escarpment to the more level prairie further out and contains the Neepawa site at 8-km range. The repeat sector at Neepawa looks northwest, first across slightly inclined terrain rising gradually towards the escarpment, and then, beginning at about 5-km range, up the side of the escarpment to the Polonia site at 8km range. The terrain slopes on the side of the escarpment are about 2°. The land cover throughout the area is primarily cropland, but there is a significant secondary component of woodland, mainly aspen, that occurs in patches and groves. At Neepawa, the rising escarpment is viewed in the distance over a relatively open lowrelief terrain surface that would be expected to be supportive of multipath. At VHF, the terrain at long ranges high up on the escarpment is not high enough to reach maximum illumination at the peak gain of the first multipath lobe. Nevertheless, the fact that the terrain rises away from the Phase One site at a gradually increasing rate results in much of this terrain being well illuminated, not down in the horizon plane null as on level terrain, but well up on the side of the first multipath lobe, although not as high as the peak. At UHF, the peak of the first multipath lobe does fully illuminate the steeply rising terrain up the side of the escarpment, theoretically providing as much as a 12-dB peak gain over free space. At L-band, the first two multipath lobes illuminate the rising terrain up the side of the escarpment. Indeed, in the Neepawa results of Figure 3.27, mean strengths at UHF and L-band are about 10 dB stronger than at VHF, which is indicative of the fuller illumination of the escarpment at the higher frequencies. Discussion now turns to Polonia. Looking down from Polonia, multipath is still expected to occur from the side of the escarpment below the radar, but the side of the escarpment is tilted away from the radar by ≈2°. As a result (see Section 3.B.2) the peak of the first lobe illuminates the prairie at 25.8, 9.2, and 7.2 km at VHF, UHF, and L-band, respectively. Mean clutter strengths in Figure 3.27 were computed only over the 1- to 10-km repeat sector range interval. Thus, the Polonia repeat sector is illuminated on the underside of the first multipath lobe at VHF, but at UHF and L-band parts of this range interval are illuminated at the peak gain of the multipath pattern. This explains why the effective mean clutter strengths from Polonia in Figure 3.27 are much stronger at UHF and L-band than at VHF. The Polonia clutter data discussed to this point are for the 1- to 10-km range interval in the repeat sector. Since the Polonia site was quite high, clutter measurements were made there over low-relief prairie farmland to much longer ranges than 10 km. Appendix 3.B, Section 3.B.2 discusses how it is often multipath from the local hillslope that dominates propagation in situations such that the illumination of clutter sources at long-range is the result of the direct ray in the horizontal direction interfering with a horizontally directed multipath ray from the local hillslope. At Polonia, the local hillside terrain slope involved, namely, ≈2°, happens to be just such that it is the peak of the second multipath lobe at UHF that horizontally illuminates the long-range clutter sources, with a resultant theoretical 12-dB multipath gain augmentation in clutter strength. This situation is depicted in Figure 3.28. Measured clutter statistics for the Polonia repeat sector over a longer range interval from 1 to 47 km indeed show mean clutter strengths are 5 to 8 dB stronger at UHF than in the other four bands, which is the result of this multipath augmentation at UHF.

188 Repeat Sector Clutter Measurements

No Lobing

12 dB 15 m 2° 120 m

0.7° 2° Riding Mountain Escarpment 3.25 km

Low-Relief Prairie

48 km

Figure 3.28 UHF multipath lobing at Polonia, Manitoba.

Thus specific propagation effects are seen to cause both significantly stronger and weaker clutter in what are otherwise tightly clustered multifrequency clutter measurements in this prairie farmland terrain. Despite such propagation induced specificities, evidence of general similarity in the mean strengths of the clutter from Plateau Mountain (a), Neepawa, and Polonia is seen in Figure 3.27. The specific propagation effects at Polonia and Neepawa, and their lack at Plateau Mountain (a), serve as good examples of the significant role propagation plays in low-angle ground clutter from open terrain.

3.4.1.4.2 Moderately Low-Relief Agricultural Terrain Table 3.3 includes three sites within the category of moderately low-relief agricultural terrain. Moderately low-relief terrain is defined as having terrain slopes between 1° and 2°. In Table 3.3, it is the presence of inclined terrain (of landform class = 2) at all three sites that results in them being grouped together as moderately low-relief. Multifrequency mean clutter strengths measured over the repeat sectors at the three moderately low-relief agricultural sites are shown in Figure 3.29. The data in Figure 3.29 are relatively frequency-independent at an overall level of about –30 dB (their median level = –29.6 dB). All three moderately low-relief agricultural sites were on agricultural terrain which had significant relief. At each site, the Phase One radar was set up on a local topographic high such that the antenna looked out into a repeat sector in which the terrain elevation fell off down the side of the hill that the radar was set up on and up the side of the next hill. The significant “inclined” component in landform classification arose in these repeat sectors by the land first being inclined away from the radar and then, farther out in the repeat sector, being inclined towards the radar. Even though strong multipath generally occurred on these open farmland landscapes, the terrain inclinations between 1° and 2° were enough to first steer the multipath lobes down (the angle to the peak of the first multipath lobe above the local ground slope is nominally at 1.5°, 0.6°, and 0.2° at VHF, UHF, and L-band, respectively, for the 60-ft antenna mast, see Figure 3.B.4), and then to result in the more distant terrain rising up through them. That is, the distant rising terrain in these repeat sectors was well illuminated at all frequencies on the multipath lobing pattern, giving rise to roughly frequency-independent mean clutter strengths at about the –30-dB level.

Repeat Sector Clutter Measurements 189

−10

Range Res. (m) Pol. 150 150 15/36 15/36

Mean of σ°F4 (dB)

−20

H V H V

−30

−40

−50 VHF

UHF

L-

S-

X-Band

Frequency (MHz) 19-Magrath 28-Beiseker (4) 42-Beulah 15-Beis (2)-VHF 36 m V-Pol Only

Figure 3.29 Mean clutter strength vs frequency for agricultural/moderately low-relief terrain. See Table 3.3.

Beiseker. Beiseker was one of the most intensively investigated of the Phase One sites. The Phase One radar made four visits to Beiseker to establish seasonal variations in clutter. Ground-based and helicopter-borne propagation tests were conducted there for three of the four visits to establish the multipath properties at the site. At Beiseker, the measurement position was on a local topographic high point. In the direction of the repeat sector, terrain elevations gradually fell away by ~400 ft at ~9-km range, and then the terrain elevations gradually rose back up by ~350 ft at ~17-km range. Land cover in the repeat sector was 88% farmland, 11% rangeland, and 1% wetland. An aerial photo of the terrain in the Beiseker repeat sector at 1:50,000 scale is shown in Figure 3.30. Figure 3.31 shows mean clutter strength vs frequency for the Beiseker repeat sector for the four seasonal Phase One visits. The first visit to Beiseker was a fall (October/November) visit, with stubbly and plowed fields without much snow. Crops had been harvested. Light snow occasionally fell during early morning hours but disappeared later in the day. The second visit to Beiseker was a winter (February) visit. At this time the fields were snowcovered with 2 to 10 cm of old crusted snow on all the field surfaces. In the stubble fields,

190 Repeat Sector Clutter Measurements

Figure 3.30 Aerial photo of repeat sector at Beiseker. Scale = 1:50,000. North is up.

the stubble stuck up through the snow. The third visit to Beiseker was a summer (August) visit with fields containing mature crops, primarily grains (e.g., wheat, barley, oats) but also canola and alfalfa. Some crops were being harvested. The fourth visit to Beiseker was a later fall (late November) visit, with quite wintry fields as in the February visit, but without the old crusted snow. During this visit, the view was primarily of white fields, although with thin snow cover and with stubble sticking through. Thus, across the four Beiseker visits, quite different seasonal status of the agricultural field surfaces occurred. A major reason Beiseker was selected for four seasonal visits was because the clutter returns at Beiseker were strongly affected by multipath at all

Repeat Sector Clutter Measurements 191

–10

Range Res. (m) Pol. 150 150 15/36 15/36

Mean of σ°F4 (dB)

–20

H V H V

–30

–40

–50 VHF

UHF

L-

S-

X-Band

Frequency (MHz)

Figure 3.31 Seasonal variations in mean clutter strength at Beiseker. Repeat sector data. First visit, fall (18 October to 13 November). Second visit, winter (12 February to 24 February). Third visit, summer (6 August to 24 August). Fourth visit, late fall (16 November to 26 November of the following year). Second, third, and fourth visit results indicated by superscripts to the upper-right.

frequencies. It was believed that the varying seasonal states of the field surfaces might more significantly affect clutter returns through varying terrain reflection coefficients and hence varying multipath effects than through seasonal effects on the clutter sources themselves, many of which tend to be discrete vertical objects. The seasonal variations in mean clutter strength at Beiseker, as shown in Figure 3.31, do little to support the view that very significant changes in multipath occurred with changing season at Beiseker. One can find occasional 5- and 6-dB differences in mean strength with season in these data, but most of the Beiseker seasonal variations in mean strength are less than 3 or 4 dB (median difference = 1.7 dB). Furthermore, these variations do not exhibit any particular pattern. For example, the summer visit results (i.e., third visit) with crops in the fields do not stand out from the other three visits without crops. It is fair to conclude from the data of Figure 3.31 that seasonal variations in clutter returns at a given site are quite small (e.g., several decibels) compared to the sorts of variations that can occur in similar terrain from site to site. Multipath effects in the Beiseker repeat sector explain the UHF dip in the data of Figure 3.31. The situation is illustrated by the sketch in Figure 3.32. From the Beiseker site center, looking into the repeat sector, for the first kilometer out from the radar the terrain was inclined away from the radar at a relatively constant angle of 1.4°, like a tilted flat surface. For the next 700 m the terrain leveled out, and then beyond 1.7 km proceeded to continue to

192 Repeat Sector Clutter Measurements

fall off in elevation. Thus, the first kilometer of 1.4° tilted flat surface would be expected to dominate multipath characteristics. Indeed, for the 57-ft antenna mast height, the second null (i.e., the first null above the horizon plane null) on the UHF multipath lobing pattern in elevation occurs at 1.12° above the plane of this tilted surface, assuming unity reflection coefficient from the tilted surface (see Figure 3.B.4). Thus, with respect to local horizontal at the Phase One antenna, this null occurs at 0.28° depression angle below the horizontal, which is close to the depression angle at which the centroid of the repeat sector range interval was illuminated. As a result, at UHF, the rising terrain from 8 to 17 km that constitutes the repeat sector range interval is weakly illuminated in a null of the multipath lobing pattern in which there is a propagation loss (i.e., F < 1). The angular width of this null covers most of the repeat sector range interval from 8 to 17 km and explains the approximately 6 dB weaker mean clutter strengths at UHF over this interval, compared with the other bands.

VHF

UHF

170

430

L

S

X

1.7°

15 m

1.4° 0.55°

1.4° 1 km

UHF Lobing

17 km

Mean of σ°F4 (dB)

Free Space –30

–40

–50 1250

3250

9000

Frequency (MHz) Frequency Dependence

• Landform: Undulating/Rolling; Moderate (125 m) Relief • Land Cover: Agricultural; Very Few Trees

Figure 3.32 Effects of UHF multipath on clutter strength at Beiseker, Alberta.

In considering multipath effects on clutter strengths, it is often important to know the terrain slope near the radar. Obtaining terrain slope from topographic contour maps is often relatively imprecise (e.g., typical contour interval = 25 ft) and results in approximating the actual terrain with sloped facets running from contour line to contour line. One is left with the question of determining which facets provide active reflecting Fresnel zones causing the multipath. Then the effective Phase One antenna mast height that controls the periodicity of the multipath lobing is the height above the plane of this facet, which can be less than or greater than the actual mast height. These matters are discussed in Section 3.B.2 of Appendix 3.B. At Beiseker, the imprecise faceted topographic map model left ambiguity in explaining the UHF dip in mean clutter strengths in Figure 3.31. As a result, a more precise and accurate land survey of terrain elevations was conducted into the repeat sector, nominally every 50 m for the first 6 km. This survey unambiguously provided the actual 1.4° terrain slope causing multipath that explains the relatively weak effective clutter strengths at UHF in Figure 3.31.

Repeat Sector Clutter Measurements 193

3.4.1.4.3 Very Low-Relief Agricultural Terrain Table 3.3 indicates that there are six sites within the category of very low-relief agricultural terrain with terrain slopes of less than 1°. In Table 3.3, the only landform classes occurring for the repeat sectors at these sites are 1, level, and 3, undulating. Note, in particular, the absence of landform class 2, inclined, or any other landform classes of greater relief. The only land cover classes occurring are 21, cropland, with occasional secondary occurrence of 31, herbaceous rangeland (no occurrences of any other, dramatically different, types of land cover). Thus, this group of repeat sectors is unequivocally general low-relief farmland without the sorts of specific terrain features in relief or land cover that so often dominate clutter measurements. As with any six different locations on the surface of the earth, there are detailed differences among these six sites. Some have significant incidences of trees (e.g., Wolseley, Shilo) and some do not. Some are dry and approaching rangeland conditions; others are black-earth cropland with plentiful average rainfall. Some are on hills, some are not, and one site, Corinne, is situated on the extremely level Regina Plain in southern Saskatchewan. Pakowki Lake and Orion occur in relatively dry prairie grassland terrain under irrigation for agriculture in southeastern Alberta (note that each has a secondary land cover component of rangeland). From the Orion site, the Phase One antenna looks down from its hilltop location out across undulating terrain in the repeat sector, which falls off fairly quickly in the first 2 km, but then falls off much more slowly at an average slope of about 0.2°. At Pakowki Lake, the terrain very gradually rises through the repeat sector at 0.17°. Multifrequency mean clutter strengths measured over the repeat sectors at the six very lowrelief agricultural sites are shown in Figure 3.33. This characteristic is remarkably different from that of Figure 3.29 for moderately low-relief agricultural sites. As in the moderately low-relief data, the very low-relief data show essential invariance of mean clutter strength with frequency at L-, S-, and X-bands; but unlike the moderately low-relief data that also hold this level at UHF and VHF, the very low-relief data drop to lower levels at UHF and much lower levels at VHF. Consider the median value of the set of mean strengths plotted in each band in Figure 3.33 (see Table 3.6); this value holds constant within a few tenths of a decibel of –31 dB at L-, S-, and X-bands, but drops 10 dB to –41 dB at UHF, and drops 25 dB to –56 dB at VHF. These large decreases in effective clutter strength at UHF and VHF on very low-relief agricultural terrain are due to multipath loss entering through the pattern propagation factor. At these open agricultural sites, forward terrain reflections cause multipath lobing on the vertical elevation beam of the antenna. In this very low-relief terrain, in contrast to the previously discussed moderately low-relief terrain, first the terrain does not slope away from the site enough to tilt the lobing pattern down very much, and second, terrain elevation variations farther out are not large enough to cause the far-out illuminated terrain to rise back up through the lobing pattern with increasing range through the repeat sector. Rather, the levelness of the terrain at very low-relief sites constrains the effective gain of the illumination to be locked deep into the horizon plane null at VHF and UHF. The terrain classification system employed here effectively finds such level sites by separating inclined terrain of landform = 2 (1° < terrain slopes < 2°) from level or undulating terrain of landform = 1 or 3 (terrain slopes < 1°).

194 Repeat Sector Clutter Measurements

−10

Mean of σ°F4 (dB)

−20

−30

−40 Range Pol. Res. (m) −50

150 150 15/36 15/36

−60

H V H V

−70 VHF

UHF

L-

S-

X-Band

Frequency (MHz) 2-Shilo 13-Pakowki Lake 14-Orion

29-Wolseley 35-Rosetown Hill 38-Corinne

Figure 3.33 Mean clutter strength vs frequency for agricultural/very low-relief terrain. See Table 3.3.

Hilltop vs Level Sites. There is a large range of depression angles for the six very lowrelief agricultural sites in Table 3.3, from 1.2° to 0.15°. Three of these sites, Orion, Wolseley, and Rosetown Hill, although providing level and/or undulating cropland in their repeat sectors, were set up on hills 335, 180, and 98 ft above their repeat sectors, leading to depression angles of 1.2°, 0.5°, and 0.4°, respectively. The other three sites all had little or no terrain elevation advantage over their repeat sectors, which were illuminated at 0.3°, 0.2°, and 0.15° depression angle. Within the very low-relief sites, the multifrequency mean strength characteristics of the hilltop sites separate as a group from those of the level sites. For the three hilltop sites, Orion, Rosetown Hill, and Wolseley, the mean strengths at UHF cluster very tightly at a median level of mean strength of –39 dB. This cluster provides good site-to-site repeatability such that all 12 measurements fall within a range of +4 dB and –6 dB about the median. For two of these hilltop sites, Orion and Rosetown Hill, the mean strengths at VHF also cluster closely at a median level of –48 dB. For the three level sites, Corinne, Shilo, and Pakowki Lake, the UHF and VHF groups of mean strengths also cluster quite well, at median levels of –46 dB and –57.5 dB, respectively. Thus, in terms of median values of clustered groups of measurements of mean

Repeat Sector Clutter Measurements 195

strength, level sites provide 7-dB and 9.5-dB lower mean strengths, or increased multipath propagation losses, compared with hilltop sites, at UHF and VHF, respectively, all in very low-relief agricultural terrain with terrain slopes < 1°. The reason for this (see Section 3.B.2) is that, for the hilltop sites, the terrain sloping away from the site tilts the multipath lobing pattern down, causing the effective antenna gain against the more distant level terrain to start to rise, but not enough to clearly get out of the null and up on the peak of the pattern, as happens in moderately low-relief terrain with terrain slopes between 1° and 2°. Rosetown Hill is a classic example of this situation, with a definite local hill rising 100 ft or so above level surrounding terrain. Thus, in the repeat sector direction, the terrain drops 98 ft in the first 2.5 km away from the site (i.e., 0.7° terrain slope), and then levels out, with the repeat sector range interval starting at 4 km. On the other hand, the situation at Wolseley is somewhat different. Wolseley does not provide a clear-cut local hilltop situation, but instead provides a general topographic high, with the terrain gradually falling away in the repeat sector direction towards a river valley at 25-km range. The terrain falls faster (150 ft) over the first 6 km (0.4° terrain slope), and slower (25 ft) over the next 4 km that constitute the repeat sector range interval. At VHF, with its broader horizon plane null, these terrain variations are not enough to substantially increase the illumination, and at VHF the Wolseley mean strength data fit the level terrain group better than the hilltop group. At UHF, however, the Wolseley terrain elevation fall-off is enough to provide illumination at increased gain on the elevation lobing pattern and bring Wolseley into coincidence with the other hilltop sites in very low-relief agricultural terrain. At the Phase One microwave frequencies, L-, S-, and X-band, mean strengths for these very low-relief agricultural sites are invariant with frequency (as discussed ) and invariant between the hilltop and level sites. The fact that mean strengths separate between these two groups at VHF and UHF is an indication that depression angle can be used as the separation parameter (i.e., 0.4° ≤ depression angle ≤ 1.2° for the hilltop sites, 0.15° ≤ depression angle ≤ 0.3° for the level sites; see Table 3.3). The fact that depression angle does not separate mean strengths in low-relief agricultural terrain in the microwave bands was observed in Chapter 2 in the Phase Zero X-band data. Although mean strengths of clutter amplitude distributions do not vary with depression angle in agricultural terrain in the microwave bands, the spreads in these distributions vary extremely rapidly with depression angle, decreasing as depression angle rises. This was also observed in the Phase Zero data in Chapter 2. Thus, subsequent models for the behavior of these distributions in agricultural terrain are based on small gradations in depression angle, even though microwave mean strengths are invariant with both frequency and depression angle in such terrain.

Shilo. The terrain at Shilo is open prairie farmland strongly supportive of multipath. Terrain relief is low, less than 50 m over 10- to 20-km range, but the terrain is not absolutely level. The site position provided little elevation advantage over surrounding terrain, only 20 ft over the midpoint of the repeat sector. In such terrain, dominant clutter sources are vertical discretes. Phase Zero X-band clutter results from Shilo showing the discrete nature of the clutter and the typical discrete clutter sources that occurred there are discussed in Chapter 2. A strong trend of increasing strength with increasing frequency occurred in the Shilo clutter amplitude statistics as a result of multipath decreasing the effective illumination of the clutter sources at the lower frequencies. This is illustrated in Figure 3.34. To the right in

196 Repeat Sector Clutter Measurements

Figure 3.34, mean clutter strength is plotted vs frequency for the Shilo repeat sector. To the left in Figure 3.34 are notional graphics illustrating how multipath causes the strong trend in mean clutter strength. Thus, on low-relief open terrain such as that at Shilo, strong forward terrain reflections cause multipath lobing on the free-space antenna pattern. At VHF these lobes are broad. As a result, backscatter from typical clutter sources such as trees and buildings is received well on the underside of the first multipath lobe, and effective clutter strengths are much reduced. This is entirely the result of propagation effects (i.e., multipath) entering clutter strength σ °F4 through the pattern propagation factor F. Now, as indicated in the upper graphic in Figure 3.34, as frequency increases, the multipath lobes become narrower, and the first lobe is pressed closer and closer to the ground. As a result effective clutter strengths rise until, in the microwave regime, typical clutter sources such as trees and buildings start to subtend a number of lobes, and the effect starts to average out.

VHF

Free Space

UHF L

5°

20 dB 15 m 22km

VHF Lobing

1.7°

Mean of σ°F4 (dB)

VHF −30

UHF

L

S

X

1250

3250

9000

150-H

−40 −50 −60 170

430

Frequency (MHz)

Frequency Dependence • Landform: Level/Undulating; Low (50 m) Relief • Land Cover: Agricultural; Up to 30% Tree Cover

Figure 3.34 Effects of multipath on clutter strength at Shilo, Manitoba.

At Shilo, some repeat sector measurements were made with only one antenna tower section extended, resulting in a reduced tower height of nominally 30 ft, as well as more complete measurements at a nominal height of 60 ft. Table 3.4 indicates that, at X-band, out of five comparisons where similar measurements (i.e., same waveforms, same ranges) were available at both short and tall tower heights, the short tower resulted in slightly stronger mean clutter strength three times, the tall tower gave slightly stronger clutter one time, and both towers gave the same mean strength one time. Thus, at X-band, these antenna tower heights appear to have little effect on measured clutter strength over the ranges indicated in Table 3.4. Whether the tower is tall or short, the propagation lobes are narrow enough so that numerous lobes are subtended over typical sources such as trees and buildings, and changes in antenna height cause only minor variations in clutter strength as the lobes shift around over the sources. However, at UHF in Table 3.4, out of two available comparisons, the shorter tower in both cases resulted in much decreased (i.e., by 9 dB and by 13 dB) mean clutter strength, even though the tall tower mean clutter strength was 10 to 15 dB weaker than that at X-band. That is, at UHF, even with the tall tower, there is a 10- to 15-dB multipath loss caused by

Repeat Sector Clutter Measurements 197

Table 3.4 Short Tower and Tall Tower Clutter Strengths at Shiloa Band

Waveformb

Range (km)

Tower Heightc with Stronger Clutter

How Much Stronger (dB)

X

150 H 150 H 150 V

1–21.7 1–10.3 1–10.4

Short Short —

2 3 0

15 H 15 V

1–5.7 1–10.4

Short Tall

3 3

36 H 36 V

1–12.3 1–12.3

Tall Tall

9 13

UHF

a

b c

Approximate Mean Strength of Stronger Clutter (dB) –30 ± 3

–45 ± 5

Low-relief farmland Some tree cover (up to 30 percent) Snow cover Range resolution = 15, 36, 150 m; polarization = horizontal (H) or vertical (V) Short = 30 ft; Tall = 60 ft

illumination on the underside of the first propagation lobe, and this loss increases to 23 dB as tower height decreases from 60 to 30 ft and the first null-width broadens. This 9- to 13-dB decrease in mean clutter strength shown in the UHF data of Table 3.4 is calculable by evaluating the pattern propagation factor in the simple situation of multipath on a plane conducting surface, assuming a clutter source height of 15 m (i.e., like a tree or a house) at 5-km range. As expected in these Shilo measurements, where multipath propagation loss substantially reduces clutter strength at VHF and UHF on open low-relief agricultural terrain, the amount of the loss depends significantly on antenna height. At Suffield and Lethbridge West, as at Shilo, some repeat sector measurements were obtained with both one and three antenna tower sections extended (see Table 3.A.1 and [1]). In the Suffield repeat sector (i.e., grassland, 7 to 11.9 km; see Chapter 4, Section 4.5.3), differences of the tall tower minus the short tower repeat sector mean strengths were 5.1, 2.5, –0.7, and 1.8 dB at VHF, UHF, L-, and X-band, respectively. In the Lethbridge West repeat sector (i.e., urban, 6 to 11.9 km; see Section 3.4.1.1), differences of the tall tower minus the short tower repeat sector mean strengths were 9.3, 10.2, 5.2, and –3.5 dB at VHF, UHF, L-, and X-band, respectively. These differences are averages of differences between individual experiments of like waveform in each band. As expected, the differences are more significant at the lower frequencies and are greater at Lethbridge West where the terrain is quite level than at Suffield where the relief, although low, is significant (i.e., 50 m). Comparing Suffield results with those from Shilo where the terrain profiles are quite similar, the tall tower UHF mean strength is 9 to 13 dB stronger than the short tower mean strength at Shilo, but only 2 to 3 dB stronger at Suffield. Such differences result from multipath illumination specifics (i.e., different local terrain inclinations, different clutter source heights, etc.).

Antenna Height Variations at Corinne. In a multipath-dominated situation, the geometrical factors of antenna height, range, and clutter source height affect the amplitudes of received clutter returns. It is impracticable, however, to compute accurately the actual

198 Repeat Sector Clutter Measurements

varying multipath illumination across the vertical extent of every clutter source. To provide empirical statistical insight into these matters, multifrequency measurements of mean clutter strength are now shown for the Corinne repeat sector using three different Phase One antenna tower heights. An aerial photo of the repeat sector at Corinne is shown in Figure 3.35. Corinne comprises canonically level farmland with only farmland discretes rising as clutter sources above level fields. The repeat sector azimuth extent at Corinne is 60°, broad enough to allow significant statistical averaging to take place (i.e., more clutter sources). In such a “laboratory demonstration” type of environment, the effects of multipath propagation on ground clutter become readily apparent. Figure 3.36 shows mean clutter strengths vs frequency for the Corinne repeat sector with three antenna tower heights. In this figure the superscripts “L” and “M” appended usually to the upper-right (but occasionally to the upper-left) of a data point stand for low tower (one antenna tower section) and medium tower (two sections), respectively. The three-section (standard height) tower data are not superscripted. Figure 3.36 shows relatively strong dependence of mean strength on frequency but relatively weak dependence of mean strength on antenna height. Additional results are provided in Table 3.5. Median levels of mean strength over all repeat sector experiments in each band at both polarizations and pulse lengths are shown in Table 3.5, whereas Figure 3.36 shows mean strengths from only one representative experiment for each polarization and pulse length in each band. Based on the many experiments underlying Table 3.5, differences of the tall tower (three sections) minus the low tower (one section) mean strengths were 5.1, 6.7, 5.6, 1.6, and 3.9 dB at VHF, UHF, L-, S-, and X-bands, respectively. Differences of the tall tower (three sections) minus the medium tower (two sections) mean strengths were 2.8, 2.2, 1.7, –1.2, and 2.6 dB at VHF, UHF, L-, S-, and X-bands, respectively. Differences of the medium tower (2 sections) minus the low tower (one section) mean strengths were 2.3, 4.5, 3.9, 2.8, and 1.3 dB at VHF, UHF, L-, S-, and X-bands, respectively. These differences are averages of differences between individual experiments of like waveform (i.e., like polarization and pulse length) in each band (i.e., they are not the differences of the median numbers entered in Table 3.5). These differences in repeat sector mean clutter strength with antenna height at Corinne are less at VHF and UHF than those observed at Shilo and Lethbridge West. Over the Corinne repeat sector, mean clutter strengths increase with antenna height by 5 to 7 dB in the low bands and by 2 to 4 dB in the high bands. On the other hand, for any antenna height, mean strengths increase strongly and monotonically with frequency, by 28 dB overall for both the high and medium antennas and by 32 dB overall for the low antenna. These results can be understood on the basis of multipath lobing on the Phase One antenna pattern. Consider the height to the peak of the first multipath lobe. Assuming perfect reflection from a flat surface at all frequencies, a not unreasonable assumption at Corinne, the height to the peak of the first lobe varies directly with range and inversely with frequency and antenna height. The range interval of the Corinne repeat sector is from 1 to 8.9 km. Line-of-sight geometric visibility of the complete repeat sector exists from all antenna positions. The frequencies vary over a 55:1 range, from 167 to 9200 MHz. On the other hand, the tower heights, with from one to three tower sections extended, vary only over a 2:1 range. This is the reason why frequency has such a strong effect in Figure 3.36, and tower height a much weaker effect. At VHF, for all ranges within the repeat sector and the three antenna heights, most clutter sources, such as buildings, telephone poles, fence lines, etc., are well below the peak of the

Repeat Sector Clutter Measurements 199

Figure 3.35 Aerial photo of repeat sector at Corinne. Scale = 1:50,000. North is to the left.

first lobe. The gain at which such objects are illuminated is well down on the underside of the first multipath lobe, accounting for the weak clutter strengths there. The increases in antenna height over a 2:1 range only cause relatively minor 5- or 7-dB increases in the overall VHF illumination, which overall is very weak due to 30-dB multipath loss. At Xband, on the other hand, for all ranges within the repeat sector and the three antenna heights, many clutter sources are higher than the peak of the first multipath lobe and are fully illuminated by multiple lobes. Thus, less variation with antenna height occurs at Xband. L-band provides an in-between situation, with clutter sources fully illuminated at

200 Repeat Sector Clutter Measurements

–20

Mean of σ°F4 (dB)

–30

–40

–50 Range Pol. Res. (m) 150 H 150 V 15/36 H 15/36 V

–60

–70 VHF

UHF

L-

S-

X-Band

Frequency (MHz)

Figure 3.36 Mean clutter strength vs frequency at Corinne for three antenna heights. Repeat sector data; level farmland; antenna heights = 54–59 ft (3 tower sections, no superscript), = 41–46 ft (2 tower sections, superscript “M”), and = 27–32 ft (1 tower section, superscript “L”); at S-band, the high resolution range interval (4.0–8.9 km) is shorter than that for the other 18 frequency band/ waveform combinations (1.0–8.9 km). Table 3.5 Median Values of Mean Clutter Strength vs Antenna Height for the Corinne Repeat Sector Median Level of Mean Clutter Strength Values (dB) VHF

UHF

L-Band

S-Band

X-Band

High Tower

–55

–46

–34

–30

–27

Medium Tower

–57

–48

–34

–31

–29

Low Tower

–62

–53

–38

–33

–30

Note: Medianized over all measurements at both polarizations and both pulse lengths for each antenna height in each band.

Repeat Sector Clutter Measurements 201

close ranges at all three antenna heights. However, with increasing range and decreasing antenna height, the illumination gradually decreases until at longer ranges there exists weak illumination at all three antenna heights. Thus, at L-band, 5- to 8-dB average multipath loss occurs over the complete sector for the three antenna heights, and a 4-dB increase in mean strength occurs with increasing antenna height.

Antenna Height Effects: Phase Zero vs Phase One. Phase Zero and Phase One mean clutter strength results are now compared at similar and differing antenna heights for repeat sectors at various sites covering many terrain types. From all the sites, there is available a set of 30 sites where the Phase Zero and Phase One radars made measurements from nearly identical locations. At all 30 sites, Phase Zero used its 50-ft antenna mast height. For 22 of these sites, Phase One used its 59.1-ft X-band mast height, which is regarded as reasonably close to the Phase Zero height. For the remaining eight of these sites, Phase One used its 99-ft X-band mast height, which is twice as high as the Phase Zero mast height. For each site, the difference is computed of the Phase One mean clutter strength in the repeat sector minus the Phase Zero mean clutter strength in the repeat sector (both at 150-m pulse length, horizontal polarization). Across the 22 sites for which Phase One and Phase Zero had similar antenna heights, of the 22 differences in mean strength, the mean difference was –0.01 dB, and the standard deviation was 3.9 dB. However, across the eight sites for which Phase One had twice as high an antenna as Phase Zero, of the eight differences in mean strength, the mean difference was 4.9 dB, with a standard deviation of 3.2 dB. This study provides two important results. First, it provides an answer to the question, do the Phase One and Phase Zero radars get the same answers when they measure the same clutter? This study answers yes, even to a precision (obviously somewhat fortuitous) of 0.01 dB. It provides reassurance regarding calibration of both instruments. Second, this study shows that a 100-ft mast measures X-band clutter, on the average, 4.9 dB stronger than a 50- or 60-ft mast. This extends a previous study of Phase Zero mast height on the level open farmland at Corinne, where mean clutter strengths rose an average of 6 dB when the Phase Zero mast was raised from 20 to 50 ft. In the Phase One repeat sector data at Corinne, the average difference of the tall 59-ft tower minus the low 32-ft tower Xband mean clutter strengths over many repeated measured differences was 3.9 dB. Here, in this Phase Zero/Phase One comparison, a similar mast height effect exists covering eight sites with much more general terrain types.

3.4.1.5 Desert, Marsh, or Grassland Table 3.3 includes four sites within the category of desert, marsh, or grassland. These sites are quite different from one another in specific terrain characteristics. They are discussed in two regimes of depression angle, high and low, with each depression angle regime containing two sites. These four sites are all open or nonforested sites. This alone does not distinguish them from the previously discussed agricultural sites, which, taken together, cover a very wide variety of different scenes in open terrain. What distinguishes these four sites from agricultural sites is their lack of a cultural overlay of discrete man-made objects. These four open sites are largely in their original natural states, and their repeat sectors have the original natural vegetation as land cover on generally level or low-relief terrain. The multifrequency

202 Repeat Sector Clutter Measurements

characteristics of mean clutter strength at these four sites are different from any of the other sites. As a group they all have considerably lower mean clutter strengths than other terrain categories at corresponding depression angles, with one exception (pointed out in the following pages). The situations at these sites are as follows. At Booker Mountain, the site was on a high peak in Nevada; its repeat sector began at 12-km range on the relatively level (but slightly undulating) desert floor 1,570 ft below. This desert repeat sector is barren in places and covered with desert brush vegetation (e.g., sagebrush, greasewood) in other places. At Vananda East, the site was on the edge of a 350-ft-high bluff in Montana, from which the view was down off the steep edge of the bluff and out 3.6 km to the beginning of the repeat sector. The terrain below the bluff is low-relief undulating grassland without roads, buildings, or other cultural discretes (but with infrequent small occurrences of pine trees). Significant relief exists within the repeat sector, from 100 to 150 ft, with maximum slopes between 1° and 2°. At Knolls, the site was on the Great Salt Lake Desert in Utah. From a 25-ft-high local hill, the antenna looked into a very level repeat sector (relief < 5 ft) beginning at 3-km range, containing mostly barren salt and mud flats, but with some scrubby desert vegetation in places. At Big Grass Marsh, the site was in the middle of a large, level wetland area in Manitoba, approximately 20 miles long in the north-south direction by 10 miles across. The Big Grass Marsh measurements were made in winter (February) with the marsh frozen and snow-covered. Some of the marsh is used for pasture or for growing hay in summer. The terrain is somewhat rough and bumpy. The repeat sector began at 1-km range and extended 6 km across nonforested wetland, with some minor hayfields. Several very small patches of trees occurred near the boundaries of the repeat sector. Otherwise, the natural vegetation was dormant marshland grasses and tall aquatic vegetation (e.g., cattails and bulrushes) over most of the sector, with much of the higher vegetation sticking through the snow cover. The center area of the sector was slightly higher (≈3 ft) than the setup position. Multifrequency mean clutter strengths measured over the repeat sectors at Booker Mountain, Vananda East, Knolls, and Big Grass Marsh are shown in Figure 3.37. Mean strengths range over 53 dB in Figure 3.37, from –23.1 dB at X-band (Nevada desert at high depression angle) to –76.1 dB at UHF (Big Grass Marsh at grazing incidence). This is a much greater range of mean clutter strengths for this set of relatively open, discrete-free sites than for any of the other groups of sites. These somewhat similar surfaces were observed at quite different geometries, with effective site elevation advantages of –3, 25, 342, and 1,570 ft, and depression angles of 0.2°, 0.3°, 1.0°, and 1.8°, for Big Grass Marsh, Knolls, Vananda East, and Booker Mountain, respectively. Driving these strengths over wide ranges are large amounts of multipath loss at the lower frequencies at the two sites, Knolls and Big Grass Marsh, with little or no elevation advantage. The two high sites, Vananda East and Booker Mountain, provide what are largely intrinsic σ°’s in Figure 3.37. Note that, just due to multipath effects alone, mean strengths at VHF should be weaker than at UHF. Surprisingly, at both Big Grass Marsh and Knolls, mean strengths at VHF are generally 5 to 10 dB stronger than at UHF. Looking at the multipath-free situations of Booker Mountain and Vananda East, mean strengths are also substantially stronger at VHF than at UHF at Booker Mountain, and at least equal at Vananda East. Thus, across three of these four sites, intrinsic σ°’s at VHF are substantially greater than at UHF (with substantial equivalence at the fourth site, Vananda East).

Repeat Sector Clutter Measurements 203

–20 Low D.A. – 32-Big Grass Marsh Low D.A. – 43-Knolls High D.A. – 44-Booker Mtn. High D.A. – 45-Vananda East

–30

Mean of σ°F4 (dB)

–40

–50

–60 Range Res. (m) 150 150 15/36 15/36

–70

Pol. H V H V

–80 VHF

UHF

L-

S-

X-Band

Frequency (MHz)

Figure 3.37 Mean clutter strength vs frequency for desert, marsh, or grassland (few discretes) at high and low depression angle. See Table 3.3.

Depression angle largely accounts for the variability in Figure 3.37, both where large multipath loss exists (e.g., at VHF, by over 40 dB), and where it does not (e.g., at X-band, by over 20 dB). Similar Phase Zero range of variation of X-band mean clutter strength with depression angle over similar terrain types was discussed in Chapter 2. Reasonable similarity is seen in mean strength vs frequency characteristics at Booker Mountain and Vananda East, where Booker Mountain provides a higher depression angle, but Vananda East has higher terrain slopes. Remarkable similarity is seen in the L-band data at these two high sites. At both high sites X-band mean strengths as a tight group have abruptly increased to be 12 or 14 dB stronger than in the lower bands, providing exceptionally strong clutter from these otherwise relatively weak-clutter terrain types (this is the exception mentioned previously). At the two lower sites, grazing incidence backscatter from the mud flats at Knolls or from the frozen marsh in Manitoba provides significantly lower mean strengths than higher incidence backscatter from the Nevada desert (2°) or the Montana grassland (1°).

204 Repeat Sector Clutter Measurements

3.4.2 Twelve Multifrequency Clutter Strength Characteristics A major objective of Chapter 3 is to show how mean ground clutter strength varies with frequency for various terrain types. The approach taken for achieving this objective is to combine measurements from different sites within broad classes of similar terrain and depression angle, such that the results cluster within each category and separate between different categories. In the foregoing subsections of Section 3.4, the clustering of the multifrequency mean strength data within 12 terrain categories has been presented and discussed in detail. Such clusters were developed based on the repeat sector database. Within each terrain category, the median level of the cluster of measured mean strengths in each of the five frequency bands, VHF, UHF, L-, S-, and X-band, is now specified as a general measure of mean strength at that frequency for that terrain category. In so doing, overly specific terrain and propagation effects in individual measurements are averaged out. The results are plotted in Figure 3.38 and tabulated in Table 3.6. The results of Figure 3.38 and Table 3.6 generalize how mean ground clutter strength varies with frequency as a function of terrain type. These results are based on one unified program of measurements with accurate calibration and consistent data reduction throughout. Figure 3.38 and Table 3.6 provide five broadly different terrain groups, namely, urban, mountains, forest, farmland, and a combined discrete-free category of desert, marsh, or grassland. Many of these groups are further partitioned within several regimes of depression angle and/or terrain relief, such that there are 12 subcategories in all. A great deal of variability of mean clutter strength is observed in Figure 3.38—in total 66 dB between mountains at VHF and desert or marshland at UHF. This extreme variability is what has plagued investigators attempting to understand and predict the performance of ground-based radars operating against clutter interference over the years. It is apparent that an orderly rationale of sorting through this variability on the basis of terrain type, depression angle, relief, and radar frequency reduces variability within class to within a one-sigma range of ≈± 3.2 dB (see Figure 3.50), and provides the separation between classes as observed in Figure 3.38. The results in Figure 3.38 and Table 3.6 are now discussed. For the most part, all of the measurement-specific qualifications of these data are left to the preceding site-by-site discussions in Section 3.4 so as to focus here more on pointing out the messages in these data. The clusters of mean strengths from which the median levels of Figure 3.38 and Table 3.6 were obtained include mean strengths at both vertical and horizontal polarization and short and long pulse length. Variations with polarization and resolution, usually small, are more generally discussed subsequently in Section 3.5. In what follows, discussion for the first time dwells on comparing and contrasting mean clutter strengths between classes, not on the degree of clustering of measurements from different sites within classes. First, in Figure 3.38, focus on the two short-dashed curves at the top of the figure for mountain and urban clutter, providing very strong mean strengths in the –10-dB to –20-dB range. Mountain clutter at VHF provides the strongest mean clutter strengths measured at –7.6 dB. This falls rapidly by 14 dB with increasing frequency to levels of –21 and –22 dB at S- and Xbands. Much of this trend of decreasing strength with increasing frequency in mountain terrain is caused by forest vegetation on steep mountain slopes. Urban complexes observed, as in the repeat sector measurements of Chapter 3, on low-relief open terrain provide large mean clutter strengths at high frequencies in the –10-dB to –12-dB range, partly because of their broadside aspect. At low frequencies these large returns are decreased significantly by up to 10 dB

Repeat Sector Clutter Measurements 205

0

Mou

ntain

≥1

Urban

s

°

−10 Forest/ HighRelief

> 1° ° ≤ 0.2

−20

0.4° To

σ°F4 (dB)

−30

1°

Farmland

Terrain Slopes

Forest/ Low-Relief

> 1°

Terrain Slopes < 1° ≥ 1°

−40

Desert, Marsh, or −50 Grassland (Few Discretes)

≤ 0.3°

−60 ≤ 0.3°

1,000

10,000

Depression Angle 100

−70

−80 VHF

UHF

L- Band

S-Band

X-Band

Frequency (MHz)

Figure 3.38 Mean clutter strength vs frequency for all measured terrain types. See Table 3.6 for numeric values.

through multipath loss. On the basis of the Phase Zero measurements, in more general composite urban terrain, mean clutter strength from urban complexes at X-band is 12 dB weaker than on low-relief open terrain (see Chapter 2, Section 2.4.2.2). Next, in Figure 3.38, focus on the two long-dashed forest/high-relief curves near the top of the figure. These curves also show mean strengths decreasing with increasing frequency, as in mountains, but generally a few decibels weaker, partly due to less steep terrain slopes. Relatively little difference is seen between high and low depression angle in high-relief

206 Repeat Sector Clutter Measurements

Table 3.6 Median Values of Mean Land Clutter Strength by Terrain Type and Radar Frequency Median* Value of σ°F4 (dB) Terrain Type

Urban Mountains Forest/High-Relief (Terrain Slopes > 2 °) High Depression Angle ( > 1°) Low Depression Angle ( ≤ 0.2 °) Forest/Low-Relief (Terrain Slopes < 2°) High Depression Angle ( > 1°) Intermediate Depression Angle (0.4 ° to 1°) Low Depression Angle ( ≤ 0.3 °) Agricultural/High-Relief (Terrain Slopes > 2 °) Agricultural/Low-Relief Moderately Low-Relief (1°< Terrain Slopes < 2 °) Very Low-Relief (Terrain Slopes <1°) Desert, Marsh, or Grassland (Few Discretes) High Depression Angle ( ≥1°) Low Depression Angle ( ≤ 0.3 °)

Frequency Band VHF

UHF

L-Band S-Band X-Band

–20.9 –7.6

–16.0 –10.6

–12.6 –17.5

–10.1 –21.4

–10.8 –21.6

–10.5 –19.5

–16.1 –16.8

–18.2 –22.6

–23.6 –24.6

–19.9 –25.0

–14.2 –26.2

–15.7 –29.2

–20.8 –28.6

–29.3 –32.1

–26.5 –29.7

–43.6

–44.1

–41.4

–38.9

–35.4

–32.4

–27.3

–26.9

–34.8

–28.8

–27.5

–30.9

–28.1

–32.5

–28.4

–56.0

–41.1

–31.6

–30.9

–31.5

–38.2 –66.8

–39.4 –74.0

–39.6 –68.6

–37.9 –54.4

–25.6 –42.0

* Medianized (central) values within groups of like-classified measurements in a given frequency band, including both VV- and HH-polarizations and high (15 or 36 m) and low (150 m) range resolution.

forest terrain at UHF, L-, and S-bands, indicating that terrain slopes are steep enough to largely overwhelm depression angle leverage on total illumination angle in such terrain. However, at VHF and X-band, depression angle is shown to be of more effect in high-relief forest terrain. At VHF, many of the measurement scenarios with low depression angle in high-relief forest terrain supported forward terrain reflections from the terrain between the radar and the farther out steep forest, and this led to multipath propagation loss in mean clutter strength from the steep forest. Thus, in Figure 3.38, mean clutter strengths in forest/ high-relief/low depression angle terrain show a local countertrend decreasing from UHF to VHF by 3 dB. At X-band, the mean clutter strength in forest/high-relief terrain at high depression angle also shows a countertrend of increasing by 3 dB from S-band, and, in fact, is slightly higher than for mountains at X-band. It has been previously mentioned that 42 repeat sector terrain macropatches are not enough to average out all site specificities in the repeat sector results, and that this is the major reason why all of the 360° full coverage Phase One survey data were processed to provide results from many more patches in

Repeat Sector Clutter Measurements 207

Chapter 5. In Figure 3.38, the fact that, at X-band, forest/high-relief/high depression angle mean strength rises above that of mountains is such a specificity. Phase Zero X-band measurements across many more patches show forest/high-relief/high depression angle mean strength to continue to decrease from its S-band value of –23.6 dB to an X-band value of –24.5 dB. Next, in Figure 3.38, focus on the three low-relief forest curves indicated by plus sign symbols. In such terrain, mean clutter strengths vary strongly both with depression angle and radar frequency. At high depression angles in low-relief forest, mean clutter strengths decrease with increasing frequency. At low depression angles in low-relief forest, mean clutter strengths increase with increasing frequency. At any of the five frequencies, mean strength increases significantly with depression angle, more so at VHF (by 29 dB, from low to high depression angle) than at X-band (by 9 dB, from low to high depression angle). If a comparison is made between low-relief forest (plus signs) and high-relief forest (long dashes) both at high depression angle > 1°, little difference is seen with relief at VHF, UHF, and L-band, but large 6-dB differences are seen with relief at S- and X-band. This difference indicates that the degree of separation of clutter mean strength by terrain class can be a function of radar frequency; therefore, selection or specification of optimum terrain categories to separate clutter statistics can be frequency dependent. The rise in mean strengths from S- to X-band in low-relief forest at both high and intermediate depression angles is borne out in the Phase One survey data of Chapter 5. Next, in Figure 3.38, focus on the two farmland curves indicated by heavy solid lines midway in the figure. Then, in Table 3.6, notice that there is not significant separation in mean strengths between high-relief agricultural terrain (with terrain slopes > 2°) and moderately low-relief agricultural terrain (with terrain slopes between 1° and 2°). In these two terrain groups, there are random variations of the median level of mean strength by frequency band, with the former stronger at UHF and L-band, the latter stronger at VHF and S-band, and virtually identical levels at X-band, all within several decibels of –30 dB. Hence, results are combined from these two groups into one terrain category with terrain slopes > 1°; in Figure 3.38 the farmland curve annotated as “terrain slopes > 1°” plots the median levels of the combined results in each band. This curve is essentially invariant with frequency at the –30-dB level, with band-to-band fluctuations of at most 1 or 2 dB about this level. As previously discussed, mean clutter strengths do not vary with depression angle in high-relief or moderately low-relief agricultural terrain, although the spreads in clutter amplitude distributions in such terrain are a very strong function of depression angle. Thus, in contrast to low-relief forest, in which mean clutter strengths vary strongly with both frequency and depression angle, in low-relief farmland mean strengths are invariant both with frequency and depression angle, except for very low-relief farmland. As indicated in Figure 3.38, in very low-relief farmland, terrain slopes are less than 1° (and so usually is depression angle, i.e., in such terrain there are few hills high enough to give higher depression angles), and as a result there is a large multipath propagation loss at UHF (≈10 dB) and VHF (≈25 dB) in mean clutter strength below the nominal –30-dB level. The multipath propagation loss is very significantly dependent on the precise terrain slope of the hill upon which the radar is located, even in very low-relief terrain in which terrain slopes are less than 1°. In addition, the multipath propagation loss is theoretically dependent on geometric factors of antenna height, clutter source height, and distance between antenna and clutter source. In very broad measure, the Phase One clutter results do

208 Repeat Sector Clutter Measurements

not show extreme sensitivity to clutter source height and range extent variations as they occur over the repeat sector matrix of patches. However, higher antennas generally provide somewhat stronger clutter (Section 4.1.4.3). Note that there are remarkably small differences in mean clutter strength between farmland of moderate relief or greater (terrain slopes > 1°) and low-relief forest at intermediate depression angles. There are many sites in each of these two terrain classes (see Table 3.3). Thus, in much commonly occurring low-relief rural terrain, neither very level nor very steep, at intermediate depression angles, mean clutter strengths hover around the –30-dB level, irrespective of whether the terrain is forest or farmland. These results are closely corroborated by the Phase One survey data in Chapter 5. Next, in Figure 3.38, focus on the two short-dashed curves at the bottom of the figure for desert, marsh, or grassland, that is, for open terrain with very few discrete sources compared with farmland. On discrete-free desert, marsh, or grassland, mean clutter strength is weaker than for other terrain types. Again, at low depression angles, there is a large multipath loss due to decreased illumination at the lower frequencies, and this loss is greater and extends to higher frequencies than in farmland because the clutter sources are much lower in such terrain (e.g., a sagebrush bush) than in farmland (e.g., a feed storage silo). Note that propagation loss alone would continue to decrease mean clutter strength from UHF to VHF at low depression angles on open desert, marsh, or grassland. However, the data from desert and frozen marshland indicate that intrinsic σ°’s actually rise substantially from UHF to VHF in such terrain, enough to more than compensate for increased propagation loss at low angles from UHF to VHF and to result in greater mean clutter strengths at VHF compared to UHF at both high and low depression angles. These results are also corroborated by the Phase One survey data in Chapter 5. The repeat sector data from grassland indicate intrinsic σ°’s at VHF equal to those at UHF. Mean clutter strength is observed to increase very strongly with depression angle in discrete-free desert, marsh, or grassland in all frequency bands, including VHF where much of the effect is caused by multipath propagation, and X-band where multipath has less effect. More specifically, mean clutter strengths in Figure 3.38 for desert, marsh, or grassland increase from low to high depression angle by 30 dB or more at low frequencies and 16 dB at X-band as depression angle increases over the small but highly significant range from ≤ 0.3° to 1° or 2°. If mean clutter strength is compared between desert, marsh, or grassland and forest at Xband in Figure 3.38, it is observed that at low depression angles mean strength in desert or marshland terrain is 5 or 6 dB weaker than in forest terrain. However, at high depression angles greater than 1° (and on the basis of two different Phase One measurement sites), mean strength in desert or grassland is equal to that in low-relief forest terrain (i.e., at Xband, looking down at sagebrush vegetation is equivalent to looking down at a forest canopy). This strong X-band desert or grassland clutter at high depression angle is 12 to 14 dB greater than at S-band and lower frequencies. This summary section has focused on median levels of clusters of measured mean clutter strengths for each combination of terrain type and frequency. Similar information showing median differences in mean strength with polarization and resolution within clusters by terrain type and radar frequency is provided in Section 3.5. Subsequently, in Section 3.6,

Repeat Sector Clutter Measurements 209

medianized levels of higher moments and percentiles of clutter amplitude distributions are provided within the same measurement clusters as specified here, by terrain type and radar frequency band.

3.5 Dependencies of Mean Land Clutter Strength with Radar Parameters The repeat sector database consists of 4,465 measurements of ground clutter amplitude distributions from repeat sector clutter patches selected at 42 different places on the surface of the earth. Each repeat sector clutter patch was measured a number of times (nominally, four) across the Phase One radar parameter matrix (five radar frequencies, two polarizations, two pulse lengths). It is evident that the repeat sector database must contain a considerable amount of general information concerning dependencies of ground clutter on the main radar parameters of frequency, polarization, and resolution over and above specific variations from site to site and terrain type to terrain type. What can be said about such general radar parameter dependencies of ground clutter, for example, for the benefit of radar engineers who need to design radars to perform in a variety of terrain types? In Section 3.5, repeat sector data are reduced to provide general information on how mean ground clutter strength varies with frequency, polarization, and resolution, independent of terrain type.

3.5.1 Frequency Dependence A generalized non-terrain-specific frequency dependence of ground clutter is now determined by combining measurement results over a large set of sites encompassing a wide variety of terrain types. In doing so, should all terrain types be included in the encompassing set, or should some terrain types be excluded from the general set as being overly specific? For example, there are urban and rural terrain types. Within rural, there are extreme terrain types such as mountains and deserts as well as more commonly occurring general types of farmland and forest. Should urban terrain types be included? Urban stands apart as a special man-made terrain type. Should mountains and desert be included? It turns out that, in terms of overall mean clutter strength, mountains influence the overall level to be somewhat higher, desert to be somewhat lower, and these two influences tend to cancel. So, somewhat arbitrarily, all rural sites including mountains and desert are included for the sake of generality, but urban is deleted as being different in kind, not just degree, from rural. All the rural mean strengths from the repeat sector database are now assembled in a scatter plot vs frequency, VHF through X-band. Five urban sites and six seasonal repeats are not included, leaving 37 rural sites. Multifrequency mean clutter strength data from these 37 rural sites for both pulse lengths and polarizations are plotted together in Figure 3.39. It is observed that the resultant scatter plot is basically funnel shaped— discounting the desert (Knolls) and marsh (Big Grass Marsh) results that tend to separate out at the bottom of the plot at UHF, L-, and S-bands22— with wide scatter at VHF and decreasing scatter as frequency increases to X-band.

22. Figure 1.8 in Chapter 1 is the same scatter plot as Figure 3.39 except that the desert and marsh results are deleted in Figure 1.8.

Repeat Sector Clutter Measurements 209

medianized levels of higher moments and percentiles of clutter amplitude distributions are provided within the same measurement clusters as specified here, by terrain type and radar frequency band.

3.5 Dependencies of Mean Land Clutter Strength with Radar Parameters The repeat sector database consists of 4,465 measurements of ground clutter amplitude distributions from repeat sector clutter patches selected at 42 different places on the surface of the earth. Each repeat sector clutter patch was measured a number of times (nominally, four) across the Phase One radar parameter matrix (five radar frequencies, two polarizations, two pulse lengths). It is evident that the repeat sector database must contain a considerable amount of general information concerning dependencies of ground clutter on the main radar parameters of frequency, polarization, and resolution over and above specific variations from site to site and terrain type to terrain type. What can be said about such general radar parameter dependencies of ground clutter, for example, for the benefit of radar engineers who need to design radars to perform in a variety of terrain types? In Section 3.5, repeat sector data are reduced to provide general information on how mean ground clutter strength varies with frequency, polarization, and resolution, independent of terrain type.

3.5.1 Frequency Dependence A generalized non-terrain-specific frequency dependence of ground clutter is now determined by combining measurement results over a large set of sites encompassing a wide variety of terrain types. In doing so, should all terrain types be included in the encompassing set, or should some terrain types be excluded from the general set as being overly specific? For example, there are urban and rural terrain types. Within rural, there are extreme terrain types such as mountains and deserts as well as more commonly occurring general types of farmland and forest. Should urban terrain types be included? Urban stands apart as a special man-made terrain type. Should mountains and desert be included? It turns out that, in terms of overall mean clutter strength, mountains influence the overall level to be somewhat higher, desert to be somewhat lower, and these two influences tend to cancel. So, somewhat arbitrarily, all rural sites including mountains and desert are included for the sake of generality, but urban is deleted as being different in kind, not just degree, from rural. All the rural mean strengths from the repeat sector database are now assembled in a scatter plot vs frequency, VHF through X-band. Five urban sites and six seasonal repeats are not included, leaving 37 rural sites. Multifrequency mean clutter strength data from these 37 rural sites for both pulse lengths and polarizations are plotted together in Figure 3.39. It is observed that the resultant scatter plot is basically funnel shaped—discounting the desert (Knolls) and marsh (Big Grass Marsh) results that tend to separate out at the bottom of the plot at UHF, L-, and S-bands22—with wide scatter at VHF and decreasing scatter as frequency increases to X-band.

22. Figure 1.8 in Chapter 1 is the same scatter plot as Figure 3.39 except that the desert and marsh results are deleted in Figure 1.8.

210 Repeat Sector Clutter Measurements

0

–10

–20

Mean of σ°F4 (dB)

–30

–40

–50

–60

Range Pol. Res. (m) 150 H 150 V 15/36 H 15/36 V

100

1,000

10,000

–70

–80

VHF

UHF

L-

S-

X-Band

Frequency (MHz)

Figure 3.39 Mean clutter strength at 37 rural sites. Five-frequency repeat sector data.

Next the central or median position of this scatter plot is specified (including values for both pulse lengths and polarizations) in each frequency band, as a general non-terrainspecific measure of mean ground clutter strength. The results are tabulated in Table 3.7 and plotted in Figure 3.40. In overall terms, these results indicate that general mean ground clutter strength is remarkably invariant with radar frequency, VHF through X-band, at or about the –30-dB level, with no strong trend. More specifically, the mean of all five clutter strength numbers in Table 3.7 and Figure 3.40 is –29.2 dB, and all five numbers lie within

Repeat Sector Clutter Measurements 211

1.7 dB of this. Mean strengths at VHF, UHF, and S-band are all within a fraction of 1 dB of –30 dB; mean strengths at L-band and X-band are closer to –27.5 dB. These results are strongly confirmed in Chapter 5; i.e., see Figure 5.12 and Table 5.10. In generally averaging across many terrain types in this manner, care must be taken in case the result is unlike any particular terrain type. In that case, design would never be for a real situation. In preceding terrain-specific discussions, approximate frequency invariance of mean clutter strength was occasionally observed near the –30-dB level. For example, Wainwright mean clutter strengths as shown in Figure 3.5 are remarkably invariant near the –30-dB level; so also are mean clutter strengths at Turtle Mountain and Beulah. Table 3.7 General Dependence of Mean Land Clutter Strength on Frequency Frequency Band VHF

UHF

L-Band

S-Band

X-Band

Median value of mean clutter strength (dB)

–29.6

–30.3

–27.8

–30.7

–27.5

Standard deviation in mean clutter strength (dB) (i.e., one-sigma variation)

16.6

13.6

9.7

7.1

5.8

Number of repeat sector measurements

144

146

146

110

129

Notes: Median values of mean clutter strength over 37 rural sites. Also, one-sigma variations of mean strength in each band. Phase One repeat sector data, seasonal repeats not included.

Besides characterizing the central level in the funnel plot, it is also desirable to quantify the spread whereby the funnel is wide at VHF and narrow at X-band. This is done by computing, for each band, the standard deviation or one-sigma range of variation of all the contributing mean strengths. These results are also shown in Table 3.7 and Figure 3.40—this figure includes indications of the extreme values from this set of sites, excluding the results from the two very weak sites, desert (Knolls) and marsh (Big Grass Marsh); cf. Figure 3.39 and Figure 1.8. To the extent that the mean strengths are distributed normally in each band (a fair approximation), the one-sigma variation is the range within which 68% of the values fall. There is a strong clear monotonic trend in Table 3.7 and Figure 3.40 whereby this onesigma range of variation decreases with increasing frequency, from 16.6 dB at VHF to 5.8 dB at X-band. That is, mean clutter strengths in rural terrain vary much more at VHF than at X-band. The reasons—described in more detail in Section 3.3.2—are associated with VHF clutter strengths increasing in forest due to decreased vegetative absorption at VHF compared to the microwave bands, and with VHF clutter strengths decreasing in open level farmland because of multipath loss. The previously discussed terrain-specific characteristics of mean strength with frequency do not have this problem of greatly increased variability at VHF (see Section 3.7.3 for quantitative information).

212 Repeat Sector Clutter Measurements

0

Median Value of Mean Clutter Strength (dB)

−10

−20

X-Band

L-Band

VHF −30 UHF

S-Band

−40

−50

−60

−70 100

200

300

500

700 1,000

2,000 3,000

5,000

10,00

Frequency (MHz)

Figure 3.40 General dependence of mean low-angle land clutter strength (circles) and its standard deviation (vertical lines) as a function of frequency over 37 rural sites. Extreme values shown as horizontal bars (excluding results from two very weak sites, desert and marsh). (After Skolnik [5]; by permission, © 2001 The McGraw-Hill Companies, Inc.)

3.5.2 Polarization Dependence Central (medianized) differences in mean clutter strength with polarization across all repeat sectors including seasonally repeated measurements are shown in Table 3.8. Each difference is computed as mean strength at vertical (VV) polarization in decibels minus mean strength at horizontal (HH) polarization in decibels.23 That is, each decibel difference represents the ratio of power received at vertical polarization to power received 23. Left to right, VV means transmit vertical, receive vertical; HH means transmit horizontal, receive horizontal, etc.

Repeat Sector Clutter Measurements 213

at horizontal polarization for otherwise comparable measurements. The medianized differences across all sites are shown in Table 3.8 for each radar frequency band, each range resolution, and for both range resolutions combined. Table 3.8 Median Differences in Mean Clutter Strength with Polarization, VV-HH Difference (dB) in Mean Clutter Strength with Polarization, VV-HH (One-Sigma Variation, dB) Range Resolution

Frequency Band VHF

UHF

L-Band

S-Band

X-Band

Low (150-m pulse length)

1.0 (4.5)

1.8 (2.8)

0.3 (2.3)

2.3 (1.8)

1.7 (1.6)

High (15 m at L-, S-, X-bands; 36 m at VHF and UHF)

1.6 (3.8)

2.0 (3.2)

0.4 (2.9)

2.3 (1.8)

1.7 (2.3)

Both

1.2 (4.1)

2.0 (3.0)

0.4 (2.6)

2.3 (1.8)

1.7 (2.0)

Notes: Phase One repeat sector data. All site visits. One-sigma variations are shown in parentheses.

The median differences of mean clutter strength with polarization in Table 3.8 are small, on the order of 2 dB or less. Specifically, the median differences with polarization in Table 3.8 are quite close to 2 dB, VV–HH, at UHF, S-, and X-bands, but are slightly less at VHF, and nearly zero at L-band. Note that there is very little difference in these median differences with range resolution, allowing emphasis to be on the bottom row, which shows median differences across the set of experiments including both resolutions. Even though general Phase One calibration accuracy is specified to be 2 dB rms over all sites, Table 3.8 is based on differences in two measurements always conducted at the same site, often one immediately following the other, with calibration differences between them being much less than 1 dB. Thus, on the average, mean ground clutter strength is often one to two dB stronger at vertical polarization than at horizontal, presumably because of the preferred vertical orientation of many discrete clutter sources. Although average differences in mean clutter strength with polarization are small, individual differences in specific pairs of measurements can be greater. For example, if on the basis of all of the repeat sector measurements, still separated by frequency band but including measurements at both pulse lengths, the largest but one difference in mean clutter strength with polarization in each direction, VV > HH and HH > VV, respectively, is as follows: at VHF, 11.1 and 7.0 dB; at UHF, 6.8 and 3.2 dB; at L-band, 5.1 and 6.5 dB; at Sband, 5.1 and 4.6 dB; and at X-band, 5.5 and 4.0 dB—discount the largest difference in each direction as the extreme statistical outlier. Because of these occasional larger differences in mean strength with polarization, consider now the one-sigma range of variation shown in Table 3.8 specifying the range over which larger, more significant, differences with polarization commonly occur. It is observed that the one-sigma range of variation in mean strength with polarization about the mean difference decreases from 4.1 dB at VHF to 2.0 dB at X-band.

214 Repeat Sector Clutter Measurements

The polarization differences in mean strength at all five bands and both pulse lengths are now combined into one overall histogram as shown in Figure 3.41. The corresponding cumulative distribution is shown in Figure 3.42. The overall median polarization difference in mean clutter strength across all bands is 1.5 dB, VV > HH. The overall one-sigma range of variation across all bands is 2.8 dB. This histogram also demonstrates that larger polarization differences in mean clutter strength occur significantly frequently in ground clutter. The cumulative distribution of polarization differences in mean clutter strength in Figure 3.42 allows the reading of probability of occurrence directly. For example, in 3% of the measurements, mean strength at horizontal polarization was stronger than at vertical by 5 dB or more (left tail); in another 3% of the measurements, mean strength at vertical was stronger than at horizontal by 7 dB or more (right tail). The remaining 94% of measurements had lesser differences in mean strength with polarization. Seventy-five percent of measurements had differences within the 2.8-dB one-sigma range of variation about the mean difference. 15 416 Differences in Mean Clutter Strength with Polarization, VV-HH (all frequencies, VHF, UHF, L-, S-, X-band; both pulse lengths, 150 m and 15/36 m)

Difference (dB) Median = +1.48 Mean = +1.40 1σ = 2.81

Percent

10

5

0 –15

–10

–5

0

5

10

15

Difference in Mean Clutter Strength with Polarization, VV-HH (dB)

Figure 3.41 Histogram of differences in mean ground clutter strength with polarization, VV-HH. Phase One repeat sector data. All site visits, all five radar frequencies, both range resolutions.

Repeat Sector Clutter Measurements 215

Normal Scale

Probability That Difference in Mean Clutter Strength, VV-HH

Abscissa

0.999 416 Differences in Mean Clutter Strength with Polarization, VV-HH (all frequencies, VHF, UHF, L-, S-, X-band; both pulse lengths, 150 m and 15/36 m)

0.99

0.9 Difference (dB) Median = +1.48 Mean = +1.40 1σ = 2.81

0.7

0.5

0.3

0.1

0.01

0.001 –12

–10

–8

–6

–4

–2

0

2

4

6

8

10

12

Difference in Mean Clutter Strength with Polarization, VV-HH (dB)

Figure 3.42 Cumulative distribution of differences in mean ground clutter strength with polarization, VV-HH. Phase One repeat sector data. All site visits, all five radar frequencies, both range resolutions.

Next, differences in mean strength with polarization are presented broken down by terrain type. Table 3.9 shows differences in mean clutter strength with polarization for the 12 repeat-sector terrain categories, averaged across all five frequencies and both pulse lengths. On the whole, differences with polarization remain small when broken down into these 12 individual terrain categories. An exception is high-relief agricultural terrain, for which mean clutter strength at vertical polarization is, on the median average, 4.8 dB stronger than at horizontal polarization. Other weak trends are observable in the data of Table 3.9. For example, differences in mean strength with polarization increase with increasing depression angle in low-relief forest and in desert, marsh, or grassland; increase with increasing relief in low-relief agricultural terrain, but decrease with increasing depression angle in high-relief forest.

216 Repeat Sector Clutter Measurements

Table 3.9 Differences in Mean Clutter Strength with Polarization, VV-HH, by Terrain Type Difference (dB) in Mean Clutter Strength with Polarization, VV-HH Terrain Type Median

Mean

Standard Deviation

Urban

1.1

0.7

2.8

Mountain

1.2

2.4

2.8

Forest/High-Relief High Depression Angle Low Depression Angle

0.6

1.2

1.8

1.7

1.8

1.9

Forest/Low-Relief High Depression Angle Intermediate Depression Angle Low Depression Angle

1.2 1.0 0.2

1.2 0.6 –0.1

2.0 2.5 2.0

Agricultural/High-Relief

4.8

3.6

3.8

Agricultural/Low-Relief Moderately Low-Relief Very Low-Relief

2.5 1.6

1.7 1.4

3.2 3.1

Desert, Marsh, or Grassland (Few Discretes) High Depression Angle Low Depression Angle

2.4 0.2

2.2 0.1

2.5 2.2

Notes: Repeat sector data. All sites, five frequencies, both pulse lengths.

3.5.3 Resolution Dependence The clutter coefficient σ ° is equal to the RCS of the resolution cell divided by the area of the cell. This normalization by cell area means that, in homogeneous clutter where RCS increases directly with cell size, there is no dependence of σ ° on spatial resolution. The real world of ground clutter is the antithesis of homogeneity. With real clutter, one needs to think of distributions of varying σ ° over a spatial region, not of constant σ °. The spreads of these distributions are fundamentally dependent on spatial resolution, where increasing resolution results in less averaging within a cell and thus more cell-to-cell variability. However, even for real heterogeneous clutter, the mean clutter strength of the spatial amplitude distribution over a fixed region, unlike any other statistical attribute of the distribution, is often relatively independent of spatial resolution. To see why this is so, consider the following arguments. First, imagine a resolution cell of 150-m range resolution containing one telephone pole of 1-m2 RCS in a clutter-free background. Let the σ° of the cell be x. Now imagine increasing range resolution to 15 m, so that 10 cells cover the region previously covered by the 150-m cell. Of these 10 cells, one will have a σ° of 10x (i.e., pole RCS stays the same at 1 m2, cell size smaller by a factor

Repeat Sector Clutter Measurements 217

of 10), and the other nine cells will have σ°’s of zero. The mean clutter strength over all 10 cells at 15-m resolution is still x (i.e., one value of 10x averaged together with nine values of zero), the value for the 150-m cell. Second, imagine a 150-m resolution cell containing 10 approximately equispaced telephone poles, each of 1-m2 RCS. Assume that the 10 returns from these poles are of random phase (i.e., the exact position of each pole within its 15-m domain is random with respect to carrier wavelength). Imagine illuminating all 10 poles in one large 150-m resolution cell. Because the phases of the 10 returns are random, powers are additive, and the measured RCS from the 150-m cell is 10 m2. Let the resultant σ°, obtained by dividing by the area of the 150-m cell, be x. Now imagine increasing range resolution to 15 m, so that there is only one pole per cell. The RCS of each 15-m cell is now 1 m2, or one-tenth that of the large cell, but the area of each small 15-m cell is also one-tenth that of the large 150-m cell, so that σ° of each small cell remains x as does the mean over all 10 small cells. Thus, in power-additive situations where clutter sources within cells are randomly phased, mean clutter strengths over fixed spatial regions are independent of resolution. In voltageadditive situations, where only several sources exist within a cell of fixed phases that can interfere constructively or destructively, separating the returns with higher resolution and averaging the resultant σ°'s will not yield a mean σ° equal to the original single-cell value. To the extent that differences with resolution are seen in mean clutter strengths in the Phase One repeat sector results, it indicates once more the domination of low-angle clutter by discrete sources with several (not one, not many) interfering discretes per cell. Such arguments, however, provide no basis for expecting any overall dependence of mean strength on resolution across many measurements (i.e., sometimes constructive interference, sometimes destructive). Discussion now turns to the measurement results showing differences in mean strength with range resolution. Table 3.10 shows such differences, medianized across all of the repeat sector measurements, for vertical polarization, horizontal polarization, and both polarizations combined. These medianized differences with resolution are very small, less than 2 dB everywhere. These slight differences include any contributing small calibration offsets. Table 3.10 Median Differences in Mean Ground Clutter Strength with Range Resolution, High-Low

Polarization

Difference (dB) in Mean Clutter Strength with Pulse Length, 15/36 m – 150 m (One-Sigma Variation, dB) Frequency Band VHF

UHF

L-Band

S-Band

X-Band

Vertical

1.9 (2.1)

1.5 (3.0)

0.9 (1.5)

–1.2 (1.8)

0.2 (2.5)

Horizontal

2.0 (1.6)

1.4 (1.4)

0.7 (3.0)

–0.9 (1.7)

0.0 (1.4)

Both

2.0 (1.9)

1.4 (2.3)

0.9 (2.3)

–1.0 (1.8)

0.2 (2.0)

Notes: Phase One repeat sector data. All site visits. One-sigma variations are shown in parentheses.

218 Repeat Sector Clutter Measurements

Now consider how changing polarization affects the results in Table 3.10. In a clutter measurement, if the polarization is switched (e.g., from vertical to horizontal), the ensemble of effective scatterers is changed in the resolution cell. Therefore, individual resolution differences in mean clutter strength would be expected to change with changing polarization, as would the one-sigma variation of resolution differences with polarization over many experiments. Indeed, significant differences are observed in the one-sigma ranges of variation in Table 3.10, between vertical and horizontal polarization in each band. However, in changing polarization, if there were a constant small calibration offset with range resolution, it would be the same at vertical or horizontal polarization. Indeed, in Table 3.10, medianized differences with resolution are observed to be very nearly the same at vertical and horizontal polarization in each band. If, therefore, these differences are taken as relative calibration offsets, essentially no offset is observed at X-band, plus and minus 1-dB offsets are observed at L- and S-bands, respectively, and 1.4- and 2-dB offsets are observed at UHF and VHF, respectively. In this presumed equivalence of median difference with resolution to calibration offset, it is relative calibration that is being considered—i.e., on the average over many measurements, no difference with pulse length is expected. Now consider again the one-sigma range of variations of differences in mean strength with resolution, shown in parentheses in Table 3.10. Although relatively randomly differing between vertical and horizontal polarization in each frequency band, there is no trend with frequency, unlike the previous corresponding variations with polarization in Table 3.8 where larger differences occurred at lower frequencies. Overall, in Table 3.10, the one-sigma range of variation in mean strength between Phase One range resolutions, i.e., 150 m vs 15/36 m, indicative of the phasing in and out of several dominant discrete scatterers per cell, is ≈2 dB in each band. This result illustrates from another perspective that low-angle clutter contains discretes of stable phase and the extent to which a few such interfering discretes per resolution cell often occur. Cells containing many randomly phased contributors would not show such one-sigma differences with resolution. Next, all of the differences in mean strength with resolution are combined across all repeat sectors, including all bands and both polarizations, in one histogram, as shown in Figure 3.43. The corresponding cumulative distribution is shown in Figure 3.44. The overall mean and median differences in this distribution are 0.81 and 0.85 dB, respectively; but these small numbers may be less significant than the corresponding specific numbers by frequency band just discussed. General differences by terrain type in the tails of these distributions are now discussed. There is a predominance of farmland sites in these tails, and a lack of woodland sites, which tends to support previous arguments that resolution differences are caused by dominant cells containing several interfering discretes. There is only one clear exception to this, where a purely forested site with no qualifying second- and third-order classifiers appears only once—namely, Puskwaskau, with a –4.15-dB resolution difference, 15-m result minus 150-m result, at L-band and horizontal polarization—within the most extreme 15 measurements in either tail. In contrast, in the center of the distribution where differences with resolution are small, the sites are predominantly forested. For example, over the 12 measurements where absolute differences in mean strength with resolution were ≤ 0.1 dB, eight came from forested sites, one from grassland, and one from desert (all with relatively fewer discretes) and only two from agricultural sites (both Beiseker, with

Repeat Sector Clutter Measurements 219

more discretes). Probabilities of occurrence of differences in mean strength with Phase One resolution, 15/36 m vs 150 m, across the complete repeat sector database may be quantified from Figure 3.44. For example, 79% of measurements had differences within the 2.16-dB one-sigma range of variation about the mean difference.

15 Difference (dB)

413 differences in mean clutter strength with range resolution, high-low (all frequencies VHF, UHF, L-, S-, X-Band; both polarizations VV and HH)

Median = +0.85 Mean = +0.81 1σ = 2.16

Percent

10

High Range Resolution = 15 m at L-, S-, X-Bands; = 36 m at VHF, UHF Low Resolution = 150 m

5

0 –15

–10

–5

0

5

10

15

Difference in Mean Clutter Strength with Range Resolution, High-Low (dB)

Figure 3.43 Histogram of differences in mean ground clutter strength with range resolution, high-low. Phase One repeat sector data. All site visits, all five radar frequencies, both polarizations.

Pursuing the general observation that discrete-dominated farmland terrain shows greater variation in mean clutter strength with resolution than does more homogeneous forest terrain, the repeat sector mean strength data are now reduced to show differences with resolution by terrain class. The results are shown in Table 3.11. Recall that little meaning can be ascribed to average differences in mean clutter strength with pulse length, but that larger standard deviations of these differences are expected in discrete-dominated terrain where a few major scatterers per resolution cell might provide returns that are voltage additive and which, therefore, could sum differently for different cell sizes. Indeed, Table 3.11 illustrates relatively large standard deviations of differences with resolution for urban terrain and agricultural terrain (especially very low-relief agricultural terrain, namely,

220 Repeat Sector Clutter Measurements

413 differences in mean clutter strength with range resolution, high-low (all frequencies,VHF, UHF, L-, S-, X-Band; both polarizations, VV and HH)

0.999

Probability That Difference in Mean Clutter Strength, High-Low ≤ Abscissa

0.99

0.9

Difference (dB) Median = +0.85 Mean = +0.81 1σ = 2.16

0.7 0.5 0.3

0.1

0.01 High Range Resolution = 15 m at L-, S-, X-Bands; = 36 m at VHF, UHF Low Range Resolution = 150 m

0.001

0.0001 –12

–10

–8

–6

–4

–2

0

2

4

6

8

10

12

Difference in Mean Clutter Strength with Range Resolution, High-Low (dB)

Figure 3.44 Cumulative distribution of differences in mean ground clutter strength with range resolution, high-low. Phase One repeat sector data. All site visits, all five radar frequencies, both polarizations.

3.41 dB). Both terrain types, urban and agricultural, are obviously dominated by cultural (i.e., man-made) discrete clutter sources. In addition, a large value of standard deviation of differences in mean strength with resolution for desert, marsh, or grassland at low depression angle (i.e., Knolls and Big Grass Marsh), namely, 3.32 dB, is seen in Table 3.11. It has been stated that this terrain class is discrete-free, but this simply means free of the large cultural discretes that dominate farmland. The result of Table 3.11 indicates that for radiation skimming at grazing incidence over the desert at Knolls or the frozen wetland at Big Grass Marsh, the backscatter is also, perhaps not unsurprisingly, dominated by

Repeat Sector Clutter Measurements 221

discretes (i.e., voltage-additive situations); where here the discretes are minor variations in microtopography (i.e., small hillocks and hummocks) in the desert and marsh terrain. That is, at grazing incidence, ground clutter is grainy; discretes can be large (i.e., water tower) or small (e.g., hillock), but whatever rises above the mean plane of the surface becomes the localized source of the backscatter. Note that, as depression angle changes from low to high for desert, marsh, or grassland in Table 3.11, the standard deviation of differences in mean strength with resolution abruptly drops from 3.32 dB to 1.12 dB, indicating that the desert, marsh, or grassland floor stops being grainy and becomes much more homogeneous as the depression angle rises from grazing incidence to 1° or 2°. Also, forested terrain is expected to be less discrete-dominated than urban or farmland terrain, and indeed, generally smaller standard deviations of differences in mean strength with resolution are observed in forest (and in mountains, which are primarily forest covered) than in urban or agricultural terrain in Table 3.11. In addition, these standard deviations of differences are significantly lower in high-relief forest (higher slopes, more homogeneous) than in low-relief forest. Table 3.11 Differences in Mean Clutter Strength with Phase One Range Resolution, HIgh-Low, by Terrain Type

Difference (dB) in Mean Clutter Strength with Pulse Length 15/36 m – 150 m Terrain Type Median

Mean

Standard Deviation

Urban

0.8

0.9

2.1

Mountain

0.9

0.8

1.5

Forest/High-Relief High Depression Angle Low Depression Angle

0.1 1.3

0.2 1.0

1.2 1.6

Forest/Low-Relief High Depression Angle Intermediate Depression Angle Low Depression Angle

0.0 1.1 1.1

0.4 1.2 1.2

2.0 1.8 1.9

Agricultural/High-Relief

2.0

1.5

2.9

Agricultural/Low-Relief Moderately Low-Relief Very Low-Relief

–0.5 1.3

–0.2 1.0

2.0 3.4

Desert, Marsh, or Grassland (Few Discretes) High Depression Angle Low Depression Angle

0.6 1.8

0.6 1.8

1.1 3.3

Notes: Repeat sector data. All sites, all five frequencies, both polarizations.

222 Repeat Sector Clutter Measurements

3.6 Higher Moments and Percentiles in Measured Land Clutter Spatial Amplitude Distributions The subject matter of Chapter 3 is multifrequency low-angle land clutter amplitude distributions as measured from large, repeat sector, spatial macroregions of visible terrain. Previously, the mean levels (i.e., first moments) in these distributions have been under discussion. Here, in Section 3.6, the repeat sector clutter distributions are brought under more complete description by numerically specifying their higher moments, namely, the ratio of standard deviation-to-mean (which is a normalized measure of the second moment), the coefficient of skewness (or normalized third moment), and the coefficient of kurtosis (or normalized fourth moment), and several particular percentile levels in them, namely, the 50- (or median), 70-, and 90-percentile levels. These six statistical attributes are defined in Appendix 2.C. Each of them is provided as a median value of the particular attribute over a number of repeat sectors and measurements by frequency band within the same terrain groups as in Table 3.6. Thus, these higher moments and percentiles are generalized (i.e., central) values by terrain class and radar frequency band. Whereas the means of the clutter amplitude distributions are largely independent of resolution, the spreads in these distributions are fundamentally dependent on radar spatial resolution. As a result, all of the higher attributes presented in this section depend strongly on resolution. Therefore, in what follows, the generalized results by terrain class for higher moments and percentiles are separated, in different tables, between those applicable for the wide pulse (i.e., 150 m) and those applicable for the narrow pulse (i.e., 15 m at L-, S-, and X-bands; 36 m at VHF and UHF). In these tables, the variations with range resolution are observable by comparing and contrasting between pairs of tables, and the essential variations with azimuth resolution are observable by comparing and contrasting between different frequency bands in any given table. Many of the trends with resolution in these tables by terrain type and depression angle are carried over into the clutter models developed in Chapters 4 and 5. The medianized results by terrain class for skewness, kurtosis, and 50-, 70-, and 90percentiles presented in Section 3.6 are obtained somewhat differently than are the similar generalized results for means and standard deviations. The fundamental difference is that the repeat sector results for higher moments and percentiles are medianized over all the repeat sector experiments, including the day-to-day repeats of which there are nominally four per experiment; whereas, the results for mean and standard deviation are medianized over a selected subset in which only a single, centrally selected (best) experiment from each set of day-to-day repeats is included. To the extent that the repeated experiments repeat exactly (usually, a good approximation), the statistics do not change.

3.6.1 Ratio of Standard Deviation-to-Mean Values for ratios of standard deviation-to-mean in repeat sector ground clutter amplitude distributions at all Phase One measurement sites are plotted in Figures 3.45 and 3.46 for urban sites and rural sites, respectively. For each repeat sector, values are plotted for each of the 20 combinations in the radar parameter matrix (i.e., five frequencies, two polarizations, two resolutions). In Figures 3.45 and 3.46, very large values of ratio of standard deviationto-mean are generally observed in both urban and rural terrain, resulting from the long

Repeat Sector Clutter Measurements 223

high-side tail in these amplitude distributions caused by isolated strong returns from discrete sources over a wide range of amplitudes. In particular, in the urban data of Figure 3.45 at X-band, there is a clear-cut separation between narrow pulse and wide pulse results such that the narrow pulse data have much higher spreads than the wide pulse data; in the lower frequency bands there remains relatively good separation (i.e., little overlap) between narrow pulse and wide pulse results. Spreads in the urban data, as given by ratio of standard deviation-to-mean, are never less than ≈5 dB in Figure 3.45. 16

Range Pol. Res. (m) 150 H 150 V 15/36 H 15/36 V

14

Ratio of SD/Mean (dB)

12

10

8

100

1,000

10,000

6

4 VHF

UHF

L-

S-

X-Band

Frequency (MHz)

Figure 3.45 Ratio of standard deviation-to-mean in clutter amplitude distributions at five urban sites. Five-frequency repeat sector data.

Maximum spreads in the rural data in Figure 3.46 can be approximately as large as in the urban data. The average spreads in the rural data are less than in the urban data, but minimum observed spreads in the rural data are much less than in urban data, and in a number of measurements, approach values close to unity (i.e., ratios of standard deviationto-mean near zero dB) indicative of Rayleigh statistics.

224 Repeat Sector Clutter Measurements

15.5

13.5

Range Pol. Res. (m) 150 150 15/36 15/36

H V H V

11.5

Ratio of SD/Mean (dB)

9.5

7.5

5.5

3.5

100

1,000

10,000

1.5

–0.5 VHF

UHF

L-

S-

X-Band

Frequency (MHz)

Figure 3.46 Ratio of standard deviation-to-mean in clutter amplitude distributions at 37 rural sites. Five-frequency repeat sector data.

Figures 3.45 and 3.46 separate the measured values of ratio of standard deviation-to-mean into only two terrain types, urban and rural. These values are next separated within the total 12-category set of terrain types as given by Table 3.3. Tables 3.12 and 3.13 show ratios of

Repeat Sector Clutter Measurements 225

standard deviation-to-mean for ground clutter spatial amplitude distributions, by frequency band in all 12 terrain classes, for the Phase One wide pulse and narrow pulse, respectively. These numbers are medianized and, hence, generalized from groups of repeat sector measurements with a variable number of measurements in each group. Measurements at both polarizations are included in these groups. Table 3.12 Median Values of Ratio of Standard Deviation-to-Mean in Ground Clutter Amplitude Distributions over Many Repeat Sector Measurements by Terrain Type for the Phase One Low Range Resolution Waveform* Median Value of SD/Mean (dB) Frequency Band

Terrain Type VHF

UHF

L-Band

S-Band

X-Band

Urban

5.7

7.6

7.7

9.5

8.7

Mountains

2.7

4.1

3.4

4.5

3.6

Forest/High-Relief (Terrain Slopes > 2 °) High Depression Angle ( > 1°) Low Depression Angle ( ≤ 0.2 °)

2.9 5.0

3.1 5.3

4.2 4.3

4.6 2.1

4.3 4.8

3.5 2.9

3.7 4.3

3.6 4.2

3.5 4.7

3.8 4.6

5.3

3.7

4.6

5.2

4.6

4.9

5.8

6.1

6.4

7.1

5.8

5.5

7.4

6.7

5.8

4.4

6.7

7.7

9.3

6.7

3.8 1.7

5.7 2.7

5.6 5.9

2.2 7.2

0.9 4.6

Forest/Low-Relief (Terrain Slopes < 2°) High Depression Angle ( > 1°) Intermediate Depression Angle (0.4 ° to 1°) Low Depression Angle ( ≤ 0.3 °) Agricultural/High-Relief (Terrain Slopes > 2 °) Agricultural/Low-Relief Moderately Low-Relief (1°< Terrain Slopes < 2 °) Very Low-Relief (Terrain Slopes <1°) Desert, Marsh, or Grassland (Few Discretes) High Depression Angle ( ≥1°) Low Depression Angle ( ≤ 0.3 °) *Low range resolution = 150 m.

The ratio of standard deviation-to-mean is the fundamental statistical measure of spread (or statistical dispersion) in the distribution. When the ratio is equal to unity, it is indicative of Rayleigh statistics. Most of the results in Tables 3.12 and 3.13 are considerably greater than unity, indicating that extreme cell-to-cell variability exists in low-angle ground clutter statistics. This variability occurs because, at angles near grazing incidence, returns are

226 Repeat Sector Clutter Measurements

Table 3.13 Median Values of Ratio of Standard Deviation-to-Mean in Ground Clutter Amplitude Distribution over Many Repeat Sector Measurements by Terrain Type for the Phase One High Range Resolution Waveform* Median Value of SD/Mean (dB) Terrain Type

Frequency Band VHF

UHF

Urban

8.7

10.3

10.7

14.1

12.5

Mountains

3.4

5.4

2.8

4.0

4.1

Forest/High-Relief (Terrain Slopes > 2 °) High Depression Angle ( > 1°) Low Depression Angle ( ≤ 0.2 °)

4.2 5.5

4.3 5.5

6.1 4.2

7.3 2.7

6.7 5.4

2.8 3.6

5.2 5.6

3.9 6.0

4.7 6.5

5.4 6.1

6.1

4.5

8.3

7.6

6.6

5.8

7.4

8.6

—

9.3

7.5

7.9

9.7

8.3

7.2

5.1

8.6

11.1

13.6

10.4

5.5 1.6

8.2 3.5

9.2 1.7

3.7 11.6

1.7 7.3

Forest/Low-Relief (Terrain Slopes < 2°) High Depression Angle ( > 1°) Intermediate Depression Angle (0.4 ° to 1°) Low Depression Angle ( ≤ 0.3 °) Agricultural/High-Relief (Terrain Slopes > 2 °) Agricultural/Low-Relief Moderately Low-Relief (1°< Terrain Slopes < 2 °) Very Low-Relief (Terrain Slopes <1°) Desert, Marsh, or Grassland (Few Discretes) High Depression Angle ( ≥1°) Low Depression Angle ( ≤ 0.3 °)

L-Band S-Band X-Band

* High range resolution = 15 m at L-, S-, and X-bands, and = 36 m at VHF and UHF.

measured over a wide range of strengths from all of the vertical features rising above the mean elevation of the clutter patch. The underlying trends observed in Tables 3.12 and 3.13 are as follows. A comparison of Tables 3.12 and 3.13 shows that the ratio of standard deviation-to-mean usually increases with increasing range resolution. In either table, a weak trend is observed where the ratio of standard deviation-to-mean tends to increase as azimuth beamwidth decreases from VHF to X-band (e.g., agricultural/high-relief; marsh/low depression angle). For a given spatial resolution (i.e., for a given frequency band in either table), the ratio of standard deviationto-mean usually decreases with increasing depression angle. Large ratios of standard deviation-to-mean are observed in urban and agricultural terrain because these terrain types are dominated by discrete objects; smaller ratios occur in forest, particularly at high angles,

Repeat Sector Clutter Measurements 227

and in mountains, where steep forested slopes also prevail. As angle of illumination increases in forested terrain, the phenomenon gradually transitions from a widespread Weibull regime towards a more narrowly-spread Rayleigh regime. It is evident that these observed trends in ratios of standard deviation-to-mean in Tables 3.12 and 3.13 are less well defined than the trends in mean strength previously discussed. The more comprehensive Phase One survey data considered in Chapter 5 provide improved accuracy of such observed second-moment trends.

3.6.2 Skewness and Kurtosis The coefficients of skewness and kurtosis are normalized measures of the third and fourth central moments, respectively, of any distribution (see Appendix 2.C). Skewness is a measure of asymmetry in the distribution. Kurtosis is a measure of concentration about the mean. General values of skewness for the measured low-angle ground clutter amplitude distributions for the low and high range resolution waveforms are given in Tables 3.14 and 3.15, respectively. Corresponding values of kurtosis are given in Tables 3.16 and 3.17. All these values in Tables 3.14–3.17 are medianized over groups of individual repeat sector measurements within each of the 12 general terrain classes for each radar frequency band. The number of different repeat sectors in each group is shown in Table 3.3. Measurements at both vertical and horizontal polarizations are included. These higher moments can be of particular interest to theoretical workers in ground clutter who treat clutter as a correlated noise process. Such workers may model the process, for example, such that the scatterers follow a correlated Gamma distribution. Then the clutter amplitude returns are K-distributed (see Appendix 5.A). The K-distribution has built into it the mechanisms to handle the correlation physics of the underlying phenomenon [3]. This is in contrast to the approach taken here of providing empirical descriptions of these distributions and their important observed parametric dependencies. The way higher moments are often used in theoretical studies is as follows. Any measured amplitude distribution can be normalized to have zero mean (by subtracting the actual mean from each sample) and unity standard deviation (by dividing each sample by the actual standard deviation). It is then straightforward to match mean and standard deviation of the measured normalized distribution to appropriate analytic distributions such as Weibull, lognormal, or K-. The goodness-of-fit then depends on how well the higher moments follow the match. Such theoretical studies into clutter correlation are thus based on the behavior of third and fourth moments. Clutter correlation is important to radar detection performance. For example, false alarm rates can rise dramatically in spatially correlated clutter as opposed to uncorrelated clutter with the same amplitude distribution [4]. Rayleigh statistics may be taken as a point-of-departure in interpreting coefficients of skewness and kurtosis. For Rayleigh statistics, skewness = 2 (or 3.01 dB) and kurtosis = 9 (or 9.54 dB). The numbers in Tables 3.14–3.17 usually show skewness and kurtosis to be considerably greater than Rayleigh, a consequence of the widely dispersed high-side tail caused by the fundamental discrete and spiky nature of low-angle clutter. As with ratio of standard deviation-to-mean, where more Rayleigh-like conditions would be expected—for example, with increasing illumination angle in forest—these numbers tend to be smaller; and where a more discrete-dominated spiky process would be expected—for example, at low angles in agricultural terrain or in urban terrain—these numbers tend to be larger. A strong

228 Repeat Sector Clutter Measurements

Table 3.14 Median Values of Skewness over All Repeat Sector Measurements by Terrain Type for the Low Resolution Waveform* Median Value of Skewness (dB) Terrain Type

Frequency Band VHF

UHF

L-Band

S-Band

X-Band

Urban

6.9

8.9

9.8

12.7

11.1

Mountains

2.9

4.4

5.5

5.6

6.1

Forest/High-Relief High Depression Angle Low Depression Angle

6.6 6.1

6.5 6.1

9.3 7.8

9.6 8.5

9.9 7.3

Forest/Low-Relief High Depression Angle Intermediate Depression Angle Low Depression Angle

6.5 5.3 6.3

5.1 7.9 5.7

6.1 7.7 7.0

6.9 9.0 7.8

7.9 8.2 8.1

Agricultural/High-Relief

7.2

8.0

10.0

11.8

11.4

Agricultural/Low-Relief Moderately Low-Relief Very Low-Relief

8.1 6.9

7.2 8.8

9.5 10.1

11.0 10.6

9.7 11.1

5.4 4.2

8.2 5.0

8.7 12.4

5.8 11.1

4.1 7.9

Desert, Marsh, or Grassland (Few Discretes) High Depression Angle Low Depression Angle * Low range resolution = 150 m.

dependence is seen on range resolution, where the numbers are larger for higher resolution. The observed tendency of the skewness and kurtosis numbers to increase with increasing radar frequency is due to the decreasing azimuth beamwidth with increasing frequency. The observed skewness and kurtosis numbers for mountains at VHF and low range resolution (viz., 2.9 dB and 7.9 dB, respectively) are relatively close to Rayleigh. Ratios of standard deviation-to-mean and ratios of percentile levels also indicate statistics approaching Rayleigh in this situation. The reason for this is that, in looking at mountains, the radar is looking predominantly at steeply forested slopes under full illumination. In addition, low range resolution and VHF reduces the spatial resolution to the minimum available within the Phase One radar parameter matrix, thus providing more scatterers in each cell and giving Rayleigh statistics a better chance for realization.

3.6.3 Fifty-, 70-, and 90-Percentile Levels Central (medianized) values of 50-, 70-, and 90-percentile levels in the measured lowangle ground clutter amplitude distributions for the low and high range resolution waveforms are given in Tables 3.18 and 3.19, respectively. These numbers are medianized over groups of individual repeat sector measurements within each of the 12 general terrain classes (see Table 3.3) for each radar frequency band. These results were obtained

Repeat Sector Clutter Measurements 229

Table 3.15 Median Values of Skewness over All Repeat Sector Measurements by Terrain Type for the High Resolution Waveform* Median Value of Skewness (dB) Frequency Band

Terrain Type VHF

UHF

L-Band

S-Band

X-Band

10.6

12.5

13.2

16.6

16.0

Mountains

5.7

8.1

7.1

9.8

7.5

Forest/High-Relief High Depression Angle Low Depression Angle

8.9 7.2

8.6 7.8

11.7 10.7

14.2 12.3

14.8 10.0

Forest/Low-Relief High Depression Angle Intermediate Depression Angle Low Depression Angle

6.8 6.8 9.2

8.4 9.6 7.9

8.5 10.2 9.7

9.6 11.3 10.8

11.9 10.6 11.6

Agricultural/High-Relief

9.4

9.9

13.0

—

15.6

Agricultural/Low-Relief Moderately Low-Relief Very Low-Relief

9.4 7.9

11.7 10.6

13.6 13.4

13.4 15.4

13.0 15.6

Desert, Marsh, or Grassland (Few Discretes) High Depression Angle Low Depression Angle

8.1 5.8

10.0 8.0

14.0 22.4

19.3 16.2

7.7 10.8

Urban

* High range resolution = 15 m at L-, S-, and X-bands, and = 36 m at VHF and UHF.

including measurements at both vertical and horizontal polarizations and day-to-day repeated measurements. The 50-percentile level is the median level in the distribution. Percentile level is defined in Appendix 2.C. These percentile levels provide additional information describing the clutter amplitude distributions over and above that provided by the moments. In particular, they provide a simple direct way of envisioning the shape of the histogram, at least at three specific points. To interpret the results in terms of departure from Rayleigh statistics, it is necessary to know that for Rayleigh statistics, the ratios of 90- to 50-percentile, 70- to 50-percentile, and mean-to-median are 5.2, 2.4, and 1.6 dB, respectively. Although indications of the same trends are vaguely discernible in the percentile level numbers of Tables 3.18 and 3.19 as were observed previously in the moments, the percentile level numbers provide less well defined trends than the moment numbers. It is evident that if one were to work with median clutter strengths instead of means, one would not be able to show trends with terrain type, relief, depression angle, and frequency as clear-cut, smooth, and converged as are the trends with means. The reason for this is that any percentile level, in contrast to a moment, is just a threshold at one particular level of strength indicating relative proportions in numbers of samples above and below the

230 Repeat Sector Clutter Measurements

Table 3.16 Median Values of Kurtosis over All Repeat Sector Measurements by Terrain Type for the Low Resolution Waveform* Median Value of Kurtosis (dB) Frequency Band

Terrain Type VHF

UHF

L-Band

S-Band

X-Band

14.3

18.1

20.3

25.5

23.0

7.9

10.8

12.3

13.2

13.9

Forest/High-Relief High Depression Angle Low Depression Angle

14.4 13.4

15.2 13.4

20.2 17.1

21.0 18.5

21.8 16.2

Forest/Low-Relief High Depression Angle Intermediate Depression Angle Low Depression Angle

13.8 11.9 13.8

11.2 17.0 13.0

13.7 17.2 15.1

15.5 20.0 17.3

17.7 18.5 18.2

Agricultural/High-Relief

15.2

17.0

20.9

25.4

24.0

Agricultural/Low-Relief Moderately Low-Relief Very Low-Relief

17.0 14.9

15.4 18.2

19.6 21.0

22.9 21.7

21.0 23.3

Desert, Marsh, or Grassland (Few Discretes) High Depression Angle Low Depression Angle

11.7 10.7

17.0 11.8

18.4 27.8

13.6 23.2

11.1 17.6

Urban Mountains

* Low range resolution = 150 m.

threshold, but unweighted by the actual values of the samples. Thus, the percentile levels are illustrative but less statistically meaningful than the moments. Nevertheless, there is a great deal of additional specific information bound up in the numbers of Tables 3.18 and 3.19. For example, showing these three percentile level numbers together as a triad for each combination of frequency and terrain type illustrates again the extreme range of variability that exists in low-angle ground clutter spatial amplitude distributions. These triads of numbers typically range over 20 dB in Tables 3.18 and 3.19—i.e., clutter is not well represented as a constant-σ° phenomenon. Mean clutter strengths in Table 3.6 are usually much greater than median clutter strengths in Tables 3.18 and 3.19, often by as much as 20 dB or so. For Rayleigh statistics, the meanto-median ratio is 1.6 dB. The observed large mean-to-median ratios are another indication of large spread in the low-angle clutter amplitude distributions. Often, in Tables 3.18 and 3.19, it is the 90-percentile levels that are closest to the means, occasionally the 70percentile levels. One exceptional situation where the mean is very nearly equal to the median at both low and high range resolution is for the desert, marsh, or grassland terrain class at high depression angle and X-band. It was indicated earlier that the X-band mean level of this terrain class was unusual in that it was much higher than at the other

Repeat Sector Clutter Measurements 231

Table 3.17 Median Values of Kurtosis over All Repeat Sector Measurements by Terrain Type for the High Resolution Waveform* Median Value of Kurtosis (dB) Frequency Band

Terrain Type VHF

UHF

L-Band

S-Band

X-Band

Urban

21.5

25.3

27.3

33.9

32.7

Mountains

13.8

17.5

16.4

21.4

17.2

Forest/High-Relief High Depression Angle Low Depression Angle

19.0 15.8

18.6 16.8

25.2 22.9

29.7 26.3

31.4 21.4

Forest/Low-Relief High Depression Angle Intermediate Depression Angle Low Depression Angle

14.8 15.2 19.1

17.8 20.5 16.6

19.0 22.5 20.5

20.9 24.7 23.6

26.0 23.7 25.6

Agricultural/High-Relief

20.0

21.0

27.3

—

32.9

Agricultural/Low-Relief Moderately Low-Relief Very Low-Relief

20.1 17.2

24.2 21.8

28.5 27.4

28.6 31.2

28.1 32.1

Desert, Marsh, or Grassland (Few Discretes) High Depression Angle Low Depression Angle

17.6 13.9

21.1 18.6

29.5 45.5

40.6 34.6

18.4 24.2

* High range resolution = 15 m at L-, S-, and X-bands, and = 36 m at VHF and UHF.

frequencies and nearly matched low-relief forest at high depression angle (i.e., at X-band, looking down at low-relief forest is like looking down at desert vegetation or grassland). Another exceptional situation where the mean is close to the median is again for the desert, marsh, or grassland terrain class, this time at low depression angle at VHF, UHF, and Lband, particularly at high range resolution.

3.7 Effects of Weather and Season Preceding general information has been provided in Chapter 3 showing how the mean strength of ground clutter varies with radar frequency for various terrain types. Although specific seasonal variations in measurements at Gull Lake West (Sections 3.2.2.2 and 3.4.1.3.4), Brazeau (Section 3.4.1.3.3), and Beiseker (Section 3.4.1.4.2) were discussed, no mechanism was included for taking into account the effects of weather and season in the resultant generalized information, obtained by combining measurements from similar sites in whatever conditions of weather and season those measurements happened to be made. Are there important trends in the Phase One clutter measurements as a result of weather-related or seasonal change? What are the ranges of variability or error bounds in the modeling information presented as a result of effects of weather and season?

Table 3.18 Median Values of 50-, 70-, and 90-Percentile Levels in Ground Clutter Amplitude Distributions over All Repeat Sector Measurements by Terrain Type for the Phase One Low Range Resolution Waveform* Median Value of 50-, 70-, and 90-Percentiles (dB) Frequency Band

Terrain Type VHF Urban Mountains

UHF

L-Band

S-Band

X-Band

– 43, – 37, – 28

– 38.5, – 32.5, – 21.5

– 32, – 26, – 14.5

– 44, – 32, – 17

– 41, – 32, – 15

– 14, – 9, – 3

– 18, – 13, – 8

– 22, – 18, – 12.5

– 27, – 20, – 14

– 35, – 24, – 16

– 16, – 12, – 7

– 22.5, – 17, – 12

– 24.5, – 20, – 14.5

– 30, – 24, – 18

– 27, – 22, – 16

– 29, – 25, – 21

– 29, – 22, – 13

– 28, – 24, – 18

– 33, – 26, – 20

– 33, – 26.5, – 21

– 21, – 16.5, – 10.5

– 25, – 19, – 10

– 27, – 23, – 17

– 36, – 31, – 25

– 33, – 28.5, – 23

– 37, – 29, – 23

– 42, – 33, – 25

– 42, – 31, – 25

– 48, – 37, – 28.5

– 44, – 34.5, – 26.5

–52, –49, –44

– 55, – 48.5, – 40

– 59, – 52, – 41

– 54, – 47, – 36.5

– 45, – 38, – 31

– 44, – 39, – 30

– 41, – 36, – 28.5

– 41, – 34.5, – 27

-43.5, -37.5, -31.5

– 40.5, – 36, – 26

– 52, – 45, – 29

– 49, – 39, – 27

– 48.5, – 40, – 30

– 385, – 32.5, – 25

– 68, – 64, – 56

– 60, – 51, – 41

– 55, – 45, – 35

– 65, – 59, – 45

– 49, – 41, – 30

– 47, – 41.5, – 34

– 58, – 50, – 39.5

– 51.5, – 46.5, – 36.5

– 40, – 36.5, – 32

– 25, – 23, – 20

– 72, – 69, – 65

– 78.5, – 75, – 70

– 75, – 71.5, – 66.5

– 63, – 55.5, – 47

– 47, – 43.5, – 38

Forest/High-Relief (Terrain Slopes > 2°) High Depression Angle (> 1°) Low Depression Angle (≤ 0.2 °) Forest/Low-Relief (Terrain Slopes < 2°) High Depression Angle (> 1°) Intermediate Depression Angle (0.4° to 1°) Low Depression Angle (≤ 0.3 °) Agricultural/High-Relief (Terrain Slopes > 2°) Agricultural/Low-Relief Moderately Low-Relief (1°< Terrain Slopes < 2 °)

– 48.5, – 40.5, – 29.5

Very Low-Relief (Terrain Slopes < 1°) Desert, Marsh, or Grassland (Few Discretes) High Depression Angle (≥ 1°) Low Depression Angle (≤ 0.3 °) *Low range resolution = 150 m.

Table 3.19 Median Value of 50-, 70-, and 90-Percentile Levels in Ground Clutter Amplitude Distributions over All Repeat Sector Measurements by Terrain Type for the Phase One High Range Resolution Waveform* Median Value of 50-, 70-, and 90-Percentiles (dB) Frequency Band

Terrain Type VHF Urban Mountains

UHF

L-Band

S-Band

X-Band

–45, –39, –31.5

–46, –38, –23

–40, –33, –18

–39.5, –34, –24.5

–33, –30, –24

–13, –9, –2

–16, –12, –5.5

–28, –18.5, –12

–40, –27.5, –18.5

–36.5, –25, –16.5

Forest/High-Relief (Terrain Slopes > 2°) High Depression Angle (> 1°) Low Depression Angle (≤ 0.2 °)

–15, –11, –5

–26, –20.5, –13

–25.5, –20, –14.5

–34, –28, –21

–29, –23, –16.5

–27, –23, –15.5

–26, –20, –12.5

–29, –24, –18

–38, –30, –22

–37, –29, –21

Forest/Low-Relief (Terrain Slopes < 2°) High Depression Angle (> 1°) Intermediate Depression Angle

–18, –13, –6

–24, –19, –10.5

–28, –23, –17

–39, –33, –27

–35, –29, –23

–35, –29, –22

–42, –32, –23

–43, –31, –24

–49, –39, –29.5

–45, –37, –27

–52, –49, –44

–64, –56, –46

–58, –52.5, –44

–62, –56.5, –43.5

–59, –51, –36

–38.5, –34.5, –28

–44, –39, –29.5

–41, –36, –25

–47, –41, –31

–53, –46, –33

–51, –43, –30

–55, –46, –33

–45.5, –35.5, –26

–59, –56, –51

–62.5, –52, –40.5

–57, –50, –37

–63, –59, –54

–54, –46, –34

–49, –45, –38

–59.5, –54.5, –44.5

–48.5, –44.5, –38

–42.5, –39.5, –34

–27.5, –24, –20

–65, –62.5, –59

–74.5, –72.5, –68

–66.5, –62.5, –58

–63.5, –60, –53.5

–49, –45, –39

(0.4° to 1°) Low Depression Angle (≤ 0.3 °) Agricultural/High-Relief (Terrain Slopes > 2°)

—

–44, –37.5, –29

Agricultural/Low-Relief Moderately Low-Relief (1°< Terrain Slopes < 2 °) Very Low-Relief (Terrain Slopes < 1°) Desert, Marsh, or Grassland (Few Discretes) High Depression Angle (≥ 1°) Low Depression Angle (≤ 0.3 °)

* High range resolution = 15 m at L-, S-, and X-bands, and = 36 m at VHF and UHF.

234 Repeat Sector Clutter Measurements

No significant trends with weather or season are observable in the Phase Zero (see Section 2.4.6) or Phase One clutter data. Reflect on why this is so. In preceding discussions, the importance of spatially localized or discrete sources in low-angle clutter statistics was emphasized. Many of the measurement sites were on low-relief prairie farmland in western Canada. At the beginning of the program, for example, when standing in an Alberta wheat field and seeing nothing but wheat to far horizons, clutter modeling was thought of in terms of dielectric constant of wheat, moisture content of soil, and fields high in mature wheat vs harvested fields in stubble vs plowed fields and snow-covered fields, all of which led to an expectation of significant seasonal variations in clutter strength. Vertical discrete objects were not considered to be of foremost importance because, visually, they seemed relatively sparse. It turned out that when radar measurements were subsequently made at such sites to ranges of 25 or 50 km or more, the incidence of discrete sources was large and their effect was dominant. In the early days of radar, general acceptance of the idea that “angels” (i.e., nonzero Doppler echos) were caused by birds came slowly because there did not appear to be that many birds; but over hundreds and thousands of square kilometers of radar coverage, there can be enormous numbers of birds to account for angels. Similarly, there are enormous numbers of stationary discrete or localized vertical scattering features dominating zeroDoppler ground clutter statistics. Thus, it is not so much the wheat field itself as the fence around it, the road and telephone line through it, and occasional storage granaries or trees around ponds in it, that act as clutter sources. The dramatic seasonal variations that occur in the physical appearance of the surface of the wheat field have relatively little effect on the returned clutter statistics. The actual vertical sources tend to be there relatively unchanged, summer and winter. Thus, in general, little seasonal variation occurs in low-angle ground clutter strengths, generally on the order of 3 dB or so, with no noticeable trends. Tree lines are very common discrete clutter sources. A tree line within a large regional clutter patch contributes strong clutter cells to the overall patch amplitude distribution, independent of whether the trees happen to be in leaf or bare, or wet or dry. Weather-related and seasonal effects only cause minor variations in these strong contributions. Of more significance in the distributions is whether the tree line exists or not, or more generally, the relative incidence of occurrence of tree lines on landscapes. Chapter 2 provides information showing how clutter amplitude distributions vary with percent tree cover, which indicates that the dominant sources causing much of the wide spread typically observed in these distributions for agricultural terrain are isolated trees (see Section 2.4.2.5). Nevertheless, weather and season do act to introduce variation in ground clutter. What are the ranges of variability or error bounds in prediction caused by these changes? Sections 3.7.1 and 3.7.2 show the ranges of variability of mean clutter strength with weather and season, respectively, based on the repeat sector database of measurements. In these results, differences in Phase One repeat sector measurements in all five frequency bands, at both polarizations and at both range resolutions, are combined.

3.7.1 Diurnal Variability Elsewhere in this chapter it has been discussed that, in the repeat sector at each site, measurements were repeated a number of times during the Phase One radar’s time on site. One purpose of these repeated measurements was to indicate the variability in ground clutter that occurs due to changes in weather and other environmental factors. During the

Repeat Sector Clutter Measurements 235

measurement period at each site, weather conditions in the repeat sector were monitored and recorded. In general, little obvious correlation of changes in clutter statistics with changes in weather was observed. Thus, in what follows, all the day-to-day or diurnal differences in mean strength between repeated experiments are combined. The difference taken in each case is the absolute difference in decibels of a particular measurement from each of the other measurements in the set of repeated measurements at a given frequency, polarization, and resolution at that site. A histogram of all such diurnal differences in mean clutter strength from the repeat sector measurements is shown in Figure 3.47. Note that the ordinate is a logarithmic scale. All day-to-day differences are bound up in this histogram, including possible differences due to calibration variation, and minor differences due to variation of underlying system parameters that would not be expected to affect clutter strength (e.g., antenna step/scan vs continuous scan in azimuth, or high PRF vs low PRF). Day-to-day calibration consistency as shown by repeatability of returns from a discrete reference target of opportunity at each site was usually well within 1 dB. Differences due to variation of underlying system parameters have been shown to be very minor (see Section 3.C.4). Thus, when large differences occur in the histogram of Figure 3.47, they are caused by actual changes in the clutter patch being measured. As mentioned above, it is not attempted here to actually correlate or attribute these differences with changes in weather in a deterministic (causative) manner. Dynamic processes of change in landscape are complex. For example, should the change that was caused by a train crossing the flat Corinne farmland repeat sector during data taking be counted as legitimate? Most of the changes in the histogram are not due to such singular events and indeed are due to weather. However, it is more correct to associate the histogram with all environmental changes, including man-made and natural, and with all day-to-day system and calibration variations. The results of Figure 3.47 indicate that the most likely diurnal difference (i.e., the mode of the distribution) in mean clutter strength is 0.2 dB, the average difference is ≈1 dB (i.e., median difference = 0.8 dB, mean difference = 1.2 dB), and the one-sigma range of variability beyond the mean is to 2.5 dB (i.e., 84% of the day-to-day differences ≤ 2.5 dB). The tail of the distribution of day-to-day differences shows occasional (i.e., at a few onehundredths of 1% probability of occurrence) day-to-day differences near 10 dB, but some or all of these may be due to undetected measurement equipment malfunctions or singular events like train passings. It may be concluded that changes in clutter mean strength due to weather are usually relatively small.

3.7.2 Six Repeated Visits Results here are based on six seasonal revisits of the Phase One radar to four different sites. Three of these sites, Cochrane, Brazeau, and Gull Lake West, had one revisit each. Beiseker had three revisits. Some of the individual seasonal variations in mean strengths in these measurements were discussed in Sections 3.2 and 3.4. Here, the accumulation of all the differences in mean strength at these sites, as exist between seasonally different pairs of corresponding measurements, each pair at the same site, frequency, polarization, and resolution, are presented. Figure 3.48 shows the histogram formed from this accumulation of seasonal differences in mean strength. The difference taken in every case is the absolute difference in decibels

236 Repeat Sector Clutter Measurements

100 7152 Day-to-Day Differences in Mean Clutter Strength

Difference (dB) Mode = 0.2 Median = 0.8 Mean = 1.2 1σ = 1.3

Percent

10

1

0.1

0.01 0

2

4

6

8

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Figure 3.47 Histogram of diurnal differences in mean ground clutter strength. Phase One repeat sector data. All five radar frequencies, both polarizations, and both pulse lengths. All 49 site visits.

between the later and earlier measurements at a particular site at the same frequency, polarization, and resolution. As mentioned, Beiseker had three revisits. If differences are allowed for all combinations of Beiseker visit numbers, two at a time (viz., six), the Beiseker results would swamp out the results from the other sites. It is preferable that each Beiseker revisit count once, allowing the three revisits to Beiseker to count the same together as the three revisits to the Cochrane, Brazeau, and Gull Lake West sites. Thus, for Beiseker, it was arbitrarily determined to only include absolute differences of each subsequent visit from the first visit in the histogram of Figure 3.48. The results of Figure 3.48 for seasonal variation of mean clutter strength indicate that the most likely seasonal variation in mean clutter strength in the Phase One repeat sector measurements (i.e., the mode of the distribution) is 1.5 dB, the average variation is ≈2 dB (i.e., median difference = 1.8 dB, mean difference = 2.3 dB), and the one-sigma range of variability beyond the mean is to 4.1 dB (i.e., 84% of the seasonal differences ≤ 4.1 dB). This value of 4.1 dB is considerably larger than the corresponding value of 2.5 dB in the day-to-day variations, as would be expected. Even so, seasonal changes remain small

Repeat Sector Clutter Measurements 237

16

87 Seasonal Differences in Mean Clutter Strength at Four Phase One Sites Difference (dB)

13.5

Mode = 1.5 Median = 1.8 Mean = 2.3 1σ = 1.7

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6

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1 0

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Figure 3.48 Histogram of seasonal differences in mean ground clutter strength. Phase One repeat sector data. All five radar frequencies, both polarizations, and both pulse lengths. Sites are Cochrane, Brazeau, and Gull Lake West, two seasonal visits each; and Beiseker, four seasonal visits.

compared with the total range of variation of mean clutter strength shown in Figure 3.38. The maximum observed seasonal difference in Figure 3.48 is 8.1 dB from Gull Lake West. The maximum seasonal difference at Beiseker is 7.1 dB. For Beiseker alone, the seasonal differences across four visits are just slightly less than the corresponding differences in the four-site data of Figure 3.48. This indicates that seasonal variation is not too different from one site to another.

3.7.3 Temporal and Spatial Variation Figure 3.49 shows cumulative distributions of both diurnal and seasonal variations in mean clutter strength as measured by the Phase One radar. These data come from the histograms of Figures 3.47 and 3.48, respectively. Thus, the diurnal variations shown in Figure 3.49 are based on repeat sector measurements over the two- to three-week stay at every Phase One site. In Figure 3.48, 71% of diurnal variations, largely due to changes in weather, are less than 1.5 dB. The seasonal variations shown in Figure 3.48 are based on six repeated visits

238 Repeat Sector Clutter Measurements

Normal Scale

0.99

Probability That Variation in Mean Clutter Strength ≤ Abscissa

0.98 Day-to-Day Variations (42 Sites)

0.95 0.9 0.8 0.7 0.6 0.5 0.4

Seasonal Variations (Repeated visits to 4 sites)

0.3 0.2 0.1 71% of Variations are Less Than:

0.05 0.02

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0

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Figure 3.49 Diurnal and seasonal variability in mean ground clutter strength. Phase One repeat sector data. All five radar frequencies, both polarizations, and both pulse lengths. Cumulative distributions of data histogrammed in Figures 3.47 and 3.48.

by the Phase One equipment to four sites for the purpose of investigating seasonal variability. In Figure 3.49, 71% of seasonal variations are less than 3 dB. In the foregoing discussion (i.e., Figures 3.47, 3.48, and 3.49), diurnal and seasonal variability in mean clutter strength over repeat sectors are characterized by forming singlesided distributions of absolute values of differences between measurements. This is the natural thing to do when there are only two in the cluster of repeated measurements, for example, two seasonal repeats. When there are more than two in the cluster (e.g., four seasonal repeats at Beiseker), this approach provides all combinations of differences (e.g., six differences among the four Beiseker repeats, although only four were allowed) including the large difference between the two outliers. The resultant one-sided histogram of absolute values of differences is primarily characterized by the mean, median, and mode of the distribution. In particular, the standard deviation in this one-sided distribution is a secondary or relative attribute that gives the

Repeat Sector Clutter Measurements 239

range of variation about the mean difference but, unless quoted with the mean difference, by itself does not provide any absolute information on typically occurring diurnal or seasonal differences. These one-sided histograms are a very satisfactory way to show diurnal and seasonal differences. Even though the number of samples in them grows combinatorially with number of repeated measurements in the cluster (although restricted in the seasonal differences at Beiseker), they do include the difference between each measurement and every other measurement in the cluster (i.e., equal weight to every pair). Diurnal and seasonal variability in mean clutter strength over repeat sectors may also be characterized, not by forming single-sided distributions of absolute values of differences between measurements, but by forming two-sided distributions of differences of individual measurements from central values within groups of measurements of common frequency, polarization, and resolution. These two-sided distributions of differences from central values provide one-sigma ranges of variability that may be compared with the one-sigma numbers used to specify spatial variability. That is, in considering spatial variation, the distribution of mean strengths is formed from all repeat sector patches of a given terrain class, a central value is determined in the distribution, and variability in the distribution is characterized by the one-sigma range of variation about the central value. To follow a parallel approach for temporal (i.e., diurnal or seasonal) variation, where there are clusters of repeated measurements of each repeat sector patch, it is first necessary to normalize the central value of each cluster to zero to remove patch-to-patch spatial variation. Thus, for each repeated cluster, the central value in the cluster is first specified, then the differences (both positive and negative) of each measurement in the cluster from the central value are determined, and finally all such temporal differences from all clusters are accrued into one aggregate histogram. The resultant histogram of differences is two-sided, approximately symmetric, and approximately normal (i.e., law of large numbers). To repeat, it is showing differences from central values of clusters of repeated measurements, not differences between pairs of measurements in the cluster. It is a two-sided or polarized distribution centered at (or very near) zero. The mean, median, and mode in this two-sided distribution are all at (or very near) zero. This two-sided distribution is primarily characterized by the standard deviation or one-sigma value of the distribution. To the extent that the distribution is normal, 68% of the diurnal or seasonal differences lie within the one-sigma range of variation. Such two-sided distributions are now provided for diurnal, seasonal, and patch-to-patch variations in repeat sector clutter patch mean clutter strength, respectively. Diurnal and seasonal variations constitute long-term temporal variations for a given patch. Patch-topatch variations constitute spatial variations from one patch to another within a given category of terrain classification and for a given radar frequency band. These three distributions of variability in mean ground clutter strength are shown in Figure 3.50. In each case, the variation is the difference in mean clutter strength from a central value within a group of measurements repeated in time (i.e., diurnal or seasonal) or in space (patch to patch, for a specific terrain class). Because these data are all similarly derived to show central differences, the three distributions of Figure 3.50 showing diurnal, seasonal, and spatial variability are all primarily characterized by their one-sigma ranges of variability. As is indicated in Figure 3.50, these one-sigma ranges of variability for diurnal, seasonal, and patch-to-patch variations are 1.1, 1.6, and 3.2 dB, respectively. When all is said and done, the same set of diurnal and seasonal repeat sector measurements exist whether one-sided or two-sided distributions of differences are formed. Thus, aside

240 Repeat Sector Clutter Measurements

Normal Scale 0.999 Diurnal Variations (3436 repeated measurements from 42 sites)

0.99 0.98

Seasonal Variations (153 repeated measurements from 4 seasonally revisited sites)

Probability That Variation in Mean Clutter Strength ≤ Abscissa

0.95 0.9 0.8 0.7 0.6 0.5 0.4

Patch-to-Patch Variations within Specific Terrain Groups (714 measurements from 42 sites)

0.3 0.2 0.1 0.05

1σ Variation (dB)

0.02

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Figure 3.50 Temporal and spatial variability in mean ground clutter strength. Central differences. Phase One repeat sector data. All five radar frequencies, both polarizations, and both pulse lengths.

from statistical niceties, similar numbers should be obtained to characterize typically occurring diurnal and seasonal variations in distributions. To observe the extent to which this is so, consider that the ±1.1 dB and ±1.6 dB one-sigma numbers from the two-sided diurnal and seasonal distributions, respectively, as shown in Figure 3.50, which encompass 79% and 65% of central difference variations, respectively, when doubled to represent absolute differences between individual measurements encompass 80% and 71% of variations, respectively, in the one-sided distributions shown in Figure 3.49. Each distribution in Figure 3.50 will be discussed in turn. First, the seasonal variations in Figure 3.49 are based on differences in the subset of centrally selected (best) measurements among the day-to-day repeats for the four seasonally revisited sites. The approximate linearity of this curve indicates that the decibel values of seasonal central differences are approximately normally distributed. To the extent that they are, 68% and 95% of them are within one-sigma (i.e., ±1.6 dB) and two-sigma (i.e., ±3.2 dB) ranges of variation, respectively. These percentages are closely approximated by the actual percentages of

Repeat Sector Clutter Measurements 241

differences within these ranges of variation, which may be obtained directly from the ordinate in Figure 3.49, as 65% and 94.5%, respectively. Next, the diurnal variations in Figure 3.50 are based on all repeated experiments at each site, not just the best experiments. In establishing these diurnal variations, experiments with parametric variations that would not be appropriate to attribute to day-to-day variability were eliminated, as were obviously bad experiments due to equipment malfunction. The resultant distribution of diurnal central differences is seen to be approximately normal over its central 60% (from 0.2–0.8 cumulative probability). However, the spreads in the tails (approximately 0–20% cumulative probability on the left side; approximately 80–100% cumulative probability on the right side) of this distribution are considerably greater than would be provided by linear extrapolation of the central quasi-normal distribution. It is apparent in Figure 3.50 that, in the extreme tails (i.e., 1% or 2% on each side), the diurnal differences approach and nearly coincide with the seasonal differences. That is, whatever the mechanisms at work that cause the largest (although infrequent) seasonal changes, mechanisms are also at work to cause similarly large (but infrequent) changes on a day-today or weekly basis. Finally, as were the seasonal variations, the patch-to-patch variations in Figure 3.50 are based upon the subset of centrally selected (best) measurements among the day-to-day repeats. These variations are the differences from the central values given in Table 3.6 of the cluster of measurements in each frequency band in the 12 scatter plots showing mean clutter strength vs frequency by terrain class presented in Section 3.4. In other words, this distribution characterizes the prediction accuracy that may be associated with the generalized values of mean clutter strength by frequency band and terrain type as given in Table 3.6. As with the seasonal variations, the distribution of patch-to-patch decibel central differences in Figure 3.50 is approximately normal over its complete range (i.e., 72% and 94% of differences lie within one-sigma and two-sigma ranges, respectively, compared with 68% and 95% for the normal distribution). However, as would be expected, the distribution of central differences is considerably broader than the distributions of diurnal and seasonal variations (i.e., the one-sigma and two-sigma ranges for patch-to-patch differences are ±3.2 dB and ±6.4 dB, respectively). The temporal and spatial variability of clutter as given by the distributions of Figure 3.50 is the variability that remains after the data have been separated by terrain type. It is interesting to compare this residual variability with the overall range of variability in the clutter phenomenon without distinguishing terrain type, for example, as is illustrated in Figure 3.39. It is the 3.2-dB one-sigma patch-to-patch spatial variability that determines prediction accuracy based upon repeat sector measurements. The one-sigma patch-to-patch spatial variability in mean ground clutter strength by frequency band before terrain classification is as follows: 16.6, 13.6, 9.7, 7.1, and 5.8 dB, at VHF, UHF, L-, S-, and Xband, respectively (see Table 3.7). In contrast, the corresponding one-sigma patch-to-patch spatial variability in mean clutter strength by frequency band after terrain classification is: 3.9, 3.8, 2.9, 2.7, and 2.3 dB at VHF, UHF, L-, S-, and X-band, respectively. These latter five numbers indicate how the overall 3.2-dB one-sigma spatial variability in Figure 3.50 splits up by frequency band.

242 Repeat Sector Clutter Measurements

In comparing these measures of patch-to-patch spatial variability in mean clutter strength before and after terrain classification, the following observations are made: •

Terrain classification substantially reduces variability in all bands

•

The amount of the reduction is greatest at VHF and decreases with increasing radar frequency (i.e., amount of reduction = 12.7, 9.8, 6.8, 4.4, and 3.5 dB at VHF, UHF, L-, S-, and X-bands, respectively)

•

The variability after terrain classification still decreases somewhat with increasing radar frequency from 3.9 dB at VHF to 2.3 dB at X-band, but this decrease is very much less than the corresponding decrease before terrain classification

Thus, it is clear that specifying terrain type, terrain relief, and the depression angle at which the terrain is illuminated, as is done in Chapter 3, greatly improves the accuracy to which the mean clutter strength from terrain can be predicted, and that non-terrain-specific approaches to clutter modeling must inherently involve large uncertainties.

3.8 Summary How strong is radar land clutter? How does the strength of the clutter vary with the type of terrain in which the radar is situated? In particular, whatever the terrain, how does the strength of the clutter vary with radar carrier frequency over the range of frequencies used in modern surface radar operations? These questions have perplexed radar engineers since the advent of radar during World War II. Answers to these questions are important because the performance of surface-sited radar against low-flying targets is often limited by land clutter interference even when state-of-the-art MTI clutter cancellation processing is employed. Because of this importance, many specific clutter measurements have been performed and reported over the years, but they have not led to a characterization of clutter providing generally accepted answers to the above questions. Central to the difficulty in clutter characterization and prediction is the fact that terrain is essentially infinitely variable, and every clutter measurement scenario is different. Hence, ground clutter’s most salient attribute is variability. As a result, questions concerning clutter strength need to be answered statistically. As is amply illustrated by discussions of individual measurements in Chapter 3, the underlying physics in any given measurement can usually be understood. However, every measurement is fraught with terrain and propagation specifics, and generalization on the basis of any one measurement is usually not possible. The clutter literature, seemingly characterized by inconsistency and contradiction, is really just reflecting the fact that clutter is an extremely variable statistical process. The literature frustrates us with single-point measurements of which the broader significance is not understood. Thus, a major new program of ground clutter measurements was undertaken at Lincoln Laboratory to provide new general understandings and predictability of the low-angle ground clutter statistical phenomenon. Large amounts of data were collected in the belief that averaging over large amounts of data would allow underlying fundamental trends to emerge that are often obscured by specific effects in individual measurements. The fivefrequency Phase One clutter measurement radar system was operated continuously in the field over a three-year period, collecting multifrequency clutter data at 42 different sites.

Repeat Sector Clutter Measurements 243

Many of the measurement sites were in western Canada, in terrain of relatively low-relief and at northern latitudes. In addition to this emphasis, however, many other important terrain types were measured, including mountains, cities, desert, marshland, farmland, and woodland. Many of the Phase One sites and the measurements obtained there are described in Chapter 3. Altogether in this measurement program, approximately 475 gigabytes of accurately calibrated, pulse-by-pulse ground clutter data were collected. Chapter 3 provides multifrequency results of low-angle clutter based on the repeat sector database which altogether comprises 4,465 clutter measurements. The repeat sector at each site was an azimuth sector of concentration in which measurements were repeated a number of times to increase the reliability of the results. As an easy-to-comprehend summary, Figure 3.38 and Table 3.6 represent the best repeat-sector answers to the most pressing high-level questions for which answers were sought in the Phase One clutter measurement program. The results of Figure 3.38 and Table 3.6 have a number of advantages. First, underlying them is a universally applicable terrain classification system consistently applied across 42 different repeat sectors. This classification system causes the clutter statistics to cluster within class and to properly separate between classes. This system separates differences in terrain or measurement scenario that are enough to cause significant variation (i.e., different classes) in the clutter returns. The terrain classification system utilized is basically formulated at 1:50,000 scale to classify both land-surface form and land cover, and quantifies important parameters such as terrain relief, terrain slope, depression angle, and percent tree cover. Second, the data shown in Figure 3.38 and Table 3.6 are medianized and hence generalized central values within terrain classes. Even at best, terrain is variable within class, and any single measurement in a given terrain class comes from a spectrum of all possible measurements in such terrain. The data shown in Figure 3.38 and Table 3.6 are medianized central values over many measurements and thus represent generally occurring levels of clutter strength in each terrain class. Third, the data of Figure 3.38 and Table 3.6 were accurately calibrated and reduced using consistent data reduction procedures. Complicating factors in data reduction, such as electromagnetic propagation (ground clutter is not a freespace measurement), geometric shadowing (a dominant influence in the low-angle regime), radar sensitivity limitation, radar noise contamination, and differing degrees of coherency in clutter returns are explained in Chapter 3. Finally, each measurement underlying the medianized data of Figure 3.38 and Table 3.6 is itself a centrally selected measurement from a group of identically repeated measurements in which occasional anomalous outliers have been removed. Thus, the summary results of Figure 3.38 and Table 3.6 are the product of much effort devoted to concerns with accuracy, generality, and statistical consistency. The results of Figure 3.38 and Table 3.6 are now summarized. First, these results indicate 66 dB of variability in mean strength of ground clutter from mountains at VHF to marshland or desert at UHF. However, these results also provide a rational means of sorting through this variability, through specification of terrain type, relief, depression angle, and radar frequency. In general terms, it is seen that just five major, easy-to-distinguish terrain categories are utilized; namely, mountains, cities, forest, farmland, and, as an encompassing fifth category, desert, marsh, or grassland with few large discrete clutter sources. As expected, mountains and cities produce strong clutter returns, and desert,

244 Repeat Sector Clutter Measurements

marsh, and grassland produce weak clutter returns. Results from the preceding Phase Zero X-band program of ground clutter measurements described in Chapter 2 show that, at the very low angles of ground-based radar, depression angle as it affects shadowing on a sea of discrete clutter sources is of dominant importance to clutter statistics. The Phase Zero findings are essentially duplicated in the Phase One X-band results of Figure 3.38 and Table 3.6. In addition, similar important dependencies on depression angle at the other frequencies, VHF, UHF, L-, and S-bands, are observed, such that fractional variations of depression angle cause major variations in clutter statistics in all these bands. However, the purpose of Chapter 3 is not so much to dwell on the previously emphasized important role of depression angle, which also fundamentally affects statistical spreads in distributions, but to take up the question of frequency dependence in these distributions. The question of frequency dependence requires an empirical approach. The summary data of Figure 3.38 and Table 3.6 show that in forest of high relief and/or at high depression angle, mean ground clutter strengths decrease significantly with increasing frequency; whereas, in very low-relief farmland, mean ground clutter strengths increase significantly with increasing frequency. The frequency dependence of mountain clutter mirrors the behavior of high-relief forest clutter, except that it is stronger; the frequency dependence of desert or marshland clutter mirrors that of very low-relief farmland, except that it is weaker. (An exception occurs where, at high depression angle at X-band, desert clutter is as strong as forest clutter.) For much commonly occurring terrain, either farmland or forest of moderately low-relief leading to intermediate illumination angles, little general dependence of mean clutter strength with frequency is observed. In such terrain, mean clutter strengths hover around the –30-dB level, VHF to X-band. In summary, the data of Figure 3.38 and Table 3.6 bring much statistical order to the problem of predicting mean clutter strengths from spatial macroregions of terrain. They answer the questions of how strong clutter is for various terrain types and for radar frequencies varying from VHF to X-band. These numbers are subsequently refined in the clutter modeling information presented in Chapter 5. Within any spatial macroregion consisting of hundreds or thousands of resolution cells, extreme cell-to-cell fluctuation occurs about the mean value as provided by Figure 3.38 and Table 3.6. A proper clutter model will model these statistical fluctuations. The clutter models subsequently developed in Chapters 4 and 5 do so by modeling the clutter returns as random numbers from Weibull distributions. Each modeled Weibull distribution is characterized by a mean strength and a shape parameter. Any model needs to reach towards simplicity and generality. Thus, in the clutter model of Chapter 4, some subjective smoothing of trends is performed as complementary results from the Phase Zero and Phase One programs are merged and minor variations that are judged to be statistically insignificant are removed. The results of Figure 3.38 and Table 3.6 are exact results as delivered by the repeat sector measurements, medianized within terrain class and including both vertical and horizontal polarizations and high and low range resolutions. Chapter 3 provides general information on the effects of polarization, range resolution, weather, and season on mean clutter strength. The effects of each of these parameters are generally small, primarily because mean clutter strength is dominated by strong discrete clutter sources that are physically complex with respect to polarization and relatively invariant with weather and season. With polarization, only a slight overall trend exists where vertical polarization provides stronger mean clutter than horizontal by 1.4 dB on the average. However, the one-sigma variability about this average is 2.8 dB, and occasional

Repeat Sector Clutter Measurements 245

differences in mean strength with polarization can occur in the 5- to 10-dB range, with either vertical or horizontal being stronger. Radar resolution fundamentally affects spreads in clutter amplitude distributions, not the means which are emphasized in Chapter 3. Across all the repeat sector measurements, the mean strength measured at high resolution is only 0.8 dB stronger on the average than that measured at low resolution. The one-sigma variability with resolution about this average is 2.2 dB. Variations of mean strength with resolution indicate the existence of small numbers of discrete interfering scatterers within a resolution cell. Weather and season act to introduce statistical variability in mean clutter strength without apparent trend. On the basis of the repeated measurements at each site, the one-sigma variability due to short-term changes with weather is specified at 1.1 dB, with occasional variations (i.e., 10%) greater than 3 dB. On the basis of the seasonal revisits to six sites, the one-sigma variability due to long-term changes with season is specified at 1.6 dB with occasional variations (i.e., 10%) greater than 4.8 dB. These specifications of diurnal and seasonal variability in terms of probability of occurrence bring statistical order to a historical literature characterized more by individual examples. The long-term diurnal and seasonal temporal variabilities of mean strength in the repeat sector measurements of 1.1 dB and 1.6 dB, respectively, may be contrasted with the sector-to-sector spatial variability within groups of common terrain type in the measurements. This spatial variability has a one-sigma range of 3.2 dB, which represents a measure of prediction accuracy based on repeat sector measurements. In light of such variability (seasonal, weather related, and spatial), the reader is cautioned that the numbers comprising the clutter modeling information of this book need to be regarded as statistical averages. These averages certainly establish important trends. Any specific clutter measurement, however, whether new or historical, may vary considerably from these predicted average numbers. Chapter 3 emphasizes mean clutter strengths over spatial macroregions consisting of many contiguous resolution cells. The most basic descriptive measure of any statistical distribution is the mean of the distribution, which is the average of all the samples in the distribution, each sample weighted by just its own strength. The means usually occur high in the measured clutter amplitude distributions, often near the 90-percentile level, driven there by occasional strong returns from discrete sources. However, because the distributions are not simply behaved does not mean that the standard techniques of statistical science for bringing them under general description should be discarded. This seemingly self-evident fact is mentioned here because means at high percentile levels can occasion a sense that they should be discounted. Returns from discrete sources over a wide range of strengths comprise the phenomenon for which a description is sought. The phenomenon is not so simple that, for example, moving to the median can rid it of a few classical, water-tower type of contaminating discretes and thus provide a better central measure of a well-behaved, discrete-free clutter background. For complete descriptions of the repeat sector clutter amplitude distributions in addition to mean levels, general information is also provided in Chapter 3 on higher moments and percentile levels, medianized over a number of individual repeat sector measurements within the same terrain groups as the means. The higher moments provided are standard deviation, skewness, and kurtosis. The standard deviation is the basic statistical measure of spread, and from it the Weibull shape parameter of the clutter models developed in Chapters 4 and 5 is completely determined. Skewness and kurtosis are normalized third and

246 Repeat Sector Clutter Measurements

fourth central moments, respectively. These quantities are of particular importance in theoretical investigations. The percentiles provided in Chapter 3 are the 50-, 70-, and 90percentile levels in the clutter amplitude distributions. They provide an easy descriptive means of visualizing the distributions, although otherwise they contain less meaningful statistical information in three or four numbers than do the moments. Chapter 3 provides mean land clutter strength vs radar frequency, VHF through X-band, as measured over repeat sector spatial macroregions of terrain at 42 different sites. These results were obtained under one unified program of measurements utilizing consistent and accurate calibration throughout. As such, they provide much information on the frequency dependence of radar land clutter and in totality bring connecting tissue to a disjointed literature. Many of the results, at least in detail, are specific to the site at which they were obtained. Chapter 3 averages out such specificity by combining results from sites of similar terrain class. In this manner, generalized characteristics of mean land clutter strength vs frequency are arrived at for most important terrain types. The information in Chapter 3 on the frequency dependence of low-angle land clutter is based on a statistical population of just 42 repeat sector clutter patches. When these 42 samples are divided up among five major categories of terrain and then further partitioned by relief and depression angle, they do not leave very many samples per category. The Phase One multifrequency 360° survey data at each site provide clutter amplitude distributions for many more patches, on the order of 80 patches per site as opposed to the one patch per site provided by the repeat sector database. Results based on survey data are subsequently provided in Chapter 5, substantially improving the statistical rigor with which multifrequency clutter characteristics are specified.

References 1.

J. B. Billingsley and J. F. Larrabee, “Multifrequency Measurements of Radar Ground Clutter at 42 Sites,” Lexington, MA: MIT Lincoln Laboratory, Technical Report 916, Volumes 1, 2, 3; 15 November 1991; DTIC AD-A246710.

2.

J. B. Billingsley, “Exponential Decay in Windblown Radar Ground Clutter Doppler Spectra: Multifrequency Measurements and Model,” Lexington, MA: MIT Lincoln Laboratory, Technical Report 997, 29 July 1996; DTIC AD-A312399.

3.

E. Jakeman, “On the statistics of K-distributed noise,” J. Phys. A 13, 31-48 (1980).

4.

S. Watts and K. D. Ward, “Spatial correlation in K-distributed sea clutter,” Proc. Inst. Electr. Eng. 134, 526-531 (1987).

5.

M. I. Skolnik, Introduction to Radar Systems (3rd ed.), New York: McGraw-Hill (2001).

4 Approaches to Clutter Modeling 4.1 Introduction The historical technical literature on low-angle land clutter includes a number of different past approaches for attempting to model this complex phenomenon, as reviewed in Chapter 1. Thus, most simply, low-angle clutter has been characterized as a single-variable characteristic or functional relationship between the dependent variable σ ° and any one of the following three independent variables: (1) illumination angle to the backscattering terrain point; (2) radar carrier frequency; and (3) range to the backscattering terrain point. Chapters 2 and 3 illustrate at some length the strong dependencies of low-angle clutter on illumination (i.e., depression) angle and radar carrier frequency based on Phase Zero Xband data and Phase One five-frequency repeat sector data, respectively. Although providing new useful clutter modeling information, the results of Chapters 2 and 3 in themselves do not constitute a clutter model generalized to be applicable to any surface-sited radar. The objective of such a model is to provide a description of the amplitude statistics of the clutter returns received by an arbitrary radar in a specified environment. As has been discussed previously in this book, the mean strength (first moment) of the clutter amplitude distribution depends strongly on (1) depression angle and (2) radar frequency. However, the equally important shape parameter (derived from the ratio of second to first moments) of the clutter amplitude distribution is fundamentally dependent on the spatial resolution of the radar. The modeling information of Chapters 2 and 3 is restricted to Phase Zero and Phase One pulse lengths and beamwidths. As such, this modeling information may be used to replicate clutter in radars of Phase Zero or Phase One spatial resolution, but is not generalized there to be applicable to radars of spatial resolution significantly different from the Phase Zero and Phase One radars. Chapter 4 provides an interim angle-specific clutter model fully generalized to be applicable to radars of arbitrary spatial resolution. This interim model is presented in Section 4.2. It is based on the Phase Zero X-band database (Chapter 2) and the Phase One repeat sector database (Chapter 3) and includes all important trends of variation of lowangle clutter amplitude statistics seen in these two databases, including the general dependency of shape parameter on the spatial resolution or cell size of the radar. The interim clutter model is thus a complete model applicable to any surface-sited radar in any ground environment. This model is labelled “interim” because it does not have the statistical depth of the spatially comprehensive 360° Phase One survey data. The identical

286 Approaches to Clutter Modeling

structure of the interim clutter model carries forward to the more comprehensive modeling information of Chapter 5 which is based on the Phase One survey data. The presentation of material in Chapter 4 is as follows. First, Section 4.1.1 describes an important clutter modeling objective, namely, the prediction or simulation of plan-position indicator (PPI) clutter maps in surface-sited radars. Then Section 4.1.2 discusses the clutter modeling rationale of this book, distinguishing between angle-specific clutter modeling information suitable for site-specific clutter prediction using digitized terrain elevation data (DTED) and non-angle-specific modeling information suitable for more generic clutter prediction. Section 4.1.3 discusses clutter as a statistical random process and briefly describes the scope of included material within the context of available random-process statistical attributes. Section 4.2 presents the angle-specific interim clutter model, which requires specification of the depression angle to each clutter patch. This model explicitly incorporates the interdependent effects on clutter of (1) depression angle and (2) radar frequency, but the effects of (3) range occur implicitly in its site-specific application whereby the occurrences of visible clutter patches decrease with increasing range at each specific site. PPI clutter maps in surface-sited radars are inherently patchy in character. The details of the patchiness are specific to each site. There remains a need, however, for a generic non-sitespecific approach to clutter modeling in which the spatial character of the clutter field is not patchy. An important feature of a PPI clutter map for a surface-sited radar, disregarding the specificities of patchiness in each such map, is the obvious dissipation of the clutter with increasing range. Section 4.3 takes up the subject of non-angle-specific clutter modeling information suitable for use in non-patchy prediction. This naturally leads to the explicit introduction of (3) range as the important independent variable affecting the clutter, in contrast to effects of range occurring implicitly in site-specific modeling. What becomes apparent based on clutter measurements at many sites is that the occurrence of clutter fundamentally depends upon (i.e., decreases with) range, for a given site height; and that the strength of the clutter where it occurs is fundamentally dependent upon terrain type but not upon range. Section 4.3 provides a simple, generic, non-patchy clutter model based upon these observations in the measurement data. Section 4.4 discusses the intimate interrelationship at low angles between geometrically visible terrain and clutter occurrence. Section 4.5 discusses the difficulties involved at low angles in attempting to distinguish discrete from distributed clutter and takes up the issue of how best to reduce the measurement data. Section 4.6 provides additional insight into the clutter phenomenon and the ramifications in its modeling by providing brief introductory discussions of its temporal statistics, its spectral characteristics, and its correlative properties. Section 4.7 summarizes many of the insights developed in Chapter 4. Appendices 4.A, 4.B, and 4.C further develop the effects of radar height and range in lowangle clutter and discuss the complications introduced by range-dependent sensitivity limitations and the corresponding range-dependent effects of radar noise corruption in clutter measurement data. Appendix 4.D describes a more computationally intensive approach to low-angle clutter modeling in which spatial cells that are locally strong (i.e., “discretes”) compared to their neighbors are modeled separately from the weaker neighboring (i.e., “background”) cells.

Approaches to Clutter Modeling 287

4.1.1 Modeling Objective Figure 4.1 shows measured PPI ground clutter maps for all five Phase One frequencies at the Peace River South measurement site, located high on the east bank of the Peace River in Alberta. The maximum range in these maps is 23 km; north is at zenith. Clutter is shown as white where σ °F4 > –40 dB. These five-frequency Peace River clutter maps may be compared with the five-frequency Gull Lake West clutter maps previously shown in Figure 3.9. To the west in each map in Figure 4.1 is the well-illuminated river valley; to the east, level terrain is illuminated at grazing incidence. As with the Gull Lake West measurements, as patterns of spatial occurrence of ground clutter, all five clutter maps at Peace River are quite similar. As previously discussed, the reason for this similarity is that the relatively strong clutter shown in Figure 4.1 largely comes from visible terrain. At all five frequencies in the figure, the nature of the clutter tends to be granular and patchy. However, the granularity is greater at grazing incidence to the east, less at the higher depression angles to the west. Also as has been discussed, such effects are principally due to depression angle as it affects microshadowing. Obvious in Figure 4.1 is the effect of increasing beamwidth with decreasing frequency causing increased azimuthal smearing of the clutter. This effect is of spatial resolution, such that decreasing resolution results in decreased spreads in clutter amplitude distributions.

VHF

UHF

S-Band

L-Band

X-Band

Figure 4.1 Measured multifrequency ground clutter maps at Peace River, Alberta.

A main modeling objective of this book is the site-specific prediction of clutter maps such as those shown in Figure 4.1 using DTED. This objective is illustrated by Figure 4.2 which compares predicted terrain visibility and measured X-band clutter at Katahdin Hill,

288 Approaches to Clutter Modeling

Predicted

Digitized Terrain Elevation Data

Measured

X-Band Clutter Map σ° > –40 dB

Percent Circumference Visible

Massachusetts. To the left is predicted terrain visibility with a 5-m antenna on the basis of geometric line-of-sight visibility in DTED. To the right is the measured Phase Zero clutter map at the same site. In approximate measure, the two spatial patterns are quite similar;24 this similarity is borne out in the plot showing percent circumference visible compared with percent circumference in measured clutter vs range. DTED are used to deterministically predict where the clutter occurs, and a statistical depression-angle-specific and terraintype-specific clutter model is used to predict the strength of the clutter in each visible cell.

100 30 Measured

10 3 1.0

Predicted

0.3 0

10

20

30

40

Range (km)

Modeling Procedure 1) Use DTED for deterministictatistical prediction of where the clutter is 2) Subsequently use empirical statistical model to predict how strong the clutter is

Figure 4.2 Predicted clutter visibility at Katahdin Hill. Maximum range = 35 km.

The interim clutter model presented in Section 4.2 is suitable for such site-specific clutter prediction as well as other applications. The interim clutter model structure is illustrated by the schematic diagram of Figure 4.3. To model site-specific clutter, Weibull random numbers are distributed cell-by-cell over visible terrain as determined by DTED. As indicated in Figure 4.3, the Weibull numbers are drawn from distributions characterized by a Weibull mean strength σ w° and a Weibull shape parameter aw. These two coefficients vary with terrain type, depression angle, and the important radar parameters of frequency and resolution. Mean strength σ w° varies with frequency, aw varies with resolution, and both σ w° and aw vary with depression angle and terrain type. The actual interim clutter model matrix of numbers organized as shown in Figure 4.3 is provided in Section 4.2.

4.1.2 Modeling Rationale Low-angle ground clutter is a patchy phenomenon. Areas of the ground that are directly visible to the radar usually cause relatively strong clutter returns, and areas of the ground that are shadowed or masked to the radar usually cause relatively weak clutter returns, often below the sensitivity of the radar. Using DTED allows the deterministic prediction

24. But see also Figure 2.11, a similar comparison at finer resolution.

Approaches to Clutter Modeling 289

1) Weibull distribution specifies spatial variability of clutter strengths

Table

Terrain

w (dB) Dep Frequency Band Ang (deg) VHF UHF L- S- X-

aw Resolution (m2) 103 106

Forest

— — —

— — —

— — —

— — —

— — —

— — —

— — —

— — —

Farmland

— — —

— — —

— — —

— — —

— — —

— — —

— — —

— — —

• • •

• • •

• • •

• • •

• • •

• • •

• • •

• • •

— — —

— — —

— — —

— — —

— — —

— — —

— — —

— — —

aw

Clutter Strength 4

• • • Mountains

F w

2) Parameters Terrain Type; Depression Angle; Frequency; Resolution; Polarization

Figure 4.3 Interim clutter model structure (table look-up).

and distinction between macroregions of general geometric visibility and macroregions of shadow, where macro implies kilometer-sized regions that encompass hundreds or thousands of spatial resolution cells. Such deterministic prediction of the specific pattern of spatial occurrence of ground clutter at a given site is essentially what is meant here by site-specific study. Predicting, in this manner, the existence of a macropatch of clutter at some site, a description is subsequently needed of the statistics of the clutter returns that are expected from within the patch. Thus Section 4.2 provides modeling information to describe clutter amplitude distributions occurring over macrosized spatial regions of visible terrain. These distributions are characterized by broad spread. The degree of spread in the distribution is fundamentally controlled by depression angle, that is, the angle below the horizontal at which the patch is observed at the radar. Depression angle is a quantity that can be computed relatively rigorously and unambiguously from DTED, depending as it does simply on range and relative elevation difference between the radar antenna and the patch. The fundamental dependence of spread in the clutter amplitude distribution on depression angle is significant even for the very low depression angles (i.e., typically < 1°) and small patch-to-patch differences in depression angle (i.e., typically fractions of 1°) that occur in surface-sited radar. The patch-specific modeling information for ground clutter amplitudes presented in Section 4.2 is tied tightly to this basic dependence on depression angle, such that amplitude distributions are specified in terms of small and precise gradations of depression angle for various terrain types. Let us reflect on this approach to modeling low-angle ground clutter. As a physical phenomenon, the most salient attribute of low-angle ground clutter is variability. This variability is manifested in two important ways: first, as patchiness in spatial occurrence and second, as extremely wide cell-to-cell statistical fluctuation in strength (i.e., spikiness) within a patch. Concerning spatial patchiness, it is emphasized that clutter does not always exist, and it is the patch-specific on-again, off-again macrobehavior of clutter that at first level determines the performance of a given radar against a given low-altitude aircraft at a given site. Concerning wide cell-to-cell variations of clutter strength within macropatches,

290 Approaches to Clutter Modeling

it is emphasized that what appears at first consideration to be a phenomenon of extreme variability and little predictability turns out in the end, after much data analysis, to be generally dependent on very fine differences in depression angle. Use of site-specific DTED allows the capture of both these basic attributes of low-angle ground clutter, its spatial patchiness (approximately computed simply as geometric visibility), and (through depression angle) its expected range of amplitudes within a patch. Therefore, this approach to modeling low-angle clutter is regarded as a major advance over more general non-patchy approaches that do not distinguish between macroregions of clutter occurrence and macroregions of shadow. This approach allows an analyst to predict, within macroregions, where a surface-sited radar can be expected to encounter clutter interference and where the radar will be free of such interference; and, given that the radar is experiencing clutter, what, on the average, the expected statistics of signal-to-clutter ratio will be across the macroregion of clutter. Clutter returns within patches are often highly spatially correlated. This book discusses the fact that the dominant clutter sources within macroregions of general geometric visibility are usually spatially localized or discrete, such that groups of cells providing strong returns are often separated by cells providing weak or noise-level returns. The occurrence of noiselevel returns distributed within macroregions of general geometric visibility is referred to as “microshadowing,” where micro implies resolution-cell-sized areas (see Figure 2.11 and its accompanying discussion in Chapter 2). The high degree of spatial microcorrelation of strong discrete sources within macropatches results from the fact that such sources exist as vertical features of landscape discontinuity that often occur in definite patterns, for example, along the leading edge of a tree line or the clustering of vertical objects along roads and field boundaries. If an analyst is interested in the actual microstatistics, for example, of break-lock in a surface radar tracking a target across a given clutter patch, the information in this book does not go that far. The kind of detail and fidelity in terrain description that are required to predict microstatistics of spatial correlation of clutter amplitudes within macropatches are regarded as a second sequential major hurdle to cross in clutter modeling. Limitations encountered in attempting this second advance have been explored. It has been found that prediction of microspatial correlation is a very challenging task that immediately takes exploratory operations out to the limits of current resources in terms of available information and computer processing. In contrast, the first major advance in low-angle clutter fidelity, which is the field-of-investigation of this book, comes relatively easily once DTED are in play. The above allusion to general non-patchy approaches to clutter modeling does not imply that such approaches are without value. Section 4.3 moves from measurements in which the patch-specific parameter of depression angle is the fundamental controlling parameter to non-angle-specific modeling information based on relatively general parameters such as site height, terrain roughness, and terrain type (e.g., forest, agricultural, etc.). However, it is true that non-patchy approaches to clutter modeling are, indeed, relatively abstract and conceptually vague in quantitative study. This is the logical penalty that non-patchy approaches must pay as the price for generality. This penalty comes about because, instead of aggregating system performance measures after realistic clutter computations at many individual sites, the non-patchy approach attempts to aggregate and generalize clutter influences before a one-time assessment of system performance. That is, the non-patchy

Approaches to Clutter Modeling 291

approach takes the easy way of attempting to a priori average the clutter first, whereas the site-specific patchy approach takes the harder but more rigorous way of a posteriori averaging the actual site-specific performance measures to reach generality.

4.1.3 Modeling Scope Low-angle radar ground clutter is a complex phenomenon. Nevertheless, as a random process, all of its descriptive attributes must fall somewhere within the list shown in Table 4.1. First, consider variation that occurs from point to point in space. The question of how strong the clutter is across an ensemble of spatial points is answered statistically in terms of a histogram of clutter amplitudes, one from each spatial point. The other pertinent question concerning spatial variation is, how far must the sampling point move for the clutter amplitude to change significantly? This question is answered statistically in terms of correlation distance in the random process. Second, consider variation that occurs at any given point with passing time. As with spatial variation, the question of temporal variation of clutter strength is answered in terms of a statistical histogram of clutter amplitudes measured consecutively in time at a given point. With temporal variation, the remaining question is, how long does it take for the clutter amplitude to change significantly? This question is answered statistically in terms of correlation time. The spatial information contained in correlation distance and the temporal information contained in correlation time are equivalent to the spectral information in the random process in space and time, respectively—i.e., the Fourier transform of the autocorrelation function is the power spectrum. Table 4.1 Radar Ground Clutter Statistics Spatial Variations Amplitude Statistics Correlation Distances Temporal Variations Amplitude Statistics Correlation Times/Spectra

The simple overall scheme illustrated in Table 4.1 for describing low-angle ground clutter becomes complicated because of matters to do with scale. Clutter is spatially nonhomogeneous. That is, it varies spatially in a complex way. As a result, it presents many different observable attributes depending on the scale at which it is observed. For example, consider a wood lot adjacent to an open agricultural field. At microscale, the clutter statistics applicable to the wooded area constitute a different process and need to be investigated separately from those applicable to the open field—where here, as before, the prefix micro implies resolution cell-sized areas. But consider the clutter statistics applicable to the important boundary region between wood lot and agricultural field. The strong clutter returns from such boundary regions, and other features of vertical discontinuity that exist pervasively over almost all landscapes, dominate in low-angle clutter. In this regard, the field of low-angle clutter is akin to other modern fields of investigation in which spatial feature is important, such as digitized map processing, synthetic-aperture radar (SAR) image data compression, pattern recognition, and artificial intelligence. All such fields attach more importance to edges of features and to defining, storing, and recognizing such edges than to the more homogeneous regions within bounding edges.

292 Approaches to Clutter Modeling

Thus, the field of low-angle clutter leads an investigator from microscale to macroscale, where here, also as before, the prefix macro implies kilometer-sized regions encompassing hundreds or thousands of spatial resolution cells and many vertical features. As discussed in Chapter 2, the correct empirical approach in dealing with many edges of features existing as discontinuous or discrete clutter sources is to collect meaningful numbers of them together within macropatches, allowing the terrain classification system to describe their statistical attributes at an overall level of description. This book provides modeling information allowing the prediction of the spatial amplitude statistics of low-angle clutter as they occur for ground-based radar distributed over macroregions of visible terrain. Development of this information requires clutter measurements from many different sites and macropatches to build up an appropriate supportive empirical statistical database. This book does not address statistical issues of patch length and separation, but Chapter 4 and its appendices address how, as a result of spatial patchiness, the occurrence of clutter generally decreases with increasing range. An example showing microscale correlation distance in farmland terrain is provided in Section 4.6. Such microspatial correlation is important, for example, in the detailed processing algorithms of constant-false-alarm rate (CFAR) radars. Issues of temporal variation of low-angle ground clutter generally stand apart from the more stressing problem of modeling the spatial statistics of clutter. The subjects overlap somewhat in that clutter spatial amplitude statistics vary with long-term temporal variation associated with weather and season. Long-term temporal variation is discussed in Chapter 3. Concerning short-term temporal variation, some brief information describing the relative frequency of occurrence of temporal amplitude statistics between cells with Rayleigh (i.e., windblown foliage) and Ricean (i.e., fixed discretes embedded in foliage) statistics is provided in Section 4.6. Section 4.6 also introduces the subject of intrinsic-motion Doppler frequency spectra of windblown ground clutter; the accurate characterization of windblown clutter spectra is more extensively addressed as the subject of Chapter 6.

4.2 An Interim Angle-Specific Clutter Model 4.2.1 Model Basis Section 4.2 presents an interim angle-specific clutter model for predicting ground clutter amplitude statistics as they occur over spatial macroregions of directly visible terrain at low depression angles. The interim clutter model is based upon Phase Zero X-band and Phase One five-frequency measurements as discussed in Chapters 2 and 3, respectively. The results of Chapters 2 and 3 apply specifically to cell sizes as defined by Phase Zero and Phase One pulse lengths and beamwidths. The interim model generalizes these results such that the spatial resolution of the radar becomes an important—and, within limits, arbitrarily specifiable—independent variable upon which the clutter statistics strongly depend. The spread in the clutter amplitude distribution as defined by the shape parameter of the distribution is fundamentally dependent on the spatial resolution of the radar. Spatial resolution or cell size A in m2 is defined by A = r·∆r·∆θ where r is range, ∆r is range resolution, and ∆θ is beamwidth (see Section 2.3.1.1). The range of cell sizes empirically available in the Phase Zero and Phase One data is determined not only by the different pulse lengths provided by the Phase Zero and Phase One radars (viz., 0.06, 0.1, 0.25, 0.5, and 1.0 µs), but also and very importantly by the different azimuth beamwidths available (viz., 1°, 3°, 5°, 13°) and by the different ranges over which clutter patch amplitude

Approaches to Clutter Modeling 293

distributions were acquired (viz., from 1 to > 50 km). Of course, each azimuth beamwidth is generally available in only one radar frequency band in the clutter measurement data, but it turns out that the spread in the clutter amplitude distribution, determined, for example, by the ratio of standard deviation-to-mean, is relatively independent of the radar frequency at which it is measured. The spatial spikiness causing spread in low-angle clutter—a characteristic feature easily observed in A-scope sector displays—is relatively independent of radar frequency because the same large discrete sources causing the spikes exist whatever the frequency band employed in the measurement. Therefore, observed spreads in clutter amplitude distributions, which are fundamentally and strongly dependent on cell size, may be considered as independent of frequency and thus may be combined and interpolated across the beamwidths available in the various frequency bands to provide a much wider range of spatial resolution than would be available in any one frequency band alone. By this means, the interim clutter model, and also the clutter modeling information provided subsequently in Chapter 5, are generalized such that the highly significant spreads in clutter amplitude distributions apply to radar cell sizes ranging over the relatively wide extent from ~103 m2 to ~106 m2 in any frequency band. This matter is further discussed in Chapter 5. The Phase Zero X-band results of Chapter 2 underlying the interim clutter model comprise measurements from 2,177 different clutter patches. With this large number of terrain samples, even after separating into different categories of terrain type and depression angle, there are still many samples left in any given category and hence good statistical definition in the results. That is, with a large amount of averaging at work in these data, even small differences in results are statistically significant. In contrast, the Phase One five-frequency results of Chapter 3 underlying the interim clutter model comprise measurements from just 42 repeat sector terrain patches, one per site from each of the 42 Phase One sites. Because backscatter measurements were performed on each repeat sector patch a number of times across a 20-element radar parameter matrix, the Phase One repeat sector database of Chapter 3 constitutes a comparable amount of data to the Phase Zero database and allowed determination of trends of variation with frequency, pulse length and polarization. It is important to realize, however, that when looking for such trends and separating the 42 repeat sector patches into various categories of terrain type and depression angle, in contrast to Phase Zero there often are not very many terrain samples per category. As a result, the interim clutter model reaches for multifrequency characteristics often on the basis of a few examples of an observed trend rather than with the statistical rigor of Phase Zero. This lack of statistical depth in the interim clutter model is evidenced by the fact that the interim model is presented as a simple one-page table of numbers. There are obvious advantages to this simplicity, both in ease of comprehension and ease of implementation. As a result of such advantages, the interim clutter model has received and continues to receive extensive usage at Lincoln Laboratory and elsewhere. The disadvantages of this simplicity are less statistical rigor and diminished prediction accuracy. Chapter 5 brings all the Phase One 360º survey data at each site under analysis, in addition to the repeat sector data, utilizing the same model construct as employed by the interim clutter model. In doing so, the Phase One modeling information of Chapter 5 obtains the important Phase Zero statistical advantage of many terrain samples and increased prediction accuracy.

294 Approaches to Clutter Modeling

4.2.2 Interim Model The interim angle-specific clutter model is presented in Table 4.2. The clutter modeling information in Table 4.2 is provided within a context of Weibull statistics [1, 2], where σ w° is the Weibull mean strength and aw is the Weibull shape parameter. Weibull statistics are defined and discussed in Appendices 2.B and 5.A. The interim model is based upon the three main categories of descriptive parameter of low-angle clutter previously introduced in Section 3.4. First are parameters which are descriptive of the radar. The important radar parameters affecting clutter statistics as employed in the interim model are radar frequency as it affects σ w° and radar spatial resolution as it affects aw. Second are parameters descriptive of the geometry of illumination of the clutter patch. As in Chapters 2 and 3, the interim model utilizes depression angle, a relatively simple and unambiguous quantity to determine, depending only on range and relative elevation difference between the radar antenna and the backscattering terrain point. Recall that attempts in Chapter 2 to use grazing angle met with little additional success, partly due to difficulties associated with scale, precision, and accuracy in unambiguously defining local terrain slope and partly because dominant clutter sources tend to be vertical discrete objects associated with the land cover. Use of grazing angle in clutter modeling is further discussed in Appendix 4.D. Formulating the interim clutter model in terms of depression angle involves the possibility of occurrence of negative depression angles wherein terrain is observed by the radar at elevations above the antenna. For terrain to be visible at negative depression angle requires the terrain to be of terrain slope greater than the absolute value of the depression angle at which it is observed. Third are parameters descriptive of the terrain within the clutter patch. The interim clutter model of Table 4.2 is comprehensive in that, whatever terrain is under consideration, it must fall within one of the terrain types of the model. Most terrain types in the model involve several depression angle regimes. As introduced in Chapter 2, the important general terrain types of the interim model are threefold, namely (1) rural/low-relief terrain in which terrain slopes are < 2°; (2) rural/high-relief terrain in which terrain slopes are > 2°; and (3) urban terrain. Within general rural/low-relief terrain, the interim model further distinguishes three specific important subclass terrain types as discussed in Chapter 3, namely, continuous forest, open farmland, and open wasteland (e.g., desert, marsh) or grazing land with very low incidence of large discrete vertical objects (e.g., farmstead buildings, feed storage silos, isolated trees, etc.) such as typically occur in farmland. Within rural/high-relief terrain, particularly separated out are the two subclass terrain types of continuous forest and mountains. Within urban terrain, separated out is the subclass of urban areas as observed over open low-relief terrain supportive of multipath (see Chapter 3). Concerning the several subcategories of terrain contained within each of the three general terrain types in Table 4.2, the general category (a) is applicable only if the terrain in question fails to meet the specification of any of the subsequent specific subcategories within a group. That is, the general category applies to mixed or composite terrain that is neither completely open nor completely tree-covered. The subcategorization of terrain within each major group becomes increasingly important with decreasing frequency. For completeness, a fourth general category comprising terrain observed at negative depression angle is required. Terrain observed at negative depression angle is usually relatively steep.

Approaches to Clutter Modeling 295

Table 4.2 Multifrequency Weibull Parameters of Land Clutter Amplitude Distributions aw ° (dB) σw Depression Terrain Type

Frequency Band

Resolution(m2 ) X-Band 103 106

Angle (deg)

VHF

UHF

L-

S-

a) General rural

0.00 to 0.25 0.25 to 0.75 0.75 to 1.50 1.50 to 4.00 > 4.00

-33 -32 -30 -27 -25

-33 -32 -30 -27 -25

-33 -32 -30 -27 -25

-33 -32 -30 -27 -25

-33 -32 -30 -27 -25

3.8 3.5 3.0 2.7 2.6

2.5 2.2 1.8 1.6 1.5

b) Continuous forest

0.00 to 0.30 0.30 to 1.00 > 1.00

-45 -30 -15

-42 -30 -19

-40 -30 -22

-39 -30 -24

-37 -30 -26

3.2 2.7 2.0

1.8 1.6 1.3

c) Open farmland

0.00 to 0.40 0.40 to 0.75 0.75 to 1.50

-51 -30 -30

-39 -30 -30

-30 -30 -30

-30 -30 -30

-30 -30 -30

5.4 4.0 3.3

2.8 2.6 2.4

d)

0.00 to 0.25 0.25 to 0.75 > 0.75

-68 -56 -38

-74 -58 -40

-68 -46 -40

-51 -41 -38

-42 -36 -26

3.8 2.7 2.0

1.8 1.6 1.3

Rural/Low-Relief

Desert, marsh, or grassland (few discretes)

Rural/High-Relief a)

General rural

0 to 2 2 to 4 4 to 6 >6

-27 -24 -21 -19

-27 -24 -21 -19

-27 -24 -21 -19

-27 -24 -21 -19

-27 -24 -21 -19

2.2 1.8 1.6 1.5

1.4 1.3 1.2 1.1

b)

Continuous forest

any

-15

-19

-22

-22

-22

1.8

1.3

c)

Mountains

any

-8

-11

-18

-20

-20

2.8

1.6

Urban a)

General urban

0.00 to 0.25 0.25 to 0.75 > 0.75

-20 -20 -20

-20 -20 -20

-20 -20 -20

-20 -20 -20

-20 -20 -20

4.3 3.7 3.0

2.8 2.4 2.0

b)

Urban, observed on open low-relief terrain

0.00 to 0.25

-32

-24

-15

-10

-10

4.3

2.8

0.00 to -0.25 -0.25 to -0.75 < -0.75

-31 -27 -26

-31 -27 -26

-31 -27 -26

-31 -27 -26

-31 -27 -26

3.4 3.3 2.3

2.0 1.9 1.7

Negative Depression Angle a)

All, except mountains and high-relief continuous forest

The interim clutter model of Table 4.2 consists of 27 combinations of terrain type and depression angle. For each combination, the model provides Weibull mean clutter strength as a function of radar frequency f, VHF through X-band, as σ w° ( f ) , and provides the Weibull shape parameter as a function of radar spatial resolution A over the range between 103 and 106 m2, as aw(A). The shape parameter is obtained from linear interpolation on log10(A) between the values provided for A = 103 m2 and A = 106 m2. The total matrix of information in Table 4.2 contains all the important trends that are observed in the measured clutter amplitude distributions as discussed in Chapters 2 and 3.

296 Approaches to Clutter Modeling

Many of the important trends of variation in the σ w° data of Table 4.2 are plotted in Figure 4.4. These trends are now discussed in some detail. This discussion to some extent summarizes and reiterates previous discussions of the clutter measurement data in Chapters 2 and 3. Thus, in Figure 4.4, in general rural terrain of both low and high relief, mean clutter strength increases with depression angle but is invariant with frequency. That is, within the shaded region clutter strength rises with increasing depression angle both within the rural/low-relief and within the rural/high-relief regimes. In continuous forest, however, mean clutter strength depends both on depression angle and frequency; whereas in open farmland, mean clutter strength is invariant both with depression angle and frequency, except at low depression angle on level terrain where a significant multipath propagation loss occurs at low frequencies. Note that at intermediate depression angles in Figure 4.4, both forest and farmland fall in closely with general rural/low-relief terrain in terms of mean clutter strength. 0 Urban (Open Terrain)

Mtns Hi D.A

.

–20 Urban

σ °w (dB)

Cont For XXX

–40 Des, Marsh, Grass

Rur/ Hi Rel

Int D.A.

Neg. D.A.

Rur/Lo Rel

Open Fmlnd Hi D.A. Lo D.A. . D.A Lo

Int D.A.

–60

Lo D

1000

100

–80

10,000

.A.

VHF

UHF

L-

S-

X-BAND

Frequency (MHz) D.A. Hi Int Lo Neg

= = = = =

Depression Angle High Intermediate Low Negative

Cont For Des Fmlnd Marsh Mtns

= = = = =

Continuous Forest Desert Farmland Marshland Mountains

Rur/Hi Rel Rur/Lo Rel

= =

Rural/High Relief Rural/Low Relief

Figure 4.4 Weibull mean clutter strength vs frequency for all terrain types.

Urban complexes observed over low-relief open terrain provide large mean clutter strengths at high frequencies partly because of their broadside aspect, but at low frequencies these large returns are decreased significantly through multipath loss. However, in more general

Approaches to Clutter Modeling 297

composite terrain, mean clutter strength from urban complexes is 10 dB weaker than at high frequencies on open terrain and is frequency invariant. On discrete-free desert, marsh, or grassland, mean clutter strength is weaker than for other terrain types. Again, at low and even intermediate depression angles, there is a large multipath loss due to decreased illumination strength at the lower frequencies, and this loss is greater and extends to higher frequencies than in farmland because the clutter sources are much lower in such terrain (e.g., a sagebrush bush) than in farmland (e.g., a silo). Note that, aside from differences in intrinsic σ°, propagation loss by itself would act to continue to decrease mean clutter strength σ °F 4 from UHF to VHF at low and intermediate depression angles on open desert, marsh, or grassland; however, repeat sector data from four different sites and at all parametric variations of polarization and resolution show that mean clutter strength actually rises slightly from UHF to VHF, indicating that intrinsic σ° is considerably greater at VHF than UHF in such terrain. Next mean clutter strength is compared between desert and forest at X-band. At low and intermediate depression angles, mean strength in desert terrain is 5 or 6 dB weaker than in forest terrain, but at high depression angle >1° (and on the basis of two different desert measurement sites at all combinations of polarization and resolution), mean strength in desert is equal to that in forest terrain (i.e., at X-band, looking down at sagebrush vegetation is equivalent to looking down at a forest canopy). The data in Figure 4.4 cover 66 dB of variability in mean clutter strength, from mountains at VHF to desert at UHF. Of course, cell-to-cell variability in clutter amplitude statistics is even greater. The trends of variation in the aw data of Table 4.2 that determine cell-to-cell variability are shown in Figure 4.5 for rural/low-relief terrain. These results illustrate that spreads in clutter amplitude distributions due to cell-to-cell variability decrease both with decreasing spatial resolution and with increasing depression angle. Over and above these basic dependencies, the results in Figure 4.5 and Table 4.2 also show that aw in open farmland is greater than in general rural/low-relief terrain, whereas aw in continuous forest is less than in general rural/low-relief terrain; and that aw in rural/high-relief terrain is less than in rural/low-relief or urban terrain (see Figure 2.47).

4.2.3 Error Bounds An interim multifrequency ground clutter model is provided in Table 4.2 for determining ground clutter amplitudes from visible regions of terrain in surface-sited radars. This interim model consists of a manageable set of empirically derived numbers that in total establishes an orderly rationale for the specification of such clutter amplitudes over their many order-of-magnitude range of variations, based on terrain type, depression angle, and the important radar parameters of frequency and resolution. What are the error bounds in the interim modeling information presented in Table 4.2? The discussion of temporal and spatial variation in low-angle ground clutter previously provided in Section 3.7.3 provides some guidance in this matter. On the basis of repeat sector measurements over the two to three week stay at every Phase One site, the 1-σ diurnal variability in mean clutter strength, largely due to changes in weather, is specified in Section 3.7.3 to be 1.1 dB. The Phase One equipment made six repeated visits to selected sites to investigate seasonal variations. On the basis of these measurements, the 1-σ

298 Approaches to Clutter Modeling

6 Rural/Low-Relief General Rural

xxxxx

Continuous Forest Open Farmland Desert, Marsh, Grassland

Shown by Depression Angle (deg)

Weibull Shape Parameter aw

5

4

0.0

x 3

x

0t

x x

0.75

x

to 1.

50 x x x x 1.0 x

0.3 to

2

x x x

0.00

x x x 0.25

to 0.7

x x

>0.75

x 0.0 t

x x 1.5 to 4

>4

x x x >1 x x x

x

0.40

.25

0.0

x

0 to

x

.40

to 0

0.75 to o 0.3

5

to 0

o0

.75

1.50 0.25

0.2

5

to 0

.75

x x

x x x x x x x x x x x x x x x x x x x x x x x

1 103

104

105

106

Spatial Resolution A (m2)

Figure 4.5 Weibull shape parameter aw vs radar spatial resolution for rural/low-relief terrain types.

seasonal variability in mean clutter strength is specified in Section 3.7.3 to be 1.6 dB. Such long-term temporal variations in mean clutter strength from macroregions of terrain may be contrasted with the spatial region-to-region 1-σ variability that is specified in Section 3.7.3 to be 3.2 dB, on the basis of region-to-region variations in repeat sector mean clutter strength within similar regions. Thus, it is apparent that the numbers comprising the interim clutter model are statistical averages. These averages establish important trends, but actual realizations of clutter will deviate from the predicted average numbers of the model.

Approaches to Clutter Modeling 299

4.3 Non-Angle-Specific Modeling Considerations In Section 4.2, the measured data were used to develop an interim clutter model for use in determining site-specific radar system performance, where the actual terrain at the radar site is deterministically represented through digitized terrain elevation data. Such a sitespecific clutter model can provide, with reasonable fidelity, detailed measures of clutterlimited radar performance as a particular low-altitude airborne target is engaged by a particular radar at a particular site. At a higher level of abstraction, however, there remains a need for a non-patchy clutter model for use in computing the limiting effects of ground clutter on system performance in a generic sense, independent of how specific terrain features and resulting patchiness varies from site to site. This section brings the large database of Phase Zero ground clutter measurements statistically to bear to provide simple non-patchy clutter modeling information that captures the important statistical and parametric variations in the database. One important characteristic of a PPI clutter map is the obvious dissipation of the clutter with increasing range, which is automatically incorporated in a patchy site-specific model. Consideration of how best to implement this characteristic in a non-patchy non-site-specific model leads to discussion of explicit effects of range on low-angle clutter.

4.3.1 Phase Zero Results Figure 4.6 shows measured clutter maps to 47-km maximum range for six different sites, in order of increasing effective radar height. Figure 4.7 shows percent circumference in clutter vs range for the same six sites. The details of each pattern of spatial occurrence of clutter in Figure 4.6 are specific to the terrain features at that site. In all such patterns, however, the patches of clutter become fewer and farther between with increasing range so that, as shown in Figure 4.7, the amount of clutter that occurs gradually diminishes with increasing range from the site. These two figures also show that the amount of clutter that occurs is a strong function of the effective height of the radar. Effective radar height is defined with respect to visible terrain and includes both the height of the hill on which the radar is situated and the antenna mast height (see Section 2.2.3). The somewhat differing higherorder effects of hill height and mast height on terrain visibility are discussed in Appendix 4.B. It is apparent in Figures 4.6 and 4.7 that higher radars see clutter to longer ranges. Figure 4.8 provides general information on clutter extent and strength by averaging measurements like those of Figures 4.6 and 4.7 from many sites. Figure 4.8(a) shows percent of circumference in clutter vs range averaged across 86 sites. The resultant clutter visibility curve is approximately linear over most of its extent as displayed on the logarithmic vertical scale employed in Figure 4.8(a). This linearity indicates that in general the amount of ground clutter that occurs in surface radar decreases exponentially with increasing range, thus quantifying the observations of the preceding paragraph. The curve of Figure 4.8(a) represents the best non-site-specific information that the large Phase Zero database can deliver when brought to bear to answer the general question, how far out does ground clutter go? Because ground clutter diminishes gradually (i.e., exponentially) with increasing range, this question must be answered conditionally in terms of a threshold on how much clutter is of concern. As an example, Figure 4.8(a) indicates that in general 10% of circumference is in clutter at 19-km range.

300 Approaches to Clutter Modeling

(a) Coaldale: Effective Radar Height = 3 m

(d) Magrath: ERH = 94 m

(b) Shilo: ERH = 18 m

(c) Cold Lake: ERH = 40 m

(e) Calgary W: ERH = 124 m

(f) Equinox Mt.: ERH = 678 m

Figure 4.6 Phase Zero clutter maps for six sites. In each map, maximum range = 47 km (10-km range rings). Results shown are for full Phase Zero sensitivity.

Percent circumference in clutter represents the probability of discernible clutter Pc vs range r. Pc(r) is dependent on radar sensitivity. If it is assumed that clutter arises only from geometrically visible terrain and that over visible terrain clutter is Weibull-distributed, then it is straightforward to numerically extrapolate the Phase Zero clutter visibility data of Figure 4.8 to radars of higher sensitivity. In this extrapolation, Pc(r) = Pv(r)·PD(r), where Pv(r) is the probability that the terrain is geometrically visible, and PD(r) is the probability that the clutter strength is above radar noise level given that the terrain is visible. PD(r) is simply the Weibull cumulative (integral) distribution function obtained by integrating Eq. (2.B.18) with radar noise level at range r as the lower limit of integration [(cf. Eq. (2.B.21) obtained with zero as the lower limit of integration]. PD(r) is easily numerically evaluated, once the Weibull coefficients of the clutter and the noise level of the radar are specified. If the ratio of PD(r) for a radar of increased sensitivity to PD(r) for Phase Zero sensitivity is computed, then clutter visibility Pc(r) for the radar of increased sensitivity is simply the product of this ratio and Pc(r) for Phase Zero as given by the data in Figure 4.8. The validity of such extrapolation of Phase Zero clutter visibility data to higher sensitivity radars is dependent on the soundness of the assumptions, which deteriorate with large departure from Phase Zero sensitivity. Discussion now turns to Phase Zero clutter amplitude distributions as obtained within macropatches of visible terrain. Figure 4.8(b) shows the cumulative distribution of mean clutter strengths, one mean value per clutter patch, over all the 2,177 patches for which Phase Zero clutter amplitude distributions were determined. These 2,177 macropatches were selected from 96 different measurement sites. The curve of Figure 4.8(b), as plotted on a logarithmic (i.e., decibel) abscissa, is essentially linear over most of its central extent.

Percent Circumference in Clutter

Approaches to Clutter Modeling 301

100

10

1

0.1 0

10

20

30

40

0

Percent Circumference in Clutter

Range (km) (a) Coaldale: ERH = 3 m

10

20

30

40

Range (km) (b) Shilo: ERH = 18 m

0

10

20

30

40

Range (km) (c) Cold Lake: ERH = 40 m

100

10

1

0.1 0

10

20

30

40

Range (km) (d) Magrath: ERH = 94 m

0

10

20

30

40

Range (km) (e) Calgary W: ERH = 124 m

0

10

20

30

40

Range (km) (f) Equinox Mt: ERH = 678 m

Figure 4.7 Percent circumference in clutter vs range for six sites. Phase Zero data, 47-km maximum range, 150-m range resolution, clutter threshold is 3 dB above full sensitivity.

Abscissa

0.999

F4

0.7 0.5

Probability That

Percent of Circumference in Clutter

Normal Scale 100

0.3

10

1

0.1 0

10

30

20

Range (km) (a)

40

0.99 0.9

0.1 0.01 0.001 –60

–50

–30

–40

–20

–10

4

F (dB) (b)

Figure 4.8 General spatial extent and strength of low-angle radar ground clutter: (a) decrease of clutter occurrence with range and (b) distribution of mean strengths of ground clutter patches.

This linearity implies that the distribution of mean strengths of clutter patches (in units of m2/m2) is lognormal. The data in Figure 4.8(b) represent Phase Zero’s best answer to the

302 Approaches to Clutter Modeling

next general question, how strong is ground clutter? Figure 4.8(b) indicates that mean ground clutter strength varies over five orders of magnitude. Thus this question also must be answered conditionally in terms of probability of occurrence. The median or 50percentile value of mean clutter strength in this figure is –31 dB (i.e., half of all measured values of mean clutter strength occur above –31 dB, half below). The mode or most frequently occurring value of mean clutter strength in Figure 4.8(b) is –40 dB.

4.3.2 Simple Clutter Model In developing a simple non-site-specific clutter model, the first issue that must be confronted is terrain visibility. As previously discussed, from most places on the surface of the real earth, visibility to terrain is spatially patchy. To an observer looking out from the site, high regions are visible and intervening low regions are masked. Most of the relatively significant clutter comes from directly (geometrically) visible terrain. As range increases, the visible terrain patches become fewer and farther between until beyond some maximum range, no more terrain is visible. Thus on the real earth, terrain visibility and hence the spatial occurrence of clutter is a gradually diminishing function of increasing range. Here, a simple non-site-specific clutter model means a non-patchy model that is spatially homogeneous and isotropic. The sort of earth that provides this kind of clutter is a cue ball earth. That is, if the site-specific macroscopic terrain features that exist at every real site are suppressed, what remains is a cue ball, conceptually devoid of all macrofeature, but uniformly microrough to account for homogeneous and isotropic diffuse clutter backscatter. On such a cue ball devoid of macroscale terrain features, the clutter patches observed at real sites expand to encompass all of the terrain out to a single-valued horizon, RC. The resulting binary visibility function is imparted to the simple clutter model. There may be a temptation to spatially dilute the clutter amplitude statistics as actually measured within large macropatches of visibility with the large amounts of macroshadow that exist on the real earth between the patches. Such spatial dilution would artificially diminish clutter strengths with increasing range in a way that would certainly not be measured by a real radar, either on a real earth-sized cue ball or on the real earth itself. These matters are discussed at greater length in Appendix 4.C. Such considerations lead to the simple, non-patchy, non-site-specific clutter model shown in Figure 4.9. This simple model provides homogeneous clutter within a circular region centered at the radar. The mean clutter strength within this region is given by σ w° , and the radial extent of the region by the clutter cut-off range RC. The statistically important effect of increasing macroshadow with increasing range shown in Figure 4.8(a) is used to set the radial extent of the homogeneous clutter region RC. This setting of RC is done as a statistical threshold on clutter visibility in the measured data. That is, the user first specifies the minimum spatial amount of clutter that begins to degrade the user’s systems (e.g., 20%). Then the range at which that amount of clutter generally occurs in the measurements is used as the clutter cut-off range RC in the simple model (e.g., 12 km). The effective height of the radar above the surrounding terrain is the major parameter affecting how far ground clutter occurs. This effect is illustrated by the data of Figure 4.10, in which the exponential decrease of clutter occurrence with increasing range shown in Figure 4.8(a) is parameterized in five regimes of effective radar height, using the same 86site set of data upon which the result of Figure 4.8(a) is based. Figure 4.10 may be compared with Figure 4.7. Again, it is apparent that higher radars see clutter to longer

Approaches to Clutter Modeling 303

Smooth Spherical Earth No Specific Features Hence No Patchiness in Clutter

Two Parameters (1) Clutter Cutoff Range Rc (2) Clutter Strength σ°w

Figure 4.9 Non-site-specific clutter model.

ranges. The simple model incorporates this important effect of radar height by parameterizing the statistical procedures for setting clutter cut-off range to be dependent on radar height in the measured data. The results of these procedures for specifying clutter cut-off range RC in the non-sitespecific model are summarized in Table 4.3. If 20% of circumference in clutter on the real earth is accepted as a baseline threshold above which clutter is expected to have substantial impact on radar system performance, Table 4.3 indicates that at a general radar height of 40 m, this threshold in clutter occurrence will be exceeded at ranges ≤ 12 km. If it is known that the radar is substantially lower or higher than this general height of 40 m, the clutter cutoff range decreases to 7 km or increases to 22 km, respectively, for the same baseline threshold in clutter occurrence. If the threshold in clutter occurrence rises to as much as 50%, clutter extents above such a high threshold are relatively benign, 3 or 4 km, whereas if the threshold in clutter occurrence drops to as little as 2%, clutter extents are quite severe, ranging from 21 to 48 km depending on radar height. Note that except for this latter severe situation, clutter extents as derived empirically in Table 4.3 from clutter visibility on the real earth are usually much less than range to the spherical earth horizon on a cue ball, illustrating that on the real earth, terrain relief usually dominates over earth sphericity in influencing terrain visibility and horizons. With the radial extent of the homogeneous region determined in this manner for the simple model, the mean strength of the clutter σ w° that exists within this region must be specified.

304 Approaches to Clutter Modeling

Percent of Circumference in Clutter

100

10

Effective Radar Height (m) 1.0 120–680 60–120 30–60 15–30 0–15 0.1 0

20

10

30

40

Range (km)

Figure 4.10 Average ground clutter occurrence vs range as a function of effective radar height. Table 4.3 Clutter Cut-Off Range Rc for Use in Non-Site-Specific Clutter Modeling Percent of Circumference In Clutter for Ranges ≤ Cut-Off Empirical Threshold Underlying Model Development

Clutter Cut-Off Range Rc (km) Clutter Visibility Variations

Effective Radar Height Applicable To Cue-Ball Model

Low (15 m)

General (40 m)

High (200 m)

≥ 50

100

3

4

3

Benign (least)

≥ 20

100

7

12

22

Baseline

≥2

100

21

37

48

Severe (most)

16

26

58

Spherical Earth Horizon (km)

To do so, mean clutter strengths as measured over many macropatches in the measured data are used as illustrated by the data of Figures 2.23, 2.24, 2.35, and 4.8(b). Table 4.4 provides a resulting matrix of information showing how mean clutter strength varies with terrain type and probability of occurrence. If the 50-percentile level is accepted as a baseline probability of occurrence, then in completely general or non-terrain-specific circumstances the data suggest σ w° = –31 dB as the best single measure of mean clutter strength. However, if it is known that the terrain is either relatively low or high relief or urban, mean clutter strength σ w° may be adjusted to –33, –27, or –23 dB, respectively, at the same 50-

Approaches to Clutter Modeling 305

percentile probability of occurrence. Proceeding to a worst-case/best-case assessment, if 90- and 10-percentile probabilities of occurrence are accepted as reasonable measures of strong and weak mean clutter strengths, respectively, then by these measures the data in Table 4.4 show that strong mean clutter strength is generally 7 or 8 dB stronger than baseline, and weak clutter is generally 7 or 8 dB weaker than baseline, both in general circumstances and for the three main terrain types. Table 4.4 Mean Clutter Strength for Use in Non-Site-Specific Clutter Modeling Percent of Measured Patches ° ≤ with σw Tabulated Value

Mean Clutter Strength σ°w (dB) Clutter Strength Variations

Terrain Type Rural/ Low-Relief

General

Rural/ High-Relief

Urban

10

-41

-40

-34

-31

Benign (weakest)

50

-33

-31

-27

-23

Baseline

90

-26

-23

-20

-15

Severe (strongest)

4.3.3 Further Considerations 4.3.3.1 Clutter Strength vs Range Ground clutter strength depends principally on the depression angle at which the backscattering terrain point is illuminated as it varies with terrain elevation from point to point over a site. The simple, non-patchy, non-site-specific clutter model does not incorporate local variability in terrain elevation and hence would be able to bring in depression angle only as a very slowly diminishing function with increasing range on a spherical earth. Is this small rate of change of illumination angle with range sufficient to cause an observable general dependence of clutter strength with range in measured data? To begin to answer this question, consider again the measured clutter maps of Figure 4.6. These measurements are shown at full Phase Zero sensitivity. When the clutter in the maps is shown only above a gradually increasing threshold in clutter strength, except at very close ranges the density of the clutter sources within patches gradually diminishes relatively uniformly over the remainder of the map at longer ranges, indicating that within patches of visibility, clutter strength is relatively independent of range beyond the first few kilometers (e.g., see Figure 4.19). That is, the clutter does not disappear at the longer ranges first. Sector display plots of clutter amplitude vs range such as are shown in Figures 2.10, 2.18, 2.20, and 3.11 also do not indicate any general diminishment of clutter strength with range through patches of clutter occurrence. This matter is discussed further in Appendix 4.A, in which similar sector display plots are shown to much longer ranges. Results generalizing the lack of range dependency in clutter are provided in Figure 4.11. Clutter amplitude statistics combined from 10 different sites are separated into four annular regimes of range—from 5 to 15 km, 15 to 25 km, 25 to 35 km, and 35 to 45 km. Care must be taken to properly normalize the results. First, because the amount of clutter rapidly

306 Approaches to Clutter Modeling

diminishes with increasing range, only those cells in which discernible clutter are measured above the radar noise floor are included. Second, because radar sensitivity diminishes with increasing range, the results are normalized to range-independent sensitivity by further conditionally limiting included cells to only those in which clutter signals are stronger than system noise at the longest ranges, that is σ°F4 > –24 dB. The results of Figure 4.11 indicate that there is essentially no dependence with range in the resulting clutter amplitude statistics. These results are discussed further in Appendix 4.C. Because clutter strength shows no major dependence upon range, σ w° in the simple nonpatchy model abruptly transitions from a constant nonzero m2/m2 value within RC to zero m2/m2 beyond RC. This abrupt transition keeps before the user the simple non-site-specific nature that was initially postulated as a requirement of the model in the results of system studies implementing the model. When step function performance characteristics are unacceptable, it is not realistic to arbitrarily decrease clutter strength σ w° with increasing range in the simple model to introduce more acceptable, continuous characteristics with range and avoid step function characteristics. In reality, it is the spatial occurrence of clutter, not its strength, that diminishes with range. 0.999

0.99 0.97 0.95

35 to 45 km

Given That σ°F4 ≥ –24 dB

Probability That σ°F4 ≤ Abscissa,

0.9 5 to 15 km

0.8

15 to 25 km 0.7

25 to 35 km 35 to 45 km

0.6

5 to 15 km

0.5 0.4 0.3

0.2

0.1 –20

–10

σ°F4 (dB)

Figure 4.11 Clutter amplitude statistics in four regimes of range.

0

Approaches to Clutter Modeling 307

It is certainly incorrect to simply multiply the clutter strength by the visibility function to provide what may be thought to be a more desirable modeling characteristic of diminishing clutter strength with increasing range. Such a procedure involving azimuthal averaging (i.e., spatial dilution of clutter with macroshadow) is only applicable to an unrealistic radar with a 360° omnidirectional azimuth beam [in such circumstances, it is the shadowless mean that is multiplied by the visibility function; see Appendix 4.C for further discussion of this matter, in particular, Eq. (4.C.4) and Figures 4.C.16 and 4.C.17)]. Thus when step function performance characteristics are unacceptable, a more sophisticated clutter model incorporating a gradually diminishing clutter occurrence or visibility function must be employed. The site-specific clutter model discussed in Section 4.2 incorporates gradually diminishing terrain visibility with increasing range as determined by line-of-sight geometric terrain visibility in DTED. In addition, a patchy nonsite-specific clutter model was developed [3] by the Defence Evaluation and Research Agency/U.K. which conducted analyses of some subsets of Phase One clutter data coordinated with Lincoln Laboratory. The patchy non-site-specific clutter model was based on the empirically observed exponential decrease of clutter visibility with range as shown in Figures 4.8(a) and 4.10 to provide stochastic realizations of random patchiness representative of a particular type of terrain, as opposed to deterministic site-specific realizations of patchiness. In the stochastic approach to patchiness, the characteristics of the terrain that determine the patchiness are obtained by processing DTED over the general terrain of interest. Such stochastic techniques for providing non-site-specific patchiness in a clutter model are more appropriate for low-relief terrain, as high-relief terrain is too specific in terms of dominant terrain features within the radar coverage area to be properly characterized as a random process.

4.3.3.2 Spread in Clutter Amplitude Statistics Ground clutter amplitude distributions have wide spread resulting from cell-to-cell spatial variation within macropatches of clutter occurrence. This wide spread is illustrated by the data in Figure 4.12, which show percentile levels between 50 and 90 in ground clutter amplitude distributions both for general terrain and for the three primary terrain types. Each percentile value plotted in Figure 4.12 is the median of the set of corresponding individual percentiles from all clutter patches of that class within the overall set of 2,177 clutter patch amplitude distributions. Figure 4.12 typically shows about 16 dB of variation between 50- and 90-percentile levels. Furthermore, this figure also shows that the mean value, indicated by a vertical arrow, is usually close to the 90-percentile level (except for rural/high-relief terrain in which illumination angles are higher and hence the influence of discrete sources, which tend to dominate the mean, are reduced). Should a percentile level lower than the mean be used in selecting a value for σ w° in the simple model? This question has no simple answer. The data displayed in Figure 4.12 illustrate the conceptual difficulty of modeling a widely varying dynamic random process with a single deterministic number. However, some guidance may be offered toward answering this question. In a system study simulating the existence of low-altitude targets at a number of Phase One clutter measurement sites, the resultant radar performance, averaged over all sites, was approximately the same as would be computed if a constant clutter strength of σ w° = –38 dB was used over all visible terrain. This value of clutter strength occurs at the 70-percentile level on the general terrain curve of Figure 4.12, approximately halfway between the mean and the median. Recall that the most probable

308 Approaches to Clutter Modeling

90

Rural/ Low-Relief 80

Percentile

General

70 Rural/ High-Relief

Urban

60

OR

= Mean

50 –50

–40

–30

–20

␴°F4 (dB)

Figure 4.12 Clutter strength as a function of percentile level in the amplitude distribution.

value of mean clutter strength in the general data of Figure 4.8(b) is –40 dB, perhaps a fortuitous concurrence. The reader is cautioned that this is a particular result of only one study and that such values of constant-σ° that provide equivalent system performance as real clutter (or site-specifically simulated clutter) are highly specific to the particular radar system and performance parameters under consideration. In any case, the data of Figure 4.12 allow investigators to adjust modeling values of σ w° away from the mean values shown in Table 4.4, if they so desire.

4.3.3.3 Database Depth The easy-to-use data for RC and σw° in Tables 4.3 and 4.4 capture the most important first-level effects contained in the large database of measurements for simple non-sitespecific modeling applications. Consideration of higher-order effects can provide everincreasing specificity of information. For example, consider the distributions of mean strength in six classes of landform and land cover provided earlier in Figures 2.23 and 2.24, respectively. One can imagine similar distributions by landform and land cover for median strength or for other statistical measures of the patch amplitude distributions. The data in Tables 4.5 and 4.6 provide quantitative measures of distributions of means, ratios of standard deviation-to-mean, medians, and various percentile levels, by landform and land cover, respectively. Thus the data of Tables 4.5 and 4.6 may be drawn upon to expand the simplified information of Table 4.4 to other probabilities of occurrence, other measures of strength (e.g., median), and other landform and land cover types

Approaches to Clutter Modeling 309

The statistical attributes shown in the second column of Tables 4.5 and 4.6 are now defined more explicitly. Observe in Figures 2.23 and 2.24 that the distributions are approximately lognormal. As a result, it is useful to define the mean and standard deviation of the normally distributed logarithmic quantity. These two quantities are shown as the first (i.e., top-most) and second attributes for each patch amplitude statistic. The third attribute shown is the median, which itself just transforms logarithmically. If the logarithmic quantity is normally and hence symmetrically distributed, its mean and median must be identical. The data in Tables 4.5 and 4.6 indicate that these two quantities (i.e., the first and third attributes, respectively) are, indeed, often nearly equal. Once it is assumed that the distribution is approximately lognormal, all other attributes of the distributions of both the logarithmic quantity and the more fundamental underlying linear quantity immediately follow from the first and second attributes provided in Tables 4.5 and 4.6. However, the fourth and final attribute for each patch amplitude statistic shown is the actual empirical mean of the basic linear quantity, which can be used either directly in its own right or as a further check on the degree of goodness of the approximating lognormal distributions. Now consider some of the trends with landform contained in the data of Table 4.5, where terrain slopes rise monotonically with landform class, left to right, from less than 1° for level terrain to between 10° and 35° for steep terrain (see Figure 2.23). Consider the median of M samples within a particular landform class of a given statistic (e.g., mean) of a clutter amplitude distribution as an easy-to-understand attribute, in that half the samples occur above the median level and half below. The median attribute is shown in increasing order of landform as the third row of numbers for each patch amplitude statistic in Table 4.5. Thus, as terrain slopes rise from level to steep, the third rows of the table show that (1) mean strengths rise over the 10-dB range from –33 to –23 dB; (2) median strengths rise over the 15-dB range from –48 to –33 dB; (3) spreads in amplitude distributions as measured by ratio of standard deviation-to-mean fall from 7 to 3 dB, spreads as measured by ratio of 99.9- to 50-percentile fall from 33 to 22 dB, and spreads as measured by ratio of mean-to-median fall from 15 to 10 dB. All the trends are monotonic with increasing terrain steepness as specified by the median value from a large number M of individual patch measurements within each landform class. In considering increasing specificity of information, recall that all the non-site-specific information presented in this section has been derived from X-band measurements. However, when considering that mean strengths from the three general terrain types of rural/low-relief, rural/high-relief, and urban are largely frequency independent, and that the simple model is already averaging out much fine-scaled variation, it is not unrealistic to apply the simple model across the general microwave regime. Investigators who wish to introduce more specific frequency dependence in non-site-specific investigation may, as a beginning, be guided by the multifrequency mean data of Table 4.2.

4.3.4 Summary The considerations guiding the development of the simple, non-angle-specific clutter modeling information presented in Section 4.3 are now summarized. The objective is to invest a simple clutter model with important general attributes as they have come to be understood in investigating the large database of clutter measurements. Of first-order importance is to distinguish between where the clutter occurs and its strength, given that it occurs. The simple, non-patchy model of Section 4.3.2 maintains this distinction by first specifying clutter cut-off range based on the measurements of clutter visibility, and then

Table 4.5 Various Average Measures of Ensembles of Clutter Patch Amplitude Statistics by Landform Patch Amplitude Statistic

Attribute of Set of Patch Amplitude Statistics over M Patches

M X dB

Mean m

X

M

(

(

SD X

M

m

Xσ

dB

Xσ

Standard Deviation to Mean

(

m X50

nth Percentile to 50 Percentile m n/ 50

X

n = 90,99,99.9 Number of Patches M

M

(

(X σ dB(50M X 50

Median

M dB

SD X σ dB

Xσ

M dB M dB M

(

(

SD X 50 dB M X 50 dB 50 M X dB 50

(

(

M X n/ 50 dB

(

Undulating

Inclined

Rolling

Mod Steep

Steep

-33.1

-32.0

-30.2

-28.9

-26.4

-22.8

6.9

6.1

5.9

4.8

4.7

5.1

-33.0

-32.0

-30.0

-29.0

-26.0

-23.0

-23.9

-26.6

-26.7

-26.0

-24.5

-19.7

7.3

7.0

6.0

4.6

3.9

2.9

2.9

3.1

2.8

2.1

2.1

1.9

7.0

7.0

5.0

4.0

4.0

3.0

8.4

8.2

7.0

5.2

4.5

3.3

-47.5

-45.8

-42.7

-41.4

-38.1

-35.0

6.8

7.5

8.7

9.3

10.3

12.6

-48.0

-46.0

-44.0

-42.0

-36.0

-33.0

-41.1

-39.3

-35.1

-33.1

-30.0

-24.5

14.4, 26.2, 32.7 14.9, 25.2, 31.6 14.8, 23.6, 29.1 16.4, 23.1, 27.3 15.6, 21.8, 25.6 16.4, 22.0, 24.1 M

(

SD X n/ 50 dB M X n/ 50 dB 50 M X n/ 50 dB

(

Level

dB

(X dB(50M X

Landform

(

5.9, 7.0, 8.4

5.2, 6.9, 8.6

5.4, 7.6, 9.2

7.0, 8.0, 8.6

7.7, 9.0, 9.7 10.2, 11.5, 12.2

14.0, 26.0, 33.0 14.0, 25.0, 32.0 15.0, 23.0, 29.0 16.0, 23.0, 27.0 14.0, 20.0, 24.0 13.0, 19.0, 22.0 19.1, 32.8, 40.6 18.5, 30.6, 39.5 18.1, 30.2, 38.0 22.5, 29.8, 34.7 23.4, 30.6, 36.2 27.2, 34.4, 37.5

571

556

338

216

152

94

Table 4.6 Various Average Measures of Ensembles of Clutter Patch Amplitude Statistics by Land Cover Patch Amplitude Statistic

Attribute of Set of Patch Amplitude Statistics over M Patches M X dB M

(

(

Land Cover Wetland

Rangeland

Agricultural

Forest

Barren

Urban

-37.5

-32.0

-31.8

-30.7

-29.1

-22.4

4.9

6.0

5.1

7.3

7.8

7.0

Mean

SD X dB

m

(X dB(50M

-38.0

-32.0

-31.0

-30.0

-29.0

-23.0

X

-34.6

-27.5

-28.5

-26.2

-22.3

-16.7

5.5

5.8

7.9

4.3

6.6

7.1

2.0

2.8

2.9

2.2

3.4

2.3

5.0

5.0

8.0

4.0

6.0

7.0

6.1

6.8

8.9

5.0

8.2

7.7

-48.3

-44.7

-47.2

-41.5

-42.4

-39.0

(

6.6

8.1

6.8

10.3

10.1

8.1

(X 50 dB(50

-48.0

-46.0

-47.0

-43.0

-45.0

-38.0

-42.3

-36.6

-41.0

-31.3

-29.4

-32.7

X

M

Standard Deviation to Mean m

Xσ

dB Xσ

( σ dB(M (Xσ dB (50M SD X

Xσ X 50

Median m X 50

m X n / 50

n = 90,99,99.9

Number of Patches M

M dB M dB M

(

SD X 50

X

nth Percentile to 50 Percentile

M dB

dB M

M 50

dB

M X n / 50 dB

(

13.5, 22.5, 27.3 15.2, 23.7, 29.0 15.5, 27.1, 34.3 14.4, 21.4, 25.1 14.2, 24.3, 30.2 16.3, 29.2, 34.8

(

M

(

SD X n / 50 dB M X n / 50 dB 50 M X n / 50 dB

(

4.7, 5.7, 6.3

6.6, 7.7, 9.0

5.8, 6.5, 7.8

6.4, 7.6, 8.4

7.3, 8.5, 9.8

5.3, 8.2, 9.6

13.0, 22.0, 27.0 14.0, 23.0, 29.0 15.0, 27.0, 35.0 13.0, 21.0, 24.0 12.0, 23.0, 31.0 16.0, 29.0, 36.0 16.7, 26.2, 31.3 21.9, 31.0, 38.6 19.7, 32.2, 40.6 20.6, 28.4, 33.0 22.6, 31.6, 39.0 20.6, 35.8, 43.4

92

371

788

684

115

122

312 Approaches to Clutter Modeling

specifying clutter strength based on measurements of clutter amplitude statistics within macropatches of occurrence. Furthermore, this model brings in the important parameters of radar height as it influences clutter extent and terrain type as it influences clutter strength. In this empirical manner, the model maintains its focus on the important firstlevel parameters in the real clutter phenomenon and statistically provides baseline central values of clutter strength and extent as they occur at real sites. The simple model does more than this, however. In addition to providing central measures, the model also specifies the distributions. As a result, besides providing information on baseline values of strength and extent of clutter, the model also provides parametric information on how severe (i.e., strong clutter to long-range) or how benign (i.e., weak clutter to short-range) the clutter can become, all in terms of specifiable probability of occurrence. It is this depth of statistical information in the simple model incorporating the extreme variability of the clutter phenomenon in quantitative terms of probability of occurrence, more so than the baseline central values of the model, that sets it apart from other single-point approaches in the literature.

4.4 Terrain Visibility and Clutter Occurrence Figure 4.10 in Section 4.3.2 shows percent of circumference in discernible clutter as a function of range for five regimes of effective radar height, as measured by the Phase Zero radar with a mast height of 15 m. These clutter occurrence curves of Figure 4.10 may be compared with those of Figure 4.B.3 (in Appendix 4.B) which show percent of circumference over which terrain is visible, also from a mast height of 15 m and as a function of range, for four regimes of site advantage. The occurrence of clutter (Figure 4.10) is strongly tied to line-of-sight visibility to terrain (Figure 4.B.3). That is, clutter occurs primarily within visible terrain macroregions in which discrete clutter sources are separated by randomly occurring microshadowed cells where the radar is at its noise level. Because of the microshadowing that occurs within macroregions of general visibility, the spatial extent of terrain visibility is greater than, and can be much greater than, the spatial extent of discernible clutter, as is apparent in comparing the curves of Figure 4.B.3 with those of Figure 4.10. Figure 4.13 shows the same terrain characterized by DTED obtained from two different sources, cartographic (maps) and photogrammetric (aerial photos). It is evident that photogrammetric source DTED are more precise and provide fine-scale terrain detail not contained in the cartographic source DTED. The cartographic source DTED capture the basic first-order characteristics of the terrain land-surface form, and are highly suitable for distinguishing macroregions of visible terrain from macroregions of shadow. The increased precision of photogrammetric source DTED may begin to allow deterministic prediction of microshadowed cells within macroregions of visibility. However, land cover elements are much more involved as the predominant sources of microshadow, as is seen in the following Cold Lake results.

4.4.1 Effects of Trees on Visibility at Cold Lake Trees are often dominant components of land cover affecting low-angle clutter (see Chapter 2, Section 2.4.2.5). Figure 4.14 shows the dramatic effect on clutter visibility of

Approaches to Clutter Modeling 313

Cartographic Source Data (Maps)

(a)

Photogrammetric Source Data (Aerial Photos)

(b)

Figure 4.13 Three-dimensional oblique views of the same terrain characterized by digitized terrain elevation data derived from two sources: (a) maps and (b) aerial photos. The terrain shown is a common 30 km × 30 km test area.

predicting tree heights in individual spatial cells at the measurement site of Cold Lake, Alberta. These results incorporate cell-specific tree cover information derived from Landsat data to obtain a more precise and accurate clutter map prediction. Figure 4.14(a) shows terrain elevation contour plots at 20-m intervals at Cold Lake, obtained from cartographic source DTED which does not include tree heights. In the northeast quadrant of this plot, the large level surface at 540-m elevation is water, the surface of Cold Lake. Four small islands are visible in the southern part of the lake. Figure 4.14(b) shows geometric visibility to bare ground (or water) based on these DTED. In Figure 4.14(b), visible areas of the ground are shown as black, and masked or shadowed areas of the ground are shown as white. Large continuous regions of the ground, including much of the surface of Cold Lake itself, are indicated as being within line-of-sight visibility in Figure 4.14(b). Figure 4.14(c) shows the Phase Zero ground clutter measurement at Cold Lake. The Cold Lake area in north-central Alberta is generally forested, although considerable regions have been cleared for farming. Within the large continuous black macroregions of visibility of Figure 4.14(b), actual clutter sources of σ °F4 ≥–30 dB occur as black micropatches in Figure 4.14(c), interspersed with a considerable degree of white microshadowing. Figure 4.14(d) shows how geometric visibility to the ground is modified by cell-specific inclusion of the occurrence of trees on the landscape. Landsat data for the Cold Lake area were classified in a scheme that included deciduous and coniferous tree categories. These data were registered with the terrain elevation data at Cold Lake. Each DTED cell that Landsat indicated as containing trees was increased in effective masking elevation by a statistical increment to account for the tree heights. A Gaussian statistical tree height increment was used such that: (1) mean height = 20 m, standard deviation = 0.9 m, for deciduous classification; and (2) mean height = 25 m, standard deviation = 1.8 m, for coniferous classification.

314 Approaches to Clutter Modeling

(a)

(b)

(c)

(d)

Figure 4.14 Effects of tree heights on ground clutter visibility at Cold Lake, Alta. The maximum range in each plot is 23.5 km. (a) terrain elevation contour plot, 20-m intervals; (b) geometric visibility to ground (black), no trees; (c) Phase Zero ground clutter measurement, σ °F4 ≥ –30 dB, 75-m range resolution; (d) geometric visibility to ground (black), with Landsat trees.

Including the effects of tree heights on terrain visibility in Figure 4.14(d) in this way greatly changes the character of the bare ground visibility map of Figure 4.14(b), mainly by introducing cell-specific microshadowing effects within large macroregions of visibility. The bare-earth model at Cold Lake [Figure 4.14(b)] shows much higher terrain visibility than when trees are accounted for [Figure 4.14(d)]. Much of the water surface of Cold Lake itself, indicated as visible without trees in Figure 4.14(b), becomes shadowed when trees are included in Figure 4.14(d). Whether shadowed or not, the water surface of Cold Lake is below the clutter strength threshold in Figure 4.14(c) and is indicated as white there. Thus, careful incorporation of site-specific and cell-specific variations in elevation, for example, due to trees, can account for much detailed feature in a measured

Approaches to Clutter Modeling 315

ground clutter map, based on geometric visibility considerations alone without any recourse to propagation or scattering physics.

4.4.2 Decreasing Shadowing with Increasing Site Height Although there exists much correlation in terms of general features between the measured Cold Lake clutter map of Figure 4.14(c) and the predicted map inclusive of tree height effects of Figure 4.14(d), careful examination indicates that on a more detailed cell-by-cell basis the correlation in these maps deteriorates. Successful reduction of clutter measurement data in a cell-specific manner in which measured clutter strength in a cell is associated with cell-specific geometric effects such as tree height and grazing angle would require terrain descriptive Geographic Information System (GIS) data of very high precision and accuracy. The reduction of measured clutter data as described in this book uses available DTED more simply to predict boundaries of macroregions of general terrain visibility, which are denoted as clutter patches. Then all of the measured clutter data within the boundaries of the specified patch, including cells at radar noise level, are assembled in a histogram of clutter strengths associated with the patch. Figure 4.15 shows six such measured histograms, one for each of six different sites (including Cold Lake) in order of increasing effective radar height. In these histograms, the 50-, 90-, and 99-percentile levels are shown as vertical dotted lines; the mean strength is shown as a vertical dashed line; and bins to the left side of the histogram that are significantly contaminated by radar noise samples are doubly underlined. Figure 4.16 shows the cumulative distributions above the highest noise contaminated bin for each of these six patches. Table 4.7 shows the incidence of microshadowing within each patch and its effect on the mean clutter strength of the patch. For example, the incidence of microshadowing for the Cold Lake patch for which the clutter strength histogram is shown in Figure 4.15(c) is 35%. It is evident in these results that the incidence of microshadowing within clutter patches decreases rapidly with increasing effective radar height. At low sites such as Coaldale and Shilo, the incidence of microshadowing can be very high (74% at Coaldale), but even so the mean clutter strength of the patch as determined within the upper- and lower-bound limits remains accurate (to within 0.014 dB at Coaldale). The mean strength of the patch determined in this manner includes the effects of microshadowing and is accurate independent of the sensitivity of the measurement radar; so also is the cumulative distribution for the patch (above the highest noise contaminated bin) as is shown in Figure 4.16 and from which the Weibull shape parameter aw is obtained. The shadowless mean clutter data shown in Table 4.7 which do not include samples within the histogram at radar noise level are highly dependent on the particular sensitivity of the measurement radar utilized and are not generally useful in clutter modeling (although such data are often inappropriately used in the existing clutter literature).

4.4.3 Vertical Objects on Level Terrain at Altona Prediction of clutter strengths based on the information provided in this book proceeds on the basis of many measured patch histograms and cumulative distributions of clutter strength such as are shown in Figures 4.15 and 4.16. Given the occurrence of a visible terrain macroregion, the subsequent distribution of modeled clutter over the region is specified as a broad Weibull distribution of appropriate shape parameter aw that includes the distribution of microshadowed cells at the correct incidence of occurrence as Weibull

316 Approaches to Clutter Modeling

35139 Samples

17388 Samples 10

Percent

Effective Radar =3m Height Depression Angle = 0.2˚

ERH = 94 m DA = 0.5˚

Percent

10

0

0 –50 –40

–30 –20 –10

0

10

–50

–40

–30 –20 –10

10

d) Magrath, Patch 21

38640 Samples

5459 Samples

10

10

ERH = 124 m DA = 1.9˚

Percent

ERH = 18 m DA = 0.3˚

Percent

0

σ˚F4 (dB)

σ˚F4 (dB) a) Coaldale, Patch 3

0

0 –50 –40

–30 –20

σ˚F4

–10

0

–50 –40

10

–30

(dB)

0

10

(dB)

e) Calgary West, Patch 1/2

b) Shilo, Patch 17

33966 Samples

22274 Samples

10

10

ERH = 678 m DA = 4.2˚

Percent

ERH = 40 m DA = 0.7˚

Percent

–20 –10

σ˚F4

0

0 –50 –40 –30

–20

–10

0

10

–50

–40

–30

–20 –10

0

σ˚F4 (dB)

σ˚F4 (dB)

c) Cold Lake, Patch 14

f) Equinox Mt., Patch 8/2

10

Figure 4.15 Clutter strength histograms for six patches selected from sites in different regimes of effective radar height. Phase Zero data, 75-m range resolution.

values below the noise level of the radar under investigation. Not only is the prediction of patch mean strength independent of radar sensitivity, but the incidence of microshadowing that is predicted is appropriate to the sensitivity of the radar under investigation, which can be different from that of the measurement radar. The predicted microshadowed cells within the patch for which clutter is being predicted occur randomly within the patch. Prediction of clutter in this manner thus proceeds accurately without being dependent on the availability of highly precise and accurate cell-specific GIS terrain descriptive data. For low-relief sites at short ranges where terrain visibility is very high (e.g., Figure 4.B.3, range < 10 km, site advantage regime = 10 to 35 m), visibility of discernible clutter is very

Approaches to Clutter Modeling 317

Weibull Scale 0.999 COA-3 = Coaldale, Patch 3 and so on for other sites and patches, see Fig. 4.15

0.97

DA =

Rayle

EQU

igh S

-8/2,

lope

aw = 1

124

L-1 CA

0.3

ER

0.4

/2,

1, E

RH

0.5

H=

=9

4m

0.6

m, DA

,D A=

0.7

= 67 8 m,

0.8

.9°

.3° =0 A ,D 7° 8m 1 0. = = A RH ,E ,D m -17 I 40 SH = H ER 4, -1 L CO

4.2°

m

ERH

,

A-3 CO

=3

MA G-2

Probability That σ°F4 ≤ Abscissa

0.9

H ER

° 0.2

=1

0.95

A= ,D

0.5 °

0.995 0.99

0.2 ERH = Effective Radar Height (m) DA= Depression Angle (deg) 0.1 –70

–60

–50

–40

–30

–20

–10

0

4

σ°F (dB)

Figure 4.16 Six clutter patch cumulative amplitude distributions from sites in different regimes of effective radar height. Phase Zero data, 75-m range resolution.

low (e.g., Figure 4.10, range < 10 km, effective radar height = 0 to 30 m). The reason for this can be seen in the PPI clutter map for Altona II shown in Figure 4.17. The terrain at Altona II is very level cropland, much like that at Coaldale [see Figure 4.15(a)]. From the 15-m Phase Zero antenna mast height, virtually all of the terrain within the 6-km maximum range clutter map of Figure 4.17 is predicted as visible using bare-earth DTED to model the Altona II terrain surfaces. Yet only within the nearest 1 or 2 km is the Phase Zero radar generally sensitive to the backscatter from these terrain surfaces. The several white sectors within the central black region are due to local masking by clusters of trees near the radar site. At longer ranges, it is the vertical objects on the terrain associated with the land cover that constitute strong backscatter sources. Many of these are associated with individual farmsteads and trees around farmsteads, although roads, rail lines, power line pylons, and stream beds are also sources of discernible clutter. The predominant rectangular pattern is associated with vertical objects along field boundaries. The reason backscatter from the field surfaces, as opposed to that from vertical objects on the fields, is weak and generally below the sensitivity of the measurement radar is partly because the illumination occurring

318 Approaches to Clutter Modeling

Table 4.7 Influence of Effective Radar Height on Incidence of Microshadowing for Six Clutter Patches

Site

Coaldale

Effective Radar Height (m)

Clutter Patch Number

Mean Clutter Strength σ˚F4 (dB)b

Percent of Microshadowed Cellsa

Upper Boundc

Lower Boundd

Shadowlesse

3

3

74.4

-28.332

-28.346

-22.428

Shilo

18

2

62.7

-32.808

-32.831

-28.548

Cold Lake

40

14

34.5

-30.781

-30.784

-28.946

94

21

25.2

-31.770

-31.770

-30.517

Calgary West

124

1/2

2.3

-25.270

-25.270

-25.169

Equinox Mt.

678

8/2

8.3

-19.499

-19.499

-19.123

Magrath

a Microshadowed cells are defined to be cells within patches at radar noise level. b 2 2

Computed in units of m /m and subsequently converted to dB. c Assign noise power level to noise cells. d Assign zero power level to noise cells. e Noise cells deleted.

N

W E

S

Figure 4.17 High resolution clutter map at Altona II, Manitoba. Phase Zero X-band data, 6-km maximum range setting, 9-m range resolution. The clutter map is 3 dB from full sensitivity. Clutter is black. North is zenith.

Approaches to Clutter Modeling 319

beyond 1 or 2 km is very close to grazing incidence and partly because many of these low surfaces are shadowed by land cover features not included in DTED (e.g., road and rail beds) that are a few feet higher than the field surfaces proper. Thus, all of the terrain in Figure 4.17 is within geometric line-of-sight visibility as modeled with DTED, yet the clutter sources are predominantly vertical objects associated with land cover as they exist distributed over this nominally visible terrain. As a result, the extent of discernible clutter (black) in Figure 4.17 is much less than the extent of nominally visible terrain, and a very high incidence of white microshadowed cells occurs between the black clutter cells.

4.4.4 Summary Determination of geometric terrain visibility in a bare-earth faceted terrain model based on DTED predicts general terrain regions in which clutter sources occur. Predicting the existence of clutter thus arises from a set of conditional probabilities, in which the first and most important condition for the existence of clutter at some spatial position is for that position to be geometrically visible. Consider again (see Section 4.3.1) that the probability of discernible clutter Pc is given by the probability that the terrain is geometrically visible Pv times the probability PD that the clutter strength is discernible, given that the terrain is visible. As discussed in Section 4.3.1, PD is easily numerically evaluated, once the Weibull coefficients of the clutter and the noise level of the radar are specified. Further conditions on clutter discernibility, in addition to the radar sensitivity at the point under consideration, are those associated with land cover, as discussed for Altona II and Cold Lake, or conditions associated with propagation. For example, as discussed in Chapter 3, at low radar frequencies such as VHF, little clutter may be received from lowrelief terrain because terrain reflections prevent illumination of the terrain, even though it is within line-of-sight. Or some VHF clutter may be received from regions somewhat beyond geometric visibility due to diffraction, if the radar sensitivity is high enough to discern relatively weak clutter (clutter strength for shadowed terrain depends on depth of shadow; see Appendix 4.D). The Phase One clutter data indicate that determination of bare-earth terrain visibility is the most useful first step in understanding the spatial occurrence of ground clutter, even at VHF. Effective radar height is the single most useful parameter combining site height and mast height for specifying the extent in range to which clutter occurs. Increasingly precise and accurate terrain descriptive GIS data together with ever more available computational power will allow increasingly accurate future specification of the landform and land cover contents of individual clutter cells. Even with such increased information, the extreme complexity of terrain will likely always require that the prediction of clutter strength from a cell (as opposed to the visibility of the cell) be based on a statistical approach. Whatever the level of fidelity of the available terrain descriptive information, it is evident from the Cold Lake and Altona II results that geometrical considerations dominate the low-angle ground clutter phenomenon, and a realistic approach to clutter prediction needs to involve prediction of geometric terrain visibility as a first step, followed by a statistical determination of clutter strength based on terrain relief and the available land cover information. Although geometry is of first-order importance in this process, once the realistic geometry is specified for a given radar observing the contents of a given visible cell over a given profile, then as a higher-order matter considerations of

320 Approaches to Clutter Modeling

propagation, scattering, and absorption physics can be brought to bear to provide increased understanding of the clutter strength phenomenon for that cell. But it is apparent that attempts to model low-angle clutter based on propagation and scattering physics applied as a first step to simplified or canonical representations of the earth that do not take into account specificities of geometry are foreordained to be exercises of the imagination.

4.5 Discrete vs Distributed Clutter 4.5.1 Introduction It has long been recognized that “. . . dominant land clutter signals are from discrete isolated targets . . . ”[4]. This section addresses important considerations involving the modeling of discrete clutter, as opposed to that of distributed clutter. A discrete clutter cell is an occasional, unusually strong, spatially isolated clutter cell for which the strong return is typically associated with some large physical point object in the cell. Discrete clutter is also occasionally referred to as point clutter or specular clutter in the literature. In contrast, distributed clutter is considered to be extensive in area over the clutter-producing surface rather than being associated with particular points on the surface. Before taking up the subject of approaches to modeling discrete clutter, it is necessary to first distinguish between conceptual models and empirical models. A conceptual clutter model is defined here as a hypothetical construct of the imagination that attempts to match selected important observed features in measured clutter data. On the other hand, an empirical clutter model is tied more tightly to direct trend analyses in actual measured clutter data, where the parametric trends observed in the data and their logical interrelationships and consequences themselves constitute the predictive clutter model. An empirical model is based on reduction and analysis of measured clutter data, whereas a conceptual model can be postulated apart from measured data. In the empirical approach, any preconceived parametric relationships arising from postulated conceptualized modeling constructs that cannot be verified to exist in the measured clutter data are not allowed to have a place in the final empirical modeling apparatus. This book takes an empirical approach to generating clutter modeling information, including the modeling of discrete clutter. Discrete clutter was early addressed as being of serious systems consequence in land clutter in airborne radar. As discussed in Chapter 2 (see Sections 2.3.4.2 and 2.4.4.3), distributed land clutter occurring at higher depression angles characteristic of airborne radar is a relatively well-behaved quasi-homogeneous, quasi-Rayleigh process of relatively constant return, i.e., exhibiting only small cell-to-cell variability, for example as illustrated in the σ ° vs range data shown in Figure 2.20 as measured at Cazenovia. In such a well-behaved, relatively constant clutter background, occasional spatially isolated discrete cells of very much stronger clutter amplitude clearly stand out as being entirely different in kind from the surrounding weaker quasi-homogeneous clutter and are easily capturable in measured data via spatial filtering and amplitude thresholding. Various measurement programs were established to characterize discrete clutter in airborne radar [5, 6]. An elaborate, largely conceptual clutter model was developed at IIT Research Institute (IITRI) for ground clutter in airborne radar including distributed and discrete components [7, 8]. The distributed component was modeled in terms of the backscattering

Approaches to Clutter Modeling 321

ground area density function σ°. The discrete component was modeled in terms of the RCS levels σ of discrete point scatterers, in which σ amplitudes were allowed to vary from 102 m2 to 106 m2 and in which the spatial occurrences of the discrete scatterers was specified to be uniformly random in terms of given numbers per km2. This discrete model was considerably extended to include temporally varying fluctuation statistics from the discrete sources, their correlation times, etc. The IITRI conceptual approach to modeling land clutter in terms of both a distributed σ° component and a discrete σ component remains intuitively satisfying. In turning to low-angle clutter as it occurs in surface-sited radar, the conceptual idea of a discrete clutter component separable from a distributed background becomes less clear cut. The complete spatial field of low-angle clutter is inherently a spiky process throughout, with strong and weak cells often closely intermingled and exhibiting extreme cell-to-cell variability, as evidenced for example in the σ° vs range data shown in Figure 2.18 as measured at Shilo. A useful point of view adopted in this book thus has been to conceptualize the complete field of low-angle clutter spatial amplitude statistics as arising from a sea of discretes, where the amplitudes of the discrete scatterers range over orders of magnitude. A similar point of view was previously taken in a brief early paper by Ward [9], in which the whole clutter spatial field was modeled as comprised only of discrete sources σ, without a distributed component σ°. Table 4.8 reproduces Ward’s clutter model. The table specifies both the RCS amplitudes σ of the discrete clutter sources in dB with respect to 1 m2 (i.e., dBsm); the number of discrete sources randomly and uniformly distributed over a half-space 180° in azimuth extent and from 0 to 40 km in range extent; and the resultant spatial density of the discrete sources. If this book envisages low-angle clutter as arising from a sea of discretes, should the clutter modeling information in the book be reduced and presented in terms of σ rather than σ°? This question is answered in Section 4.5.4. Table 4.8 Ward’s Discrete Land Clutter Model RCS Level σ of Point Discrete (dBsm)

Number of Discretes: 0 to 40 km Range, 0 to 180˚ Azimuth

Density of Discretes (number/km2)

40

450

0.18

30

900

0.36

20

4500

1.8

10

6800

2.7

In the late 1960s and early 1970s, an ongoing series of investigations involving the discrete nature of low-angle land clutter at high resolution was conducted in the United Kingdom, predominantly at Admiralty Surface Weapons Establishment (ASWE) [10] but elsewhere as well [4]. It was very evident in these studies that dominant land clutter signals come from point sources. This fact led to the measured data being reduced to σ rather than σ°. As was stated in these studies, σ was considered to be a more basic quantity for representing a point source, the RCS of which is independent of the size of the cell capturing the point source, in contrast to characterizing the return from the point source by a σ° coefficient that varies with the area of the capturing cell. At first consideration, such argument seems very

322 Approaches to Clutter Modeling

reasonable. Again, should the modeling information in this book be presented in terms of σ rather than σ°? Although deferring the answer to Section 4.5.4, we begin to address such matters in what follows. Although it is possible to postulate a conceptual clutter model comprising both a distributed σ°component and a discrete σ component, it is far from straightforward to separate distributed from discrete clutter in measured low-angle clutter data. The difficulty in meaningfully or usefully effecting such a separation is not widely recognized, although Schleher does so as indicated in the following direct quotation: “Note that most experimental [land] clutter measurements . . . include composite discrete and distributed clutter, which cannot be separated into component parts, and hence measurement statistics of parameters such as σ° . . . represent combined statistical data” [11]. For example, the AWSE measurements of discrete clutter mentioned previously were entirely reduced in terms of σ, without any attempt to reduce a separate σ° component that might be more appropriate at weaker levels. The inherent spikiness of low-angle clutter is the basic reason why it is difficult to meaningfully separate discrete and distributed components in low-angle clutter simply on the basis of recognizable qualitative differences as exist in higher-angle clutter. Certainly, without recourse to detailed ground truth information, nothing can be said about how point-like any clutter source is beyond the spatial resolution of the measurement. It may be thought from a theoretical point of view that measurements of the same clutter at increasing resolution could find point sources by looking for cells, each providing a constant level of clutter RCS σ independent of the capturing cell size. In practice, Phase One measurements of the same clutter region at both 150-m and 15-m range resolution both reveal cell-to-cell variations in spikiness, with the rate of variation 10 times faster at 15-m resolution than at 150-m resolution, in which it is seldom evident that a particular 15-m cell within any 10-cell neighborhood provides an RCS level clearly standing out from its neighbors and at the same RCS level as in the encompassing 150-m cell. Such a process would not find many discretes, nor would it serve a very useful purpose in simplifying the characterization of low-angle clutter. Thus we concur with Schleher that for all intents and purposes it is practicably impossible to determine which clutter returns come from point objects and which from distributed surfaces in low-angle clutter, and in fact that it might be equally impracticable to unambiguously frame criteria for capturing what is conceptually meant by “point” and “distributed” over the myriad of physical objects and surfaces constituting landscape, especially as observed at near-grazing incidence. However, it is certainly possible to separate locally strong clutter cells in measured data irrespective of whether or not a determinable point object can be associated with each such strong return. Appendix 4.D goes forward with this approach as a point of departure for defining and separating “discrete” clutter from “background” clutter (as opposed to attempting to distinguish between point objects vs extended surfaces as the physical sources of the clutter) in order to determine what might be gained by such an approach to empirical clutter modeling. Acknowledging for now the difficulty of separating σ° and σ components in measured low-angle clutter data, it is still possible to follow, for example, the lead of the AWSE studies and the Ward model described above and reduce the measured data only in terms of clutter RCS σ, as opposed to reducing the measured data (as is done elsewhere in this book) only in terms of the normalized clutter RCS (i.e., backscattering coefficient) σ°. Figure

Approaches to Clutter Modeling 323

4.18 shows three subsets of Phase Zero X-band clutter data reduced in this manner. The three subsets constitute urban, mountain, and rural data, respectively. Within each subset, the data are shown as cumulative distributions over all the data in each subset in which the ordinate shows the number of cells per km2 with RCS ≥ the value at any given position along the abscissa. Similar to Ward’s early discrete model shown in Table 4.8, the Phase Zero results of Figure 4.18 can be tabulated as shown in Table 4.9. The Phase Zero results of Figure 4.18 and Table 4.9 include clutter RCS returns from all the resolution cells within each terrain type; no effort was made to select a subset of cells defined by some criterion to be discrete. Thus, at the larger clutter RCS levels, some of the returns in the figure undoubtedly correspond to cells actually containing large discrete scattering objects, but other returns presumably just come from large cells at long-range. At the lower clutter RCS levels, the returns come from a composite of small cells, discrete-free cells, and microshadowed cells. Such complications must always intrude when attempting to use empirically derived clutter RCS data to attempt specification of a discrete component in a conceptual clutter model. 104 103

Number of Cells per km2 with RCS Abscissa

Urban (1 Site; 179 km2) 102 101

Mountains (1 Site; 58 km2)

100 10-1 Rural (Aggregate of 5 Sites; Various Terrain Types; 2,087 km2)

10-2 10-3

Receiver Saturation

10-4 100

101

103

102

104

105

2

RCS (m )

Figure 4.18 Number of cells with large RCS in ground clutter. Phase Zero X-band data; 2- to 12-km range; 0.5-µs pulse length.

Consider again that the clutter RCS results shown in Figure 4.18 are based on all the clutter cells within each terrain type. In a similar manner, it would certainly be possible as an alternative approach to reduce all of the Phase Zero and Phase One data in terms of clutter RCS σ rather than in terms of clutter backscattering coefficient σ°. Based on the preceding arguments that low-angle clutter is spiky and discrete, and that the RCS of a point scatterer is independent of the area of the capturing cell, it might be thought, as in the Ward and AWSE studies, that a clutter model based on reducing the measurements to σ statistics

324 Approaches to Clutter Modeling

Table 4.9 Phase Zero RCS Land Clutter Model RCS Level σ (dBsm)

Density of Cells (number/km2) Urban

Mountains

Rural

40

3

0.004

0.004

30

30

3

0.3

20

100

80

10

10

300

300

100

rather than σ° statistics would be the more fundamental approach. To the contrary, Section 4.5.4 will show that σ° is the fundamental quantity to which to reduce clutter measurement data for use in a spatially extensive clutter model, whether the clutter is postulated to arise from discrete or distributed sources over the surfaces involved. Before that, Section 4.5.2 provides examples of thresholded PPI clutter maps at Cochrane, further illustrating how strong isolated discrete cells appear to be embedded in spatially extensive distributed clutter at weaker levels. Then, Section 4.5.3 provides a further example of the spikey nature of low-angle clutter as measured at the prairie grassland site of Suffield and illustrates what is involved in separating one large discrete source from the background clutter when it is known what the discrete is and where it is. Section 4.5.5 provides brief conclusions concerning the practicableness of separating discrete from distributed clutter in measured data and in empirical models.

4.5.2 Discrete Clutter Sources at Cochrane Figure 4.19 shows PPI clutter maps at Cochrane, Alberta, to 24-km maximum range based on Phase Zero X-band measurement data. The figure shows eight clutter maps at increasing thresholds of clutter strength over a dynamic range of 40 dB, from σ°F4 ≥ − 48 dB to σ°F4 ≥ –8 dB. In each clutter map, cells exceeding the clutter strength threshold for that map are painted black; cells for which clutter strength is less than the threshold are left white. It is apparent in this figure that at the lowest thresholds, much of the clutter is spatially distributed over contiguous black regions much larger than a resolution cell (resolution cell size = 1° ×75 m). With increasing threshold, however, the clutter gradually becomes more spatially granular, such that at the highest thresholds shown it is apparent that the strongest cells at Cochrane are entirely spatially isolated or discrete. Similar measurements by various investigators over the years have led to a concurrence of opinion that land clutter is dominated by discrete sources, and to its often being conceptually modeled as a distributed σ ° phenomenon at lower strengths augmented by discrete σ ’s at higher strengths. Two additional observations may be made of the data shown in Figure 4.19. First, the strong discrete clutter sources in the figure do not disappear at the long ranges first. This supports evidence and conclusions provided elsewhere in Chapter 4 that clutter strength σ° has no intrinsic dependence on range (for example, see Figure 4.11, and the plots of σ ° vs range in Appendix 4.A). Secondly, it is the indication of discrete sources at the highest thresholds such as is shown in Figure 4.19 that motivates investigators to want to determine to what extent clutter modeling can be advanced by separating the effects of discretes at

Approaches to Clutter Modeling 325

a) σ˚F4

–48 dB

b) σ˚F4

–38 dB

c) σ˚F4

–33 dB

d) σ˚F4

–28 dB

Figure 4.19(a-d) Thresholded PPI clutter plots at Cochrane, Alta. Phase Zero X-band data. Maximum range = 24 km; range resolution = 75 m. North is at zenith.

high levels from the more distributed clutter at lower levels. Appendix 4.D provides results obtained by going forward under this motivation and separately analyzing the effects of locally strong “discrete” cells in the measured data.

4.5.3 Separation of Discrete Source at Suffield This section illustrates that it is complicated to remove the effects of a single large discrete clutter source in measured clutter data, even when it is known what the discrete scatterer is and where it is situated. The investigation is conducted in repeat sector measurement data from the Suffield measurement site in southeastern Alberta. The Suffield terrain is native herbaceous rangeland. Suffield measurements were conducted in winter season with light snow cover. The landform is generally low-relief, although with some variety. From the site center the terrain gradually falls off (by 175 ft) to 7-km range, the start of the repeat sector range interval, and then gradually rises back (by 150 ft) to 13 km, the end of the

326 Approaches to Clutter Modeling

e) σ˚F4

g) σ˚F4

–23 dB

–13 dB

f) σ˚F4

h) σ˚F4

–18 dB

–8 dB

Figure 4.19(e-h) Thresholded PPI clutter plots at Cochrane, Alta. Phase Zero X-band data. Maximum range = 24 km; range resolution = 75 m. North is at zenith.

repeat sector. Within the repeat sector, the low-relief terrain is largely undulating, although in places it becomes hummocky or broken. There are some small prairie sloughs or ponds in the sector (2% by area) and some low marshland areas (5% by area) surrounded by sedge and cattails. No trees, cropland, or man-made structures (except as subsequently discussed) are known to exist in the sector. Thus, at Suffield, discrete-free clutter from winter-season grassland terrain was expected to be measured. However, the measured results appeared to be dominated by some strong discrete returns. Subsequent field surveillance determined that an Alberta Energy Corporation natural gas compressor pumping station had been built since the date of the aerial photos being utilized. The building housing the station was a large, two- to threestory, rectangular metal barn, with smaller outlying buildings and equipment, located at 8.9-km range and 127° azimuth.

Approaches to Clutter Modeling 327

The discrete clutter sources comprising the large AEC building complex were sufficient to drive the Suffield repeat sector mean clutter strengths to high levels. This is evident from the results shown in Figures 4.20 and 4.21. These figures show the same measured data reduced and plotted in different ways. Figure 4.20 shows the X-band clutter strength histogram and cumulative distribution for the Suffield repeat sector for the 15-m pulse length and at horizontal polarization. Figure 4.21 shows clutter strength vs range through the Suffield repeat sector, for the same X-band, 15-m pulse, horizontal polarization experiment, for five specific beam positions, namely, for 125.5°, 126.5°, 127.5°, and 128.5°, which are the first four contiguous beam positions in the sector, and for 134.5°, which is the last beam position in the sector (recall that the X-band beamwidth is 1°; see Table 3.A.2).

126,077 Samples 15 100

Percentiles 50 70 90

w=

10

,a

10

Lower Bound

0.5

We ibu ll

0.7

99 Mean

3.9

0.99 0.97

Percent

Abscissa

0.9

Probability That

F4

Weibull Scale

0.9999 0.999

a)

Upper Bound

5

1

b)

0.1

0.3 0.01

0.15

0 0.003

–85

–65

–45

–25

F4 (dB)

–5

15

–85

–65

–45

–25

–5

15

F4 (dB)

Figure 4.20 Clutter histogram and cumulative distribution for Suffield prairie grassland, including large discrete (metal barn). X-band, horizontal polarization, 15-m pulse. (a) Cumulative/ Weibull scale and histogram/linear percent scale. (b) Histogram/logarithmic percent scale showing high-side tail.

First consider the clutter histogram and cumulative distribution shown in Figure 4.20. These results were generated from partially integrated data in which each sample was obtained by coherently integrating 32 of the 1,024 pulses collected at a PRF of 2,000 Hz in each range gate with step/scan antenna positioning. In Figure 4.20(a), the histogram is plotted utilizing a linear percent ordinate; Figure 4.20(b) utilizes a logarithmic percent ordinate. The first thing to notice in the histogram is that in the clutter strength region from about –20 dB to about –50 dB, the histogram is very well behaved; the number of samples gradually diminishes with increasing strength in a very regular manner. In fact, over this region from –20 to –50 dB, the distribution of clutter strengths is very accurately represented by a Weibull distribution with a Weibull shape parameter of aw = 3.9. This well-behaved Weibull distribution of strengths measured from Suffield discrete-free grassland terrain well represents the area-extensive clutter background in these measurements.

328 Approaches to Clutter Modeling

10

Az = 125.5°

–10 –30 –50 –70 10

Az = 126.5°

–10 –30

Mean Clutter Strength (dB)

–50 –70 10

Az = 127.5°

Large Building

–10 –30 –50 –70 10

Az = 128.5°

–10 –30 –50 –70 10

Az = 134.5°

–10 –30 Noise Floor –50 –70 7

8

9

10

11

12

13

Range (km)

Figure 4.21 Mean clutter strength vs range at Suffield. Repeat sector data. X-band, 15-m pulse, horizontal polarization. Individual azimuth beam positions.

However, the next thing to notice in the histogram, particularly as plotted in Figure 4.20(b), is that it contains a long high-side tail over the clutter strength region from –19 to +11 dB, caused by strong discrete returns of low percent occurrence. In fact, from –19 dB to +11 dB inclusive, there are 808 samples in the histogram of Figure 4.20 coming from ~25 different spatial cells, which constitutes 0.64% of the total number of samples in the histogram. If attention is now turned to the sector display of Figure 4.21, it is evident that most of these strong values come from the vicinity of the large AEC building in the Suffield repeat sector. The data in Figure 4.21 are now described more specifically. These data involve no spatial averaging, but show clutter strength in individual resolution cells, range gate by range gate

Approaches to Clutter Modeling 329

and beam position by beam position. In each resolution cell, the clutter strength shown is the temporal mean strength resulting from averaging 32 samples, each of which is a coherent average of 32 pulses recorded at a PRF of 2,000 Hz. Generally, Figure 4.21 indicates that the clutter from this Suffield grassland terrain is of a very spiky nature, with 30-dB fluctuations common, as individual cells drop into and out of direct visibility at the low 0.3-deg depression angle involved. These data are a good example of the statistical nature of low-angle clutter, even from what is relatively homogeneous, discrete-free grassland terrain (i.e., not constant σ° or a tight Rayleigh process). Most of these clutter returns vary over the range from –20 to –50 or –60 dB. The major exception to this range of variation in the data of Figure 4.21 is the set of returns of strength >> –20 dB from cells in the near vicinity of the AEC building in the range interval from 8.8 to 9.0 km and at azimuths from 125.5° to 127.5°. For example, at the 127.5° azimuth position there is a strong specular flash directly from this building that raises the clutter return 30 dB or more above the envelope of the peaks in other cells not near the building. Although in the following beam position (i.e., 128.5°) no indication of the building remains, in the two preceding beam positions there is significant evidence of the building and associated discretes at levels > –20 dB spread over a number of range gates. Altogether, in these data there are 435 samples of strength ≥ –13 dB from the vicinity of the AEC building, which, if deleted, reduce the mean strength in the histogram of Figure 4.20 from –22.6 to –34.9 dB. Note that the general statistical nature of the grassland clutter at 134.5°, the final beam position in the sector, is relatively similar in range of fluctuation to that 6° earlier (i.e., at 128.5°) except over the region from 7 to 8.5 km. This region is shadowed terrain at the noise floor, where the noise level decreases with increasing range because r4 sensitivitytime-control (STC) attenuation was used in the experiment. The 5-dB discrete-finding algorithm utilized in Appendix 4.D clearly would specify a number of cells in Figure 4.21 as being “discrete,” i.e., as being 5 dB stronger than their neighbors, even though no obvious point-like discrete physical scattering sources other than the AEC building are known to exist in the Suffield repeat sector. Thus, the data of Figures 4.20 and 4.21 indicate that a more appropriate value of X-band mean clutter strength (at 15-m pulse length, horizontal polarization) to represent discretefree Suffield grassland is –34.9 dB, not the –22.6 dB value actually measured there and driven to be so large by the presence of the AEC building. Next, similar adjustments to Suffield repeat sector mean clutter strengths are performed in other bands. These are done at low resolution (i.e., 150-m pulse length). The low resolution data are more clear-cut as to which samples come from the AEC building. Thus, in the L-band (150-m pulse, horizontal polarization) data there are four cells at σ°F4 levels of –4, –8, –16, and –17 dB providing samples (32 each) from the AEC building. When the samples from these four cells are removed from the measured histogram, the mean strength of the histogram drops from –25.0 to –39.9 dB. Similarly in the other bands (at 150-m pulse length, horizontal polarization), it is found that mean strengths adjust as follows: at X-band, from –21.7 to –33.9 dB; at S-band, from –25.3 to –43.2 dB; at L-band, from –25.0 to –39.9 dB; at UHF, from –36.8 to –40.3 dB; and at VHF, from –51.3 to –51.7 dB. These adjusted Suffield mean clutter strengths (adjusted to be representative of grassland without the large AEC building discrete clutter source) are now compared with the grassland site of Vananda East which has similar landform (i.e., 3–5) but at which a higher depression angle occurred. This comparison is made at 150-m pulse length and horizontal polarization. At UHF, L-, and S-band, the adjusted Suffield values are remarkably close to

330 Approaches to Clutter Modeling

Vananda East values (the values are, for Suffield and Vananda East, respectively: at UHF, –40.3 dB vs –38.9 dB; at L-band, –39.9 dB vs –39.5 dB; at S-band, –43.2 dB vs –38.1 dB). Furthermore, in these three bands at both these grassland sites, mean clutter strengths are remarkably invariant with frequency at or near the –40-db level. These –40-db levels are good estimates of mean clutter strength in these bands for canonical discrete-free grassland, and therefore are what would be assigned as mean strengths to Weibull distributions for representing an area-extensive distributed clutter background. At VHF, although Vananda East mean clutter strength holds near the –40-db level (viz., –41.7 dB), adjusted Suffield mean clutter strength drops to –51.7 dB (i.e., 10 dB weaker than Vananda East). This lower Suffield value is caused by VHF multipath loss from the hillslope local to the antenna at Suffield (see Appendix 3.B, Section 3.B.2), which does not occur for the high-bluff site at Vananda East. Note that, at VHF, the adjusted Suffield mean strength is only 0.4 dB weaker than the unadjusted value. This is because at VHF the cells containing the AEC building, although 25 to 30 dB stronger than surrounding cells, were 5 dB weaker than some cells at longer range which were strong due to multipath enhancement. This resulted in the mean clutter strength, dominated by these strong long-range cells, coincidentally being about equal to the strength of the cells containing the AEC building, so whether the AEC cells are included or not has little effect on mean clutter strength at VHF. At X-band, the Vananda East mean clutter strength abruptly rises from the –40-db level in lower bands to –27.7 dB. This effect is described elsewhere in this book (viz., see Sections 3.4.1.5, 3.4.2, and 5.4.7.2). The adjusted Suffield X-band mean clutter strength also abruptly rises from –40 dB, but to –33.9 dB, a level 6 dB weaker than measured for grassland at Vananda East but still 11 dB stronger than measured for grassland at Big Grass Marsh. The repeat sector values of mean clutter strength at Suffield, adjusted to be applicable to relatively discrete-free grassland by removal of cells containing the AEC building, are thus understandable and provide additional information within the context of the other discrete-free grassland sites, Vananda East (same 3–5 landform as Suffield) and Big Grass Marsh (landform = 1, level). The depression angle at Suffield, 0.3 deg, is intermediate between the depression angle at Big Grass Marsh, 0.2 deg, and that at Vananda East, 1.0 deg. As a result, at VHF and X-band, adjusted values of Suffield mean clutter strength for grassland lie intermediate between those at Big Grass Marsh and at Vananda East. At UHF, L-, and S-band, adjusted values of Suffield mean clutter strength are very nearly equivalent to those at Vananda East. These Suffield results indicate that, in the separation of returns from a known discrete clutter source (viz., large building) in the measurement data, it is not so simple as the finding of a single large value of RCS in a single cell, but instead what is found are multiple returns from the building varying over orders of magnitude from a number of small contiguous cells, each of which partially intersects the building. This technique of separately dealing with large man-made discretes in the clutter data is usually much more demanding than at Suffield because usually many such sources exist in open terrain (e.g., farmland).

4.5.4 σ vs σ ° Normalization Section 4.5.1 raised the idea that a conceptual ground clutter model comprising (1) a σ ° component for area-extensive background clutter that is distributed over all cells, augmented by (2) a σ component for discrete clutter arising from large point sources occupying a relatively small proportion of cells, is intuitively satisfying at low or high

Approaches to Clutter Modeling 331

angle. However, Sections 4.5.1–4.5.3 further showed that in working with measured lowangle clutter data, which unlike clutter data at higher angles is spiky throughout, it is not readily feasible to separate a distributed σ ° component known a priori to arise from physically extended surfaces from a discrete σ component known a priori to arise from physical point objects. Nevertheless, and also as illustrated in Section 4.5.1, one may choose to reduce all the measured clutter data either to clutter RCS σ per resolution cell or to normalized clutter RCS or backscattering coefficient σ° (where σ ° = σ/A, A = cell area = r • ∆r • ∆θ; see Figure 2.4). Section 4.5.1 showed that the predilection of some previous investigators was to reduce all the measured clutter data to σ, on the basis that the stronger elements of low-angle clutter were spatially isolated or point-like (see Figure 4.19), and that the RCS σ of a point source is the fundamental quantity independent of the size of the capturing cell, as opposed to σ° which depends on the size of the capturing cell. Is it just a matter of subjective choice or preference on the part of the investigator, or do substantive reasons exist for making either σ or σ ° the preferable choice to which to reduce measured low-angle clutter data? For us to begin to address this question, reference is first made to the results of Section 3.5.3 in Chapter 3 showing that in measured repeat sector clutter data, the mean value of the clutter coefficient σ ° is essentially independent of cell area or spatial resolution (see Table 3.10, small differences with pulse length in all five bands). Independence of mean strength on cell area is necessary for the concept of density function to be true. It is true in the measured data, irrespective of whether descriptive adjectives like “discrete” or “distributed” are associated with the measured data, and also irrespective of whether the nature of the measured clutter is very uniform or very spiky. Thus, as described elsewhere throughout this book, the fact that σ ° is independent of cell area is fundamentally important to the structure of the modeling information presented. In contrast, if all the clutter measurement data are reduced to σ rather than σ°, the mean value of clutter RCS σ ⋅ . Clutter modeling information over a spatial region is dependent on cell area, as σ = σ° A presented in terms of σ rather than σ° would require the mean values σ of clutter amplitude distributions to be shown as functions of resolution. In other words, σ is not as fundamental a quantity for specifying clutter amplitudes over extended spatial regions as is σ°. Beyond this, care must be taken not to read too much into the fact that σ° is independent of cell area A. For example, it is easy to presume that this fact indicates that low-angle clutter is essentially not point-like but from extended surfaces—however, this is an incorrect assumption. What is indicated is that spiky clutter from discrete sources occurs distributed over surfaces; i.e., that in low-angle clutter, both adjectives apply—clutter is both “discrete” and “distributed.” It is easy to appreciate that mean clutter cross section increases linearly with cell area (i.e., σ = σ °⋅A ) in area-extensive clutter. But how does this observation square with the fact that in clutter arising from point sources, the more basic quantity for the cell capturing the clutter source is its RCS σ which is independent of the capturing cell size? A simple example may be illuminating in this regard. Imagine the existence of a hypothetical clutter spatial field in which each cell contains a single point discrete of σ = X. One might choose to characterize this clutter in terms of its mean clutter RCS such that σ = X. Now suppose the resolution of the radar to change so as to either increase or decrease by a factor of 10. If the resolution increases, one-tenth of the cells will capture a discrete and have σ = X; the other nine-tenths of cells will miss capturing a discrete and will have σ = 0. Thus if the resolution increases by

332 Approaches to Clutter Modeling

a factor of 10, σ = X/10. If, on the other hand, the resolution decreases by a factor of 10, each cell captures 10 discretes and (under the assumption that the 10 discretes combine as a power-additive process) σ = 10X. Thus even in this hypothetical discrete clutter field, mean clutter RCS σ varies linearly with cell area similarly as it does in the actual measured data. That is, σ is not an invariant irreducible quantity suitable for basing a model upon. Next consider the hypothetical clutter spatial field in σ° space. At the original range resolution, say 150 m, the σ° of each cell (each cell containing a single discrete of RCS = X) is X/( r ⋅ 150 ⋅ ∆θ ). Next, allow the range resolution to increase by a factor of 10, to 15 m. Each discrete-capturing 15-m cell still provides RCS = X, and the σ° of each discrete-capturing cell rises by a factor of 10 to σ° = X/( r ⋅ 15 ⋅∆ θ ). But in the region around each discrete-capturing cell, there are now nine empty cells with σ° = 0. Thus the mean value of σ° over each 10-cell region is σ ° = [X/( r ⋅ 15 ⋅∆θ )]/10 which is the same value of σ° as measured with the 150-m cell. Similarly, if range resolution is allowed to decrease from its original 150-m value by a factor of 10 to 1500 m, each cell captures 10 discretes; so σ ° =10X/( r ⋅ 1500 ⋅∆θ ) which is also the same value of σ ° as measured with the 150-m cell. Thus in considering ground clutter, all possibilities of cells on the ground must be specified depending on resolution, not just cells capturing single discretes, but including possibilities of cells capturing more than one discrete and cells capturing no discretes. This is the point that is missed when intuition incorrectly suggests that σ is a more basic quantity than σ° for characterizing discrete clutter. Certainly, in a backscatter measurement of any single point object in which concern is only with the cell containing the object and not the surrounding empty cells, the appropriate characterization of the object is by its RCS σ. This hypothetical situation of a clutter spatial field in which at intermediate resolution each cell contains a single discrete clutter source of RCS = X is handled by a σ° clutter model as follows. At all three resolutions, the mean value of clutter coefficient σ ° remains constant, invariant with cell size (as in the modeling information in this book). The different σ° distributions for the three variations in range resolution are theoretically handled through specification of differently shaped distributions for the three resolutions, but with σ ° for each distribution remaining unchanged (also as occurs in the modeling information in this book). Thus in these hypothetical situations, for the mid-size cell, the shape of the distribution is an impulse allowing no variation in σ°; for the small cell, the shape of the distribution is such as to define a two-impulse bipolar distribution with nine-tenths of the σ° values equal to zero and one-tenth equal to X/( r ⋅15 ⋅∆ θ ); and for the large cell, the shape of the distribution is such as to allow the variability associated with 10 interfering scatterers within the cell. For the actual measured clutter data, as opposed to the above hypothetical construct, such extreme shapes of distributions are unnecessary; the Weibull distribution of constant mean strength σ w° and varying shape parameter aw is sufficient to handle the actual variations in shape that occur with changing resolution in the actual measured data. The above reasoning indicates that when concern is with returns from all the cells defining a surface, the correct way to empirically characterize the phenomenon is to reduce the measured data to σ°, even though each return in itself may arise from a point source. Is this reasoning supported by the observed behavior of the actual measured clutter data? Consider again that since σ° is independent of cell area, σ = σ° ⋅A must increase linearly with

Approaches to Clutter Modeling 333

increasing cell area. Thus in observed clutter data, if range is allowed to increase from 1 km to, say, 64 km (that is, by six factors of 2), cell area doubles with each factor of 2 increase in range leading to the expectation that clutter RCS would increase by 18 dB over this range, certainly enough to show a noticeable trend in measured data. That is, larger cells at longer ranges capture more discretes and provide larger cross sections. But in the σ° vs range results shown in this book, for example in the sector displays of Appendix 4.A or in the thresholded PPI displays of Figure 4.19, no strong trends of σ° vs range are observed, indicating that σ° is indeed the appropriate irreducible quantity upon which to base a clutter model. In all observations, σ° within visible clutter regions (although fluctuating strongly from cell to cell) neither increases nor decreases significantly with range, but remains as a fundamental quantity with range effects properly normalized out. It is apparent from the preceding discussion that σ°, as opposed to σ, is the more fundamental quantity to which to reduce measured low-angle clutter data, despite the fact that low-angle clutter is an essentially spiky phenomenon arising from a sea of discrete clutter sources. A clutter model based on reducing all measured returns to σ is not completely reduced; such a model must include σ depending on resolution as an extra complicating dimension that is not necessary in a model based on σ°. This fact leads to the clutter data in this book being reduced to σ° as the most basic characteristic of a distributed phenomenon, despite the fact that what is distributed are discrete clutter sources.

4.5.5 Conclusions The idea behind separating discrete clutter sources in measured clutter data is that objects like water towers act as contaminants in what would otherwise be a statistically wellbehaved area-extensive clutter background from the land surface itself, and that a better clutter model results if RCS values of strong discretes are added in a separate σ process to the basic distributed σ ° component representing the background clutter. This idea has some validity at higher angles of illumination typical of airborne radar platforms. At the low angles of illumination of ground-based radars, the focus of the idea tends to dissipate for several reasons. First, low-angle clutter is spiky throughout; removal of the largest spikes still leaves a spiky background. Second, it is not possible to deterministically separate clutter arising from point objects from clutter arising from extended surfaces in the measured data. Many spikes occur only because of vicissitudes of visibility and shadowing compounded by extreme propagation variations at very low angles of illumination. Little correlation exists between locally strong clutter returns and known point objects on the ground. Third, even though low-angle clutter appears to arise from a sea of discretes, the proper way to reduce the data is to the normalized clutter coefficient σ °, as opposed to radar cross section σ, irrespective of whether one is examining so-called “distributed” or “discrete” components. Given these qualifications, if we continue to wish to examine the usefulness of separately analyzing and modeling strong clutter as an overlay to the general clutter background, it is necessary to fall back to a position in which locally strong cells are specified a posteriori in the measured clutter data as opposed to their a priori specification as the returns from known point objects. In so doing, the initial premise has changed. Rather than removing and separately modeling the returns from known point discretes such as water towers, the question now being posed is if it is useful to model the total clutter distribution from a given spatial region as two

334 Approaches to Clutter Modeling

components, one consisting of the locally strong clutter cells resulting from passing a spatial filter over the data and the other consisting of the residual clutter cells which failed to pass the filter. That is, is it useful to set a threshold so as to separate locally strong σ° from weaker surrounding σ°. The potential benefit of such a procedure hinges on the possibility of there being a difference in kind, not just degree, in the two distributions (even though each consists of spiky returns) such that each might be of a relatively simple shape, whereas their combination is of a more complex shape. Note that both components are broad distributions consisting of spiky returns of strengths differing by orders of magnitude, with the major differences being that the so-called “discrete” component consists of locally strong spiky returns and the so-called “background” component consists of the weaker neighboring spiky returns. Further, note that there is no benefit and indeed needless added complexity in moving to σ space to characterize the locally strong or socalled “discrete” component. The modeling of clutter based on the two-distribution approach allows the possibility of assigning two random variates to each clutter cell with the resulting total σ° being the phasor addition of the two components. This approach models “discrete” clutter returns statistically rather than attempting to deterministically specify returns from known point targets on the landscape. Appendix 4.D shows results obtained from separating clutter into two σ° components in this manner. The main approach of this book, however, is to characterize the total clutter from a given spatial region as a single Weibull distribution, where the broad extent of the Weibull distribution usually satisfactorily represents the measured distribution, capturing the occasional strong returns from discrete sources at appropriate probabilities of occurrence. The clutter modeling information provided in Chapter 5 and elsewhere (except in Appendix 4.D) in this book is based on the singledistribution approach involving the assignment of a single random variate to represent clutter strength in each resolution cell.

4.6 Temporal Statistics, Spectra, and Correlation For many years, in radars of low spatial resolution, the in-phase and quadrature components of the spatially varying ground clutter signal were considered to be distributed as Gaussian probability density functions, resulting in the signal amplitude being Rayleigh distributed (see, for example [12], Section 10.2). In modern radar systems, operating at low grazing angles and with resolution capabilities high enough to resolve the surface structure, the statistics of the clutter have been observed to strongly deviate from Gaussianity [13–19]. The clutter is spikier than if it were Gaussian, and the spikes are processed by the radar detector as targets, with increased false-alarm rate. Until now, Chapter 4 and the preceding chapters of this book have been primarily concerned with the characterizations and prediction of the highly non-Gaussian clutter amplitude statistics resulting from cell-to-cell spatial variations in ground clutter signals. Windblown ground clutter Doppler spectra also in early years were, like the amplitude distributions, erroneously thought to be of Gaussian shape [20–22]. The correct understanding of ground clutter and the accurate modeling of its non-Gaussian behavior, both in the spatial amplitude distribution and in the Doppler spectrum, are problems of fundamental interest to the radar community for successful radar design and performance prediction. The subject now widens to include temporal variations in the received clutter

Approaches to Clutter Modeling 335

signals returned from particular spatial cells. Important attributes of temporal statistics are (1) temporal amplitude statistics, (2) spectral characteristics, and (3) correlation times. Correlation distance in the ground clutter spatial process is also discussed. Improved knowledge of these various additional attributes of ground clutter, in addition to its spatial amplitude statistics, is required in the demanding specialized design of modern signal processors required to detect, track, and otherwise operate against ever-smaller radar targets in ground clutter backgrounds. For example, the spectral characteristics of clutter determine the design of moving target indicator (MTI) or space-time adaptive processors (STAP) [23, 24], and the amplitude statistics of clutter affect the design of constant-falsealarm rate (CFAR) processors (see e.g., [12, p. 306; 25]). Results concerning these additional important attributes of low-angle ground clutter are provided in Section 4.6 at a first or introductory level of analysis. More in-depth analyses of these attributes based on the Phase One clutter data are available elsewhere [26–31]. They show that the temporal and spatial domains of ground clutter are interrelated. However, in the specification of the spatial clutter amplitude statistics which is a principal focus of this book, each individual spatial clutter amplitude so specified may be regarded as the mean level of a temporal process in a given spatial cell. Subsequently, Chapter 6 takes up the subject of the modeling of windblown ground clutter spectral shape as a second principal focus of this book.

4.6.1 Temporal Statistics Figure 4.22 presents information describing the relative frequency of occurrence of temporal amplitude statistics between cells with Rayleigh (i.e., windblown foliage) and Ricean (i.e., fixed discretes embedded in foliage) statistics. Ricean statistics describe ground clutter temporal variations from a fixed spatial cell quite accurately as the return of a dominant steady reflector or fixed discrete in a varying background [22, 32]. Rayleigh statistics are a limiting case of Ricean statistics with steady signal equal to zero. The quantity m2 in the Ricean distribution as introduced by Goldstein [22] is the ratio of steady to random average power, or, in other words, the dominant-to-Rayleigh reflector ratio. The ratio of standard deviation-to-mean (sd/mean) in the Ricean process is related to m2 as sd/mean = [(1 + 2 m2) / (1 + m2)2]0.5 ≅ 2 /m for m2 >> 1. The data in Figure 4.22 indicate that, over a population of 988 relatively strong clutter cells selected from three rural sites, more than 40% of the cells are Rayleigh (i.e., have ratios of standard deviation-to-mean = 0 dB), and the remainder are generally Ricean (i.e., have ratios of standard deviation-to-mean < 0 dB), with increasingly strong Ricean cells occurring less frequently. For example, Figure 4.22 shows that 1% of cells are strongly enough dominated by fixed discretes to have a dominant-to-Rayleigh reflector ratio as high as 50. The reason that 40% of the clutter cells in the figure contain only windblown foliage with dominant-toRayleigh reflector ratio equal to zero is that there are some trees on these farmland landscapes. Where trees occur, even at relatively low incidence of occurrence, they tend to dominate as strong clutter sources (see Chapter 2, Section 2.4.2.5).

4.6.2 Spectral Characteristics For Rayleigh cells containing windblown trees, the wind-induced motion causes Dopplershifted energy in the power spectra of the received temporal signals. Figure 4.23 shows two examples of windblown ground clutter spectral results, each computed from a Phase One X-band long-time-dwell experiment measured from the same forested cell at 2.6-km

336 Approaches to Clutter Modeling

100 988 Cells from Three Rural Sites

30 Percent of Cells

40

m2 30

10

20

Percent of Cells

Dominant-to-Rayleigh Reflector Ratio m 2

50

3 10

1

0

–6

–4

–2

0

Standard Deviation-to-Mean of σ°F4 (dB)

Figure 4.22 Frequency of occurrence of Rayleigh vs Ricean cells in X-band ground clutter.

range on two April days about one week apart. This cell contains mixed deciduous and evergreen trees to an approximate height of 60 or 70 ft. On the first day, 17 April, the winds were quite strong; at the time of this X-band experiment, wind speed was recorded at 10 knots, gusting to 20. In contrast, the second day, 25 April, was a very still day and the winds were recorded as calm at the time of the experiment. The spectra of Figure 4.23 are computed directly as fast Fourier transforms (FFTs) of the temporal pulse-by-pulse return, including the dc component, calibrated in radar cross section (RCS) units of meters squared. The spectral content is displayed in decibels with respect to 1 m2 (i.e., in dBsm). The method used to generate these spectra is that of modified periodograms [33], where the temporal record of 30,720 pulses is divided into continuous groups of 1,024 samples, a 1,024-point complex FFT is generated for each group, and the amplitudes of the resultant set of FFTs are arithmetically averaged together in each Doppler cell to provide the spectrum illustrated. Thus in Figure 4.23 each spectrum shown is the result of averaging 30 individual spectra from an overall RCS record of 1.024min duration and 2-ms pulse repetition interval (PRI). In the generation of each spectrum, a 4-sample Blackman-Harris window or weighting function is utilized, with highest sidelobe level at –74 dB and with 6-dB per octave fall-off [34].

Approaches to Clutter Modeling 337

Forested Cell 2582 m, 235°

Range Res. = 15 m Pol. = Horizontal PRI = 2 ms

0 Windy Day 17 April 10 kn, 340° Gusts to 20 kn

X-Band

RCS (dBsm)

–20

Calm Day 25 April

–40

–60

–2

–1

0

1

2

Doppler Velocity (m/s)

Figure 4.23 Power spectra of X-band radar returns from windblown trees.

The results of Figure 4.23 illustrate the differences in spectral content of the X-band reflections from this cell between when the tree branches are relatively motionless and when they are undergoing relatively strong, wind-induced, random motion. It is graphically apparent in these results how much of the dc or zero-Doppler return on the calm day is converted to ac return distributed over Doppler velocities up to 2 m/s on the windy day. The windy day spectrum shown in the figure is one of the wider spectra found in the Phase One long-time-dwell clutter database. In this windy day data, the rate of decay of spectral energy with increasing Doppler velocity in the tail of the spectrum is approximately exponential as indicated by the straight line drawn through the left side of the spectrum. The Phase One system noise levels are evident in both the calm and windy day results of Figure 4.23 at a level of about –64 dBsm. Andrianov, Armand, and Kibardina [35] provide an earlier observation of piece-part exponential spectral decay in windblown radar ground clutter Doppler spectra (see Section 6.6.1.3). The results of Figure 4.23 are representative of much of the Lincoln Laboratory clutter spectral data, in that rates of decay of spectral power with increasing Doppler velocity in radar returns from windblown trees in these data are often observed to be reasonably well approximated as exponential. One Phase One study [26] involved fitting exponential approximations to 23 different Phase One L-band experiments obtained from nominally

338 Approaches to Clutter Modeling

once-a-week measurements over a period of nine months, to provide information on how clutter spectra vary with wind, weather, and season. Chapter 6 takes up the matter of windblown clutter spectral modeling much more extensively and completely.

4.6.3 Correlative Properties The question now is, how long does it take for radar returns from windblown trees to decorrelate? This question is complementary to that of spectral extent in such returns. The normalized autocorrelation function [36] was computed for all five Phase One frequencies for the returns from the same 2.6-km forested cell as measured on the windy day of 17 April [26] for which spectral results are shown in Figure 4.23. These autocorrelation results are shown in Figure 4.24 over a time lag from 0 to 0.5 sec. The time of day (hr:min) at which data collection commenced for each of these five long-time-dwell experiments was as follows: X-band, 10:24; S-band, 11:30; L-band, 14:12; VHF, 15:50; UHF, 15:27. Each of these five long-time-dwell experiments consisted of 30,720 pulses at PRIs of 2, 10, 10, 6, and 2 ms for VHF, UHF, L-, S-, and X-bands, respectively. For all five experiments, the polarization was horizontal and the range resolution was 150 m. At each of the five Phase One frequencies, the autocorrelation of the return from a stationary water tower reference target remains essentially at unity over the 0.5-s time lag shown in Figure 4.24. Correlation times τ1/e and τ1/2 are defined as the times required for the normalized autocorrelation function to decrease to 1/e (= 0.368) or 1/2 (= 0.5), respectively. Table 4.10 gives these measures of time required for decorrelation of the radar returns from windblown trees, as determined from the data of Figure 4.24. If the scattering centers and their motion were the same at all five frequencies, simple Doppler considerations would lead to the expectation that correlation times should decrease inversely with radar carrier frequency, all else being equal. There is an approximate trend indicative of this effect in the data of Figure 4.24 and Table 4.10. These results do not scale exactly linearly with frequency, however, because (1) the experiments were conducted at different times and thus under different specific wind conditions on 17 April, (2) the cell sizes and hence scattering center ensembles were different (e.g., due to azimuth beamwidth varying with frequency band), and (3) the scattering centers and their velocities are expected to vary with the radar transmission wavelength (i.e., twigs at Xband, branches at L-band, limbs at VHF). The correlative properties of radar returns from windblown trees shown in Figure 4.24 and Table 4.10 apply for the particularly windy day of 17 April. Correlation times from windblown trees increase with decreasing wind speed. Figure 4.25 shows the normalized autocorrelation function for the L-band returns from the same 2.6-km forested cell, measured on three different days under three quite different wind conditions. The autocorrelation function is shown in Figure 4.25 only over the correlation interval from 1.0 to 0.9 to emphasize the region where the data just begins to decorrelate. In Figure 4.25, the windy day was 17 April (wind speed = 15 to 25 kn), the breezy day was 10 April (wind speed ≈11 kn), and the light air day was 5 June (wind speed ≤ 8 kn). Each of these longtime-dwell experiments consisted of 30,720 pulses at pulse repetition intervals of 10, 2, and 10 ms for the windy, breezy, and light air days, respectively. In these results, the correlation times τ1/e on the windy, breezy, and light air days were 0.95, 2.11, and 5.56 s, respectively. These results show how temporal correlation in L-band radar returns from windblown trees increases with decreasing wind speed.

Approaches to Clutter Modeling 339

Normalized Autocorrelation Function

1.0

VHF

0.8

UHF L-Band

0.6 Windy Day 0.4

S-Band 0.2 X-Band

0.0

0

0.125

0.25

0.375

0.5

Time Lag (s)

Figure 4.24 Autocorrelation functions of radar returns from windblown trees on a windy day at five radar frequencies. Table 4.10 Correlation Times for Radar Returns from Windblown Trees on a Windy Day Frequency Band VHF UHF L-Band S-Band X-Band

Correlation Time(s)

␶ 1/2

4.01* 0.69 0.67 0.062 0.033

␶ 1/e 5.04* 0.94 0.95 0.081 0.049

Note: * = extrapolated estimate

Spatial Correlation. In contrast to temporal correlation, which addresses the question of duration in time that must pass for a clutter signal from a fixed cell to decorrelate, spatial correlation addresses the question of extent in distance (i.e., number of cell dimensions) that must be traversed in order that the clutter signal from the current cell decorrelates with respect to the signal from the original cell. Because of the general spatial heterogeneity of terrain and the spiky spatial nature of the land clutter phenomenon as observed at low angles, a number of studies over the course of the Phase Zero/Phase One activities have found that low-angle land clutter often spatially decorrelates in about one spatial cell. That is, the physical content (i.e., scattering ensemble) within each cell when observed at low

340 Approaches to Clutter Modeling

1.00 L-Band

Normalized Autocorrelation Function

0.98

Light Air 0.96

Breezy 0.94

Windy 0.92

0.90 0

0.125

0.25

0.375

0.5

Time Lag (s)

Figure 4.25 Autocorrelation functions of L-band radar returns from windblown trees for three different wind conditions.

angles is usually different enough (different set of discrete sources) from cell to cell that the signal from any one cell largely decorrelates from its spatial neighbors. Occasionally, increased correlation is observed from cell to cell, for example, at higher angles over uniform forest. As an example of cell-to-cell spatial decorrelation, results are summarized here from a statistical study [30] of Phase One X-band open farmland clutter data collected at the Wolseley, Saskatchewan site.25 Other results from this study are discussed in Appendix 5.A. The data were acquired in slow (2°/s) scan mode through one ~90° azimuth sector in which 703 azimuth samples were collected per range cell. Within the azimuth sector, data were acquired in four contiguous 4.74-km range intervals; each range interval contained 316 range cells of 15 meter sampling interval (i.e., 10 MHz sampling rate). Figures 4.26 and 4.27 show azimuth and range spatial correlation coefficients obtained in processing the fourth range interval in these data. The results were obtained by processing the entire 703 x 416 sample array of data obtained at HH-polarization in the fourth range interval (15.2 to 20.0 km from the radar).

25. Summary provided here of material originally published in [30], by permission of IEEE.

Approaches to Clutter Modeling 341

1.0 Re 0.8

Im HH Polarization 4th-Range Interval

ρz (m)

0.6

0.4

0.2

0.0

–0.2 0

2

1

3

4

5

6

7

8

9

10

12

14

16

18

20

Time (s)

0

2

4

6

8

10

Index of 1° Azimuth Cells

Figure 4.26 Azimuthal correlation coefficient, fourth-range interval, HH polarization. (Results provided by F. Gini and M. Greco, Univ. of Pisa. After [30]; by permission, © 1999 IEEE.)

The azimuthal autocorrelation sequence was estimated from the data without making any assumption, other than stationarity, about the structure of the clutter process. The sample M estimator processed M = 316 records { z k } k = 1 , one for each range cell, of N = 703 complex azimuth samples according to the following algorithm [37, Ch. 9]: M N–m–1

1 Rˆ z ( m ) = --------NM

∑ ∑

z k ( n ) zk* ( n + m ) = 2 Rˆ z ( m ) + j 2 Rˆ z I

I zQ

k=1 n=0

where zI(n) and zQ(n) are the in-phase and quadrature components, z(n) = zI(n) + jzQ(n) is the complex envelope of the observed signal, and * represents complex conjugate. In ˆ ˆ Figure 4.26 the correlation coefficient ρz(m) ∆ = R z ( m ) ⁄ R z ( 0 ) is shown for the fourth range interval. It is observed that the signal decorrelates to 0.29 in one 1°-beamwidth, and to ~0 in four beamwidths. As expected, the imaginary part of ρz(m), i.e., the crosscorrelation coefficient Rˆ z z (m)/ Rˆ Z(0), is approximately zero. I Q

To obtain the range correlation coefficient, the correlation for each azimuth cell was calculated, and then the 703 estimates were averaged. The correlation coefficient ρR(m) is plotted in Figure 4.27. Comparing this figure with Figure 4.26, the two decorrelation times

342 Approaches to Clutter Modeling

1.0 Re

0.8

Im HH Polarization 4th-Range Interval

␳R (m)

0.6

0.4

0.2

0.0

–0.2 0

100

200

300

400

500

600

700

800

900

1000

7

8

9

10

Time (nsec)

0

1

2

3

4

5

6

Index of 15-m Range Cells

Figure 4.27 Range correlation coefficient, fourth range interval, HH polarization. (Results provided by F. Gini and M. Greco, Univ. of Pisa. After [30]; by permission, © 1999 IEEE.)

are observed to be quite different. Along the azimuth direction the coefficient reduces to 0.1 in a few seconds, whereas along the range direction, the same amount of reduction occurs in a few hundreds of nanoseconds. These apparent large differences are merely the result of the different time-sampling frequencies utilized in range (10 MHz) and in azimuth (15.625 Hz). The assumption usually made in adaptive radar detection (see, e.g., [38], Ch. 3) of independence of the data from different range cells is very reasonable in these Wolseley data. Thus, the important thing to observe in considering Figures 4.26 and 4.27 is that, owing to the heterogeneity of the spatial scattering ensemble in open farmland terrain (strong discrete sources dispersed over a weakly scattering medium), the returned signal from the scanning antenna largely decorrelates from one spatial cell to the next, whether the variation is in the range direction or in the azimuth direction. Consider again the azimuth variation results of Figure 4.26. The azimuth extent of the spatial resolution cell is determined by the beamwidth of ~1°. The scan rate is 2°/s, so the expectation is that the returned signal would decorrelate in ~1 beamwidth or ~0.5 s. Figure 4.26 shows the azimuthal correlation coefficient to drop to 0.29 in 0.5 s (one beamwidth), but to take ~2 s (~4 beamwidths) to decorrelate to zero. This largely meets the expectation of decorrelation in one azimuthal interval, given that the azimuthal cell specified is the 3-dB beamwidth,

Approaches to Clutter Modeling 343

with resultant beam overlap between 1° cells. The azimuth sampling rate used in data acquisition was 15.625 samples (pulses) per second. That is, in azimuth, the sampling time (0.064 s, is much less than the cell size (~0.5 s). Now consider again the range variation results shown in Figure 4.27. The range extent of the spatial resolution cell is determined by the 3-dB pulse length which is specified to be 100 ns. This is matched to the range sampling rate of 10 MHz (i.e., in range, the sampling interval equals the cell size). Therefore, the expectation is that, in range, the returned signal would largely decorrelate, sample-to-sample, in ~100 ns. Figure 4.27 shows the range correlation coefficient to drop to 0.3 in 100 ns (one pulse length), but it takes 300 ns (3 pulse lengths) to decorrelate to zero. Thus the range results of Figure 4.27 very closely match the azimuthal results of Figure 4.26 in terms of equivalent cell-to-cell decorrelation in azimuth and range. Note that although the azimuthal decorrelation in Figure 4.26 is caused by the antenna pattern, the decorrelation data cannot be simply predicted from the pattern. Perhaps it would be useful to state a simple example as follows: if the pattern were hypothetically purely rectangular (i.e., a simple step function of width φ), and if the clutter were simply one large point scatterer, then the azimuthal correlation coefficient would be triangular of base width 2φ (i.e., would fall to 0.5 in one cell and to zero in two cells). By contrast, the measured data in Figure 4.26 falls to 0.29 in one cell and to zero in four cells.

4.7 Summary Chapter 4 describes a number of approaches for modeling low-angle land clutter in surface-sited radar. As a physical phenomenon, the most salient attribute of low-angle clutter is variability. Two important ways in which this variability is evidenced are patchiness in spatial occurrence and extremely wide cell-to-cell statistical fluctuation in clutter strength (i.e., spikiness) within patches. A site-specific approach to clutter modeling is described based on the use of digitized terrain elevation data (DTED) at each site, which captures both of these basic attributes—patchiness, via deterministic computation of geometric terrain visibility from the radar site; and spikiness, via realizations from statistical distributions in which the spread depends on the depression angle to the backscattering terrain point as computed from the DTED. An interim site-specific clutter model is provided as a table of Weibull coefficients in which the mean value of the distribution of clutter strengths varies with radar frequency, the shape parameter of the distribution varies with radar spatial resolution, and both mean strength and shape parameter vary with depression angle and terrain type. This sitespecific approach to clutter modeling in surface radar is highly realistic. Besides capturing the fundamental patchiness and spikiness of low-angle clutter, this approach: (a) ensures that the modeled clutter in surface-sited radar dissipates with increasing range in the same way that clutter actually dissipates with increasing range at real sites, namely, via the deterministic visibility function, whereby the spatial patches of occurrence of clutter become fewer and farther apart with increasing range until, beyond some maximum range, no more clutter patches are visible; and (b) raises clutter modeling to the level of a quantitative science in that a given clutter patch at a given site, and, more specifically, the distribution of clutter strengths over that patch is a real and distinct physical entity that can be measured, parameterized (e.g., by terrain type and depression angle), and modeled, thus

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allowing quantitative comparison of the measured and modeled distributions and hence a direct means for clutter model validation. Dominant sources of low-angle clutter appear to be of a point-like or spatially discrete nature, in that they occur in spatially isolated cells as opposed to being of a spatially extended nature. The basic site-specific approach to clutter modeling does not distinguish between whether clutter returns emanate from discrete or extended sources. A refinement to the basic site-specific clutter model is described involving a more computationally intensive approach that separates the modeling of dominant, locally strong clutter cells (called the discrete component) from weaker surrounding clutter cells (called the background component). Little correlation was found to exist between clutter cells that are locally stronger than their neighbors, and actual physical discrete objects on the terrain that could be identified as the sources of the strong clutter. Furthermore, it is not possible to determine in the measurement data whether a given, locally strong clutter return actually emanates from a definable, physical point object of specifiable RCS, or from a physically extended σ° clutter medium that by chance phasor reinforcement happens to produce a strong clutter return. Therefore, the separate modeling of locally strong clutter cells under this approach needed to be carried out, not as a deterministic RCS overlay, but as a second statistical σ° process in which, with a specified probability of occurrence, a given cell might have a “discrete” component added vectorally to its “background” component. That is, under this approach an investigator is not provided with a single value of σ° for a given terrain type and illumination angle, but is provided with two values of σ°, one for “discrete” clutter and one for “background” clutter. The total clutter return is comprised of two components requiring two random draws, compared to modeling the total return as a single component obtained from one random draw. In the separation of locally strong clutter cells from the weaker surrounding cells, the weaker clutter was found to be dependent at the resolution cell level on terrain slope and grazing angle, thus allowing the effect of landform on the weaker clutter to be provided at the cell level via computation of grazing angle using DTED rather than through macropatch classification of terrain relief; the locally strong (i.e., dominant) clutter, like the total clutter in the interim model, did not show correlation with grazing angle at the cell level. Another refinement to the basic site-specific clutter model obtainable with more intensive computation is the softening or blurring of shadow boundaries, as determined geometrically from DTED, whereby clutter is allowed to rapidly diminish into shadowed regions with increasing depth of shadow rather than abruptly terminating right at the shadow boundary. These site-specific approaches to clutter modeling allow the limiting effects of clutter on radar system performance at any given site to be determined to a high degree of exactitude, thereby meeting much in the way of design- and analysis-related need for quantification and prediction of radar performance in ground clutter. In today’s highly evolved and rapidly expanding era of high performance computer capability, the fact that a site-specific approach to clutter modeling is computer-dependent, requiring extensive computation based on accurate DTED for the sites in question, is no longer very restrictive, whether concern is with individual sites or complexes of sites. The nature of ground clutter is that it can affect radar performance very differently from site to site, as a consequence of the

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extreme variations in surrounding terrain that can occur from one site to another, and a quantitative approach to the accurate assessment of the effects of clutter needs to reflect this specificity. Nevertheless, the fact remains that the site-specific approach to modeling clutter provides answers one site at a time. For radar system design/analysis that requires more general information of the impact of ground clutter on system performance, the rigorous way under the site-specific approach is to first compute performance across a set of sites as specified by the particular design or analysis under consideration, and then to generalize (e.g., medianize) performance depending on how site-to-site performance varies across the set. Note that this approach to generality a posteriori averages the performance measures obtained from a number of realistic site-specific clutter computations; it does not attempt to a priori average the clutter first (a non-verifiable undertaking) followed by a one-time assessment of performance. As a conceptual alternative to accepting the computational burden required in such a rigorous approach to generality, the idea of a clutter model that retains the important element of spatial patchiness but realizes it by means of a generic stochastic process in which patch extents, separations, and obliquities are statistically representative of general types of terrain rather than specific sites is intuitively attractive. This idea, involving implementation of generalized stochastic patchiness, although beyond the range of subject matter covered in this book, was explored at some length in coordinated studies involving the Lincoln Laboratory clutter data carried out by other investigative agencies ([3] is an early citation from extended research undertaken to develop this idea). However, the specificity of terrain feature at the scale at which terrain feature affects low-angle terrain visibility and clutter patchiness makes it difficult to capture such effects statistically. Unlike the ocean, the terrain at most sites of any significant relief is not very statistical in the sense of generally repeated patterns, but is dominated by a relatively few discrete singular macrofeatures (e.g., a mountain range, a ridge of hills, a river valley, a coastal shoreline). As a result, the parameters affecting the patchiness provided by a general stochastic model could not be related to simple quantifiable measures (e.g., surface relief; correlation distance) associated with generalized terrain types; but rather required that the parameters governing patchiness be acquired by an initialization or conditioning cycle of processing in DTED over a large-scale region encompassing the site of interest. Such generalized approaches to stochastic patchiness were reasonably successful for terrain of relatively low or moderate relief; high-relief terrain is too specific for a stochastic approach to be appropriate. Since a stochastically patchy non-site-specific clutter model requires initialization using DTED from the terrain region of interest, the sought for advantages of such a model in providing non-site-specific stochastic realizations of patchiness are somewhat diminished compared with more straightforwardly obtained sitespecific realizations of patchiness. For such reasons, the initially attractive and deceptively simple notion of a generic non-site-specific clutter model invested with realistic stochastic patchiness becomes more difficult to successfully implement in actual practice than might be presupposed, although a remaining advantage of the stochastically patchy approach is that it can lead to generic analytic formulations of such system performance measures as, for example, signal-to-clutter ratio vs range for the terrain type under consideration.

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A spatially patchy clutter model, whether site-specific or non-site-specific, captures the important element of disconnectedness in spatial occurrence of low-angle terrain visibility that leads to a high degree of fidelity in the representation of ground clutter in surface radar. Such a high degree of fidelity is not always required, however, in the representation of ground clutter by radar system engineers. As a first indication of the effects of ground clutter, the radar system engineer may not be interested in the full-blown system effects of patchiness, but may require only a single value of constant σ° indicating how strong the clutter is at a given site for use in the radar range equation to estimate signal-to-clutter ratios against particular targets; and in addition may require only a single value of cut-off range to indicate the maximum extent in range to which the constant σ° applies and beyond which the radar is clutter-free. From this point of view, the modeling of patchiness in low-angle terrain visibility may be regarded as a higher order (although important) effect in low-angle clutter phenomenology compared with modeling the strength of the clutter (assuming that the ground is visible), and for a beginning all that is required of this higher-order effect is a global estimate of the maximum extent of the patchy terrain visibility in range. Furthermore, this point of view disregards the fact that low-angle σ° occurs as a statistical phenomenon with wide cell-tocell variations over a local region, but instead focuses on a single measure of strength such as the mean level; it also disregards the fact that σ° varies with depression angle since depression angle varies most significantly only within the first few kilometers of range from the radar, and usually diminishes to very near grazing incidence (e.g., 0.1° or 0.2°) over the much greater extents of clutter spatial occupancy that occur at much longer ranges. To meet these kinds of less demanding requirements in a clutter model, Chapter 4 also provides a simple, non-patchy, non-site-specific clutter model that specifies mean clutter strength σ w° depending only on general terrain type (e.g., rural/low-relief, rural/highrelief, urban) and clutter cut-off range Rc depending only on effective radar height (e.g., low, intermediate, high). Since low-angle clutter is so variable both in strength and extent, these two parameters σ w° and Rc are provided not only as baseline central values, but also as worst-case values indicative of severe or heavy clutter situations, and as best-case values indicative of benign or light clutter situations. A very large step in simplification occurs between the extremes of clutter models (viz., the full-blown site-specific statistical model vs the simple non-site-specific constant-σ° model) described in Chapter 4. Many of the difficulties that face efforts to bring realism to empirical clutter models at intermediate levels of fidelity between these two extremes are explored in ancillary discussions of the measured clutter data both in the body of Chapter 4 and its appendices. These ancillary discussions include considerations of (a) the inherent effects on terrain visibility and clutter strength of radar height and radar range; (b) the proper way to deal with unavoidable noise-level samples in clutter measurements and the important consequent effect on clutter statistics of rapidly decreasing radar sensitivity to clutter with increasing range; and (c) the wide range of variability involved in general clutter amplitude statistics and the attendant difficulty in specifying any particular σ° level for a constant-σ° clutter model. Discussions are also provided concerning the relationship between terrain visibility and clutter occurrence and concerning discrete vs distributed clutter and the appropriate parameter by which to characterize low-angle clutter. All these discussions serve to more

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fully describe the complex, multifaceted nature of low-angle clutter from different perspectives and to bring home the value of the site-specific approach to clutter modeling in that it automatically and accurately incorporates all the complicating factors that are difficult for more general modeling approaches to capture. Although the main subject of Chapter 4 is the consideration of various approaches to modeling the spatial amplitude statistics of lowangle ground clutter, brief consideration is also given to aspects of the phenomenon associated with its temporal variability and its spectral and correlative properties.

References 1.

M. Sekine and Y. Mao, Weibull Radar Clutter, London, U. K.: Peter Peregrinus Ltd. and IEE, 1990.

2.

R. R. Boothe, “The Weibull Distribution Applied to the Ground Clutter Backscatter Coefficient,” U. S. Army Missile Command Rept. No. RE-TR-69-15, Redstone Arsenal, AL, June 1969; DTIC AD-691109.

3.

S. P. Tonkin and M. A. Wood, “Stochastic model of terrain effects upon the performance of land-based radars,” AGARD Conference Proceedings on Target and Clutter Scattering and Their Effects on Military Radar Performance, AGARD-CP501, (1991).

4.

M. P. Warden and E. J. Dodsworth, “A Review of Clutter, 1974,” Royal Radar Establishment Technical Note No. 783, Malvern, U.K., September 1974; DTIC AD A014421.

5.

W. J. McEvoy, “Discrete Clutter Measurements Program: Operations in the Metropolitan Boston Area,” MITRE Corporation; Air Force Systems Command, Electronic Systems Division, Deputy for AWACS, Report ESD-TR-72-131, AD 742 298, March 1972.

6.

W. J. McEvoy, “Discrete Clutter Measurements Program: Operations in Western Massachusetts,” MITRE Corporation; Air Force Systems Command, Electronic Systems Division, Deputy for AWACS, Report ESD-TR-72-132, AD 742 297, March 1972.

7.

D. C. Schleher, MTI and Pulsed Doppler Radar, Norwood, MA: Artech House, 1991, p. 226.

8.

S. Kazel, J. Patten, J. Dabkowski, J. Pipkin, and A. Brindley, “Extensions to the ORT Clutter Model,” IIT Research Institute, Chicago, June 1971.

9.

H. R. Ward, “A model environment for search radar evaluation,” IEEE EASCON Rec, pp. 164-171, 1971.

10. C. J. Rigden, “High Resolution Land Clutter Characteristics,” Admiralty Surface Weapons Establishment Technical Report TR-73-6, Portsmouth, U.K., January 1973; DTIC AD-768412. 11. D. C. Schleher, op. cit., p. 174. 12. C. W. Helstrom, Elements of Signal Detection and Estimation, Englewood Cliffs, NJ: Prentice-Hall, 1995.

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13. T. Linell, “An experimental investigation of the amplitude distribution of radar terrain return,” 6th Conf. Swedish Natl. Comm. Sci. Radio, Research Institute of National Defence, Stockholm, March 1963. 14. F. E. Nathanson and J. P. Reilly, “Clutter statistics that affect radar performance analysis,” EASCON Proc. (supplement to IEEE Trans.), vol. AES-3, no. 6, pp. 386398, November 1967. 15. J. K. Jao, “Amplitude distribution of composite terrain radar clutter and the Kdistribution,” IEEE Transactions on Antennas and Propagation, AP-32 (Oct. 1984), 1049-1062. 16. J. B. Billingsley and J. F. Larrabee, “Multifrequency Measurements of Radar Ground Clutter at 42 Sites,” Lexington, MA: MIT Lincoln Laboratory, Technical Rep. 916, Volumes 1, 2, 3; 15 November 1991; DTIC AD-A246710. 17. K. Rajalakshmi Menon, N. Balakrishnan, M. Janakiraman, and K. Ramchand, “Characterization of fluctuating statistics of radar clutter for Indian terrain,” IEEE Transactions on Geoscience and Remote Sensing. vol. 33. no. 2 (March 1995), 317323. 18. V. Anastassopoulos and G. A. Lampropoulos, “High resolution radar clutter classification,” in Proceedings of IEEE International RADAR Conference, Washington, DC, May 1995, 662-667. 19. K. S. Chen and A. K. Fung, “Frequency dependence of backscattered signals from forest components,” IEE Proceedings, Pt. F, 142, 6 (December 1995), pp. 310-315. 20. E. J. Barlow, “Doppler Radar”, Proc. IRE, 37, 4 (1949). 21. J. L. Lawson and G. E. Uhlenbeck (eds), Threshold Signals, Vol. 24 in the MIT Radiation Laboratory Series, New York: McGraw-Hill (1950). Reprinted, Dover Publications (1965). 22. H. Goldstein, “The Fluctuations of Clutter Echoes,” pp. 550-587, in D. E. Kerr (ed.), Propagation of Short Radio Waves, Vol. 13 in the MIT Radiation Laboratory Series, New York: McGraw-Hill (1951). Reprinted, Dover Publications (1965). 23. J. B. Billingsley, A. Farina, F. Gini, M. V. Greco, and P. Lombardo, “Impact of experimentally measured Doppler spectrum of ground clutter on MTI and STAP,” in Proceedings of 1997 International Radar Conference, Edinburgh, UK, October 1416, 1997, 290-294. 24. A. Farina, F. Gini, M. V. Greco, and P. Lee, “Improvement factor for real sea-clutter Doppler frequency spectra,” IEE Proceedings, Pt. F, 143, 5 (October 1996), 341-344. 25. S. Watts, C. J. Baker, and K. D. Ward, “Maritime surveillance radar Part 2: Detection performance prediction in sea clutter,” IEE Proceedings, Pt. F, 137, 2 (April 1990), 63-72. 26. J. B. Billingsley and J. F. Larrabee, “Measured Spectral Extent of L- and X-Band Radar Reflections from Windblown Trees,” Lexington, MA: MIT Lincoln Laboratory, Project Rep. CMT-57, 6 February 1987; DTIC AD-A179942. 27. H. C. Chan, “Radar ground clutter measurements and models, part 2: Spectral characteristics and temporal statistics,” AGARD Conference Proceedings on Target

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and Clutter Scattering and Their Effects on Military Radar Performance, AGARDCP-501 (1991). 28. G. C. Sarno, “A model of coherent radar land backscatter,” AGARD Conference Proceedings on Target and Clutter Scattering and Their Effects on Military Radar Performance, AGARD-CP-501 (1991). 29. J. B. Billingsley, “Exponential Decay in Windblown Radar Ground Clutter Doppler Spectra: Multifrequency Measurements and Model,” Lexington, MA: MIT Lincoln Laboratory, Technical Report 997, 29 July 1996; DTIC AD-A312399. 30. J. B. Billingsley, A. Farina, F. Gini, M. V. Greco, and L.Verrazzani, “Statistical analyses of measured radar ground clutter data,” IEEE Trans. AES, vol. 35, no. 2 (April 1999). 31. P. Lombardo, and J. B. Billingsley, “A new model for the Doppler spectrum of windblown radar ground clutter,” in Proceedings of IEEE 1999 Radar Conference, Boston, MA, 20-22 April 1999. 32. D. P. Meyer and H. A. Mayer, Radar Target Detection—Handbook of Theory and Practice, San Diego, CA: Academic Press, 1973, pp. 66, 67. 33. L. R. Rabiner and B. Gold, Theory and Application of Digital Signal Processing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1975. 34. F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE, vol. 66, no. 1, pp. 51-83, January 1978. 35. V. A. Andrianov, N. A. Armand, and I. N. Kibardina, “Scattering of radio waves by an underlying surface covered with vegetation,” Radio Eng. and Electron. Physics (USSR), vol. 21, no. 9, September 1976. 36. C. M. Rader, “An improved algorithm for high-speed autocorrelation with applications to spectral estimation,” IEEE Trans. Audio Electrocoustic., vol. AU-18, pp. 439-441, Dec. 1970. 37. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Englewood Cliffs, NJ: Prentice-Hall, 1993. 38. S. Haykin and A. Steinhardt, Adaptive Radar Detection and Estimation, New York: Wiley, 1992.

5 MULTIFREQUENCY LAND CLUTTER MODELING INFORMATION 5.1 Introduction Chapter 5 provides land clutter modeling information for surface-sited radar based on comprehensive reduction of extensive multifrequency land clutter measurement data from 42 different sites. The survey clutter measurements upon which this information is based are described in Chapter 3 (see also [1]). The clutter modeling information that follows is provided for general terrain and for eight specific terrain types. For each terrain type, the modeling information is further partitioned by the relief of the terrain and by the depression angle below the horizontal from the radar to the backscattering terrain point. For each terrain type/relief/depression angle combination of parameters, the modeling information provided specifies the probability distribution encompassing the spatial cellto-cell variability of clutter amplitude statistics applicable to that combination of parameters. Probability distributions are specified in terms of Weibull statistics. For each terrain type/relief/depression angle combination, Weibull mean clutter strength σ w° is provided as a function of radar frequency, VHF to X-band; and Weibull shape parameter aw is provided as a function of radar spatial resolution, 103 m2 to 106 m2. The number of clutter coefficients σ w° applicable to low-angle land clutter specified in Chapter 5 is 864. These coefficients are provided within a parametric structure that allows practical application of them to surface radars sited in various terrains and situations. Most of the clutter coefficients provided are relatively general, each usually being based on numerous measurements. The number of measurements applicable to each value of σ w° is also provided. In the past, authoritative reviews of the subject [2–5] have agreed on the difficulty of characterizing low-angle land clutter with basic questions of radar frequency dependence, the role of illumination angle, and effects of varying terrain type remaining unanswered. The definitive body of new information presented in Chapter 5 now provides a condensed and unified codification of low-angle land clutter’s fundamental attributes. In what follows, Section 5.1.1 reviews the Phase One survey database, the reduction of these data into patch-specific histograms of clutter strength, and the fundamental parametric effects that emerge in the trend analyses of these histograms. Section 5.2 describes how clutter modeling information in terms of Weibull statistics is derived through the combination of many patch measurements. Section 5.3 presents clutter modeling information for general rural terrain, irrespective of land cover. Section 5.4 presents clutter modeling information for eight specific terrain types. Section 5.5 briefly discusses and

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provides an example of plan-position indicator (PPI) clutter map simulation using the modeling information of Chapter 5. Section 5.6 is a summary. Appendix 5.A presents additional information on Weibull statistics and compares them with statistics from lognormal and K-distributions.

5.1.1 Review 5.1.1.1 Clutter Measurements The results of Chapter 5 are based on Phase One five-frequency land clutter measurements at 42 different sites as described in Chapter 3. At each Phase One site, all of the discernible land clutter within the field-of-view was measured at each of five frequencies, VHF, UHF, L-, S-, and X-bands, and at both vertical and horizontal polarization and at low and high range resolution. These raw Phase One data were calibrated, pulse-by-pulse and cell-bycell, into absolute units of clutter strength. The resultant large 475-Gbyte five-frequency land clutter measurement database comprises a unique resource that is planned to be maintained indefinitely at Lincoln Laboratory. These data were provided to government authorities in Canada and the United Kingdom, and coordinated analyses took place in these countries as well as in the United States [6–9]. The results of Chapter 5 are based on the spatially comprehensive 360° survey data from all 42 Phase One sites. Previous Phase One results discussed in Chapters 3 and 4 were based on the relatively narrow (e.g., 20°) azimuth sector of repeated measurement concentration at each site called the repeat sector. Clutter experiments acquired in survey mode, as opposed to repeat sector mode, are further described in Chapter 3, Section 3.2.2.

5.1.1.1.1 Data Reduction Each raw in-phase (I) and quadrature (Q) sample pair of Phase One measured clutter data is reduced to a clutter strength number. As defined earlier in this book, clutter strength is given by σ °F4, where σ ° is the intrinsic backscattering coefficient and F is the pattern propagation factor. As previously discussed, the pattern propagation factor includes all terrain effects in low-angle land clutter caused by multipath reflections and diffraction from the terrain. Using available digitized terrain elevation data, it is not generally possible to deterministically compute F at clutter source heights sufficiently accurately to allow cell-by-cell separation of intrinsic σ ° in measured clutter data (e.g., see Chapter 1, Section 1.5.4; Chapter 3, Appendix 3.B). All of the coefficients of clutter strength tabulated as modeling information in Chapter 5 include propagation effects. All computations involving σ °F4 are performed in units of m2/m2. For convenience, the tabulated clutter coefficients have been subsequently converted to decibels with respect to 1 m2/m2. The specific computations involved in data reduction are defined more completely in Chapters 2 and 3.

5.1.1.1.2 Stored Clutter Histograms Within the PPI spatial map of measured clutter strength at each site, terrain macroregions were selected largely within line-of-sight illumination in which a relatively high percentage of resolution cells contain discernible clutter above the radar noise level. These terrain macroregions are referred to as terrain patches or clutter patches. Typically, clutter patches are several kilometers on a side (median size = 12.6 km2; see Appendix 2.B). Many examples of clutter patches and histograms of clutter strength measured from clutter patches are shown in this book, including several to follow in Chapter 5. By registering measured clutter maps with air photos and topographic maps, landform and land cover descriptive information of the terrain within the patch was provided.

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The landform and land cover classification systems utilized in this process are described in Chapter 2, Section 2.2.3. For each clutter patch, the distribution or histogram of clutter strengths occurring within the patch was formed, based upon all of the cells within the patch, including those at radar noise level. This histogram was formed at each of the 20 parameter combinations nominally available within the Phase One radar parameter matrix (five frequencies, two polarizations, two range resolutions; see Appendix 3.A, Table 3.A.2). Various statistical attributes (e.g., mean, median, variance, etc.) of each histogram were computed. The formulas used in these computations are provided in Appendices 2.B and 3.C. Each histogram together with its statistical attributes and the applicable terrain descriptors of the patch and the radar parameters was then stored in a computer file. Predictive clutter modeling information was developed by establishing general correlative properties between the stored distributions of measured clutter strength and the corresponding terrain descriptions and relevant radar parameters. The results of Chapter 5 are based on 59,804 stored histograms of measured clutter strength from 3,361 clutter patches at the 42 Phase One sites.

5.1.1.1.3 Pure and Mixed Terrain Classification of the terrain within each of the 3,361 clutter patches in terms of landform (i.e., the relief or roughness of the terrain) and land cover (e.g., urban, forest, agricultural, etc.) occurred at two levels, primary and secondary (see Sections 2.2.3 and 3.2.3 for details). As a result of terrain classification, the results of Chapter 5 are partitioned into two groups, those applicable to pure terrain and those applicable to mixed terrain. Pure terrain is terrain that requires primary classification only. Mixed terrain requires secondary as well as primary classification. Of the 3,361 clutter patches, 1,733 (i.e., 52%) are pure and 1,628 (i.e., 48%) are mixed. For pure terrain, clutter modeling results are provided in Section 5.4 for eight specific terrain types; namely, urban, agricultural, forest, shrubland, grassland, wetland, desert, and mountain categories. These specific terrain types are usually characterized principally by land cover, although mountain terrain is characterized principally by landform. For mixed terrain, general results are provided in Section 5.3. Most terrain types are further partitioned by relief, usually in terms of high relief (i.e., with terrain slopes > 2°) and low relief (i.e., with terrain slopes < 2°). Results for pure terrain are suitable for modeling at cell level or in very homogeneous terrain. Results for pure terrain are also useful for setting approximate worst-case/best-case bounds on the severity of land clutter interference. Results for mixed terrain apply more generally to large extents of composite landscape. The results in Section 5.3 for general mixed rural terrain are among the more important results of the Phase One clutter measurements program; these results show how systematic variations in terrain relief and depression angle cause corresponding variations in clutter strength in all five frequency bands for generally occurring composite terrain.

5.1.1.1.4 Clutter Patch Selection at Magrath Figure 5.126 illustrates clutter patch selection at the Phase One measurement site of Magrath, Alberta. The figure shows two Phase One X-band PPI clutter maps in both of which clutter is shown dark gray—the clutter map on the left is to 20-km maximum range, that to the right is to 50-km maximum range. In both clutter maps, the repeat sector clutter patch is shown as a narrow solid black sector to the southeast. Repeat sector clutter 26. All Chapter 5 figures occur consecutively in the figures-only, color section beginning on page 447.

410 Multifrequency Land Clutter Modeling Information

measurements, involving one patch per site at each of 42 different sites, are the basis of the Phase One results provided in Chapters 3 and 4. Also in both clutter maps, all the survey patches selected at Magrath are shown outlined and shaded to appear light gray. It is evident that the survey patches in total are much more spatially comprehensive in terms of covering almost all of the measured clutter than the repeat sector. As a result, the clutter modeling information of Chapter 5, based on survey measurements at all sites, is of increased statistical certainty and of increased prediction accuracy, both because these survey results are based on many more samples per terrain class and in addition because they are based on more terrain classes.

5.1.1.1.5 Noise Corruption It was indicated above that, in forming histograms and cumulative distributions of clutter strength σ °F 4 over clutter patches, all of the cells and samples that were measured from the patch, including those at radar noise level, need to be included. It is possible, in forming such histograms and distributions, to include only those samples for which the returned signal strength is greater than radar noise level, and to delete the noise-level samples. Such histograms and distributions have been referred to as “shadowless” previously in this book (e.g., see Section 1.4.7 and Appendices 2.B, 3.C, and 4.C for related discussions). Shadowless statistics are obviously dependent upon radar sensitivity and are thus conditional (not absolute) measures of reflectivity. Use of shadowless clutter statistics can lead to subsequent misinterpretation in analysis and significant misrepresentation of radar system performance. Thus, in forming the cumulative distribution for a given clutter patch, the noise-level samples are retained and the cumulative is plotted two ways: (1) as an upper bound in which the samples at noise level retain their noise power values, and (2) as a lower bound in which the samples at noise level are assigned zero (or a very low value of) power. These upper bound/lower bound cumulative pairs deviate from each other only over the low-end noise-corrupted interval of the distribution (where the true cumulative must lie between them); they merge to form the single true cumulative at σ °F 4 levels above the highest noise corruption. By true cumulative is meant that which would be measured by a hypothetical radar of infinite sensitivity (or at least sensitivity high enough so that all clutter samples returned from the clutter patch are well above radar noise level). In contrast, the shadowless cumulative can lie significantly apart from the true cumulative over its compete range (see Appendix 4.C). Similarly, in the computation of the moments of distributions that include noise samples, the moments are computed two ways: (1) as an upper bound in which the samples at noise level retain their noise power values, and (2) as a lower bound in which the samples at noise level are assigned zero power. Upper and lower bounds to moments of noise-corrupted clutter distributions are usually within small fractions of a decibel of each other, even when the amount of noise corruption is high; such tight bounds are the result of the extreme skewness of the distributions such that the moments are dominated by the high-end tails. Of course, the true value of the moment must lie between the upper and lower bounds. In contrast, moments of shadowless distributions are dependent on radar sensitivity (i.e., the amount of noise that was deleted) and can be significantly different from the true value. Separation of upper and lower bound values of moments by large amounts indicates a measurement too corrupted by noise to provide useful information.

Multifrequency Land Clutter Modeling Information 411

The clutter modeling results provided in Chapter 5 are based upon tight upper-bound values of moments of noise-corrupted low-angle clutter distributions and are thus absolute measures independent of radar sensitivity. The correct methodology (as discussed above) for the proper treatment of radar noise and shadowing in low-angle clutter is elaborated in more detail elsewhere (see Section 1.4.7 and Appendices 2.B, 3.C, and 4.C).

5.1.1.1.6 Two Clutter Patch Histograms The terrain within general rural clutter patches often consists of mixtures of various open (e.g., cropland, rangeland) and tree-covered components. Figures 5.2 and 5.3 show examples of measured clutter histograms and cumulative distributions from two such mixed rural patches. These two examples were selected from the 30,246 such histograms comprising the Phase One general mixed rural clutter modeling database. Figure 5.2 shows a UHF histogram measured from patch 34/2 at Wachusett Mountain, Massachusetts. Patch WM 34/2 was primarily hilly mixed-forest with secondary occurrences of cropland and lakes, and was observed at 1° depression angle. It was situated beginning at 11.9 km from the radar and extended 11.7 km in range and 35.6° in azimuth. In the histogram of Figure 5.2, 4.1% of the samples are at radar noise level (cells at noise level are indicated as black in the histogram). Figure 5.3 shows an X-band histogram measured from patch 7/1 at Spruce Home, Saskatchewan. Patch SH 7/1 was primarily level cropland with secondary occurrences of trees at 10% incidence of occurrence and was observed at a depression angle of 0.6°. It was situated beginning 2.2 km from the radar and extended 4.8 km in range and 33.6° in azimuth. In the histogram of Figure 5.3, 11.6% of the samples are at radar noise level. The histograms of Figures 5.2 and 5.3 were both measured using 150-m pulse length and horizontal polarization. The WM 34/2 and SH 7/1 clutter histograms of Figures 5.2 and 5.3 typify the many such measurements in the Phase One database in the extremely wide range of values of clutter strength σ °F 4 that each exhibits. The WM 34/2 histogram of Figure 5.2 covers over six orders of magnitude in σ °F 4; the SH 7/1 histogram of Figure 5.3 covers over eight orders of magnitude. In addition to showing these histograms, Figures 5.2 and 5.3 also show the corresponding upper-bound cumulative distributions in which the percent of samples in each histogram bin is accumulated left to right across the histogram. The cumulative distribution is shown as a solid line and is read on the left ordinate; on the right ordinate is read the percent of samples in each histogram bin. The left ordinate is a nonlinear Weibull probability scale such that theoretical Weibull cumulative distributions plot as straight lines when, as shown, the abscissa is clutter strength in decibels (see Appendix 2.B). Both the WM 34/2 UHF cumulative clutter distribution (Figure 5.2) and the SH 7/1 X-band distribution (Figure 5.3) are relatively linear and hence reasonably well approximated as Weibull distributions over much of their central extents. In this respect also, these two distributions are representative of most of the many such measurements in the Phase One database, which are generally (but not without occasional exception) more Weibull-like than, for example, lognormal-like or K-distribution-like. This matter is discussed further in Appendix 5.A. Also shown in Figures 5.2 and 5.3 is the slope that a theoretical Rayleigh distribution takes in such plots; by Rayleigh, it is meant that the received clutter voltage signal x is

412 Multifrequency Land Clutter Modeling Information

Rayleigh distributed, which means that the clutter strength x = σ °F 4 (which is a normalized measure of received clutter power) is exponentially distributed. The Rayleigh (voltage) distribution or exponential (power) distribution is a degenerate (one-parameter) case of the more general (two-parameter) Weibull distribution for which the Weibull shape parameter aw is equal to unity [see Eq. (5.2)]. A simple Rayleigh (voltage) distribution is what is expected for clutter measured at higher airborne-like angles or over more homogeneous surfaces (see discussions in Chapter 2, Sections 2.3.4.2 and 2.4.4.3). It is evident in Figures 5.2 and 5.3 that the measured cumulative distributions are of significantly lower slope and hence are significantly wider than Rayleigh. The non-Rayleigh nature of the two distributions shown in Figures 5.2 and 5.3 is also apparent from the numbers provided in Table 5.1. This table shows statistical attributes of these two measured clutter distributions and compares them with theoretical Rayleigh values. In Figures 5.2 and 5.3, the vertical dotted lines show the positions of the 50- (or median), 70-, 90-, and 99-percentile levels in the distributions, left to right, respectively; the vertical dashed line shows the position of the mean level in each distribution. For example, whereas a Rayleigh (voltage) distribution has mean/median (power) ratio equal to 1.6 dB [Eq. (5.3)], the measured WM 34/2 and SH 7/1 distributions have mean/median ratios equal to 7.8 and 21.2 dB, respectively. The other statistical attributes of these measured distributions shown in Table 5.1 are similarly indicative of very wide, highly skewed, non-Rayleigh behavior. A Rayleigh distribution may be envisaged in Figures 5.2 and 5.3 not only to be of the cumulative Rayleigh slope indicated, but also to have a 99-percentile (right-most dotted line) to median (left-most dotted line) extent of only 8.2 dB. Table 5.1 indicates that the measured distributions in Figures 5.2 and 5.3 have 99-percentile/median ratios of 18 and 34 dB, which are more than twice and more than four times the Rayleigh value, respectively. Table 5.1 Clutter Statistics for Two Mixed Rural Terrain Patches Statistic

Spruce Home Patch 7/1 X-Band

Wachusett Mt. Patch 34/2 UHF

Theoretical Rayleigh Values

aw

4.2

2.1

1.0

SD/Mean (dB)

7.2

3.7

0.0

Skewness (dB)

10.8

7.2

3.0

Kurtosis (dB)

22.8

16.4

9.5

Mean/Median (dB)

21.2

7.8

1.6

99-percentile/Median (dB)

34.0

18.0

8.2

Of particular interest in Table 5.1 are the values of Weibull shape parameter aw and the values of ratio of standard deviation-to-mean from which the aw values derive [Eq. (5.4)]. Again it is evident for the two example histograms of Figures 5.2 and 5.3 that, in terms of aw, the data depart increasingly from the Rayleigh value of unity in proceeding from the higher angle, more homogeneous WM 34/2 patch (aw = 2.1) to the lower angle, more heterogeneous SH 7/1 patch (aw = 4.2). Looking ahead to the empirical clutter modeling information given in Chapter 5, observe that: (1) an important component of the modeling

Multifrequency Land Clutter Modeling Information 413

information is the general specification of aw as a function of resolution and depression angle, and (2) the values of aw so specified for general low-angle clutter in ground-based radar over large extents of composite terrain are generally far from Rayleigh and only begin to approach the Rayleigh value of unity when cell size becomes very large or as depression angle increases to airborne-like regimes.

5.1.1.2 Parametric Effects The following review of parametric clutter dependencies summarizes earlier discussions in this book. As developed in Chapter 2, a fundamental parametric dependence in lowangle clutter amplitude statistics is that of depression angle as it affects microshadowing among dominant discrete clutter sources, such that mean clutter strengths increase and cell-to-cell fluctuations decrease with increasing angle. At very low angles, clutter is to a very great extent caused by isolated discrete sources. Numerous low-reflectivity or shadowed cells occur between cells containing discrete clutter sources, even though the overall region from which the clutter amplitude distribution is formed is under general illumination by the radar. The combination of many shadowed or low-reflectivity weak cells together with many discrete-dominated strong cells causes extensive spread in the resultant low-angle clutter amplitude distribution. As depression angle increases, the low reflectivity areas between discrete vertical features become more strongly illuminated, resulting in less shadowing and a rapid decrease in the spread of the distribution. As a result, measures of spread in the amplitude statistics such as ratio of standard deviation-to-mean and mean-to-median ratio decrease rapidly with increasing angle as the shadowed and weak samples at the low end of the distribution rise toward the stronger values that dominate the mean. However, the upper tail of the clutter distribution and mean level that is largely determined by the upper tail are still primarily caused by discrete sources and increase more slowly with increasing depression angle. These general effects of depression angle are important at all frequencies in the Phase One measurements. Because of the heterogeneous process involved, wherein groups of cells providing strong returns are often separated by cells providing weak or noise-level returns, the spatial resolution of the radar fundamentally affects the amount of spread in clutter amplitude distributions from spatial macroregions. Increasing resolution results in less averaging within a cell, more cell-to-cell variability, and hence increased spread in the distributions. This general effect of resolution is also important at all frequencies in the Phase One measurements. Within the context of the above mechanisms, radar frequency does not generally play as fundamental a role as do depression angle and resolution. However, as discussed in Chapter 3, two strong trends with frequency occur in particular circumstances. One of these is directly the result of the intrinsic backscattering coefficient σ ° having an inherent frequency-dependent characteristic. Thus, at high depression angles in forested terrain, propagation measurements show that forward reflections are minimal (i.e., F ≈1). In such terrain, intrinsic σ ° decreases strongly with increasing frequency due to the absorption characteristic of forest increasing with frequency. The other trend with frequency is the result of a general propagation effect entering clutter strength σ °F 4 through the pattern propagation factor F. At low depression angles in level

414 Multifrequency Land Clutter Modeling Information

open terrain, strong forward reflections cause multipath lobing on the free-space antenna pattern. At low frequencies such as VHF, these lobes tend to be broad so that returns from most clutter sources are received well on the underside of the first multipath lobe, and clutter strengths are much reduced. As frequency increases, the multipath lobes become narrower; typical clutter sources such as buildings or trees tend to extend over multiple lobes, with the result that at higher frequencies the overall multipath effect on illumination has less influence on the clutter strength. Thus, at low angles on level open terrain, there exists a characteristic of strongly increasing mean clutter strength with increasing frequency introduced through the pattern propagation factor. In inclined or rolling open terrain of increased relief, multipath is as likely to reinforce as to cancel clutter returns even at low radar frequencies. Polarization has little general effect on ground clutter amplitude statistics. On the average, mean ground clutter strength is often 1 or 2 dB stronger at vertical polarization than at horizontal. The reason may be associated with the preferred vertical orientation of many discrete clutter sources. As discussed in Chapter 3, occasional specific measurements can show more significant variation with polarization but almost always less than 6 or 7 dB.

5.1.1.2.1 Discretes A classical ground clutter model consists of diffuse clutter emanating from area-extensive surfaces with a few large point-like discrete scatterers added in to account for objects like water towers. The Phase One measurements reveal that, at the near grazing incidence of surface radar, over ranges of many kilometers, a more realistic construct is to imagine clutter as arising from a sea of discretes. By discretes are meant here strong, locally isolated clutter cells separated by weak cells often at the noise level of the radar. For example, over forest, it is the cells containing projecting treetops that cause the dominant backscatter, with the in-between shadowed areas of the canopy contributing much lower returns. Over agricultural terrain, it is the few projecting hillocks in the microtopography plus buildings, fence lines, and other obvious cultural discretes that dominate the backscatter. At low angles, all terrain types, open or forested, natural or cultural, are dominated by discretes that occur at approximately 20% incidence of occurrence independent of land cover. Thus the clutter modeling information of Chapter 5 is based on depression angle as it affects shadowing in a sea of patchy visibility and discrete scattering sources. As depression angle increases, there is a gradual transition from a discrete-dominated, widespread, spiky, Weibull process towards more diffuse clutter and the accompanying, narrow spread, Rayleigh process that exists in airborne radar. Physical discretes are distinguished from discrete cells in the measured clutter data. By physical discretes are meant isolated vertical objects, structures, and terrain features existing in the landscape. Discrete cells in the measured clutter data are cells which contain stronger clutter than their neighbors. As discussed in Appendix 4.D, discrete cells in the measured clutter data may be specified as 5-db discretes, by which are meant cells in which the clutter is stronger than neighboring cells by 5 dB or more. That is, a 5-db spatial filter separates locally strong cells in a very widespread continuum of clutter amplitudes. The cells that remain (i.e., that fail to pass the 5-db spatial filter) may be called background cells. To a large extent clutter in background cells also comes from discrete but weaker physical sources in the sea of discretes that tends to make up low-angle clutter (as opposed to area-

Multifrequency Land Clutter Modeling Information 415

extensive diffuse clutter), even though dependency of clutter strength on grazing angle often exists in the residual set of weaker background cells. This dependency of background clutter on grazing angle is of limited advantage since the dominant discrete clutter is not dependent on grazing angle (see Appendix 4.D). Insufficient correlation exists between strong isolated clutter cells and obvious discrete vertical elements on the landscape to allow practicable deterministic prediction of discrete clutter. The clutter modeling information of Chapter 5 does not distinguish between discrete cells and background cells, but applies to the complete spatial amplitude distribution comprising returns from both strong and weak cells.

5.1.1.2.2 Depression Angle Depression angle is of major importance in its effects on both strength and spread in land clutter spatial amplitude statistics, even for the very low depression angles (typically within a degree of grazing incidence) and small (typically fractional) variations in depression angle that occur in surface radar. Depression angle is formulated mathematically in Appendix 2.D to be the complement of incidence angle at the backscattering terrain point under consideration. Incidence angle equals the angle between the outward projection of the earth’s radius at the terrain point and the direction of illumination at that point, assuming a 4/3 earth radius to account for standard atmospheric refraction. As previously discussed, the rigorous definition of depression angle in this book is in a reference frame centered at the terrain point, not at the antenna. For convenience of reference here, the following discussion summarizes material from Chapter 2, Sections 2.3.4–2.3.6, and elsewhere in this book. Thus, if range from radar to backscattering terrain point is r, effective earth’s radius (i.e., actual earth’s radius times 4/3) is a and effective radar height (i.e., radar site elevation plus radar antenna mast height minus terrain elevation at backscattering terrain point) is h, then depression angle α is given approximately by rα ≅ h-- – ----r

2a

(5.1)

This definition of depression angle includes the effect of earth curvature on the angle of illumination but does not include any effect of the local terrain slope. At short enough ranges that earth curvature is insignificant (i.e., r << a), depression angle simplifies to be the angle below the horizontal at which the terrain point is viewed from the antenna (i.e., α ≅ h/r, see Figure 5.6). Negative depression angle occurs when steep terrain is observed by the radar at elevations above the antenna. Depression angle is a quantity relatively simple and unambiguous to determine, depending as it does simply on range and relative elevation difference between the radar antenna and the backscattering terrain point. Since depression angle depends only on terrain elevations and not terrain slopes, it is a slowly varying quantity over clutter patches and not highly sensitive to errors in digitized terrain elevation data (DTED). Thus, the complete clutter amplitude distribution from any given clutter patch can usually be associated with one narrow depression angle regime. Grazing angle is the angle between the tangent to the local terrain surface at the backscattering terrain point and the direction of illumination. Thus, grazing angle does take into account the local terrain slope. Attempts to use grazing angle in clutter data analysis met with limited additional success, partly due to difficulties associated with specifying local terrain slope (i.e., rate of change of elevation) accurately in DTED, and partly due to the fact that many clutter sources tend to be vertical discrete objects associated with the land cover (see Section 2.3.5.1 and Appendix 4.D). Thus, the

416 Multifrequency Land Clutter Modeling Information

clutter modeling information of Chapter 5 is presented in fine steps or bins of depression angle in each radar frequency band. The depression angle bins utilized are specified subsequently in Table 5.4, Section 5.2.3.5.

5.2 Derivation of Clutter Modeling Information 5.2.1 Weibull Statistics In Chapter 5 modeling information for the empirical prediction of land clutter spatial amplitude distributions is presented in terms of Weibull statistics [10, 11]. Weibull statistics are convenient for this purpose both because they can easily accommodate the wide spreads existing in many low-angle measured clutter strength distributions, and because in the limiting, narrow spread case they degenerate to Rayleigh voltage statistics (i.e., exponential power statistics) as do the measured clutter distributions at high angles. The Weibull cumulative distribution function, previously defined in Chapter 2, is repeated here as:

 ln 2 ⋅ x  P ( x ) = 1 – exp  – -----------------  b  ( σ °50 )  b

(5.2)

where σ °50

=

median value of x,

b

=

1/aw , and

aw

=

Weibull shape parameter.

Here, as elsewhere in this book, the random variable x represents clutter strength σ°F 4 in units of m2/m2, i.e., x is a power-like quantity and y = 10log10 x. Equation (5.2) degenerates to an exponential power distribution for x (corresponding to a Rayleigh voltage distribution for x ) when aw = 1. The mean-to-median ratio for Weibull statistics is Γ ( 1 + aw ) σ °w --------- = ---------------------aw σ °50 ( 1n2 )

(5.3)

where σ w° is the mean value of x and Γ is the Gamma function. From these relationships, it is seen that a Weibull distribution is characterized by σ w° and aw. The modeling information in Chapter 5 specifies these two coefficients as a function of the terrain type within the clutter patch, the depression angle at which the radar illuminates the clutter patch, and the radar parameters of radar frequency, polarization, and spatial resolution. The lognormal distribution is another analytic distribution that can provide wide spread. However, the lognormal distribution often provides somewhat too much spread. That is, the high-end tails of measured low-angle clutter spatial amplitude distributions usually fall off more rapidly than do the tails of lognormal distributions matched to the measurements by, for example, the first two moments (see Appendix 5.A).

Multifrequency Land Clutter Modeling Information 417

Figure 2.28 in Chapter 2 shows five theoretical Weibull cumulative distributions having the same median clutter strength, σ °50 = –40 dB, but having values of shape parameter aw ranging from aw = 1 to aw = 5. Figure 5.4 shows the same five distributions plotted as histograms of y; i.e., as the probability density function p(y) vs y (see Appendix 5.A). The five Weibull distributions shown in Figure 5.4 graphically indicate how highly skewed distributions of very wide spread rapidly develop as aw increases from unity. Radar detection performance is seriously degraded in the presence of land clutter as a result of large clutter distribution losses caused by such highly skewed spatial distributions [3]. Appendix 5.A provides further information describing the long high-side tails associated with Weibull distributions with aw > 1. In a Weibull distribution, the Weibull shape parameter aw and the ratio of standard deviation-to-mean (sd/mean) are also directly related [see Appendix 2.B, Eq. (2.B.20)], as: 1 ⁄2 2 [ Γ ( 1 + 2a w ) – Γ ( 1 + a w ) ]

sd/mean = -------------------------------------------------------------------Γ ( 1 + aw )

(5.4)

Thus the shape parameter aw may be determined from either the ratio of standard deviationto-mean or the mean-to-median ratio. The modeling information of Chapter 5 specifies aw both ways, from measured values of ratio of standard deviation-to-mean and from measured values of mean-to-median ratio. To the extent that the measured clutter amplitude distributions are rigorously Weibull, these two evaluations of aw will be identical. Thus, comparison of the two evaluations provides a first indication of the degree of validity of assuming Weibull statistics. Although the two evaluations of aw are often approximately equal, they are seldom identically equal. Low-angle land clutter is a messy statistical phenomenon in which returns are collected from all the discrete vertical scattering sources that occur at neargrazing incidence over composite landscape. Thus, measured low-angle clutter distributions almost never pass rigorous statistical hypothesis tests (e.g., the KolmogorovSmirnov test) for belonging to Weibull, lognormal, K-, or any other analytic distribution over their complete extents (but see Appendix 5.A). Rather than dwell on statistical rigor, emphasis is given here to engineering approximations to the measured clutter distributions using Weibull statistics. Working in this manner, rigorous Weibull statistics within specified confidence bounds are not guaranteed. However, the one-sigma variability of mean strength (an engineering indication of prediction accuracy) in the measured distributions within a given terrain type/relief/depression angle class is often on the order of 3 dB. Less concern is with specifying exact shapes of low-angle clutter distributions than in correctly establishing the levels of first moments and the amounts of spread that occur in such distributions. Besides providing aw evaluated two ways, the modeling information of Chapter 5 also includes the measured values of ratio of standard deviation-to-mean and mean-to-median ratio from which these values of aw were determined. For Weibull statistics, Figure 5.5 shows plots of the ratios of standard deviation-to-mean and mean-to-median as given by Eqs. (5.3) and (5.4), respectively, vs the Weibull shape parameter aw. For aw = 1, the Weibull distribution, which is exponential (power) in this case, provides ratio of standard deviation-to-mean = 1 (i.e., 0 dB) and mean-to-median ratio = 1.44 (i.e., 1.6 dB). The results of Figure 5.5 reinforce those of Figure 5.4 in indicating

418 Multifrequency Land Clutter Modeling Information

how distributions of very wide spread (i.e., large ratios of standard deviation-to-mean and mean-to-median) rapidly arise as aw increases from unity. The plots of Figure 5.5 are useful as graphical aids to provide quick conversion factors in using the Weibull modeling information for aw provided subsequently in Chapter 5. Information comparing the use of Weibull, lognormal, and K-distributions in the representation of measured clutter amplitude statistics is provided in Appendix 5.A.

5.2.2 Clutter Model Framework For a given clutter patch, measured clutter histograms were collected and stored for all 20 combinations of Phase One radar measurement parameters nominally available (five frequencies, two polarizations, two pulse lengths; see Appendix 3.A). Altogether the file of measured histograms upon which Chapter 5 is based numbers 59,804. Trend analysis of these stored data involved sorting out like-classified sets of patches and looking for clustering within sets and separation between sets. This trend analysis led to a general framework for predicting or modeling clutter in which the fundamental structure is as follows: (1) Weibull mean strength σ w° varies with radar frequency and polarization; (2) Weibull shape parameter aw varies with radar spatial resolution; and (3) both σ w° and aw vary with terrain type and depression angle (cf. Section 4.2.2). Note that within this modeling framework, radar frequency affects σ w° but not aw; whereas spatial resolution affects aw but not σ w° . That is, frequency and resolution decouple in their effects on clutter amplitude statistics. The basic criterion imposed in developing this modeling framework was the degree to which an expected trend or dependency was actually borne out in the measured clutter data. This modeling framework is sufficient to capture all of the important trends and dependencies observed in the data.

5.2.2.1 Mean Strength σ w° A key attribute of the first moment or mean strength in a low-angle clutter amplitude distribution is that it is independent of radar spatial resolution. This fact and its importance are often unrecognized. It is both theoretically true in power-additive spatial ensemble processes and observed to be empirically true in the Phase One measurements. That it is theoretically true was discussed in Chapter 3, Section 3.5.3, and in Chapter 4, Section 4.5.4. In the Phase One measurement data, differences in mean strength between high (15 m or 36 m) and low (150 m) range resolution across the complete matrix of repeat sector patches were often less than one decibel (i.e., in the distribution of differences of mean strength with resolution, the mean difference was 0.8 dB and the median difference was 0.9 dB; see Figure 3.43). The fact that the mean is independent of resolution in the modeling construct being utilized here has the important benefit of reducing the parametric dimensionality in this construct. Looking ahead to the tabularized modeling information of Chapter 5, if σ w° in these tables had to be further partitioned in several categories of resolution, the number of measurements in any given category would become too small to allow the development of useful general trends, and the modeling information would begin to degenerate to trendless tabularization of data. The mean is the only attribute of low-angle clutter amplitude distributions that is independent of resolution. A number of early investigations emphasized the median rather than the mean in such distributions, since means usually occur high in the distributions,

Multifrequency Land Clutter Modeling Information 419

often near the 90-percentile level, driven there by occasional strong returns from discrete sources. It was thought that the median might be a better central measure of a discrete-free area-extensive clutter background. However, attempts to characterize the changing shapes of low-angle clutter amplitude distributions using the median instead of the mean as the central measure of each distribution required unwieldy normalization procedures and did not lead to useful general results, since the median central measure of each distribution as well as its shape were strongly dependent on resolution [12]. Because the mean occurs high in a distribution is not a reason to discard standard statistical techniques of using the first two moments of any distribution as the best way to begin to bring it under general description.

5.2.2.2 Shape Parameter aw The shapes of low-angle clutter spatial amplitude distributions are strongly and fundamentally dependent on spatial resolution. However, as with the mean strengths, there is a similar savings in model dimensionality with the shape parameter. With aw, this savings is in the fact that the shapes of distributions, as observed in the clutter data, are not very sensitive to the remaining radar parameters of radar frequency and polarization. This key fact is an empirical observation here that apparently has not been advanced elsewhere. The reason why shapes of clutter amplitude distributions are largely insensitive to frequency and polarization is that essentially the same set of discrete sources on the landscape cause the dominant clutter returns, whatever the radar frequency or polarization. This is observed in PPI clutter plots showing the spatial texture of clutter. Insensitivity of distribution shape to radar frequency allows bringing to bear the varying Phase One azimuth beamwidths with frequency, from 13° at VHF to 1° at X-band, to help provide a combined broad range of spatial resolutions across which to establish trends. It can be seen in the modeling information of Chapter 5 that, in working across frequency in this manner to establish trends of spread vs spatial resolution, radar frequency is essentially undetectable in the trends observed. That is, looking ahead to Figure 5.9 and the following 18 similar figures showing measured results of sd/mean vs A, it is evident that the different colored plot symbols in each such figure which correspond to different frequency bands contribute much more towards establishing one overall scatter plot through which it is most sensible to define one overall regression line, as opposed to five individual scatter plots with five different regression lines. If it were necessary to separate aw with radar frequency and/or polarization, there would not be enough available range in resolution in the Phase One data to properly establish a trend, nor would there be enough data to properly fill the matrix. Thus two important factors upon which the success of the modeling construct employed herein is based are that σ w° is dependent on frequency and polarization but is independent of resolution; whereas aw is independent of frequency and polarization but is dependent on resolution—that is, that the important radar parameters decouple in their effects on lowangle clutter spatial amplitude distributions, much reducing the required parametric dimensionality of the model.

420 Multifrequency Land Clutter Modeling Information

5.2.3 Derivation of Results 5.2.3.1 Derivation of σ w° Results Like-classified groups of measured clutter histograms were formed in which the classifiers were: terrain type, relief, depression angle, radar frequency band (VHF, UHF, L-, S-, or Xband), and radar polarization (HH or VV). For each like-classified group, the mean clutter strengths of all the measured clutter histograms within the group were collected, one value of mean strength per histogram. The median or 50-percentile value from this set of mean strengths was selected as the representative value of mean strength by which to characterize that particular like-classified group of measurements. This 50-percentile value of mean clutter strength for each like-classified group of measurements was tabulated as the Weibull mean clutter strength coefficient σ w° in Sections 5.3 and 5.4 of Chapter 5. The number of measurements in each like-classified group was also tabulated in Sections 5.3 and 5.4, as an indication of the degree of generality of each σ w° coefficient presented. Color plots of σ w° vs frequency by depression angle regime and polarization are provided for each terrain type/relief category in Sections 5.3 and 5.4. The likeclassified sets of mean clutter strength, upon which the σ w° modeling information of Chapter 5 is based, number 864.

Information Underlying σ w° . As an example of the derivation of each value of σ w° provided as modeling information in what follows, Table 5.2 illustrates the like-classified groups of measured clutter histograms for one terrain type—namely, low-relief forest with depression angle from 0.25° to 0.75°. The data in Table 5.2 are separated by frequency band (VHF, UHF, L-, S-, X-bands), range resolution (F = fat = 150 m; T = thin = 36 m for VHF and UHF bands, = 15 m for L-, S-, X-bands), and polarization (V = vertical, H = horizontal). Each line in the table corresponds to one group of like classified histograms. In each line, the following information is provided: the number of histograms in the group (Npts) which is also the number of available like-classified values of clutter patch mean strength in dB; the median of these dB values (which is what is selected for σ w° ); the mean of these dB values; the standard deviation of these dB values (i.e., the 1-σ variability of σ w° ); the maximum of these dB values (the strongest like-classified patch measured); and the minimum of these dB values (the weakest like-classified patch measured). Looking ahead to Table 5.27 in Section 5.4.3.1, the values shown in the 0.25° to 0.75° lines in the upper and lower subtables of Table 5.27 come from Table 5.2. For example, lines 5 and 6 in Table 5.2 provide Npts = 113, 113 (4th column) and σ w° = –27.1, –28.0 dB (5th column) for vertical and horizontal polarization, respectively, at VHF. Corresponding information to that shown in Table 5.2 lies behind all terrain type/depression angle categories for which σ w° values are provided in following Sections 5.3 and 5.4.

5.2.3.2 Derivation of aw Results The spread in a clutter spatial amplitude distribution as given, for example, by the ratio of standard deviation-to-mean or by the mean-to-median ratio, is fundamentally dependent on radar spatial resolution. Radar spatial resolution A (see Section 2.3.1.1) is given by

A = r ⋅∆ r ⋅∆θ where

(5.5)

Multifrequency Land Clutter Modeling Information 421

r

=

range,

∆r

=

range resolution, and

∆θ

=

one-way 3-dB azimuth beamwidth. 4

Table 5.2 Information* on Patch Values of Mean Clutter Strength σ °F ° Underlying σ w° for Forest/ Low-Relief Terrain at 0.25° to 0.75° Depression Angle, by Frequency Band, Range Resolution, and Polarization

σ°F4 (dB)

Band

Res

Pol

Npts

VHF VHF VHF VHF VHF VHF VHF

F F T T F+T F+T F+T

V H V H V H V+H

86 82 27 31 113 113 226

Median -27.3 -29.0 -26.9 -26.9 -27.1 -28.0 -27.5

Mean -27.4 -28.9 -26.0 -25.4 -27.1 -27.9 -27.5

St. Dev. 9.1 9.8 8.0 7.8 8.8 9.4 9.1

Max. -9.1 -12.9 -10.6 -9.3 -9.1 -9.3 -9.1

Min. -54.2 -57.8 -41.6 -44.0 -54.2 -57.8 -57.8

UHF UHF UHF UHF UHF UHF UHF

F F T T F+T F+T F+T

V H V H V H V+H

102 100 49 43 151 143 294

-26.8 -29.5 -26.1 -30.3 -26.1 -29.6 -27.8

-27.2 -30.1 -26.5 -29.5 -26.9 -29.9 -28.4

6.7 6.2 7.1 6.9 6.8 6.4 6.8

-15.0 -18.5 -15.0 -17.5 -15.0 -17.5 -15.0

-46.9 -46.3 -42.7 -44.9 -46.9 -46.3 -46.9

L L L L L L L

F F T T F+T F+T F+T

V H V H V H V+H

109 107 55 55 164 162 326

-27.9 -28.2 -28.5 -28.8 -28.2 -28.5 -28.4

-28.9 -29.6 -28.9 -29.8 -28.9 -29.7 -29.3

4.9 4.8 5.1 5.4 5.0 5.0 5.0

-20.5 -21.7 -21.0 -21.6 -20.5 -21.6 -20.5

-44.8 -47.5 -46.1 -46.2 -46.1 -47.5 -47.5

S S S S S S S

F F T T F+T F+T F+T

V H V H V H V+H

107 108 56 59 163 167 330

-29.4 -32.1 -32.5 -33.8 -30.6 -32.6 -31.4

-30.7 -32.3 -32.7 -34.4 -31.4 -33.0 -32.2

6.3 3.8 4.5 4.6 5.8 4.2 5.1

-20.1 -24.7 -23.5 -25.1 -20.1 -24.7 -20.1

-70.3 -45.4 -45.9 -47.4 -70.3 -47.4 -70.3

X X X X X X X

F F T T F+T F+T F+T

V H V H V H V+H

59 59 33 35 92 94 186

-29.0 -30.1 -28.7 -31.5 -28.9 -30.3 -29.8

-29.3 -29.8 -29.6 -31.5 -29.4 -30.4 -29.9

4.2 4.5 4.8 4.7 4.4 4.7 4.6

-20.4 -14.8 -21.6 -23.4 -20.4 -14.8 -14.8

-39.4 -40.2 -40.9 -41.5 -40.9 -41.5 -41.5

* This table shows the number of patch measurements of σ°F4 available as a set for each combination of parameters, and various statistical attributes (including the median) of each set. Res = range resolution; F = 150m; T = 36m for VHF and UHF, = 15m for L-, S-, X-bands; F+T = both F and T range res. data combined. Pol = polarization; V+H = both V and H polarization data combined. Npts = number of clutter patch histograms.

422 Multifrequency Land Clutter Modeling Information

Like-classified groups of measured clutter histograms were formed in which the classifiers were: terrain type, relief, depression angle, range interval, range resolution, and azimuth beamwidth. Three range intervals were utilized, as: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km. The measured clutter histograms are approximately equally distributed within these three intervals. Two range resolutions are available, wide pulse (i.e., 150 m) or narrow pulse (i.e., 36 m at VHF and UHF, 15 m at L-, S-, and Xbands). Five azimuth beamwidths are available, one per frequency band, as: 13° at VHF, 5° at UHF, 3° at L-band, 1° at S- and X-bands. Although S- and X-bands both have ≈1° azimuth beamwidth, they are kept separate in spread analysis classification grouping to keep the frequency bands separate in the scatter plots (but not in the regression). For each like-classified group of measured clutter histograms, three parameters were collected from each of the measured clutter histograms within the group. These three parameters are: (1) the ratio of standard deviation-to-mean, (2) the mean-to-median ratio, and (3) the value of spatial resolution A applicable for the measurement. The median values of each of these three parameters were selected as representative values to characterize the spread in that particular like-classified group of measurements. Spread characterization utilizing these three parameters proceeded as follows. For each terrain type/relief/ depression angle category, two scatter plots were formed. The first scatter plot shows the ratio of standard deviation-to-mean vs log10 A. The second scatter plot shows the mean-tomedian ratio vs log10 A. Each plotted point in the first of these scatter plots shows the median value of ratio of standard deviation-to-mean vs the median value of log10 A for a particular like-classified group of measured clutter histograms. A number of these scatter plots of standard deviation-to-mean vs log10 A are shown in Sections 5.3 and 5.4, one scatter plot for a selected depression angle regime in each terrain type/relief category. Similar to the first scatter plot, each plotted point in the second scatter plot shows the median value of meanto-median ratio vs the median value of log10 A for a particular like-classified group of measured clutter histograms. The maximum number of points in a scatter plot is 30 (five azimuth beamwidths, two pulse lengths, three range intervals), but little narrow pulse data is generally available in the third range interval. Regression analysis was performed in each scatter plot. These regression analyses generally show significantly decreasing spread with decreasing resolution (i.e., increasing A) for each terrain type/relief/depression angle category. The regression line for each scatter plot is provided as modeling information for spread in clutter amplitude distributions in Chapter 5. The regression line is generally characterized by its values at A = 103 m2 and A = 106 m2, with a few noted exceptions. Modeling information characterizing spread in clutter spatial amplitude distributions based on regression analysis in the scatter plots is provided two ways: (1) based on measured ratios of standard deviation-to-mean and (2) based on measured mean-to-median ratios. For both ways, the regression line values at A = 103 m2 and A = 106 m2 are converted to the corresponding two values of Weibull shape parameter aw at A = 103 m2 and A = 106 m2 by Equations (5.3) and (5.4). These pairs of values of aw are tabulated by terrain type/relief/ depression angle category in Sections 5.3 and 5.4. In addition to the paired values of aw, the underlying paired values of ratios of standard deviation-to-mean and mean-to-median ratio

Multifrequency Land Clutter Modeling Information 423

are also tabulated. The number of clutter patches and number of measured clutter histograms that each scatter plot (i.e., regression analysis) is based on is also tabulated. This tabulated modeling information for Weibull shape parameter aw is used as follows. First, the spatial resolution A of the radar under study is calculated at the terrain point under consideration. Then linear interpolation on log10 A between the values of aw at A = 103 m2 and A = 106 m2 for the appropriate terrain type/relief/depression angle category is performed to obtain the value of aw at the radar spatial resolution A in question. Preference is given to the tabulated values of aw based on measured ratios of standard deviation-tomean. The additional provision of tabulated values of aw based on measured mean-tomedian ratios provides a first indication of the degree of validity of modeling the underlying measured data with Weibull statistics, based on how closely aw computed from measured ratios of standard deviation-to-mean approximates aw computed from measured mean-to-median ratios. The like-classified sets of measured clutter histograms, upon which the aw modeling information of Chapter 5 is based, number 1,510. Note that these are different sets than those upon which the σ w° modeling information is based.

Information Underlying aw. As described above, the aw values provided as modeling information in what follows come from regression in scatter plots. Two scatter plots were formed: one of sd/mean (dB) vs log10 A; the other of mean/median (dB) vs log10 A. Each scatter plot comes from like-classified groups of measured clutter histograms. As an example of the information underlying the two scatter plots for low-relief forest with depression angle from 0.25° to 0.75°, Table 5.3 is shown here in three parallel parts. Parts (a), (b), and (c) show results for sd/mean (dB), mean/median (dB), and patch mid-range (km), respectively. Consider first Table 5.3(a) for sd/mean (dB). The data in Table 5.3(a) are separated by frequency band (VHF, UHF, L, S, X), range resolution (Fat or Thin), and range interval (1, 2, or 3, as described previously). Each line in the table corresponds to one group of likeclassified histograms and one point in the corresponding scatter plot—note that the groups are different from those of Table 5.2. In each line of Table 5.3(a), the following information is provided: the median value of mid-range cell size A for the group (shown under X as X = log10 A and A = r ⋅∆r ⋅∆θ in m2); the number of histograms in the group (Npts), which is also the number of available like-classified values of ratio of sd/mean (dB), one from each clutter patch histogram; the median of these dB values of sd/mean (which forms the ordinate of the point in the scatter plot corresponding to this line); the mean of the dB values of sd/mean; the standard deviation of the dB values of sd/mean (i.e., the vertical 1-σ variability of this point in the scatter plot); the maximum of these dB values of sd/mean (i.e., the maximum patch value of sd/mean in this group); and the minimum of these dB values of mean/median. Thus, each line in Table 5.3(a) corresponds to the ordinate of a given point in a given scatter plot. For example, the scatter plot for low-relief forest, 0.0° to 0.25° depression angle is shown as Figure 5.27 in Section 5.4.3.2 (note: the plot corresponding to the 0.25° to 0.75° depression angle regime of Table 5.3 is not shown). Table 5.3(b) is similar to Table 5.3(a) except Table 5.3(b) provides underlying information for the ordinate of the plotted points in the scatter plots of mean/median (dB) vs log10 A. Examples of the mean/median scatter plots are not shown in this book; they appear similar to the sd/mean scatter plots, except that they employ a different y-scale.

424 Multifrequency Land Clutter Modeling Information

Table 5.3a Information* on Patch Values of SD/Mean of σ ° F 4 Underlying aw for Forest/Low-Relief Terrain at 0.25° to 0.75° Depression Angle, by Frequency Band, Range Resolution, and Range Interval Band

Res

Rng

X

Npts

VHF VHF VHF VHF VHF UHF UHF UHF UHF UHF L L L L L S S S S S X X X X X

F F F T T F F F T T F F F T T F F F T T F F F T T

1 2 3 1 2 1 2 3 1 2 1 2 3 1 2 1 2 3 1 2 1 2 3 1 2

5.21 5.93 6.12 4.55 5.14 4.79 5.51 5.70 4.17 4.70 4.45 5.30 5.48 3.45 4.13 3.98 4.82 5.00 3.02 3.65 4.08 4.83 5.00 3.06 3.70

70 93 5 49 9 70 128 4 70 22 70 138 8 71 39 71 138 6 77 38 68 48 2 58 10

Clutter Patch SD/Mean of F4 (dB) Median Mean St. Dev. Max. Min. 1.26 1.12 1.73 5.07 -4.62 1.88 2.01 1.80 8.82 -1.16 0.88 0.92 0.56 1.71 0.27 1.94 2.22 1.31 7.29 -0.26 3.39 3.43 2.24 6.41 0.08 3.32 3.23 1.72 7.47 -0.67 3.10 3.10 1.33 7.53 0.27 2.47 2.52 0.66 3.29 1.87 3.89 4.28 1.85 8.73 0.59 4.18 4.51 1.54 8.21 2.21 3.48 3.58 1.92 8.45 -1.08 3.06 3.18 1.22 7.34 0.82 3.63 3.44 0.80 4.72 2.06 4.62 4.88 1.95 11.12 1.53 3.54 3.63 1.36 6.56 0.99 3.48 3.82 2.02 9.74 -0.76 3.97 3.91 1.26 7.41 0.97 4.76 5.12 2.37 9.33 2.77 5.63 5.78 1.75 10.79 1.14 4.43 4.49 1.70 9.00 1.82 3.76 3.69 1.80 8.25 0.18 3.85 3.85 1.19 7.57 1.64 5.81 5.81 0.98 6.50 5.12 5.05 5.75 2.15 13.22 2.75 5.44 4.75 1.69 6.92 1.85

* This table shows the number of patch measurements of SD/Mean of σ°F4 available as a set for each combination of parameters, and various statistical attributes (including the median) of each set. Res = range resolution (m); F = 150m; T = 36m for VHF and UHF, = 15m for L-, S-, X-Bands. Rng = range interval: 1 (1 to 11.3 km); 2 (11.3 to 35.7 km); 3 (>35.7 km). X = log10 (A), A = r ⋅ r ⋅ , r = rang. res. (m), = az. bw. (rad), r = median range (m). Npts = number of clutter patch histograms.

Table 5.3(c) is similar to Table 5.3(a) except Table 5.3(c) provides underlying information for the abscissas of the plotted points in both kinds of scatter plots. The abscissa is 10log A where A is cell area in m2. As discussed above, A = r ⋅∆r ⋅∆θ where ∆r (range resolution) and ∆θ (azimuth beamwidth) are fixed within any like-classified group (i.e., any line in the table), but r is the range in km to the center (i.e., mid-range) of each clutter patch in the group. Thus each line in Table 5.3(c) applies to the like-classified set of patch mid-range values, and the median value of mid-range is selected as r in the computation of A and hence the value of X = log10 A shown in each line of Table 5.3(c). Thus a given point in the scatter plot of sd/mean (dB) vs log10 A for forest/low-relief/ depression angle from 0.25° to 0.75° is obtained by selecting the appropriate value of “Median” in Table 5.3(a) as the ordinate, and the corresponding value of X that comes from the corresponding value of “Median” in Table 5.3(c). Scatter plots of sd/mean vs log10 A and mean/median vs log10 A were generated for all terrain type/depression angle categories. Each pair of scatter plots came from corresponding information similar to the three parts of Table 5.3. Shape parameter aw data obtained from regression in these scatter plots is provided in Sections 5.3 and 5.4.

Multifrequency Land Clutter Modeling Information 425

Table 5.3b Information* on Patch Values of Mean/Median of σ° F4 Underlying aw for Forest/Low-Relief Terrain at 0.25° to 0.75° Depression Angle, by Frequency Band, Range Resolution, and Range Interval Band

Res

Rng

X

Npts

VHF VHF VHF VHF VHF UHF UHF UHF UHF UHF L L L L L S S S S S X X X X X

F F F T T F F F T T F F F T T F F F T T F F F T T

1 2 3 1 2 1 2 3 1 2 1 2 3 1 2 1 2 3 1 2 1 2 3 1 2

5.21 5.93 6.12 4.55 5.14 4.79 5.51 5.70 4.17 4.70 4.45 5.30 5.48 3.45 4.13 3.98 4.82 5.00 3.02 3.65 4.08 4.83 5.00 3.06 3.70

70 93 5 49 9 70 128 4 70 22 70 138 8 71 39 71 138 6 77 38 68 48 2 58 10

Clutter Patch Mean/Median of F4 (dB) Median Mean St. Dev. Max. Min. 3.84 9.54 -0.82 3.89 2.58 3.76 11.14 -0.18 4.23 2.33 2.07 3.03 1.43 2.17 0.69 4.40 8.91 1.16 4.59 1.76 5.54 7.69 1.23 5.23 2.31 7.40 17.60 1.43 7.31 3.41 6.24 13.89 1.59 6.25 2.46 4.38 5.53 3.66 4.49 0.83 7.96 19.58 1.86 8.71 3.72 5.99 11.00 3.14 2.41 6.92 7.09 16.96 0.00 3.71 7.33 6.14 18.62 1.45 2.95 6.70 5.58 10.46 4.23 2.04 6.31 9.73 20.21 2.62 4.13 9.77 5.88 11.34 2.70 2.58 6.51 9.20 21.76 3.43 4.40 9.96 8.42 22.35 2.50 4.51 9.33 9.94 11.95 5.36 2.80 9.39 14.54 26.39 2.65 5.71 14.63 8.43 14.86 3.47 3.69 8.90 8.36 22.00 2.05 4.69 9.10 8.77 23.98 3.41 5.09 9.91 8.52 8.63 8.40 0.16 8.52 14.88 29.26 4.30 5.85 14.98 10.67 14.33 3.65 4.19 9.71

* This table shows the number of patch measurements of Mean/Median of F4 available as a set for each combination of parameters, and various statistical attributes (including the median) of each set. Res = range resolution (m); F = 150m; T = 36m for VHF and UHF, = 15m for L-, S-, X-Bands. Rng = range interval: 1 (1 to 11.3 km); 2 (11.3 to 35.7 km); 3 (>35.7 km). X = log10 (A), A = r ⋅ r ⋅ , r = rang. res. (m), = az. bw. (rad), r = median range (m). Npts = number of clutter patch histograms.

5.2.3.3 Statistical Confidence In Chapter 5, some clutter modeling results are obtained from many similar measurements leading to high statistical confidence, whereas other results are obtained from fewer measurements leading to less confidence. The rationale followed in Chapter 5 is to present all of the results obtained regardless of the degree of trust, confidence coefficient, or generality associated with each. This is in contrast to the interim clutter model of Chapter 4, Section 4.2, where some smoothing of thinner data was employed. In Chapter 5, information specifying the number of like-classified measurements involved for each σ w° or aw number is included as a means of allowing assessment of statistical validity or generality of the result. Statistical sampling populations and associated confidence levels are usually large in the depression angle regimes near grazing incidence. The sampling populations decrease as depression angle moves to outlying positive or negative depression angle regimes. In the color plots of mean clutter strength σ w° vs frequency, open symbols are occasionally used to indicate σ w° numbers judged likely to be relatively measurement specific and non-representative of the general mean clutter strength applicable to that situation, on the basis of relatively few measurements and clutter strength values far removed from the general trends otherwise observed.

426 Multifrequency Land Clutter Modeling Information

Table 5.3c Information* on Patch Values of “Mid-Range to Clutter Patch” Underlying the Median Range r and Resolution A Associated with aw for Forest/Low-Relief Terrain at 0.25° to 0.75° Depression Angle, by Frequency Band, Range Resolution, and Range Interval

Band

Res

Rng

X

VHF VHF VHF VHF VHF UHF UHF UHF UHF UHF L L L L L S S S S S X X X X X

F F F T T F F F T T F F F T T F F F T T F F F T T

1 2 3 1 2 1 2 3 1 2 1 2 3 1 2 1 2 3 1 2 1 2 3 1 2

5.21 5.93 6.12 4.55 5.14 4.79 5.51 5.70 4.17 4.70 4.45 5.30 5.48 3.45 4.13 3.98 4.82 5.00 3.02 3.65 4.08 4.83 5.00 3.06 3.70

Npts 70 93 5 49 9 70 128 4 70 22 70 138 8 71 39 71 138 6 77 38 68 48 2 58 10

Mid-Range to Clutter Patch (km) Median Mean St. Dev. Max. Min. 5.20 2.69 10.51 1.67 4.75 24.90 24.46 6.25 35.48 11.42 38.63 37.71 1.90 39.89 35.71 4.35 4.73 2.43 10.47 1.61 17.08 15.03 3.55 19.23 11.40 4.75 5.27 2.74 10.51 1.67 24.83 24.67 5.59 35.48 11.42 38.63 38.21 1.77 39.89 35.71 4.69 5.21 2.74 10.47 1.61 15.88 15.89 2.65 19.66 11.40 3.63 4.57 2.37 10.51 1.67 25.51 24.70 5.55 35.48 11.42 38.63 38.21 1.64 39.89 35.71 3.60 4.71 2.52 10.47 1.61 17.07 16.89 2.83 20.57 11.38 3.63 4.62 2.33 10.51 1.67 25.51 24.70 5.55 35.48 11.42 38.63 38.08 1.92 39.89 35.71 4.01 5.03 2.79 11.10 1.61 17.07 17.22 2.48 21.63 11.38 4.56 5.15 2.60 10.51 1.67 25.76 25.96 5.30 35.48 11.42 38.63 38.63 0.00 38.63 38.63 4.35 4.94 2.53 10.47 1.61 19.21 17.79 3.71 21.63 11.38

* This table shows the number of patch measurements of mid-range available as a set for each combination of parameters, and various statistical attributes (including the median) of each set. Res = range resolution (m); F = 150m; T = 36m for VHF and UHF, = 15m for L-, S-, X-Bands. Rng = range interval: 1 (1 to 11.3 km); 2 (11.3 to 35.7 km); 3 (>35.7 km). X = log10 (A), A = r ⋅ r ⋅ , r = rang. res. (m), = az. bw. (rad), r = median range (m). Npts = number of clutter patch histograms.

5.2.3.4 Use of Modeling Information The Weibull coefficient modeling information may be employed to generate a σ °F 4 clutter strength number (i.e., realization) for a given spatial cell. First, it is determined if the cell is geometrically visible from the antenna position or if the cell is masked or shadowed by intervening terrain of higher elevation. If masked, as a first approximation, zero clutter power is assigned to the cell (the information of this book is not directly applicable to shadowed cells; but see Appendix 4.D). If visible, the depression angle from the antenna position to the cell is computed, the terrain type and relief for the cell is determined, and the radar spatial resolution A at the cell is calculated. This determination of terrain type/relief/depression angle/spatial resolution for the cell leads to the pair of Weibull coefficients, σ w° , aw , which specify the clutter amplitude distribution for that combination of terrain type, relief, depression angle, and resolution. A single random variate from this clutter amplitude distribution is assigned as clutter strength to the cell under examination. The modeler then proceeds to the next cell and repeats the process. In this manner, all visible cells at the site are assigned Weibull random variates as clutter strength, each appropriate to the radar parameters, geometry, and terrain type for the cell under consideration. The cell-to-cell spatial correlation that occurs in this process is that

Multifrequency Land Clutter Modeling Information 427

provided by the underlying land cover and DTED information; otherwise, the random variates of clutter strength occur independently from cell to cell, as indeed for the most part do the measured data (see Chapter 4, Section 4.6.3). Further explanation of this terrain-specific modeling rationale is provided in Chapter 4. Techniques for validating and improving this approach to clutter modeling are briefly described in Section 5.5. For those interested in general clutter levels (e.g., means, medians) exclusive of cell-to-cell variability, use of the modeling information provided in Chapter 5 is more direct. Mean clutter strength σ w° is directly tabulated. Median clutter strength σ °50 and other percentile levels and moments are dependent on radar spatial resolution A. Median clutter strength σ °50 is simply calculated from σ w° and the mean-to-median ratio; the mean-to-median ratio may be obtained for the radar resolution A under consideration by linear interpolation on log10 A between tabulated values at A = 103 m2 and A = 106 m2. The standard deviation may be obtained in a manner directly parallel to that by which the median is obtained. Other percentile levels may be simply calculated from the Weibull cumulative distribution function [Eq. (5.2)].

5.2.3.5 Presentation of Material Sections 5.3 and 5.4 provide extensive modeling information for low-angle land clutter spatial amplitude statistics within a standard presentation format. The format utilized follows that of the interim clutter model presented in Chapter 4, Section 4.2, and illustrated in Figure 4.3. The format of presentation of mean clutter strength σ w° is reviewed here as an aid to the presentation of the extensive modeling information that directly follows. The clutter modeling information that follows is based on depression angle. Figure 5.6 shows depression angle to be the angle below the horizontal from the radar to the backscattering terrain point. A precise mathematical definition of depression angle is given by Equation (5.1); see also Appendix 2.C of Chapter 2. As shown in Figure 5.6, terrain can occasionally rise to elevations higher than the radar which leads to negative depression angle. Approximately 30% of the clutter modeling information to follow applies to clutter measurements obtained at negative depression angle. The clutter modeling information that follows is presented within bins (i.e., narrow angular regimes) of depression angle. The depression angle bins utilized are shown in Table 5.4. As is apparent in Table 5.4, different binning is utilized in low-relief terrain (terrain slopes < 2°) than in high-relief terrain (terrain slopes > 2°). In low-relief terrain, five positive and three negative depression angle bins are used; in high-relief terrain, five positive and two negative bins are used. The bins are very narrow, particularly at low depression angle, and more so for low-relief than high-relief terrain. Each bin typically contains hundreds of clutter measurements. What is plotted is the median value of clutter patch mean strength σ w° within each bin. It will be seen in the clutter modeling information to follow that, as a result of medianizing over many measurements, the small differences in depression angle shown in Table 5.4 can account for systematic differences in mean clutter strength σ w° that in total can cover wide ranges. The bins are shown color-coded in Table 5.4; the same color coding is used in plotting mean clutter strength σ w° in color figures to follow, with different shaped symbols used to plot σ w° at VV-polarization (circles) and HH-polarization (squares). The color

428 Multifrequency Land Clutter Modeling Information

codes are as follows: for increasing positive depression angle, cyan, dark blue, purple, magenta, red for bins 1 to 5, respectively; for increasing negative depression angle, dark green, intermediate green, light green for bins –1, –2, and –3 in low-relief terrain, and dark green, intermediate green for bins –1, –2 in high-relief terrain, respectively. The category of long-range mountains requires a specialized negative depression angle category. Complete data are not always available for all terrain types at outlying depression angles. Table 5.4 Depression Angle Bins Low-Relief Terrain (Slopes < 2˚)

Depression Angle (deg)

Bin Number

High-Relief Terrain (Slopes > 2˚) Color Code VV

Depression Angle (deg)

Bin Number

Color Code VV

HH

> 4˚

5

> 6˚

5

1.5˚ to 4˚

4

4˚ to 6˚

4

0.75˚ to 1.5˚

3

2˚ to 4˚

3

0.25˚ to 0.75˚

2

1˚ to 2˚

2

0˚ to 0.25˚

1

0˚ to 1˚

1

–0.25˚ to 0˚

–1

–1˚ to 0˚

–1

–0.75˚ to –0.25˚

–2

< –1˚

–2

< – 0.75˚

–3

HH

NOTE: A color version of Table 5.4 appears on page 450.

In the clutter modeling information that follows, for each terrain type mean clutter strength σ w° is plotted vs radar frequency against a log-frequency x-axis in order to show results for all five frequency bands together. The plotting methodology is shown representationally in the diagram of Figure 5.7. Within each frequency band, σ w° results separated by depression angle bin are plotted by slightly displacing the plot symbols horizontally from bin to bin to avoid symbol overlap. This plot methodology, covering eight depression angle bins, is shown for X-band in an exaggerated way in the diagram of Figure 5.7. The sequential horizontal displacements shown in Figure 5.7 do not imply an in-band frequency shift; the cluster of sixteen plotted values of σ w° shown in Figure 5.7 all apply for a single X-band frequency. Similar bin-to-bin horizontal offsetting of plot symbols is also employed in the lower four bands. Mean clutter strength σ w° generally increases both with increasing positive depression angle and with increasing negative depression angle. As a result, the in-band clusters of plotted data in multiple depression angle bins often take on the v-shape shown representatively by the X-band cluster in Figure 5.7. Thus, as a point of departure in interpreting the results, it is suggested that the reader first look for v-shapes indicating

Multifrequency Land Clutter Modeling Information 429

whether or not consistent depression angle effects on clutter strength occur for the particular frequency band and terrain type of interest.

5.3 Land Clutter Coefficients for General Terrain A radar designer or analyst may often require that the characteristics of land clutter be specified independently of specific terrain type. There are two reasons for this requirement. First, most radars must maintain performance when sited in various terrains and situations. Second, even at individual sites much clutter producing terrain is often composite and mixed over scales of several kilometers. In Section 5.3, modeling information characterizing low-angle land clutter spatial amplitude distributions is provided based on a large set of 30,246 measured clutter histograms from 1,628 clutter patches classified as general mixed rural. These measurements comprise 51% of the multifrequency Phase One clutter measurement data. This set of measurements includes the measurements from all mixed terrain types except those primarily classified as urban. Mixed terrain is generally neither completely open nor completely tree-covered. Because of the large amount of composite terrain clutter measurement data upon which they are based, the results of Section 5.3 are very general. General effects of depression angle, terrain relief, radar frequency, polarization, and resolution are quantified independent of specific terrain type.

5.3.1 General Mixed Rural Terrain 5.3.1.1 High-Relief General Mixed Rural Terrain Table 5.5 shows the number of patches and measured clutter histograms by depression angle regime and terrain relief for general mixed rural terrain. Table 5.6 presents Weibull mean clutter strength σ w° for general mixed rural terrain of high relief, by depression angle, frequency band, and polarization. The number of measured clutter histograms upon which each value of σ w° in Table 5.6 is based is also presented in the lower of the two subtables comprising Table 5.6. High-relief terrain has terrain slopes > 2°. The σ w° data of Table 5.6 are plotted in Figure 5.8. To avoid obscuring results with overlapping plot symbols, within each frequency band in Figure 5.8 the colored plot symbols are plotted with small increasing horizontal displacements to the right as depression angle decreases from its highest positive regime through zero to its highest negative regime (i.e., top to bottom in Table 5.6). These small artificial displacements do not indicate an in-band frequency shift. In each frequency band of Figure 5.8, the resultant set of colored plot symbols has a v-shape. The consistent v-shape indicates consistent depression angle effects in each band, where σ w° increases with both increasing positive (left side of v-shape, cyan through magenta) and increasing negative (right side of v-shape, dark green through intermediate green) depression angle. In what follows in Chapter 5, the σ w° data for each terrain type are plotted in a figure in which the manner of data presentation is similar to that employed in Figure 5.8. The cyan (i.e., light blue) colored symbols in Figure 5.8 represent the lowest positive depression angle regime (0° to 1°) in high-relief terrain. These results are based on a significantly larger number of measurements than the other depression angle regimes in

430 Multifrequency Land Clutter Modeling Information

Table 5.5 Numbers of Terrain Patches and Measured Clutter Histograms for General Mixed Rural Terrain, by Relief and Depression Anglea,b,c

Terrain Relief


= Depression Angle (degrees) 6.0 ≤


High-relief

Low-relief

0

Number of Measurements 0

4.0 ≤
< 6.0

5

79

2.0 ≤
< 4.0

51

987

1.0 ≤
< 2.0

70

1,997

0.0 ≤
< 1.0

338

7,003

-1.0 ≤
< 0.0

250

2,986


< -1.0

20

183

Totals

734

13,235

4.00 ≤


1

28

1.50 ≤
< 4.00

31

747

0.75 ≤
< 1.50

114

2,659

0.25 ≤
< 0.75

275

6,130

0.00 ≤
< 0.25

292

5,353

-0.25 ≤
< 0.00

150

1,758

-0.75 ≤
< -0.25

28

285


< -0.75

3

51

894

17,011

1,628

30,246

Totals Grand Totals

Number of Patches

a Mixed terrain implies primary and secondary terrain classification. Rural terrain includes all classes except urban. 2 b A terrain patch is a land surface macroregion usually several kms on a side (median patch area = 12.62 km ). c A measured clutter histogram contains all of the temporal (pulse by pulse) and spatial (resolution cell by resolution cell) clutter samples obtained in a given measurement of a terrain patch. A terrain patch was usually measured many times (nominally 20) as RF frequency (5), polarization (2), and range resolution (2) were varied over the Phase One radar parameter matrix.

Table 5.6 and hence may be regarded as the most reliable data shown in Figure 5.8. In moving from cyan through the higher positive depression angles in Figure 5.8, there is a monotonic rise up the left side of the v-shaped cluster from cyan to dark blue (1° to 2°) to purple (2° to 4°) to magenta (4° to 6°). Thus in each frequency band Figure 5.8 shows a strong monotonic increase in σ w° with increasing positive depression angle. The number of measurements falls off with increasing positive or negative depression angle (see Table 5.5). No data are available for depression angle > 6° (red) in any band in Figure 5.8, and no data are available from 4° to 6° (magenta) at S- and X-bands in Figure 5.8 due to the limited Phase One elevation beamwidths in those bands (see Appendix 3.A).

Multifrequency Land Clutter Modeling Information 431

Table 5.6 Mean Clutter Strength σ w° and Number of Measurements for General Mixed Rural Terrain of High Relief, by Frequency Band, Polarization, and Depression Anglea

Weibull Mean Clutter Strength σ°w (dB)


= Depression Angle (degrees)

VHF

UHF

S-Band

X-Band

HH

VV

HH

VV

HH

VV

HH

VV

HH

VV

----

----

----

----

----

----

----

----

----

----

4.0 ≤
< 6.0

-17.3

-14.3

-22.9

-19.4

-22.1

-23.0

----

----

----

----

2.0 ≤
< 4.0

-19.4

-15.3

-21.0

-20.4

-23.0

-23.5

-28.7

-27.1

-25.9

-22.5

1.0 ≤
< 2.0

-24.0

-20.6

-24.7

-22.8

-26.0

-26.0

-30.3

-28.2

-25.2

-24.0

6.0 ≤


0.0 ≤
< 1.0

-27.6

-25.1

-29.0

-27.9

-29.0

-29.0

-31.7

-29.9

-29.5

-28.0

-1.0 ≤
< 0.0

-26.5

-21.7

-27.0

-25.8

-26.6

-27.7

-30.3

-28.3

-29.6

-28.5


< -1.0

-16.6

-17.0

-19.8

-16.4

-23.1

-21.0

-24.6

-23.6

-24.9

-25.9

Number of Measurements


= Depression Angle (degrees)

VHF HH

6.0 ≤


a

L-Band

0

UHF

VV 0

HH 0

L-Band VV 0

HH 0

S-Band

VV

HH

0

0

X-Band

VV

HH

VV

0

0

0

4.0 ≤
< 6.0

13

11

15

15

9

16

0

0

0

0

2.0 ≤
< 4.0

136

136

139

141

140

156

66

71

1

1

1.0 ≤
< 2.0

196

205

203

209

221

227

183

199

174

180

0.0 ≤
< 1.0

606

626

778

800

760

829

591

593

709

711

-1.0 ≤
< 0.0

252

278

350

372

321

325

232

235

305

316


< -1.0

21

23

21

21

23

21

11

9

17

16

TOTALS

1,224

1,279

1,506 1,558 1,474 1,574 1,083 1,107

1,206 1,224

Table 5.5 defines the population of terrain patches upon which these data are based.

Values of σ w° for negative depression angle are plotted in shades of green. Negative depression angle occurs when steep terrain is observed by the radar at elevations above the antenna. The darkest shade of green shows results in the lowest negative depression angle regime, which is 0° to –1° in high-relief terrain. These dark green (0° to –1°) results in Figure 5.8 are generally close to and usually slightly higher than the cyan (0° to 1°) results, as intuitively would be expected. The shade of green becomes lighter with increasing negative depression angle. In high-relief terrain, only one additional negative depression angle regime is utilized, for depression angle < –1° (intermediate green in Figure 5.8). In every band, the intermediate green values of σ w° in Figure 5.8 are significantly stronger than the dark green values, thus providing the right sides of the v-shaped clusters. There is a general trend of decreasing σ w° with increasing radar carrier frequency in Figure 5.8. At the lowest (positive or negative) depression angles, this trend is slight (e.g., for cyan, 0° to 1°, UHF, L-, and X-band results are all remarkably close in the –29 dB vicinity, with VHF slightly stronger and S-band slighter weaker). At higher (positive or negative) depression angles, the trend is stronger. This trend is largely due to increasing

432 Multifrequency Land Clutter Modeling Information

absorption of radio frequency (RF) power from the incident radar wave by tree foliage, VHF to S-band (see Chapter 3). Mixed rural terrain of high relief has a larger component of trees than at low relief. At the highest positive depression angles (magenta and purple) in Figure 5.8, the variation of σ w° with radar frequency f VHF to S-band is approximately σ w° (f) ∝ f -0.94. In the historical literature, what little information is available on the subject usually suggests a slight trend of increasing clutter strength with increasing radar frequency, for example, σ w° (f) ∝ f 1/2 or σ w° (f) ∝ f [2–5]. Thus the trend of decreasing clutter strength with increasing radar frequency seen in many of the Phase One highangle forest measurements is relatively unexpected. Note that at all positive depression angles in Figure 5.8, the trend of decreasing σ w° with increasing radar frequency from VHF to S-band reverses from S-band to X-band. That is, at all positive depression angles there is an S-band dip between L-band and X-band in Figure 5.8, indicating that over the range of frequencies shown, maximum RF absorption occurs at S-band. It is probably not entirely coincidental that S-band is also the frequency band in which the common household microwave oven operates (at 2.45 GHz). In Figure 5.8, the differences with polarization are generally small, on the order of several dB or less, with vertical polarization (VV) almost always stronger than horizontal (HH). Table 5.7 presents the Weibull shape parameter aw and ratios of standard deviation-to-mean and mean-to-median for general mixed rural terrain of high relief, by depression angle and radar spatial resolution. Whereas the information of Table 5.6 specifies the mean or first moment of the clutter spatial amplitude distribution, the information of Table 5.7 specifies the spread or variability in the distribution as determined by the second moment or other derivative quantities. Table 5.5 shows the number of terrain patches and number of measured clutter histograms for general mixed rural terrain of high relief, broken down by depression angle in a parallel manner to that of Table 5.7; that is, the statistical populations underlying the data of Table 5.7 are available in Table 5.5. The numbers of measured clutter histograms in Table 5.5 are further broken down by frequency band and polarization in Table 5.6. Table 5.5 shows no data available for depression angle > 6° for general mixed rural terrain of high relief. Generally, there is little Phase One data available at such a high depression angle, although Section 5.4 shows that there is one high-relief forest clutter patch and six mountain clutter patches at depression angles > 6°. In Table 5.7, aw is calculated two ways: (1) from the ratio of standard deviation-to-mean and (2) from the mean-to-median ratio. In Table 5.7, and in general throughout Chapter 5, no major systematic difference results between these two methods of calculation of aw , or, including as a third alternative, in the aw that comes from the least-mean-squares bestfitting true Weibull distribution that is matched to the measured distribution over a large central part (i.e., noise level to 0.999 cumulative probability) of the measured distribution. However, aw results by two different methods of calculation are shown in Table 5.7 and in all similar tables throughout Chapter 5 as a first indication of the degree to which Weibull statistics approximate the characteristics of the measured distributions; if the measured distributions were exactly Weibull, the two different methods of calculation of aw would yield identical results. Each pair of aw numbers in Table 5.7 comes from a scatter plot in which each individual point plotted shows the median value of spread vs the median value of spatial resolution in a group of like-classified measured clutter histograms. For example, for Table 5.7 the standard deviation-to-mean scatter plot for the 2° to 4° depression angle regime is shown in

Multifrequency Land Clutter Modeling Information 433

Table 5.7 Shape Parameter aw and Ratios of Standard Deviation-to-Mean (SD/Mean) and Mean-to-Median for General Mixed Rural Terrain of High Relief, by Spatial Resolution A and Depression Anglea
= Depression Angle (degrees)

Weibull Shape Parameter aw from SD/Mean

from Mean/Median

A = 103m2

A = 106m2

A = 103m2

A = 106m2

6.0 ≤


---

---

---

---

4.0 ≤
< 6.0

2.4

1.5

2.9

1.3

2.0 ≤
< 4.0

3.0

1.4

3.2

1.7

1.0 ≤
< 2.0

3.0

1.6

3.4

1.5

0.0 ≤
< 1.0

3.5

1.8

3.8

2.0

-1.0 ≤
< 0.0

3.2

1.9

3.8

2.1


< -1.0

3.6

1.9

3.4

2.3

Ratios


= Depression Angle (degrees)

a

SD/Mean (dB)

Mean/Median (dB)

A = 103m2

A = 106m2

A = 103m2

A = 106m2

6.0 ≤


---

---

---

---

4.0 ≤
< 6.0

4.6

1.9

11.6

2.8

2.0 ≤
< 4.0

6.3

1.7

14.3

4.5

1.0 ≤
< 2.0

6.4

2.3

15.6

3.8

0.0 ≤
< 1.0

7.9

2.9

18.9

6.3

-1.0 ≤
< 0.0

6.8

3.2

18.3

7.0


< -1.0

8.1

3.2

15.5

7.7

Table 5.5 defines the population of terrain patches and measurements upon which these data are based.

Figure 5.9. This scatter plot is based on 51 terrain patches and 987 measured clutter histograms, as indicated in Table 5.5. Twelve similar scatter plots underlie the 12 pairs of aw numbers in Table 5.7. The major parametric variation of aw in Table 5.7 is with radar spatial resolution. In every case, aw is much greater at 103 m2 resolution than at 106 m2 resolution. There is also a weaker trend in Table 5.7 whereby aw decreases as depression angle increases from the 0° to 1° regime (more so with increasing positive depression angle than with increasing negative depression angle). For cell-by-cell Weibull random clutter strength numbers, aw for the radar spatial resolution at the cell under consideration is required. The value of aw applicable at resolution A is obtained by linear interpolation on log10A between the tabulated values of aw at A = 103 m2 and A = 106 m2 shown in Table 5.7. For example, in general mixed rural terrain of high relief in the depression angle regime from 1° to 2°, the applicable value of aw at A = 104 m2 based on: (1) measured ratios of standard deviation-tomean is aw = 2.53, (2) measured mean-to-median ratios is aw = 2.77, and (3) equal weighting of ratios of standard deviation-to-mean and mean-to-median is aw = 2.65.

434 Multifrequency Land Clutter Modeling Information

The lower subtable of Table 5.7 shows the ratios of standard deviation-to-mean and meanto-median from which the aw numbers in the upper subtable come. The large spreads in low-angle land clutter spatial amplitude distributions at high spatial resolution are perhaps more dramatically evidenced by these lower numbers (e.g., mean-to-median ratio = 18.9 dB at 103 m2, compared to 6.3 dB at 106 m2, Table 5.7, depression angle regime from 1° to 2°). Figure 5.5 allows quick conversion between the numbers in the upper and lower subtables of Table 5.7, and similar tables throughout Chapter 5. Interpolation in these lower numbers directly yields general second moment or median values at the spatial resolution under consideration. For example, at A = 104 m2, for general mixed rural terrain of high relief in the 1° to 2° depression angle regime, the ratio of standard deviation-to-mean is 5.0 dB and the mean-to-median ratio is 11.7 dB. The applicable mean level σ w° is obtained from Table 5.6. If L-band and vertical polarization happen to be the frequency and polarization of the radar in question, then, continuing the example, in general mixed rural terrain of high relief in the 1° to 2° depression angle regime at spatial resolution of 104 m2, the applicable low-angle land clutter spatial amplitude distribution has σ w° = –26.0 dB, ° = –37.7 dB, and standard deviation equal to –21.0 dB. σ 50

5.3.1.2 Low-Relief General Mixed Rural Terrain Table 5.8 presents Weibull mean clutter strength σ w° for general mixed rural terrain of low relief by depression angle, frequency band, and polarization. The lower of the two subtables comprising Table 5.8 shows the number of measurements upon which each σ w° value in the upper subtable is based. Low-relief terrain has terrain slopes < 2°. Table 5.5 indicates that, within the Phase One general mixed rural clutter data, low relief occurs somewhat more frequently (viz., 56%) than high relief (viz., 44%). The low-relief σ w° data of Table 5.8 are plotted in Figure 5.10 in a manner similar to that employed with the high-relief σ w° data in Figure 5.8. As in Figure 5.8, in each frequency band of Figure 5.10 the set of colored plot symbols continues to have a consistent v-shape indicating consistent depression angle effects in each band. The v-shapes of the low-relief data in Figure 5.10 are, however, considerably more pronounced than those of the highrelief data in Figure 5.8. That is, depression angle effects are stronger at low relief than at high relief. The cyan colored symbols in Figure 5.10 represent the lowest positive depression angle regime (0° to 0.25°) in low-relief terrain and are based on a large number of measurements (see Table 5.8). In moving from cyan through the higher positive depression angles in Figure 5.10, in general there is a monotonic rise (with a few minor exceptions) up the left side of the v-shaped cluster from cyan to dark blue (0.25° to 0.75°) to purple (0.75° to 1.5°) to magenta (1.5° to 4°) to red (depression angle > 4°). Thus in each frequency band Figure 5.10 shows a strong increase in σ w° with increasing positive depression angle. The number of measurements falls off at outlying positive and negative depression angles (see Tables 5.5 and 5.8). No data are available for depression angle > 4° (red) at S- and X-bands in Figure 5.10 due to the limited Phase One elevation beamwidths in those bands. Values of σ w° for negative depression angle are plotted in shades of green. The darkest shade of green shows results in the lowest negative depression angle regime, which is 0° to –0.25° in low-relief terrain. These dark green (0° to –0.25°) results in Figure 5.10 are generally close to and usually slightly higher than the cyan (0° to 0.25°) results. The shade of green becomes lighter with increasing negative depression angle. In low-relief

Multifrequency Land Clutter Modeling Information 435

Table 5.8 Mean Clutter Strength σ w° and Number of Measurements for General Mixed Rural Terrain of Low Relief, by Frequency Band, Polarization, and Depression Anglea Weibull Mean Clutter Strength σ °w (dB)


= Depression

VHF

Angle (degrees)

L-Band

S-Band

VV

HH

VV

HH

VV

HH

X-Band

VV

HH

VV

4.0 ≤


-17.0

-18.5

-22.5

-21.7

-23.2

-24.8

---

---

---

---

1.50 ≤
< 4.00

-20.5

-18.7

-21.9

-20.4

-23.7

-23.6

-31.8

-28.6

-24.5

-22.5

0.75 ≤
< 1.50

-26.7

-25.4

-26.0

-23.7

-26.7

-26.5

-31.5

-29.5

-28.4

-26.9

0.25 ≤
< 0.75

-35.8

-35.9

-32.7

-31.2

-29.6

-29.6

-32.9

-31.1

-30.5

-29.4

0.00 ≤
< 0.25

-40.7

-40.7

-38.4

-38.1

-32.8

-32.1

-35.3

-33.4

-32.3

-30.8

-0.25 ≤
< 0.00

-37.5

-39.7

-36.6

-35.4

-33.3

-34.2

-34.1

-32.9

-32.3

-30.6

-0.75 ≤
< -0.25

-41.3

-39.4

-32.2

-31.7

-30.5

-31.6

-31.2

-28.4

-31.8

-29.8


< -0.75

-31.2

-25.3

-22.3

-19.9

-22.6

-18.8

---

---

-26.6

-28.4

Number of Measurements


= Depression

VHF

Angle (degrees) HH

4.0 ≤


UHF VV

4

4

HH

5

L-Band VV

HH

5

4

S-Band

VV

HH

6

0

X-Band

VV

0

HH

0

VV

0

1.50 ≤
< 4.00

84

87

90

90

89

97

67

67

38

38

0.75 ≤
< 1.50

257

270

296

301

296

309

216

218

246

250

0.25 ≤
< 0.75

566

610

689

710

640

658

458

446

665

688

0.00 ≤
< 0.25

335

392

614

657

572

595

498

462

589

639

-0.25 ≤
< 0.00

87

108

188

212

193

199

161

157

225

228

-0.75 ≤
< -0.25

13

20

32

34

34

37

22

19

37

37


< -0.75

6

6

6

6

8

8

0

0

6

5

1,352 1,497

1,920

1,909 1,422

1,369

TOTALS a

UHF

HH

2,015 1,836

1,806 1,885

Table 5.5 defines the population of terrain patches upon which these data are based.

terrain, two additional negative depression angle regimes are utilized for depression angles from –0.25° to –0.75° (intermediate green) and for depression angles < –0.75° (light green). In moving from cyan through the three green negative depression angle regimes in Figure 5.10, in general there is a strong monotonic rise (with two minor exceptions) up the right side of each v-shaped cluster. At VHF in Figure 5.10, at low depression angles (e.g., cyan, 0° to 0.25°) clutter strengths are low due to multipath loss over the open components of the low-relief mixed rural terrain—this effect is not at work in the high-relief data of Figure 5.8. Remaining with VHF in Figure 5.10, at high depression angles (e.g., red, > 4°) clutter strengths are high because of the low RF absorption at VHF by the forested components of the low-relief mixed rural terrain—this effect is at work in the high-relief data of Figure 5.8. As a result of these two effects, the amplitude of the v-shaped cluster of plot symbols at VHF in Figure 5.10 is wide, viz., 24 dB, compared to 13 dB in Figure 5.8. These are the ranges over which small changes in depression angle affect the mean strength σ w° of land clutter at VHF in general mixed rural terrain of low and high relief, respectively. In Figure 5.10, as radar carrier

436 Multifrequency Land Clutter Modeling Information

frequency f rises from VHF into the microwave regime, at low depression angle (cyan) σ w° ( f ) rises from VHF to L-band due to decreasing multipath loss with approximate dependence σ w° ( f ) ∝ f 0.95, whereas at high depression angle (red and magenta) σ w° ( f ) falls from VHF to S-band due to increasing RF absorption by tree foliage with approximate dependence σ w° ( f ) ∝ f -0.97. At intermediate depression angles, the variation with radar frequency is intermediate between these extremes. As a result of these two opposite trends with radar frequency, the data points plotted in Figure 5.10 take on a funnel shape. As in the high-relief data of Figure 5.8, there is an S-band dip between L-band and X-band in the low-relief data of Figure 5.10, with the dip more pronounced at high depression angle (magenta) than at low depression angle (cyan). This dip occurs at all positive depression angles in Figure 5.10. As in Figure 5.8 at high relief, in Figure 5.10 at low relief the differences with polarization are generally small, on the order of several dB or less, with vertical polarization (VV) almost always stronger than horizontal (HH). Comparison of Figures 5.8 and 5.10 indicates that there exist considerable differences in mean clutter strength σ w° between general mixed rural terrain of high relief (terrain slopes > 2°) and low relief (terrain slopes < 2°), respectively. A major reason for this is that lowrelief mixed rural terrain allows multipath propagation to occur, which drives down clutter strengths at low depression angle in the lower bands. Multipath propagation does not occur to any significant degree in high-relief terrain or at high depression angles in low-relief terrain. At high depression angles in the lower bands and at all depression angles in the upper bands, mean clutter strengths in high-relief terrain are somewhat greater than in lowrelief terrain, within similar depression angle regimes. Such differences are due directly to the effect of terrain relief on intrinsic σ°; they are less than the low depression angle differences in the lower bands caused by multipath. A contributing factor to all the differences in mean clutter strength with terrain relief indicated in Figures 5.8 and 5.10 is that high-relief mixed rural terrain tends to be somewhat more forested whereas low-relief mixed rural terrain tends to be somewhat more open. Classification by terrain relief in two major regimes as shown in Figures 5.8 and 5.10 is a simple and practicable approach for sorting out the complex phenomenological influences at work in low-angle land clutter. Table 5.9 presents the Weibull shape parameter aw and ratios of standard deviation-to-mean and mean-to-median for clutter amplitude distributions in general mixed rural terrain of low relief, by depression angle and radar spatial resolution. The statistical populations underlying the data of Table 5.9 are available in Table 5.5. In Table 5.9, aw is calculated two ways: (1) from the ratio of standard deviation-to-mean and (2) from the mean-to-median ratio. Many of the corresponding aw numbers resulting from these two methods of calculation are remarkably close in Table 5.9. Each pair of aw numbers in Table 5.9 comes from a scatter plot in which each individual point plotted shows the median value of spread vs the median value of spatial resolution in a group of like-classified measured clutter histograms. The standard deviation-to-mean scatter plot for the 0.25° to 0.75° depression angle regime in Table 5.9 is shown in Figure 5.11. The major parametric variation of aw in Table 5.9 is with radar spatial resolution. In every case, aw is much greater at 103 m2 resolution than at 106 m2 resolution. There is a weak trend in Table 5.9 whereby aw decreases as depression angle increases from the 0° to 0.25° regime. There is little indication for aw in terrain of high relief as shown in Table 5.7 to be lower than in terrain of low relief as shown in Table 5.9, as might be expected in these results. The lower subtable of Table 5.9 shows the ratios of standard deviation-to-mean and mean-to-median from which the aw numbers in the upper subtable come. The large spreads in low-angle land

Multifrequency Land Clutter Modeling Information 437

Table 5.9 Shape Parameter aw and Ratios of Standard Deviation-to-Mean (SD/Mean) and Mean-to-Median for General Mixed Rural Terrain of Low Relief, by Spatial Resolution A and Depression Anglea

Weibull Shape Parameter aw


= Depression Angle (degrees)

from SD/Mean

from Mean/Median

A = 103m2

A = 106m2

A = 103m2

A = 106m2

4.00 ≤


2.5

1.6

2.2

1.6

1.50 ≤
< 4.00

2.5

1.7

2.5

1.7

0.75 ≤
< 1.50

3.1

2.1

3.3

1.9

0.25 ≤
< 0.75

3.5

1.8

3.7

1.7

0.00 ≤
< 0.25

3.5

1.7

3.7

1.7

-0.25 ≤
< 0.00

4.4

1.5

4.3

1.5

-0.75 ≤
< -0.25

4.2

1.7

3.6

2.3


< -0.75

2.9

1.7

3.4

1.8

Ratios


= Depression Angle (degrees)

a

SD/Mean (dB)

Mean/Median (dB)

A = 103m2

A = 106m2

A = 103m2

A = 106m2

4.00 ≤


4.9

2.2

7.3

4.0

1.50 ≤
< 4.00

4.9

2.5

9.2

4.7

0.75 ≤
< 1.50

6.6

3.8

14.8

5.5

0.25 ≤
< 0.75

7.9

2.8

17.6

4.7

0.00 ≤
< 0.25

7.9

2.6

18.0

4.6

-0.25 ≤
< 0.00

10.2

1.9

22.7

3.7

-0.75 ≤
< -0.25

9.6

2.6

16.9

7.9


< -0.75

6.1

2.7

15.5

5.2

Table 5.5 defines the population of terrain patches and measurements upon which these data are based.

clutter spatial amplitude distributions at high spatial resolution continue to be dramatically evidenced by these lower numbers.

5.3.2 Further Reduction The previous results of Section 5.3, although applicable to a single generic terrain type (viz., mixed rural), still require specification of the relief of the terrain (in two categories, viz., high- and low-) and the depression angle at which the terrain is illuminated. A clutter modeler who is unable to specify terrain relief and depression angle may desire that the Phase One clutter measurement data be reduced so as to average together all variations of terrain relief and depression angle. The results of such reduction are presented in what follows. Table 5.10 shows mean clutter strength σ w° for general mixed rural terrain by frequency band and polarization, in which all variations with relief and depression angle are subsumed. The σ w° results of Table 5.10 are plotted in Figure 5.12. The lower subtable of Table 5.10 shows that the number of measurements upon which the mean clutter

438 Multifrequency Land Clutter Modeling Information

Table 5.10 Mean Clutter Strength σ °w and Number of Measurements for General Mixed Rural Terrain by Frequency Band and Polarization, Inclusive of Variations with Relief and Depression Anglea Weibull Mean Clutter Strength σ°w (dB) VHF

UHF

L-Band

S-Band

X-Band

HH

VV

HH

VV

HH

VV

HH

VV

HH

VV

-29.9

-29.2

-30.5

-29.1

-28.9

-28.9

-32.4

-30.4

-30.1

-28.8

Number of Measurements VHF

a

UHF

L-Band

S-Band

X-Band

HH

VV

HH

VV

HH

VV

HH

VV

HH

VV

2,576

2,776

3,426

3,573

3,310

3,483

2,505

2,476

3,012

3,109

Table 5.5 defines the population of terrain patches upon which these data are based.

strength results in Table 5.10 are based is large—on the order of 3,000 measurements for each value of σ w° . The σ w° results of Table 5.10 and Figure 5.12 hover around –30 dB in all five frequency bands and at both polarizations. There is a slight (~2 dB) S-band dip between L-band and X-band; also, results at vertical polarization are usually slightly stronger (on the order of 1 or 2 dB) than at horizontal polarization (except at L-band where σ w° VV = σ w° HH ). Such differences with frequency and polarization are small. That is, after incorporating all variations with relief and depression angle, mean clutter strength in general mixed rural terrain is remarkably invariant with frequency and polarization. The results of Table 5.10 and Figure 5.12 corroborate corresponding results obtained with repeat sector data in Chapter 3 (cf. Table 3.7 and Figure 3.40). Table 5.11 presents the Weibull shape parameter aw and ratios of standard deviation-tomean and mean-to-median for clutter amplitude distributions in general mixed rural terrain, inclusive of all variations with relief and depression angle, but retaining the dependence on radar spatial resolution. Figure 5.13 shows the sd/mean scatter plot associated with this table, in which the strong trend of decreasing spread with increasing cell size continues to be seen. The dependence of aw on spatial resolution cannot sensibly be avoided. However, a radar modeler usually can specify the parameters of his radar, including resolution (as well as frequency and polarization), even if he cannot be specific about terrain relief and depression angle. For example, linear interpolation on log10A in Table 5.11 indicates that, in general mixed rural terrain independent of relief and depression angle, for a radar that happens to have spatial resolution A = 104 m2 for the terrain region in question, the meanto-median ratio in the amplitude distribution of the land clutter for that region is 13.4 dB. Thus, largely independent of frequency (VHF to X-band) and polarization, the mean clutter strength for that region is σ w° ≈– 30 dB (as per Table 5.10), and the median clutter strength for that region is σ 50 ° ≈– 43 dB (as per Table 5.11). At some other value of spatial resolution significantly different from 104 m2, σ w° will remain at ∼ –30 dB, but σ °50 will vary significantly from ∼ –43 dB.

Multifrequency Land Clutter Modeling Information 439

Table 5.11 Shape Parameter aw and Ratios of Standard Deviation-to-Mean (SD/Mean) and Meanto-Median for General Mixed Rural Terrain by Spatial Resolution A, Inclusive of Variations with Relief and Depression Anglea

Weibull Shape Parameter aw from SD/Mean

from Mean/Median

A = 103m2

A = 106m2

A = 103m2

A = 106m2

3.4

1.8

3.7

1.9

Ratios SD/Mean (dB)

a

Mean/Median (dB)

A = 103m2

A = 106m2

A = 103m2

A = 106m2

7.6

2.8

17.4

5.5

Table 5.5 defines the population of terrain patches and measurements upon which these data are based.

Does the reduction of clutter strength results inclusive of all variations of terrain relief and depression angle constitute reductio ad absurdum? Certainly there is a price to pay for the simplicity of the resulting information. That price is the loss in variability in σ w° and aw that actually occurs with terrain relief and depression angle. The range of variation of σ w° in Figure 5.12 is very small compared to the ranges of variation of σ w° in Figures 5.8 and 5.10. It is clear from this variability that attempting to characterize low-angle land clutter independently of terrain relief and depression angle must inherently involve large uncertainties in predicting clutter strengths in any real radar operating at a particular depression angle in terrain of particular relief.

5.3.3 Validation of Clutter Model Framework In the clutter modeling framework of Chapter 5, mean clutter strength σ w° varies with radar frequency f as σ w° ( f ) , shape parameter aw varies with radar spatial resolution A as aw(A), and both σ w° (f) and aw(A) vary with terrain type and depression angle. This modeling framework was developed through evolving examination of clutter measurement data— first, the Phase Zero data at X-band in Chapter 2, and then the Phase One multifrequency repeat sector data in Chapter 3. The repeat sector data were based on one carefully selected clutter patch at each measurement site so as to represent a canonical, uncomplicated, clearcut terrain type and measurement situation. Thus an important question has been, do the trends observed in the carefully selected 42-patch repeat sector data represent those that exist in more generally occurring composite landscape? Stated differently, were the 42 repeat sector patches selected with too much care, leading to parametric dependencies not generally borne out in the spatially comprehensive 3,361-patch survey data? The results of Section 5.3 confirm that the modeling framework originally developed from preliminary measurement data continues to be appropriate for deriving modeling information from the final complete multifrequency measurement database. As shown in Section 5.3, major empirical dependencies in clutter amplitude statistics with frequency, resolution, terrain relief, and depression angle do indeed exist in general mixed rural terrain and are captured by this modeling framework. Basing the model framework on σ w° , in contrast, for example, to σ °50 , results in a considerable simplification. In any measured clutter spatial amplitude distribution, σ w° is

440 Multifrequency Land Clutter Modeling Information

the only attribute of the distribution not dependent on A. Thus basing the model framework on σ w° removes one complete parameter dimension from the model—that is, σ w° = σ w° (f), whereas σ °50 = σ °50 (f, A).

5.3.4 Simplified Clutter Prediction Digitized terrain elevation data27 may often be more readily available to radar performance modelers than digitized data descriptive of the land cover. For example, although raw Landsat data descriptive of land cover are readily available by purchase from the USGS EROS Data Center, these raw data require considerable further processing, first for geometric correction, and then for classification into standard land cover categories (e.g., forest, agricultural, etc.), before they are useful for clutter modeling. The clutter modeling information of Section 5.3, applicable to the single general land cover class of “general mixed rural,” may be directly used for site-specific clutter prediction using only digitized terrain elevation data—information descriptive of the land cover at the site is not necessary in this simplified approach to clutter modeling. Through use of the digitized terrain elevation data, (1) depression angle from the radar to the backscattering terrain point can be calculated based simply on the relative elevation differences of the radar and the terrain point, and (2) terrain relief can be estimated as high or low based on whether average terrain slope in the neighborhood of the terrain point is > 2° or < 2°, respectively. This information, together with specification of the radar parameters, is sufficient to calculate a Weibull random variate estimate of general mixed rural clutter strength σ°F 4 for the terrain cell in question from the results of Section 5.3. Of course the disadvantage of this simplified approach is the loss in prediction fidelity associated with the variations in clutter amplitude statistics that occur with changes in land cover. That such variability can be large is indicated by the clutter modeling information presented in Section 5.4 for a number of specifically different land cover classes. However, simplification to the single “general mixed rural” land cover class (i.e., doing without land cover information) while retaining variations with relief and depression angle is obviously less severe than further simplifying out variations with relief and depression angle (i.e., in addition, doing without digitized terrain elevation data) as in the results of Tables 5.10 and 5.11, and Figures 5.12 and 5.13.

5.4 Land Clutter Coefficients for Specific Terrain Types In Section 5.4, land clutter coefficients are presented for the following eight specific terrain types—urban, agricultural, forest, shrubland, grassland, wetland, desert, and mountains. These eight terrain types are characterized principally by land cover, except for mountain terrain which is characterized principally by landform. The results of Section 5.4 are based on the set of 1,733 clutter patches for which the terrain classification is pure. Pure terrain classification implies that a single primary classifier was sufficient to describe the patch; secondary classification was unnecessary. This set of 1,733 pure patches is a 27. Digitized terrain elevation data may be acquired from the U. S. Geological Survey (USGS) or the U. S. National Imagery and Mapping Agency (NIMA). Such data are called Digital Elevation Models (DEMs) by USGS, and Digital Terrain Elevation Data (DTED) by NIMA. In the past, the data from both sources were commonly available at 3 arc-seconds (i.e., ≈100 m) sampling interval, but data at smaller sampling intervals (e.g., 1 arc-second) are now increasingly available.

440 Multifrequency Land Clutter Modeling Information

the only attribute of the distribution not dependent on A. Thus basing the model framework on σ w° removes one complete parameter dimension from the model—that is, σ w° = σ w° (f), whereas σ °50 = σ °50 (f, A).

5.3.4 Simplified Clutter Prediction Digitized terrain elevation data27 may often be more readily available to radar performance modelers than digitized data descriptive of the land cover. For example, although raw Landsat data descriptive of land cover are readily available by purchase from the USGS EROS Data Center, these raw data require considerable further processing, first for geometric correction, and then for classification into standard land cover categories (e.g., forest, agricultural, etc.), before they are useful for clutter modeling. The clutter modeling information of Section 5.3, applicable to the single general land cover class of “general mixed rural,” may be directly used for site-specific clutter prediction using only digitized terrain elevation data—information descriptive of the land cover at the site is not necessary in this simplified approach to clutter modeling. Through use of the digitized terrain elevation data, (1) depression angle from the radar to the backscattering terrain point can be calculated based simply on the relative elevation differences of the radar and the terrain point, and (2) terrain relief can be estimated as high or low based on whether average terrain slope in the neighborhood of the terrain point is > 2° or < 2°, respectively. This information, together with specification of the radar parameters, is sufficient to calculate a Weibull random variate estimate of general mixed rural clutter strength σ°F 4 for the terrain cell in question from the results of Section 5.3. Of course the disadvantage of this simplified approach is the loss in prediction fidelity associated with the variations in clutter amplitude statistics that occur with changes in land cover. That such variability can be large is indicated by the clutter modeling information presented in Section 5.4 for a number of specifically different land cover classes. However, simplification to the single “general mixed rural” land cover class (i.e., doing without land cover information) while retaining variations with relief and depression angle is obviously less severe than further simplifying out variations with relief and depression angle (i.e., in addition, doing without digitized terrain elevation data) as in the results of Tables 5.10 and 5.11, and Figures 5.12 and 5.13.

5.4 Land Clutter Coefficients for Specific Terrain Types In Section 5.4, land clutter coefficients are presented for the following eight specific terrain types—urban, agricultural, forest, shrubland, grassland, wetland, desert, and mountains. These eight terrain types are characterized principally by land cover, except for mountain terrain which is characterized principally by landform. The results of Section 5.4 are based on the set of 1,733 clutter patches for which the terrain classification is pure. Pure terrain classification implies that a single primary classifier was sufficient to describe the patch; secondary classification was unnecessary. This set of 1,733 pure patches is a 27. Digitized terrain elevation data may be acquired from the U. S. Geological Survey (USGS) or the U. S. National Imagery and Mapping Agency (NIMA). Such data are called Digital Elevation Models (DEMs) by USGS, and Digital Terrain Elevation Data (DTED) by NIMA. In the past, the data from both sources were commonly available at 3 arc-seconds (i.e., ≈100 m) sampling interval, but data at smaller sampling intervals (e.g., 1 arc-second) are now increasingly available.

Multifrequency Land Clutter Modeling Information 441

completely separate, nonoverlapping set from the 1,628 mixed patches upon which the results of Section 5.3 are based. The clutter modeling information presented in Section 5.4 is based on 29,558 measured clutter histograms from the 1,733 pure patches. These measurements comprise 49% of the multifrequency Phase One clutter measurement data. Specification of land clutter by specific terrain type is useful for various reasons, three of which are mentioned in what follows. First, for radar sites in which the surrounding terrain is entirely of one homogenous type, improved radar performance predictions are obtained by constraining clutter predictions to the terrain type that exists there. In homogeneous terrain, such improvement is gained without losing the significant advantage of general mixed rural classification—namely, the use of a single land cover class over the complete site, so that region- or pixel-specific land cover information is not required. Second, if pixel-specific land cover information is available (e.g., 30-m Landsat pixels), much improved fidelity in clutter prediction can result. The degree of improvement in fidelity when the prediction is specific to (i.e., matches) the terrain class at the pixel level depends on the extent to which the terrain at the site is of mixed land cover. In mixed terrain, individual pixels are usually of purer intrinsic land cover than are large regions. Over large radar coverage regions, most sites have some occurrence of mixed land cover. Third, in the design and simulation of radars required to operate in land clutter, although specification of clutter from general mixed rural terrain is suitable to establish baseline central performance measures, there is also need to establish what variations in performance result from operating in clutter that is stronger or weaker than the baseline. Review of the clutter modeling information presented by specific terrain type in Section 5.4 can establish how strong and how weak land clutter can become in specific circumstances. Strongest values of σ w° generally occur in urban and mountain terrain. Weakest values of σ w° generally occur in low-relief open terrain such as level wetland and level desert. Recall that the σ w° values presented in Chapter 5 represent the median level of mean clutter strength from groups of like-classified patches—that is, individual patches from the groups can have stronger or weaker values of σ w° than the median level. For example: (1) the single strongest clutter patch measured was an urban clutter patch at VHF for which σ w° = 9.8 dB; (2) the strongest mountain patch was also measured at VHF for which σ w° = 4.1 dB; (3) the weakest clutter patch measured was frozen level wetland at depression angle = 0.22° at UHF for which σ w° = –81.2 dB; and (4) the next weakest clutter patch measured was level desert at depression angle = 0.27° also at UHF for which σ w° = –78.3 dB. Thus the range of mean clutter strength in the Phase One database of measurements from 3,361 clutter patches covers nine orders of magnitude. In what follows in Section 5.4, σ w° and aw land clutter coefficients are specified for the eight specific terrain types listed above in a similar manner to how the same coefficients were presented in Section 5.3 for general mixed rural terrain. Since many of the details of this presentation are the same as in Section 5.3, a complete description of them is not repeated here.

Two Pure Clutter Patches. The modeling information to follow is based on 29,558 measured spatial clutter amplitude distributions from 1,733 clutter patches for which the terrain is classified as pure. Figures 5.14 and 5.15 show examples of measured clutter histograms and cumulative distributions from two of these pure patches. Figure 5.14

442 Multifrequency Land Clutter Modeling Information

shows a pure forest histogram measured at VHF from patch 4/2 at Wachusett Mountain, Massachusetts. Patch WM 4/2 was hilly terrain (landform = 4) observed at 6° depression angle. It was situated beginning at 2 km from the radar and extended 3 km in range and 36° in azimuth. In the histogram of Figure 5.14, 6.3% of the samples are at radar noise level (shown in black). Figure 5.15 shows a pure farmland histogram measured at X-band from patch 7/1 at Wolseley, Saskatchewan. Patch WO 7/1 was undulating terrain (landform = 3/1) observed at a depression angle of 0.7°. It was situated beginning 3.2 km from the radar, and extended 4.2 km in range and 52° in azimuth. In the histogram of Figure 5.15, 48.3% of the samples are at radar noise level (black). The histograms of Figures 5.14 and 5.15 were measured using 36-m and 15-m pulse length, respectively; both used horizontal polarization. Clutter statistics for these two clutter patches are given in Table 5.12. Table 5.12 Clutter Statistics for Two Pure Terrain Patches

Statistics

Wolseley Farmland Patch 7/1 X-Band

Wachusett Mt. Forest Patch 4/2 VHF

Theoretical Rayleigh Values

4.7

1.7

1

SD/Mean (dB)

10.4

2.5

0

Skewness (dB)

14.5

6.0

3

Kurtosis (dB)

30.2

14.0

9.5

Mean/Median (dB)

23.3

4.6

1.6

99-percentile/Median (dB)

35.0

14.0

8.2

aw

The two histograms of Figures 5.14 and 5.15 are both quite well behaved but are of extremely different shapes. In both figures, the measured cumulative distribution is plotted against a Weibull probability scale to the left. Both cumulatives are quite linear as plotted against this scale and hence are very well modeled as Weibull distributions [their coefficients of determination are 0.9994 and 0.9996, respectively; see Equation (2.B.30)]. The shape parameter aw of the Weibull distribution for the pure forest patch in Figure 5.14 is of value 1.7; it may be compared with the slope of the Rayleigh distribution of aw = 1 also shown in the figure. Although aw = 1.7 is significantly removed from aw = 1.0 (i.e., the distribution of Figure 5.14 is not a Rayleigh distribution, compare its sd/mean and mean/ median numbers of 2.5 and 4.6 dB with Rayleigh values of 0 and 1.6 dB; see Table 5.12), still the distribution of Figure 5.14 approaches Rayleigh about as closely as routinely occurs in the Phase One measurements. The reasons that the pure forest distribution of Figure 5.14 approaches Rayleigh are: (1) the forested land cover (which constitutes a relatively homogeneous scattering medium compared with farmland), (2) the relatively large cell sizes resulting from the 13° VHF azimuth beamwidth, and (3) the high depression angle (i.e., 6°) at which the measurement was obtained.

Multifrequency Land Clutter Modeling Information 443

In contrast, the pure farmland distribution of Figure 5.15 is very spread out, with a shape parameter of aw = 4.7. This value of aw is about as high as routinely occurs in the Phase One data. The reasons that this distribution is of such high spread are: (1) it is discretedominated farmland, (2) it is of high spatial resolution (i.e., 15-m range resolution and 1° azimuth beamwidth), and (3) it is of relatively low depression angle (i.e., 0.7°). The reason the cumulative tails off at its left end in Figure 5.15 is because it is being drawn down by the noise contamination (shown in black) at the low end of the histogram. As discussed previously, such noise contamination when included properly in computations does not adversely affect the moments, or the cumulative in the region to the right of the contamination. The two pure clutter patch measurements shown in Figures 5.14 and 5.15 may be compared with the two mixed-terrain measurements shown previously in Chapter 5 in Figures 5.2 and 5.3. Both pairs of measurements exhibit extremely wide ranges in clutter strength (i.e., > 5 and > 8 orders of magnitude in Figures 5.14 and 5.15, respectively); and both pairs are reasonably well modeled as Weibull distributions over these wide ranges. The pure forest histogram of Figure 5.14 approaches Rayleigh more closely than the mixed forest/ agricultural histogram of Figure 5.2, and the pure farmland histogram of Figure 5.15 is of greater spread (i.e., further from Rayleigh) than the mixed farmland/forest histogram of Figure 5.3. As discussed elsewhere in this book, every clutter patch measurement is different. Rather than rely on individual measurements such as are shown in Figures 5.14 and 5.15 for pure-terrain modeling information, what is done subsequently in Section 5.4 (as heretofore in Section 5.3) is to assemble large numbers of like-classified pure-terrain patch measurements, and to seek general modeling trends in the medianized results of σ w° and aw over many measurements.

Uncertain Outliers. There are generally large numbers of clutter patches within each terrain type/depression angle/radar parameter category. In processing clutter measurement results involving large numbers of patches, criteria are automatically applied ensuring that each patch measurement is valid (e.g., precluding excessive amounts of noise and/or saturation contamination, requiring close upper and lower mean bounds, etc.). Beyond this, it is generally not practicable to individually examine the measurement results from each clutter patch within a category. When the number of patch measurements within a category is large, occasional borderline measurements which, if individually examined, might be deleted as inappropriate to that category generally have negligible effect on the resulting median value of σ w° or aw for that category. When the number of patch measurements within a category is small and the median value appears out-of-line with the expected trend, an open plot symbol is used to indicate that the value is an uncertain outlier (see Section 5.2.3.3). Since the number of patch measurements associated with uncertain outliers is small, it becomes practicable to occasionally examine individual patch measurements in such cases to determine if there is a discernible reason for the out-of-trend result. Some examples of such individual examination of uncertain outlier results are provided in following subsections addressing urban, agricultural, and forest terrain types.

5.4.1 Urban or Built-Up Terrain By urban terrain is meant any kind of built-up land predominantly covered with structures, from high-rise centers of large cities (e.g., Calgary, Winnipeg, Scranton) to small country

444 Multifrequency Land Clutter Modeling Information

villages and remote military bases or industrial complexes. The urban clutter modeling information of Section 5.4.1 is based on 1,282 measured clutter histograms from 64 pure urban clutter patches at 18 measurement sites. Table 5.13 shows how these numbers of urban clutter patches and measured clutter histograms break down by depression angle in five regimes of depression angle. All of these urban clutter measurements were in pure low-relief terrain of terrain slope < 2°. Table 5.13 Numbers of Terrain Patches and Measured Clutter Histograms for Urban or Built-up Terrain, by Depression Anglea,b,c

Terrain Relief

Low-relief


= Depression Angle (degrees)

Number of Patches

Number of Measurements

4.00 ≤


0

0

1.50 ≤
< 4.00

6

121

0.75 ≤
< 1.50

9

176

0.25 ≤
< 0.75

18

432

0.00 ≤
< 0.25

23

487

-0.25 ≤
< 0.00

8

66


< -0.25

0

0

Totals

64

1,282

a A single (primary) classifier only is sufficient to describe these patches. b A terrain patch is a land surface macroregion usually several kms on a side (median patch area = 2 12.62 km ). c A measured clutter histogram contains all of the temporal (pulse by pulse) and spatial (resolution cell by resolution cell) clutter samples obtained in a given measurement of a terrain patch. A terrain patch was usually measured many times (nominally 20) as RF frequency (5), polarization (2), and range resolution (2) were varied over the Phase One radar parameter matrix.

Trends in σ w° . Table 5.14 presents mean clutter strength σ w° for urban terrain by frequency band, polarization, and depression angle, and includes the number of measurements upon which each value of σ w° is based. The σ w° data of Table 5.14 are plotted in Figure 5.16. In Figure 5.16, consider first the σ w° data at positive depression angle (i.e., cyan, dark blue, purple, magenta). These data show two trends with frequency. The cyan and dark blue, low depression angle data (i.e., 0° to 0.25° and 0.25° to 0.75°) show increasing σ w° with increasing frequency, from about –35 dB at VHF to about –16 dB at X-band. The purple and magenta, high depression angle data (i.e., 0.75° to 1.5° and 1.5° to 4°) show frequency invariance of σ w° largely within the –15 to –20 dB range in all five frequency bands. The low depression angle data were almost entirely measured at low site elevations over low-relief open terrain supportive of multipath; thus the lower σ w° levels in the lower bands at low depression angles are due to multipath loss entering clutter strength σ°F 4 through the propagation factor F. The high depression angle data were largely measured at higher site elevations in forested terrain not conducive to multipath; hence these high depression angle σ w° data are more indicative of intrinsic σ° levels. At X-band, both high and low depression angle data indicate σ w° at vertical polarization to be significantly stronger (viz., by 3 to 6 dB) than at horizontal polarization. This clear-cut difference with polarization at X-band is much less evident in the lower bands.

Multifrequency Land Clutter Modeling Information 445

Table 5.14 Mean Clutter Strength σ w° and Number of Measurements for Urban or Built-up Terrain, by Frequency Band, Polarization, and Depression Anglea

Weibull Mean Clutter Strength σ°w (dB)


= Depression Angle (degrees)

VHF

UHF

S-Band

X-Band

HH

VV

HH

VV

HH

VV

HH

VV

HH

VV

4.0 ≤


----

----

----

----

----

----

----

----

----

----

1.50 ≤
< 4.00

-16.3

-18.3

-17.5

-16.3

-18.4

-18.5

-20.8

-19.0

-22.7

-17.0

0.75 ≤
< 1.50

-20.6

-16.7

-17.1

-15.1

-16.4

-17.1

-20.7

-15.4

-20.0

-15.2

0.25 ≤
< 0.75

-33.9

-33.9

-28.9

-28.7

-25.9

-26.3

-22.7

-20.8

-19.5

-16.0

0.00 ≤
< 0.25

-35.3

-36.5

-30.3

-28.4

-14.9

-18.1

-18.2

-18.6

-16.0

-12.9

-0.25 ≤
< 0.00

-42.6

----

-40.0

-37.6

-35.0

-37.9

-37.1

-34.9

-31.2

-29.3


< -0.25

----

----

----

----

----

----

----

----

----

----

Number of Measurements


= Depression Angle (degrees)

VHF HH

4.0 ≤


a

L-Band

UHF

VV

HH

L-Band VV

HH

S-Band

VV

HH

X-Band

VV

HH

VV

0

0

0

0

0

0

0

0

0

0

1.50 ≤
< 4.00

17

15

18

18

20

23

2

2

3

3

0.75 ≤
< 1.50

26

24

24

24

15

21

9

9

12

12

0.25 ≤
< 0.75

38

43

52

54

45

49

34

34

44

39

0.00 ≤
< 0.25

34

41

62

63

55

64

52

30

39

47

-0.25 ≤
< 0.00

2

0

5

5

8

8

9

7

11

11


< -0.25

0

0

0

0

0

0

0

0

0

0

TOTALS

117

123

161

164

143

165

106

82

109

112

Table 5.13 defines the population of terrain patches upon which these data are based.

Uncertain Outliers. Next, in Figure 5.16, consider the σ w° data at negative depression angle (dark green, 0° to –0.25°). These data come from seven clutter patches at three sites. These dark green, negative depression angle σ w° data are considerably weaker in all bands than the corresponding σ w° data at positive depression angles. The reason for the low levels in the dark green, negative depression angle σ w° data in Figure 5.16 is that all seven clutter patches contributing to the dark green data were measured with positive effective radar height h, but at long ranges r of 20 to 40 km which were beyond the imaginary28 spherical earth horizon r′ in all cases. Thus the negative depression angle is the result of geometry on the spherical earth, not the result of negative effective radar height (see Appendix 2.C). This is not to suggest that the negative depression angle that results at long ranges r > r′ on the spherical earth with h > 0 is any less real than that resulting from h < 0 at short ranges r < r′—but that considerable propagation loss occurs over the long intervening ranges, which accounts for the low levels of the dark green, negative depression angle σ w° data in Figure 5.16. Such propagation loss would not exist in short range, 28. These seven clutter patches were all within line-of-sight visibility to the radar on the real earth.

446 Multifrequency Land Clutter Modeling Information

negative depression angle urban σ w° data in h < 0 situations. Therefore, the dark green, negative depression angle σ w° data in Figure 5.16 are plotted as open symbols to indicate that urban clutter that might be measured from steep slopes at higher elevations than the radar antenna (N.B., no such measurements exist in the Phase One database) should not be assumed to be generally weaker than urban clutter at positive depression angle.

Strong Urban (and Mountain) Clutter. The high depression angle, urban σ w° data in Table 5.14 and Figure 5.16 (plotted as purple and magenta) represent very strong values of mean land clutter strength. Among the eight specific terrain types discussed in Section 5.4, mountain terrain also provides strong values of σ w° . The purple and magenta, urban σ w° data of Figure 5.16 are stronger than the mountain σ w° data of Section 5.4.8 at X- and Sband, approximately equal to (or slightly stronger than) the strongest values of mountain σ w° at L-band, and weaker than the strongest values of mountain σ w° at UHF and VHF—slightly weaker at UHF and much weaker at VHF. That is, urban clutter is generally strongest in the high bands, and mountain clutter is generally strongest in the low bands. In each of the five Phase One frequency bands, either urban or mountain terrain provides the maximum value of σ w° among the eight specific terrain types of Section 5.4. By frequency band, these five maximum values of σ w° are: at VHF, –5.8 dB (mountains); at UHF, –12.4 dB (mountains); at L-band, –14.9 dB (urban); at S-band, –15.4 dB (urban); and at X-band, –12.9 dB (urban). The urban σ w° values of Table 5.14 and Figure 5.16 represent median levels of mean clutter strength from groups of like-classified clutter patches—individual patches can be stronger. In each of the five Phase One frequency bands, the strongest mean clutter strength from a pure urban clutter patch was: at VHF, 9.8 dB; at UHF, 0.3 dB; at L-band, 0.0 dB; at S-band, –5.8 dB; and at X-band, –0.5 dB. The urban σ w° data of Table 5.14 and Figure 5.16 indicate a strong depression angle dependence in the lower bands. As discussed previously, this effect is largely due to multipath loss in the results at low depression angles. However, intrinsic σ° at VHF may also increase with depression angle in urban terrain. At one site, Cochrane, five clutter histograms at VHF were measured from one urban clutter patch at the high depression angle of 7.8° (these data are not included in Figure 5.16). The range of mean strengths in these five histograms was 4.0 to 6.1 dB, considerably stronger than the –16.3 to –20.6 dB VHF levels in the 0.75° to 4° depression angle range in Table 5.14 and Figure 5.16. Besides the high depression angle, another factor that contributed to these high VHF urban clutter levels at Cochrane is that the terrain of the patch was of mixed landform—generally level, but with a moderately steep component along the bank of a river dissecting the patch. In the higher bands, there is little indication of depression angle dependence in the urban σ w° data of Table 5.14 and Figure 5.16.

Shape Parameter aw. Table 5.15 presents the Weibull shape parameter aw and ratios of standard deviation-to-mean and mean-to-median for clutter amplitude distributions in lowrelief urban terrain by depression angle and radar spatial resolution. The statistical populations underlying the data of Table 5.15 are shown in Table 5.13. In Table 5.15 and other similar tables in Chapter 5, aw is calculated two ways: (1) from the ratio of standard deviation-to-mean and (2) from the mean-to-median ratio. Many of the corresponding aw numbers resulting from these two methods of calculation are relatively close in Table 5.15; however, several of these corresponding aw numbers in Table 5.15 are not close, indicating that urban clutter can in some situations be less well approximated as Weibull distributed than other types of land clutter.

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Multifrequency Land Clutter Modeling Information 447

20 km →

20 km 15-m Pulse

50 km 150-m Pulse

Figure 5.1 Comparison of repeat sector patch and survey patches at Magrath, Alta. Phase One X-band data; clutter maps thresholded at σ°F 4 ≥ –40 dB. The repeat sector patch is shown black; the survey patches are shown light gray; clutter is shown dark gray. .

10920 Samples 15

0.9999 Weibull Scale

0.99 0.97

pe

10

0.8 0.7

Percent

igh Slo

0.9

Rayle

Probability That σ°F4 ≤ Abscissa

0.999

0.6 0.5

5

0.4 0.3 0.2 0.15

0 –80

–70

–60 –50

–40

–30

–20

–10

0

10

σ°F4 (dB) Figure 5.2 A measured UHF clutter histogram and cumulative distribution for a mixed rural terrain patch (WM 34/2) at Wachusett Mt., Mass.

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448 Multifrequency Land Clutter Modeling Information

8395 Samples 0.9999

15 Weibull Scale

0.99 0.97

Rayleig h Slop e

0.9 0.8 0.7

10

Percent

Probability That σ°F4 ≤ Abscissa

0.999

0.6 0.5

5

0.4 0.3 0.2 0.15 –80

0 –70

–60 –50

–40 –30 σ°F4 (dB)

–20

–10

0

10

Figure 5.3 A measured X-band clutter histogram and cumulative distribution for a mixed rural terrain patch (SH 7/1) at Spruce Home, Sask.

0.020

p(y)

0.015

0.010

0.005

aw = 1

2

3

4

5

0.000 –80

–60

–40

–20

0

y Figure 5.4 The logarithmically transformed Weibull probability density function p(y); aw = 1, 2, 3, 4, 5.

Ch05b.fm Page 449 Tuesday, December 11, 2001 11:13 AM

15

40

10

30

Mean/Median (dB)

SD/Mean (dB)

Multifrequency Land Clutter Modeling Information 449

5

0

20

10

0

5

10

10 0

2

4

6

0

aw

2

4

6

aw

(a)

(b)

Figure 5.5 Ratios of (a) standard deviation-to-mean and (b) mean-to-median vs aw for Weibull statistics.

Depression Angle Negative Positive Depression Angle

Figure 5.6 Positive and negative depression angle.

Ch05b.fm Page 450 Tuesday, December 11, 2001 11:13 AM

450 Multifrequency Land Clutter Modeling Information

⬚ (dB) Mean Clutter Strength σw

–20

X-Band Presentation (Representative)

Similar Presentations for Lower Bands

–30

5 –40

4

2 1

1.0

VHF

1 2

3

Depression Angle Bin Number*

*No In-Band Frequency Shift

0.1

3

UHF

L-

10.0

S-

X-Band

Frequency (GHz) Figure 5.7 Five-frequency plot methodology showing depression angle color coding. Circles represent VV-polarization; squares represent HH-polarization. Each plot symbol is a median value of mean clutter strength over many clutter patch measurements. Table 5.4 Depression Angle Bins Low-Relief Terrain (Slopes < 2˚)

Depression Angle (deg)

Bin Number

High-Relief Terrain (Slopes > 2˚) Color Code VV

Depression Angle (deg)

Bin Number

Color Code VV

HH

> 4˚

5

> 6˚

5

1.5˚ to 4˚

4

4˚ to 6˚

4

0.75˚ to 1.5˚

3

2˚ to 4˚

3

0.25˚ to 0.75˚

2

1˚ to 2˚

2

0˚ to 0.25˚

1

0˚ to 1˚

1

–0.25˚ to 0˚

–1

–1˚ to 0˚

–1

–0.75˚ to –0.25˚

–2

< –1˚

–2

< – 0.75˚

–3

HH

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Multifrequency Land Clutter Modeling Information 451

0

High-Relief General Mixed Rural Terrain −10

Mean Clutter Strength σw (dB)

−20

°

−30

−40

−50


= Depression Angle (deg)

Polarization HH VV

4.0 ≤
< 6.0 2.0 ≤
< 4.0 1.0 ≤
< 2.0 0.0 ≤
< 1.0 −1.0 ≤
< 0.0
< −1.0

−60

−70 0.1

1.0

10.0

−80 VHF

UHF

L-Band

S-Band

X-Band

Frequency (GHz) NOTE: Within each of the five frequency bands, the horizontal displacement of the different colored plot symbols is just a convenient way to separate the various depression angle regimes to avoid overlapping plot symbols. This displacement does not imply a systematic in-band frequency shift with depression angle.

Figure 5.8 Mean clutter strength σ°w vs frequency for general mixed rural terrain of high relief.

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452 Multifrequency Land Clutter Modeling Information

15

High-Relief General Mixed Rural Terrain 2i° ≤ Depression Angle < 4i°

SD/Mean (dB)

10

5

VHF UHF L-Band S-Band X-Band Range Interval 1 Wide Pulse Narrow Pulse Regression Line

0

102

103

2

3

104

105

A

106

10

(m2)

NOTES: Each plotted symbol represents median values of SD/Mean and A over a group of similar patch measurements. A = r • ∆r • ∆θ r = range (data are separated into three range intervals: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km). ∆r = range resolution (data are wide pulse, i.e., 150 m, or narrow pulse, i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands ∆θ = one way 3 dB azimuth beamwidth (13 degrees at VHF, 5 degrees at UHF, 3 degrees at L-band, 1 degree at S- and X-bands) Each plot symbol can appear five times, once for each radar frequency, in order of decreasing frequency left-to-right as beam width increases. Little narrow pulse data is available in the third range interval.

Figure 5.9 Ratio of standard deviation-to-mean (SD/Mean) vs radar spatial resolution A for general mixed rural terrain of high relief with depression angle between 2.0 and 4.0 degrees.

Ch05b.fm Page 453 Tuesday, December 11, 2001 11:13 AM

Multifrequency Land Clutter Modeling Information 453

0

Low-Relief General Mixed Rural Terrain −10

Mean Clutter Strength σw (dB)

−20

°

−30

−40

−50


= Depression Polarization

Angle (deg) 4.00 ≤
1.50 ≤
< 4.00 0.75 ≤
< 1.50 0.25 ≤
< 0.75 0.00 ≤
< 0.25 −0.25 ≤
< 0.00 −0.75 ≤
< −0.25
< −0.75

−60

−70

1.0

0.1

HH

VV

10.0

−80 VHF

UHF

L-Band

S-Band

X-Band

Frequency (GHz) NOTES: 1. Open symbols indicate results that may be atypical. 2. Within each of the five frequency bands, the horizontal displacement of the different colored plot symbols is just a convenient way to separate the various depression angle regimes to avoid overlapping plot symbols. This displacement does not imply a systematic in-band frequency shift with depression angle.

Figure 5.10 Mean clutter strength σ °w vs frequency for general mixed rural terrain of low relief.

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454 Multifrequency Land Clutter Modeling Information

15 Low-Relief General Mixed Rural Terrain 0.25i° ≤ Depression Angle < 0.75i°

SD/Mean (dB)

10

5

VHF UHF L-Band S-Band X-Band Range Interval 1 Wide Pulse Narrow Pulse Regression Line

0

102

103

2

3

104

105

A

106

107

(m2)

NOTES: Each plotted symbol represents median values of SD/Mean and A over a group of similar patch measurements. A = r • ∆r • ∆θ r = range (data are separated into three range intervals: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km). ∆r = range resolution (data are wide pulse, i.e., 150 m, or narrow pulse, i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands). ∆θ = one way 3 dB azimuth beamwidth (13 degrees at VHF, 5 degrees at UHF, 3 degrees at L-band, 1 degree at S- and X-bands). Each plot symbol can appear five times, once for each radar frequency, in order of decreasing frequency left-to-right as beamwidth increases. Little narrow pulse data is available in the third range interval.

Figure 5.11 Ratio of standard deviation-to-mean (SD/Mean) vs radar spatial resolution A for general mixed rural terrain of low relief with depression angle between 0.25 and 0.75 degrees.

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Multifrequency Land Clutter Modeling Information 455

0 General Mixed Rural Terrain −10

° (dB) Mean Clutter Strength σw

−20

−30

−40

−50

−60

Polarization HH VV

−70 0.1

1.0

10.0

−80 VHF

UHF

L-Band

S-Band

X-Band

Frequency (GHz) Figure 5.12 Mean clutter strength σ°w vs frequency for general mixed rural terrain, inclusive of variations with relief and depression angle.

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15

General Mixed Rural Terrain

SD/Mean (dB)

10

5

VHF UHF L-Band S-Band X-Band Range Interval 1 Wide Pulse Narrow Pulse Regression Line

0

102

103

2

3

104

105

106

107

A (m2)

NOTES: Each plotted symbol represents median values of SD/Mean and A over a group of similar patch measurements. A = r • ∆r • ∆θ r = range (data are separated into three range intervals: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km). ∆r = range resolution (data are wide pulse, i.e., 150 m, or narrow pulse, i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands ∆θ = one way 3 dB azimuth beamwidth (13 degrees at VHF, 5 degrees at UHF, 3 degrees at L-band, 1 degree at S- and X-bands) Each plot symbol can appear five times, once for each radar frequency, in order of decreasing frequency left-to-right as beam width increases. Little narrow pulse data is available in the third range interval.

Figure 5.13 Ratio of standard deviation-to-mean (SD/Mean) vs radar spatial resolution A for general mixed rural terrain inclusive of variations with relief and depression angle.

-

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Multifrequency Land Clutter Modeling Information 457

13916 Samples 0.9999

15 Weibull Scale

0.99

Slope

0.97 0.9 0.8

0.6

Percent

0.7

Probability That

10

Rayle igh

F4 Abscissa

0.999

0.5

5

0.4 0.3 0.2 0.15

0 –75

–65

–55

–45

–35

–25

–15

5

–5

15

F4 (dB) Figure 5.14 A measured VHF clutter histogram and cumulative distribution for a pure forest patch (WM/4/2) at Wachusett Mt., Mass.

114535

Samples 15

0.9999 Weibull Scale

0.99 0.97

10

Percent

igh Slo

Rayle ig

0.8

pe

h Slop

e

0.9

0.7 0.6

Rayle

Probability That σ°F4 ≤ Abscissa

0.999

0.5

5

0.4 0.3 0.2 0

0.15 –90

–80

–70

–60

–50

–40

–30

–20

–10

0

σ°F4 (dB) Figure 5.15 A measured X-band clutter histogram and cumulative distribution for a pure farmland patch (WO 7/1) at Wolseley, Sask.

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458 Multifrequency Land Clutter Modeling Information

0

Urban or Built-up Terrain −10

Mean Clutter Strength σ°w (dB)

−20

−30

−40

−50


= Depression

Polarization HH VV

Angle (deg)

−60

1.50 ≤
< 4.00 0.75 ≤
< 1.50 0.25 ≤
< 0.75 0.00 ≤
< 0.25 −0.25 ≤
< 0.00

−70 0.1

1.0

10.0

−80 VHF

UHF

L-Band

S-Band

X-Band

Frequency (GHz) NOTES: 1. Open symbols indicate results that may be atypical. 2. Within each of the five frequency bands, the horizontal displacement of the different colored plot symbols is just a convenient way to separate the various depression angle regimes to avoid overlapping plot symbols. This displacement does not imply a systematic in-band frequency shift with depression angle.

Figure 5.16 Mean clutter strength σ°w vs frequency for urban or built-up terrain.

Ch05b.fm Page 459 Tuesday, December 11, 2001 11:13 AM

Multifrequency Land Clutter Modeling Information 459

15

Urban or Built-up Terrain 0.0i° ≤ Depression Angle < 0.25i°

SD/Mean (dB)

10

5

VHF UHF L-Band S-Band X-Band Range Interval 1 Wide Pulse Narrow Pulse Regression Line

0

102

103

2

3

104

105

A

106

107

(m2)

NOTES: Each plotted symbol represents median values of SD/Mean and A over a group of similar patch measurements. A = r • ∆r • ∆θ r = range (data are separated into three range intervals: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km). ∆r = range resolution (data are wide pulse, i.e., 150 m, or narrow pulse, i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands ∆θ = one way 3 dB azimuth beamwidth (13 degrees at VHF, 5 degrees at UHF, 3 degrees at L-band, 1 degree at S- and X-bands) Each plot symbol can appear five times, once for each radar frequency, in order of decreasing frequency left-to-right as beam width increases. Little narrow pulse data is available in the third range interval.

Figure 5.17 Ratio of standard deviation-to-mean (SD/Mean) vs radar spatial resolution A for urban or built-up terrain with depression angle between 0.0 and 0.25 degrees.

Ch05b.fm Page 460 Tuesday, December 11, 2001 11:13 AM

460 Multifrequency Land Clutter Modeling Information

0

High-Relief Agricultural Terrain −10

° (dB) Mean Clutter Strength σw

−20

−30

−40

−50

−60


= Depression Angle (deg) 2.0 ≤
< 4.0 1.0 ≤
< 2.0 0.0 ≤
< 1.0 −1.0 ≤
< 0.0

−70

0.1

1.0

Polarization HH VV

10.0

−80

VHF

UHF

L-Band

S-Band

X-Band

Frequency (GHz) NOTES: 1. Open symbols indicate results that may be atypical. 2. Within each of the five frequency bands, the horizontal displacement of the different colored plot symbols is just a convenient way to separate the various depression angle regimes to avoid overlapping plot symbols. This displacement does not imply a systematic in-band frequency shift with depression angle.

Figure 5.18 Mean clutter strength σ°w vs frequency for high-relief agricultural terrain.

Ch05b.fm Page 461 Tuesday, December 11, 2001 11:13 AM

Multifrequency Land Clutter Modeling Information 461

15 High-Relief Agricultural Terrain 1.0i∞ ≤ Depression Angle < 2.0i∞

SD/Mean (dB)

10

5

VHF UHF L-Band S-Band X-Band Range Interval 1 Wide Pulse Narrow Pulse Regression Line

0

102

103

2

3

104

105

106

107

A (m2) NOTES: Each plotted symbol represents median values of SD/Mean and A over a group of similar patch measurements. A = r • ∆r • ∆θ r = range (data are separated into three range intervals: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km). ∆r = range resolution (data are wide pulse, i.e., 150 m, or narrow pulse, i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands). ∆θ = one way 3 dB azimuth beamwidth (13 degrees at VHF, 5 degrees at UHF, 3 degrees at L-band, 1 degree at S- and X-bands). Each plot symbol can appear five times, once for each radar frequency, in order of decreasing frequency left-to-right as beamwidth increases. Little narrow pulse data is available in the third range interval.

Figure 5.19 Ratio of standard deviation-to-mean (SD/Mean) vs radar spatial resolution A for high-relief agricultural terrain with depression angle between 1.0 and 2.0 degrees.

.

Ch05b.fm Page 462 Tuesday, December 11, 2001 11:13 AM

462 Multifrequency Land Clutter Modeling Information

0

Low-Relief Agricultural Terrain −10

Mean Clutter Strength σ°w (dB)

−20

−30

−40

−50


= Depression

Angle (deg) 1.50 ≤
< 4.00 0.75 ≤
< 1.50 0.25 ≤
< 0.75 0.00 ≤
< 0.25 −0.25 ≤
< 0.00 −0.75 ≤
< −0.25

−60

−70 0.1

1.0

Polarization HH VV

10.0

−80 VHF

UHF

L-Band

S-Band

X-Band

Frequency (GHz) NOTES: 1. Open symbols indicate results that may be atypical. 2. Within each of the five frequency bands, the horizontal displacement of the different colored plot symbols is just a convenient way to separate the various depression angle regimes to avoid overlapping plot symbols. This displacement does not imply a systematic in-band frequency shift with depression angle.

Figure 5.20 Mean clutter strength σ°w vs frequency for low-relief agricultural terrain.

Ch05b.fm Page 463 Tuesday, December 11, 2001 11:13 AM

Multifrequency Land Clutter Modeling Information 463

15

Low-Relief Agricultural Terrain 0.0i° ≤ Depression Angle < 0.25i°

SD/Mean (dB)

10

5

VHF UHF L-Band S-Band X-Band Range Interval 1 Wide Pulse Narrow Pulse Regression Line

0

102

103

2

3

104

105

A

106

107

(m2)

NOTES: Each plotted symbol represents median values of SD/Mean and A over a group of similar patch measurements. A = r • ∆r • ∆θ r = range (data are separated into three range intervals: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km). ∆r = range resolution (data are wide pulse, i.e., 150 m, or narrow pulse, i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands ∆θ = one way 3 dB azimuth beamwidth (13 degrees at VHF, 5 degrees at UHF, 3 degrees at L-band, 1 degree at S- and X-bands) Each plot symbol can appear five times, once for each radar frequency, in order of decreasing frequency left-to-right as beam width increases. Little narrow pulse data is available in the third range interval.

Figure 5.21 Ratio of standard deviation-to-mean (SD/Mean) vs radar spatial resolution A for low-relief agricultural terrain with depression angle between 0.0 and 0.25 degrees.

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464 Multifrequency Land Clutter Modeling Information

0

Level Agricultural Terrain −10

° (dB) Mean Clutter Strength σw

−20

−30

−40

−50


= Depression Polarization

Angle (deg) 0.75 ≤
< 1.50 0.25 ≤
< 0.75 0.00 ≤
< 0.25 −0.25 ≤
< 0.00

−60

−70 0.1

1.0

HH VV

10.0

−80 VHF

UHF

L-Band

S-Band

X-Band

Frequency (GHz) NOTES: 1. Open symbols indicate results that may be atypical. 2. Within each of the five frequency bands, the horizontal displacement of the different colored plot symbols is just a convenient way to separate the various depression angle regimes to avoid overlapping plot symbols. This displacement does not imply a systematic in-band frequency shift with depression angle.

Figure 5.22 Mean clutter strength σ°w vs frequency for level agricultural terrain.

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Multifrequency Land Clutter Modeling Information 465

15

Level Agricultural Terrain 0.0i° ≤ Depression Angle < 0.25i°

SD/Mean (dB)

10

5

VHF UHF L-Band S-Band X-Band Range Interval 1 Wide Pulse Narrow Pulse Regression Line

0

102

103

2

3

104

105

106

107

A (m2) NOTES: Each plotted symbol represents median values of SD/Mean and A over a group of similar patch measurements. A = r • ∆r • ∆θ r = range (data are separated into three range intervals: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km). ∆r = range resolution (data are wide pulse, i.e., 150 m, or narrow pulse, i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands ∆θ = one way 3 dB azimuth beamwidth (13 degrees at VHF, 5 degrees at UHF, 3 degrees at L-band, 1 degree at S- and X-bands) Each plot symbol can appear five times, once for each radar frequency, in order of decreasing frequency left-to-right as beam width increases. Little narrow pulse data is available in the third range interval.

Figure 5.23 Ratio of standard deviation-to-mean (SD/Mean) vs radar spatial resolution A for level agricultural terrain with depression angle between 0.0 and 0.25 degrees.

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466 Multifrequency Land Clutter Modeling Information

0

High-Relief Forest −10

° (dB) Mean Clutter Strength σw

−20

−30

−40

−50


= Depression Angle (deg) 6.0 ≤
4.0 ≤
< 6.0 2.0 ≤
< 4.0 1.0 ≤
< 2.0 0.0 ≤
< 1.0 −1.0 ≤
< 0.0
< −1.0

−60

−70 0.1

Polarization HH VV

10.0

1.0

−80 VHF

UHF

L-Band

S-Band

X-Band

Frequency (GHz) NOTES: 1. Open symbols indicate results that may be atypical. 2. Within each of the five frequency bands, the horizontal displacement of the different colored plot symbols is just a convenient way to separate the various depression angle regimes to avoid overlapping plot symbols. This displacement does not imply a systematic in-band frequency shift with depression angle.

Figure 5.24 Mean clutter strength σ°w vs frequency for high-relief forest.

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Multifrequency Land Clutter Modeling Information 467

15

High-Relief Forest 2.0i° ≤ Depression Angle < 4.0i°

SD/Mean (dB)

10

5

VHF UHF L-Band S-Band Range Interval 1 Wide Pulse Narrow Pulse Regression Line

0

102

103

2

3

104

105

106

107

A (m2)

NOTES: Each plotted symbol represents median values of SD/Mean and A over a group of similar patch measurements. A = r • ∆r • ∆θ r = range (data are separated into three range intervals: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km). ∆r = range resolution (data are wide pulse, i.e., 150 m, or narrow pulse, i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands ∆θ = one way 3 dB azimuth beamwidth (13 degrees at VHF, 5 degrees at UHF, 3 degrees at L-band, 1 degree at S- and X-bands) Each plot symbol can appear five times, once for each radar frequency, in order of decreasing frequency left-to-right as beam width increases. Little narrow pulse data is available in the third range interval.

Figure 5.25 Ratio of standard deviation-to-mean (SD/Mean) vs radar spatial resolution A for high-relief forest with depression angle between 2.0 and 4.0 degrees.

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468 Multifrequency Land Clutter Modeling Information

0

Low-Relief Forest −10

Mean Clutter Strength σ°w (dB)

−20

−30

−40

−50


= Depression

Angle (deg) 4.00 ≤
1.50 ≤
< 4.00 0.75 ≤
< 1.50 0.25 ≤
< 0.75 0.00 ≤
< 0.25 −0.25 ≤
< 0.00 −0.75 ≤
< −0.25

−60

−70

0.1

1.0

Polarization HH VV

10.0

−80 VHF

UHF

L-Band

S-Band

X-Band

Frequency (GHz) NOTE: Within each of the five frequency bands, the horizontal displacement of the different colored plot symbols is just a convenient way to separate the various depression angle regimes to avoid overlapping plot symbols. This displacement does not imply a systematic in-band frequency shift with depression angle.

Figure 5.26 Mean clutter strength σ°w vs frequency for low-relief forest.

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Multifrequency Land Clutter Modeling Information 469

15 Low-Relief Forest 0.0i° ≤ Depression Angle < 0.25 °

SD/Mean (dB)

10

5

VHF UHF L-Band S-Band X-Band 1 Range Interval Wide Pulse Narrow Pulse Regression Line

0

102

103

2

3

104

105

A

106

107

(m2)

NOTES: Each plotted symbol represents median values of SD/Mean and A over a group of similar patch measurements. A = r • ∆r • ∆θ r = range (data are separated into three range intervals: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km). ∆r = range resolution (data are wide pulse, i.e., 150 m, or narrow pulse, i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands ∆θ = one way 3 dB azimuth beamwidth (13 degrees at VHF, 5 degrees at UHF, 3 degrees at L-band, 1 degree at S- and X-bands) Each plot symbol can appear five times, once for each radar frequency, in order of decreasing frequency left-to-right as beam width increases. Little narrow pulse data is available in the third range interval.

Figure 5.27 Ratio of standard deviation-to-mean (SD/Mean) vs radar spatial resolution A for low-relief forest with depression angle between 0.0 and 0.25 degrees.

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470 Multifrequency Land Clutter Modeling Information

0

High-Relief Shrubland −10

Mean Clutter Strength σ°w (dB)

−20

−30

−40

−50


= Depression Angle (deg) 1.0 ≤
< 2.0 0.0 ≤
< 1.0 1.0 ≤
< 0.0

−60

Polarization HH VV

−70 0.1

1.0

10.0

−80 VHF

UHF

L-Band

S-Band

X-Band

Frequency (GHz) NOTES: 1. Open symbols indicate results that may be atypical. 2. Within each of the five frequency bands, the horizontal displacement of the different colored plot symbols is just a convenient way to separate the various depression angle regimes to avoid overlapping plot symbols. This displacement does not imply a systematic in-band frequency shift with depression angle.

Figure 5.28 Mean clutter strength σ°w vs frequency for high-relief shrubland.

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Multifrequency Land Clutter Modeling Information 471

15

High-Relief Shrubland 0.0i° ≤ Depression Angle < 1.0i°

SD/Mean (dB)

10

5

VHF UHF L-Band S-Band X-Band Range Interval 1 Wide Pulse Narrow Pulse Regression Line

0

102

103

2

3

104

105

106

107

A (m2)

NOTES: Each plotted symbol represents median values of SD/Mean and A over a group of similar patch measurements. A = r • ∆r • ∆θ r = range (data are separated into three range intervals: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km). ∆r = range resolution (data are wide pulse, i.e., 150 m, or narrow pulse, i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands ∆θ = one way 3 dB azimuth beamwidth (13 degrees at VHF, 5 degrees at UHF, 3 degrees at L-band, 1 degree at S- and X-bands) Each plot symbol can appear five times, once for each radar frequency, in order of decreasing frequency left-to-right as beam width increases. Little narrow pulse data is available in the third range interval.

Figure 5.29 Ratio of standard deviation-to-mean (SD/Mean) vs radar spatial resolution A for high-relief shrubland with depression angle between 0.0 and 1.0 degrees.

Ch05b.fm Page 472 Tuesday, December 11, 2001 11:13 AM

472 Multifrequency Land Clutter Modeling Information

0

Low-Relief Shrubland −10

° (dB) Mean Clutter Strength σw

−20

−30

−40

−50


= Depression

Angle (deg) 1.50 ≤
< 4.00 0.75 ≤
< 1.50 0.25 ≤
< 0.75 0.00 ≤
< 0.25 −0.25 ≤
< 0.00

−60

−70 0.1

1.0

Polarization HH VV

10.0

−80 VHF

UHF

L-Band

S-Band

X-Band

Frequency (GHz)

NOTES: 1. Open symbols indicate results that may be atypical. 2. Within each of the five frequency bands, the horizontal displacement of the different colored plot symbols is just a convenient way to separate the various depression angle regimes to avoid overlapping plot symbols. This displacement does not imply a systematic in-band frequency shift with depression angle.

Figure 5.30 Mean clutter strength σ°w vs frequency for low-relief shrubland.

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Multifrequency Land Clutter Modeling Information 473

15

Low-Relief Shrubland 0.25i° ≤ Depression Angle < 0.75i°

SD/Mean (dB)

10

5

VHF UHF L-Band S-Band X-Band 1 Range Interval Wide Pulse Narrow Pulse Regression Line

0

102

103

2

3

104

105

A

106

107

(m2)

NOTES: Each plotted symbol represents median values of SD/Mean and A over a group of similar patch measurements. A = r • ∆r • ∆θ r = range (data are separated into three range intervals: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km). ∆r = range resolution (data are wide pulse, i.e., 150 m, or narrow pulse, i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands ∆θ = one way 3 dB azimuth beamwidth (13 degrees at VHF, 5 degrees at UHF, 3 degrees at L-band, 1 degree at S- and X-bands) Each plot symbol can appear five times, once for each radar frequency, in order of decreasing frequency left-to-right as beam width increases. Little narrow pulse data is available in the third range interval.

Figure 5.31 Ratio of standard deviation-to-mean (SD/Mean) vs radar spatial resolution A for low-relief shrubland with depression angle between 0.25 and 0.75 degrees.

Ch05b.fm Page 474 Tuesday, December 11, 2001 11:13 AM

474 Multifrequency Land Clutter Modeling Information

0

High-Relief Grassland −10

Mean Clutter Strength σ°w (dB)

−20

−30

−40

−50


= Depression

Polarization HH VV

Angle (deg) 2.0 ≤
< 4.0 1.0 ≤
< 2.0 0.0 ≤
< 1.0 −1.0 ≤
< 0.0

−60

−70 0.1

1.0

10.0

−80 VHF

UHF

L-Band

S-Band

X-Band

Frequency (GHz) NOTES: 1. Open symbols indicate results that may be atypical. 2. Within each of the five frequency bands, the horizontal displacement of the different colored plot symbols is just a convenient way to separate the various depression angle regimes to avoid overlapping plot symbols. This displacement does not imply a systematic in-band frequency shift with depression angle.

Figure 5.32 Mean clutter strength σ°w vs frequency for high-relief grassland.

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Multifrequency Land Clutter Modeling Information 475

15 High-Relief Grassland 0.0i° ≤ Depression Angle < 1.0i°

SD/Mean (dB)

10

5

VHF UHF L-Band S-Band X-Band Range Interval 1 Wide Pulse Narrow Pulse Regression Line

0

102

103

2

3

104

105

A

106

107

(m2)

NOTES: Each plotted symbol represents median values of SD/Mean and A over a group of similar patch measurements. A = r • ∆r • ∆θ r = range (data are separated into three range intervals: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km). ∆r = range resolution (data are wide pulse, i.e., 150 m, or narrow pulse, i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands ∆θ = one way 3 dB azimuth beamwidth (13 degrees at VHF, 5 degrees at UHF, 3 degrees at L-band, 1 degree at S- and X-bands) Each plot symbol can appear five times, once for each radar frequency, in order of decreasing frequency left-to-right as beam width increases. Little narrow pulse data is available in the third range interval.

Figure 5.33 Ratio of standard deviation-to-mean (SD/Mean) vs radar spatial resolution A for high-relief grassland with depression angle between 0.0 and 1.0 degrees.

Ch05b.fm Page 476 Tuesday, December 11, 2001 11:13 AM

476 Multifrequency Land Clutter Modeling Information

0

Low-Relief Grassland −10

Mean Clutter Strength σ°w (dB)

−20

−30

−40

−50


= Depression

Angle (deg) 1.50 ≤
< 4.00 0.75 ≤
< 1.50 0.25 ≤
< 0.75 0.00 ≤
< 0.25 −0.25 ≤
< 0.00 −0.75 ≤
< −0.25

−60

−70 0.1

1.0

Polarization HH VV

10.0

−80 VHF

UHF

L-Band

S-Band

X-Band

Frequency (GHz) NOTES: 1. Open symbols indicate results that may be atypical. 2. Within each of the five frequency bands, the horizontal displacement of the different colored plot symbols is just a convenient way to separate the various depression angle regimes to avoid overlapping plot symbols. This displacement does not imply a systematic in-band frequency shift with depression angle.

Figure 5.34 Mean clutter strength σ°w vs frequency for low-relief grassland.

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Multifrequency Land Clutter Modeling Information 477

15

Low-Relief Grassland 0.0i° ≤ Depression Angle < 0.25i°

SD/Mean (dB)

10

5

VHF UHF L-Band S-Band X-Band 1 Range Interval Wide Pulse Narrow Pulse Regression Line

0

102

103

2

3

104

105

106

107

A (m2) NOTES: Each plotted symbol represents median values of SD/Mean and A over a group of similar patch measurements. A = r • ∆r • ∆θ r = range (data are separated into three range intervals: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km). ∆r = range resolution (data are wide pulse, i.e., 150 m, or narrow pulse, i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands ∆θ = one way 3 dB azimuth beamwidth (13 degrees at VHF, 5 degrees at UHF, 3 degrees at L-band, 1 degree at S- and X-bands) Each plot symbol can appear five times, once for each radar frequency, in order of decreasing frequency left-to-right as beam width increases. Little narrow pulse data is available in the third range interval.

Figure 5.35 Ratio of standard deviation-to-mean (SD/Mean) vs radar spatial resolution A for low-relief grassland with depression angle between 0.0 and 0.25 degrees.

Ch05b.fm Page 478 Tuesday, December 11, 2001 11:13 AM

478 Multifrequency Land Clutter Modeling Information

0

Wetland −10

Mean Clutter Strength σ°w (dB)

−20

−30

−40

−50


= Depression Angle (deg) 0.25 ≤
< 0.75 0.00 ≤
< 0.25

−60

Polarization HH VV

−70

0.1

1.0

10.0

−80

VHF

UHF

L-Band

S-Band

X-Band

Frequency (GHz) NOTE: Within each of the five frequency bands, the horizontal displacement of the different colored plot symbols is just a convenient way to separate the various depression angle regimes to avoid overlapping plot symbols. This displacement does not imply a systematic in-band frequency shift with depression angle.

Figure 5.36 Mean clutter strength σ°w vs frequency for wetland.

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Multifrequency Land Clutter Modeling Information 479

15

Wetland 0.0i° ≤ Depression Angle < 0.25i°

SD/Mean (dB)

10

5

VHF UHF L-Band S-Band X-Band Range Interval Wide Pulse Narrow Pulse Regression Line

0

102

1

103

2

3

104

105

106

107

A (m2)

NOTES: Each plotted symbol represents median values of SD/Mean and A over a group of similar patch measurements. A = r • ∆r • ∆θ r = range (data are separated into three range intervals: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km). ∆r = range resolution (data are wide pulse, i.e., 150 m, or narrow pulse, i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands ∆θ = one way 3 dB azimuth beamwidth (13 degrees at VHF, 5 degrees at UHF, 3 degrees at L-band, 1 degree at S- and X-bands) Each plot symbol can appear five times, once for each radar frequency, in order of decreasing frequency left-to-right as beam width increases. Little narrow pulse data is available in the third range interval.

Figure 5.37 Ratio of standard deviation-to-mean (SD/Mean) vs radar spatial resolution A for wetland with depression angle between 0.0 and 0.25 degrees.

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480 Multifrequency Land Clutter Modeling Information

0

High-Relief Desert −10

Mean Clutter Strength σ°w (dB)

−20

−30

−40

−50


= Depression Angle (deg) 4.0 ≤
< 6.0 2.0 ≤
< 4.0 1.0 ≤
< 2.0 0.0 ≤
< 1.0 −1.0 ≤
< 0.0
< −1.0

−60

−70

0.1

1.0

Polarization HH VV

10.0

−80

VHF

UHF

L-Band

S-Band

X-Band

Frequency (GHz) NOTES: 1. Open symbols indicate results that may be atypical. 2. Within each of the five frequency bands, the horizontal displacement of the different colored plot symbols is just a convenient way to separate the various depression angle regimes to avoid overlapping plot symbols. This displacement does not imply a systematic in-band frequency shift with depression angle.

Figure 5.38 Mean clutter strength σ°w vs frequency for high-relief desert.

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Multifrequency Land Clutter Modeling Information 481

15

High-Relief Desert –1.0i° ≤ Depression Angle < 0.0i°

SD/Mean (dB)

10

5

VHF UHF L-Band S-Band X-Band 1 Range Interval Wide Pulse Narrow Pulse Regression Line

0

102

103

2

3

104

105

A

106

107

(m2)

NOTES: Each plotted symbol represents median values of SD/Mean and A over a group of similar patch measurements. A = r • ∆r • ∆θ r = range (data are separated into three range intervals: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km). ∆r = range resolution (data are wide pulse, i.e., 150 m, or narrow pulse, i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands ∆θ = one way 3 dB azimuth beamwidth (13 degrees at VHF, 5 degrees at UHF, 3 degrees at L-band, 1 degree at S- and X-bands) Each plot symbol can appear five times, once for each radar frequency, in order of decreasing frequency left-to-right as beam width increases. Little narrow pulse data is available in the third range interval.

Figure 5.39 Ratio of standard deviation-to-mean (SD/Mean) vs radar spatial resolution A for high-relief desert with depression angle between –1.0 and 0.0 degrees.

Ch05b.fm Page 482 Tuesday, December 11, 2001 11:13 AM

482 Multifrequency Land Clutter Modeling Information

0

Low-Relief Desert −10

Mean Clutter Strength σ°w (dB)

−20

−30

−40

−50


= Depression

Angle (deg) 1.50 ≤
< 4.00 0.75 ≤
< 1.50 0.25 ≤
< 0.75 0.00 ≤
< 0.25 −0.25 ≤
< 0.00 −0.75 ≤
< −0.25

−60

−70 0.1

1.0

Polarization HH VV

10.0

−80 VHF

UHF

L-Band

S-Band

X-Band

Frequency (GHz) NOTES: 1. Open symbols indicate results that may be atypical. 2. Within each of the five frequency bands, the horizontal displacement of the different colored plot symbols is just a convenient way to separate the various depression angle regimes to avoid overlapping plot symbols. This displacement does not imply a systematic in-band frequency shift with depression angle.

Figure 5.40 Mean clutter strength σ°w vs frequency for low-relief desert.

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Multifrequency Land Clutter Modeling Information 483

15 Low-Relief Desert 0.0 ° ≤ Depression Angle < 0.25 °

SD/Mean (dB)

10

5

VHF UHF L-Band S-Band X-Band Range Interval 1 Wide Pulse Narrow Pulse Regression Line

0

102

103

2

3

104

105

A

106

107

(m2)

NOTES: Each plotted symbol represents median values of SD/Mean and A over a group of similar patch measurements. A = r • ∆r • ∆θ r = range (data are separated into three range intervals: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km). ∆r = range resolution (data are wide pulse, i.e., 150 m, or narrow pulse, i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands ∆θ = one way 3 dB azimuth beamwidth (13 degrees at VHF, 5 degrees at UHF, 3 degrees at L-band, 1 degree at S- and X-bands) Each plot symbol can appear five times, once for each radar frequency, in order of decreasing frequency left-to-right as beam width increases. Little narrow pulse data is available in the third range interval.

Figure 5.41 Ratio of standard deviation-to-mean (SD/Mean) vs radar spatial resolution A for low-relief desert with depression angle between 0.0 and 0.25 degrees.

Ch05b.fm Page 484 Tuesday, December 11, 2001 11:13 AM

484 Multifrequency Land Clutter Modeling Information

0

Level Desert −10

Mean Clutter Strength σ°w (dB)

−20

−30

−40

−50


= Depression

Angle (deg) 1.50 ≤
< 4.00 0.75 ≤
< 1.50 0.25 ≤
< 0.75 0.00 ≤
< 0.25 −0.25 ≤
< 0.00 −0.75 ≤
< −0.25

−60

−70 0.1

1.0

Polarization HH VV

10.0

−80 VHF

UHF

L-Band

S-Band

X-Band

Frequency (GHz) NOTES: 1. Open symbols indicate results that may be atypical. 2. Within each of the five frequency bands, the horizontal displacement of the different colored plot symbols is just a convenient way to separate the various depression angle regimes to avoid overlapping plot symbols. This displacement does not imply a systematic in-band frequency shift with depression angle.

Figure 5.42 Mean clutter strength σ°w vs frequency for level desert.

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Multifrequency Land Clutter Modeling Information 485

15

Level Desert 0.0i° ≤ Depression Angle < 0.25i°

SD/Mean (dB)

10

5

VHF UHF L-Band S-Band X-Band 1 Range Interval Wide Pulse Narrow Pulse Regression Line

0

102

103

2

3

104

105

106

107

A (m2)

NOTES: Each plotted symbol represents median values of SD/Mean and A over a group of similar patch measurements. A = r • ∆r • ∆θ r = range (data are separated into three range intervals: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km). ∆r = range resolution (data are wide pulse, i.e., 150 m, or narrow pulse, i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands ∆θ = one way 3 dB azimuth beamwidth (13 degrees at VHF, 5 degrees at UHF, 3 degrees at L-band, 1 degree at S- and X-bands) Each plot symbol can appear five times, once for each radar frequency, in order of decreasing frequency left-to-right as beam width increases. Little narrow pulse data is available in the third range interval.

Figure 5.43 Ratio of standard deviation-to-mean (SD/Mean) vs radar spatial resolution A for level desert with depression angle between 0.0 and 0.25 degrees.

Ch05b.fm Page 486 Tuesday, December 11, 2001 11:13 AM

486 Multifrequency Land Clutter Modeling Information

0

Mountains −10

Mean Clutter Strength σ°w (dB)

−20

−30

−40

−50


= Depression Angle (deg) 6.0 ≤
4.0 ≤
< 6.0 2.0 ≤
< 4.0 1.0 ≤
< 2.0 0.0 ≤
< 1.0 −1.0 ≤
< 0.0
< −1.0

−60

−70 0.1

1.0

Polarization HH VV

10.0

−80 VHF

UHF

L-Band

S-Band

X-Band

Frequency (GHz) NOTES: 1. Open symbols indicate results that may be atypical. 2. Within each of the five frequency bands, the horizontal displacement of the different colored plot symbols is just a convenient way to separate the various depression angle regimes to avoid overlapping plot symbols. This displacement does not imply a systematic in-band frequency shift with depression angle.

Figure 5.44 Mean clutter strength σ°w vs frequency for mountain terrain.

Ch05b.fm Page 487 Tuesday, December 11, 2001 11:13 AM

Multifrequency Land Clutter Modeling Information 487

15

Mountains 2.0 ° ≤ Depression Angle < 4.0 °

SD/Mean (dB)

10

5

VHF UHF L-Band S-Band Range Interval 1 Wide Pulse Narrow Pulse Regression Line

0

102

103

2

3

104

105

A

106

107

(m2)

NOTES: Each plotted symbol represents median values of SD/Mean and A over a group of similar patch measurements. A = r • ∆r • ∆θ r = range (data are separated into three range intervals: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km). ∆r = range resolution (data are wide pulse, i.e., 150 m, or narrow pulse, i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands ∆θ = one way 3 dB azimuth beamwidth (13 degrees at VHF, 5 degrees at UHF, 3 degrees at L-band, 1 degree at S- and X-bands) Each plot symbol can appear five times, once for each radar frequency, in order of decreasing frequency left-to-right as beam width increases. Little narrow pulse data is available in the third range interval.

Figure 5.45 Ratio of standard deviation-to-mean (SD/Mean) vs radar spatial resolution A for mountain terrain with depression angle between 2.0 and 4.0 degrees.

Ch05b.fm Page 488 Tuesday, December 11, 2001 11:13 AM

488 Multifrequency Land Clutter Modeling Information

0 Long-Range Mountains −10

Mean Clutter Strength σ°w (dB)

−20

−30

−40

−50 α = Depression Angle (deg) −1.6 ≤ α < −0.75

−60

Polarization HH VV

−70 0.1

1.0

10.0

−80 VHF

UHF

L-Band

S-Band

X-Band

Frequency (GHz) Figure 5.46 Mean clutter strength σ°w vs frequency for long-range mountain terrain.

Ch05b.fm Page 489 Tuesday, December 11, 2001 11:13 AM

Multifrequency Land Clutter Modeling Information 489

15

Long-Range Mountains −1.6i° ≤ Depression Angle < −0.75i°

SD/Mean (dB)

10

5

VHF UHF L-Band S-Band X-Band Range Interval 1 Wide Pulse Narrow Pulse Regression Line

0

102

103

2

3

104

105

A

106

107

(m2)

NOTES: Each plotted symbol represents median values of SD/Mean and A over a group of similar patch measurements. A = r • ∆r • ∆θ r = range (data are separated into three range intervals: interval 1, 1 to 11.3 km; interval 2, 11.3 to 35.7 km; interval 3, range > 35.7 km). ∆r = range resolution (data are wide pulse, i.e., 150 m, or narrow pulse, i.e., 36 m at VHF and UHF, 15 m at L-, S-, and X-bands ∆θ = one way 3 dB azimuth beamwidth (13 degrees at VHF, 5 degrees at UHF, 3 degrees at L-band, 1 degree at S- and X-bands) Each plot symbol can appear five times, once for each radar frequency, in order of decreasing frequency left-to-right as beam width increases. Little narrow pulse data is available in the third range interval.

Figure 5.47 Ratio of standard deviation-to-mean (SD/Mean) vs radar spatial resolution A for long-range mountain terrain with depression angle between –1.6 and –0.75 degrees.

Ch05b.fm Page 490 Tuesday, December 11, 2001 11:13 AM

490 Multifrequency Land Clutter Modeling Information

Measured

— 70

Modeled

— 60 — 50 — 40

— 30

— 20

σ°F4 (dB) Figure 5.48 Comparison of measured and modeled PPI ground clutter maps at Brazeau, Alta. Maximum range = 24 km. X-band, 150-m range resolution, horizontal polarization.

Multifrequency Land Clutter Modeling Information 491

Table 5.15 Shape Parameter aw and Ratios of Standard Deviation-to-Mean (SD/Mean) and Meanto-Median for Urban or Built-up Terrain, by Spatial Resolution A and Depression Angle*


= Depression Angle (degrees)

Weibull Shape Parameter aw from SD/Mean

from Mean/Median

A = 103m2

A = 106m2

A = 103m2

A = 106m2

4.00 ≤


---

---

---

---

1.50 ≤
< 4.00

4.6

1.7a

3.4

2.0a

0.75 ≤
< 1.50

4.7

1.5

4.5

1.8

0.25 ≤
< 0.75

3.3

1.9

3.5

2.0

0.00 ≤
< 0.25

3.8

2.0

4.3

2.1

-0.25 ≤
< 0.00

3.3b

1.8

4.1b

1.8


< -0.25

---

---

---

---

Ratios


= Depression Angle (degrees)

SD/Mean (dB) A = 103m2

A = 106m2

Mean/Median (dB) A = 103m2

A = 106m2

4.00 ≤


---

---

---

---

1.50 ≤
< 4.00

10.9

2.7a

15.6

6.2a

0.75 ≤
< 1.50

11.0

1.8

24.5

5.0

0.25 ≤
< 0.75

7.2

3.2

16.3

6.5

0.00 ≤
< 0.25

8.5

3.5

22.3

6.5

-0.25 ≤
< 0.00

7.2b

2.9

21.3b

5.2


< -0.25

---

---

---

---

a Footnoted values apply at A = 105 m2, not 106 m2. b 4 2 3 2

M l

Footnoted values apply at A = 10 m , not 10 m .

* Table 5.13 defines the population of terrain patches and measurements upon which these data are based.

The major parametric variation of aw in Table 5.15 is with radar spatial resolution. In every case, aw is much greater at 103 m2 resolution than at 106 m2 resolution. At low depression angle (i.e., 0° to 0.25°), Table 5.15 indicates that spreads in urban terrain, although high, are not unusually high compared to many other terrain types. However, most terrain types show significantly smaller spreads at high depression angle. In contrast, Table 5.15 indicates that in urban terrain at high spatial resolution (i.e., A = 103 m2), spreads remain high at high depression angle. Each pair of aw numbers in Table 5.15 comes from a scatter plot of spread vs spatial resolution. The standard deviation-to-mean scatter plot for the 0° to 0.25° depression angle regime in Table 5.15 is shown in Figure 5.17. The main trend in Figure 5.17 is decreasing spread with decreasing resolution. In the wide pulse data in the lower frequency bands, spreads in the first range interval are less than in the second and third range intervals, contrary to expectation. This tendency is not borne out in the narrow pulse data.

492 Multifrequency Land Clutter Modeling Information

5.4.2 Agricultural Terrain As in urban terrain, the dominant clutter sources in agricultural terrain are often specific discrete vertical objects associated with man’s use of the land. Clutter strengths can depend quite specifically on what particular discretes exist and how they are distributed over a clutter patch. Unlike urban terrain, however, in agricultural terrain the occasional (e.g., 20% incidence) strong isolated discrete cells occur in a weakly scattering background. Many of the strong cells occur in definite, culturally determined, spatial patterns. Thus farmland clutter is quite a different, more heterogeneous, statistical random process than clutter from terrain with more natural land cover—for example, forest. Furthermore, multipath exists in many of the Phase One farmland clutter measurements to cause additional specific variations in clutter strength through the propagation factor, depending on the specific variations of terrain elevation involved (see Section 3.4.1.4). As a result of this multifold specificity affecting clutter strengths in agricultural terrain, more measurements are required to establish generality in agricultural terrain than in more homogeneous terrain such as forest. As shown in Table 5.16, the farmland clutter modeling information of Section 5.4.2 is based on 10,357 measured clutter histograms Table 5.16 Numbers of Terrain Patches and Measured Clutter Histograms for Agricultural Terrain, by Relief and Depression Anglea,b,c

Terrain Relief

␣ = Depression Angle

Number of Patches

Number of Measurements

4.0 ≤ ␣

0

0

2.0 ≤ ␣ < 4.0

1

23

1.0 ≤ ␣ < 2.0

4

72

0.0 ≤ ␣ < 1.0

6

95

-1.0 ≤ ␣ < 0.0

9

60

␣ < -1.0

0

0

Totals

20

250

4.00 ≤ ␣

0

0

1.50 ≤ ␣ < 4.00

22

681

0.75 ≤ ␣ < 1.50

65

2,505

0.25 ≤ ␣ < 0.75

131

2,987

0.00 ≤ ␣ < 0.25

161

2,334

-0.25 ≤ ␣ < 0.00

111

1,452

-0.75 ≤ ␣ < -0.25

15

148

High-relief

Low-relief

(degrees)

␣ < -0.75 Totals Grand Totals

0

0

505

10,107

525

10,357

a A single (primary) classifier only is sufficient to describe these patches. 2 b A terrain patch is a land surface macroregion usually several kms on a side (median patch area = 12.62 km ). c A measured clutter histogram contains all of the temporal (pulse by pulse) and spatial (resolution cell by resolution cell) clutter samples obtained in a given measurement of a terrain patch. A terrain patch was usually measured many times (nominally 20) as RF frequency (5), polarization (2), and range resolution (2) were varied over the Phase One radar parameter matrix.

Multifrequency Land Clutter Modeling Information 493

from 525 clutter patches. These results come from 30 measurement sites. These are the largest numbers of measurements, patches, and sites among the eight specific terrain types of Section 5.4. In what follows, multifrequency clutter coefficients are presented for agricultural terrain in three regimes of relief: (1) high-relief, (2) low-relief, and (3) level.

Seasonal Effects. Agricultural terrain is primarily cropland. The status of the crops in the fields depends upon season. During summer season, changes from before to after harvest occur. During winter season, cropland fields are generally fallow or stubble, often with various degrees of snow cover. Approximately 45% of the clutter measurements occurred in winter season. Perhaps surprisingly, farmland clutter is not highly sensitive to the changing seasonal status of the fields because it is dominated by isolated discrete sources that exist independent of season. The field surfaces contribute to low-level background clutter whatever their seasonal status. Seasonal variations in the land clutter measurements, including agricultural terrain, are discussed in Chapters 2 and 3. Since general seasonal effects in land clutter are small, the clutter modeling information presented in Chapter 5 does not include season as a parametric dimension. 5.4.2.1 High-Relief Agricultural Terrain Trends in σ w° . Table 5.17 presents mean clutter strength for high-relief agricultural terrain by frequency band, polarization, and depression angle and includes the number of measurements upon which each value of σ w° is based. Relatively little Phase One measurement data exists for high-relief agricultural terrain—just 250 measured clutter histograms from 20 clutter patches at eight measurement sites. The primary reason for this sparsity of data is that little high-relief farmland exists; farm machinery cannot easily access high-relief terrain. The σ w° data of Table 5.17 are plotted in Figure 5.18. Except for the uncertain outliers plotted as open symbols, the data of Figure 5.18 lie largely in the –29- to –36-dB range without major trends with frequency or depression angle. At first consideration, the cluster of L-band results appears 3 or 4 dB stronger than the other bands; however, the more reliable cyan (0° to 1°) results do not show stronger σ w° at L-band. In these results, σ w° at vertical polarization is usually several decibels stronger than at horizontal polarization.

Uncertain Outliers. Now consider the uncertain outliers in the σ w° results for highrelief agricultural terrain of Table 5.17. These uncertain results are plotted as open plot symbols in Figure 5.18. Within these uncertain outlier results in high-relief agricultural terrain, three particular clutter patch measurements are discussed. Two of these patch measurements involve borderline-high incidences of trees occurring within patches classified as pure farmland terrain causing stronger than expected outlier values of σ w° ; and one patch measurement involves a terrain inclination away from the radar causing a weaker than expected outlier value of σ w° . First consider the very strong, green (0° to –1°) results at VHF in Figure 5.18. These results are dominated by one strong clutter patch, viz., patch 37 at the Penhold measurement site in Alberta. This patch is classified as pure farmland, although with ~10% tree cover. These patch 37 σ w° results agree very closely with corresponding results (not shown here) at VHF for high-relief mixed terrain classified as open/forest, these latter results being based on a large number of measurements. Thus it would appear that patch 37 at Penhold may have been more appropriately classified as mixed terrain with a secondary component of

494 Multifrequency Land Clutter Modeling Information

Table 5.17 Mean Clutter Strength σ w° and Number of Measurements for High-Relief Agricultural Terrain, by Frequency Band, Polarization, and Depression Anglea Weibull Mean Clutter Strength σ°w (dB)

␣ = Depression Angle (degrees)

VHF

L-Band

S-Band

X-Band

VV

HH

VV

HH

VV

HH

VV

HH

VV

4.0 ≤ ␣

----

----

----

----

----

----

----

----

----

----

2.0 ≤ ␣ < 4.0

-36.0

-34.4

-26.1

-22.8

-31.3

-26.7

----

----

----

----

1.0 ≤ ␣ < 2.0

-50.2

-46.1

-33.4

-35.9

-29.0

-25.3

-46.8

-43.8

-38.9

-34.6

0.0 ≤ ␣ < 1.0

-35.9

-31.9

-32.2

-30.4

-31.4

-31.9

-32.5

-30.3

-31.3

-29.2

-1.0 ≤ ␣ < 0.0

-19.9

-14.1

-34.5

-30.7

-27.7

-28.6

-34.8

-32.8

-33.6

-32.0

␣ < -1.0

----

----

----

----

----

----

----

----

----

----

Number of Measurements

␣ = Depression

UHF

VHF

Angle (degrees)

a

UHF

HH

L-Band

S-Band

X-Band

HH

VV

HH

VV

HH

VV

HH

VV

HH

VV

4.0 ≤ ␣

0

0

0

0

0

0

0

0

0

0

2.0 ≤ ␣ < 4.0

4

3

4

4

4

4

0

0

0

0

1.0 ≤ ␣ < 2.0

7

5

7

8

6

7

8

8

8

8

0.0 ≤ ␣ < 1.0

5

7

12

12

10

9

9

9

11

11

-1.0 ≤ ␣ < 0.0

3

3

9

9

5

5

4

4

9

9

␣ < -1.0

0

0

0

0

0

0

0

0

0

0

TOTAL

19

18

32

33

25

25

21

21

28

28

Table 5.16 defines the population of terrain patches upon which these data are based.

forest. Misclassification of occasional single patches is usually of little consequence in the general (i.e., medianized) results of Chapter 5 that are more typically based on measurements from many patches. Next, consider the relatively strong, purple (2° to 4°) results at UHF in Figure 5.18. These results are based on measurements from one clutter patch, viz., patch 30 at the Polonia measurement site in Manitoba. Again, this patch is classified as pure farmland with ~10% tree cover. Comparison with other results indicates that the clutter from patch 30 at Polonia was also very likely dominated by trees. That is, patch 30 at Polonia may also have been more appropriately classified as mixed open/forest. Most farmland has some small incidence of occurrence of trees. The percentage incidence at which trees begin to dominate the backscatter from farmland landscapes can be quite low. The results from these two patches show the importance in clutter prediction of accurately depicting the relative proportion of trees on generally open landscapes. Finally, consider the relatively weak, dark blue (1° to 2°) results at VHF, S-, and X-band in Figure 5.18. These results are based almost entirely on three clutter patches, and, at S- and X-bands, on just two clutter patches. One of these patches, viz., patch 12 at the Magrath measurement site in Alberta, was relatively weak in all bands. Patch 12 was at close range (1.2 to 2.2 km) on the side of the slope at the top of which the Phase One radar was situated,

Multifrequency Land Clutter Modeling Information 495

and as a result may be weak due to its outward inclination and/or due to it being borderlineshadowed by intervening higher terrain (brow-of-hill effect; see Appendix 4.B). More measurements were made from patch 12 than the other contributing patches in the dark blue (1° to 2°) results in Figure 5.18 at VHF, S-, and X-band—hence the median result from the set is low in these bands. In contrast, more measurements were made from the other two contributing patches than from patch 12 at UHF and L-band—hence the median results from these sets are higher and in line with the data from the other depression angle regimes in Figure 5.18. It is evident from such considerations that caution must be exercised in using any Chapter 5 open-symbol results based on sparse data.

Shape Parameter aw. Table 5.18 presents the Weibull shape parameter aw and ratios of standard deviation-to-mean and mean-to-median for clutter amplitude distributions in highrelief agricultural terrain by depression angle and radar spatial resolution. The statistical populations underlying the data of Table 5.18 are shown in Table 5.16. Table 5.18 shows that very large values of spread occur in spatial clutter amplitude distributions at low angles and high resolution in high-relief agricultural terrain. In every case, aw is greater at 103 m2 resolution than at 106 (or 105) m2 resolution. At the higher resolution of 103 m2, aw also strongly depends on depression angle. In high-relief agricultural terrain, aw at high Table 5.18 Shape Parameter aw and Ratios of Standard Deviation-to-Mean (SD/Mean) and Meanto-Median for High-Relief Agricultural Terrain, by Spatial Resolution A and Depression Angle*

␣ = Depression Angle (degrees)

Weibull Shape Parameter aw from SD/Mean

from Mean/Median

A = 103m2

A = 106m2

A = 103m2

A = 106m2

---

---

---

---

2.0 ≤ ␣ < 4.0

3.3

2.1a

3.1

2.1a

1.0 ≤ ␣ < 2.0

3.9

1.6

4.7

2.0a

4.0 ≤ ␣

0.0 ≤ ␣ < 1.0

5.8

1.6

4.8

2.1

-1.0 ≤ ␣ < 0.0

2.6

2.1

3.8

2.4

␣ < -1.0

---

---

---

---

Ratios

␣ = Depression Angle (degrees)

SD/Mean (dB) A = 103m2

a *

A = 106m2

Mean/Median (dB) A = 103m2

A = 106m2

4.0 ≤ ␣

---

---

---

---

2.0 ≤ ␣ < 4.0

7.2

3.8a

13.2

6.9a

1.0 ≤ ␣ < 2.0

9.0

2.3

26.4

5.9a

0.0 ≤ ␣ < 1.0

14.1

2.2

27.2

6.5

-1.0 ≤ ␣ < 0.0

5.3

3.8

18.7

8.4

␣ < -1.0

---

---

---

---

Footnoted values apply at A = 105 m2, not 106 m2.

Table 5.16 defines the population of terrain patches and measurements upon which these data are based.

496 Multifrequency Land Clutter Modeling Information

resolution decreases strongly from large values at grazing incidence (i.e., 0° to 1°) to much smaller values at higher angles (e.g., 2° to 4°). Therefore, modeling of clutter from highrelief agricultural terrain must be done in narrow regimes of depression angle to accommodate this strong trend of decreasing spread in clutter amplitude distributions with increasing angle of illumination, even though mean clutter strengths in high-relief agricultural terrain are relatively insensitive to angle of illumination. Each pair of aw numbers in Table 5.18 comes from a scatter plot of spread vs spatial resolution. The standard deviation-to-mean scatter plot for the 1° to 2° depression angle regime in Table 5.18 is shown in Figure 5.19. The data in Figure 5.19 show a strong trend of decreasing spread with decreasing resolution (i.e., increasing A). Note that all of the results in Figure 5.19 happen to come from the first range interval, 1 to 11.3 km. As a result, it is easier to follow the variations with frequency and pulse length in this figure than in many of the similar scatter plots in Chapter 5. Further note that although the measured data extend only to A ≅ 105 m 2 in Figure 5.19, it is reasonable to extend the regression line to A = 106 m2; indeed, this was done to provide the sd/mean based results at A = 106 m2 for the 1° to 2° depression angle interval in Table 5.18. However, for the corresponding mean/ median scatter plot, it was not reasonable to extend the regression line to A = 106 m2; hence the mean/median based results are shown at A = 105 m2, not A = 106 m2, for the 1° to 2° depression angle regime in Table 5.18.

5.4.2.2 Low-Relief Agricultural Terrain Trends in σ w° . Table 5.19 presents mean clutter strength σ w° for low-relief agricultural terrain by frequency band, polarization, and depression angle and includes the number of measurements upon which each value of σ w° is based. These results are based on a very large amount of Phase One measurement data—10,107 measured clutter histograms from 505 clutter patches; see Table 5.16. These measurements come from 30 sites. The σ w° data of Table 5.19 are plotted in Figure 5.20. The main parametric trend observed in Figure 5.20 is that σ w° increases significantly—by about 10 dB—with increasing frequency, VHF through L-band, then levels off, L-band through X-band. Weaker values of σ w° at VHF and UHF are due to multipath loss from forward reflections on generally open, low-relief, agricultural terrain. At the lower frequencies, the multipath lobes on the elevation pattern are broad, and returns from clutter sources are typically received at reduced gain well on the underside of the first multipath lobe. At the higher frequencies, the multipath lobes are narrower and clutter sources tend to be more fully illuminated. The details of the multipath depend on the terrain between the clutter patch and the radar. Some patches will experience more multipath loss and some less (see Section 3.4.1.4). Figure 5.20 shows medianized results from many measurements in generally low-relief agricultural terrain. The σ w° results of Figure 5.20 show little variation with depression angle. The results at Xband form a very tight cluster. The results from L-band through X-band are remarkably invariant with both frequency and depression angle, all largely in the –29 dB to –33 dB range. At first consideration, the results at UHF appear to show increasing σ w° with increasing positive depression angle. However, further consideration of these UHF data reveals that, in the cyan, 0° to 0.25° results, large multipath loss exists, as large as that which exists in the cyan results at VHF, but in the dark blue, purple, and magenta, higher

Multifrequency Land Clutter Modeling Information 497

Table 5.19 Mean Clutter Strength σ w° and Number of Measurements for Low-Relief Agricultural Terrain, by Frequency Band, Polarization, and Depression Anglea

Weibull Mean Clutter Strength σ°w (dB)

␣ = Depression VHF

Angle (degrees) HH

VV

HH

VV

HH

S-Band

VV

HH

X-Band

VV

HH

VV

4.0 ≤ ␣

----

----

----

----

----

----

----

----

----

----

1.50 ≤ ␣ < 4.00

-39.8

-41.0

-35.4 -32.4

-32.2

-30.5 -37.0

-37.4

-32.2

-31.4

0.75 ≤ ␣ < 1.50

-39.3

-39.3

-33.3 -32.2

-29.1

-31.1 -34.0

-32.1

-32.3

-30.2

0.25 ≤ ␣ < 0.75

-41.9

-41.2

-36.3 -34.1

-30.3

-31.2 -32.0

-30.4

-31.5

-29.4

0.00 ≤ ␣ < 0.25

-39.5

-40.8

-42.7 -41.1

-32.6

-32.6 -32.0

-30.8

-31.5

-29.8

-0.25 ≤ ␣ < 0.00

-37.8

-41.2

-37.9 -39.5

-32.8

-32.8 -32.7

-31.6

-31.9

-30.3

-0.75 ≤ ␣ < -0.25

-33.7

-46.9

-43.9 -43.4

-31.9

-32.4 -34.6

-32.5

-34.7

-31.9

␣ < -0.75

----

----

----

----

----

----

----

----

----

HH

VV

0

0

HH 0

HH

VV 0

0

X-Band

S-Band

L-Band

UHF

VHF

Angle (degrees) 4.0 ≤ ␣

----

Number of Measurements

␣ = Depression

a

L-Band

UHF

VV 0

HH

VV

HH

0

0

0

VV 0

1.50 ≤ ␣ < 4.00

84

86

81

79

82

83

45

47

47

47

0.75 ≤ ␣ < 1.50

260

271

289

294

280

277

187

194

227

226

0.25 ≤ ␣ < 0.75

229

279

335

357

341

345

256

259

294

292

0.00 ≤ ␣ < 0.25

100

135

251

280

258

278

253

257

256

266

-0.25 ≤ ␣ < 0.00

54

106

155

174

177

189

142

135

148

172

-0.75 ≤ ␣ < -0.25

5

2

14

18

19

19

17

17

19

18

0

0

0

0

0

0

0

0

1,125 1,202 1,157 1,191

900

909

991

1,021

␣ < -0.75

0

0

TOTALS

732

879

Table 5.16 defines the population of terrain patches upon which these data are based.

depression angle UHF results, the multipath loss is less and little or no variation of σ w° occurs with depression angle in these higher angle results. Note that in the dark blue, 0.25° to 0.75° results in Figure 5.20, σ w° at S-band is approximately equal to σ w° at L-band and X-band, but with increasing depression angle, purple, 0.75° to 1.5°, through magenta, 1.5° to 4°, σ w° at S-band increasingly dips below σ w° at L-band and X-band. A more significant S-band dip at high depression angle was discussed in the low-relief general mixed rural results of Figure 5.10. At X-band in Figure 5.20, σ w° VV is one or two dB stronger than σ w° HH in every depression angle regime. This slight polarization bias continues to be largely true at S-band but is less evident at the lower frequencies, and at VHF is reversed such that σ w° HH is generally slightly stronger than σ w° VV .

Uncertain Outliers. Now consider the uncertain outliers in σ w° results for low-relief agricultural terrain which are plotted as open plot symbols in Figure 5.20. First consider the light green, –0.25° to –0.75° results. Table 5.19 shows that these results are based on

498 Multifrequency Land Clutter Modeling Information

Table 5.20 Shape Parameter aw and Ratios of Standard Deviation-to-Mean (SD/Mean) and Meanto-Median for Low-Relief Agricultural Terrain, by Spatial Resolution A and Depression Angle*

Weibull Shape Parameter aw

␣ = Depression Angle (degrees)

from SD/Mean

from Mean/Median

A = 103m2

A = 106m2

A = 103m2

A = 106m2

---

---

---

---

1.50 ≤ ␣ < 4.00

3.8

2.2a

3.8

2.9a

0.75 ≤ ␣ < 1.50

3.9

1.9

4.4

1.8

0.25 ≤ ␣ < 0.75

4.9

1.9

4.5

2.0

0.00 ≤ ␣ < 0.25

5.6

2.0

5.1

1.8

4.00 ≤ ␣

-0.25 ≤ ␣ < 0.00

4.5

2.1

4.6

2.2

-0.75 ≤ ␣ < -0.25

4.4

2.3

3.7

2.6

␣ < -0.75

---

---

---

---

Ratios

␣ = Depression Angle (degrees)

4.00 ≤ ␣

a

SD/Mean (dB)

Mean/Median (dB)

A = 103m2

A = 106m2

A = 103m2

A = 106m2

---

---

---

---

18.5

12.1a

1.50 ≤ ␣ < 4.00

8.7

4.2

0.75 ≤ ␣ < 1.50

8.9

3.2

23.3

5.3

0.25 ≤ ␣ < 0.75

11.6

3.1

24.6

6.0

0.00 ≤ ␣ < 0.25

13.7

3.4

29.5

5.1

a

-0.25 ≤ ␣ < 0.00

10.6

3.7

25.0

7.2

-0.75 ≤ ␣ < -0.25

10.4

4.4

17.8

10.1

␣ < -0.75

---

---

---

---

5

2

6

2

Footnoted values apply at A = 10 m , not 10 m .

*

Table 5.16 defines the population of terrain patches and measurements upon which these data are based.

significantly fewer measurements than the other depression angle regimes. At VHF these light green results show a very significant difference with polarization, with σ w° HH stronger than σ w° VV by 13 dB. At horizontal polarization, the light green result at VHF comes from five measurements, four from the Altona site and one from a very weak clutter patch at the Neepawa site. Thus at horizontal polarization, the median measurement is an Altona measurement. At vertical polarization, however, the light green result at VHF comes from only two measurements, both from the weak Neepawa patch. Thus at vertical polarization, the median measurement is an atypically weak Neepawa measurement. At UHF the light green, –0.25° to –0.75° results in Figure 5.20 no longer show a polarization difference, but remain dependent on relatively few samples, and are significantly weaker than the dark green, 0° to –0.25° results. One reason that the light green, –0.25° to –0.75° σ w° results are relatively weak at UHF and, indeed, also relatively weak at S-band and Xband is that among the 15 clutter patches contributing to these results are three clutter

Multifrequency Land Clutter Modeling Information 499

patches that exist at long ranges, from 35 to 65 km. For these three patches, effective radar height is negative, on the order of several hundred feet. Even so, these three patches are at ranges nearly as great as (i.e., one patch) or significantly greater than (i.e., two patches) the quantity r′ = 2aH (see Appendix 2.C). Therefore, much of the negative depression angle to these three patches is caused by geometry on the spherical earth. These patches are weak because of diffraction loss due to propagation over the long ranges of intervening terrain at near grazing incidence. Similarly weak clutter occurring for long-range urban patches is discussed in Section 5.4.1. Now consider the magenta, 1.5° to 4° results in Figure 5.20. At S-band these magenta results show a significant dip of 5 to 6 dB below the magenta results at L-band and X-band. These magenta results also are based on fewer measurements than in the lower depression angle regimes in Figure 5.20. Among these measurements are those from one relatively weak clutter patch, viz., patch 31, at the Beiseker measurement site. Patch 31 was at close range (1.0 to 2.2 km) on the side of the long hill upon which the Phase One radar was situated at Beiseker and, therefore, may have been borderline-shadowed (brow-of-hill effect). Deleting the patch 31 measurements would significantly raise the magenta S-band results in Figure 5.20 but would have less effect at X-band. Thus the exaggerated S-band dip in the magenta results in Figure 5.20 may partially reflect a real effect, but in addition may be partially due to atypically weak S-band clutter from patch 31 at Beiseker.

Shape Parameter aw. Table 5.20 presents the Weibull shape parameter aw and ratios of standard deviation-to-mean and mean-to-median for clutter amplitude distributions in lowrelief agricultural terrain by depression angle and radar spatial resolution. The statistical populations underlying the data of Table 5.20 are shown in Table 5.16. Table 5.20 shows that very large values of spread occur in spatial clutter amplitude distributions at low angles and high resolution in low-relief agricultural terrain. For example, at near grazing incidence (i.e., 0° to 0.25° depression angle) and at high resolution (i.e., A = 103 m2), ratios of meanto-median and standard deviation-to-mean of 29.5 dB and 13.7 dB, respectively, indicate a very highly skewed distribution. The main parametric trend of aw in Table 5.20 is with radar spatial resolution. In every case, aw is greater at 103 m2 resolution that at 106 m2 resolution. However, at the higher resolution of 103 m2, aw also strongly depends on depression angle. That is, in low-relief agricultural terrain, although σ w° is largely invariant with depression angle, aw at high resolution decreases strongly from large values at grazing incidence (i.e., 0° to 0.25°) to much smaller values at higher angles. Consideration of Table 5.16 and comparison of Table 5.20 with Table 5.18 indicates that this trend in low-relief agricultural terrain is supported by a much larger population of measurements separated into more finely graduated depression angle regimes than the corresponding trend in high-relief agricultural terrain. Therefore, as in high-relief agricultural terrain, modeling of clutter in low-relief agricultural terrain must still be done in narrow regimes of depression angle to accommodate this strong trend of decreasing spread in clutter amplitude distributions with increasing angle of illumination, even though mean clutter strengths in low-relief agricultural terrain are relatively insensitive to angle of illumination. The reasons that depression angle affects spread (see Table 5.20) but not mean strength (see Figure 5.20 and Table 5.19) in clutter spatial amplitude distributions in low-relief farmland are as follows. In low-relief farmland, dominant clutter sources are large, discrete, vertical objects. At low angles strong returns are received from these discrete sources, but much

500 Multifrequency Land Clutter Modeling Information

(e.g., 75%) of the intervening terrain is either shadowed or provides very weak returns due to the illumination being at grazing incidence. As a result, in low-relief farmland at low depression angle clutter amplitude distributions have very large spread. As depression angle increases, the intervening terrain between strong discrete sources comes under stronger illumination. The weak returns from these regions rapidly increase, and as a result spreads in amplitude distributions rapidly decrease, as shown in Table 5.20. However, the strong returns from the discrete objects at the high ends of the distributions tend to be relatively independent of depression angle and continue to dominate their mean strengths, with the result that the mean strengths in low-relief farmland as shown in Table 5.19 and Figure 5.20 are largely independent of depression angle (cf. Chapter 2, Figure 2.47). Each pair of aw numbers in Table 5.20 comes from a scatter plot of spread vs spatial resolution. The standard deviation-to-mean scatter plot for the 0° to 0.25° depression angle regime in Table 5.20 is shown in Figure 5.21. The data in Figure 5.21 show a very strong trend of decreasing spread with decreasing resolution (i.e., increasing A). There is a very large amount of measurement data underlying the scatter plot of Figure 5.21; see Table 5.16. In terms of plot symbols, Figure 5.21 is more highly populated than most similar scatter plots in Chapter 5, only missing three plot symbols, i.e., only missing narrow pulse data in the third range interval in the three high bands. Not only does the regression line in Figure 5.21 show a very strong trend whereby the ratio of standard deviation-to-mean rapidly drops from very high values—among the highest of any presented in Chapter 5—to very low values with increasing A, but in addition the plot symbols are for the most part tightly correlated to the regression line and show relatively little scatter away from this line.

Underlying Variability. In low-angle land clutter there is considerable patch-to-patch variability for any given specification of terrain type, relief, depression angle, and radar parameters. This is particularly true in low-relief agricultural terrain where specific influences of discrete sources and propagation prevail. For example, consider the results in the dark blue, 0.25° to 0.75° depression angle regime in Figure 5.20 and Table 5.19, which is the depression angle regime containing the largest number of measurements in low-relief agricultural terrain. In Figure 5.20, these dark blue results show a smooth trend of increasing σ w° with frequency, VHF to L-band, which levels off from L-band through X-band. Underlying this smooth general trend is considerable patch-to-patch variability. Within these dark blue data, the maximum and minimum values of mean clutter strength within the set of contributing like-classified measurements26 in each frequency band are as follows: at VHF, –6.1 and –72.2 dB; at UHF, –10.7 and –74.4 dB; at L-band, –7.8 and –75.7 dB; at S-band, –10.9 and –73.5 dB; and at X-band, –15.1 and –50.0 dB. The standard deviation of the decibel values of mean clutter strength as a measure of spread in each frequency band is: at VHF, 12.7 dB; at UHF, 11.0 dB; at L-band, 8.8 dB; at S-band, 7.2 dB; and at X-band, 4.8 dB. Thus significantly decreasing patch-to-patch variability in mean clutter strength occurs with increasing frequency VHF through X-band in lowrelief agricultural terrain (cf. corresponding discussion based on repeat sector data in Chapter 3 at the end of Section 3.7.3). The principal reason for this decreasing variability with increasing frequency is that propagation influences diminish with increasing frequency. Such underlying patch-to-patch variability makes clear why selected individual measurements historically did not lead to a very clear overall picture of the

26. That is, from the underlying information for this terrain/depression angle category corresponding to that shown in Table 5.2.

Multifrequency Land Clutter Modeling Information 501

general characteristics of low-angle land clutter. As indicated here, a large amount of measurement data is required to find general trends.

5.4.2.3 Level Agricultural Terrain The previous section showed that at lower frequencies (viz., VHF and UHF) in open lowrelief agricultural terrain, mean clutter strengths σ w° are reduced due to multipath loss entering effective clutter strength σ°F 4 through the propagation factor F. In such situations, the direct ray tends to be canceled by the multipath ray that reflects from terrain with 180° phase reversal. The interference between the direct ray and multipath ray causes lobing on the antenna elevation pattern as from a two-element interferometer, resulting in a null in the horizon plane which is the general direction of clutter sources. The details of the multipath loss depend on the terrain between the clutter patch and the radar. For the Phase One 60-ft antenna mast height, the elevation angle to the peak of the first multipath lobe above a level surface is 1.5° at VHF, 0.6° at UHF, and 0.2° at L-band. Depending on the particular undulations and inclinations of the terrain between the radar and the clutter patch, differing amounts of multipath loss or even gain can occur depending upon where on the lobing pattern the clutter patch is illuminated. Since terrain slopes in low-relief terrain are less than 2°, these undulations and inclinations are seldom extreme enough to raise VHF illumination completely out of the horizon plane null. Differing amounts of VHF multipath loss will occur depending from where on the underside of the first multipath lobe (i.e., how deeply into the null) the patch is illuminated (see Section 3.4.1.4 for specific examples). From these considerations, it is clear that maximum multipath loss occurs in very level open terrain such that clutter sources are constrained to lie deep in the horizon plane null. What is the frequency characteristic of land clutter—how much multipath loss occurs and how high in frequency is the effect seen—in very level agricultural terrain, in contrast to the generally low-relief agricultural terrain of the preceding section? If the terrain is level enough (no terrain is perfectly level), the only factor involved in raising clutter sources into illumination is the heights of the clutter producing objects on the terrain surface. To provide empirical information on this matter, results are provided in Section 5.4.2.3 from the Phase One measurement site situated at Corinne on the Regina Plain in southcentral Saskatchewan. Corinne is selected because it is a canonically level farmland site with only farmland discretes rising as clutter sources above level fields. Repeat sector clutter measurements at Corinne were discussed in Chapter 3, e.g., Sections 3.3.2.1 and 3.4.1.4.3; see also Figure 3.7. Corinne was one of the 30 measurement sites contributing to the low-relief agricultural land clutter results of Section 5.4.2.2. Table 5.21 indicates that the Corinne database for level agricultural terrain consists of 345 measured clutter histograms from 14 different clutter patches. Of these 14 pure level farmland clutter patches, five occurred at ranges from 1 to 2 km, seven occurred at ranges from 2 to 12 km, one extended from 12 to 24 km, and one extended from 24 to 28 km. Within 12 km, terrain elevations over contributing patches varied by no more than 15 ft from site center. Terrain elevations of the two clutter patches beyond 12 km were about 100 ft higher than site center. Of the 14 contributing clutter patches at Corinne, three were classified with 0% incidence of trees, and the remaining 11 were classified with 1 to 3% incidence of trees. A significant portion of the

502 Multifrequency Land Clutter Modeling Information

Table 5.21 Numbers of Terrain Patches and Measured Clutter Histograms for Level Agricultural Terrain, by Depression Anglea,b,c

␣ = Depression

Number of Patches

Number of Measurements

Terrain Relief

Angle (degrees) 1.50 ≤ ␣

0

0

Level

0.75 ≤ ␣ < 1.50

1

2

0.25 ≤ ␣ < 0.75

4

174

0.00 ≤ ␣ < 0.25

7

153

-0.25 ≤ ␣ < 0.00

2

16

␣ < -0.25

0

0

Totals

14

345

a A single (primary) classifier only is sufficient to describe these patches. Corinne site. Level is included within low-relief. b A terrain patch is a land surface macroregion usually several kms on a side (median patch area = 12.62 km2 ). c A measured clutter histogram contains all of the temporal (pulse by pulse) and spatial (resolution cell by resolution cell) clutter samples obtained in a given measurement of a terrain patch. A terrain patch was usually measured many times (nominally 20) as RF frequency (5), polarization (2), and range resolution (2) were varied over the Phase One radar parameter matrix.

Corinne terrain was mixed farmland/herbaceous rangeland; this mixed open terrain was not included in the Corinne level farmland results presented here. By “level” at Corinne is meant terrain with slopes < 1°; that is, terrain that is of landform class 1 or 3; see Table 2.2. Corinne patches of landform classes other than 1 or 3 are also excluded in the results presented here. An aerial photo of the Corinne terrain is provided in Figure 3.35. Phase One measurements were conducted at Corinne with three different antenna heights, nominally, 30, 45, and 60 ft. All of the results presented here are for the 60-ft antenna height. Results are presented in Figure 3.36 and Table 3.5 for all three antenna heights at Corinne.

Trends in σ w° . Table 5.22 presents mean clutter strength σ w° for level agricultural terrain by frequency band, polarization, and depression angle and includes the number of measurements upon which each value of σ w° is based. The σ w° data of Table 5.22 are plotted in Figure 5.22. The mean strength results of Figure 5.22 may be compared with the Corinne repeat sector mean strength results shown in Figure 3.7 of Chapter 3. The main parametric trend observed in Figure 5.22 is that in level farmland σ w° increases strongly with increasing frequency, VHF through X-band. The amount of the increase in σ w° from VHF to X-band is 25 to 30 dB. No leveling off of this level farmland characteristic occurs in the microwave bands, in contrast to the corresponding characteristic for general lowrelief farmland—see Figure 5.20. The strong trend of increasing σ w° with increasing frequency in level farmland is entirely due to multipath loss entering clutter strength through the propagation factor. There appears to be no multipath loss in σ w° at X-band on level farmland (compare Table 5.22 with Tables 5.19 and 5.17), but multipath loss occurs on level farmland for all bands below X-band. By frequency band, the approximate amount of multipath loss in σ w° on level farmland in Table 5.22 and Figure 5.22 is: several dB at Sband, 10 dB at L-band, 20 dB at UHF, and 25 to 30 dB at VHF. The resulting, very weak, –

Multifrequency Land Clutter Modeling Information 503

Table 5.22 Mean Clutter Strength σ w° and Number of Measurements for Level Agricultural Terrain, by Frequency Band, Polarization, and Depression Anglea

Weibull Mean Clutter Strength σ°w (dB)

␣ = Depression Angle (degrees)

VHF HH

HH

L-Band VV

HH

S-Band

VV

HH

X-Band

VV

HH

VV

0.75 ≤ ␣

----

----

----

----

----

----

----

----

-37.1

-34.2

0.25 ≤ ␣ < 0.75

-53.2

-57.6

-49.6

-49.6

-39.8

-39.8

-42.1

-41.4

-35.0

-31.5

0.00 ≤ ␣ < 0.25

-58.8

-59.1

-53.5

-48.0

-37.4

-40.3

-34.3

-33.3

-31.4

-30.0

-0.25 ≤ ␣ < 0.00

----

----

----

----

-48.4

-48.9

-35.8

-35.1

-34.4

-33.0

␣ < -0.25

----

----

----

----

----

----

----

----

----

----

Number of Measurements

␣ = Depression

UHF

VHF

Angle (degrees) HH

a

UHF VV

VV

HH

L-Band VV

HH

S-Band

VV

HH

X-Band

VV

HH

VV

0.75 ≤ ␣

0

0

0

0

0

0

0

0

1

1

0.25 ≤ ␣ < 0.75

13

18

18

18

16

17

20

20

17

17

0.00 ≤ ␣ < 0.25

5

5

16

17

14

16

18

22

20

20

-0.25 ≤ ␣ < 0.00

0

0

0

0

1

1

2

4

4

4

␣ < -0.25

0

0

0

0

0

0

0

0

0

0

TOTALS

18

23

34

35

31

34

40

46

42

42

Table 5.21 defines the population of terrain patches upon which these data are based.

50 to –60 dB levels of σ w° at VHF in level farmland are approximately equal to corresponding clutter strengths in level desert and low-relief grassland, and somewhat stronger than corresponding clutter strengths in wetland. At X-band, the level farmland σ w° clutter strengths in the –30 to –35 dB range are somewhat stronger—by 5 to 10 dB— than corresponding clutter strengths in level desert, low-relief grassland, and wetland. The weak, level farmland values of σ w° at VHF—in the –50 to –60 dB range—remain accurate, even though they are so weak. Almost all of the Phase One measured clutter histograms contain some samples at radar noise level. Mean clutter strength in the histogram is always computed two ways—first, as an upper bound, where the noise samples retain their noise power values, and second, as a lower bound, where the noise samples are given received power values equal to zero. The true value of mean clutter strength that would be measured by an infinitely sensitive radar, such that no noise samples would occur, must lie between these bounding limits. Only those measured clutter histograms are retained for which the differences between the upper bound and lower bound to mean clutter strength are < 1.5 dB. Usually these bounding estimates of mean clutter strength are within a small fraction of a dB. In any case, all values of mean clutter strength upon which Chapter 5 is based, even very weak ones, cannot be in error by more than 1.5 dB, and usually the error is much less. Coherent integration is utilized in processing the Phase One data to increase sensitivity to weak clutter returns (see Appendix 3.C).

504 Multifrequency Land Clutter Modeling Information

Now consider more closely what is happening in the level farmland σ w° data of Table 5.22 and Figure 5.22. First consider the dark blue, 0.25° to 0.75° results. On the level Corinne landscape, such relatively high depression angles occur only because of the effect of antenna mast height over very near-range clutter patches. Thus the dark blue, 0.25° to 0.75° results come from the five level clutter patches all in the 1- to 2-km range interval from the radar. Clutter returns from these near-range clutter patches are clearly discernible well above system noise level at all five Phase One frequencies. However, clutter patches at longer ranges rapidly become too weak for Phase One measurement at the lower frequencies due to multipath loss. Thus at VHF, of the seven patches in the 2- to 12-km range interval, only two provided clutter strong enough to be measured (given by the cyan, 0° to 0.25° results in Figure 5.22), and neither of the two longer range patches beyond 12 km were measurable above radar noise. At UHF, in addition to the five 1- to 2-km patches (dark blue, 0.25° to 0.75°), all seven patches between 2 and 12 km were measurable (cyan, 0° to 0.25°), but the two longer range patches continued to not provide measurable returns at UHF. At L-band, all 1- to 2-km patches (dark blue, 0° to 0.75°) and 2- to 12-km patches (cyan, 0° to 0.25°) remained measurable, and the single, 12- to 24-km patch at 100ft higher elevation also became measurable (dark green, 0° to –0.25°). At S- and X-bands, all 14 patches provided valid measurements, including the longest range, 24- to 28-km patch; this last patch was also at 100-ft higher elevation and also contributes to the dark green, 0° to –0.25° results in these bands. Thus in Figure 5.22, with increasing frequency the clutter results come from patches enclosed within a gradually enlarging terrain region centered at the radar. This region is bounded by 4 km at VHF, 12 km at UHF, 24 km at L-band, and 28 km at S- and X-bands. Consider that, at VHF, the height to the peak of the first (1.5°) multipath lobe at 4 km is 105 m; obviously few clutter sources (e.g., farm buildings, grain storage silos, trees) reach this high, which explains the lack of discernible clutter beyond 4 km at VHF. In contrast, at X-band, the height to the peak of the first (0.03°) multipath lobe is only 6.3 m at 12 km. Thus at X-band, most clutter sources within 12 km are high enough to be fully illuminated. The strength of the illumination decreases with decreasing frequency from X-band. The only common terrain region to all frequency bands in the results of Figure 5.22 is the close-range, 1 to 2 km region. Results from this close-range region are given by the dark blue, 0.25° to 0.75° plot symbols in Figure 5.22. Although the dark blue results generally show increasing clutter strength, VHF to X-band, they also show an S-band dip between Land X-bands. The cyan, 0° to 0.25° results come from patches within the 2- to 12-km region, with fewer patches from within this region contributing at VHF than in the higher bands. The somewhat higher terrain beyond 12 km provides the dark green, 0° to –0.25° results. At L-band, these dark green results are shown as open plot symbols because they are based on single measurements. However, although relatively weak, these single L-band, dark green measurements may not be atypical, since at UHF and VHF the clutter returns from the terrain beyond 12 km drop to such low levels that they could not be measured with the Phase One equipment. The purple, 0.75° to 1.5° results at X-band in Figure 5.22 are also shown as open plot symbols because they also come from single measurements. These results arose as follows. One of the patches in the 1- to 2-km region was at somewhat closer range than the others and had a depression angle close to 0.75°. In these particular (purple) X-band measurements of this patch which are at high range resolution, the precise positions of the

Multifrequency Land Clutter Modeling Information 505

range gates on the ground together with the precise X-band antenna height (slightly higher than the other bands) were such as to cause the depression angle to just exceed 0.75° (viz., 0.78°). For the corresponding low resolution X-band measurements of this patch, the range gate positions were at somewhat greater distances, and the depression angle was less than 0.75° (viz., 0.71°). Thus the low resolution X-band measurements from this patch are included in the dark blue results in Figure 5.22, as are all other measurements of the patch. Similar migration of particular patch measurements across depression angle regime boundaries occasionally happens elsewhere in the results of Chapter 5. Specific discussion of individual sites such as is given here for Corinne is not possible in most other results of Chapter 5, which are generally based upon numerous sites in each terrain category. However, specific discussion of repeat sector results by individual site is given for many sites (including Corinne) in Section 3.4.

Shape Parameter aw. Table 5.23 presents the Weibull shape parameter aw and ratios of standard deviation-to-mean and mean-to-median for clutter amplitude distributions in level agricultural terrain by depression angle and radar spatial resolution. The statistical populations underlying the data of Table 5.23 are shown in Table 5.21. Since the level farmland results of Chapter 5 come from just one site (viz., Corinne), the populations shown in Table 5.21 are much lower than for most other terrain types. Table 5.23 shows that very large values of spread occur in spatial clutter amplitude distributions at low angles and high resolution in level agricultural terrain. For example, at near grazing incidence (i.e., 0° Table 5.23 Shape Parameter aw and Ratios of Standard Deviation-to-Mean (SD/Mean) and Meanto-Median for Level Agricultural Terrain, by Spatial Resolution A and Depression Angle*

Weibull Shape Parameter aw

= Depression Angle (degrees)

from SD/Mean A=

103m2

A=

from Mean/Median

106m2

A = 103m2

A = 106m2

0.75 ≤ ␣

---

---

---

---

0.25 ≤ ␣ < 0.75

3.4

1.9a

4.5

2.5a

0.00 ≤ ␣ < 0.25

5.5

2.4

5.8

3.3

-0.25 ≤ ␣ < 0.00

5.9

3.2

4.1

4.5

␣ < -0.25

---

---

---

---

Ratios = Depression Angle (degrees)

SD/Mean (dB)

Mean/Median (dB)

A = 103m2

A = 106m2

A = 103m2

A = 106m2

0.75 ≤ ␣

---

---

---

---

0.25 ≤ ␣ < 0.75

7.5

3.3a

24.5

8.9a

0.00 ≤ ␣ < 0.25

13.4

4.6

36.4

14.5

-0.25 ≤ ␣ < 0.00

14.4

7.0

20.6

24.3

␣ < -0.25

---

---

---

---

a Footnoted values apply at A = 105 m2, not 106 m2.

* Table 5.21 defines the population of terrain patches and measurements upon which these data are based.

506 Multifrequency Land Clutter Modeling Information

to 0.25° depression angle) and at high resolution (i.e., A = 103 m2), ratios of mean-tomedian and standard deviation-to-mean of 36.4 and 13.4 dB, respectively, indicate a very highly skewed distribution. The main parametric trend of aw in Table 5.23 is with radar spatial resolution. In every case, aw is greater at 103 m2 resolution that at 106 m2 resolution. However, at the higher resolution of 103 m2, aw also strongly depends on depression angle. That is, in level agricultural terrain, although σ w° is largely invariant with depression angle, aw at high resolution decreases strongly from large values at grazing incidence (i.e., 0° to 0.25°) to much smaller values at higher angles. Each pair of aw numbers in Table 5.23 comes from a scatter plot of spread vs spatial resolution. The standard deviation-to-mean scatter plot for the 0° to 0.25° depression angle regime in Table 5.23 is shown in Figure 5.23. The data in Figure 5.23 show a very strong trend of decreasing spread with decreasing resolution (i.e., increasing A). There is a relatively small amount of measurement data underlying the scatter plot of Figure 5.23; see Table 5.16. In terms of plot symbols, Figure 5.23 is less populated than most similar scatter plots in Chapter 5, with results coming only from the first range interval at Corinne. The five individual frequency bands and the two pulse lengths per frequency band are easy to follow in these results. There is very tight correlation of these data to the regression line. These Corinne data strongly make the case, upon which all the results in Chapter 5 are based, that spread is predominantly affected by resolution and that direct effects of radar frequency on spread are small.

5.4.3 Forest Terrain Much natural terrain is forested. The characteristics of land clutter from forested terrain are very different than from open terrain. Section 5.4.3 specifies the characteristics of forest land clutter based on 8,611 measured clutter histograms from 466 forest clutter patches. These measurements break down in two regimes of relief, high (terrain slopes > 2°) and low (terrain slopes < 2°), and in multiple depression angle regimes as shown in Table 5.24. These forest clutter measurements come from 27 different sites. Because forest is much less supportive of multipath than is open terrain, particularly at high illumination angles, many of these forest measurements are much more measurements of relatively pure intrinsic σ° and are much less contaminated by dispersive propagation influences than are measurements in open terrain. To the extent that this is true, fewer measurements can establish trends in forest terrain than in farmland terrain. Nevertheless, the Phase One forest clutter measurements constitute 29% of all Phase One measurements in pure terrain. Thus, after farmland at 35%, forest stands as far and away the second most highly sampled terrain type among the eight pure terrain types of Chapter 5. Classification of forest clutter patches was in three separate categories, viz., deciduous, coniferous, and mixed (see Table 2.1). However, the clutter measurements showed no significant variation among these classes. The results presented here are inclusive of all three classes. Little seasonal variation was observed in the Phase One clutter measurements from forested terrain. One forested wilderness site—Brazeau, Alberta—was visited twice by the Phase One equipment, once in summer and once in winter. Typically, mean clutter strengths at

Multifrequency Land Clutter Modeling Information 507

Table 5.24 Numbers of Terrain Patches and Measured Clutter Histograms for Forest, by Relief and Depression Anglea,b,c

Terrain Relief

␣ = Depression Angle

High-relief

(degrees) 6.0 ≤ ␣

1

Number of Measurements 8

4.0 ≤ ␣ < 6.0

3

70

2.0 ≤ ␣ < 4.0

10

238

1.0 ≤ ␣ < 2.0

27

609

0.0 ≤ ␣ < 1.0

86

1,732

-1.0 ≤ ␣ < 0.0

109

1,261

2

21

238

3,939

␣ < -1.0 Totals Low-relief

Number of Patches

4.00 ≤ ␣

1

71

1.50 ≤ ␣ < 4.00

13

470

0.75 ≤ ␣ < 1.50

27

949

0.25 ≤ ␣ < 0.75

65

1,362

0.00 ≤ ␣ < 0.25

67

1,241

-0.25 ≤ ␣ < 0.00

51

540

-0.75 ≤ ␣ < -0.25

4

39

␣ < -0.75

0

0

228

4,672

466

8,611

Totals Grand Totals

a A single (primary) classifier only is sufficient to describe these patches. 2 b A terrain patch is a land surface macroregion usually several kms on a side (median patch area = 12.62 km ). c A measured clutter histogram contains all of the temporal (pulse by pulse) and spatial (resolution cell by resolution cell) clutter samples obtained in a given measurement of a terrain patch. A terrain patch was usually measured many times (nominally 20) as RF frequency (5), polarization (2), and range resolution (2) were varied over the Phase One radar parameter matrix.

Brazeau between summer and winter seasons differed by only 1 or 2 dB with the summer measurements usually (but not always) being stronger (see Section 3.4.1.3.3 and Figure 3.24). The results presented in Section 5.4.3 are inclusive of all Phase One forest measurements independent of the season in which the measurement was made. As was provided for agricultural terrain, some interpretative discussion involving individual patch measurements continues to be provided concerning the uncertain outliers that occur in the following results for forest terrain. It is interesting to compare the high- and low-relief forest mean clutter strength data to follow with the site-specific repeat-sector forest mean clutter strength characteristics from Blue Knob and Wachusett Mountain shown in Figures 3.3 and 3.4, respectively, in Chapter 3.

5.4.3.1 High-Relief Forest Trends in σ w° . Table 5.25 presents mean clutter strength σ w° for high-relief forest by frequency band, polarization, and depression angle and includes the number of

508 Multifrequency Land Clutter Modeling Information

Table 5.25 Mean Clutter Strength σ w° and Number of Measurements for High-Relief Forest, by Frequency Band, Polarization, and Depression Anglea

Weibull Mean Clutter Strength σ°w (dB)

␣ = Depression

VHF

Angle (degrees) 6.0 ≤ ␣

-17.4

-13.5

-18.7 -16.9

4.0 ≤ ␣ < 6.0

-17.7

-13.4

-21.3 -21.2

2.0 ≤ ␣ < 4.0

-20.1

-17.3

-25.2 -22.1

1.0 ≤ ␣ < 2.0

-17.3

-15.0

-22.6 -20.1

0.0 ≤ ␣ < 1.0

-20.6

-19.3

-1.0 ≤ ␣ < 0.0

-23.8

-16.8

␣ < -1.0

-14.5

-5.5

Angle (degrees)

VV

X-Band

S-Band

VV

HH

VV

HH

VV

----

----

----

----

----

----

-23.3

-23.6

----

----

----

----

-26.2

-24.3 -33.4

-31.3

----

----

-24.2

-24.5 -28.9

-27.2

-23.2

-22.7

-25.1 -22.9

-26.7

-25.9 -29.5

-27.8

-27.1

-26.6

-19.8 -17.1

-22.8

-22.2 -28.9

-27.0

-27.3

-27.2

-14.9

-14.3

----

-22.6

-24.5

-8.2

-7.3

HH

----

Number of Measurements

2

VV 2

HH 2

VV 2

HH 0

X-Band

S-Band

L-Band

UHF

VHF HH

6.0 ≤ ␣

HH

L-Band

VV

␣ = Depression

VV 0

HH 0

VV

HH

VV

0

0

0 0 0

4.0 ≤ ␣ < 6.0

9

12

9

10

11

19

0

0

0

2.0 ≤ ␣ < 4.0

32

31

34

34

33

39

17

18

0

39

1.0 ≤ ␣ < 2.0

67

56

68

67

68

67

68

68

41

0.0 ≤ ␣ < 1.0

149

142

171

172

185

206

201

205

147

154

-1.0 ≤ ␣ < 0.0

148

167

161

174

144

136

71

67

96

97

5

4

3

3

2

2

0

0

1

1

358

285

291

x < -1.0 TOTALS a

UHF

HH

412

414

448

462

443

469

357

Table 5.24 defines the population of terrain patches upon which these data are based.

measurements upon which each value of σ w° is based. A relatively large amount of Phase One measurement data exists for high-relief forest—more than 10 times that which exists for high-relief farmland, for example (compare Tables 5.16 and 5.24), and approximately the same as exists for low-relief forest (see Table 5.24). Much of these data exist in the lower, 0° to 1° and 0° to –1°, depression angle regimes. At higher depression angles the amount of available data falls off rapidly. In particular, Table 5.25 shows that no data exist above 2° at X-band, above 4° at S-band, and above 6° at L-band. This lack of data at high angles results from the fact that the Phase One antenna elevation beam is always directed horizontally and is of decreasing beamwidth with increasing frequency, e.g., 10° at L-band (i.e., the half-power point is 5° above the horizontal), 4° at S-band, and 3° at X-band (see Table 3.A.2). Of course, all σ°F4 measurement data upon which Chapter 5 is based are corrected for antenna gain depending exactly where on the vertical pattern the particular measurement is made. Data requiring a two-way correction of more than about 10 dB are not utilized. Although the Phase One equipment is constrained to relatively narrow vertical beamwidths in the higher bands, with corresponding lack of measurement data at higher depression angles, the Phase Zero equipment had a much broader vertical beamwidth (viz., 23°), and as a result the Phase Zero database does provide land clutter results—albeit at Xband only—to higher depression angles (e.g., 8°, see Chapter 2).

Multifrequency Land Clutter Modeling Information 509

The high-relief forest σ w° data of Table 5.25 are plotted in Figure 5.24. The main characteristics of the data in Figure 5.24 are similar to those of high-relief general mixed rural terrain shown in Figure 5.8 and discussed in Section 5.3. In particular, like the highrelief general mixed rural σ w° data, the high-relief forest σ w° data show significantly decreasing strength with increasing frequency, VHF to S-band, with a subsequent small increase, S-band to X-band; and also, like the high-relief general mixed rural data, the highrelief forest data show the v-shapes within frequency bands indicating strong effects from depression angle. Next, consider the effects of depression angle on the high-relief forest σ w° data in Figure 5.24 more closely. Focus first on the cyan, 0° to 1° results. In each frequency band, there is a general trend of increasing σ w° with increasing positive depression angle, from cyan (0° to 1°) to dark blue (1° to 2°) to purple (2° to 4°) to magenta (4° to 6°) to red (>6°); and also a general trend of increasing σ w° with increasing negative depression angle, from cyan (0° to 1°) to dark green (0° to –1°) to intermediate green (< –1°). These trends of increasing σ w° with increasing positive and negative depression angle in high-relief forest terrain, although very significant, are not quite as smooth or as nearly monotonic as in high-relief general mixed rural terrain (notably, there is a reversal in trend between the dark blue, 1° to 2°, high-relief forest σ w° results and the purple, 2° to 4°, high-relief forest σ w° results at VHF and UHF, and to a lesser degree in the horizontal polarization results at L-band; the weak, purple, 2° to 4° results at S-band plotted as open plot symbols will be discussed presently). This may be due to the fact that the amount of Phase One clutter measurement data available for high-relief forest, although large, is still only about 30% of the amount of data available for high-relief general mixed rural terrain (e.g., there are only 10 patches contributing to the 2° to 4° regime; see Table 5.24). The v-shapes of the set of colored plot symbols in each frequency band for the high-relief forest σ w° data in Figure 5.24 have less vertical extent (disregarding the open plot symbols) than the corresponding v-shapes for the high-relief general mixed rural data of Figure 5.8. Both Figure 5.24 and Figure 5.8 provide σ w° results in the same ranges at high positive depression angles. The differences accounting for less in-band vertical extent in Figure 5.24 are in the low depression angle (i.e., cyan) results. In each frequency band, the cyan, 0 to 1°, σ w° results for high-relief forest are greater than for high-relief general mixed rural terrain, by 6 or 7 dB at VHF, by 4 or 5 dB at UHF, by 2 or 3 dB at L-band, by about 2 dB at S-band, and by 1 or 2 dB at X-band. The fact that high-relief general mixed rural terrain is partially open reduces its clutter strength compared to high-relief forested terrain at low depression angle but not at high depression angle. At low angles more shadowing occurs of the open areas between forested areas in general mixed rural terrain than occurs in forested terrain, which is more uniformly illuminated; whereas, at high angles, relatively complete illumination occurs in mixed as well as forested terrain. In the high-relief forest σ w° data of Table 5.25 and Figure 5.24, σ w° VV is generally greater than σ w° HH by several dB at VHF and UHF, and by a lesser amount at S-band. This polarization bias is less evident at L-band and X-band. Radars are frequently situated in rural terrain that is often either forest or farmland. How important is the difference in land cover between forest and farmland in affecting the clutter amplitude statistics in the radar? Comparison between Figures 5.18 and 5.24 (and Tables 5.17 and 5.25) indicates that in high-relief terrain σ w° is significantly stronger in forest

510 Multifrequency Land Clutter Modeling Information

than in farmland. In broad measure, the amount of the difference by frequency band is: at VHF, 15 dB; at UHF, 10 dB; and at L-, S-, and X-bands, 3 to 6 dB.

Uncertain Outliers. Now consider the uncertain outliers in σ w° in high-relief forest terrain which are plotted as open plot symbols in Figure 5.24. First consider the light green, <–1° results. These light green results are very strong at VHF, UHF, and L-band. Table 5.25 shows that these light green results are based on relatively few measurements. Table 5.24 shows that these few measurements come from just two patches. Both patches are of steep forested terrain in the region where the prairie transitions into the Rocky Mountains. Both patches were measured at relatively long range from Alberta prairie sites. Specifically, these patches are patch 105 at the Phase One measurement site of Strathcona, and patch 50 at the Phase One measurement site of Pakowki Lake. Patch 105 is moderately steep, pure forest terrain measured at 48-km range and at a 3000 ft higher elevation than the Strathcona site location. Patch 50 is steep, pure forest terrain measured at 65-km range and at a 3,300 ft higher elevation than the Pakowki Lake site location. The depression angle to patch 105 is –1.2°; to patch 50 is –1.1°. The clutter from these two patches is very strong at VHF, UHF, and L-band (open, light green, plot symbols; Figure 5.24). The terrain from which this strong clutter arises is steep enough that it might be thought of as being mountainous. However, the term “mountains” is relatively vague and imprecise in terrain classification. In Chapter 5, mountain clutter data are constrained to come from two canonical Rocky Mountain clutter sites in which steep, barren (or snow-covered) mountain peaks and rock faces are visually and unambiguously present at close range—see Section 5.4.8. Other steep terrain from which Phase One measurements were made, for example, in the American Intermontane desert regions in the west or in the Appalachian Mountains in the east, is simply classified as high-relief, of whatever land cover type is appropriate. Thus it is apparent that considerable overlap exists between the classification categories of “high-relief” and “mountains” in Chapter 5— “mountains” being a relatively arbitrary subset of the general category of “high-relief.” A further subcategory of long-range mountains is employed in Section 5.4.8.1, within which the two patches under present discussion would fall in terms of their range and depression angle values if it were not that their land covers were pure forest. The two patches in question, patch 105 at Strathcona and patch 50 at Pakowki Lake, properly meet the criteria for pure forest terrain (i.e., no barren peaks) of very high-relief. In fact, the clutter strengths from these two patches at VHF (vertical polarization only), UHF, and L-band are somewhat stronger than the corresponding general σ w° levels for mountains specified in Section 5.4.8 and much stronger in these bands than the corresponding levels for long-range mountains specified in Section 5.4.8.1. The results for these two patches are shown as open plot symbols in Figure 5.24 because, being from only two patches, these results cannot be considered general. No measurements of these two patches are available at S-band. At X-band, of these two patches only measurements of the Pakowki Lake patch are available; although not overly strong at X-band, these light green X-band results are still shown as open plot symbols in Figure 5.24 because of the little data involved (i.e., only one measurement at each polarization). At S-band in Figure 5.24, the purple, 2° to 4° results are weaker and out-of-line with the other S-band results. Table 5.25 shows that none of the 2° to 4° results are based on a very large number of measurements, and that the S-band results in particular are based upon about one-half the number of measurements as the VHF, UHF, and L-band results.

Multifrequency Land Clutter Modeling Information 511

Therefore, the S-band results are plotted as open plot symbols to indicate that they should be used with caution. Nevertheless, the purple, 2° to 4° high-relief forest σ w° data provide another indication of an S-band dip at high depression angle, similar, for example, to that previously discussed for general rural terrain.

VHF Polarization Bias. In the intermediate green, <–1°, VHF σ w° results in Figure 5.24 and Table 5.25, σ w° VV > σ w° HH by 9 dB. This large polarization bias at VHF disappears at UHF and L-band. This VHF polarization bias exists throughout the set of nine measurements from the two patches, patch 50 at Pakowki Lake and patch 105 at Strathcona, upon which these results are based; that is, this polarization bias is not a peculiarity of data reduction but exists in each corresponding pair of measurements from these two patches. Now consider the dark green, 0° to –1°, VHF σ w° results in Figure 5.24 and Table 5.25. These dark green VHF results also exhibit a large polarization bias, σ w° VV > σ w° HH by 7 dB. However, the dark green, 0° to –1° VHF results are based on many measurements from a large number of patches. A similar strong polarization bias, σ w° VV > σ w° HH at VHF in high-relief terrain, is discussed in Section 3.4.1.2. This previous discussion is based on Phase One repeat sector measurements at the two Phase One mountain sites in Alberta, Plateau Mountain and Waterton. In the repeat sector measurements at these two mountain sites, σ w° VV > σ w° HH by 7 to 8 dB. This bias is very similar to that exhibited in the light green (< –1°) and dark green (0° to –1°) high-relief forest data of Figure 5.24. In Chapter 5, which is based on the spatially comprehensive Phase One 360° survey data, similar strong VHF polarization biases occur for other high-relief forested terrain types. Usually the bias is much more pronounced in the dark green, 0° to –1° depression angle regime than at other depression angles, although similar but smaller biases of 2 or 3 dB, σ w° VV > σ w° HH , frequently exist in the other depression angle regimes also. Thus, at VHF in the dark green, 0° to –1° results, σ w° VV > σ w° HH : by 4.8 dB in high-relief general mixed rural terrain, by 7.0 dB in high-relief forest, by 9.8 dB in high-relief shrubland, by 9.6 dB in mountains, by 6.2 dB in high-relief mixed forest/open terrain, and by 6.8 dB in high-relief mixed open/forest terrain (forest/open and open/forest results are not included in this book). Thus, a large polarization bias at VHF occurs generally in highrelief forested terrain, predominantly in the 0° to –1° depression angle regime.

Shape Parameter aw. Table 5.26 presents the Weibull shape parameter aw and ratios of standard deviation-to-mean and mean-to-median for clutter amplitude distributions in highrelief forest terrain by depression angle and radar spatial resolution. The statistical populations underlying the data of Table 5.26 are shown in Table 5.24. Table 5.26 shows that the spread in spatial clutter amplitude distributions in high-relief forest terrain is much lower than in open terrain. Thus, for example, high-relief forest clutter is distinguished from high-relief farmland clutter, not just in terms of mean clutter strength as discussed previously in Section 5.4.3.1, but also in terms of spread—mean strengths are higher (i.e., more severe) and spreads are lower (i.e., less severe) in forest than in farmland. Spreads are lower in forest than in farmland because forest is a much more homogeneous scattering medium than farmland. Although the spreads shown in Table 5.26 for high-relief forest are lower than for most other terrain types, they still indicate a statistical process with considerable more spread than a Rayleigh (i.e., exponential power) process. In Rayleigh statistics, the Weibull shape

512 Multifrequency Land Clutter Modeling Information

Table 5.26 Shape Parameter aw and Ratios of Standard Deviation-to-Mean (SD/Mean) and Meanto-Median for High-Relief Forest, by Spatial Resolution A and Depression Angle* Weibull Shape Parameter aw

␣ = Depression Angle (degrees)

from SD/Mean

from Mean/Median

A = 103m2

A = 106m2

A = 103m2

A = 106m2

6.0 ≤ ␣

1.8b

1.8a

2.2b

1.9a

4.0 ≤ ␣ < 6.0

1.9

1.3

2.0

1.5

2.0 ≤ ␣ < 4.0

2.7

1.8

3.1

2.5

1.0 ≤ ␣ < 2.0

2.5

1.8

3.5

2.0

0.0 ≤ ␣ < 1.0

2.5

1.6

2.9

1.9

-1.0 ≤ ␣ < 0.0

2.6

1.7

3.5

␣ < -1.0

2.8

c

1.9

3.5

2.2 c

2.9

Ratios

␣ = Depression Angle (degrees)

a

SD/Mean (dB)

Mean/Median (dB)

A = 103m2

A = 106m2

6.0 ≤ ␣

2.9b

2.9a

4.0 ≤ ␣ < 6.0

3.1

2.0 ≤ ␣ < 4.0

5.5

1.0 ≤ ␣ < 2.0 0.0 ≤ ␣ < 1.0

A = 103m2

A = 106m2

7.5b

5.8a

1.2

6.1

3.6

3.0

13.4

9.0

5.0

2.8

16.0

6.2

4.9

2.3

11.7

5.8

-1.0 ≤ ␣ < 0.0

5.2

2.6

15.9

7.1

␣ < -1.0

5.8c

3.3

16.4c

12.1

5

2

6

2

Footnoted values apply at A = 10 m , not 10 m . 4 2 3 2 b Footnoted values apply at A = 10 m , not 10 m . 5 2 3 2 c Footnoted values apply at A = 10 m , not 10 m . *

Table 5.24 defines the population of terrain patches and measurements upon which these data are based.

parameter aw equals unity, and the ratios of mean-to-median and standard deviation-tomean are 1.6 and 0 dB, respectively. Even at A = 106 m2 in Table 5.26, where spreads are least, they still generally remain much greater than Rayleigh. Although at the higher illumination angles of airborne radar, land clutter is in large measure a Rayleigh process, the data of Table 5.26 indicate that, for surface radar, land clutter is not a Rayleigh process, even at relatively high angles (for surface radar) in homogeneous forest terrain and with large resolution cells. Modeling of land clutter in surface radars as a Rayleigh process results in overestimates of radar detection performance. The actual clutter distributions that exist, skewed significantly more highly than Rayleigh even in forest terrain, cause, for example, higher numbers of false alarms for a given detection probability. The main trend of parametric variation of aw in Table 5.26 is with radar spatial resolution. In almost every case, aw is greater at 103 m2 resolution than at 106 m2 resolution. However, this trend of decreasing aw with decreasing resolution is weaker in high-relief forest than in high-relief farmland. Values of aw at A = 103 m2 are generally considerably less in high-

Multifrequency Land Clutter Modeling Information 513

relief forest than in high-relief farmland; values of aw at A = 106 m2 are much closer for the two terrain types. There is only a secondary trend, relatively weak and erratic, whereby aw decreases with increasing depression angle in Table 5.26, although the numbers of measurements are quite low at the higher depression angles. Each pair of aw numbers in Table 5.26 comes from a scatter plot of spread vs spatial resolution. The standard deviation-to-mean scatter plot for the 2° to 4° depression angle regime in Table 5.26 is shown in Figure 5.25. The data in Figure 5.25 show a significant trend of decreasing spread with decreasing resolution (i.e., increasing A), although the trend is by no means as strong as that shown previously for high-relief farmland, 1° to 2°, in Figure 5.19. Comparison of Figures 5.25 and 5.19 provides graphic indication of the much lower spreads that exist in land clutter spatial amplitude distributions for forest terrain compared to farmland.

5.4.3.2 Low-Relief Forest Visibility and Shadow. Low-relief forest is a simple scattering surface compared with other terrain types. There are several contributing aspects to this simplicity. First, low-relief forest is not dominated by large cultural discrete scattering sources spatially distributed in deterministic patterns as is farmland, but is much more a natural homogeneous random scattering medium. Second, low-relief forest is a diffusely scattering medium and does not, to any significant degree, support forward multipath reflections that cause high complexity in illumination and resulting clutter strength in open terrain. Third, low-relief forest, being of low-relief, is not dominated by particular large-scale terrain features, but has only minor undulations, inclinations, and waviness in the surface. Because of these various aspects of simplicity, and because it is a very commonly occurring terrain type, low-relief forest represents a good starting point from which to understand a basic mechanism at work in all low-angle clutter. Although low-relief forest is a simple scattering surface, it is by no means approximated by a theoretical planar surface or planar slab of random scattering medium. The difference is in the fact that the real terrain surface, even though of low-relief, remains wavy. As a result, at very low angles of terrain illumination such as exist in surface radar, the terrain backscattering statistics are dominated by relative incidences of illumination and shadow. At near grazing incidence, a theoretical planar surface remains fully illuminated, whereas a natural, low-relief, wavy terrain surface is mostly in shadow. As angle of illumination increases, just in very small increments above grazing incidence, the low-relief terrain surface rapidly comes into much fuller view. Some quantification of this fast onset of visibility in terms of a rapidly decreasing incidence of noise-level cells in low-angle clutter data with increasing depression angle is provided in Chapter 2 (see Figure 2.46). This rapid change in the relative proportions of shadowed cells vs illuminated cells with very small changes in angle of illumination of the low-relief forest surface dominates the low-angle clutter statistics of the surface, affecting both the mean strength σ w° and the shape parameter aw of these statistics. For low-relief forest terrain near grazing incidence, terrain elevation data and descriptive information describing the land cover are not precise and accurate enough to deterministically predict the shadowing statistics. For example, consider the shadowing that occurs from one tree crown to the next. Thus at low angles in low-relief terrain, geometric shadowing represents a statistical random process highly dependent on depression angle. In

514 Multifrequency Land Clutter Modeling Information

this book, such shadowing is referred to as microshadowing, by which is implied: (a) that the terrain under consideration is under general illumination (i.e., is not deep in macroshadow) and (b) that within the generally illuminated region, the shadowing occurs at microscale (i.e., at a scale associated with resolution cell size and even RF wavelength). The microshadowing statistics are embedded in and dominate low-angle clutter statistics. High-resolution SAR images dramatically indicate how the incidence of microshadowing is a very strong function of depression angle at very low angles. Over the range of depression angles, viz., 0° to 4°, for which clutter results for low-relief forest are provided in this section, full illumination of the terrain is not achieved. Although the clutter statistics change with angle over this range of angles, moving from a widespread spiky Weibull process at low angles and high resolution towards a more Rayleigh-like process at higher angles, Rayleigh statistics are not achieved over this range of angles. At higher angles, for example, 8° and above, nearly full illumination is achieved and the process does become essentially Rayleigh (see Section 2.4.4.3). Thus very significant geometric effects associated with depression angle, illumination, and shadow occur in clutter statistics from low-relief forest. The local inclination of the surface is important mostly as to whether it raises the surface into visibility or drops it into shadow. The effect of the local slope of the surface on its scattering strength is secondary. Associating clutter strength with terrain slope through grazing angle is more appropriate under conditions of full illumination of the terrain, which seldom prevail for surface radar. Associating clutter strength with depression angle ties clutter strength more directly to the dominating statistics of microshadowing at low angles on complex low-relief surfaces.

Trends in σ w° . Table 5.27 presents mean clutter strength σ w° for low-relief forest by frequency band, polarization, and depression angle and includes the number of measurements upon which each value of σ w° is based. The low-relief forest σ w° data of Table 5.27 are plotted in Figure 5.26. The main characteristics of the data in Figure 5.26 are similar to those of low-relief general mixed rural terrain shown in Figure 5.10 and discussed in Section 5.3.1.2. In particular, like the low-relief general mixed rural σ w° data, the low-relief forest σ w° data show the v-shapes within frequency bands indicating strong effects from depression angle. In Figure 5.26, the v-shape at X-band is particularly well-formed. Mean strength σ w° rises smoothly and uniformly with increasing depression angle through positive (i.e., left side of v-shape) depression angles from cyan (0° to 0.25°) to dark blue (0.25° to 0.75°) to purple (0.75° to 1.5°) to magenta (1.5° to 4°), and through negative (i.e., right side of v-shape) depression angles from cyan (0° to 0.25°) to dark green (0° to –0.25°) to intermediate green (–0.25° to –0.75°). This systematic behavior of increasing σ w° with increasing positive or negative depression angle is to a significant extent caused by decreasing incidence of microshadowing with increasing depression angle in low-relief forest, although the intrinsic effect of increasing clutter strength with increasing illumination angle is also at work in these results. Similar systematic behavior with small changes in depression angle is observed in the Phase Zero X-band data (e.g., see Figures 1.9, 2.44, and 2.47). A very large amount of measurement data from many sites underlies these very well-formed X-band vshapes, both for low-relief general mixed rural terrain in Figure 5.10 and for low-relief forest in Figure 5.26. A large amount of data is necessary for this systematic behavior with depression angle to emerge.

Multifrequency Land Clutter Modeling Information 515

Table 5.27 Mean Clutter Strength σ °w and Number of Measurements for Low-Relief Forest, by Frequency Band, Polarization, and Depression Anglea

° (dB) Weibull Mean Clutter Strength σw

␣ = Depression VHF

Angle (degrees) HH

VV

HH

L-Band

VV

X-Band

S-Band

HH

VV

HH

VV

HH

VV

4.0 ≤ ␣

-19.2

-20.7

-26.0 -24.2

-24.1

-25.0

----

----

----

----

1.50 ≤ ␣ < 4.00

-22.4

-22.7

-25.4 -21.5

-25.8

-26.2 -32.3

-30.7

-25.1

-23.8

0.75 ≤ ␣ < 1.50

-20.6

-22.9

-26.0 -24.1

-26.7

-25.5 -32.6

-30.5

-27.7

-26.8

0.25 ≤ ␣ < 0.75

-28.0

-27.1

-29.6 -26.1

-28.5

-28.2 -32.6

-30.6

-30.3

-28.9

0.00 ≤ ␣ < 0.25

-34.4

-35.4

-37.4 -34.8

-32.4

-31.8 -35.5

-33.3

-32.7

-32.3

-0.25 ≤ ␣ < 0.00

-27.6

-23.7

-35.0 -34.9

-29.6

-29.8 -35.5

-33.1

-31.9

-30.7

-0.75 ≤ ␣ < -0.25

-34.9

-32.1

-22.6 -24.7

-29.1

-31.2 -32.7

-28.6

-30.7

-29.1

␣ < -0.75

----

----

----

----

----

----

----

----

----

----

Number of Measurements

␣ = Depression HH

X-Band

S-Band

L-Band

UHF

VHF

Angle (degrees)

a

UHF

VV

HH

VV

HH

VV

HH

VV

HH

VV

4.0 ≤ ␣

12

13

12

11

12

11

0

0

0

0

1.50 ≤ ␣ < 4.00

49

53

60

60

60

59

50

49

15

15

0.75 ≤ ␣ < 1.50

92

97

106

107

94

98

104

105

74

72

0.25 ≤ ␣ < 0.75

113

113

143

151

162

164

167

163

94

92

0.00 ≤ ␣ < 0.25

79

83

152

142

127

142

135

134

118

129

-0.25 ≤ ␣ < 0.00

32

35

61

74

55

57

66

64

48

48

-0.75 ≤ ␣ < -0.25

4

4

2

4

4

5

3

3

5

5

␣ < -0.75

0

0

0

0

0

0

0

0

0

0

381

398

536

549

514

536

525

518

354

361

Table 5.24 defines the population of terrain patches upon which these data are based.

In Figure 5.26, mean clutter strengths at L-band are very similar to those at X-band. At Sband, the low depression angle (i.e., cyan, dark green, dark blue) σ w° data are slightly weaker than at L- and X-band, but the high depression angle (i.e., magenta, purple) S-band data are much weaker than at L- and X-band. In fact, the high depression angle dependence from dark blue (0.25° to 0.75°) through purple (0.75° to 1.5°), magenta (1.5° to 4°), and red (> 4°) that exists in other bands in Figure 5.26 is completely lacking at S-band. That is, at high angles at S-band, σ w° does not rise with depression angle. This lack of depression angle dependence at high angles in S-band σ w° data from low-relief forest indicates that, with increasing angle, the forest is becoming increasingly absorptive of the RF energy at Sband. Looking across all five frequency bands in Figure 5.26, this increased absorptivity at S-band is made very evident by lower values of σ w° (i.e., an S-band dip), particularly at the higher angles of illumination. The grazing incidence, 0° to 0.25° (cyan) low-relief forest σ w° results in Figure 5.26 show little variation with frequency band. At L-band and X-band, these results are at about the –32 dB level, with S-band slightly lower; at VHF and UHF, these results are at about the –35 dB level. However, in the lower bands there is a much larger increase from

516 Multifrequency Land Clutter Modeling Information

the cyan, 0° to 0.25° results to the dark blue, 0.25° to 0.75° results than in the upper bands. This increase is about 8 dB at VHF and UHF, about 4 dB at L-band, and about 3 dB at S- and X-band. This changing difference may indicate that there is a more rapid onset of illumination with increasing depression angle (or, in other words, that microshadow disappears faster) in the lower bands than in the upper bands, possibly due to increased diffractive effects at the lower frequencies. In the pure low-relief forest σ w° data of Figure 5.26, significant multipath is not generally at work to reduce the low-angle, cyan (0° to 0.25°) and dark blue (0.25° to 0.75°) σ w° results to much lower levels at VHF and UHF. In contrast, multipath does have significant influence in partially open, general mixed rural terrain to reduce the cyan and dark blue, VHF and UHF σ w° results of Figure 5.10 to lower levels. The existence of multipath in the low-relief general mixed rural σ w° results of Figure 5.10 is particularly evidenced by the fact that the low-angle cyan (0° to 0.25°) and dark blue (0.25° to 0.75°) σ w° results increase strongly with increasing frequency, VHF through L-band; a comparable strong uniform increase is lacking in the low-relief forest σ w° results of Figure 5.26. The v-shaped clusters in Figure 5.26 showing low-relief forest σ w° data are significantly lower in each frequency band than the v-shaped clusters in Figure 5.24 showing high-relief forest σ w° data. That is, in forested terrain, which constitutes a relatively simple, diffusely reflective scattering surface uncomplicated by questions of significant coherent reflection, separating terrain in two regimes of relief, high (terrain slopes > 2°) and low (terrain slopes < 2°), results in significant separation of mean clutter strengths; and in each regime of relief, the influence of microshadowing in low-angle clutter results in strong effects of depression angle on mean clutter strength. As expected, these effects of depression angle are more significant in low-relief than in high-relief forest terrain because the increased terrain slopes in high-relief terrain reduce the amount of microshadowing. Section 5.4.3.1 compared low-angle clutter statistics from high-relief forest and farmland. Comparison between Figures 5.20 and 5.26 (and Tables 5.19 and 5.27) indicates that lowrelief forest σ w° ranges from being substantially greater than low-relief farmland σ w° to being nearly equivalent to low-relief farmland σ w° , depending on frequency band and depression angle regime. More specifically, the amount by which low-relief forest σ w° exceeds low-relief farmland σ w° by frequency band and depression angle regime is: at VHF, from 20 dB at high angle to 6 dB at low angle; at UHF, from 10 dB at high angle to 6 dB at low angle; at L-band and X-band, by 6 or 7 dB at high angle to near equivalence at low angle; and at S-band, near equivalence at all angles. In broad measure, polarization differences are very small in the low-relief forest σ w° data of Figure 5.26. There is a slight overall bias whereby σ w° VV is slightly greater than σ w° HH —true in all depression angle regimes at S- and X-band, and, except for –0.25° to –0.75°, also at UHF; less generally true at VHF and L-band. The somewhat larger polarization differences in the –0.25° to –0.75° depression angle regime reflect the fact that little data are available in this regime.

Uncertain Outliers. In Figure 5.26 showing σ w° results for low-relief forest, there are relatively little data available in the light green, –0.25° to –0.75° depression angle regime (viz., 39 measured clutter histograms from four clutter patches; see Table 5.24). Nevertheless, in the three upper frequency bands these light green σ w° results fall in quite closely with the cyan and dark green results, and show a trend of increasing σ w° with

Multifrequency Land Clutter Modeling Information 517

increasing negative depression angle, cyan to dark green to light green. However, at VHF and UHF, larger differences occur between the light green and dark green σ w° results than in the upper bands, and the relative behavior of the light green and dark green results with respect to each other and with respect to the cyan results is more erratic. The light green results largely come from three patches (patch 39 at the Cold Lake measurement site and patches 46 and 47 at the Woking measurement site) which exist at relatively long ranges (33 to 47 km) with some mix of open and forested terrain occurring between the radar and the clutter patches. Thus some degree of multipath may be occurring in these light green VHF and UHF measurements, possibly acting to reduce clutter strength at VHF and to augment clutter strength at UHF. This possibility of multipath in the light green results does not explain why the dark green results, which are based on many more measurements than the light green results, are relatively strong at VHF and relatively weak at UHF. This discussion brings forward the fact that classification of a clutter patch as forest does not necessarily imply that all of the terrain between the patch and the radar is forested.

Shape Parameter aw. Table 5.28 provides the Weibull shape parameter aw and associated information for clutter amplitude distributions in low-relief forest terrain. Each Table 5.28 Shape Parameter aw and Ratios of Standard Deviation-to-Mean (SD/Mean) and Meanto-Median for Low-Relief Forest, by Spatial Resolution A and Depression Angle* Weibull Shape Parameter aw

␣ = Depression

from SD/Mean

Angle (degrees)

A = 103m2

from Mean/Median

A = 106m2

A = 103m2

A = 106m2

2.0

1.5a

2.4

1.3a

1.50 ≤ ␣ < 4.00

2.4

1.6a

2.8

1.6a

0.75 ≤ ␣ < 1.50

2.4

1.7

3.0

1.7

0.25 ≤ ␣ < 0.75

2.6

1.6

3.0

1.5

0.0 ≤ ␣ < 0.25

2.8

1.5

2.9

1.6

4.00 ≤ ␣

-0.25 ≤ ␣ < 0.00

3.1

1.7

3.1

1.9

-0.75 ≤ ␣ < -0.25

2.1b

1.5

2.7b

1.5

␣ < -0.75

----

----

----

----

Ratios

␣ = Depression Angle (degrees)

SD/Mean (dB) A=

103m2

A=

106m2

Mean/Median (dB) A = 103m2

A = 106m2

4.00 ≤ ␣

3.6

2.0a

8.7

2.7a

1.50 ≤ ␣ < 4.00

4.8

2.2a

11.0

4.1a

0.75 ≤ ␣ < 1.50

4.6

2.5

12.2

4.4

0.25 ≤ ␣ < 0.75

5.3

2.3

12.3

3.5

0.0 ≤ ␣ < 0.25

5.9

1.9

12.2

4.2

-0.25 ≤ ␣ < 0.00

6.7

2.6

13.3

5.6

-0.75 ≤ ␣ < -0.25

3.7b

1.9

10.2b

3.8

␣ < -0.75

----

----

----

----

a 5 2 6 2 Footnoted values apply at A = 10 m , not 10 m . b 5 2 3 2

Footnoted values apply at A = 10 m , not 10 m .

*

Table 5.24 defines the population of terrain patches and measurements upon which these data are based.

518 Multifrequency Land Clutter Modeling Information

pair of aw numbers in Table 5.28 comes from a scatter plot of sd/mean or mean/median vs spatial resolution A. Figure 5.27 shows the sd/mean scatter plot for the 0.0° to 0.25° depression angle regime. As in high-relief forest, spreads in clutter amplitude distributions continue to be relatively low in low-relief forest, compared with other terrain types. There continues to be a strong trend of decreasing spread with increasing cell size A, and a weak trend of decreasing spread with increasing depression angle. Spreads in low-relief forest are similar to spreads in high-relief forest. In Figure 5.27, the five VHF data points separate out as being of less spread than shown in the other bands and as being of little variation with A.

5.4.4 Shrubland Terrain Less discussion is provided for following terrain types in Section 5.4—shrubland, grassland, wetland, desert, mountains—than was provided for foregoing terrain types of urban, agricultural, and forest. The reason for this is to avoid redundant discussion—many of the points to be made have already been dealt with in previous discussions. Uncertain outliers continue to be indicated with open plot symbols for the terrain types that follow, although they are not discussed in the text. The land cover classification system utilized provides rangeland as a major land cover category (see Table 2.1). Within rangeland, there are three specific subcategories— herbaceous rangeland, shrubby rangeland, and mixed herbaceous/shrubby rangeland. Hereafter, pure herbaceous rangeland clutter patches are referred to as grassland, and patches classified as shrubby or herbaceous/shrubby mixtures are referred to as shrubland. Forest, shrubland, and grassland thus comprise three land cover classes involving natural vegetation for which the height of the vegetation significantly decreases from forest to shrubland to grassland. As will be seen, this decrease in vegetation height results in significantly differing clutter characteristics from these three terrain types. Table 5.29 shows the statistical populations underlying the shrubland clutter modeling information to follow. These populations are relatively low, involving only 1,030 measured clutter amplitude distributions from 51 patches. The high-relief shrubland patches come from three different sites, the low-relief shrubland patches from seven different sites.

5.4.4.1 High-Relief Shrubland Clutter modeling information for high-relief shrubland is given in Tables 5.30 and 5.31 and Figures 5.28 and 5.29. Mean clutter strengths at VHF and UHF in Figure 5.28 vary somewhat erratically. Mean strengths at L- and S-bands cluster more tightly. In general, high-relief shrubland mean clutter strengths in Figure 5.28 are relatively invariant with frequency, VHF to S-band, but increase at X-band. The X-band data are also tightly clustered by polarization and depression angle. Comparison with Figure 5.24 shows that mean clutter strength in high-relief forest is generally much greater than in high-relief shrubland, with the differences most pronounced in the lower bands and least at X-band. Comparison with Figure 5.18 shows that mean clutter strength in high-relief agricultural terrain is overall somewhat similar to that in high-relief shrubland. Table 5.31 indicates relatively little trend of decreasing spread with increasing cell size A, for high-relief shrubland, in contrast to most other terrain types. In particular, in the 0° to 1° depression angle regime, Figure 5.29 shows extreme variability in the scatter plot of sd/mean vs A, with a regression line in this case actually showing gradually increasing spread with A.

Multifrequency Land Clutter Modeling Information 519

Table 5.29 Numbers of Terrain Patches and Measured Clutter Histograms for Shrubland, by Relief and Depression Anglea,b,c

Terrain Relief

High-relief

Low-relief

␣ = Depression Angle (degrees) 2.0 ≤ ␣

Number of Patches 0

Number of Measurements 0

1.0 ≤ ␣ < 2.0

3

84

0.0 ≤ ␣ < 1.0

11

251

-1.0 ≤ ␣ < 0.0

3

33

␣ < -1.0

0

0

Totals

17

368

4.00 ≤ ␣

0

0

1.50 ≤ ␣ < 4.00

2

20

0.75 ≤ ␣ < 1.50

2

54

0.25 ≤ ␣ < 0.75

12

256

0.00 ≤ ␣ < 0.25

15

301

-0.25 ≤ ␣ < 0.00

3

31

␣ < -0.25

0

0

Totals

34

662

51

1,030

Grand Totals

a A single (primary) classifier only is sufficient to describe these patches.

b A terrain patch is a land surface macroregion usually several kms on a side (median patch area = 12.62 km2 ). c A measured clutter histogram contains all of the temporal (pulse by pulse) and spatial (resolution cell by resolution cell) clutter samples obtained in a given measurement of a terrain patch. A terrain patch was usually measured many times (nominally 20) as RF frequency (5), polarization (2), and range resolution (2) were varied over the Phase One radar parameter matrix.

This indicates that high-relief shrubland is extremely heterogeneous in character—the shrubland is not a homogeneous vegetative cover of uniform height and density.

5.4.4.2 Low-Relief Shrubland Clutter modeling information for low-relief shrubland is given in Tables 5.32 and 5.33 and Figures 5.30 and 5.31. Figure 5.30 indicates that mean clutter strength in low-relief shrubland has strong, well-behaved trends of variation with frequency and depression angle. In the 0° to 0.25° degree depression angle regime, mean clutter strengths rise from –52 or –54 dB at UHF to –33 or –34 dB at X-band; this 20 dB rise is due to decreasing multipath propagation loss with increasing frequency, UHF to X-band. The X-band data show a particularly well-behaved trend with depression angle rising from –33 dB at low angle to –23 dB at high angle. The VHF mean strengths at low angle (cyan) being stronger than at UHF indicates much stronger intrinsic σ ° at VHF than UHF, enough to overcome increased multipath propagation loss at VHF. In general these low-relief shrubland data are much weaker than low-relief forest except at X-band; they are also generally weaker than low-relief farmland. Table 5.33 and Figure 5.31 show that spreads in low-relief shrubland are somewhat better behaved than in high-relief shrubland—there are at least consistent trends of decreasing

520 Multifrequency Land Clutter Modeling Information

Table 5.30 Mean Clutter Strength σ °w and Number of Measurements for High-Relief Shrubland, by Frequency Band, Polarization, and Depression Anglea

Weibull Mean Clutter Strength σ°w (dB)

␣ = Depression Angle (degrees)

VHF

UHF

L-Band

S-Band

X-Band

HH

VV

HH

VV

HH

VV

HH

VV

HH

VV

2.0 ≤ ␣

----

----

----

----

----

----

----

----

----

----

1.0 ≤ ␣ < 2.0

-32.8

-31.4

-33.0

-35.6

-30.9

-36.1

-36.3

-35.1

-27.7

-25.4

0.0 ≤ ␣ < 1.0

-36.3

-28.0

-29.4

-28.8

-31.8

-33.5

-34.0

-31.8

-28.3

-26.5

-1.0 ≤ ␣ < 0.0

-32.9

-23.1

-41.1

-37.8

-35.7

-36.0

-34.3

-33.8

-33.6

-31.3

␣ < -1.0

----

----

----

----

----

----

----

----

----

----

Number of Measurements

␣ = Depression

VHF

Angle (degrees)

HH

VV

HH

L-Band VV

HH

S-Band

VV

HH

X-Band

VV

HH

VV

2.0 ≤ ␣

0

0

0

0

0

0

0

0

0

1.0 ≤ ␣ < 2.0

10

9

8

8

9

9

9

8

8

6

0.0 ≤ ␣ < 1.0

22

21

26

26

24

26

28

27

28

23

-1.0 ≤ ␣ < 0.0

1

2

3

4

3

4

4

4

4

4

␣ < -1.0

0

0

0

0

0

0

0

0

0

0

39

40

33

33

TOTALS a

UHF

32

37

38

36

39

41

0

Table 5.29 defines the population of terrain patches upon which these data are based.

Table 5.31 Shape Parameter aw and Ratios of Standard Deviation-to-Mean (SD/Mean) and Meanto-Median for High-Relief Shrubland, by Spatial Resolution A and Depression Anglea

␣ = Depression Angle (degrees)

Weibull Shape Parameter aw from SD/Mean A = 103m2

A = 106m2

A = 103m2

A = 106m2

2.0 ≤ ␣

---

---

---

---

1.0 ≤ ␣ < 2.0

3.3

2.0

3.5

2.8

0.0 ≤ ␣ < 1.0

2.4

3.2

3.6

3.2

-1.0 ≤ ␣ < 0.0

3.2

1.8

4.2

2.3

␣ < -1.0

---

---

---

---

␣ = Depression Angle (degrees)

Ratios SD/Mean (dB) 3

2

A = 10 m

a

from Mean/Median

A=

Mean/Median (dB)

106

2

m

A = 103m2

A = 106m2

2.0 ≤ ␣

---

---

---

---

1.0 ≤ ␣ < 2.0

7.2

3.5

16.3

11.4

0.0 ≤ ␣ < 1.0

4.8

6.8

16.6

14.0

-1.0 ≤ ␣ < 0.0

7.0

3.0

21.8

8.1

␣ < -1.0

---

---

---

---

Table 5.29 defines the population of terrain patches and measurements upon which these data are based.

Multifrequency Land Clutter Modeling Information 521

Table 5.32 Mean Clutter Strength σ w° and Number of Measurements for Low-Relief Shrubland, by Frequency Band, Polarization, and Depression Anglea

Weibull Mean Clutter Strength σ°w (dB)

␣ = Depression VHF

Angle (degrees)

HH

VV

L-Band

HH

VV

HH

S-Band

VV

HH

X-Band

VV

HH

VV

4.0 ≤ ␣

----

----

----

----

----

----

----

----

----

----

1.50 ≤ ␣ < 4.00

-29.1

-26.5

-28.9 -29.3

-28.8

-29.8 -36.5

-33.5

-23.8

-22.4

0.75 ≤ ␣ < 1.50

-34.1

-36.1

-34.8 -43.1

-43.4

-40.3 -39.8

-35.0

-26.9

-25.0

0.25 ≤ ␣ < 0.75

-49.9

-41.5

-39.4 -43.9

-36.3

-34.8 -38.2

-34.9

-31.1

-29.6

0.00 ≤ ␣ < 0.25

-40.3

-44.5

-54.0 -52.2

-45.1

-44.8 -42.9

-39.5

-34.0

-32.7

-0.25 ≤ ␣ < 0.00

----

-36.6

-47.2

50.2

-40.3

-40.9 -36.7

-32.7

-33.1

-32.0

␣ < -0.25

----

----

----

----

----

----

----

----

----

----

Number of Measurements

␣ = Depression

UHF

VHF

Angle (degrees)

a

UHF

S-Band

L-Band

HH

X-Band

VV

HH

VV

HH

VV

HH

VV

HH

VV

4.0 ≤ ␣

0

0

0

0

0

0

0

0

0

0

1.50 ≤ ␣ < 4.00

3

2

2

2

2

2

2

2

2

1

0.75 ≤ ␣ < 1.50

4

5

5

6

5

6

6

6

6

5

0.25 ≤ ␣ < 0.75

13

20

22

28

24

29

26

26

35

33

0.00 ≤ ␣ < 0.25

15

19

33

34

36

35

25

26

40

38

-0.25 ≤ ␣ < 0.00

0

1

2

4

4

4

4

4

4

4

␣ < -0.25

0

0

0

0

0

0

0

0

0

0

TOTALS

35

47

64

74

71

76

63

64

87

81

Table 5.29 defines the population of terrain patches upon which these data are based.

spread with increasing A, but the trends are weaker than in other terrain types. The scatter plot of Figure 5.31 for low-relief shrubland continues to show extreme variability, although the weak regression line shown is of the expected slope.

5.4.5 Grassland Terrain Table 5.34 shows the statistical populations underlying the grassland clutter modeling information to follow. As with shrubland, the high-relief grassland populations remain small, but the low-relief grassland populations are significantly higher. High-relief grassland patches come from six different sites, the low-relief grassland patches from nine different sites.

5.4.5.1 High-Relief Grassland Clutter modeling information for high-relief grassland is given in Tables 5.35 and 5.36 and Figures 5.32 and 5.33. Much of the high-relief grassland mean clutter strength data is in the 0° to 1° or 0° to –1° depression angle regimes. In contrast to high-relief shrubland, mean clutter strength in high-relief grassland shows a strong trend of increasing strength with increasing frequency, VHF to X-band; and is generally much weaker than high-relief

522 Multifrequency Land Clutter Modeling Information

Table 5.33 Shape Parameter aw and Ratios of Standard Deviation-to-Mean (SD/Mean) and Meanto-Median for Low-Relief Shrubland, by Spatial Resolution A and Depression Angle*

␣ = Depression Angle (degrees)

Weibull Shape Parameter aw from SD/Mean

from Mean/Median

A = 103m2

A = 106m2

A = 103m2

A = 106m2

4.00 ≤ ␣

----

----

----

----

1.50 ≤ ␣ < 4.00

3.4

1.7

2.9

3.4

0.75 ≤ ␣ < 1.50

2.6

2.2

2.8

2.2

0.25 ≤ ␣ < 0.75

3.1

2.7

3.6

2.7

0.00 ≤ ␣ < 0.25

2.9

2.8

2.5

2.5

-0.25 ≤ ␣ < 0.00

2.9a

2.9

3.8a

2.0

␣ < -0.25

----

----

----

----

Ratios

␣ = Depression Angle (degrees)

SD/Mean (dB)

Mean/Median (dB)

A = 103m2

A = 106m2

4.00 ≤ ␣

----

----

----

----

1.50 ≤ ␣ < 4.00

7.7

2.7

11.6

15.2

0.75 ≤ ␣ < 1.50

5.3

4.2

10.9

7.3

0.25 ≤ ␣ < 0.75

6.7

5.4

17.0

10.8

0.00 ≤ ␣ < 0.25

6.2

5.8

16.5

9.3

-0.25 ≤ ␣ < 0.00

6.2a

6.2

18.3a

6.0

␣ < -0.25

----

----

----

----

a

5

2

3

A = 103m2

A = 106m2

2

Footnoted values apply at A = 10 m , not 10 m .

*

Table 5.29 defines the population of terrain patches and measurements upon which these data are based.

shrubland, particularly in the lower bands. Also in marked contrast to high-relief shrubland, the information describing spread in clutter amplitude distributions in highrelief grassland in Table 5.36 and Figure 5.33 is well behaved, showing strong trends of decreasing spread with increasing cell size A, and a weaker trend of decreasing spread with increasing depression angle. The scatter plot of Figure 5.33 shows a strong trend of decreasing sd/mean with increasing A and little variability about its regression line, in marked contrast with the extreme shrubland scatter shown in Figures 5.29 and 5.31.

5.4.5.2 Low-Relief Grassland Clutter modeling information for low-relief grassland is given in Tables 5.37 and 5.38 and Figures 5.34 and 5.35. As in high-relief grassland, the low-relief grassland mean clutter strength data of Figure 5.34 continue to show a strong trend of increasing strength with increasing frequency, VHF to X-band. There is little variation in these results with depression angle. Mean clutter strength in low-relief grassland is somewhat weaker than in high-relief grassland in every band. Comparison with low-relief shrubland is interesting in

Multifrequency Land Clutter Modeling Information 523

Table 5.34 Numbers of Terrain Patches and Measured Clutter Histograms for Grassland, by Relief and Depression Anglea,b,c

Terrain Relief

␣ = Depression Angle (degrees)

High-relief

Low-relief

Number of Patches

Number of Measurements

4.0 ≤ ␣

0

2.0 ≤ ␣ < 4.0

1

8

1.0 ≤ ␣ < 2.0

5

34

0

0.0 ≤ ␣ < 1.0

3

76

-1.0 ≤ ␣ < 0.0

14

115

␣ < -1.0

0

0

Totals

23

233

4.00 ≤ ␣

0

0

1.50 ≤ ␣ < 4.00

2

39

0.75 ≤ ␣ < 1.50

11

377

0.25 ≤ ␣ < 0.75

36

1,021

0.00 ≤ ␣ < 0.25

27

706

-0.25 ≤ ␣ < 0.00

14

168

-0.75 ≤ ␣ < -0.25

5

29

Grand Totals

␣ < -0.75

0

0

Totals

95

2,340

118

2,573

a A single (primary) classifier only is sufficient to describe these patches. b 2 A terrain patch is a land surface macroregion usually several kms on a side (median patch area = 12.62 km ). c

A measured clutter histogram contains all of the temporal (pulse by pulse) and spatial (resolution cell by resolution cell) clutter samples obtained in a given measurement of a terrain patch. A terrain patch was usually measured many times (nominally 20) as RF frequency (5), polarization (2), and range resolution (2) were varied over the Phase One radar parameter matrix.

that mean clutter strength in low-relief shrubland has such a strong dependency on depression angle in every band, whereas in low-relief grassland it has none. At higher angles, low-relief shrubland is stronger than low-relief grassland in every band; but at grazing incidence the picture is more complicated, with grassland equal or stronger in the upper bands, but shrubland stronger at VHF. The spreads in clutter amplitude distributions in low-relief grassland given in Table 5.38 and Figure 5.35, as in high-relief grassland, continue to show strong trends of decreasing spread with increasing cell size A. The scatter plot of Figure 5.35 shows strong correlation about the regression line.

524 Multifrequency Land Clutter Modeling Information

Table 5.35 Mean Clutter Strength σ w° and Number of Measurements for High-Relief Grassland, by Frequency Band, Polarization, and Depression Anglea

Weibull Mean Clutter Strength σ°w (dB)

␣ = Depression

VHF

Angle (degrees)

S-Band

L-Band

X-Band

VV

HH

VV

HH

VV

HH

VV

HH

VV

4.0 ≤ ␣

----

----

----

----

----

----

----

----

----

----

2.0 ≤ ␣ < 4.0

-32.8

-24.4

----

----

-29.3

-29.7 -38.0

-33.3

----

----

1.0 ≤ ␣ < 2.0

-31.2

-26.3

-23.3 -22.6

-31.3

-32.2 -35.0

-32.9

----

----

0.0 ≤ ␣ < 1.0

-52.8

-50.4

-46.6 -41.5

-33.7

-34.0 -28.4

-27.2

-26.1

-25.0

-1.0 ≤ ␣ < 0.0

-53.4

-53.6

-38.8 -44.3

-33.3

-37.2 -31.9

-27.3

-32.9

-30.6

␣ < -1.0

----

----

----

----

----

----

----

----

----

----

Number of Measurements

␣ = Depression HH

VV

HH

VV

HH

X-Band

S-Band

L-Band

UHF

VHF

Angle (degrees)

a

UHF

HH

VV

HH

VV

HH

VV

4.0 ≤ ␣

0

0

0

0

0

0

0

0

0

0

2.0 ≤ ␣ < 4.0

1

1

0

0

1

1

2

2

0

0

1.0 ≤ ␣ < 2.0

4

5

2

1

5

5

6

6

0

0

0.0 ≤ ␣ < 1.0

1

4

8

8

8

8

10

9

10

10

-1.0 ≤ ␣ < 0.0

4

6

16

16

17

14

8

6

15

13

␣ < -1.0

0

0

0

0

0

0

0

0

0

0

TOTALS

10

16

26

25

31

28

26

23

25

23

Table 5.34 defines the population of terrain patches upon which these data are based.

Multifrequency Land Clutter Modeling Information 525

Table 5.36 Shape Parameter aw and Ratios of Standard Deviation-to-Mean (SD/Mean) and Meanto-Median for High-Relief Grassland, by Spatial Resolution A and Depression Angle*

␣ = Depression Angle (degrees)

4.0 ≤ ␣

Weibull Shape Parameter aw from SD/Mean

from Mean/Median

A = 103m2

A = 106m2

A = 103m2

----

A = 106m2

----

----

----

2.0 ≤ ␣ < 4.0

2.0

a

1.6

2.3a

1.4

1.0 ≤ ␣ < 2.0

2.1a

1.9

3.1a

2.0

0.0 ≤ ␣ < 1.0

3.3

1.8b

3.8

2.2b

-1.0 ≤ ␣ < 0.0

3.4

1.7

3.6

2.2

␣ < -1.0

----

----

----

----

Ratios

␣ = Depression Angle (degrees)

SD/Mean (dB)

Mean/Median (dB)

A = 103m2

A = 106m2

A = 103m2

A = 106m2

4.0 ≤ ␣

----

----

----

----

2.0 ≤ ␣ < 4.0

3.6a

2.2

8.0a

3.0

1.0 ≤ ␣ < 2.0

3.8a

3.2

13.4a

6.4

0.0 ≤ ␣ < 1.0

7.2

2.7b

18.9

7.6b

-1.0 ≤ ␣ < 0.0

7.6

2.7

17.3

7.5

␣ < -1.0

----

----

----

----

a 5 2 3 2 Footnoted values apply at A = 10 m , not 10 m . b 5 2 6 2

Footnoted values apply at A = 10 m , not 10 m .

*

Table 5.34 defines the population of terrain patches and measurements upon which these data are based.

526 Multifrequency Land Clutter Modeling Information

Table 5.37 Mean Clutter Strength σ w° and Number of Measurements for Low-Relief Grassland, by Frequency Band, Polarization, and Depression Anglea

Weibull Mean Clutter Strength σ°w (dB)

␣ = Depression Angle (degrees)

VHF HH

VV

HH

VV

HH

X-Band

S-Band

VV

HH

VV

HH

VV

4.0 ≤ ␣

----

----

----

----

----

----

----

----

----

----

1.50 ≤ ␣ < 4.00

-63.3

-41.7

-55.2 -51.5

-40.7

-39.5 -37.3

-36.2

-39.1

-36.8

0.75 ≤ ␣ < 1.50

-52.9

-54.6

-47.5 -47.6

-40.7

-42.4 -41.4

-41.4

-36.8

-35.1

0.25 ≤ ␣ < 0.75

-57.9

-54.5

-41.9 -40.8

-37.3

-37.0 -41.3

-39.5

-35.4

-34.1

0.00 ≤ ␣ < 0.25

-57.7

-60.3

-45.3 -43.2

-41.8

-42.6 -40.8

-39.9

-37.2

-36.2

-0.25 ≤ ␣ < 0.00

-60.7

-48.8

-45.3 -42.5

-43.1

-39.9 -40.3

-35.9

-32.8

-33.7

-0.75 ≤ ␣ < -0.25

-15.8

-33.5

-26.9 -22.4

-35.2

-39.5

----

----

-27.5

-28.7

␣ < -0.75

----

----

----

----

----

----

----

----

----

----

␣ = Depression Angle (degrees) 4.0 ≤ ␣

a

L-Band

UHF

Number of Measurements

VV

HH

VV

HH

0

0

0

0

0

X-Band

S-Band

L-Band

UHF

VHF HH

VV

HH 0

0

VV

HH

VV

0

0

4

0

1.50 ≤ ␣ < 4.00

3

4

4

5

6

6

2

2

3

0.75 ≤ ␣ < 1.50

26

36

30

30

47

41

32

31

49

55

0.25 ≤ ␣ < 0.75

72

87

109

114

116

112

57

58

141

155

0.00 ≤ ␣ < 0.25

27

31

66

66

84

93

55

59

114

111 32 4

-0.25 ≤ ␣ < 0.00

3

6

16

17

19

23

12

10

30

-0.75 ≤ ␣ < -0.25

2

3

4

4

4

4

0

0

4

0 361

␣ < -0.75

0

0

0

0

0

0

0

0

0

TOTALS

133

167

229

236

276

279

158

160

341

Table 5.34 defines the population of terrain patches upon which these data are based.

Shrubland vs Grassland. The classification system separating shrubland from grassland as specific subcategories of general rangeland has found significant differences in the low-angle clutter characteristics of shrubland and grassland. Shrubland shows a strong trend of mean strength on depression angle (Figure 5.30), but is poorly behaved in its spread characteristics (Figure 5.31), whereas grassland shows little or no variation of mean strength with depression angle (Figure 5.34), but is well behaved in its spread characteristics with strong trends of decreasing spread with increasing cell size A (Figure 5.35). It is interesting to compare and contrast the grassland and shrubland mean clutter strength data provided here in Chapter 5 with the well-behaved Vananda East repeat sector mean clutter strength characteristic shown in Figure 3.6 in Chapter 3—the Vananda East repeat sector was transitional between grassland (LC = 31) and shrubland (LC = 32) in lowrelief terrain with undulating (LF = 3) and hummocky (LF = 5) components; see Figure 3.6.

5.4.6 Wetland Terrain Table 5.39 shows the statistical population underlying the wetland clutter modeling information to follow. This population comprises 447 measured clutter amplitude

Multifrequency Land Clutter Modeling Information 527

Table 5.38 Shape Parameter aw and Ratios of Standard Deviation-to-Mean (SD/Mean) and Meanto-Median for Low-Relief Grassland, by Spatial Resolution A and Depression Angle*

␣ = Depression Angle (degrees)

Weibull Shape Parameter aw from SD/Mean

from Mean/Median

A = 103m2

A = 106m2

A = 103m2

A = 106m2

4.00 ≤ ␣

----

----

----

----

1.50 ≤ ␣ < 4.00

3.2

1.4a

3.8

1.8a

0.75 ≤ ␣ < 1.50

3.5

2.0a

2.9

3.0a

0.25 ≤ ␣ < 0.75

3.9

1.5

3.7

1.9

0.00 ≤ ␣ < 0.25

4.1

1.7

3.7

2.2

-0.25 ≤ ␣ < 0.00

3.2

2.1

3.6

2.5

-0.75 ≤ ␣ < -0.25

2.8b

2.3

3.0b

3.1

␣ < -0.75

----

----

----

----

Ratios

␣ = Depression Angle (degrees)

SD/Mean (dB)

Mean/Median (dB)

A = 103m2

A = 106m2

A = 103m2

A = 106m2

4.00 ≤ ␣

----

----

----

----

1.50 ≤ ␣ < 4.00

7.1

1.7a

18.4

5.2a

0.75 ≤ ␣ < 1.50

7.8

3.6

a

11.8

12.4a

0.25 ≤ ␣ < 0.75

8.9

1.8

17.5

5.9

0.0 ≤ ␣ < 0.25

9.6

2.4

17.6

7.4

-0.25 ≤ ␣ < 0.00

6.9

3.9

17.3

9.0

-0.75 ≤ ␣ < -0.25

5.8b

4.3

12.5b

13.0

␣ < -0.75

----

----

----

----

a 5 2 6 2 Footnoted values apply at A = 10 m , not 10 m . b 5 2 3 2

Footnoted values apply at A = 10 m , not 10 m .

*

Table 5.34 defines the population of terrain patches and measurements upon which these data are based.

distributions from 17 clutter patches at three different sites. Many of these measurements occurred at Big Grass Marsh, Manitoba, which was visited by Phase One in winter weather (see Chapter 3, Section 3.4.1.5). All wetland clutter patches were of “level” landform classification. Clutter modeling information for wetland is provided in Tables 5.40 and 5.41 and Figures 5.36 and 5.37. As shown in Figure 5.36, mean clutter strength for wetland is very weak—in fact, it is the weakest clutter strength in every band of any of the terrain types examined. The results of Figure 5.37 correspond quite closely with the Big Grass Marsh repeat sector results shown in Figure 3.8 in Chapter 3. Mean clutter strength is particularly weak at VHF and UHF in Figure 5.36, hovering in the neighborhood of –67 to –72 dB. Although very weak, these are accurate measured clutter strength numbers unaffected by Phase One

528 Multifrequency Land Clutter Modeling Information

Table 5.39 Numbers of Terrain Patches and Measured Clutter Histograms for Wetland, by Depression Anglea,b,c

Terrain Relief

␣ = Depression Angle

Level

(degrees)

Number of Patches

Number of Measurements

0.75 ≤ ␣

0

0

0.25 ≤ ␣ < 0.75

9

311

0.00 ≤ ␣ < 0.25

8

136

␣ < 0.00

0

0

Totals

17

447

a A single (primary) classifier only is sufficient to describe these patches. b

A terrain patch is a land surface macroregion usually several kms on a side (median patch area = 12.62 km2 ). c A measured clutter histogram contains all of the temporal (pulse by pulse) and spatial (resolution cell by resolution cell) clutter samples obtained in a given measurement of a terrain patch. A terrain patch was usually measured many times (nominally 20) as RF frequency (5), polarization (2), and range resolution (2) were varied over the Phase One radar parameter matrix.

Table 5.40 Mean Clutter Strength σ w° and Number of Measurements for Wetland, by Frequency Band, Polarization, and Depression Anglea

Weibull Mean Clutter Strength σ°w (dB)

␣ = Depression Angle (degrees)

VHF

L-Band

S-Band

X-Band

HH

VV

HH

VV

HH

VV

HH

VV

HH

VV

0.75 ≤ ␣

----

----

----

----

----

----

----

----

----

----

0.25 ≤ ␣ < 0.75

-63.5

-70.1

-68.5

-68.2

-56.3

-55.8

-42.2

-41.0

-39.0

-37.4

0.0 ≤ ␣ < 0.25

-67.3

-66.9

-72.4

-68.9

-61.9

-60.4

-49.6

-49.5

-39.5

-39.0

␣ < 0.0

----

----

----

----

----

----

----

----

----

----

Number of Measurements

␣ = Depression

UHF

VHF

Angle (degrees) HH

a

UHF

VV

HH

L-Band VV

HH

S-Band

VV

HH

X-Band

VV

HH

VV

0.75 ≤ ␣

0

0

0

0

0

0

0

0

0

0

0.25 ≤ ␣ < 0.75

27

19

27

28

35

36

34

34

33

38

0.0 ≤ ␣ < 0.25

1

7

8

12

9

13

19

17

22

28

␣ < 0.0

0

0

0

0

0

0

0

0

0

0

TOTALS

28

26

35

40

44

49

53

51

55

66

Table 5.39 defines the population of terrain patches upon which these data are based.

Multifrequency Land Clutter Modeling Information 529

Table 5.41 Shape Parameter aw and Ratios of Standard Deviation-to-Mean (SD/Mean) and Meanto-Median for Wetland, by Spatial Resolution A and Depression Angle*

Weibull Shape Parameter aw

␣ = Depression

from SD/Mean

Angle (degrees)

3

2

A=

A = 10 m

2

m

A = 103m2

A = 106m2

0.75 ≤ ␣

---

---

---

---

0.25 ≤ ␣ < 0.75

3.1

1.7

3.4

1.6

0.00 ≤ ␣ < 0.25

4.2

2.4a

4.0

3.1a

␣ < 0.00

---

---

---

---

Ratios

␣ = Depression

SD/Mean (dB)

Angle (degrees)

3

2

A=

A = 10 m

a

from Mean/Median

106

Mean/Median (dB)

106

2

m

A = 103m2

A = 106m2 ---

0.75 ≤ ␣

---

---

---

0.25 ≤ ␣ < 0.75

6.6

2.5

15.8

4.1

0.00 ≤ ␣ < 0.25

9.7

4.8a

19.9

13.1a

␣ < 0.00

---

---

---

---

5

2

6

2

Footnoted values apply at A = 10 m , not 10 m .

* Table 5.39 defines the population of terrain patches and measurements upon which these data are based.

sensitivity limitations and noise corruption (see Appendix 3.C for examples of accurate weak clutter computation at Big Grass Marsh). The wetland mean strength data show a strong trend of increasing strength with increasing frequency, UHF to X-band—obviously due to multipath propagation, and a weaker trend in most bands of increasing strength with increasing depression angle between 0° to 0.25° and 0.25° to 0.75°—the only depression angle regimes in which data exist for wetland. The fact that VHF mean clutter strengths are somewhat stronger than at UHF indicates that intrinsic σ° is significantly greater at VHF than UHF for wetland, a result previously seen in repeat sector data in Chapter 3. Table 5.41 and Figure 5.37 indicate strong trends of decreasing spread in level wetland clutter amplitude distributions with increasing cell size A. In this respect, level wetland is like low-relief grassland (compare Figure 5.37 with Figure 5.35).

5.4.7 Desert Terrain Desert terrain does not explicitly appear in the land cover and landform terrain classification systems employed herein (see Section 2.2.3, Tables 2.1 and 2.2). A criterion utilized to specify desert clutter within the Phase One measurement database is that the desert clutter must come from two Phase One sites—Booker Mountain, Nevada, and Knolls, Utah—that were situated in typical western desert terrain (see Section 3.4.1.5). Booker Mountain was a high site; Knolls was a low site. At both sites, low-relief desert valleys were surrounded by steep terrain at much higher elevations. The low-relief valley floors were typically covered with sparse desert vegetation, but with occasional barren dry lake beds or salt flats. The surrounding high-relief terrain had occasional occurrences of

530 Multifrequency Land Clutter Modeling Information

patches of trees, principally on steep slopes at higher elevations. A further criterion for a clutter patch to be accepted as desert at either of these two sites is that, if low relief, its land cover classification be predominantly rangeland or barren; if high-relief, a component of trees was also allowed. Table 5.42 indicates that, for desert terrain thusly defined, there are available 2,884 measured Phase One clutter amplitude distributions from 279 desert clutter patches. These desert patches and histograms are approximately equally distributed between high-relief patches and low-relief patches. Repeat sector desert clutter measurements at Booker Mountain and Knolls were previously discussed in Chapter 3, Section 3.4.1.5 (in particular, see Figure 3.37). Table 5.42 Numbers of Terrain Patches and Measured Clutter Histograms for Desert, by Relief and Depression Anglea,b,c

Terrain Relief


= Depression Angle (degrees)

High-relief

Number of Measurements

6.0 ≤


0

0

4.0 ≤
< 6.0

1

21

2.0 ≤
< 4.0

3

46

1.0 ≤
< 2.0

3

66

0.0 ≤
< 1.0

30

358

-1.0 ≤
< 0.0

113

1,062


< -1.0 Totals Low-relief

Number of Patches

2

10

152

1,563

4.00 ≤


0

0

1.50 ≤
< 4.00

7

147

0.75 ≤
< 1.50

10

161

0.25 ≤
< 0.75

34

346

0.00 ≤
< 0.25

53

484

-0.25 ≤
< 0.00

18

159

-0.75 ≤
< -0.25

5

24


< -0.75

0

0

127

1,321

279

2,884

Totals Grand Totals

a American Intermontane West terrain. Knolls and Booker Mountain sites. Predominantly with shrubby

desert vegetation or barren. b A terrain patch is a land surface macroregion usually several kms on a side (median patch area 2

= 12.62 km ). c A measured clutter histogram contains all of the temporal (pulse by pulse) and spatial (resolution cell

by resolution cell) clutter samples obtained in a given measurement of a terrain patch. A terrain patch was usually measured many times (nominally 20) as RF frequency (5), polarization (2), and range resolution (2) were varied over the Phase One radar parameter matrix.

Multifrequency Land Clutter Modeling Information 531

5.4.7.1 High-Relief Desert Clutter modeling information for high-relief desert is given in Tables 5.43 and 5.44 and Figures 5.38 and 5.39. In Figure 5.38, mean clutter strengths at low angles (cyan and green) are observed to be relatively frequency independent, VHF to S-band—but perhaps a little stronger at X-band. In this respect these data are very different from high-relief forest, even though high-relief desert terrain has significant occurrences of trees. In the lower bands in Figure 5.38 there is an unusual strong, inverse dependence with depression angle wherein clutter strengths decrease with increasing depression angle, from cyan through dark blue, and purple, to magenta. The reason for this unusual trend in these data is as follows. High-relief desert terrain observed at low angles comes from either steep surrounding mountains at the low Knolls site or steep neighboring mountain peaks at the high Booker Mountain site. Such steep terrain observed at near broadside incidence (i.e., low depression angle) results in strong clutter. In contrast, high-relief desert observed at high depression angle comes from terrain of lower elevations—albeit of high relief—at the higher Booker Mountain site. Looking down at surrounding, lower elevation, mountainous patches provides significantly weaker clutter in Figure 5.38 (dark blue, Table 5.43 Mean Clutter Strength σ w° and Number of Measurements for High-Relief Desert, by Frequency Band, Polarization, and Depression Anglea

° (dB) Weibull Mean Clutter Strength σw


= Depression VHF

Angle (degrees) HH

L-Band

HH

VV

HH

S-Band

X-Band

VV

HH

VV

HH

VV

6.0 ≤


----

----

----

----

----

----

----

----

----

----

4.0 ≤
< 6.0

-45.8

-42.9

-54.2 -47.4

-40.7

-41.7

----

----

----

----

2.0 ≤
< 4.0

-36.6

-34.6

-30.0 -29.6

-29.1

-30.9 -42.4

-39.8

----

----

1.0 ≤
< 2.0

-37.0

-32.0

-32.7 -32.2

-30.7

-32.3 -38.7

-37.3

-23.9

-22.9

0.0 ≤
< 1.0

-25.5

-29.3

-28.4 -28.0

-26.9

-28.4 -28.3

-27.9

-22.9

-22.8

-1.0 ≤
< 0.0

-24.4

-27.2

-24.7 -26.2

-24.6

-25.7 -24.5

-23.0

-24.5

-24.8


< -1.0

-26.6

-28.1

-22.3 -27.5

-24.8

-28.9 -24.4

-21.4

-25.0

-23.0


= Depression Angle (degrees) 6.0 ≤


Number of Measurements X-Band

S-Band

L-Band

UHF

VHF HH

VV

HH

VV

HH

VV

0

0

0

0

0

0

HH 0

VV

HH

VV

0

0

0 0 0

4.0 ≤
< 6.0

3

4

4

4

3

3

0

0

0

2.0 ≤
< 4.0

8

8

8

8

5

5

2

2

0

6

1.0 ≤
< 2.0

6

7

7

7

6

7

7

7

6

0.0 ≤
< 1.0

34

36

36

35

33

33

36

36

36

43

-1.0 ≤
< 0.0

98

98

104

103

102

101

105

106

113

132


< -1.0

1

1

1

1

1

1

1

1

1

1

152

156

182

TOTALS a

UHF VV

150

154

160

158

150

150

151

Table 5.42 defines the population of terrain patches upon which these data are based.

532 Multifrequency Land Clutter Modeling Information

Table 5.44 Shape Parameter aw and Ratios of Standard Deviation-to-Mean (SD/Mean) and Meanto-Median for High-Relief Desert, by Spatial Resolution A and Depression Angle*

Weibull Shape Parameter aw


= Depression Angle (degrees)

from SD/Mean

from Mean/Median

A = 103m2

A = 106m2

A = 103m2

A = 106m2

6.0 ≤


----

----

----

----

4.0 ≤
< 6.0

3.1

1.8

2.3

2.3

2.0 ≤
< 4.0

2.4

2.2

3.0

2.3

1.0 ≤
< 2.0

3.5

2.2

3.5

2.7

0.0 ≤
< 1.0

4.1

1.9

4.7

2.3

-1.0 ≤
< 0.0

3.8

2.0

5.3

2.6


< -1.0

3.3a

2.1

5.4a

3.1

Ratios


= Depression Angle (degrees)

a

SD/Mean (dB)

Mean/Median (dB)

A = 103m2

A = 106m2

A = 103m2

A = 106m2

6.0 ≤


----

----

----

----

4.0 ≤
< 6.0

6.8

2.7

7.7

8.2

2.0 ≤
< 4.0

4.6

4.1

12.9

7.9

1.0 ≤
< 2.0

7.9

4.1

16.1

10.7

0.0 ≤
< 1.0

9.4

3.1

26.4

8.1

-1.0 ≤
< 0.0

8.7

3.6

31.4

9.9


< -1.0

7.2a

3.7

32.4a

13.5

5

2

3

2

Footnoted values apply at A = 10 m , not 10 m .

*

Table 5.42 defines the population of terrain patches and measurements upon which these data are based.

purple, magenta) than when surrounding mountainous patches at more nearly equal or even greater elevation are viewed nearer broadside incidence (cyan, dark green). The Xband data in Figure 5.38 do not show this trend, or any trend with depression angle— rather, they form a very tight cluster. In Section 5.4.8 which follows, a similar inverse trend of mean clutter strength with depression angle for mountain terrain is observed, and for the same reasons. Table 5.44 and Figure 5.39 provide information on the spread of clutter amplitude distributions in high-relief desert terrain. There is seen to be a strong general trend of decreasing spread with increasing cell size A; there is also a weaker trend whereby spread diminishes with increasing depression angle.

Multifrequency Land Clutter Modeling Information 533

5.4.7.2 Low-Relief Desert Clutter modeling information for low-relief desert is given in Tables 5.45 and 5.46 and Figures 5.40 and 5.41. Comparison of Figure 5.40 with Figure 5.38 shows mean clutter strength in low-relief desert to be generally very much weaker than in high-relief desert. Also, in marked contrast to high-relief desert, in low-relief desert there is a strong, positive, trend—not inverse here—of increasing clutter strength with increasing depression angle. This expected trend indicates that clutter strength from low-relief desert valley floors is stronger as observed at high depression angle from Booker Mountain, but is weaker as observed at low depression angle from Knolls. A number of other interesting observations may be made of the low-relief desert data of Figure 5.40. First note that at low positive depression angles (cyan, dark blue), mean clutter strength is relatively invariant with frequency band, VHF to X-band (a little weaker at UHF, a little stronger at X-band). Furthermore, at higher angles (purple, magenta), mean clutter strength (although generally somewhat higher than at low angles) is also remarkably Table 5.45 Mean Clutter Strength σ w° and Number of Measurements for Low-Relief Desert, by Frequency Band, Polarization, and Depression Anglea

Weibull Mean Clutter Strength σ°w (dB)

␣ = Depression Angle (degrees)

VHF HH

VV

HH

VV

HH

S-Band

VV

HH

X-Band

VV

HH

VV

4.0 ≤ ␣

----

----

----

----

----

----

----

----

----

----

1.50 ≤ ␣ < 4.00

-35.8

-35.6

-37.7 -35.5

-34.6

-38.1 -38.0

-37.1

-19.4

-22.1

0.75 ≤ ␣ < 1.50

-35.3

-34.5

-36.7 -36.6

-34.1

-35.5 -32.4

-33.5

-22.5

-22.3

0.25 ≤ ␣ < 0.75

-40.8

-40.6

-40.4 -46.3

-36.9

-41.2 -38.5

-36.3

-33.3

-33.7

0.00 ≤ ␣ < 0.25

-42.3

-36.5

-45.0 -45.1

-38.5

-40.0 -39.0

-38.0

-32.9

-34.3

-0.25 ≤ ␣ < 0.00

-29.7

-31.0

-32.6 -34.9

-32.0

-34.0 -30.4

-27.6

-28.1

-27.0

-0.75 ≤ ␣ < -0.25

-34.8

-28.7

-37.2 -40.5

-32.8

-24.0 -37.8

-38.3

-30.9

-35.1

␣ < -0.75

----

----

----

----

----

----

----

----

----

----

Number of Measurements

␣ = Depression

4.0 ≤ ␣

X-Band

S-Band

L-Band

UHF

VHF

Angle (degrees)

a

L-Band

UHF

HH

VV

HH

VV

HH

VV

0

0

0

0

0

0

HH 0

VV

HH

VV

0

0

5

0

1.50 ≤ ␣ < 4.00

18

18

17

17

12

15

21

20

4

0.75 ≤ ␣ < 1.50

16

17

15

16

14

14

16

17

15

21

0.25 ≤ ␣ < 0.75

29

43

31

34

30

31

37

33

39

39

0.00 ≤ ␣ < 0.25

33

54

39

47

39

39

50

51

70

62 17 3

-0.25 ≤ ␣ < 0.00

15

14

16

16

16

16

15

16

18

-0.75 ≤ ␣ < -0.25

3

4

3

3

1

1

2

1

3

0 147

␣ < -0.75

0

0

0

0

0

0

0

0

0

TOTALS

114

150

121

133

112

116

141

138

149

Table 5.42 defines the population of terrain patches upon which these data are based.

534 Multifrequency Land Clutter Modeling Information

Table 5.46 Shape Parameter aw and Ratios of Standard Deviation-to-Mean (SD/Mean) and Meanto-Median for Low-Relief Desert, by Spatial Resolution A and Depression Angle*

Weibull Shape Parameter aw

␣ = Depression Angle (degrees)

from SD/Mean

from Mean/Median

A = 103m2

A = 106m2

A = 103m2

A = 106m2

4.00 ≤ ␣

----

----

----

----

1.50 ≤ ␣ < 4.00

2.9

2.7

2.3

3.1

0.75 ≤ ␣ < 1.50

2.7

2.5

2.4

2.6

0.25 ≤ ␣ < 0.75

4.1

2.3

3.5

2.3

0.00 ≤ ␣ < 0.25

4.5

1.9

4.4

1.5 2.4

-0.25 ≤ ␣ < 0.00

3.8

2.0

4.3a

-0.75 ≤ ␣ < -0.25

3.3b

2.7

3.1b

2.4

␣ < -0.75

----

----

----

----

Ratios

␣ = Depression Angle (degrees)

SD/Mean (dB)

Mean/Median (dB)

A = 103m2

A = 106m2

A = 103m2

A = 106m2

4.00 ≤ ␣

----

----

----

----

1.50 ≤ ␣ < 4.00

6.0

5.6

8.0

13.4

0.75 ≤ ␣ < 1.50

5.5

5.1

8.5

10.1

0.25 ≤ ␣ < 0.75

9.5

4.3

15.9

8.2

0.0 ≤ ␣ < 0.25

10.7

3.2

23.7

3.9

-0.25 ≤ ␣ < 0.00

8.7

3.4

22.4

-0.75 ≤ ␣ < -0.25

7.2b

5.4

13.1b

8.4

␣ < -0.75

----

----

----

----

a

8.3

a 4 2 3 2 Footnoted values apply at A = 10 m , not 10 m . b 5 2 3 2

Footnoted values apply at A = 10 m , not 10 m .

*

Table 5.42 defines the population of terrain patches and measurements upon which these data are based.

invariant with frequency, in this case VHF to S-band, but jumps ~15 dB in clutter strength, S-band to X-band. This remarkable increase in mean clutter strength from S-band to Xband in high-angle data, and from low angle to high angle in X-band data, when looking down at high angle to a low-relief desert valley floor, was discussed earlier in the repeat sector results of Chapter 3 (Sections 3.4.1.5 and 3.4.2). In these survey data of Chapter 5, looking down at desert vegetation at high angle at X-band is even somewhat stronger than looking down at forest vegetation at high angle at X-band (see Figure 5.26), although otherwise mean clutter strength in low-relief forest is generally much greater than mean clutter strength in low-relief desert. This unusually strong, X-band only and high angle only, mean clutter strength of low-relief desert is even marginally higher than the corresponding mean strength in high-relief desert (see Figure 5.38). Finally, in Figure 5.40, note that mean clutter strength in low-relief desert at low negative depression angle (dark

Multifrequency Land Clutter Modeling Information 535

green) is relatively frequency invariant and relatively strong in all bands, VHF to X-band. For the most part, these data come from the higher terrain surrounding the valley at Knolls. Table 5.46 and Figure 5.41 show clutter modeling information for spreads of clutter amplitude distributions in low-relief desert. These data are similar to those in high-relief desert, with strong trends of decreasing spread with increasing cell size A and a weaker trend of decreasing spread with increasing depression angle. That is, whereas first moment mean clutter strengths of high-relief and low-relief desert are quite different (e.g., exhibit opposite trends with depression angle), second moments (i.e., spreads) in clutter amplitude distributions of high- and low-relief desert are quite similar.

5.4.7.3 Level Desert Level desert is a subcategory of low-relief desert. Level desert clutter patches are required to be of level landform (see Table 2.2) and of either rangeland or barren land cover (see Table 2.1). Table 5.47 indicates the availability of 537 measured Phase One clutter amplitude distributions from 38 level desert clutter patches. This subset represents about one-third of the available measurements for low-relief desert (see Table 5.42). Clutter modeling information for level desert is provided in Tables 5.48 and 5.49 and Figures 5.42 and 5.43. As in low-relief desert, the mean clutter strength data for level desert in Figure 5.42 continue to show a strong trend of increasing strength with increasing depression angle in each band—here the low angle data (cyan, dark blue) are much weaker, with a significant multipath-induced trend of increasing strength with frequency, UHF to X-band. As with wetland (see Figure 5.36), this multipath trend in the low angle data does not extend to VHF, indicating (as with wetland and low-relief shrubland) much greater intrinsic σ °’s in low angle VHF level desert data than at UHF (enough greater to Table 5.47 Numbers of Terrain Patches and Measured Clutter Histograms for Level Desert, by Depression Anglea,b,c

Terrain Relief

Level


= Depression Angle (degrees)

Number of Patches

Number of Measurements

4.00 ≤


0

0

1.50 ≤
< 4.00

3

57

0.75 ≤
< 1.50

3

31

0.25 ≤
< 0.75

11

166

0.00 ≤
< 0.25

18

253

-0.25 ≤
< 0.00

1

18

-0.75 ≤
< -0.25

2

12


< -0.75

0

0

Totals

38

537

a American Intermontane West terrain. Knolls and Booker Mountain sites. Predominantly with shrubby

desert vegetation or barren. Level is included within low-relief. b A terrain patch is a land surface macroregion usually several kms on a side (median patch area 2

= 12.62 km ). c A measured clutter histogram contains all of the temporal (pulse by pulse) and spatial (resolution cell

by resolution cell) clutter samples obtained in a given measurement of a terrain patch. A terrain patch was usually measured many times (nominally 20) as RF frequency (5), polarization (2), and range resolution (2) were varied over the Phase One radar parameter matrix.

536 Multifrequency Land Clutter Modeling Information

Table 5.48 Mean Clutter Strength σ w° and Number of Measurements for Level Desert, by Frequency Band, Polarization, and Depression Anglea

Weibull Mean Clutter Strength σ°w (dB)


= Depression

VHF

Angle (degrees)

HH

VV

L-Band

HH

VV

HH

X-Band

S-Band

VV

HH

VV

HH

VV

4.0 ≤


----

----

----

----

----

----

----

----

----

----

1.50 ≤
< 4.00

-37.6

-39.2

-38.5 -36.2

-35.6

-39.2 -38.0

-37.2

-23.8

-23.5

0.75 ≤
< 1.50

-35.9

-34.6

-33.8 -31.9

-34.1

-35.1 -31.8

-26.5

-21.2

-21.3

0.25 ≤
< 0.75

-51.3

-54.7

-54.9 -60.7

-45.1

-51.9 -41.4

-42.3

-35.3

-35.5

0.00 ≤
< 0.25

-52.7

-53.4

-57.2 -54.0

-53.6

-54.2 -42.1

-40.9

-33.0

-33.3

-0.25 ≤
< 0.00

-43.8

----

-33.5 -35.6

-35.1

-36.1 -33.9

-33.5

-27.9

-25.6

-0.75 ≤
< -0.25

----

-32.2

-35.1 -38.1

-32.8

-24.0 -36.8

-38.3

-29.0

-31.1


< -0.75

----

----

----

----

----

----

----

----


= Depression Angle (degrees)

----

----

Number of Measurements X-Band

S-Band

L-Band

UHF

VHF HH

a

UHF

VV

HH

VV

HH

VV

HH

VV

HH

VV

4.0 ≤


0

0

0

0

0

0

0

0

0

0

1.50 ≤
< 4.00

6

6

6

6

5

6

9

8

2

3

0.75 ≤
< 1.50

3

3

3

3

3

3

3

3

3

4

0.25 ≤
< 0.75

14

20

15

17

16

15

17

16

18

18

0.00 ≤
< 0.25

16

24

16

21

21

23

31

32

35

34

-0.25 ≤
< 0.00

2

0

2

2

2

2

2

2

2

2

-0.75 ≤
< -0.25

0

2

2

2

1

1

1

1

1

1


< -0.75

0

0

0

0

0

0

0

0

0

0

TOTALS

41

55

44

51

48

50

63

62

61

62

Table 5.47 defines the population of terrain patches upon which these data are based.

overcome the increased multipath loss at VHF). Although weak and similar to wetland results, the low angle (cyan, dark blue) level desert results in Figure 5.42 are not as weak as the level wetland results of Figure 5.36. The low angle (cyan, dark blue) level desert mean clutter strength results in Figure 5.42 for the most part come from Knolls. In contrast, the high angle (purple, magenta) level desert mean clutter strength results in Figure 5.42 for the most part come from Booker Mountain.The high angle level desert results are very similar to the high angle low-relief desert results of Figure 5.40. The high angle level desert results also show the very remarkable ~15 dB increase in mean clutter strength from S-band to X-band at high angles and from low angle to high angle at X-band previously described in the low-relief desert results of Figure 5.40. Modeling information for spreads in clutter amplitude distributions from level desert is given in Table 5.49 and Figure 5.43. A strong trend is shown of decreasing spread with increasing cell size. A weaker trend is shown of decreasing spread with increasing

Multifrequency Land Clutter Modeling Information 537

Table 5.49 Numbers of Terrain Patches and Measured Clutter Histograms for Mountain Terrain, by Depression Anglea,b,c

Weibull Shape Parameter aw


= Depression Angle (degrees)

from SD/Mean

from Mean/Median

A = 103m2

A = 106m2

A = 103m2

A = 106m2

4.00 ≤


----

----

----

----

1.50 ≤
< 4.00

3.2

3.3

2.6

2.8

0.75 ≤
< 1.50

2.1a

3.7

1.5a

3.3

0.25 ≤
< 0.75

4.7

2.0

4.0

1.7

0.00 ≤
< 0.25

4.4

2.1

4.3

1.6 2.0

-0.25 ≤
< 0.00

3.3

2.2

3.9a

-0.75 ≤
< -0.25

3.4b

2.5

3.5b

2.4


< -0.75

----

----

----

----

Ratios


= Depression Angle (degrees)

SD/Mean (dB)

Mean/Median (dB)

A = 103m2

A = 106m2

A = 103m2

A = 106m2

4.00 ≤


----

----

----

----

1.50 ≤
< 4.00

6.9

7.2

9.8

10.9

0.75 ≤
< 1.50

3.9a

8.4

3.8a

14.9

0.25 ≤
< 0.75

11.0

3.5

20.3

4.7

0.0 ≤
< 0.25

10.4

3.7

22.7

3.9 6.3

-0.25 ≤
< 0.00

7.3

4.0

19.8a

-0.75 ≤
< -0.25

7.6b

4.8

16.1b

8.6

----

----

----


< -0.75

----

a 4 2 3 2 Footnoted values apply at A = 10 m , not 10 m . b 5 2 3 2

Footnoted values apply at A = 10 m , not 10 m .

*

Table 5.47 defines the population of terrain patches and measurements upon which these data are based.

depression angle. The scatter plot of Figure 5.43 shows relatively tight correlation about the regression line. This plot is very similar to that of low-relief desert in Figure 5.41.

5.4.8 Mountainous Terrain As with desert terrain, mountain terrain does not overtly appear in the terrain classification systems employed herein (see Tables 2.1 and 2.2). A criterion utilized to specify mountain clutter within the Phase One measurement database is that the mountain clutter must come from two Phase One sites—viz., Plateau Mountain and Waterton—that were situated in what is obviously extremely mountainous terrain in the Canadian Rocky Mountains. Plateau Mountain was a high site; Waterton was a low site; both sites are further described in Sections 2.4.2.1 and 3.4.1.2. Further criteria for a clutter patch to be accepted as mountainous at either of these two sites are that its landform classification must be ridged,

538 Multifrequency Land Clutter Modeling Information

moderately steep, or steep (see Table 2.2); and its land cover classification must be barren (e.g., perennial-snow-and-ice), rangeland, or forest (see Table 2.1). Table 5.50 indicates that, for mountain terrain thusly defined, there are available 1,653 measured Phase One clutter amplitude distributions from 133 clutter patches for which the terrain within the patch meets these criteria for being mountainous. Table 5.50 Numbers of Terrain Patches and Measured Clutter Histograms for Mountain Terrain, by Depression Anglea,b,c

Terrain Relief

Mountains

␣ = Depression Angle (degrees)

Number of Patches

Number of Measurements

6.0 ≤ ␣

6

54

4.0 ≤ ␣ < 6.0

8

110

2.0 ≤ ␣ < 4.0

31

461

1.0 ≤ ␣ < 2.0

25

320

0.0 ≤ ␣ < 1.0

38

421

-1.0 ≤ ␣ < 0.0

11

92

␣ < -1.0

14

195

Totals

133

1,653

a Canadian Rocky Mountain terrain. Waterton and Plateau Mountain sites. Predominantly barren or

forested land cover. Mountain terrain does not include long-range mountain terrain. b A terrain patch is a land surface macroregion usually several kms on a side (median patch area 2

= 12.62 km ). c A measured clutter histogram contains all of the temporal (pulse by pulse) and spatial (resolution cell

by resolution cell) clutter samples obtained in a given measurement of a terrain patch. A terrain patch was usually measured many times (nominally 20) as RF frequency (5), polarization (2), and range resolution (2) were varied over the Phase One radar parameter matrix.

Clutter modeling information for mountains is given in Tables 5.51 and 5.52 and Figures 5.44 and 5.45. In Figure 5.44, mean clutter strengths for mountains are seen to be very strong, and, like high-relief forest (Figure 5.24), to show a significant trend of decreasing clutter strength with increasing frequency VHF to X-band (compare with the repeat sector mountain data of Figure 3.21; see also Figure 3.2). This trend in mountain terrain is due to increasing absorption of RF power from the incident radar wave by tree foliage with increasing frequency as discussed in Chapter 3, Section 3.4.1.2. As discussed there, when the mountain slopes are not forested, this trend disappears. Also, as in high-relief forest (Figure 5.24), there are significant trends with depression angle in most bands in the mountain data of Figure 5.44, but the trends are more complicated than those of increasing strength with increasing angle exhibited in forest. In fact, there is an inverse trend of decreasing strength with increasing angle in the mountain data of Figure 5.44 similar to the inverse trend shown in the high-relief desert data of Figure 5.38, which exists for the same reason in the mountain data as previously explained for the high-relief desert data. However, in the lower three bands in the mountain data of Figure 5.44 where depression angle effects are significant, the inverse trend is from the 1° to 2° depression angle regime (dark blue) through 2° to 4° (purple) to 4° to 6° (magenta) and > 6° (red); the trend does not include the 0° to 1° (cyan) data. In fact, looking closely at the mountain data in the lower three bands in Figure 5.44, an opposite, more common trend of increasing strength with increasing angle is seen from the –1° to 0° depression angle regime (dark green) to

Multifrequency Land Clutter Modeling Information 539

Table 5.51 Mean Clutter Strength σ w° and Number of Measurements for Mountain Terrain, by Frequency Band, Polarization, and Depression Anglea

Weibull Mean Clutter Strength σ°w (dB)

␣ = Depression VHF

Angle (degrees)

VV

6.0 ≤ ␣

-31.1

-31.8

4.0 ≤ ␣ < 6.0

-20.7

-18.4

2.0 ≤ ␣ < 4.0

-16.4

1.0 ≤ ␣ < 2.0 0.0 ≤ ␣ < 1.0

VV

S-Band

X-Band

VV

HH

VV

HH

VV

-31.3 -28.0

-27.6

-28.3

----

----

----

----

-17.3 -16.5

-21.2

-24.3

----

----

----

----

-13.2

-17.7 -12.8

-18.2

-18.0 -24.4

-24.7

----

----

-14.7

-10.8

-15.1 -12.4

-17.6

-17.5 -22.9

-24.4

----

----

-14.8

-14.0

-18.8 -16.2

-20.0

-19.7 -22.4

-22.2

----

----

-1.0 ≤ ␣ < 0.0

-15.4

-5.8

-23.1 -20.6

-25.6

-27.4 -25.2

-25.5

-26.1

-25.6

␣ < -1.0

-11.2

-7.6

-13.9 -13.3

-17.8

-18.7 -19.2

-19.4

-21.1

-22.0

Angle (degrees)

HH

L-Band HH

␣ = Depression

a

UHF

HH

Number of Measurements X-Band

S-Band

L-Band

UHF

VHF HH

VV

HH

VV

HH

VV

6.0 ≤ ␣

12

14

9

10

4

5

4.0 ≤ ␣ < 6.0

17

17

17

17

21

21

2.0 ≤ ␣ < 4.0

61

64

64

64

57

64

1.0 ≤ ␣ < 2.0

40

41

41

41

34

40

0.0 ≤ ␣ < 1.0

48

53

53

51

48

55

HH

VV

HH

VV

0

0

0

0

0

0

0

44

43

0

0

42

41

0

0

57

56

0

0

0

-1.0 ≤ ␣ < 0.0

5

7

11

11

12

13

13

12

4

4

␣ < -1.0

20

25

26

26

22

24

17

17

9

9

TOTALS

203

221

221

220

198

222

173

169

13

13

Table 5.50 defines the population of terrain patches upon which these data are based.

0° to 1° (cyan) to 1° to 2° (dark blue). So the strongest mountain clutter occurs in all three lower bands in the 1° to 2° depression angle regime (dark blue), with mean strengths decreasing both with increasing depression angle (lower terrain) and decreasing depression angle (higher terrain) from there. Modeling information for spreads in clutter amplitude distributions from mountain terrain is given in Table 5.52 and Figure 5.45. Spreads in mountain clutter amplitude distributions are small (although generally still significantly wider than Rayleigh statistics)—in fact, spreads in mountain clutter are the least of any terrain type (high-relief forest has the next lowest spread). In particular, the mountain spreads for large A (A = 106 m2) are nearer unity (i.e., more approaching Rayleigh) in Table 5.52 than any other terrain type (compare with highrelief forest, Table 5.26). These low spreads in mountain clutter amplitude distributions are due to the high terrain slopes and corresponding full illumination of the mountain clutter patches. As with most other terrain types, there exists a significant trend of decreasing spread with increasing cell size A in the mountain data of Table 5.52 and Figure 5.45.

540 Multifrequency Land Clutter Modeling Information

Table 5.52 Shape Parameter aw and Ratios of Standard Deviation-to-Mean (SD/Mean) and Meanto-Median for Mountain Terrain, by Spatial Resolution A and Depression Angle* Weibull Shape Parameter aw


= Depression Angle (degrees)

from SD/Mean

from Mean/Median

A = 103m2

A = 106m2

A = 103m2

A = 106m2

6.0 ≤


2.3b

1.4a

3.1b

1.2a

4.0 ≤
< 6.0

1.9b

1.0a

2.1b

1.3a

2.0 ≤
< 4.0

2.1

1.1

2.6

1.1

1.0 ≤
< 2.0

2.3

1.2

2.8

1.7

0.0 ≤
< 1.0

2.0

1.5

2.8

1.9 2.4 1.9

-1.0 ≤
< 0.0

2.5

1.8

3.8b


< -1.0

2.8

1.8

3.9 Ratios


= Depression Angle (degrees)

SD/Mean (dB)

Mean/Median (dB)

A = 103m2

A = 106m2

A = 103m2

A = 106m2

6.0 ≤


4.5b

1.4a

13.2b

2.4a

4.0 ≤
< 6.0

3.0b

0.0a

6.5b

2.7a

2.0 ≤
< 4.0

3.8

0.5

9.7

2.1

1.0 ≤
< 2.0

4.3

0.7

11.2

4.5

0.0 ≤
< 1.0

3.6

1.8

11.3

5.8 8.7 5.6

-1.0 ≤
< 0.0

4.9

3.0

18.0b


< -1.0

5.7

2.9

19.3

a Footnoted values apply at A = 105 m2 , not 106 m2 . b Footnoted values apply at A = 104 m2 , not 103 m2 .

*

Table 5.50 defines the population of terrain patches and measurements upon which these data are based.

5.4.8.1 Long-Range Mountains When strong clutter from visible terrain at long range occurs in surface-sited radars, it usually comes from mountains because only mountains are high enough to be visible at long range over the spherical earth. Long-range mountain clutter is discussed at some length in Chapter 3, Appendix 3.B, Section 3.B.3. The long-range mountain clutter data discussed in Chapter 3 were measured over broad azimuth sectors from the Canadian Rocky mountains at three Alberta sites. In what follows, long-range mountain clutter data are presented, also from the Canadian Rocky mountains, but as measured within clutter patches as selected from six Alberta measurement sites. Table 5.53 indicates that there are available 721 measured Phase One clutter amplitude distributions from 80 long-range mountain clutter patches at these six sites. These long-range mountain clutter patches were predominantly of barren or perennial-snow-and-ice land cover classification, with some secondary occurrences of forest. Ranges to these 80 patches varied from 45 to 143 km. As shown in Table 5.53, all 80 long-range mountain clutter patches were observed in a narrow negative depression angle regime, from – 0.75° to –1.6°.

Multifrequency Land Clutter Modeling Information 541

Table 5.53 Numbers of Terrain Patches and Measured Clutter Histograms for Long-Range Mountain Terrain, by Depression Anglea,b,c


= Depression Angle

Terrain Relief

Number of Patches

(degrees)

Long-range mountains

Number of Measurements

-0.75 ≤


0

0

-1.6 ≤
< -0.75

80

721


< -1.6

0

0

Totals

80

721

a Ranges from 45 to 143 kilometers. Canadian Rocky Mountain terrain. Six sites. Predominantly barren or forested land

cover. Long-range mountain terrain is not included within mountain terrain.

b A terrain patch is a land surface macroregion usually several kms on a side (median patch area = 12.62 km2 ). c A measured clutter histogram contains all of the temporal (pulse by pulse) and spatial (resolution cell by resolution cell )

clutter samples obtained in a given measurement of a terrain patch. A terrain patch was usually measured many times (nominally 20) as RF frequency (5), polarization (2), and range resolution (2) were varied over the Phase One radar parameter matrix.

Mean clutter strengths for long-range mountains are given in Table 5.54 and plotted in Figure 5.46. Mean clutter strengths for long-range mountains are strong, but not as strong as mountains at closer ranges (compare with Figure 5.44), particularly in the lower bands. A gentle trend of decreasing clutter strength with increasing frequency, VHF to S-band, is observed in Figure 5.46, with X-band increasing slightly over S-band. These results may be compared with the generally weaker long-range mountain clutter as reduced over very large azimuth sectors shown in Figure 3.B.10 of Appendix 3.B—these latter data are weaker because they are not patch-specific but instead incorporate significant amounts of macroshadow, particularly at the higher radar frequencies. The long-range mountain clutter of Figure 5.46 is weaker than mountain clutter at shorter ranges (Figure 5.44), particularly in the lower bands, because of propagation losses over the long ranges at near grazing incidence. Table 5.54 Mean Clutter Strength σ w° and Number of Measurements for Long-Range Mountain Terrain, by Frequency Band, Polarization, and Depression Anglea

Weibull Mean Clutter Strength σ°w (dB)


= Depression VHF

Angle (degrees)

HH

VV

L-Band

HH

VV

HH

S-Band

VV

HH

X-Band

VV

HH

VV

-0.75 ≤


----

----

----

----

----

----

----

----

----

----

-1.6 ≤
< -0.75

-16.7

-17.5

-19.6 -21.2

-21.6

-21.7 -23.9

-23.4

-23.0

-22.4


< -1.6

----

----

----

----

----

----

----

----


= Depression Angle (degrees)

a

UHF

----

----

Number of Measurements X-Band

S-Band

L-Band

UHF

VHF

VV

VV

HH

VV

HH

VV

HH

-0.75 ≤


0

0

0

0

0

0

0

0

0

0

-1.6 ≤
< -0.75

73

75

82

91

84

77

70

53

58

58


< -1.6

0

0

0

0

0

0

0

0

0

0

TOTALS

73

75

82

91

84

77

70

53

58

58

Table 5.53 defines the population of terrain patches upon which these data are based.

VV

HH

HH

542 Multifrequency Land Clutter Modeling Information

Modeling information for spreads in clutter amplitude distributions from long-range mountains is given in Table 5.55 and Figure 5.47. Cell area A is very large in all these longrange data. However, over the range of large cell areas available, there remains a significant trend of decreasing spread with increasing cell size. Table 5.55 Shape Parameter aw and Ratios of Standard Deviation-to-Mean (SD/Mean) and Meanto-Median for Long-Range Mountain Terrain, by Spatial Resolution A and Depression Angle*

Weibull Shape Parameter aw

␣ = Depression

from SD/Mean

Angle (degrees) A=

103m2

A=

from Mean/Median

106m2

A = 103m2

A = 106m2

-0.75 ≤ ␣

----

----

----

----

-1.6 ≤ ␣ < -0.75

2.7a

1.9

3.7a

2.3

␣ < -1.6

----

----

----

----

Ratios

␣ = Depression Angle (degrees)

SD/Mean (dB)

Mean/Median (dB)

A = 103m2

A = 106m2

-0.75 ≤ ␣

----

----

----

----

-1.6 ≤ ␣ < -0.75

5.6a

3.1

18.0a

8.1

␣ < -1.6

----

----

----

----

a

5

2

3

A = 103m2

A = 106m2

2

Footnoted values apply at A = 10 m , not 10 m .

*

Table 5.53 defines the population of terrain patches and measurements upon which these data are based.

5.5 PPI Clutter Map Prediction Of particular interest is the site-specific prediction of plan-position indicator (PPI) land clutter maps for ground-sited radars. Such prediction involves simulating the spatial variation of land clutter. As previously discussed, first DTED is used to establish geometric line-of-sight terrain visibility from the radar antenna position, then the strength of the clutter in each visible cell is provided as a random realization from a Weibull distribution for which the coefficients σ w° and aw are appropriately selected from the tables provided in Sections 5.3 or 5.4. An example of this procedure for predicting a PPI clutter map is shown in Figure 5.48. This figure compares modeled and measured clutter maps for an X-band radar of horizontal polarization and 150-m range resolution situated at Brazeau, a forested wilderness site in Alberta, Canada at latitude 53.04° N and longitude 115.43° W (see Chapter 3). The maximum range of the clutter maps in Figure 5.48 is 24 km; the clutter map measured by the Phase One radar is to the left, the simulated map is to the right. The black regions in the simulated map are masked terrain regions as predicted using DTED. They correspond reasonably well with black regions in the measured map where the radar is at or close to its noise floor. As the quality of available DTED continues to improve, so does the fidelity of

Multifrequency Land Clutter Modeling Information 543

prediction of the black masked regions in such maps. Within the visible colored regions in the modeled map of Figure 5.48, there is generally good agreement with measurement in the general range of colors predicted in any particular region, although the cell-to-cell spatial correlation in the measured map is not precisely followed in the modeled map. The validity of such predictions is not based on subjective judgment of how good a modeled clutter map appears, or even on how closely modeled and measured cumulative σ ° distributions compare within regions or over whole sites. Rather the validity of such predictions is based in the final analysis on how closely a particular radar system performance measure computed using modeled clutter compares to the corresponding performance measure computed using measured clutter. When tested in this manner, the Weibull statistical clutter models generally perform with highly satisfactory accuracy in computing clutter-limited system performance.

5.5.1 Model Validation The Weibull clutter model has been in use at Lincoln Laboratory for a number of years in radar system studies involving clutter-limited operation against various airborne targets. These studies have involved radar systems ranging in frequency from VHF to X-band. Since the clutter model directly affects the outcomes of such studies, strong and ongoing interest exists in validating and improving the clutter model. In validating a clutter model, a radar engagement with a target is hypothesized to take place at one of the Phase One clutter measurement sites, and system performance is computed in two ways: (1) using the actual measured clutter at that site, and (2) using the clutter model to simulate clutter at that site. Successful validation requires that the performance measure computed using modeled clutter be acceptably similar to that computed using the actual clutter. Model validation encompasses many measurement sites. For X-band tracking systems, the Weibull model generally works well in predicting the performance parameters employed in such studies. System performance is then generalized by computing the median performance parameter of the system over many sites. A simple spherical earth, constant-σ ° clutter model cannot deliver the same general performance as the more in-depth Weibull model. That is, the constant σ ° required in the simple model is system and performance-parameter dependent, whereas the Weibull statistical model is adaptive and resilient enough to work well for any clutter-limited system or performance parameter. For VHF surveillance systems, radar performance parameters can be more difficult to predict due to propagation effects. The Weibull VHF model remains accurate in terrain of significant relief where propagation effects are not severe. However, in level open terrain, the accuracy of the Weibull model can, in some circumstances, be improved by adding deterministic computations of multipath propagation.

5.5.2 Model Improvement The clutter modeling information of Chapter 5 represents low-angle land clutter as a Weibull statistical process occurring over visible terrain regions. The Weibull distributions aggregate the widely varying returns received predominantly from an infinitude of spatially localized discrete sources. Studies have been conducted to shed further light on higherorder parametric effects that occur in low-angle land clutter beyond the level at which clutter modeling information is provided in Chapter 5. These studies include the following:

544 Multifrequency Land Clutter Modeling Information

1.

separating the strongest discretes and introducing grazing angle dependence on the residual clutter background (see Appendix 4.D);

2.

introducing clutter into shadowed regions (see Appendix 4.D);

3.

utilizing improved cell-specific land cover information (e.g., Landsat data, see Section 4.4.1);

4.

improving propagation prediction (e.g., SEKE; Parabolic Equation techniques; Method of Moments techniques) at clutter source heights (see Section 1.5.4 and Appendix 3.B);

5.

investigating non-site-specific clutter modeling approaches which incorporate spatial patchiness on the basis of mathematically derived stochastic processes as opposed to deterministic site-specific visibility in DTED (see Sections 1.4.2 and 4.3.3.1).

As indicated, each of these subjects has been mentioned or discussed elsewhere in this book. Figure 4.3 (in Chapter 4) conveniently represents the structure of the Weibull statistical clutter model. Within this structure, what actually exists is an adaptive computer-resident modeling capability. That is, 59,804 measured clutter spatial amplitude distributions exist as computer files together with their terrain descriptive parameters. The clutter model is the template by which these data are sorted. Not only can general templates be provided for general terrain types such as are given in Sections 5.3 and 5.4, but also the template can be adjusted to provide more detailed results for terrain types highly specific to an individual user’s particular interests.

5.6 Summary Chapter 5 provides land clutter modeling information for surface radar on the basis of extensive Phase One five-frequency 360° survey clutter measurements at 42 different sites of widely varying terrain type (see Chapter 3). The modeling information provided specifies the probability distribution encompassing the spatial cell-to-cell variability of clutter amplitudes for a given set of parametric conditions. Important parameters are of three types: (1) those of the radar—frequency, resolution, polarization; (2) the angle of illumination of the terrain—that is, the depression angle below the horizontal at which the radar views the terrain; and (3) parameters descriptive of the terrain—its relief and land cover. The probability distributions are specified in terms of Weibull statistics. A modeling approach is followed, as developed in earlier chapters of this book, in which radar spatial resolution affects only the shape parameter aw of the Weibull distribution, and radar frequency affects only the mean of the distribution σ w° . This decoupling of the effects of resolution and frequency on the modeled clutter distributions is central to the success of this approach to clutter modeling. The fact that aw depends only on radar resolution and not radar frequency means that results from the various Phase One radar frequency bands and corresponding widely varying azimuth beamwidths are able to be combined to generalize effects with spatial resolution across a wide range of resolutions. The fact that the mean strength σ w° depends only on radar frequency and not resolution ( σ w° is the only resolution-invariant attribute of the clutter amplitude distribution) reduces the

Multifrequency Land Clutter Modeling Information 545

dimensionality of the modeling construct and allows fundamental trends in σ w° to emerge. Both σ w° and aw are dependent on depression angle and terrain type. In contrast to the much simpler interim clutter model presented in Chapter 4 (which was of the same modeling structure as the information presented in Chapter 5), the information in Chapter 5 is presented without any smoothing or extrapolation as was necessary in the interim model. The number of measurements underlying each value of σ w° and aw in Chapter 5 is also provided as a first assessment of generality. Occasionally, open plot symbols are used in the mean strength figures of Chapter 5 to indicate lightly-sampled σ w° values that appear to be non-general. Clutter modeling information is provided in Chapter 5 for both general rural terrain and for a number of specific terrain types. In general rural terrain, consistent general trends emerge of increasing mean clutter strength σ w° with increasing depression angle, in all five frequency bands and for both high- and low-relief terrain. The reason these trends emerge so consistently in the general rural terrain results of Chapter 5 is that each plotted point is typically based on hundreds of measurements, among which there is much individual variability. Concerning radar frequency dependence in general rural terrain, at high depression angles mean clutter strength decreases with increasing radar carrier frequency as ~(1/f); at low depression angles mean strength increases with increasing carrier frequency as ~f; there is no single simple frequency dependence in low-angle land clutter. Mean strengths at HH-polarization are usually 1 or 2 dB weaker than at VV-polarization (a full matrix of information is available at both polarizations). Mean clutter strength rises rapidly with increasing negative depression angle (i.e., terrain observed at higher elevations than the radar). A large amount of generalized clutter modeling information is presented in Chapter 5 for general rural terrain. These results are among the more important of the Phase One findings. They show consistent general trends, especially with depression angle, but also with terrain relief and radar frequency, to sort out a phenomenon of which the most salient characteristic is variability. Chapter 5 also provides generalized clutter modeling information for eight specific terrain types—urban, farmland, forest, shrubland, grassland, wetland, desert, and mountains. As expected, these results show that clutter is strong in urban and mountain terrain, and weaker in desert and wetland terrain. In urban terrain at high depression angle, mean clutter strength σ w° is relatively frequency invariant in the –15 to –20 dB range. Mountain clutter shows a trend of decreasing strength with increasing radar frequency, so that it is stronger than urban clutter at VHF and UHF, weaker at S- and X-bands. Mountain clutter also shows a countertrend of decreasing strength with increasing depression angle—looking broadside at high peaks causes stronger clutter than looking down at lower peaks. Desert clutter at high depression angles is approximately frequency invariant VHF to S-band (at σ w° ≅ –35 dB), but increases dramatically by ~15 dB (to σ w° ≅ –20 dB) at X-band. At low angles, desert clutter is much weaker, but level desert at low angles (with σ w° = –50 to –60 dB in the lower bands) is not as weak as wetland at low angles (with σ w° = –60 to –70 dB in the lower bands). Both level desert and wetland clutter at low angles show intrinsic σ° (aside from multipath losses) to be significantly stronger at VHF (170 MHz) than UHF (430 MHz). Many other general effects may be seen in the clutter modeling information for mean clutter strengths provided for specific terrain types in Chapter 5. In total there is 70 dB of variability in mean clutter strength between the strongest and weakest measurements of land clutter. However, specification of terrain type, terrain relief, and the depression angle at which the

546 Multifrequency Land Clutter Modeling Information

terrain is illuminated allows the mean clutter strength from that terrain to be accurately predicted, even over such a wide range. It is evident that non-terrain-specific approaches to land clutter modeling must inherently involve large uncertainties. In addition to mean clutter strength σ w° , the land clutter modeling information of Chapter 5 also specifies the shapes aw of clutter amplitude distributions. As mentioned, the shape or spread of the distribution is fundamentally dependent on the spatial resolution of the radar. The modeling information of Chapter 5 shows that for almost all terrain, there exists a strong trend of decreasing spread (decreasing aw) with increasing area A of the radar resolution cell. Spreads in forested terrain—including forested mountain terrain—are much less than spreads in open terrain for given values of cell size A, although both forested and open terrain show the strong trends of decreasing aw with increasing A. Values of aw are generally specified over the range from A = 103 m2 to A = 106 m2. Many of the results appear to indicate that the extremely widely spread Weibull distributions (e.g., aw = 5) that exist for small cell sizes rapidly diminish in spread with increasing A and appear to be approximately approaching Rayleigh statistics (aw = 1) for very large cells (e.g., A ≅ 107 or 108 m2) beyond the available range of the data. However, what occurs for larger cell sizes (A > 106 m2) or smaller SAR-like cell sizes (A < 103 m2) is unknown—there are physical reasons to expect that the linear trends observed of aw vs log A should not extrapolate to very small cell sizes. In addition to the strong trend of decreasing spread with increasing cell size, there also often exist suggestions of a weaker trend of decreasing spread with increasing depression angle particularly for smaller cell sizes. In totality, the clutter modeling information of Chapter 5 provides a condensed and unified, general codification of the properties of low-angle land clutter. Historically, there has been little indication of connectivity or unity among the many measurements reported by many different investigators. The main reason that has allowed Chapter 5 to successfully generalize low-angle land clutter is the large amounts of measurement data involved. Averaging over (medianizing) large amounts of data has allowed fundamental trends to emerge that are often obscured by specific effects in individual measurements.

References 1.

J. B. Billingsley and J. F. Larrabee, “Multifrequency Measurements of Radar Ground Clutter at 42 Sites,” Lexington, MA: MIT Lincoln Laboratory, Technical Rep. 916, Volumes 1, 2, 3; 15 November 1991; DTIC AD-A246710.

2.

F. E. Nathanson (with J. P. Reilly and M. N. Cohen), Radar Design Principles (2nd ed.), New York: McGraw-Hill, 1991.

3.

D. K. Barton, Modern Radar System Analysis, Norwood, MA: Artech House, 1988.

4.

M. W. Long, Radar Reflectivity of Land and Sea (3rd ed.), Boston: Artech House, 2001.

5.

M. I. Skolnik, Introduction to Radar Systems (3rd ed.), New York: McGraw-Hill, 2001.

6.

J. B. Billingsley, “Radar ground clutter measurements and models, part 1: Spatial amplitude statistics,” AGARD Conf. Proc. Target and Clutter Scattering and Their

Multifrequency Land Clutter Modeling Information 547

Effects on Military Radar Performance, Ottawa, AGARD-CP-501, 1991; DTIC ADP006 373. 7.

H. C. Chan, “Radar ground clutter measurements and models, part 2: Spectral characteristics and temporal statistics,” AGARD Conference Proceedings on Target and Clutter Scattering and Their Effects on Military Radar Performance, AGARDCP-501 (1991).

8.

G. C. Sarno, “A model of coherent radar land backscatter,” AGARD Conference Proceedings on Target and Clutter Scattering and Their Effects on Military Radar Performance, AGARD-CP-501 (1991).

9.

S. P. Tonkin and M. A. Wood, “Stochastic model of terrain effects upon the performance of land-based radars,” AGARD Conference Proceedings on Target and Clutter Scattering and Their Effects on Military Radar Performance, AGARD-CP501 (1991).

10. M. Sekine and Y. Mao, Weibull Radar Clutter, London, U. K.: Peter Peregrinus Ltd. and IEE, 1990. 11. R. R. Boothe, “The Weibull Distribution Applied to the Ground Clutter Backscatterer Coefficient,” U. S. Army Missile Command Rept. No. RE-TR-69-15, Redstone Arsenal, AL, June 1969; DTIC AD- 691109. 12. M. P. Warden and E. J. Dodsworth, “A Review of Clutter, 1974,” Royal Radar Establishment Technical Note No. 783, Malvern, U. K., September 1974; DTIC AD A014421.

6 Windblown Clutter Spectral Measurements 6.1 Introduction Moving target indication (MTI) radar utilizes Doppler processing to separate small moving targets from large clutter returns. Any intrinsic motion of the clutter sources causes the clutter returns to fluctuate with time and the received clutter power to spread from zero-Doppler in the frequency domain. As a result, intrinsic clutter motion degrades and limits MTI performance. MTI design objectives can require clutter rejection in the 60to 80-dB range or more, and can be implemented not only by using conventional fixedparameter MTI filter design [1, 2] but also through modern adaptive Doppler-processing techniques [3–5]. However implemented, successful clutter rejection to such low levels requires accurate definition of the detailed shape of the intrinsic-motion clutter power spectrum. The most pervasive source of intrinsic fluctuation in ground clutter is the windinduced motion of tree foliage and branches or other vegetative land cover. The shape of windblown tree clutter power spectra has been a subject of investigation since the early days of radar development. Although this subject continues to be important, it has generally remained rather poorly understood, largely because of the difficulty of accurately measuring clutter spectra to very low spectral power levels. Radar ground clutter power spectra were originally thought to be of Gaussian shape [6–9]. Later, with measurement radars of increased spectral sensitivity, it became apparent that spectral tails wider than Gaussian existed that could be modeled as power law over the spectral ranges of power—typically 35 to 40 dB below the peak zero-Doppler level—then available [10, 11]. A number of measurements of clutter spectra all generally characterized as power law followed [12–20], and much discussion at the time focused on power-law representation of clutter spectral shape. If real when extrapolated to low levels, power-law spectral tails would severely limit MTI Doppler-processor performance against small targets and would reduce motivation for suppressing radar phase noise to lower levels. Measurements of windblown ground clutter power spectra at Lincoln Laboratory to levels substantially lower (i.e., 60 to 80 dB down) than most earlier measurements indicate spectral shapes that fall off much more rapidly than constant power-law at rates of decay often approaching exponential [21–26]. How are these observations of exponential spectral shape reconcilable with the earlier power-law observations? One purpose of Chapter 6 is to resolve these apparently conflicting results. The most salient aspect of Lincoln Laboratory’s measurements of windblown ground clutter power spectra is their rapid decay to levels 60 to 80 dB down from zero Doppler. Chapter 6

576 Windblown Clutter Spectral Measurements

provides a simple model with exponential decay characteristics for the Doppler-velocity power spectrum of radar returns from cells containing windblown trees. This exponential model empirically captures, at least in general measure and occasionally very accurately, the major attributes of the measured phenomenon. The exponential shape (a) is somewhat wider than the historic Gaussian shape, as required by the general consensus of experimental evidence; (b) is very much narrower at lower power levels (i.e., 60 to 80 dB down) than the subsequent power-law representations when they are extrapolated to such low levels; and (c) at higher power levels (35 to 40 dB down) finds approximate equivalence in spectral level and extent with a number of reported results modeled as power law at these higher levels. Important effects of wind speed and radar frequency (VHF to X-band) on windblown ground clutter spectra are also described and incorporated in the model. Chapter 6 presents the exponential model in Section 6.2. The general validity of the postulated model is demonstrated in Section 6.3 by comparing it with numerous measurements. Section 6.4 briefly discusses (a) how to use the exponential clutter spectral model to calculate the absolute level of clutter power in any radar Doppler cell; (b) differentiation of quasi-dc and ac regions of spectral approximation; (c) how the exponential model can perform adequately not only in forested but also in nonforested terrain (farmland, desert) by suitably adjusting the dc/ac term of the model; and (d) comparison of the MTI improvement factors for a single delay-line canceller in exponential vs Gaussian clutter. Section 6.5 investigates the impact of assigning the correct shape for the clutter power spectral density (PSD) on modern radar signal processing techniques that use coherent adaptive processing for target detection in clutter; and further validates the exponential clutter spectral model by showing that the differences between using measured windblown clutter data as input to the processor, and using modeled data of various spectral shapes, are minimized when the modeled data are of exponential spectral shape. Section 6.6 is a thorough tutorial review of the historical literature concerning intrinsic-motion ground clutter spectral spreading that compares and contrasts current clutter spectral results with those previously reported. Section 6.7 is a summary.

6.2 Exponential Windblown Clutter Spectral Model Consider a radar spatial resolution cell containing windblown trees. Such a cell contains both fixed scatterers (ground, rocks, tree trunks) and moving scatterers (leaves, branches). The returned signal correspondingly contains both a constant (or steady) and a varying component. The steady component gives rise to a dc or zero-Doppler term in the power spectrum of the returned signal, and the varying component gives rise to an ac term in the spectrum. Thus a suitable general analytic representation for the total spectral power density Ptot(v) in the Doppler-velocity power spectrum from a cell containing windblown vegetation is provided by r 1 P tot ( v ) = ----------- ⋅ δ ( v ) + ----------- P ac ( v ) , – ∞ < v < ∞ r+1 r+1

(6.1)

Windblown Clutter Spectral Measurements 577

where v is Doppler velocity32 in m/s, r is the ratio of dc power to ac power in the spectrum,33 δ(v) is the Dirac delta function, which properly represents the shape of the dc component in the spectrum, and Pac(v) represents the shape of the ac component of the spectrum, normalized such that ∞

∫ –∞

P ac ( v ) dv = 1 .

Since by definition ∞

∫ –∞

δ ( v ) dv = 1 ,

it follows that normalization in Eq. (6.1) is to unit total spectral power, i.e., ∞

∫

–∞

P tot ( v ) dv = 1 .

It is apparent from Eq. (6.1) that for |v| > 0, Ptot(v) = [1/(r + 1)]Pac(v). In considering analytic spectral shapes, Pac(v) is the fundamental quantity, whereas in measured results Ptot(v) is the fundamental quantity. On a decibel scale, the level of an analytic spectral shape function 10 log1 0 Pac must be reduced by 10 log1 0 (r + 1) before comparison with directly measured data 10 log1 0 Ptot, or the level of directly measured data 10 log1 0 Ptot must be raised by 10 log1 0 (r + 1) before considering its ac spectral shape. Such normalization adjustments obviously depend on the dc/ac ratio r, a highly variable quantity in measured clutter spectra. In Chapter 6, either Ptot or Pac can represent measured or modeled data, depending on context.

6.2.1 ac Spectral Shape Radar ground clutter spectral measurements at Lincoln Laboratory to levels 60 to 80 dB below the peak zero-Doppler level indicate that the shapes of the spectra often decay at rates close to exponential. The two-sided exponential spectral shape may be represented analytically as β P ac ( v ) = --- ⋅ exp ( – β v ) , – ∞ < v < ∞ 2

(6.2)

where β is the exponential shape parameter. Table 6.1 provides values of β as a function of wind conditions such that spectral width increases with increasing wind speed as generally observed in the measurement data. The exponential shapes specified in Table 6.1 are plotted in Figure 6.1. The terminology used here to describe wind conditions borrows from but does not strictly adhere to that of the Beaufort wind scale [27, 28]. The measurements indicate that the values of β in Table 6.1 and Figure 6.1 are largely independent of radar carrier frequency over the range from VHF to X-band (see Figures 6.10 and 6.11). 32. The term “Doppler velocity” as used herein is equivalent to scatterer radial velocity. 33. In Chapter 6, r represents dc/ac ratio. In preceding chapters, r represents radar range (see Section 2.3.1.1).

578 Windblown Clutter Spectral Measurements

Table 6.1 Exponential ac Shape Parameter β vs Wind Speed

Wind Conditions

Wind Speed (mph)

Exponential ac Shape Parameter β (m/s)-1 Typical

Worst Case

1-7

12

—

Breezy

7-15

8

—

Windy

15-30

5.7

5.2

Gale force (est.)

30-60

4.3

3.8

Light air

The basis of the “worst-case, windy” specification of β = 5.2 is the highly exponential forest/windy spectrum subsequently shown in Figure 6.5, which is among the widest in the current Lincoln Laboratory database of clutter spectral measurements. The basis of the “typical, gale force” specification of β = 4.3 is the scaled estimate of a forest clutter spectrum in gale force winds subsequently shown in Figure 6.9. Increasing gale force β from its typical specification based on this scaled estimate to a worst-case specification of β = 3.8 brings it into very close agreement (in terms of spectral extent at the –14-dB level) with the only known measurements of windblown clutter under actual gale force wind conditions, namely, the very early measurements of Goldstein [9] that are further discussed in Section 6.6.3.5. Many measurements similar to the forest/light air spectrum subsequently shown in Figure 6.16 are the basis of the “light air, typical” specification of β = 12. Consideration of the β numbers in Table 6.1 reveals that spectral width as given by the quantity β-1 varies approximately linearly with the logarithm of the wind speed. Note that v = β-1 is the point on the spectrum that is 10 log10 (1/e) = –4.34 dB down from its zeroDoppler peak. Dependency of spectral width on the logarithm of wind speed is directly illustrated in some particular measurements to follow (see Figures 6.8 and 6.9). An algebraic expression for β that incorporates linear dependency of spectral width on the logarithm of the wind speed w as observed in these data is β-1 = 0.1048 [log10 w + 0.4147]

(6.3)

where w is wind speed in statute miles per hour. Equation (6.3) provides a reasonable match to the values of β shown in Table 6.1 and Figure 6.1. However, β is a highly variable quantity in measured clutter spectra. The tabulated values of β are for the most part medianized values within broad regimes of wind speed and hence portray more realistically than Eq. (6.3) what was actually observed across the spectral database as a whole. The implementation of a rigorous linear dependence of spectral width on the logarithm of wind speed in Eq. (6.3) provides a good fit to the data for windy conditions, but somewhat overestimates the higher wind speeds necessary for given values of β in gale force conditions and slightly underestimates the lower wind speeds necessary for given values of β in breezy and light air conditions. Equation (6.3) can nevertheless be useful in trend analysis studies that require an analytic approximation for the dependency of β on w.

Windblown Clutter Spectral Measurements 579

Typical Worst Case

20

Light Air Breezy Windy Gale Force (Est.)

(a) (b) (c) (d) (e) (f)

Pac (dB)

0

–20

(d) (e) (f)

–40

(a) (b) Windblown Vegetation

–60

VHF to X-Band

0.10

(c) β = 12

8

5.7 4.3 5.2 3.8

1.00

10.00

Doppler Velocity v (m/s)

Figure 6.1 Exponential model for ac clutter spectral shape from windblown vegetation, parameterized by wind speed. Applicable VHF to X-band.

Doppler frequency f in Hertz and scatterer radial velocity v in m/s are fundamentally related as f = –2v/λ, where λ is the radar transmission wavelength.34 It follows that if the Doppler velocity extent of measured clutter spectra from windblown vegetation is largely invariant with radar frequency, the Doppler frequency extent from windblown vegetation must scale approximately linearly with radar frequency. In Chapter 6, clutter spectra are usually plotted using a Doppler velocity abscissa as opposed to the more conventional Doppler frequency abscissa to allow direct comparison of spectral shape and extent at different radar frequencies with the linear scaling factor normalized out. Of course, for any particular radar system, it is the quantity Pac(f), not Pac(v), that is of direct interest. To convert to Pac(f) in Eq. (6.2), i.e., Pac(f) df = Pac(v) dv, replace v by f and β by (λ/2) β. To convert from v to f in Eq. (6.1), replace v by f.

6.2.2 dc/ac Ratio Although Pac(v) is largely independent of radar frequency, the value of dc/ac ratio r in Eq. (6.1) is strongly dependent on both wind speed and radar frequency, as subsequently shown in Figures 6.17 and 6.19. An analytic expression for r empirically derived from such results which generally captures these dependencies is provided by

34. In Chapter 6, f represents Doppler frequency and fo represents radar carrier frequency. In preceding chapters, f represents radar carrier frequency.

580 Windblown Clutter Spectral Measurements

r = 489.8 w-1.55 fo-1.21

(6.4)

where, as before, w is wind speed in statute miles per hour, and fo is radar carrier frequency in gigahertz.3 4 Equation (6.4) applies to cells containing windblown trees. The database from which it was derived covers the frequency range from 170 MHz (i.e., VHF) to 9.2 GHz (i.e., X-band) and includes measurements from many forested cells under various wind conditions. The variation of r with wind speed and radar frequency as specified by Eq. (6.4) is plotted in Figure 6.2. The quantity r in Eq. (6.4) is also the ratio of steady to random average power (originally defined as m2 by Goldstein [9]) in the Ricean distribution describing the temporal amplitude statistics of the clutter (see Chapter 4, Section 4.6.1).

30 10

0

Fr

,00

nd

10

Seq ue Lnc y

00

Ba

10

10

X-

dc/ac Ratio r (dB)

20

UH F o ( VH MH F z)

0

0

Forest

–10

2

5

10

20

30 40 50

Wind Speed w (mph)

Figure 6.2 Modeling information specifying ratio of dc to ac spectral power in windblown forest clutter spectra vs wind speed and radar frequency.

In measured clutter spectra from windblown trees, not only does the maximum spectral power almost always occur in the zero-th Doppler bin, but high spectral power levels are also often resolved in neighboring Doppler bins that are very near but not right at zero Doppler. Hereafter, such near zero-Doppler spectral power is called quasi-dc power. The near zero-Doppler regime of quasi-dc power is usually 0 < |v| < 0.25 m/s. Excess quasi-dc power exists in the quasi-dc region when the spectral power initially decays rapidly but continuously from the peak power level right at zero Doppler at a rate much faster than the exponential rate evident at lower power levels in the spectral tail. The spectral power that is resolved in the zero-th Doppler bin in such spectra comes from relatively motionless parts

Windblown Clutter Spectral Measurements 581

of the tree trunks near ground level as well as from the ground surface itself, whereas the spectral power resolved as quasi-dc comes from higher parts of tree trunks and major limbs flexing slightly at very slow rates. Including the excess quasi-dc spectral power as part of the ac spectral power degrades the goodness-of-fit of the exponential shape function in the spectral tail. That is, in these circumstances even though the value of β in Eq. (6.2) is correctly selected to match the relative shape Pac(v) in the spectral tail, the value of r will be too low, with the result that the absolute level [1/(r + 1)]Pac(v) will be too high. Furthermore, to the extent that windblown clutter statistics are nonstationary, besides being too high, this level can also be dependent on the length of coherent processing interval (CPI) employed. Therefore, in what follows, where excess (above the approximating exponential) quasi-dc power occurs in the data, it is included with the Dirac delta function as dc power in the model. This approach to quantifying dc/ac ratio r has been followed in the processing underlying the statistics upon which Eq. (6.2) is based (see Section 6.4.2). The major consequence of this approach is that the preceding spectral model approximates the exponential spectral tail region correctly, in both relative shape and absolute level, and independently of the length of CPI employed. Examples of windblown forest clutter spectra containing excess quasi-dc power are presented subsequently, as well as examples of desert and cropland clutter spectra in which a dc component from the absolutely stationary underlying ground surface (as opposed to the moving vegetation) exists as a discrete delta function.

6.2.3 Model Scope Equations (6.1), (6.2), (6.3), and (6.4) constitute a simple but complete empirical model for characterizing the complex physical phenomenon of radar ground clutter power spectra from windblown trees based on extensive measurements. Total backscattered clutter power is represented including both dc and ac spectral components. The test of any model of a physical phenomenon is the degree to which it generally represents the phenomenon while avoiding complicating detail. The important parameters incorporated in the model of Eqs. (6.1), (6.2), (6.3), and (6.4) are wind speed and radar frequency; others that might be thought to strongly influence clutter spectra from windblown trees, but which appear to be generally subsumed within the ranges of statistical variability over the relatively large cell sizes utilized in the measurement data, include: (a) the types of trees involved (species, density, growth stage), (b) season of the year (e.g., leaves on vs leaves off), (c) wind direction, (d) polarization, and (e) angle of illumination. It is not possible to generalize information for dc/ac spectral power ratio r for all possible varieties of vegetated (or partially vegetated) ground clutter cells from which significant proportions of backscattered clutter power come from stationary scattering elements. Subsequently discussed Lincoln Laboratory measurements of clutter spectra in scrub desert, rangeland, and cropland terrain, although indicating much larger values of dc/ac spectral power ratio when compared with forest terrain, also indicate that the residual ac spectral shape function Pac(v) is similar to that of forest. Thus the spectral model of Eqs. (6.1), (6.2), and (6.3), although explicitly derived for windblown trees, may be considered generally applicable not only to forested cells but also, at least as a first-order approximation, to cells in partially open or open terrain (desert, rangeland, cropland) as long as the value of r is increased appropriately. However, Eq. (6.4) specifying r was derived only from forested cells, and only some particular examples are provided in what

582 Windblown Clutter Spectral Measurements

follows indicating how r increases for cells incompletely filled with trees or in open agricultural terrain. Although the exponential spectral shapes Pac(v) in Figure 6.1 are modeled to be invariant with radar frequency and vegetation type, two important ramifications are: (1) modeled widths of clutter frequency spectra Pac(f) increase linearly with radar frequency from VHF to X-band, and (2) increasing values of dc to ac ratio r in increasingly open terrain (desert, cropland) and/or with decreasing radar frequency cause absolute ac power levels [1/(r+1)] Pac(v) to decrease even though the Pac(v) shape function itself remains invariant under such circumstances. An important requirement in the development of the current model was that its predictions of spectral extent be in the correct general Doppler regime at spectral power levels 60 to 80 dB down from zero-Doppler peaks. Much uncertainty has existed concerning the location of this regime. The extensive Lincoln Laboratory database of windblown clutter spectral measurements, without exception, indicates ever increasing rates of spectral decay (i.e., downward curvature) with decreasing spectral power level as observed on log-Doppler velocity axes such that maximum spectral extents 60 to 80 dB down are limited to Doppler velocities of 3 to 4 m/s. The exponential shape function properly reflects this important fundamental feature of the measurements. The exponential model for Pac(v) provides windblown clutter spectra wider than Gaussian as required by experiment and supported by theory [29]. An alternative popular spectral shape function Pac(v) has been power-law [10]. The measurement data clearly indicate that observed rates of decay modeled as power law at upper levels of spectral power do not continue as power law to lower levels of spectral power but fall off much faster at the lower levels. In contrast, an exponential representation generally captures, at least approximately and occasionally highly accurately, the major attributes of the windblown clutter ac spectral shape function over the entire range from near the zero-Doppler peak to measured levels 60 to 80 dB down. The exponential model for Pac(v) is validated in Section 6.5 (see also [30, 31]) by showing that the differences in matched filter and clutter cancellation system performance between using actual measured in-phase (I) and quadrature (Q) Phase One clutter data as input to the processors, and modeled clutter spectral data of various spectral shapes (viz., Gaussian, power law, and exponential), are minimized when the spectral model employed is of exponential shape. Section 6.5 also evaluates the impact of using the exponential model for Pac(v), as opposed to Gaussian and power-law models, on the prediction of detection performance of airborne and ground-based surveillance radar using coherent adaptive processing [32, 33].

6.3 Measurement Basis for Clutter Spectral Model 6.3.1 Radar Instrumentation and Data Reduction Lincoln Laboratory has measured and characterized ground clutter power spectra over wide spectral dynamic ranges using the Phase One and LCE (L-Band Clutter Experiment) instrumentation radars [21, 25]. Both of these radars were conventional analog coherent

Windblown Clutter Spectral Measurements 583

radars. These two radars are first mentioned in this book in Chapter 1, Section 1.3. The Phase One radar and its program of clutter measurements are subsequently described more completely in Chapter 3. Important system parameters of these two radars are shown in Table 6.2. As shown in the table, the Phase One radar operated in five frequency bands, whereas the LCE radar operated at L-band only. With both radars, the basic type of clutter experiment suitable for examining temporal and spectral characteristics of ground clutter was the long-time-dwell experiment (see Section 3.2.2) in which relatively long sequences of pulses at low pulse repetition frequency (PRF) were recorded over a contiguous set of range gates with a stationary antenna beam. Each radar activated one combination at a time of frequency, polarization, and pulse length for any particular long-time-dwell clutter experiment. Many of the Phase One clutter spectra shown in Chapter 6 are from long-time-dwell data collected at Katahdin Hill, a forested site in eastern Massachusetts, during April and early May before leaf emergence on deciduous trees. The forested cells from which backscatter was measured at Katahdin Hill are typical of the eastern mixed hardwood forest (oak, maple, beech) with occasional occurrences of conifers (hemlock, pine), all generally 50 or 60 ft high. For the Katahdin Hill measurements, general wind conditions in the neighborhood of the principle cells from which backscatter was recorded were taken from weather information continuously broadcast from a nearby airfield. At other sites, wind conditions were measured by anemometers located at the radar site and, in many instances, also in the clutter measurement sector. Table 6.2 Radar System Parameters Parameter Frequency Band (MHz)

LCE

Phase One

L-Band (1230)

VHF (169)

UHF (435)

L-Band (1230)

S-Band (3230)

X-Band (9100)

Antenna gain (dBi)

31

13

25

28.5

35.5

38.5

Antenna beamwidth Az (deg) EI (deg)

6 3

13 42

5 15

3 10

1 4

1 3

Peak power (kW)

8

10

10

10

10

50

Polarization PRF (Hz) Pulse width (µs) Waveform A/D converter No. of bits Sampling rate (MHz)

HH, VV, HV, VH

HH, VV

500

500

1

0.1, 0.25, 1

Uncoded CW pulse

Uncoded CW pulse

14 2

13 10, 5, 1

584 Windblown Clutter Spectral Measurements

The LCE radar was a major upgrade at L-band only of the Phase One measurement equipment with substantially reduced phase noise levels [34, 35]. A primary design objective of the LCE radar was to achieve low enough phase noise such that the lowfrequency Doppler components of windblown clutter could be measured to levels ≈ 80 dB below the dc or stationary component of the clutter at zero-Doppler. This objective was met by using a combination of low phase-noise local oscillators (viz., Hewlett-Packard models 8662A and 8663A) locked to a common source, a low phase-noise transmitter, and system clocks with low jitter. The transmitter used two planar triodes (viz., Eimac Y-793F) in a grounded-grid amplifier configuration providing inherently low noise sensitivity [36]. The LCE radar receiver achieved high dynamic range through careful gain distribution and proper choice of mixers and amplifiers, with particular attention paid to maintaining overall system linearity. The two channels of the analog in-phase and quadrature (I/Q) detector, which operated at a receiver IF of 3 GHz, were balanced to within approximately 0.1 dB in amplitude and 1 degree of phase. This balance provided approximately 40 dB of image rejection. The receiver baseband I/Q outputs were digitized by 14-bit analog-to-digital (A/ D) converters chosen for their linearity and speed (i.e., maximum clock speed = 10 MHz). The I/Q detector dc bias was temperature-regulated to approximately 100 µV variation (i.e., to less than the least-significant bit of the A/D converter). Many of the LCE clutter spectra shown in Chapter 6 are from long-time-dwell data collected at Wachusett Mountain, Massachusetts, 32 miles west of Katahdin Hill, with similar tree cover. A photograph of the LCE radar on Wachusett Mountain is shown in Figure 6.3. Another LCE measurement site was in Nevada, where backscatter data were recorded from sparse scrub vegetation typical of the western desert. In contrast with Phase One, the LCE radar could measure both the copolarized and the cross-polarized returns, although not simultaneously. For LCE clutter measurements at Wachusett Mountain, wind conditions were measured simultaneously with the clutter measurements at 10-s update intervals with an anemometer stationed on top of a 75-ft tower in a treed clutter cell along one of the three azimuth positions selected for clutter measurements. These measurements were performed in August with the deciduous trees fully in leaf.

6.3.1.1 Spectral Processing LCE long-time-dwell clutter data were acquired with a stationary antenna over 70-s data recording intervals called experiments. Each LCE experiment involved the recording of 80 I and Q sample pairs per pulse repetition interval (PRI) at 2- MHz sampling frequency (i.e., 75-m range gate spacing), leading to a 6-km total recorded range swath. Clutter experiments were usually taken in sequential groups covering the various LCE polarization combinations. Phase One long-time-dwell clutter data were acquired similarly to LCE data. Table 6.3 provides the specific Phase One clutter data acquisition and spectral processing parameters applicable to the Phase One spectral results shown herein from Katahdin Hill. All the LCE clutter power spectra shown subsequently were computed directly as fast Fourier transforms (FFTs) of the sampled temporal pulse-by-pulse return, including the dc component. A four-term Blackman-Harris window function was utilized, with highest sidelobe level at –92 dB [37]. Each temporal record of 30,720 pulses (first 61.44 s of each 70-s experiment) was divided into contiguous groups of 5,120 samples; a 1,024-point complex FFT was generated for each group by utilizing every fifth pulse; and the amplitudes of the resultant set of FFTs were arithmetically averaged together in each

Windblown Clutter Spectral Measurements 585

Figure 6.3 The LCE radar.

Doppler cell to provide the spectrum illustrated. Thus each LCE spectrum shown is the result of averaging six individual spectra (each from a 1,024-point FFT) from an overall record of 1.024-min duration, using an effective 10-ms PRI and an effective 100-Hz PRF. The CPI for each FFT was 10.24 s. Table 4.10 in Chapter 4 indicates that the typical correlation time for windblown trees at Lband is ∼ 1 s (see also Table 6.3). Thus the CPI utilized in LCE spectral formation, usually being ∼ 10 times the correlation time, is more than adequate to allow the random process to fully develop. The Phase One clutter spectra shown were computed similarly to the LCE spectra. Table 6.3 provides the particular Phase One spectral processing parameters utilized in generating the Phase One clutter spectra from Katahdin Hill. Table 6.3 includes both the CPI (i.e., time dwell per FFT) used and the typical correlation time of windblown trees for each Phase One frequency band, as specified by Table 4.10. These numbers indicate that the CPI covers many correlation periods at each of the five Phase One radar frequencies.

6.3.1.2 System Stability For a steady target, the spectral processing of either the Phase One or LCE radar yields a very narrow spectrum containing only dc power at zero-Doppler velocity. Figure 6.4 shows results from such steady targets. Figure 6.4(a) shows the measured LCE clutter spectrum from a desert terrain cell under very still (0 mph) wind conditions. Figures 6.4(b) and (c) show measured Phase One spectra from a large municipal water tower at L- and Xbands, respectively; in each case, clutter from trees in the same cell as the water tower just

586 Windblown Clutter Spectral Measurements

Table 6.3 Phase One Clutter Spectra Parameters (Katahdin Hill) Frequency Band Parameter VHF

UHF

L-Band

S-Band

X-Band

Polarization

HH

HH

VV, HH

HH

VV

Range resolution (m)

150

150

15

150

150

No. of pulses recorded

30,720

30,720

30,720

30,720

30,720

PRF (Hz)

33.33

33.33

100

167

500

Time dwell(s) Total recorded Per FFT

61.44 61.44

307.20 61.44

307.20 20.48

184.32 12.29

61.44 4.096

Typical correlation time(s)

5.04

0.94

0.95

0.081

0.049

1

5

15

15

15

No. of FFTs averaged per spectral plot

begins to broaden the spectrum near the base of the water-tower dc spike. Figure 6.4(d) shows the measured Phase One VHF spectrum from a cell containing tall grass; the windblown motion of the grass is indiscernible in this VHF measurement. In all these results, the width of the dc spectral component from the steady target is essentially the limit of spectral resolution provided by the Blackman-Harris window function, which is cleanly maintained over the full spectral dynamic range of the radar down to the system noise level (i.e., 71 to 77 dB down for Phase One, 80 dB down for LCE). The window function sidelobes occur below the noise level of either system.

6.3.1.3 Spectral Normalization Chapter 6 shows measured clutter spectra normalized to compare with analytic representations of clutter spectral density. The first step in spectral normalization is to convert the FFT output from power per spectral resolution cell to power/(m/s) so as to be directly comparable with analytic spectral shapes defining continuous density functions. This conversion is performed by dividing each point in the FFT velocity spectrum by the width of the Doppler velocity resolution cell ∆v. The Doppler velocity resolution cell is wider than the sampling interval by a factor equal to the equivalent noise bandwidth ENBW of the window function. Thus ∆v = (λ/2) ⋅(PRF/N) ⋅ENBW, where N is the number of points in the FFT. For the four-term Blackman-Harris window used here, ENBW = 2.004 [37]. The second step in spectral normalization is to bring the power in the measured spectrum to unity for comparison with analytic spectral shapes for which the integral over the entire velocity domain is unity. In some circumstances, total power in the spectrum is brought to unity by dividing each spectral point by total spectral power. In other circumstances, where concern is only with the ac spectral shape and not the particular amount of dc power present, the ac power in the spectrum is brought to unity by dividing each spectral point by total spectral power times 1/(r + 1).

Windblown Clutter Spectral Measurements 587

20

20

LCE (4.0 km)

Phase One (6.4 km) L-Band

Desert Still Air

(a)

0

Water Tower

(b)

–20

–20

–40 Noise Level

71 dB

80 dB

0

–40

Tree Clutter

Noise Level

–60

–2

20

–1

0

1

2

–2

20

Water Tower

Phase One (6.4 km) X-Band

(c)

–20

0

2

(d)

–20

Tree Clutter

Noise Level

Noise Level

–40

1

Tall Grass (~3' high) 8/12 mph Winds

Phase One (6.3 km) VHF

0

77 dB

0

–1

71 dB

Ptot (dB)

–60

–40

–60

–60 –2

–1

0

1

2

–2

–1

0

1

2

Doppler Velocity v (m/s)

Figure 6.4 Four measured power spectra from “stationary” targets exhibiting little or no discernible spectral spreading to levels 70 to 80 dB down: (a) LCE, (b), (c), (d) Phase One L-, X-, VHF bands, respectively.

6.3.1.4 Spectral Power Total, dc, and ac spectral power were computed in the time domain for the Phase One and LCE spectral results. Total power over the temporal record of each FFT is 1/N times the sum of the squares of the I and Q samples of received power. The dc power over the same temporal record is the square of 1/N times the sum of the I samples plus the square of 1/N times the sum of the Q samples (i.e., coherent sum). The ac power over the same temporal record is total power minus dc power. These computations were performed over each FFT contributing to each spectrum. The final time-domain quantities for total, dc, and ac spectral power are each means of the resulting set of values, one value per FFT, applicable to each spectrum.

588 Windblown Clutter Spectral Measurements

The dc power obtained by summing coherently over a temporal record of backscatter from windblown trees depends on the length of the record (the CPI) over which the summation is performed. If the random process were well behaved (i.e., stationary), the coherent sum would converge and be largely independent of record length for lengths much greater than the correlation period of the process. However, windblown clutter backscatter records are not rigorously stationary. The statistics of the process sometimes appear to be characterized as intervals of stability separated by abrupt transitions from one stable state to another. Such abrupt changes can be caused, for example, by large tree limbs suddenly shifting position. Because the coherent sum does not always converge, the ratio of dc/ac power computed in the time domain is dependent on CPI duration. Table 6.4 provides two examples of the dc/ac ratio obtained as a function of CPI duration for two LCE long-time-dwell backscatter measurements from cells containing windblown trees, one taken under very light wind conditions and the other under very windy conditions. The correlation times for these two experiments are estimated to be ∼ 4 s for the light-air data and ∼ 1 s for the windy data. The clutter spectra from these two measurements are discussed in Section 6.3.2.1. It is evident that a significant dc component exists in the light-air data in Table 6.4 and very little dc power exists in the windy data. The results in the table may be interpreted in terms of decreasing sampling bandwidth of the zero-velocity Doppler filter with increasing CPI, where sampling interval bandwidth is given by λ/(2 × CPI). Because no weighting is employed in these time-domain computations, the filter has a sin x/x response. Table 6.4 Variation of dc/ac Ratio with Length of CPI for LCE Clutter Measurements from Windblown Trees

CPI (s)

No. of Points per CPI (PRF = 500 Hz)

No. of CPIs Averaged

Ratio of dc to ac Power (dB) (Time-Domain Computation) Light-Air Measurement (5 Sep, 4.7 km)

Windy Measurement (11 Sep, 7.7 km)

0.032

16

2048

47.2

20.8

0.064 0.128 0.256 0.512 1.02 2.05 4.10 8.19 16.4 32.8 65.5

32 64 128 256 512 1024 2048 4096 8192 16384 32768

1024 512 256 128 64 32 16 8 4 2 1

43.1 37.9 32.4 27.1 22.4 18.9 15.7 14.0 13.2 12.0 10.5

15.0 9.8 5.1 1.8 –1.0 –3.6 –5.8 –9.1 –10.7 –18.6 –19.0

In the frequency domain, the zero-th Doppler bin can contain both a singular dc power component existing as a discrete delta function and ac power existing as a continuous density function. The ac power in the zero-th Doppler bin decreases with increasing resolution (i.e., with increasing CPI duration), whereas the singular dc component is

Windblown Clutter Spectral Measurements 589

theoretically independent of resolution. However, in all the measured clutter spectra shown here, normalization (division) of power/cell by ∆v was performed for all cells, including the zero-Doppler cell. First-order credibility checks of the reasonableness of dc/ac ratios provided herein for spectra containing strong dc components (i.e., strong dc spikes, for example, in desert or cropland or at VHF) should therefore be performed by first decreasing the height of the spike by |∆v| dB before estimating the resultant dc/ac ratio. Note that the peak spectral level at zero Doppler (before or after division by ∆v) is not itself used in any direct way in Chapter 6 to normalize measured spectral data (measured spectra are never simply aligned by peak level). One reason that the zero-Doppler cell is not normalized differently from others is to maintain the relative shape of the raw FFT before normalization (whatever is done to one cell is done to all cells). Another reason is that the power in the zero-Doppler cell of windblown foliage spectra is often not dominated by a singular dc (i.e., delta function) component, in which circumstances the continuous power in the zero-Doppler cell requires normalization by ∆v similarly to all other Doppler cells. Excess quasi-dc power in Doppler resolution cells near the zero-Doppler cell is included as dc power in computing the dc/ac power ratio used as spectral modeling information in spectra where excess quasi-dc power exists. The dc/ac ratio in which the excess quasi-dc component is included in the singular dc term is obtained in the frequency domain by best-fitting the spectral tail at high Doppler velocities with an exponential ac shape function. The excess quasi-dc power is that which exists above the approximating exponential in cells of very low Doppler velocity close to zero Doppler. The fitting process is largely independent of spectral resolution as long as the resolution is adequate to define the exponential spectral tail. As a result, the dc/ac ratio used herein, which is that required for the ac exponential shape function to match the measured spectral tail both in relative shape and in absolute level, is also largely independent of CPI duration and spectral resolution. This fitting process is discussed in Section 6.4.2.

6.3.2 Measurements Illustrating ac Spectral Shape 6.3.2.1 Variations with Wind Speed Figures 6.5–6.7 are examples of LCE-measured windblown forest clutter spectra under windy, breezy, and light-air conditions, respectively. The data in these figures are normalized to show ac spectral shape Pac(v) plotted against a logarithmic Doppler velocity axis similar to the modeled curves of Figure 6.1. Each figure compares the measured ac spectral shape with several exponential shape functions of various values of shape parameter β. In Figure 6.5, the measured data follow the exponential curve of shape factor β = 5.2 remarkably closely over the full spectral dynamic range shown. This match of measured ac spectral shape with exponential is among the best in the Lincoln Laboratory database, although other examples exist both of LCE and Phase One windy-day clutter spectra with equally good fits to exponential. Furthermore, the spectrum of Figure 6.5 is among the widest measured; its shape factor β = 5.2 is the basis of the “worst case, windy” specification in Table 6.1 and Figure 6.1. Also shown in Figure 6.5 is a narrower Gaussian spectral shape function. The particular Gaussian shape shown corresponds to Barlow’s [7] much-referenced 20-dB dynamic range historical measurement (see Section 6.6.1.1). It is evident in Figure 6.5 that the overall rate of decay in the LCE data is much more exponential than Gaussian in character. Thus these LCE data support the general consensus of agreement subsequently arrived at

590 Windblown Clutter Spectral Measurements

[10–20, 27, 28] of spectral tails wider than Gaussian in windblown clutter spectra. Li [19] explains that tails wider than Gaussian are theoretically required by branches and leaves in oscillatory—as opposed to merely translational—motion.

Forest Windy

20

Pac (dB)

0

–20

Noise Level

–40

–60

LCE (7.7 km, 166 )

0.10

Gaussian, g = 20

= 8 5.2 4 1.00

10.00

Doppler Velocity v (m/s)

Figure 6.5 Highly exponential decay (β = 5.2) in a forest clutter spectrum measured under windy conditions.

The LCE spectral data of Figures 6.6 and 6.7 indicate that measured ac spectral shapes remain reasonably well represented by exponential shape functions under less windy conditions, with increasing values of exponential shape factor with decreasing winds (i.e., β ≅ 8 for breezy conditions, β ≅ 12 for light-air conditions). The results of Figures 6.6 and 6.7 are representative of many similar spectra measured in other cells on other days. Recall that normalization to Pac(v) requires raising the Ptot(v) spectrum by 10 log1 0 (r + 1) decibels on the vertical ordinate. The value of r applicable in Figures 6.5, 6.6, and 6.7 is 0.7, 18.9, and 29.8 dB, respectively. It is evident in Figures 6.6 and 6.7 that the measured data begin to depart from the approximating exponentials for v < 0.2 m/s as they begin to rise into the quasi-dc region, contributing to the large values of r in these data. As the amount of dc spectral power increases, less spectral dynamic range is left for measuring the ac power in the spectral tail, indicated by the rapidly rising effective system noise levels with respect to Pac(v) as wind speed decreases and dc/ac ratio increases in Figures 6.5–6.7. As discussed later (Sections 6.6.1 and 6.6.2), power-law spectral tails plot as straight lines in plots of 10 log1 0 P vs log1 0 v such as those of Figures 6.5–6.7. Thus a power law of shape n = 3 (30 dB/decade) fits the data of Figure 6.6 reasonably well down to the Pac = –20-dB level.

Windblown Clutter Spectral Measurements 591

Forest Breezy

20

Pac (dB)

0

–20 Noise

–40

–60

LCE (7.6 km, 294 ) = 12 9 7

0.10

1.00

10.00

Doppler Velocity v (m/s)

Figure 6.6 Approximate exponential decay in a forest clutter spectrum measured under breezy conditions.

However, this n = 3 power law cannot be extrapolated to lower levels. The local power-law (local slope tangent to the data curve) rate of decay in Figure 6.6 strongly increases (to n ≅ 6 or 7) at the lower spectral power levels in Figure 6.6. Likewise, at first consideration, an n = 4 power law (40 dB/decade) might be thought to be a reasonable match to the measured data of Figure 6.7. The apparent goodness of this straight-line fit to the data in Figure 6.7 is heightened by the data beginning to rise above the exponential in the low-Doppler quasi-dc region v < 0.2 m/s and by the data flaring away from the exponential toward the noise level as they become limited in signal-to-noise (S/N) ratio when approaching to within 10 dB of the noise floor at higher Doppler velocities around 1 m/s. However, these two effects tend to obscure a more fundamental exponential-like rate of decay (increasing local tangent slope with decreasing power level) as shown in the region 0.2 < v < 0.7 m/s in Figure 6.7, and the upper-level power-law rate of decay can no more be extrapolated to lower levels in the lightair data of Figure 6.7 than in the windier data of Figures 6.5 and 6.6. To do so would lead to physical implausibility as the upper-level light-air power law would extrapolate to lowerlevel ac power levels (e.g., Pac = –60 dB) exceeding in spectral width those measured under windy conditions at the same lower levels. Not all the Phase One and LCE clutter spectra measured under breezy and windy conditions are as closely exponential as the measured spectrum in Figure 6.5. However, like that spectrum, they all demonstrate increasing downward curvature (convex from above) with increasing Doppler velocity and decreasing power level as their most characteristic general feature in plots of 10 log P vs log v such as that of Figure 6.5. The main reason the

592 Windblown Clutter Spectral Measurements

Forest Light Air

20

Pac (dB)

0

–20

Noise

–40

–60

LCE (4.7 km, 166°) β = 16 12 9

0.10

1.00

10.00

Doppler Velocity v (m/s)

Figure 6.7 Approximate exponential decay in a forest clutter spectrum measured under light wind conditions.

exponential form is used herein for modeling clutter spectral shapes is that it, too, when plotted as 10 log P vs log v, possesses this increasingly downward curving shape (see Figure 6.1) while remaining wider than Gaussian as required by the measured data (see Figure 6.5). In contrast, the spectral tails of power-law functions do not have increasing downward curvature on 10 log P vs log v axes but plot linearly (i.e., extrapolate rapidly to excessive spectral width) on such axes. This matter is further discussed in Sections 6.6.1 and 6.6.2. Most of the Phase One- and LCE-measured clutter spectra are not completely and precisely representable by any simple analytic function over their full spectral ranges. Many of these measured spectra are somewhat wider than exponential (i.e., are concave from above in 10 log P vs v plots), but they are almost always much narrower than power law (i.e., are convex from above in 10 log P vs log v plots). In such circumstances, absorbing excess quasi-dc power in the dc term usually gives the exponential model the flexibility to match the relative shapes and absolute levels of the measured spectra over extensive spectral tail regions.

Gale Force Winds (Scaled Estimate). Figure 6.8 shows a different set of three LCE-measured windblown-forest clutter spectra under light-air, breezy, and windy conditions, displayed as 10 log Ptot vs v. In contrast to the light-air, breezy, and windy spectra of Figures 6.5–6.7 (which come from three different range cells) the spectra shown

Windblown Clutter Spectral Measurements 593

in Figure 6.8 are from the same 7-km range cell on three different measurement days. These Figure 6.8 spectra clearly indicate that spectral extent from a given range cell increases strongly with increasing wind speed. In approximate measure, the data of Figure 6.8 indicate similar-sized steps of increasing spectral width for wind speeds increasing by approximate factors of 3 (from 1–2 to 6–7 mph, and from 6–7 to 18–20 mph). This observation implies that spectral width increases approximately linearly with the logarithm of wind speed [28, 38]. Such data are the basis of Eq. (6.3) specifying spectral width as a function of wind speed in the clutter model of Section 6.2. In Figure 6.8, the maximum spectral extent in the data 70 dB down from their zero-Doppler peaks is ∼ 1, 2, and 3 m/s for the light-air, breezy, and windy spectra, respectively. In these results, as ac clutter power increases and spreads out with increasing wind speed, dc clutter power decreases, as indicated by dc/ac ratios r of 0.1, –1.5, and –4.5 dB for the light-air, breezy, and windy spectra, respectively.

20

LCE (7.0 km, 166 ) Forest

Wind (mph) (a) 1 – 2 (b) 6 – 7 (c) 18 – 20

(c) Windy 70 dB

Ptot (dB)

0

–20

Noise

–40 (b) Breezy

–60 (a) Light Air –3

–2

–1

0

1

2

3

Doppler Velocity v (m/s)

Figure 6.8 Variation of LCE windblown forest clutter spectra with wind speed. Common range gate (7 km).

Figure 6.9 shows the same three spectra of Figure 6.8, now displayed as 10 log Ptot vs log v. Figure 6.9 also shows a scaled extrapolation to higher wind speeds by a further factor of 3, that is, from the 18–20 mph of the “windy” spectrum to 54–60 mph gale force wind speeds. This estimate was obtained by finite-difference extrapolation of the light-air, breezy, and windy Doppler velocities, say va, vb, and vc, to vd, the estimated gale force Doppler velocity, at multiple spectral power levels, assuming constant factors-of-3 increases in wind speed throughout. It is evident in the figure that the gale force spectral estimate is well

594 Windblown Clutter Spectral Measurements

modeled by an exponential curve of shape factor β = 4.3; this is the basis of the “typical” gale force exponential ac shape parameter specification β = 4.3 in the clutter model of Section 6.2. Increasing gale force β in this model from its typical specification based on the scaled estimate shown in Figure 6.9 to a worst-case specification of β = 3.8 brings it into very close agreement (in terms of gross spectral extent at the –14-dB level) with the only known measurements of windblown clutter under actual gale wind conditions, namely, the very early measurements of Goldstein [9] that are further discussed in Section 6.6.3.5.

Gale Force Estimate 20

Windy

Ptot (dB)

0

–20

Breezy –40

Noise

Light Air

–60

= 4.3

0.10

1.00

10.00

Doppler Velocity v (m/s)

Figure 6.9 Scaled estimate of windblown forest clutter spectrum under gale force winds (54–60 mph).

6.3.2.2 Invariance with Radar Frequency The idea that spectral extents of windblown ground clutter Doppler-velocity spectra are in large measure invariant with radar frequency, or equivalently, that spectral widths in Doppler-frequency spectra are approximately proportional to radar frequency, has been discussed in the technical literature of the subject since the early days of radar development [6, 8, 9]. For example, early work in comparing spectral widths with radar frequency conducted at the MIT Radiation Laboratory during World War II by Herbert Goldstein and others is summarized by Goldstein’s conclusion that “The widths of the [Doppler-frequency] spectra . . . increase with wind speed and . . . appear to be essentially proportional to [radar] frequency” [8, 9]. This idea remains true in the LCE and Phase One spectral results, as indicated in Figures 6.10 and 6.11—Figure 6.10 shows VHF, L-, and X-band Doppler-velocity forest spectra under windy conditions; Figure 6.11 shows UHF, L-, and S-band forest spectra under breezy conditions.

Windblown Clutter Spectral Measurements 595

However, the early results were mainly in the 1- to 10-cm range of wavelengths and, by today’s standards, over very limited spectral dynamic ranges (∼ 20 dB). Results such as those of Figures 6.10 and 6.11 extend the idea of frequency invariance of windblown clutter Doppler-velocity ac spectral shape over very much greater spectral dynamic ranges (> 60 dB) and to very much longer radar wavelengths [from X-band (λ = 3.3 cm) to VHF (1.8 m)]. These results are rather surprising, since the dominant, wavelength-sized scatterers at VHF (large branches, limbs) are presumably different than those at X-band (leaves, twigs). As will be shown, much more dc power exists in VHF windblown clutter spectra than at higher radar frequencies, for one reason because the VHF energy partially penetrates the foliage to reach the underlying stationary tree trunks and ground surface. As a result, the ac spectral power at VHF is measured at lower levels in the available spectral dynamic range. Still, over very many spectral measurements of windblown trees at VHF and UHF, ac spectral spreading caused by internal motion in windblown clutter generally exists at VHF and UHF at lower absolute levels of Ptot(v) but roughly equivalently in the relative shape and extent of Pac(v) to that observed in the higher, L, S, and X microwave bands.

Forest Windy

20

Pac (dB)

0

–20

Noise Level –40 (a) VHF (b) L-Band (c) X-Band

(a) (b),(c)

–60 = 9 0.06 0.10

6

1.00

10.00

Doppler Velocity v (m/s)

Figure 6.10 Variations of windblown forest clutter spectra with radar frequency under windy conditions: (a) VHF, Phase One, (b) L-band, LCE, and (c) X-band, Phase One.

In Figure 6.10, the VHF and X-band spectra were measured by the Phase One radar at Katahdin Hill under windy conditions on two different days in April at 2.8-km range. The Lband spectrum was measured by the LCE radar at Wachusett Mt. on 11 September at 6-km range. The Figure 6.11 spectra were all measured by the Phase One radar at Katahdin Hill also at 2.8-km range under breezy conditions in late April or early May. In general measure, the three windy-day spectra of Figure 6.10 are essentially identical in overall ac spectral

596 Windblown Clutter Spectral Measurements

Forest Breezy

20

Pac (dB)

0

–20

Noise Level

–40

(c) (b)

–60

(a) UHF (b) L-Band (c) S-Band

0.07 0.10

(a) = 16 12 9 1.00

10.00

Doppler Velocity v (m/s)

Figure 6.11 Variations of Phase One windblown forest clutter spectra with radar frequency under breezy conditions, UHF, L-, and S-bands.

shape, as are the three breezy-day spectra of Figure 6.11. Of course, temporal (minute-tominute, hour-to-hour) and spatial (cell-to-cell, site-to-site) variability exist in LCE- and Phase One-measured clutter spectra under nominally similar wind conditions, and not all such measurements overlay one another as exactly as those shown in Figures 6.10 and 6.11. Concerning variability, even in the results of Figures 6.10 and 6.11 for which the same nominal range and azimuth apply, the spatial cells still encompass different overlapping ground areas due to the different azimuth beamwidths. Also, “. . . there are the usual uncertainties [because of the lack of]. . . simultaneity of the measurements in time” [9]. In considering possible means by which variations with radar frequency might be introduced in clutter velocity spectra, amplitude fluctuations caused by scatterer rotation and the wig-wag shadowing of background leaves by leaves in the foreground have been discussed [14, 19, 29, 39] as possible mechanisms that might complicate clutter spectra over and above phase fluctuations caused by the scatterer velocity distribution. However, one theoretical model exists [14] that incorporates scatterer rotational and shadowing effects and still provides radar frequency-independent clutter Doppler-velocity spectral shapes (i.e., “to a first approximation, the spectrum . . . depends only on the product λf ” [14]). It is not suggested here that if multifrequency spectra could somehow be measured simultaneously from exactly the same spatial assemblage of windblown foliage, fine-scaled specific differences would not be observed in ac spectral shape with radar frequency. However, in looking across all the LCE- and Phase One-measured spectral data and the variations that exist therein, no significant trend is observed in ac Doppler-velocity spectral

Windblown Clutter Spectral Measurements 597

shape with radar frequency, VHF to X-band, as opposed, for example, to the strong trend seen in ac spectral shape with wind speed.

6.3.2.3 Invariance with Polarization The LCE and Phase One clutter spectral data indicate that clutter spectral shape from windblown vegetation is largely independent of radar polarization, to the extent that this can be determined in non-simultaneous measurements. Figure 6.12 shows one set of three sequential LCE measurements of windblown treed-cell ground clutter spectra at VV-, HH-, and HV-polarizations obtained at approximately 2-min intervals, which are of essentially identical spectral shape. The spectral artifact in the HV-pol. spectrum of Figure 6.12 at ∼ 2.8 m/s is probably a bird. Many other LCE and Phase One VV- and HH-pol. spectra were compared from common cells selected from other sites and experiments [21]. These usually showed little or no variation in spectral shape with polarization. When variations of spectral shape with polarization did occur, such variations were usually relatively random with little evidence for the existence of any strong general effect on spectral shape with polarization.

LCE (7.4 km, 166 )

20

Forest Windy

Ptot (dB)

0

–20

Noise Level Polarization

–40

(a) HH (b) VV (c) HV

–60

0.03

0.10

1.00

10.00

Doppler Velocity v (m/s)

Figure 6.12 Variations of LCE windblown forest clutter spectra with polarization: (a) pol. = HH, winds (mean/gusts) = 10/18 mph; (b) pol. = VV, 2 min later, winds = 13/19 mph; (c) pol. = HV, 4 min later, winds = 10/16 mph.

Other investigators have also found little effect on windblown clutter spectral shape with polarization. For example, Kapitanov et al. [13] observed that “The spectra of [X-band] echo signals from forest for different polarizations [vertical and circular]. . . are on the

598 Windblown Clutter Spectral Measurements

average similar.” Unpublished X-band windblown clutter spectral results obtained at Lincoln Laboratory by Ewell [20] at VV-, HH-, and circular polarizations in shrubby desert terrain also indicated no consistent differences in the spectral shapes obtained at the various polarizations.

6.3.2.4 Temporal Variation All LCE clutter spectra in Chapter 6 are averages of six individual 1,024-point FFTs, each formed from a 10.24-s duration temporal backscatter record. Windy-day wind conditions frequently vary considerably from one 10-s interval to the next. Such variability of windyday conditions within a treed resolution cell from one 10.24-s interval to the next often leads to significant variability in successive individual 10.24-s dwell FFTs [21]. However, the results of Figures 6.13 and 6.14 indicate that over longer periods of 60- to 80-s, windyday treed-cell clutter spectra can be expected to become more stationary. Figure 6.13 shows LCE treed-cell clutter spectra for three repeated experiments on a windy day, each of which is formed from an overall temporal record of 61.44 s (100-Hz PRF, 1024-point FFTs, 6 FFTs averaged). The shape of the spectrum from the first experiment is essentially identically replicated by the shape of the spectrum from a following experiment begun 65 min later, suggesting that enough averaging of wind variations occurs within 1 min to lead to some degree of convergence in average spectral shape. But wind is an extremely nonstationary dynamic random process with complex short- and long-term variation. For example, on the windy/gusty day on which the data of Figure 6.13 were collected, the gusts happened to die down over the 70-s interval covering the second experiment (begun 9 min after the first), and the spectrum formed from that data is indeed considerably narrower than the other two. Figure 6.14 shows Phase One L-band clutter spectra for three repeated breezy-day experiments for very nearly the same treed cell at Wachusett Mt. for which the LCE data of Figure 6.13 apply. Each of these Phase One spectra is formed from a temporal record of 81.9-s duration (125-Hz PRF, 2048-point FFTs, 5 FFTs averaged). The spectrum from the first experiment is nearly identical to that of the second experiment, begun 4 min later. The spectrum from the third experiment, begun 9 min after the first, is somewhat narrower. In a similar set of five sequential experiments begun 15 min before those of Figure 6.14, the range of variability of spectral shape was similar. The slightly changing average wind conditions within 81.9-s intervals over 4- or 5-min periods resulted in only very small changes in the measured spectra, such as shown in Figure 6.14. Such results indicate that the range of variability in clutter spectra formed by averaging over 60- to 80-s data intervals under nominally similar wind conditions generally is quite low, compared with the more variable individual FFTs formed from 10- to 16-s data intervals during the same period.

6.3.2.5 Effects of Site/Season/Tree Species/Cell Size It is not difficult to find Phase One and LCE spectra of essentially identical exponential spectral shape—two are shown in Figure 6.15. The LCE spectrum (a) measured on September 10 (leaves on deciduous trees) at Wachusett Mt. at 7.9-km range, HH-pol., 150-m range resolution, and 2° depression angle essentially overlays and replicates the Phase One spectrum (b) which was measured on May 3 (leaves not yet emerged) at Katahdin Hill at 2.4-km range, VV-pol., 15-m range resolution, and 0.5° depression angle. These two measurements were obtained with different radar receivers, and the two spectra were produced using different data reduction and processing software. Thus commonality can

Windblown Clutter Spectral Measurements 599

LCE (7.6 km, 166 )

20

Gusts

0

Ptot (dB)

Forest Windy/Gusty

No Gusts

–20

–40

Experiment

–60

Wind Speed (mph) Mean/ Gusts

Noise Level

First 9 min Later 65 min Later

10/18 8/None 13/18 (Exp. Duration = 61.44 s) 0.03

0.10

1.00

10.00

Doppler Velocity v (m/s)

Figure 6.13 Variations of LCE windblown forest clutter spectra with time: Wachusett Mt., 11 September.

exist in spectral shape, in large measure because of the large cells and large degree of spatial averaging involved, despite a host of underlying differences including measurement instrumentation and parameters (range, cell size, illumination angle, polarization), site, and time of year. The Phase One and LCE radars mimic long-range ground-based surveillance radars in the relatively long ranges, large resolution cell sizes, and low illumination angles of their measurements. Cell sizes, typically several hundred meters on a side, are large enough to encompass a large spatial ensemble of scatterers (many trees) as well as variable local wind currents within the cell. Because of the complexity of the scattering ensemble and nonuniform winds within such large cells and the temporal and spatial variability of the ensemble from cell to cell over large numbers of cells, it is difficult to discern significant site-to-site differences or significant trends with season and/or tree species in the Phase One and LCE spectral data. Other, more fine-scaled investigations, both historical [13–16] and recent [40–42], involving small illumination spot sizes (e.g., 1.8-m diameter [42]) on individual trees at short ranges (e.g., 30 m [42], 50 m [16]), provide results showing variation on treed-cell spectral shape with the type or species of trees. However, such small differences are largely absorbed within the general ranges of statistical variability in the Phase One and LCE measurements and are thus of limited consequence for the longer ranges and larger cells of surveillance radars.

600 Windblown Clutter Spectral Measurements

40 Phase One L-Band (7.7 km, 166 )

Forest Breezy

20

Ptot (dB)

0

–20 First Experiment

Noise Level

4 min Later –40

9 min Later (Exp. Duration = 81.9 s)

–60 0.01

0.10

1.00

10.00

Doppler Velocity v (m/s)

Figure 6.14 Variations of Phase One L-band windblown forest clutter spectra with time: Wachusett Mt., 22 August.

From Phase One Katahdin Hill measurements acquired from a specific set of forested cells once a week over a nine-month period [21], L-band spectra were examined for seasonal variations in three wind regimes, viz., calm to light-air conditions, light-air to breezy, and windy. These results marginally showed that in each wind regime, spectral widths 60 to 70 dB down were only very slightly wider by no more than ≈0.5 m/s for summer measurements (leaves on deciduous trees) than for winter measurements (leaves off deciduous trees). An early study of Phase One spectra involved eight forested sites, four in western Canada and four in the eastern U.S. For the western Canadian sites, the dominant tree species were aspen and spruce. For the eastern U.S. sites, the forest was mixed (oak, beech, maple, hemlock, pine). Measured Doppler-velocity spectra generally showed no significant major differences in shape or extent from one forested measurement site to another, either within each group or from group to group. No significant discernible difference has been observed in the shapes of Phase One spectra from cells of 150-m range resolution compared with cells of 15-m range resolution.

6.3.3 Measured Ratios of dc/ac Spectral Power 6.3.3.1 Variation with Wind Speed Forested ground clutter cells contain many scatterers. Each scatterer is positioned randomly within the cell and hence produces an elemental scattered signal of random relative phase with respect to the other scatterers. Some of the scatterers, such as leaves

Windblown Clutter Spectral Measurements 601

20

(b)

L-Band Windblown Trees

0

Pac (dB)

(a)

–20

Noise

–40

(a) LCE, Wachusett Mountain

–60

0.03

(b) Phase One, Katahdin Hill

0.10

1.00

10.00

Doppler Velocity (m/s)

Figure 6.15 Similar LCE and Phase One forest clutter spectra measured under windy conditions at two different sites: (a) LCE, Wachusett Mt., 10 September, and (b) Phase One (L-band), Katahdin Hill, 3 May.

and smaller branches, move in the wind, producing fluctuating signals with time-varying phases. Other scatterers, such as tree trunks and larger limbs, are more stationary, producing steady signals of fixed phase. The total clutter signal is the sum of all the elemental backscattered signals, both steady and fluctuating. At high wind speeds, most of the foliage is in motion, and the ratio r of dc to ac power in the clutter spectrum is relatively low. In such circumstances, and in the higher microwave bands where little foliage penetration occurs, the steady component can become vanishingly small, whereupon Eq. (6.1) simplifies to Ptot(v) ≅ Pac(v). Goldstein correctly anticipated, however, that “As the wind velocity decreases, . . . the steady-to-random ratio [i.e., r] would be expected to increase” [9]. Thus under light winds, a large proportion r/(r + 1) of the clutter power is at dc. Even so, the small proportion of clutter power 1/(r + 1) that, under light winds, remains at ac can still troublesomely interfere with desired target signals. Therefore, it is necessary that a windblown clutter spectral model quantify the dc/ac ratio r expected from forested or other types of vegetated cells as a function of wind speed. Figure 6.16 shows an LCE-measured clutter spectrum from a treed cell under very light wind conditions. The most striking characteristic of this light winds spectrum is its extreme narrowness, with spectral spreading occurring only at relatively low power levels and to relatively small extent in Doppler. This spectrum contains a large steady or dc component,

602 Windblown Clutter Spectral Measurements

and since the spectral density decays smoothly and continuously (albeit rapidly) away from the peak zero-Doppler level, it also contains high levels of quasi-dc power at very low but non-zero Doppler velocities. This spectrum may be approximately modeled utilizing a value of r = 29.8 dB, in which excess quasi-dc power is included in the dc term, and an exponential shape function for the spectral tail of shape parameter β = 12. The spectrum of Figure 6.16 is generally representative of many similarly narrow LCE and Phase One clutter spectra measured in other treed cells and on other light wind days.

LCE (4.7 km, 166 ) dc/ac = 29.8 dB

20

Forest Light Air

78 dB

Ptot (dB)

0

–20

–40

Noise

–60

–3

–2

–1

0

1

2

3

Doppler Velocity v (m/s)

Figure 6.16 An LCE windblown forest clutter spectrum measured under light wind conditions.

The particular value of dc/ac ratio r applicable to any given treed clutter cell is highly variable. Such variability is illustrated in the results shown in Figure 6.17, in which ratios of dc to ac spectral power obtained from LCE clutter measurements from many treed cells are shown as a function of wind speed. There is some difficulty in precise specification of wind speed in such results since anemometer measurements usually provide only a onepoint-in-space indication of wind conditions for the total test area. Over and above the inherent variability in these data, Figure 6.17 indicates a strong trend such that the ratio of dc to ac spectral power in dB decreases approximately linearly with the logarithm of wind speed w.

6.3.3.2 Variation with Radar Frequency Whether a scatterer in a forested clutter cell is classified as stationary or in motion depends on the radar wavelength. A back-and-forth scatterer motion of 3 cm would produce a steady signal of essentially fixed phase at VHF, but a fluctuating signal passing through all

Windblown Clutter Spectral Measurements 603

Forest L-Band

dc/ac Ratio r (dB)

30

20

10

0

Light Air Breezy Windy

2

5

10

20

Wind Speed w (mph)

Figure 6.17 LCE measurements showing ratio of dc to ac spectral power vs wind speed in Lband windblown forest clutter spectra.

possible phases at X-band. Furthermore, at VHF and UHF, significant energy penetrates the foliage to scatter from the stationary underlying ground surface, whereas at X-band little or no energy reaches the ground. Again, Goldstein correctly anticipated that, because of such effects, the dc to ac ratio in windblown clutter spectra “. . . should therefore decrease with [decreasing] wavelength” [9]. Figure 6.18 shows a Phase One-measured spectrum at VHF from a treed cell under windy conditions (same spectrum as shown in Figure 6.10). It is evident in Figure 6.18 that a large dc component exists in this VHF clutter signal such that the ratio of dc to ac power in the spectrum is 14.8 dB. In contrast to the large dc component in the light winds spectrum of Figure 6.16, in which significant quasi-dc spectral power also occurs, in the lower frequency VHF spectrum of Figure 6.18 the dc component exists largely as a discrete delta function at the spectral resolution of the processing in the zero-Doppler bin. Much smaller dc components occurred in measured spectra at higher radar frequencies from the same forested cell under similarly windy conditions. Although there is a large dc component in the VHF spectrum, it also contains a significant amount of ac power of considerable spectral extent. This VHF spectrum comes from a single FFT of 61.44-s CPI (i.e., no averaging), this relatively long CPI being required to provide adequate spectral resolution at this relatively low radar frequency. The VHF spectrum of Figure 6.18 is representative of many other Phase One-measured VHF clutter spectra from other forested cells and on other windy days.

604 Windblown Clutter Spectral Measurements

VHF dc/ac = 14.8 dB

20

Forest Windy

76 dB

Ptot (dB)

0

–20

Noise

–40

–60

–3

–2

–1

0

1

2

3

Doppler Velocity v (m/s)

Figure 6.18 A Phase One windblown forest clutter spectrum at VHF.

Figure 6.19 shows ratios of dc to ac spectral power vs radar frequency, VHF to X-band, obtained from Phase One clutter measurements under windy conditions at three forested sites. The solid line in the figure joins the median positions of each in-band cluster of data points; the dashed line joins the median positions of the bounding VHF and X-band clusters only. These lines indicate, over and above the inherent variability in the data, a strong trend such that the dc to ac ratio in dB decreases approximately linearly with the logarithm of the radar carrier frequency fo. Thus at X-band in Figure 6.19, virtually all the spectral power is ac, whereas at VHF the ac power occurs at levels 15 to 25 dB below the dc power. The information shown in Figures 6.17 and 6.19 substantiates the early expectations [9] in these matters. Such information was used to develop the empirical relationship given by Eq. (6.4), which relates dc to ac ratio in windblown clutter spectra with wind speed and radar frequency.

6.4 Use of Clutter Spectral Model 6.4.1 Spreading of σ ° in Doppler Two important issues concerning the effects of ground clutter on radar system performance are the strength of the clutter, which determines how much interfering clutter power is received, and the spreading of received clutter power in Doppler. Thus predicting ac clutter power in a given Doppler cell requires predicting the backscattering clutter coefficient σ° in the spatial resolution cell under consideration (see Section 2.3.1.1),

Windblown Clutter Spectral Measurements 605

25

Blue Knob Wachusett Mt. Katahdin Hill

20

dc/ac Ratio r (dB)

15

10

5 0

–5

Forest Windy

–10 0.1

1

VHF

UHF

10

L-

S-

X-Band

Frequency (GHz)

Figure 6.19 Phase One measurements showing ratio of dc to ac spectral power vs radar frequency under windy conditions at three forested sites.

predicting the dc to ac power ratio r in the spectrum, and predicting the ac spectral shape factor Pac(v). Let σ °trees be the clutter coefficient for windblown trees. Equation (6.1) shows that [ σ °trees ⋅ P tot ( v ) ] specifies the spreading of σ °trees in Doppler, i.e., ∞

∫

–∞

[ σ °trees ⋅ P tot ( v ) ] dv = σ °trees ,

so [ σ °trees ⋅ P tot ( v ) ] represents the normalized density of windblown tree clutter power occurring at Doppler velocity v in units of [(m2 /m2 )/(m/s)]. For |v| > 0, [ σ °trees ⋅ P tot ( v ) ] becomes

[ ( σ °trees ⁄ ( r + 1 ) ) ⋅ P ac ( v ) ] . Let n = 0, 1, 2, . . ., N be the Doppler cell index, where n = 0 is the zero-Doppler cell. Then the amount of windblown-tree clutter cross section σ trees (n) that occurs in the nth Doppler cell is given by:

606 Windblown Clutter Spectral Measurements

σ °trees λ σ trees ( n ) = ------------------⋅ ∆ f ⋅ A ⋅ P ac ( f n ), 2(r + 1)

n>0

(6.5)

where σ trees(n) is in units of [m2 ], and fn is the Doppler frequency [Hz] in the center of the nth Doppler cell. In Eq. (6.5), ∆f = Doppler cell width [Hz]; λ = radar wavelength [m]; A = spatial resolution cell area [m2 ]; r = ratio of dc/ac spectral power [as given by Eq. (6.4)]; and Pac(fn) is the value at f = fn of the ac spectral shape function [as given by Eqs. (6.2) and (6.3)]. Comprehensive information specifying the clutter coefficient σ °trees in Eq. (6.5) is provided in earlier chapters for the low illumination angles typical of ground-sited radar, for radar frequencies from VHF to X-band, and for both VV- and HH-polarizations, on the basis of the Phase Zero and Phase One clutter measurement databases. These clutter data are not available at cross-polarization. However, the LCE clutter data at Wachusett Mt. indicate that in forest, cross-pol. clutter coefficients are generally 3 to 6 dB but occasionally as little as 0 dB or as much as 8 dB less than the co-pol. clutter coefficients. Similar depolarization effects in forest clutter data have been observed elsewhere [13, 27, 43].

6.4.2 Two Regions of Spectral Approximation Figure 6.20 shows an idealized representation of a typical windblown clutter spectrum (solid line). As is often observed in measured clutter spectral data, this representation consists of two distinct regions, namely, a quasi-dc region near zero-Doppler velocity and an ac spectral tail region at greater Doppler velocities. Also shown is a spectral model (dashed lines) as given by Eq. (6.1). The model uses a delta function at v = 0 to represent the dc spectral component and the exponential shape function as given by Eq. (6.2) to represent the ac spectral tail. In a plot of 10 log10 Ptot vs v such as that of the figure, the exponential shape plots as a straight line of slope 4.34 β (where 4.34 = 10 log10 e and e = 2.718 ...). Also, both the data and the model in Figure 6.20 are normalized to unit total spectral power, i.e., ∞

∫ –∞

P tot ( v ) dv = 1 .

In these circumstances, the model is matched to the data as follows: first, β is selected so that the slope [i.e., dB/(m/s)] of the model matches that of the data in the ac spectral tail region. Next, the value of dc/ac ratio r in the model is assigned to provide a y-intercept [1/ (r + 1)](β/2) so that the exponential model overlays and matches the ac region of the data in absolute power level Ptot (v) (i.e., vertical position) as well as slope. Because of the normalizations involved, this procedure results in the excess power from the quasi-dc region of the data being included in the dc Dirac delta function term [r/(r + 1)]δ(v) of the model, where excess quasi-dc power means the power in the quasi-dc region of the data that exists above the approximating exponential of the model. Figure 6.21 shows four examples of measured windblown clutter spectra presented as 10 log Ptot (v) vs v to illustrate quasi-dc and ac spectral regions in actual measured data. Figure 6.21(a) shows an LCE spectrum; Figures 6.21(b) through (d) show Phase One spectra at L-, X-, and UHF bands, respectively. Each spectrum has an approximating exponential model shown as a straight line through the right side of the data. Each spectrum in Figure 6.21 contains excess power above the approximating exponential in a quasi-dc

Windblown Clutter Spectral Measurements 607

Data

Ptot (dB)

Model

1

β

r +1

2

Quasi-dc Region

ac Region, Slope = 4.34 β

(dB)

Exponential ac Model

dc Model r = δ (v) r +1

0

Doppler Velocity v (Linear Scale)

Figure 6.20 Modeling of clutter spectra.

region near zero-Doppler. The resolution in these spectra is very fine (≈ 0.01 m/s, see Table 6.3), so in each case quasi-dc spectral power is resolved at levels well above the zeroDoppler window function limiting resolution. It is evident that absorbing the excess quasidc power of the data in the delta function dc term of the model in such results allows extremely good fits of the ac spectral tail regions with exponential shape functions over regions of wide Doppler extent in the spectral tails. As computed directly in the time domain, the zero-Doppler cell contains relatively little dc power compared with the total ac power from all the non-zero Doppler cells, for each of the examples shown in Figure 6.21. However, the quantity rmodeled increases compared with rmeasured as a result of absorbing the excess quasi-dc power in the modeled dc term. For the spectra of Figure 6.21, the values used for rmodeled are 0.7, 4.3, 2.9, and 8.0 dB for spectra (a), (b), (c), and (d), respectively. Use of these values causes the exponential straight-line fits to the data in the examples of Figure 6.21 to be shifted downwards by 10 log (rmodeled + 1) – 10 log (rmeasured + 1) decibels, resulting in the exponential models overlaying the measured data in these examples throughout the extensive ac spectral tail regions [25]. Equation (6.4) which specifies rmodeled was developed from data in which excess quasi-dc power was absorbed in the dc term to gain the benefit of improved fidelity in modeling spectral tails. No simple ac model (i.e., analytic expression), including exponential, can adequately represent both the quasi-dc region |v| < 0.25 m/s and the ac region |v| > 0.25 m/s of the data in Figures 6.20 and 6.21. The objective of Chapter 6 is realistic representation of the ac region or spectral tail of the data. Even the simplest single-delay-line MTI filter can usually

608 Windblown Clutter Spectral Measurements

LCE (7.7 km)

Forest Windy

(a)

20

(b)

Quasi-dc

0

Quasi-dc

0

66 dB

–20

–40

–20

Noise

–40

Noise

–60

–60 Exponential

Ptot (dB)

Phase One (2.4 km) Forest L-Band Breezy/Windy

61 dB

20

–4

–2

0

2

Phase One (2.8 km) X-Band

20

Exponential

= 5.2

4

–3

Forest Windy

20

–2

–1

= 7.1

0

1

Phase One (2.8 km) UHF

Quasi-dc

2

3

Forest Breezy Quasi-dc

(d)

(c)

65 dB

–20

Noise

–40

75 dB

0

0

–20

Noise

–40

–60

–60 Exponential –3

–2

–1

0

= 5.9 1

Exponential 2

3

–3

–2

–1

= 9.7 0

1

2

3

Doppler Velocity v (m/s)

Figure 6.21 Highly exponential decay in four measured windblown forest clutter spectra: (a) LCE; (b), (c), and (d) are Phase One L-, X-, and UHF bands, respectively. Regions of excess quasidc power are also indicated.

sufficiently reject dc and quasi-dc clutter power in the region |v| < 0.25 m/s. It is the tail of the clutter spectrum that requires definition to enable, for example, knowledgeable design of the skirts of MTI filter characteristics or other Doppler signal-processing ground clutter rejection techniques in the region |v| > 0.25 m/s (see Section 6.5). In the modeling information provided herein, excess quasi-dc power is included in the dc term in situations where including it as ac power would degrade representation of the ac spectral tail. Users of this information whose interests in clutter spectra may differ from those just stipulated need to be aware that some of the dc power in the delta function of the current model is often spread slightly into a near-in quasi-dc region |v| < 0.25 m/s in actual measurements. As an alternative to absorbing the excess quasi-dc power in the dc delta function, the quasi-dc

Windblown Clutter Spectral Measurements 609

region in each specific measured clutter spectrum can instead be represented by a second, very sharply declining, measurement-specific exponential function [31]. This alternative can be helpful in analysis situations in which the Dirac delta function is not of sufficient analytic tractability.

6.4.3 Cells in Partially Open or Open Terrain 6.4.3.1 Desert Ground clutter spatial resolution cells in which some of the backscattered power comes from stationary scattering elements such as the underlying terrain surface itself or large fixed discrete objects (water towers, rock faces) provide correspondingly larger values of dc/ac ratio r in the resulting clutter spectra. In the ground clutter spectral measurements conducted by the LCE radar at its desert site, portions of barren desert floor were visible between the sparse desert bushes (greasewood, creosote) typically of heights of 3 or 4 ft. Figure 6.22 illustrates a typical LCE clutter spectrum measured at this desert site under windy conditions (wind speed ≅ 20 mph). It is evident that this desert clutter spectrum contains a large dc component at zero-Doppler velocity, the result of backscatter from the stationary desert floor.

L-Band dc/ac = 24.1 dB

20

Desert Windy

76 dB

Ptot (dB)

0

–20

–40

Noise

–60

–3

–2

–1

0

1

2

3

Doppler Velocity v (m/s)

Figure 6.22 An LCE-measured clutter spectrum from desert terrain (scrub/brush, partially open) under windy conditions.

The ratio of dc/ac power computed directly in the time domain for the desert spectrum of Figure 6.22 is 24.1 dB. Normalization of measured spectral data to Ptot(v) involves division

610 Windblown Clutter Spectral Measurements

of power per resolution cell by the width of the cell ∆v. For the data of Figure 6.22, ∆v equals –16.22 dB, so this procedure raises the power in each cell by 16.22 dB. For spectra like that of this figure with a large dc component, the power in the zero-Doppler cell is not distributed over ∆v but exists as a singular dc component. Reducing the zero-Doppler peak by 16.2 dB allows more straightforward interpretation of r = 24.1 dB as simply the ratio of the reduced zero-Doppler peak to the total ac power (i.e., the power level of the step function existing in the unit interval –0.5 < v < +0.5 m/s and containing the same total ac spectral power as the measured spectrum). The desert/windy clutter spectrum of Figure 6.22 contains extensive ac spectral spreading at lower power levels. The low-level ac spectral spreading in these data is due to wind-induced motion of the desert foliage. Other LCE-measured desert spectra from similar cells under light or calm wind conditions showed little or no spectral spreading over as much as 80 dB of spectral dynamic range [see Figure 6.4(a)]. Unlike the forest/light wind spectrum of Figure 6.16, which also contains a large dc component but in which the spectral power decays rapidly but broadens continuously away from the zero-Doppler peak, the dc component in the desert/windy spectrum of Figure 6.22 exists more as a discrete delta function at the spectral resolution of the window function over the higher levels of spectral power. Figure 6.23 shows the ac spectral tail region of the desert/windy spectrum of Figure 6.22 at higher Doppler velocities as 10 log Pac(v) vs log v. Also shown in Figure 6.23 is the forest/ windy spectrum previously shown in Figure 6.5. Both measured spectra in Figure 6.23 are normalized to Pac(v). The 24-dB dc/ac ratio in the desert spectrum (a) of Figure 6.23 results in an effective 24-dB loss of sensitivity (i.e., higher noise level) compared with the forest spectrum (b) in measuring ac spectral shape. Otherwise, the ac spectral shape of the desert/ windy spectrum in Figure 6.23 almost exactly overlays that of the forest/windy spectrum over their common interval of available spectral dynamic range. It was previously shown that the exponential shape factor β = 5.2 provides an excellent match to the forest/windy spectrum of Figure 6.23. On the basis of these data, the windblown clutter ac spectral shape that applies for densely forest-vegetated clutter cells under windy conditions also applies for more open desert-vegetated cells. That is, these data suggest that the ac spectral shape function caused by windblown vegetation in a cell may be, at least to a first-order approximation, somewhat independent of the type of vegetation in the cell. However, this equivalence does not extend to include dc/ac ratio; the dc to ac ratio of clutter spectral power is much higher in partially open desert than in forest terrain.

Knolls, Utah. Figure 6.24 shows X-band desert clutter spectra measured by the Phase One radar at two western U. S. desert measurement sites—Booker Mt., Nevada, and Knolls, Utah—in summer season. At both sites these spectra were obtained as eight-gate averages, 15 FFTs per gate (2,048-point FFTs, PRF = 500 Hz, hor. pol., gate width = pulse length = 150 m). The Booker Mt. spectrum of Figure 6.24(a) was measured from barren level mud flats under calm wind conditions and light rain at 12- to 13.2-km range and 2.3° grazing angle. This Booker Mt. spectrum shows essentially no spectral spreading beyond the window-function resolution over a 60-dB spectral dynamic range (except for the small residual spur indicated at the base of the dc-spike 56 dB down), and again evidences the field capability of the Phase One radar for making X-band clutter spectral measurements at low Doppler frequencies [compare with Figure 6.4(c)].

Windblown Clutter Spectral Measurements 611

20

L-Band Windy

Pac (dB)

0

–20

Noise Levels

(a) –40

(a) Desert (b) Forest

–60

(b) β= 8

0.3

6 5

1.00

10.00

Doppler Velocity v (m/s)

Figure 6.23 Comparison of ac spectral shapes of LCE (a) desert (scrub/brush) and (b) forest clutter spectra under windy conditions.

In contrast to no spectral spreading at Booker Mt. in Figure 6.24(a), Figures 6.24(b) and (c) show an X-band desert spectrum from Knolls with significant spectral spreading. The Knolls spectrum was measured from very level terrain containing sparse, low, desert scrub vegetation under 11- to 16-mph wind conditions at 2.5- to 3.7-km range and 0.5° grazing angle. This X-band desert spectrum, although containing a significant dc component, contains less dc power than the LCE L-band Nevada desert spectrum of Figure 6.22. As a result, more ac spectral dynamic range is available for defining the shape of the X-band desert spectrum in Figure 6.24(c) than was available for defining the shape of the L-band desert spectrum in Figure 6.23. This X-band Knolls desert spectrum [Figures 6.24(b), (c)] is very similar to other Phase One and LCE windblown clutter spectra observed at other radar frequencies and from other types of vegetation. The basic similarities of the Knolls spectrum to other Phase One- and LCE-measured spectra are in the increasing downward curvature with increasing Doppler velocity and decreasing power level displayed in Figure 6.24(c) on 10 log P vs log v axes. This downward curvature also characterizes the exponential shape factor. Thus through a broad central region of increasing downward curvature in the data of Figure 6.24(c), the exponential shape factor β = 11.2 overlays the data and captures its general shape. At upper levels, the data rise somewhat above the approximating exponential in the quasi-dc region |v| < 0.21 m/s; this excess quasi-dc power is included as dc power in the dc/ac ratio of 5.2 dB ascribed in modeling this spectrum. The slight broadening beyond exponential at

612 Windblown Clutter Spectral Measurements

20 20 June 16 mph Winds 2.5–3.7 km

(a)

12–13.2 km dc/ac = 29 dB

(c)

(b) n = 2.0 n = 4.1

0 60 dB

Ptot (dB)

0

22 July Calm

n = 6.4 dc/ac = 5.2 dB Noise Level

–20

66 dB

20

S/N Limited

Quasi-dc

–20 Noise Level

–40 = 11.2

–40

Noise Level

X-Band

X-Band –55

–45

–0.5 0 0.5 Nevada Desert (Barren Mud Flats)

–1

0

1

0.04

0.10

1.00

Doppler Velocity v (m/s) Utah Desert (Sparse, Low, Desert Scrub Vegetation)

Figure 6.24 Phase One X-band desert clutter spectral measurements: (a) Booker Mt., Nevada, and (b), (c) Knolls, Utah.

very low levels in Figure 6.24(c) as the measured data approach to within 10 dB of the noise level is partially the result of S/N limitations in this region. In contrast to the exponential shape factor generally capturing the shape of this spectrum, power-law rates of decay [Figure 6.24(c)] increase from n ≅ 2 (20 dB/decade) at upper levels to n ≅ 4 (i.e., 40 dB/decade) at intermediate levels to n > 6 (> 60 dB/decade) at the lowest levels; in other words, no single power law comes close to capturing the general shape of the X-band desert spectrum shown in Figures 6.24(b) and (c).

6.4.3.2 Cropland The Phase One radar acquired clutter measurement data at the farmland site of Beulah, N. Dakota, during the first two weeks of June [44]. The open agricultural fields in the measurement sectors around Beulah were mostly in wheat; in early June, the wheat was not yet very high. Trees occurred at ~1% to 3% incidence by area, for the most part at lowlying elevations along creekbeds. The primary Beulah measurement swath examined comprised 16 contiguous 150-m gates from 4.5- to 6.75-km range. Over this swath, the terrain was well illuminated by the Phase One radar at a depression angle of ~ 0.4°. Windblown wheatland clutter spectra were generated for all 16 primary-swath gates at vertical polarization and 1-µs pulsewidth in all five Phase One frequency bands. In each band, 2048-point FFTs were generated and averaged to form the spectrum for each gate. The effective PRF and number of FFTs averaged in each band were at X-band, 500-Hz PRF, 15 FFTs; at S-band, 167-Hz PRF, 5 FFTs; at L-band, 100-Hz PRF, 3 FFTs; at UHF, 33.3-Hz PRF, 1 FFT; and at VHF, 12.5-Hz PRF, 1 FFT. Considerable gate-to-gate variation occurred in the resultant clutter spectra. Six particular gates (10–12 and 14–16) at longer ranges in the primary swath were selected as under strong illumination and essentially containing pure wheat fields within the azimuth main beamwidth in all bands. Spectra from these gates were averaged together in each band to provide a generalized indication of pure windblown wheatland clutter spectra.

Windblown Clutter Spectral Measurements 613

Figure 6.25 shows the resultant generalized clutter spectra from pure windblown wheatland in all five Phase One frequency bands. These measurements were obtained on four different days under relatively windy conditions. The results show significant spectral spreading in each of the four upper bands (X, S, L, and UHF) to either side of a strong dc component. Spectral spreading in these bands extends to power levels 60 to 70 dB below zero-Doppler peaks and to corresponding Doppler velocities generally < ~1 m/s. In contrast, the VHF wheatland spectrum shows absolutely no spectral spreading to a level 65 dB down under 12-mph winds. This complete lack of VHF spectral spreading is due to a combination of (a) a high degree of penetration of the VHF radiation through the wheat stalks to the underlying stationary ground, and (b) the amplitude of the 12-mph windblown motion of the wheat stems being << 1λ at VHF (<< 1.7 m). Note that the UHF wheatland spectrum, which shows the greatest degree of spreading of any of the four upper-band spectra to a maximum Doppler velocity of ~1.25 m/s, was measured under much windier conditions (27 mph). The ac spectral spreading in the four upper-band wheatland clutter spectra of Figure 6.25 is highly exponential in shape, as indicated by the relatively linear decay displayed on the 10 log P vs v axes used in Figure 6.25. The three ac spectral shapes at S-, L-, and UHFbands are remarkably exponential, and in fact are reasonably well-fitted by the exponential shape factor β = 9, which is not out of line with the values of exponential shape parameter appropriate for windblown forest at similar wind speeds (see Table 6.1). Each spectrum also shows a strong dc component. However, the X-band spectrum in Figure 6.25 shows a much decreased dc component, such that much of the pure dc power in the lower bands has spread into a quasi-dc region |v| ≤ ~ 0.25 m/s at X-band. The dc to ac ratios in these spectra for X-, S-, L-band, and UHF are: 4, 17, 21, and 17 dB respectively.

Beiseker, Alberta. Another agricultural site visited by the Phase One radar in summer season was Beiseker, Alberta (see Section 3.4.1.4.2). The Phase One summer visit to Beiseker was in August when the crops (mostly wheat and other grains) were mature and thus higher than for the June visit to Beulah. Figure 6.26 shows an S-band summer Beiseker cropland clutter spectrum measured as a 16- gate average of 150-m range gates at vertical polarization (5 FFTs per gate, 2048-point FFTs, PRF = 500 Hz). The PRF of 500 Hz used to make this spectrum was higher than the 167 Hz generally used at S-band, resulting in somewhat reduced spectral resolution. This Beiseker spectrum is from measurements at 10- to 12.4-km range under 7- to 12-mph winds. The measurement geometry resulted in illumination at a depression angle of ~0.4°. The 2.4-km Beiseker measurement sector was almost entirely in mature wheat, although it was somewhat broken in places and dissected with a stream bed, resulting in small secondary incidences of herbaceous rangeland and minor scrub/brush. The 16-gate, mature-wheat, Beiseker S-band spectrum of Figure 6.26 is well represented as exponential, although containing less dc power than the 6-gate, young-wheat, Beulah S-band spectrum included in Figure 6.25. The exponential shape factor that best represents the Beiseker spectral shape is β = 13, greater than the β = 9 Beulah value as a result of the lighter winds at Beiseker. Power-law rates of decay shown in Figure 6.26(b) increase from n ≅ 3 (30 dB per decade) at intermediate levels to n ≅ 5 (50 dB per decade) at lower levels. The dc/ac ratio in which excess quasi-dc power is included as dc power to enable the β = 13 shape factor to fit the spectral tail in Figure 6.26 is 12.2 dB.

614 Windblown Clutter Spectral Measurements

20

12 June 12 mph winds

7 June 19 mph winds

8 June 14 mph winds

72 dB

61 dB

67 dB

Ptot (dB)

0

–20

–40 X-Band

S-Band

L-Band

–60 –1

0

1

–1

v (m/s) 20

0

1

–1

0

v (m/s)

8 June 27 mph winds

1

v (m/s)

10 June 12 mph winds 65 dB

63 dB

Ptot (dB)

0

–20

–40

UHF

–60 –1

0

VHF 1

–1

0

1

Doppler Velocity v (m/s) N. Dakota Cropland (Wheat)

Figure 6.25 Phase One five-frequency clutter spectra from North Dakota wheatland measured on four different days in early June under strong breezy or windy conditions.

The Beiseker 16-gate spectrum of Figure 6.26 is essentially identical in all respects to a corresponding Beulah wheatland 16-gate spectrum35 (not shown). That is, although detailed gate-to-gate differences exist in these data caused by variations in topography, crops, and wind speeds, when averaged over broad 2.4-km swaths these results indicate that exponential spectral spreading generally occurs in open cropland terrain without much sitespecific variation.

de Loor’s Results. Much earlier measurements of clutter spectra from windblown crops (including wheat) made with a noncoherent X-band system were reported by de Loor, Jurriens, and Gravesteijn [45]. The one example shown by de Loor et al. is an ac spectrum for full-grown wheat under 5- to 7-mph winds of ~ 40-dB spectral dynamic range. This 35. Formed from all 16 primary-swath gates at Beulah, not just the six pure-wheat gates for which results are shown in Figure 6.25.

Windblown Clutter Spectral Measurements 615

20 13 August

(a)

(b)

12 mph winds 10 –12.4 km 0

dc/ac = 12.2 dB

n=3

61 dB

Ptot (dB)

n=5

–20

Noise Level

Noise Level

LimS/N ite d –40

β = 13

S-Band

–1

0

1

0.03

0.10

1.00

Doppler Velocity v (m/s) Alberta Cropland (Mature Wheat, Minor Scrub/Brush Areas)

Figure 6.26 Phase One S-band cropland clutter spectrum from Beiseker, Alberta.

spectrum appears to be highly exponential and is very similar in shape to the Phase Onemeasured Beulah pure-wheat spectra of Figure 6.25. Spectral widths at the –3- and –10-dB levels as a function of wind speed for winds up to 22 mph are also provided by de Loor et al. in composite plots covering four different crop types (wheat, alfalfa, sugar beets, potatoes). The maximal extent points in these results fall in closely with the predictions of the current windblown clutter exponential model at corresponding –10- and –25-dB levels under windy conditions (see Figure 6.1), after taking into account that de Loor’s results are noncoherent (i.e., wider spectra by a factor of ~1.4, see Section 6.6.1.1). However, de Loor et al. “could not conclusively [show] significant [spectral] differences between different crop types.” Detailed comparisons of Phase One spectral results with those of de Loor et al. reinforce Phase One indications suggesting no large differences in ac spectral shape or extent at microwave frequencies between windblown tree spectra and windblown crop spectra, or indeed, between windblown crops at different stages of maturity, from different sites, and of different crop types, under windy conditions.

6.4.3.3 Rangeland Clutter spectral results were obtained for rangeland terrain in which patches of trees (45-ft high aspen) and patches of shrubs (15-ft high willow) occurred over open areas of herbaceous (grassy) rangeland [24, 25]. Five-frequency spectra were obtained, each averaged over 76 contiguous 15-m range gates, in which a number of FFTs per gate were also averaged. A significant dc component existed in these spectra (e.g., of dc/ac ratio as much as 15 to 20 dB), largely the result of geometrically visible open ground occurring between the patches of trees and shrubs. “Shoulders” were evident in the spectral shapes at the onset of the ac spreading just at the base of the dc spikes [cf. Figures 6.22, 6.24(b),

616 Windblown Clutter Spectral Measurements

6.25]. Such shoulders in spectral shape have been associated with the natural resonant frequency of the trees (see Section 6.6.1.3). Beyond these shoulders, the rates of decay over the ac spectral tail regions in the rangeland spectra were highly exponential. See [25] for plots of these rangeland spectra, as well as other considerations involved in their modeling including their dc/ac ratios.

6.4.4 MTI Improvement Factor A significant advantage of an exponential spectral model for clutter is its analytic tractability. Here an example of this tractability is provided by deriving the MTI improvement factor of a single delay-line canceller operating in an environment of windblown clutter exponentially distributed in Doppler. Also derived is the single delay-line canceller MTI improvement factor that results under the more traditional assumption of Gaussian-distributed clutter, which is then compared with the improvement factor pertaining to exponentially distributed clutter. In deriving those improvement factors, the earlier approaches of Skolnik [1] and Narayanan et al. [42] are followed for deriving improvement factors for Gaussian spectral shapes. However, also explicitly included in the derivations here is the effect of the dc spectral component on the improvement factor. The expression for n cascaded delay-line cancellers operating in exponential clutter is also presented. Note that the power-law function [see Eq. (6.18)] is not so analytically tractable as the exponential and Gaussian functions. For example, attempting to follow the preceding approach to obtain the single delay-line canceller improvement factor for power-lawdistributed clutter leads to an infinite integral expression that cannot be simply evaluated analytically.

6.4.4.1 Preliminary Analysis The input clutter power within one pulse repetition interval T entering the single delay-line canceller is given by f p 2⁄

P ic =

∫

– f p 2⁄

P tot ( f ) df

where fp = 1/T is the PRF and Ptot(f) is the total clutter spectral power density as given by Eq. (6.1) (transformed from Doppler velocity v to Doppler frequency f). Since fp must be much greater than the clutter spectral extent of Ptot(f) for successful MTI operation, the limits of integration in the preceding integral can be further expanded to ± ∞ without practical consequence on Pic, whereupon ∞

P ic =

∫

–∞

P tot ( f ) df = 1

The equivalence of the infinite integral expression to unity in this equation is required by the definition of Ptot(f) in Eq. (6.1). The frequency response function in the power domain for a delay line of time delay T is given [1] by H(f)

2

= sin 2 ( 2πfT )

Thus the residual clutter power after cancellation is given by

Windblown Clutter Spectral Measurements 617

P oc =

∞

∫ Ptot ( f ) H ( f ) –∞

2

df

In this equation, the sine function in |H(f)|2 may be replaced by its small-angle approximation (i.e., its argument), again because fp = 1/T greatly exceeds the practical spectral extent of Ptot(f). The result of this substitution is 2 2

P oc = 4π T

∞

∫ f –∞

2

P tot ( f ) df

The total clutter spectral power density Ptot(f) is given by Eq. (6.1) as r 1 P tot ( f ) = ----------- δ ( f ) + ----------- P ac ( f ) r+1 r+1 where r is the ratio of dc to ac power in the clutter spectrum and Pac(f) is the ac spectral shape factor. Substituting this expression for Ptot(f) into the above equation for Poc and recognizing that the term involving integration over the delta function term vanishes, the general result is that the output clutter power from a single delay-line canceller is given by 2 2 4π T ∞ 2 P oc = -------------- f P ac ( f ) df r + 1 –∞

∫

(6.6)

The MTI improvement factor I of the single delay-line canceller is given [1,42] by P ic I = G -------P oc where G , the average gain of the canceller, can be shown [1] to equal 2. Therefore, I of the single delay-line canceller is given by 2 I = -------P oc where Poc is given by Eq. (6.6).

6.4.4.2 Exponential Clutter Clutter distributed exponentially in Doppler frequency f is given by Eq. (6.2) as β' P ac ( f ) = --- exp ( – β' f ) 2 where β' = (λ/2)β and β is as specified in Eq. (6.3) or Table 6.1. It follows that 4π T ∞ 2 P oc = -------------- β' f exp ( – β'f ) df r+1 0 2 2

∫

618 Windblown Clutter Spectral Measurements ∞

Using the standard result

∫x 0

2

exp ( – ax ) dx = 2a

–3

, the preceding equation reduces to

2 2

8π T 2 2 P oc = --------------------2 ⋅ ---   ( r + 1 )λ β Representing I of the single delay-line canceller in exponentially distributed clutter as I β , it follows that vp 2 β 2 I β = ( r + 1 )  -----  ---  π   2

(6.7)

where v p = ( λ ⁄ 2 )f p . Skolnik has extended Eq. (6.7) to apply to n delay line cancellers in cascade (see [1], p. 158), as: v p β 2n I β ( n ) = ( r + 1 )  --------  π 

1 × 3 × 5 × ... ( 2n – 1 ) ---------------------------------------------------n 2 n! ( 2n )!

(6.8)

6.4.4.3 Gaussian Clutter Clutter distributed Gaussianly in Doppler frequency f is given by Eq. (6.17) as P ac ( f ) =

2 g' --- exp ( – g'f ) π

2

where g' = ( λ ⁄2 ) g . It follows that 8π T g' ∞ 2 2 P oc = --------------- --- f exp ( – g'f ) df r+1 π 0 2 2

∫

∞ 2 2 2 π x exp ( – a x ) dx = ------------ , the preceding equation reduces Using the standard result 3 0 ( 4a ) to:

∫

2 2

8π T 1 P oc = --------------------2 ⋅ --( r + 1 )λ g If I of the single delay-line canceller in Gaussianly distributed clutter is represented as I g , it follows that vp 2 I g = ( r + 1 )  ---- g  π

(6.9)

Except for the inclusion of the term (r+1), which explicitly shows the effect on Ig of nonzero dc/ac spectral power ratio r, this expression for Ig is otherwise identical to that provided elsewhere [1,42]. Both Eqs. (6.7) and (6.9) reduce to

Windblown Clutter Spectral Measurements 619

vp 2 1 I = ( r + 1 )  -----  ---------  π   2 2σ

(6.10)

where σ is the standard deviation in the respective spectrum [i.e., in Gaussian-distributed clutter, σ = σ g = 1 (⁄ 2g ) ; in exponentially distributed clutter, σ = σ β = ( 2 ⁄ β ) ].

6.4.4.4 Numerical Examples It is evident from Eqs. (6.7), (6.9), and (6.10) that I obtained in Gaussian clutter exceeds that obtained in exponential clutter by a decibel amount given by 10 log10(Ig/Iβ) = 10 log10(4g/β2) = 10 log10(σ β /σ g)2

(6.11)

assuming that the radar parameters λ and fp and the clutter dc/ac ratio r are the same in both cases. As a numerical example, consider Barlow’s [7] much-referenced Gaussian clutter spectrum under windy (20-mph) conditions for which g = 20 (see Section 6.6.1.1). The value of β from the exponential clutter model of Section 6.2 for similar windy (15- to 30-mph) conditions is specified in Table 6.1 as β = 5.7. Applying Eq. (6.11) using these clutter parameters shows that the single delay-line canceller improvement factor obtained in g = 20 Gaussian clutter is 3.9 dB greater than that obtained in β = 5.7 exponential clutter, independent of radar frequency and processing-specific parameters such as pulse repetition frequency. That is, the fact that exponential clutter spreads the clutter in Doppler beyond that of the more usually assumed Gaussian clutter results in a 3.9 dB loss in improvement factor. As a further numerical example, the values of Iβ obtained by an X-band radar (i.e., λ = 3 cm) of fp = 1000 Hz operating in exponential clutter are shown in Table 6.5 as computed from Eq. (6.7). The exponential clutter for which Table 6.5 applies is that of the model of Eqs. (6.1), (6.2), (6.4) and Table 6.1 under various wind conditions. Table 6.5 Improvement Factor Iβ in Exponential Clutter for an X-Band Radar (λ = 3 cm) with PRF = 1000 Hz

Wind Speed (mph)

Exponential ac Spectral Shape Factor βa

5 10 20 40

12 8 5.7 4.3

a. From Table 6.1 b. From Equation (6.4) c. From Equation (6.7)

Ratio of dc/ac Spectral Power r (dB) b 40 –0.7 –5.4 –10.0

Single Delay-Line Canceller Improvement Factor Iβ (dB)c 34.6 28.3 23.8 20.6

620 Windblown Clutter Spectral Measurements

6.5 Impact on MTI and STAP 6.5.1 Introduction The shape of the windblown radar ground clutter Doppler spectrum is important in determining the performance of target detection in ground clutter. In modern radar that operates with wide dynamic range and low noise floor, the decay of the spectral tails of ground clutter has significant impact on the detection of small moving targets. In such systems, detection performance can be clutter limited, even to relatively high Doppler frequencies. Therefore, the rate at which the clutter spectral tails decay (i.e., the spectral shape) with increasing Doppler frequency is an essential issue for the realistic prediction of detection performance. The preceding section (Section 6.4.4) shows that the use of a realistic exponential ground clutter spectral shape causes significant loss in single-delay-line improvement factor I, e.g., 3.9 dB, compared to use of the more conventional Gaussian ground clutter spectral shape. Section 6.5 expands this previous discussion to consider the impact of ground clutter spectral shape on the prediction of detection performance of ground-based and airborne surveillance radar using modern coherent signal processing. It is shown that, with such processing, detection losses much greater than 3.9 dB can occur using incorrect clutter spectral shapes for performance prediction. The results presented summarize the work in this area of Professor Alfonso Farina of Alenia Marconi Systems, Rome, Italy, and his Italian colleagues, Professor Fulvio Gini and Dr. Maria V. Sabrina Greco at the University of Pisa and Professor Pierfrancesco Lombardo at the University of Rome, who took up the Lincoln Laboratory findings concerning ground clutter spectral shape and investigated the impact of these findings on radar signal processing techniques for target detection in clutter. What follows summarizes36 these investigations; for more extensive discussion and results describing this work, refer to the original technical journal articles [30–33]. Following subsections first review the derivation of how ground clutter spectral shape affects the performance of optimum coherent detectors, both for ground-based and airborne early-warning (AEW) surveillance radars, when such radars operate in a ground clutter environment of Rayleigh clutter amplitudes (i.e., I and Q components of Gaussian pdf). It has previously been shown in this book that temporal clutter amplitude statistics from windblown vegetation (particularly, windblown trees) indeed tend to be Rayleigh distributed—see Figure 5.A.16. The expressions for detection performance in Gaussian clutter, as discussed in what follows, can also apply to adaptive coherent detection in nonhomogeneous and nonstationary clutter environments, providing the I and Q clutter pdf’s remain Gaussian [46]. Numerical results are provided both at X-band and L-band in which the predicted performance of the MTI improvement factor I is compared between using an exponential shape for the ground clutter spectrum, as illustrated and modeled heretofore in Chapter 6, and using Gaussian and power-law shapes for the ground clutter spectrum, such as have been previously employed in the technical literature and which are defined and discussed subsequently in Section 6.6.1. This allows evaluation of the sensitivity of detection system performance prediction to the use of incorrect ground clutter spectral models. It is shown 36. The summary provided here includes material originally published in [30, 31, and 33] by permission of IEEE, and in [32] by permission of IEE.

Windblown Clutter Spectral Measurements 621

that the Gaussian shape can significantly overestimate system performance, whereas the power-law shape can significantly underestimate system performance, compared to the more correct exponential clutter spectral shape.

6.5.2 Impact on Performance of Optimum MTI To evaluate the impact of the measured clutter Doppler spectrum on the detection performance, we proceed as follows. Consider a ground-based surveillance radar in which the radar receiver demodulates, filters the incoming narrowband waveform, and uniformly samples each pulse return, thus obtaining N complex samples {z[i]} iN=– 10 spaced by T seconds, where T = 1/PRF is the PRI. The N samples are assembled into the N-dimensional vector z = zI + jzQ = [z[0] ... z[N – 1]]T, where zI and zQ represent the vectors of the I and Q components, and the superscript “T” stands for “transpose of.” Assuming an exact knowledge of the clutter covariance matrix, the optimum MTI processor is a coherent linear transversal filter with complex coefficient vector w = [w1, w2, ..., wN]T. To test a range cell for detection, the quantity wHz is evaluated (where the superscript “H” stands for “conjugate transpose of”), and the envelope of the result is compared to a detection threshold, thus ascertaining whether a target is present or not. The target signal is modeled by the N-dimensional complex-valued vector s = α p, where α is a complex parameter accounting for target amplitude and initial phase and pi = e j 2π i fT, 0 ≤ i ≤ N− 1; f being the target Doppler frequency. The interference (i.e., clutter plus noise) is given by the vector d, where PC is clutter power; and PN is white noise power. The parameters that characterize the clutter interference are: the clutter to noise power ratio (CNR), the shape of the clutter spectrum, and the width of the clutter spectrum for given shape. In the results to follow, the shape of the clutter spectrum is specified to be either Gaussian, exponential, or power law; and the width of the clutter spectrum is characterized by either the one-lag autocorrelation coefficient ρ (X-band results), or by the –3-dB spectral width (L-band results). In all results, the mean Doppler frequency of the clutter spectrum is assumed to be zero. The signal to interference power ratio SIRo at the output of the filter is given by: H

w Sw SIR o = -----------------H w Mw

(6.12)

where S = E {ssH} is the covariance matrix of the target signal and M = E {ddH} = (PC + PN) Mn is the covariance matrix of the interference d (i.e., clutter and noise). Mn is the normalized covariance matrix, i.e., [Mn]i, i = 1; i = 0, 1, ..., N–1. The performance of the filter is described by the definition of clutter improvement factor I, as SIR I = -----------oSIR i

(6.13)

where SIRi is the signal-to-interference power ratio referred to a single pulse at the input of the filter. For the optimum MTI processor (i.e., one having the weight vector w = cM-1p), the improvement factor is given by Ic = pHMn-1p

(6.14)

622 Windblown Clutter Spectral Measurements

The above discussion is applicable to the one-dimensional (1-D) ground-based case (i.e., single antenna) parameterized by f only, as opposed to the two-dimensional (2-D) airborne case (i.e., multiple effective antenna elements) parameterized by f and direction-of-arrival θ discussed in Section 6.5.3. As will be shown, Eq. (6.14) also applies to the airborne (2-D) case and to Kelly’s adaptive processor [46], for expressions of p and Mn extended to apply to these cases (see Section 6.5.3). To obtain assigned values of probability of detection PD and probability of false alarm PFA, a specified level of SIRo at the output of the detection filter must be provided. The SIRi which is required at the input of this filter (in dB) to ensure the required performance is given by SIRi|dB = SIRo|dB – Ic(f)|dB. The improvement factor of the filter is different for any Doppler frequency, while SIRo is constant. Thus a normalized visibility plot is provided by showing [–Ic(f)|dB] for given N. In what follows, two sets of plots are used to represent performance: (i) visibility curves: the inverse of Ic (i.e., SIRi required to leave SIRo = 0 dB) as a function of the Doppler frequency f for given N; (ii) improvement factor plots: Ic as a function of N, for given Doppler frequency f. The visibility curve (the inverse of Ic) is a scaled (normalized) version of the required SIRi for given N as a function of target Doppler frequency necessary to provide a specific SIRo as required, for any given detector and target model, to ensure an assigned performance level (for example PD = 0.8 with PFA = 10-6), for the differing clutter spectral shapes. That is, the visibility curve allows the determination for given N of the SIRi that is required at the input of the radar detector to ensure the desired performance as given by SIRi = SIRo/Ic, where SIRo is a constant. The improvement factor plot allows the determination of the minimum number of radar pulses N for given f that is required to provide a desired value of Ic, also for the differing clutter spectral shapes.

6.5.2.1 X-Band Results (1-D) The X-band results to follow compare optimum MTI filter performance as given by Eq. (6.14) for corresponding Gaussian and exponential windblown ground clutter spectral shapes under breezy wind conditions. The model utilized for clutter power spectral density (PSD) is that specified in Section 6.2, particularly by Eq. (6.1) which specifies Ptot(v) in terms of dc/ac ratio r and the ac shape factor Pac(v). The exponential spectral shape is modeled as specified in Section 6.2.1, particularly by Eq. (6.2) which specifies exponential spectral shape in terms of the exponential shape parameter β,β being specified as a function of wind speed (e.g., breezy, windy) in Table 6.1 and Figure 6.1. The Gaussian spectral shape is modeled as specified by Eq. (6.17) in Section 6.6.1.1, where the Gaussian shape parameter g is that required to give the same one-lag temporal autocorrelation coefficient ρ as that of the exponential spectrum under given wind conditions. This procedure is one way of normalizing the Gaussian and exponential shapes to be of equivalent extent in Doppler as a function of wind speed, the autocorrelation function being the inverse Fourier transform of the clutter power spectrum. The dc/ac ratio r in the clutter spectrum is modeled as specified in Section 6.2.2, particular by Eq. (6.4) which models r as a function of wind speed w and radar carrier frequency fo (see also Figure 6.2). In the results to follow, fo = 9.2 GHz (X-band), PRF = 1/T = 500 Hz, and CNR = 50 dB.

Windblown Clutter Spectral Measurements 623

Figure 6.27 shows two visibility curves, corresponding to exponential and Gaussian clutter spectra under breezy conditions with dc/ac ratio r = unity, and for N = 16 coherently integrated pulses. For the exponential spectrum, β = 8 s/m; for both spectra, ρ = 0.9908, and r = 0 dB. Each curve shows the SIRi necessary to obtain PD = 0.8 and PFA = 10-6 vs normalized Doppler separation fT. Both curves decay from large required values of SIRi at low values of fT, where clutter strength is high, to bottom out at a much lower floor value of SIRi ≅ –61 dB at higher values of fT, the floor level being determined by the thermal noise limit. The curve for the Gaussian PSD decays much faster than the curve for the exponential PSD. That is, the MTI filter operating under the standard assumption of Gaussian clutter spectral shape significantly outperforms the MTI filter operating under the more realistic assumption of exponential clutter spectral shape. The loss in detection performance due to the exponential PSD is given by the signal power increase required by the disturbance with exponential PSD to match the performance of the disturbance with Gaussian PSD. It is evident in Figure 6.27 that this loss in detection performance caused by the exponential PSD is significant over a wide range in fT (i.e., for 0.05 < fT < 0.3) and at its maximum becomes as large as 15 dB. Corresponding results under windy conditions (not shown here) show larger differences in performance between Gaussian and exponential PSDs, with significant detection loss due to the exponential PSD spanning 0.07 < fT < 0.4, and becoming as large as 18 dB [32]. It is apparent that the predicted performance of the MTI processor is very sensitive to the assumed shape of the clutter Doppler spectrum. Figures 6.28 and 6.29 show improvement factor plots under assumptions of exponential and Gaussian clutter spectra, respectively (i.e., corresponding to the visibility curves of Figure 6.27). As in Figure 6.27, wind conditions for the results of Figures 6.28 and 6.29 are breezy. Comparison between the two figures indicates that, for a normalized target Doppler frequency of fT = 0.2, (i.e., well within the main clutter spectral region), to obtain Ic = –50 dB in the presence of an exponential spectrum requires the coherent integration of N = 10 pulses, while integration of only 6–7 pulses is sufficient for a Gaussian spectrum. In passing from breezy to windy conditions, the achievable improvement factor significantly degrades (i.e., under the assumption of an exponential PSD and close to zero Doppler at fT = 0.1, the loss in improvement factor in passing from breezy to windy is on the order of 9 dB [32]).

6.5.2.2 L-Band Results (1-D) The L-band results that follow parallel the X-band results of the previous subsection, except that the comparison of optimum MTI filter performance [Eq. (6.14)] is now extended to include power-law—as well as Gaussian and exponential—windblown ground clutter spectral shapes. The power-law PSD is modeled as specified by Eq. (6.18) in Section 6.6.1.2; i.e., as parameterized by the power-law exponent n which typically takes on values of n = 3 or 4. Equivalent spectral extent for given wind conditions among the three spectral shapes of Gaussian, exponential, and power-law is now specified in these Lband results in terms of equal –3-dB frequency bandwidth in the three shapes, rather than specifying equal temporal correlation coefficients as in the X-band results. A further distinction is that the L-band results are provided for “windy” (as opposed to “breezy”) wind conditions, with wind speed specified at 30 mph. In the L-band results to follow, fo = 1.23 GHz, PRF = 500 Hz, and CNR = 70 dB (as opposed to 50 dB in the X-band results). These parameters are appropriate for an L-band ground-based surveillance radar.

624 Windblown Clutter Spectral Measurements

0 Exponential Gaussian –10

SIRi (dB)

–20

–30

–40

–50

–60

–70 0.0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.5

fT

Figure 6.27 Comparison of X-band visibility curves (1-D case) showing SIRi vs normalized Doppler offset fT (with SIRo = 0 dB) for Gaussian and exponential clutter spectral shapes under breezy conditions and N = 16 coherent pulses. (Results provided by P. Lombardo, Univ. of Rome. After [32]; by permission, © 1997 IEE.)

Figure 6.30 shows L-band visibility curves for Gaussian, exponential, and power-law clutter spectral shapes under windy conditions, for integration of N = 32 coherent pulses. For the exponential clutter PSD, the shape parameter for windy conditions is given by β = 5.7 (see Table 6.1). The Gaussian and power-law clutter PSDs have shape parameters providing equivalent –3 dB spectral width to that of the exponential PSD. The dc/ac ratio is as specified by Eq. (6.4) for w = 30 mph and fo = 1.23 GHz. As in the X-band results, the curve for the Gaussian-shaped clutter PSD decays much faster in Figure 6.30 than that for the more realistic exponentially-shaped clutter PSD. In the region fT < 0.1, performance prediction based on the exponential model requires SIRi up to 22 dB greater than that specified by the Gaussian model. In the region fT > 0.1, both Gaussian and exponential PSDs are below the thermal noise level, which determines the required SCRi ≅ − 84 dB in this region. The n = 3 power-law clutter PSD has a much higher spectral tail than the Gaussian or exponential PSDs (see Figures 6.44 and 6.55), resulting in much greater SCRi being required over the complete range 0 < fT < 0.5 to ensure the same detection performance. Performance prediction based on the n = 3 power-law clutter PSD is excessively pessimistic, compared to that based on the more realistic exponential clutter PSD. The n = 4 power-law prediction in Figure 6.30 is less pessimistic but still results in significant performance mismatch.

Windblown Clutter Spectral Measurements 625

70

60

50

Ic (dB)

40

30 fT = 0.0 fT = 0.1 fT = 0.2 fT = 0.3 fT = 0.4 fT = 0.5

20

10

0 5

10

15

20

25

30

Number of Coherent Pulses, N

Figure 6.28 X-band improvement factor plots (1-D case) showing Ic vs N for breezy exponential clutter, parameterized by fT. (Results provided by P. Lombardo, Univ. of Rome. After [32]; by permission, © 1997 IEE.)

Figure 6.31 shows L-band improvement factor plots for clutter of exponential spectral shape under windy conditions (i.e., corresponding to the exponential curve of Figure 6.30) but here showing variability with number of integrated pulses N; the results are parameterized by fT. It is apparent that for high target Doppler frequencies, a small number of pulses is sufficient to yield the best performance achievable, namely, Ic|MAX = CNR|dB + 10 log10(N); whereas for lower Doppler frequencies, larger numbers of pulses are necessary to converge to the same condition. Figure 6.32 compares improvement factor plots at fT = 0.5 and fT = 1/16, assuming corresponding Gaussian, exponential, and n = 3 power-law clutter PSDs. Unlike Ic for the Gaussian and exponential clutter PSDs, Ic for the power-law clutter PSD does not converge to the ideal performance, even at high Doppler frequencies.

6.5.3 Impact on STAP Performance Consider an AEW radar equipped with an array of antennas with digital beam-forming capability. The detection problem is analyzed in the two-dimensional (2-D) plane of Doppler f and direction-of-arrival (DOA) θ (i.e., space-time approach [3, 4]). Assume that K channels demodulate and filter the incoming narrowband waveform received by either K antennas or K subarrays of antennas. Each channel samples the N returning pulses, thus obtaining N complex K-dimensional vectors {zk[i]} iN=– 10 spaced by T seconds. The N T vectors are assembled into the NK-dimensional vector, z = [ z 1 , ..., z T ]T. Again, the K detection problem is to determine, after the vector z has been received, whether it consists

626 Windblown Clutter Spectral Measurements

70

60

50

Ic (dB)

40

30 fT = 0.0 fT = 0.1 fT = 0.2 fT = 0.3 fT = 0.4 fT = 0.5

20

10

0 5

10

15

20

25

30

N

Figure 6.29 X-band improvement factor plots (1-D case) for breezy Gaussian clutter, parameterized by fT. (Results provided by P. Lombardo, Univ. of Rome. After [32]; by permission, © 1997 IEE.)

only of disturbance d, or, in addition to d, a 2-D target signal vector s is also received. The (N×K) ×1 target signal vector with Doppler frequency = f, DOA = θ, and complex amplitude = α is now defined as: s(f, θ) = α p = α[pT1(f,θ), pT2(f,θ), ... pTK(f,θ)]T where pk(f,θ) = e j2π(2d/λ sinθ)k [1, e j2π fT, ..., ej2π fT(N-1)]T, where d is the antenna spacing. The normalized clutter covariance matrix Mc is a block Toeplitz matrix with blocks related to the antenna array elements. The elements of Mc are obtained from the space-time clutter correlation coefficient, which is usually expressed as: ρ(∆t, ∆s) = ρt(∆t)

⋅

∆s ρs(∆t + ------- ) 2V

(6.15)

where for simplicity the antenna spacing is set such that d = λ/2 = 2VT where V is the platform velocity [47, 48]. In Eq. (6.15), ρt(∆t) is the temporal correlation coefficient, which depends on the temporal displacement ∆t of two sequential clutter echoes. This is the only term that depends on clutter internal motion, i.e., on the clutter spectral behavior under analysis herein, which is assumed to be of either Gaussian, exponential, or power-law

Windblown Clutter Spectral Measurements 627

0

Exponential Gaussian Power Law n = 4 Power Law n = 3

–10

–20

SIRi (dB)

–30

–40

–50

–60

–70

–80

–90 0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

fT

Figure 6.30 Comparison of L-band visibility curves (1-D case) showing SIRi vs normalized Doppler offset fT (with SIRo = 0 dB) for Gaussian, exponential, and power-law (n = 3,4) clutter spectral shapes under windy conditions and N = 32 coherent pulses. (Results provided by P. Lombardo, Univ. of Rome. After [33]; by permission, © 2001 IEEE.)

shape. The term ρs(∆t + ∆s/(2V)) is the spatial correlation coefficient, which encodes the decorrelation due to the combined effect of: (i) the motion of the radar platform (and thus of the different viewing angles over the scene) and (ii) the antenna pattern. Since this term depends on the spatial position of the receivers, it is a function of both the temporal displacement ∆t (which follows from the differing sequential positions of the platform in flight) and the spatial displacement ∆s of the antennas in the array. The optimum detector for the signal s embedded in correlated Gaussian-distributed interference is given by the same matched filter as for the 1-D case that now operates in the 2-D Doppler-DOA plane with corresponding 2-D definition of target vector and interference covariance matrix [33]. As is well known, the presence of multiple receivers, corresponding to displaced phase centers, makes it possible through space-time adaptive processing (STAP) to compensate for spectral spreading due to the platform motion, thus providing a significant improvement in detection performance [3, 4, 47]. As for the 1-D case, the optimum detector for the radar target s embedded in Gaussian distributed clutter with zero mean value and covariance matrix M is given by the filter weight vector M-1np, utilizing the 2-D definition of target vector and clutter covariance matrix. The performance parameter of interest is still Ic as specified by Eq. (6.14), which in the 2-D case is dependent on DOA θ as well as f. This same expression for Ic also characterizes the performance of a well-known adaptive detector [46] applicable to both

628 Windblown Clutter Spectral Measurements

90 Ic

MAX

80 70

Ic (dB)

60

50 40 30 fT = 0.0 fT = 1/64 fT = 1/32 fT = 1/16 fT = 1/8 fT = 1/4 fT = 1/2

20 10 0 100

101

102

Number of Coherent Pulses, N

Figure 6.31 L-band improvement factor plots (1-D case) showing Ic vs N for windy exponential clutter, parameterized by fT. Dotted curve indicates best performance theoretically achievable, given by Ic|MAX = CNR|dB + 10 log10 N. (Results provided by P. Lombardo, Univ. of Rome. After [33]; by permission, © 2001 IEEE.)

ground-based and airborne surveillance radar designed to work in nonhomogeneous and nonstationary clutter environments [33]. For simplicity, results to follow are presented for detection of a target at antenna broadside aspect (DOA = θ = 0). Compared to the 1-D case of ground-based radar, the 2-D case of airborne radar has an extra parameter that influences detection performance, namely, the number of receivers K. In consequence, the two kinds of results, i.e., visibility curves and improvement factor plots described in Section 6.5.2, now each replicate for all possible values of K. However, it is usual in space-time processing to consider detection performance as a function of the number of degrees of freedom (DOF) given by the product N × K [3, 33, 47–49]. This product corresponds to the number of parameters that can be arbitrarily selected in the detection filter, this number having direct implication on the complexity of the required signal processor. Therefore, the results to follow compare the effect of different clutter spectral shapes on radar performance, assuming N × K = 64. As in the 1-D case, two sets of plots are also used to represent system performance in the 2-D case: (i) visibility curves: inverse of Ic as a function of the Doppler frequency f for given N (with constant N × K = 64 and θ = 0);

Windblown Clutter Spectral Measurements 629

90 80 70

Ic (dB)

60

50

40 30 fT = 1/16, Expo fT = 1/16, Gauss fT = 1/16, PL3 fT = 1/2, Expo fT = 1/2, Gauss fT = 1/2, PL3

20

10 0 100

100.5

101

101.5

N

Figure 6.32 Comparison of L-band improvement factor plots (1-D case) for Gaussian, exponential, and power-law (n = 3) clutter spectral shapes under windy conditions, at fT = 1/16 and 1/2. (Results provided by P. Lombardo, Univ. of Rome. After [33]; by permission, © 2001 IEEE.)

(ii) improvement factor plots: Ic as a function of N (with constant N × K = 64 and θ = 0), for given Doppler frequency f. In the generation of these plots for the airborne (2-D) case, it is necessary to quantify the spatial correlation coefficient ρs. This term is independent of clutter spectral behavior and depends mainly on the along-track antenna pattern. The results to follow assume a transmitter antenna pattern with a Gaussian main lobe and two Gaussian sidelobes, 25 and 40 dB, respectively, below the peak, and at normalized angles of 0.2 and 0.4, respectively, on both sides of the peak. These five antenna lobes are characterized by the same width, which corresponds to a one-lag spatial correlation coefficient of 0.995 [47].

6.5.3.1 X-Band Results (2-D) The X-band results to follow compare STAP system performance (i.e., 2-D case) for corresponding Gaussian and exponential windblown ground clutter spectral shapes under breezy conditions. The same methodology for modeling the clutter spectra and the same values of radar parameters are utilized as specified at the beginning of Section 6.5.2.1 in the 1-D X-band case. Figures 6.33 and 6.34 show visibility plots for exponential and Gaussian clutter PSDs, respectively, under breezy conditions with dc/ac ratio r = unity. Various curves are shown in these two figures for different combinations of N and K, thus exchanging temporal DOF for spatial DOF. The optimum number of pulses is on the order of N = ~16, which provides the lowest SIRi value needed to achieve assigned values of PD

630 Windblown Clutter Spectral Measurements

for fixed values of PFA. The undulations of the curve for N = 64 are caused by the two antenna sidelobes in this degenerate case of K = 1. Such undulations appear when the number of spatial DOF is so low as to allow little cancellation to be possible. Comparison 0

–10

SIRi (dB)

–20

–30

–40

N=1 N=2

–50

N=4 N=8 N = 16 N = 32 N = 64

–60

–70

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

fT

Figure 6.33 X-band visibility curves (2-D case) showing SIRi vs fT (with SIRo = 0 dB) for breezy exponential clutter, parameterized by number of coherent pulses N (where N × K = 64, θ = 0). (Results provided by P. Lombardo, Univ. of Rome. After [32]; by permission, © 1997 IEE.)

between the results of Figures 6.33 and 6.34 reveals that the detection loss incurred by the airborne MTI processor in this 2-D example under the realistic assumption of an exponential clutter PSD as opposed to the more common assumption of a Gaussian clutter PSD can be as much as 10 dB. Figures 6.35 and 6.36 show improvement factor plots assuming exponential and Gaussian clutter PSDs, respectively, corresponding to the visibility curves of Figures 6.33 and 6.34. These figures indicate that for target Doppler frequencies well within the main clutter spectral region, i.e., for fT = 0.1 or 0.2, the MTI performance assuming Gaussian clutter significantly exceeds that assuming exponential clutter by amounts on the order of 8 to 10 dB for various numbers N of pulses integrated. In addition, the improvement factor Ic is much less sensitive to the number of temporal DOF N with the exponential spectrum than with the Gaussian spectrum, indicating that selection of the optimum ratio of temporal to spatial DOF depends on the assumed shape of the clutter spectrum. As in the 1-D case, in passing from breezy to windy conditions, the achievable improvement factor significantly degrades (i.e., under the assumption of an exponential PSD, and close to zero-Doppler at fT = 0.1, the loss in 2-D improvement factor in passing from breezy to windy is ≈10 dB [32]).

Windblown Clutter Spectral Measurements 631

0

–10

SIRi (dB)

–20

–30

–40 N=1 N=2

–50

N=4 N=8 N = 16

–60

N = 32 N = 64

–70 0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

fT

Figure 6.34 X-band visibility curves (2-D case) for breezy Gaussian clutter, parameterized by N (where N × K = 64, θ = 0). (Results provided by P. Lombardo, Univ. of Rome. After [32]; by permission, © 1997 IEE.)

6.5.3.2 L-Band Results (2-D) The 2-D L-band results to follow compare STAP system performance for different assumed shapes of clutter spectra using the same methodology for modeling the clutter spectra and using the same values of radar parameters as specified at the beginning of Section 6.5.2.2 for the 1-D L-band case. Figures 6.37, 6.38, and 6.39 show 2-D L-band visibility plots for exponential, Gaussian, and n = 3 power-law clutter PSDs, respectively, under windy conditions and for various numbers N of coherently integrated pulses as processed by the optimum space-time processor. In all three figures, the undulations in the curve for N = 64 are caused by effects of the two antenna sidelobes in this single-antennaelement case, as mentioned in the previous subsection. For the Gaussian and exponential clutter PSDs, the optimum number of pulses to provide the lowest SIRi needed to achieve assigned values of PD for fixed values of PFA is N = 8. In contrast, for the n = 3 power-law clutter PSD, the optimum number of pulses is N = 32. Figure 6.40 compares the Gaussian, exponential, and n = 3 power-law visibility plots for N = 8 and N = 32 together in one figure. At N = 32, the results for Gaussian and exponential clutter still show residuals of the space-time cancelled sidelobes. It is apparent in these results that a significant loss in performance (i.e., as much as 10 dB) occurs over a wide range in target Doppler frequencies (i.e., 0 < fT < 0.3) when using the realistic exponential spectrum compared to the more commonly used Gaussian spectrum. However, the additional loss in performance that occurs in utilizing an n = 3 power-law clutter spectrum is generally very much greater (i.e., as much as 30 dB) and extends over all available Doppler frequencies (i.e., 0 < fT < 0.5). That is, the predictions based on the power-law model require a very much higher SIRi at the system input to obtain the same

632 Windblown Clutter Spectral Measurements

70

60

50

Ic (dB)

40

30 fT = 0.0 fT = 0.1

20

fT = 0.2 fT = 0.3 fT = 0.4 fT = 0.5

10

0 1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

log2 N

Figure 6.35 X-band improvement factor plots (2-D case) showing Ic vs log2N for breezy exponential clutter, parameterized by fT (with N × K = 64, θ = 0). (Results provided by P. Lombardo, Univ. of Rome. After [32]; by permission, © 1997 IEE.)

detection performance as with the Gaussian or exponential models, and the impact of the space-time cancellation is very much lower for the power-law model due to the very slow decay of the power-law spectral tails. This slow decay also masks the effects of the antenna sidelobes at K = 2 using the power-law model, such effects being clearly evident in the corresponding results using the other two models. Figure 6.41 shows 2-D L-band improvement factor plots for windy exponential clutter PSD corresponding to the visibility plots for exponential clutter shown in Figures 6.37 and 6.40. Since clutter PSD modeled to be of exponential shape most closely matches the measured spectral clutter data as discussed elsewhere throughout Chapter 6 (e.g., see Figures 6.5, 6.21, 6.54), the modeled results for Ic under windy conditions shown in Figure 6.41 are the best estimate of actual L-band clutter cancellation performance to be expected. The data indicate that the optimum number of integrated pulses N to maximize Ic for the various parameterized values of target Doppler frequency fT shown is usually such that N ≅Κ, in agreement with approximate theoretical expectations discussed elsewhere [48, 49] in this regard. Figure 6.42 compares 2-D L-band improvement factor plots for windy Gaussian, exponential, and n = 3 power-law clutter PSDs at two values of fT, viz., fT = 1/32 and 1/2. At fT = 1/32 (i.e., well within the main region of clutter Doppler extent and, in fact, quite close to zero-Doppler), the prediction based on Gaussian clutter significantly overestimates Ic (by 13 dB for N = 8 pulses) and the prediction based on n = 3 power-law clutter significantly underestimates Ic (by 10 dB at N = 8 pulses) compared to the more realistic prediction based on exponential clutter PSD. At fT = 1/2 (i.e., at the highest target Doppler

Windblown Clutter Spectral Measurements 633

70

60

50

Ic (dB)

40

30

fT = 0.0 fT = 0.1

20

fT = 0.2 fT = 0.3 fT = 0.4 fT = 0.5

10

0 1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

log2 N

Figure 6.36 X-band improvement factor plots (2-D case) for breezy Gaussian clutter, parameterized by fT (with N × K = 64, θ = 0). (Results provided by P. Lombardo, Univ. of Rome. After [32]; by permission, © 1997 IEE.) 0 N=1 N=2 N=4 N=8 N = 16 N = 32 N = 64

–10

–20

SIRi (dB)

–30

–40

–50

–60

–70

–80

–90

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

fT

Figure 6.37 L-band visibility curves (2-D case) showing SIRi vs fT (with SIRo = 0 dB) for windy exponential clutter, parameterized by number of coherent pulses N (where N × K = 64, θ = 0). (Results provided by P. Lombardo, Univ. of Rome. After [33]; by permission, © 2001 IEEE.)

634 Windblown Clutter Spectral Measurements

0 N=1 N=2 N=4 N=8 N = 16 N = 32 N = 64

–10 –20

SIRi (dB)

–30 –40 –50 –60 –70 –80 –90 0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

fT

Figure 6.38 L-band visibility curves (2-D case) for windy Gaussian clutter, parameterized by N (where N × K = 64, θ = 0). (Results provided by P. Lombardo, Univ. of Rome. After [33]; by permission, © 2001 IEEE.) 0 N=1 N=2 N=4 N=8 N = 16 N = 32 N = 64

–10

–20

SIRi (dB)

–30

–40

–50

–60

–70

–80

–90 0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

fT

Figure 6.39 L-band visibility curves (2-D case) for windy power-law (n = 3) clutter, parameterized by N (where N × K = 64, θ = 0). (Results provided by P. Lombardo, Univ. of Rome. After [33]; by permission, © 2001 IEEE.)

Windblown Clutter Spectral Measurements 635

0

N = 8, Gauss N = 8, Exp N = 8, PL3 N = 32, Gauss N = 32, Exp N = 32, PL3

–10 –20

SIRi (dB)

–30 –40 –50 –60 –70 –80 –90 0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

fT

Figure 6.40 Comparison of L-band visibility curves (2-D case) for Gaussian, exponential, and power law (n = 3) clutter spectral shapes under windy conditions, for N = 8 and 32 coherent pulses (where N × K = 64, θ = 0). (Results provided by P. Lombardo, Univ. of Rome. After [33]; by permission, © 2001 IEEE.)

frequency), the predictions for Ic based on the Gaussian and exponential models are essentially identical since the clutter for both these models is well below thermal noise at such high Doppler, with the result that the performance for these two models at fT = 1/2 is dependent only on thermal noise. In contrast, the estimated clutter cancellation performance using the n = 3 power-law clutter PSD model at fT = 1/2 is much poorer (i.e., is far too pessimistic, by 25 dB for N = 8 pulses) since the power-law clutter spectral tail is still well above thermal noise even at such high Doppler.

6.5.4 Validation of Exponential Clutter Spectral Model Elsewhere, Chapter 6 (e.g., Figures 6.5, 6.21, 6.54) shows that measured shapes of windblown ground clutter Doppler spectra appear to be much more closely matched by an exponential approximation than by Gaussian (too narrow) or power-law (too wide) approximations. The preceding subsections in Section 6.5 show that large differences exist in predictions of MTI clutter improvement factor Ic between that based on what appears to be a realistic exponential clutter spectral shape and those based on more traditional Gaussian and power-law clutter spectral shapes. Compared to the exponential shape, the Gaussian shape substantially underpredicts the effects of clutter, and the power-law shape substantially overpredicts the effects of clutter. This section validates the exponential spectral model for windblown foliage by showing that the differences in improvement factor performance prediction between using actual measured I/Q data as input to the clutter canceller, and modeled clutter data of Gaussian, exponential, or power-law spectral shape, are minimized when the spectral model employed is of exponential shape.

636 Windblown Clutter Spectral Measurements

90

80

70

Ic (dB)

60

50

40

30 fT = 0 fT = 1/32 fT = 1/16 fT = 1/8 fT = 1/4 fT = 1/2

20

10

0

0

1

2

3

4

5

6

log2N

Figure 6.41 L-band improvement factor plots (2-D case) showing Ic vs log2N for windy exponential clutter, parameterized by fT (where N × K = 64, θ = 0). (Results provided by P. Lombardo, Univ. of Rome. After [33]; by permission, © 2001 IEEE.)

To compare performance predictions obtained by using each of the three clutter spectral models (i.e., Gaussian, exponential, and power-law) to the performance actually obtained using measured I/Q clutter data, the following procedure is established. First, within the database of long-time-dwell clutter measurements from windblown trees, a typical experiment is selected, within which a typical clutter cell (i.e., range gate) is further selected such that the temporally-varying I/Q data from the cell are Gaussian-distributed (i.e., the clutter amplitude is Rayleigh-distributed—see Figure 5.A.16—indicative of purely windblown foliage within the cell, without significant contributions from stationary discrete sources embedded within the trees which would lead to Ricean-distributed clutter amplitudes—see Figure 4.22). The clutter Doppler spectrum from the selected cell is generated from the measured I/Q data for that cell. This measured clutter spectrum is then best-fitted [i.e., utilizing a minimum least squares (MLS) procedure] by each of the three clutter spectral models in turn, resulting in three sets of fit parameters defining theoretical clutter models of Gaussian, exponential, and power-law spectral shape. The parameters for each theoretical clutter model are used to define a corresponding clutter covariance matrix for each model. Each theoretical clutter model is then used to specify an optimum MTI matched filter such that the covariance matrix of the theoretical clutter at the filter input and the filter design covariance matrix are identical. Next, the actual measured I/Q ground clutter data from the cell under consideration is input to each of these three filters in turn, and the measured improvement factor Im is determined for each filter as the ratio between input and output clutter power. Note that, in each of the three cases, Im is based on a mismatch between the actual measured I/Q input data (which do not provide perfect Gaussian, exponential, or

Windblown Clutter Spectral Measurements 637

90

80

70

Ic (dB)

60

50

40

30 fT = 1/2, Gauss fT = 1/2, Exp fT = 1/2, PL3 fT = 1/32, Gauss fT = 1/32, Exp fT = 1/32, PL3

20

10

0 0

1

2

3

4

5

6

log2N

Figure 6.42 Comparison of L-band improvement factor plots (2-D case) for Gaussian, exponential, and power-law (n = 3) clutter spectral shapes under windy conditions, for fT = 1/32 and 1/2 (where N × K = 64, θ = 0). (Results provided by P. Lombardo, Univ. of Rome. After [33]; by permission, © 2001 IEEE.)

power-law spectral shape) and the filter (which is specified based on a theoretical clutter model of perfect Gaussian, exponential, or power-law spectral shape). It is now necessary, in each of the three cases, to compare the measured value of Im obtained as described above using the actual measured I/Q clutter data as input to the filter with the theoretical value Ic that applies, assuming the filter is perfectly matched; i.e., assuming that the input data are synthetic data such as to give the perfect Gaussian, exponential, or powerlaw spectral shapes obtained by best-fitting each to the measured spectrum. Also assumed is that the temporal variation is Gaussian. In each of the three cases, Ic is given by Eq. (6.14), which assumes that the covariance matrix of the theoretical clutter at the filter input and the filter design matrix are the same. In each case, the appropriate figure of merit is the ratio ∆I of the measured improvement factor Im in the mismatched case to the theoretical improvement factor Ic in the matched case. Thus, in each case, ∆I = Im /Ic; and, in turn, ∆I|Gaussian, ∆I|exponential, and ∆I|power-law are computed for the particular clutter cell under consideration. For the specific technical details involved in carrying out these computations, refer to the original technical journal articles [30, 31, 33]. The figure of merit ∆I indicates the error in MTI filter performance resulting from the mismatch between the actual measured I/Q data and the assumption that the data are of

638 Windblown Clutter Spectral Measurements

either Gaussian, exponential, or power-law in spectral shape. The closer ∆I is to unity (i.e., 0 dB), the better that the particular clutter spectral model (Gaussian, exponential, or powerlaw) represents the measured clutter data in terms of the impact of the clutter data on the clutter canceller. If ∆I = unity (i.e., 0 dB), it indicates that the input I/Q clutter data provide a clutter spectral shape that is perfectly Gaussian, exponential, or power-law. Figure 6.43 shows typical results for ∆I|Gaussian, ∆I|exponential, and ∆I|power-law, for one particular clutter cell containing windblown trees, utilizing N = 8 coherently integrated 20

Gauss Exp

15

PL3

∆I (dB)

10

5

0

–5

–10 0

0.1

0.2

0.3

0.4

0.5

fT Figure 6.43 Differences in improvement factor (i.e., ∆I) between using measured X-band I/Q clutter data (35th range cell) as input to processor (1-D case), and theoretical clutter data of Gaussian, exponential, and power-law (n = 3) spectral shapes (each best fitted to the measured spectrum), vs normalized Doppler frequency fT, for N = 8 coherent pulses. (Results provided by P. Lombardo, Univ. of Rome, and F. Gini and M. Greco, Univ. of Pisa. After [33]; by permission, © 2001 IEEE.)

pulses. The measurement cell utilized is the 35th range cell in an X-band experiment (of HH-polarization) that was conducted at Katahdin Hill under windy conditions (20 to 30 mph). It is clearly evident in Figure 6.43 that the exponential model exhibits the lowest ∆I; i.e., for the exponential model, the predicted improvement factor Ic and the actual improvement factor Im (as obtained using the measured I/Q clutter data to feed the clutter canceller) are very nearly equal. The errors ∆I for the Gaussian model occur, as expected, at lower values of fT; at higher values of fT, the predictions based on both Gaussian and exponential clutter models transition to limitations caused by thermal noise. Also as expected, the errors in ∆I for the power-law model (of power-law exponent n = 3) occur over the full range 0 < fT < 0.5 due to the slow decay of the power-law spectral tails.

Windblown Clutter Spectral Measurements 639

The results for ∆I shown in Figure 6.43 are generally representative of similar results for other numbers N of integrated pulses, and for data from other tested range cells and other tested experiments at L-band as well as X-band. Such results validate the exponential clutter spectral model as described in Section 6.2 as being most realistic with which to model windblown radar ground clutter spectra, and indicate that the more commonly used Gaussian and power-law models (as described hereafter in Section 6.6) are comparatively unsatisfactory. The ramifications of improvement factor prediction error ∆I to prediction error in PD and PFA are discussed in the references [30, 31, 33].

6.6 Historical Review 6.6.1 Three Analytic Spectral Shapes In comparing different analytic forms for the shape of the ac component of the windblown clutter Doppler velocity spectrum Pac(v) [see Eq. (6.1)], it is necessary to base the comparison on equivalent total ac spectral power, and it is convenient to maintain total ac spectral power at unity. Such normalization is seldom implemented in representations of clutter spectra. Figure 6.44 shows examples of the three forms for Pac(v) to be discussed subsequently, namely Gaussian, power law, and exponential, in each of which ∞

∫

–∞

P ac ( v ) dv = 1 .

As a result, the power density levels at any value v for these three spectral shapes as shown in Figure 6.44 are directly comparable on an equivalent total ac power basis. The ac spectral shape function Pac(v) may be decomposed as

P ac ( v ) = K η ⋅ k η ( v )

(6.16)

where η is a shape parameter, Kη is a normalization constant set so that ∞

∫

∞

P ac ( v ) dv = 1 ,

and kη (v) is the unnormalized shape function with kη (0) = 1. Often, historically, Kη is omitted and only kη (v) is shown in plots such as Figure 6.44 with the zero-Doppler peak at 0 dB. In such cases, at best the shape parameter η of each individual spectral representation is all that remains for adjustment to equivalent total ac spectral power, where in fact it is the shape parameter that should be used to match to experimental data, or at worst (often the case) no attempt is made to compare spectra on an equivalent total ac spectral power basis at all. In short, in comparing different analytic spectral representations, it is not rigorously proper to simply set their zero-Doppler peaks each at unity (i.e., 0 dB). In the examples shown in Figure 6.44, spectral extent of the exponential representation lies between that of the Gaussian (narrow) and that of the power law (wide). The following subsections consider the origins of these three analytic expressions that have been used in the past to represent the shape of the Doppler frequency or velocity spectrum of windblown ground clutter, and in particular the rate of decay with increasing Doppler in the tail of the spectrum. It is evident in Figure 6.44 that the historical Gaussian and power-law representations match the Lincoln Laboratory-based exponential representation reasonably

640 Windblown Clutter Spectral Measurements

20

Extrapolation

0

Pac (dB)

–20

n

–40

Po 3,

we

v

1

0.1

rL

=

aw

0.

10

7

ntial one =6

Exp

ian Gauss g = 20

c

–60

–80

=

10

Doppler Velocity v (m/s)

Figure 6.44 Three analytic spectral shapes, each normalized to unit spectral power. The g = 20 Gaussian curve corresponds to Barlow’s [7] measurement. The n = 3 power-law curve corresponds to Fishbein et al.’s [10] measurement. The β = 6 exponential curve represents much of the Phase One and LCE data.

well (i.e., at least to within an order of magnitude) over the upper levels of clutter spectral power that lie within the dynamic ranges (solid lines) of these historical measurements; but that extrapolations of the historical representations (dotted lines) to much lower levels of spectral power differ by many orders of magnitude from the Lincoln Laboratory measurements at these low levels.

6.6.1.1 Gaussian Spectral Shape Radar ground clutter power spectra were originally thought to be of approximately Gaussian shape [6–9]. The Gaussian spectral shape may be represented analytically as 2 --g- ⋅ exp ( – gv ) , –∞ < v < ∞ π

P ac ( v ) =

where g is the Gaussian shape parameter, K = = exp(–gv2 ), and ∞

∫

–∞

g π⁄

P ac ( v ) dv = 1 .

(6.17)

is the normalization constant, k(v)

Windblown Clutter Spectral Measurements 641

To convert to Pac(f) in Eq. (6.17) where f is Doppler frequency, i.e., Pac(f) df = Pac(v)dv, replace v by f and g by (λ/2)2 g. The standard deviation of the Gaussian spectrum of Eq. (6.17) is given by σ g = 1 ⁄ ( 2g ) in units of m/s. In a much-referenced [1, 27, 50] early paper, Barlow [7] presents measured L-band ground clutter power spectra approximated by the Gaussian shape to a level 20 dB below the peak zero-Doppler level and to a maximum Doppler velocity of 0.67 m/s. Figure 6.45 shows Barlow’s ground clutter spectra k(v) as plotted originally, except here vs Doppler velocity v rather than Doppler frequency f. Recall that k(v) is the unnormalized ac shape function such that k(0) = 1, so the spectra plotted in Figure 6.45 are not shown on an equivalent total ac power basis. 0 Heavily Wooded Hills Wind Speed = 20 mph g = 10.2 (env.) g = 20.0 (coh.)

Relative Power k (dB)

–5

From Envelope Measurements Coherent Processing Estimate

–10

Sparsely Wooded Hills Wind Speed = 20 mph g = 1730 (env.)

–15

g = 3400 (coh.) L-Band

k (v) = exp [–gv 2 ] Gaussian –20 0

0.25

0.50

0.75

Doppler Velocity v (m/s)

Figure 6.45 Measurements of radar ground clutter power spectra by Barlow. (After [7]; by permission, © 1949 IEEE.)

Barlow’s spectral results were obtained from radar envelope measurements as opposed to coherent processing. For a Gaussian-shaped spectrum, the width of the envelope spectrum is approximately 1.4 times the width of the coherent spectrum [51,52]. That is, in Eq. (6.17), gcoherent ≈ (1.4)2 gen v elo p e . On this basis, estimates of the shapes of the coherent spectra corresponding to Barlow’s envelope spectra are also shown in Figure 6.45. The resulting g = 20.04 coherent-spectrum k(v) curve shown in Figure 6.45 for heavily wooded hills under 20 mph winds corresponds to the Gaussian g = 20 Pac(v) curve shown in Figure 6.44. Early observations at the MIT Radiation Laboratory [8, 9] were that the shapes of power spectra from precipitation, chaff, and sea echo were “roughly Gaussian” and that the shape of the spectrum from land clutter was “roughly similar” but with differences from Gaussian

642 Windblown Clutter Spectral Measurements

shape “somewhat more pronounced.” The explanation for clutter spectra of approximately Gaussian shape is loosely based on the idea that windblown vegetation consists fundamentally of a random array of elemental moving scatterers, each with a constant translational drift velocity. If the distribution of radial velocities of such a group of scatterers were approximately Gaussian, they would generate an approximately Gaussianshaped power spectrum. However, consider if the motion of the scatterers also were to include an oscillatory component to represent branches and leaves blowing back and forth in the wind. It is well known [53] that simple harmonic angle modulation (frequency or phase) generates an infinite series of sidebands so that an array of oscillating scatterers would be expected to generate a wider spectrum than an array of scatterers each with only a constant drift velocity. Indeed, in 1967 Wong, Reed, and Kaprielian [29] provided an analysis of the scattered signal and power spectrum from an array of scatterers, each with random rotational (oscillatory) motion as well as a constant random drift velocity. Under assumptions of Gaussianly distributed drift and rotational velocities, Wong et al. [29] showed that the power spectrum of the scattered signal is the sum of six components. Li [19] subsequently provided further interpretation of these six components, as follows. If scatterer rotation is absent, the Wong et al. expression for the clutter spectrum degenerates to Barlow’s simple Gaussian expression, i.e., Eq. (6.17). However, with scatterer rotation present, five additional Gaussian components arise, all of which decay more slowly and all but one of which are offset from zero-Doppler (by ± 2 and ± 4 times the rotational velocity). As a result, these five additional Gaussian terms that come into play with scatterer rotation act to “spread” the spectrum beyond that of the simple Gaussian of Eq. (6.17). Narayanan et al. [42] returned to Wong’s formulation of offset Gaussians in modeling some later-acquired X-band windblown clutter spectral measurements. In 1965, two years before the publication of the Wong et al. paper [29], Bass, Bliokh, and Fuks [54] also provided a theoretical study of scattering from oscillating reradiators to model scattering from windblown vegetation. In the Bass et al. paper, the reradiators were modeled to be decaying oscillators randomly positioned on a planar surface. In their analysis, Bass et al. showed that the power spectrum of the scattered radiation from the oscillating reradiators consists of a doubly infinite sum of offset Gaussian functions, but when the reradiators do not oscillate, the power spectrum simplifies to a sum of simple non-offset Gaussians. It is evident that these results have some degree of similarity with those of Wong et al. [29] in that both represent the power spectrum from a group of oscillating random scatterers as sums of Gaussians, the peaks of which are offset from zero-Doppler and for which the offsets collapse in the absence of oscillation. Some years following both the Wong et al. [29] and the Bass et al. papers [54], Rosenbaum and Bowles [55] derived theoretical expressions for windblown clutter spectra based on a physical model in which the backscattering was associated with random permittivity fluctuations superimposed on a lossy background slab. Again with overtones of similarity to both the Wong et al. and the Bass et al. analyses, Rosenbaum and Bowles modeled scatterer motion two ways, first, as a Gaussian process, and second, assuming scatterer motion to be quasi-harmonic, so that the scatterers behave as decaying simple-harmonic oscillators. It has been observed that the Rosenbaum and Bowles spectral results “are . . . too complex for radar engineers to use in design practice” [19].

Windblown Clutter Spectral Measurements 643

Status (Gaussian Spectral Shape). As will be shown, essentially all measurements of ground clutter spectra from 1967 on, of increased sensitivity compared with those of Barlow and the other early investigators, without exception show spectral shapes wider in their tails than Barlow’s simple Gaussian. Also, as indicated in the preceding discussion, it had become theoretically well understood, also from 1965–67 on, that scatterer rotational and/or oscillatory motion generates spectra wider than Gaussian. Nevertheless, Barlow’s simple Gaussian representation continues to be how clutter spectra are usually represented in radar system engineering, at least as a method of first-approach in representing the effects of intrinsic clutter motion. Thus many of the standard radar system engineering and phenomenology textbooks continue to reference Barlow’s early results [1, 27, 50]. Also, Nathanson [28] characterizes ground clutter spectral width in a scatter plot of data from many different sources in which the standard deviation in the best fit of each data source to a Gaussian shape is plotted vs wind velocity. Although it is stated in Nathanson that these results are not intended as a recommendation for the use of Gaussian spectral shape in any system design in which the detailed shape of the spectrum is of consequence, nevertheless Nathanson’s results continue to be referenced as justification for the “common assumption . . . ” [4] that the internal-motion clutter spectral shape is Gaussian (see also [56] for a similar remark). This continuing representation is understandably based on reasons of simplicity, i.e., “the clutter spectrum is often modeled as Gaussian for convenience, but is usually more complex” [57], and analytic tractability, e.g., the Gaussian function is its own Fourier transform [51].

6.6.1.2 Power-Law Spectral Shape MTI system performance predicted by the assumption of a Gaussian-shaped clutter spectrum was not achieved in practice. In a much referenced later report, Fishbein, Graveline, and Rittenbach [10] introduced the power-law clutter spectral shape. The power-law spectral shape may be generally represented analytically as 1 ⁄ ) n sin ( π n P ac ( v ) = ------------------------- ⋅----------------------2πv c v n 1 + ----vc

, –∞ < v < ∞

(6.18)

Equation (6.18) has two power-law shape parameters—n, the power-law exponent, and vc, the break-point Doppler velocity where the shape function is 3 dB below its peak zeroDoppler level. The normalization constant K is equal to nsin(π/n)/(2πvc); n k ( v ) = 1 ⁄ [ 1 + ( v ⁄ v c ) ] ; and ∞

∫ –∞

P ac ( v ) dv = 1 .

To convert to Pac(f) in Eq. (6.18), i.e., Pac(f)df = Pac(v) dv, replace v by f and vc by fc = –n (2/λ)vc. For velocities v >> vc, Eq. (6.18) simplifies to P ac ( v ) = ( K ⋅ v cn )v , which plots as a straight line in a plot of 10 log Pac vs log v. In such a plot, n defines the slope of the straight-line v-n power-law spectral tail (slope = dB/decade = 10 n). Because of its two shape parameters, the power-law shape function of Eq. (6.18) has an additional degree of freedom for fitting experimental data compared with the single-parameter Gaussian and exponential shape functions of Eqs. (6.17) and (6.2), respectively. For any power of n, the power-law shape function may be made as narrow as desired by making vc small

644 Windblown Clutter Spectral Measurements

enough. Still, whatever the values of n and vc , ultimately at low enough power levels (i.e., as 10 log P → – ∞ ) the power-law shape always becomes wider than Gaussian or exponential. Fishbein et al. [10] indicate that measured clutter rejection ratios up to 40 dB are matched under the assumption of a theoretical power-law spectral shape with n = 3. They also made one actual X-band clutter spectral measurement in 12 knot winds verifying that an n = 3 spectral tail did exist down to a level 35 dB below the zero-Doppler level and out to a maximum Doppler velocity of 1.6 m/s. The graph of these results, shown in Figure 6.46, appears to very convincingly show the clutter spectrum to be an n = 3 power law, as opposed to Gaussian, and it is widely referenced [27, 28]. 0 X-Band (9.375 GHz) 12 Knot Winds –5

Relative Power k (dB)

–10 Power Law, n = 3 –15

–20 Gaussian –25 1 –30

1 + ( vv

c

)3

; vc = 0.107 m/s

exp [–gv 2]; g = 46.9 (m/s)–2 –35 0.016

0.03

0.06

0.1

0.2

0.4 0.6

1.0

1.6

Doppler Velocity v (m/s)

Figure 6.46 A measured radar ground clutter power spectrum by Fishbein, Graveline, and Rittenbach of the U. S. Army Electronics Command. After [10], 1967.

The Gaussian and power-law curves in Figure 6.46 are k(v) curves as originally presented by Fishbein et al. [10] with their zero-Doppler peaks at 0 dB. Such k(v) curves are generally not of equivalent total ac power. However, the particular Gaussian curve shown in Figure 6.46 is the one resulting when its shape parameter g is adjusted to the necessary value, viz., g = 46.9, to provide equivalent power (not unity) to that contained by the power-law curve of Figure 6.46. That is, the Gaussian curve in this figure did not arise from direct fitting to measured data. In contrast, Barlow’s Gaussian curves of Figure 6.45 did arise from direct fitting to measured data. It is more fair to compare the Fishbein et al. n = 3 power-law curve of Figure 6.46 with Barlow’s g = 10 and 20 Gaussian curves of Figure 6.45, all as Pac curves normalized to unit total ac spectral power for whatever values of shape parameter

Windblown Clutter Spectral Measurements 645

were required to fit to measured data. The g = 20 Gaussian curve and n = 3, vc = 0.107 power-law curve shown in Figure 6.44 are Barlow and Fishbein et al. curves, respectively, plotted as Pac functions, each properly normalized to equivalent unit total ac spectral power. It is evident that Barlow’s g = 20 Gaussian curve would be considerably wider than (i.e., would lie to the right of) the g = 46.9 Gaussian plotted in Figure 6.46, with the result that the data in Figure 6.46 become somewhat less convincingly power law. The Fishbein et al. [10] results were important in establishing the existence of low-level tails wider than Gaussian in ground clutter spectra. Other ground clutter spectral measurements followed in which power-law spectral shapes were observed. For example, shortly after publication of the Fishbein et al. report, Warden and Wyndham [11] briefly mentioned two S-band measurements of clutter spectra, shown in Figure 6.47. The first was a clutter spectrum for a wooded hillside in 14- to 16-knot winds. The shape of this spectrum, to –29 dB at a maximum Doppler velocity of 0.82 m/s, is wider than Gaussian but narrower than an n = 3 power law. The second was a clutter spectrum for a bare hill in 10- to 12-knot winds. This spectrum is slightly narrower than the first, although still wider than Gaussian in the tail. The authors concluded that an n = 3 power law best fitted their data overall. 0 Wooded Hillside 14–16 Knot Winds

Bare Hill 10–12 Knot Winds

Relative Power k (dB)

–5

–10

Power Law n=2 n=3

–15

Power Law n=2 n=3

–20

–25

Gaussian Gaussian

–30 0

0.2

0.4

0.6

0.8 0

0.2

0.4

0.6

Doppler Velocity v (m/s) S-Band (3 GHz) Experimental Points

Figure 6.47 Two measurements of radar ground clutter power spectra by Warden and Wyndham of the Royal Radar Establishment (U. K.). After [11], 1969.

Several years later, Currie, Dyer, and Hayes [12] provided measurements of noncoherent clutter spectra from deciduous trees under light air and breezy conditions over a spectral

646 Windblown Clutter Spectral Measurements

dynamic range of 20 dB at frequencies of 9.5, 16, 35, and 95 GHz. Over this limited spectral dynamic range, they also found their results to be well fitted with power laws of n = 3 in the lower bands and n = 4 at 95 GHz. At both 9.5 and 16.5 GHz, maximum spectral extents under breezy 6- to 15-mph winds at the –20-dB level were ~0.8 m/s, which is a close match both to the Fishbein et al. results and to the Phase One and LCE measurements and exponential model (see Figure 6.1) of Chapter 6 over similar spectral dynamic ranges and under similar breezy conditions—especially if the Currie et al. spectral widths are reduced by a factor of ~1.4 to account for the fact that their measurements were noncoherent. At 35 and 95 GHz, maximum spectral extents under breezy conditions at the –20-dB level were ~0.5 m/s, that is, ~40% narrower than at the lower X- and Ku-band frequencies. These narrower upper-band spectra appear to indicate that the frequency invariance, VHF to X-band, of Doppler-velocity ac spectral shape of the current exponential model may not extend to frequencies as high as 35 GHz (Ka-band) and 95 GHz (W-band). The Currie et al. [12] results are also discussed in Long [27] and in Currie and Brown [58]; in the latter discussion, Currie remarks that “curve-fitting is an inexact science” and raises the possibility that other spectral shapes might also have been used to equally well fit these data. A set of papers in the Russian literature [13–16] from the same time period included power law among various analytic representations used in fitting experimental data in different Doppler regimes. Results taken from these Russian papers are shown in Figures 6.48, 6.49, and 6.50. In these Russian studies, spectral power was observed to decay at first according 0

Relative Power (dB)

–10

–20

–30 Power Law, ~4 n=

–40 X-Band, Forest Three Measurements under Different Wind Conditions –50 0.015

0.15

1.50

Doppler Velocity v (m/s)

Figure 6.48 Measurements of radar ground clutter power spectra by Kapitanov, Mel’nichuk, and Chernikov of the Russian Academy of Sciences. After [13], 1973.

Windblown Clutter Spectral Measurements 647

0

Relative Power k (dB)

X-Band, Forest

–20

–40

Power Law n≅6

–60

–70 0.0015

0.015

0.15

1.5

Doppler Velocityv (m/s) Measurement Interval 1 2 3 4

Amplifier Bandwidth (Hz) 0 – 2000 0 – 2000 20 – 2000 20 – 2000

Figure 6.49 Measurements of radar ground clutter power spectra by Andrianov et al. of the Russian Academy of Sciences. After [15], 1976.

to Gaussian [13] or exponential [16] laws to spectral power levels down 10 to 20 dB from zero-Doppler. This initial region of decay was followed by subsequent power-law decay to lower levels and higher Doppler velocities. Spectral widths in these Russian measurements closely match those measured by the Phase One and LCE radars near their limits of sensitivity (down ∼ 70 dB). The Russian investigations included theoretical [13,14] as well as empirical characterizations of windblown clutter spectra. The theoretical studies concluded that shadowing effects (of background leaves and branches by those in the foreground under turbulent wind-induced motion) were important in determining the shapes of spectral tails, over and above oscillatory and rotational effects. A physical model of windblown vegetation was initially discussed by Kapitanov et al. [13], which included random oscillation of elementary reflectors (leaves, branches) causing phase fluctuation of returned signals and shadowing of some elementary reflectors by others causing amplitude

648 Windblown Clutter Spectral Measurements

0

Relative Power k (dB)

1

–20 0 2

–40

Exponential

–10 3

–60 –70

X-Band

0.015

0.15

1.5

Doppler Velocity v (m/s)

Curve

Tree Species

1 2 3

Birch Alder Pine

Wind Speed (mph) 6 11 13

–20 X-Band –23.5 0.15 0.015

0.30

Doppler Velocity v (m/s)

Tree Species

Wind Speed (mph)

Birch

4

0.45 0.4875

Figure 6.50 Measurements of radar ground clutter power spectra by Andrianov, Armand, and Kibardina of the Russian Academy of Sciences. After [16], 1976.

fluctuation of returns. An expression for the clutter spectrum was obtained based on the correlation properties of the returned signals. This expression consisted of four terms—the first dependent on the initial positions of the reflectors, the second representing the spectrum of the amplitude fluctuations, and the third describing the spectrum of the phase fluctuations; the fourth term was the convolution of the amplitude and phase fluctuations of the elementary signals and was said to determine “the behavior of the wings [i.e., tails] of the spectrum”[13]. It was believed in this study that the interaction of foliage with turbulent wind flow was beyond the scope of accurate mathematical description, so the authors resorted to experimental measurement of the oscillatory motion of branches in winds through photographic methods. These measurements of branch oscillatory motion led to the prediction of an n = 4 power-law clutter spectral decay associated with phase fluctuation up to a Doppler velocity of ∼ 0.5 m/s, with a faster phase fluctuation-induced rate of decay expected at higher Doppler velocities. Since their measurements indicated an n = 4 power-law decay to higher Doppler velocities (i.e., to 1.5 to 3 m/s near their system limits of –36 to –40 dB down from zero-Doppler peaks), they concluded that shadowinginduced amplitude fluctuation must have caused the n = 4 power-law decay continuing to be observed beyond ∼ 0.5 m/s.

Windblown Clutter Spectral Measurements 649

Armand et al. [14] further developed the Kapitanov et al. [13] physical model by assuming that the elemental scatterers at X-band were primarily leaves and modeling them as metal disks. These elemental scatterers introduced phase fluctuation in returned signals due to oscillatory motion, and amplitude fluctuation due to rotational motion and shadowing effects. A mathematical model of wind-induced scatterer motion including these effects was assumed. The resultant tail of the clutter spectrum was shown to be describable by a negative power series in Doppler frequency f, including both integer and fractional powers. In the absence of shadowing effects, this expression simplified considerably, leaving only a single dominant power-law term of n ≅ 5.66. Since the authors observed experimental power-law spectral decay of n ≅ 3, they also concluded that shadowing effects had to be at work in determining the shape and extent of windblown clutter spectral tails. Other results in which power-law spectral decay was observed are those of Simkins, Vannicola, and Ryan [17]. These measurements of ground clutter spectra were obtained at L-band at Alaskan surveillance radar sites as shown in Figure 6.51. In these results, powerlaw shapes with exponents n of 3 and 4 were attributed to the measured data which exist to levels 40 to 45 dB below the zero-Doppler peaks. In Figure 6.51, the “partially wooded hills” power law (given by n = 4, vc = 0.058 m/s) provides spectral widths comparable with those measured by other investigators, but the “heavily wooded valley” power law (given by n = 3, vc = 0.34 m/s) for which the bounding envelope is shown to reach 10.6 m/s at the –45 dB point provides spectral widths very much wider than any other known ground clutter spectral measurement at equivalent spectral power levels. The particular four points in the “heavily wooded valley” data that show excessive spectral width for windblown forest in 20 knot winds are indicated as a, b, c, and d in Figure 6.51; they deviate from the general rule as determined by the vast preponderance of other measurements reported in the literature of the subject. The position of the widest LCEmeasured clutter spectrum is also shown in Figure 6.51 for comparison. These results of Simkins et al. were subsequently extrapolated as n = 3 and n = 4 power laws to lower levels in clutter models (see subsequent discussion in Section 6.6.3.4). In the 1980s, several research institutes in China investigated backscattering power spectra from windblown vegetation in various microwave radar bands, including X, S, and L [18, 19]. In all plots presented, spectral dynamic ranges were ≤ 30 dB below zero-Doppler peaks. The focus of interest in these Chinese investigations was on the fact that power spectra from windblown vegetation over such limited spectral dynamic ranges are typically well approximated by power laws, but that no simple physical model or underlying fundamental principle is known that requires spectral shapes to be of power-law form. Thus they wished to bring the power-law basis for spectral decay into better understanding and onto firmer theoretical footing. Jiankang, Zhongzhi, and Zhong [18] presented a first-principles theoretical model for backscattering from vegetation to represent the intrinsic motion or time variation of σ ° that occurs in microwave surface remote sensing. This model was based on representing the vegetation as a random medium in which the dielectric constant varied with space and time. A general formulation for the backscattering power spectrum was obtained based on the assumed leaf velocity distribution. Assumptions that the wind was an impulse function and that the leaves were Rayleigh-distributed elemental masses led to a leaf velocity distribution that was shown to be closely similar in form (but not exactly equal) to an n = 3

650 Windblown Clutter Spectral Measurements

10

L-Band 10–20 Knot Winds

Relative Power (dB)

0 Power Law, n n=3

a –10

b

–20 c –30

n=4 n=4

d

–40 –45 0.02

0.1

0.2

0.6 1

2 3 4 6 8 10

Doppler Velocity v (m/s) Measurements

Models

Mountains Partially Wooded Hills Heavily Wooded Valleys (Lowlands) a, b, c, d: Extrema : Widest Lincoln Measurement

Figure 6.51 Measurements of radar ground clutter power spectra by Simkins, Vannicola, and Ryan of the USAF Rome Air Development Center. After [17], 1977.

power law. However, the resulting backscattering power spectrum was of “quite complex form” [18]. Its numerical evaluation and comparison with three measured spectra indicated n = 3 power-law spectral decay over spectral dynamic ranges reaching 30 dB down from zero-Doppler peaks. A further assumption restricting the originally specified elliptic spatial distribution of leaf motion to motion only along the wind direction reduced the complex expression for backscattering power spectrum to the same n = 3 quasi-power-law form as the leaf velocity distribution. This expression was compared with the Fishbein n = 3 powerlaw results and found to be in good agreement. The authors concluded by claiming that their model provides a theoretical basis for power-law spectral decay and, in addition, allows generalization of parametric effects such as wind speed on spectral shape. What their model appears to show, however, is less far-reaching—only that a postulated n = 3 quasi-power-law distribution of leaf velocities results in similar n = 3 quasi-power-law clutter spectral shapes.

Windblown Clutter Spectral Measurements 651

In a later paper, Li [19] summarized L-band investigations at the Chinese Airforce Radar Institute to characterize Doppler spectra from windblown vegetation to improve design and performance of MTI and MTD (moving target detector) clutter filters. According to Li, the common position reached by Chinese researchers from several research institutes in China was that the radar land clutter spectrum could be represented as a power law with n ranging from < 2 to > 3, but that no direct physical explanation for the power-law spectral shape was available in published papers. To help provide such an explanation, Li started with the complex theoretical formulation for the power spectrum from an assemblage of randomly translating and rotating scatterers expressed as a sum of offset Gaussian functions as derived much earlier by Wong et al. [29], and argued heuristically that the rotational components that spread the spectrum resulted in power-law spectral shapes. To illustrate this hypothesis, Li numerically evaluated Wong et al.’s expression for three different cases in which Wong et al.’s statistical parameters were changed to ostensibly show effects of varying wind speed and for two different cases in which the statistical parameters were changed to ostensibly show effects of changing radar frequency. For all five cases, Li showed that the changing spectral shapes resulting from such parameter variations in Wong et al.’s formula could be well tracked by changing n in a simple power-law approximation. All such comparisons were shown over spectral dynamic ranges reaching 30 dB below zero-Doppler peaks. Li finally showed that two of his power-law approximations closely fit, respectively, two spectral measurements taken from the much earlier Rosenbaum and Bowles paper [55]. These two measurements were at UHF and L-band and were available to Rosenbaum and Bowles (who were Lincoln Laboratory investigators) from a 1972-era Lincoln Laboratory clutter spectral measurement program [59] to be discussed later. Li selectively showed the Rosenbaum and Bowles data only over upper ranges of spectral power (i.e., to –30 dB and –20 dB, respectively, or only over about one-half the spectral dynamic ranges of the original data), and Li also converted the Rosenbaum and Bowles data from a logarithmic to a linear Doppler frequency axis. Li’s resulting plots show results, including both Rosenbaum and Bowles’ experimental data and the power-law approximations to them, which are very linear on 10 log P vs f axes—that is, all would be reasonably matched with exponential functions, although Li matched them with power-law functions. Measurements of decorrelation times [40], bistatic scattering patterns [41], and power spectra [42] of continuous-wave X-band backscatter from windblown trees were obtained by Narayanan and others at the University of Nebraska. These measurements were of individual trees (1.8-m-diameter illumination spot size on the tree crown) of various species at very short ranges (e.g., 30 m). Radar system noise is evident in these spectral data at levels 35 to 45 dB below the zero-Doppler spectral peaks and for Doppler frequencies f corresponding to Doppler velocities v ≤ ~1 m/s [42]. Over these relatively limited spectral dynamic ranges and corresponding low Doppler velocities, many of the measured spectral data appear to closely follow power-law behavior (i.e., the spectral data are very linear as presented on 10 log P vs log f axes), although this apparent near-power-law behavior was not commented upon in the paper. As with Li [19], the Narayanan et al. starting point in modeling these data was the Wong et al. [29] formulation of the power spectrum for a group of moving scatterers, each with random rotational as well as translational motion. As previously discussed, Wong et al.’s spectral

652 Windblown Clutter Spectral Measurements

result consists of six Gaussian terms of which four are offset from zero-Doppler. Wong et al.’s expression depends on three parameters, the standard deviation σ d of the translational drift velocity components, and the mean ω r and standard deviation σ r of the rotational components. Thus in Wong et al.’s expression σ d determines the spectral width of the central Gaussian peak at zero-Doppler arising just from translation; ω r determines the locations of the four offset peaks at ± 2 ω r and ± 4 ω r , respectively; and σ d and σ r together determine the slower-decaying spectral widths of all five additional Gaussians (four offset and one not offset from zero-Doppler) arising from rotation. In modeling his measured power spectral data from windblown trees using Wong et al.’s theoretical expression, Narayanan postulated each of the three parameters σ d , ω r , and σ r to be linearly dependent on wind speed and specified the coefficients of proportionality for each specifically by tree type based on least-squared fits to measured autocovariance data. Narayanan et al. also provided extensive conjectural discussion associating σ d with branch translational motion and ω r and σ r with leaf/needle rotational motion, although their results do not appear to be dependent on the validity of these associations. In this manner, Narayanan et al. arrived at a six-term Gaussian expression for the power spectrum from windblown trees based on three coefficients of proportionality to wind speed for which the coefficients are empirically specified for six different species of trees. This expression provided reasonable matches to measured clutter spectral data from individual trees over spectral dynamic ranges reaching 35 to 45 dB below the zero-Doppler peaks. Narayanan et al. also derived an expression for the MTI improvement factor for a single delay-line canceller based on their six-term Gaussian expression for the clutter power spectrum from windblown vegetation, and provided numerical results showing significant degradation in tree-species-specific delay-line canceller performance using their six-term (i.e., with rotation) spectral expression compared with the corresponding single-Gaussian (i.e., without rotation) spectral expression. In both spectral and improvement factor results, there is considerable variation in these results between different tree species. These shortrange small-spot-size deterministic results applicable to specific tree species are in major contradistinction to the Phase One and LCE statistical results, which are applicable to larger cells at longer ranges and over greater spectral dynamic ranges, each cell containing a number of trees, often of mixed species. A limited set of coherent X-band measurements of ground clutter spectra were obtained by Ewell [20] utilizing a different Lincoln Laboratory radar unrelated to the Phase One and LCE radars. This radar (1° beamwidth and 1-µs pulsewidth) was not specifically designed for measuring very-low-Doppler clutter signals—e.g., it used a cavity-stabilized klystron as the stable microwave oscillator, which is less stable at low Doppler frequencies than modern solid state oscillators. The available ac spectral dynamic range provided by this radar for measuring clutter signals at low Doppler offsets was ~40 to 45 dB. Measurements were made of three desert terrain types at ranges for the most part from 3 to 12 km on three different measurement days under winds gusting from 9 to 12 mph. Results were provided for both circular and linear polarizations. Over the available ~40-dB spectral dynamic range, these measured data appeared to follow power-law spectral shapes, although with occasional hints in the data of faster decay at lower levels. Table 6.6 shows the resulting power-law shape parameters, averaged over a number of measurements within each of the three terrain types. These three desert clutter

Windblown Clutter Spectral Measurements 653

spectral shapes are quite similar; that is, when each is normalized to equivalent unit spectral power as per Eq. (6.18) and the set of three is plotted together, they form a relatively tight cluster to levels ~40 dB down. For example, all three curves reach the –30-dB level at v ≅ 1 m/s, which point is very closely matched by the β = 8 exponential shape factor provided by the spectral model of Section 6.2 for similar breezy wind conditions (see Figure 6.1). Also included for comparison in Table 6.6 are Fishbein et al.’s original power-law spectral shape parameters. The Fishbein et al. power law is wider than the three desert power laws in Table 6.6 (e.g., the Fishbein et al. power law reaches the –30-dB level at v = 1.7 m/s), although part of the reason for the wider Fishbein et al. data is that they were noncoherent. Besides corroborating gross spectral extents of Phase One and LCE clutter spectra measured at upper ranges of spectral power under breezy conditions, the results of Ewell’s spectral measurements shown in Table 6.6 also tend to substantiate the Phase One and LCE findings that ac clutter spectral shape, at least to first-order, tends to be approximately independent of terrain type and that clutter spectral shape tends to be largely independent of polarization. Table 6.6 Comparison of Ewell [20] and Fishbein et al. [10] Power-Law Clutter Spectral Shape Parameters

Clutter Spectrum

Power-Law Spectral Shape Parameters n

v c (m/s)

Ewell [20] a 4.1

0.11

3.7

0.10

3) Low-growing cedar trees

3.3

0.07

Fishbein et al. [10] b

3.0

0.11

1) Scrub/brush 2) Mountain slopes (sparse vegetation/rocks)

a. Spectral shape parameters shown are valid for approximating clutter spectra over ac spectral dynamic ranges reaching ~40 to 45 dB down from the zero-Doppler peak. b. Valid to ~ 35 dB down

Status (Power-Law Spectral Shape). Many measurements of windblown clutter spectra obtained following the very early measurements of Barlow and others provide spectral dynamic ranges typically reaching ∼ 30 or ∼ 40 dB below zero-Doppler peaks. Such measurements, as reviewed in the preceding discussion, provide clutter spectral shapes that are frequently well represented as power laws. In contrast to the Gaussian spectral shape which theoretically arises from a random group of scatterers each of constant translational drift velocity, there is no simple physical model or fundamental underlying reason requiring clutter spectral shapes to be power law. All

654 Windblown Clutter Spectral Measurements

theoretical investigations of clutter spectra based on physical models that include oscillation and/or rotation in addition to translation of clutter elements provide expressions for clutter spectra that are to greater or lesser degree of complex mathematical form [14, 18, 29, 39, 54, 55], although one such expression [14] is derived to be a negative power series in f (i.e., as a sum of elemental power laws) which at least does have a general power lawlike behavior. Because the preponderance of the empirical evidence in spectral measurements to levels 30 or 40 dB down from zero-Doppler peaks has been for simple power-law spectral shapes, there has been some motivation by theoreticians either to reduce an initially derived complex formulation for clutter spectral shape to a simpler, approximately power-law formulation [18] or to show that numerical evaluation of the complex formulation provides results that closely match a simple power law [19]. However, the evidence that clutter spectra have power-law shapes over spectral dynamic ranges reaching 30 to 40 dB below zero-Doppler peaks is essentially empirical, not theoretical.

6.6.1.3 Exponential Spectral Shape Phase One and LCE ground clutter spectral measurements to levels 60 to 80 dB down indicate that the shapes of the spectra decay at rates often close to exponential [21, 25]. The two-sided exponential spectral shape is given by Eq. (6.2), repeated here as: β P ac ( v ) = --- ⋅ exp ( – β v ) ,–∞ < v < ∞ 2

(6.19)

where β is the exponential shape parameter, K = β/2 is the normalization constant, k ( v ) = exp ( – β v ) , and ∞

∫

–∞

P ac ( v ) dv = 1 .

To convert to Pac(f) in Eq. (6.2), i.e., Pac(f)df = Pac(v) dv, replace v by f and β by (λ/2)β. The standard deviation of the exponential spectrum of Eq. (6.2) is given by σ β = 2 ⁄β in units of m/s. The exponential shape is wider than Gaussian, but in the limit much narrower than power law whatever the value of the power-law exponent n. Like the Gaussian, the exponential is simple and analytically tractable. For example, the Fourier transform of the exponential function is a power-law function of power-law exponent n = 2 [8, 51]. The exponential shape is easy to observe as a linear relationship in a plot of 10 log Pac vs v. Figure 6.21 shows four cases of measured Phase One and LCE spectra that are remarkably close to exponential over most of their Doppler extents, and other examples of Phase One and LCE exponential or quasi-exponential clutter spectral decay are provided elsewhere in Chapter 6. There is no known underlying fundamental physical principle requiring clutter spectra to be of exponential shape. Rather, the exponential shape is a convenient analytic envelope approximating the shapes of many of the Phase One and LCE measurements to levels 60 to 80 dB down. In Eq. (6.2), the independent variable v may itself be raised to a power, say n, as: exp (–β|v|n) to provide an additional degree of freedom in curve-fitting to measured data. When n > 1, this results in convex-from-above spectral shapes on 10 log P vs v axes, that is, in shapes that decay faster than exponential (e.g., when n = 2 the shape becomes Gaussian). On the other hand, n < 1 (i.e., fractional) results in concave-from-above spectral shapes on 10 log P

Windblown Clutter Spectral Measurements 655

vs v axes, which is the direction away from purely exponential that measured Phase One and LCE spectra usually tend towards, especially at lower wind speeds. Provision of a more complex exponential-like expression to possibly enable improved curve-fitting capability to particular empirical data sets is not further pursued here since the simple exponential form (i.e., n = 1) satisfactorily captures the general shapes and trends in the data. The Phase One clutter data were shared with the Canadian government. Chan of Defence Research Establishment Ottawa (DREO) issued a report [22] and subsequent paper [23] on the spectral characteristics of ground clutter as determined largely from his investigations of the Phase One data, but also including measured ground clutter spectra from a DREO rooftop S-band phased-array radar. Figure 6.52 shows some of Chan’s results comparing clutter spectra from the same two resolution cells under windy and breezy conditions. In the main, Chan’s results agree with those of Lincoln Laboratory. In arriving at these results, Chan used a different set of the Phase One data than the long-time-dwell experiments used at Lincoln Laboratory in spectral processing. That is, to obtain a larger set of measurements, Chan used repeat sector Phase One data (see Chapter 3) which provided more spatial cells but shorter dwells, and performed maximum entropy spectral estimation on these data to obtain the necessary spectral resolution. Thus with different data, different processing, and, in the case of the DREO phased-array instrumentation, a different radar, Chan also arrived at exponential spectral decay for what he calls the “slow-diffuse” component of the ground clutter spectrum. Indeed, the spectra from the DREO radar shown in Figure 6.52 appear for the most part to be highly exponential in spectral shape. Stewart [43] has also shown a measured ground clutter spectral shape of relatively wide spectral extent that appears highly exponential. The empirical observations of exponential decay in the Phase One and LCE clutter spectra motivated White [39] to develop a new first-principles physical model for radar backscatter from moving vegetation that also provides exponential spectral decay to conform in this respect with the experimental evidence. White’s model assumes that an important element of the scattering arises from the tree branches. The key feature of the model is the representation of each branch as a cantilever beam clamped at one end. Distributions of branch lengths is Gaussian. Distribution of branch angles with respect to horizontal is uniform over π radians. Scattering centers are distributed uniformly over an outer (specifiable) portion of each branch. A mathematical expression for the Doppler spectrum of the radar return from such an assemblage of branches under a distributed wind forcing function is derived. This expression is a complex five-part multiple integral requiring numerical evaluation. When numerically evaluated, the resultant Doppler spectrum is shown to very closely provide exponential decay with increasing Doppler frequency. In addition, the sensitivity of White’s exponential spectral shape to a number of his model assumptions was tested numerically. It was found that the exponential shape was not very sensitive to a number of underlying assumptions concerning the beam modes of oscillation, but much faster than exponential decay occurred when the beams were not clamped (i.e., simple translation), when a nondistributed wind force was used, and when branch lengths were uniformly (as opposed to Gaussianly) distributed. Besides this exponential spectral component arising from branch motion, the model also postulates a rectangular wideband background spectral component at lower power levels arising from leaf motion (see Section 6.6.3.3). Although White’s main thrust was the development of a theoretical clutter spectral model, he also provided a small amount of measured radar clutter spectral data acquired

656 Windblown Clutter Spectral Measurements

40

50 Wind Speed = 25 mph 40

(a)

30

Spectral Density (dB)

Wind Speed = 12 mph

Spectrum A az = 36° 6.35 km

30

20

Spectrum B az = –40° 6.65 km

(b) Spectrum A az = 36° 6.35 km

20 Spectrum B az = –40° 6.65 km

10 10 0 0

–10

–10

–20

–20 –1

0

1

–1

0

1

Doppler Velocity v (m/s) Site: DREO Freq. = 2.97 GHz Pol. = Horizontal Range Res. = 150 m PRF = 100 Hz

Figure 6.52 Measurements of radar ground clutter power spectra by Chan of DREO (Canada) showing results from the same two resolution cells under windy conditions (a), and breezy conditions (b). After [22], 1989.

using a rooftop C-band radar of spectral dynamic range reaching ≈30 to 40 dB below zero-Doppler peaks. White concluded from curve-fitting studies comparing power-law with exponential approximations to his measured data that “ . . . the exponential model is the better fit” [39]. Using a different method of analysis than that of White, Lombardo [60] presents a mathematical formulation for ground clutter spectral shape derived from a phenomenologically representative negative binomial probability distribution of scatterer velocities that also can yield an exponential decay characteristic in the tail. Measured results very similar to those of Phase One and LCE but over less wide, 40- to 60-dB dynamic ranges were obtained in a much earlier set of Lincoln Laboratory measurements of ground clutter spectra at UHF and L-band [59]. Clutter spectra from this earlier program averaged over a number (e.g., 5) of range cells and displayed on log-Doppler velocity axes typically show an increasing rate of downward curvature (convex from above) as in the LCE and Phase One measurements. By coincidence, this early Lincoln Laboratory program [59] of 1972 and the Russian X-band investigations [13] going forward in very nearly the same time period (1973) both developed first-principles physical models of clutter spectra from forest. In

Windblown Clutter Spectral Measurements 657

both studies, the tree was modeled as a mechanical resonator excited by a turbulent wind field of known spectral content. Both programs involved measurements of tree motion. In both programs, the spectral content of tree motion decayed at low frequencies below a resonance maximum according to an n = 5/3 power law; at higher frequencies above the resonance maximum, the decay was faster. The slightly later (1974), largely theoretical paper by Lincoln Laboratory authors [55] concerning electromagnetic scattering from vegetative regions included three measured clutter spectra from the 1972-era measurement program. Shoulders before the onset of faster decay, such as those shown in some of the LCE- and Phase One-measured clutter spectra (e.g., see Figures 6.22, 6.24, and 6.25), are similar to those observed previously in the earlier Lincoln Laboratory program [59] and explained as local resonance maxima associated with the natural resonant frequency of trees. The resonance shoulder was more pronounced at lower frequencies and lower wind speeds, and tended to diminish at higher frequencies and higher wind speeds. The reason is that, at lower wind speeds and longer wavelengths, the motion of the tree is a small fraction of a radar wavelength. Thus under these conditions the tree motion superimposes a phase modulation with low index of modulation, and as a result the clutter spectrum directly corresponds with that of the tree’s physical motion. At higher frequencies and under stronger winds, the degree of phase modulation increases and the clutter spectrum no longer simply replicates that of the tree motion. These observations tend to be corroborated in LCE and Phase One results. In addition, the LCE and Phase One data tend to have resonance shoulders to somewhat higher frequencies in measurements from partially open or open terrain (desert, farmland, rangeland) in which there is a significant dc component; the measurements from forested terrain tend to have distinct resonance shoulders only at the lower radar frequencies (VHF and UHF). The earlier Lincoln Laboratory program observed, in passing, that the shapes of some measured spectra beyond the resonance shoulder were highly exponential, but this observation was not elaborated upon. Another early, more explicit, observation of exponential spectral shape is in the results of Andrianov, Armand, and Kibardina [16] (see Figure 6.50). In these results, exponential decay was initially observed from the maximum zero-Doppler level down to –20 dB, followed by power-law decay thereafter to –70 dB with reported values of n equal to 3.4, 3.8, and 5.6 for pine, alder, and birch, respectively. The equipment used was ostensibly of 70-dB dynamic range [15] although, to use their words translated to English, two dynamic range intervals were “sewn together” [16], as shown in Figure 6.49, to provide the full 70-dB range. In terms of gross spectral extent (e.g., 1.5 m/s, 70 dB down; 0.4 m/s, 20 dB down), these results of Andrianov et al. [15, 16] fall closely within the range of measured LCE and Phase One spectral extents over similar spectral dynamic ranges. The earlier results of Kapitanov, Mel’nichuk, and Chernikov [13], as shown in Figure 6.48, were said to exhibit Gaussian decay down 10 to 15 dB, followed by power-law decay with n = 4 down to –40 dB. The initial Gaussian decay was later stated to be erroneous by Andrianov et al. [16] because of early equipment limitations and that initial exponential decay as reported by them (see Figure 6.50) was more correct. The exponent n of the power law is easy to estimate in measured spectral data as simply onetenth the slope of the approximating straight line on 10 log P vs log v axes in dB/decade. In Figure 6.50, the three measured spectral curves for pine, alder, and birch shown to the left do not exhibit decay anything like the quoted power-law slopes of n = 3.4, 3.8, and 5.6, respectively. These three curves are stated by the authors to be three particular examples of

658 Windblown Clutter Spectral Measurements

measured spectra, whereas their quoted values of n are averages over all measurements in which the value of n varies from 2.6 to 6.8. The rates of decay in the spectral tails of the data to the left in Figure 6.50 are much greater than any of these quoted values of n and, at least in qualitative appearance (increasing downward curvature), appear to be more exponential than power law. The data of Figure 6.49 appear to be more credibly of power-law behavior (n ≈6) in their tails, but the data plotted at the –68-dB level indicate slightly increasing curvature (rate of decay > n ≈6) at the lowest power levels shown. The data of Figure 6.48 closely match the n = 4 power law attributed by the authors to these data. Some confusion may arise because these Russian investigators [13–16] associate powerlaw shapes with lower ranges of spectral power in their measured data, whereas other investigators [10–12, 17–20] match their data to power-law shapes over upper ranges of spectral power. Measured clutter data in any particular regime of spectral power may be fitted with a power law, but the danger lies in extrapolating the power law beyond its regime of applicability. An additional, somewhat more significant, past use of the exponential function to characterize clutter spectra from windblown vegetation occurred in experimental work performed at the Laboratoire Central de Telecommunications in France [38]. These French measurements were also performed during the 1970s using coherent-on-receive radars, spectrum analyzers with limited (i.e., 50 dB) dynamic range, and a limited number of vegetation clutter types. In this work, the MTI filter cutoff frequency was adjusted so as to be just sufficient to remove the clutter to the –40-dB level. It was found that the cutoff frequency just sufficient to remove the clutter was best predicted by hypothesizing an exponential spectral clutter model. The cutoff frequency predicted by a Gaussian spectral model was too low (i.e., optimistic—if there was even a light wind, significant clutter was passed by the filter); whereas the cutoff frequency predicted by a power-law spectral model was too high (i.e., pessimistic—at X-band, all targets with radial speed < 50 km/h were missed). In contrast, cutoff frequencies in the range predicted by an exponential spectral model were successfully used as the standard specification for many service radars in the French military and elsewhere.

Status (Exponential Spectral Shape). The significantly increasing rate of downward curvature (i.e., convex from above) observed in the general shapes of Phase One- and LCE-measured windblown ground clutter Doppler spectra on 10 log P vs log v axes over spectral dynamic ranges reaching 60 to 80 dB below zero-Doppler peaks points to a general exponential characterization rather than a power-law characterization that plots linearly on such axes. Increasing rate of downward curvature in such plots has always been observed without exception in all measurements examined of clutter spectra from windblown trees and other vegetation under breezy or windy conditions taken from these extensive databases. Other investigators [22, 24] have corroborated that the exponential shape factor is generally representative of these data and is not the result of processingspecific particulars. In early studies, theoretical investigators attempted to reduce complex mathematical formulations of clutter spectra based on physical models incorporating oscillation and/or shadowing of elemental scatterers to simple power-law forms to conform with the experimental evidence then available at upper levels of spectral power (down 30 or 40 dB from zero-Doppler peaks). Subsequent awareness of investigators of the Lincoln Laboratory clutter spectral results provided motivation to develop theoretical bases for the

Windblown Clutter Spectral Measurements 659

observed exponential spectral shapes. Thus there exist the interesting works of White [39] and Lombardo [60] in which formulations are developed for the clutter Doppler spectrum, that, although mathematically complex, provide close to exponential decay under numerical evaluation. In addition, White observed that “the series solutions produced by Bass et al. [54], Armand et al. [14], and Wong et al. [29] probably have sufficient degrees of freedom to produce a function that would be a close approximation to . . . exponential . . . ” [39]. Nevertheless, as for the power law for spectral dynamic ranges 30 to 40 dB down, the evidence of exponential clutter spectral shape for spectral dynamic ranges reaching 60 to 80 dB down is essentially empirical. The only known measurements of windblown clutter spectra of spectral dynamic ranges equal to or exceeding those of the Phase One and LCE instruments are the Russian measurements of the 1970s [13–16], for which the results over lower ranges of spectral power were approximated as power laws. However, these results are power law only in a piece-part sense; the upper range of spectral power was concluded to be exponential. Hence these results are not very useful or analytically tractable, in that no single simple analytic function was provided to describe the complete clutter spectral shape over its full measured spectral dynamic range. Furthermore, little actual measurement data were shown in these papers, thus restricting possibilities for independent assessment of the data and conclusions by present-day readers. Like the Gaussian function, the exponential function is simple and analytically tractable. The exponential function provides spectral shapes that are wider than Gaussian, as required by all the empirical evidence and by theoretical constructs involving oscillation, rotation, and shadowing of clutter elements; that are very much narrower at lower power levels (60 to 80 dB down) than extrapolations to lower levels of power-law representations of measurements accurate at higher levels of spectral power (30 to 40 dB down); and that are reasonably equivalent to the measurement data at high and low levels of spectral power.

6.6.2 Reconciliation of Exponential Shape with Historical Results 6.6.2.1 Current vs Historical Clutter Spectral Measurements Figure 6.5 (Section 6.3.2.1) shows a measured LCE clutter spectrum from windblown trees and compares it with several exponential shape functions (dotted lines) of various values of exponential shape parameter β. In Figure 6.5, the measured data closely follow the exponential curve of shape parameter β = 5.2 over the full spectral dynamic range shown. Also shown in Figure 6.5 is a narrower Gaussian spectral shape function (dashed line) corresponding to Barlow’s much-referenced historical measurement [7] (see Figure 6.45). The Gaussian curve in the figure is shown extrapolated to low spectral power levels much below Barlow’s measured spectral dynamic range, which reached only 20 dB below the zero-Doppler peak. The overall rate of decay in the LCE data of Figure 6.5 is much more exponential than Gaussian in character. Spectral tails wider than Gaussian are theoretically required by branches and leaves in oscillatory motion [19, 29] (see Section 6.6.1). Figure 6.53 shows another LCE windblown-tree clutter spectrum different from that of Figure 6.5. The spectrum of Figure 6.53 was measured at vertical polarization on 11

660 Windblown Clutter Spectral Measurements

September at Wachusett Mt. at range = 8.0 km. Also shown in the figure is the n = 3, vc = 0.107 power-law curve introduced by Fishbein et al. [10] to match their data (Figure 6.46). This Fishbein et al. power-law curve is shown dashed in Figure 6.53 to a level 35 dB down from the zero-Doppler peak, which is the region for which Fishbein et al. had data; at lower levels in Figure 6.53 the Fishbein et al. power-law curve is shown dotted to indicate extrapolation to levels below Fishbein et al.’s noise floor. The LCE data in Figure 6.53 provide a remarkably close match to the Fishbein et al. power-law curve at upper levels (viz., down 35 dB) over which Fishbein et al. had data. That is, these LCE spectral data confirm the historic Fishbein et al. spectral measurement with modern measurement instrumentation. However, it is also very clear in Figure 6.53 that the Fishbein et al. powerlaw curve cannot be extrapolated to lower levels. At lower levels, the LCE measured spectrum in this figure decays much more rapidly than at upper levels. In overall shape, the LCE data of Figure 6.53 are not very different from Figure 6.5 and are better modeled as exponential over their complete range than as any power law.

Fishbein et al. Match Down 35 dB 20

Pac (dB)

0

–20 n

=

–40

3,

vc

=

0.

10

7

LCE (8.0 km) Noise

Fishbein et al. Power Law

–60

0.03

0.10

1.00

10.00

Doppler Velocity v (m/s)

Figure 6.53 Comparison of an LCE windblown forest clutter spectrum with the Fishbein et al. power-law model [10].

The Fishbein et al. measurement (Figure 6.46) was made with noncoherent instrumentation; thus the Fishbein et al. power-law approximation shown in Figure 6.53 is ~1.4 times wider than would be expected if the measurement had been coherent (see Section 6.6.1.1; the 1.4 factor is specifically applicable to spectra of Gaussian shape, but a similar factor is expected to apply to spectra of power-law shape). The LCE coherent measurement shown in Figure 6.53, although of similar relative shape to what would be expected if Fishbein et al. had made

Windblown Clutter Spectral Measurements 661

a coherent measurement, is thus wider in absolute terms at upper power levels (> –35 dB) than what would be expected in such a measurement. Even so, the narrower Fishbein et al. coherent measurement, if modeled as an n = 3 power law, would still extrapolate at lower levels (<< –35 dB) to spectral extents much broader than any LCE measurement at these lower levels, including LCE narrower measurements selected to match the coherent Fishbein et al. measurement at upper power levels. Figure 6.21 (Section 6.4.2) shows measured LCE and Phase One clutter spectra as 10 log Ptot vs v from cells containing windblown trees on breezy and windy days. These results are among the widest windblown clutter spectra measured by these instruments. In contrast with most of the other historical spectral measurements discussed in Section 6.6.1, the measurements of Figure 6.21 over greater spectral dynamic ranges than were available in most of the other measurements have spectral shapes that are accurately representable as exponential. This accurate exponential representation is indicated by the good fits of the data to the straight lines drawn through the right sides of the spectra in Figure 6.21. Figure 6.54 shows the right sides of Figures 6.21(a), (b), respectively, plotted as 10 log Ptot vs log v. Recall that the power-law spectral shape [Eq. (6.18)] plots as a straight line in the spectral tail region v >> vc using a log-Doppler velocity axis as in Figure 6.54. Certainly no single power-law straight line fits either of the spectral data traces in Figure 6.54, both of which exhibit strong downward curvature (convex from above) over their complete spectral extents. Even though the measurement data in Figure 6.54 exhibit strong downward curvature, a local power-law rate of decay can be defined for such data in a small Doppler interval δv as the value of power-law exponent n corresponding to the slope of the straight line tangent to the data curve in the region δv. The local power laws that thus fit the upper levels over historic dynamic range intervals in Figure 6.54 (n = 3 or 3.5) cannot be extrapolated to lower levels. Much faster decaying local power laws (n = 7, 8, or 10.5) fit the lower levels. In both Figures 6.53 and 6.54, the more sensitive Phase One and LCE measurement instruments confirm measured rates of spectral power decay reported by other investigators at upper power levels, but in addition find that much faster local power-law rates of decay occur at lower power levels. Close examination of the spectral data in Figures 6.53 and 6.54 appear to indicate, in fact, two or more distinct rates of decay in the spectra, perhaps indicating different phenomenological regimes with different sets of scatterers and/or different mechanisms of scatter dominating at different spectral power levels. On the basis of these results, it is not surprising that many previous investigators have characterized the rate of ground clutter spectral decay at relatively high spectral power levels (i.e., 35 to 45 dB down) as n = 3 or n = 4 power laws. In Figure 6.54, exponential fits to the data are shown lightly dotted. The exponential shape β = 7.1 closely fits the Phase One data of Figure 6.54(b) over its full ac spectral range away from its quasi-dc region (i.e., |v| > ≈0.2 m/s), including both regions of local power-law fits; similarly, the exponential shape β = 5.2 closely fits the LCE data of Figure 6.54(a) over its full ac range (i.e., |v| > ≈0.1 m/s). In Figure 6.44, the exponential β = 6 curve lying between Barlow’s g = 20 Gaussian curve and the Fishbein et al. n = 3 power-law curve is now seen as reasonably representative of the data shown in Figure 6.54 from two different instruments at two different sites across more than six orders of magnitude of diminishing spectral power.

662 Windblown Clutter Spectral Measurements

(a)

Power Law, n

Power Law, n

(b)

20 n =3

Ptot (dB)

0

n = 3.5 n =7 n =8

–20

n = 10.5

Exponential = 5.2

Noise

–40 Noise Exponential = 7.1

–60

0.10

1.00

10.00 0.10

1.00

10.00

Doppler Velocity v (m/s)

Figure 6.54 Two windblown forest clutter spectra for which exponential fits are compared with power-law fits: (a) LCE data, Wachusett Mt. (September) and (b) Phase One (L-band) data, Katahdin Hill (May).

6.6.2.2 Matching Measured Clutter Spectra with Analytic Shapes Figure 6.55 compares the β = 6 exponential shape with vc = 0.1; n = 3, 4, 5 power-law shapes both on 10 log P vs v axes [Figure 6.55(a)] and on 10 log P vs log v axes [Figure 6.55(b)]. Each of the four spectral shapes shown is normalized to equivalent unit spectral power as per Eqs. (6.2) and (6.18). Figure 6.55(a) uses a linear Doppler velocity axis, making evident how all power-law shapes become slowly decaying at low levels of spectral power, whatever the value of n. Given that the maximum Doppler velocities observed in Phase One- and LCE-measured clutter spectra were in the 3- to 4-m/s range at levels 60 to 80 dB down, the power-law parameters vc and n can certainly be adjusted to provide similar spectral extents at similar power levels. However, the resultant power-law shapes will not match Phase One- and LCE-measured data at higher levels of spectral power and will rapidly extrapolate to excessive spectral width at lower levels. As plotted against the logarithmic Doppler velocity axis in Figure 6.55(b), the β = 6 exponential shape demonstrates the increasing downward curvature (convex from above) with increasing Doppler velocity and decreasing power level that characterizes all the Phase One- and LCE-measured clutter spectra when plotted on such axes. In contrast, the power-law shapes in Figure 6.55(b) have little curvature. That is, on 10 log P vs log v axes, power-law shapes are asymptotic to two straight lines with a maximum departure in curvature below these asymptotes of only 3 dB at the v = vc breakpoint between them. This rapid rotation from near-horizontal to straight line spectral tails in which rapidly increasing downward curvature is constrained to a very narrow v ≅ vc Doppler regime is not generally characteristic of the Phase One- and LCE-measured clutter spectral shapes.

Windblown Clutter Spectral Measurements 663

Power Law, n vc = 0.1 m/s

0

(a)

–20

Pac (dB)

Power Law, n vc = 0.1 m/s

(b)

n

–40

=

n=3

3

n = 4

–60

n=4 n = 5

–80

n=5

=6

0

5

Exponential

10

0.10

=6

1.00

10.00

Doppler Velocity v (m/s)

Figure 6.55 Comparison of exponential and power-law spectral shapes: (a) linear and (b) logarithmic Doppler velocity axes.

6.6.2.3 Summary The Phase One and LCE measurements of ground clutter spectra presented in Chapter 6 are displayed on both linear and logarithmic Doppler velocity axes. What is clear in these presentations, and what has not been generally recognized, is that if the clutter ac spectral shape Pac is represented as a power law, the power-law exponent n is not constant but gradually increases from n = 3 or 4 when Pac is 35 or 40 dB down from its maximum to n = 5 or 6 or even higher when Pac is 60 to 80 dB down from its maximum. Uncertainty about whether “the law” of spectral decay is “n = 3 or n = 6 (or even exponential)” is abetted by the additional lack of general recognition that the shape of the spectrum to levels 60 to 80 dB down is usually not precisely representable by any single analytic expression. In the results presented herein, slight upward curvature (concave from above) often occurs on the 10 log Pac vs v plots, hence the shape can be slightly broader than exponential; whereas strong downward curvature (convex from above) almost always occurs on the 10 log Pac vs log v plots, hence the shape is much narrower than constant power law. Thus there is no argument with Andrianov, Armand, and Kibardina that “It is [usually] impossible to [precisely match] the spectral density of the scattered signal by a single analytical function in the entire range of [Doppler] frequencies” [16]. However, much of the potentially ensuing difficulty in the general modeling of clutter spectra is overcome in Chapter 6 not just by utilizing exponential shapes, but also by introducing the concept of a quasi-dc region and absorbing excess power in this region into the dc delta function term of the model (see also [31]). However the spectrum is modeled, the Phase One and LCE results support the general existence of windblown clutter Doppler velocities only as great as ∼ 3 to 4 m/s for 15- to 30-mph winds to levels 70 to 80 dB down.

664 Windblown Clutter Spectral Measurements

The evidence for both power-law and exponential clutter spectral shapes is essentially empirical. The concern in Chapter 6 is not which of these two forms fits the data best over spectral dynamic ranges of –30 or –40 dB, or even whether such a question can be definitively answered. Chapter 6 provides good examples of both power-law and exponential fits to measured clutter spectral data to levels 30 or 40 dB down, and in reviewing the technical literature finds it to be similarly bipartite on this matter. The concern is, however, in determining an appropriate functional form to describe clutter spectra over greater spectral dynamic ranges. The main observation in this regard, based on the Phase One and LCE databases, is that no matter how good the power-law fits are over spectral dynamic ranges extending 30 to 40 dB below zero-Doppler peaks, they cannot be extrapolated to lower levels. That is, power-law shapes extrapolate rapidly to excessive spectral width. In contrast, the exponential form generally represents the Phase One and LCE measurements not only over their upper ranges of spectral power but also over their complete spectral dynamic ranges extending to levels 60 to 80 dB below zero-Doppler peaks. Thus radar system design for which ground clutter interference is of consequence at such low levels of spectral power is much more accurately based on an exponential clutter spectral shape approximation than on an extrapolated power-law approximation. The validity of the exponential shape on the basis of best matching coherent detection system performance to that obtained using actual measured I/Q clutter data as input to the clutter processor is demonstrated in Section 6.5.4.

6.6.3 Reports of Unusually Long Spectral Tails Several historical reports of spectral tails in ground clutter at unusually high power levels and/ or extending to unusually high Doppler velocities are considered in the following subsections.

6.6.3.1 Total Environment Clutter There exists significant concern with how to characterize the clutter residues left in Doppler filter banks in high sensitivity radars after MTI cancellation that might cause false targets for subsequent multitarget tracking algorithms. Thus there is interest in specifying an overall environment clutter model that would include the Doppler interference from such things as aurora, meteor trails, cosmic noise, windblown material (leaves, dust, spray), birds and insects, rotating structures, rain and other precipitation, lightning, clear air turbulence, fluctuations of refractive index, etc. Often such phenomena are highly transient as they occur in measurements of radar Doppler spectra, so that it is difficult to causally and quantitatively associate unusual spectral artifacts directly with their sources. It is not suggested here that a specific program dedicated to measuring any one of these phenomena would not be successful—rather, that in a general database of spectral measurements collected from spatial ensembles of remote ground clutter cells, the occasional occurrence of causative agents different from windblown vegetation is difficult to determine. The main focus of interest in the Phase One and LCE spectral measurements is the general and continuous spectral spreading that occurs in ground clutter due to wind-induced motion of tree foliage and branches or other vegetative land cover. These clutter databases have not been very extensively used for systematic searching for infrequent, spatially unusual, narrowband, or transient spectral features resulting from other causative agents in the total clutter environment because of their ephemeral nature and uncertain signature characteristics, although occasional evidence of birds, airplanes, automobiles, and other anomalies has been encountered in the spectral analyses of these data. The one concrete example encountered by the LCE radar of clutter from the total environment over land with

Windblown Clutter Spectral Measurements 665

atypical spectral behavior was strong Bragg resonance at small, but nonzero Doppler frequencies in the returns from a small inland body of water [34, 35]. Some of the unusually long spectral tails attributed to windblown clutter in the following discussions may have originated from external sources other than windblown vegetation or from internal instrumentation or data processing effects of which the investigators were unaware.

6.6.3.2 Chan’s “Fast-Diffuse” Component In addition to a “slow-diffuse” exponential component in ground clutter spectra, Chan [22, 23] also introduced a “fast-diffuse” component at a relatively weak but constant power level out to a higher Doppler frequency cutoff than the slow-diffuse component. Both components are indicated in Chan’s idealized diagram of a composite ground clutter model shown in Figure 6.56. The fast-diffuse component is based on the observation of very infrequent or narrowband spectral features usually observed in isolated cells and for short-duration time intervals. The amplitude and cutoff frequency of the fast-diffuse component are not specified by Chan; however, for all his fast-diffuse examples, the maximum, or cutoff Doppler velocity, although greater than the slow-diffuse component present, was ≤ 2.5 m/s. Such occasional spectral features may often be caused by total environment clutter (birds, etc.). Magnitude in dB Scale Co Coherent Component, Slope = kc s

Do Slow Diffuse Component, Slope = ks Fast Diffuse Component

Dof –fc

fc

Doppler Frequency

Figure 6.56 Chan’s conceptual composite clutter model, including a fast-diffuse component. From [22], 1989. See also [23].

Transient, isolated, narrowband spectral features at low Doppler that do not exist symmetrically to either side of zero-Doppler can often, with some degree of confidence, be attributed to birds. Chan speculated that “regular oscillatory motion of [crop] vegetation, arising from restricted freedom of travel and natural elasticity” [22] might explain some unusual symmetrical features. Similar features have not been observed at Lincoln Laboratory, although Chan was using different Phase One data (repeat sector) and different processing (maximum entropy). Nonlinear superresolution processing techniques (such as maximum entropy) usually require large S/N ratios—not available at low levels in measured clutter spectra—to avoid spurious results. Spectral contaminants from the measurement instrument or from external RF sources of interference may also be present.

666 Windblown Clutter Spectral Measurements

Spectral features that are not isolated but exist in all spatial resolution cells, and/or that exist symmetrically to either side of zero-Doppler, are likely to be instrumentation or processing contaminants. Probabilities of occurrence, which would be difficult to determine, would eventually be required in a model for fast-diffuse spectral features. In any event, experience has indicated that Chan’s fast-diffuse spectral component is easily misunderstood to imply the existence of a long, continuous, low-level, uniform amplitude spectral tail in ground clutter that is always there for all cells and all times. In fact, the fast-diffuse component was based on the observation of infrequent spectral artifacts.

6.6.3.3 White’s Wideband Background Component White’s physical model [39] for windblown trees, which provides an exponential spectral component, also provides a rectangular wideband background spectral component at lower power levels. White essentially postulated the existence of his background component on the basis of Chan’s fast-diffuse component [22, 23]. In so doing, White—as others have done—appears to have misinterpreted Chan’s fast-diffuse component in the manner discussed above. Thus, whereas Chan’s fast-diffuse component was based on the observation of infrequent spectral artifacts out to a maximum observed Doppler velocity of 2.5 m/s, White took this as the basis for postulating a wideband noise-like spectral component with “. . . a uniform spread of spectral power over all [Doppler] frequencies up to about 1 kHz” [39]. A cutoff frequency of 1 kHz corresponds to Doppler velocities of 15 and 50 m/s for the X- and S-band radars, respectively, that White was considering, which is well beyond Chan’s observed cutoff. White provided heuristic argument for the existence of a wideband background spectral component based on leaf (as opposed to branch) motion. In particular, he argued that rapid decorrelation in the returned signal resulting from the shadowing of one leaf by another and by leaf rotation can be expected to give rise to a wideband noise component. White did not derive a mathematical expression for the wideband component, and its absolute level was not specified. White attempted to provide some experimental evidence for the wideband background spectral component in his limited set of C-band measured ground clutter data. This experimental evidence is unconvincing. The spectral dynamic range of the measurement radar was not shown or specified, but it was stated that the radar had a “. . . reasonably high radar noise floor” [39]. Results were provided for a quiet day and a windy day. In both sets of results, what was claimed to be the wideband background component also has the appearance of a system or processing noise floor. In both sets of results, cells with significantly spread clutter spectra, cells with little, and cells with no clutter Doppler spread were separately combined to provide averaged clutter spectra with wide, some, and no clutter spread. It was observed that the noise-like background component was somewhat higher in spectral power level for the wide averaged spectrum than for the other two averaged spectra with little or no spread. In the quiet-day results, this difference in background level was small, and it was concluded that “the apparent white noise component . . . is due to . . . Fourier sidelobes and system noise” [39]. In the windy-day results, the difference was somewhat greater. It was argued that in this case this difference indicates “a real white-noise scatterer

Windblown Clutter Spectral Measurements 667

motion within the band limits of the radar” [39]. In White’s plotted results, what was claimed to be the white-noise spectral component occurs about 38 dB below the zeroDoppler peak. The Phase One and LCE databases of clutter spectral measurements provide no evidence for the existence of a noise-like wideband background spectral component within the spectral dynamic ranges of these instruments, which reach 60 to 80 dB below the zeroDoppler spectral peaks. The Armand et al. [14] measured clutter spectral data (discussed subsequently in Section 6.6.3.6) at 4-mph wind speed show a noise-like component at a constant level of ~ –115 dB extending over the range 2.5 < v < 20 m/s. At the higher wind speeds of 13 and 31 mph, the Armand et al. data decay continuously and reach the –115-dB level only at the limit of the measured data as v reaches ~20 m/s. No convincing evidence is provided by Armand et al. that the –115-dB level in these data is not a noise level. The bare-hill data of Warden and Wyndham [11] show a hint of a possible constant noise-like tail beginning at the –24-dB level (0.55 < v < 0.65 m/s), which is almost certainly a noise level or other corruptive influence (see Figure 6.47). In a private communication, White agreed that some degree of skepticism was warranted concerning his postulated wideband noise-like background component [61].

6.6.3.4 Simkins’ “Lowland” Data of Wide Spectral Extent This discussion concerns the L-band measurements of clutter spectra by Simkins, Vannicola, and Ryan [17] shown in Figure 6.51. Modeling information for spectral shape derived from these measurements was based on upper-bound approximations to worstcase spectra.These worst-case spectra came from resolution cells causing false alarms in a three-pulse-canceller MTI channel. These cells causing false alarms led to v-3 and v-4 power-law estimates of spectral shape. Spectra from adjacent cells with similar intensity but which did not cause false alarms were narrower, with v-5 or exponential shape. Relative frequencies of occurrence of false alarm cells compared with non-false alarm cells were not specified. False alarms can be caused by transient events in the total clutter environment other than generally pervasive windblown vegetation. False alarms that moved measurable distances over several PPI scans were called angels; possible associations of angels, primarily with birds, but also with insects, clear air turbulence, and aurora, were discussed. Other false alarms were due to anomalous propagation, for which no spectral data were taken. Stationary false alarm cells were assumed to be caused directly by areaextensive ground clutter (as opposed to having less direct total environment origins) and used to develop ground clutter spectral modeling information. Consider first the Simkins et al. ground clutter spectral data for “partially wooded hills” in 10- to 20-knot winds. The v-4 power-law shape attributed to these data in Figure 6.51 is an approximate upper-bound to an underlying scatter plot of data points. These data points, as typified by ≈–30 dB at 0.25 m/s and ≈–40 dB at 0.5 m/s, are not out of line with Phase One and LCE data. It is not the characterization of the bounding shape of these data as v-4 over the indicated 45-dB dynamic range that leads to difficulty, but the extrapolation of a constant v-4 power-law shape to power density levels significantly lower than –45 dB. Phase One and LCE also often show v-3 and v-4 rates of decay 35 to 40 dB down, but these become v-5 and v-6 rates of decay 60 to 80 dB down.

668 Windblown Clutter Spectral Measurements

Consider next the Simkins et al. ground clutter spectral data for “heavily wooded valleys” or “lowlands” in 10- to 20-knot winds also shown in Figure 6.51. A wider v-3 power-law shape was attributed as an upper bound approximation to these data. These heavilywooded-valley data, as typified by ∼ –7 dB at 0.5 m/s and ∼ –15 dB at 1 m/s, are significantly wider than Phase One- and LCE-measured spectra (the widest LCE spectrum is ∼ − 20 dB at 0.5 m/s and ∼ –30 dB at 1 m/s). The maximum measured Doppler velocity among the heavily-wooded-valley spectral data points is 5.8 m/s, 40 dB down; 5.8 m/s is almost twice the maximum Doppler velocity of ∼ 3 m/s for windblown trees consistently seen by LCE in 15- to 30-mph winds, 70 to 80 dB down, and almost four times the Doppler velocity of 1.5 m/s seen in the widest LCE spectrum, 40 dB down. No other known measurement of a ground clutter spectrum approaches such high spectral power at such high Doppler velocity as given by the 5.8 m/s, –40-dB point of the Simkins et al. heavilywooded-valley data. On the basis of the many Phase One and LCE results in 15- to 30-mph winds, attributing Doppler velocities of 5.8 m/s, 40 dB down, to windblown trees would conjecturally require wind velocities much greater than the nominal 10 to 20 knots associated with the heavilywooded-valley data. The only other known measurements of ground clutter spectra in which spectral power decays as slowly with increasing Doppler velocity as in the Simkins et al. heavily-wooded-valley data are early results reported by Goldstein [9] for trees in gale-force winds, discussed next in Section 6.6.3.5; however, these measurements only extend to a maximum Doppler velocity of 1 m/s. The only other known measurements of ground clutter Doppler velocities approaching or exceeding the 5.8 m/s maximum Doppler velocity shown at the –40-dB spectral power level in the Simkins et al. heavily-woodedvalley data (besides White’s improbable wideband noise-like component) are the highly questionable results of Armand et al. [14] discussed in Section 6.6.3.6; however, spectral extent ≥ 5.8 m/s in the Armand et al. data is at dubiously low spectral power levels in the range of –90 to –120 dB. Otherwise, the Phase One and LCE measurements and the rest of the published literature [7, 10–13, 15, 16, 18–20, 22, 38, 42, 43, 45], including the other Simkins et al. data [17] and the Armand et al. data [14] at higher, less questionable spectral power levels, are in general agreement in terms of gross spectral extent (as opposed to details of spectral shape), measured over equivalent spectral dynamic ranges. Since these high Doppler-velocity heavily-wooded-valley or lowland data are worst-case results from occasional false alarm cells, they are probably caused by some phenomenon other than windblown trees. The fact that a v-3 power-law spectrum at low Doppler frequencies typically results from poor stability in a radar (in particular, the oscillator) might suggest possible equipment limitations. Simkins, Vannicola, and Ryan [17] discuss efforts to quantify the spectral contamination contributed by their measurement instrumentation, including spreading of observed spectra due to oscillator instability. Further assurance that the heavily-wooded-valley data were indeed of external origin and important consequence would be provided if they could be confirmed through routine replication in independent measurements. In any event, whether internally or externally caused, these high Doppler-velocity heavily-wooded-valley data should not be misconstrued as generally representative of clutter spectra from windblown trees. The further extrapolation of these heavily-wooded-valley data as an upper bound, v-3 constant power-law dependency to levels significantly below –40 dB (e.g., to Doppler velocities of 30 m/s, 60 dB down), while retaining their general association with windblown trees, is highly unrealistic on the basis of the LCE and Phase One measurements.

Windblown Clutter Spectral Measurements 669

6.6.3.5 Goldstein’s Spectral Measurements in Gale Winds Goldstein [9] describes three measurements in “gale winds or higher.”37 The actual maximum Doppler velocities to which spectral power was measured in these results are low (≤ 1 m/s), but the corresponding power levels are very high. The first two measurements were at X- and K-bands for which the power spectra are shown much as originally plotted in Figure 6.57 on linear scales of normalized spectral power density (0 to 1) vs Doppler velocity. The two spectra are quite similar; both are typical bell curves. The X-band spectrum is slightly wider than the K-band spectrum. At 0.5 m/s, the power levels in those spectra are 0.36 (–4.4 dB) and 0.28 (–5.5 dB) for X- and K-bands, respectively. At higher Doppler velocities, power levels in these bell-curve spectra diminish: at 0.85 m/s, the Kband curve is shown to reach zero power (–∞ dB); and at 1 m/s the X-band curve is at power level = 0.04 (–14 dB), this latter point being the maximum Doppler velocity provided in Goldstein’s gale force spectral results. This point is nearly equivalent to corresponding points provided by the exponential spectral model of Section 6.2 for gale force winds at 1 m/s (i.e., –15.4 and –13.7 dB for β = 4.3 and 3.8, respectively; see Section 6.2). 1.0

Relative Power k (Linear Scale)

0.8

0.6 X-Band 0.4

0.2

K-Band

0 0

0.2

0.4

0.6

0.8

1.0

Doppler Velocity v (m/s) Heavily Wooded Terrain “Gale Winds” [9] X-Band ( λ = 3.2 cm) and K-Band ( λ = 1.25 cm)

Figure 6.57 Measurements of radar ground clutter power spectra by Goldstein under gale winds. (After Goldstein [9]; by permission, The McGraw-Hill Companies, Inc.)

37. The Beaufort scale of wind velocities covers 13 Beaufort force numbers [from (0) Calm and (1) Light air to (12) Hurricane], including the following “gale force” numbers: (7) Moderate gale, winds from 32 to 38 mph; (8) Fresh gale, 39 to 46 mph winds; (9) Strong gale, 47 to 54 mph winds; and (10) Whole gale, 55 to 63 mph winds.

670 Windblown Clutter Spectral Measurements

Goldstein’s third measurement was at S-band in “winds of whole gale force.” This spectrum, reported by Goldstein to be of “strange shape” and “markedly out of line with the others” [9], was not shown, although three measured points38 were provided, viz., –1 dB at 0.1 m/s, –3 dB at 0.2 m/s, and –10 dB at 0.7 m/s. However, the autocorrelation function for this measurement was provided by Goldstein and shows a long, slowly diminishing tail plotted on linear scales. Subsequently, Wong, Reed, and Kaprielian [29] computed a corresponding power spectrum as the Fourier transform of a theoretical autocorrelation function incorporating scatterer rotational motion that was a very close match to Goldstein’s unusual experimental autocorrelation function. Wong, Reed, and Kaprielian’s computed spectrum is reproduced in Figure 6.58 together with the three actual spectral points specified by Goldstein. The computed spectrum shows a long, slowly diminishing tail. Initially, it rapidly drops to power level = 0.2 (–7 dB) at 0.5 m/s, and thereafter slowly diminishes at a rate approximated by a power law of n = 3.3 1.0

Relative Power k (Linear Scale)

0.8

0.6

0.4

0.2

0 0

0.5

1

1.5

2.0

Doppler Velocity v (m/s) Goldstein's Three Measured Points Wooded Terrain “Winds of Whole Gale Force” [9] S-Band ( λ = 9.2 cm)

Figure 6.58 A radar ground clutter power spectrum computed from Goldstein’s measured correlation function by Wong, Reed, and Kaprielian showing a long spectral tail under winds of whole gale force. (Computed spectrum (solid curve) after [29]; by permission, © 1967 IEEE. Three plotted points from Table 6.8 in Goldstein [9]; by permission, The McGraw-Hill Companies, Inc.)

38. Labelled as occurring at wind speed of 50 mph in Goldstein’s Table 6.8 [9].

Windblown Clutter Spectral Measurements 671

to power level = 0.02 (–17 dB) at 2 m/s. In comparison, at 2 m/s the widest measured LCE spectrum is at –53 dB. In discussing these curves of correlation function and power spectrum, Wong, Reed, and Kaprielian noted that they “deviate significantly from the usual expected Gaussian shape. Instead, they drop very slowly toward zero” [29]. Thus these data have contributed to the concept of a long spectral tail, here at an usually high power level. Some reservations must be accorded to Goldstein’s results, due to their very early origin. Goldstein was attempting to establish only the most basic general characteristics and, indeed, just the very existence of spectral spreading of ground clutter in these early results. Conversion of values from near the limits of Goldstein’s plots on linear scales to decibel quantities for comparison with modern measurements to much lower power levels where the concern is with detailed behavior of spectral tails is using Goldstein’s data out of historical context. In particular, Goldstein’s unusual S-band gale force data and their further elaboration by Wong, Reed, and Kaprielian [29] now appear to be best regarded as an anomalous occurrence in an isolated measurement. No modern measurements of windblown tree clutter spectra under gale force winds are known to exist.

6.6.3.6 Armand’s Long, Low-Level Clutter Spectral Tail Armand et al. [14] ostensibly measured X-band clutter spectra from windblown trees to very low levels of spectral power (–120 dB) and correspondingly very high Doppler velocities (20 m/s). Their results are reproduced in Figure 6.59. Armand et al. stated that these ground clutter spectra were measured with CW equipment in which the power received from the sidelobes of the transmitter was an order of magnitude higher than that reflected from the trees. Instabilities were reported to be eliminated through use of klystrons stabilized by cooling with liquid helium. Results were obtained in the 40- to 2,500- Hz Doppler frequency band (i.e., not near the carrier). Spectral results are shown for three wind speeds—4, 13, and 31 mph—over the range from 40 to ∼ 1,300 Hz (0.6 to ∼ 20 m/s). Over this range, the spectral power density levels are between –50 and –120 dB (i.e., are much lower than any other known spectral measurements). For the 4-mph spectrum, the power drops to –120 dB at 2.5 m/s, and thereafter stays at ∼ –120 dB all the way out to 20 m/s (i.e., exhibits a long spectral tail at a uniform low level, like White’s [39] conceptual wideband noise-like spectral component). The 13- and 31-mph spectra drop gradually from –63 and –52 dB, respectively, at 0.6 m/s to ∼ –115 dB at 20 m/s. At power levels 80 dB down, Doppler velocities in the Armand et al. results of Figure 6.59 are ∼ 0.9, 1.4, and 2.5 m/s for 4-, 13-, and 31-mph winds, respectively; these spectral widths are a very close match to those measured by Phase One and LCE at similar levels of spectral power (i.e., near their limits of sensitivity). Armand et al. [14] claimed that their spectral shapes were power-law, with an average value of power-law exponent n = 3 in the 110- to 2,500-Hz band averaged over all tests and with n varying inversely with wind velocity between 3 and 6 in the 40- to 110-Hz band. The authenticity of these very long, very low-level clutter spectral tails is open to question; what was measured may have been effects of sidelobes, internal system instabilities, etc. Before undue credibility is ascribed to these results, they need to be confirmed by independent and consistent replication using modern measurement instrumentation. However, these results arguably keep open the possibility of long spectral tails at very low power levels below Phase One and LCE sensitivities. As previously discussed, spectral power at large Doppler velocities is theoretically accounted for by Armand et al. through amplitude modulation via

672 Windblown Clutter Spectral Measurements

(a) Wind Speed = 4 mph

–90 –100

Relative Power k (dB)

–110

(b) Wind Speed = 13 mph

–70 –80 –90 –100 –110

–60 –70

(c) Wind Speed = 31 mph

–80 –90 –100 0.6

1.2

2.4

4.8

9.6

19.2

Doppler Velocity v (m/s) Wooded Area (Leaves on Trees) X-Band (λ = 3 cm)

Figure 6.59 Measurements of radar ground clutter spectra by Armand et al. of the Russian Academy of Sciences showing very long, low-level spectral tails. After [14], 1975.

leaf rotation and shadowing of one leaf by another, in addition to phase modulation caused by leaf oscillatory motion in the direction of the radar. Note that the Russian spectral measurements [15, 16] that followed those of Armand et al. [14] were performed specifically to obtain information close to the carrier. Although the Phase One and LCE results do not agree with this series of Russian results [13–16] in their assessments of spectral shape as power-law, none of these Russian measurements show inordinately wide spectra over the ranges of spectral power measured by the Phase One and LCE instruments.

6.6.3.7 Instrumentation and Processing Effects Internal effects from the measurement radar often have contaminated and corrupted attempted measurements of clutter frequency spectra to low spectral power levels. The fact that the shape of the spectrum resulting from oscillator instability is an n = 3 power law can raise suspicion of measured clutter spectra with n = 3 power-law characteristics. For example, the Simkins et al. [17] heavily-wooded-valley data of unusually wide spectral extent follow an n = 3 power-law shape, as do the Armand et al. [14] data at very low power levels (70 to 120 dB down) and high Doppler velocities (1.65 to 37.5 m/s). Care must be taken to isolate and avoid spectral contamination from system instabilities. Quantification of spectral contamination is required for every measurement at the actual range at which the clutter measurement is performed, since instability of the stable local oscillator (STALO) produces a greater effect at longer ranges (the phase has more time to

Windblown Clutter Spectral Measurements 673

change when the STALO is used to upconvert on transmit and downconvert on receive). If the STALO is not used on receive, but the signal is merely envelope-detected prior to spectral analysis (as in the results of Goldstein [9] and Fishbein et al. [10]), the full STALO instability spectrum or that of the transmitter is impressed on the received clutter signal. Goldstein’s [9] early measurements were undoubtedly made using a klystron or magnetron as the transmitter, resulting in relatively poor stability. In the Armand et al. [14] results, transitions are observable in the spectral data at low power levels (at 1.5 m/s Doppler velocity for 4-mph wind speed, and at 2.4 m/s Doppler velocity for 13-mph wind speed). For Doppler velocities greater than those of these transition points, it is conceivable that the data result from system instabilities. Note that the results of Armand et al. were obtained using a CW transmitter; use of pulsed radar can introduce additional instability due to noise contamination of trigger pulses. Nonlinearities in circuitry or processing (e.g., lin-limit amplifier) can also limit and spread the frequency spectrum, especially under strong signal (strong clutter) conditions. Data in saturation result in significant spectral spreading caused by the actual spectrum convolving with itself in such circumstances. Discounting this possibility for the stationary false alarm cells underlying the Simkins et al. heavily-wooded-valley data is the reported fact that spectra from adjacent non-false alarm cells of similar intensity were narrower. Unwanted antenna motion caused mechanically, and/or by the wind, can also spread the frequency spectrum by modulating the clutter signal. This modulation may go unobserved if stability testing is performed in low-wind conditions. A few cases of long spectral tails extending to Doppler velocities >> 3 m/s were observed during the course of examining the Phase One database of spectral measurements. In every case, the long spectral tail was isolated to some sort of instrumentation problem (e.g., sticking bits on the A/D converter generating minute sample-and-hold stairsteps on the temporal signal, occasional saturations, external interference). One excessively wide Phase One spectral measurement caused by undetected saturation was inadvertently included in a set of “windy” spectra in a previous publication (spectrum 4, Figure 6.9, in [21]). Thus any unusually wide measured spectra should always be very carefully examined in the time domain before accepting the wide frequency domain result. Attempts to improve Phase One stability by sampling the transmitted signal and correcting (i.e., subtracting) transmitted phase variations in the received signal were unsuccessful (i.e., proved to be not simple to implement). The LCE radar was a spectrally purer system than the Phase One radar and was never observed to generate an excessively wide spectral tail due to system or processing contamination. A number of windblown clutter spectral measurements by other investigators reviewed from time to time by the author have at first contained obviously corrupted clutter spectral tails of excessive width and extremely slow (e.g., n ≅ 3) decay; subsequent investigation has always found these long spectral tails to be caused by errors in instrumentation or processing. In considering all the possible ways in which instrumentation limitations or processing errors can broaden measured clutter spectra, it is well to bear in mind that of two measured spectra—one narrow and one wide—ostensibly characterizing the same clutter phenomenon, the narrower spectrum is always more credible since all corruptive influences due to instrumentation limitations or processing errors can only broaden the spectrum, not narrow it. Because of all the potential uncertainties (i.e., potential contaminants of internal and external origin) in radar ground clutter spectral measurements as exemplified in the

674 Windblown Clutter Spectral Measurements

preceding discussions of Section 6.6.3, the use of such data requires the exercise of judgment. Ground clutter spectral models should reflect, for the most part, central repeatable trends in measured data, not unusual or isolated artifacts or aberrations.

6.7 Summary Accurate characterization of radar ground clutter spectral shape is important in radar technology applications in which target signals compete with strong ground clutter returns. Ground clutter spectral spreading can limit the performance of MTI/Doppler processors, including both conventional one-dimensional fixed-parameter designs [1, 2] and modern two-dimensional displaced phase-centered antenna or space-time adaptive techniques [3–5] for detecting and tracking moving targets in clutter backgrounds. Internal clutter motion can also cause defocusing in SAR processing [62] and indeed can degrade any radar processing technique that assumes the clutter to be stationary. Such reasons provide motivation to obtain a proper understanding of clutter spectral spreading and to obtain an accurate characterization of the shapes of clutter spectra to very low levels of spectral power. Historically, the state of knowledge of windblown ground clutter spectral shape has been rather poor, and considerable disagreement has existed concerning the extent to which Doppler spreading occurs in such spectra. Lincoln Laboratory measurement data indicate that ground clutter power spectra over spectral dynamic ranges reaching 60 to 80 dB below the zero-Doppler peaks are relatively narrow and reasonably characterized as of exponential shape. First observation of exponential spectral decay in the clutter studies discussed herein occurred in the early examination of windblown foliage clutter spectra obtained with the Phase One clutter measurement radar at western Canadian sites. These first observations of exponential decay remained valid in the general representation of a much more complete set of L-band spectral measurements over various regimes of wind speed obtained with the Phase One radar at the Lincoln Laboratory measurement site of Katahdin Hill in eastern Massachusetts [21]. Exponential decay was also concluded to be the best overall characterization of windblown ground clutter spectral shape covering Phase One measurements at other frequencies (i.e., VHF, UHF, S-, and X-bands), from other sites, and over several thousand spectral observations taken from the extensive L-band database of clutter spectral measurements subsequently obtained with the LCE clutter measurement radar [25]. The LCE radar was a major L-band-only upgrade of the five-frequency Phase One radar with new, much improved receiver and data recording units, lower phase noise levels, and very clean and reliable spectral response. Analyses of Phase One clutter data in Canada [22, 23] and in the U. K. [24] also concluded that ground clutter spectra were generally best-fitted with exponential shapes. On the basis of the Phase One and LCE clutter data, two different first-principles theoretical models [39, 60] were independently developed for the windblown clutter Doppler spectrum that, although mathematically complex, in both cases provide close to exponential decay under numerical evaluation. Other previous references to exponential (or quasi- or partially-exponential) clutter spectral decay exist in a much earlier Lincoln Laboratory measurement program [59] of the 1970s, and in Russian measurements [13–16] and French measurements [38] of the same early time period.

Windblown Clutter Spectral Measurements 675

The very earliest indications were that windblown ground clutter spectra were of Gaussian spectral shape [6–9]. Many subsequent measurements to lower power levels 30 to 40 dB below the peak zero-Doppler level indicated spectral shapes that were significantly wider than Gaussian in their tails and that appeared to be well approximated with power-law functions [10–20]. The Phase One and LCE ground clutter spectral measurements, over such limited spectral dynamic ranges, also can be adequately modeled as of power-law shapes. However, the Phase One and LCE measurement data also clearly indicate that the power-law rates of decay at upper levels of spectral power do not continue to lower levels of spectral power reaching 60 to 80 dB down from the zero-Doppler peak. The measured power-law rates of decay at lower power levels are always much faster than at the upper levels. An exponential representation generally captures, at least approximately and occasionally highly accurately, the major attributes of the windblown clutter ac spectral shape function over the entire range from near the zero-Doppler peak to measured levels 60 to 80 dB down. In contrast, the windblown clutter ac spectral shape is not at all representable by any power law over such a wide spectral dynamic range. The maximum Phase One- and LCEmeasured Doppler velocity spectral extents from windblown foliage at levels 60 to 80 dB down are ≈3 to 4 m/s. Power-law models can extrapolate data of 40-dB spectral dynamic range to spectral extent as great as 30 m/s, 60 dB down. Such extreme windblown foliage spectral extents have never been corroborated by any results in the extensive Phase One and LCE databases of windblown clutter spectral measurements. Chapter 6 provides a new empirical model for windblown ground clutter Doppler spectra based on many clutter spectral measurements obtained with the Lincoln Laboratory LCE and Phase One five-frequency (VHF, UHF, L-, S-, and X-band) radars. This model is complete, including both ac and dc components of the spectrum. The important parameters incorporated in the model are wind speed and radar carrier frequency. Ac spectral shape is specified as exponential, with the Doppler-velocity exponential shape factor strongly dependent on wind speed but independent of radar frequency, VHF to X-band. The fact that ac spectral spreading occurs at VHF in windblown clutter Doppler-velocity spectra more or less equivalently as at X-band is illustrated through representative measurement results; many other examples of VHF-measured clutter spectra with similar spectral spreading exist in the Phase One and LCE databases. The major difference between VHF and X-band clutter spectra is that a much larger dc spectral component exists at VHF compared with X-band. The ratio of dc to ac spectral power in the model is determined by an analytic expression empirically derived from the measurements that captures the strong dependencies of dc/ac ratio on both wind speed and radar frequency. Chapter 6 includes both a complete specification of the clutter spectral model and a thorough comparison of model predictions with many examples of measured windblown clutter spectra under various combinations of radar parameters and measurement circumstances. Besides wind speed and radar frequency, other parameters that might be thought to significantly influence clutter spectra, but that appear to be largely subsumed within general ranges of statistical variability in the measurement data, include tree species, season of the year, wind direction, cell size, polarization, range, and grazing angle. The exponential model is explicitly derived to be applicable to windblown trees, but examples are also provided of measured clutter spectra from scrub desert, cropland, and rangeland that indicate the model can also perform adequately for other windblown vegetation types by suitably adjusting its dc/ac term.

676 Windblown Clutter Spectral Measurements

Although it is now generally accepted that radar ground clutter spectral shapes are wider than Gaussian in their tails, the simple Gaussian continues to be how clutter spectra are usually represented in radar system engineering (at least as a method of first approach in representing effects of intrinsic clutter motion) because of its simplicity and analytic tractability. The Gaussian spectral shape is theoretically generated by a group of moving scatterers, each of random translational drift velocity [19]. Theory also suggests that the origin of the increased spreading observed in measured ground clutter spectra beyond that predicted by Gaussian is largely due to the random oscillatory motion of leaves and branches, in contrast to simple random translational motion [19, 29, 42]. Like the Gaussian spectral shape, the exponential spectral shape is also simple and analytically tractable and has the advantage of being wider than Gaussian as required by experiment and supported by theory. There is no underlying fundamental physical principle requiring clutter spectra to be precisely of exponential shape. Many of the Phase One and LCE clutter spectral measurements, particularly many of the narrower spectra occurring at lower wind speeds, are less exponential overall than some of the wider measured spectra. To be clear on this matter, almost none of the Phase One- and LCE-measured clutter spectra can be accurately represented by any single simple analytic function, including exponential [31], over their complete spectral dynamic ranges, from the point of view of passing rigorous statistical hypothesis tests. Use of the exponential shape in Chapter 6 is as a convenient analytic bounding envelope that empirically approximates, occasionally very accurately, many of the LCE and Phase One measurements over most of their spectral dynamic ranges, including the lowest power levels measured. The resulting model overcomes much of the difficulty in modeling clutter spectra not only by using exponential shapes, but also by introducing the concept of a quasi-dc region and absorbing the excess power measured in the quasi-dc region into the dc delta function term of the model. This approach allows the model the flexibility of using the exponential representation to optimally match the measured spectral spreading in the spectral tail regions without regard to the narrow nearzero-Doppler quasi-dc region, which often displays a different rate of decay than occurs in the broad spectral tail [31]. In addition to showing that measured shapes of windblown ground clutter Doppler spectra appear to be much more closely matched by an exponential approximation than by Gaussian (too narrow) or power-law (too wide) approximations, Chapter 6 also investigates the impact of assigning the correct clutter spectral shape on MTI and STAP coherent target detection. Compared to the exponential shape, the Gaussian shape substantially underpredicts the effects of clutter on detection, and the power-law shape substantially overpredicts the effects of clutter on detection. The exponential spectral model for windblown foliage is validated by showing that the differences in clutter improvement factor performance prediction between using actual measured I/Q data as input to the clutter canceller, and modeled clutter data of Gaussian, exponential, or power-law spectral shape, are minimized when the spectral model employed is of exponential shape. It is evident on the basis of the Phase One and LCE measurements that the current state of knowledge regarding the extent of spectral spreading in windblown ground clutter has been advanced to the point where it is relatively incontrovertible that clutter spectra from windblown vegetation, although wider than Gaussian, are still generally relatively narrow and spread to Doppler velocities < ≈3 or 4 m/s over spectral power levels reaching to 80 dB below zero-Doppler peaks for wind speeds in the 15- to 30-mph range. Investigators

Windblown Clutter Spectral Measurements 677

who may wish to continue to argue for much wider clutter spectra from windblown foliage over such ranges are faced with proving spectral purity in their wider measurements, since unknown corruptive instrumentation or processing effects can only widen spectra, not narrow them. Presumably, most of the spectral spreading that occurs in the Phase One and LCE data is caused by the velocity distribution (translational and/or oscillatory) of the foliage, that is, by the radial motion of individual scatterers (leaves and branches) toward and away from the radar causing phase modulation in the returned signal. To whatever extent other effects are also at work in the Phase One and LCE data, such as leaf rotation or the shadowing of one leaf by another causing more complex amplitude modulation effects, such effects are also constrained to cause limited spreading to levels 80 dB down. Chapter 6 also provides a relatively thorough review of the available literature of clutter spectral measurements, which generally brings it and the Phase One and LCE results into conformity and agreement. There remain hints in the literature, however, not only from theoretical reasoning but also in various poorly substantiated measurement results, of long spectral tails existing in ground clutter data to Doppler velocities greatly exceeding the maximum ≈3 to 4 m/s observed in the Phase One and LCE data. Arguments for the existence of such wide tails often are based on postulated leaf-rotation and leaf-shadowing effects. Such long tails have never been observed, whether as slowly decaying power laws or as uniform-amplitude wideband noise-like components, in any of the several thousand spectra that have been examined from the extensive Phase One and LCE databases of ground clutter spectral measurements to levels reaching 60 to 80 dB below zero-Doppler peaks. What might occur at lower levels remains conjectural.

References 1.

M. I. Skolnik, Introduction to Radar Systems, 3rd ed., New York: McGraw-Hill (2001).

2.

J. A. Scheer and J. L. Kurtz (eds.), Coherent Radar Performance Estimation, Boston, MA: Artech House, Inc. (1993).

3.

R. Klemm, Space-Time Adaptive Processing: Principles and Applications, IEE Press, Radar, Sonar, Navigation and Avionics Series, 1999.

4.

J. Ward, “Space-Time Adaptive Processing for Airborne Radar,” Lexington, MA: MIT Lincoln Laboratory, Technical Rep. 1015 (13 December 1994), DTIC ADA293032.

5.

P. Richardson, “Relationships between DPCA and adaptive space-time processing techniques for clutter suppression,” Proc. International Conf. Radar, SEE 48 rue de la Procession, 75724 Paris Cedex 15 (May 1994), pp. 295–300.

6.

L. N. Ridenour (ed.), Radar System Engineering, Vol. 1 in the MIT Radiation Laboratory Series, New York: McGraw-Hill (1947). Reprinted, Dover Publications (1965).

7.

E. J. Barlow, “Doppler Radar,” Proc. IRE 37, 4 (1949).

8.

J. L. Lawson and G. E. Uhlenbeck (eds.), Threshold Signals, Vol. 24 in the MIT Radiation Laboratory Series, New York: McGraw-Hill (1950).

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9.

H. Goldstein, “The Fluctuations of Clutter Echoes,” pp. 550–587, in D. E. Kerr (ed.), Propagation of Short Radio Waves, Vol. 13 in the MIT Radiation Laboratory Series, New York: McGraw-Hill (1951).

10. W. Fishbein, S. W. Graveline, and O. E. Rittenbach. “Clutter Attenuation Analysis,” Fort Monmouth, NJ: U.S. Army Electronics Command, Technical Rep. ECOM-2808 (March 1967). Reprinted in MTI Radar, D.C. Schleher (ed.), Boston, MA: Artech House, Inc. (1978). 11. M. P. Warden and B. A. Wyndham, “A Study of Ground Clutter Using a 10-cm Surveillance Radar,” Royal Radar Establishment, Technical Note No. 745, Malvern, U. K. (1969). DTIC AD 704874. 12. N. C. Currie, F. B. Dyer, and R. D. Hayes, “Radar Land Clutter Measurements at Frequencies of 9.5, 16, 35, and 95 GHz,” Engineering Experiment Station, Georgia Institute of Technology, Technical Report No. 3, United States Army, Contract DAAA-25-73-C-0256, April 1975. DTIC AD-A012709. 13. V. A. Kapitanov, V. Mel’nichuk, and A. A. Chernikov, “Spectra of radar signals reflected from forests at centimeter waves,” Radio Eng. and Electron. Phys., 18, 9 (1973). 14. N. A. Armand, V. A. Dyakin, I. N. Kibardina, A. G. Pavel’ev, and V. D. Shuba, “The change in the spectrum of a monochromatic wave when reflected from moving scatterers,” Radio Eng. and Electron. Phys., 20, 7 (1975). 15. V. A. Andrianov, I. S. Bondarenko, I. N. Kibardina, V. K. Prosshin, and D. Y. Shtern, “Characteristics of measurement of spectra of radio signals scattered by an underlying surface,” Radio Eng. and Electron. Phys., 21, 2 (1976). 16. V. A. Andrianov, N. A. Armand, and I. M. Kibardina, “Scattering of radio waves by an underlying surface covered with vegetation,” Radio Eng. and Electron. Phys., 21, 9 (1976). 17. W. L. Simkins, V. C. Vannicola, and J. P. Ryan, “Seek Igloo Radar Clutter Study,” Rome Air Development Center, Technical Rep. RADC-TR-77-338 (October 1977). Updated in FAA-E-2763b Specification, Appendix A (May 1988). See also FAA-E2763a (September 1987), FAA-E-2763 (January 1986, July 1985). 18. J. Jiankang, Z. Zhongzhi, and S. Zhong, “Backscattering power spectrum for randomly moving vegetation,” Proc. IGARSS Symposium, Zurich (August 1986), pp. 1129–1132. 19. N. J. Li, “A study of land clutter spectrum,” Proc. 1989 International Symp. on Noise and Clutter Rejection in Radars and Imaging Sensors, T. Suzuki, H. Ogura, and S. Fujimura (eds.), IEICE, Kyoto (1989), pp. 48–53. 20. G. W. Ewell, private communication (December 1995). 21. J. B. Billingsley and J. F. Larrabee, “Measured Spectral Extent of L- and X-Band Radar Reflections from Windblown Trees,” Lexington, MA: MIT Lincoln Laboratory, Project Rep. CMT-57 (6 February 1987), DTIC AD-A179942. 22. H. C. Chan, “Spectral Characteristics of Low-Angle Radar Ground Clutter,” Ottawa, Canada: Defence Research Establishment Ottawa, Report No. 1020 (December 1989), DTIC AD-A220817.

Windblown Clutter Spectral Measurements 679

23. H. C. Chan, “Radar ground clutter measurements and models, part 2: Spectral characteristics and temporal statistics,” AGARD Conf. Proc. Target and Clutter Scattering and Their Effects on Military Radar Performance, Ottawa, AGARD-CP501 (1991), AD-P006374. 24. G. C. Sarno, “A model of coherent radar land backscatter,” AGARD Conf. Proc. Target and Clutter Scattering and Their Effects on Military Radar Performance, Ottawa, AGARD-CP-501 (1991), AD-P006375. 25. J. B. Billingsley, “Exponential Decay in Windblown Radar Ground Clutter Doppler Spectra: Multifrequency Measurements and Model,” Lexington, MA: MIT Lincoln Laboratory, Technical Report 997, 29 July 1996; DTIC AD-A312399. 26. J. B. Billingsley, “Windblown radar ground clutter Doppler spectra: measurements and model,” submitted to IEEE Trans. AES, May 2000, accepted subject to minor revision, October 2000. 27. M. W. Long, Radar Reflectivity of Land and Sea, 3rd ed., Boston: Artech House, Inc. (2001). 28. F. E. Nathanson, Radar Design Principles, 2nd ed., New York: McGraw-Hill (1991). Reprinted, SciTech Publishing, Inc., 1999. 29. J. L. Wong, I. S. Reed, and Z. A. Kaprielian, “A model for the radar echo from a random collection of rotating dipole scatterers,” IEEE Trans. AES 3, 2 (1967). 30. M. V. Greco, F. Gini, A. Farina, and J. B. Billingsley, “Analysis of clutter cancellation in the presence of measured L-band radar ground clutter data,” in Proceedings of IEEE International Radar Conference (Radar 2000), Alexandria, VA, May 8–12, 2000. 31. M. V. Greco, F. Gini, A. Farina, and J. B. Billingsley, “Validation of windblown radar ground clutter spectral shape,” IEEE Trans. AES, vol. 37, no. 2, April 2001. 32. J. B. Billingsley, A. Farina, F. Gini, M. V. Greco, and P. Lombardo, “Impact of experimentally measured Doppler spectrum of ground clutter on MTI and STAP,” in Proceedings of IEE International Radar Conference (Radar ‘97), IEE Conf. Pub. No. 449, pp. 290-294, Edinburgh, 14–16 October 1997. 33. P. Lombardo, M. V. Greco, F. Gini, A. Farina, and J. B. Billingsley, “Impact of clutter spectra on radar performance prediction,” IEEE Trans. AES, vol. 37, no. 3, July 2001. 34. J. B. Billingsley and J. F. Larrabee, “Bragg Resonance in Measured L-band Radar Clutter Doppler Spectra from Inland Water,” Lexington, MA: MIT Lincoln Laboratory, Technical Rep. 1019 (1 August 1995), DTIC AD-A297680. 35. J. B. Billingsley, “Measurements of L-band inland-water surface-clutter Doppler spectra,” IEEE Trans AES, Vol. 34, No. 2, April 1998, pp. 378–390. 36. R. L. Ferranti, “Very low phase noise in a pulsed 10-kw L-band triode power amplifier,” Santa Clara, CA: Proc. RF Expo West, 59-66 (February 1991). 37. F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66, 51–83 (January 1978).

680 Windblown Clutter Spectral Measurements

38. R. Basard, “Vegetation clutter Doppler spectrum models,” International Conference on Radar, (Session II), Paris, pp. 28-31, 4–8 December 1978. 39. R. G. White, “A model for MTI radar clutter,” Proc. SEE Int. Radar Conf., Paris (May 1994), pp. 540–545. 40. R. M. Narayanan, D. W. Doerr, and D. C. Rundquist, “Temporal decorrelation of Xband backscatter from wind-influenced vegetation,” IEEE Trans. Aerosp. Electron. Syst. 28, 2 (1992), pp. 404–412. 41. R. M. Narayanan, S. E. Nelson, and J. P. Dalton, “Azimuthal scattering pattern of trees at X-band,” IEEE Trans. Aerosp. Electron. Syst. 29, 2 (1993), pp. 588–593. 42. R. M. Narayanan, D. W. Doerr, and D. C. Rundquist, “Power spectrum of windinfluenced vegetation backscatter at X-band,” IEE Proc.-Radar, Sonar Navig., 141, 2 (1994), pp. 125–131. 43. N. A. Stewart, “Use of crosspolar returns to enhance target detectability,” in J. Clarke (ed.), Advances in Radar Techniques, IEE Electromagnetic Wave Series 20, Peter Peregrinus, Ltd., London, U.K., 1985, pp. 449–454. 44. J. B. Billingsley and J. F. Larrabee, “Multifrequency Measurements of Radar Ground Clutter at 42 Sites,” Lexington, MA: MIT Lincoln Laboratory, Technical Rep. 916, Volumes 1, 2, 3 (15 November 1991), DTIC AD-A246710. 45. G. P. de Loor, A. A. Jurriens, and H. Gravesteijn, “The radar backscatter from selected agricultural crops,” IEEE Trans. on Geoscience Electronics, 12, 70–77 (April 1974). 46. E. J. Kelly, “An adaptive detection algorithm,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 22, No. 2, pp. 115–127, March 1986. 47. A. Farina, P. Lombardo, M. Pirri, “Non-linear space-time processing for airborne early warning radar,” IEE Proc. on Radar, Sonar and Navigation, Vol. 145, No. 1, pp. 9–18, February 1998. 48. R. Klemm, “Adaptive clutter suppression for airborne phased-array radars,” IEE Proceedings-F, Vol. 130, No. 1, pp. 125–132, February 1983. 49. S. Barbarossa and A. Farina, “Space-time-frequency processing of synthetic aperture radar signals,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 30, No. 2, pp. 341–358, April 1994. 50. D. K. Barton, Modern Radar System Analysis, Boston, MA: Artech House, Inc. (1988), p. 246. 51. A. Papoulis, The Fourier Integral and Its Applications, New York: McGraw-Hill (1962). 52. W. B. Davenport, Jr., and W. L. Root, An Introduction to the Theory of Random Signals and Noise, New York: McGraw-Hill (1958). 53. S. Goldman, Frequency Analysis, Modulation, and Noise, New York: McGraw-Hill (1948). Reprinted, Dover Publications (1967).

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54. F. G. Bass, P. V. Bliokh, and I. M. Fuks, “Statistical characteristics of a signal scattered from randomly moving reradiators on a plane section,” translated from Radiotechnika i Electronika (USSR), 10, 5 (May 1965), pp. 731–739. 55. S. Rosenbaum and L.W. Bowles, “Clutter return from vegetated areas,” IEEE Trans. Ant. Propag., AP-22, 2 (March 1974), pp. 227–236. 56. D. C. Schleher, MTI and Pulsed Doppler Radar, Norwood, MA: Artech House, 1991, p. 127. 57. J. A. Scheer, “Coherent Radar Performance Estimation,” IEEE National Radar Conference, Tutorial Notes, Atlanta (1994). 58. N. C. Currie and C. E. Brown, eds., Principles and Applications of Millimeter-Wave Radar, Norwood, MA: Artech House, Inc. (1987). 59. L. Cartledge, M. Labitt, J. H. Teele, and R. D. Yates, “An Experimental UHF Ground Surveillance Radar, Volume 2,” Lexington, MA: MIT Lincoln Laboratory, Technical Rep. 497 (12 October 1972), DTIC AD-757565. 60. P. Lombardo and J. B. Billingsley, “A new model for the Doppler spectrum of windblown radar ground clutter,” in Proceedings of 1999 IEEE Radar Conference, Boston, MA, 20-22 April 1999, pp. 142–147. 61. R. G. White, private communication (11 September 1995). 62. C. Elachi and D. D. Evans “Effects of random phase changes on the formation of synthetic aperture radar imagery,” IEEE Trans. on Antennas and Propagation, Vol. AP-25, No. 1, pp. 149–153, January 1977.

118 Appendix 2.A Phase Zero Radar

Appendix 2.A Phase Zero Radar 2.A.1 Phase Zero Radar The Phase Zero clutter measurement radar was based on an X-band commercial marine navigation radar—the Raytheon Mariners Pathfinder Model 1650/9XR. This radar was acquired and installed in an all-wheel drive, one-ton truck. The truck was equipped with a 50-ft pneumatically extendable antenna mast and self-contained prime power. An onboard clutter data digital recording capability was implemented under computer control. The resultant clutter measurement instrument was referred to as Phase Zero. The Phase Zero instrument made measurements at 106 sites widely distributed over the North American continent. The schedule of Phase Zero ground clutter measurements is shown in Table 2.A.1. A simple schematic diagram of the Phase Zero radar is shown in Figure 2.A.1. The salient system parameters of this radar are displayed in Table 2.A.2. A precision IF attenuator was installed in the Phase Zero receiver to measure clutter strength by recording sequential 360° azimuth scans in stepped levels of IF attenuation. Clutter strength was determined from these data subsequently using thresholding techniques. This procedure was facilitated by the fact that the large, 16-inch diameter, primary PPI display unit of the radar was digitally driven. For each attenuator setting, each pixel in the PPI display was either lit (i.e., above the minimum detectable signal) or unlit (i.e., below the minimum detectable signal). The lit/ unlit state of each pixel was set by determining if the corresponding signal strength exceeded a threshold (i.e., single bit A/D converter). The results of this thresholding process for all 320 range gates in each range sweep of the radar were stored as ones and zeros in its binary buffer unit. Hence the binary buffer unit controlling the contents of the PPI could be unloaded onto tape to provide a direct digital record of each scan of data. This entire scheme was brought under control of a minicomputer which was installed in the box of the Phase Zero truck. In this manner a digital record of a PPI stack of azimuth scans in stepped levels of attenuation (usually about 45 or 50 dB in 1-dB steps) was obtained at each site. These raw data were later processed at Lincoln Laboratory to provide calibrated clutter data.

Phase Zero Experiment Set. The Phase Zero data set collected at each site is shown in Table 2.A.3. The radar operated under mode control where the only parameter normally set by the operator was the maximum range. The maximum range was selected from the set indicated in the first column of Table 2.A.3 with a knob on the face of the PPI console. The underlying important parameters which changed with maximum range setting are indicated in the other columns of Table 2.A.3. Each maximum range setting is referred to as a Phase Zero experiment. At each measurement site, stepped attenuation data were recorded for the seven experiments shown in Table 2.A.3 (200 × 106 binary samples on two tape reels). The primary Phase Zero 2,177 patch file of modeling information involved clutter patches selected from the nominal 6 nmi (11.76 km) maximum range experiment.

Appendix 2.A Phase Zero Radar 119

Table 2.A.1 Summary Schedule of Phase Zero Ground Clutter Measurements No. of Sites Measured Measurement Sequence

Active Measurement Period

Location

Duration (days)

Analog Data Only

Digital First

Repeated

Year 1 Autumn

12 Oct - 29 Oct

N. Dak., Man., Sask., Alta.

18

Year 2 Winter/ Spring/ Summer

18 Feb - 11 Mar 2 Apr - 14 Apr 13 May - 7 Jun 8 Jul - 12 Jul 30 Jul - 2 Aug 11 Dec - 16 Dec

Man., Sask. Sask., Alta. Alta., N.W.T. Alta. Nev. N. Mex.

23 13 26 5 4 6

Year 3 Spring/ Summer

14 May - 4 Jun 9 Jun - 27 Jun

Mass. Mass., Vt., N.Y., Ont., Penna., Mich., Iowa, Wisc., N. Dak., Man. Man., Sask., Alta., N.W.T.

2 19

1 18

1 2

12

12

1

12

8

4

4 15

1

2 14

25 Jul - 5 Aug

Year 4 Summer/ Autumn

26 Jun - 7 Jul

Nev., Utah, Wyo., Mont., N. Dak., Man., Sask. 28 Jul - 31 Jul Alta. 27 Oct - 14 Nov Alta., Sask., Man.

20

1

23 13 18 6 1 1

Year 5 Summer/ Autumn

10 Aug Alta. 16 Nov - 20 Nov Sask., Alta.

1 5

1 3

Year 6 Summer/ Autumn

23 Jun 30 Oct

1 1

1 1

Utah Mass.

Totals

102*

30

* No digital data at 4 sites.

2.A.2 Phase Zero Calibration Angle Calibration. Phase Zero angle calibration was performed as follows. At each attenuation level, 14 angular sectors of data were recorded, each consisting of 128 radials, with 320 range gates recorded per radial. Each radial corresponds to one recorded pulse repetition interval (PRI) of the radar. The nominal rate at which pulses were recorded is 450 pulses per second in all operating modes. A sector is 30° wide; 14 sectors cover 420°. The angle interval per radial (or per pulse) is thus 0.2344°. The end of an azimuth sweep provided about 60° of data which overlapped with and repeated the beginning of an azimuth sweep. Correlation procedures were used in the overlap region to determine the exact radial where the data started to repeat (i.e., corresponding to 360° azimuth). This radial varied slightly from site to site, experiment to experiment, and azimuth sweep to azimuth sweep due to wind loads on the antenna, power loads on the generator, etc.

120 Appendix 2.A Phase Zero Radar

Rotary Joint Antenna 20-dB Coupler

Varian 620/L-100 Minicomputer

Calibrated Source

Transmitter

PPI

TR Switch

Mixer

L.O.

Mode Control Adjustable IF Attenuator Bandpass Amplifier Detector Camera

Binary Threshold Determination PPI Binary Buffer

Figure 2.A.1

A-Scope

Phase Zero radar schematic.

In early calibration techniques, angle calibration was done once per experiment on a single azimuth sweep in the PPI stack. Later, in improved techniques, every sweep in the stack was calibrated, and in addition, angle information recorded from shaft encoders at the beginning of each sector was used to reduce variations within a sweep and ensure uniform initial alignment from sweep to sweep. An indication of the improvement in data quality that resulted is illustrated in Figure 2.A.2. This figure gives a sectional view into the raw PPI stack. Thus it shows 50 levels of attenuation vs 320 range gates for a given radial. It is at the resolution of the data; a black dot indicates an above-threshold (or lit) sample, the absence of a black dot indicates a below-threshold (or unlit) sample. The data shown at the top are unaligned. There are obvious anomalies in these data. The data at the bottom have been aligned through angle calibration processing. A clear improvement in data quality has been realized with the investment in processing.

Range Calibration. Experiments were conducted with the Phase Zero radar to determine the actual position in range from the radar of the 320 range gate positions in the receiver. Special range calibration experiments were conducted using oil drums deployed on flat terrain, and telephone poles, power pylons, and road markers along roads. In general it was determined that there was an initial, negative, 3 or 4 range gate positional bias (i.e., the radar position is in the 3rd or 4th range gate, see Table 2.A.3), with a subsequent gate sampling interval also as indicated in Table 2.A.3.

Appendix 2.A Phase Zero Radar 121

Table 2.A.2 Phase Zero Radar Parameters Transmitter Frequency Power

9375 + 30 MHz 50 kW peak; 45 W average

Operating Modes

Max Range (nmi)*

0.75, 1.5, 3

6, 12

24, 48

Pulsewidth ( s)

0.06

0.5

1

Transmit PRF (pps)

3600

1800

900

Receiver Type

Noncoherent (amplitude only)

Intermediate Frequency

45 MHz

IF Amplifier Bandwidth

24 MHz (0.06 s pulsewidth) 4 MHz (0.5, 1 s pulsewidth) 10 dB

Noise Figure

IF Attenuation (dB)**

F 4 = –45 dB at 10km (0.5 s pulsewidth) 0 to 50 in 1 dB steps

Recording** Record PRF (pps)

Digital recording of stepped attenuation PPI displays 450

Nominal Sensitivity

Antenna Type

9-ft, end fed, slotted array

Polarization Mast Height Scan

Horizontal 50 feet Continuous azimuth scan only (horizontal beam)

Rotation Beamwidth

17.6 rpm 0.9 Az; 23 El

Gain Sidelobes

32.5 dB below peak

32.5 dB

* Manually set by operator ** Computer controlled

Signal Strength Calibration. The method of thresholding in the PPI stack to determine signal strength is indicated in Figure 2.A.3. Experimentation with various thresholding algorithms led to a “top-down, 2-out-of-3” thresholding algorithm. In this algorithm, for each PPI pixel location, a sliding attenuation window 3-dB wide was first positioned at the maximum attenuation level (nominally 50 dB) and then allowed to move in 1-dB steps toward lower attenuations, with the threshold set at the first position where two of the three windowed levels became lit. Thresholding in a binary PPI stack of stepped levels of attenuation is essentially a slow A/D conversion process in which the clutter signal

122 Appendix 2.A Phase Zero Radar

Attenuation (dB)

50 40 30 20 10 0 0

50

100

150

200

250

300

250

300

Range Gate a) Before Alignment

Attenuation (dB)

50 40 30 20 10 0 0

50

100

150

200

Range Gate b) After Alignment

Figure 2.A.2 Angle alignment of the Phase Zero data. The data are from sector 11, radial 64 (i.e., 315° azimuth) of the 12-km maximum range experiment at Shilo, Manitoba. Compare with Figure 2.18.

varies temporally over the conversion period. The conversion period is determined by the following factors: 1.

The scan period for one azimuth rotation was about 3.4 s

2.

Every data-recording azimuth scan was followed by a buffer scan in which IF attenuation was switched

3.

Assembling the entire 50-dB stack of PPIs took about 6 minutes

4.

Data recording over several scans near the threshold level where scintillation has most effect in the binary result took about one-half minute

With the thresholded attenuation value in hand, computation of received signal strength followed from knowledge of the minimum detectable signal, which was measured and recorded by injection of a calibration RF test signal at the input to the Phase Zero receiver for each experiment. The calibration procedures incorporated correction in this process for gain compression in the IF amplifier. Received power was converted to clutter strength using a calibration equation.

Appendix 2.A Phase Zero Radar 123

Table 2.A.3 Phase Zero Experiment Set p PPI Nominal Maximum Range Setting* (nmi)

PPI Binary Buffer Unit** Actual Maximum Range (km)

Range Origin (range gate number)

Pulse Length

Sampling Interval (m)

(m)

( s)

9

0.06

75

0.5

150

1.0

0.75

1.47

4

4.6379

1.5

2.94

3

9.2758

3.

5.88

3

18.5515

6.

11.76

4

37.1030

12.

23.52

3

74.2061

24.

47.05

3

148.4121

48.

94.09

3

296.8243

* Manually set by operator. ** 320 range gates per pulse.

A calibration constant relating received signal strength to radar cross section was obtained through Phase Zero backscatter measurements from external test targets of known radar cross section. Determination of the calibration constant is challenging with a radar that always illuminates the ground (i.e., the elevation beams were not controllable but fixed horizontally for both the Phase Zero and Phase One systems). External calibration experiments sometimes involving balloon-borne spheres, and other times involving towermounted calibrated repeaters, were conducted in the Phase Zero program to determine the calibration factors. Two methods for minimizing competing ground clutter were developed for such experiments. The first involved deploying the target in a shadowed area behind a hill; in this case diffraction from the hilltop complicated data extraction. The second involved deploying the target in a smooth level area where forward scatter was enhanced and backscatter was minimal; in this case foreground terrain reflection and multipath complicated data extraction. Such external calibration tests were difficult to perform and interpret. However, perseverance with them eventually led to consistent and accurate calibrations across the entire Phase Zero data set. A flow chart illustrating the processing performed on the raw Phase Zero data tapes to generate calibrated clutter tapes is shown in Figure 2.A.4.

Elevation Pattern Gain Variation. For both the Phase Zero and Phase One radars, the backscatter from a clutter patch is measured at some angular position on the fixed elevation antenna pattern. Although this angle is usually small and usually within the oneway 3-dB points on the free-space elevation pattern, it is rigorously zero (i.e., on-boresight) only if the source of clutter backscatter is at the same elevation as the antenna phase center. Since this is seldom rigorously true, computations of clutter strength were corrected for elevation gain variations. To do this requires knowledge of the relative difference in terrain elevation between the radar and the clutter patch.

124 Appendix 2.A Phase Zero Radar

1. Raw Data 51 Binary (r, θ) PPI Maps

•

0 dB

1 dB

50 dB

2. Thresholding Process Establish threshold attenuation α for each (r, θ) sample cell

•

Binary Raw Data

Amplitude <1

1

2

3

4

48

49

50 >50

Binary Amplitude <1

1

2

3

α

4

48

49 50 >50

ATTn

Equivalent Step Function Thresholded ATTn Data

3. Calibrated Clutter Data Convert threshold attenuation α to σ°F4 for each (r, θ) sample cell

•

σ°F4 Single σ°F4 (r, θ) PPI Map

θ

Figure 2.A.3

Thresholding of the Phase Zero raw data.

This relative difference in mean height above sea level between the radar position and the clutter patch, as well as antenna mast height, range to the clutter patch, and the decrease in the effective elevation of the clutter patch due to a 4/3 radius spherical earth, were used to compute the off-axis angle on the elevation pattern at which the clutter measurement was made. The two-way gain adjustment due to this non-zero off-axis angle was accounted for in computation of absolute clutter strength. This off-axis angle, which is defined in a Cartesian coordinate system locally centered and horizontal at the antenna phase center, is different from the depression angle used in this book as a major parameter in clutter modeling. Depression angle is rigorously defined in a Cartesian coordinate system locally centered and horizontal at the terrain point from which backscatter is emanating. These two

Appendix 2.A Phase Zero Radar 125

Raw Tapes

Header Maintenance

Header Printout

1 Range Sweep, Unfiltered and Unaligned

Condition

Edited Raw Tapes Azimuth Filter

Angle Anomaly Search Stack Angle Alignment (Relative)

Range Anomaly Search Final Angle Adjust Override

Relative Angle Calibration Factor

Phase Zero Van Magnetic Heading

1 PPI Plot, Filtered and Aligned

Aligned Raw Tapes

4 Range Sweeps, Filtered and Aligned Table Look-Up

Stack Collapse (2 out of 3 Thresholding Algorithm)

Calibration

Site Magnetic Declination

Gain Compression

Amplitude Calibration Constant Override

Range Calibration Constant Override

Absolute Relative Angle Angle Calibration Alignment Factor Factor (True North)

Amplitude Calibration Constant Chrono Flag

Calibration

σ°F4 Calibrated Clutter Tapes

Figure 2.A.4

Application Programs • Sector • Patch • Ensemble • σ°F4 Map etc.

Phase Zero data reduction flow chart.

angles differ by the amount that the two Cartesian reference frames (i.e., local horizontals) in which they are respectively defined are rotated with respect to each other due to the spherical earth (see Appendix 2.C).

126 Appendix 2.B Formulation of Clutter Statistics

Appendix 2.B Formulation of Clutter Statistics 2.B.1 Overview of Patch Data Modeling investigations of clutter amplitude statistics in this book are based on the concept of a clutter patch. A clutter patch is a spatial macroregion selected within radar line-of-sight in which substantial clutter is discernible above the radar noise level. To provide detailed and accurate terrain descriptive information for the process of patch specification and description, measured clutter maps were overlaid and registered onto stereo air photos and topographic maps of the terrain, typically at about 1:50,000 scale. For each clutter patch selected, typically from several thousands to several tens of thousands of Phase Zero samples of clutter strength σ °F4 were obtained as range and azimuth position varied throughout the patch. The histogram of all the spatial samples of σ °F4 measured within the patch was formed, and various statistical attributes of this histogram or distribution were computed. The histogram together with its statistical attributes and associated terrain descriptive information for the patch was then stored in a computer file. The data upon which Chapter 2 is based are from 2,177 clutter patches selected from the 11.8-km maximum range Phase Zero experiment (see Table 2.A.3) at each of 96 measurement sites. The median patch size of these patches is 5.3 km2, or about 2.3 km on a side. Measurements of these patches led to a Phase Zero modeling file of 2,177 stored histograms of clutter strength, one histogram per patch. Phase One clutter patches were selected in a similar manner but were not limited in maximum range to 11.8 km. In total 3,361 Phase One clutter patches were selected from the 42 Phase One sites, extending in range to cover all the clutter that was measured, which led to substantial numbers of patches selected to ranges of 50 km, and in some cases to 100 km or more. The median patch size of these patches is 12.6 km2, or about 3.5 km on a side. Phase One patches were measured a number of times across the Phase One radar parameter matrix (5 frequencies, 2 polarizations, 2 pulse lengths), which led to a Phase One clutter modeling file of 59,804 stored histograms. The results of Chapter 5 are based on analysis of this stored file of Phase One data. The results of Chapter 3 are based on analysis of 42 Phase One repeat sector patches of median patch size equal to 12 km2, providing a modeling file of 4,465 stored histograms.

σ °F4 Histograms. Figure 2.B.1 shows examples of six Phase Zero clutter patch histograms from the Cold Lake site in western Canada. Similar results exist for each clutter patch histogram in the Phase Zero and Phase One stored histogram modeling files. The results in Figure 2.B.1, being representative of these large databases, are now described in some detail. Histograms of σ °F4 are shown for each patch at the top of the figure. The identifying patch number is shown in the upper-right corner of each histogram box. Fifty-, 90-, and 99-percentile levels are shown as three vertical dotted lines in each histogram,

Appendix 2.B Formulation of Clutter Statistics 127

progressing left to right, respectively, across the histogram. The n-th percentile level of σ °F4 indicates that n percent of the samples (n = 50, 90, or 99) in the histogram lie to the left of the dotted line at σ °F4 levels less than or equal to that indicated by the dotted line. The mean value of clutter strength σ °F4 within each patch is shown as a vertical dashed line in the histogram. The number of samples in each histogram including samples at radar noise level is printed above each histogram box. Oversampling exists in these Phase Zero results (nominally, 2:1 in range, 4:1 in azimuth, see Appendix 2.A), although some degree of independence exists between adjoining samples due to tapering beamwidth, pulse length, and thresholding effects. The resolution of σ °F4 in each histogram is in 1-dB increments or bins. Bins that contain one or more samples at radar noise level are doubly underlined at the bottom edge of the histogram to indicate radar noise contamination—they usually occur to the left side of the histogram. Bins that contain one or more saturated samples are triply underlined—when they occur, which is infrequently, they are to the right side of the histogram. The histograms are stored in computer files as three-dimensional arrays containing: (1) the total number of samples per bin, (2) the number of noise samples per bin, and (3) the number of saturated samples per bin.

σ °F4 Cumulatives. To the right of the histograms, cumulative distributions are shown obtained by cumulatively summing across each histogram from left to right. These cumulative distributions are shown both on a nonlinear lognormal scale and a nonlinear Weibull scale. If an empirical distribution is rigorously lognormal or Weibull, it plots as a straight line on a non-linear lognormal or Weibull scale, respectively. To the extent that empirical distributions are approximately linear on either of these scales, they may be approximated analytically by Weibull or lognormal statistics. On the whole, but not without exception, the empirical clutter distributions tend to be somewhat more linear on the Weibull scale than the lognormal scale. Lognormal statistics tend to overemphasize the spreads that actually occur in low-angle clutter (see Appendix 5.A). Percentile levels for any σ °F4 value may be read directly from the left-hand, non-linear vertical scale on either the lognormal or Weibull plot—for a given distribution the same levels are read on either plot. The cumulative distributions shown are absolute measures independent of noise contamination at σ °F4 levels above the maximum (i.e., strongest) noise-contaminated bin. The percentile level indicates the relative proportion of samples below a given strength. As long as the given strength is above the noise, it does not matter whether samples below that are at noise level (the true levels for samples measured at noise level must be less than or equal to the noise level). The cumulative plots are only shown as they emerge above (i.e., to the right of) the maximum noise-contaminated bin. However, their formation includes the samples at radar noise level to the left of this point of emergence. As a result, to the right of the point of emergence, over the region where the cumulative is displayed in the plots, the cumulatives are absolute measures of reflectivity independent of sensitivity.

Terrain Descriptive Information. In the box immediately below the histograms in Figure 2.B.1, terrain descriptive or ground truth information is provided as stored in the computer files for each patch. Terrain classification by land cover and landform is indicated (see Tables 2.1 and 2.2). Up to three levels of land cover may be specified (primary, secondary, and tertiary), and up to two levels of landform may be specified (primary and secondary), where the higher levels indicate decreasing relative incidence of those terrain types within the patch. These various levels of classification reflect the heterogeneity of

Percent

33966

Samples

Samples

7

0.999

14

0.99

Lognormal Scale

6

7 5

2.0

8

1.6

0.97 0 0

–50 –40 –30 –20 –10 22496

Samples

6

Percent

10

0

10

Samples

8

15

0 –50 –40 –30 –20 –10

0

–50 –40 –30 –20 –10

10

0

10

–50 –40 –30 –20 –10

0

σ°F4 (dB) Terrain Classification Patch Number

Land Cover

Landform

5 6 7 8 14 15

43-21 43-52 11-21 11-43 21-43 21-43

7 7 1-3 3-2 1-3 3-1

Depression Angle (deg)

Tree Cover (%)

Supplementary Terrain Descriptors Major road Heavy forest, major road Cropland surrounds town, major road, railway Town: patch contains part of CFB Cold Lake, major roads, railway Major highway, sewage plant, ponds, trees along creek Major highway, roads, creek

>50 >50 1-3 11-30 4-10 11-30

0.02 0.08 0.88 0.45 0.65 0.26 σ°F4 (dB)*

Regression Coefficients† Y = m • σ°F4 (dB)+b

Percentiles

Mean

Standard Deviation

Mean

Kurtosis

50

90

99

Slope (m)

Intercept (b)

Coefficient of Determination

Sum of Squared Deviations

5 6 7 8 14 15

-25.9 (-34.7) -26.8 (-33.7) -23.0 (-32.3) -23.3 (-39.2) -30.8 (-46.0) -37.0 (-45.6)

-22.9 (11.0) -24.7 (9.6) -18.7 (11.2) -14.5 (11.8) -25.4 (13.5) -30.9 (7.1)

7.59 (-0.18) 4.92 (-0.25) 7.34 (-0.66) 12.9 (0.23) 10.6 (0.31) 10.1 (1.28)

18.2 (1.63) 12.0 (1.66) 15.9 (3.17) 27.0 (2.46) 24.5 (1.85) 21.6 (3.98)

-32 -31 -30 -38 -48 -48††

-21 -22 -20 -25 -27 -34

-16 -18 -11 -10 -19 -25

0.042 (0.078) 0.049 (0.089) 0.046 (0.074) 0.030 (0.057) 0.026 (0.057) 0.030 (0.073)

1.30 (2.71) 1.49 (3.06) 1.25 (2.45) 1.02 (2.29) 1.17 (2.61) 1.42 (3.51)

0.968 (0.906) 0.959 (0.883) 0.997 (0.974) 0.982 (0.996) 0.977 (0.926) 0.994 (0.975)

0.192 (3.06) 0.208 (2.10) 0.031 (0.78) 0.147 (0.14) 0.080 (1.07) 0.008 (0.20)

† Weibull (Lognormal)

0.5 0.3 0.1

15

0.4 0

14 8 56 7 –50 –40 –30 –20 –10

0.999 0.99 0.97 0.9 0.7

Weibull Scale

6

0.1

†† Upper Bound

Figure 2.B.1 Phase Zero clutter statistics and terrain classification for selected patches at the Cold Lake site.

0

–0.8 10 0.8

7 5 8

15 14

0.3

–0.4

Linear Scale

0.5

Patch Number

* Of Linear Values (of dB Values)

10

0.7

0.8

0.6 0.4

e

10260

Slop

–50 –40 –30 –20 –10

0.2 0

eigh

10

–0.2

Rayl

10

0

Samples

4998

Probability That σ°F4 (dB) ≤ Abscissa

–50 –40 –30 –20 –10

1.2

0.9

8 56

–0.4 –0.6

Linear Scale

7 –50 –40 –30 –20 –10

σ°F4

(dB)

Y = m • σ°F4 (dB) + b

8580

5

0

–0.8 10

Y = m • σ°F4 (dB) + b

Samples

9168 10

Appendix 2.B Formulation of Clutter Statistics 129

terrain within kilometer-sized patches. Also included in the ground truth box for each stored clutter patch histogram are depression angle, percent tree cover, and supplementary terrain descriptors as provided in stereo air photo interpretation.

2.B.2 Formulation of Clutter Statistics Below the ground truth box in Figure 2.B.1 is a box containing a number of computed statistical attributes of the clutter amplitude distribution for each patch. These are computed from the stored, three-dimensional, clutter patch histogram. The differences between statistics computations based on the actual array of non-rounded-off, individual samples of σ °F4, and the more efficient computations based on the rounded-off, binned groups of the histogram, were shown to be insignificant. In what follows, each quantity in the statistics box is defined in turn. First, let x represent clutter strength σ °F4 in units of m2/m2. Let y represent the dB value of σ °F4, such that y = 10log10 x

(2.B.1)

In forming the histogram of spatial samples of clutter strength within a clutter patch, measured values of y are sorted into bins 1 dB wide. A sketch of such a histogram is shown in Figure 2.B.2. In this histogram, let i be the bin index, which runs in increasing order from i = 1 at the minimum value of y, y = ymin in the histogram, to i = I at the maximum value of y, y = ymax in the histogram. The clutter strength in the i-th bin is xi m2/m2, where xi = 10 yi ⁄ 10 . Let i = i' represent the bin containing the maximum value of y that is noise contaminated, y = y'. Let the number of samples in the i-th bin be ni. Let the total number of samples in the histogram be N. Then I

N =

∑

ni i=1

(2.B.2)

The sketch of Figure 2.B.2 shows these relationships.

Definitions of Moments. Moment-dependent quantities are computed from linear values xi and subsequently converted to dB. These quantities are defined as follows: 1 mean = x = ---N

I

∑

(2.B.3)

ni xi i=1

1 standard deviation = sd ( x ) = ------------N–1

I

∑

1 --2

ni ( xi – x ) 2

i=1

(2.B.4)

Number of Samples

130 Appendix 2.B Formulation of Clutter Statistics

Double underline indicates bins containing one or more samples at radar noise level

ni

Histogram of clutter strengths within a patch; contains N spatial samples,

I

where: N = Σ ni i=1

1 dB Bins 0 Minimum value of y in histogram, ymin

123

y = Clutter Strength Maximum value of y in histogram, ymax i = Bin Index

Maximum value of y that is noise contaminated, y '

i'

I

i

Figure 2.B.2 Sketch of patch clutter strength histogram showing nomenclature. Here, y = 10 log10(σ°F4).

M3 ( x ) coefficient of skewness = g 3 ( x ) = ------------------------3⁄2 [ M2 ( x ) ]

(2.B.5)

M4 ( x ) coefficient of kurtosis = g 4 ( x ) = -------------------2 [ M2 ( x ) ]

(2.B.6)

q 1 I q-th moment about the mean = M q ( x ) = --n i ( x i – x ) ; q = 2, 3, 4. N

(2.B.7)

where

∑

i=1

In clutter amplitude statistics, these quantities dependent on the first four moments of xi are almost always much less than unity. For convenience, these quantities shown in Eqs. (2.B.3) through (2.B.6) are converted to dB units, as: x dB = 10 log10 x

(2.B.8)

sd ( x ) dB = 10 log10[sd(x)]

(2.B.9)

g3 ( x )

= 10 log10[g3(x)]

(2.B.10)

g 4 ( x ) dB = 10 log10[g4(x)]

(2.B.11)

dB

Appendix 2.B Formulation of Clutter Statistics 131

These quantities dependent on the first four moments of xi and converted after computation to dB units are shown to the left (i.e., not within parentheses) in the 2nd through 5th columns from the left, respectively, in Figure 2.B.1. These are primary quantities fundamentally representative of the clutter amplitude distributions and upon which is based much of the expected value modeling information in this book. A second set of moment-dependent quantities is computed from dB values yi. These quantities are defined as follows: 1 mean of dB values = y = --N

I

∑ ni yi

(2.B.12)

i=1

1⁄ 2

standard deviation of dB values = sd ( y ) =

1

-----------N–1

I

∑ ni ( yi – y )2

(2.B.13)

i=1

M3 ( y ) coefficient of skewness of dB values = g 3 ( y ) = --------------------------3⁄2 [ M2 ( y ) ]

(2.B.14)

M4 ( y ) coefficient of kurtosis of dB values = g 4 ( y ) = ---------------------2 [ M2 ( y ) ]

(2.B.15)

where 1 M q ( y ) = --N

I

∑ ni ( yi – y )

q

; q = 2, 3, 4.

(2.B.16)

i=1

These quantities dependent on the first four moments of dB values yi are shown within parentheses in the 2nd through 5th columns from the left, respectively, in Figure 2.B.1. These are adjunct quantities occasionally useful in working with clutter statistics.

Upper Bounds to Moments. Some of the samples in the histograms are at noise level. In all moment computations, upper bounds are computed assigning noise power values to these samples, and lower bounds are computed assigning zero power values to these samples. Both upper and lower bounds for each moment-derived quantity were stored for each clutter patch histogram in the computer files of modeling information. Even when the amount of microshadowing (i.e., noise contamination) within a clutter patch becomes extensive, upper and lower bounds to mean clutter strength usually remain close (within a small fraction of a decibel) because of domination by strong discrete clutter sources. Significant divergence of mean bounds indicates a clutter patch measurement too contaminated by radar noise to be useful. Only upper bounds are shown in the statistics box of Figure 2.B.1.

132 Appendix 2.B Formulation of Clutter Statistics

Interpretation of Moments. The quantities dependent on the first four moments of linear values xi in the statistics box are briefly interpreted as follows: the spread in the distribution is fundamentally indicated by the ratio of standard deviation-to-mean. For example, in the limiting case of Rayleigh statistics,19 sd(x) = x and 10 log10(sd(x)/ x ) = sd(x)|dB – x |dB = 0. Thus the quantity sd(x)|dB – x |dB (i.e., value in 3rd column minus value in 2nd column of the statistics box) indicates the degree of spread in the amplitude distribution beyond Rayleigh. Low-angle clutter amplitude distributions are usually characterized by wide spreads. Occasional patch amplitude distributions may be found, almost always at higher depression angles, that are close to Rayleigh. Rayleigh may also be taken as a point-of-departure in interpreting coefficient of skewness and kurtosis. Skewness is a measure of asymmetry in the distribution. Kurtosis is a measure of concentration about the mean. For Rayleigh statistics, g3(x) = 2 and g4(x) = 9, so that g3(x)|dB = 3.01 and g4(x)|dB = 9.54. Usually the values listed for g3(x)|dB and g4(x)|dB in the 4th and 5th columns, respectively, of the statistics box are considerably greater than 3 and 9.5, respectively, again the result of a widely dispersed high-side tail in low-angle clutter amplitude distributions. However, occasional patch amplitude distributions may be found close to Rayleigh. For example, the high depression angles at the Equinox Mountain site in Vermont resulted in some of the measured clutter patch statistics there approaching Rayleigh. Equinox Mountain patches with homogeneous forest as land cover provided measured statistics which approach Rayleigh values, whereas Equinox Mountain patches that include cropland on the valley floor as a secondary component of land cover in addition to forest provided measured statistics that remain far from Rayleigh (cf. Figure 2.20 and its discussion). In Table 2.B.1, two patches at Equinox Mountain, patch numbers 1/2 and 8/2, are selected for detailed comparison of attributes of their spatial amplitude statistics with theoretical Rayleigh values (cf., Table 2.15). The empirical attributes shown for these two patches in Table 2.B.1 are within a few dB of theoretical Rayleigh values.

Percentiles. Next, in the 6th through 8th columns from the left of the statistics box in Figure 2.B.1 are shown the 50-, 90-, and 99-percentile levels of σ °F4, respectively, of the six clutter patch amplitude distributions shown. In Figure 2.B.2, let Pi represent the probability that y ≤ yi (or, equivalently, that x ≤ xi). Then 1 P i = ---N

i

∑ nj

(2.B.17)

j=1

and the corresponding percentile level is 100 · Pi.20 The 50-, 90-, and 99-percentile levels, besides being tabulated in the statistics box, may be read directly from the histograms (as vertical dotted lines) or from the cumulatives (as the σ °F4 values for probabilities of 0.5, 19. More precisely, if the voltage (x)1/2 is Rayleigh distributed, then the power x follows an exponential distribution in which x = sd(x). 20. If the n-th percentile level (0 ≤ n ≤ 100) occurs at xi = x i in the distribution of xi, it occurs at y i = 10 log10 n n ( x ) in the distribution yi, since percentile level only indicates relative position in the distribution. This is in not true of moment-dependent quantities. That is, Mq(y) ≠ 10 log10 Mq (x).

Appendix 2.B Formulation of Clutter Statistics 133

Table 2.B.1 Approximately Rayleigh Spatial Amplitude Statistics for Two Patches at Equinox Mountain, Vermonta

Statistical Attribute of Spatial Amplitude Distribution Mean

c

Measured Values Patch No. 1/2b

Patch No. 8/2c

Theoretical Rayleigh Values

–17.9

–15.5

–

Standard Deviationto-Mean

1.5

0.6

0

Skewness

4.3

4.3

3

11.1

12.4

9.5

Mean-to-Median

3.1

1.5

1.6

90 Percentile-toMedian

7

5

5.2

99 Percentile-toMedian

11

9

8.2

Kurtosis

a b

σ° F4 (dB)

Phase Zero X-band data, range resolution = 75 m. Moderately steep mixed forest. Depression angle = 7.6°. Range limits are from 2.0 to 6.6 km. Azimuth limits are from 327° to 360°. Moderately steep to steep mixed forest. Depression angle = 4.3°. Range limits are from 6.2 to 9.3 km. Azimuth limits are from 110° to 171°.

0.9, and 0.99, respectively). In the statistics box, if the median (i.e., 50 percentile) is at a level of σ °F4 contaminated by noise, it is indicated by footnote as only representing an upper bound to the true median. Otherwise, the percentile levels tabulated are uncontaminated by noise.

2.B.3 Fitting of Measured Clutter Data to Weibull and Lognormal Distributions The right-most four columns of the statistics box in Figure 2.B.1 provide linear regression and goodness of fit coefficients to either Weibull (left entry in each column) or lognormal (right entry in each column within parentheses) approximations to each of the six actual empirical clutter patch amplitude distributions shown. That is, if an empirical patch amplitude distribution is approximately linear in the lower Weibull graph or in the upper lognormal graph, the regression coefficients provide the best fitting straight line approximation to the empirical distribution. In what follows, information is provided defining the regression coefficients and goodness of fit parameters.

Weibull Relationships. The Weibull probability density function may be written b

b–1

( b ) ⋅ ln 2 ⋅ x - ⋅e p ( x ) = ---------------------------------b x 50

ln 2 ⋅ x – ----------------b x 50

(2.B.18)

134 Appendix 2.B Formulation of Clutter Statistics

where x50 =

median value of x,

b=

1/aw

aw =

Weibull shape parameter,

and, as before, x represents σ °F4 in units of m2/m2. The mean-to-median ratio of a Weibull distribution is given by Γ(1 + a )

x w ------ = ----------------------

x 50

( ln 2 )

(2.B.19)

aw

where Γ is the Gamma function. The ratio of standard deviation-to-mean of a Weibull distribution is given by 2

[ Γ ( 1 + 2a w ) – Γ ( 1 + a w ) ] sd ( x ) ------------- = -------------------------------------------------------------x Γ ( 1 + aw )

1 ⁄2

(2.B.20)

The Weibull distribution degenerates to a Rayleigh21 distribution when aw = 1. The Weibull cumulative distribution function is b

P(x) = 1 – e

ln 2 ⋅ x – --------------b x 50

(2.B.21)

where x

P(x) =

∫ p ( ξ ) dξ 0

Equation (2.B.21) may be rearranged, as

 1 1 1  log10  ln  ------------  = ------------ ⋅ 10 log10 x +{log10(ln2) – ------------ 10 ⋅ log10x50} (2.B.22)  1 – P 10a w   10a w In Eq. (2.B.22), if we let Y = log10

1 ln  ------------  1 – P

(2.B.23)

21. That is, voltage-like quantities are Rayleigh distributed; power-like quantities are exponentially distributed. Here, x is a power-like quantity.

Appendix 2.B Formulation of Clutter Statistics 135

and recall that y = 10 log10 x, we obtain Y = m⋅y+d

(2.B.24)

1 m = ------------10a w

(2.B.25)

1 d = log10(ln2) – ------------- ⋅ y 50 10a w

(2.B.26)

y50 = 10 log10(x50)

(2.B.27)

where

and

That is, Eq. (2.B.24) is a linear relationship between Y and y. Equation (2.B.17) shows that for each patch there exists an empirical cumulative amplitude distribution given by an ordered pair (Pi , yi ), i = 1,2, . . . I. In this ordered pair, the dependent variable Pi is transformed to Yi by Eq. (2.B.23). The cumulative distributions (Yi , yi ) are then plotted, as shown in Figure 2.B.1 in the Weibull graph to the lower-right. The abscissa of this graph, shown as σ °F4 (dB), is what is represented here as y. The linear ordinate on the right side of this graph is Y given by Eq. (2.B.24). The nonlinear ordinate on the left side of this graph is P, obtained from the corresponding value of Y by Eq. (2.B.23).

Linear Regression. A standard linear regression fit to the plot of (Yi , yi) was performed for each stored clutter patch amplitude distribution, as shown in the Weibull graph to the lower-right of in Figure 2.B.1. That is, for each clutter patch amplitude distribution, the slope m and Y-intercept d of the best-fitting straight line to (Yi, yi) was obtained. This regression analysis was performed only over the region of (Yi, yi) above (i.e., to the right of) the maximum noise-contaminated bin (i.e., yi > y', see Figure 2.B.2) and within the limits of probability shown in the graph (i.e., 0.1 ≤ Pi ≤ 0.999). As the standard measure of goodness of fit in regression analysis, the coefficient of determination (i.e., the square of the correlation coefficient) was obtained. Also obtained was the sum of the squared deviations. These regression computations are defined by the following standard formulas [1]: 1 I -( y i Y i ) – yY I

∑

i=1

m = --------------------------------------2 σy

(2.B.28)

d = Y – my

(2.B.29)

 m σ y coefficient of determination =  ---------  σY  and

2

(2.B.30)

136 Appendix 2.B Formulation of Clutter Statistics

I

∑ [ Yi – ( myi + d ) ]

sum of squared deviations =

2

(2.B.31)

i=1

1 y = --I

1 Y = --I



2 1 σ y =  --I

I

∑ yi

(2.B.32)

i=1 I

∑ Yi

(2.B.33)

i=1

I



∑

yi  – y

I

Yi  – Y

2

  i=1 

2

(2.B.34)

and



2 1 σ Y =  --I

∑



2

  i=1 

2

(2.B.35)

The regression quantities m, d, coefficient of determination, and sum of squared deviations were tabulated as the left-most entries in the 4th through 1st columns from the right in the statistics box of Figure 2.B.1. A rigorously exact Weibull distribution plots as a straight line in the lower right-hand Weibull graph of Figure 2.B.1, as shown by Eqs. (2.B.22) and (2.B.24). To the extent that any particular patch amplitude distribution is fairly linear in this graph, it is reasonably approximated by a Weibull distribution over the range indicated with Weibull coefficients m and d as given by the left-hand entries in the 4th and 3rd columns from the right in the statistics box. This approximating Weibull distribution may be drawn in the Weibull graph as a straight line with slope m and Y-intercept d using the right-hand ordinate in the graph. Direct qualitative comparison of the empirical curve with its approximating straight line is the most useful method of assessing goodness of fit; the coefficient of determination and the sum of the squared deviations quantify the goodness of fit. The parameters aw and x50 in the analytical Weibull distribution of Eqs. (2.B.18) and (2.B.21) are obtained from Eqs. (2.B.25), (2.B.26), and (2.B.27). Weibull random variates distributed according to this approximating best-fit distribution may be obtained by generating uniformly distributed random variates Pk, k = 1,2,3, . . . and using Eq. (2.B.22) to convert each to a corresponding Weibull distributed variate xk, k = 1,2,3, . . . , where the parameters aw and x50 in Eq. (2.B.22) are obtained as discussed previously.

Lognormal Relationships. As before, let y = 10 logl0x, and let x = σ °F4 in units of m2/

m2. Suppose y is normally distributed with variance s2. Then x is lognormally distributed, with probability density function

Appendix 2.B Formulation of Clutter Statistics 137

x 2 log  -------- 10 x 50

p(x) =

1 2⁄ 1 N ----------------------⋅ --- ⋅ e x 4π log 10ρ

– ----------------------4N log 10ρ

(2.B.36)

where x50 = median value of x x = mean value of x x ρ = ------x 50

(2.B.37) 2

s 10 log 10ρ = --------20N

(2.B.38)

and N = log 10e = 0.4343 The mean-to-median ratio of a lognormal distribution is given by ρ (see Eq. (2.B.37) and (2.B.38)). The ratio of standard deviation-to-mean is given by (ρ2 – 1)1/2. The coefficient of skewness is given by (ρ2 – 1)1/2(ρ2 + 2). The coefficient of kurtosis is given by ρ8 + 2ρ6 + 3ρ4 – 3. The lognormal cumulative distribution function is x   ----- 50 1 P ( x ) = --- 1 + erf --------------------------------1 2⁄ log

2

10  x

2 ( N log 10ρ )

(2.B.39)

where erf = error function Equation (2.B.39) may be rearranged as x   ----- 50 erf -1 { 2P ( x ) – 1 } = ---------------------------------1 ⁄2 2 ( N log 10ρ ) log

10  x

where erf -1 = inverse error function.

(2.B.40)

138 Appendix 2.B Formulation of Clutter Statistics

In Eq. (2.B.40), if we let Y = erf -1 { 2P ( x ) – 1 }

(2.B.41)

Y = m ⋅y + d

(2.B.42)

we obtain

where 1 m = ---------------------------------------1 ⁄2 20 ( N log 10ρ )

(2.B.43)

and log ( x 50 ) 10 d = -----------------------------------1 ⁄2 2 ( N log 10ρ )

(2.B.44)

Equation (2.B.42) indicates that Y is linearly dependent on y, with slope equal to m and Yintercept equal to d. In the empirical cumulative amplitude distribution (Pi , yi), i = 1, 2, . . . I, of each patch, the dependent variables Pi were transformed to Yi by Eq. (2.B.41), the resultant distribution (Yi, yi) was plotted in the lognormal graph to the upper-right in Figure 2.B.1, and a standard linear regression fit to the plot of (Yi, yi) was performed for each patch distribution over the range given by yi > y' and 0.1 < Pi < 0.999. As with the Weibull regression analyses, lognormal regression computations were performed using Eqs. (2.B.28) through (2.B.35) to yield lognormal regression quantities m, d, coefficient of determination, and sum of squared deviations. These are tabulated as the right-most entries (i.e., within parentheses) in the 4th through 1st columns from the right in the statistics box of Figure 2.B.1. The approximating lognormal distribution to any empirical patch distribution may be drawn in the upper-right lognormal graph as a straight line with slope m and Y-intercept d using the right-hand ordinate in the graph. The parameters ρ and x50 in the analytical lognormal distribution of Eqs. (2.B.36) and (2.B.39) are obtained from Eqs. (2.B.43) and (2.B.44). Lognormal random variates distributed according to the lognormal approximation to the empirical patch amplitude distribution may be obtained by generating uniformly distributed random variates Pk(x), k = 1,2,3 . . . and using Eq. (2.B.40) to convert each to a corresponding lognormal distributed variate xk, k = 1,2,3, . . . , where the parameters ρ and x50 in Eq. (2.B.40) are obtained as discussed previously.

Reference 1.

G. W. Snedecor and W. G. Cochrane, Statistical Methods (7th ed.), Iowa State University Press, Ames, IA, 1980.

Appendix 2.C Depression Angle Computation 139

Appendix 2.C Depression Angle Computation Figure 2.C.1 shows geometrical relationships involved in considerations of depression angle on a spherical earth. Range from radar to backscattering terrain point is r. Effective earth’s radius (i.e., actual earth’s radius times 4/3 to account for standard atmospheric refraction) is a. The actual earth’s radius is approximately 6,370 km. Effective radar height (i.e., site elevation above mean sea level plus radar antenna mast height minus terrain elevation above mean sea level at backscattering terrain point) is h. The quantities h and r are small compared to a.

Radar Antenna γ

S

LO

h

α β r

he Backscattering Terrain Point a

φ

4/3 Earth

Figure 2.C.1 Geometrical relationships involving depression angle on a spherical earth.

Depression angle α on a spherical earth is defined to be the complement of incidence angle β at the backscattering terrain point. Incidence angle β is the angle between the outward

140 Appendix 2.C Depression Angle Computation

projection of the earth’s radius at the backscattering terrain point and the direction of illumination (or line-of-sight to the radar antenna) at the backscattering terrain point. The spherical earth has two effects in the computation of depression angle. The first effect is the effective decrease in terrain elevation of the backscattering terrain point due to the sphericity of the earth, whereby the surface of the earth (i.e., an imaginary sphere with height above mean sea level constant and equal to that of the backscattering terrain point) drops off with increasing range from the radar. This effective decrease in terrain elevation of the backscattering terrain point is denoted as he. On a spherical earth of radius a, he is computed as 2

r h e = -----2a

(2.C.1)

Including he, the angle below the local horizontal at the radar antenna at which the backscattering terrain point is observed, denoted γ, is computed as h + he rγ = tan – 1  ------------- ≅ h --- + ---- r  r 2a

(2.C.2)

Angle γ is referred to as the off-axis angle. It is the angle for which elevation gain correction on the elevation pattern of the radar antenna is performed in computation of clutter strength. The second effect of the spherical earth on depression angle is the rotation of the local Cartesian reference frame at the backscattering terrain point with respect to that at the radar antenna. This angle of rotation, denoted by ϕ, is computed as r ϕ = --a

(2.C.3)

That is, the correct illumination angle to be associated with the clutter measured from the backscattering terrain point is the angle α above the local horizontal at which an observer at the backscattering terrain point sees the radar, not the angle γ at which an observer at the radar sees the terrain point. Incorporating both effects, depression angle α is computed as h r α = γ – ϕ ≅ --- – -----r 2a

(2.C.4)

It is depression angle α which is computed for each clutter patch in this book and associated thereafter with the measured amplitude distribution of the clutter patch. For r < a, both α (seen by the observer at the terrain point) and γ (seen by the observer at the radar) simplify to ≈h/r. See [1], Section 1.11 for related discussion (N.B., the angle nomenclature in [1] differs from that utilized here; the term “grazing angle” herein means the angle between the tangent to the local terrain surface at the backscattering terrain point and the direction of illumination; [1] does not utilize or define the term “grazing angle” as used herein; “grazing

Appendix 2.C Depression Angle Computation 141

angle” in [1] is equivalent to “depression angle” here, and “depression angle” in [1] is equivalent to “off-axis angle” here).

Positive h. For the majority of the clutter patches of this book, effective radar height h is positive, i.e., h > 0. For h > 0, range to the spherical earth horizon, denoted by r′, is given by r′ = 2ah . At the spherical earth horizon (i.e., r = r′), depression angle α = 0, and off-axis angle γ = 2ha⁄ . Beyond the spherical earth horizon (i.e., r > r′), α is negative. That is, due to the spherical earth, at long enough ranges depression angle α becomes negative even though effective radar height h is positive. Most of the clutter patches of this book occur at ranges within the spherical earth horizon (i.e., r < r′) which, for h > 0, leads to positive values of depression angle α. However, occasional long-range clutter patches occur at ranges beyond the imaginary spherical earth horizon (i.e., r > r′), but still remain within line-of-sight visibility to the radar on the real earth. Such long-range clutter patches lead, properly, to negative values of α, even though h > 0. Such clutter patches are often weak due to diffraction loss over the long ranges of intervening terrain at near grazing incidence. Some examples of such long-range patches for urban terrain are discussed in Chapter 5. Negative h. For a significant number of the clutter patches of this book, effective radar height h is negative, i.e., h < 0. When h < 0, the terrain elevation of the clutter patch is higher than the radar antenna. To be within line-of-sight visibility in such circumstances, the terrain within the clutter patch must be of steep slope greater than the absolute value of the depression angle at which it is observed. For this reason, clutter strengths often rise quickly with increasing negative depression angle. For convenience, when h < 0, let H = –h, so that H is a positive number. Also, for h < 0 let r′ = 2aH . Then, when h < 0, Eq. (2.C.4) for depression angle α becomes H r α ≅ – ---- – -----r 2a

(2.C.5)

Equation (2.C.5) indicates that α is always negative for h < 0. If the magnitude of α is represented as |α|, then Eq. (2.C.5) further indicates that, for h < 0, with increasing range r, |α| first decreases from a large value determined by H/r to a minimum value of ( 2H ) a⁄ at r = r′; and then as r continues to increase (i.e., r > r′), |α| begins to increase as r/2a. Almost all of the clutter patches of this book with h < 0 occur at ranges r < r′; that is, the negative values of depression angle associated with them are primarily the result of negative values of effective radar height h, and are only secondarily the result of the longrange spherical earth effect r/2a. This is true even for the long-range mountain patches for which results are provided in Chapter 5. Although many of the long-range mountain patches occur at ranges of 100 km or more, these mountain patches occur at elevations 4000 to 5000 ft above the prairie site elevations at which they were measured, so that their long ranges remain less than 2aH .

Reference 1.

F. E. Nathanson (with J. P. Reilly and M. N. Cohen), Radar Design Principles (2nd ed.), New York: McGraw-Hill, 1991.

Appendix 3.A Phase One Radar 247

Appendix 3.A Phase One Radar 3.A.1 Phase One Sites A photograph of the Phase One ground clutter measurement equipment deployed at the Katahdin Hill site at Lincoln Laboratory is shown in Figure 3.A.1. The Phase One measurement program consisted of setting up and acquiring clutter measurement data with this equipment 49 times at 42 different sites. Table 3.A.1 lists the 49 Phase One site visits, and for each provides the site location by latitude and longitude, the time of year of the measurements, the number of sections that were extended in the expandable Phase One antenna tower, and whether the visit was a repeated visit (n) to the site to establish seasonal variations.

3.A.2 Phase One Measurement Equipment Important Phase One system parameters are shown in Table 3.A.2. The five Phase One frequency bands—VHF, UHF, L-, S-, and X-bands—shared three antenna reflectors. The large 10-ft by 30-ft reflector was a shared dual-frequency antenna between VHF and UHF with each band having its own set of crossed dipole feeds. A photograph of this VHF/UHF feed system is shown mounted in position in front of the VHF/UHF reflector in Figure 3.A.2. The intermediate-sized reflector was a similar shared reflector between L- and Sbands, with a crossed dipole feed at L-band and a dual polarized waveguide feed at S-band. The L- and S-band feeds were protected by a radome. A smaller reflector was dedicated to X-band, which was fed with a dual-polarized horn. A close-up view of the L-/S-band radome and the X-band reflector above it is shown in Figure 3.A.3. Visible above the Xband reflector in this photograph is a TV camera that provided a boresight video display at the operating console in the electronics trailer. The antenna tower upon which the three reflectors were mounted was expandable in six sections to a nominal maximum height of 100 ft. The weight on top of this tower due to the five antenna systems and associated equipment was 3,000 lbs. The antenna wind load was 8,000 lbs at the specified survival wind velocity of 75 knots. The tower was guyed with 28 cables, each tensioned to 1,000 or 2,000 lbs. Eight guy anchors were emplaced at each site and each was tested to 20,000 lbs withholding capacity. Motion at the center of mass on top of the tower, critical to system stability and phase coherence, was tested to within a specified tolerance (viz., 0.1035 in/sec) under dynamic wind loading using a vertically directed laser. Table 3.A.2 shows gains, beamwidths, and rms sidelobe levels of the Phase One antenna beams at a particular selected frequency within each band. The Phase One system was capable of operating within a 5% bandwidth in each of its five radar bands. The frequencies shown in Table 3.A.2 were those most commonly used in Phase One data acquisition. The antenna beams were relatively wide in elevation and were fixed with boresight horizontal at 0° depression angle (i.e., no control was provided on the position of the elevation beam).

248 Appendix 3.A Phase One Radar

Figure 3.A.1

Phase One equipment at Katahdin Hill. Antenna tower is erected to 100 ft.

The azimuth and elevation beamwidths specified are as measured at the 3-dB one-way points (6-dB two-way). For most sites and landscapes, the terrain at all ranges from 1 to many kilometers was usually illuminated within the 3-dB points of the fixed elevation beamwidth. The measured clutter statistics are corrected for gain variations on the elevation beam both within and beyond the 3-dB points, depending on the off-boresight angle to the backscattering terrain point. At almost all sites, either three antenna tower sections were raised to provide a nominal height of 60 ft or six tower sections were raised to provide a nominal height of 100 ft. Occasionally, some clutter data were acquired with only one or

Appendix 3.A Phase One Radar 249

Table 3.A.1 Forty-nine Phase One Ground Clutter Measurement Setups Setup Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

Site Name Katahdin Hill, MA Shilo, Man. Neepawa, Man. Polonia, Man. North Truro, MA Cochrane, Alta. Strathcona, Alta. Penhold II, Alta. Beiseker, Alta. Westlock, Alta. Cold Lake, Alta. Suffield, Alta. Pakowki Lake, Alta. Orion, Alta. Beiseker (2), Alta. Cochrane (2), Alta. Brazeau, Alta. Lethbridge W., Alta. Magrath, Alta. Waterton, Alta. Plateau Mt., Alta. Picture Butte II, Alta. Beiseker (3), Alta. Brazeau (2), Alta. Puskwaskau, Alta. Peace River S. II, Alta. Woking, Alta. Beiseker (4), Alta. Wolseley, Sask. Headingley, Man. Altona II, Man. Big Grass Marsh, Man. Gull Lake W., Man. Spruce Home, Sask. Rosetown Hill, Sask. Wainwright, Alta. Dundurn, Sask. Corinne, Sask. Gull Lake W. (2), Man. Sandridge, Man. Turtle Mt., Man. Beulah, ND Knolls, UT Booker Mt., NV Vananda E., MT Wachusett Mt., MA Scranton, PA Blue Knob, PA Katahdin Hill, MA

(n) n-th visit (repeated)

Latitude (°N)

Longitude (°W)

42.46 71.27 49.75 99.63 50.33 99.50 50.36 99.61 40.03 70.05 51.20 114.45 51.02 114.17 52.18 113.97 51.39 113.27 54.16 113.70 54.43 110.18 50.27 111.14 49.32 110.85 49.50 110.81 Seasonal Revisit Seasonal Revisit 53.04 115.43 49.71 112.93 49.41 112.97 49.15 113.83 50.22 114.52 49.92 112.82 Seasonal Revisit Seasonal Revisit 55.22 117.49 56.20 117.27 55.55 118.75 Seasonal Revisit 50.36 103.15 49.88 97.40 49.19 97.66 50.39 98.85 50.40 96.53 53.45 105.76 51.54 107.93 52.82 111.06 51.85 105.57 50.05 104.62 Seasonal Revisit 50.61 97.51 49.06 100.18 47.30 101.74 40.74 113.28 38.10 117.19 46.45 106.98 42.49 71.89 41.38 75.59 40.29 78.55 Seasonal Revisit

Time of Year Nov/Dec Feb/Mar Mar Mar Jun/Jul Aug Sep Sep/Oct Oct/Nov Nov Nov/Dec Dec/Jan Jan/Feb Feb Feb Feb/Mar Mar/Apr Apr/May May/Jun Jun Jun Jul/Aug Aug Aug/Sep Sep/Oct Oct/Nov Nov Nov Nov/Dec Dec Jan Feb Feb Feb/Mar Mar Mar/Apr Apr Apr May May May/Jun Jun Jun Jul Jul/Aug Aug Aug/Sep Sep Sep/Oct

Number of Antenna Tower Sections 6 3, 1 3 3 6 3 3 6 3 6 6 3, 1 3 3 3 3 6 3, 1 3 3 3 3 3 6 6 6 3 3 3 3 6 3 6 3 3 1 3 3, 2, 1 6 3 6 3 3 3 3 3 3 3 6

250 Appendix 3.A Phase One Radar

Table 3.A.2 Phase y One System Parameters a) Frequency-Dependent Parameters Frequency Band

Parameter VHF

UHF

L-Band

S-Band

X-Band

MHz (Nominal)

167

435

1230

3240

9200

Azimuth Beamwidth (deg) Elevation Beamwidth (deg) RMS Sidelobes (dB) Antenna Gain (dBi) Peak Power (kW) Pulse Length (µs) Clutter Improvement Factor (dB)

13 42 –25 13 10 0.25, 1 60

5 15 –25 25 10 0.25, 1 60

3 10 –30 28.5 10 0.1, 1 60

1 4 –30 35.5 10 0.1, 1 55

1 3 −30 38.5 50 0.1, 1 55

b) Parameters Not Dependent on Frequency Polarization Emit PRF 10-km Sensitivity A/D Sampling Rate A/D Number of Bits Waveform Data Recording Rate Output Data RCS Accuracy Minimum Range Dynamic Range Instantaneous Attenuator Controlled Data Collection Modes

Azimuth Scan Rate Tower Height

Either VV or HH 500, 1000, 1500, 2000, --- 4000 Hz σ°F4 ≅ –60 dB 1, 2, 5 or 10 MHz 13 Uncoded CW Pulse 625 Kbytes/s Pulse-by-Pulse I and Q 2 dB rms 1 km 60 dB 40 dB Beam Scan Parked Beam Beam Step 0 to 3 deg/s 30, 45, 60, 100 ft

two tower sections raised to provide nominal heights of 30 ft or 45 ft, respectively. The number of tower sections used at each site is shown in Table 3.A.1. The Phase One equipment constituted a self-contained transportable five-frequency radar system transported by three tractor/trailers (see Figure 3.A.1). The white electronics trailer contained the five transmitters, receivers, exciter, analog-to-digital (A/D) converters, signal processors, a digital computer, displays, and high-speed data recorders. The flat-bed tower trailer transported the tower, antenna reflector midsections, antenna feeds, and a dieseloperated winch system used to erect the tower. The tarpaulin-covered equipment trailer transported a 60-kW diesel generator, waveguide sections, coaxial RF cables, power cables, a man-portable 75-ft tower used during system calibration, and portions of the antenna reflectors. The overall radar system block diagram is shown in Figure 3.A.4. The system exciter supplied all transmit and receive local oscillator (LO) frequencies and provided the basic timing reference for the system. The basic frequency reference for the exciter was a Hewlett Packard 8662A synthesizer signal generator, which had sufficient stability to support an overall system clutter improvement factor of 60 dB. There were five transmitters

Appendix 3.A Phase One Radar 251

Figure 3.A.2

Crossed-dipole feeds of the Phase One VHF/UHF reflector.

in the system. The two higher frequency transmitters (S- and X-bands) had traveling wave tubes (TWTs) as final high-power output stages. The intermediate and final stages of the three low band transmitters (VHF, UHF, and L-band) used Eimac type Y-739F planar triodes with Eimac CV-8030 series resonant cavities. A single low-band transmitter power supply was used for intermediate and final stages of the three low-band transmitters. The cavities could be manually tuned over a few megahertz in each of the three low-band transmitters. The signals from each of the five high-power transmitters were fed through their respective circulators to transmission lines. The S- and X-band signals were

252 Appendix 3.A Phase One Radar

Figure 3.A.3

L- and S-band feed radome, X-band antenna, and tower-top TV camera.

transmitted to their antennas in separate waveguides. The two waveguide runs consisted of 12-ft sections connected together during tower erection. A single 7/8-inch coaxial line was used to carry the VHF, UHF, and L-band signals to their antennas. The appropriate low band signal was switched into the coaxial line by two three-way band-select switches, one located near the top of the tower, and the other inside the electronics van. The signal received from each antenna was fed to a separate preamplifier for each frequency band. The

Antenna

(5) Transmitters

Exciter

Preamplifiers

5:1 Switch

(5)

IF Receiver

(5)

A/D’s

Buffer Interface

System Triggers

System Control

MiniComputer Recorder

Figure 3.A.4

Phase One instrument block diagram.

Appendix 3.A Phase One Radar 253

first intermediate frequency (IF) for all frequency bands was 740 MHz. The first IF entered into a common receiver used for all frequencies. The diagram of the receiver and signal processor is shown in Figure 3.A.5. The receiver IF gain could be varied dynamically according to an r3 or r4 (where r = range) sensitivity time control (STC) function. Both STC functions provided 40-dB attenuation at 1 km. In addition, the preamplifiers shown in Figure 3.A.4 could be bypassed, and fixed attenuation could be switched into the system to avoid system saturation by large target returns. The 740-MHz IF signal was mixed to l50 MHz where the matched filtering was accomplished. Additional IF amplification was also provided. The l50-MHz IF signal was converted to in-phase and quadrature (I and Q) signals at baseband where the A/D conversion was performed. The Data Collection Unit provided real-time buffering of the I and Q data and routed the clutter data to the PDP-11 computer or tape recorder. The Radar Data Processor (RDP) performed envelope detection, or the I and Q samples were fed to a digital-to-analog (D/A) converter which drove the A-scope as shown. In addition, the RDP performed real-time noncoherent integration of 128 pulse returns. The integrated data were saved by the computer, which, in non-real time could generate a range/azimuth display. The Radar Control Unit consisted of timing and data control logic that accepted commands from the computer and converted them to radar control signals. Data collection was controlled automatically by the computer. The system operator input parameters via keyboard or floppy disk which established the range and azimuth limits, radar frequency, scan rate, waveform, sampling rate, and polarization to be used for each experiment (see Table 3.A.8). The Phase One system performance parameters listed in Table 3.A.2 are now described more fully. System stability and dynamic range are commensurate with a clutter Control

590-MHz LO 740 MHz from Microwave

150-MHz IF

STC Attenuator

Filter

Select: r 3, r 4, Fixed

Test

150 MHz A Scope Control Buses

15, 36, 150-m Filter

SYNC Detector

SYNC Detector

A/D

A/D

Strobe Radar Data Processor

Radar Control Unit

PDP 11/34 Computer

Range/Az Display

Figure 3.A.5

Phase One receiver and signal processor.

Data Collection Unit

Tape Recorders

150 MHz

Strobe

254 Appendix 3.A Phase One Radar

improvement factor of 60 dB at VHF, UHF, and L-band and 55 dB at S- and X-bands for a two-pulse cancellation technique. These specified clutter improvement factor levels assume that pulse-to-pulse variations in transmitter amplitude and phase due to antenna motion are small. The pulse-to-pulse variations in transmitter amplitude and phase were measured in real time and stored on tape in the calibration block of the clutter data record. Experimental tests showed that antenna motion was minimal and that 60-dB clutter improvement performance was achieved in winds up to 20 knots. The Phase One system was capable of transmitting and receiving vertical or horizontal polarization. There were two waveforms available at each frequency, one at low resolution (150 m) and one at high resolution (15 m at L-, S-, and X-bands; 36 m at VHF and UHF). The waveforms were short uncoded pulses of 1-µs duration for low resolution and of 0.1-µs or 0.25-µs duration for high resolution. The minimum range of 1 km is the closest range from the radar at which clutter data could be collected. The calibration accuracy specification of 2-dB rms reflects the capability of maintaining this accuracy across all sites (see Section 3.A.3). The instantaneous dynamic range was the amplitude range of clutter strength that could be collected with a signal-to-noise (S/N) ratio of 12 dB or greater without saturating or exceeding the linear range of the receiver and A/D converter. The center of the 60-dB instantaneous range could be adjusted in 1-dB steps from 0 to 40 dB. For example, the total dynamic range could be expanded to 100 dB by first collecting data with 40 dB of attenuation over a particular area and then repeating the data collection over the same area with no attenuation. Additional control of dynamic range could be effected through bypassing the preamp. The clutter data were recorded in I and Q format at the A/D converter outputs. The maximum A/D converter sampling rate was 107 I and Q samples per second with 13 bits each. The A/D data were then buffered for the recorders, which had a maximum recording rate of ≈625 Kbytes per second. The system sensitivities shown in Table 3.A.2 apply to the 150-m waveform. The sensitivity to clutter for the high resolution waveforms was 20 dB lower (10 dB reduction in pulse energy, and 10 dB reduction in area illuminated). There were three basic data collection modes available: the beam scan mode, the parked beam mode, and the beam step mode. During the beam scan mode, data were collected as the antenna beam scanned from one azimuth limit to the next. In the parked beam mode, data were collected while the beam was held at a fixed azimuth—long-time-dwell data were collected with a parked beam. In the beam step mode, the beam was stepped through the measurement sector, beam position by beam position, with the beam held fixed at each step while data were recorded. Approximately 15 s were required for antenna stabilization at each step during step beam data collection. Largely because of this antenna stabilization wait time in step mode, most of the 360° survey data were recorded in scan mode to keep data volume and data acquisition time reasonable. However, many of the repeat sector measurements were conducted in step mode. See Section 3.C.4 for computational comparison of clutter measured in these various modes. The antenna scan was limited to 360° due to cable wrap.

3.A.3 Phase One Calibration Each operating mode of the Phase One radar had an adjustable system range bias associated with it. These range biases were accurately adjusted when the equipment was

Appendix 3.A Phase One Radar 255

first set up at Katahdin Hill at Lincoln Laboratory. These initial adjustments were made by measuring radar reflections from known discrete targets in the neighborhood for which the positions had been accurately surveyed. Range calibration was checked at every Phase One site in a boresight test using a prominent discrete object of opportunity (such as a water tower) as a radar target, the radar range of which was obtained from large-scale maps. Azimuth information was provided in the Phase One system by a precision azimuth encoder in the servo drive mechanism for steering the antennas. Every recorded pulse had associated with it in header information an azimuth position read from this encoder. The quantization interval of the encoder was 0.01°. Occasionally, even with a fixed beam position, wind forces could cause very small positional variations which, even though small, were picked up by the encoder and precisely recorded on tape. The raw azimuth-encoded data indicated relative angle information only and had to be corrected by an additive offset to provide absolute azimuth with respect to true north. The correction angle varied from site to site, depending on the particular setup geometry realized by the trailer configuration at each site. The same boresight test that checked range calibration at each site using a prominent discrete target also was used to provide the azimuth servo correction angle. Phase One signal strength calibration involved both internal and external procedures. Every recorded clutter experiment carried with it on the raw data tape both pre- and postcalibration files containing internally measured values of transmitter and receiver parameters. Table 3.A.3 lists the parameters that were internally measured and recorded with each experiment and indicates the frequency at which these measurements were performed. These parameters were subsequently used at Lincoln Laboratory to reduce the data to units of absolute clutter strength on calibrated clutter tapes. The automatic internal calibration measurements shown in Table 3.A.3 calibrated the Phase One system up to the transmit and receive couplers. Beyond these couplers, the RF transmission line losses and antenna gains were checked by external tests. Table 3.A.4 summarizes these external tests, which include range and azimuth calibration as discussed above. External signal strength calibration checks were conducted using standard gain antennas and corner reflectors. The standard gain antenna tests were conducted as both receive tests and transmit tests at VHF, UHF, and L-band; corner reflector tests were conducted at S-band and X-band. The lower band receive tests consisted of radiating a signal from a standard gain antenna (horn at L-band, Yagis at VHF and UHF) located on a tower approximately 100 m from the radar tower, and receiving this radiated signal at the Phase One receiver. In these procedures, the standard gain antenna was located on the fringe of the near field of each of the three low band Phase One radar antennas. A Hewlett Packard 866A signal generator was used for the RF source. The RF signal was transmitted through a 100-ft coaxial cable to the standard gain antenna on top of the calibration tower which could be expanded from 37 to 75 ft. By raising and lowering the tower, the multipath effects were accounted for by measuring the maximum and minimum signal level and calculating the free-space signal assuming a relatively constant terrain reflection coefficient. At the 100-ft radar tower height the multipath was usually less than 2 dB at all of the low band frequencies. At the 60-ft radar tower height the multipath effects remained small at UHF and L-band but were somewhat more significant at VHF. The lower band transmit tests were conducted by transmitting from the Phase One radar and receiving at the standard gain antenna. The equipment and procedures were identical to the receive tests except that a Hewlett Packard 1/36A power meter was used to measure the power received at the standard gain antenna.

256 Appendix 3.A Phase One Radar

Table 3.A.3 Internal Calibration Tests Test

Frequency

Receiver gain

Each experiment

Transmitter average power

Each experiment

Transmit amplitude and phase

Each pulse

Antenna VSWR

Operator request

Receiver noise figure

Half hour

Synchronous detector balance

Half hour

DC correction loop

Half hour

Fixed attenuator

Each experiment

Sensitivity Time Control (STC)

Each experiment

Table 3.A.4 External Calibration Tests Test

Frequency Bands

Purpose

Standard gain antenna tests (receive and transmit)

VHF, UHF, L-Band

Signal strength calibration

Corner reflector tests

S-Band, X-Band

Signal strength calibration

Boresighting tests

All bands

Range and azimuth calibration

Reference object tests

All bands

Signal strength monitoring

The external calibration tests at S- and X-band were conducted using a corner reflector for which the RCS was +35.7 dBsm (i.e., dB with respect to 1 m2) at X-band and +27.5 dBsm at S-band. The corner reflector was mounted on the calibration tower approximately 3 km from the radar tower and was raised and lowered to account for multipath reflections similarly to the transmit and receive standard gain antenna tests. Where possible a line of brush or small trees was used to block the terrain multipath. The X-band returns seldom varied by more than 2 dB, but the S-band returns more frequently varied by more than 2 dB. Measurements of the calibration tower without the corner reflector indicated that the tower RCS was approximately 10 dB lower than the corner reflector RCS at S-band. Calibration constants were not individually adjusted at each site on the basis of each site’s external calibration tests because the calibration tests were always conducted in a nonfreespace propagation environment and hence had some associated site-specific variation. Instead, average results over a multisite history of external tests were used to set calibration constants. This leaves site-to-site variations over the history of the external tests. Table 3.A.5 shows the standard deviation by band and polarization in the site-to-site variations in the Phase One external calibration measurements over the history of the program. Table 3.A.6 shows similar data from a single reference target for the Phase One radar’s

Appendix 3.A Phase One Radar 257

Table 3.A.5 Standard Deviations (dB) of External Calibration Measurements over the Three-Year History of the Phase One Radar*

Frequency Band Polarization VHF

UHF

L-Band

S-Band

X-Band

Vertical

1.5

1.3

1.2

2.3

1.5

Horizontal

2.0

1.6

1.4

2.4

1.6

* External calibrations were performed at 36 Phase One sites using a corner reflector and standard gain antennas. The standard deviations are of differences between expected and measured results. Calibration constants were set such that mean values of these differences over multiple sites were zero.

Table 3.A.6 Standard Deviations (dB) of Measurements of Reference Target RCS at Katahdin Hill over Nine-Month Period*

Frequency Band Polarization

VHF†

UHF

L-Band

S-Band

X-Band

Vertical

1.2

0.7

0.7

1.0

1.0

Horizontal

1.7

0.8

0.9

1.2

0.9

* The Phase One radar collected ground clutter and reference target data once a week over a nine-month period at the Katahdin Hill site. The referenced target was a 120-ft tall, 40-ft diameter cylindrical water tank located at a range of 6.5 km. † Severe VHF interference frequently occurred at the Katahdin Hill site, which may have affected the consistency of the VHF measurements.

subsequent nine-month setup on Katahdin Hill. As expected, the variations occurring at a fixed site (Table 3.A.6) are less than those occurring across many sites (Table 3.A.5). The variations shown in both Tables 3.A.5 and 3.A.6 are small and validate the quoted estimate for calibration accuracy of ≈2 dB rms across the complete set of Phase One sites. At each site, the discrete reflecting object such as a water tower used in boresight range and angle calibration was also used as a signal strength reference target prior to and throughout clutter data collection (see Table 3.A.4). The return from the reference object was repeatedly measured and recorded to ensure that no changes occurred in system calibration. As a result, a set of measurements of reference target RCS in each band was available from each site. For each site and band, the standard deviation across this set of measurements was computed. Table 3.A.7 shows the mean values of these standard deviation numbers in each band across all sites. The data in Table 3.A.7, which summarize many more measurements than Tables 3.A.5 and 3.A.6, confirm day-to-day calibration repeatability based on measurements from reference objects such as water towers.

3.A.4 Phase One Data Collection The basic entity in which Phase One data were recorded was as a Clutter Data Collection (CDC) experiment. In each experiment, clutter returns were measured pulse by pulse from every resolution cell on the ground over some area defined by beginning and ending limits

258 Appendix 3.A Phase One Radar

Table 3.A.7 Standard Deviations (dB) of Measurements of Reference Target RCS at 33 Sites* Frequency Band

Mean

VHF

UHF

L-Band

S-Band

X-Band

0.6

0.5

0.7

1.2

1.8

* Daily reference target data were collected at 33 Phase One sites over the radar's three-year history. At each of these sites, a strong discrete reference target of opportunity, such as a nearby water tower, was selected to check day-to-day system repeatability.

on both range and azimuth for a given antenna mode and for a fixed set of radar parameters. Each experiment was defined by a Radar Directive File (RDF). The RDF controlled the Phase One measurement system during acquisition of the clutter data within each experiment. The RDF parameters requiring specification for each CDC experiment are shown in Table 3.A.8. The measured clutter data were obtained as either survey, repeat, or long-time-dwell data. Table 3.A.8 Radar Directive File Parameters for Clutter Data Collection Experiments Measurement Sector

Radar Parameters

Range (km):

(a) START

(b) EXTENT

Frequency:

Azimuth (deg):

(a) START

(b) STOP

Polarization:

Antenna Mode (1) Step:

(a) Azimuth increment (deg) (b) Number of recorded pulses ≤ 30,720

or (2) Scan:

(a) Scan velocity ≤ 3 deg/s

VHF, UHF, L-, S-, X-Band VV or HH

Resolution (m): 15, 36, 150 Range Sampling Rate (MHz): PRF (Hz):

1, 2, 5, 10 500, 1000, 1500, … 4000

Record 1 out of N Pulses:

N = 1, 2, 4, 8, 16

Attenuation: Fixed:

1, 2, 3, … 40 dB

STC:

r 3 or r 4; 40 dB at 1 km

Appendix 3.B Multipath Propagation 259

Appendix 3.B Multipath Propagation 3.B.1 Background In considering the physics of the low-angle clutter phenomenon, an important factor is the effect of the intervening terrain on the illumination at the backscattering cell. As is indicated in Figure 3.B.1, the terrain between the radar and the clutter patch influences the illumination of the clutter patch. For example, multipath reflections can interfere with the direct illumination and cause lobing on the free-space antenna pattern. All terrain propagation effects including reflection and diffraction are included within the pattern propagation factor F (see Section 2.3.1.2). Ideally, one would wish to separate effects of propagation from the backscatter measurement. Free-Space Antenna Pattern X-Band Lobing VHF Lobing Depression Angle α ρ

12 d

B

Microshadowing

Propagation Factor F

Clutter Coefficient σ°

Clutter Strength = σ°F4

Figure 3.B.1

Clutter physics.

However, the actual effects of terrain on illumination cannot be easily separated out. To do so experimentally would require a separate measurement of illumination strength in every clutter cell. As to what this would entail, consider that the illuminating field strength is often a rapid function of elevation near the ground, making it difficult to determine the actual illuminating field distributions over typical vertical clutter features (e.g., tree, silo). To do so theoretically requires use of radar propagation prediction computer codes, utilizing digitized terrain elevation data, such as those based on SEKE [1, 2], Parabolic Equation [3–5], or Method of Moments [6]. At X-band, such codes are useful for providing physical insight on the statistical average over large spatial regions at clutter source heights, but are not accurate enough to allow deterministic cell-by-cell computation and separation of F in clutter measurement data. At VHF, however, propagation variation exhibits less scintillation and some efforts were made to use propagation prediction codes to predict and separate F from Phase One VHF clutter measurements. However, these attempts to separate

260 Appendix 3.B Multipath Propagation

F in VHF clutter data generally met with little success because the local cell-to-cell variations in clutter strength σ°F4 were not well correlated with the predictions of F—the resultant separated distributions of intrinsic σ ° usually became broader instead of narrower than the corresponding distributions of σ°F4. Therefore, what is measured as real-world clutter strength is the product of the clutter coefficient, σ°, defined (see Section 2.3.1.1) to be RCS per unit ground area in the resolution cell, and the fourth power of the pattern propagation factor. The propagation factor is raised to the fourth power as it enters into clutter strength because clutter strength (actually clutter intensity) is proportional to power (i.e., the square of the field strength), and a two-way propagation path is involved. Implicit in this definition of clutter strength is the proper assumption of unit plane wave illumination in the definition of RCS, as well as the proper incorporation of the real unknown illumination within the propagation factor. Throughout this book clutter strength is represented by the symbols σ°F4 to demonstrate explicitly that clutter strength depends on two important factors, the intrinsic backscatter and the illumination. These two factors are not separated in the clutter measurement data or clutter results in this book. Within the Phase One clutter measurement program, measurements of illumination strength and the effects of propagation on illumination were made at a number of Phase One sites. These propagation measurements were recorded in a helicopter (i.e., Phase One radar used as transmitter; receiver in helicopter) flying vertical ascents and descents above selected clutter cells. The important findings from these propagation measurements are incorporated in the interpretation of the clutter measurement data in this book. At X-band, terrain reflection coefficients are often lower and hence multipath effects are diminished from those that can exist at lower radar frequencies. The Phase One propagation measurements revealed, however, that significant multipath lobing does exist at X-band on typical low-relief open prairie landscapes. When they exist at X-band, propagation lobes are relatively narrow—for example, the height to the first maximum on the X-band lobing pattern is 14.6 ft at 10-km range with a 60-ft antenna tower over a level reflecting surface. Typical clutter sources such as trees and buildings over most visible terrain often subtend a number of such lobes when they exist. As a result, the effects of propagation are further diminished at X-band when compared with lower frequencies. As carrier frequency decreases, especially below L-band to UHF and VHF, influences of terrain on propagation and illumination strength can become dominant. First, at the lower frequencies, terrain reflection coefficients increase so that multipath lobing becomes stronger. Second, for a given antenna height, as carrier frequency decreases, the widths of the multipath lobes become broader—for example, the height to the first maximum on the VHF lobing pattern is 864 ft at 10-km range with a 60-ft antenna tower over a level reflecting surface. This result may be understood on the basis of the lobing pattern simply being an interference pattern between the actual source of radiation and its image in the reflecting terrain surface. For a given antenna height, as carrier frequency decreases, the effective separation of the source point and its image measured in wavelengths decreases, and the angular periodicity (i.e., lobe width) in the interference pattern increases. Even at X-band, there can be a region at long enough range where strengths from even relatively high clutter sources are generally reduced because of illumination from the

Appendix 3.B Multipath Propagation 261

underside of just the first propagation lobe. In contrast to such a relatively unusual X-band situation, however, at lower frequencies these broad multipath lobes can be of dominant influence even at short ranges over typical sources and patches. That is, they can strongly change (either increase or decrease) the effective gain over whole clutter patches and over the complete vertical extents of typical clutter sources within patches. This situation is illustrated in Figure 3.B.1 where a strong low-frequency multipath lobe caused by a terrain reflection coefficient ρ of unity increases effective antenna gain over the whole patch by 12 dB. Such an increase is evident in the Strathcona repeat sector clutter measurements at VHF. The theoretical upper limit to gain increase over free space caused by a single Fresnel multipath reflection is 12 dB, which is the result of both incident and scattered field strengths being doubled by terrain reflection, although terrain focusing effects can occasionally result in gain increases > 12 dB. The Phase One clutter data are analyzed to determine important fundamental trends in clutter strength σ°F4 as measured from regions of visible terrain. Except at low frequencies on level open terrain, the effects of multipath propagation on clutter strength are usually specific to the particular terrain profile occurring for any given measurement and hence statistically dispersive across a set of nominally similar measurements as the details of the multipath lobing vary from measurement to measurement. Thus, the measurement program requires many sites and patches to overcome such specific influences. As noted, it might be initially supposed that the theoretical high ground would be to separate propagation from backscatter. This becomes even more the case upon considering that illumination strength of a discrete vertical clutter source in the presence of multipath is a function of geometrical factors such as antenna height and range to the clutter source. The practical goal in this book is to move in a statistical fashion past this impracticable position requiring the separation of propagation effects to provide useful results for predicting low-angle ground clutter strengths as actually experienced in ground-based radar. The process involves gathering statistics as much on propagation F as on terrain backscatter σ°. It is evident from the above discussion that the propagation factor F significantly affects clutter strength σ°F4. It is oversimplifying, however, to attribute most of the variability in σ°F4 over any given spatial macroregion to propagation. The Phase One measured clutter histograms over such macroregions reveal up to 60 dB of cell-to-cell variability in intrinsic σ° over forested terrain where effects of propagation are minimal (i.e., F ≅1); this variability increases to 80 dB over open terrain supportive of multipath. Thus the measurements indicate that most of the cell-to-cell variability within patches in the measured clutter data is associated with variations in intrinsic σ°, although variations in propagation F further increase the variability in clutter strength σ°F4. Preliminary attempts [7] to model the low-angle clutter phenomenon as constant σ° with a subsequent overlay of propagation computation were not in the end generally successful in accurately replicating measured clutter amplitude distributions. Of course attempts to model low-angle clutter as constant σ° without including effects of propagation are even more unrealistic—studies have shown that the value of constant σ° (i.e., the percentile level in the measured clutter distribution) that provides equivalent system performance as real clutter is highly specific to the particular system, performance parameter, and terrain being modeled. The idea of extreme variability in intrinsic clutter σ° is not always intuitive. For example, consider two similar pine trees—how can their intrinsic σ°’s be very different from each other? Hence it must be propagation-induced variations in the illumination of the trees that

262 Appendix 3.B Multipath Propagation

cause such wide variations in measured clutter strength. However, what is not accounted for in such an argument is that the clutter measurement is made at low angles over a spatial macroregion encompassing a number of square kilometers of forested terrain with all of the cell-to-cell variability that naturally occurs over such terrain including local effects of shadowing where the treetops drop out of visibility and discretes where tall trees rise into visibility. It is true that cell-to-cell variations in illumination within and over a forest canopy are largely propagation induced, but such microscale variations involving inter- and intra-tree propagation effects are properly subsumed within intrinsic σ°, and are not the sort of macroscale propagation effects caused by significant variations in terrain elevation that can realistically be predicted by available propagation prediction codes and included in the propagation factor in the measurement data. Such discussion makes clear the futility of attempting to too finely distinguish effects of propagation from those of intrinsic clutter—at low angles, both clutter and propagation are to a significant degree bound up as one integrated and inseparable phenomenon, as put forward in a theoretical discussion of lowangle scatter by Barrick [8]. The SEKE propagation code [1, 2] was utilized to estimate propagation at clutter source heights in many of the repeat sectors at VHF, UHF, and L-band. These SEKE estimates were usually within appropriate general propagation regimes; for example, they usually successfully separated strongly multipath-dominated situations from nonmultipath situations. However, from a more specific cell-by-cell point of view, the SEKE estimates were seldom useful in assisting in quantitatively understanding the clutter measurements. Local variations in SEKE propagation estimates in a given repeat sector were not accurately borne out in the clutter measurement data. Multifrequency differences in measured clutter strength were not accurately predicted. Such propagation predictions at the very low heights of clutter sources tend to be highly sensitive to artificial nuances in the DTED upon which they are based. Because most of the repeat sector clutter measurements occur at relatively short ranges, typically of less than 10 or 20 km, the dominant mechanism of propagation entering the measurements is multipath reflection. At many sites, the multipath enters in a manner very specific to the terrain involved. Section 3.B.2 shows how to estimate the multifrequency effects of multipath in the repeat sector measurements by considering multipath from a flat surface local to the Phase One antenna but tilted at the hillside slope where the measurements are taken. Such multipath estimates apply at relatively short-range where earth sphericity effects are relatively inconsequential. Section 3.B.3 provides some Phase One measurements of long-range mountain clutter obtained in survey data acquisition mode. These long-range mountain clutter data expand the understanding of how propagation effects, not only reflective but also diffractive, can dominate low-angle clutter from visible terrain.

3.B.2 Hillside Multipath The Phase One radar was often set up to make clutter measurements on a local topographic high point in open, low-relief terrain. In such situations, the radar initially looked down the side of the hill it was set up on over terrain outwardly inclined at angle α with respect to horizontal, and then out to clutter sources distributed over more level terrain at longer range in the repeat sector clutter patch. In this book, multifrequency clutter strength results are interpreted in a number of such measurement situations under

Appendix 3.B Multipath Propagation 263

the assumption that dominant multipath occurred from the side of the hill at relatively close range. That is, a multipath lobing pattern was assumed to be set up by the presence of a plane reflecting ground surface outwardly inclined at angle α. The effect of the inclination of this plane was to tilt the lobing pattern down by angle α. As a result, clutter sources on level terrain at much longer range were illuminated up on the pattern at positive elevation angle α rather than deep in the horizon plane null as they are when the reflecting surface is level. This rotation of the multipath lobing pattern by the local terrain slope in the direction of the repeat sector was often a dominant influence in the multifrequency clutter strength characteristic of the repeat sector clutter patch, even for what were often relatively small terrain slopes. This effect is now analyzed more thoroughly. First, assume a situation involving an antenna at ha above a tilted, perfectly reflecting, infinite planar surface tilted at angle α with respect to horizontal, as depicted in Figure 3.B.2. Also shown dashed in Figure 3.B.2 is the profile of the actual terrain as it deviates from the inclined planar surface, both at the hilltop and into more level terrain far out in the clutter patch. This simple model allows backscatter from clutter sources distributed on this more level terrain but does not allow additional multipath from it (i.e., multipath is allowed only from the tilted plane). In Figure 3.B.2, the height of the antenna above the tilted plane is ha, the height of the clutter source above the tilted plane is ht, the range along the reflecting plane from the antenna to the clutter source is R, and the range along the reflecting plane from the antenna to the bottom of the hill is r. It is desired to know the clutter strength σ °F4 from the indicated clutter source, where σ ° is the intrinsic reflectivity of the source and F is the propagation factor. Under the conditions that R>>ha, ht>>ha, and the reflection coefficient equals –1, the factor F4 is given by F4 = 16 sin4  2π ------h ⋅ θ   λ a h

(3.B.1)

where λ equals carrier wavelength and θh = ht/R.

ha

Antenna

Hill

Direct R

Antenna Image

ay

Multipa

Clutter Sources

th Ray

α r

Terrain

ht Tilted Reflecting Plane

R Ran Ant ge from enn a

Figure 3.B.2

Multipath from a tilted reflecting plane.

264 Appendix 3.B Multipath Propagation

Note that, in Equation (3.B.1), θh varies with every clutter source position. Thus, so far, little progress in simplification has occurred—the situation requires a separate computation of F4 for every clutter source position. Rather than compute F4 at every clutter source position in a repeat sector clutter patch, what is desired here is to perform a simple one-time computation to help provide an understanding, at least in general terms, of the effect of multipath in causing large variations in mean clutter strength vs frequency over the whole repeat sector clutter patch. A first step towards such generality is to assume that R is very large, or, in other words, that the range to the clutter patch R is much greater than the range to the bottom of the hill r. Let x equal the range from the bottom of the hill to the clutter patch, i.e., let x = R–r. Then, for large R, ht ht h θ h = ----t = ----------- ≅ ---- = α x+r x R

(3.B.2)

Thus, when R is large, α may be substituted for θh in Equation (3.B.1). The quantity α is a fixed quantity, equal to the hillside slope upon which the Phase One radar is set up and down which the radar looks in the direction of the repeat sector clutter patch. Now substantial progress has been made in simplification because in Equation (3.B.1) θh, a quantity which varies with clutter source position, has been replaced with α, a fixed quantity. This substitution assumes that all the clutter sources in the repeat sector clutter patch are at long enough range that they are essentially illuminated by a horizontal direct ray and an interfering horizontal multipath ray reflected from the hillside slope below the Phase One radar. This situation is depicted in Figure 3.B.3.

Far-field Clutter Source Antenna

Hill

Figure 3.B.3

Direct Multipath

Far-field interference between a direct ray and a hillside slope multipath ray.

A number of the Phase One repeat sector measurement situations are reasonably well modeled by the situation illustrated in Figure 3.B.3. At a number of other sites, the terrain is more bowl-shaped; rather than leveling off beyond the foot of the hill, the terrain rises back up to the repeat sector clutter patch, but the assumption of near-horizontal direct and multipath rays illuminating the clutter patch remains a good first approximation. In Section 3.4 of Chapter 3, when multifrequency clutter measurement characteristics are interpreted on the basis of local terrain slope tilting a multipath lobing pattern down by the amount of the terrain slope, it is assumed that the multipath originates only from a tilted plane, and that clutter sources in the repeat sector clutter patch are illuminated at near-zero depression angle, either because they are on nominally level terrain at long-range or because a bowlshaped terrain profile raises the clutter sources back up.

Appendix 3.B Multipath Propagation 265

Figures 3.B.4 and 3.B.5 show F4 vs θh as given by Equation (3.B.1) for the Phase One VHF, UHF, and L-band antennas, for three tower sections expanded in Figure 3.B.4 and for six tower sections expanded in Figure 3.B.5. To apply the above model as depicted in Figure 3.B.3, estimate α, the slope of the hill the radar is on in the direction of the clutter patch, and read multipath loss (or gain) F4 at VHF, UHF, and L-band at θh = α in Figures 3.B.4 or 3.B.5, depending on antenna height. That is, in these circumstances, Figures 3.B.4 and 3.B.5 give multipath loss vs hillside slope angle θh. In farmland situations, intrinsic σ ° is roughly frequency independent (see Section 3.4), so a frequency band that provides a considerably different value of mean clutter strength than the other bands, either higher or lower, is often explained on the basis of its being at a peak or null in the multipath lobing pattern. Next, the question of estimating the slope of the ground on the hill running down from the antenna is addressed. What is usually available is either a contour topographic map or 20 L-Band

VHF

UHF

10

F4 (dB)

0

–10

–20

–30

–40 0

1

2

Elevation Angle θh (deg)

Figure 3.B.4 Two-way multipath propagation loss F4 vs hillside slope angle θh for the Phase One antennas with three tower section extended. Computed by Equation (3.B.1), ha = 17.4 m, 17.4 m, and 16.6 m for VHF, UHF, and L-band, respectively.

3

266 Appendix 3.B Multipath Propagation

20 L-Band

VHF

UHF

10

F4 (dB)

0

–10

–20

–30

–40 0

1

2

3

Elevation Angle θh (deg)

Figure 3.B.5 Two-way multipath propagation loss F4 vs hillside slope θh for the Phase One antennas with six tower sections extended. Computed by Equation (3.B.1), ha = 29.6 m, 29.6 m, and 28.7 m for VHF, UHF, and L-band, respectively.

digitized terrain elevation data, both of which in effect model the side of the hill in the direction of the repeat sector as a number of tilted straight line segments or facets along the outward radial from the radar site position into the repeat sector. Each facet has a different tilt angle. It is necessary to determine which facet results in a horizontally reflected multipath ray. This is the active facet, which provides a first Fresnel zone of specular reflection in the horizontal direction, and at the tilt angle for which Figures 3.B.4 and 3.B.5 are entered to determine multipath loss. To determine which is the active facet, an iterative procedure is conducted examining each facet. The geometry for this process is shown in Figure 3.B.6. As is shown there, let the start range of the facet from the antenna position be r1, the stop range of the facet be r2, the decrease in terrain elevation from the antenna position to the beginning of the facet be y1, the subsequent decrease in terrain elevation from the beginning of the facet to the end of the facet be y2, and let the vertical antenna mast height be q. Let the slope of the facet with

Appendix 3.B Multipath Propagation 267

respect to horizontal be α, i.e., tan α = y2/(r2–r1). Imagine the planar facet surface to expand so as to be of infinite extent (i.e., the facet line is extended both to left and to right). The question is then posed, at what range r' on this expanded facet does the specular reflection point occur for an observer infinitely removed in the horizontal direction (i.e., horizontal specularly reflected ray)? The condition for specular reflection is that the angle of incidence equals the angle of reflection from the tilted planar surface. The range to this specular point r' is given by y1 + h – r1 r' = cos2α ----------------------tan α

(3.B.3)

The quantity r' is computed for every facet down the side of the hill. The active facet is the particular facet for which r1 < r' < r2. The value of α from the active facet is what is used for θh to compute propagation loss in Equation (3.B.1). Direct

Antenna

q

Ac

y1

tive

Fa

ce

y2

Image

t

α

Multipath Reflecting Plane

r 0

Figure 3.B.6

r1

r`

r2

Active facet geometry.

One other task remains. The height of the antenna ha in Equation (3.B.1) is the height of the antenna above the infinitely extended active facet surface in a direction normal to this surface (see Figure 3.B.2). This height ha may be significantly greater than or less than the actual antenna mast height q, depending on α and the details of the terrain profile out to the active facet. The quantity ha is given by ha = (q + y1) cos α – r1 sin α

(3.B.4)

268 Appendix 3.B Multipath Propagation

Thus, after the active facet is determined, its parameters are used to determine ha by means of Equation (3.B.4), and then the active facet slope α and ha are used in Equation (3.B.1) to determine multipath loss F4. Figures 3.B.4 and 3.B.5 plot F4 from Equation (3.B.1) as a function of facet slope, but they do so only for values of ha equal to antenna mast height q. However, in going from q to ha, the only difference in Figures 3.B.4 and 3.B.5 is that the abscissa scale changes by a fixed multiplicative factor, according to the relationship ha θh = q θh', where θh is the new scale applicable for height ha and θh' is the old scale as plotted in Figures 3.B.4 and 3.B.5 applicable for ha = q. Thus if ha > q, the rate of lobing with increasing angle is faster by qa/ha, and vice versa if ha < q. In this manner, Figures 3.B.4 and 3.B.5 may still be used to estimate a multipath loss for values of ha different than the actual mast heights explicitly applicable in these figures. A simple method (model) has been described for estimating the effects of multipath on observed clutter strength when a radar is situated at a topographic high point in open, lowrelief terrain. This simple model has proven useful to explain a number of particular features in the Phase One repeat sector measurements. In the next section, this model is used to help understand long-range mountain clutter measured from open low-relief sites.

3.B.3 Long-Range Mountain Clutter Ground clutter observed from visible terrain at long ranges of 100 km or more comes from mountains because only mountains rise high enough to be visible at such long ranges. Even so, visible mountains at such long ranges barely rise above a distant horizon and are usually observed at elevation angles of less than 1° above the local horizontal at the antenna. This being the case, one might assume that when such long-range mountains are observed from open, low-relief sites, their X-band clutter strengths would be substantially greater than their VHF clutter strengths due to significant multipath propagation loss being expected at VHF at such low angles. In fact, the measurements of long-range mountain clutter from open, low-relief sites show just the opposite—mountain clutter strength at VHF is 10 or 12 dB stronger than at X-band. The reason for this difference is that the inclined surface away from the topographic high point upon which the radar is located rotates the VHF multipath pattern downward and hence brings the long-range mountains at the horizon into stronger illumination, as discussed in the previous section. This section presents multifrequency long-range mountain clutter strengths from high peaks and ranges in the Canadian Rocky Mountains as measured looking west from three different Phase One sites in Alberta, Canada. Two of these sites, Magrath and Lethbridge West, were on open, low-relief prairie in southern Alberta. The third site, Brazeau, was located farther north in Alberta in low-relief boreal forest. At each site, mountain clutter data were reduced from within a 45° azimuth sector to ranges extending well beyond 100 km. At each site, the mountain ranges observed within the sector include steep barren rock faces and snow-clad jagged peaks, as well as steep forested slopes at lower elevations. However, the specific mountain terrain from which clutter was measured was different for each site (i.e., there was no overlap on the ground in 45° sector coverage at the three sites). At each site, multifrequency mean clutter strengths are compared at relatively near ranges (i.e., ≤ 24.7 km) within the 45° sector with multifrequency mean strengths at longer ranges (i.e., from 24.7 km out to more than 100 km) in the sector. At the near ranges, the mean clutter strengths so obtained are specific to the terrain type in which the radar was located,

Appendix 3.B Multipath Propagation 269

either dense boreal forest or open prairie farmland and rangeland; whereas, at the long ranges, the mean clutter strengths are for mountainous terrain at all three sites. All of the clutter results in this section are based on clutter data measured in survey mode. These survey mode data were acquired under continuous azimuth scan of the antenna, as opposed to the step scan of the antenna used in much of the repeat sector data, and with fewer pulses per cell recorded (typically 125) than in the repeat sector data (typically 1,024). In these continuous scan data, coherent integration was performed over a period of time corresponding to antenna rotation of one-eighth of the antenna beamwidth (typically 16 pulses) to arrive at each sample of clutter strength. Then all of the clutter strengths were assembled from over the 45° sector and specified range interval, either near or far, into a histogram of clutter strengths from which the mean clutter strength was obtained. Multifrequency mean clutter strength results as measured in survey data to long ranges in 45° azimuth sectors at these three sites are shown in Figures 3.B.7, 3.B.8, and 3.B.9, both for the short-range interval at each site and the long-range interval containing mountains. In the Brazeau data of Figure 3.B.7, the low-relief forest data results measured at short-range have the same inverse frequency dependence that is seen in the general low-relief forest, high depression angle, repeat sector results (e.g., see Table 3.6). The Brazeau long-range mountain results in Figure 3.B.7 also have a similar inverse frequency dependence to that of the general mountain repeat sector results (see Table 3.6), except that the Brazeau longrange mountain results are 10 to 12 dB weaker in every band. This significant decrease in clutter strength of long-range mountains compared with short-range mountains is caused by a substantial diffraction loss occurring at the very long ranges and near grazing incidence illumination of the long-range mountains over this poorly reflecting forested terrain. At all three measurement sites under consideration here, although the terrain is of low relief within the first 25 km, as range increases well beyond 25 km, the terrain becomes increasingly rough and ridged as the wooded foothills of the Rockies are encountered prior to the mountain peaks. The propagation paths near grazing incidence suffered diffraction loss over these ridges. The theoretical two-way diffraction loss along the shadow boundary of a single knife edge is 12 dB, which is very nearly the exact loss observed in the longrange mountain data of Figure 3.B.7 compared with the short-range mountain data of Table 3.6. Propagation measurements at Brazeau indicated little or no forward multipath reflection from the forest at all five Phase One frequencies. It is coincidental that the shortrange forest and long-range mountain results for Brazeau in Figure 3.B.7 are so similar. It is apparent in the Magrath and Lethbridge West results plotted in Figures 3.B.8 and 3.B.9, respectively, that the measurement data obtained at these two sites are very similar (note: VHF mountain data were not collected at Lethbridge West). In comparing the data from both these sites with the Brazeau data of Figure 3.B.7, it is observed that the longrange mountain data at all three sites are very similar but that the short-range data are very different at Brazeau from those at Magrath and Lethbridge West. Propagation measurements at both Magrath and Lethbridge West indicated that the open prairie farmland and rangeland terrain at both of these sites were strongly supportive of forward multipath reflections at all five Phase One frequencies. Hence, the short-range data in Figures 3.B.8 and 3.B.9 both show mean strengths that fall off rapidly with decreasing frequency due to increasing multipath loss with decreasing frequency, similar to the repeat sector results in very low-relief agricultural terrain. However, the long-range mountain

270 Appendix 3.B Multipath Propagation

−20

Forest

Mean of σ°F4 (dB)

−30

Mountains

−40

Short-Range Forest (1 to 24.7 km) Long-Range Mountains (24.7 to 143 km)

−50

−60 VHF

UHF

L-

S-

X-Band

Frequency (MHz)

Figure 3.B.7 Multifrequency mean clutter strengths from short-range forest and long-range mountains as measured at Brazeau. Azimuth interval = 225 to 270 deg; pulse length = 150 m; vertical polarization.

clutter data measured at Magrath and Lethbridge West have no multipath loss on the basis of their near equivalence to the data measured at Brazeau in a multipath-free situation. The mean strengths of long-range mountain clutter from all three sites are shown plotted together in Figure 3.B.10. These multifrequency results from three different sites are remarkably similar. A substantial ~12-dB diffraction loss exists in all three sets of measurements of long-range mountain clutter in Figure 3.B.10, with no apparent multipath loss. Thus, relatively full illumination of the long-range mountains occurred in all bands at both prairie sites, even though very large low-frequency multipath losses occurred at shorter ranges at the prairie sites. The simple multipath model of the previous section is next used to show how this is, indeed, the case. At Magrath, the active facet providing Fresnel reflection at 0° depression angle to the farfield, as found from Equation (3.B.3), is at a terrain slope α = 1.85°. The effective height of the antenna ha = 30.6 ft above the plane of the reflecting facet as given by Equation (3.B.4) is substantially reduced from the mast height q = 57 ft. The heights of the longrange mountains seen from Magrath in terms of elevation angle above the local horizontal were determined to reach to 0.7° to 0.8°. Multipath lobing patterns of F4 at VHF, UHF, and L-band for the Phase One antennas above a reflecting plane tilted at α = 1.85° were computed from Equation (3.B.1) using the effective antenna height ha = 30.6 ft as

Appendix 3.B Multipath Propagation 271

−20

Mountains

Mean of σ°F4 (dB)

−30

−40 Prairie

Short-Range Prairie (1 to 24.7 km) Long-Range Mountains (24.7 to 120.6 km)

−50

−60 VHF

UHF

L-

S-

X-Band

Frequency (MHz)

Figure 3.B.8 Multifrequency mean clutter strengths from short-range prairie and long-range mountains as measured at Magrath. Azimuth interval = 225 to 270 deg; pulse length = 150 m; vertical polarization.

described in the previous section. The elevation angles of the long-range mountain peaks above the local horizontal occurred well up on these computed lobing patterns indicating that the mountain peaks were well illuminated in all bands. Even at VHF the mountain peaks reached to nearly the first maximum of the VHF lobing pattern. At Lethbridge West the local terrain in the direction of the mountains in the survey data sector inclines away from the site at a terrain slope α = 0.87°. The mountain peaks appeared at 0.4° to 0.6° above the local horizontal. The effective antenna height above the plane of the reflecting facet was reduced to 27.2 ft, compared with the 57-ft mast height. The terrain slope of 0.87° and reduced antenna height lead to lobing patterns in which the long-range mountain peaks are not illuminated as high as at Magrath, but still high enough to provide full illumination at gains greater than free space in all three bands. If either the Magrath situation or Lethbridge West situation is merely modeled as multipath lobing above a level (i.e., not tilted) reflecting surface using the 57-ft antenna mast height, the elevation angles at which the mountain peaks appear are low enough on the lobing patterns to result in significantly increasing strength of illumination of long-range mountain clutter, VHF to UHF to L-band, as F4 monotonically rises with frequency on the underside of the first propagation lobe in all three bands. There is no evidence of such a countertrend of decreasing clutter strength with increasing frequency due to multipath loss in the longrange mountain clutter measured at either of these two prairie sites.

272 Appendix 3.B Multipath Propagation

−20

Mountains

Mean of σ°F4 (dB)

−30

−40 Prairie

Short-Range Prairie (1 to 24.7 km) Long-Range Mountains (24.7 to 141 km)

−50

−60 VHF

UHF

L-

S-

X-Band

Frequency (MHz)

Figure 3.B.9 Multifrequency mean clutter strengths from short-range prairie and long-range mountains as measured at Lethbridge West. Azimuth interval = 272 to 317 deg; pulse length = 150 m; vertical polarization.

At Lethbridge West compared with Magrath, the lower terrain slope is insufficient to bring the short-range terrain into illumination at UHF, so in Figure 3.B.9 the short-range Lethbridge West clutter strengths at UHF remain low near the VHF levels. At Magrath, due to the higher terrain slope, the short-range terrain is much more strongly illuminated at UHF, so in Figure 3.B.8 the short-range Magrath clutter strengths at UHF are much higher than the VHF levels and nearer the microwave band levels. The long-range mountain clutter measurements over large sectors at three different sites shown in Figure 3.B.10 and described and analyzed in this section may be compared with the long-range mountain data based on 80 specific clutter patches at six sites presented in Chapter 5, Section 5.4.8.1.

3.B.4 References 1.

S. Ayasli, “A computer model for low altitude radar propagation over irregular terrain,” IEEE Trans. Ant. Prop., vol. AP-34, no. 8, pp. 1013-1023 (August 1986).

2.

M. P. Shatz and G. H. Polychronopoulos, “An algorithm for the evaluation of radar propagation in the spherical earth diffraction region,” The Lincoln Laboratory Journal, vol. 1, no. 2, 145-152 (fall 1988).

Appendix 3.B Multipath Propagation 273

−20

Long-Range Mountain Clutter

Mean of σ°F4 (dB)

−30

−40

Measured from: Brazeau Magrath Lethbridge West

−50

−60 VHF

UHF

L-

S-

X-Band

Frequency (MHz)

Figure 3.B.10 Multifrequency mean clutter strengths from long-range mountains as measured from three sites. Brazeau, 25 to 143 km; Magrath, 25 to 121 km; Lethbridge West, 25 to 141 km. 45degree azimuth sectors. Pulse length = 150 m, vertical polarization.

3.

G. D. Dockery and J. R. Kuttler, “An improved impedance boundary algorithm for Fourier split-step solutions of the parabolic wave equation,” IEEE Trans. Ant. Prop., 44 (12), 1592-1599 (1996).

4.

A. E. Barrios, “A terrain parabolic equation model for propagation in the troposphere,” IEEE Trans. Ant. Prop., 42 (1), 90-98 (January 1994).

5.

D. J. Donohue and J. R. Kuttler, “Modeling radar propagation over terrain,” Johns Hopkins APL Technical Digest, vol. 18, no. 2, 279-287 (April-June 1997).

6.

J. T. Johnson, R. T. Shin, J. C. Eidson, L. Tsang, and J. A. Kong, “A method of moments model for VHF propagation,” IEEE Trans. Ant. Prop., 45 (1), 115-125 (January 1997).

7.

S. Ayasli, “Propagation effects on radar ground clutter,” Proceedings of the IEEE National Radar Conference, Los Angeles, pp. 127-132 (March 1986).

8.

D.E. Barrick, “Grazing behavior of scatter and propagation above any rough surface,” IEEE Trans. Ant. Prop., vol. 46, no. 1, pp. 73-83 (January 1998).

274 Appendix 3.C Clutter Computations

Appendix 3.C Clutter Computations 3.C.1 Introduction Chapter 3 is based on clutter measurements within repeat sector macropatches. The repeat sector at each clutter measurement site is a sector of concentration in which each measurement was repeated a number of times to provide a database of increased parametric depth (i.e., more samples per cell, more variations in data collection parameters such as data sampling rate and duration) than could be provided in the more spatially comprehensive survey data. As a result, the values of mean strength and other statistical attributes of repeat sector clutter amplitude distributions upon which Chapter 3 is based are generally well understood, highly accurate, and reliable. Definitions for mean, standard deviation, and other attributes in measured clutter amplitude distributions are provided in Appendix 2.B. This present appendix discusses and illustrates effects of noise corruption on the computation of mean clutter strength and the role of coherent integration in improving radar sensitivity to provide a valid computation of mean strength when the clutter returns are weak. This appendix also illustrates that typical effects of hour-to-hour and day-to-day variations, sampling rate variations, and antenna scan motion on the computations of mean strength are quite small by showing selected groups of experiment-by-experiment repeat sector mean clutter strength at three sites, holding the main radar parameters of frequency, polarization, and resolution constant within each group. Chapter 3 provides values of mean strength for repeat sector clutter amplitude distributions measured across the 20-element Phase One radar parameter matrix (i.e., five frequencies, two polarizations, two range resolutions) at each site. Each value was selected as being centrally representative from a group of repeated measurements of the same frequency, polarization, and resolution. Thus all values of mean strength and other attributes of repeat sector clutter amplitude distributions presented in Chapter 3 are buttressed by underlying information in the measurement database such as is illustrated by a few examples in this appendix. For convenience, each repeat sector patch was selected to be a range interval of an angular sector in a polar grid centered at the radar. The median repeat sector patch is 2.4 km in azimuth extent at its midrange point and 6 km in range extent. Repeat sector patches were selected only within terrain that was under general illumination by the radar, and over which macroscale shadows cast by large terrain features were avoided. Nevertheless, the measurement of ground backscatter by means of a radar on the ground almost always involves microscale shadowing as an important underlying phenomenon even within regions that are generally well illuminated. In fact, for low-relief terrain in which the radar wave skims the surface and backscatters significantly from vertical features only, regions under general illumination contain a high percentage of low return and/or shadowed cells at radar noise level. The reduced clutter data shown in this book incorporate all the cells within generally illuminated patches, including the cells at radar noise level.

Appendix 3.C Clutter Computations 275

Seldom used in this book are “shadowless” statistics in which, within a repeat sector patch, only those clutter return samples above radar noise level are collected into histograms and distributions. Shadowless statistics are sensitivity dependent and are conditional, not absolute, measures of reflectivity. They are often incorrectly used in the clutter literature and misinterpreted in analysis in ways that can significantly misrepresent real system performance. A few examples of shadowless data are presented in Tables 3.C.1–3.C.4, but all of the major clutter results of this book are based on computations involving all samples in the histogram, including those at radar noise level. A major advantage of including all the samples within the distribution, including those at radar noise level, is that the resultant cumulative distributions, once they emerge from the noise, are independent of the sensitivity of the measurement radar. In other words, any percentile level in an amplitude distribution, to be an absolute measure, needs only to reflect how many samples exist below it, not the particular strengths of those samples. These matters of shadowing and sensitivity are discussed at greater length elsewhere in this book. Section 3.C.2 discusses how the corrupting influence of noise-level samples in ground clutter spatial amplitude distributions is dealt with in computing their moments. Section 3.C.3 discusses the computational ramifications of coherency in the measured data. Section 3.C.4 expands upon these discussions by providing a number of examples of repeat sector mean clutter strength computed in various ways.

3.C.2 Upper and Lower Bounds The measured clutter amplitude distributions upon which this book is based include all of the clutter samples returned from within a clutter spatial macroregion or patch, including those at radar noise level. To determine the extent to which these noise samples corrupt the results, the moments of these distributions are computed in two ways: as an upper bound and as a lower bound. The upper bound is computed by assigning the actual received power values to the noise level samples. That is, the actual clutter return for a noise level cell has to be less than or equal to the noise level; if it were greater, it would be measured above the noise floor. The lower bound is computed by assigning zero power to the noise level samples. That is, the actual clutter return for a noise level cell, even if only weakly illuminated through diffraction, theoretically has to be greater than zero. Every computation of clutter mean strength, ratio of standard deviation-to-mean, and higher moment in this book has been performed both ways, as an upper bound and as a lower bound. The values provided are upper bounds unless indicated otherwise. Even when the amount of microshadowing within a patch is extensive (i.e., when a large percentage of returns are at radar noise level), it usually has very little effect on the estimates of these moments. The upper and lower bounds to these quantities are usually within a tenth or even a few hundredths of a decibel of one another because these calculations are dominated by the strong returns from the discrete clutter sources within the patch. Examples of upper and lower bounds to mean patch clutter strength are provided in Tables 3.C.1 through 3.C.4. The shadowless moments can be significantly higher than the upper and lower bounds to the moments because the shadowless moments are computed over a conditional sample population of cells that can be significantly less than the total number of cells. If N is the

276 Appendix 3.C Clutter Computations

total number of cells in the patch, and Nc is the number of shadowless cells above radar noise level, then the shadowless mean is greater than the lower bound mean by 10 log10(N/ Nc) dB. That is, the conditionally defined shadowless mean is highly sensitivity dependent because Nc is highly sensitivity dependent; whereas the upper and lower bounds to the absolute mean (both normalized to the complete population of N cells) are usually not very sensitivity dependent. The shadowless mean is also provided in Tables 3.C.1 through 3.C.4. Note that the percentage of noise samples in each underlying histogram in these tables, although not tabulated, can be computed using the above relationship.

3.C.3 Coherency The Phase One system measured radar reflections coherently, meaning that the radar return from each range sample of each pulse is available on the calibrated clutter tapes as an in-phase and quadrature number pair. A useful benefit of coherency in radar data is the increase in sensitivity that can be obtained by coherently integrating over a number of pulses. This increase in sensitivity depends on the relative phase of the returned signal from the target remaining constant over the integration period while the pulse-to-pulse phase variation in the system noise is random. However, ground clutter is generally not a deterministic targetlike signal but is a noiselike random process with some degree of temporal and spatial correlation. Care must be taken in coherent integration of clutter returns to avoid unintentionally reducing the clutter as though it were noise while attempting to realize increased sensitivity to clutter returns. Let Ii and Qi be the in-phase and quadrature samples for the i-th pulse on a given resolution cell in units of {σ°}1/2. Let the mean σ° of that cell, coherently averaged over N pulses, be σ° coherent. Then 2

N   N  1  I i +  σ °coherent = -----2-  Q i i=1  N i=1 

∑

2

∑

(3.C.1)

Let the mean σ ° of the same cell, noncoherently averaged over the N pulses, be σ ° noncoherent. Then 1 σ °noncoherent = ---N

N

∑

2

( Ii ) +

i=1

N

∑ ( Qi )

2

(3.C.2)

i=1

It is apparent that coherent averaging sums voltage-like quantities; whereas noncoherent averaging sums power-like quantities. Furthermore, it is apparent that coherent averaging of a noncorrelated random process will incorrectly reduce the estimated mean clutter strength by a factor of N. In attempting to improve clutter measurement radar system sensitivity through coherent integration, it is necessary to restrict the integration interval to be substantially less than the correlation time in the clutter process. Clutter correlation time is a strongly varying function of space and time, and, for example, can vary considerably from cell to cell within a repeat sector. Specification of correlation

Appendix 3.C Clutter Computations 277

time statistics in measured data can be a major data reduction undertaking. Alternatively, what can be done is to observe the behavior of spatially averaged coherent mean clutter strength as a function of number of pulses integrated over very long intervals in long-timedwell data, keeping the number of pulses integrated on each cell the same for a given computation of spatially averaged coherent mean strength. This was done in the Phase One data to build up a base of information illustrating how spatially averaged coherent mean clutter strength gradually diminishes with increasing integration time, depending on parameters such as frequency band and terrain type. These results were used to determine how to proceed in repeat sector situations involving weak clutter backscatter where integration gain was required to obtain accurate measures of mean, standard deviation, and other attributes in the measured clutter amplitude distributions. The foregoing discussion indicates that noncoherent computation of clutter strength is preferable if integration gain is not required because noncoherent computation avoids the complex issue of variable temporal correlation characteristics in a noiselike process. Therefore, as the baseline operation in obtaining results for mean strength and other attributes in the clutter spatial amplitude distributions of this book, the coherency available in the data was not utilized, and, for each return sample, the Ii2 and Qi2 clutter strength estimate for that sample was simply binned in a histogram containing all such samples from the clutter patch. The mean and higher moments of the resultant “all-sample” distribution was then computed, both as an upper bound and as a lower bound with respect to the noise level samples in the distribution. As long as these two bounds remain tight, within 0.1 dB or so, the resultant all-sample values of mean and higher moments are definitive. As a standard procedure, a coherent computation of the same results was also routinely performed. In all cases where the all-sample clutter bounds were tight and the integration interval in the coherent computation was much less than the clutter correlation time, the coherent bounds were within a few tenths of a decibel of the corresponding all-sample bounds and provided an amplitude distribution with increased sensitivity at low percentile levels. At a very few sites, particularly with the reduced sensitivity of the high range resolution waveforms, repeat sector all-sample mean bounds diverged by many decibels. Such sites were characterized by being open (i.e., nonforested) and without large discrete clutter sources. Examples of such sites are the desert site of Knolls, Utah, and the wetland site of Big Grass Marsh, Manitoba. In both situations, it was attempted to measure very weak backscatter at grazing incidence from what would be characterized more as a statistical rough surface and less as a sea of discretes. In these circumstances, particularly at high range resolution, the increased sensitivity available through integration gain is necessary to obtain accurate measures of mean and higher moments in the measured Phase One clutter amplitude distributions. At these sites, although the high resolution all-sample mean bounds diverged by many decibels, the high resolution coherent mean bounds remained relatively tight to within a few decibels, even at the weak mean clutter strength levels involved (e.g., –70 dB). The all-sample distribution discussed above is obtained by setting N = 1 in Equation (3.C.2); that is, each clutter return sample is individually binned in the histogram. Noncoherent averaging over a number N of return samples [N > 1 in Equation (3.C.2)] prior to assembling the histogram results in reduced spread in the distribution. Noncoherent

278 Appendix 3.C Clutter Computations

averaging does not affect the mean of the resultant distribution compared with the allsample distribution.

3.C.4 Repeat Sector Computational Examples Some examples are now provided of the set of results obtained for computing mean clutter strength within a repeat sector. As discussed previously, each repeat sector clutter measurement involved computation of upper and lower bounds to the absolute mean clutter strength in the repeat sector including noise-level cells, and also computation of the shadowless mean clutter strength excluding noise-level cells, the latter being a conditional or nonabsolute measure of repeat sector mean clutter strength dependent on radar sensitivity. Furthermore, for each measurement this set of three quantities was computed two ways, as a noncoherent all-sample computation and as a coherent integration computation. Thus, for each repeat sector clutter measurement selected, this section shows these six computed quantities for mean clutter strength. At each site, for a given radar frequency band, polarization, and range resolution, each repeat sector measurement was performed a number of times during the period of time that the Phase One equipment was at the site. Although a major purpose of this procedure was to show diurnal variations in clutter strength, within these repeated measurements underlying parameters involving data sampling rate and data acquisition interval or dwell time were also varied. A relatively high data sampling rate (i.e., PRF) is beneficial for the purpose of improving sensitivity through coherent integration, which requires many samples within a clutter correlation period. On the other hand, a low sampling rate is beneficial so that the set of samples covers many clutter correlation periods, thereby introducing a desirable element of temporal averaging in the statistics such that the repeat sector spatial mean clutter strength is based on a temporal mean clutter strength in each spatial resolution cell within the repeat sector. A burst mode of data collection that would provide fast sampling within a burst for coherent integration, and slow sampling between bursts for time averaging was not available. Instead, some repeat sector experiments were measured with fast sampling and others with slow sampling, but always with a constant sampling rate within each experiment. Repeat sector experiments with relatively high sampling rates are referred to as type 1 experiments, which were usually performed using the Phase One beam step antenna azimuth positioning mode. In the beam step mode, the beam was held stationary at each azimuth during data collection and was then stepped to the next azimuth until complete coverage through the repeat sector was completed. Beam step experiments with low sampling rate for time averaging are referred to as type 2 experiments. In addition, type 3 experiments were implemented which, like type 2 experiments, also involved a low data sampling rate, but in conjunction with a continuous slow azimuth scan through the repeat sector during data collection to introduce continuous spatial averaging in the data stream. Computations of mean clutter strength are now shown for the farmland repeat sector at the Beulah, North Dakota site. Table 3.C.1 shows Beulah results at L-band; Table 3.C.2 shows Beulah results at VHF. This site and these two bands are arbitrarily selected to show typical examples of mean clutter strength computations as observed at most sites. Many of the effects discussed previously in Appendix 3.C are quantified in the data of Tables 3.C.1 and 3.C.2. Thus, at Beulah, the all-sample mean bounds are always quite tight for all three

Appendix 3.C Clutter Computations 279

experiment types. Further, in the high sampling rate type 1 experiments, the coherently integrated mean bounds are very close to the all-sample mean bounds. Theoretically, the coherently integrated result should always be less than or equal to the equivalent noncoherently integrated result. Occasionally, in these type 1 experiments, the coherently integrated result is very slightly (i.e., insignificantly) greater than the noncoherent allsamples result, an effect attributable to round-off as all the individual samples are individually binned in the histogram. The increase in sensitivity through coherent integration is observed in the data in Tables 3.C.1 and 3.C.2 in that the coherently integrated shadowless mean is much closer to the corresponding coherently integrated upper and lower bounds than is the noncoherent all sample shadowless mean. This reflects the existence of fewer noise samples when coherent integration is employed. The number of noise samples may be calculated from the ratio of the shadowless mean to the mean lower bound (see Section 3.C.2), also given that N = 128. In contrast to the high sampling rate type 1 experiments, in the low sampling rate experiments of type 2 or type 3, the coherently integrated mean is generally significantly less than the noncoherent all-samples mean, particularly at the higher frequencies (e.g., L-band), reflecting the fact that in these experiments the coherent integration interval can span many correlation periods. In general, Tables 3.C.1 and 3.C.2 indicate good repeatability in the results from hour-tohour and day-to-day, and little noticeable effect with increased temporal (type 2 experiments) or spatial (type 3 experiments) averaging. At occasional sites, more repeat sector experiments were recorded than at typical sites such as Beulah. One such site was Peace River South II, a river valley site in northern Alberta. Table 3.C.3 shows mean clutter strength computations for the Peace River repeat sector for all the L-band experiments at 150-m range resolution and horizontal polarization. This larger set of repeated experiments continues to show very close hour-to-hour and day-to-day repeatability in mean clutter strength. For example, the one-sigma value for the variations in the noncoherent, all-sample, mean upper bound in Table 3.C.3 is 0.17 dB. Such variations in these data include variations in calibration accuracy as well as true variations in the clutter due, for example, to weather-related effects. Day-to-day calibration variations were monitored through measurement of returns from a discrete reference target of opportunity such as a water tower (see Appendix 3.A). Standard Phase One procedures called for the reference target return to be measured each day in each band that was used that day. Big Grass Marsh, Manitoba, was a weak clutter site where Phase One radar sensitivity needed to be increased by means of coherent integration to obtain accurate values of repeat sector mean clutter strength. This is illustrated by the L-band data in Table 3.C.4. These data show that at low range resolution, the Phase One sensitivity before improvement through integration provides mean bounds separated by as much as 5 dB, but after improvement through integration this separation reduces to 0.13 dB. More dramatically, however, at high range resolution before integration gain the mean bounds are separated by as much as 22.5 dB, which reduces to 2.8 dB after integration.

Table 3.C.1 Computations of L-Band Repeat Sector Mean Clutter Strength at Beulah, North Dakota (Repeat sector azimuth extent = 20 deg; range extent = 5.9 km; terrain type = farmland)

Date/Time (hr:min)

Experiment Type*

σ°F4 (dB) Non-Coherent Binning of 128 samples/cell

Coherent Integration of 128 samples/cell

Upper Bound

Lower Bound

Shadowless

Upper Bound

Lower Bound

Shadowless

1 3 2 1

–30.07 –28.34 –30.54 –28.49

–30.07 –28.35 –30.55 –28.50

–27.38 –25.42 –27.85 –25.78

–30.08 –28.90 –30.83 –28.46

–30.08 –28.90 –30.83 –28.46

–29.81 –28.52 –30.50 –28.05

1 3 2 1

–30.64 –27.76 –28.20 –27.72

–30.64 –27.76 –28.21 –27.72

–28.40 –25.41 –25.81 –25.43

–30.65 –28.33 –28.59 –27.69

–30.65 –28.33 –28.59 –27.69

–30.38 –28.12 –28.30 –27.42

1 3 2 1

–28.06 –28.05 –28.80 –28.87

–28.09 –28.11 –28.87 –29.25

–23.04 –22.67 –23.47 –23.90

–28.09 –28.61 –29.29 –28.86

–28.09 –28.61 –29.29 –28.86

–27.07 –26.94 –27.81 –27.35

1 3 2 1

–28.18 –28.01 –28.60 –28.85

–28.19 –28.04 –28.64 –28.86

–24.20 –23.93 –24.45 –24.56

–28.18 –28.55 –29.23 –28.86

–28.19 –28.55 –29.24 –28.86

–27.55 –27.44 –28.27 –27.82

Range res = 150 m Pol = HH 7 June 14 June 14 June 14 June

09:29 15:10 15:48 16:22

Range res = 150 m Pol = VV 7 June 14 June 14 June 14 June

09:21 15:04 15:40 16:15

Range res = 15 m Pol = HH 7 June 14 June 14 June 14 June

09:43 14:59 15:16 16:04

Range res = 15 m Pol = VV 7 June 14 June 14 June 14 June

09:33 14:53 15:28 15:57

* Experiment Type 1. High sampling rate, step scan. PRF= 2000 Hz, 1024 pulses/step, dwell time = 0.512 s/step. Azimuth step size = 2°, azimuth reposition time = 15 s/step. 2. Low sampling rate, step scan. PRF = 31.25 Hz, 512 pulses/step, dwell time = 16.38 s/step. Azimuth step size = 2°, azimuth reposition time = 15 s/step. 3. Low sampling rate, continuous scan. PRF= 31.25 Hz, 500 pulses/beamwidth, scan rate = 0.125°/s, dwell time = 16 s/beamwidth.

Table 3.C.2 Computations of VHF Repeat Sector Mean Clutter Strength at Beulah, North Dakota (Repeat sector azimuth extent = 20 deg; range extent = 5.9 km; terrain type = farmland) σ°F4 (dB) Date/Time (hr:min)

Experiment Type*

Non-Coherent Binning of 128 samples/cell

Coherent Integration of 128 samples/cell

Upper Bound

Lower Bound

Shadowless

Upper Bound

Lower Bound

Shadowless

1 3 2 1 1

–34.30 –35.07 –34.26 –34.06 –34.70

–34.30 –35.07 –34.26 –34.06 –34.71

–33.53 –34.36 –33.49 –33.48 –34.31

–34.18 –35.12 –34.42 –34.12 –34.72

–34.18 –35.12 –34.42 –34.12 –34.72

–34.13 –35.10 –34.42 –34.12 –34.61

1 3 2 1 1

–26.73 –27.43 –26.90 –27.16 –27.35

–26.73 –27.43 –26.90 –27.16 –27.35

–26.73 –27.34 –26.79 –27.11 –27.24

–26.78 –27.50 –26.95 –27.17 –27.34

–26.78 –27.50 –26.95 –27.17 –27.34

–26.78 –27.50 –26.95 –27.17 –27.34

1 3 2 1

–32.74 –33.99 –33.11 –32.32

–33.11 –34.82 –33.59 –32.73

–27.16 –27.81 –26.93 –26.78

–32.98 –34.34 –33.49 –32.65

–32.98 –34.34 –33.51 –32.65

–32.30 –33.21 –31.28 –30.91

1 3 2 1

–26.81 –27.91 –26.85 –27.24

–26.98 –28.19 –27.20 –27.41

–22.64 –23.74 –20.64 –23.13

–26.92 –28.10 –26.95 –27.33

–26.92 –28.10 –26.95 –27.33

–26.84 –27.99 –26.48 –27.03

Range res = 150 m Pol = HH 10 June 10 June 10 June 13 June 13 June

05:58 07:18 07:49 10:44 18:40

Range res = 150 m Pol = VV 10 June 10 June 10 June 10 June 13 June

05:52 07:10 07:37 10:41 18:37

Range res = 36 m Pol = HH 10 June 10 June 10 June 10 June

05:55 07:14 07:42 10:38

Range res = 36 m Pol = VV 10 June 10 June 10 June 10 June

05:48 07:04 17:29 10:33

* Experiment Type 1. High sampling rate, step scan. PRF= 500 Hz, 1024 pulses/step, dwell time = 2.048 s/step. Azimuth step size = 10°, azimuth reposition time = 15 s/step. 2. Low sampling rate, step scan. PRF = 31.25 Hz, 1920 pulses/step, dwell time = 61.44 s/step. Azimuth step size = 10°, azimuth reposition time = 15 s/step. 3. Low sampling rate, continuous scan. PRF= 31.25 Hz, 2500 pulses/beamwidth, scan rate = 0.125°/s, dwell time = 80 s/beamwidth.

Table 3.C.3 Computations of L-Band Repeat Sector Mean Clutter Strength at Peace River South II, Alberta (Repeat sector azimuth extent = 10 deg; range extent = 5.9 km; terrain type = forested river valley and farmland)

σ°F4 (dB) Date/Time (hr:min)

Experiment Type*

Non-Coherent Binning of 128 samples/cell Upper Bound

Lower Bound

Shadowless

Coherent Integration of 128 samples/cell Upper Bound

Lower Bound

Shadowless

Range res = 150 m Pol = HH 15 Oct

17:22

1

–19.73

–19.73

–19.53

–19.74

–19.74

–19.74

18 Oct

14:40

1

–20.44

–20.44

–20.21

–20.46

–20.46

–20.46

19 Oct

13:38

1

–19.78

–19.78

–19.60

–19.80

–19.80

–19.77

20 Oct

15:04

1

–20.23

–20.23

–20.07

–20.21

–20.21

–20.21

21 Oct

15:44

1

–20.28

–20.28

–20.14

–20.28

–20.28

–20.28

22 Oct

14:57

1

–19.58

–19.58

–19.30

–19.62

–19.62

–19.59

28 Oct

11:32

1

–20.24

–20.24

–20.13

–20.25

–20.25

–20.23

–19.68

–19.45

–19.66

–19.66

–19.66

28 Oct

14:51

1

–19.68

29 Oct

14:06

1

–20.36

–20.36

–20.13

–20.35

–20.35

–20.35

31 Oct 2 Nov

14:39 18:57

1 1

–19.17 –20.47

–19.17 –20.47

–19.04 –20.29

–19.18 –20.46

–19.18 –20.46

–19.18 –20.46

* Experiment Type 1. High sampling rate, step scan. PRF = 2000 Hz, 1024 pulses/step, dwell time = 0.512 s/step. Azimuth step size = 2°, azimuth reposition time = 15 s/step.

Table 3.C.4 Computations of L-Band Repeat Sector Mean Clutter Strength at Big Grass Marsh, Manitoba (Repeat sector azimuth extent = 20 deg; range extent = 5.9 km; terrain type = wetland) σ°F4 (dB) Date/Time (hr:min)

Experiment Type*

Non-Coherent Binning of 128 samples/cell Upper Bound

Coherent Integration of 128 samples/cell

Lower Bound

Shadowless

Upper Bound

Lower Bound

Shadowless

Range res = 150 m Pol = HH 4 Feb 16:04

1

–66.94

–71.73

–62.59

–69.60

–69.73

–68.97

Range res = 150 m Pol = VV 4 Feb 15:59

1

–67.84

–69.15

–63.04

–68.69

–68.71

–68.11

Range res = 15 m Pol = HH 4 Feb 16:19

1

–50.97

–73.50

—

–63.38

–66.17

–62.04

Range res = 15 m Pol = VV 4 Feb 15:54

1

–55.51

–71.36

–54.22

–66.00

–67.32

–63.53

* Experiment Type 1. High sampling rate, step scan. PRF = 2000 Hz, 1024 pulses/step, dwell time = 0.512 s/step. Azimuth step size = 2°, azimuth reposition time = 15 s/step.

350 Appendix 4.A Clutter Strength vs Range

Appendix 4.A Clutter Strength vs Range 4.A.1 Introduction An important characteristic of land clutter in a surface-sited radar as first perceived on the radar’s PPI display is that its occurrence dissipates rapidly with increasing range from the radar. Cannot this obvious general characteristic be simply modeled? The PPI display shows the spatial occupancy of the clutter, but otherwise (without introducing an intensity dimension to the basic plan-position display) does not directly show clutter strength within occupied regions. A simple, azimuthally-isotropic, non-spatially-patchy clutter model provides clutter everywhere and hence does not have variable clutter occurrence as an available parameter by which to properly diminish the clutter with increasing range. Clutter strength being the only available parameter of such a simple model, the question arises as to whether diminishing clutter strength with increasing range is a suitable way to provide the obvious general dissipation of clutter with increasing range as first perceived on a PPI display. The correct way to answer this question is to look for such effects in measured clutter data. Thus Appendix 4.A shows mean clutter strength as a function of range at six selected sites. The basic A-scope or sector display format in which clutter strength variation is shown vs range is complementary with PPI clutter map presentations in advancing comprehension of the low-angle clutter phenomenon, so that besides addressing the basic question of clutter strength vs range, these results also provide additional insight into the general nature of low-angle clutter. Specifically, the sector display format shows the spikiness, clumpiness, and heterogeneity of clutter in which wide dynamic range in clutter strength is evident. This format shows from another perspective how low-angle clutter is dominated by discrete sources and provides intuitive understanding of why low-angle clutter often spatially decorrelates in one resolution cell. Furthermore, this format provides graphic evidence that low-angle clutter is essentially a line-of-sight phenomenon; where terrain is within line-ofsight, clutter spikes are observed occurring above the radar noise floor, and where terrain is geometrically masked, the return is usually at or near the noise floor. The data in Appendix 4.A show no significant general trends of decreasing strength with increasing range that could be incorporated as the basis of a simple non-patchy clutter model. Table 4.A.1 lists the sites for which sector display results are shown in this appendix. The criterion for their selection was that ground clutter be discernible to relatively long-range. As a result, all six of these sites are of relatively high effective site height. For each site, a narrow azimuth sector was selected containing clutter to long-range, and a sector display was generated showing clutter strength vs range, range gate by range gate, from the beginning to the end of the sector. Figures 4.A.2–4.A.8 show these sector displays. Also shown in each of these figures is a Phase Zero PPI clutter map at close to (i.e., 3 dB from) full sensitivity in which the azimuth sector for which sector display results are presented is indicated.

Appendix 4.A Clutter Strength vs Range 351

Table 4.A.1 Sites for Which Mean Clutter Strength vs Range Results are Presented in Appendix 4.A

Sector Display ( σ˚ F4 vs Range)

Site Name

Effective Site Height (m)

Katahdin Hill Picture Butte II Picture Butte II Cochrane Polonia Wachusett Mt. Blue Knob

31 54 54 104 128 333 338

Maximum Range (km)

Azimuth Extent (deg)

24 24 44 47 47 47 47

20 3 3 20 20 45 20

No. of Azimuth Samples per Range Gate 86 14 375 87 86 193 87

4.A.2 Clutter Visibility vs Range The six sectors in this appendix are selected at relatively high sites so as to contain significant amounts of clutter. Although selected in this manner to avoid the occurrence of macroshadow where the radar is at its noise floor over large spatial regions, nevertheless, and as typically occurs in ground clutter returns especially at longer ranges, a large amount of microshadowing occurs within the sectors. For each sector, the percent of cells at or within 3 dB of the noise floor is quantified as a function of range in Figure 4.A.1. This is done in two ways. First, the percentage of cells in clutter (i.e., the complement of percentage of cells at or near noise level) at each range gate position over the azimuthal extent of the sector is shown, range gate by range gate, across the 320 Phase Zero range gates in each sector. This quantity is denoted as percent circumference (or more precisely, percent of circumferential arc length spanning the azimuth extent of the sector) in clutter. The number of azimuth samples in each range gate for each of the six sectors is shown in Table 4.A.1. Second, the percentage of cells in clutter included within the sector out to and including the range under consideration is shown, also range gate by range gate across the 320 range gates in each sector. This quantity is denoted as percent of area in clutter (more precisely, it is the percentage of included cells in clutter—the percentage of included cells is not proportional to included area because cell area is range dependent). The quantity indicated as percent area in clutter is the cumulative sum of the quantity indicated as percent circumference in clutter from the first range gate out to the range gate under consideration. In Figure 4.A.1, all sectors show an initial rapid decrease, followed by a slower falloff, of percent of cells in clutter with increasing range. The details of this variation depend on the specific nature of the terrain and the effective radar height at each site. In all six cases, the percent of cells in clutter throughout the complete sector to its maximum range varies from about 10% to about 35%. That is, over such long ranges, the majority of cells occur at or near noise level, even within sectors selected to contain substantial amounts of clutter. The effects of these noise level cells on the mean clutter strength computed range gate by range gate in each sector are ascertained through computation of upper and lower bounds to mean clutter strength (see Appendices 2.B and 3.C) in selected range gates. The differences between these bounds are labelled as “mean deviation” for these selected range gates in Figures 4.A.2–4.A.8.

Percent Circumference

100 80 60 40 20 0

Percent Area

352 Appendix 4.A Clutter Strength vs Range

100 80 60 40 20 0 0

5

10

15

20

0

10

20

30

40

0

10

20

30

40

Percent Circumference

100 80 60 40 20 0

Percent Area

Range (km) Range (km) Range (km) a) Katahdin Hill, 270°–290° b) Picture Butte II, 144°–147° c) Cochrane, 200°–220°

100 80 60 40 20 0 0

10

20

30

40

Range (km) d) Polonia, 90°–110°

0

10

20

30

40

0

10

20

30

40

Range (km) Range (km) e) Wachusett Mt., 45°–90° f) Blue Knob, 190°–210°

Figure 4.A.1 Percent of included circumferential arc length and percent of included area in clutter for selected sectors at six sites. Phase Zero X-band data.

40 Depression Angle (deg)

σ°F4 (dB)

20

4 32 1

0.5

0.2

0

0.1 Mean Deviation (dB) 0.0 1.0

–20 –40 Mean 99 Percentile

–60 –80 5

10

15

20

Range (km)

Figure 4.A.2 Phase Zero sector display plot for Katahdin Hill showing σ °F 4 vs range between 270° and 290° azimuth. Available dynamic range is indicated by solid lines bracketing the data. Mean (upper bound) and 99-percentile levels are shown for each range gate, averaged over 86 azimuth samples. Mean deviation is the difference between upper and lower mean bounds. A Phase Zero clutter map (clutter is black) is also shown, indicating the azimuth sector under consideration. The clutter map is 3 dB from full sensitivity; maximum range = 23.5 km; 5-km range rings; north is zenith.

Appendix 4.A Clutter Strength vs Range 353

40

Depression Angle (deg)

σ°F4 (dB)

20

1.0

0.8

Mean Deviation (dB)

0.6

0.0

0

0.0

0.0

–20 –40 Village Oldman River Mean Valley Small 99 Percentile Lake

–60 –80

5

10

15

20

Range (km)

Figure 4.A.3 Phase Zero sector display plot for Picture Butte II showing σ °F 4 vs range between 144° and 147° azimuth. Mean (upper bound) and 99-percentile levels are shown for each range gate, averaged over 14 azimuth samples. Mean deviation is the difference between upper and lower mean bounds. A Phase Zero clutter map (clutter is black) is also shown indicating the azimuth sector under consideration. The clutter map is 3 dB from full sensitivity; maximum range = 23.5 km; 5-km range rings; north is zenith.

S-Band H-Polarization 150-m Range Resolution

–20

Picture Butte II

Old Man RiverValley

σ°F4 (dB)

10 0

–40 –60 –80 5

10

15

20

25

30

35

40

Range (km) 4

Figure 4.A.4 Phase One sector display plot for Picture Butte II showing σ °F vs range between 147° and 150° azimuth. Mean clutter strength is shown for each range gate, averaged over 375 azimuth samples. A Phase Zero clutter map (clutter is black) is also shown indicating the azimuth sector under consideration. The clutter map is 3 dB from full sensitivity; maximum range = 47.1 km; 10-km range rings; north is zenith.

Over the set of 2,177 Phase Zero clutter patches lying between 2 and 12 km from the radar and upon which Chapter 2 is based, the percentage of cells at radar noise level is 47.1%. In the percent area results of Figure 4.A.1, the average percentage of included cells at radar noise level within these six sectors to 12-km range is indeed about 50% (i.e., on the order of the average clutter patch value), but increases to about 75% to the longest ranges shown. The increase in percentage of included cells at radar noise level in Figure 4.A.1 (i.e., the percent area curves) with increasing range is largely due to increasing geometrical shadowing of terrain with increasing range. Increasing geometrical shadowing with increasing range can theoretically result in gradually decreasing clutter strength with increasing range due to the spatial dilution of clutter cells with shadowed cells at noise level. In Figures 4.A.2–4.A.8, the mean strength in each range gate is accurate to the

354 Appendix 4.A Clutter Strength vs Range

40 Depression Angle (deg) 4 321 0.75 0.5 Mean Deviation (dB)

20 0

1.0

1.0

1.0

3.0

–20 –40 Mean 99 Percentile

–60 –80 10

20

30

40

Range (km)

Figure 4.A.5 Phase Zero sector display plot for Cochrane showing σ °F 4 vs range between 200° and 220° azimuth. Mean (upper bound) and 99-percentile levels are shown for each range gate, averaged over 87 azimuth samples. Mean deviation is the difference between upper and lower mean bounds. A Phase Zero clutter map (clutter is black) is also shown indicating the azimuth sector under consideration. The clutter map is 3 dB from full sensitivity; maximum range = 47.1 km; 10-km range rings; north is zenith.

σ°F4 (dB)

40 20 0

Depression Angle (deg) 1.0 0.5 Mean Deviation (dB) 0.0 3.0 2.0 3.0 2.0

2.0 1.5

–20 –40 Mean 99 Percentile

–60 –80 10

20

30

40

Range (km)

Figure 4.A.6 Phase Zero sector display plot for Polonia showing σ °F 4 vs range between 90° and 110° azimuth. Mean (upper bound) and 99-percentile levels are shown for each range gate, averaged over 86 azimuth samples. Mean deviation is the difference between upper and lower mean bounds. A Phase Zero clutter map (clutter is black) is also shown indicating the azimuth sector under consideration. The clutter map is 3 dB from full sensitivity; maximum range = 47.1 km; 10-km range rings; north is zenith.

tolerances indicated by the mean deviation independent of sensitivity or number of noise samples in the range gate. No significant falloff of mean strength with increasing range occurs over the longer ranges in the sectors of Figures 4.A.2–4.A.8 because these sectors were selected to contain substantial discernible clutter, and as a result the occurrence of noise level cells in these sectors, although rising to relatively large values at long ranges, is not enough to significantly erode the accuracy of the mean strength computation or reduce it through spatial dilution. Appendix 4.C discusses effects of shadowing and sensitivity on clutter strength in more detail. There, analysis is not restricted to narrow sectors of substantial clutter visibility, but

Appendix 4.A Clutter Strength vs Range 355

σ°F4 (dB)

40 20 0

Depression Angle (deg) 1 2 7654 3 Mean Deviation (dB) 1.0

1.0

9.0

1.0

–20 –40 Mean 99 Percentile

–60 –80 10

20

30

40

Range (km)

Figure 4.A.7 Phase Zero sector display plot for Wachusett Mt. showing σ °F 4 vs range between 45° and 90° azimuth. Mean (upper bound) and 99-percentile levels are shown for each range gate, averaged over 193 azimuth samples. Mean deviation is the difference between upper and lower mean bounds. A Phase Zero clutter map (clutter is black) is also shown indicating the azimuth sector under consideration. The clutter map is 3 dB from full sensitivity; maximum range = 47.1 km; 10-km range rings; north is zenith.

σ°F4 (dB)

40 20

Depression Angle(deg) 4.2 3.2

0 –20 –40 Mean 99 Percentile

–60 –80 10

20

30

40

Range (km)

Figure 4.A.8 Phase Zero sector display plot for Blue Knob showing σ °F 4 vs range between 190° and 210° azimuth. Mean (upper bound) and 99-percentile levels are shown for each range gate, averaged over 87 azimuth samples. Mean deviation is the difference between upper and lower mean bounds. A Phase Zero clutter map (clutter is black) is also shown indicating the azimuth sector under consideration. The clutter map is 3 dB from full sensitivity; maximum range = 47.1 km; 10-km range rings; north is zenith.

instead large amounts of macroshadow are absorbed through 360° in azimuth. As a result, the percentage of cells at radar noise level rises to 99% at 47 km, and this constitutes enough spatial dilution to cause a significant reduction in mean clutter strength with increasing range (see Figure 4.C.16).

4.A.3 Clutter Strength vs Range Sector display plots showing clutter strength vs range at six sites are presented in Figures 4.A.2–4.A.8. These plots show clutter strength σ °F 4 vs range, range gate by gate. The Phase Zero radar utilized 320 range gates (see Appendix 2.A). In each range gate, all of

356 Appendix 4.A Clutter Strength vs Range

the clutter strength samples obtained from the beginning azimuth position of the sector to the ending azimuth position of the sector were binned in a histogram of clutter strengths. For each sector, the number of azimuth samples in the histogram is given in Table 4.A.1. Various statistical measures of this histogram were computed. In the sector display plots of Figures 4.A.2–4.A.8, the upper bound mean is shown as a solid line, and the 99-percentile level is shown as a dotted line. The noise floor or sensitivity limit is indicated as a monotonically increasing lower bound to the measurements which increases as the third power of range, and above it the saturation ceiling is indicated as a monotonically increasing upper bound to the measurements. These two limits define the available dynamic range of the clutter measurements. Also indicated for a few range gate positions on most of these sector display plots are numbers labelled “mean deviation (dB).” The mean deviation indicates the difference between the upper and lower bounds to the mean, where in the upper bound computation, noise power values are assigned to samples at radar noise level; and in the lower bound computation, zero power values are assigned to these samples. Tight mean bounds indicate an accurate assessment of mean clutter strength to within the bounds indicated, irrespective of radar sensitivity or the number of corrupting radar noise samples involved in the calculation. The mean deviation also indicates to what extent significant clutter occurs in the range gate. In clutter patch selections to 12 km in range, the mean bounds are maintained within 1 dB of each other. The extent to which they drift apart beyond 1 dB in the sector display results of Figures 4.A.2–4.A.8 indicates to what extent macroshadowing begins to influence these results at longer ranges. In this appendix, narrow sectors containing relatively high spatial densities of clutter are selected to minimize macroshadowing. Appendix 4.C presents similar plots in which results are obtained by averaging over 360° to show the effects of macroshadowing and for which the upper and lower bounds to mean clutter strength are shown by individual range gate for all range gates. For each sector display plot, depression angle was estimated at a few points in each sector from 1:50,000 scale or l:25,000 scale topographic maps; the results are indicated on the plots. At Katahdin Hill, the sector display of Figure 4.A.2 shows strongly decreasing mean strength as depression angle decreases from about 3° to about 1° in the first few kilometers in range. Similar effects are seen in the Cochrane and Wachusett Mountain results. However, in all of these sector display results, once the depression angle has dropped to < ~1° in the first few kilometers, no further significant decrease of clutter strength with increasing range occurs. It is evident in these data that the controlling parameter on clutter strength is angle, not range, and that this effect of angle on clutter strength is of primary importance only within the first several kilometers of range from the radar. That is, once the depression angle falls off with increasing range into the near grazing incidence regime, then no further significant decreases of clutter strength occur with further extensive increases in range.

Picture Butte II. Picture Butte II is a prairie site for which terrain visibility occurs to very long distances, even though the site position is not on a local hill. The distant terrain remains visible due to long gradual terrain slopes such that terrain elevations gradually diminish over many kilometers to the southeast, as indicated in the terrain profile of Figure 4.A.9. Thus clutter occurs to long distances in the Picture Butte II sector unaccounted for by antenna mast height or local hill height, but simply because of geometric visibility down a long incline that overrides local earth curvature.

Elevation (20-m Increments)

Appendix 4.A Clutter Strength vs Range 357

165 Masked Unmasked –165 0

10

20

Range (km)

Figure 4.A.9 Picture Butte II terrain profile in southeast sector. Masked and unmasked terrain profiles are shown for 50-ft antenna.

Two Picture Butte II sector display results are provided. The first, shown in Figure 4.A.3, is a Phase Zero result to 23-km maximum range. In Figure 4.A.3, masked terrain in the Oldman River valley occurs from 9 to 13 km where the radar is at its noise floor; a cluster of buildings comprising the small village of Picture Butte occurs at 7-km range where mean clutter strength rises 20 dB over the surrounding cropland; and a small lake occurs at 6-km range where again the radar is at its noise level for a few gates. Next, Figure 4.A.4 shows an S-band Phase One sector display result for Picture Butte II to 44-km maximum range. In these S-band data, the polarization is horizontal and the range resolution is 150 m. The data were acquired in scan mode, scanning at 2°/s, at an effective PRF of 250 Hz. Thus in the 3° azimuth sector shown, each range gate receives 375 pulses. The mean strength shown is the result of binning 375 samples into an amplitude distribution for each gate and computing the mean of the distribution. The increased sensitivity of the Phase One radar compared to the Phase Zero radar is evident. The predominant character of the clutter on this agricultural landscape is similar in both Phase Zero and Phase One data. It is very spiky and discrete dominated, exhibiting wide dynamic range and occurring from terrain within line-of-sight. There is little suggestion of any significant general trend of σ°F4 with range to long ranges in these data.

4.A.4 Summary This appendix shows examples of mean clutter strength σ°F4 vs range for six high sites with clutter extending to long ranges. For each site, mean clutter strength is averaged over a number of azimuth samples within a fixed azimuth sector, range gate by range gate. In these results, a general trend of significantly decreasing clutter strength with increasing range is observed only over the first few kilometers, where depression angle significantly decreases with increasing range. At longer ranges where depression angle has very nearly reached zero degrees, mean clutter strength (although scintillating strongly from gate to gate) shows no general trend with range in the results. Two conclusions concerning clutter modeling can be made from these results. First, since no strong general trend of decreasing σ° with increasing range occurs over long ranges in these data, the data provide no support to the idea of gradually dissipating clutter strength in a simple non-patchy clutter model by simply reducing σ° with increasing range. Second, even though low-angle clutter is dominated by discretes, the density function σ° normalized by cell area is the appropriate measure by which to characterize clutter strength. In contrast, clutter RCS per resolution cell does not isolate single discretes but generally

358 Appendix 4.A Clutter Strength vs Range

increases approximately linearly with increasing range due to linearly increasing cell area (see related discussions in Section 4.5 and Appendix 4.D).

Appendix 4.B Terrain Visibility as a Function of Site Height and Antenna Mast Height 359

Appendix 4.B Terrain Visibility as a Function of Site Height and Antenna Mast Height 4.B.1 Introduction Ground-based radars are often situated on hills to improve their coverage. The relative height of the hill with respect to the surrounding terrain is an important parameter affecting the ground clutter received by the radar. Relative height directly affects the distance to which clutter occurs and indirectly, through illumination angle, affects the strength of the clutter received. These matters are discussed and illustrated with empirical data elsewhere in this book. In addition to the height of the hill itself, the antenna mast height of the radar also contributes to the overall effective height of the radar. In this book, a single height parameter is associated with the ground clutter data acquired at each clutter measurement site, namely, effective radar height, obtained by simply summing site height and mast height. Effective radar height is defined in Chapter 2, Section 2.2.3. On first consideration, the summation of site height and mast height would appear to require little justification. However, raising mast height on a given site is not the same as moving to a higher site. In raising an antenna to higher positions at a given site, the surrounding terrain does not change, and simple geometrical considerations require that in such circumstances terrain visibility must monotonically increase with increasing mast height. Whereas, in moving to a higher site, the surrounding terrain does change, and, for example, terrain visibility at short ranges can decrease because the terrain slopes down the side of the hill upon which the radar is positioned can be increasingly shadowed for increasingly high hills. Except for very level terrain, increasing mast height through the ranges of practical heights typically used by ground-based radars only slowly increases visibility. The increases in long-range terrain visibility available from increasing site height are much greater than those available from increasing mast height. For practical purposes, mast height is for the most part useful for raising the antenna into the clear above immediately surrounding vertical obstructions such as trees. However, in practice some very high radar antenna masts have been used purposefully to increase radar coverage of low-flying targets; and, in contrast, some very low radar sites have been purposefully selected to minimize terrain visibility and associated clutter effects in operations against high-altitude targets. This appendix investigates effects of site height and mast height on terrain visibility. The investigation is based on geometric visibility of terrain as modeled by available digitized terrain elevation data (DTED) at 43 hilltop sites. The investigation provides generalized effects of site height and mast height on geometric line-of-sight visibility to terrain by

360 Appendix 4.B Terrain Visibility as a Function of Site Height and Antenna Mast Height

averaging results across the 43 hilltop sites. To effect this process, first the sites are binned into four classes of site height, then terrain visibility results are averaged within class, and in this manner terrain visibility is generalized both by site height and mast height. As expected, the results show that increasing height on a given site monotonically increases visibility, although the rate of increase is usually small. The results also show that high sites see much more terrain at long ranges than low sites, and that this effect is much stronger than effects of mast height on visibility. However, the curves of visibility vs site height are not monotonically increasing. This book associates the general spatial occurrence of the strongest elements of ground clutter with line-of-sight visibility to terrain. The study of terrain visibility of this appendix allows improved understanding of this association, in which low-angle ground clutter arises from discrete sources distributed over surfaces within line-of-sight visibility. In what follows, Section 4.B.2 describes the terrain elevation data employed in the study, and Section 4.B.3 provides the numerical results of the study.

4.B.2 Terrain Elevation Data This appendix uses DTED to characterize 43 hypothetical hilltop sites. These data are cartographic source data generated from 1:250,000 scale maps to provide terrain elevation in integer meters on an approximately 100 m grid. These DTED do not include tree heights or heights associated with any other land cover features. Thus, they are bare-earth DTED, and comprise a faceted terrain model as discussed in Section 1.2. The 43 sites were selected from a large contiguous geographic region approximately 1,000 km in extent, including plains and plateaus, uplands and lowlands. Hence, a considerable variety of terrain types is included within the set of sites, from relatively level to moderately hilly, although the study region does not include any mountainous terrain. Each of these sites was selected to be the highest hill within a radius of 10 km. These are hypothetical sites, in that no consideration was given to the practical accessibility of sites, or to whether or not there was any pre-existing utilization of the site for any purpose. For each site, statistical computations on the DTED were performed. In particular, the relative height of each site was computed as site height above the best-fit plane over a 50 × 50 km site-centered area. This measure of relative site height is designated as site advantage. The resultant site advantages of all 43 hypothetical hilltop sites are plotted in increasing order of site advantage in Figure 4.B.1. Four regimes of site advantage and the number of sites in each from the 43-site set are shown in Table 4.B.1. These regimes are also demarcated in Figure 4.B.1. The next section shows terrain visibility results for each of the four regimes of site advantage shown in Table 4.B.1, averaged over the sites within each regime, and as a function of antenna mast height.

4.B.3 Terrain Visibility Results This section presents terrain visibility results showing the effects of: (1) varying site height and (2) varying antenna mast height. Terrain visibility is shown as percent of circumference around site center in which the terrain is within line-of-sight visibility as a function of range. Percent of circumference visible as a function of range is computed from the DTED at each site through creation of a site-centered polar array of terrain elevation data of 80-km radius and grid spacing of 100 m by one deg. In the geometric determination of visibility of

Appendix 4.B Terrain Visibility as a Function of Site Height and Antenna Mast Height 361

200

180

160

Site Advantage (m)

140

120

100

80

60

40

20

0 0

10

20

30

40

50

Site No.

Figure 4.B.1 Site advantages for 43 hypothetical hilltop sites plotted in order of increasing site advantage. Table 4.B.1 Number of Hypothetical Hilltop Sites in Four Regimes of Site Advantage Site Advantage (m)

Number of Sites

10 to 35

8

40 to 65

13

70 to 95

14

100 to 200

8

Total

43

each point in this array, an earth of 4/3 the radius of the actual earth is used to account for standard atmospheric refraction. At each range position, the percent of circumference visible at each site is averaged together over all the sites within a given regime of site heights to provide the mean percent of circumference visible at that range for that site height regime. The computation of mean percent of circumference visible as a function of range for various site height regimes is performed for various antenna mast heights. This

362 Appendix 4.B Terrain Visibility as a Function of Site Height and Antenna Mast Height

procedure generalizes terrain visibility as a function of relative site height and antenna mast height on the basis of the available 43-site set of DTED. In these visibility computations, four antenna mast heights are used, as follows: (1) 5 m, (2) 15 m, (3) 30 m, and (4) 50 m. The 5-m mast height is rather low, for which visibility in many cases would be limited by land cover features. The 50-m mast height is a very high mast, impracticably so in most ground-based radar applications. Thus the 5-m and 50-m antenna mast heights approximate lower- and upper-bound limiting cases, whereas the 15-m and 30-m mast heights are of more practical interest. The four regimes of site advantage defined in Table 4.B.1 are of common occurrence. Next, 16 curves are computed showing mean percent of circumference visible as a function of range for four site height regimes and four antenna mast heights. In each of these curves, visibility data is presented to a maximum range of 50 km. These curves are presented in two ways, as follows. First, in Figures 4.B.2–4.B.5, curves are shown for the four site height regimes in each figure, for a given mast height of 5, 15, 30, or 50 m, respectively. Then, in Figures 4.B.6–4.B.9, curves are shown for the four antenna mast heights in each figure, for a given site advantage regime of 10 to 35 m, 40 to 65 m, 70 to 95 m, or 100 to 200 m, respectively. Each curve includes an arrow indicating the horizon range on a smooth, spherical, 4/3 radius earth as seen from a height given by the sum of the antenna mast height and the median site advantage within the appropriate site advantage regime. If the spherical earth horizon range is greater than 50 km, it is not shown. Thus, Figures 4.B.2–4.B.9 directly show the effect on terrain visibility of either increasing site height for a given antenna mast height or increasing mast height for a given site height. Three important observations from these results are as follows: 1.

Higher masts incrementally increase terrain visibility at all ranges (see Figures 4.B.6–4.B.9). The influence of mast height on terrain visibility is stronger for low sites (Figure 4.B.6) than for moderate or high sites (Figures 4.B.7–4.B.9).

2.

Higher sites strongly increase terrain visibility at long ranges (see Figures 4.B.2– 4.B.5).This effect is generally much stronger than that of mast height at long ranges.

3.

Increasing mast height on a given site is not the same as moving to a higher site. Increasing mast height gradually but monotonically increases terrain visibility at all ranges (Figures 4.B.6–4.B.9). Increasing site height results in slightly decreasing terrain visibility at short ranges, strongly increasing visibility at long ranges, and either slightly decreasing or slightly increasing visibility at intermediate ranges (Figures 4.B.2–4.B.5).

Observations 1 and 2, and the data supporting them, confirm intuitive expectation. Increasing mast height on a given site has to monotonically increase visibility, but this effect is relatively small for realistic mast heights. Furthermore, much more terrain in the distance must be visible from high sites than from low sites. This latter effect is stronger than the increased visibility obtainable through increasing mast height at a given site, high or low. This strong effect is largely due to the fact that high sites (e.g., 100 to 200 m) are much higher than high masts (e.g., 50 m), but the fact that high sites occur in high-relief terrain where the relief tends to dominate visibility to ranges far beyond a smooth spherical earth horizon also contributes.

Appendix 4.B Terrain Visibility as a Function of Site Height and Antenna Mast Height 363

100 Antenna Mast Height = 5 m

80

Mean Percent of Circumference Visible

60

40 30

20

10

Site Advantage (m) 100 to 200 70 to 95 40 to 65 10 to 35

7 5

= Spherical Earth Horizon 3 0

10

20

30

40

50

Range (km)

Figure 4.B.2 Mean terrain visibility vs range for four regimes of site advantage, with a 5-m antenna mast height. Based on bare-earth DTED for 43 hilltop sites. The DTED are derived from cartographic source.

Observation 3, however, is not so intuitive. The fact that, in moving to higher sites, terrain visibility actually decreases at short ranges (less than ~10 km) is directly opposite to the effect caused by increasing mast height. Decreasing visibility with increasing site height at short-range is due to the “brow of the hill” effect whereby the terrain down the side of the hill upon which the radar is situated is masked to the radar. In contrast, for very low relief sites at short ranges, almost all of the terrain is visible. Since at long ranges (e.g., greater than 25 km for a 15-m mast height, see Figure 4.B.3) the expected effect of strongly increasing visibility with increasing site height comes into play, it is necessary that there be an intermediate range region in which site height has little effect and no clear-cut trend on visibility (e.g., between 10 and 20 km, high sites of 100 to 200 m site advantage and low sites of 10 to 35 m site advantage have about the same terrain visibility for 15-m mast heights, see Figure 4.B.3). Note that the “brow-of-the-hill” effect exists in the highest effective radar height regime in the 15-m mast clutter occurrence data of Figure 4.10, as well as in the highest site advantage regime in the corresponding 15-m mast terrain visibility data of Figure 4.B.3. In Figures 4.B.2–4.B.5, the curves for the middle two regimes of site advantage (viz., 40 to 65 m, and 70 to 95 m) are not too different from each other and could be combined into one curve generally representative of most terrain. Further to this, it may be observed in Figures 4.B.2–4.B.5 that the upper envelope of all the visibility data is almost always given by the

364 Appendix 4.B Terrain Visibility as a Function of Site Height and Antenna Mast Height

100 Antenna Mast Height = 15 m

80

Mean Percent of Circumference Visible

60

40 30

20

Site Advantage (m)

10

100 to 200 70 to 95 40 to 65 10 to 35

7 5

= Spherical Earth Horizon 3 0

10

20

30

40

50

Range (km)

Figure 4.B.3 Mean terrain visibility vs range for four regimes of site advantage, with a 15-m antenna mast height. Based on bare-earth DTED for 43 hilltop sites.

lowest (10- to 35-m site advantage) or highest (100- to 200-m site advantage) sites. Generally, lowest sites see most terrain at closer ranges, and highest sites see most terrain at long ranges. In these data, there is not a crossover range regime where sites of intermediate height see most terrain. On the other hand, there is a crossover range regime where sites of intermediate height (70- to 95-m site advantage) see least terrain. Otherwise, generally, highest sites see least terrain at close ranges, and lowest sites see least terrain at long ranges. Sites of 40- to 65-m site advantage never see most terrain or least terrain in these data.

Appendix 4.B Terrain Visibility as a Function of Site Height and Antenna Mast Height 365

100 Antenna Mast Height = 30 m

80

Mean Percent of Circumference Visible

60

40 30

20

10

Site Advantage (m) 100 to 200 70 to 95 40 to 65 10 to 35

7 5

= Spherical Earth Horizon 3 0

10

20

30

40

50

Range (km)

Figure 4.B.4 Mean terrain visibility vs range for four regimes of site advantage, with a 30-m antenna mast height. Based on bare-earth DTED for 43 hilltop sites.

366 Appendix 4.B Terrain Visibility as a Function of Site Height and Antenna Mast Height

100 Antenna Mast Height = 50 m

80

Mean Percent of Circumference Visible

60

40 30

20

Site Advantage (m) 100 to 200 70 to 95 40 to 65 10 to 35

10 7 5

= Spherical Earth Horizon 3 0

10

20

30

40

50

Range (km)

Figure 4.B.5 Mean terrain visibility vs range for four regimes of site advantage, with a 50-m antenna mast height. Based on bare-earth DTED for 43 hilltop sites.

Appendix 4.B Terrain Visibility as a Function of Site Height and Antenna Mast Height 367

100 Site Advantage 10 to 35 m

Mean Percent of Circumference Visible

80 60

40 30

20

Antenna Mast Height (m)

5

15

30

50

10 7 5 = Spherical Earth Horizon 3 0

10

20

30

40

50

Range (km)

Figure 4.B.6 Mean terrain visibility vs range for four antenna mast heights, for sites with site advantage lying between 10 and 35 m. Based on bare-earth DTED for 43 hilltop sites.

368 Appendix 4.B Terrain Visibility as a Function of Site Height and Antenna Mast Height

100 80

Site Advantage 40 to 65 m

Mean Percent of Circumference Visible

60

40 30

20

Antenna Mast Height (m)

5

15

30

50

10 7 5 = Spherical Earth Horizon 3 0

10

20

30

40

50

Range (km)

Figure 4.B.7 Mean terrain visibility vs range for four antenna mast heights, for sites with site advantage lying between 40 and 65 m. Based on bare-earth DTED for 43 hilltop sites.

Appendix 4.B Terrain Visibility as a Function of Site Height and Antenna Mast Height 369

100 Site Advantage 70 to 95 m

80

Mean Percent of Circumference Visible

60

40 30

50 30 15

20 Antenna Mast Height (m)

5

10 7 5 = Spherical Earth Horizon 3 0

10

20

30

40

50

Range (km)

Figure 4.B.8 Mean terrain visibility vs range for four antenna mast heights, for sites with site advantage lying between 70 and 95 m. Based on bare-earth DTED for 43 hilltop sites.

370 Appendix 4.B Terrain Visibility as a Function of Site Height and Antenna Mast Height

100 Site Advantage 100 to 200 m

80

Mean Percent of Circumference Visible

60 50 40

30 15

30 Antenna Mast Height (m)

5

20

10 7 5 = Spherical Earth Horizon 3 0

10

20

30

40

50

Range (km)

Figure 4.B.9 Mean terrain visibility vs range for four antenna mast heights, for sites with site advantage lying between 100 and 200 m. Based on bare-earth DTED for 43 hilltop sites.

Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity 371

Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity 4.C.1 Introduction This appendix investigates effects of terrain shadowing and radar sensitivity limitations on measurements of low-angle ground clutter strength. Shadowed terrain is terrain that is not directly illuminated or within geometrical line-of-sight to the radar. As range increases, the amount of terrain shadowing increases. Furthermore, as range increases, radar sensitivity decreases. For real radars with finite sensitivity limits, the increased terrain shadowing that occurs with increasing range is accompanied by increased numbers of samples at radar noise level in measured ground clutter distributions. These noise samples can introduce undesirable biases in clutter strength estimates. This appendix inquires into the effects of large numbers of noise samples on measured ground clutter distributions when large amounts of shadowing at long ranges occur. Section 4.C.2 shows the general qualitative effects to be expected of these influences on measured clutter distributions. In Section 4.C.3 clutter is reduced to long ranges within wide annular rings subsuming large amounts of shadow. In Section 4.C.4, clutter is reduced to long ranges within 360° range gates, similarly subsuming large amounts of shadow.

4.C.2 General Effects on Measured Ground Clutter Distributions For a theoretically infinitely sensitive radar, increased terrain shadowing with increasing range can cause clutter strengths to decrease with increasing range because of the weak returns received from the shadowed cells illuminated only indirectly through diffraction. If strong clutter returns from visible regions are averaged together with weak clutter returns from shadowed regions, and if the shadowing is extensive, the resultant diminution of average clutter strength may be referred to as being caused by spatial dilution. That is, the strong clutter received from directly illuminated cells is diluted by spreading it out over many shadowed cells. This effect of spatial dilution of clutter strength is theoretically independent of sensitivity, although, practically, shadowed cells are often measured at radar noise level. Real radars with narrow azimuth beams usually operate either within directly illuminated macroregions of visible terrain or free of strong clutter in macroregions of shadowed terrain; the radar receiver does not average together or spatially dilute strong clutter from visible regions with extensive amounts of weak clutter from shadowed terrain. Estimates of clutter strength within macroregions of visibility allow these estimates to remain on solid

372 Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity

quantitative footing. The selection of clutter patches to lie in macroregions of clutter and not macroregions of shadow avoids their degradation by spatial dilution. Even within macroregions of visibility, many clutter return samples may occur on the noise floor of the radar. However, their numbers within patches are not so large as to prevent acceptable absolute measures of clutter strength from being obtained, either in terms of percentile levels in cumulative distributions, or in terms of mean strengths and higher moments (e.g., see Table 4.7, Figures 4.15, 4.16). To achieve solid footing for estimates of clutter strength in the patch world in an absolute sense independent of radar sensitivity, all of the cells within the patch need to be included in the computation, including those for which the received clutter power measurement is at the noise floor of the radar. Appendix 4.A illustrates that within sectors that contain significant amounts of visible terrain, clutter strength does not diminish significantly with increasing range. This appendix moves beyond the patch world, such that very large numbers of noise samples are accepted into measured clutter distributions because of the inclusion of macroshadowing. Incorporation of large numbers of noise samples in the distributions requires careful interpretation of the results to avoid incorrectly assuming that observed relative biases caused by limited sensitivity are actual trends in absolute clutter strength. Figure 4.C.1 shows sketches of clutter histograms including effects of noise and saturation. Here, as in Appendix 2.B, x is used to represent clutter strength σ°F 4 in units of m2/m2, and y to represent 10 log10(x), i.e., y represents clutter strength in dB. Figure 4.C.1(a) shows an idealized sketch of a histogram of clutter strengths within some spatial region, as this histogram actually exists without reference as to how it might be measured. A perfect measurement radar with infinite dynamic range would measure this histogram, as shown in Figure 4.C.1(a), without introducing any spurious or contaminating effects. Note that Figure 4.C.1(a) shows definite limits both to the maximum clutter strength y*max (less than infinity) and the minimum clutter strength y*min (greater than zero) occurring in the histogram. Any actual histogram of measured clutter strengths is limited both in maximum and minimum in this way. On a dB scale for measuring clutter strength y, most theoretical distributions (e.g., Weibull, lognormal, K-) are not limited but stretch from minus infinity (i.e., zero power) to plus infinity. In what follows, the word “actual” is reserved to mean the distribution as it actually exists without reference to measurement considerations, as opposed to what is “measured” with a real radar limited in dynamic range. All real radars are sensitivity limited. As a result, it is not unusual for some of the cells within a clutter region to be at the radar noise level. Thus many measured patch histograms are contaminated by noise at their weaker or lower levels. The noise samples do not all occur at a common clutter strength since the sensitivity limit is range dependent. Figure 4.15 shows examples of patch histograms with noise contamination where bins containing one or more noise samples are indicated with a double underline. In any measurement, it is known which samples are at radar noise level, so that they can be separated and dealt with as desired. Besides overestimating the returns from weak cells at noise level, the radar may saturate on and thus underestimate the strength of some strong cells. Figure 4.C.1(b) shows a sketch representing the “measured” histogram of clutter strengths for the same clutter region for which the “actual” histogram of Figure 4.C.1(a) applies. The measurement is assumed to be performed by a real radar with limited dynamic range. In this measured histogram, the

Percent of Samples

Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity 373

"Actual" Histogram

Clutter Strength y y*min

y*max

Percent of Samples

"Measured" Histogram

Percent of Samples

(a) Histogram that would be measured by a radar with infinite dynamic range.

Limited Dynamic Range Infinite Dynamic Range

y Noise Contamination

sat y * = y sig ymin max max= ymax Saturation Contamination

y sig * y ymin min ymin

noi = y' ymax

sat y sig y ymin max max y*max

Percent of Samples

(b) Histogram as measured by a real radar with limited dynamic range.

"Shadowless" Histogram

y sig ymin

ymax

(c) Shadowless histogram containing only samples measured above the noise floor of a real radar.

Figure 4.C.1 Sketches and nomenclature for clutter strength histograms.

minimum measured strength ymin may be greater than y*min (i.e., ymin ≥ y*min) because of limiting from above at noise level, and the maximum measured clutter strength ymax may be less than y*max (i.e., ymax ≤ y*max) because of limiting from below at saturation level. The noise floor and saturation ceiling, in terms of absolute strength levels, are range dependent.

374 Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity

Figure 4.C.l(b) shows the strongest noise level sample reaching up into the histogram to a noi level denoted as y max . In Appendix 2.B, Figure 2.B.2, this maximum noise level is designed as y', and this designation is continued here for this important quantity. Similarly, the minimum saturation level is shown reaching down to a level denoted as y sat min . To complete the nomenclature of various clutter strength levels, the minimum actual sig sig noi clutter strength measured above radar noise is denoted as y min , where y min ≤ y max , and the maximum actual clutter strength measured below saturation is denoted as y sig max sat where y sig max ≥ y min . In point of fact, saturation is usually much less a contaminating influence in clutter strength computation than noise, and, as indicated in the insert in Figure 4.C.1(b), often the highest bin in the histogram can contain both saturated and unsaturated samples, so that y sig max = ymax = y*max. In what follows, the focus will be on noise contamination in considering effects of sensitivity limitations, requiring the use of y' and y sig min . Figure 4.C.1(c) shows a sketch of the “shadowless” histogram obtained as just the subset of measured samples from the histogram of Figure 4.C.1(b) containing discernible clutter above radar noise level. Figure 4.C.2 shows a sketch of the cumulative distribution function of the measured histogram of clutter strengths shown in Figure 4.C.1(b). This cumulative distribution function is obtained by integrating (or accumulating) across the histogram of Figure 4.C.1(b) left-to-right, but identical conclusions apply whether cumulative distributions are formed by integrating left-to-right or right-to-left across histograms. Many cumulative clutter distributions are shown in this book displayed on nonlinear Weibull or lognormal cumulative probability scales. All such cumulative distributions increase monotonically from zero at ymin to unity at ymax. In Figure 4.C.2 and elsewhere in this section, these limits of zero and unity are shown on the vertical cumulative probability scale, and for simplicity the cumulative distribution functions are shown to plot linearly (or piecewise linearly) against this otherwise arbitrary scale. Note that, as drawn in Figure 4.C.2, there is a break in slope in the measured cumulative distribution between the noise-contaminated region and the uncontaminated region. This is seen in many measured distributions. Since it is known in any measurement what the maximum measured noise clutter power level y' is, the investigator may choose to only consider the uncontaminated upper region of the distribution at percentile levels greater than P'.

Cumulative Probability P

1 Actual Distribution (Unlimited Sensitivity)

Measured Distribution

noi P max = P' Noise Contamination Due to Sensitivity Limit

0 y*min

ymin

noi ymax = y'

ymax

Clutter Strength y

Figure 4.C.2 Idealized cumulative distribution of clutter strengths within a clutter patch.

Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity 375

Suppose a particular clutter region is selected and repeatedly measured in steps of increasing sensitivity. The resultant clutter strength histograms would be as shown in Figure 4.C.3. As the sensitivity increases, the region of noise contamination is pushed to lower levels further to the left. The resultant cumulative distribution functions are shown in Figure 4.C.4 from which an important observation may be made. As the sensitivity increases, the measured distribution in Figure 4.C.4 matches the actual (unlimited sensitivity) distribution to lower and lower y levels. At any sensitivity, the cumulative distribution matches the actual distribution for (y, P) values greater than the (y', P') values at that sensitivity. This is one important reason why noise-level cells must be retained in measured clutter distributions. By doing so, absolute or sensitivity-independent percentile measures of clutter strength are obtained for y > y'. As shall be seen, distributions formed of only those samples above radar noise level within a region, or what are referred to here as shadowless distributions, do not have this attribute.

Percent

Measured Histograms of Varying Sensitivity Low

Actual Histogram (Unlimited Sensitivity)

Moderate High Actual

0 ymax

ymin

Clutter Strength y

y*min

Figure 4.C.3 Behavior of measured histograms of clutter strength with varying radar sensitivity.

Actual Distribution (Unlimited Sensitivity)

Cumulative Probability P

1

Low Sensitivity

Actual

Moderate Sensitivity High Sensitivity 0 ymin

ymax

Measured Distributions Clutter Strength y

y*min

Figure 4.C.4 Behavior of measured cumulative distributions of clutter strength with varying radar sensitivity.

In working within a patch world of clutter amplitude statistics, an analyst keeps on solid footing by working with the complete distribution for any patch including samples at radar noise level. As discussed, doing so keeps percentile results sensitivity independent. That is, any percentile levels P so provided are absolute measures as long as P > P'. If P < P', the

376 Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity

corresponding clutter strength y < y' is an upper bound to true or absolute clutter strength. It is the continuous sequence of increasing values of P with increasing y that forms the cumulative distribution function. These functions are valid absolute measures of clutter strength only over the uncontaminated region P > P'. With respect to the moments (e.g., mean, standard deviation, etc.) of measured clutter patch amplitude distributions, which depend upon y < y' as well as y > y', the analyst keeps on solid footing by computing upper- and lower-bound estimates for each moment. The upper bound is computed by assigning y = ynoise to noise cells, where ynoise is range dependent. The lower bound is computed by assigning x = 0 power to all noise cells. For clutter patches in visible regions of terrain, these bounds are usually within a fraction of a dB of each other, even for large amounts of microshadowing (see Table 4.7). The reason the noise values have such little influence on moments of clutter amplitude statistics from patches is that the strong clutter cells dominate the computations. This would be more intuitively obvious if a linear abscissa x were employed, rather than a logarithmic abscissa y. Close upper and lower bounds to amplitude moments do not always occur in investigations of clutter amplitude statistics. These bounds are close to each other in the patch world because patches are purposefully selected to contain substantial visible clutter. If these bounds drift apart from each other for a patch, it is an indication that the patch was poorly selected. However, when the patch world is departed from and macroshadowing is allowed to contaminate clutter amplitude distributions and measures of clutter strength, these bounds can be widely separated. To provide some insight into these macroshadowing matters, consider the shadowless histograms of clutter strength sketched in Figure 4.C.5, as measured from a given clutter region by radars of increasing sensitivity. Shadowless distributions are formed of only those samples within a region above the radar noise level. When examining a large macroscopic region of spatial extent containing a high percentage of cells at radar noise level, an analyst may feel motivated to consider only the subset of shadowless cells in which actual ground clutter is discerned above radar noise level. As shown in Figure 4.C.l(c), shadowless histograms contain only y values greater than y sig min , and the typical secondary lobe due to noise contamination is not evident in them. Note that the number of samples in a shadowless histogram is sensitivity dependent, as shown in Figure 4.C.5. The more sensitive the measurement radar, the more cells in a given clutter patch that will be measured above the noise level. Thus, in Figure 4.C.5, the left side of the histogram extends further to the left and includes more samples with increasing sensitivity. Since the computation of moments (e.g., mean) of these shadowless distributions obviously depends on the number of clutter samples Nc above the noise level (e.g., x

shadowless

1 = -----Nc

Nc

c

∑ xi , see Section 4.C.3),

i=1

moment computations of shadowless distributions are not fixed in any absolute sense, but vary with sensitivity. On the other hand, when the noise cells are included in the distributions as in Figure 4.C.1(b), there always exists a fixed total number of cells within the patch which are used in all upper and lower bound moment computations; thus, such computations are fixed as absolute measures independent of sensitivity.

Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity 377

Increasing Sensitivity

Percent

Actual Histogram (Unlimited Sensitivity) Actual Measured Shadowless Histograms

Clutter Strength y

0 y*min

sig ymin

ymax

Figure 4.C.5 Behavior of measured shadowless histograms of clutter strength with varying sensitivity.

Figure 4.C.6 shows how the cumulative shadowless distribution function for a given region varies as a function of sensitivity. The distributions sketched in Figure 4.C.6 are formed by integrating left-to-right across the shadowless histograms of Figure 4.C.5. Each distribution in Figure 4.C.6 begins to rise from P = 0 at the minimum discernible clutter strength level sig y min applicable for a particular sensitivity. As a result, the shape or slope of the shadowless cumulative clutter distribution varies with radar sensitivity over the complete extent of the distribution. The shadowless distributions of Figure 4.C.6 may be compared with the distributions of Figure 4.C.4 which include noise samples and are not sensitivity dependent for (y, P) greater than (y', P'). The sensitivity dependence of the shadowless distributions in Figure 4.C.6 is clearly undesirable.

Low

Moderate

1 High

Cumulative Probability P

Sensitivity

Increasing Sensitivity

0

ymax

Clutter Strength y

y sig min

Figure 4.C.6 Sensitivity dependence of shadowless distribution of clutter strengths for a given clutter patch.

Until now, this section has been considering how noise and sensitivity affect measures of clutter strength within a given clutter region. It has been shown that, for a given region of spatial extent with fixed boundaries, the resultant distributions of clutter strength within those boundaries are independent of sensitivity for y > y' as long as they include the noise

378 Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity

level cells. The question now raised is, what happens when those boundaries are allowed to vary? Imagine a hypothetical circular spatial region of strong clutter in which all cells are above radar noise level, as shown by region 1 in Figure 4.C.7. The cumulative clutter distribution for region 1 would be as shown (idealized) by the zero percent shadowing curve in Figure 4.C.8. Now let the boundary of the circular region expand to position 2 in Figure 4.C.4., in which all the cells in the additional annular region are at radar noise level. The cumulative clutter amplitude distribution for this larger region containing a low degree of shadowing is as indicated by the low percent shadowing curve in Figure 4.C.8. Similarly, if the circular boundary of the clutter region continues to expand to regions 3 and 4 as shown in Figure 4.C.7, the cumulative clutter distributions become noise contaminated to higher and higher percentile levels as shown in Figure 4.C.8. As more and more shadowing is included within a region with a center core of discernible clutter, the uncontaminated part of the distribution of (y, P) greater than (y', P') changes shape or slope depending on the amount of shadowing included. Thus the distribution, even in its region of validity, is not absolute and independent of the choice of boundary. An important point emerges here. Measures and distributions of clutter strength within a clutter patch theoretically depend upon the selection of the patch boundaries. Only after the boundaries are set does the distribution within those boundaries, which includes the noise cells, become an absolutely specifiable quantity independent of sensitivity for y > y'. The theoretical dependence of clutter patch spatial amplitude distributions on selection of patch boundaries reflects the basic heterogeneity of terrain.

Region*

1 2 3 4 3

Percent of Shadowed Cells Zero Low Moderate High

4

2

1 Clutter

Macroshadow Macroshadow Macroshadow * Region n+1 Includes Region n, n = 1, 2, 3

Figure 4.C.7 A circular clutter region surrounded by macroshadow.

Clutter Shadow

Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity 379

High Moderate Low None

P'

Cumulative Probability P

1 Percent of Shadowed Cells

0 y'

ymax

Clutter Strength y

Figure 4.C.8 Dependence of clutter strength distribution on the amount of shadowing.

In actual practice, most clutter patch amplitude distributions are not too sensitive to boundary specification because patch boundaries are selected to encompass relatively uniform terrain regions such that small changes in boundaries usually do not cause abrupt changes in relative clutter and shadow densities within patches. Thus a patch world keeps an analyst on solid quantitative footing in this matter also, in that the specification of boundaries for most patches is not a major factor influencing shapes and strengths of resultant distributions. This is not the case in the following sections of this appendix, in which patch analysis is bypassed to allow consideration of clutter distributions containing increasingly large amounts of macroshadow with increasing range. This section concludes by comparing the idealized clutter distributions of Figure 4.C.6 with those of Figure 4.C.8. In Figure 4.C.6, increasing sensitivity strongly affects the shape of the shadowless distribution for a fixed clutter region by moving the starting strength y sig min of the distribution increasingly to the left or to lower values. In Figure 4.C.8, increasing the relative amount of shadowing within a region while maintaining a non-changing shadowless core distribution of discernible clutter within the region strongly affects the shape of the resultant clutter distribution that includes radar noise cells. In this latter case, increasing shadowing affects the shape by moving the starting percentile level P' of the uncontaminated range of the distribution y > y' increasingly up the vertical scale to higher values. In the next section, it will be seen how the incorporation of increasing macroshadowing in measured cumulative clutter distributions with increasing range results in both of these strong effects associated with variations in sensitivity and shadowing undesirably influencing the shapes and strengths of the measured distributions.

4.C.3 long-range Clutter within Wide Annular Regions The world of clutter patches, upon which much of the analysis of this book is based, avoids undesirable consequences of shadowing in estimates of low-angle ground clutter strength, even though some degree of shadowing is unavoidable even within patches (see Table 4.7). Although shadowing of clutter increases and radar sensitivity to clutter decreases with increasing radar range, the measures of clutter strength within patches remain absolute measures accurate at long ranges as well as short ranges. Such patch measures of clutter strength show no significant general trend with increasing range over the long ranges beyond that at which the onset of the grazing incidence depression angle regime occurs. This is shown in the sector display results of Appendix 4.A, in which the

380 Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity

long-range narrow-azimuth sectors employed may be thought of as long narrow patches over largely visible terrain containing significant amounts of clutter. The work of patch selection eliminates macroshadow in estimates of clutter strength. If macroshadow is not eliminated, its effects intrude in analyses of clutter strength. This section and the next show how clutter strength varies with range, including the effects of macroshadow, either as the macroshadow occurs in wide annular rings in this section, or as the macroshadow occurs within individual range gates in the next section. Ground clutter is now analyzed in large annular regions, using Phase Zero measurements at 47-km maximum range setting (see Appendix 2.A, Table 2.A.3). At this range setting, the radar RF pulse length is 1 µs, and the resultant range resolution is 150 m. Ten sites were selected, as listed in Table 4.C.1, of varying land cover, landform, and effective site height, but all with substantial amounts of measured clutter to long range. Measured PPI clutter plots to 47-km maximum range are shown for each site in Figure 4.C.9. Four annular regions were specified with range extents as follows: (1) 5 to 15 km, (2) 15 to 25 km, (3) 25 to 35 km, and (4) 35 to 45 km. For each of these four annular regions, all of the individual spatial samples of clutter strength from all 10 sites were aggregatively combined to form four ensemble histograms of clutter strength, each applying to a general annular region. Standard procedures for characterizing clutter amplitude statistics over spatial regions (see Appendix 2.B) were then applied to each of these four histograms. Table 4.C.1 Ten Sites for Which Substantial Amounts of Ground Clutter to 47-km Range Were Measured

Site

Land Cover

Landform

Effective Site Height (m)

Neepawa

2-4

2

-30

Shilo

2-4

1-3

3

Pakowki Lake

3

1

11

Peace River South

2-4

3-7

19

Spruce Home

2-4

3

25

Rosetown Hill

2

3

28

Thompson

2

1

35

Orion

3

3

41

Vananda East

3

4

94

Wachusett Mt.

4

4-7

333

Figure 4.C.10 shows the resultant four cumulative amplitude distributions, each one containing all measured samples over 10 sites within the indicated range interval or annular region, including all samples at radar noise level. There is an obvious trend in the relative shapes and positions of these distributions with increasing range. Table 4.C.2 shows some statistical attributes of these four distributions which help provide understanding of how clutter strength varies across these distributions. First, the 99-percentile level shows a clear trend of decreasing strength with increasing range. This trend reflects the fact that the relative positioning of these distributions is ordered by range, with the long-range distribution left-most (i.e., weakest), and the short-range distribution right-most (i.e.,

Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity 381

(a) Neepawa; Effective Site Height = –30 m

(b) Shilo; ESH = 3 m

(d) Peace River South; ESH = 19 m

(c) Pakowki Lake; ESH = 11 m

(e) Spruce Home; ESH = 25 m

Figure 4.C.9 Ground clutter maps at 10 sites, selected for investigating clutter strength dependencies on range. Phase Zero X-band data. In each map, maximum range = 47 km, north is zenith, range resolution = 150 m, clutter is black, clutter threshold is 3 dB from full sensitivity. Figure continued on next page.

strongest) in Figure 4.C.10. This trend, however, is primarily just a direct consequence of the relative number of samples at radar noise level in each distribution. As is shown in Table 4.C.2, the percent of samples at radar noise level increases strongly with increasing range, from 54% at short-range to 97% at long-range. Clearly, as a radar looks out to longer and longer ranges, it will see less and less clutter above its sensitivity limit, and this will always drive any given percentile level of clutter strength down with increasing range, until, in the limit at long enough range, all percentile levels lie on the noise floor. The ordered positions with range of the distributions in Figure 4.C.10 are explained by the sketch of Figure 4.C.8. The latter indicates how distributions vary when a central core of clutter is surrounded by more and more shadow. This is similar to the situation with the four annulae of measured data, where, as range increases, the samples of discernible clutter are immersed in more and more macroshadow. Thus, the relative positions of the distributions in Figure 4.C.10 are primarily controlled by macroshadowing. Recall that these distributions, as shown in Figure 4.C.10 only above their regions of noise contamination y > y', are sensitivity independent and reflect absolute levels, as do those in Figure 4.C.8.

382 Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity

(f) Rosetown Hill; Effective Site Height = 28 m

(g) Thompson; ESH = 35 m

(i) Vananda East; ESH = 94 m

(h) Orion; ESH = 41 m

(j) Wachusett Mt; ESH = 333 m

Figure 4.C.9, cont’d. Ground clutter maps at 10 sites, selected for investigating clutter strength dependencies on range. Phase Zero X-band data. In each map, maximum range = 47 km, north is zenith, range resolution = 150 m, clutter is black, clutter threshold is 3 dB from full sensitivity. Results above conclude this figure.

Next, consider the mean strengths of the clutter distributions in Figure 4.C.10. Upper and lower bounds to the mean strengths of these distributions are included in Table 4.C.2. Consideration of upper and lower bounds keeps analysis on solid footing here in the face of macroshadowing, as it does within patches in the face of microshadowing. In either case, an infinitely sensitive radar that would measure discernible clutter return in every resolution cell (i.e., no noise samples) would find a mean clutter strength between these bounds. Overall, the mean bounds shown in Table 4.C.2 indicate decreasing mean clutter strength with increasing range. If an infinitely sensitive radar looks to longer and longer ranges, the mean clutter strength must eventually strongly decrease as more and more cells become lit only by diffraction. The percent of samples at radar noise level in the outer two annulae is 94% in the 25- to 35-km annulus and 97% in the 35- to 45-km annulus. Since the total number of samples combined from 10 sites in each annular region is large (i.e., approximately 106, see Table 4.C.2), even small percentages of discernible clutter samples (i.e., 6.2% in the 25- to 35-km annulus; 2.6% in the 35- to 45-km annulus) still result in sizeable sample populations of clutter (66,138 clutter samples in the 25- to 35-km annulus; 27,169 clutter samples in the 35- to 45-km annulus) from which general conclusions may be drawn regarding clutter strength vs range.

Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity 383

Weibull Scale 0.99999

Probability That σ°F4 ≤ Abscissa

0.9999 0.999

45

o 5t

0.995 0.99

km

3

0.95

m

0.9 0.8

15

0.7 o 5t

0.6

k 35 to 5 2 km 25 to 15

km

0.5 0.4 0.3 –50

–40

–30

–20

–10

0

10

σ°F4(dB)

Figure 4.C.10 Cumulative distributions of clutter amplitude statistics, conglomeratively combined from 10 sites into four annular regions. These four distributions include all spatial samples including those at radar noise level. The distributions are shown only as they emerge to the right of their noise-contaminated regions for σ °F4 levels greater than the maximum σ °F4 level in which noise occurs in each distribution. Phase Zero X-band data, 150-m range resolution. Compare with Figure 4.C.8. Table 4.C.2 Clutter Strengths by Annular Regiona Including Noise-Level Samples σ°F4 (dB)

a b c d e f

Lower Bounde

Percent of Samples at Radar Noise Level

Samplesf

Meanc

Range (km)

99 Percentileb

Upper Boundd

No. of x 106

5 to 15

-17

-28.4

-28.4

54.0

1.045

15 to 25

-21

-30.4

-30.9

82.6

1.045

25 to 35

-23

-31.9

-34.7

93.8

1.061

35 to 45

-25

-30.2

-37.1

97.4

1.045

Averaged over ten sites, see Table 4.C.1. Lower percentiles are noise contaminated. Computed in units of m2 /m2 and subsequently converted to dB. Noise samples assigned noise power values. Noise samples assigned zero power values. Range sample interval = 148.41 m; azimuth sample interval = 0.234°.

Figure 4.C.11 shows the four cumulative shadowless clutter amplitude distributions that result from collecting just the samples in these annulae in which discernible clutter occurs above the noise floor. Each distribution in Figure 4.C.11 contains all samples of discernible clutter from 10 sites within the indicated range interval. No samples at radar noise level are included in these shadowless distributions. Here, as in Figure 4.C.10, an obvious trend is

384 Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity

seen in the relative shapes and positions of these shadowless distributions, although each is quite different from its counterpart in Figure 4.C.10. Table 4.C.3 shows some statistical attributes of these shadowless distributions. There is a clear indication of increasing clutter strength with increasing range in these shadowless clutter statistics. The true trend of decreasing clutter strength with increasing range as would be measured by an infinitely sensitive radar is masked in these shadowless data by the effects of decreasing sensitivity with increasing range. This is seen by comparing the actual empirical shadowless distributions of Figure 4.C.11 with the idealized shadowless distributions sketched in Figure 4.C.6. The latter indicate how shadowless distributions vary with decreasing sensitivity for a given clutter region. This idealized variation as sketched in Figure 4.C.6 explains the dominant trend observed with range in the distributions of Figure 4.C.11.

4 Probability That σ°F ≤ Abscissa, 4 Given That σ°F > Radar Noise Level

Weibull Scale 0.99999 0.9999 0.999 0.995 0.99 0.95 0.9 0.8

Range (km)

25 to 35 km

5 to 15 15 to 25 25 to 35 35 to 45

15 to 25 km

0.7 0.6

5 to 15 km

σ°F4 (dB) Mini- Maximum* mum –58 6† –43 10 –37 8 –32 8

* Shadowless † Saturated

0.5 0.4

35 to 45 km

0.3 –50

–40

–30

–20

–10

0

10

4

σ°F (dB)

Figure 4.C.11 Cumulative distributions of shadowless clutter amplitude statistics, conglomeratively combined from 10 sites into four annular regions. These distributions include only those spatial samples in which discernible clutter above the radar noise floor was measured. Phase Zero X-band data, 150-m range resolution. Compare with Figure 4.C.6.

We wish to determine how ground clutter strength varies with range in an absolute sense not dependent on radar sensitivity. The data of Figure 4.C.10, although absolute measures, are biased by spatial dilution; these data are dominated by the fact that as a radar looks to longer ranges, it sees increasingly less ground clutter and is at its noise level over increasingly large spatial regions. If, as in Figure 4.C.11, we attempt to resolve this problem by considering only discernible clutter samples above radar noise level, these shadowless data are also biased (i.e., they are relative, not absolute, measures), dominated by the fact that radar sensitivity decreases with range so that at far ranges the radar only measures very strong clutter. Working with clutter strengths within visible terrain patches

Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity 385

Table 4.C.3 Shadowless Clutter Strengths by Annular Regiona Range (km) 5 to 15 15 to 25 25 to 35 35 to 45

σ°F4 (dB)b 99 Percentile -15 -15 -13 -11

Meanc -25.1 -23.3 -22.7 -21.2

No. of Samples 480,475 181,881 66,138 27,169

Percent of Total No. of Samples within Annulus 46.0 17.4 6.2 2.6

a Averaged over ten sites, see Table 4.C.1. b These are not true σ°F4 statistics but are conditional on clutter strength being above noise

level. For example, multiplying mean σ°F4 given here by cell area does not yield true mean clutter cross section or allow the computation of the true mean clutter power. c Computed in units of m2/m2 and subsequently converted to dB.

and employing a model that keeps separate the ideas of where the clutter is and how strong it is avoids such problems. In what follows, the analysis of ground clutter within large annular regions is continued in order to find an unbiased answer in these results on how clutter strength varies with range, such that the strong biasing effects caused by increasing shadowing and decreasing sensitivity with increasing range are normalized out. To do this, shadowless statistics are employed but the same radar sensitivity is artificially enforced in all annulae as exists in the farthest range annulus. That is, the radar sensitivity is decreased in the first three annulae to equal that in the fourth annulus. In Figure 4.C.10, which shows the distributions only above the maximum noise-contaminated bin y > y' [see Figure 4.C.1(b)], the maximum noise-contaminated bin in the 35- to 45-km annulus is σ°F4 = –27 dB. Thus, for each annular regime, the distributions are formed of all clutter samples of measured strength σ°F4 ≥ –24 dB, thereby providing a buffer of 3 dB to be well clear of the noise in the 35- to 45-km regime. The resultant distributions are shown in Figure 4.C.12. They are very nearly identical. They indicate that strong clutter, as it occurs for σ°F4 ≥ –24 dB, exists independently of range from the radar. This annular region result is necessarily restricted to apply only to strong clutter in order that it avoid biases introduced by effects of varying sensitivity or degree of shadowing with range. Table 4.C.4 provides some additional quantitative measures of the distributions shown in Figure 4.C.12. These measures reinforce the obvious rangeindependence of the data in Figure 4.C.12. Care must be taken in the use of these conditional data in Figure 4.C.12 or Table 4.C.4, since they portray only conditional σ°F4 statistics that occur equal to or stronger than –24 dB. In this respect, note that the conditional mean clutter strength values in Table 4.C.4 are much higher than the true unconditional means as indicated by the mean bounds in Table 4.C.2. Another way of showing the σ°F4 ≥ –24 dB data of Figure 4.C.12 is in the normalized histograms shown in Figure 4.C.13. These histograms are normalized to show the relative number of samples at a given σ°F4 level greater than –24 dB compared to the number of samples at –24 dB. This normalization is in contrast to that of the cumulative distributions in Figure 4.C.12, which is with respect to the total number of samples of σ°F4 ≥ –24 dB. The data in both Figures 4.C.12 and 4.C.13 are strongly indicative of range-independence of clutter samples for which σ°F4 ≥ –24 dB. Many of these samples are doubtlessly caused by the existence of strong discrete backscattering sources on the landscape. There is no

386 Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity

0.999

Probability That σ°F4 ≤ Abscissa, Given That σ°F4 ≥ –24 dB

0.99 0.97 0.95 0.9

35 to 45 km 5 to 15 km 15 to 25 km 25 to 35 km 35 to 45 km

0.8 0.7 0.6 5 to 15 km

0.5 0.4 0.3

0.2

0.1 –20

–10

σ°F4

0

(dB)

Figure 4.C.12 Cumulative distributions of clutter amplitude statistics with strength σ °F4 ≥ –24 dB, conglomeratively combined from 10 sites into four annular regions. These distributions include only those spatial samples in which σ °F4 ≥ –24 dB was measured. Phase Zero X-band data, 150-m range resolution. Table 4.C.4 Statistical Attributes of the Distributions of Clutter Strength of σ°F4 ≥ –24 dB, by Annular Regiona

σ°F4 (dB)b Range (km)

No. of Samples

Percent of Total No. of Samples within Annulus

Mean

Maximum

Standard Deviationto-Mean

5 to 15

-17.9

6c

6.3

75,201

7.2

15 to 25

-16.1

10c

4.3

29,486

2.8

25 to 35

-17.0

8

8.3

141,731

1.4

35 to 45

-16.9

8

7.9

9,275

0.9

a Averaged over ten sites, see Table 4.C.1. b Computed in units of m2/m2 and subsequently converted to dB; these are not general spatial amplitude

statistics but are conditional on σ°F4 ≥ -24 dB; multiplying mean of σ°F4 as given here by ground area does not yield true mean clutter cross section. c Saturated.

Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity 387

reason to expect that the distribution of such strong cells on the landscape would show any general preference with respect to range from the radar, and this is borne out by the data in Figures 4.C.12 and 4.C.13.

Number of Samples of σ°F4 = –24 dB

1.0 5 to 15 km 0.3

5 to 15 km 15 to 25 km 25 to 35 km 35 to 45 km

0.1

0.03

Number of Samples of σ°F4 = Abscissa

0.01 0.003

0.001 35 to 45 km 0.0003 0.0001 –20

–10

0

10

4 σ°F (dB)

Figure 4.C.13 Normalized histograms of clutter amplitude statistics with strength σ °F4 ≥ –24 dB, conglomeratively combined from ten sites into four annular regions. These histograms contain only those spatial samples in which σ °F4 ≥ –24 dB was measured. Phase Zero X-band data, 150-m range resolution.

4.C.4 Long-Range Clutter within 360° Range Gates The previous section presented ground clutter data from 10 sites averaged azimuthally within four broad annular range rings to 45-km maximum range. In the analysis of these data, shadowing and sensitivity were major factors. This section expands these previous insights into range dependencies of measured clutter data by considering the same 10-site set of clutter data in the limiting case as an annular ring shrinks in width to a single range gate. Average clutter strength vs range is shown, range gate by range gate, to 47-km maximum range. This approach provides continuous range dependencies in the results. The constant radar noise level within each range gate allows a more straightforward determination of the effects of sensitivity on mean clutter levels. These results, like those of the previous section, continue to entail 360° azimuth averaging through macroshadow. The resulting spatial dilution of clutter strengths causes trends of decreasing clutter strength with increasing range in the results. These results apply to the hypothetical situation of a radar with an azimuthally omnidirectional antenna pattern in which mean clutter power levels received would, indeed, include effects of macroshadowing through 360°.

388 Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity

First, some analytical relationships are developed applicable to this range gate by range gate investigation. Assume that, in a given range gate from the radar, all azimuth samples from one complete azimuth scan of the radar are binned in a histogram and averaged. Let the total number of azimuth samples from one complete 360° azimuth scan be N. For the Phase Zero radar, N = 1,536 (see Appendix 2.A). The notation here follows that first developed in Appendix 2.B, where x represents clutter strength σ °F 4 in units of m2/m2, and y = 10 log10 (x). Thus clutter strength from each of the N azimuth samples is represented as xi, i = 1 to N. The overall mean of these N samples, denoted x , is given simply by N

1 x = ---N

∑ xi

(4.C.1)

i=1

Of these N samples, some will be true measurements of clutter strength above the sensitivity of the radar at that range, and some will be at the noise floor of the radar due to shadowing. Suppose there are Nc true measurements of clutter, and Nn measurements at noise level. Then, N = Nc + Nn. The ratio Nc /N is the fraction of the circumference in clutter at the range gate under consideration. That is, the quantity (Nc /N × 100) is what is referred to as percent circumference in clutter elsewhere in this book (see Section 4.3.2, Figures 4.8 c and 4.10). If xi is a true clutter measurement, let it be represented by x i , and if x i is a noise n measurement, let it be represented by x i . With this, the mean of just the set of samples constituting true clutter measurements, which is denoted here as the shadowless mean, is s given by x , where 1 s x = ----Nc

Nc c

∑ xi

(4.C.2)

i=1

Since at a given range, all Nn samples of noise are of equal clutter strength, the notation n n simplifies, as x i ≡ x . With this terminology, Eq. (4.C.1) may be expressed as: Nn n Nc s x = ------ ⋅ x + ------ ⋅ x N N

(4.C.3)

Now consider the meaning of the various terms and factors in Eq. (4.C.3). The shadowless s mean x is the mean of the clutter samples only, without any shadowed cells at radar noise level. It is obviously dependent on the sensitivity of the radar and hence range, and as a s result is by itself not an absolute measure of clutter strength. When x is multiplied by the fraction of circumference in clutter, however, the result is an absolute lower bound to the overall mean clutter strength in the range gate under consideration. This may be seen in Eq. (4.C.3), where there are Nn samples at the noise floor xn contributing to the overall mean x . These Nn noise samples of strength xn are not true measures of clutter strength, but represent upper bounds only to the true clutter strengths that would have been measured if there were no sensitivity limit. That is, if the true clutter value of a sample measured at xn is n n denoted as x true , then 0 ≤ x true ≤ xn. Thus, in Eq. (4.C.3), if the xn values are approximated by their known lower bound of zero (i.e., clutter power cannot be less than

Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity 389

zero), the result is an absolute overall lower bound of mean clutter strength in the range gate under consideration, as: Nc s x lower bound = ----- ⋅ x N

(4.C.4)

On the other hand, if the noise samples are assigned their actual measured values, this is known to be an upper bound approximation (i.e., if the clutter strength is greater than xn, it is measured as xc). Thus x in Eq. (4.C.3) is more precisely denoted as x upper bound . Equation (4.C.3) indicates that an absolute upper bound on mean clutter strength for the range gate under consideration (left hand side) is given by the product of the shadowless mean and the fraction of the circumference in clutter (the product constituting an absolute lower bound on the mean clutter strength) augmented by noise power contributions from all the shadowed samples, as: Nn n x upper bound = ------ ⋅ x + x lower bound N

(4.C.5)

In conceiving a simple non-patchy clutter model, there can be an inclination to want to diminish the mean clutter strength [Figure 4.8(b)] by multiplying it by the ratio of circumference in clutter Nc /N [Figure 4.8(a)] in order to provide a characteristic of diminishing clutter strength with increasing range in the model. Equations (4.C.3), (4.C.4), s and (4.C.5) show that the only correct procedure along these lines is to multiply x by Nc / N to obtain a rigorous lower bound on true mean clutter strength, but that to multiply either upper or lower bounds to true mean clutter strength by Nc /N to provide a characteristic of diminishing clutter strength with increasing range in a simple non-patchy clutter model is arbitrary and without analytical justification. These relationships are now illustrated using clutter measurements from the set of 10 sites shown in Table 4.C.1. For a given range gate, the 15,360 azimuth samples obtained from all 10 sites are combined into a histogram of clutter strengths. Figure 4.C.14 shows various percentile levels in this histogram, as a function of range, range gate by range gate through 320 range gates, where the data were obtained from the 47-km maximum range Phase Zero experiment (see Table 2.A.3). In Figure 4.C.14, five percentile levels are shown, namely: (1) the 50-percentile level, (2) the 90-percentile level, (3) the 99-percentile level, (4) the 99.5-percentile level, and (5) the maximum measured clutter strength level, in each histogram. For example, of the 15,360 samples in each histogram, 77 samples exceed the clutter strength indicated by the 99.5-percentile level. These five levels are shown as measured within the Phase Zero measurement dynamic range between the noise floor and saturation ceiling. The noise floor and saturation ceiling of the Phase Zero radar vary slightly from site to site—the noise floor and saturation ceiling shown are those for a representative site among the 10-site set. The percentile levels of clutter strength shown in Figure 4.C.14 gradually diminish with increasing range, with the lower percentile levels falling off faster. As long as these percentile levels lie above the noise floor, they are absolute measures independent of radar sensitivity. The 90-percentile level diminishes in strength by about 12 dB in the first 25 km. As a radar looks out to farther and farther ranges, the sensitivity of the radar decreases and the amount of macroshadowing of terrain increases. If it were just a matter of decreasing

390 Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity

30 Saturation Ceiling

20

Percentile Level

σ°F4 (dB)

10

Maximum

0 –10

99.5

–20 99

–30 90

–40 –50

Noise Floor

50

–60 3

7

11

15

19

23

27

31

35

39

43

Range (km) * Within each range gate, the percentile levels shown apply to the combined distribution of amplitude samples obtained from 10 sites and through 360 azimuth degrees at each site.

Figure 4.C.14 Selected percentile levels of ground clutter strength vs range, averaged through 360° in azimuth and over 10 sites. Phase Zero X-band data, horizontal polarization, 150-m range resolution, 0.9° azimuth beamwidth. Range sampling interval = 148.4 m, azimuth sampling interval = 0.2344°, 1,536 azimuth samples/range gate/site.

sensitivity for otherwise unchanging clutter, any percentile level in the resulting clutter strength histogram would stay constant with decreasing sensitivity until the noise level reached that percentile level, beyond which that percentile level would ride up on the noise floor. In Figure 4.C.14, the percentile levels do not stay constant but diminish with increasing range before they start to ride up on the noise floor. This diminishment is because of increased terrain shadowing (see Figure 4.C.8). That is, even if sensitivity were to remain constant independent of range, an increasing percentage of cells would occur on the noise floor with increasing range just because less terrain is visible at longer ranges (see Appendix 4.B). The maximum level shown in Figure 4.C.14 shows a downward trend of ~3 dB per octave with increasing range resulting in an ~12 dB overall decrease over the 47-km range extent shown. The maximum level is not a percentile level and is not affected by varying amounts of shadowing in the same way that percentile levels are. The maximum level indicates the strongest clutter cell observed in a given range gate. Although the clutter RCS of a lowangle ground clutter cell usually increases with cell area, the single strongest cell out of the 15,360 azimuth samples in each range gate might be expected to contain a spatially isolated discrete object (such as a water tower) large enough to dominate the clutter RCS independent of cell size. Such cells containing dominant discretes are expected to be uniformly distributed with respect to range and azimuth from the radar (see Figure 4.19). For such cells, the clutter coefficient σ°(where σ ° = clutter RCS ÷ cell area) would decrease with increasing range by 3 dB per octave due to the cell area increasing linearly

Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity 391

with range as a result of the fixed azimuth beamwidth. This explains the decreasing trend of maximum σ ° with increasing range in the results of Figure 4.C.14. The step increase in maximum level beyond 43 km in Figure 4.C.14 is due to a specific feature in the contributing Wachusett Mountain measurement (see Figure 4.C.9) where, at these ranges to the southeast, the urban area of Framingham, Massachusetts, causes strong backscatter (this effect is also evident in Figure 4.C.16). The peaks of the maximum level curve in Figure 4.C.14 near the σ ° = +10-dB level match reasonably closely those of the overall Phase Zero clutter amplitude distribution for 2- to 12-km range clutter patches shown in Chapter 2, Figure 2.29. Figure 4.C.15 shows five individual range gate histograms of clutter strength selected from the 320 range gates shown in Figure 4.C.14. The five range gates selected, namely, gates 40, 100, 160, 220, and 280, are evenly spread over the 47 km shown in Figure 4.C.14. It is from 320 histograms like those in Figure 4.C.15 that the curves in Figure 4.C.14 are generated. The 50-, 90-, and 99-percentile levels are shown as dotted vertical lines in the histograms of Figure 4.C.15, and are printed to the right of each histogram. Samples in these histograms that are at or within 2 dB of the noise floor are shown as black. The strengths of these samples spread over several dB, even though the data come from individual range gates, because the radar noise level varies slightly from site to site over the 10 sites from which data is combined in these histograms. The decreasing sensitivity of the radar with increasing range is clearly evident in these histograms as the black samples move to the right (cf. Figure 4.C.4). The effect of increasing terrain shadowing with increasing range is also evident in these histograms as a given percentile level above the noise, for example, the right-most 99-percentile level, decreases with increasing range (cf. Figure 4.C.8). Mean clutter levels are also indicated in Figure 4.C.15. The mean upper bound level [Eqs. (4.C.3), (4.C.5)] is shown as a vertical dashed line in each histogram. Both the mean lower bound [Eq. (4.C.4)] and the mean upper bound [Eqs. (4.C.3), (4.C.5)] are printed to the right of each histogram. Note that these mean computations are performed on distributions of clutter samples in units of m2/m2 [as per Eq. (2.B.3)], and subsequently converted to dB [as per Eq. (2.B.8)], although the histograms are shown with a dB abscissa (as per Figure 2.B.2). Each histogram in Figure 4.C.15 contains 15,360 samples. The percent of samples in each bin of each histogram is given on a logarithmic vertical scale so that small values of percent of samples may be read. This scale is terminated at 0.1% to present five histograms in one figure. However, the plot of each histogram is continued to lower percent levels where they occur to the right on the high-side tail of the histogram. Where the histogram is shown below the limit of the vertical scale, the same vertical scale (extended unshown) applies. Examples of bins containing only one sample and only two samples are shown in the histogram for gate 100. Figure 4.C.16 shows mean levels as determined from histograms like those in Figure 4.C.15 for all 320 range gates. The shadowless mean is the mean of only those spatial samples in which discernible clutter was measured (i.e., the mean of only the white samples in the histograms of Figure 4.C.15). Theoretically, as sensitivity decreases with increasing range, the shadowless mean must gradually increase. This effect is only very gradual in the data of Figure 4.C.16 in that the shadowless mean rises only a few dB for ranges to 47 km.

392 Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity

100 Gate 280 41.1 km –39 –30 –31 –30 –25

10 1

0.1 100 Gate 220 32.2 km –38 –32 –34 –34 –24

10

Percent of Samples

1

0.1 100 10

Gate 160 23.3 km –31 –30 –39 –35 –22

1

0.1 100 10

1 Sample 2 Samples

1

Gate 100 14.4 km –31 –31 –45 –29 –19

0.1 100 10

Percentiles

90

50

99

Mean Upper Bound

Gate 40 5.5 km –27 –27 –44 –24 –16

1

0.1 –50

–40

–30

–20

–10

4

σ°F (dB) Mean Lower Bound, Mean Upper Bound (dB) Percentile Levels; 50, 90, 99 (dB) Samples at Radar Noise Level

Figure 4.C.15 Histograms of ground clutter strength in five selected range gates, combined from 10 sites and through 360 azimuth deg at each site. Phase Zero X-band data, horizontal polarization, 150-m range resolution, 0.9° azimuth beamwidth. Range sampling interval = 148.4 m, azimuth sampling interval = 0.2344°, 1,536 azimuth samples/range gate/site, 15,360 samples/histogram.

(The abrupt rise in the shadowless mean beyond 44 km is due to urban clutter in the Wachusett Mountain measurement previously mentioned.) The reason that the shadowless mean does not rise more quickly with increasing range and decreasing sensitivity is that the computation is dominated by the high side tail of very strong clutter values, see Figure 4.C.15. The shadowless data in Figure 4.C.16 may be compared and contrasted with the idealized sketches of Figures 4.C.5 and 4.C.6 and with

Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity 393

the shadowless data reduced in broad annulae in Figure 4.C.10 and Table 4.C.3. The proviso of Note b in Table 4.C.3 also applies to the shadowless mean data of Figure 4.C.16.

30 Saturation Ceiling

20

Mean Level

F4 (dB)

10 Upper Bound

0 Shadowless

–10 –20 –30 Noise Floor

–40

Lower Bound

–50 –60 4

8

12

16

20

24

28

32

36

40

44

Range (km) * Within each range gate, the mean levels shown apply to the combined distribution of amplitude samples obtained from 10 sites and through 360 azimuth degrees at each site.

Figure 4.C.16 Mean levels (upper bound, lower bound, and shadowless) of ground clutter strength vs range, averaged omnidirectionally over 10 sites. Phase Zero X-band data, horizontal polarization, 150-m range resolution, 0.9° azimuth beamwidth. Range sampling interval = 148.4 m, azimuth sampling interval = 0.2344°, 1,536 azimuth samples/range gate/site.

Figure 4.C.17 shows the fraction of circumference in clutter Nc /N as a function of range averaged over the 10-site set. This quantity is shown on the same dB ordinate as used in Figures 4.C.14 and 4.C.16 so that its effect may be directly observed in the data of Figure 4.C.16. A very clean exponential decrease of clutter occurrence with increasing range is observed in the empirical data of Figure 4.C.17. These data, averaged over 10 sites, are essentially identical to similar data averaged over 86 sites shown in Figure 4.8(a). The implication is that generality with respect to clutter occurrence has been reached in the 10site set. Now consider the mean upper-bound data and the mean lower-bound data shown in Figure 4.C.16. The mean lower bound is simply the shadowless mean reduced by the fraction of circumference in clutter [see Eq. (4.C.4)]. That is, the vertical displacement in Figure 4.C.17 is exactly the separation between shadowless mean and lower-bound mean in Figure 4.C.16. In effect, the same shadowless clutter is spread over many more samples—viz., it is spread over all N samples including the Nn noise-level samples—to arrive at the spatially diluted lower-bound mean level. The mean upper-bound level in any range gate in Figure 4.C.16 is equal to the mean lower-bound level augmented by weighting the noise samples to the noise level rather than to zero [see Eq. (4.C.5)]. In Figure 4.C.16 the mean bounds do not significantly diverge out to ~25 km in range. Their tightly bounded level to 25 km is what a hypothetical infinitely sensitive, azimuthally omnidirectional radar would measure

10 Log10 [Fraction of Circumference in Clutter]

394 Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity

40 30 20 10

0 –10 –20 –30 –40 –50 –60 4

8

12

16

20

24

28

32

36

40

44

Range (km) * Within each range gate, the fraction of circumference in discernible clutter above radar noise level applies to the combined distribution of amplitude samples obtained from 10 sites and through 360 azimuth degrees at each site.

Figure 4.C.17 Fraction of circumference in clutter vs range, averaged omnidirectionally over 10 sites. Phase Zero X-band data, horizontal polarization, 150-m range resolution, 0.9° azimuth beamwidth. Range sampling interval = 148.4 m, azimuth sampling interval = 0.2344°, 1,536 azimuth samples/range gate/site.

as mean clutter level. The shadowless mean is not such an absolute quantity. An infinitely sensitive, onmidirectional radar would result in only one curve in Figure 4.C.16—the shadowless mean, upper-bound mean, and lower-bound mean would all coalesce to the single curve defined by the upper-bound/lower-bound curve out to its point of divergence at ~25 km. Beyond ~25 km in Figure 4.C.16, the mean bounds start to diverge as a result of sensitivity limitation. When the mean bounds start to diverge, it cannot be theoretically known where the true onmidirectional mean level lies, except that it must lie between the upper and lower bounds. Assumption of continuity in the rate of decrease of mean level with increasing range and the obvious riding up of the upper bound onto the noise floor at long ranges indicate that the lower bound may be the better estimate in Figure 4.C.16. The relatively continuous rate of falloff of the mean lower bound, which constitutes about 20 dB over the 47 km indicated in Figure 4.C.16, does not extend indefinitely to longer ranges. This falloff is essentially due to geometrical spatial dilution (as per Figure 4.C.17). Beyond the maximum range at which discernible clutter from visible cells occurs, the lower bound curve of Figure 4.C.16 must abruptly drop to minus infinity as the result of assigning zero clutter power to all N cells. This discontinuity would be softened somewhat into a steep but finite rate of falloff if the radar were sensitive enough to discern weak (but non-zero) clutter from the diffraction zone beyond direct illumination. The mean clutter strengths shown in Figure 4.C.16 may be compared with those provided in Chapter 2. Chapter 2 focuses on Phase Zero measurements of clutter strength within

Appendix 4.C Effects of Terrain Shadowing and Finite Sensitivity 395

clutter patches at ranges between 2 and 12 km from the radar. The histograms within range gates upon which the results of Figure 4.C.16 are based are large Phase Zero ensemble histograms. Thus, it is appropriate to compare mean clutter strength for ranges ≤ 12 km in Figure 4.C.16 with the overall patch ensemble mean level, which is ~ –27.6 dB (see Figure 2.29 and Table 2.5). Over the 2- to 12-km range interval in Figure 4.C.16, the true mean clutter level indicated by the coalesced upper-bound/lower-bound curve in this interval decreases from ~ –25 dB at 3 km to ~ –30 dB at 12 km. This decrease in clutter strength with increasing range is due to decreasing depression angle and increasing terrain shadowing (spatial dilution) over this range interval. The range of true clutter strengths between –25 and –30 dB in this range interval in Figure 4.C.16 compare closely to the overall ensemble value of –27.6 dB, which was measured over many more sites. The decreasing trend in mean clutter strength with decreasing range for range < 3 km shown in Figure 4.C.16 is an incorrect artifact caused by increasing numbers of saturations at very near ranges in these long-range experiments. True mean clutter strength for range < 3 km as measured correctly in other saturation-free short-range experiments continues to gradually increase with decreasing range for range < 3 km due to increasing depression angle. This appendix provides general information on effects of terrain shadowing and radar sensitivity limitations on measurements of ground clutter strength in surface-sited radar. Theoretically, shadowing and sensitivity are independent; an infinitely sensitive radar can never be noise limited, but will experience more and more shadowing as range increases, with accompanying weak clutter strengths in shadowed cells. In practical terms, a radar of finite sensitivity often measures shadowed cells at its noise level. In the Phase Zero results of Figures 4.C.14–4.C.17 there is little dependence on sensitivity out to 25 km, but significant dependence on shadowing in the same range region. In these results, as elsewhere in this book, geometrical effects (i.e., effects of illuminated vs shadowed terrain) provide the best point of departure from which to understand low-angle clutter.

396 Appendix 4.D Separation of Discretes in Clutter Modeling

Appendix 4.D Separation of Discretes in Clutter Modeling 4.D.1 Introduction Low-angle land clutter is dominated by spatially isolated, strong clutter cells typically thought to be associated with strongly backscattering, physically discrete, point objects on the landscape such as buildings, water towers, rock faces, individual trees or small stands of trees, etc. The main purpose of this appendix is to determine what advantages can be gained in clutter modeling by analyzing locally strong, discrete cells in the measured clutter data separately from the more pervasive background cells typically associated with area-extensive or distributed clutter. A secondary purpose is to consider the possibility of clutter from visible sources spilling over into DTED-predicted shadow regions.

4.D.2 Investigation of Higher-Order Effects A significant effort was expended to identify physical point objects on the landscape accounting for locally strong cells in the clutter measurement data. For this purpose, highresolution color infrared stereo aerial photography was acquired in flights over selected sectors at many Phase One clutter measurement sites. The photography was registered to the clutter measurement data. In general, relatively poor correlation was found to exist between locally strong clutter cells and physically discrete point objects that could account for the strong clutter. In many locally strong clutter cells, no obvious physical object could be identified in the cell to account for its high strength; and many large physical objects in the photography did not correspond to a strong clutter cell in the measurement data. This poor correlation is largely attributed to the fact that the background clutter is itself spiky clutter, in which a particular spike stronger than the neighboring spikes is attempted to be identified with a recognizable point source. Complicating matters is the difficult-to-predict visibility/masking of terrain surfaces (and the objects on them) at low grazing angles, as well as the associated highly variable values of propagation factor F at the low heights of clutter sources (where F can vary as the fourth power of clutter source height). For these reasons, accurate deterministic prediction of discrete clutter sources proved to be impracticable at the level of effort available. Therefore the study of this appendix is carried forward as a statistical study in the clutter measurement data, in which the σ °’s from strong isolated clutter cells are separated, collected into distributions, and statistically characterized without further attempts to deterministically predict individual strong cells or to identify them with particular physical point objects on the landscape. The results of this appendix are largely based on analyses of the Phase One clutter data (coordinated with those taking place at Lincoln Laboratory)

Appendix 4.D Separation of Discretes in Clutter Modeling 397

conducted at Defence Research Establishment Ottawa by Dr. H. C. Chan, in which possibilities of higher-order effects in the data were investigated. Figure 4.D.1 illustrates the concepts involved in dealing separately with locally strong σ° cells in the measurement data. Such cells are denoted as being discrete cells, or “discretes.” Thus, as shown in Figure 4.D.1, “discretes” are defined here to be σ° cells that are 5 dB or more stronger than their neighbors in the measured clutter data. By a cell 5 dB stronger is meant a cell in which the clutter magnitude is 5 dB or more higher than the average between its four immediate neighbors (two on each side), either in range or in azimuth. Cells that fail to pass the 5-dB spatial filter are called “background” cells. Thus all σ° clutter cells in visible terrain regions are labeled either “discrete” or “background” on the basis of whether or not they pass the 5-dB spatial filter. Various other discrete-finding algorithms were tried, but the 5-dB algorithm proved most efficacious.

–1 Discrete Cell: 5 dB > Neighbor –1 +4 –1

–1 Background cells: All clutter cells that are not discrete Depression Background Angle Discrete Grazing Angle

Visible

Depth of Shadow

Shadow

Higher-Order Effects 1. Grazing angle dependence of background σ˚ in visible region 2. Spillover of visible σ˚ into shadow region – Spillover depends on depth of shadow

Figure 4.D.1 Separation of discrete clutter sources.

As indicated in Figure 4.D.1, the main approach of this book is the determination of strong trends in the total clutter with depression angle, where the total clutter consists of both discrete clutter and background clutter. If, however, the discrete cells are dealt with separately, an advantage is that background σ° can be shown to depend on grazing angle. Grazing angle effects are not empirically observed in total clutter because discrete clutter does not depend on grazing angle and discrete clutter dominates over the background clutter. Since grazing angle is defined here to be the illumination angle above the local terrain slope as provided by DTED for each clutter cell (see Chapter 2, Section 2.3.4), a model based on grazing angle does not require the classification of landform. That is, in

398 Appendix 4.D Separation of Discretes in Clutter Modeling

determining terrain slope and grazing angle, the DTED carries the landform information content necessary for describing the relief of the terrain, with respect to background clutter. With respect to discrete clutter, land-surface form may be thought to be of less influence on discrete clutter than background clutter because discrete clutter is more associated with vertical elements of land cover (although this hypothesis was not directly tested in the measurement data). In any event, these ideas allow the possibility of removing the terraindescriptive dimension of landform from a clutter model, leaving only land cover as the remaining necessary terrain-descriptive element and thus significantly simplifying the model. Also as shown in Figure 4.D.1, another important higher-order effect to investigate is the spilling of relatively strong clutter from visible sources over into DTED-predicted shadowed regions, thus improving model fidelity by having less sharp shadow boundaries. What is under consideration here is the possibility of a vertical source of clutter located in a DTED-predicted shadowed cell rising up into visibility above the DTED-predicted shadow boundary; not under consideration here is weaker diffraction-illuminated clutter from terrain that is entirely in shadow (including shadowed objects on the shadowed terrain). The controlling parameter affecting clutter spillover into shadow is the depth of shadow as determined in DTED. DTED accuracy also affects shadow boundary prediction; some shadowed cells as determined by DTED are actually visible, and vice-versa (see Figure 2.22). The objective here is to explore the possibility of extending clutter marginally beyond DTED-predicted shadow boundaries into regions in which predicted shadow depth is shallow—not to extend clutter globally over regions of deep macroshadow. In what follows, the above-described higher-order effects (viz., separation of discrete σ°; grazing angle dependence of background σ°; and the spilling of σ° into shadowed regions) are illustrated in the Phase One clutter measurement data to test their empirical validity (as opposed to their being simply attractive modeling concepts, see Section 4.5.1). The modeling structure that computationally implements these concepts is referred to as the three-layered modeling approach, in which three sequential computational passes involving (1) background clutter in visible terrain regions, (2) discrete clutter in visible terrain regions, and (3) total clutter (background plus discrete) in shadowed terrain regions are required to simulate the overall clutter as it occurs at any given site. In contrast to the main approach of this book, which is based on expected-value estimates of clutter strength as reduced from clutter patches (macroregions of visible terrain), the three-layered model is based on ensemble distributions of like-classified clutter cells collected from many sites and patches, where the site- and patch-based identity and origin of each sample cell are merged in the overall conglomerative ensemble (see Chapter 2, Section 2.4.3.1). Such distributions can be too broad (i.e., can over-emphasize the degree of spread required, see Section 2.4.3), compared with the mainline expected-value approach of this book. Ensemble distributions were collected for discrete clutter, background clutter, and shadowed clutter, for each of the 20 combinations of radar parameters in the Phase One radar parameter matrix (five frequencies, two polarizations, two pulse lengths). Discrete and background clutter were further partitioned in a number of land cover classes—shadowed clutter is postulated to be independent of land cover. All higher-ordereffect data reduction underlying the three-layered model occurred in σ° space as determined by the range/azimuth resolution cell grid in the Phase One measured data.

Appendix 4.D Separation of Discretes in Clutter Modeling 399

There was no attempt to reduce discrete clutter in terms of RCS rather than σ° (see Section 4.5.4). Although discrete clutter ensembles were collected at both 150-m and 15-m range resolution, no effort was made to determine if the discrete cells determined at one resolution correspond at all to those determined at the other resolution in terms of either spatial location or RCS amplitude. Such correspondence would be expected if the locally strong discrete cells actually correlated significantly with point objects on the ground. Clutter modeling on the basis of these ensemble distributions takes place on the basis of random draws from theoretical distributions (Weibull, K-, lognormal) in which the mean levels and shapes of the modeled distributions match those of the empirical ensemble distributions of like-classified cells collected over many patches and sites. Clutter predictions are restricted to radar parameter combinations available in the Phase One radar (frequency, polarization, range resolution, azimuth beamwidth) for the purpose of comparing with Phase One measurements. A general three-layered clutter model allowing arbitrary specification of radar spatial resolution was not developed. In the process of clutter prediction using the three-layered model, a random sample of background σ° is assigned to every visible cell; following which, a random sample of discrete σ° may be added (phasor addition) to the background σ° under a specified probability of occurrence. Random samples of shadowed σ° are assigned to shadowed cells, depending on depth of shadow, with a specified probability of occurrence.

Separation of Discretes. Figure 4.D.2 shows X-band results at the Phase One prairie farmland site of Magrath, Alberta. To the left is shown geometric visibility in DTED. In the center is shown separated background clutter in visible regions, thresholded at σ°F 4 ≥ –40 dB. To the right is shown the occurrence of 5-dB discretes in visible regions. It is evident that there are many such discretes at Magrath; they constitute 25% of the total clutter in visible regions. Background in Visible

DTED Visibility

X-Band Clutter Map (σ˚F4 ≥ –40 dB)

Discretes in Visible (25%)

5-dB Discretes

Figure 4.D.2 Comparison of discernible clutter and visible terrain at Magrath, Alta. Maximum range = 50 km. (Results courtesy of H. C. Chan, DREO.)

Figure 4.D.3 shows the effect of grazing angle on visible clutter at Magrath in Phase One Sband data. In (a) are shown cumulative distributions over visible regions of total clutter (background plus discretes), background cells only (weaker; more linear on the Weibull

400 Appendix 4.D Separation of Discretes in Clutter Modeling

Agricultural S-Band

–40

y

Onl

isc

lls

Dis

cre

te C

ells

sD

Ce

Plu nd

nd

ckg rou

ckg rou

Ba

.8 .7 .6 .5 –60

ret

On

ly

es

.99 .95 .9

Agricultural S-Band

a)

Mean of σ°F4 (dB)

.9999 .999

Ba

Probability That σ°F4 ≤ Abscissa

scale), and discrete cells only (stronger, less linear). To the right in (b), these three distributions are further separated into grazing angle regimes, for which mean clutter strengths are plotted. In the total clutter on the right, there is no trend with grazing angle. If, however, the discrete cells (also trendless with grazing angle) are first separated out, the background cells that remain show a significant trend of increasing mean clutter strength with increasing grazing angle. This is the only way in which trends of low-angle clutter strength with grazing angle are able to be found in measured clutter data—by first separating out discretes (cf. Section 2.3.5.1). In what follows, such information is generalized.

–20

Magrath 0

–20

b)

ete Discr

Only tes re isc D s lu

Cells dP

n grou

Back

–30

oun

kgr Bac

Magrath

–40

0

1

2

nly

lls O

e dC

3

4

Grazing Angle (deg)

σ°F4 (dB)

Figure 4.D.3 Influence of grazing angle on background clutter at Magrath, Alta. Visible region. (a) Cumulative distributions. (b) Grazing angle dependence. (Results courtesy of H. C. Chan, DREO.)

Figure 4.D.4 shows the occurrence of 5-dB discretes in measured X-band clutter maps at three different sites of very different terrain types. It is not surprising that many discretes occur in farmland (left map), but the center and right maps indicate that 5-dB discretes exist pervasively and extensively in other, more natural, terrain types as well—namely, forest and desert. The numbers at the bottom indicate that the average strength of the discretes above the background is greater in farmland than in forest or desert. Discretes in visible regions usually occur at about 20% or 25% incidence of occurrence, irrespective of terrain type.

Grazing Angle Dependence of Background σ °. The results of Figure 4.D.5

generalize the grazing angle dependence of background σ° in visible regions, across all Phase One sites, for both agricultural and forested terrain and for both X- and S-bands at two resolutions. Each plotted point is the mean of an ensemble distribution consisting of the aggregate of the individual σ°’s from all cells of a particular terrain type, grazing angle regime, and radar frequency and resolution. In Figure 4.D.5, the variation in mean strength with grazing angle covers 6 or 7 dB in agricultural terrain and 10 or 11 dB in forested terrain. Significant separation exists between the forest and farmland characteristics, with forest 3 or 4 dB stronger than farmland at the lower grazing angles, rising to 6 or 7 dB stronger at the higher grazing angles. The models developed from such characteristics are statistical. Results such as are shown in Figure 4.D.5 characterize the means of statistical distributions from which random draws are taken to provide a value of clutter strength for a

Appendix 4.D Separation of Discretes in Clutter Modeling 401

Farmland (Magrath)

12

Forest (Brazeau)

Desert (Booker Mt.)

7

9

Average Clutter Strength of Discretes Minus Background (dB)

Figure 4.D.4 5-dB discretes in farmland, forest, and desert. Phase One X-band data. Maximum range = 50 km. (Results courtesy of H. C. Chan, DREO.)

particular DTED cell of given terrain slope/grazing angle and terrain type. Other results, not shown here, similar to Figure 4.D.5 but characterizing the shapes of the ensemble distributions rather than their means, are also required.

–20 X-Band 150 m 15 m

Forested

Mean σ°F4 (dB)

S-Band 150 m 15 m

–30

Agricultural

–40 0

1

2

3

4

5

Grazing Angle (deg)

Figure 4.D.5 General grazing angle dependence across many sites. Background σ ° in visible regions. (Results courtesy of H. C. Chan, DREO.)

402 Appendix 4.D Separation of Discretes in Clutter Modeling

Spillover of Clutter into Shadowed Regions. Figure 4.D.6 shows Magrath results paralleling those of Figure 4.D.2, but here the central and right clutter maps show only clutter in geometrically shadowed regions. The central clutter map in Figure 4.D.6 shows total clutter in shadow. Comparison with Figure 4.D.2 indicates that total clutter in shadow is significant compared to total clutter in visible terrain—the total clutter in shadow at Magrath constitutes 16% of the total clutter in both visible and shadowed terrain. The rightmost clutter map in Figure 4.D.6 indicates those clutter cells in shadow that pass the spatial filter test of being 5-dB discretes. It is observed that most, i.e., 88%, of clutter cells in DTED shadow at Magrath are 5-dB discretes. The clutter modeling approach developed from such data assumes all clutter in shadow is land-cover invariant. Earlier discussions and examples of DTED accuracy in Chapter 2 (see Figure 2.22) lead to the expectation that some of the DTED-predicted shadowed clutter in Figure 4.D.6 is actually from visible regions incorrectly predicted as shadowed, particularly in shallow shadowed regions where shadow depth is small.

Clutter in Shadow

DTED Visibility

X-Band Clutter Map (σ°F4 ≥ –40 dB)

Discretes in Shadow (88%)

5-dB Discretes

Figure 4.D.6 Occurrence of clutter in shadowed regions at Magrath, Alta. Maximum range = 50 km. (Results courtesy of H. C. Chan, DREO.)

Table 4.D.1 shows the number of cells containing discernible clutter in shadowed terrain at Magrath utilizing the same X-band data as shown in Figure 4.D.6. In the table, the number of clutter cells is separated into six shadow regimes in which shadow depth is increased in 10-m intervals from 0 to 10 meters to > 50 meters. It is evident that most shadowed clutter cells occur in the first transitional zone of shallow (0 to 10 m) shadow depth, with the number of clutter cells rapidly diminishing with increasing depth of shadow. Figure 4.D.7 shows generalized results for modeling the spillover of discretes into shadowed regions. It is assumed that clutter in DTED shadow is independent of land cover. To the left in (a) are shown 14 cumulative distributions of clutter-in-shadow distributions for X-band, VV-polarization, and 150-m pulse length. These distributions were formed as ensemble aggregates of all shadowed cells from all Phase One sites irrespective of terrain type. In these shadowed distributions, where they abruptly change slope to become of steeper slope at their left-hand ends is where they encounter radar noise; to the left of the breakpoint they show noise-level returns rather than discernible clutter returns within

Appendix 4.D Separation of Discretes in Clutter Modeling 403

Table 4.D.1 Number of Cells Containing Discernible Clutter vs Shadow Depth at Magrath, Alta. Phase One X-Band; Maximum Range = 50 km

Shadow Depth (m)

Number of Clutter Cells

0 – 10

3463

10 – 20

263

20 – 30

111

30 – 40

50

40 – 50

29

> 50

11

Results courtesy of H.C. Chan, DREO.

0.9999 0.999

–35

a)

b)

F4 (dB)

0.99 0.95 0.90 0.80 0.70 0.60 0.50 0.40

X-Band VV Pol 150 m

150 m

0.20 –70

S-Band VV Pol HH Pol –45

Increasing Shadow Depth

0.30

X-Band VV Pol HH Pol

Mean

Probability That

F4

Abscissa

shadowed regions. To the right of their breakpoint, it is observed that with increasing shadow depth these distributions become weaker (i.e., they move to the left) and of decreasing slope (i.e., of increasing spread) as the clutter becomes more discrete-like withincreasing depth of shadow.

–55 –50

–30 4

F (dB)

–10

10

0

10

20

30

40

50

60

70

Shadow Depth (m)

Figure 4.D.7 Occurrence of discernible clutter in shadowed regions. (a) Cumulative distributions. (b) Shadow depth dependence. (Results courtesy of H. C. Chan, DREO.)

Figure 4.D.7(b) shows the mean strengths of the shadowed distributions shown in Figure 4.D.7(a), but also includes similar distributions at HH-polarization and at S-band. These results indicate how mean clutter strength decreases with increasing depth of shadow. Where these curves flatten out at the larger values of shadow depth indicates where the mean strength becomes noise dominated—for example, note in the cumulative distributions

Ch04.fm Page 404 Monday, January 7, 2002 4:13 PM

404 Appendix 4.D Separation of Discretes in Clutter Modeling

to the left that the left-most distribution for the maximum shadow depth contains almost 99% of cells at noise level.

4.D.3 Results

Probability That σ°F4 ≥ Abscissa

The three-layered approach to clutter modeling was tested by comparing predicted and measured X-band clutter at three Phase One measurement sites. Figure 4.D.8 shows cumulative distributions inclusive of all cells to 24-km range for both measured and modeled clutter at each of the three sites. At each site, excellent correspondence is observed in Figure 4.D.8 between measured and modeled clutter based on cumulative distributions over all cells at each site. Patch-specific prediction in subregions at each site is the next logical step for examination, but is not considered here.

Weibull Scale 0.9999 0.999 0.99 0.9

Modeled

0.7

Measured

Modeled

Measured

Measured

0.5 0.3

Modeled

0.15 –80

–60

–40

–20

0 10 –80

Clutter Strength σ°F4 (dB) a) Scranton, PA

–60

–40

–20

0 10 –80

Clutter Strength σ°F4 (dB) b) Brazeau, Alta.

–60

–40

–20

0 10

Clutter Strength σ°F4 (dB) c) Spruce Home, Sask.

Figure 4.D.8 Modeled and measured site cumulative clutter amplitude distributions at three sites. Phase One X-band data, HH-polarization, 24-km maximum range. (Results courtesy of H. C. Chan, DREO.)

The results of Figure 4.D.8 indicate that the three-layered approach to clutter modeling results in accurate predictions of X-band clutter in the Phase One radar. A more general objective of a clutter model is to predict clutter in any radar. The three-layered approach as developed here allows replication of Phase One clutter through trend analyses of the various Phase One parameter combinations (i.e., VHF, UHF, L-, S-, or X-band frequency; 150-m or 15-m pulse length; VV or HH polarization). To move beyond the Phase One parameter matrix would require the determination of the dependency of the shape parameter of the ensemble clutter amplitude distribution on spatial resolution, as in the mainline approach to clutter modeling based on depression angle as discussed throughout this book.

4.D.4 Summary The possibility of obtaining higher-order improvements to clutter models was investigated. The result is a three-layered approach to modeling in which clutter is predicted separately for locally strong “discrete” clutter cells in visible regions, weaker

Appendix 4.D Separation of Discretes in Clutter Modeling 405

residual “background” cells in visible regions, and total clutter (discrete plus background) in shadowed regions. In this three-layered approach, a dependence of low-angle clutter on grazing angle—the angle between the tangent to the local terrain surface and the direction of illumination—is established. The dependence exists only for the background clutter in visible regions. The dominant (≥5 dB stronger) discrete clutter is not dependent on grazing angle. Because of this dependence of background clutter on grazing angle, the model was implemented without explicit dependency on landform or relief (e.g., plains, hills, mountains). The three-layered model does not provide a single value of σ° for a given terrain type and illumination angle, and is thus suitable principally for computer implementation allowing the cell-by-cell running phasor addition of discrete and background clutter components. Computations in DTED are required to determine whether a cell is visible or shadowed; if visible, to determine the grazing angle to the DTED facet which requires knowledge of the slope of the facet; and if shadowed, to determine the depth of shadow. Terrain relief or landform class only enters the model through DTED-computed cell-level terrain slopes as they affect grazing angle and thereby the weaker background clutter. The sensitivity of the model’s predicted total clutter amplitude distributions to the accuracy of the DTEDcomputed terrain slopes affecting the subordinate background clutter was not tested. Results obtained with the three-layered approach to modeling were based on across-siteaggregation of individual cell-level σ°’s into ensemble modeling distributions. The threelayered model was basically set up to replicate Phase One measurements and was not generalized for clutter prediction in radars of other spatial resolution than Phase One. The results of the studies summarized in this appendix provide useful insights into higherorder ramifications in low-angle land clutter. The main result is that the influence of grazing angle—long thought to be a necessary parametric effect on low-angle clutter strength—was finally winnowed out of the measurement data. It is a significantly more insightful position to be able to say (positive statement) that grazing angle does indeed affect low-angle clutter strength, but only the weaker background clutter, not the dominant discrete clutter, than to just be able to say (negative statement) that grazing angle cannot be shown to have any significant effect on total (background plus discrete) clutter strength. The additional concept of allowing clutter to statistically occur in shadowed cells in which clutter strength is parameterized by depth of shadow basically attempts to overcome both lack of information on heights of land cover features occurring in shadowed regions and limitations in accuracy of available DTED. This concept remains consonant with a major tenet of this book, namely, that at low angles the most significant clutter comes from geometrically visible clutter sources (e.g., in this case, vertical features rising into visibility from shadowed terrain). The availability of increasingly accurate DTED and increasingly precise information about land cover features and their heights may gradually allow the occurrence of visible land-cover features in DTED-predicted shadow to be deterministically predicted, as opposed to statistically, as in this appendix. As stated elsewhere in this book (e.g., see Chapter 1, Section 1.5), weaker diffraction-illuminated ground clutter from regions deep in shadow, while not necessarily inconsequential, is understood fundamentally as clutter reduced by large propagation losses for which propagation modeling is required.

548 Appendix 5.A Weibull Statistics

Appendix 5.A Weibull Statistics 5.A.1 Introduction Chapter 5 provides empirical modeling information for low-angle radar land clutter spatial amplitude statistics in terms of Weibull probability distributions [1]. The purpose of this appendix is to provide information indicating why Weibull distributions were selected to model low-angle clutter in Chapter 5 and elsewhere in this book, as opposed to other possible distribution functions, including in particular the lognormal distribution and the K-distribution. The reasons for using Weibull distributions are as follows: 1.

The Weibull distribution is a simple two-parameter distribution that can accommodate the extreme spreads that occur in low-angle clutter spatial amplitude statistics.

2.

The Weibull distribution generally (but not without occasional exception) fits the measured low-angle distributions better than other candidate distributions that can also accommodate wide spread, including the lognormal and K-distributions.

3.

The Weibull distribution is analytically simple and tractable, more so than the lognormal or K-distributions.

4.

A Weibull distribution of clutter power (as used here in representing clutter strength σ °F 4) of shape parameter aw remains a Weibull distribution when transformed to clutter voltage, of shape parameter aw /2.

5.

The Weibull distribution provides decreasing spread with decreasing values of shape parameter aw and in the limiting case degenerates to an exponential distribution [exponential for clutter power = σ °; Rayleigh for clutter voltage = (σ °)1/2]. This mimics the behavior of measured clutter amplitude distributions which, with increasing depression angle and cell size, also show decreasing spread and, in the limiting high-angle case for surface radar (viz., 8° or so), also often degenerate to approximately Rayleigh distributions (e.g., see Table 2.B.1).

This appendix covers the following material. Section 5.A.2 further describes Weibull distributions. A number of plots are provided which give added insight into the behavior of Weibull distributions, and which make the clutter modeling information of Chapter 5— given in terms of Weibull coefficients—easier to work with. Section 5.A.3 numerically examines the shapes of the cumulative distribution function (cdf) of theoretical Weibull distributions as plotted against nonlinear Weibull and lognormal probability ordinates, and compares them with lognormal and K-distribution shapes plotted against the same ordinates. This provides understanding on how to interpret upwards and downwards curvature in cdf shapes of measured spatial clutter amplitude distributions when plotted against these ordinates, as to whether they are tending towards Weibull, lognormal, or Kshapes. Examination of the shapes in the extreme high tails is also included. Section 5.A.4 illustrates how Weibull distributions often fit measured low-angle clutter amplitude distributions better than other analytic distributions by comparing fits obtained with

Appendix 5.A Weibull Statistics 549

Weibull, lognormal, and K-distributions to some measured Phase One X-band farmland clutter data.

5.A.2 Weibull Distributions; a w = 1, 2, 3, 4, 5 The Weibull probability density function (pdf) may be written p ( x ) = b ⋅c ⋅ x

b – 1 – cx

b

(5.A.1)

e

In Eq. (5.A.1), as elsewhere in this book, the random variable x represents clutter strength σ °F4, where F is the pattern propagation factor [2]. The quantity x = σ °F4 is in some places abbreviated as σ ° in this appendix. Also, as represented elsewhere in this book, the Weibull shape parameter aw is related to b in Eq. (5.A.1) as 1 a w = --b

(5.A.2)

The scale parameter c in Eq. (5.A.1) is related to the median value of clutter strength x50 (or σ °50) as ln2 c = ------b x 50

(5.A.3)

[cf. Eq. (2.B.18)]. The Weibull cumulative distribution function (cdf) follows from Eq. (5.A.1), as P(x) =

x

∫

p ( ξ ) d( ξ ) = 1 – e

– cx

b

(5.A.4)

o

The ratio of variance to the square of the mean for a Weibull distribution is given by var ( x )

Γ ( 1 + 2a )

w -------------- = ------------------------–1 2 2 Γ ( 1 + aw ) (x)

(5.A.5)

where Γ is the Gamma function, x is the mean of x, and var(x) is the variance of x. The ratio of standard deviation-to-mean in a Weibull distribution, i.e., sd/mean = sd(x)/ x , which is much used in Chapter 5, is sd ( x ) ------------- = x

var ( x ) 1 2⁄ ---------------2 (x)

(5.A.6)

The ratio of mean-to-median in a Weibull distribution is given by Γ(1 + a )

x w ------ = ---------------------

x 50

( ln 2 )

aw

(5.A.7)

550 Appendix 5.A Weibull Statistics

Definitions, relationships, and other matters involving the Weibull distribution are also discussed in Appendix 2.B. Figure 5.A.1 plots the shape of the Weibull pdf as given by Eq. (5.A.1) for four values of shape parameter aw—namely, aw = 0.666, 0.5, 1, and 2, following Sekine and Mao [1]. Table 5.A.1 shows the aw shape regimes of Weibull distributions. It is apparent in Figure 5.A.1 that, for aw < 1, the shapes are peaked at a positive modal value of x [for the Weibull b – 1 1 b⁄ distribution of Eq. (5.A.1), mode (x) =  ------------ ], and the pdf decays from its modal  cb  peak to zero at both x = 0 and x = ∞. In contrast, for aw ≥ 1, the shapes are not peaked. For aw = 1, the pdf is a negative exponential and decays from its maximum value of unity at x = 0 to reach zero at x = ∞. For aw >1, the shapes are like the negative exponential in that they also decay from maximum values at x = 0 to reach zero at x = ∞. These shapes for aw > 1 are called subexponential because their exponents b = 1/aw are less than unity. Although similar to the negative exponential shape for aw = 1, the subexponential shapes for aw > 1 decay with increasing x from maximum values at x = 0 greater than unity, first at rates faster than the negative exponential, and then for large values of x at rates slower than the negative exponential. It is these slow rates of decay and long tails for large values of x that are of interest here in that they mirror the behavior of low-angle land clutter spatial amplitude distributions. Thus interest is in the subexponential Weibull pdf’s for which aw > 1. Note that for aw simplicity, Figure 5.A.1 is plotted for c = 1 which means for x 50 = ( ln2 ) —see Eqs. (5.A.1) and (5.A.3). This is done in the interest of making a simple plot, but the plot is not representative of realistic clutter amplitudes. In a number of results to follow in Sections 5.A.2 and 5.A.3, this appendix sets x50 = 0.0001 (i.e., median clutter strength = –40 dB) and lets the Weibull shape parameter range subexponentially over the five values aw = 1, 2, 3, 4, 5. These values of x50 and aw are representative of the values occurring for these parameters in many of the actual measured clutter spatial amplitude distributions shown in the main body of Chapter 5 and elsewhere in this book. Thus Figure 5.A.2 plots the shape of the Weibull pdf as given by Eq. (5.A.1) for Weibull parameters x50 = 0.0001 and aw = 1, 2, 3, 4, 5. To accommodate these realistic parameters, logarithmic scales are used for both abscissa and ordinate (i.e., log-log paper). The median value x50 = 0.0001 is shown at the extreme left end of the abscissa. Long decaying tails are seen over increasing values of x from the median value, of increasing length and decreasing rate of decay with increasing aw. The label “Gaussian” on the aw = 1 curve means that the in-phase (I) and quadrature (Q) clutter voltage components are each of zero-mean equalvariance Gaussian shape, which implies that the amplitude of the clutter voltage [I2 + Q2]1/2 is Rayleigh distributed, and the clutter power σ ° = I2 + Q2 is exponentially distributed. The distributions of Figure 5.A.2 are not similar to these actually observed or plotted in this book, when histograms of measured clutter spatial amplitude statistics are formed. The reason is that the clutter histograms as shown herein are formed of decibel values of clutter strength to keep them manageable because of the wide ranges of clutter power that are involved. Thus the histograms are formed in bins of width specified in decibels, typically in bins 1 dB wide (see Appendix 2.B). This constitutes a logarithmic transformation y =

Appendix 5.A Weibull Statistics 551

1.0

aw = 1/b

.666 0.8

0.5 1.0

0.6

p(x)

2.0

aw < 1, peaked aw = 1, negative exponential aw > 1, subexponential

0.4

0.2

0 0

1

2

x a

b

Figure 5.A.1 Weibull pdf p(x) = bxb–1 e–x . Here x50 = (ln 2) w, so c ≡ 1. (After Sekine and Mao [1]; by permission, © 1990 IEE.) Table 5.A.1 Shape Regimes of Weibull Distribution aw

Shape

<1

Peaked

=1

Negative Exponential

>1

Subexponential

10log10x. Figure 5.A.3 shows the logarithmically transformed Weibull pdf of Eq. (5.A.1) such that p(x)dx = p(y)dy. Like Figure 5.A.2, Figure 5.A.3 continues to show results for x50 = 0.0001 and aw = 1, 2, 3, 4, 5. The pdf shapes in Figure 5.A.3 look like the typical shapes of the measured clutter histograms, examples of which are shown in a number of places in this book. These pdf shapes show a long, slowly diminishing, high-side tail of increasing extent and decreasing rate of decay with increasing value of aw, which mimics the behavior of the measured histograms. All five pdf’s in Figure 5.A.3 are of bell shape, between narrow and high (aw = 1) and wide and low (aw = 5). The median value of 10log10x50 = y50 = –40 dB is evident near the peaks of the bell shapes. Many of the measured histograms do not show much or any of the diminishing shape for low values of y to the left because the histograms become noise-limited for low values of y. Figure 2.28 in Chapter 2 plots the shape of the Weibull cdf as given by Eq. (5.A.4) against a Weibull ordinate, also for x50 = σ °50 = 0.0001 and aw = 1, 2, 3, 4, 5. The increasing extent of the high-side tail with increasing values of aw is evident in Figure 2.28, as are the increasingly strong values of mean clutter strength in these distributions as a result of the high-side tails, and the increasingly large values of mean/median ratio with increasing aw.

552 Appendix 5.A Weibull Statistics

104

p(x) =

b • In 2 • x b–1 b

x 50

• exp

–In 2 • x b x b50

b = 1/aw x50 = Median = 0.0001

100

p(x)

sia Gaus n

10-4

aw = 1 10-8

2

3

10-2

10-4

4

5

100

102

x

Figure 5.A.2 The Weibull probability density function p(x); x50 = 0.0001; aw = 1, ...5.

0.020

p(y) = 0.015

b • In 2 • log e • (10 y/10 ) –In 2 (10 y/10 ) b

Gaussian

• exp

10 • x b50

b

•

xb50

p(y)

y = 10 logx, b = 1/aw, 0.010

x50 = Median = 0.0001, y50 = 10 logx50 = –40

0.005

aw = 1

2

3

4

5

0.000 –80

–60

–40

–20

0

y

Figure 5.A.3 The logarithmically transformed Weibull probability density function p(y); y50 = –40; aw = 1, . . . 5.

Appendix 5.A Weibull Statistics 553

Figure 5.A.4 shows plots of the ratio of standard deviation-to-mean [sd(x)/ x ] vs aw, and of the ratio of mean-to-median ( x /x50) vs aw, as given by Eqs. (5.A.6) and (5.A.7), respectively. Note that these relationships are transcendental, involving the Gamma function. The plots are shown over the range 0 ≤ aw ≤ 6, although principal interest here is in the subexponential range aw > 1. It is apparent that both measures of Weibull spread in Figure 5.A.4—sd/mean and mean/median—increase very rapidly with increasing aw; they are shown as decibel quantities in Figure 5.A.4 to accommodate their rapid increase. As indicated in Figure 5.A.4, when aw = 1 the Weibull distribution degenerates to a simple negative exponential distribution for clutter power and power-like quantities including σ °, which means the in-phase and quadrature components of clutter voltage are distributed as zero-mean equal-variance Gaussians.

SD/Mean

30

5

0

10

1.6 0

SD/Mean = –5

20

Gaussian

Mean/Median (dB)

SD/Mean (dB)

10

Mean/Median

40

Gaussian

15

[(1+2aw )–2(1+aw)]1/2 (1+aw)

Mean/Median =

–10

(1+aw ) (ln 2)aw

–10 0

1

2

3 aw

4

5

6

0

1

2

3 aw

4

5

6

Figure 5.A.4 Ratios of standard deviation-to-mean and mean-to-median vs aw for Weibull statistics.

Extensive modeling information for spread in low-angle land clutter distributions is given in Chapter 5 in terms of tabulated and plotted values of both the actual measured quantities of spread in these distributions—namely, ratios of sd/mean and mean/median—and in terms of the modeling parameter used to capture these quantities—namely, the Weibull shape parameter aw. The two plots in Figure 5.A.4 are useful in allowing quick, back-andforth conversion between these transcendentally-related quantities. The modeling information for spread in clutter amplitude distributions given in Chapter 5 is given in terms of linear regression between spread values for limiting cell sizes A = 103 m2 and A = 106 m2. The linear regression actually took place in the measured quantities of spread—sd/mean (dB) vs log10 A and mean/median (dB) vs log10 A. Many examples of the scatter plots of sd/mean (dB) vs log10 A and the resulting regression lines are shown in

554 Appendix 5.A Weibull Statistics

Chapter 5; similar scatter plots and regression lines were formed of mean/median (dB) vs log10 A. The exact use of the modeling information for spread requires linear interpolation on log10 A of the provided underlying measured values of spread—sd/mean (dB) or mean/ median (dB)—rather than aw directly. However, as shown in the left-hand plot of Figure 5.A.4, the relationship between sd/mean (dB) and aw is essentially linear for values of aw such that aw > 1.5. The value of aw = 1.5 corresponds to a value of sd/mean = 1.90 dB. Almost all values of clutter spread given in Chapter 5 exceed aw = 1.5 and/or sd/mean = 1.90 dB. Since the relationship between sd/mean (dB) and aw is essentially linear for aw > 1.5 and sd/mean > 1.90 dB, it does not matter whether the linear regression is done on aw vs log10 A or sd/mean (dB) vs log10 A. By contrast, the right-hand plot in Figure 5.A.4 is less linear, so it matters more that, if modeling values of aw are selected as derived from mean/ median (dB), in this case the interpolation be of mean/median (dB) vs log10 A, not aw vs log10 A.

5.A.3 Comparison of Weibull, Lognormal, and K-Distributions This section discusses what observed curvature can imply in plots of cdf’s of clutter strength on nonlinear probability scales. The two nonlinear scales of interest are the Weibull scale (if the measured cdf is linear when plotted on a Weibull scale, the measured distribution is Weibull) and the lognormal scale (if the measured cdf is linear when plotted on a lognormal scale, the measured distribution is lognormal). All measured spatial clutter amplitude distributions from clutter patches were plotted on both Weibull and lognormal cumulative probability scales. The derivation of the plot axes in such Weibull and lognormal plots, the plotting of measured clutter distributions in the plots, and the regression analyses to obtain modeling information in the plots are all described in detail in Appendix 2.B. The question of interest here is, what does observed curvature in such plots imply about whether such clutter amplitude distributions are more accurately represented as Weibull, lognormal, or K-distributions? Figure 5.A.5 is a notional diagram showing the kinds of curvature exhibited by Weibull, lognormal, and K-distributions when plotted as cdf’s using a nonlinear Weibull probability scale as the y-axis. As shown, a Weibull distribution plots as a straight line, a lognormal distribution plots with convex curvature as observed from above (i.e., is downward curving), and a K-distribution plots with concave curvature as observed from above (i.e., is upward curving). The plots of measured clutter cdf’s in overall measure tend more toward linearity on Weibull plots than they tend to be of strong general upwards or strong general downwards curvature, although examples of all three kinds of curvature occur in the data. The notional diagrams of Figure 5.A.6 expand the discussion of Figure 5.A.5. Part (a) shows a Weibull distribution, which as required plots linearly against the Weibull y-axis used there; part (b) shows the same Weibull distribution which exhibits upward curvature (concave from above) when plotted against the lognormal y-axis used there. A lognormal distribution is also shown in (b) as the straight dashed line. It is apparent in (b) that a Weibull distribution has less high-end spread and more low-end spread than a lognormal distribution. Part (d) shows a lognormal distribution, which as required plots linearly against the lognormal y-axis used there; and part (c) shows the same lognormal distribution, which exhibits downward curvature (convex from above) when plotted against the Weibull y-axis used there. A Weibull distribution is also shown in (c) as the straight

Appendix 5.A Weibull Statistics 555

Weibull Scale Concave from above

K

Lognormal

P(x)

Convex from above

W

ei

bu

ll

K

Lognormal

x(dB) Figure 5.A.5 Weibull, lognormal, and K-distribution comparative cdf shapes plotted on a Weibull scale.

dashed line. It is apparent in (c) that a lognormal distribution has more high-end spread and less low-end spread than a Weibull distribution.

Two Clutter Patch Measurements. Figure 5.A.7 shows measured ground clutter amplitude histograms and cdf’s from two clutter patches, a Peace River patch in part (a) at the top, and a Magrath patch in part (b) at the bottom. At both top and bottom, the cdf (read on the left ordinate of each plot) is shown plotted against a Weibull y-axis in the left plot and against a lognormal y-axis in the right plot. At the top, the same Peace River histogram is repeated both to left and right, and likewise for the Magrath histogram at the bottom (the percent of samples per histogram bin is read on the right ordinate of each plot). In either part (a) or part (b), for any given value of σ ° on the x-axis, the same value of cumulative probability P(σ °) is read from the (left plot) Weibull scale or the (right plot) lognormal scale. The presentation format used in each of the four plots in Figure 5.A.7 is similar to that used for Figures 5.2 and 5.3, and Figures 5.14 and 5.15; this format is described more fully in the discussions relating to these preceding figures in the main body of Chapter 5. For example, the vertical dotted lines show the positions of the 50-, 70-, 90-, and 99percentiles in each distribution; and the vertical dashed line shows the position of the mean in the distribution. The upper part of Figure 5.A.7 [i.e., part (a)] shows the histogram and cdf resulting from an L-band measurement of a clutter patch at Peace River, Alberta. This Peace River patch was of agricultural land cover with a secondary component of trees (~10% incidence of trees)

556 Appendix 5.A Weibull Statistics

Weibull

Lognormal

P(x)

P(x)

Less High-end Spread

Lognormal

More Low-end Spread Weibull

(a)

(b)

x(dB)

x(dB)

Weibull

Lognormal Weibull

P(x)

More High-end Spread

P(x)

Lognormal

Less Low-end Spread

(c)

x(dB)

(d)

x(dB)

Figure 5.A.6 Weibull cdf shape on (a) Weibull and (b) lognormal scales, vs lognormal cdf shape on (c) Weibull and (d) lognormal scales.

and was observed at 0° depression angle. It was situated beginning at 3.9 km from the radar, and extended 4.1 km in range and 79.5° in azimuth. In this measurement, 4% of the samples are at radar noise level (black). The measurement was conducted at 150-m pulse length and vertical polarization. The lower part of Figure 5.A.7 [i.e., part (b)] shows the histogram and cdf resulting from an X-band measurement of a clutter patch at Magrath, Alberta. This Magrath patch was also of agricultural land cover (but in this case with only ~1% incidence of trees) and was observed at 1° depression angle. It was situated beginning at 5.7 km from the radar, and extended 6.2 km in range and 46° in azimuth. In this measurement, 57.3% of the samples are at radar noise level. This measurement was also conducted at 150-m pulse length, but at horizontal polarization. The Peace River cdf in part (a) of Figure 5.A.7 is extremely linear as plotted against the Weibull y-axis to the left, and hence shows upwards curvature plotted against the lognormal y-axis to the right (cf. Figure 5.A.6, top). Therefore, this measured distribution is accurately modeled as a Weibull distribution of shape parameter aw = 2.85 [this value of aw obtained through a regression analysis least-mean-squares fit of the cdf shown to the left in (a) to a straight line; see Appendix 2.B]. Many measured clutter cdf’s, while not as linear as (a) (left) on a Weibull axis, show some degree of upwards curvature like (a) (right) on a lognormal axis. The histogram in the upper plots is indeed of similar shape to the theoretical Weibull pdf shown in Figure 5.A.3 for aw = 3. The Magrath cdf in part (b) of Figure 5.A.7 is highly linear as plotted against the lognormal y-axis to the right, and hence

Appendix 5.A Weibull Statistics 557

Weibull Scale

Lognormal Scale

0.9999 0.999

15

15

10

Peace River L-Band aw= 2.85

0.99 10

0.97 0.9

5

0.3 0.2 0.15

0

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.15

P

P(σ⬚)

0.8 0.7 0.6 0.5 0.4

Samples 8,392

0.999

0.99 0.97 0.9

0.9999

5

0

–90 –80 –70 –60 –50 –40 –30 –20 –10 0

–90 –80 –70 –60 –50 –40 –30 –20 –10 0

σ⬚(dB)

σ⬚(dB)

(a) Approximate Weibull Distribution Weibull Scale

Lognormal Scale 15

0.9999 0.999

0.99

10

0.97

t

10

Magrath X-Band =19.53

0.9 5

0.3 0.2 0.15 –80 –70 –60 –50 –40 –30 –20 –10 0

σ⬚(dB)

0 10

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.15

P

P(σ⬚)

0.8 0.7 0.6 0.5 0.4

15

0.999

0.99 0.97 0.9

Samples 14,752

0.9999

5

0 –80 –70 –60 –50 –40 –30 –20 –10 0

10

σ⬚(dB)

(b) Approximate Lognormal Distribution

Figure 5.A.7 Two measured ground clutter amplitude distributions; (a) approximate Weibull distribution; (b) approximate lognormal distribution.

shows downward curvature plotted against the Weibull y-axis to the left (cf. Figure 5.A.6, bottom). Therefore, this measured distribution is accurately modeled as a lognormal distribution with mean-to-median ratio ρ = 19.53 [also obtained through linear regression of the cdf shown to the right in (b), see Appendix 2.B]. Although not all measured clutter cdf’s are as linear on Weibull or lognormal axes as those shown in Figure 5.A.7 (a) (left) or (b) (right), considerably fewer measured clutter cdf’s show some degree of downwards curvature on a Weibull axis [like (b) (left)] than show some degree of upwards curvature on a lognormal axis [like (a) (right)]. That is, considerably more measured cdf’s tend towards Weibull curvature than towards lognormal curvature. Table 5.A.2 shows additional statistical attributes relating to the Peace River and Magrath clutter measurements shown in Figure 5.A.7. The indicated measured values of sd/mean and mean/median of 5.5 and 11.1 dB, respectively, in the Peace River measured distribution

558 Appendix 5.A Weibull Statistics

compare relatively closely to the corresponding values of 6.0 and 11.5 dB that are applicable to an ideal analytic Weibull distribution of shape parameter aw = 2.85. This close comparison confirms the Weibull fit to be a good approximation to the Peace River clutter distribution, as does the high value of the coefficient of determination obtained in this fit, equal to 0.9993 (see Table 5.A.2). Similarly, the indicated measured values of sd/mean and mean/median of 10.7 and 13.2 dB, respectively, for the Magrath measurement shown in Table 5.A.2 compare reasonably well to the corresponding value of 12.9 dB applicable to each in an ideal analytic lognormal distribution of shape parameter ρ = 19.53. Note that, in a lognormal-like distribution [Table 5.A.2(b)], the values of sd/mean [theoretically equal to (ρ2–1)1/2; see Appendix 2.B] and mean/median (theoretically equal to ρ) are nearly equal for ρ >> 1; whereas, in a Weibull-like distribution [Table 5.A.2(a)], the value of mean/median far exceeds the value of sd/mean (see Figure 5.A.4). As with the Weibull fit in Figure 5.A.7(a), the lognormal fit in Figure 5.A.7(b) is confirmed by the reasonable comparison between measured and analytic values of sd/mean and mean/ median and by the high value of the coefficient of determination applicable to this fit, equal to 0.9955 (see Table 5.A.2). Attempting to fit the Peace River distribution as lognormal (upper-right) or the Magrath distribution as Weibull (lower-left) results in gross mismatches between measured and analytic values of sd/mean and mean/median, and significantly lower values of coefficient of determination. Table 5.A.2 Clutter Statistics for Two Measured Clutter Patches; (a) Peace River, (b) Magrath (a) Peace River Agricultural/~ 10% Trees L-Band

Statistic

Mean (dB)

(b) Magrath Agricultural/~ 1% Trees X-Band

-26.9

-28.8

SD/Mean (dB)

5.5

10.7

Mean/Median (dB)

11.1

13.2

Shape Parameter Weibull aw Lognormal ρ

2.85 

— 19.53

0.9993 

— 0.9955

Coef. of Determination Weibull Fit Lognormal Fit

K-Distribution. The Weibull distribution is defined in Appendix 2.B and in Section 5.A.2 of this appendix. The lognormal distribution is defined in Appendix 2.B. It now remains to define the K-distribution. The cumulative distribution function (cdf) of the Kdistribution is given by [3–5] 2 d x ν P ( x ) = 1 – -----------  ---------- K ν ( d x ) Γ(ν) 2 

(5.A.8)

Appendix 5.A Weibull Statistics 559

where Γ is the Gamma function and Kν is the modified Bessel function of second kind of order ν. The parameter ν is the shape parameter of the K-distribution; 1/d is a scale parameter. The first two moments of the K-distribution are 2

2 x =  --- ν  d

(5.A.9)

and x

2

= 2  1 + --1- ( x ) ν

2

(5.A.10)

The quantity d is given by ν d = 2 --x

(5.A.11)

The K-distribution shape parameter ν is given by 2

2(x) ν = -----------------------2

x – 2(x)

(5.A.12)

2

In this book, spread in distributions is often defined by the ratio of sd(x)/ x , where sd(x) = var ( x ) and var ( x ) = x 2 – ( x ) 2 . An important relationship for the K-distribution is var ( x -) = 1 + --2--------------2 ν (x)

(5.A.13)

If spread in a Weibull distribution [from Eq. (5.A.5)] is equated with spread in a Kdistribution [from Eq. (5.A.13)], the following equation is arrived at Γ ( 1 + 2a w ) 1 -–1 --- = ----------------------------2 ν 2Γ ( 1 + a w )

(5.A.14)

that relates the Weibull shape parameter aw with the K-distribution shape parameter ν.

Comparison of Analytic cdf Shapes. This section graphically compares the shapes of Weibull, lognormal, and K-distributions. In what follows, numerical plots of theoretical Weibull, lognormal, and K-cdf’s are provided to show how the previously introduced ideas of cdf curvature as plotted on Weibull and lognormal ordinates (see the notional diagrams, Figures 5.A.5 and 5.A.6) develop in actual numeric data.27 The basis of the comparison is the same as used heretofore—namely, the median value x50 of the distribution is always set 2 to x50 = 0.0001 (i.e., to –40 dB), and the spreads [i.e., ratios of sd(x)/ x or var(x)/ ( x ) ] are those of Weibull distributions with values of shape parameter aw = 1, 2, 3, 4, 5. Table 5.A.3

560 Appendix 5.A Weibull Statistics

shows expressions for the shape parameters for the Weibull, lognormal, and K2 distributions, and the relationship of each to spread as given by var(x)/ ( x ) . Table 5.A.4 illustrates the distributions to be compared. The basic set of distributions are the Weibull distributions of x50 = 0.0001 and aw = 1, 2, 3, 4, 5. Table 5.A.4 shows the value of var(x)/ 2 ( x ) for each one of these distributions. Then Table 5.A.4 shows the five values of ρ for 2 the five corresponding lognormal distributions with the same values of var(x)/ ( x ) ; and similarly the five values of ν for the five corresponding K-distributions. Table 5.A.3 Relationship of Shape Parameter to var ( x ) ⁄ ( x )

2

for Weibull,

Lognormal, and K-Distributions

Distribution Weibull

Shape Parameter

Relationship to var (x)/(x)2

aw = Weibull shape parameter

Lognormal

Γ(1+2aw) Γ 2 (1+aw)

var (x) (x)

2

+1

ρ 2 = var (x) +1 2 (x)

ρ = x / x 50

ν = K-distribution shape parameter

K-

=

ν =

2 var (x) (x)

2

−1

Table 5.A.4 Weibull, Lognormal, and K-Distribution Shape Parameters Corresponding to Weibull aw = 1,2,3,4,5

ρ (Lognormal)

ν (K-distribution)

aw (Weibull)

Var (x)/(x)

1

1

ρ = 1.414 1

ν1 = ∞

2

5

ρ = 2.449 2

ν2 = 0.5

3

19

ρ = 4.472 3

ν3 = 0.111

4

69

ρ = 8.367 4

ν4 = 0.029*

5

251

ρ = 15.875 5

ν5 = 0.008*

2

* Numerical results not provided.

Figure 5.A.8(a) shows the five basic Weibull distributions plotted against a Weibull y-axis. Figure 5.A.8(b) shows the five corresponding lognormal distributions with values of ρ as 27. These results, shown in Figures 5.A.8–5.A.12, were generated by Mr. Tejan K.Tingling who at the time was an undergraduate student from Norfolk State University, Norfolk, VA, participating in the Lincoln Laboratory Summer Internship Program.

Appendix 5.A Weibull Statistics 561

given by Table 5.A.4 and of equal spread to the Weibull distributions, plotted against a lognormal y-axis. The lognormal distributions in Figure 5.A.8 are more tightly clustered than the Weibull distributions over the range shown because the lognormal spreads are more strongly affected by the lognormal high tails beyond the range plotted. That is, at high enough cumulative probability levels each lognormal distribution in Figure 5.A.8 eventually has a longer high tail than the corresponding Weibull distribution. This will be seen in what follows. Figure 5.A.9 plots equivalent Weibull, lognormal, and K-distributions on Weibull y-axes for σ °50 = –40 dB, and for the first three values of spread specified in Table 5.A.4. The upward and downward curvatures sketched in Figure 5.A.5 are evident in Figure 5.A.9. Note that the K-distribution corresponding to aw = 1 (i.e., ν = ∞) degenerates to negative exponential (or Rayleigh voltage) as does the Weibull for aw = 1; and the K-distribution corresponding to aw = 2 (i.e., ν = 0.5) also is identically equal to the Weibull distribution of aw = 2. For the aw = 3 plot in Figure 5.A.9, the curvatures are as sketched in Figure 5.A.5. Figure 5.A.10 shows the five basic Weibull and five basic lognormal distributions, each with σ °50 = –40 dB and with values of sd/mean as specified in Table 5.A.4, in which each distribution is plotted against a Weibull y-axis. These plots show each Weibull distribution to be a straight line as required when plotted against a Weibull probability ordinate (see Appendix 2.B), and show each lognormal distribution to be of downwards curvature as indicated in the sketch of Figure 5.A.6(c) [compare also with the measured data in Figure 5.A.7(a) (left) and (b) (left)]. Figure 5.A.11 shows the same Weibull and lognormal distributions as in Figure 5.A.10, but here plotted against a lognormal y-axis. These plots show each lognormal distribution to be a straight line as required when plotted against a lognormal probability ordinate (see Appendix 2.B), and show each Weibull distribution to be of upwards curvature as indicated in the sketch of Figure 5.A.6(b) [compare also with the measured data in Figure 5.A.7(a) (right) and (b) (right)]. Considerably more low-angle measured clutter data tend to be Weibull-like or quasi-Weibull (i.e., displaying a significant degree of upwards curvature when plotted against lognormal ordinates, as shown by the Weibull plots in Figure 5.A.11), than appear to be lognormal-like or quasi-lognormal (i.e., displaying a significant degree of downwards curvature when plotted against Weibull ordinates, as shown by the lognormal plots in Figure 5.A.10). In Figures 5.A.10 and 5.A.11, the crossover points in the high-end distribution tails where the lognormal distribution starts to extend to higher values of σ ° compared with the Weibull [see Figures 5.A.6(c) and (b)] only explicitly appear in the first two plots of each figure. Figure 5.A.12 shows the first four of the five basic Weibull and five basic lognormal distributions (see Table 5.A.4) plotted to very high values of cumulative probability to better show the behavior of the high-end tails. It is apparent in these plots that, at high enough probability levels, the lognormal distribution always reaches to higher values of σ ° (i.e., always has a longer high-end tail) than the corresponding Weibull distribution, for a given ratio of sd/mean.

5.A.4 Fits to Measured Farmland Clutter: Weibull vs Lognormal vs KMany distributions have been proposed in the literature to model the amplitude pdf of spiky clutter; see, for example [1, 3–13]. This section provides results from a study (for

562 Appendix 5.A Weibull Statistics

Weibull Scale

aw = 1

2

3

4

5

P( )

0.9999 0.999 0.99 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Median Value 50 = –40 0.01 –80

–40

–60

–20

0

20

(dB) (a) Weibull Distributions ␳1

Lognormal Scale

␳2

␳3 ␳4 ␳5

0.9999 0.999 0.99

P( )

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 Median Value 50 = –40

0.1

0.01 –70

–60

–50

–40

–30

–20

–10

0

(dB) (b) Lognormal Distributions

Figure 5.A.8 Weibull and lognormal distributions. (a) Weibull distributions on a Weibull scale; σ °50 = –40 dB, aw = 1, ... 5. (b) Lognormal distributions on a lognormal scale; σ °50 = –40 dB; (sd/ mean) for lognormal distributions = (sd/mean) for corresponding Weibull distributions of given aw.

which [14] is a summary) of two particular experiments of Phase One ground clutter that show that in these data Weibull statistics usually (but not without occasional exception) provide better fits to the clutter amplitude distributions than do lognormal or K-

Appendix 5.A Weibull Statistics 563

Weibull Scale

Weibull Scale

Weibull Lognormal

Weibull Lognormal K-statistics

1–10-7 0.9999 0.9 0.7 0.5 0.3

=2 ;

2

P( )

0.99

a

w

aw = 1

0.1

2

1

0.01 –120 –100 –80 –60 –40 –20

0

20

–120 –100 –80 –60 –40

(dB) 1–10-7 0.9999 0.9 0.7 0.5

20

Weibull Scale Weibull Lognormal K-statistics

3

0.3

a

w

0.1

0

=3

P( )

0.99

–20

(dB)

3 0.01 –120 –100 –80 –60 –40 –20

0

20

(dB)

Figure 5.A.9 Weibull vs lognormal vs K-distributions; Weibull scale; σ °50 = –40 dB; aw = 1,2,3; (sd/ mean) for lognormal and K-distributions = (sd/mean) for corresponding Weibull distributions of given aw.

distributions.28 Other results from this study are discussed in Chapter 4, Section 4.6.3, under the heading “Spatial Correlation.” In this study, the term clutter amplitude refers to the clutter voltage amplitude, that is, to the square root of the sum of the squares of the I and Q voltage components. In what follows, the empirical pdf is compared with the Weibull, lognormal, and K- pdf’s having the same first- and second-order moments, and with the Rayleigh pdf having the same variance. Additional details are available in [14], including expressions for the first- and second-order moments of the Weibull, lognormal, and K- pdf’s ([12, 15]; see also Appendix 2.B). The two clutter experiments studied were of open farmland X-band clutter obtained at the clutter measurement site of Wolseley, Saskatchewan; one experiment is at VV-polarization, 28. The summary provided here includes material originally published in [14], by permission of IEEE.

564 Appendix 5.A Weibull Statistics

Weibull Scale

Weibull Scale

Weibull Scale

Weibull Lognormal

Weibull Lognormal

Weibull Lognormal

3 a

a

w

w

=

w

a

0.1

=

=

2

1

P(

)

1–10–7 0.9999 0.99 0.9 0.7 0.5 0.3

2

1

3

0.01 –55 –50 –45 –40 –35 –30

(dB)

–20

0

(dB)

Weibull Scale

Weibull Scale

Weibull Lognormal

Weibull Lognormal

5 a

w

a

0.1

w

=

=

4

P(

)

1–10–7 0.9999 0.99 0.9 0.7 0.5 0.3

–60 –40

–80

–70 –60 –50 –40 –30 –20

(dB)

4

5

0.01 –100 –80 –60 –40 –20 0

(dB)

–100

–50

0

(dB)

Figure 5.A.10 Weibull vs lognormal distributions; Weibull scale, variable abscissas; σ °50 = –40 dB, aw = 1, . . . 5; (sd/mean) for lognormal distribution = (sd/mean) for corresponding Weibull distribution of given aw.

the other at HH-polarization. Both experiments are of Phase One survey data taken in slow scan mode (see Chapter 3) through one ~90° azimuth sector in which 703 azimuth samples were collected per range cell. Each experiment contains four range intervals, and each range interval contains 316 range cells of 15-m sampling interval. Thus each range interval covers 4.74 km, and the four contiguous range intervals cover from 1 to 20 km. Figure 5.A.13 shows a three-dimensional clutter map covering the first range interval at VVpolarization; the spiky nature of the discrete farmland clutter is evident. Figure 5.A.14 shows the histogram of the I component of the clutter voltage signal from the fourth range interval at VV-polarization—the histogram of the Q component is similar. Long, drawn-out, slowly diminishing tails are evident in the histogram of Figure 5.A.14. The histogram (or empirical pdf) of Figure 5.A.14 is compared in the figure with the Gaussian pdf having the same variance as the empirical pdf and zero mean (the very small, residual dc offset of each measured channel was estimated in each range interval and subtracted from the data). It is apparent that the I (and Q) components of spatially varying clutter amplitudes do not follow Gaussian distributions (i.e., the voltage amplitude is not Rayleigh, and the clutter strength distribution is not exponential). An X-band histogram and cumulative distribution of clutter strength σ °F4 from a clutter patch at this same Wolseley

Appendix 5.A Weibull Statistics 565

1–10–7

P( )

0.9999 0.999 0.99

Lognormal Scale

Lognormal Scale

Lognormal Weibull

0.9 0.7 0.5 0.3 0.1

Lognormal Scale Lognormal Weibull

Lognormal Weibull

aw = 3

aw = 1 aw = 2 1

2

3

0.01 –45

–40 –35 –30

–25

–50

–40

(dB) 1–10–7

P(σ°)

0.9999 0.999 0.99 0.9 0.7 0.5 0.3 0.1

–30

–70 –60 –50–40–30–20–10 0 10

–20

(dB)

(dB)

Lognormal Scale

Lognormal Scale Lognormal Weibull

Lognormal Weibull

aw = 4

4

0.01 –70 –60–50–40 –30–20 –10 0 10

(dB)

aw = 5

5

–70–60–50–40–30–20–10 0 10

(dB)

Figure 5.A.11 Lognormal vs Weibull distributions; lognormal scale; σ °50 = –40 dB, aw = 1, . . . 5; (sd/mean) for lognormal distribution = sd/mean) for corresponding Weibull distribution of given aw.

site were shown previously in Figure 5.15 of Chapter 5; these data of Figure 5.15 appear to be well modeled as a Weibull distribution. To be determined here is if this previous indication of Weibull is borne out in the following more analytically rigorous results. Figure 5.A.15 plots clutter amplitude histograms for the second and fourth range intervals, both at HH-polarization, and compares them with Rayleigh, Weibull, lognormal, and Kdistributions. In this figure, the measured pdf is compared with the Weibull, lognormal, and K- pdf’s having the same first and second order moments, and with the Rayleigh pdf having the same variance. For the second range interval (a), the data are very well fitted by the Weibull approximation over the full range of amplitudes shown. For the fourth interval (b), the data appear to generally lie between the Weibull and lognormal approximations. Figure 5.A.16 shows an X-band clutter amplitude histogram obtained as temporal variations from a fixed cell containing windblown trees. These data were obtained at the Katahdin Hill measurement site; they constitute long-time-dwell data (see Chapter 3) in which 30,720 samples per cell were recorded at 500 Hz PRF (stationary antenna, VVpolarization; 15-m pulse length). These temporal data are shown here to indicate the profound differences in clutter statistics that result when the clutter is collected as spatial variations over many cells of open farmland, on the one hand (Figure 5.A.15), and as temporal variations from windblown foliage, on the other (Figure 5.A.16). The temporal

566 Appendix 5.A Weibull Statistics

Weibull Scale

Weibull Scale

Weibull Lognormal

Weibull Lognormal

1–10-20 1–10-15 1–10-12

= w

=

a

w

1–10-8 1–10-7

a

P( )

1

2

1–10-10

0.999999 0.99999

␳2

0.9999

␳1

0.999 –30

–26

–28

–24

–10

–15

–22 –20

(dB)

–5

(dB)

Weibull Scale

Weibull Scale

Weibull Lognormal

Weibull Lognormal

1–10-20 1–10-15 1–10-12

P( )

1–10-10

␳4 ␳3

1–10-8 1–10-7

a

w

a

w

=

3

0.99999

=

4

0.999999

0.9999 0.999 –10

–5

0

5

(dB)

10

0

5

10

15

20

25

30

(dB)

Figure 5.A.12 Weibull vs lognormal distributions, high tails, variable abscissas; Weibull scale; σ °50 = –40 dB, aw = 1, ... 4; (sd/mean) for lognormal distribution = (sd/mean) for corresponding Weibull distribution of given aw.

data in Figure 5.A.16 very closely follow the Rayleigh distribution—the I and Q components of these data follow Gaussian pdf’s as shown in Figure 5.A.14. The theoretical Rayleigh pdf in Figure 5.A.16 which the empirical data so closely follow is normalized to have the same variance as the data. For the Wolseley farmland spatial clutter data, Figure 5.A.17 shows the first six normalized moments as computed from the data and compares them to the theoretical higher moments of Weibull, lognormal, and K-distributions [12, 14, 15]. In these results, the parameters of the theoretical distributions are set by matching the first two moments of the theoretical

Appendix 5.A Weibull Statistics 567

703 (360°)

th imu Az ples m Sa 1 (270°) 1 (1 km)

ge Ran les p m a S

316 (5.7 km)

Figure 5.A.13 3D clutter map of clutter spatial amplitude statistics from open farmland. 1st range interval; VV-polarization. (Results provided by F. Gini and M. Greco, Univ. of Pisa. After [14]; by permission, © 1999 IEEE.)

distributions to the first two computed moments in the empirical clutter data. As in Figure 5.A.15, results are shown for the second and fourth range intervals at HH-polarization. For the second range interval (a), all four higher moments of orders 3, 4, 5, and 6 computed in the measured data match those of the Weibull distribution very closely—in fact, the measured moments actually overlay the Weibull theoretical moments in this plot. For the fourth range interval (b), the four higher moments computed in the measured data lie between the corresponding Weibull and lognormal moments—but somewhat more closely to Weibull. These results substantiate what initially appears to be true in the histograms of Figure 5.A.15. Note in Figure 5.A.17 that Weibull higher moments lying between lognormal and K-distribution higher moments shows in another way how Weibull distributions lie intermediate between lognormal and K-distributions in terms of degree of spread involved (compare with the figures showing distribution shape in Section 5.A.3). Figure 5.A.18 plots the measured cdf’s, here for the third and fourth range intervals both at HH-polarization, on Weibull paper. The Weibull paper utilized is such that the abscissa is 10log10 σ ° , and the ordinate is 10log10{− ln[1− P( σ ° )]}. In such a plot, a Weibull distribution for clutter amplitude σ ° plots as a straight line with slope given by the shape

568 Appendix 5.A Weibull Statistics

1000 VV Polarization 4th-Range Interval

Clutter Histogram Gaussian PDF

100

PDF

10

1

0.1

0.01 –0.05 –0.04

–0.03

–0.02

–0.01

0

0.01

0.02

0.03

0.04

0.05

I Component 

Figure 5.A.14 Histogram of I component of clutter spatial amplitude statistics from open farmland. (Results provided by F. Gini and M. Greco, Univ. of Pisa. After [14]; by permission, © 1999 IEEE.)

parameter of the Weibull distribution [14]. These matters are explained more fully in Appendix 2.B. The empirical cdf for the third range interval is quite linear when plotted on the Weibull paper of Figure 5.A.18(a), indicating that a Weibull distribution accurately fits these data. The empirical cdf for the fourth range interval is also quite linear in Figure 5.A.18(b). In Figure 5.A.18, each measured clutter cumulative or cdf is compared with the method of moments (MoM) line representing the Weibull cdf with the same mean and mean square values as the measured data, and with the line obtained by linear least squares (LS) fitting to the data [16]. For each range interval, it is apparent in Figure 5.A.18 that the MoM and LS techniques provide very similar values for coefficients (i.e., slope, intercept) of Weibull distributions to match the measured cdf’s. Note that the Weibull distributions shown in Figure 5.A.18 are for the clutter amplitude σ ° ; the shape parameter aw for the corresponding cdf of clutter strength σ o is twice that obtained directly from Figure 5.A.18. Thus, the LS value of aw applicable to the σ o cdf in both (a) and (b) of Figure 5.A.18 is aw = 4.55.29 This value compares closely with the value pertaining to the Wolseley data of Figure 5.15, viz., aw = 4.7 (see Table 5.12), for which the applicable clutter patch straddles the first and second range intervals. In both parts (a) and

29. Table IV in [14] gives Weibull shape parameter c = 0.44 for both empirical

σ ° cdf’s in Figure 5.A.18; aw = 2/c.

Appendix 5.A Weibull Statistics 569

103 HH Polarization 2nd Range Interval

Clutter Histogram K Lognormal

102

Rayleigh Weibull

PDF

10

1

10-1

(a) 10-2 0

0.05

0.1

0.15

0.2

Amplitude  (a) 103 Clutter Histogram K Lognormal

HH Polarization 4th Range Interval 102

Rayleigh Weibull

PDF

10

1

10-1

(b) 10-2 0

0.05

0.1

0.15

0.2

Amplitude  (b)

Figure 5.A.15 Histograms of clutter spatial amplitude statistics from open farmland. (a) 2nd range interval; (b) 4th range interval. (Results provided by F. Gini and M. Greco, Univ. of Pisa. Part (b) after [14]; by permission, © 1999 IEEE.)

570 Appendix 5.A Weibull Statistics

102 Windblown Trees

Clutter Histogram Rayleigh

PDF

10

1

10-1

10-2 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Amplitude 

Figure 5.A.16 Histogram of clutter temporal amplitude statistics from a cell containing windblown trees. (Results provided by F. Gini and M. Greco, Univ. of Pisa. After [14]; by permission, © 1999 IEEE.)

(b) of Figure 5.A.18, the regions where the data tails off at the left are the result of radar noise contamination and should be ignored. A goodness-of-fit hypothesis test was applied to each of the eight sets of Wolseley X-band farmland clutter data—i.e., four range intervals, two polarizations. This test determines which distribution, Weibull, lognormal, or K-, best fits each set of data. Over their complete extents, measured low-angle clutter distributions almost never pass rigorous statistical hypothesis tests for belonging to any practicable theoretical distribution. Therefore, a modified Kolmogorov-Smirnoff test was employed such that only the data in the upper tail region σ ° > 0.03 was taken into account. The test is characterized by the parameter α that represents the probability of Type I error. Probability of Type I error is the probability of error that occurs in rejecting the null hypothesis when true. Here, the null hypothesis is that the measured (empirical) clutter distribution is equal to the hypothesized theoretical distribution under test. If this probability is low, the hypothesis that the empirical distribution is equal to the theoretical distribution should be rejected; if this probability is high, this same hypothesis should be accepted [17]. Results are shown in Table 5.A.5. The high probabilities under Weibull indicate that all eight data sets are reasonably well fitted by Weibull distributions in the region σ ° > 0.03, some very closely. Only in three cases is the lognormal probability higher than Weibull, but the Weibull probability is still high in each of these three cases. Some of the lognormal probabilities are very low. All of the Kdistribution probabilities are low or very low, indicating that none of the eight distributions are well fitted by K-distributions in their upper tails.

Appendix 5.A Weibull Statistics 571

1020 Measured Clutter Value K Lognormal

HH Polarization 2nd Range Interval 1016

Normalized Moments

Weibull

1012

(a)

108

104

1 2

1

4

3

5

6

Moment Order 1012 Measured Clutter Value K

HH Polarization 4th Range Interval

1010

Lognormal

Normalized Moments

Weibull 108

(b)

106

104

102

1 2

3

4

5

6

Moment Order

Figure 5.A.17 Normalized moments of clutter spatial amplitude distributions from open farmland. (a) 2nd range interval; (b) 4th range interval. (Results provided by F. Gini and M. Greco, Univ. of Pisa. Part (b) after [14]; by permission, © 1999 IEEE.)

572 Appendix 5.A Weibull Statistics

10 HH Polarization 3rd Range Interval

10 log{–ln[1–P(
)]}

5

0 (a) Noise Contamination –5

Measured Clutter Cumulative MoM Line LS Line

–10 –30

–25

–20

–15

–10

10 log
10 HH Polarization 4th Range Interval

10 log{–ln[1–P(
)]}

5

0 (b)

Noise Contamination

–5

Measured Clutter Cumulative MoM line LS line

–10 –30

–25

–20

–15

–10

10 log


Figure 5.A.18 Cumulative clutter spatial amplitude distributions plotted on Weibull paper. (a) 3rd range interval; (b) 4th range interval. (Results provided by F. Gini and M. Greco, Univ. of Pisa. Part (b) after [14]; by permission, © 1999 IEEE.)

Appendix 5.A Weibull Statistics 573

Table 5.A.5 Results of Kolmogorov-Smirnoff Hypothesis Test Modified to Upper Tail Region ( σ ° > 0.03) of Clutter Spatial Amplitude Distribution* Range Interval/ Polarization

st

1

st

1 2

nd

2 3

nd rd rd

3 4

th

4

th

Probability That Measured Clutter Distribution Equals Hypothesized Theoretical Distribution ( σ > 0.03)

˚

Lognormal

Weibull

K-

/HH

0.99

0.99

0.19

/VV

0.06

0.96

0.04

/HH

0.01

0.96

0.31

/VV

0.15

0.99

0.03

/HH

0.11

0.87

0.01

/VV

0.62

0.55

< 0.01

/HH

0.84

0.97

0.02

/VV

0.94

0.79

< 0.01

________________ *R esults provided by F. G ini and M . G reco, U niv. of P isa. A fter [14]; by perm ission, © 1999 IE E E .

As a result of the various preceding analyses of the empirical Wolseley farmland spatial clutter amplitude distributions provided in Section 5.A.4, it is evident that, in the first and second range intervals, these clutter data are accurately represented and much better fitted by Weibull distributions than by lognormal or K-distributions. In the third and fourth range intervals, the empirical data show behavior intermediate between Weibull and lognormal.

5.A.5 References 1.

M. Sekine and Y. Mao, Weibull Radar Clutter, London, U. K.: Peter Peregrinus Ltd. and IEE, 1990.

2.

L. V. Blake, Radar Range-Performance Analysis (2nd ed.), Silver Spring, MD: Monroe Publishing, 1991.

3.

E. Jakeman, “On the statistics of K-distributed noise,” J. Physics A: Math. Gen., vol. 13, 31-48 (1980).

4.

J. K. Jao, “Amplitude distribution of composite terrain radar clutter and the Kdistribution,” IEEE Trans. Ant. Prop., vol. AP-32, no. 10, 1049-1062 (October 1984).

5.

K. D. Ward, “Application of the K-distribution to radar clutter—A review,” Proc. Internat. Symp. on Noise and Clutter Rejection in Radars and Imaging Sensors, pp. 15-21, IEICE, Tokyo (1989).

6.

E. M. Holliday, E. W. Wood, D. E. Powell, and C. E. Basham, “L-Band Clutter Measurements,” U. S. Army Missile Command Report RE-TR-65-1, Redstone Arsenal, AL, November 1964; DTIC AD-461590.

574 Appendix 5.A Weibull Statistics

7.

F. E. Nathanson and J. P. Reilly, “Clutter statistics that affect radar performance analysis,” EASCON Proc. (supplement to IEEE Trans.), vol. AES-3, no. 6, pp. 386398 (November 1967).

8.

W. L. Simkins, V. C. Vannicola, and J. P. Ryan, “Seek Igloo Radar Clutter Study,” Rome Air Development Center, Technical Rep. RADC-TR-77-338, October 1977. Updated in FAA-E-2763b Specification, Appendix A, May 1988. See also FAA-E2763a, September 1987; FAA-E-27263, January 1986, July 1985.

9.

V. Anastassopoulos and G. A. Lampropoulos, “High resolution radar clutter classification,” in Proceedings of IEEE International RADAR Conference, Washington, DC, 662-66 (May 1995).

10. H. C. Chan, “Radar sea-clutter at low grazing angles,” IEE Proceedings, Pt. F, 137, 2, 102-112 (Apr. 1990). 11. K. S. Chen and A. K. Fung, “Frequency dependence of backscattered signals from forest components,” IEE Proceedings, Pt. F, 142, 6, 310-315 (Dec. 1995). 12. T. J. Nohara and S. Haykin, “Canadian East Coast radar trials and the Kdistribution,” IEE Proceedings, Pt. F, 138, 2, 80-88 (Apr. 1991). 13. K. Rajalakshmi Menon, N. Balakrishnan, M. Janakiraman, and K. Ramchand, “Characterization of fluctuating statistics of radar clutter for Indian terrain,” IEEE Transactions on Geoscience and Remote Sensing, vol. 33, no. 2, 317-323 (Mar. 1995). 14. J. B. Billingsley, A. Farina, F. Gini, M. V. Greco, and L. Verrazzani, “Statistical analyses of measured radar ground clutter data,” IEEE Trans. AES, vol. 35, no. 2 (April 1999). 15. A. Stuart and J. K. Ord, Kendall’s Advanced Theory of Statistics, London: Griffin, 1987. 16. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Englewood Cliffs, NJ: Prentice-Hall, 1993. 17. P. J. Kim and R. I. Jennrick, “Tables of the exact sampling distribution of the two sample Kolmogorov-Smirnoff criterion Dmn(m
Index A A/D (analog-to-digital) converters, 14, 250 Admiralty Surface Weapons Establishment (ASWE), 321 AEW (airborne early-warning) radar, 620 detection problem analysis of, 625 agricultural fields, 112 agricultural terrain, 492–493 high-relief, 185–188, 493–496 level, 88, 501–506 low-relief, 167, 496–501 mean clutter strength, 106 moderately low-relief, 167, 188–192 multifrequency clutter measurements, 184–201 very low-relief, 168, 193 See also terrain air defense, 2 air turbulence, 664 airborne clutter, 106–108, 320 depression angles, 108 airborne radar, 60 phenomenology, 82 aircraft Convair 580, 106 design, 2 low-observable technology in, 2 alfalfa, 190 Allegheny Range, 176 Altona, Manitoba, 44 clutter strength measurements at, 317– 319 American Intermontane desert, 510 analog-to-digital (A/D) converters, 14, 250 anemometers, 583 angle calibration, 119–120 angle of illumination vs microshadowing, 43 X-band effects of, 160 antenna elevation pattern, 123–125 K subarrays of, 625 mast heights, 38, 58, 154 omnidirectional, 387

phase center, 123 reflectors, 247 tower height, 145 transportable, 143 wind load, 247 See also radar antenna heights effects on clutter strength, 201 variations in, 197–201 visibility and, 157 Appalachian Mountains, 175 area density function, 110 artificial intelligence, 291 aspen, 182 ASWE (Admiralty Surface Weapons Establishment), 321 atmospheric refraction, 157 attenuators, 14 aurora, 664 autocorrelation function, 338 azimuthal, 341 Fourier transform of, 291 azimuth beamwidths, 9, 292, 422 in backscattering measurements, 14 one-way 3-dB, 43 Phase One, 419 two-way 3-dB, 43 azimuth cell, 341 azimuth encoder, 255

B background cells, 414 background clutter, 397 grazing angle dependence of, 400, 415 in visible terrain regions, 398 background components, 344 backscattering coefficient, 162 discrete sources and, 414 from vegetation, 650 in level farmland terrain, 92 localized sources of, 221 measurement of, 14, 115 microwave, 111–114 seasonal effects on, 112

684

Index

backscattering (continued) terrain and, 11 terrain point, 62, 165 VHF (very high frequency), 162 barley, 190 barns, 44 beam parked mode, 254 scan mode, 254 step mode, 254 Beaufort wind scale, 577 Beiseker, Alberta, 11 clutter strength vs radar frequency, 189–192 cropland clutter spectra, 613–614 repeat sector measurements, 189–192 Bessel function, 559 Beulah, North Dakota, 278 cropland clutter measurements, 612– 613 Big Grass Marsh, 202 bimodal distribution, 80–82 bins, 427 birch, 182 birds, 234, 664 bistatic scattering patterns, 651 Blackman-Harris window function, 584 Blue Knob, Pennsylvania, 81 clutter strength vs frequency, 148 repeat sector measurements, 163–164 Booker Mountain, Nevada, 529 desert clutter spectra, 610–612 repeat sector measurements, 202 boundary cells, 50 boundary regions, 291 branches, 576 Brazeau, Alberta, 62 PPI clutter maps, 542 radar site, 178 seasonal variations at, 180 buildings, 8 as clutter sources, 58 built-up terrain. See urban terrain bulrushes, 202 Burnstick, 45 burr oak, 182 bushes, 58

C Calgary, Alberta, 82

clutter measurement sites near, 37 calibration, 254–257 angle, 119–120 range, 120 signal strength, 121–123 Camp Wainwright, 182 Canadian Rocky Mountains, 37 canola, 190 carrier wavelength, 263 cattails, 202 Cazenovia, New York, 56 C-band radar, 656 CDC (Clutter Data Collection), 257 cell area, 9 dimensions, 339 size, 292 cell-level aggregation, 99 CFAR (constant-false-alarm rate), 292, 314 China, 650–651 circular polarization, 598 clutter, 23 airborne, 106–108 amplitude, 1 amplitude distributions, 22 azimuthal smearing of, 287 cancellers, 3 correlation, 227 correlation time, 276 covariance matrix, 636 data recording, 37 discrete sources of, 8–9 distributed, 320–324 early measurements of, 1 early models of, 1 environment, 664 exponential, 617–618 Gaussian, 618–619 granularity, 287 histograms, 5, 420 in shadowed terrain regions, 398 lack of range dependency in, 305 low-angle, 333 macroscale, 18 measurements, 13–16 mountain, 77–82, 446 overview, 23 percent circumference in, 300, 351

Index

percent of area in, 351 percent of circumference vs range in, 299, 312 percentage of cells in, 351 point source of, 9 prediction of, 16–22 propagation, 24–25 seasonal effects on, 111–114 shadowless, 393 simulation of, 2 spectral power density, 616, 617 spillover into shadowed regions, 402– 403 stationary, 1 urban, 82–85, 446 voltage signals, 411 wetland, 85–87 windblown, 576–582 within wide annular regions, 379–387 clutter amplitude distributions angle of illumination and, 43 at negative depression angles, 95 dependence of spread on depression angle, 289 depression angle and, 68–71 depression angle vs shadowing, 59 high tails in, 77 high-relief agricultural terrain, 495 high-relief desert, 532 high-relief forest, 511 level agricultural terrain, 505–506 level desert, 535, 536 low-relief agricultural terrain, 499 low-relief desert, 535 low-relief forest, 517 mean strength, 418 moments of, 376 mountain terrain, 539 parametric effects on, 413–414 repeat sector patches, 209 rural/low-relief patches, 100 shape parameter, 419 spread, 292, 307, 420, 422 standard deviation-to-mean ratio, 222–227 statistical attributes of, 129–132 upper and lower bounds, 275 urban terrain, 446 wetland terrain, 526

685

X-band, 69 clutter amplitudes from visible regions of terrain, 297 histograms, 96, 291 K-distribution of, 53 non-Raleigh, 7 overall ensemble distribution of, 74–75 overview, 126 parametric dependencies in, 24 probability distributions, 544 spatial cell-to-cell variability of, 544 spatial correlation of, 290 statistical measures of, 24 clutter cancellers, 3 MTI improvement factor of, 617 single delay-line, 616 clutter cells, 44 area, 9, 331 background, 397 discrete, 320–324, 397, 414–415 false-alarm, 667 noise level, 59 parametric effects, 413–414 radiation between radar and, 24 sizes, 292, 581 spectral power ratio in, 581 vertical scatterers in, 25 clutter coefficient, 216 as area-density function, 6 definition of, 5, 42 in resolution cells, 604–606 measurement of, 5 clutter correlation, 227 Clutter Data Collection (CDC), 257 clutter maps, 46 correlation in, 315 Magrath, Alberta, 409–410 Phase Zero sites, 299–302 site-specific prediction of, 287 clutter measurements, 5, 13–16 effect of radar resolution on, 110–111 higher-order effects in, 396–399 multifrequency, 145–146 repeat sector, 154–156, 274 statistical models in, 2 See also clutter statistics clutter modeling, 426 conceptual, 320 discrete components, 330–333

686

Index

clutter modeling (continued) distributed components, 330–333 DTED (digitized terrain elevation data) in, 65–67 empirical, 320 ensemble aggregations of cell-level statistics in, 98 framework for, 418, 439–440 grazing angle in, 294 improvements in, 543–544 low-angle, 10 non-angle-specific, 297–299 non-patchy approaches to, 290 non-site specific, 302–305 objective, 287–288 one-component, 18–19 presentation format for, 427–429 rationale for, 288–290 scope of, 291–292 site-specific approach to, 23, 343 three-layered approach to, 398–399, 404–405 two-distribution approach, 334 validation in, 543 See also clutter spectral model See also interim clutter model clutter patches cell-to-cell variability within, 16 classification by terrain slope, 65 Gull Lake West, Manitoba, 47–50 histograms, 126–127, 411–413, 418 illumination of, 44 in terms of landform, 409 interclutter visibility and, 7 Magrath, Alberta, 409–410 mapping of, 46 measurements of, 555–558 microshadowing within, 275, 317 overview, 126, 408–409 Plateau Mountain, 77–80 pure, 441–443 terrain descriptive information, 127 Waterton, Alberta, 80 Wolseley, Saskatchewan, 442 clutter physics, 160–162 low-angle clutter, 42–43 clutter power, 604–606 output from single delay-line canceller, 617

predicting in Doppler cells, 604 residual, 616 clutter prediction, 16–22 empirical approach to, 17 simplified approach to, 440 clutter returns coherency of, 145 correlation in, 290, 648 from area-extensive terrain surfaces, 46 clutter spatial field, 7 clutter spectra current vs historical measurements, 659–661 effects of instrumentation on, 672– 674 exponential shape, 654–659 fast-diffuse exponential component, 665 Gaussian shape, 640–643 in gale winds, 669–671 L-band measurements of, 667 lowland data, 667–668 matching with analytic shapes, 662 noncoherent, 645 power-law shape, 643–654 regions of approximation, 606–609 VHF vs X-band, 675 wideband background component, 666 X-band, 671–672 See also windblown clutter spectra clutter spectral model exponential, 635–639 measurement basis for, 582–604 scope of, 581–582 use of, 604–619 validation of, 635–639 See also clutter spectra clutter statistics confidence levels, 425 kurtosis, coefficient of, 130 linear regression, 135–136 lognormal, 136–138 mean, 129 mean deviation, 130 moments, 129 percentiles, 132 sampling populations, 425

Index

shadowless, 410 skewness, coefficient of, 130 standard deviation, 129 Weibull, 416–418 clutter strength, 408 calibration of, 37 cell-to-cell variability in, 261 classification by land cover, 65 classification by landform, 65 coefficient of, 25 cumulative distributions of, 127 definition of, 24, 44 depression angle and, 20, 415 desert vs forest, 297 determination of, 118 diurnal variability and, 235 effects of antenna height on, 201 effects of illumination angle on, 66 effects of microshadowing on, 317 effects of polarization on, 414 effects of weather and season on, 231– 234 frequency dependence of, 209–211 mean, 427 mean vs median, 102 median, 427 multifrequency, 204–209 percentile levels of, 389 polarization dependence on, 212–215 propagation effect in, 44, 163, 413 resolution dependence of, 216–221 saturation levels, 373–374 seasonal differences in, 235 shadowless, 22 spatial dilution of, 371 spatial variations, 237–242 temporal variations, 237–242 urban, 84 vs grazing angle, 11, 60–62 vs radar frequency, 144, 162–163 vs range, 58, 305–307, 350, 355–357 clutter strength number, 408 clutter to noise power ratio (See CNR) clutter visibility, 300 range and, 351–354 clutter voltage, 564 amplitude, 563 CNR (clutter to noise power ratio), 621 Coaldale, 317

687

coaxial RF cables,, 250 Cochrane, Alberta, 324–325 coefficient of determination, 135 coefficient of kurtosis, 130, 137, 222, 227– 228 of dB values, 131 coefficient of skewness, 130, 137, 222, 227–228 of dB values, 131 coherency, 276–277 coherent processing interval (See CPI) Cold Lake, Alberta clutter patch histograms, 126 low-angle clutter measurements, 312– 314 multifrequency clutter measurements, 177 terrain elevation data at, 313 color codes, 427 composite terrain, 294 computers, 250 confidence levels, 425 constant-false-alarm rate (See CFAR) Convair 580 aircraft, 106 Corinne, Saskatchewan antenna height variations at, 197–201 level farmland at, 166 repeat sector measurements, 163–164 corner reflectors, 256 correlation distance, 335 correlation time, 276 vs radar carrier frequency, 338 cosmic noise, 664 CPI (coherent processing interval), 581 creosote, 609 cropland, 46, 189, 411 windblown clutter spectra, 612–615 cultural objects, 46 cumulative distribution function, 127, 548 lognormal, 136–138 Weibull, 134, 549

D data collection beam scan mode, 254 beam step mode, 254 parked beam mode, 254 decibels, 102, 300 decorrelation, 627 azimuthal, 343

688

Index

decorrelation time, 651 Defence Evaluation and Research Agency, 307 Defence Research Establishment Ottawa (See DREO) degrees of freedom (See DOF) density function, 331 depression angle, 19–20 bins of, 427 calculation of, 440 clutter strength and, 20, 59, 415 computing from DTED, 289 definition of, 55–56 effects on clutter histogram shapes, 56 effects on microshadowing, 413–414 effects on spread in clutter amplitude statistics, 415 equation for computing, 56 farmland vs forest, 104–106 general characteristics, 101–104 hilltop vs level sites, 194–195 negative, 36, 94–95, 431 terrain elevation and, 415 terrain slopes and, 165–168 desert, 201 clutter strength vs depression angle, 297 high-relief, 531–532 land clutter coefficient, 529–530 LCE clutter spectrum for, 585 low-relief, 533–535 repeat sector, 202 spatial resolution cells, 609–612 windblown clutter spectra, 609–612 See also terrain desert clutter, 244 strength vs radar frequency, 545 detection, probability of, 622 dielectric constant, 234 diffraction, 259 digital-to-analog (D/A) converter, 253 digitized maps, 291 digitized terrain elevation data (See DTED) Dirac delta function, 577 direction-of-arrival (See DOA) discrete cells, 414 discrete clutter, 397 Cochrane, Alberta, 324–325 in visible terrain regions,, 398

modeling of, 320 overview, 320–324, 414–415 separation of, 399–400 See also clutter discrete components, 344 discrete sources, 414–415 physical discretes, 414 RCS amplitudes of, 321 separation of, 325–330, 333 within macropatches, 290 distributed clutter, 320–324 diurnal variability, 111 of clutter strength, 235 DOA (direction-of-arrival), 625 DOF (degrees of freedom), 628 dominant-to-Rayleigh reflector ratio, 335 Doppler echos, 234 frequency, 616 signal processing, 1 spectra, 334 Doppler cells clutter cross section in, 605 clutter power in, 604 index, 605 non-zero, 607 Doppler frequency exponential clutter distribution in, 617–618 Gaussian clutter distribution in, 618– 619 transformation from Doppler velocity, 616 Doppler velocity, 577 abscissa, 579 break-point, 643 gale force, 593 of windblown clutter spectra, 579 resolution cell, 586 transformation to Dopper frequency, 616 DREO (Defence Research Establishment Ottawa), 397, 655 DTED (digitized terrain elevation data), 2, 62–64 accuracy, 63–64 cartographic source, 312 clutter strength vs grazing angle, 62–63 for hypotheitical hilltop sites, 360

Index

geometric terrain visibility in, 307 in clutter modeling, 10, 65–67 in clutter prediction, 45, 542 in defining depression angle, 19 photogrammetric source, 312 prediction of shadowed regions, 398 site-specific, 290 Dundurn, 183

E earth’s radius effective, 56, 415 incidence angle and, 55 effective radar height, 38, 415 effect on ground clutter, 302 equation for, 56 effective site height, 38 Eimac resonant cavity, 251 electromagnetic propagation, 243 elevation beam, 14 encoder, 255 ensemble amplitude distributions, 96–100 cell-level aggregative, 98 from clutter patches, 94 radar spatial resolution and, 110–111 wetland terrain, 87 See also clutter amplitude distributions environment clutter, 664 Equinox Mountain, Vermont, 132 equivalent noise bandwidth, 586 error bounds, 297–298 error function, 137 inverse, 137 exciter, 250 exponential clutter single delay-line canceller in, 617– 618 spectral model, 635–639 spectral shape, 654–659 exponential power statistics, 416 exponential shape parameter, 659 equation for, 577, 654 exponential spectral shape, 577–579, 654– 659 historical results and, 659–661 improvement factor and, 620 tractability of, 616 See also spectral shape

689

F facets, 266 false alarm clutter cells, 667 probability of, 622 rates, 227, 334 farm machinery, 493 farmland clutter, 492 K-distributions, 561–573 lognormal distributions, 561–573 seasonal effects on, 493 strength vs radar frequency, 244 Weibull distributions, 561–573 See also agricultural terrain See also clutter farmsteads, 91, 318 fast Fourier transform (See FFT) fence lines, 58 FFT (fast Fourier transform), 584 of temporal pulse-by-pulse returns, 336 relative shape of, 589 fixed scatterers, 576 forest, 506–507 forest clutter, 18, 244 frequency dependencies of, 163–165 multifrequency measurements of, 175–183 forested wetlands, 48 forest canopies, 262 clutter strength vs radar frequency, 175–183, 244 frequency dependencies of clutter in, 163–165 high-relief, 507–513 level, 88 low-relief, 513–518 percent tree cover, 92 RF (radio frequency) absorption in, 163 See also forest clutter See also terrain fractal phenomenon, 65 Framingham, Massachusetts, 391 France, 658 frequency response function, 616 Fresnel zones, 192

690

Index

G gale winds, 578 clutter spectra in, 592–594 spectral measurements in, 669–671 gamma function, 72, 134, 416 gas pumping station, 326 Gaussian clutter, 618–619 numerical examples, 619 Gaussian shape parameter, 622, 640 general mixed rural terrain high-relief, 429–434 land clutter coefficients for, 429–436 low relief, 434–436 geometric shadowing, 243 clutter strength and, 353 GIS (geographic information system), 316 glacial deposit, 182 goodness-of-fit hypothesis test, 570 grain, 190 grain storage elevators, 74 grassland, 201, 521 clutter strength vs depression angle, 297 high-relief, 521–522 low-relief, 522–523 vs shrubland, 526 See also terrain grazing angle, 9–11 antenna mast height and, 58 definition of, 55, 415 dependence of background clutter on, 400 in clutter data analysis, 415 in clutter modeling, 294 terrain slopes and, 62 vs clutter strength, 11, 60–62 grazing incidence, 53 greasewood, 609 Great Salt Lake Desert, 202 ground, 576 ground clutter airborne, 106–108 backscatter in, 115 effects of polarization, 414 effects of terrain shadowing, 371–379 frequency dependence of, 209–211 high-range resolution, 46 low-angle, 291 low-range resolution, 44–46

measurement sites, 37 measurements, 13–16 overview, 23 power spectra, 575 seasonal effects on, 111–114 source of intrinsic fluctuation, 575 sources of, 8–9 variability in mean strength of, 243 X-band, 44, 68–71 See also clutter See also land clutter ground clutter measurements, 13–16 ground-based radar, 1 dominant clutter sources, 43 location of, 359 Gull Lake East, Manitoba, 52 Gull Lake West, Manitoba, 47–50 multifrequency ground clutter maps, 154 repeat sector measurements, 155 seasonal effects on clutter measurements in, 112

H harmonic oscillators, 642 Hewlett Packard signal generator, 250 high-angle clutter modelling, 60 strength vs radar range, 58–60 higher-order effects in, 396–399 high-range resolution, 46 high-relief agricultural terrain clutter amplitude distributions, 495 land clutter coefficients, 493–496 mean clutter strength for, 493 uncertain outliers in, 493–495 See also agricultural terrain high-relief desert clutter amplitude distributions, 532 land clutter coefficient, 531–532 mean clutter strengths, 531 See also desert high-relief forest clutter amplitude distributions, 511 high depression angle and, 175–177 land clutter coefficients, 507–513 low depression angle and, 177–178 mean clutter strength, 507–509 uncertain outliers in, 510–511 VHF polarization bias in, 511

Index

See also forest high-relief landform, 158 high-relief terrain, 82 agricultural, 185–188 rural, 75 slopes, 66 high-resolution radar, 7, 8 high-speed data recorders, 250 hillock, 221 hilltops, 9 radar sites, 360 histograms, 5 clutter patches, 126–127, 411–413 computation of clutter statistics, 129 ensemble, 96 of classified groups, 420 of clutter strength, 408–409 parameters, 422 shadowless, 376 See also clutter measurements homogeneous clutter, 7 horizontal polarization, 212, 563–573 vs vertical polarization, 432 hummocks, 9

I I/Q (in-phase/quadrature) signals, 14, 253, 584 coherency of, 276 IF (intermediate frequency), 14, 253 IIT Research Institute (IITRI), 320 illumination angle, 9–11, 62, 116 effects on low-angle clutter strength, 66 fundamental measure of, 62 low, 333 improvement factor plots, 622, 629 incidence angle, 55, 415 incident fields, 44 insects, 664 interclutter visibility, 7 interim clutter model angle-specific, 292–297 error bounds in, 297–298 general terrain types in, 294 multifrequency, 297–298 overview, 294–295 statistical depth of, 293 subclass terrain types in, 294 Weibull coefficients in, 343

691

See also clutter modeling intermediate frequency (See IF) intrinsic backscattering coefficient, 162, 408

K K channels, 625 Katahdin Hill, Massachusetts, 51, 182 backscatter measurements at, 583 clutter strength vs depression angle, 356 clutter strength vs range, 11 clutter visibility at, 288 X-band clutter and terrain visibility at, 287 K-distributions, 74 cumulative distribution function of, 558 of farmland clutter, 561–573 vs Weibull distribution, 558–561 klystron, 671 Knolls, Utah, 529 desert clutter spectra, 610–612 Kolmogorov-Smirnov test, 417, 570 kurtosis, 227 coefficient of, 137 definition of, 132 radar frequency and, 228

L Laboratoire Central de Telecommunications, 658 Lackawanna River, 176 Lake Winnipeg, 181 shoreline, 146 lakes, 411 land, 25 land clutter, 242 backscattering coefficient, 42 in surface radar, 544 long-range diffraction-illuminated, 25 low-angle, 396 low-range resolution, 44–46 maps, 44–46 measurement data, 2 model, 9 seasonal effects on, 111–114 spatial field of, 19 spatial homegeneity of, 6 strength vs radar frequency, 168

692

Index

land clutter (continued) surface-sited radar, 350 See also ground clutter land clutter coefficients desert, 529–530 grassland terrain, 521 high-relief agricultural terrain, 493– 496 high-relief desert, 531–532 high-relief forest, 507–513 high-relief general mixed rural terrain, 429–434 high-relief grassland, 521–522 high-relief shrubland, 518–519 level agricultural terrain, 501–506 level desert, 535–536 low-relief agricultural terrain, 496– 501 low-relief desert, 533–535 low-relief forest, 513–518 low-relief general mixed rural terrain, 434–436 low-relief grassland, 522–523 low-relief shrubland, 519–521 mountains, 537–539 overview, 429 pure terrain, 440–441 shrubland terrain, 518 urban terrain, 443–491 wetland terrain, 526–529 land clutter measurements overview, 408 program for, 2 land cover, 37 as backscatter sources, 318 discrete vertical features in, 62 mean clutter strength in classes of, 308–309 raw Landsat data, 440 variations in, 60 land use, 111 landform, 37 classes, 158 clutter patches in, 409 high-relief, 158 low-relief, 158 mean clutter strength in classes of, 308–309 Landsat, 313

landscape, 2 scales, 5 vertical features on, 43, 62 land-surface form, 3 larch, 48 L-band, 14, 174 desert clutter spectra, 611 dipole feed, 247 mean clutter strength vs polarization at, 213 MTI filter performance at, 623–625 STAP system performance at, 631– 635 L-band Clutter Experiment. See LCE LCE (L-band Clutter Experiment), 15, 582, 584–585 LCE radar, 583–584 primary design objective of, 584 spectral processing in, 584–585 leaf velocity distribution, 650 leaves, 576 Lethbridge, Alberta, 82 mountain clutter measurements at, 268–272 repeat sector measurements, 172 level agricultural terrain clutter amplitude distributions, 505– 506 land clutter coefficients, 501–506 mean clutter strength, 502–505 level desert, 535–536 clutter amplitude distributions, 535, 536 land clutter coefficients, 535–536 mean clutter strength, 536 level farmland, 88 frequency dependencies of clutter in, 163–165 level forest, 88 level terrain, 87–91 vertical objects on, 317–319 lightning, 664 Lincoln Laboratory, 2, 242 clutter measurement program, 3, 13– 16 linear regression, 135–136 liquid helium, 671 local oscillator, 250, 584 lognormal distributions, 416

Index

equations, 136–138 of farmland clutter, 561–573 lognormal scale, 51 long-range clutter within 360° range gates, 387–395 within wide annular regions, 379–387 long-range mountain clutter land clutter coefficients, 540–542 overview, 145 low range resolution, 44–46 low reflectivity areas, 115 low-altitude targets, 10 low-angle clutter, 2, 56–58 amplitudes, 58 attributes of, 3 cell-to-cell variability in, 110 clutter physics, 42–43 clutter strength vs range, 58 depression angle characteristics of, 104 dominant sources of, 43, 344 effects of trees on, 91–93 granularity in, 9 high-relief terrain in, 82 low-relief terrain in, 82 major elements in, 43–44 modeling of, 289 multifrequency results of, 243 overview, 396 patchiness, 7 phenomenology, 2 spatial amplitude distributions, 115 spatial extents, 7 spatial resolution in, 18 spikiness of, 322 statistical models, 2 variability, 289, 343 See also clutter lower bounds, 275 lowlands, 668 low-observable technology, 2 low-relief agricultural terrain clutter amplitude distributions, 499 land clutter coefficients, 496–501 mean clutter strength, 496 patch-to-patch variability in, 500 uncertain outliers in, 497 See also agricultural terrain low-relief desert

693

clutter amplitude distributions, 535 land clutter coefficients, 533–535, 535–536 mean clutter strength, 533–534 low-relief forest clutter amplitude distributions, 517 high depression angle and, 178–179 intermediate depression angle and, 180–182 land clutter coefficients, 513–518 low depression angle, 183 mean clutter strength, 514–516 microshadowing in, 514 terrain elevation data, 513 uncertain outliers in, 516 visibility and shadow in, 513–514 See also forest low-relief landform, 158 low-relief terrain, 66, 75, 82 low-resolution radar, 7

M macropatches, 20, 50 discrete sources, 290 predicting the existence of, 289 macroregions, 21, 43 macroshadow azimuth averaging through, 387 spatial dilution of clutter with, 307 Magrath, Alberta, 399 clutter patch measurements, 555–558 clutter patch selection at, 409–410 mountain clutter measurements at, 268–272 man-made structures, 8 marsh, 201 clutter strength vs depression angle, 297 mast height, 359 effect on terrain visibility, 360–364 mean clutter strength, 130, 418, 427 agricultural terrain, 106 high-relief agricultural terrain, 493 lower bound of, 389 low-relief agricultural terrain, 496 one-sigma variability of, 417 shadowless, 388 urban areas, 84 vs median clutter strength, 102 Weibull, 73

694

Index

mean deviation, 356 mean-to-median ratio, 427 in clutter histograms, 422 median clutter strength, 427 vs mean clutter strength, 102 vs percent tree cover, 92 Weibull, 72 median position, 210 meteor trails, 664 method of moments, 25, 259 microshadowing, 290 black, 52 effects of depression angle on, 413– 414 effects on clutter strength, 317 in clutter measurements, 51–52 in clutter patches, 275, 317 in low-angle clutter, 22 in low-relief forest, 514 vs angle of illumination, 43 vs depression angle in clutter patches, 102 microstatistics, 290 microtopography, 414 microwave backscatter, 111–114 microwave bands, 195 microwave clutter, 44 minimum least squares (See MLS) MIT Radiation Laboratory, 594 mixed terrain, 294, 409 classification of, 409 MLS (minimum least squares), 636 model validation, 543 moments, 129 computation of, 410 interpretation of, 132 lower bounds, 275, 410 method of, 259 of clutter amplitude distributions, 376 shadowless, 275 upper bounds, 131, 275, 410 mountain clutter, 77–82, 446, 537–539 bi-modal distributions of, 80–82 long-range, 145, 268–272 multifrequency measurements of, 172–174 phenomenology, 82 vs depression angle, 545 vs radar frequency, 545

See also clutter mountains, 37 clutter amplitude distributions, 539 clutter strength vs radar frequency in, 172–174 land clutter coefficients, 537–539 long-range, 540–542 mean clutter strength, 538–539 See also terrain moving scatterers, 576 moving target indicator (See MTI) MTI (moving target indicator), 23 cutoff frequency, 658 impact of windblown clutter spectra on, 621–623 improvement factors, 616 L-band results, 623–625 signal-to-interference power ratio, 621–623 single-delay-line, 607 X-band results, 622–623 multifrequency clutter measurements agricultural terrain, 184–201 Cold Lake, Alberta, 177 data collection, 146 Dundurn, 183 equipment, 146 forest, 175–183 Gull Lake West, Manitoba, 155 L-band, 204–209 mountains, 172–174 overview, 145–146 Sandridge, 183 S-band, 204–209 UHF band, 204–209 urban terrain, 170–172 VHF band, 204–209 Woking, Alberta, 177 See also clutter measurements See also Phase One clutter measurements See also repeat sector measurements multipath lobes, 163 radar frequency and, 414 multipath propagation, 259–262 hillside, 262–268 overview, 145 multipath reflections, 44 interference on direct illumination, 161

Index

N natural vegetation, 518 Neepawa, Manitoba, 186–188 negative depression angle, 94–95 no tree distribution, 92 noise contamination, 131 corruption, 410–411 noise floor, 350, 356 at high Doppler velocities, 591 noise level in clutter cells, 59 zero power, 275 noise power, 22 assigning values to, 131 from shadowed samples, 389 non-site-specific clutter model, 302–305 clutter cut-off range, 303 database of measurements for, 308–309 definition of, 302 normalization, 330–333 normalization constant, 640, 654 North American continent, 2

O oats, 190 oil drums, 120 open plot symbol, 443 Orion, Saskatchewan, 194 oscillators, 642

P Pakowki Lake, 193 parabolic equation, 25, 259 patch amplitude distributions, 308 patch histograms, 372 patches boundaries, 22 classification by terrain slope, 65 histograms, 372 separation, 8 sizes, 8 statistical convergence, 100 patchiness, 7, 286 deterministic, 18 spatial, 289 pattern propagation factor F, 16, 161 clutter strength and, 163, 413 definition of, 24, 44

695

pattern recognition, 291 Peace River, Alberta, 287 clutter patch measurements, 555–558 Pembina Hills, 44 Penhold II, 177 percent area, 351 percent circumference, 351 percent tree cover, 92 percentile levels, 229–231 of long-range clutter strength, 389 percentiles, 132, 245 periodograms, 336 phase modulation, 657 Phase One clutter measurements 360-degree survey data, 146 clutter patches, 126 clutter strength vs antenna height, 201 data collection, 146, 257–258 equipment, 143, 247–254 histograms, 418 instruments, 13–16 L-band experiments, 337 multifrequency, 143 objectives, 143 overview, 242 repeat sector, 154–156 repeat sector patches, 160 seasonal revisits, 235 sites, 247 spatial variations, 237–242 temporal variations, 237–242 See also multifrequency clutter measurements See also repeat sector measurements Phase One radar, 146, 583–584 calibration, 254–257 overview, 14 seasonal revisits of, 235 spectral processing in, 584–585 See also radar Phase Zero clutter maps, 299–302 Plateau Mountain, 77 Shilo, 58 Phase Zero clutter measurements, 115, 299–302 clutter patches, 46, 65, 126 clutter strength vs antenna height, 201 microshadowing vs depression angle, 102

696

Index

Phase Zero clutter measurements (cont.) oversampling in, 127 site heights, 38–39 sites of, 37 standard deviation-to-mean vs depression angle, 101 summer vs winter data, 112 Phase Zero radar angle calibration, 119–120 description of, 36–37, 118 elevation pattern gain variation, 123– 125 instrument, 13–15 overview, 14 primary display of, 36 range calibration, 120 receiver, 58 schematic diagram of, 118 signal strength calibration, 121–123 See also radar physical discretes, 414 Picture Butte II, 356 pixels, 118, 441 plan position indicator. See PPI plant morphology, 111 Plateau Mountain, 37, 45 clutter patches at, 77–80 repeat sector measurements, 172–174 point objects, 322 point source, 9 Poisson distribution, 53 polarization, 162, 244 circular, 598 dependence of clutter strength on, 212–215 effects on ground clutter strength, 414 horizontal, 146, 212 invariance with clutter spectra shape, 597–598 overview, 144 vertical, 146, 214 Weibull mean strength and, 418 Polonia, Manitoba, 186–187 ponds, 91, 326 poplar, 182 potatoes, 615 power law, 575 exponent, 643, 657 in clutter spectral shape, 643–654

rate of decay, 661 Russian studies, 646–650 spectral decay, 649 spectral shape function, 582 power line pylons, 120, 318 power meters, 255 power spectral density (See PSD) PPI (plan position indicator), 4, 36 PPI clutter maps, 13, 408–409 Altona, Manitoba, 318 Brazeau, Alberta, 542 Cochrane, Alberta, 324–325 overview, 286 Peace River, Alberta, 287 site-specific prediction, 542–543 PPI display, 350 prairie, 4 Beiseker, Alberta, 11 farmland, 56 grassland, 58 low-relief, 83 sloughs, 326 precipitation, 664 precision IF attenuator, 14, 36 in Phase Zero receiver, 118 PRF (pulse repetition frequency), 327, 583 PRI (pulse repetition interval), 336 input clutter power within, 616 of radar, 119 probability density function, 136 probability of detection, 622 probability of false alarm, 622 propagation, 24–25 electromagnetic, 243 lobes, 44 multipath, 145, 259–262 velocity of, 42 PSD (power spectral density), 576 equation, 576 pulse length, 42 pulse repetition frequency. See PRF pulse repetition interval. See PRI pure terrain, 409 classification of, 409 land clutter coefficients for, 440 Puskwaskau, Alberta, 178

Q quadrangle maps, 64

Index

quasi-dc power, 580 near-zero Doppler regime of, 580

R radar AEW (airborne early-warning), 620 angle calibration, 119–120 antenna mast height, 359 azimuth scan of, 388 carrier wavelength, 263 C-band, 656 detection performance of, 417, 621 effective height, 38, 56 finite sensitivity limits, 371 frequency, 20–21 ground-based, 359 high-resolution, 7 line-of-sight, 126 low-resolution, 7 noise floor, 350 noise level, 21–22, 300 polarization, 27 PPI display, 350 PRI (pulse repetition interval), 119 pulse length, 43 range calibration, 120 Raytheon Mariners Pathfinder 1650/ 9XR, 118 shipboard, 25 signal strength calibration, 121–123 spatial resolution, 20–21, 27 wavelength, 3, 10 radar cross section (See RCS) Radar Data Processor, 253 Radar Directive File, 258 radar frequency correlation times and, 338 decoupling of, 20–21 dependence of ground clutter on, 209– 211 insensitivity of distribution shape to, 419 vs clutter strength, 144, 162–163, 168 vs spectral power ratio, 602–604 vs spectral widths, 594–597 Weibull mean strength and, 418 radar noise, 275 corruption, 21–22 measurement of, 410–411

697

radar spatial resolution, 27 calculation of, 426 decoupling of, 20–21 effects on spread in clutter amplitude distributions, 413 ensemble amplitude distributions and, 110–111 equation, 420 Weibull shape parameter and, 418 windblown trees and, 576–582 radials, 119 radio frequency. See RF radome, 247 rail lines, 318 as discrete clutter sources, 115 rain, 664 range, 286 clutter strength vs, 58 correlation coefficient, 341 dependence on, 11–13 extent, 155 gates, 355, 636 intervals, 422 range calibration, 120 range gates, 355, 636 thresholding process for, 118 range resolution, 244 dependence of clutter strength on, 216–221 high, 46 low, 44–46 rangeland grassy, 182 herbaceous, 325 prairie, 182 subcategories of, 518 windblown clutter spectra for, 615–616 ratio of standard deviation-to-mean, 222 Rayleigh, 48 distribution, 5, 7, 50 slope, 48 statistics, 335 voltage distribution, 412, 416 RCS (radar cross section), 5 discrete sources of clutter and, 9 prediction of, 19 receivers, 250 noise level, 5

698

Index

reflection, 259 specular, 267 reflectors, 247, 648 elementary, 647 refractive index, 664 Regina Plain, Saskatchewan, 193 regression analysis, 422 remote sensing, 650 repeat sector measurements, 154–156, 274 azimuth extent, 155 Booker Mountain, Nevada, 202 computational examples, 278–279 Corinne, Saskatchewan, 197–201 data collection, 146 database, 209 diurnial variability and, 235 forest, 175–183 Gull Lake West, Manitoba, 155 mean strength vs polarization, 212– 215 mountains, 172–174 Neepawa, Manitoba, 186–188 objectives, 154 overview, 143, 145–146 Polonia, Manitoba, 186–187 range extent, 155 start range, 155 terrain classification in, 158 urban terrain, 170–172 Wainwright, 150 See also multifrequency clutter measurements See also Phase one clutter measurements reradiators, 642 resolution cell, 1, 216–217, 245 clutter coefficient in, 604–606 desert, 609–612 Dopple velocity, 586 windblown trees in, 576–582 resonant cavities, 251 RF (radio frequency), 154 Ricean statistics, 335 ridge, 47 ridge tops, 112 Riding Mountain, 187 river bluffs, 9 river valley, 56, 115 road markers, 120

roads, 318 rock faces, 9, 174 rocks, 576 Rocky Mountains, 45 Rosetown, Saskatchewan, 82 repeat sector measurements, 194 rotating structures, 664 rural terrain, 68 clutter modeling for, 545 high-relief, 68, 75 low-relief, 68, 75 rural/high-relief terrain clutter strength vs depression angle, 296 depression angle distributions for, 68– 70 general mixed, 429–434 overall amplitude distribution in, 75– 77 subclass types, 294 rural/low-relief terrain clutter amplitude distributions, 100 clutter strength vs depression angle, 296 depression angle distributions for, 68– 70 general mixed, 434–436 overall amplitude distribution in, 75– 77 Russia, 646–650

S sagebrush, 297 sampling populations, 425 sand dunes, 46 Sandridge, 183 SAR (synthetic aperture radar), 106 image data compression in, 291 X-band, 106 S-band, 14, 174 mean clutter strength vs polarization at, 213 mean clutter strengths at, 185 waveguide feed at, 247 scatter plots, 106, 210 regression analysis, 422 scatterers, 600 elemental, 649 oscillatory motions in, 642 radial velocity of, 579

Index

rotation of, 642 scattering ensemble, 339 scintillation, 10 Scranton, Pennsylvania clutter strength from steep forest at, 166 season, 111–114, 145, 244 effects on ground clutter strength of, 231–234 SEKE propagation code, 262 sensitivity limits, 356 sensitivity time control. See STC servodrives, 255 shadowed distribution, 402–403 shadowed terrain clutter spillover into, 402–403 clutter strength for, 319 definition of, 371 total clutter in, 398 shadowless distribution shape of, 379 statistical attributes of, 384 vs radar sensitivity, 377 shadowless mean, 391–394 definition of, 276 equation, 388 shape parameter, 419 exponential, 577, 654 Shilo, Manitoba low-angle clutter at, 56 multifrequency clutter measurements at, 195–197 shipboard radar, 25 shrubland terrain high-relief, 518–519 land clutter coefficients, 518 low-relief, 519–521 vs grassland, 526 sidelobes, 247 signal generators, 255 signal processors, 250 signal-to-clutter ratios estimation of, 346 measurement of, 5 time histories of, 2 signal-to-interference power ratio, 621 signal-to-noise ratio, 254 silos, 44, 297 site height, 359 effect on terrain visibility of, 360–364

effective, 38 site-specific clutter model, 307 advantages of, 343 description of, 343 skewness, 227 coefficient of, 137 definition of, 132 radar frequency and, 228 slant range, 56 snow, 189 soil, moisture content of, 234 space-time adaptive processing (See STAP) space-time correlation coefficient, 626 spatial amplitude distributions, 7 for general terrain types, 68–70 parametric dependence in, 115 spatial cells, 9 spatial correlation, 339–343 cell-to-cell, 426 coefficient, 627 spatial density, 9 spatial extent lack of uniformity in, 7 vs signal-strength threshold, 8 spatial filters, 397 spatial incidence, 9 spatial occupancy map, 18 spatial patches, 3 spatial resolution, 292 azimuth extent of, 342 in clutter histograms, 422 spatial variability, 245 patch-to-patch, 241 spatial variations, 237–242 spectral decay, 337 Doppler velocity and, 668 exponential, 674 power-law, 649 spectral power, 577 computation of, 587–589 dc, 587, 587–588 decay, 646 near zero-Doppler, 580 ratio, 581 total, 587 spectral power ratio vs radar frequency, 602–604 vs wind speed, 600–602

699

700

Index

spectral shape effects of cell size on, 598–600 effects of season on, 598–600 effects of site on, 598–600 effects of tree species on, 598–600 exponential, 577–579, 654–659, 664 function, 639 Gaussian, 589, 640–643, 675 invariance with radar frequency, 594– 597 invariance with radar polarization, 597–598 power-law, 643–654, 664 shoulders in, 615 temporal variation, 598 variations with wind speed, 589–594 vs Doppler velocity, 589 See also clutter spectra spectral tails ac power in, 590 high-level, 664 low-level, 645, 671–672 power-law, 643 rate of decay, 620 specular reflection, 267 spread, 292, 307 derivation of, 420 in amplitude statistics, 413 spruce, 48, 112 Spruce Home, Saskatchewan, 411–413 STALO (stable local oscillator), 672 standard deviation, 129 of dB values, 131 standard deviation-to-mean ratio, 222–227 in clutter histograms, 422 Weibull shape parameter and, 417 STAP (space-time adaptive processing), 23 effect of windblown clutter on, 625– 629 L-band results, 631–635 X-band results, 629–630 stationary clutter, 1 statistical clutter amplitude distributions, 23 statistical estimation theory, 100 statistical models, 2 statistics confidence level, 425

Rayleigh, 335 Ricean, 335 sampling populations, 425 shadowless, 410 temporal, 335 Weibull, 416–418 STC (sensitivity time control), 253, 329 step discontinuity, 53 step function, 307 stereo aerial photographs, 37, 396 overlaying clutter maps onto, 46 Strathcona, 171 stream beds, 318 Suffield, Alberta clutter strength vs range, 327 discrete clutter sources at, 325–330 repeat sector clutter measurements at, 330 terrain, 325 sugar beets, 615 sum of squared deviations, 136 surface relief, 37 surface wave, 10 surface-area density function, 5 surface-sited radar, 1 land clutter in, 350, 544 survival wind velocity, 247 synthetic aperture radar. See SAR system clocks, 584

T tamarack, 48 target detection, 5 targets detection statistics, 5 low-altitude, 10 low-flying, 1 telephone poles, 44 as clutter sources, 58, 216 in range calibration of radars, 120 temporal correlation coefficient, 626 temporal statistics, 335 attributes of, 335 temporal variations, 237–242 in spectral shapes, 598 in windblown clutter spectra, 598 of clutter strength, 291 terrain, 10 agricultural, 167, 184–201, 492–493 classification of, 37–41

Index

classification system, 243 clutter patches, 61 clutter strength vs frequency, 168 composite, 294 description methodology, 156–159 desert, 529–530 effects on clutter, 24 effects on illumination, 259 elevation profile, 56 forest, 506–507 geometric visibility of, 359 grassland, 521 heterogeneity, 65 high-relief, 82 land clutter coefficients, 429 level, 87–91 low-relief, 82 microwave backscatter from, 111–114 mixed, 294, 409 mountain, 537–539 negative depression angle, 94–95 pure, 409 pure vs mixed, 50–54 reflection coefficients, 44, 260 rural, 68 rural/high-relief, 68 rural/low-relief, 68 shrubland, 518 subcategorization of, 294 urban, 68, 443–491 variability within class, 243 wetland, 85–87, 526–529 terrain elevation, 360 depression angle and, 415 terrain patches. See clutter patches terrain reflection coefficients, 44 terrain relief, 440 terrain shadowing, 371 effects on ground clutter distributions, 371–379 terrain slopes, 56–57 depression angle and, 165–168 from topographic contour maps, 192 grazing angle and, 62 high-relief, 66 low-relief, 66 patch classification by, 65 terrain visibility, 51, 312 determination of, 319

701

effects of varying mast heights on, 360–364 effects of varying site heights on, 360– 364 geometric, 319 macroregions of, 64, 316 thermal noise, 5 Toeplitz matrix, 626 topographic maps, 37 overlaying clutter maps onto, 46 quadrangle, 64 towers, 9 towns, 112 transmitters, 250, 584 traveling wave tubes, 251 tree foliage, 48 tree lines, 52, 112 backscattering from, 52 tree lots, 91 tree trunks, 576 trees, 8 as discrete clutter source, 115 effects on low-angle clutter, 91–93 effects on visibility, 312–314 in spatial resolution cells, 62 wind-induced motion of, 575 triodes, 251, 584 Turtle Mountain, 182 clutter strengths at, 211

U UHF (ultra high frequency), 14, 174, 196 clutter strength at, 177 mean clutter strengths at, 194 UHF clutter, 411–413 uncertain outliers, 443 upper bounds, 275 urban clutter, 82–85, 446 multifrequency measurements of, 170–172 residential vs commercial, 84–85 strength, 84 vs radar frequency, 545 urban terrain, 68 clutter amplitude distributions, 446 clutter modeling for, 545 clutter strength vs radar frequency, 170–172 depression angle distributions for, 68– 70

702

Index

urban terrain (continued) land clutter coefficients, 443–491 mean clutter strength for, 444 overall amplitude distribution in, 75– 77 uncertain outliers, 445–446 Weibull shape parameter, 446 See also terrain USGS EROS Data Center, 440 utility poles, 9

V Vananda East clutter strength vs frequency at, 151 velocity of propagation, 42 vertical polarization, 214, 244, 563–573 mean clutter strength at, 215 vs horizontal polarization, 432 vertical scatterers, 25, 115 VHF (very high frequency), 13 clutter strength at, 177 mean clutter strengths at, 194 multipath loss, 330 polarization bias, 511 VHF clutter, 163, 259, 319 multipath propagation in, 172 VHF/UHF feed system, 247 visibility, 300 antenna heights and, 157 effect of trees on, 312–314 interclutter, 7 of terrain, 312 visibility curves, 622, 628 voltages, 44, 411

W Wachusett Mountain clutter patches at, 411–413 clutter strength vs depression angle at, 356 clutter strength vs frequency at, 149 LCE clutter spectral measurements at, 584 Wainwrigh, 150 water tower, 221, 390, 609 as clutter source, 74 Waterton, Alberta clutter patches at, 80 repeat sector measurements at, 172– 174

waveforms, 254 high-range resolution, 228 low-range resolution, 228 pulsed, 146 wavefront, 52 waveguides, 247 weather, 111, 145, 244 effects on ground clutter strength, 231–234 Weibull clutter model, 543 Weibull cumulative distribution function, 71, 134, 416 equation, 549 Weibull mean strength, 73, 294, 420 polarization and, 418 radar frequency and, 418 Weibull median strength, 72 Weibull probability density function equation, 133, 549 Weibull probability distribution mean-to-median ratio, 134 of farmland clutter, 561–573 overview, 548 ratio of mean-to-median in, 549 ratio of standard deviation-to-mean, 549 ratio of variance to the square of the mean in, 549 standard deviation-to-mean ratio, 134 vs K-distribution, 554–561 vs lognormal distribution, 554–561 Weibull scale, 51 Weibull shape parameter, 7, 20, 72 calculation of, 432 equation, 549 radar spatial resolution and, 418, 433 standard deviation-to-mean ratio and, 417 urban terrain and, 446 vs radar spatial resolution, 295 Weibull statistics, 71, 416–418 in probability distributions, 544 mean-to-median ratio for, 72, 416 Westlock, 182 wetland clutter, 85–87 clutter amplitude distributions, 526 land clutter coefficient, 526–529 mean clutter strength, 527–529 vs level forest clutter, 91

Index

wheat, 190, 615 dielectric constant of, 234 white noise power, 621 willow, 48 wind scale, 577 wind speed, 576, 578 logarithm of, 578 spectral power ratio and, 600–602 spectral shape and, 589–594 spectral width and, 578 windblown clutter, 576–582 Doppler spectra, 334 effect on STAP (space-time adaptive processing), 625–629 regions of spectral approximation, 606–609 spectra vs radar frequency, 594–597 spectral decay of, 337 spectral measurements of, 582 spectral processing, 584–585 spectral shape vs radar polarization, 597–598 spectral shape vs windspeed, 589–594 See also clutter windblown clutter spectra Beulah, North Dakota, 612–613 Chinese studies of, 650–651 cropland, 612–615 desert, 609–612 Doppler velocity extent of, 579 effects of cell size on, 598–600 effects of season on, 598–600 effects of site on, 598–600 effects of system instabilities on, 672 effects of tree species on, 598–600 impact on MTI filter performance, 621–623 in breezy conditions, 592–594 in gale winds, 592–594 in light-air conditions, 592–594 in windy conditions, 592–594 invariance with radar frequency of, 594–597 model, 581–582 normalization of, 586 rangeland, 615–616 Russian studies of, 647 temporal variation in, 598 See also clutter spectra

703

windblown trees, 335, 575 physical model for, 666 spatial resolutions cells with, 576–582 X-band clutter spectra for, 671–672 Woking, Alberta, 177 Wolseley, Saskatchewan, 442 farmland clutter data from, 340 repeat sector measurements at, 194 X-band clutter measurements at, 563– 573 woodlots, 112, 291 World War II, 1

X X-band, 13 backscattering, 651 clutter amplitude distributions, 69 clutter strength vs grazing angle, 11 desert clutter spectra, 611 elemental scatterers at, 649 MTI filter performance at, 622–623 SAR (synthetic-aperture radar), 106 STAP system performance at, 629– 630 terrrain reflection coefficients at, 260 tracking systems, 543 transmitters, 179 X-band clutter amplitude distributions by depression angle, 68–71 amplitude histogram, 565 effects of trees on, 91–93 level terrain, 87–91 mountain terrain, 77–82 overall distribution of, 74–75 parametric variation in, 103 spatial amplitude statistics for, 68 urban, 82–85 Weibull parameters, 71–74 wetland terrain, 85–87 See also Phase Zero clutter measurements X-band radar, 68 X-band reflector, 247

Z zero-Doppler returns, 337, 575 zero-th Doppler bin, 580