Cirrus

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cirrus

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cirrus

Edited by DAVID K. LYNCH KENNETH SASSEN DAVID O'C. STARR GRAEME STEPHENS

OXPORD UNIVERSITY PRESS 2002

OXFORD UNIVERSITY PRESS Oxford New York Athens Auckland Bangkok Bogota Buenos Aires Cape Town Chennai Dar es Salaam Delhi Florence Hong Kong Istanbul Karachi Kolkata Kuala Lumpur Madrid Melbourne Mexico City Mumbai Nairobi Paris Sao Paulo Shanghai Singapore Taipei Tokyo Toronto Warsaw and associated companies in Berlin Ibadan

Copyright © 2002 by Oxford University Press, Inc. Published by Oxford University Press, Inc. 198 Madison Avenue, New York, New York 10016 Oxford is a registered trademark of Oxford University Press. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Cirrus / edited by David K. Lynch ... [et al.]. p. cm. Includes bibliographical references and index. ISBN 0-19-513072-3 1. Cirrus clouds. I. Lynch, David K., 1946QC921.43.C57 C58 2000 551.57'6-dc21 00-021315

987654321 Printed in the United States of America on acid-free paper

Preface

Until the 1980s, cirrus clouds were viewed with curious disinterest by most atmospheric scientists. They were interesting to look at, sometimes foretelling the coming of storms, and occasionally producing pretty optical phenomena such as halos and sun dogs. But cirrus did not rain or snow and were therefore perceived as having no impact on commerce, agriculture, transportation, recreation, or the ability to wage war. Thus, cloud research largely ignored cirrus and focused on the denser clouds associated with weather systems, rain, snow, and damaging winds. With the growing recognition that global climate change was a subject worthy of scientific inquiry and potentially a public concern, scientific interest in cirrus clouds began to increase. This interest was founded in the early works of scientists such as Julius London, Fritz Moller, and Kiril Yakolevich Kondratyev in the late 1950s and Sukyo Manabe in the 1960s, who demonstrated the important radiative effect of cirrus clouds on the global heat budget and therefore in the climate system. In the late 1960s and 1970s, meteorologists began to acquire and analyze quantitative measurements of cirrus cloud radiative and microphysical properties. The efforts of these early cirrus scientists, along with the continuing growth in scientific and public concern with global climate change and the advent of improved observation technology, built the momentum for creation of significant research programs with a focus on cirrus cloud systems. The first of these was the FIRE program (First ISCCP Regional Experiment; ISCCP is the International Satellite Cloud Climatology Project), initiated in the early 1980s and led by NASA with the participation of other U.S. agencies such as the National Science Foundation and the National Oceanographic and

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Preface

Atmospheric Administration. Later, a comparable program was developed in Europe. A series of increasingly comprehensive field experiments was conducted in the United States beginning with FIRE Cirrus-I in 1986 and then FIRE CirrusII in 1991, a pilot tropical cirrus experiment as part of TOGA-COARE in 1993, and SUCCESS (Subsonic Aircraft: Contrail and Cloud Effects Special Study) in 1996. A similar, though somewhat smaller scale, series of experiments (EUCREX/ICE) were conducted in Europe during the mid-1990s under the leadership of Ehrhard Raschke. More recent activity there has focused on study of contrails under the leadership of Ulrich Schumann. The U.S. Department of Energy's Atmospheric Measurements Program (ARM) has recently made significant contributions, though the programmatic interest is much broader. Since 1994, intensive observation periods have been conducted on a roughly biennial basis at the Southern Great Plains ARM site in Oklahoma, during which extensive cirrus observations have been obtained. Extensive surface-based remote sensing cloud measurements are also obtained on a continuous basis. Interest in cirrus clouds has continued to grow, motivated by the need to understand cirrus impacts on the global radiation budget, climate and spacebased remote sensing systems, and now also by the possibility that contrails and associated anthropogenic effects, specifically effluent from aircraft, may be altering the regional and global occurrence and properties of cirrus. Recent concern that processes occurring on ice crystal surfaces may be significant in regulating upper tropospheric chemistry is an additional motivating factor. The next major planned cirrus experiment is an international multiagency tropical cirrus experiment, CRYSTAL, in the tropical western Pacific. Other smaller scale field work, airborne and surface based, is on-going. In 1997, we realized that there had never been an international scientific meeting devoted to cirrus clouds, and, worse yet, there was no single source of information about cirrus. The literature was scattered throughout journals and government reports. What was needed was a meeting where the world's cirrus experts could gather and produce a book that covered all aspects of cirrus clouds. The Optical Society of America (OSA) agreed to sponsor the meeting in cooperation with the American Meteorological Society (AMS) and the American Geophysical Union (AGU). The meeting was held in Baltimore on October 6-8, 1998 and was an intense, upbeat conference. There were more than 100 attendees, with 18 invited speakers and 30 contributed poster papers. Oxford University Press enthusiastically agreed to publish the invited papers from the meeting in book form. All of the invited speakers at the OSA meeting submitted manuscripts, and each was reviewed and revised. It was not enough, however, simply to collect the invited papers. They had to be edited so that the book was a more or less homogeneous monograph in which one chapter logically led to the next and in which there was little or no duplication of coverage. Notation had to be made uniform throughout the book, and figures had to be made to the same standard, at least to the extent possible when drawn from the technical literature. This book is a technical survey of cirrus clouds. It is intended to fill the large gap between elementary treatments of cirrus and advanced forefront research papers. It will be useful for cirrus researchers and scientists in any field who are

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interested in cirrus but who have not worked in the field before: students, meteorologists, atmospheric chemists, nucleation specialists, crystallographers, aerodynamicists, and so on. Being a review, most of the material has been previously published in one form or another. Thus it has passed the test of accuracy and reliability. But there are also many areas of uncertainty. We took particular care to highlight these areas so that people new to the field can gain some perspective on the important areas for future study. The editors are indebted to many people who took the time and effort to carefully review the manuscripts and make suggestions for improvements: Kenneth A. Campana, Allan I. Carswell, William Cotton, Anthony DelGenio, Andrew Detwiler, Stanley Gedzelman, Leo J. Donner, Ismael Gultepe, George Isaac, Eric Jensen, Richard Lindzen, David K. Lynch, Paul Menzel, Robert T. Menzies, Michael Mishchenko, Steven Ou, Martin Platt, Sergey Matrosov, William Rossow, Ken Sassen, Cynthia Twohy, Gabor Vali, and Donald Wiley. We also thank Joyce Berry at Oxford University Press, Rosemary Dwyer at the OSA, and Steve Moss of The Aerospace Corporation for help and encouragement with this project. We hope that readers will find CIRRUS to be a useful and enjoyable book. Los Angeles Salt Lake City Greenbelt Ft. Collins June 2001

D.K.L. K.S. D.S. G.S.

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Contents

First Authors, xiii 1. Cirrus: History and Definition, 3 David K. Lynch 2. Cirrus: A Modern Perspective, 11 Kenneth Sassen 3. Ice Crystals in Cirrus, 41 John Hallett, William P. Arnott, Matthew P. Bailey, and Joan T. Hallett 4. Mid-latitude and Tropical Cirrus: Microphysical Properties, 78 Andrew J. Heymsfield and Greg M. McFarquhar 5. Laboratory Studies of Cirrus Cloud Processes, 102 Paul DeMott 6. Cirrus and Weather: A Satellite Perspective, 136 Donald P. Wylie 7. Satellite Remote Sensing of Cirrus, 147 Patrick Minnis

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Contents

8. Ground-based Remote Sensing of Cirrus Clouds, 168 Kenneth Sassen and Gerald Mace 9. Molecular-Backscatter Lidar Profiling of the Volume-Scattering Coefficient in Cirrus, 197 Albert Ansmann 10. Structural and Optical Properties of Cirrus from LIRAD-type Observations, 211 C. Martin R. Platt 11. Contrail Cirrus, 231 Ulrich Schumann 12. Subvisual Cirrus, 256 David K. Lynch and Kenneth Sassen 13. Radiative Transfer in Cirrus Clouds: Light Scatting and Spectral Information, 265 K.N. Liou, Y. Takano, P. Yang, and Y. Gu 14. On Cirrus Modeling for General Circulation and Climate Models, 297 Hilding Sundqvist 15. GCM Simulations of Cirrus for Climate Studies, 310 Anthony D. Del Genio 16. Ice Clouds in Numerical Weather Prediction Models: Progress, Problems, and Prospects, 327 Christian Jakob 17. Dynamic Processes in Cirrus Clouds: A Review of Observational Results, 346 Markus Quante and David O'C. Starr 18. Dynamic Processes in Cirrus Clouds: Concepts and Models, 375 David O'C. Starr and Markus Quante 19. Microphysical Processes in Cirrus and Their Impact on Radiation: A Mesoscale Modeling Perspective, 397 Vitaly I. Khvorostyanov and Kenneth Sassen 20. Cirrus, Climate, and Global Change, 433 Graeme Stephens

Contents

21. Cirrus: The Future, 449 David K. Lynch, Kenneth Sassen, Anthony Del Genio, Andrew Heymsfield, Patrick Minnis, Martin Platt, Markus Quante, Ulrich Schumann, and Hilding Sundqvist Appendix: Chapter 2 Plates - Cirrus Case Studies, 457 Index, 469

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First Authors

David K. Lynch The Aerospace Corp. P.O. Box 92957 Los Angeles, CA 90009 [email protected]

Andrew J. Heymsfield NCAR P.O. Box 3000 Boulder, CO 80307 heyms 1 @ucar.edu

Kenneth Sassen Dept. of Meteorology 135 S 146OE 819 WBB University of Utah Salt Lake City, UT 84112 [email protected]

Kuo-Nan Liou Dept. of Atmospheric Sciences UCLA Los Angeles, CA [email protected]

David O'C. Starr Code 913 NASA Goddard Space Flight Center Greenbelt, MD 20771 [email protected]

Patrick Minnis NASALRC ASD/RSB Hampton, VA 23665-5225 [email protected]

Graeme Stephens Dept. of Atmospheric Science Colorado State University Fort Collins, CO 80523 [email protected]

C. Martin R. Platt 47 Koetong Parade Mt. Eliza, Victoria, 3930, Australia [email protected] xiii

xiv

Contributors

Donald Wylie CIMSS 1225 West Dayton Street University of Wisconsin—Madison Madison, WI 53706 [email protected]

Hilding Sundquist Dept. of Meteorology Univ. of Stockholm Arrheiniuslab, S-106 91 Stockholm, Sweden [email protected]

John Hallett Atmospheric Ice Physics Laboratory Desert Research Institute P.O. Box 60220 5625 Fox Ave. Reno, NV 89506-0220 [email protected]

Vitaly Khvorostyanov Bldg.8,Corpl,Apt.473rd Mikhalkovsky per. Moscow 125008, Russia [email protected]

Markus Quante GKSS Research Center Institute of Atmospheric Physics Max-Planck-Strasse D-21502 Geesthacht, Germany [email protected]

Christian Jakob ECMWF Shinfield Park Reading Berkshire RG2 9AX, UK [email protected]

Albert Ansmann Deutscher Wetterdienst Meteorologisches Observatorium Albin-Schwaiger-Weg 10 82383 Hohenpeibenberg, Germany albert. ansmann@tropos. de

Anthony Del Genio Goddard Institute for Space Studies 2880 Broadway New York, NY 10025 [email protected]

Paul J. DeMott Research Scientist Department of Atmospheric Science Colorado State University Fort Collins, CO 80523-1371 [email protected]

Ulrich Schumann DLR-Institut fur Physik der Atmosphere Oberpfaffenhofen D-82234 Wessling, Germany [email protected]

Acronyms

To avoid interrupting the text flow, frequently used acronyms are defined only here. ADEOS AERI AGU AMS ARES ARM ATSR AVHRR AVIRIS CAPE CART CAT CCN CCOPE CEPEX CERES COARE CPMC CRYSTAL CSIRO DMSP

Advanced Earth Observing Satellite Atmospheric Emittance Radiance Interferometer American Geophysical Union American Meteorological Society Airborne Remote Earth Sensing System Atmospheric Radiation Measurement Along Track Scanning Radiometer Advanced Very High Resolution Radiometer Airborne Visible Infrared Imaging Spectrometer convective available potential energy Clouds and Radiation Testbed clear air turbulence cloud condensation nuclei Cooperative Convection Precipitation Experiment Central Equatorial Pacific Experiment Clouds and the Earth's Radiant Energy System Coupled Ocean-Atmosphere Response Experiment Cirrus Parcel Model Comparison Project Cirrus Regional Study of Tropical Anvils and Layers (FIRE IV) Commonwealth Scientific and Industrial Research Organization (Australia) Defense Meteorological Satellite System xv

xvi

Acronyms

DOC DOE ECLIPS ECMWF EOS EOSP ERBE EUCREX PARS FDTD FIRE FTIR GARP GASP GATE GCM GCSS GEWEX GOES GPS HAT HIRS HIS HSRL HYVIS ICE ICMC IFO ISCCP ITCZ IWC JPL LANDSAT LIRAD LITE MISR MODIS MODTRAN MOZAIC NASA NCAR NCEP NOAA NWP NWS OLR PICASSOCENA OSA

Department of Commerce US Department of Energy Experimental Cloud Lidar Pilot Study European Centre for Medium-Range Weather Forecasts Earth Observation Satellites Earth Observing Scanning Polarimeter Earth Radiation Budget Experiment European Cloud and Radiation Experiment Facility for Atmospheric Remote Sensing finite-difference time domain First ISCCP Regional Experiment Fourier transform infrared spectroscopy Global Atlantic Research Program Global Atmospheric Sampling Program Global Atmospheric Tropical Experiment general circulation model Global Cloud System Study Global Energy and Water Cycle Experiment Geostationary Operational Environmental Satellite Global Positioning System high altitude tropical cirrus High Resolution Infrared Radiation Sounder High Spectral Resolution Infrared Spectrometer high spectral resolution lidar hydrometeor videosonde International Cirrus Experiment Idealized Cirrus Model Comparision Project Intensive Field Observations International Satellite Cloud Climatology Project Intertropical convergence zone ice water content Jet Propulsion Laboratory Land Satellite combined Lidar & RADar Lidar In-Space Technology Experiment Multi-angle Imaging Spectroradiometer Moderate Resolution Imaging Spectroradiometer MODerate resolution TRANsmittance code Measurement of Ozone by Airbus In-Service Aircraft National Aeronautics and space Administration National Center for Atmospheric Research National Center for Environmental Prediction National Oceanic and Atmospheric Administration numerical weather prediction National Weather Service outgoing longwave radiation Pathfinder Instruments for Cloud and Aerosol Spacebourne Observations—Climatologie Etendue des Nuages et des Aerosols Optical Society of America

Acronyms

POLDER POLINAT PROBE SAGE SHEBA SUCCESS TEFLUN TIROS TOA TOGA TOGA/ COARE TRMM VAS VIPS WMO

Polarization and Directionality of the Earth's Reflectances Pollution from Aircraft Emissions in the North Atlantic Flight Corridor Pilot Radiation Observation Experiment Stratospheric Aerosol and Gas Experiment Surface Heat Budget of the Arctic Ocean Subsonic Aircraft: Contrails and Cloud Effects Special Study Texas Florida Underflights Television and Infrared Observations Satellite Top-of Atmosphere Tropical Ocean Global Atmosphere Tropical Ocean/Global Atmosphere Coupled Ocean/Atmosphere Response Experiment Tropical Rain Measurement Mission Visible Atmospheric Sounder Video Ice Particle Sampler World Meteorological Organization

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cirrus

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I Cirrus History and Definition

DAVID K. LYNCH

I.I. The Historical View of Cirrus The most distinguishing physical property of cirrus (cirrostratus and cirrocumulus) is their composition. Cirrus are made predominantly or wholly of ice, whereas the majority of clouds (both in name and number) are composed of water droplets. That most clouds were composed of water droplets was probably well known to the ancients, who must surely have encountered fog in valleys and mountains. Yet the presence of ice in cirrus is not easily experienced in everyday life. To answer the question Who discovered that cirrus are made of ice? we have to trace developments in meteorology back almost 2500 years. Anaxagoras of Clazomenae (c. 500-428 B.C.) might have deduced that cirrus were made of ice. Using an inductive approach based on measurements and observations, Anaxagoras knew that clouds were made of water and that air was colder aloft. He believed that warm, moist air convected upward and that the water vapor cooled, condensed, and ultimately froze at great heights to become hail. We do not know if Anaxagoras considered cirrus explicitly because what little is left of his writings do not mention any cloud recognizable as cirrus (Gershenson and Greenberg 1964). Two thousand years passed before any substantial progress was made on cirrus. In 1637 Descartes (1596-1650) published Discours de la methode (Descartes 1637) in three parts: Dioptrics, Meteorology, and Geometry. In Dioptrics he set forth the law of refraction (Snell's law) and in Meteorology he applied the law to the rainbows by performing numerical ray traces. Although he 3

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Cirrus

almost certainly knew the principle of minimum deviation, there is nothing in his writings that explicitly refers to it. In the ninth discourse on Meteorology, Descartes conjectures that the common 22° halo was due to refraction through ice crystals. around the heavenly bodies there sometimes appear certain circles... they are round . . . and always surround the sun or some other heavenly body . . . they are colored, which shows that there is refraction. But the circles are never seen where it rains, which shows that they are not caused by the refraction which occurs in drops of water or in hail, but by that which is caused in those small little stars of transparent ice ... those that we have observed most often have had their diameters at around 45°... (Olscamp 1965) Descartes was obviously referring to the common 22° (radius) halo, whose diameter is about 45°. He recognized that the circles were visible on clear days and were not related in any way to rainbows. There is no evidence that Descartes actually ray traced an ice crystal. Still, Descartes almost surely recognized the existence of thin clouds when the halos were present, and he probably deserves the credit for identifying ice in cirrus. In 1681, Edme Mariotte (1620-1684) explained several halos as being due to refraction through crystals (Mariotte 1681).This confirmed Descartes' conjecture and later led Venturi (1794) and Young (1802) to set forth the modern basis of halo theory. Mariotte's framework of geometrical optics is still in place today (Pernter and Exner 1910, Tricker 1970, Greenler 1980, Tape 1994). Curiously, however, the notion of ice high in the atmosphere and the implication for temperature did not take root in the minds of seventeenth-century meteorologists. Around 1600, Fludd, Drebbel, Santorio, and Galileo were inventing what was to become the thermometer (Middleton 1966). Although the historical record does not tell us who was the first person to take a thermometer up in the air and record freezing temperatures, such an outcome would surely have been a reasonable expectation and possibly a known fact by the early seventeenth century. Thus, by the middle of the seventeenth century, all the supporting evidence was available: Descartes had optically linked cirrus with ice, even though cirrus had not yet been named or classified as a cloud type. Galileo and Santorio had established the quantitative relation between altitude and temperatures; what was necessary to complete the concept was empirical evidence that cirrus clouds were very high in the atmosphere. This had to wait almost two centuries before systematic cloud classifications began.

1.2. Modern Cloud Classification In 1802 Jean-Baptist Lamarck (1744-1829) published the first scientific cloud classification based on morphology. Though not intended as a complete system, one of his classes was nuages en balayures, or "sweep clouds," referring to what we now call "cirrus uncinus." Lamarck's French terminology was never adopted. The year after Lamarck's work, Luke Howard (1803) published a cloud classifi-

History and Definition

5

cation using Latin names. He was the first person to use the term "cirrus" to refer to wispy, fibrous clouds. Both Lamarck and Howard had biological backgrounds, and it is not surprising that "cirrus" was already used in taxonomy to describe various "dangling" or "prehensile" appendages. Howard's cloud classification is still in use. The next advance in understanding cirrus came more than 50 years after Howard's work. In 1855 Renou recognized the importance of cloud height, and researchers began triangulation measurements. Later, Hildebrandsson (1887) and Abercrombie (1887) firmly established height as an important classification parameter when they introduced 5 families of 10 cloud genera. Their work was immediately adopted as the standard for cloud classification. In 1879 Hildebrandsson published an atlas of 16 cloud photographs. A few years later he and Abercrombie published a more extensive cloud classification stressing cloud vertical height and structures and established "low," "middle," and "high" clouds as a useful classification overlay. Their work became the standard in cloud classification and was closely followed by Hildebrandsson, Riggenbach and Teisserenc de Bort (1896). Since this time, our understanding of the composition, height, and temperature of cirrus clouds was not changed significantly, nor, in general, has our definition of cirrus, except for the addition of several varieties. The period 1957-1964 was pivotal in cirrus research because satellites, lidars, and new forecasting tools became available. The first infrared cloud satellite, Television and Infrared Observations Satellite (TIROS-I), was launched April 1,1960 (Vaeth 1965). The first geosynchronous weather satellite was the Geostationary Operational Environmental Satellite (GOES), launched in May 1974 (Berlin 1988). Both TIROS and GOES had the ability to make visible and thermal infrared measurements, and thus the concept of a two-parameter classification was born. Clouds could be bright or dark in the visible and hot or cold in the infrared. Cirrus clouds were classified as "dark and cold," indicating both their relatively low optical thickness and low temperatures (i.e., thin and cold; Schiffer and Rossow 1983; Rossow and Gardner 1993). This classification, however, is not a definition, but rather a convenient way of classifying clouds based purely on their radiative properties. The fact that radiative properties correlate to some degree with ice phase, temperature, morphology, and so on makes sense but in no way is a perfect means to identify only cirrus clouds. Radiative properties may be considered a definition within the confines and restrictions of a particular satellite program, but they are in no way relevant to the morphological or physical definitions. Along with satellites came lasers (Maiman et al. 1960), and shortly thereafter, the first lidars were in operation (Ligda 1963; Fiocco and Grams 1964). Lidar provided height, density, polarization, and, eventually, velocity information. All added dramatically to our understanding of cirrus but did little to change the definition. Until the satellite age, cirrus prediction was limited to old weather sayings. In 1957 Stone reviewed all aspects of cirrus and began formulating prediction rules. A few years later Appleman (1961) reported the first cirrus climatology and was

6

Cirrus Table I . I . Cirrus cloud properties Property Thickness Altitude Concentration Ice content Size (length) Shape3

Mean 1.5km 9km 30/L 0.025 gm~3 250 urn variable

Range

Ratio3

0.1-8 km 4-20 km Kr*-10*/L IffM. 2 g/m3 1-8000 um highly variable

80:1

5:1 108:1 104:1 8000:1 large

Adapted from Dowling and Radke (1990). * Added by author.

able to identify the conditions under which cirrus formed. Their work laid the foundation for much of the modern prognostic schemes (Schmidt and Lynch 1995; chapter 2, this volume). The average properties of cirrus and their differences from water drop clouds are discussed by Dowling and Radke (1990) and summarized in table 1.1. 1.3. Definition of Cirrus By international agreement, the World Meteorological Organization (WMO) has the responsibility and authority to classify clouds. Clouds are classified primarily by morphology. Their most recent classification system (1975 [1995], p. 16,1987) gives the following definitions: Cirrus: Detached clouds in the form of white, delicate filaments or white or mostly white patches or narrow bands. These clouds have a fibrous (hair-like) appearance, or a silky sheen, or both. Cirrocumulus: Thin, white patch, sheet or layer of cloud without shading, composed of very small elements in the form of grains, ripples, etc., merged or separate, and more or less regularly arranged; most of the elements have an apparent width of less than one degree. Cirrostratus: Transparent, whitish cloud veil of fibrous (hair-like) or smooth appearance, totally or partly covering the sky, and generally producing halo phenomena.

These definitions are entirely morphological and are based on visual appearance during the day time. Properties such as ice content, temperature, altitude, color, and optical depth are not explicitly part of the definition, although all are recognized as relevant. The three genera are further divided into species, again based on morphology. These are listed in table 1.2. "Subvisual cirrus" (Uthe and Russell 1977; Barnes 1980,1982; Heymfield 1986; Sassen et al. 1989; Sassen and Cho 1992; see review by Lynch 1993) and "contrail cirrus" (see review by Schumann, this volume) are well recognized in meteorology but as yet they have no Latin designation and are not currently included in the WMO classification. Subvisual cirrrus are defined as cirrus with optical depths in the visible (0.694 urn) of less than 0.03. Such clouds are often found at the

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Table 1 .2. Cirrus cloud names Family

Genus

Species

Varieties

High

Cirrus

castellanus

duplicatus intortus radiatus vertebratus

floccus

Cirrostratus Circocumulus

spissatus uncinus fibratus nebulosus fibratus lenticularis castellanus floccus stratiformis

undulatus duplicatus undulatus lacunosus

tropopause and in some parts of the world (namely, the tropics) they may be nearly ubiquitous (see review by Wylie, this volume). Within the conventional meteorological community, associated properties of cirrus include ice content (large), height (high), and optical depth (small). Yet these cloud properties have not been quantified. The high etage usually refers to clouds whose mean lower level is 6km or higher, although there is some latitudinal variation. Altitude, of course, is correlated with temperature in the troposphere, and a high cloud would be expected to be cold, perhaps even colder than the homogeneous nucleation temperature for water of -41 °C. Although cirrus are relatively transparent, no upper limit to the optical depth has yet been offered which has a physical basis. Sassen and Cho (1993) place the upper limit of 0.03 on optical depth for subvisual cirrus. 1.4. Ice as a Classification Indicator

In any scientific field, morphology is the first guide to classification. Such an approach is simple and obvious. But with later physical insight, morphology usually gives way, at least in part, to physical classifications. Were this not the case, then whales would still be called fish and planets would be classified as stars. We now know that a fundamental physical property of cirrus and certain other clouds is ice content. This suggests that ice may be a good basis for classification. The presence of ice, as opposed to water, has tremendous significance. It means that the temperature is probably well below freezing. If the temperature is below -41 °C, then homogeneous nucleation takes place and no liquid can exist. The vapor pressure of water over ice is so low compared to that over water that most vapor is locked up in the crystals, and even small vertical excursions may force the vapor far out of equilibrium with the particles, at least for a while. Ice crystals are usually much larger than water droplets and therefore have much larger fall velocities, a factor in determining cloud morphology and evolution. Crystal habit is determined by at least three parameters: temperature, humidity, and ventilation. Thus, the existence of ice in a cloud can and often is the dominating factor

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Table 1.3. Principle cloud types that can contain ice Cirrus

Cirrus clouds are composed of ice crystals.

Cirrostratus

Cirrostratus is composed mainly of ice crystals.

Cirroculumlus

Cirrocumulus is composed, almost exclusively, of ice crystals.

Stratus

Generally grey cloud layer with a fairly uniform base, which may give drizzle, ice prisms, or snow grains. Stratus does not produce halo phenomena, except possibly at very low temperatures.

Nimbostratus

Grey cloud layer, often dark, the appearance of which is rendered diffuse by more or less continuosly falling rain or snow . . .

Altocumulus

Altocumulus is, at least in the main, almost invariably composed of water droplets. At very low temperatures, however, ice crystals may form.

Cumulonimbus

At least part of its upper portion is usually smooth, or fibrous or striated, and nearly always flattened; this part often spreads out in the shape of an anvil or vast plume.

From the WMO International Cloud Atlas (1987).

in both the cloud's evolution and its interactions with its surroundings. Table 1.3 lists those clouds that are not classified as cirrus (or Cirrostratus or cirroculumlus) which can contain ice. From table 1.3, we see that 7 of the 10 cloud genera can contain ice or sometimes shows fibrous or striated morphologies which are suggestive of cirrus (and hence ice). Incus (anvil), the supplementary features of cumulonimbus, are made predominantly of ice. Virga is often made of ice and is a prominent component of uncinus. Although no one doubts that most stratus and nimbostratus clouds are entirely made of water, it is important to realize that most genera of clouds can contain ice. According to Huschke (1959 [1980]), all clouds types can contain ice: "Of the cloud genera, only Cirrostratus and cirrus are always ice-crystal clouds; cirrocumulus can also be mixed; and only cumulonimbus is always mixed. Altostratus nearly always is mixed, but can occasionally be ice crystal. All the rest of the genera are usually water clouds, occasionally mixed: altocumulus, cumulus, nimbostratus and stratocumulus." We therefore recognize that a cloud classification could be devised and formalized based solely on ice content. Such an approach might help unify research and cross-link work in different fields concerned with ice: nucleation, crystallography, remote sensing, spectroscopy, and planetary physics. The WMO has already recognized classification by height, a scheme that crosses over morphological boundaries. In support of such a grouping, it may be valuable to perform a modern, visible, and infrared (10 um window) imaging study coupled to a polarization lidar-based survey of all clouds that are cold enough for ice to form. The survey would include simultaneous optical and infrared imagery. Such a survey would produce polarization images of clouds that would unequivocally identify ice in the clouds, measure the temperature distribution, and provide the visual observer with clues as to the state of the water. In effect, the survey could produce water-phase images of the outer layers of clouds.

History and Definition 9

1.5. Summary and Conclusions

All cirrus clouds are composed of ice, but not all ice clouds are cirrus. This is a consequence of the WMO's classification scheme, which is based on morphology rather than on physical content or dynamics. Current classifications do not include subvisual cirrus or contrail cirrus. Developing a subclassification based on ice content could prove useful. Acknowledgments I thank Kenneth Sassen for many discussions concerning the nature of cirrus and ice. This work was supported by The Aerospace Corporation's Independent Research and Development Program. References Abercromby, R., 1887. "Suggestions for an international nomenclature of clouds," Quarterly Journal of the Royal Meteorological Society, vol 13, London, pp. 154-166. Appleman, H.S., 1961. Occurrence and forecasting of cirrostratus clouds. World Meteorological Organization Technical Note No. 40. WMO, Geneva. Barnes, A.A., 1980. Observations of ice particles in clear air, /. Rech. Atmos., 14(3-4), 311-315. Barnes, A.A., 1982. "The cirrus and sub-visible cirrus background," AFGL-TR-82-0193, Hanscomb Air Force Base, MA. Berlin, P., 1988. The Geostationary Applications Satellite. Cambridge Aerospace Series. Cambridge University Press, Cambridge, MA. Descartes, R., 1637. Discours de la Method ... I Doptrique, II Geometrie, III Meteores. Dowling, D.R., and L.F. Radke, 1990. A summary of the physical properties of cirrus clouds, /. Appl Met., 29, 970-978. Fiocco, G., and G. Grams, 1964. Observations of the aerosol layer at 20km by optical radar, /. Atmos. Sci., 21,323. Gershenson, D.E., and DA. Greenberg, 1964. Anaxagoras and the Birth of Scientific Method. Blaisdell Publishing Co., New York. Greenler, R., 1980. Rainbows, Haloes and Glories. Cambridge University Press, Cambridge. Heymsfield, A.J., 1986. Ice particles observed in a cirriform cloud at -83°C and implications for polar stratospheric clouds. /. Atmos. Sci., 43, 851-855. Hildebrandsson, H., 1879. "Sur la classification des nuages employee a 1'Observatoire Meteorologique d'Upsala," Upsala, Sweden, p. 9. Hildebrandsson, H., 1887. "Remarks conserning the nomenclature of clouds for ordinary use." Quarterly Journal of the Royal Meteorological Society, vol 13, London, pp. 140-146. Hildebrandsson, H., Riggenbach, A. et Teisserenc de Bort, L., 1896 [1910]. "Atlas International des Nuages", Paris. Howard, L., 1803. On the Modification of Clouds, and on the Principles of Their Production, Suspension and Destruction. Philisophical Magazine, J. Taylor, London. [Reprinted in Neudrucke von Schriften und Karten iiber Meteorologie und Erdmagnetismus, Tome III, Berlin, 1894 p. 6.] Huschke, R.E., 1959 [1980]. Glossary of Meteorology. American Meteorological Society Press, Boston, MA.

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Lamarck, J.B., 1802. Sur la forme des nuages. In Annuaire Meteorologique pour 1'an XI de la Republic Francois, Paris, no. 3, pp. 149-164. Ligda, M.G.H., 1963. Proceedings of the First Conference on Laser Technology, U.S. Navy Office of Naval Research, Washington, D.C., pp. 63-72. Lynch, D.K., 1993. Subvisual cirrus: what it is and where you find it. In Proceedings of Passive Infrared Remote Sensing of Clouds and the Atmosphere (D.K. Lynch, ed.). SPIE Conference 1934, Bellingham, WA, pp. 264-274. Maiman,T.H., 1960. Stimulated optical emission in ruby, Nature, 187,493^494. Marriotte, E., 1681. De la Nature des Couleurs, Paris. Middleton, W.E.K., 1966. A History of the Thermometer and Its Uses in Meteorology. The Johns Hopkins Press, Baltimore, MD. Olscamp, P.J., 1965. Discourse on Method, Optics, Geometry and Meteorology. The BobbsMerrill Company, Indianapolis, IN. Pernter, J.J., and P.M. Exner, 1910. Meteorologische Optik. Wilhelm Braumuller, Wein. Renou, E., 1855. Insrtuctions Meteorologiques. In Annuaire de la Societe Meteorologique de France, Tome 3, Paris, pp. 142-146. Rossow, W.B., and L.C. Gardner, 1993. "Cloud detection using satellite measurements of infrared and visible radiances for ISCCP," /. Climate, 6,2370-2393. Sassen, K., and B.S. Cho, 1992. Subvisual-thin cirrus lidar dataset for satellite verification and climatological research. /. Appl. Meterol, 31,1275-1285. Sassen, K., M.K. Griffin, and G.C. Dodd, 1989. Optical scattering and microphysical properties of subvisual cirrus clouds, and climatic implications, /. Appl. Met., 28, 91-98. Schiffer, R.A., and W.B. Rossow, 1983. The international satellite cloud climatology project (ISCCP): The first project of the World Climate Research program, Bull. Amer. Meteor. Soc., 64, 779-784. Schmidt, E.O., and D.K. Lynch, 1995. Subvisual cirrus: associations to the dynamic atmosphere and radiative effects. In European Symposium on Satellite Remote Sensing II, Proceedings of Passive Infrared Remote Sensing of Clouds and the Atmosphere III, SPIE 2578 (D. Lynch, ed.). Sept. 25-28, Paris, pp. 68-75. Stone, R.G., 1956. A Compendium on Cirrus and Cirrus Forecasting. AWS TR 105-130, Air Weather Service, Scott Air Force Base, IL. Tape, W, 1994. Atmospheric Halos. Antarctic Research Series, vol. 64. American Geophysical Union. Washington, D.C. Tricker, R.A.R., 1970. Introduction to Meteorological Optics. Mills and Boon, London. Uthe, E., and P.B. Russell, 1977. Lidar observations of tropical high altitude cirrus clouds. In Proceedings of the IAMAP Symposium on Radiation in the Atmosphere, GarmischPartenkirchen, Science Press, pp. 242-244. Vaeth, J.G., 1965. Weather Eyes in Sky: America's Meteorological Satellites. Ronald Press. Venturi, G.B., 1794. "Indagine fisica sui colori (Modena)," Soc. Ital. Mem. VIII, 699-754. World Meteorological Organization (WMO), 1975 [1995]. International Cloud Atlas, vol. I, Manual on the Observation of Clouds and Other Meteors. WMO, Geneva. World Meteorological Organization (WMO), 1987. International Cloud Atlas, vol. II, Plates. WMO no. 407, Geneva. Young, T, 1802. An account of some cases of the production of colours, not hitherto described, Phil. Trans. Roy. Soc., 92,378-397.

2

Cirrus Clouds A Modern Perspective

K E N N E T H SASSEN

2.1. Growing Importance of Cirrus Research

It is now understood that the cirrus clouds inhabiting the upper troposphere play a significant role in regulating the radiation balance of the earth-atmosphere system and so must be recognized as a crucial component in solving the humaninduced climate change puzzle (Liou 1986). Because of their high altitudes, these cold, ice-dominated clouds act as a thermal blanket by trapping the outgoing terrestrial (infrared) radiation, but, at the same time, they can be effective at reflecting the incoming solar radiation back out to space. The balance between these two radiative processes, the greenhouse and albedo effects, respectively, determines the net impact of cirrus on our climate system. Which process dominates appears to be quite sensitive to the cloud microphysical and macrophysical properties (e.g., see Stephans et al. 1990). These properties in turn depend on the weather processes that generate cirrus, a function of geographic location, thereby complicating the global view. Of current concern is comprehending how cirrus clouds will respond, or feedback, to the effects of global warming caused by the buildup of carbon dioxide and other greenhouse gases. Would the changing atmosphere produce alterations in cirrus clouds that reinforce, or act to negate, the theoretically predicted global warming surmised from fundamental physics? One must also ask whether increasing jet aircraft traffic is creating more cirrus cloud cover, and if this traffic and agricultural activities are increasing the transport of dust and smoke particles into the upper troposphere and affecting, in a radiatively important sense, those cirrus formed naturally. Settling these issues could be pivotal to making difficult decisions on the future use of the Earth's resources.

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Cirrus

Fortunately, a new generation of meteorological instrumentation has become available. The need for these new measurement capabilities has helped to spawn and adapt instrumentation for cirrus research. Sophisticated cloud measurement capabilities using in situ probes on jet aircraft, satellite multispectral imaging, and remote sensing with lidar, short-wavelength radar, and passive radiometers, have all greatly facilitated cirrus cloud research. Major advancements have also been made in the field of numerical cloud modeling. As will be reviewed briefly here and in depth in following chapters, these developments have significantly advanced our knowledge of the characteristic properties of cirrus clouds over the past few decades. Chapter 1 of this book gave the historical view of our understanding of cirrus clouds. Here in chapter 2, the emphasis is on what can be revealed about the basic nature of cirrus clouds using modern instrumentation, as illustrated by findings from the ground-based remote sensors at the Facility for Atmospheric Remote Sensing (PARS). In these introductory chapters we are attempting to provide a working definition for what are and are not cirrus clouds, based on the traditional view, but with some input from modern research to refine our knowledge. As pointed out by Sassen and Krueger (1993), modern remote sensors can be relied on to provide incredibly detailed information on clouds to supplement visual inspection. At the same time, although defining cirrus may seem straightforward to any trained professional weather observer, today clouds are viewed from aircraft and satellites and probed with laser and radar beams in portions of the electromagnetic spectrum that are far beyond the capacity of the human eye. This sophistication may present certain difficulties. This is not to say that remote probing techniques should not be used to identify and characterize cirrus clouds—such techniques are critically important due to the remoteness of cirrus—but we must first learn how our modern instruments respond to this class of clouds. We consider it vital for modern climate research that a consistent terminology for cirrus clouds be adopted to facilitate intercomparison of ground-based visual, remote sensing, in situ, and satellite top-of-atmosphere measurements. To end this introduction and begin a modern examination of cirrus clouds, I provide in figure 2.1 a typical image of a mid-latitude cirrus cloud, variety cirrostratus fibratus, drawn at random from the extensive record of lidar height-time displays to be discussed here. The data were collected using a vertically pointing lidar on the afternoon of May 15, 1992, as the cirrus clouds advected over our field site in Salt Lake City, Utah. I will return to this image several times.

2.2. Modern Cirrus Research: Capabilities and Limitations The recent advances in cirrus cloud research capabilities have included aircraft probes, ground-based (and airborne) active remote sensing using lidar and radar, and passive radiometric probing, either from Earth-orbiting satellites or from the ground as part of multiple active/passive remote sensor techniques. The major breakthroughs occurred during the 1960s, which saw the launching of the first weather satellite, the use of more sophisticated cloud radars, and the invention

Figure 2.1. A typical lidar returned energy display of the troposphere on May 15, 1992, when cirrus clouds were observed at PARS over Salt Lake City, Utah. Note the stratification in aerosol backscattering with height and consider the clouds that form in these regimes—low-level cumulus, mid-level altocumulus, and high-level cirrus clouds.

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Cirrus

of the laser. Although these technologies are still evolving, it must be recognized that each method has its advantages and disadvantages. Because these instruments are being increasingly relied on to improve our knowledge of cirrus clouds, it is important to consider what these techniques actually measure. In situ instruments have come a long way since the pioneering cirrus cloud studies were carried out over World War II Germany in Luftewaffer fighter planes, amid growing concerns over the military consequences of contrail formation (Weickmann 1947). By the early 1970s laser-based probes with sophisticated electronic processors were developed to facilitate analysis of cirrus cloud content (Knollenberg 1976). These Particle Measurement System probes are now widely used to determine the ice crystal size-distribution for particles ranging from about 25 to 4000 urn maximum dimension. Another device based on the forward-scattering spectrometer principle has shown utility in sampling relatively minute ice particles as small as a few microns in diameter, but only under limited conditions (Gayet et al. 1996). However, these probes cannot generally determine the three-dimensional shape and mass of the particles. The direct sampling of cirrus ice crystals on treated substrates for later microscopic examination has certain advantages in determining particle shape and density and has been popular since the mid-1940s (Arnott et al. 1994; Sassen et al. 1994,1995,1998). These devices have not been widely used, though, because methods to electronically analyze the data in the laboratory are still in their infancy. The main drawbacks of existing instrumentation are their inability to effectively characterize the small (< 200 |im) crystal component and to directly measure ice water content and important optical parameters. Aircraft operations also inherently suffer from limited spatial coverage and limited instrument sampling volumes. Nonetheless, summaries of cirrus cloud microphysical properties derived from aircraft research can be found in Heymsfield and Platt (1984), Liou (1986), and Dowling and Radke (1990), and a number of new devices have recently appeared that attempt to tackle the current limitations. Chapter 4 provides a review of aircraft cirrus research. The ability to view cloud formations from outer space can be traced back to the polar-orbiting Television and Infared Observations Satellite (TIROS-I), launched in 1960, and the Geostationary Operational Environmental Satellite (GOES) series, first launched in 1974. Even these early satellites took advantage of visible and thermal infrared measurements, and such multispectral techniques are becoming more sophisticated as additional bands, and increased resolutions, are incorporated into the suite of orbiting sensors (Rossow and Garder 1993). Most prominent is the Advanced Very High Resolution Radiometer (AVHRR), as well as the new generations of radiometers to be flown on the Earth Observation Satellites (EOS). Attempts to identify and characterize cirrus cloud properties are based on increasingly advanced algorithms that exploit differences in measured multispectral radiances, as predicted by radiative transfer models. Essentially, the methods attempt to identify cirrus as appropriately high, cold, and optically thin clouds by relating solar and terrestrial radiances (see chapter 7). It is well known that cirrus clouds present unique challenges to satellite researchers. Among the weaknesses in satellite cirrus cloud retrieval are prop-

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erly accounting for the effects of cloud fraction and spatial inhomogeneities; characterizing the background (i.e., due to surface, clear sky and/or lower cloud) radiances; understanding nonspherical ice-particle scattering behavior (and their variations with size and habit); problems inherent in inferring cloud optical depth; and maintaining accurate instrument calibrations (Minnis 1998). Most fundamental are the questions of how many cirrus clouds go undetected because they are too thin, and how many cold and high clouds are characterized as cirrus even though the clouds are the tops of deep cloud systems such as altostratus or cumulonimbus. Recalling the traditional definition of cirrus based on their visual appearance from the ground, it can be appreciated that new problems are created when cloud systems are viewed by cameras from the top. Lidars and millimeter-wave radars have also reshaped the remote sensing landscape. Lidars were applied to the study of cirrus clouds not long after the invention of the laser (Schotland et al. 1971). Although weather radar has been popular since the post World War II period, it was only more recently that sufficient effort was given to improving the millimeter-wave radar technologies best suited for probing nonprecipitating clouds and cirrus (Pasqualucci et al. 1983), as a result of the wavelength Ar4 Rayleigh scattering law. As active remote sensors, lidar and radar provide accurate range resolution, down to the scale of meters and tens of meters, and come with a variety of techniques such as polarization diversity and Doppler velocity (see, e.g., Sassen et al. 1989a). By the time cirrus were recognized as worthy of a major field study, the 1986 First ISCCP (International Satellite Cloud Climatology Project) Regional Experiment Intensive Field Observation (FIRE IFO I) program in the central United States, it was clear that ground-based and airborne lidars and millimeter-wave radars were indispensable for studying the properties of cirrus clouds (Sassen et al. 1990). It is important to recognize that due to fundamental differences in the scattering of light and microwaves by hydrometeors of diameter d (i.e., the d2 Mie/geometric optics versus the d6 Rayleigh domains), lidars and radars sense quite different cloud properties (see chapter 8). Although lidar probing seems ideally suited for cirrus research because of the great sensitivity of laser light to all sizes of hydrometeors, and it can even detect subvisual cirrus from the ground (Sassen et al. 1989b; Sassen and Cho 1992) or from orbit (Winkler and Trepte 1998), the consequence of this sensitivity can be strong range-limiting optical attenuation. Fortunately, this is typically not a problem in penetrating cirrus with modern lidars, but the presence of most lower cloud layers is a barrier for lidar probing. Moreover, the basic uncertainties in interpreting the backscattered signal in simple lidars can be largely overcome with Raman or high spectral resolution lidar techniques, which use complementary spectroscopic data to derive quantitative optical coefficients. The polarization lidar technique is particularly well suited for sensing the composition of cirrus (Spinhirne et al. 1983, Sassen 1991, 2000b; Platt et al. 1998). Lidar linear depolarization ratios are inherently sensitive to ice-particle shape and orientation (Takano and Liou 1995), and the ability to discriminate cloud thermodynamic phase is unambiguous. The use of microwave radar in cirrus research is ultimately limited by the Rayleigh scattering response of small ice particles due to the d6 dependence (thus

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Cirrus

the push to improve the performance of W- and K-band radars at about 3 and 10mm wavelengths). Fortunately, even at millimeter wavelengths, attenuation in cirrus is small, and the non-Rayleigh effects from the largest particles present do not have a significant impact on the quantitative analysis of the returned signal using Rayleigh theory (Liao and Sassen 1994), the inherent advantage of radar studies. The basic problem remains, however, that where cirrus particle generation is taking place, or at extremely low temperatures, such as typically near cloud top, the small particles present impose perhaps insurmountable difficulties for radar detection (Sassen and Khvorostyanov 1998). Nonetheless, it is possible to accumulate large, climatologically representative data sets of cirrus cloud properties at high temporal and spatial resolutions using dedicated ground-based, remote sensing facilities such as the University of Utah PARS (Sassen 1997) and the Department of Energy Clouds and Radiation Testbed (CART) sites (Stokes and Schwartz 1994). Although the findings from such extended-time data sets are restricted to single locations, a number of geographically representative sites can be relied on to yield characterizations on a more global scale. At this time, extended ground-based cirrus cloud property data sets of various lengths have been reported from southern and northern Australia (Platt et al. 1987), the tropical western Pacific region (Platt et al. 1998), southern Japan (Imasu and Iwaska 1991), and the eastern Great Basin of the United States (Sassen and Cho 1992). By far the most comprehensive study is the 12+-year lidar measurement program from PARS, discussed below. Finally, the soundest approach to research cirrus is to synergistically combine as many remote sensor observations as possible. In addition to lidar and radar, it is often advantageous to use radiometers sensing in the visible, infrared, and microwave region. For example, the combined lidar and mid-infrared radiometer (LIRAD) method is useful not only to determine the cloud infrared emittance, but also to improve lidar optical depth assessment (Platt 1979; Platt et al. 1987,1998). The unitless emissitivy parameter e is used to characterize the grayness of an emitter with respect to a black body at the same temperature. Details of this and other cirrus remote-sensing methods are given in chapters 8 and 10. 2.3. Fundamental Cirrus Cloud Properties

The internationally accepted definitions for the family of cirrus clouds are at the foundation of our FARS research program and this chapter. As discussed in chapter 1, according to the World Meteorological Organization, the operational reporting of the low, middle, and high (i.e., cirrus) cloud categories is made by trained ground observers based on visual appearance. The only way of comprehending the morphological distinctions between the various species and varieties of the cloud genera is to study a cloud atlas book (e.g., WMO, 1975). Here I consider additional characterizations, based on cloud height, optical depth, thermodynamic phase, and formation mechanism. The rational scheme for discriminating between cloud types based on visual observations has been in practice for more than a century. As a corollary, the low,

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middle, and high cloud categories are divided (loosely) on ranges of cloud height (for a given latitude and season), and so by analogy on cloud phase. Although not all ice clouds are cirrus, a basic postulate is that despite the fact that some cirrus may contain patches of supercooled liquid water (SLW) clouds or even form with the aid of transient SLW (see 2.6), they are predominantly ice-phase clouds. Other types of ice clouds that occur in the polar boundary layer or stratosphere are not cirrus: they may at times closely resemble proper cirrus in terms of content or laser-scattering signature (Gobbi et al. 1998), but they have been assigned other designations. The altostratus cloud is also ice dominated and often results from deepening cirrostratus, but it is classified as a mid-level cloud because of its considerable depth and dark appearance. Low-level ice clouds derived from glaciated water clouds often generate exceptional optical displays in Arctic and Antarctic regions (see Greenler 1980; Tape 1994). In comparison, complex halo/arc displays are rarely observed in cirrus, although the common 22° halo and associated arcs are frequent at many mid-latitude locations. It has been pointed out (Sassen 1999) that cirrus halo frequency appears to be a function of geographic location, and thus of the regional weather conditions and the nature of the cloud-forming particles that generate the local cirrus. It is suggested, then, that one of the distinguishing features of cirrus is the background aerosol in the relatively clean upper troposphere, on which the cirrus ice crystals form and take shape. Note the vertical distribution of the weakly scattering aerosol component in figure 2.1. Portrayed are the relatively dense materials near the surface, where convection from solar heating is gradually raising aerosols up to approximately 4km above mean sea level (or -2.5 km above ground level at PARS), the height of the previous day's convective boundary layer. Above this lies a diffuse regime of more aged aerosols in the planetary boundary layer, extending to nearly 6 km, and above that is molecular-dominated scattering. Although this example may be unusually clear cut, the low, middle, and high cloud categories form and dwell in different temperature and aerosol regimes. Cirrus are ice-dominated clouds that by definition inhabit the upper troposphere, where it is so cold that cloud droplets are only transient and cannot be primarily responsible for cirrus generation. Thus, it is now accepted that the precursors to cloud droplets (i.e., minute haze particles composed of aqueous solutions), are involved in the production of cirrus. Because the height of the tropopause marking the top of the troposphere depends on latitude and season, the maximum heights of cirrus will similarly vary, but what of their minimum heights? Unfortunately, the seasonal variability of both the cirrus cloud top and base heights derived in PARS lidar data is so great that we cannot attempt to specify the minimum and maximum heights that distinguish the three main cloud categories. In other words, winter cirrus-cloud top heights can lie below the base heights of summertime middle level altocumulus clouds, so cloud identification criteria based strictly on height would be ambiguous. Although weather observer cloud-height reports are routinely made, it must be recognized that the heights are based on conventional estimations for cirrus clouds (in the absence of sufficiently powerful laser ceilometers), and so do not necessarily

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Cirrus

reflect the actual cloud base heights or the ceiling altitudes of importance to aviation. Another component used in identifying middle and high clouds is color or cloud transparency. The terms "translucidous" and "opaquis" are applied to layers through which the blue sky color can and cannot be seen by a ground observer, respectively. As a cirrostratus cloud gradually thickens from thin to opaque in response to developing weather patterns, they often evolve into altostratus clouds. Such mid-level clouds are operationally distinguished from cirrus by the visual loss of sharpness (or disappearance) of the solar (or lunar) disk, accompanied by descending cloud base heights. These useful distinctions have been related to approximate ranges in lidar-derived cloud optical thickness t. Characteristic T limits for subvisual cirrus, a category that obviously had to await the introduction of lidar, the thin-to-opaque cirrus change, and the cirrostratus/altostratus transition are shown in table 2.1. The backscattered signals from powerful laser beams become completely attenuated in ice clouds when T exceeds about 3.0 using anolog photodetectors (Kinne et al. 1992), which corresponds to the point where the sun visually becomes dim and irregular (Sassen and Cho 1992). This upper limit in i for cirrostratus, however, may not always hold for some varieties of cirrus. The chief problem is related to optically thick but spatially limited portions of cirrus layers, especially in cirrus derived from deep convection. In surface weather reports, a cumulonimbus cloud with spreading anvil is listed only in the low cloud category as long as the associated clouds are clearly a part of the thunderstorm. An obvious gray area arises as the cumulonimbus further develops and eventually decays, for at some point the anvil may spread significantly and become detached from the originating turrets, at which time it is appropriate to designate the remnants of the anvil as some variety of cirrus. Once the low and middle portions of the decaying cumulonimbus have eroded away in the precipitation process, the remaining high cloud is referred to as cirrus spissatus. So, at some point the maintenance of the cirrus initially generated by deep convection is no longer dominated by the effects of strong updrafts (although the injection of boundary layer moisture and aerosols may have lasting effects), and this should be used as the working definition for the cirrus derived from anvils. Unfortunately, it is often difficult to judge this turning point from surface observations. The classic picture of an isolated spissatus derived from a thunderstorm, however, often contains a central ice fallstreak that is relatively dense and could obscure the sun. Thus, in the case of cirrus spissatus, the tradiTable 2. 1 . Cirrus cloud categories and approximate optical depths based on cloud transparency and color Category Subvisual Thin Opaque Altostratus

T range <0.03 0.03-0.3 0.3-3.0 >3.0

Description Invisible against the blue sky Translucent, retains a bluish color Usually appears white Disk of sun becomes indistinct

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tional cloud identification implies that a portion of the cloud mass could exceed the T limit derived for the cirrostratus/altostratus transition. Given that cirrus cloud type identification and species refinement can be aided by knowledge of the cloud-generating mechanism, cloud genesis is also important to shed light on fundamental cloud properties. Principally, these properties, such as cloud layer thickness and structure and ice particle number size distribution, will depend on the magnitude of the updraft velocity and the temperature in the generating region, as constrained by the action of the adiabatic and nucleation processes. Obviously, cloud content has a large impact on their radiative and climatic properties. To help understand the nature of cirrus cloud varieties, table 2.2 provides a breakdown of cirrus cloud-generating mechanisms into one human-made and four basic natural categories. The aircraft-induced cirrus category involves the initial rapid formation of a condensation trail (contrail) from aircraft-supplied moisture and nuclei (likely sulfur-based haze particles, which freeze homogeneously during the mixing process), typically resulting in the creation of high numbers of minute ice crystals (Sassen 1997). Subsequent development into cirrostratus can occur under some ambient conditions as a result of contrail-spreading processes, until the layer can no longer be distinguished from natural cirrus as observed from the ground or satellites. Note, however, that it is unknown how long the contrail-cirrus cloud composition will remain distinct because of the extra cloud-particle-forming nuclei introduced by jet engines. Of the four additional cirrus cloud-generating mechanisms in table 2.2, both the orographic and thunderstorm cases can involve ice formation in relatively strong updrafts of a few meters per second or more, which tends to increase ice particle concentrations according to model studies (e.g., Jensen et al. 1994). Ice nucleation from highly supercooled cloud droplets is also possible at certain temperatures. As in the case for contrail-cirrus, anvil cirrus in the maintenance stage should remain affected by the "foreign" nuclei lifted essentially from the boundary layer. (They are foreign in the sense that convectively-raised aerosols may normally represent a portion of the background aerosol in the upper troposphere, but depending on season and latitude, other nuclei derived from the stratosphere, for example, may be more numerous.) The synoptic cirrus category is a catch-all for the usual varieties of cirrus clouds that form in situ in the upper troposphere in response to weather disturbances. Updraft speeds can range

Table 2.2. Breakdown of cirrus clouds by generating mechanism Category

Mechanism

Synoptic (jet stream, frontal, etc.) Injection cirrus Mountain-wave updraft Cold trap Contrail-cirrus

Top-down generation Thunderstorm anvil Orographic, terrain-induced Tropopause-topped thin layer Rapid cooling of aircraft exhausts

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Cirrus

widely from the centimeter per second scale typical of gradual uplift (i.e., frontal overriding) to the meter per second scale of the single convective uncinus cell. Models show that such cirrus typically form from the top (where particle generation occurs) down, due to the strength of the particle sedimentation process (Starr and Cox 1985; Khvorostyanov and Sassen 1998). The particle precipitation and evaporation processes can destabilize regions of the atmosphere, however, contributing to additional cirrus cloud development below the original generating layer. The final category of tropical thin-to-subvisual tropopause cirrus has only been recently recognized. Their large spatial extent has been illustrated by spaceborne lidar measurements (Winker and Trepte 1998). We refer to such clouds as "cold trap" cirrus in view of their quintessential properties: they occur under uniquely cold (-70° to -90°C) and high (15-20 km) conditions, which are rarely encountered outside the tropics. These tenuous layers appear to be composed of relatively small ice crystals (Heymsfield 1986) and may be maintained by moisture supplied by deep convection. 2.4. Cirrus Cloud Characterization from PARS: A Modern Conception

To help improve our understanding of cirrus cloud properties, their connection to weather, and provide graphic illustrations of their structures, I draw here from the results of a 12+-year cirrus cloud study using lidar and other remote sensors from PARS (see Sassen 1997). PARS is a unique university-based research station located at 40°49'00" N, 111°49'38" E on the bench of the Wasatch Mountains (1.52km mean sea level), overlooking Salt Lake City, Utah. Since 1987 PARS has housed the ruby cloud polarization lidar (CPL) and a growing number of remote sensors, including a suite of visible, infrared, and microwave radiometers, all-sky imagery, a 3.2-mm polarimetric Doppler radar, and the dualwavelength scanning polarization diversity lidar (PDL). All the active remote sensors use polarization diversity to enhance the information content of the backscattered signals. For the purpose of the cirrus climatology described below, we rely mainly on data collected by the "turnkey" CPL system, which consists of a high-power (1.5 J per pulse) ruby (0.694 jam) laser with a low pulse repetition frequency (PRF) of 0.1 Hz and a recorded range resolution of 7.5m. The CPL generates a manageable amount of digitized data, which facilitates the management of an extended data set, but its sensitivity is sufficient to treat each pulse as independent. In comparison, the PDL is truly a high-resolution device: it can record the four polarization channels (at the 0.532 and 1.06 urn wavelengths) at a maximum resolution of 1.5m and a PRF of 10 Hz (Sassen 1994). Since its inception, PARS has been applied to the regular study of cirrus clouds in support of basic research and the satellite validation effort of the FIRE extended-time observation program (Schiffer and Rossow 1983). Currently in its 12th year, the PARS cirrus cloud data record is unique in that it is both long term and sufficiently large to be considered statistically significant on a monthly level. As of March 1997 (the cutoff for the current climatological analysis), more than

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2200 h of ruby lidar data had been collected. PARS data collection goals emphasized the afternoon and evening hours corresponding to local National Oceanic and Atmospheric Administration polar orbiting satellite overpasses and hourly GOES imagery. Normally, the goal of collecting 20 h of PARS data per month was achieved, typically in 1- to 3-h periods. Note that for the special study described in section 2.4.2, a cirrus data period is defined as a 10-min average of cloud layer properties obtained from 0-10 min past the hour within ±3h of the 0000 UTC Salt Lake City sounding, in order to ensure representative atmospheric state data. It is clear from the preceding discussion that the basic criteria long relied on to identify cirrus clouds is their visual appearance: texture, color, spatial extent and variability, apparent phase, and optical depth. Thus, PARS cloud categorization has been consistently accomplished through visual inspection by an observer trained by the National Weather Service (then the Weather Bureau) as a Meteorological Technician. Importantly, no a priori constraints involving cloud height or temperature, or such other factors as lidar or radar signal intensity ranges, are used at PARS to define cirrus. However, the ability of polarization lidar to provide extra information (e.g., cloud phase and height) is exploited to corroborate the initial categorization, particularly at night. 2.4.1. Cirrus Cloud Case Studies Here I provide remote sensing displays of the typical structures and laser depolarizing properties of the principal cirrus cloud types studied at our midlatitude location—cirrus fibratus, cirrostratus, cirrocumulus, and cirrus spissatus—also illustrated are high-resolution views of frequent substructures such as "mares tails" and cirrus mammatta. To give a pictorial view of these cirrus case studies, plate 2.1 includes 180° fisheye photographs obtained during daylight observations at PARS. (Note: All plates can be found in the appendix which begins on p. 457) Each subsequent plate shows zenith-pointing lidar height-versus-time displays of attenuated backscattering (in relative units based on a logarithmic gray scale) and linear depolarization ratios (5, using the color scale at bottom right of plate), along with the closest radiosonde temperature and dewpoint profiles. Note that the cloud structure depicted in the returned laser power displays are not equivalent to snapshots of the entire cirrus cloud field because of the temporal alterations that occur in the clouds as they advect over the lidar. However, the resultant changes in individual cirrus structures are probably not major: generally speaking, cirrus cloud elements develop more slowly than they advect in the relatively rapid transport of the upper troposphere. As for the interpretation of the 8 value displays, this is a complex issue, facets of which I attempt to illuminate below. Reviews of this topic are given in Sassen (1991, 2000); it must suffice to say here that ice clouds generate a wide variety of 8 values that depend explicitly on ice-particle shape and orientation: polarization lidar studies indicate that cirrus produce 8 > 0.3, up to approximately 0.7, although much lower values are possible when oriented plate crystals are probed in the zenith direction. A trend that is becoming increasingly apparent, however, is that laser backscatter depolarization increases with decreasing cloud

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Cirrus

temperature, and so indicates that ice crystal shape is in some manner fundamentally dependent on temperature. It has long been known that a fundamental generating structure is the ubiquitous cirrus uncinus cell (Ludlam 1956;Harimaya 1968;Heymsfield 1975). Cirrus uncinus display a relatively dense generating cell "head" and a "tail" of precipitating ice crystals, often referred to as "mares tails" because of their plumelike appearance. (They equally resemble the barnacle appendage "cirrus", the biological source term for this cloud genera.) The width of the uncinus cell head is on the order of 1.0km (Heymsfield 1975; Sassen et al. 1989b). However, individual uncinus cells can be composed of groups of much smaller (~100m) sporadic updrafts, and they can also be assembled into mesoscale uncinus complexes (MUC) with dimensions of tens to hundreds of kilometers. The necessary condition for uncinus development should involve some slight instability in the atmospheric profile, which spawns convection and updrafts up to about 1ms"1. However, a convective appearance to cirrus cloud-top is often detected by lidar (see fig. 2.1 and below) without indications of instability, so cloud-scale convective processes may be more important in cirrus clouds than soundings would predict. This progression, from the scale of the mares tail to the synoptic arc of prefrontal cirrus clearly visible from satellites, is portrayed in the following figures and plates. Figure 2.2 is the high-resolution PDL view of a relatively narrow cirrus layer embedded in a 4-km deep jet-stream cirrus (Sassen et al. 1995), which consists of a series of uncinus cell heads generating a layer of sheared fallstreaks. The height and time coordinates have been adjusted using the wind speed to yield a 1:1 correspondence in height and distance (time is shown). Although the cell heads are 0.5-1.Okm across, at this resolution they can be seen to be composed of smaller substructures, each of which produces a thin fallstreak that combine to define (i.e., at coarser resolution) the main solid cirrus layer. Plates 2.2-2.4 depict the progression in the development of cirrus fibratus, cirrostratus, and cirrus spissatus from the apparent action of cirrus uncinus as

Figure 2.2. A high resolution (6m by O.ls) gray-scale display of 0.532 urn polarization diversity lidar backscattering (in arbitrary units) revealing the structure of a cirrus layer created by complexes of cirrus uncinus cells. Data were collected on December 5,1991 during the FIRE IFO II at Coffeeville, Kansas.

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observed at FARS. Plates 2.la and 2.2 show a classic fibratus case. Even at the 0.1 Hz temporal resolution, there is evidence for convective cell-generating structures present at the top of the fibratus streaks with massive tails of sheared particle fallstreaks below. The zenith lidar depolarization data indicate that a wide range of particle shapes and orientations were present, including the quite low (8 < 0.05) values typical of horizontally oriented plate crystals. Plate 2.3 represents the transition from a cirrostratus overcast to a series of serrated cirrus fibratus masses. Here, particularly at the right, the concept of the MUC is well portrayed, with each cloud-top generating region producing a sheared mesoscale fallstreak. As is typical for cirrus clouds, note the tendency for the highest depolarizations to occur near cloud top, with decreasing values (at warmer temperatures) below. Also note the three embedded aircraft contrails at an altitude of about 12km revealed by the strongly scattering streaks near the beginning of the period, and the cirrus cloud mammatta-like structures at cloud base from 0140 to 0210 UTC, which, as examined in more detail below, are not uncommon in deep cirrus clouds. Plate 2.4 further develops this scenario from CPL data in cirrus fibratus, in this case showing the periodic production of optically dense ice particle fallstreaks from cloud-top mesoscale generating structures. The apparent decreases in lidar cloud top heights at 1905,1925, and 2005 UTC were probably caused by strong optical attenuation, and these cloud elements were visually identified as cirrus spissatus (plate 2.1b). This example also shows the characteristic depolarization increase with height, and the presence of cirrus mammatta near the end of the period. Figure 2.3 is a high-resolution PDL returned power display of a particularly intense mammatta protruding from the base of a dense cirrus fibratus cloud. This unusual image represents a cross-section of a mammatta that apparently passed directly above the lidar, and which produced such strong optical attenuation that the lidar penetration depth was momentarily restricted to about 0.5 km in the 4.0-km deep spissatus layer. Note the depiction of various scales of turbulent eddies during its downward penetration into dry subcloud air. Plate 2.5 is a CPL image of the development of cirrus spissatus from a cirrostratus layer, which may have been derived from a distant thunderstorm anvil (see plate 2.1c). This case depicts a number of additional, common cirrus cloud structural properties, including a fetch of wave motions embedded at cloud top and base at the beginning of the period, and the range-limiting attenuation generated by the major precipitation streak around 2230 UTC, which was successful at moisturizing the subcloud environment and establishing a new lower cirrus layer (see also Sassen et al. 1990,1995,1998). The depolarization record is particularly diverse showing 5-value variations in association with the cloud wave motions, unusually high 8-values in portions of the anvil, and 8-values < 0.05 in the lower cirrus from oriented ice plates. Plates 2.6 and 2.7 ilustrate proper cirrostratus cloud conditions. Plate 2.6 depicts a rather extreme example of how vertically pointing lidar 8-values respond to cloud regions containing randomly and horizontally oriented ice plates. Note the strongly scattering and low-depolarizing cloud streaks in this thin, 22° halo-producing cirrostratus layer (see fisheye in plate 2.1d). Several contrails are at times present near the cloud top height. Plates 2.1e and 2.7 show a

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Cirrus

Figure 2.3. A very high resolution (1.5m by O.ls) polarization diversity lidar display of a vigorous cirrus spissatus mammatta probed on April 21,1996 from the DOE CART site near Lament, Oklahoma.

classic cold mid-latitude cirrostratus derived from the advection of subtropical moisture, whose cloud tops extended into the bottom of the stratosphere. This cloud generated frequent solar corona, indicative of 10-30 um effective diameter ice particles (Sassen et al. 1998). Also note the relatively strong 5-values in this cold cirrus and the strongly scattering laminae within the cloud. As for cirrocumulus, after many years of PARS cirrus cloud observations, our group has concluded that the classic small-celled cloud depicted in cloud atlases does not apply to ice-phase cirrus clouds. Rather, when such cirrocumulus clouds are probed by polarization lidar, they invariably turn out to be unusually high-altitude altocumulus composed primarily of supercooled cloud droplets. Thus, although some cirrus layers have an obvious cellular appearance, particularly in contrails, orographic, and anvil cirrus, the classic ice-phase analog of the attractive array of cells covering the sky with dimensions of 1° (the approximate diameter of the sun or moon) do not appear to exist, at least not at our midlatitude location. Figure 2.4 is a high-resolution PDL returned energy display of a 1-h-old contrail, or group of contrails, studied during the SUCCESS field campaign in Oklahoma (Sassen and Hsueh 1998), which resembles cirrocumulus. However, such cellular structures are so common in contrails that they may be more a result of frozen contrail formation processes than atmospheric instability effects. An example of a typical, relatively wide-cellular cirrus that can be referred to as cirrocumulus is given in plate 2.8 for a PDL case study of an orographic cirrus wave cloud. Embedded within the complexly structured wave cloud are several

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Figure 2.4. High resolution image of spreading contrails, resembling cirrocumulus, and natural cirrus probed in the 1.06 urn polarization diversity lidar channel at the CART site on May 2,1996.

layers showing pronounced cellularity, which often gave this cloud the appearance of cirrocumulus (see corresponding fisheye in plate 2.1f).The expanded view of one of these regions given in figure 2.5 takes advantage of the high-resolution (10 Hz by 1.5m) lidar capabilities, revealing the detailed structures of the elements. 2.4.2. Cirrus Cloud Statistical Properties Provided in table 2.3 are the seasonal and yearly (total) averages of a number of cirrus cloud properties characteristic of the PARS location on the eastern edge of the Great Basin. The method for determining the statistics for the cirrus cloud base and cloud top heights is based on the envelope method, in which either the top and bottom of a single layer or the top of the highest layer and base of the lowest cirrus layer are used. Also included in table 2.3 are the average cirrus layer thickness when multiple layers are present and the average thickness of all combined single and multiple layers. These distinctions result from the propensity of some cirrus systems to form and maintain multiple cloud layers (i.e., using the criterion of a >0.5-km gap in lidar signals), although it must be recognized that in many instances a single 10-min observation period may yield multiple layers that merely represent breaks in a vertically continuous layer that are due to the effects of wind shear on fallstreaks. This sample also uses only those cirrus that did not appear to be affected by a loss of cloud-top signals due to rangelimiting laser attenuation in dense cirrus or, more commonly, the limited (8bit) dynamic range of the detector package in the presence of a strongly backscattering layer. The data in table 2.3 represent the most comprehensive examination of cirrus cloud properties ever assembled from a particular location using modern remote sensors. In addition to the atmospheric parameters characterized, supplemental information on the prevailing cirrus all-sky coverage and the visual appearance of the cirrus in the zenith are included. Note that the visual appearance

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Table 2.3. Seasonal and yearly averages of various cirrus cloud properties derived from the 10-year PARS data set

Cloud base Height (km) Pressure (mb) Temperature (°C) Wind direction (°) Wind speed (m/s) Cloud top Height (km) Pressure (mb) Temperature (°C) Wind direction (°) Wind speed (m/s) Cloud thickness (km) Layer envelope Multiple layer All cases Sky coverage (%) Overcast Broken Scattered Visual appearance (%) Opaque Thin Very thin

Jan-Mar

Apr-Jun

Jul-Sep

Oct-Dec

Total

8.40 353.4 -38.9 288.7 17.9

8.89 329.9 -38.4 272.5 16.0

9.10 326.9 -32.6 252.2 13.9

8.89 332.0 -39.0 281.8 18.8

8.79 336.3 -37.4 276.3 16.4

10.71 248.2 -55.8 285.0 23.9

11.14 235.1 -55.3 270.8 19.8

11.12 243.5 -47.6 252.9 17.0

11.15 233.9 -55.9 284.9 21.3

11.02 240.2 -53.9 275.7 20.2

2.31 1.32 1.93

2.25 1.13 1.72

2.02 1.17 1.60

2.26 1.38 1.91

2.23 1.24 1.81

75.7 19.4 4.9

63.9 30.8 5.0

40.5 49.4 10.1

69.2 22.6 4.8

64.9 29.0 6.0

42.7 39.9 17.2

54.3 28.9 17.7

59.8 33.8 6.4

41.6 38.0 20.5

48.2 35.4 16.4

For sky coverage, overcast applies to >90%, broken to 50-90%, and scattered to 10-50% cirrus cloud coverage.

Figure 2.5. Expanded polarization diversity lidar view of a cellular orographic cirrus layer (see plate 2.8) studied at PARS.

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Figure 2.6. Comparison of monthly-averaged PARS cirrus cloud base and top heights (circles), compared with Salt Lake City tropopause heights averaged for all days and those in the cirrus sample (open and solid squares).

categories are analogous to those in table 2.1, except a combined very thin to subvisual group (with i < -0.05) is used. In this sample the opaque and thin-tovery-thin cloud categories are about equally divided. This is a significant finding, because if some satellite measurements, for example, cannot detect "thin" cirrus with i < 0.3 (Minnis 1998), then one-half of regional cirrus clouds would go undetected. This is obviously an area that deserves more careful study, particularly in view of the enhanced capabilities of the next generation of satellite probes. However, it is not the mean yearly or even seasonal properties that provide the most important information defining cirrus, but rather their variability on shorter time scales: the PARS high cloud data set is of sufficient size to permit the monthly variability in cirrus properties to be understood. Figure 2.6 contrasts the mean monthly values for cirrus cloud-base and cloud-top heights with the Salt Lake City sounding tropopause heights derived from a 10-year average and the same sample of cirrus days. The variability in monthly cirrus cloud top and base heights and temperatures (for the envelope data set) is shown in figures 2.7 and 2.8, respectively. Clearly, the accumulation of similarly comprehensive information from a number of surface sites would be highly useful in the context of testing and providing inputs for modern climate models.

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Cirrus

Figure 2.7. Contoured monthly frequencies in percent of PARS cirrus cloud (a) top and (b) base heights, based on 0.5-km height intervals.

2.4.3. Cirrus and Weather over the Eastern Great Basin It is obvious that considerable seasonality exists in the PARS high cloud data set. The seasonal dependence on cirrus frequency and characteristics is clearly a reflection of the basic synoptic patterns that control the weather of the Great Basin. There is a strong correlation between the relative frequency of occurrence of PARS cirrus cloud observations (in percent of monthly to total observations), Salt Lake City National Weather Service reports of high cloud amounts (in terms of cirrus coverage-weighted amounts), and monthly Salt Lake City precipitation as shown in fig. 2.9. In other words, the synoptic weather patterns responsible for rain and snow are naturally also the harbingers for the cirrus cloud systems that sweep across the Great Basin. The crucial consequence is that cirrus properties will vary with season as the dominant weather patterns shift, as is well illustrated here for our particular geographic location. The PARS data compiled in table 2.3 and figures 2.6-2.9 exhibit a strong seasonal influence. A principal division in cirrus properties stems from the

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Figure 2.8. Contoured monthly frequencies in percent of PARS cirrus cloud (a) top and (b) base temperatures, based on 2.5°C intervals.

distinct upper tropospheric circulations associated with advecting baroclinic systems versus the relatively quiescent summer monsoonal period, which draws Gulf and Pacific moisture through the desert Southwest northward into the Great Basin (Davis and Walker 1992; Adams and Comrie 1997). Thus, the distinction is mainly one of anvil-generated cirrus versus those generated by synoptic scale disturbances, although thunderstorms occur locally without monsoonal flow and local factors such as orography may not directly reflect the action of storm systems. A breakdown of observed PARS cirrus generation according to synoptic disturbances yields 24% in split jet flow/cutoff lows, 23% in zonal flow, and 6% under troughs (Campbell 1997). (Recall that PARS cirrus observations are confined to nonprecipitating conditions.) A total of 47% of the cirrus occurs under ridges, including 10% in flat ridges representative of deamplified upper level flow, typical of summer conditions. In other words, nearly one-half of the PARS cirrus clouds occur under conditions not normally associated with active cirrus cloud formation: these cirrus are simply advected

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Cirrus

Figure 2.9. Contrasting 10-year monthly-averaged Salt Lake City NWS high cloud reports (black bars, weighted by cloud amount), PARS observation hours (by percent of total), and precipitation amounts for SLC. into our region. The majority of our cirrus are associated with maritime Pacific storm systems along the west coast of the United States, although subtropical moisture sources are often tapped in early spring and late fall. Occasionally, cirrus from subtropical jet streams and decayed Pacific hurricanes are also observed. The distinguishing summer cirrus properties result from the fact that the regional or local monsoonal thunderstorms tend to be rather weak because of their high cloud bases in the relatively dry desert environment. It is clear that average PARS cirrus cloud-top altitudes fall far below the tropopause height during the summer period (fig. 2.6). Thus, the average cloud-top heights above sea level are not noticeably dependent on season. In contrast to the relatively strong northwesterly flow encountered during most of the year when jet streams are typically nearby, table 2.3 shows that the monsoon brings weaker and more southerly flow. It is clear that during the summer months the cirrus layers are physically thinner but more opaque and less widespread (table 2.3), all attributes of cirrus derived from thunderstorms. In other words, the anvil cirrus clouds are distinct. It is appropriate to stress here that the basic connection between cirrus and weather means that other regions of the globe will likely have different cirrus cloud characteristics because of the local prevalence of weather patterns: cirrus cloud properties are fundamentally dependent on season and geographic location.

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2.5. The Altostratus Transition During the development of synoptic weather disturbances, the classic gradual thickening in cloud cover from cirrostratus to altostratus to nimbostratus often occurs. As already mentioned, the cirrostratus-altostratus transition, which is actually observed in association with a variety of weather situations, is identified operationally by the loss of the sharpness of the solar or lunar disk due to attenuation effects in the cloud. In this section I provide a recent comprehensive PARS case study analysis that illustrates the nature of the cirrostratus-altostratus transition. Plate 2.9 provides PDL height-time displays of relative 0.532 jim backscattering and linear depolarization over the 2040-2300 UTC period of the transformation of a cirrostratus into altostratus (see the fisheye photograph in plate 2.1g). Note that the approximately 1-km deep, weakly scattering aerosol layer just below the cloud represents the remnants of a dust storm advected over the north Pacific Ocean from the Gobi Desert: the low <0.05 8-values suggest that the nonspherical dust particles were too small to generate much depolarization (Sassen 2000). Figure 2.10 shows the corresponding cloud optical properties derived from the coaligned mid-infrared radiometer (see top panel giving the effective column brightness temperature) and lidar data, using the LIRAD approach. Finally, figure 2.11 provides the 95-GHz radar reflectivity factor display from 2150 to 2300 UTC, which includes for comparison the lidar-derived cloud base and apparent cloud-top heights (as symbols) derived from the latest FARS cloud boundary algorithm (see chapter 8). Note that although the radar often failed to detect the optically thinner cirrus parts because of the small ice particles prevalent there, toward the end it measured strong radar reflectivities and higher cloud signals than the lidar because of the effects of the correspondingly strong optical attenuation.

Figure 2.10. Derived cloud optical properties from the polarization diversity lidar data of plate 2.9, showing the mid-infrared effective black body temperature Teff, visible optical depth, T, at the 0.532 urn laser wavelength, and the LIRAD cloud emittance, e.

Figure 2.11. Comparison of polarization diversity lidar cloud boundary heights (symbols, see plate 2.9) with 95-GHz radar reflectivities (see key) during the cirrostratus-to-altostratus cloud transition at PARS on March 29,1999.

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Putting together these sources of information, we have the classic description of the cirrostratus-altostratus transition. Briefly at about 2230 and then again after 2245 UTC, there is an apparent loss of cloud-top lidar signal from laser-pulse attenuation effects (fig. 2.11), strong downwelling infrared radiances, visible optical depth T approaching the lidar limit of about 3.0, and infrared cloud emittance of £ approaching 1.0 (fig. 2.10). With regard to this last finding, we can now add that cirrus are characteristically gray emitters with e < 1 (see chapter 10). 2.6. Cirrus and Supercooled Liquid Water

As for the assertion that the liquid phase may not be predominantly responsible for cirrus cloud formation and maintenance, there are three cases that need elaboration. The first is the production of anvil cirrus, where strong updrafts may raise frozen cloud drops from the lower cloud into the upper troposphere. Because this form of ice nucleation would cease by about -40°C, when haze particle homogeneous freezing would take over, it is likely that large ice particles from the lower portions of a cumulonimbus would soon settle out and not have a significant impact on the future anvil cirrus cloud in the maintenance stage. On the other hand, the introduction of numerous boundary layer aerosols would likely have a more lasting effect on the composition of the anvil cirrus cloud, which is at least partly responsible for their distinct optical properties. Another condition where SLW may initially play a role in cirrus cloud formation is in standing lenticular wave clouds, in which highly supercooled cloud droplets have been detected in strong updrafts down to about -37°C (Sassen and Dodd 1988; Heymsfield and Miloshevich 1995). The leading edges of cirrus wave clouds sometimes show the iridescence phenomenon characteristic of small, growing droplets, but the resulting cirrus clouds can exist for extended periods (and advect over areas as large as several states), so the lasting effects of the first few seconds of cloud growth are arguable. An in-depth study using in situ and polarization lidar of such conditions is given in Sassen et al. (1989b). Finally, there is the case of what we have defined as cirrostratus altocumulogenitus, in which highly supercooled altocumulus cells are sporadically detected by polarization lidar at the approximate cloud-top position of what appears to be normal-looking cirrus. This represents the extreme case of a supercooled altocumulus cloud that produces ice virga. At temperatures < -35°C, liquid droplets will not persist for long and should be confined to regions with relatively strong updrafts and low ice content (in order to compete successfully for the available moisture with ice particles). Otherwise, ice formation results from minute haze-particle freezing at cloud top. A PARS ruby lidar case study of such a cloud is given in plate 2.10. The small, strongly scattering, and nearly nondepolarizing cloud cells intermittently noted atop the ice fallstreaks represent individual supercooled altocumulus cells. The low 8-values often present in the lower cloud regions, however, signify the presence of horizontally oriented plate crystals, an especially common occurrence in ice clouds derived from growth

34

Cirrus

close to water saturation. Nonetheless, such clouds can clearly resemble cirrostratus, meeting the basic criterion for identifying cirrus clouds. Although in this case I consider this cloud a proper form of cirrus, the glaciation of warmer liquid-phase clouds can be a cause of false cirrus. In PARS measurements (in mountainous terrain), we frequently detect lidar backscattering from subvisual ice layers, typically composed of horizontally oriented ice plates, that were formed from the heterogeneous drop-freezing process in upwind altocumulus standing lenticular clouds. Due to the obvious connection with relatively warm altocumulus clouds, however, our group has not classified these targets as cirrus but has given them a separate category (i.e., crystal layers). Such crystal layers appear to be geographically widespread, to the extent that Vaisala laser ceilometers are now being routinely installed pointing a few degrees off the zenith in order to limit the detection of these targets (P. K. Piironen, 1998, personal communication). Nonetheless, their lower altitudes and tenuous nature suggests that their radiative effects are probably not significant in comparison to proper cirrus, while the detection of crystal layers with lidars is exaggerated simply because of the artifact of the zenith probing effect. It should also be pointed out that the SLW-cirrus cloud interaction appears to work both ways. The literature contains several references to water clouds being associated with or embedded in the lower (warmer) portions of cirrus (Sassen et al. 1989b, 1991,1995). In some cases the SLW clouds may owe their existence to the cirrus cloud development process. That is, we can hypothesize the reverse variety of altocumulus cirrogenitus, which is explained by the adiabatic parcel cloud model predictions given in figure 2.12. Here is shown the ver-

Figure 2.12. The cloud model-predicted relation between initial parcel temperature and vertical distance from ice to water saturation, showing how cirrus cloud precipitation can condition the subcloud environment for subsequent altocumulus development in updrafts.

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tical distance that a parcel must be lifted to reach water saturation, when it starts its ascent at ice saturation, as a function of initial temperature. In other words, this model assumes that a cirrus cloud precipitation shaft has penetrated dry subcloud air and evaporated (leading to ice saturation), with subsequent uplift leading to SLW cloud formation as long as heterogeneous ice nucleation is not significant. Thus, starting at -25°C, for example, ice saturation will be converted adabiatically to water saturation after a vertical ascent of about 300m, which appears to help to explain the frequently observed relationship between cirrus and subcloud altocumulus formation. A CPL case study of such repeated cirrus/altocumulus interactions is presented in plates 2.1h and 2.11. Here it can be visualized how intermittent cirrus precipitation streaks can condition the middle atmosphere for subsequent altocumulus formation. Also note how active cirrus precipitation has disrupted the altocumulus, particularly near the end of the observation period: supercooled water cannot exist long in the presence of much ice due to the overwhelming ice competition for the available water vapor supply. In summary, empirical evidence indicates that under certain circumstances cirrus can be initially generated with the aid of transient SLW-dominated cloud regions. Although the debate continues whether these highly supercooled cloud droplets freeze into ice crystals via the homogeneous or heterogeneous mechanism, it is revealing that SLW clouds appear to completely glaciate beginning at about -35°C, when the homogeneous freezing process starts to become important (Sassen and Dodd 1988). FARS cirrus cloud top temperature climatology demonstrates that visually identified cirrus clouds form infrequently with the aid of SLW. Only about 2% of the cirrus have cloud-top temperatures warmer than -40°C, and most of these have likely resulted from the sampling of sheared precipitation streaks generated at considerably colder temperatures. So, it appears that the transition from long-lived, mixed-phase clouds (e.g., supercooled altocumulus) to proper cirrus occurs at about -37°C. Thus, this approximate level should delineate the warmest cloud-top temperature generally permissible during cirrus cloud formation. 2.7. Summary and Conclusions

From the information compiled here, an attempt can be made to create, or more accurately, reiterate in consideration of modern information, a versatile definition of a cirrus cloud. Cirrus comprise the highest tropospheric cloud category. Pictorial cloud atlas books illustrate the differences between cloud genera and species. The criteria for the identification of cirrus have traditionally relied on visual appearance, including morphology and color, which make them distinct from the clouds of the middle and lower troposphere. After establishing that cirrus were cold, and thus high, attempts were made to confine the three main cloud groups into vertical height and latitude brackets, but these do not appear to be sufficiently versatile with regard to FARS lidar cloud samples (using 7.5-m resolution). Such criteria were developed before the advent of modern cloud height-resolving instrumentation and do not display the flexibility needed to

36

Cirrus

account for the often significant day-to-day and seasonal oscillations in cloud heights; they are only useful guidelines. Perhaps the most important distinguishing feature of cirrus is their optical thinness: cirrus layers can be subvisual and are frequently translucent with a bluish appearance from transmitted skylight. They may also become increasingly opaque until the solar (or lunar) disk becomes irregular and indistinct. This defines the transition to the midlevel altostratus cloud that often results from the vertical thickening of cirrostratus. Modern research findings indicate that the corresponding visible optical thicknesses, i, vary from upper limits of approximately 0.03 for subvisible, 0.3 for thin, to 3.0 for opaque cirrus (Sassen and Cho 1992). Considering that parts of cirrus spissatus can contain optically denser regions, the transition between cirrus and other cloud types should occur in the 3.0-5.0 x range. A similar argument can be made with regard to the infrared emittances of thickening high-level clouds: cirrus clouds are characterized by their grayness, so the altostratus transition will also become apparent as emittances begin to approach unity. Cirrus must not be confused with boundary-layer ice fogs, diamond dust, or glaciating stratus clouds. With few exceptions, ice cloud virga derived from the freezing of supercooled cloud droplets do not visually resemble cirrus: microphysically, it follows that the heterogeneous/homogeneous freezing of haze particles (i.e., generally submicron-sized solution droplets) derived from cloud nuclei in the upper troposphere are predominantly responsible for cirrus cloud formation. The sources for these nuclei include stratospheric and/or volcanic sulfuric acid droplets, terrestrial and marine particles lofted by thunderstorms, and perhaps in increasing numbers the human by-products of aircraft emissions and land use. Land-use emissions include the consequences of desertification and deforestation, which result in dust storms and smoke plumes from biomass burning that potentially may artificially influence the properties of cirrus even in the distant upper troposphere. In practice, this nucleation scenario means that cirrus cloud-top temperatures must be colder than about -37°C, essentially the point where pure water drops will freeze spontaneously, as the results of our extensive 10-year remote sensing data set corroborates. Our data set from Salt Lake City, Utah, also shows that mid-latitude cirrus cloud-top heights typically correspond to the tropopause, except during the summer season under conditions of weak monsoonal thunderstorms. Although the cirrus properties vary significantly in response to seasonally prevalent weather patterns, 10-year average values for local cirrus cloud-base/top properties are 8.79/11.2 km height, 336.3/240.2 mb pressure, -34.4/-53.9°C temperature, 16.4/20.2 ms'1 wind speed, and 276.3/275.7° wind direction. The average cirrus layer physical thickness is 1.81km. Because cirrus clouds are a product of the regional weather processes that inject water vapor into the dry upper troposphere (only to be subsequently removed through cirrus particle sedimentation), it is expected that local cirrus cloud properties will depend significantly on geographic location. Finally, distinctions in cloud microphysical, macrophysical, and radiative properties will result from basic cirrus cloud-generating mechanisms, which are essentially functions of ambient temperature, the strength of the updraft velo-

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city, and the source of the cloud-forming nuclei. A breakdown of cirrus cloudgenerating mechanisms includes 1) a variety of synoptic-scale disturbances (jet streams, closed upper-level lows, frontal overriding, etc.) that have in common relatively weak average vertical lifting rates and generally involve top-down cirrus growth; 2) injection, or anvil-cirrus from strong thunderstorm updrafts; 3) orographic wave cloud cirrus induced by local terrain also with potentially strong vertical motions; 4) cold-trap cirrus that seem to inhabit vast geographical regions at the extremely cold tropical tropopause; and 5) the recent artificial contrailcirrus produced by the spreading of contrails formed when water vapor-enriched aircraft exhausts are mixed into an ice-saturated environment. It is vital for climate research that a consistent terminology for cirrus clouds be adopted to facilitate the intercomparison of ground-based visual records, remote sensing, in situ, and satellite top-of-atmosphere radiance data. Therefore, I suggest that when uncertainty exists about whether a particular cloud would fall into the traditional cirrus category based on its visual appearance, the terms "high" or "ice" clouds be used to avoid confusing cirrus characteristics with those of midlevel altostratus/altocumulus, or even nimbostratus and cumulonimbus clouds, as viewed from satellites. Even with active remote sensors, special terms such as "apparent lidar," or "radar echo" cloud-top heights should be used unless there is clear evidence that the actual cirrus cloud-top height is determined. A healthy skepticism must be given to any case study or climatology that is not firmly based on the traditional visual definition of cirrus. All cirrus research approaches have their advantages and disadvantages, but it must be kept foremost in mind that the cloud type needs to be confirmed, either visually or based on particular cirrus characterizations derived from extended observations and surface meteorological data. In the near future, combinations of passive and active (lidar and millimeterwave radar) remote sensors will make the characterization of cirrus clouds from earth orbit more reliable and precise, and on a global scale. A greater understanding of our climate and its cloud feedback mechanisms should result from such technological developments. Understanding the effects of cirrus clouds, in particular, will certainly remain important in this endeavor.

Acknowledgments Recent PARS cirrus cloud research has been funded by National Science Foundation grant ATM-9528287, National Aeronautics and Space Administration grants NAG-1-1314 and NAG-2-1106, and Department of Energy grant DEFG0394 ER61747 from the Atmospheric Radiation Measurement program. I sincerely thank my staff and colleagues for their assistance.

Note I have widely shown this figure at meetings to exemplify the essential qualities of cirrus clouds. Its random selection results from the fact that it was the first lidar data displayed with a new software package, and I was so impressed that I photographed the monitor.

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Cirrus

References Adams, K., and A.C. Comrie, 1997. The North American monsoon. Bull. Am. Meteor. Soc., 78,2197-2213. Arnott, W.P., Y.Y. Dong, and J. Hallett, 1994. Role of small ice crystals in radiative properties of cirrus: A case study, FIRE II, November 22, 1991. /. Geophys. Res., 99, 1371-1381. Campbell, J.R., 1997. A midlatitude cirrus climatology from the ten-year Facility for Atmospheric Remote Sensing high cloud dataset. M.S. thesis. University of Utah, Salt Lake City. Davis, R.E., and D.R. Walker, 1992. An upper-air synoptic climatology of the western United States. /. Climate, 5,1449-1467. Dowling, D.R., and L.F. Radke, 1990. A summary of the physical properties of cirrus clouds. /. AppL Meteor., 29, 970-978. Gayet, J.-F, G. Febvre, and H. Larson, 1996. The reliability of the PMS FSSP in the presence of small ice crystals. /. Atmos. Ocean. Tech., 13,1300-1310. Gobbi, G.P., G. Di Donfrancesco, and A. Adriani, 1998. Physical properties of stratospheric clouds during the Antarctic winter of 1995. /. Geophys. Res., 103,10859-10873. Greenler, R., 1980. Rainbows, Haloes and Glories. Cambridge University Press, Cambridge. Harimaya, I., 1968. On the shape of cirrus uncinus clouds: A numerical computation. Studies of cirrus clouds, Part III. /. Meteor. Soc. Jpn., 46,272-279. Heymsfield, A.J., 1975. Cirrus uncinus generating cells and the evolution of cirriform clouds. Part III: Numerical computations of the growth of the ice phase. J. Atmos. Sci., 32, 820-830. Heymsfield, A.J., 1986. Ice particles observed in a cirriform cloud at -83°C and implications for polar stratospheric clouds. / Atmos. Sci., 43,851-855. Heymsfield, A.J., and C.M.R. Platt, 1984. A parameterization of the particle size spectrum of ice clouds in terms of the ambient temperature and ice water content. J. Appl. Meteor., 18,1130-1143. Heymsfield, A.J., and L.M. Miloshevich, 1995. Relative humidity and temperature influences on cirrus formation and evolution: Observations from wave clouds and FIREII. /. Atmos. Sci., 52, 4302-4326. Imasu, R., and Y. Iwaska, 1991. Characteristics of cirrus clouds observed by laser radar (lidar) during the spring of 1987 and the winter of 1987/88. J. Meteor. Soc. Jpn., 69, 401-411. Jensen, E.J., O.B. Toon, D.L. Westphal, S. Kinne, and A. J. Heymsfield, 1994. Microphysical modeling of cirrus, 1. Comparison with 1986 FIRE IFO measurements./. Geophys. Res., 99,10421-10442. Khvorostyanov, V.I., and K. Sassen, 1998. Cirrus cloud simulation using explicit microphysics and radiation. Part II: Microphysics, vapor and mass budgets, and optical and radiative properties. /. Atmos. Sci., 55,1822-1845. Kinne, S., T.P. Ackerman, A. J. Heymsfield, P.P. J. Valero, K. Sassen, and J.D. Spinhirne, 1992. Cirrus microphysics and radiative transfer: Cloud field study on 28 October 1986. Mon. Wea. Rev., 120, 661-684. Knollenberg, R.G., 1976. Three new instruments for cloud physics measurements: The 2D spectrometer, the forward scattering spectrometer probe, and the active scattering aerosol spectrometer. In Proceedings of the International Conference on Cloud Physics, pp. 554-561. American Meteorological Society, Boston. Liao, L., and K. Sassen, 1994. Investigation of relationships between Ka-band radar reflectivity and ice and liquid water contents. Atmos. Res., 34,231-248.

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Liou, K.-N. 1986. The influence of cirrus on weather and climate process: A global perspective. Mon. Wea. Rev., 114,1167-1199. Ludlam, F.H., 1956. The forms of ice clouds: II. Quart. J. Roy. Meteor. Soc., 82,257-265. Minnis, P., 1998. Retrieval of cloud properties from satellite data for weather and climate forecasting. In Proceedings of WMO Workshop on Cloud Measurements for the Forecast of Weather and Climate, Mexico City, Mexico, June 23-27, 1997. WMO Report no. 30, WMO, Geneva, pp. 60-72. Pasqualucci, E, B. Bartram, R.A. Kropfli, and W.R. Moninger, 1983. A millimeterwavelength dual-polarization Doppler radar for cloud and precipitation studies. J. Climate Appl. Meteor., 22,758-765. Platt, C.M.R., 1979. Remote sounding of high cloud. Part I: Calculation of visible and infrared optical properties from lidar and radiometer measurements. /. Appl. Meteor., 18,1130-1143. Platt, C.M.R., J.C. Scott, and A.C. Dilley, 1987. Remote sounding of high clouds. Part VI: Optical properties of midlatitude and tropical cirrus. /. Atmos. Sci., 44, 729-747. Platt, C.M.R., S.A. Young, PJ. Manson, G.R. Patterson, S.C. Marsden, R.T. Austin, and J.H. Churnside, 1998. The optical properties of equatorial cirrus from observations in the ARM Pilot Radiation Observation Experiment. /. Atmos. Sci., 55,1977-1996. Rossow, W.B., and L.C. Garder, 1993. Cloud detection using satellite measurements of infrared and visible radiances for ISCCP. /. Climate, 6,2370-2393. Sassen, K., 1991. The polarization lidar technique for cloud research: A review and current assessment. Bull. Amer. Meteor. Soc., 72,1848-1866. Sassen, K., 1994. Advances in polarization diversity lidar for cloud remote sensing. Proc. IEEE, 82,1907-1914. Sassen, K., 1997. Contrail-cirrus and their potential for regional climate change. Bull. Amer. Meteor. Soc., 78,1885-1904. Sassen, K., 1999. Cirrus clouds and haloes: A closer look. Optics & Photonics News, 10, 39-42. Sassen, K., 2000. The lidar backscatter depolarization technique for cloud and aerosol research, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Geophysical Applications, M.L. Mischenko, J.W. Hovenier, and L.D. Travis (eds). Academic Press, New York pp. 393^16. Sassen, K., and B.S. Cho, 1992. Subvisual-thin cirrus lidar dataset for satellite verification and climatological research. J. Appl. Meteor., 31,1275-1285. Sassen, K., and G.C. Dodd, 1988. Homogeneous nucleation rate for highly supercooled cirrus cloud droplets. /. Atmos. Sci., 45,1357-1369. Sassen, K., M.K. Griffin, and G.C. Dodd, 1989a. Optical scattering and microphysical properties of subvisual cirrus clouds, and climatic implications. J. Appl. Meteor., 28,91-98. Sassen, K., CJ. Grund, J.D. Spinhirne, M. Hardesty, and J.M. Alvarez, 1990. The 27-28 October 1986 FIRE IFO cirrus case study: A five lidar overview of cloud structure and evolution. Mon. Wea. Rev., 118, 2288-2311. Sassen, K., and C. Hsueh, 1998. Contrail properties derived from high-resolution polarization lidar studies during SUCCESS. Geophys. Res. Lett., 25,1165-1168. Sassen, K., and V.I. Khvorostyanov, 1998. Radar probing of cirrus and contrails: Insights from 2D model simulations. Geophys. Res. Lett., 25, 975-978. Sassen, K., N.C. Knight, Y. Takano, and A.J. Heymsfield, 1994. Effects of ice crystal structure on halo formation: Cirrus cloud experimental and ray-tracing modeling studies. Appl Opt., 30, 4590-4601. Sassen, K., and S.K. Krueger, 1993. Toward an empirical definition of virga: Comments on "Is virga rain that evaporates before reaching the ground?" Mon. Wea. Rev., 121, 2426-2428.

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Sassen, K., G.G. Mace, J. Hallett, and M.R. Poellot, 1998. Corona-producing ice clouds: A case study of a cold cirrus layer. Appl. Opt., 37,1477-1585. Sassen, K., D.O'C. Starr, G.G. Mace, M.R. Poellot, S.H. Melfi, W.L. Eberhard, J.D. Spinhirne, E.W. Eloranta, D.E. Hagen, and J. Hallett, 1995. The 5-6 December 1991 FIRE IFO II jet stream cirrus case study: Possible influences of volcanic aerosols. /. Atmos. Sci., 52,97-123. Sassen, K., D.O'C. Starr, and T. Uttal, 1989b. Mesoscale and microscale structure of cirrus clouds: Three case studies. J. Atmos. Sci., 46,371-396. Schiffer, R.A., and W.B. Rossow, 1983. The International Satellite Cloud Climatology project (ISCCP): The first project of the World Climate Research program. Bull. Amer. Meteor. Soc., 64,779-784. Schotland, R.M., K. Sassen, and R.J. Stone, 1971. Observations by lidar of linear depolarization ratios by hydrometeors. /. Appl. Meteor., 10,1011-1017. Spinhirne, J.D., M.Z. Hansen, and J. Simpson, 1983. The structure and phase of cloud tops as observed by polarization lidar. / Climate Appl. Meteor., 22,1319-1331. Starr, D.O'C, and S. K. Cox, 1985. Cirrus clouds. Part II: Numerical experiment on the formation and maintenance of cirrus. J. Atmos. Sci., 42,2682-2694. Stephens, G.L., S. Tsay, P.W. Stackhouse, Jr., and P.J. Flatau, 1990. The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback. /. Atmos. Sci., 47,1742-1753. Stokes, G.M., and S.E. Schwartz, 1994. The Atmospheric Radiation Measurement (ARM) program: Programmatic background and design of the cloud and radiation testbed. Bull. Amer. Meteor. Soc., 75,1201-1221. Takano, Y., and K.-N. Liou, 1995. Solar radiative transfer in cirrus clouds. Part III: Light scattering by irregular ice crystals. /. Atmos. Sci., 52, 818-837. Tape, W. 1994. Atmospheric Halos. Antarctic Research Series, vol. 64, American Geophysical Union, Washington DC. Weickmann, H., 1947. Die Eisphase in der Atmosphere. Lib. Trans. 273, Royal Aircraft Establishment, Farnsborough, UK. Winker, D.M., and C.R.Trepte, 1998. Laminar cirrus observed near the tropical tropopause by LITE. Geophys. Res. Lett., 25, 3351-3354. World Meteorological Organization (WMO), 1975. International Cloud Atlas, vol. I, Manual on the Observation of Clouds and Other Meteors. WMO no. 407,WMO, Geneva.

3

Ice Crystals in Cirrus

JOHN HALLETT W I L L I A M P. A R N O T T MATTHEW P. B A I L E Y JOAN T. H A L L E T T

Cirrus is conventionally considered as cloud forming in the Earth's upper troposphere at temperatures somewhat below -40°C, composed of ice crystals and forming long, wispy trails. This characteristic shape, in the form of a curl of hair, results from evaporation in vertical shear of horizontal winds, and leads to its Latin name—originally proposed by Luke Howard in 1803. Here we address the nucleation, growth, and evaporation processes that influence the concentration and shape of individual particles and their role in specific atmospheric phenomena. To set the scene, figure 3.1 shows examples of such crystals collected by aircraft. In this chapter, we also address the radiation and dynamic environment in which crystals grow and subsequently evaporate. Crystal growth depends on the location of a crystal with respect to the cloud edge and the intervening cloud optical thickness; evaporation depends on larger scale processes as at fronts and cumulonimbus anvils and also at inversion interfaces where shear instability and resulting gravity waves produce significant effects over a range of scales. These effects lead to differing cloud radiative properties and ultimately control of the earth's radiation budget and overall climate (Liou 1986; Stephens et al. 1990; Liou and Takano 1994; Takano and Liou 1995; Mishchenko et al. 1996; Strauss et al. 1997; Macke et al. 1998). 3.1. Crystal Growth A growing crystal implies a supersaturated or supercooled environment with respect to the solid phase and can, in general, be considered as growth from either 41

Figure 3.1. a. Reproduction from the translation Die Eisphase in der Atmosphare (Weickmann 1947) of replicas on a microscope slide coated with Zapon Laquer, showing bullet rosettes. Collected from the open cockpit of a single engined reconnaissance Heinkel aircraft in 1943. Small division scale = 10 urn. b. Simultaneous occurrence of many crystal habits in the same sample of air at cirrus levels (Weickmann 1947). c. Formvar replica of scalene plates with three-fold symmetry from frontal cirrus, UND Citation aircraft; Kansas, temperature -63°C, December 5,1991. Alternate faces are slightly indented. Fragments to right result from shatter of another crystal on impact, d. Replica of a scalene crystal with 42

Ice Crystals in Cirrus

43

three-fold symmetry overlying a needle, (NASA DC-8,TOGA COARE,-48°C, deep tropical convection, 1993). The replica visually shows a uniformity of color in vertical illumination, indicating a thin crystal a few micrometers thick, uniform to ±0.05 urn. e. Replica of needles, small scalene and triangular three-fold symmetry plates, hexagonal plates, columns, and irregular crystals collected by D.L.R. Falcon in thin cirrus over the Alps, temperature -55°C, October 29,1992. (Courtesy Dr. P. Wendling.) f. Replica of crystals from the evaporating tip of a contrail formed 50 s earlier by the NASA 757 aircraft sampled from the NASA DC-8. Multiple trigonal symmetry crystals are present, with a 60° rotation (left side), along with hexagonal and scalene and triangle crystals, concentration 10/cm3. Clear sky environment over Kansas, temperature -52°C, 1840-1900Z, 4 May 1996. 43

Figure 3.1. (continued)

Ice Crystals in Cirrus

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Figure 3.1. (continued)

vapor or liquid. Any growth mechanism implies a process at an atomic or molecular level whereby individual atoms, molecules, or assemblages of molecules are added to the solid, moving from a disordered or locally ordered state in the environment to a highly long-range ordered state in the crystal lattice. On a local scale is implied a translation of a growth unit from the environment to the crystal surface followed (for a nonspherical molecule, as water) by a rotation to fit into a suitable lattice site. In the case of growth from a liquid, transport may be restricted by the presence of an inert component such as a sodium chloride crystal

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growing from a solution in water or an ice crystal growing from a sodium chloride solution; in the case of a growth from the vapor, transport may similarly be restricted, as in the case of growth of ice crystals in air. In both cases released latent heat of crystallization is transported away to the environment, although in general, diffusion in a liquid is much less rapid than in a gas and is therefore rate controlling. In balance, heat transport away from the growing crystal is equivalent to the latent heat of the mass influx incorporated into the crystal lattice, leading to equations of the form:

which combine in equilibrium to give

where ra = particle mass, r - particle radius; q - particle heat content; L = the appropriate latent heat (somewhat temperature dependent); K = environment thermal conductivity, D = environment diffusivity; T= temperature, and p = vapor or solute concentration at equilibrium with the crystal surface (s) or environment (E). Critical assumptions are that the boundary conditions are in equilibrium between the temperature and vapor pressure or density as given by the ClausiusClapyeron equation, and surface conditions are uniform, which may not always be the case (see below). A correction is necessary for other than spherical shape and for mean free-path effects in rarefied gases (for general references for these growth equations, see Pruppacher and Klett 1997). Equation 3 gives a first-order estimate of the excess temperature of the crystal during growth, which we shall later compare with estimated radiation effects. Growth rate therefore depends on heat transport through the thermal conductivity of the environment and mass transport through the vapor or solution diffusivity. In the case of ice growth in air, the thermal conductivity is weakly dependent on temperature and almost independent of air pressure, whereas vapor diffusivity is inversely related to air pressure and weakly to temperature. Each process is enhanced by ventilation—either as terminal velocity of the crystal, as terminal velocity of a larger hydrometeor on which a crystal element is growing, or as an air velocity independent of crystal size for a frost crystal growing on a fixed ground site. To a first approximation, the ventilation terms are of the form

where Re is the Reynolds number of the flow appropriate to the growing crystal. For a crystal falling at terminal velocity, to sufficient approximation we may take:

The growth equation is of the form:

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47

where m = the crystal mass; C = a geometric factor; and o = the supersaturation. The term A is inversely related to thermal conductivity, and B is inversely to vapor pressure and water vapor diffusivity in air. Figure 3.2 shows the form of A and B related to temperature for different pressures and a standard atmosphere (Bailey and Hallett 1998). A varies slowly with temperature and pressure. For a standard atmosphere, the variation of B is dominated by the inverse pressure variation of the diffusion coefficient and the exponential variation of vapor pressure with temperature through the Clausius-Clapyeron equation. We distinguish several regimes: 1. A about the same as B: near 0°C and 1000mb; -45°C, altitude 12mb; 2. A (air conductivity) dominant: temperature above +10°C, pressure 1000mb; air pressure below 5mb; -80°C, O.lmb, noctilucent clouds. 3. B (diffusivity, saturated vapor pressure) dominant: temperature below -10°C, 500mb; temperature down to -80°C, 100-15 mb; polar stratospheric (nacreous) clouds.

Thus, conventional cirrus particle growth is limited by vapor diffusion flux, as is diamond dust growing at a higher pressure (1000-700 mb) in the same range

Figure 3.2. Limitation of the growth rate of an ice crystal (equation 5, A + B) through the influence of temperature and air pressure on the (A) heat conductivity term and (B) term vapor diffusivity term (including the saturation pressure of ice) for ice crystal growth in air. Thin background lines represent the B term at the indicated air pressure. The full line represents B for a standard atmosphere; conditions for diamond dust near the surface, high level tropical convection and noctilucent clouds and cirrus under various conditions are shown. The vapor diffusivity term dominates for all situations above except noctilucent clouds and comparable level rocket exhausts, and ice growth at temperatures above -10°C.

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Cirrus

of temperature. Similar considerations apply to stratospheric ice crystals (high vapor diffusivity, low vapor pressure) associated with the observation of wellformed columns (Goodman et al. 1989). An estimate of the excess temperature of the crystal during growth or evaporation may be computed from rearranging the steady-state mass and heat balance equations given above: This is best visualized from the ps, Ts plot, on which the above equation (neglecting the temperature variation of LDIK) represents a straight line through the environmental conditions (pE, TE) intersecting the ps, Ts plot (ps = saturation vapor density over ice, water as a function of temperatureT s). For a water-saturated environment, the excess temperature is about 0.4 K near -12°C at surface pressure 1000mb and falls to lower values at both lower and higher temperature (fig. 3.3). There is a basic assumption that the vapor density (or pressure) at the ice-vapor interface is a function only of temperature. This may not be the case for a molecularly smooth or strained ice interface, which could have an arbitrary vapor pressure depending on the environmental conditions. This is discussed later in section 3.2.

Figure 3.3. Equilibrium water vapor density over ice and supercooled liquid water over a range of temperatures and range of slopes of the parameter K/LD (equation 6) for the standard atmosphere (pressure shown at top of figure) and 1000mb. The lines originating on the water equilibrium curve intersect the ice curve to give the local ice surface conditions and indicate the temperature excess of the growing crystal, maximum about 0.5 K. The lines originating at an ambient saturation ratio of 10% over ice give a temperature deficit for evaporation of about 1K near -40°C.

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The range of atmospheric variables for ice formation leads to different physical considerations for ice crystal growth. In particular, crystals growing near the surface at low temperature (below -40° C, pressure near 1000mb) as diamond dust or surface frost are limited by a lower vapor diffusivity than in layers conventionally giving cirrus, so the B term for the same temperature range varies by a factor of 4-5 (fig. 3.2). Because the diffusivity term dominates over the conductivity term, the crystal growth rates at cirrus levels and surface are determined by this term through the air pressure. Crystals grown at lower air pressure and thus higher vapor diffusivity are therefore expected to have a corresponding greater rate of growth. There is also a greater tendency for such crystals to have more complete facets and greater crystal density in association with the higher diffusivity (Gonda 1980; Gonda and Koike 1982). This consideration could lead to a definition of cirrus crystal growth dependent on altitude, in as far as growth at high pressure is distinctive from growth at low pressure at the same temperature and ambient supersaturation and fall velocity. The rate is related to fall velocity enhancement of growth as an independent parameter, equivalent to a correction for the supersaturation in equation 5. Terminal fall speed for identical shapes is also altitude dependent through pressure (see section 3.5). A complexity arises as the radiation environment of the crystal changes, as could be the case at the top of an anvil or frontal cirrus and in the interior of any optically thin cloud. In an optically thick cloud, such as a water cloud under many conditions and a lenticular cloud transformed to ice or undiluted contrails, the radiation environment is unlikely to change substantially from the ambient air temperature under the former conditions. However, for a thin cloud, the radiation temperature below could well be some tens of degrees warmer and above some tens of degrees colder than the crystal environment (Roach 1976; Stephens 1983; Hallett 1987). The radiation temperature of the crystal will thus be regulated by the solid angle distribution of cloud optical depth for solar wavelengths and with respect to temperature for thermal infrared wavelengths. The optical thickness of the crystal itself in near infrared and thermal infrared wavelengths is also important. The functional dependence of heat exchange for a sphere for gas transport processes is radius dependent for the unventilated case and (radius)1 5 for high ventilation rates. For radiation effects, it is proportional to the area of the sphere, (radius)2, so that the heat-exchange process and the functional dependence changes as the particle grows (fig. 3.4). The particle shape and spatial orientation are also important. The heat balance is represented for a spherical particle by an equation of form:

where a = Stefan's constant, and Te is the radiation temperature of the environment, which may differ from TE, the environmental air temperature. The radiation component is to be adjusted for solid angle as appropriate, with Te varying with direction. Thus, for cirrus crystal growth/evaporation, the crystal temperature differs from the environmental air temperature by a fraction of a degree (fig. 3.3), whereas for different radiation temperature environments this value

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Cirrus

Figure 3.4. Comparison between heat loss by conduction and/or convection and radiation heat transfer for an ice crystal (approximated as a sphere) in an environment with a radiation temperature close to crystal temperature (1K difference as in a water cloud with visual range of order 10m) and at the top of a cirrus layer with a radiation temperature difference of 30 K.

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may increase to several degrees. This could lead to ice particle growth under apparently undersaturated conditions or evaporation under apparent growth conditions, the effect becoming important for sizes greater than a few hundred micrometers (fig. 3.4). For detailed calculation, emissivity related to radiation wavelength must be considered (see section 3.6). The Rayleigh number gives a criterion for the onset of natural convection (Turner 1973): where v = dynamic viscosity of air, K = thermal diffusivity of air, g = acceleration of gravity, and g&T/T is the buoyancy. Ra is approximately 200d3, (d = cm), well below the criterion of 1800 for the occurrence of natural convection, so that enhancement of heat loss by such convection can be neglected under these circumstances. 3.2. Crystal Growth: Kinetic Considerations

A further consideration is the occurrence of faceted and skeletal crystals and the implication of such forms for the mechanism of growth and setting the crystal-air interface boundary conditions. It has long been known that ice crystals growing from the vapor do so by macroscopic steps, often oriented in a low-index crystallographic direction, which propagate across the crystal surface (Hallett 1961). Interference microscopy of growing crystals has shown that such layers have thickness down to at least 30 nm and are nucleated at specific sites on the crystal, spreading with velocity inversely related to thickness. They maintain constant thickness during growth, showing that a local supersaturation must exist over the nongrowing basal crystal facet. Such a facet can be considered smooth on a molecular scale and requires a definite ice supersaturation to nucleate twodimensional clusters which can grow (Keller et al. 1980; Cho and Hallett 1984). There is some evidence that the critical value approaches water saturation (Hallett 1961, Dong et al. 1995). A similar argument can be made for layer evaporation (Anderson and Hallett 1979). Dislocations have been observed in vaporgrown ice (McKnight and Hallett 1978), but there is evidence that they are important for the growth process only at modest ice supersaturations. Under these conditions another growth process becomes evident involving a bicrystal (with a distinct crystallographic relationship) in the form of a spike with growth velocity well in excess of neighboring single crystals (Furukawa and Kobayashi 1978; Yamashita et al. 1984). These forms tend to occur more frequently at low temperatures and may be identified in some forms of cirrus and aircraft contrails (Bailey and Hallett 1998; Meyers and Hallett 1998). Another important factor is that the surface of a molecularly smooth, nongrowing ice surface is a base for an adsorption of water molecules that are in some dynamic equilibrium with the environmental vapor. The existence of such a layer at temperatures near 0°C is confirmed by optical ellipsometry (Furukawa et al. 1987). Thin ice layers— however nucleated—grow from this adsorbed layer and also directly from the vapor, but less so for thinner layers <1 urn, as implied from the observation that

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Cirrus

the growth velocity is inversely related to thickness. Such thin layers grow primary by diffusion from the surface adsorbed molecules. The observations imply that the adsorbed layer must change in properties with ambient saturation ratio until either a hole nucleates, leading to evaporation, or an island nucleates, leading to growth on the molecularly smooth surface. Edge or corner evaporation is necessarily independent of these considerations. Edge growth may occur because the supersaturation is somewhat higher than in the crystal interior because less vapor is removed by local competitive effects. For any crystal to have grown in the first place, either a high supersaturation must have been present or the initial nucleation process must have produced defect-containing surfaces (Hallett 1987; Penn and Banfield 1998). Observations also imply that the layer changes its characteristics, such as a surface migration distance for interacting layers, with temperature, at least on the basal plane. The variation may be invoked as giving rise to the complex variation of habit observed in the lower tropospheric range of temperature (Hallett and Mason 1958). A horizontal thermal diffusion chamber with control of air pressure provides a convenient way to study habit and growth rate under controlled temperature and supersaturation typical of cirrus conditions (Bailey and Hallett 2000). Figure 3.5 shows a map of these parameters with linear growth rate on the third axis. Further insight into these processes may be obtained from consideration of habit extremes and crystal symmetries other than hexagonal which are sometimes observed. Ice plates and dendrites and also column-type crystals sometimes have habits (defined in terms of the ratio of lengths in the principal growth directions, c/a), as extreme as 1:: 100 or 100:: 1. These habits are difficult to interpret in terms of surface properties alone, and an alternative explanation must be sought. Observations of ice crystals, both in field and laboratory, show the presence of three-fold (trigonal) symmetry extending from scalene hexagons (threefold symmetry, alternate sides shorter) to thin triangles and three-fold symmetry dendrites (see fig. 3.1; Scoresby 1820; Bentley and Humphries 1931,1962; Nakaya 1954;Yamashita 1973; Heymsfield 1986). A possible way of introducing such symmetry in a hexagonal lattice is to introduce stacking faults into the basal plane such that regions of cubic symmetry exist (Kobayashi 1976; Kobayashi et al. 1976). The unit of packing can conveniently be taken as five water molecules (a central molecule surrounded by a near tetrahedron of four others) to be stacked in close packing in the c axis direction normal to the hexagonal basal plane. Using the convention of A representing the first layer and B the layer above, the next layer above is represented as A, identical to the first layer for a hexagonal structure, or C, differing from both A and B for a cubic structure: . . . ABABABABAB . . . hexagonal . . . ABCABCABCABC . . . cubic The stacking leads to (111) planes (implying eight possibilities) in a cubic structure, the layers AB, BC, or AC being identical in each case. It may be hypothesized that a sufficiently thick sequence must be present in either hexagonal basal or cubic (111) planes to give a layer sufficiently thick for nucleation; simple nucleation theory with reasonable assumptions of embryo surface energy suggests

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53

Figure 3.5. Map of ice crystal growth rates and habits related to temperature and supersaturation at air pressures of 150 to 400mb (at center of figure, based on the standard atmosphere) from measurements made in the water vapor diffusion chamber. The observed habit of ice crystals in cirrus under known temperature may be used to infer ambient supersaturation and growth rate. Different growth rates and habits sometimes occur under the same conditions depending on the nucleation mechanism and defect structure of the ice embryo. At low supersaturations (bottom of the graph) minimum detectable growth rates are 0.005 (ims"1. The habits are mixed between -60 and -40°C, with 85% polycrystals, 15% plates and 5% short columns. Spearheads are superficially similar to dorites occurring near -15°C but with more lateral development. (A) T = -30°C, ice supersaturation 0.02, small plates and polycrystals, including two tabular columns (arrowed), a term invented by Tape (1994) to describe a type of flattened short column (see text) observed in the Antarctic. (B) A readily observable transition from predominantly plate-like to predominantly column-like crystals which occurs atT = -38° C near and above water saturation. (C) Thick column and bullet rosette at T = -40°C and ice supersaturation 0.5. (D) Transition from short to moderate to long length columns between -40°C and -50°C near water saturation. (E) Transition from long columns to needles at -55°C, ice supersaturation 1.0. (F) Needle rosettes growing at -60°C, ice supersaturation 0.5.

some tens of layers as being sufficient to nucleate and grow the trigonal symmetry associated with a cubic structure. A cube viewed symmetrically at its corner clearly shows such symmetry. The stacking becomes:

... ABAEABAEABCABC. .. ABCABCAEAEAE ... Evidence for the existence of such stacking faults is given by x-ray studies of McKnight and Hallett (1978). Stacking Faults existing preferentially in specific

54

Cirrus

(111) planes (for example in opposing symmetry) may arise and could be responsible for the more rarely observed crystals as hexagonal plates or columns with opposing long or short lengths on just two opposing faces of the hexagon. (See examples in Tape 1994.) Such effects would be expected to occur more readily at lower temperature where cubic faults would be more likely. An alternative way of visualizing the geometry is that a series of faults can be regarded as twins on the hexagonal ice basal plane or the (111) plane of the cubic ice, which gives rise to self-perpetuating steps as occurs for germanium and is a source of a rapid growth direction for germanium dendrites (Hamilton and Seidensticker 1960). It is not impossible that all thin dendrites seen in ice originate in this way. Figure 3.5 shows that a range of linear growth rates occur for identical temperature and supersaturation. This is to be interpreted in terms of different defect structure and nucleation processes for growth in different crystallographic directions. These effects also occur at higher temperature; the dorites of Hallett and Mason (1958) are an example of such growth in the temperature range -15 to -25 °C. Ice exists both in hexagonal and cubic form, with a transition near -120°C, so that lattice energy of the two structures must be almost the same. Early field observations showed the occasional presence of trigonal symmetry ice (Scoresby 1820; Bentley and Humphries 1962; Nakaya 1954). Laboratory work shows a lack of trigonal symmetry in growth of larger (100 u,m) crystals but in rapid nucleation a presence of small crystals (Yamashita 1973) and also under rapid nucleation processes in contrails (fig. 3.Id; Meyers and Hallett 1998). The occasional occurrence of four-fold symmetry in ice (Heymsfield 1986) is not inconsistent with this idea. Schaefer (1949) found trigonal symmetry with the presence of HNO3 vapor during growth. Other substances show similar effects: silver halides (Maskasky 1986) and C60 from solution in benzene (Hallett and Moore, in preparation). Thus, extreme habits in two dimensions are to be interpreted in terms of planar arrays of defects as stacking faults, and extreme habits in one dimension are to be interpreted in terms of intersection of two planes or in terms of the termination of screw dislocations. The role of supersaturation (influenced by fall velocity as discussed in section 3.1) is thus seen to lie in activation of each of these mechanisms for growth, with the relative importance of each depending in a complex way on the initial (as for droplet nucleation) and subsequent (as for freezing of a supercooled droplet on accretion) nucleation processes. A pristine crystal, in the sense of having a well-defined habit of just one crystallographic orientation and well-defined facets, such as a solid column or plate, leading to spectacular optical effects (Tape 1994), is to be expected when (1) the nucleation process leads to just a single-crystal orientation, (2) there are no defects leading to rapid growth as discussed above, and (3) the supersaturation is low enough such that skeletal growth (dendrites, needles) does not develop (Hallett and Knight 1994). This in general implies that the local supersaturation near the crystal interface does not exceed water saturation. The ambient supersaturation may exceed water saturation, but it may only approach water saturation at the surface as the crystal fall-speed approaches a value such that the air boundary layer thickness becomes small with respect to the crystal dimensions and of the order of the mean free path at the crystal tip (Dong et al. 1995). For

Ice Crystals in Cirrus

55

a crystal to grow at all at low supersaturation, some level of defect concentrations are necessary for layer nucleation; a faceted crystal implies either that such defects are present to give a nearly flat facet or that the situation of fall speed and ambient supersaturation just allow nucleation of layers at the crystal edges which spread back toward the center of the crystal. Should they not reach the center of the crystal before the supersaturation is reduced by further edge nucleation and growth, a skeletal or hopper crystal results. 3.3. Crystal Growth: Nucleation

In the case of cirrus forming at temperatures near or below -40° C, it may be argued that the prime mechanism of ice nucleation is homogeneous. This is particularly true under conditions where equivalent cooling rates are in excess of those in an updraft of a few centimeters per second (Sassen and Dodd 1988; Heymsfield and Sabin 1989; Jensen et al. 1998; chapter 5). The process for nucleation lies in dilution of the largest cloud condensation nuclei (CCN) along the Kohler curve such that the depression of the equilibrium freezing point enables homogeneous nucleation to occur at temperatures not too far below -40°C (Pueschel et al. 1997). The consequences of this argument are that the low supersaturation-large particle tail of the CCN spectrum may be crucial to the detail of the ice spectrum. In particular, the larger particles >0.5|im dry diameter responsible for ice formation with a concentration of a few per cubic centmeters may be beyond the capabilities of CCN measurement (Hallett et al. 1997; Hudson and Xie 1998) and may be in the range of giant hygroscopic particles (Meyers et al. 1999). Such particles are measured by an instrument such as the cloudscope (Arnott et al. 1995; Hallett et al. 1998). A question to be answered is whether the extreme tail can be inferred from the measured CCN tail with any reliability. Measurements from cirrus levels and also in an aircraft contrail (fig. 3.6) may be extrapolated to give likely concentrations in the contrail at high values of supersaturation (>25% water) and to low values to give the concentrations of giant CCN likely to freeze first homogeneously as they dilute at water saturation of above 70% to 90%. Such extrapolations are indicated in figure 3.6. 3.4. Concept for a Cirrus Crystal Classification

Nucleation events under different conditions can lead to single or polycrystalline growth. In general it appears that nucleation of liquid droplets by accretion on an ice single crystal gives rise to orientation identical with the ice surface with greater probability for higher temperatures and for smaller droplets (Hallett 1964; Fitter and Pruppacher 1973). An intermediate case could give rise to nucleation oriented in preferred directions, with c axes at either 70° or 90° (Furukawa and Kobayashi 1978; Furukawa 1982), with random orientation under more extreme conditions (Penn and Banfield 1998). The overall effect is that subsequent vapor growth gives changed and often multiple orientations. The number of individual crystals from such a nucleation event necessarily is a competitive

27 April 1996-SUCCESS

Figure 3.6. CCN spectra, measured by the Hudson CCN spectrometer from ambient air and near an old aircraft contrail over Kansas (after Hudson and Xie 1998). Extrapolation (within error uncertainties) to lower supersaturation indicates the large particle tail, which dilutes at subwater saturation to form haze droplets that nucleate homogeneously to form the initial ice crystals. Extrapolation to high supersaturation gives the concentration of droplets forming in a cooling contrail at specified water supersaturations, usually some 25 % over water which subsequently dilute, and nucleate homogeneously as the temperature falls below -40°C. In an environment between ice and water saturation, such crystals grow and may lead to significant cirrus appearance over extensive areas of many hundreds of kilometers, (a) Measurements in ambient air, April 27,1996, 20:40Z -43°C, 288mb, in a clean layer sandwiched between other layers with values varying over X2 to X5. Measurements near a contrail (b) show much higher concentrations, particularly in higher sulfur containing fuel; May 3,1996 20:40Z, -58°C, 208mb.

Ice Crystals in Cirrus

Figure 3.6. (continued)

57

58

Cirrus

process and results in a small number of individual crystal orientations as observed in bullet rosettes and spatial dendrites and plates (Juisto and Weickmann 1973; Gonda and Yamazaki 1978,1982,1984), dependent on supersaturation growth conditions following nucleation. Such considerations are important for laboratory simulation of atmospheric processes, where single, poly-, or multiple crystals may form depending on the local temperature gradient under the chosen nucleation conditions (solid CO2, LN2, cold wire, adiabatic expansion, insoluble ice nucleus). Such considerations limit the utility of laboratory studies for studying habit and electrical and radiation effects in application to the atmosphere unless the nucleation processes are carefully controlled. For accreted droplets that nucleate polycrystals, growth occurs from each droplet as several crystals of differing orientation (Kikuchi 1970). Hence, in general, a one- or twodimensional crystal, such as a plate or column, results from a single monocrystal nucleation event, and a three-dimensional structure results from a single or multiply polycrystalline nucleation, as occurs when riming of a plate by individual separated droplets at low temperature. A further consideration is what happens to crystals as they fall from the base of a moist layer into a dry layer below. Evaporation leads to rounding of the crystal edges, although slow evaporation at a few percent subsaturation may leave substantial regions of faceted crystal, as nucleation of holes requires a defect or a critical undersaturation. Thus, faceted columns may be indicative of growth under conditions of figure 3.5, but also of evaporation under small subsaturation. Figure 3.7a shows a crystal collected on the cloudscope evaporating under dynamic heating conditions, temperature about -50°C, yet maintaining a columnlike appearance. Breakup occurs toward the end of evaporation (fig. 3.7b). Experiments at higher temperatures (Oraltay and Hallett 1989; Dong et al. 1994; Swanson et al. 1998; Nelson 1998) show that crystals become rounded and sometimes break up on evaporation, and it appears that similar effects occur under cirrus conditions. A thin column may lead to as many as 10 crystals when evaporating under intermediate ice undersaturation of some tens of percent. Thus, a cirrus layer may maintain itself from the viewpoint of crystal numbers by recycling fragmented particles under the right conditions. Such particles appear to be single crystalline and could regrow to single-faceted crystals; it would be difficult to distinguish between a single crystal frozen drop and small crystal origin from a microscopic analysis. The classification of snow by Magono and Lee (1966) provides a background for a useful description of ice particle morphology. Laboratory work of Nakaya (1954), Kobayashi (1957), and Hallett and Mason (1958) provides a physical basis for such classification where crystal morphology is related to growth conditions (temperature and supersaturation), and, more important, complex morphology (such as capped columns) is related to changing growth conditions. The work of Keller and Hallett (1982), Alena et al. (1990), and Dong et al. (1995), combined with that of Bailey and Hallett (2000) demonstrate that the concept can be readily extended to cirrus crystals. It is necessary to take into account the influence on habit and polycrystal nucleation and growth related to defect structure, particularly at low supersaturations of a few percent over ice. The implication is

Ice Crystals in Cirrus

59

Figure 3.7. Time sequence of thin ice columns, 50 um length, captured on the cloudscope mounted on the NASA DC-8, video recorded at 1/30 s intervals. Images shown are at 1/10 s intervals. The crystals are from an old contrail made by the DC-8 off the California coast and was shown by satellite observation to grow extensively as it moved over the southwestern United States; 11:22:31Z, May 12,1996, -48°C. (a) Some columnar crystals show a uniform thinning and little shortening during evaporation, maintaining crystal facets, (b) Some column crystals become irregular and rounded on evaporation, suggesting breakup. Images digitized and filtered.

that it should be possible, with aid of a diagram such as figure 3.5, to interpret the changing growth conditions of any given crystal. Clearly, ambiguities arise in as far as similar habits may be produced under a range of conditions, and this needs to be taken into account for the interpretation. The fact that many crystals fail to conform to the idealized crystalline forms discussed here is of major importance (Korolev et al. 1999,2000). This may result from complications from different nucleation, growth and evaporation processes; herein lies a future challenge. From the viewpoint of interpreting aircraft samples of ice crystals, the situation yields constraints and opportunity. In general, temperature is well measured from an aircraft, particularly at cirrus levels with low ice content. A crystal collected at a given level will necessarily represent a history of growth over a range of conditions—its (largely unknown) trajectory since nucleation. What can be

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Figure 3.7. (continued)

readily observed is the growth form at the growing crystal periphery at the time of collection, which together with the temperature, gives a point or surface on the temperature-growth rate-supersaturation diagram, as in figure 3.5. Measurements over an appropriate time (space) interval yield a spectrum of particle sizes and shapes that can be used to derive a range of nucleation processes, under a given set of environmental conditions. A consistency check (we hesitate to use the term "validation") lies in inferring a vertical velocity to give a deduced ambient supersaturation for growth and comparison with measurement or a local range of velocities inferred by measurements by, for example, Doppler techniques (Mace et al. 1998). Thus, ambient supersaturation will be given by a difference of vapor made available by cooling resulting from vertical motion and that removed by the growing crystals. This leads to a relation of the form:

Ice Crystals in Cirrus

61

where U - a vertical velocity; a includes terms to give the amount of vapor available by cooling at the ambient lapse rate; r = a crystal dimension; c - geometric factor used to compute mass growth rate; and Z represents summation over all particles in the sampled volume. As an alternative, laboratory results may be used to give the growth rate. A fall-velocity correction to supersaturation is necessary for larger particles. A further consideration lies in comparing the crystals observed at the earth's surface formed from a strong low level inversion at the relatively high surface pressure with higher level crystals in cirrus. One possibility is that wave vertical velocity aloft may be greater than below, in the lower density air as a wave disturbance propagates upward from below. Thus, more nuclei may be activated, leading to a lower ambient supersaturation. The spectrum of CCN may also differ significantly between the two locations. It is obvious that prediction of cirrus characteristics is complex. High level aircraft observations show that on occasion high concentrations of ice crystals are present (Knollenberg et al. 1993), suggesting a locally high vertical velocity to give a transient high supersaturation leading to dilution and homogeneous ice nucleation of the larger hygroscopic particles. 3.5. Crystal Orientation and Fall

Most ice particles are nonspherical, and their fall orientation at terminal velocity depends on the detail of the shape and the particle density and, under some circumstances, the spatial distribution of density. A preferred fall orientation of nonspherical particles is important in producing natural optical phenomena such as sun dogs and arcs (Greenler 1980) and is also of importance for remote sensing both by lidar at visible or near-visible wavelengths and radar wavelengths for larger particles (Hendry and McCormick 1976; Weinheimer and Few 1983; Lynch et al. 1994; Metcalf 1995; Pekkola et al. 1998; chapter 2, this volume). Particl <10um are subject to Brownian rotation (Hallett 1987) and smaller particles to Brownian displacement, which is comparable to terminal fall velocity for particles of diameters a few tenths of a micrometer (Frazer 1979). Such particles tend to be oriented at random and fall along a long axis. Larger particles become oriented as the terminal fall velocity increases (possibly with an intermediate region where platelike particles fall at an angle along the direction of their plane; Willmarth et al. 1964; Jayaweera and Mason 1966; List and Schemenauer 1971; Katz 1998. The air flow around the particle establishes torques sufficiently large to dominate the Brownian effects. Local electric fields, >1000 to 2000 Volts/m have a similar effect in orienting ice crystals (Foster and Hallett, 2000). For Reynolds numbers at terminal velocity >0.5-5, the asymmetry of the flow is increasingly important, and flat crystals tend to orient with their plane horizontal, stabilized by attached rear eddies >20. For larger crystals and Reynolds numbers, the attached eddies are shed, and particles oscillate and fall along a helical path. Orientation sometimes occurs for smaller particles and Reynolds numbers with suitable geometry. The most striking example is for pine pollen

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Cirrus

grains (diameter, 106um), with low density "ears," which are seen to be oriented by the ellipticity of the halo produced by diffraction around the sun (Parviainen et al. 1994). One may speculate that the ears serve to reduce the fall speed, thus giving the grains a greater dispersal range, the orientation effect being incidental—unless it helps entry into the appropriate pollination site in the flower. In this case the Brownian rotation angle is 0.05°, insufficient to remove the effect. Thus, particle orientation under terminal fall velocity results from the direct effect of flow, related to Reynolds number, and the effect of gradient of density and shape of the particle. The latter effect is more important for smaller particles and gives orientation when conventional wisdom would dictate otherwise (fig. 3.8). The results obtained from pollen grains are of particular interest because nature so contrives through the genetic code to give a low variability of size and shape, in contrast to situations for cloud droplets and particularly ice crystals in different stages of growth. Similar orientation effects may occur for ice as edge growth out of the plane of a dendrite or plate on one side, as might occur from an accreted droplet with changed crystallographic orientation, and may serve a similar purpose. A question arises as to when random orientation is produced, as is often assumed in numerical calculations of halo light intensity and radiation transfer (Greenler 1980). Clearly, Brownian rotational motion of smaller particles should produce such an effect, as also could a region of mixing leading to turbulent decay. With a viscous limit of a few millimeters, ice particles could be subject to these effects. It is unclear how much of the atmosphere where cirrus forms could be so influenced. A perfectly symmetrical 22° halo often forms in

Figure 3.8. Flow around falling plates and columns (a,c,d) characterized by terminal fall speed Reynolds number (Re). Horizontal orientation of the particles at Re 20-200 results from asymmetry of the flow and lee eddy effects, (b) A pollen grain falling at a much lower Re oriented by low-density "mouse ears" giving addition edge drag; asymmetry in ice crystals may have a similar orienting effect at low Reynolds numbers.

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63

apparently quiescent conditions in the region of thin cirrus well ahead of a frontal system—why? Of interest is the fraction of crystals that need to be oriented to provide a specular reflection for a vertically pointing lidar. It is clear that many samples of ice in a region of several cubic meters from which a lidar pulse is scattered may contain a fraction of flat platelets whose density distribution (or size) leads to horizontal orientation to a fraction of a degree on fall. With crystal concentrations on the order of hundreds per liter, only a small fraction (a few percent) need to be oriented so such a phenomenon is a fairly frequent event and is indicative of such a size and shape spread. Estimating terminal velocity to give particle and mass vertical flux is complicated. Empirical relations between mass, dimension, and crystal form are commonly used. Considerations of measurements in figure 3.5 suggest that measurements of crystals under one set of growth conditions are unlikely to be transferable to other conditions, particularly if a significant change of pressure and hence vapor diffusivity is involved (equation 5). An approach to this problem has been made using a similarity argument (Mitchell 1996). An alternative approach is to use a laboratory-measured habit and inferred density as a variant of figure 3.5 together with estimated or measured drag coefficients for observed crystal shapes. A simplistic approach for a constant shape and drag coefficient is to assume a fall velocity (U) related to particle density (p() and air density (pa): where Cd - drag coefficient and a and p are shape factors. For variable density with radius, an integration may be necessary. Application of the above approach depends on further laboratory work. It also depends critically on measurement techniques available from aircraft to provide meaningful statistics of the larger particles together with direct measurements of properties used in the above analysis. 3.6. Radiative Properties of Cirrus Ice

The optical properties of ice crystals are determined in part by the refractive index of bulk ice, and in part by the ice crystal shape and size. One of the most frequently used tabulations of the refractive index for ice is that due to sources quoted in Warren (1984). Deviations from the Warren tabulation were found by Toon et al. (1994). These deviations were evaluated by Clapp et al. (1995) and were found to be related to the temperature at which the refractive index measurements were obtained. What are the consequences of imperfect knowledge of the refractive index of ice and water, especially in the thermal infrared? To partially evaluate this question, consider various literature measurements of the refractive index of water, as shown in figure 3.9. The real and imaginary parts are shown. Note especially the uncertainty in the refractive index between 3500 and 4000 cm'1. This variation in refractive index can lead to variations in the modeled infrared forcing and remote sensing of clouds. For example, figure 3.10 shows true and retrieved size distributions using the various refractive indices of figure 3.9, and the DW

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Figure 3.9. Real and imaginary refractive index of water from various measurements (DW Downing and Williams 1975; HQ Hale and Querry 1973; WWQ Wieliczka et al. 1989).

(Downing and Williams) refractive index is taken to be exact. Figure 3.10a shows first that the retrieval algorithm is reasonable in that the DW refractive index retrieves the true size distribution; second, note the strong deviation of the WWQ (Wieliczka, Weng, and Querry) retrieval from the true distribution. Yet, the obtained optical depths shown in figure 3.10b are in reasonable agreement. Errors in refractive index can, unfortunately, be translated into errors of retrieved particle information, even though the obtained optical depth is quite satisfactory. This example is from Liu et al. (1999). Though cirrus clouds generally have a warming influence on surface temperature, the presence of small (<50um) ice crystals can complicate matters (Fu and Liou 1993). For low optical depths, the infrared emission at cold temperatures by cirrus dominates solar scattering, and the radiative impact is warming. However, as the optical depth increases, the solar albedo effect of small crystals in cirrus begins to dominate, and these clouds can have a cooling influence on climate.

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65

Figure 3.10. (a) True and retrieved droplet size spectra for the various refractive indices of figure 3.8. (b) All retrieved optical depths are similar to the eye. Note in panel a the large deviation of the WWQ-retrieved size distributions.

Although the solar influence can be modeled reasonably well with the use of the geometrical optics approximation, the infrared radiative properties cannot be handled by these means. Direct measurements (Arnott et al. 1995a; Schmitt et al. 1998; Schmitt and Arnott 1999) of the extinction and emission cross-sections of small ice crystals in cirrus are useful for evaluating new numerical methods (Yang et al. 1997). The large measured spectral variability of extinction (Prabhakara et al. 1990) and emission (Smith et al. 1998) of unusual cirrus clouds can be understood in relation to the laboratory measurements and is due to the presence of copious numbers of small ice crystals relative to the number of large crystals. Schmitt et al. (1998) and Schmitt and Arnott (1999) have shown that the emission from laboratory ice clouds, crystals <30u.m diameter, can be modeled

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adequately using modified Mie theory. The single scattering cross-sections for absorption and extinction are computed from Mie theory with the proviso that the efficiencies are computed for spheres with equivalent ratios of volume to projected area as the ice crystals, and the cross-section is formed by the product of thus computed efficiencies and the actual particle cross-section. Some caution may be necessary because measurements show that significant regions of cirrus may be composed of intimate mixtures of crystals of different habit, as shown in figure 3.1. Other regions may be more uniform on a small scale but patchy on a much larger scale. Relating cirrus crystals to satellite sensing requires evaluation of such phenomena. 3.7. Crystal Measurement Technology

Pioneering work of cirrus crystal forms was carried out from an open cockpit using a hand-held, varnish-coated slide to give impressions for subsequent microscopic observation (Weickmann 1947) (figure 3.1a,b).This technique clearly showed the presence of three-dimensional bullet rosettes. Yet, even in this work it is clear that an assessment of the relative occurrence of various crystal forms in the atmosphere, both as pristine and as complex crystal shapes, is a major undertaking because of the intrinsic variability of their nucleation and growth conditions. The early surface measurements tended to select ideal forms as being of greater aesthetic value for sketching or photography and later observations have similarly selected regions where crystal forms are relatively uniform. The occurrence of multiple habits and multipeaked size spectra at a point measurement is well documented in aircraft measurement with a continuous former coated film (Hallett, 1976; Arnott et al. 1994) and simplistically may be attributed initially to different nucleation and growth processes and subsequently to different fall speeds as well as the effects of mixing in lateral shear, as in Kelvin-Helmholtz instability at an inversion top. A more fundamental question to be addressed is the meaning of any data set of crystal shape, size, and habit distribution in a given measurement. The question of time and spatial scale of the sample is of major importance, and the detail of the averaging process is crucial to how the data may be used. From a fundamental viewpoint, we may be interested in the nucleation and growth processes in a given volume of air which retains some coherence over growth times of interest—say some hundreds of seconds—with some hope of characterizing individual crystals over such a period. A Lagrangian observation strategy is therefore attractive, if not easily accomplished. From an applied viewpoint, crystals need to be characterized over, say, a volume of a lidar pulse, some cubic meters; the volume of a radar pulse some 106m3; or the volume of a satellite footprint some 100km3. To assess precipitation from a frontal system over its precipitation history, a volume of air some 108km3 is more realistic; a precipitation of 1 cm over 1 km2 requires some 1016 individual crystals. The realities of individ ual crystal measurement cannot compete, and the question of what is necessary for a meaningful sample arises. Surface collection and microscopy obviously give a remarkably small sample and cannot provide a realistic sample for such a use. Electro-optical systems (PMS 2DC, PMS 2DP) give greater ease of data

Ice Crystals in Cirrus

67

collection and are subject to some degree of automation, yet they still provide a meager sample in relation to the above numbers (Strom et al. 1997). A similar consideration applies to more recent systems (Lawson et al. 1998; Korolev et al. 1999). Some idea on variability in cirrus can be obtained on a broad scale from microwave radar (Mace et al. 1998), and it is clear that a cellular size on the order of at least 100m exists, as can readily be seen from a cursory visual inspection of any field of cirrus. One may resort to a broader approach by assuming that in a sufficiently large volume of space, particle concentration, or indeed any other characteristic, results from a combination of random events such that Shannon's maximum entropy principle applies. In this case, a Weibull distribution results (Liu and Hallett 1998), implying that any spectrum measurement is but one of a family and a sufficient data set may be specified to provide the best (most probable) distribution. It is necessary to specify a time or spatial boundary for such measurements. It may be convenient to do this on physical grounds, for example, limiting time by a well-determined effect (sea breeze/convection life time, Rossby wave transition time in Eulerian frame, a field of wave clouds, etc). Any individual measurement necessarily departs from this ideal. The reality of any particle measurement lies in the statistics of the numbers in each size bin. In general, there are fewer larger particles, and an upper limit is set for realism by Poisson statistics for the large, rare particles. Radar scattering relates to £jVr6, mass vertical flux to H/Vr5'4'3-5, depending on fall regime, mass to SA^r3, optical effects to ENr2, particle diffusion growth rate to L/Vr, and nucleation processes to Z7V (E = sum over all particles). Uncertainties arise in derived quantities at different sizes depending on where the size cut off in the measurements occurs for the selected sampling time and spatial average. A further consideration lies in direct measurement of properties of individual particles—as impurity content and mean density or density related to radius. The cloudscope class of instruments are candidate for these measurements (Hallett et al. 1998). It is of interest that the images collected by these instruments also show how ice particles evaporate and break up on collection. Measurement of mass may be made directly by impacting the particle on a heated forward-facing optical flat and recording the rate of change of area, inversely related to density. This is alternative operation of the cloudscope (Arnott et al. 1995; Hallett et al. 1998).The integral to complete evaporation gives particle mass. An alternative approach is to measure the power required to maintain the window at constant temperature during evaporation, with mass related to the added power through a latent heat. From the viewpoint of an aircraft measurement (necessarily a long, thin ribbon along its flight path), a longer flight path improves the statistics, but necessarily implies the likelihood of leaving the area (defined in space or in time) where particles are occurring—meters or some tens of kilometers at most for a cirrus regime or hundreds of kilometers for a field of convective storms. Hence, some formal definition of the spatial and volume scale and geometry of measurement becomes imperative for synthesizing data from any set of observations, whether it be area of cloud cover or a particle distribution having the moments discussed above. It may be desirable under some circumstances to average particles by updraft location (updrafts in the upshear of convective clouds have quite

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Cirrus

different microphysical structure from the downshear; Black and Hallett 1999) and combine the two averages for remote-sensing comparison. Other combinations may be required to achieve a sufficient approach to reality. 3.8. Conditions for Uniformity in Ice Formation

From the viewpoint of idealizing ice particle formation and linking the physics of the individual particle nucleation and growth with ambient conditions, specific situations may be identified. A mountain wave lenticular cloud, formed under conditions of high stability, has the merit of having low turbulence levels with traceable air trajectories from conservative variables. There is a well-defined rate of change of relative humidity ahead of the cloud and rate of availability of water vapor in the cloud itself, enabling specification of growth conditions. This situation also occurs for orographic clouds in upslope flow, which can lead to continuous production of uniform crystal type and size under quasi-steady conditions (Liu and Hallett 1998). Conditions change along such trajectories over times on the order of several minutes. Shallower clouds formed in gravity waves on frontal surfaces give somewhat longer growth times. Of present interest is the ability to produce relatively low ice supersaturations which persist over a long time, giving low nucleation rates of CCN (figure 3.6). Such particles freeze homogeneously as they dilute at temperatures somewhat below -40°C (Pueschel et al. 1997). Small droplets freeze as single crystals and grow slowly under ambient conditions in the form of crystals with uniform, flat facets to give well-defined and bright optical effects. The stability is important as it maintains conditions; we outline a conceptional model. Spectacular optical effects are reported extensively in polar regions and are known to be associated with such pristine crystals, both plates and columns (Tape 1994). Less well reported are spectacular mid-latitude summer displays at low temperatures and high levels. A way of producing a low supersaturation is a rapid overrunning of a cold layer by a warmer, moister layer, followed by a slow diffusion of properties from one to the other. Such effects can be idealized by a time-dependent solution of the heat/vapor diffusion equation in one dimension, with initial boundary conditions being uniform temperature and mixing ratio with an initial sharp discontinuity at the interface (Carlsaw and Jaeger 1980). Heat and vapor diffuse almost together (vapor is a little faster) and because the saturation vapor pressure (density) of ice is near exponential with respect to IIT (T Kelvin), a pulse of supersaturation spreads into the cold air (Nix and Fukuta 1974) with time constant: where X - the distance from the interface, D = water vapor diffusivity in air, and K = the thermal diffusivity. For distances of tens of centimeters, the times are of the order of 100sec; for meters the time is a few hours (fig. 3.11). The numerical values may be scaled according to equation 11. Shear can influence the boundary conditions and change these times, but maintaining stability is important to the process. The computed supersaturations

Ice Crystals in Cirrus

Figure 3.11. Computed time-dependent supersaturation produced by heat and vapor diffusion in a strong vertical gradient of temperature and water vapor density (100,1000, and 10,000s). In the case chosen, ice-saturated warm air overlies ice-saturated cold air and extends to infinity in the horizontal. Values of heat and vapor diffusivity are equivalent to the standard atmosphere, taken as the mean over the range of values (K = 0.421, D = 0.473 cm2/s). Profiles are shown for temperature, actual vapor density, saturation vapor density, and ice supersaturation. This situation is idealized from penetrating convection outflow or larger scale upper flow overrunning an inversion or a density current underrunning a warm layer aloft. The calculation begins at t = 0 and runs for 10,000s over a length scale of ±250 cm. The supersaturation peak moves into the cold air and remains constant with time, a consequence of the assumed assumption of horizontal homogeneity extending to infinity. Other scenarios, with a linear or spherical warm moist region, give a supersaturation ratio that attenuates with time as it propagates. Gravity waves on the inversion of appropriate wavelength, and amplitude may maintain crystals in nearconstant growth conditions to provide growth to sizes large enough to give spectacular optical effects.

Figure 3.12. Replica of individual crystals collected by the University of North Dakota Citation aircraft in the outflow of Tropical Storm Nora, having moved north-northeast from Baja California to southern California. Moist air, near ice saturation existed between 9 and 13km. Selected crystals (a) show well-formed facets and little internal structure, (b) show hexagonal, scalene, triangular, and columnar shapes. There is similarity to crystals found in diamond dust, as in Antarctica (Tape 1994). Spectacular optical effects resulted from these regions of upper-level ice. Less well-formed crystals of other shapes and habits were also present.

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shown in figure 3.11 for different times of 100, 1000, and 10,000 seconds do not decay with distance and therefore lead to nucleation and growth of particles at differing distances from the original inversion discontinuity. This behavior results from the assumption of infinite lateral extent; in reality the discontinuity may be linear or circular, giving a decreasing supersaturation as the disturbance propagates. Crystals grow at a rate of a few tenths of a micrometer per second under these conditions (fig. 3.5), so that a crystal of diameter 100 um requires some few hundred seconds for growth, equivalent to a fall distance of some tens of meters. Thus, to maintain a crystal in growth conditions would require a special combination of progressive gravity waves having such a diffusion supersaturation field but descending with the growing crystal. This is necessarily an infrequent occurrence (the sky is not universally covered with spectacular optical events), but may be sufficiently frequent to explain the occasional occurrence of spectacular optical displays under both high cirrus and boundary layer diamond dust conditions. Figure 3.12 shows a replica of pristine crystals collected in the outflow from an old hurricane as it passed from Utah to Kansas. It is clear that such pristine crystals do not readily form under changing and certainly convective conditions where crystals are lofted to fall out and grow under a wide range of temperature, supersaturation, and riming conditions. Kelvin-Helmholtz instability at an inversion top also fails to provide the right conditions. The detailed structure of inversions is far from well known. Discontinuities can be extremely sharp, with 10 K sometimes extending over a meter or less (Edinger and Wurtele 1972). Such sharp discontinuities would not appear in any standard sounding analysis (Hallett and Hallett 2000). The spatial distribution of supersaturation under these conditions is an interesting topic for further study. 3.9. Conclusions

The trail of defining and specifying cirrus clouds has followed the process of nucleation, growth, and evaporation of individual crystals. It requires a knowledge of the dynamic and radiation conditions under which cirrus evolve and ultimately specification on physical grounds of a spatial and temporal averaging domain. This domain is related to the time and spatial resolution of the instruments both for in situ and remote sensing. For multiple instruments, measurements of the same volume and geometry of air by the different techniques is crucial to a combination of observations. A comparison of the properties of crystals in high level and low level cloud (as cirrus near the tropopause and ice clouds near the surface formed under similar temperature and supersaturation) is possible providing pressuredependent variables such as vapor diffusivity and radiation field are taken into account as well as the likely mechanism of nucleation. For similar mechanisms, the individual particle evolution does not differ between altitudes, and comparison of dynamical processes is the controlling difference. Specification of any field of ice crystal cloud (high level cirrus or low level cirrus type near a thermal inversion at the surface) is dependent on the CCN spectrum and the initial nucleation

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dynamics, with the later growth dependent on the evolution of the dynamical processes as providing the time scale. The shape and density distribution in each crystal influences the radiation field; there is related influence on the vertical flux of water substance through fallout, which may be even more critical in the overall scheme of things. All need to be considered in any numerical comparison. It is a difficult but not impossible undertaking.

Acknowledgments Laboratory work and partial support for participation in FIRE were supported by grant ATM-9413437, & ATM-9900360 Physical Meteorology Program, National Science Foundation. Field observations are drawn from programs supported by the National Aeronauatics and Space Administration: TOGA COARE 1993 (NAG-2663); SUCCESS 1996 (NAG-2-923); and FIRE, 1991,1998, (NAG-1-2046); DOE, ARM, 1994,1998 (353799-AQ5). We thank Ken De Pauli and Matthew Meyers for their assistance in data analysis.

References Anderson, B.J., and J. Hallett, 1979. Influence of environmental saturation and electrical field on growth and evaporation of epitaxial ice crystals, /. Cryst. Growth, 46, 427^44. Alena, T, J. Hallett, and C.P.R. Saunders, 1990. On the facet-skeletal transition of snow crystals: experiments in high and low gravity. /. Cryst. Growth, 104, 539-555. Arnott, W.P., Y.Y. Dong, and J. Hallett, 1995a. Extinction efficiency in the infrared (2-18 um) of laboratory ice clouds: observations of scattering minima in the Christiansen bands of ice. Appl. Opt., 34, 541-551. Arnott, W.P., Y.Y. Dong, J. Hallett, and M.R. Poellot, 1994. Observations and importance of small ice crystals in a cirrus cloud from FIRE II data, 22 Nov 1994. J. Geophys. Res., 99,1371-1381. Arnott, W.P., Y. Dong, R. Purcell, and J. Hallett, 1995b. Direct airborne sampling of small ice crystals and the concentration and phase of haze particles, in Preprints of the AMS Ninth Symposium on Meteorological Observations and Instrumentation, W.F. Dabberdt Ed. American Meterological Society, Boston, MA, pp. 415-420. Bailey, M.P., and J. Hallett, 1998. Laboratory investigation of ice growth from the vapor under cirrus conditions between -30°C and -70°C. in Preprints of the AMS Conference on Cloud Physics, R.M. Rauber and J.L. Stith Eds. American Meterological Society, Boston, MA, pp. 434-437. Bailey, M., and J. Hallett, 2000. Nucleation, growth and habit distributions of cirrus type crystals under controlled laboratory conditions. 13th International Conference on Clouds and Precipitation. Desert Research Institute, Reno, NV; J. Hallett and G.A. Isaac (eds.), pp. 629-632. Bentley, W.A., and W.J. Humphreys, 1962. Snow Crystals. Dover Publications, New York. Originally published McGraw-Hill Book Company Inc. New York and London 1931, 227p. Black, R.A., and J. Hallett, 1999. Electrification of the hurricane. /. Atmos. Sci., 56, 2004-2028. Carslaw, H.S., and J.C. Jaeger, 1980. Conduction of Heat in Solids. Oxford University Press, New York.

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Cho, N., and J. Hallett, 1984. Epitaxial ice crystal growth on covellite (CuS) II. Growth characteristics of basal plane steps. /. Cryst. Growth, 69,325-334. Clapp, M.L., D.R. Worsnop, and R.E. Miller, 1995. Frequency-dependent optical constants of water ice obtained directly from aerosol extinction spectra. /. Phys. Chem., 99, 6317-6326. Dong, Y., J. Hallett, and C. Knight, 1995. Snow dendrite growth, in Preprints of the AMS Conference on Cloud Physics, H. Ochs and R. Rasmussen Eds. American Meterological Society, Boston, MA, pp. 118-121. Dong, Y.Y., R.G. Oraltay, and J. Hallett, 1994. Ice particle generation during evaporation. /. Atmos. Res., 32, 45-53. Downing, H.D., and D. Williams, 1975. Optical constants of water in the infrared. / Geophys. Res., 80,1656-1661. Edinger, J.G., and M.G. Wurtele, 1972. Interpretation of some phenomena observed in Southern California Stratus. Month. Weather Rev., 100, 389-398. Foster, T.C., and J. Hallett, 2000. A laboratory investigation of the orientation, alignment, and oscillation of ice crystals. 13th International Conference on Clouds and Precipitation, J. Hallett and G.A. Isaac, (eds.), Desert Research Institute, Reno, NV, pp. 641-644. Frazer, A.B., 1979. Which size of ice crystals causes halos? /. Opt. Soc. Am., 69, 11121118. Fu, Q., and K.N. Liou, 1993. Parameterization of the radiative properties of cirrus clouds. /. Atmos. Sci., 50,2008-2025. Furukawa, Y, 1982. Structures and formation mechanisms of snow polycrystals./. Meteor. Soc. Japan, 60, 535-547. Furukawa, Y, and T. Kobayashi, 1978. On the growth mechanisms of polycrystalline snow crystals with a specific grain boundary. /. Cryst. Growth, 45,57-65. Furukawa, Y, M. Yamamoto, and T. Kuroda, 1987. Ellipsometric study of the transition layer on the surface of an ice crystal. J. Cryst. Growth, 82, 665-677. Gonda, T., 1980. The influence of the diffusion of vapor and heat on the morphology of ice crystals grown from the vapor./ Cryst. Growth, 49,173-181. Gonda, T., and T. Koike, 1982. Growth rates and growth forms of ice crystals grown from the vapor phase. / Cryst. Growth, 56, 259-264. Gonda, T., and T. Yamazaki, 1978. Morphology of ice droxtals grown from supercooled water droplets. /. Cryst. Growth, 45, 66-69. Gonda, T., and T. Yamazaki, 1982. Morphological stability of polyhedral ice crystals growing from the vapor phase. /. Cryst. Growth, 60,259-263. Gonda, T., and T. Yamazaki, 1984. Notes and correspondence. Initial growth forms of snow crystals growing from frozen cloud droplets. /. Meteor. Soc. Japan, 62, 190-192. Goodman, J., O.B. Toon, R.F. Pueschel, K.G. Snetsinger, and S. Verma, 1989. Antarctic stratospheric ice crystals. /. Geophys. Res., 94,16449-16457. Greenler, R., 1980. Rainbows, Halos, and Glories. Cambridge University Press, Cambridge. Hale, G.M., and M.R. Querry, 1973. Optical constants of water in the 200-nm to 200-um wavelength region. Appl. Opt, 12, 555-563. Hallett, J., 1961. The growth of ice crystals on freshly cleaved covellite surfaces. Philos. Mag., 6,1073-1087. Hallett, J., 1964. Experimental studies of the crystallization of supercooled water. /. Atmos. Sci., 21, 671-682. Hallett, J., 1976. Measurement of size, concentration and structure of atmospheric particulates by the airborne continuous particle replicator. AFGL-TR-76-0149. Air Force Geophysics Laboratory, Hanscom AFB, MA 61731. Hallett, J., 1987. Faceted snow crystals. /. Opt. Soc. Amer., 4,581-588.

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Hallett, J., W.P. Arnott, R. Purcell, and C. Schmidt, 1998. A technique for characterizing aerosol and cloud particles by real time processing, in PM2.^:A Fine Particle Standard. Proceedings of an International Specialty Conference, Vol. 1. J. Chow and P. Koutrakis, Eds. Air & Waste Management Association, Pittsburgh, PA, 318-325. Hallett, J. and J.T. Hallett, 2000. The scale and role of spatial discontinities of particles in clouds. 13th International Conference on Clouds and Precipitation, Desert Research Institute, Reno, Nevada. J. Hallett and G.A. Isaac, (eds.), 633-636. Hallett, J., J.G. Hudson, F. Rogers, E. Teets, S.S. Yum, and Y. Xie, 1997. The influence of natural and aircraft exhaust on aerosol and cirrus formation, in Preprints of the Third Conference on Atmospheric Chemistry, C.J. Walcek Ed. American Meterological Society, Boston, MA, pp. 45-53. Hallett, I, and A.C. Knight, 1994. On the symmetry of snow dendrites. J. Atmos. Sci., 32, 1-11. Hallett, J., and BJ. Mason, 1958. The influence of temperature and saturation on the habit of ice crystals grown from the vapour. Proc. Roy. Soc. A, 247, 440-453. Hamilton, D.R., and R.G. Seidensticker, 1960. Propagation mechanism of germanium dendrites. J. Appl. Phys., 31,1165-1168. Hendry, A., and G.C. McCormick, 1976. Radar observations of the alignment of precipitation particles for electrostatic fields in thunderstorms. / Geophys. Res., 81, 53535357. Heymsfield, A.J., 1986. Ice particles observed in a cirriform cloud at -83°C and implications for polar stratospheric clouds. J. Atmos. Sci., 43,851-855. Heymsfield, A.J., and R.M. Sabin, 1989. Cirrus crystal nucleation by homogeneous freezing of solution droplets. J. Atmos. Sci., 46,2252-2264. Howard, L., 1803. On the Modifications of Clouds. J.Taylor, London. Hudson, J.G, and Y. Xie, 1998. Cloud condensation nuclei measurements in the high troposphere and in jet aircraft exhaust. Geophys. Res. Lett., 25,1395-1398. Jayaweera, K.O.L.F., and B.J. Mason, 1966. The falling motions of loaded cylinders and discs simulating snow crystals. Quart. J. Roy. Meteor. Soc., 92, 151-156. Jayaweera, K.O.L.F., and B.J. Mason, 1985. The behaviour of freely falling cylinders and cones in a viscous fluid. /. Fluid Mech., 22, 709-720. Jensen, E.J., O.B.Toon, A.Tabazadeh, G.W. Sachse, B.E.Anderson, K.R. Chan, C.W.Twohy, B. Gandrud, S.M. Aulenbach, A. Heymsfield, J. Hallett, and B. Gary, 1998. Ice nucleation processes in upper tropospheric waveclouds observed during SUCCESS. Geophys. Res. Letters, 25, 1363-1366. Jiusto, J.E., and H.K. Weickmann, 1973. Types of snowfall. AMS Bull., 54, 1148-1162. Katz, J.I., 1998. Subsuns and low Reynolds number flow. J. Atmos. Sci., 55, 3358-3362. Keller, V., and J. Hallett, 1982. Influence of air velocity on the habit of ice crystal growth from the vapor. J. Cryst. Growth, 60, 91-106. Keller, V., C.V. McKnight, and J. Hallett, 1980. Growth of ice discs from the vapor and the mechanism of habit change of ice crystals. J. Cryst. Growth, 49,458-464. Kikuchi, K., 1970. Peculiar shapes of solid precipitation observed at Syowa Station, Antarctica. /. Meteor. Soc. Japan, 48,243-249. Knollenberg, R.G, K. Kelly, and J.C. Wilson, 1993. Measurements of high number densities of ice crystals in the tops of tropical cumulonimbus. /. Geophys. Res., 98, 8639-8664. Kobayashi, T, 1957. Experimental researches on the snow crystal habit and growth by means of a diffusion cloud chamber. /. Meterol. Soc. Japan, 75, 38^49. Kobayashi,T, 1976. On twinned structures in snow crystals./ Cryst. Growth,32,233-249. Kobayashi, T, Y. Furakawa, K. Kikuchi, and H. Uyeda, 1976. On the twinned structure of snow crystals. /. Cryst. Growth, 32, 233-249.

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Korolev, A.V., G.A. Isaac, and J. Hallett, 1999. Ice particle habits in Arctic clouds. Geophys. Res. Lett., 26,1299-1302. Korolev, A.V., G.A. Isaac, and J. Hallett, 2000. Ice particle habits in Stratiform clouds. Quart. J. Roy. Meteor. Soc., 126,2873-2902. Lawson, P.R., A.V. Korolev, S.G. Cober, T. Huang, J.W. Strapp, and G.A. Isaac, 1998. Improved measurements of the droplet size distribution of a freezing drizzle event. Atmos. Res., 47,181-191. Lin, H., K.J. Noone, J. Strom, and A.J. Heymsfield, 1998. Dynamical influences on cirrus cloud formation process. /. Atmos. Sci., 55,1940-1949. Liou, K.N., and Y.Takano, 1994. Light scattered by non-spherical particles: Remote sensing and climate implications. /. Atmos. Res., 31,271-298. Liou, K.N., 1986. Influence of cirrus clouds on weather and climate processes: A global perspective. Month. Weather Rev., 114,1167-1199. List, R., and R.S. Schemenauer, 1971. Freefall behavior of planar snow crystals, conical graupel, and small hail. /. Atmos. Sci., 28,110-115. Liu, Y., W.P. Arnott, and J. Hallett, 1999. Particle size distribution retrieval from multispectral optical depth: Influences of particle nonsphericity and refractive index. J. Geophys. Res., 104 (D24): 31753-31762. Liu, Y., and J. Hallett, 1998. On size distributions of cloud droplets growing by condensation: A new conceptual model. /. Atmos. Sci., 55, 527-536. Lynch, D.K., S.D. Gedzelman, and A.B. Fraser, 1994. Subsuns, Bottlinger's rings, and elliptical halos. Appl. Opt., 33, 4580-4589. Mace, G.G., K. Sassen, S. Kinne, and T.P. Ackerman, 1998. An examination of cirrus cloud characteristics using data from millimeter wave radar and lidar: The 24 April SUCCESS case study. Geophys. Res. Lett., 25,1133-1136. Macke, A., PR Francis, G.M. McFarquhar, and S. Kinne, 1998. The role of ice particle shapes and size distributions in the single scattering properties of cirrus clouds. J. Atmos. Sci., 55, 2874-2883. Magono, C., and C. Lee, 1966. Meteorological classification of natural snow crystals. /. Fac. Sci., Hokkaido Univ.,Ser. VII, 2, 321-335. Maskasky, I.E., 1986. An enhanced understanding of silver halide tabular-grain growth. /. Imaging Sci., 31, 15-26. McKnight, C.V., and J. Hallett, 1978. X-ray topographic studies of dislocations in vapor-grown ice crystals. J. Glaciol., 21, 397-407. Metcalf, J.I., 1995. Radar observations of changing orientations of hydrometeors in thunderstorms. /. Appl. Meteor., 34, 757-772. Meyers, M., and J. Hallett, 1998. Ice crystal morphology in aircraft contrails and cirrus. in Preprints, AMS Conference on Cloud Physics, Everett, Washington, 14th Conference on Planned and Inadvertent Weather Modification, August 17-21, pp. 1720. Meyers, M., and J. Hallett, W.P. Arnott, and J. Niehues-Brooks, 1999. Aircraft observations of giant nuclei in arctic regions. Preprints AMS Conference on Polar Meteorology, Dallas, TX, January, 188-191. Mishchenko, M.I., W.B. Rossow, A. Macke, and A.A. Lacis, 1996. Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape./. Geophys. Res., 101,16973-16985. Mitchell, D.L., 1996. Use of mass- and area-dimensional power laws for determining precipitation particle terminal velocities./. Atmos. Sci., 53,1710-1723. Nakaya, U, 1954. Snow crystals, natural and artificial. Harvard University Press, Cambridge, MA. Nelson, I,1998. Sublimation of ice crystals. /. Atmos. Sci., 55, 910-919.

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4

Mid-latitude and Tropical Cirrus Microphysical Properties

A N D R E W J. H E Y M S F I E L D GREG M. M C F A R Q U H A R

4.1. Cirrus Structure and Types

Cirrus, a principal cloud type that forms at low temperatures in the upper troposphere, is composed almost always of ice crystals (Heymsfield and Miloshevich 1989) and on average cover about 20% of the earth's surface (Hartmann et al. 1992). The purpose of this chapter is to characterize the microphysical properties of cirrus clouds. The Glossary of Meteorology (Huschke 1970) defines cirrus clouds as detached clouds in the form of white, delicate filaments, or white or mostly white patches, which are composed of ice crystals. This cloud type forms primarily in the upper troposphere, above about 8km (25,000 feet), where temperatures are generally below -30° C. There are a number of types of cirrus clouds, with the most frequent ones occurring in layers or sheets with horizontal dimensions of hundreds or even thousands of kilometers. Because horizontal dimensions are much greater than vertical extent, this particular type of cirrus cloud is called cirrostratus. Cirrus can also form in a patchy or tufted shape, when the ice crystals are large enough to acquire an appreciable fall velocity (the rate at which ice crystals fall in the vertical) so that trails of considerable vertical extent may form. These trails curve irregularly or slant, sometimes with a commalike shape, as a result of changes in the horizontal wind velocity with height and variations in the fall velocity of the ice crystals. A wispy, layered cloud that forms at the top of a cumulonimbus cloud, termed an "anvil" because of its shape, is a cirrus that consists essentially of ice debris which spreads outward from the convective parts of the storm. Anvils do not include the white, dense portions of thunderstorms or the active convective 78

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column. Anvils can spread to form large, widespread cloud layers. Tropical cirrus clouds are thought to arise primarily from cumulonimbus clouds. Unlike the thin, wispy cirrus typifying mid-latitudes, the high altitudes and extensive lateral and vertical development that often characterize tropical cirrus impose substantial large-scale radiative effects in the atmosphere and at the earth's surface (Hartmann et al. 1992; Collins et al. 1996). The cirrus-like low-level ice clouds and ice fogs of the Arctic are not considered cirrus. Neither are altocumulus clouds, which form in distinct layers, often less than 100m thick, in the mid-troposphere at about 5-8 km. They are identified from the ground as sharply outlined clouds reflecting their tendency to consist of a liquid water composition containing rounded, often bubblelike convective elements. Cirrus often merge with altocumulus clouds, producing a deep ice-cloud layer. In this chapter, we draw upon microphysical data collected in situ from a variety of sources and in a number of primary cirrus cloud types to describe the principal microphysical properties of cirrus. The description includes crystal shapes, bulk properties such as ice water content, and general characteristics such as profiles of properties in the vertical. 4.2. Overview of Principal in situ Measurements

Figure 4.1 illustrates locations where in situ microphysical data were collected during field campaigns by a wide variety of investigators using a variety of instruments. The earliest measurements are those of Weickmann (1947), who characterized the shapes of cirrus crystals above Germany. There have been many other mid-latitude campaigns, including measurements of cirrus and cirrostratus made during the First International Satellite Cloud and Climatology Project (ISCCP) Regional Experiments (FIRE I and FIRE II) over Wisconsin and Kansas (e.g., Heymsfield et al. 1990; Arnott et al. 1994; Heymsfield and Miloshevich 1995), the Environmental Definition Program (EDP) over the continental United States (Heymsfield 1977), the Subsonic Aircraft: Contrail and Cloud Effects Special Study (SUCCESS), and flights over the continental United States between 1979 and 1984 described by Jeck (1986). Mid-latitude measurements made in Europe include those from the European Cloud and Radiation Experiment (EUCREX; Raschke et al. 1998), the International Cirrus Experiment (ICE) and pre-ICE (e.g., Personne et al. 1990; Raschke et al. 1990; Krupp 1992), observations of young cirrus clouds over southern Germany (Strom et al. 1997), and those made by Mazin and co-investigators over a 20-year period in the former Soviet Union (Mazin 1995). Matsuo et al. (1992), Mizuno et al. (1994), and more recently Murakami and Orikasa (personal communication, 1998) have also made observations of cirrus clouds over Japan. Microphysical knowledge of anvil cirrus is less complete than that of cirrus formed in situ because anvils, particularly their upper regions, are not as accessible to aircraft, and where they are accessible, the ice crystals have often been too small or irregular in shape to be accurately counted and sized with optical cloud particle spectrometers. Nevertheless, measurements of anvil cirrus over Montana

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Figure 4.1. Locations where in-situ microphysical measurements of cirrus have been made. Acronyms of projects are denned in text; labels are listed in approximate chronological order. Measurements not identified by project name are listed by location (e.g., Japan, Kwajalein), or by principal investigator (e.g., Jeck, Mazin).

during the Cooperative Convection Precipitation Experiment (CCOPE; Heymsfield 1993) and over Oklahoma and Kansas during PRESTORM (Meitin and Cunning 1985) have been made. Bennetts and Ouldridge (1984) have also described aircraft measurements in the anvil of a winter maritime cumulonimbus near England (fig. 4.1). The Texas Florida Underpass (TEFLUN) experiments A and B in Texas and Florida collected data in anvil cirrus. Measurements of tropical cirrus have been even more difficult to make because these clouds often extend to very high altitudes in locations far removed

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from aircraft landing sites, and again often consist of small and irregular particles. The measurements made in the tropics include cirrus sampled in the vicinity of Kwajalein, Marshall Islands (Heymsfield 1986a), cirrus sampled during the Global Atlantic Research Program (GARP) and Global Atlantic Tropical Experiment (GATE; Griffith et al. 1980), measurements near the tops of thunderstorm cirrus in the vicinity of Panama (Knollenberg et al. 1982), cirrus associated with tropical cyclones and related cloud systems off the northern coast of Australia during the Stratospheric-Tropospheric Exchange Project (STEP) (Knollenberg et al. 1993), cirrus and deep convection sampled during the Tropical Ocean Global Atmosphere/Coupled Ocean-Atmosphere Response Experiment (TOGA-COARE; although the data quality is poor), and outflow anvils characterized during the Central Equatorial Pacific Experiment (CEPEX; Heymsfield and McFarquhar 1996). Measurements made in Arctic cirrus during the Surface Heat Budget of the Arctic Ocean (SHEBA) experiment and the Beaufort Arctic Storms Experiment (BASE) are also depicted in figure 4.1. Although measurements in cirrus not depicted in figure 4.1 have been made, the figure does represent most focused field campaigns. The wide diversity in the measured microphysical properties described in section 4.6 is presumably due to both natural variability and differences in the characteristics of the instrumentation used. Dowling and Radke (1990) attempted to summarize the microphysical data from a wide number of projects, but found that the data were widely scattered. The cloud-center altitude ranged from 4 to 20km, cloud thickness from 0.1 to 8km, crystal number densities from 10"4 to 104/liter, condensed water contents from 10"4 to 1.2g/m3, and crystal sizes from 1 to 8000 jim. 4.3. Instrumentation

The particle measurement system's (PMS) two-dimensional imaging probes, the 2D-C cloud probe and, to a lesser extent, the 2D-P precipitation probe, have been the cornerstones for measuring microphysical properties of cirrus clouds. The 2D probes collect electronic, two-dimensional images of particles from about 50 um (2D-C) to >4mm (2D-P), from which size spectra can be readily obtained and ice crystal shape ("habit") information may be inferred. Hereafter, size refers to dimension, which for the 2D-C and 2D-P is usually the maximum particle dimension either parallel or normal to the aircraft flight direction. The measurement principal and the various configurations of probes are described by Knollenberg (1976), Gordon and Marwitz (1984), Joe and List (1987), Korolev et al. (1998), and Baumgardner and Korolev (1997). These probes have prevailed because they are relatively reliable, data processing is straightforward and quick, and because spectral moments (e.g., effective radius, extinction coefficient, ice water content, radar reflectivity factor) are readily derived. Possible errors or uncertainties in the moments arise from errors inherent in the measurement of the particle size distributions because of uncertainty in the sampling volume at small crystal sizes and high air speeds (Baumgardner and Korolev 1997), a lack of information on ice crystals below the

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2D-C size detection threshold, particle habit determination, and errors or variability in the relationships used to convert size distributions to extinction coefficients and mass. In addition, investigators treat sampling volume and particle sizing differently; for example, the National Center for Atmospheric Research (NCAR) processing routines add one-and-a-half slices to each particle (the probe begins to record data only after a particle fully occults at least one photodiode, and there is additional one-half slice uncertainty in particle length) to get the particle's size and account for the probe's response time (whereas some other processing routines do not), which in turn affects the sample volume. As detection threshold and probe resolution are an inverse function of aircraft true airspeed, the high airspeeds of some research aircraft (e.g., the NASA DC-8 and Learjets) lead to degradation of performance. Other probes have been used to measure size distributions of ice crystals. The one-dimensional cloud probe (1D-C) is an earlier version of the 2D-C which gives only a one-dimensional picture of crystals because it lacks the fast response electronics of the 2D-C probe. A forward-scattering spectrometer probe (FSSP) measures crystals with diameters between 0.4 and 75 jam, with the exact limits depending on the model and probe settings, by interpreting forward-scattered light from cloud particles as originating from Mie scatterers. An axial scattering spectrometer probe (ASSP) has also been used. From several passes through a line of cumulus congestus, Gardiner and Hallett (1985) showed that ice particle concentrations measured by an FSSP model 100 were 2-3 orders of magnitude larger than the actual ice concentrations measured using a formvar replicator and a 2D-C probe. This amplification could have resulted from a variety of factors, most importantly the detection of scattered light from ice particles larger than those which the probe was designed to sense. The FSSP-300 has a masked-slit aperture and a laser light source with a Gaussian-shaped intensity distribution, designed to provide a well-determined sample volume and to reduce or eliminate counts produced by ice particles outside the sample volume. The probe appears to measure droplets and ice crystals associated with orographic wave clouds well, where particles are at most tens of microns (Heymsfield and Miloshevich 1995), but there are suggestions that it still responds to the larger ice crystals (e.g., Gayet et al. 1996; Heymsfield and McFarquhar 1996). In addition to electronic probes, impactor-type probes can obtain ice crystal size distributions. These probes are especially important for supplementing the optical probes with information about crystal sizes smaller than 50 um or so. A video ice particle sampler (VIPS), developed at NCAR, can be used to obtain images of particles larger than about 5 urn (Heymsfield and McFarquhar 1996) by collecting particles in silicone oil on an 8-mm wide film, and then imaging them with video microscopes at two different magnifications. Collection efficiencies derived from Ranz and Wong (1952) are near unity for particle sizes >5 urn at aircraft speeds of 200 m/s. An ice particle replicator developed at the Desert Research Institute (DRI; Hallett 1976) can also size particles down to 5um by imaging crystals that impact on a formvar-coated film. The cloudscope, also developed at DRI, is an imaging microscope that detects particles from 5 um up to a few hundred micrometers (Arnott et al. 1995). Others (e.g., Weickmann 1947) have simply exposed coated slides to determine typical particle habits in cirrus.

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Newer instruments for measuring cloud microphysical properties include the cloud particle imager (CPI), which casts an image of a particle on a solidstate, 1-million pixel CCD camera by freezing the motion of the particle using a 20-ns pulsed, high-power laser diode (Lawson and Jensen 1998); a particle imaging nephelometer, which simultaneously records the particle image and measures the scattering phase function of the imaged particle (Lawson et al. 1998); and a multi-angle scattering probe (MASP), which determines the size and concentration of particles 0.3-20 um diameter by measuring the scattered light from individual particles between 30 and 60° in the forward direction and 120 to 150° in the backward direction (Baumgardner et al. 1996). Use of these probes should considerably enhance knowledge about the microphysical properties of cirrus clouds. Balloon-borne instruments have also been used to obtain in situ microphysical measurements. For example, Miloshevich and Heymsfield (1997) describe how balloon-borne Formvar ice crystal replicators were used to measure vertical profiles of ice crystal size distributions and detailed ice crystal shapes down to sizes of 10 um. Orikasa and Murakami (1997) have also devised an improved hydrometeor videosonde (HYVIS), which measures vertical distributions of hydrometeors by transmitting particle images, between 7 um and 5 mm size, obtained by small video cameras by 1.6-GHz microwaves to a ground station. There are probes that provide a direct measure of the total water content of a cloud without integrating the size distribution. The Nevzorov total water content probe is a hot-wire-type probe, kept at a constant temperature, that evaporates captured crystals. Its shape is designed to allow the capture of droplets and ice crystals. The detection threshold is as low as 0.003 g/m3, and the accuracy of the water content is 10-20% when the collection efficiency is known (Mazin 1995). Brown and Francis (1995) have also measured the mass content of cirrus using a total water content (TWC) probe, which evaporates all liquid- or solidphase water by a heater system and then measures the humidity of the resulting air by a Lyman-absorption hygrometer; the mass content is obtained by subtracting water vapor obtained from a fast-response Lyman-fluorescence water vapor sensor. A counterflow virtual impactor (CVI) provides a measure of total water content in the cloud using a Lyman-alpha hygrometer after cloud particles are separated from water vapor and heated within an inlet (e.g., Strom and Heintzenberg 1994; Twohy et al. 1997). The CVI can also measure crystal number concentration when the size distribution is composed primarily of small (<50um) crystals. The particulate volume monitor (PVM) (Gerber et al. 1994) also measures the ice water content (IWC) and surface area of ice crystals directly by using spatial filtering of forward-scattering light weighted by the second and third moment of the particle distribution. 4.4. Cirrus Particle Shapes

Weickmann (1947) first characterized the shapes of cirrus crystals from data collected in a variety of cirrus cloud types. The following relationships between

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crystal shape, relative humidity, and cloud types were noted in the temperature range -30 to -60°C: for cirrus castellatus, cirrocumulus, and cirrus uncinus generating cells, where he inferred that the conditions were close to water saturation, the crystals had prismatic skeleton shapes, occurring in hollow and cluster crystals, called "bullet rosettes" (fig. 4.2) or side planes. In cirrus filosus and cirrus densus, where crystals grow somewhere between ice and water saturation, Weickmann found the crystals to be prisms (fig. 4.2), with air enclosures but not of the typical skeleton shape. In cirrostratus, where relative humidities are somewhere near ice saturation, he found the crystals to be primarily individual and full crystals such as prisms and plates. Heymsfield and Platt (1984) described the crystal shapes in mid-latitude cirrus for three temperatures ranges: above -40°C, from -40 to -50°C, and below -50°C, subdividing the results according to whether there were cirrus-generating cells ("convective" cirrus) or were formed by slow uplift ("stable" clouds). For all situations, hollow columns and hexagonal plates predominated near cloud top; spatial crystals (e.g., bullet rosettes) were the predominant forms above -40°C; and hollow or solid columns prevailed below -50°C. In the intermediate temperature range -40 to -50°C, convective cirrus contained predominantly spatial crystal forms, while stable cirrus contained predominantly hollow columns. More recent studies (e.g., Heymsfield et al. 1990; Kinne et al. 1992; Arnott et al. 1994) have reported on particular aspects of cirrus crystal shapes, including the occurrence of unexpected crystal forms and the habits in specific temperature and relative humidity conditions. The shapes of ice crystals are poorly known for the tropics. Some examples of simple columnar and trigonally shaped ice crystals tens of microns in size, at about -83°C in cirrus at the base of the tropopause, have been observed (Heymsfield 1986a). Additionally, Heymsfield and McFarquhar (1996) found lots of examples of highly irregular, large crystals in blow-off anvils associated with deep convection. Crystals smaller than 100 urn measured by the VIPS during CEPEX tended to have a quasi-spherical shape (Heymsfield and McFarquhar 1996), but Heymsfield (1986a) reported an approximately 50% mixture of trigonal plates and columns in thin tropopause cirrus near Kwajalein, Marshall Islands. High-resolution images of ice crystals have been obtained in anvils with the CPI during TEFLUN-A and TEFLUN-B. Figure 4.3 shows examples of crystals imaged by the CPI on August 13,1998 during TEFLUN-B in an anvil between temperatures of -37 and -50°C. Examples of plates, columns, and aggregates of these pristine crystals are seen. For other anvil penetrations during TEFLUN, rimed particles were also seen, frequently in close proximity to the pristine crystals. Ample examples of small crystals, which tend to have quasi-circular shapes suggesting that they may be frozen droplets, are also seen. The complexity and variety of crystal shapes in anvils, also seen during CCOPE (Heymsfield 1986b), is anticipated given the greater amount of moisture available for deposition and the mixing and turbulence associated with the vertical motions (e.g., Lilly 1988). For radiative transfer modeling and for determining cirrus formation mechanisms, the vertical structure of cirrus needs to be known. It is problematic to

Microphysical Properties

Figure 4.2. Examples of crystals collected by Weickmann (1947) in variety of cirrus.

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Figure 4.3. Crystal images recorded by CPI on August 13,1998 during TEFLUN-B in anvil at temperatures between -37 and -50°C.

Microphysical Properties 87

obtain such information with aircraft because their high speeds prohibit vertical sampling at the same horizontal location within cloud; vertical profiles derived from gradual ascents or stacked flight legs may not be true vertical profiles due to a cloud's horizontal inhomogeneities. However, during FIRE I, the NCAR King Air penetrated through cirrus in 11 Lagrangian-type spiral descents on 7 days, a flight pattern which allowed the aircraft to drift with the same parts of the clouds while descending, thereby capturing the essence of the vertical variation. Cloud top temperatures spanned the range -40 to -45°C. The King Air 2D probe had a minimum detectable size of about 20 urn as a result of the aircraft's low true air speed. Kajikawa and Heymsfield (1989) categorized the habits from each of these spiral descents, and the results of their analyses are depicted in figure 4.4 and table 4.1. Figure 4.4 shows the fractional contribution of different habits to the extinction coefficient, an important radiative parameter, for different temperature ranges for different dates. Considerable variability between dates can be noted. For example, columns are more frequent for the cirrus sampled on November 1. On October 19, rosettes are more important to the extinction at higher altitudes than at lower altitudes. Table 4.1 gives the fractional contributions of different-shaped crystals to the total number by integrating particle size spectra over the entire descent. Contributions to number for crystals with maximum dimensions greater than and less than 150 um are depicted separately. Again, there is large variability between the different dates and also between the typical shapes of the large and small crystals. Vertical profiles can also be obtained from replicator launches.

Table 4.1. Percentage of different habits observed during Lagrangian-style descents during FIRE 1 Date

Oct. 19, 1986 Oct. 22, 1986 Oct. 25, 1986, 14:36 Oct. 25, 1986, 19:55 Oct. 28, 1986 Nov. 1, 1986, 19:47 Nov. 1, 1986, 21:01 Nov. 2, 1986

Crystal sizes (d)

% Columns

% Plates

% Compact spatial

% Branched spatial

% Bullet rosettes

<150u.m >150(im <150um >150p,m <150um >150um <150um >150|im <150(^m >150um <150p.ni >150um <150nm >150|u,m <150um >150jxm

70 25 70 20 70 25 70 20 15 5 55 50 75 40 70 20

0 5 0 5 0 5 0 10 0 0 0 15 0 25 0 5

30 10 30 30 30 20 30 40 85 40 45 10 25 15 30 40

0 25 0 35 0 35 0 30 0 30 0 20 0 15 0 25

0 30 0 10 0 10 0 0 0 20 0 0 0 0 0 10

Habits obtained by integrating over entire descent, using habits identified by Kajikawa and Heymsfield (1989). Contributions for large and small crystals depicted separately.

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Figure 4.4. Percentage of different habit crystals, identified by Kajikawa and Heymsfield (1989), contributing to extinction coefficient obtained during four Lagrangian-type spiral descents through cirrus during FIRE 1.

4.5. Overview of Measurements of Ice Water Contents Increasing attention has focused on the contributions of small particles to cirrus ice water contents. To place the size distribution measurements, which generally begin at 25-50 urn, into perspective, we estimate the contributions and importance of the small crystals. Even though the CVI and PVM both measure IWC directly, they respond to different sizes of ice crystals. Because the CVI measures IWC from all sizes of crystals, whereas the PVM is only sensitive to crystals smaller than about 50 um, a comparison of their IWCs provides information about the spectral distribution of mass. The two probes were used on the NASA DC-8 during SUCCESS to make measurements of contrail cirrus, natural cirrus,

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Figure 4.5. Fraction of ice water content (IWC) measured by PVM to IWC measured by counterflow virtual impactor (CVI) against IWC measured by CVI for all coincident measurements during SUCCESS in 1996, plotted for different temperature ranges.

and wave clouds. Figure 4.5 plots the temperature-dependent fraction of IWCpvM/IWCcvi versus IWCCvi for coincident measurements. The IWCs are larger at higher temperatures, and smaller crystals constitute a lower fraction of the IWC for higher total IWC and for higher temperatures. There are fractionally more small crystals for temperatures below -50°C. The comparison suggests that the size distribution data, from 2D imaging probes, and the related moments to be presented in subsequent sections for temperatures less than -50°C, should be viewed with caution. 4.6. Size Distributions

Characteristics of cirrus ice particle size distributions and associated spectral moments have been reported in a number of studies (e.g., Heymsfield and Knollenberg 1972; Heymsfield 1975; Varley 1978; Griffith et al. 1980; Sassen et al. 1989; Heymsfield et al. 1990). The results have been presented in summary form by Liou (1986), Dowling and Radke (1990), and Jeck (1986). Parameterizations of the size distributions, useful for modeling studies, have been developed by Welch et al. (1980), Heymsfield and Platt (1984), and Kosarev and Mazin (1991) for mid-latitude cirrus and by McFarquhar and Heymsfield (1997) for tropical cirrus. Figure 4.6 shows examples of how the concentration of crystals with maximum dimensions larger than 100 jim vary as a function of temperature for different

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Figure 4.6. Concentration of crystals with maximum dimension greater than lOOum as function of temperature for different projects. Acronyms are defined in text. Symbols represent median values; horizontal bars span quartiles of the distributions. Data obtained from optical array probes.

projects at different locations. Because the 2D probes, which were used in most of the earlier cirrus studies, begin to size particles somewhere between 25 and 50 urn and determine concentrations reliably above about 100 urn, we restrict our discussion here to concentrations above 100 urn. Ice crystal concentrations (N) fall in the range lO^-lO4/!, but are usually from 0.01 to 0.1/cm3. There is a wide scatter in the data, both for an individual project and between projects. Some of these differences may be caused by probe calibration differences (e.g., Gayet et al. 1993) and differences in the manner in which the data are processed. The magnitude of the total concentrations of the size spectra are uncertain because of the inability to reliably measure ice crystals with maximum dimensions below about 25 um (Brown 1989; Dowling and Radke 1990; Heymsfield et al. 1990; Wielicki et al. 1990), especially before the advent of more sophisticated instrumentation, and fundamental questions about the 2D probe sampling volume (Baumgardner and Korolev 1997). There is evidence of high concentrations of ice crystals with length less than 25 um, especially at temperatures below about -45°C (e.g., SUCCESS mea-

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surements in fig. 4.5), or when cirrus form in an ice-free region. Using the DRI replicator during FIRE II, Arnott et al. (1994) found the presence of large numbers of ice crystals smaller than 66|im below the detection threshold of the 2D-C. Strom et al. (1997) found a diameter of mean mass of only 16 um and high crystal concentrations averaging 2.5/cm3 in cold (-35 to -60°C) young cirrus clouds over southern Germany. Heymsfield and Miloshevich (1993) measured ice crystal concentrations in excess of 100/cm3 in orographic lenticular wave clouds at temperatures of -37°C and below. In this situation, the high crystal concentrations could be attributed to the homogeneous freezing of solution drops. Homogeneous nucleation may have also been involved in the production of high ice concentrations in the Strom et al. (1997) study and in some of the other studies. In the tropics, during STEP, Knollenberg et al. (1993) found particle mass modes at sizes of 20-40 um and rarely found particles larger than 100 urn in the tops of cirrus associated with a typhoon. Heymsfield and McFarquhar (1996) found that small crystals typically dominated over the contributions of larger crystals for cirrus with temperatures lower than -60°C during CEPEX, and Heymsfield (1986a) reported a similar observation in tropical cirrus at about -80°C. However, there is still debate as to the importance of smaller crystals for both mass budgets and for determining the radiative properties of clouds. For example, McFarquhar and Heymsfield (1997) showed that for the majority of tropical anvils in TOGA COARE and CEPEX, small crystals do not dominate the mass and radiative properties of cirrus. Further, Heymsfield et al. (1998) showed that the upper parts of cirrus, where small crystals dominate, cannot alone account for the high optical depths, IWC, and albedos for the most climatologically significant population of tropical cirrus. The predominantly large particles in the lower, warmer parts of the cirrus contain at least an order of magnitude greater mass and are dominant in producing the high observed albedos. The measured particle size distributions in cirrus mirror the variation of the saturation water vapor density with temperature; at low temperatures, particles are smaller, and at higher temperatures particles are larger. A secondary factor is ice crystal fallout; the larger crystals at lower temperatures fall to warmer temperatures, depleting the larger crystals at the lower temperatures while adding to the larger crystals at warmer temperatures. In mid-latitudes, number concentrations have been observed to decrease exponentially or in a power-law form with increasing size, and the exponential slope of the size distribution steepens with decreasing temperature (Heymsfield and Platt 1984), meaning that there are fewer of the larger ice crystals on average at lower temperatures. Figure 4.7 illustrates how the maximum-detected particle dimension varies with temperature for many different projects. For temperatures lower than -40°C, substantially more large crystals have been observed in tropical cirrus (McFarquhar and Heymsfield 1997) and in CCOPE anvils (Heymsfield 1986b) than in mid-latitude cirrus. However, in both the tropics and mid-latitudes, the largest particles in a given size distribution always increase with increasing temperature: when temperatures exceed -40°C, the largest particles often exceed 1mm in length, whereas below about -60°C they are at most 10-100 um.

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Figure 4.7. Maximum-detected particle dimension as function of temperature. Symbols and horizontal bars represent median values and quartiles of distributions, respectively. Data obtained from optical array probes and replicators.

4.7. Cross-Sectional Area/Extinction Coefficient

Cross-sectional area is directly measured by the 2D-C, 2D-P, VIPS, CPI, and many other in situ probes from the two-dimensional images of crystals. For typical ice crystal sizes and visible wavelengths, the volume extinction coefficient, aext, is simply twice the cross-sectional area because then extinction efficiency is approximately 2. Integrating extinction efficiency over cloud depth yields extinction optical depth, an important radiative parameter. Scattering cross-sections also depend critically on cross-sectional area. Thus, this second moment of the size distribution must be known to adequately characterize a cloud's radiative properties. Figure 4.8 shows how extinction coefficient, determined as twice crosssectional area, varies with temperature for cirrus from a wide variety of field projects. Despite some differences between projects, caused by use of varying instrumentation and samplings of different types of cirrus, there is a clear trend

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Figure 4.8. Volume extinction coefficient as function of temperature. Symbols and horizontal bars represent median values and quartiles of distributions, respectively. See text for details. of oext increasing toward higher temperatures, and consequently, toward the lower levels of cirrus. This is also seen on a case-by-case base using Heymsfield and Miloshevich's (1995) vertical replicator profiles, the FIRE I Lagrangian descents, and vertical descents through tropopause tropical cirrus (Heymsfield 1986a).

4.8. Ice Water Content from Size Distributions The third moment of the size distribution approximately represents the mass or IWC contained within the cirrus clouds. There are greater uncertainties in the estimate of IWC than that of cross-sectional area with most in situ probes because a direct measurement is not obtained. Typically, particle mass is estimated from the maximum dimension and shape or habit of the particle using known relationships among mass, area, and dimension. A habit is assigned to each particle based on its dimensions and shape characteristics, such as area ratio, which is the area of a particle compared to that of a circumscribed circle. In the

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Cirrus

absence of a direct IWC measurement, of which there have been few, it is problematic to determine the accuracy of the IWC calculation. However, comparison studies between different algorithms and different probes and comparisons with radar suggest that IWC is known within a factor of approximately 2 (Heymsfield and McFarquhar 1996) for the warmer temperatures, with larger errors possible for the lower temperatures where small crystals contribute relatively greater IWC percentages. A summary of ice content data collected in a variety of cirrus types, locations, and time of year are presented in figure 4.9. For reference, liquid water content in stratus clouds is typically in the range 0.1-0.3 g/m3, whereas in altostratus it is less than 0.1 g/m3. The ice content in cirrus generally decreases with decreasing temperature, for reasons cited earlier. The measurements in continental cirrus formed in situ indicate the expected decrease in IWC with decreasing temperature, from as large as 0.1 g/m3 above -40°C to about lO^g/m3 below about -60°C (FIRE I, FIRE II, and EDP). The

Figure 4.9. Ice water content as function of temperature for different projects. Symbols and horizontal bars represent median values and quartiles of distributions. See text for details.

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two data sets differ at the higher temperatures because the cirrus in the deeper case (EDP) merged into middle and lower-level clouds, whereas in the shallower case (FIRE) cirrus base and top were well defined. The EDP data represent averages over about 20km horizontal distance; the FIRE data span a distance of about 0.5km. A study of the water contents of Russian continental clouds of various types during the period 1977-1984 was conducted by Mazin (1995) using data from Nevzorov total water content probe. If it is assumed that all water below -20°C is in the form of ice, distributions of ice water content with temperature can be obtained (see discussion of instrument uncertainties in section 4.3). These data are also included in the figure 4.9. Differences between the other IWC measurements may be somewhat attributed to the different instruments used to make the measurements. As a result of the high vertical velocities in convective clouds over the high plains, the largest ice contents are noted in anvils associated with the high plains storms (CCOPE).The anvils in the tropics which are known to be associated with weaker updrafts have intermediate ice contents. For penetrations near deep convection in the tropics, examples of large IWCs have also been noted such as those between -60 and -70°C during CEPEX. Additional measurements in the tropics, not depicted in figure 4.9, have been made. Griffith et al. (1980) found that the IWC estimated from the particle size spectra above about 20 urn ranged from a few hundredths to a few tenths of a gram per cubic meter in cirrus sampled between -30 and -60°C during GATE. Knollenberg et al. (1982) measured IWC from particles larger than 40 urn of a few thousandths to a few hundredths of a gram per cubic meter at about -70°C near the tops of thunderstorm cirrus in the vicinity of Panama. Using a dual size-range spectrometer, Knollenberg et al. measured IWCs as high as 0.07 g/m3 in the tops of cirrus (13-18 km, -60 to -90°C) associated with tropical cyclones and related cloud systems off the northern coast of Australia during STEP. These measurements must be viewed with caution because most of the particles were smaller than 30 um, where spectrometers are known to be unreliable. From cirrus sampled in the vicinity of Kwajalein, Marshall Islands, Heymsfield (1993) found a general decrease in IWC with decreasing temperature, with mean values ranging from about 0.2 g/m3 at -5°C to 0.0001 g/m3 at-85°C. 4.9. Three-Layer Cirrus Conceptual Model

Vertical profiles of microphysical data from aircraft Lagrangian spiral descents during FIRE I and balloon-borne ice crystal replicator launches from FIRE II indicate that average ice crystal sizes increase from cloud top downward to near cloud base, where they decrease abruptly to produce cloud base. These observations suggest a conceptual view of the formation and development of cirrus clouds. In-situ-generated cirrus clouds can be represented by three distinct layers in the vertical: the nucleation layer (layer 1) is the uppermost part of the cloud, composed of small ice crystals, where the relative humidity (RH) exceeds the relative humidity required for ice initiation, and ice production occurs; the growth

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Cirrus

layer (layer 2) is a thicker layer, composed of pristine ice crystal shapes, where ice-supersaturation sustains crystal growth; and the sublimation layer (layer 3) is a thinner layer, composed of rounded crystals of indescript shape, where ice subsaturation causes crystals to sublimate and eventually disappear. There can be variations in the number of layers; for example, cirrus that are initially developing contains no sublimation layer and cirrus that are decaying will have no nucleation layer. According to this model, nucleation occurs in layer 1 and may be either discrete or continuous, depending on the vertical velocities and temperature. Layer 2 is a deeper region of ice supersaturation, where ice crystals can grow from tens of microns to hundreds and even a thousand microns. Layer 3 is the sublimation zone, where ice crystals generated aloft fall into dry air, lowering the cloud base and moistening the air below. The thickness of layer 3 depends on the IWC and particle sizes near the base of layer 2 and the RH and temperature profiles in layer 3. This conceptual model is consistent with earlier observations of ice development in cirrus convective elements or generating cells. Ludlam (1980) postulated that ascent in the updrafts of generating cells may lead to ice particles produced by heterogeneous nucleation a little below water saturation, which represents an ice-supersaturated region several hundred meters deep above the level of ice saturation. Sassen et al. (1990) noted from lidar observations that cirrus frequently developed in the vertical from particle fallstreaks emanating from generating regions at or near cloud top. Mace et al. (1997) showed that the radar reflectivity factor in wintertime cirrus, roughly proportional to the square of the ice-water content, tends to increase between cloud top and the middle regions of the cloud and then decreases in the lower third of the layer. This is consistent with the trends seen from replicator launches during FIRE II—namely, crystal growth occurring in the upper two-thirds of moist cirrus layers while the lower third is dominated by sublimation.

4.10. Summary and Future Problems

In this chapter, cirrus cloud microphysical data acquired in mid-latitude and tropical locations by many researchers have been summarized, and the principal instruments and measurement techniques used by them to collect the data have been described. Some of the principal findings are outlined below. • Ice particle shapes vary considerably from one cloud to another. Polycrystals, especially bullet rosettes, are the predominant ice particle form in mid-latitude, in situ-generated cirrus, although columns and single bullets are found frequently. There is some suggestion that columns predominate with cloud top temperatures below -55 or -60°C. Near cloud base, crystal edges round in response to sublimation. Particles in anvils can be aggregated and rimed, and shapes can be more complex. • Cirrus cloud properties (e.g., concentration, extinction coefficient, and ice water content) can be highly variable from one cloud to another and within a single cloud. However, there does appear to be a tendency for the mean and maximum

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crystal size, extinction coefficient, and ice water content to increase with temperature. • Ice crystals smaller than 100 |im dominate the number concentration, especially near cloud top where the predominant ice particle nucleation occurs. Ice particle size tends to increase downward to near cloud base. The lowermost parts of cirrus tend to be sublimation regions. • Although small ice crystals dominate extinction near cloud top, larger particles in the mid- and lower-cloud levels are responsible for most of the cloud optical depth on average. Similar findings are noted for ice water content. • Parameterizations of the size spectra in terms of the ice water content and temperature have been developed. They are broad averages and cannot represent the variability from one cloud to another.

Most of the cirrus cloud microphysical data have been acquired with PMS 2D imaging probes. The concentrations below 100 urn, and the derived microphysical properties from these probes, have been significantly underestimated for temperatures below -55°C. Probes have been developed to provide habit and concentration information in the smaller sizes. Future studies of cirrus clouds should focus on the upper parts of tropical and mid-latitude anvils, which are very important for the earth's heat and radiation budget but have not been adequately studied. Studies at high altitudes may require a new generation of cloud physics aircraft with higher altitude sampling capabilities. Impacts of jet aircraft on cirrus cloud coverage and microphysical properties also need to be better defined. Although remote sensing techniques for retrieving cirrus cloud properties offer great promise for building global cirrus cloud climatologies, more intercomparisons are needed to evaluate the performance of these techniques. Laboratory studies are needed to determine the ice crystal nucleation rates, the conditions (temperature, relative humidity) when homogeneous versus heterogeneous ice nucleation dominate, and the dependence of ice crystal growth rates and shapes on supersaturation. Modeling studies can yield insight into the conditions when heterogeneous versus homogeneous ice nucleation predominate, as well as concentrations and size spectra in the vertical and horizontal. Acknowledgments We thank Martine Bunting, Steve Aulenbach, Lesley Smith, and Won-Seok Ryu for their assistance in preparing the manuscript and figures. Several individuals helped by allowing their data to be included in our investigation, including Larry Miloshevich and Cynthia Twohy from NCAR, Phil Brown and Peter Francis from the U.K. Meteorological Office, Richard Jeck from the Naval Research Laboratory, Ilia Mazin formerly from the Central Aerological Observatory, Pat Arnott and John Hallett from the Desert Research Institute, Hermann Gerber of Gerber Scientific, Paul Lawson of SPEC Inc., and Mike Poellot of the University of North Dakota. The assistance of funding from the Air Force, AFOSR grant number F49620-96-C-0024, is acknowledged. References Arnott, W.P., Y. Dong, J. Hallett, and M.R. Poellot, 1994. Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22,1991./. Geophys. Res., 99,1371-1381.

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Arnott, W.P., Y. Dong, R. Purcell, and J. Hallett, 1995. Direct airborne sampling of small ice crystals and the concentration and phase of haze particles. 9th Symp Met. Observ. Instr., American Meteorological Society, Charlotte, N.C., pp. 415-420. Baumgardner, D., J.E. Dye, B. Gandrud, K. Barr, K. Kelly, and R.K. Chan, 1996. Refractive indices of aerosols in the upper troposphere and lower stratosphere. Geophys. Res. Lett., 23,749-752. Baumgardner, D., and A. Korolev 1997. Airspeed corrections for optical array probe sample volumes. /. Atmos. Ocean. Tech., 14,1224-1229. Bennetts, D.A., and M. Ouldridge, 1984. Observational study of the anvil of a winter maritime cumulonimbus cloud. Quart. J. Roy. Meteor. Soc., 110, 85-103. Brown, P.R.A., 1989. The use of holography for airborne cloud physics measurements. J. Atmos. Ocean. Tech., 6, 293-306. Brown, P.R.A., and P.N. Francis, 1995. Improved measurements of the ice water content in cirrus using a total-water probe. /. Atmos. Ocean. Tech., 12, 410-414. Collins, W.D., F.P.J. Valero, PJ. Flatau, D. Lubin, H. Grassl, and P. Pilewskie, 1996. Radiative effects of convection in the tropical Pacific. J. Geophys. Res., 101,14999-15012. Dowling, D.R., and L.F. Radke, 1990. A summary of the physical properties of cirrus clouds. /. Appl. Meteor., 29, 970-978. Gardiner, B.A., and J. Hallett, 1985. Degradation of in-cloud forward scattering spectrometer probe measurements in the presence of ice particles. /. Atmos. Ocean. Tech., 2,171-180. Gayet, J.F., P.R.A. Brown, and F. Albers, 1993. A comparison of in-cloud measurements obtained with six PMS 2D-C probes. /. Atmos. Ocean. Tech., 10,180-194. Gayet, J.-F, G. Febvre, and H. Larsen, 1996. The reliability of the PMS FSSP in the presence of small ice crystals. /. Atmos. Ocean. Tech., 13,1300-1310. Gerber, H., E.G. Arends, and A.S. Ackerman, 1994. New microphysics sensor for aircraft use. Atmos. Res., 31,235-252. Gordon, G.L., and J.D. Marwitz, 1984. An airborne comparison of three PMS probes. J. Atmos. Ocean. Tech., 1, 22-27. Griffith, K.T., S.K. Cox, and R.G. Knollenberg, 1980. Infrared radiative properties of tropical cirrus clouds inferred from aircraft measurements. J. Atmos. Sci., 37,1077-1087. Hallett, J., 1976. Measurements of size, concentration and structure of atmospheric particulates by the airborne continuous replicator, final report, cloud particle replicator for use on a p pressurized aircraft, 92 pp., I, II, supplementary final report. Contract AFGL-TR-76-0149, Air Force Geophysics Laboratory, Hanscom AFB, MA. Hartmann, D.L., M.E. Ockert-Bell, and M.L. Michelsen, 1992. The effect of cloud type on earth's energy balance: Global analysis. /. dim., 5,1281-1304. Heymsfield, A.J., 1975. Cirrus uncinus generating cells and the evolution of cirriform clouds. Part I: Aircraft observations of the growth of the ice phase. /. Atmos. Sci., 32, 799-808. Heymsfield, A.J., 1977. Precipitation development in stratiform ice clouds: a microphysical and dynamical study. /. Atmos. Sci., 34, 367-381. Heymsfield, A.J., 1986a. Ice particles observed in a cirriform cloud at -83C and implications for polar stratospheric clouds. /. Atmos. Sci., 43, 851-855. Heymsfield, A.J., 1986b. Ice particle evolution in the anvil of a severe thunderstorm during CCOPE. /. Atmos. Sci., 43,2463-2478. Heymsfield, A. J., 1993. Microphysical structures of stratiform and cirrus clouds. In AerosolCloud-Climate Interactions (P.V. Hobbs, ed.). Academic Press, New York, pp. 97-121. Heymsfield, A.J., and R.G. Knollenberg, 1972. Properties of cirrus generating cells. /. Atmos. Sci., 9,1358-1366.

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Heymsfield, A.J., and G.M. McFarquhar, 1996. High albedos of cirrus in the tropical Pacific warm pool: microphysical interpretations from CEPEX and from Kwajalein, Marshall Islands. /. Atmos. Sci., 53,2424-2451. Heymsfield, A.J., G.M. McFarquhar, W.D. Collins, J.A. Goldstein, F.P.J. Valero, J. Spinhirne, W. Hart, and P. Pilewskie, 1998. Cloud properties leading to highly reflective tropical cirrus: Interpretations from CEPEX, TOGA COARE, and Kwajalein, Marshall Islands. /. Geophys. Res., 103,8805-8812. Heymsfield, A.J.,K.M. Miller, and J.D. Spinhirne, 1990. The 27-28 October 1986 FIRE IFO cirrus case study: cloud microstructure. Mon. Wea. Rev., 118,2313-2328. Heymsfield, A.X, and L. Miloshevich, 1989. Evaluation of liquid measuring instruments in cold clouds sampled during FIRE. /. Atmos. Ocean. Tech., 6, 378-388. Heymsfield, A.J., and L. Miloshevich, 1993. Homogeneous ice nucleation and supercooled liquid water in orographic wave clouds. /. Atmos. Sci., 50,2335-2353. Heymsfield, A.J., and L. Miloshevich, 1995. Relative humidity and temperature influences on cirrus formation and evolution: observations from wave clouds and FIRE II. J. Atmos. Sci., 52,4302^326. Heymsfield, A.J., and C.M.R. Platt, 1984. A parameterization of the particle size spectrum of ice clouds in terms of ambient temperature and their ice water content. /. Atmos. Sci., 41, 846-855. Huschke, R.E., 1970. Glossary of Meteorology. American Meteorological Society, Boston, MA. Jeck, R.K., 1986. Airborne cloud physics projects from 1974 through 1984. Bull. Amer. Meteor. Soc., 67,1473-1477. Joe, P., and R. List, 1987. Testing and performance of a two-dimensional optical array spectrometer with greyscale. J. Atmos. Sci., 4,139-150. Kajikawa, M., and AJ. Heymsfield, 1989. Aggregation of ice crystals in cirrus. J. Atmos. Sci., 46,3108-3121. Kinne, S.,T.P. Ackerman, AJ. Heymsfield, F.P.J. Valero, K. Sassen, and J.D. Spinhirne, 1992. Cirrus microphysics and radiative transfer: cloud field study on 28 October 1986. Mon. Wea. Rev., 120,661-684. Knollenberg, R.G., 1976. Three new instruments for cloud physics measurements: the 2-D spectrometer, the forward scattering spectrometer probe and the active scattering aerosol spectrometer. In Proceedings of the International Conference on Cloud Physics, Boulder, CO., American Meteorological Society, 554-561. Knollenberg, R.G., AJ. Dascher, and D. Huffman, 1982. Measurements of the aerosol and ice crystal populations in tropical stratospheric cumulonimbus anvils. Geophys. Res. Lett., 9, 613-616. Knollenberg, R.G., K. Kelly, and J.C. Wilson, 1993. Measurements of high number densities of ice crystals in the tops of tropical cumulonimbus. /. Geophys. Res., 98, 8639-8664. Korolev, A. V, J.W. Strapp, and G.A. Isaac, 1998. Evaluation of the accuracy of PMS optical array probes. /. Atmos. Ocean. Tech., 15,708-720. Kosarev, A.L., and I.P. Mazin, 1991. An empirical model of physical structure of upperlayer clouds. In Radiation Properties of Cirrus Clouds, Nauka, pp. 29-52. Atmospheric Research, 26,213-228. Krupp, G, 1992. Holographische Messungen an Eiskristallen in Cirruswolkn wahrend des Internationalen Cirrus Experiments ICE. GKSS 92/E/14. Lawson, R.P., and T.L. Jensen, 1998. Improved microphysical observations in mixed phase clouds. In Conf. Cloud Phys., American Meteorological Society, Everett, WA, pp. 451-454.

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Lawson, R.P., A.J. Heymsfield, S.M. Aulenbach, and T.L. Jensen, 1998. Shapes, sizes and light scattering properties of ice crystals in cirrus and a persistent contrail during SUCCESS. Geophys. Res. Lett., 25,1331-1334. Lilly, D.K., 1988. Cirrus outflow dynamics. /. Atmos. Sci., 45,1594-1605. Liou, K.N., 1986. Influence of cirrus clouds on weather and climate processes: a global perspective. Man. Wea. Rev., 114,1167-1199. Ludlam, F.H., 1980. Clouds and Storms. The Behavior and Effect of Water in the Atmosphere. The Pennsylvania State University Press, University Park. Mace, G.G., T.P. Ackerman, E.E. Clothiaux, and B.A. Albrecht, 1997. A study of composite cirrus morphology using data from a 94-GHz radar and correlations with temperature and large-scale vertical motion. /. Geophys. Res., 102,13581-13593. Matsuo, T., H. Mizuno, M. Murakami, and Y. Yamada, 1992. Ice crystal formation in cirrus cloud. In Nucleation and Atmospheric Aerosols (N. Fukuta, and P.E. Wagner, eds.). Deepak Publishing, pp. 283-286. Mazin, I.P., 1995. Cloud water content in continental clouds of middle latitudes. Atmos. Res., 35,283-297. McFarquhar, G.M., and A.J. Heymsfield, 1997. Parameterization of tropical cirrus ice crystal size distributions and implications for radiative transfer: results from CEPEX. /. Atmos. Sci., 54,2187-2200. Meitin, J.G. Jr., and J.B. Cunning, 1985. Oklahoma-Kansas preliminary regional experiment for storm-central (O-K PRESTORM), Vol. 1, Daily operations summary. National Oceanic and Atmospheric Administration Technical Memorandum (NOAA TM ERL ESG-20), NOAA, Washington, DC. Miloshevich, L.M., and A.J. Heymsfield, 1997. A balloon-borne continuous cloud particle replicator for measuring vertical profiles of cloud microphysical properties: Instrument design, performance, and collection efficiency analysis. J. Atmos. Ocean. Tech., 14,753-768. Mizuno, H.,T. Matsuo, M. Murakami, and Y. Yamada, 1994. Microstructure of cirrus clouds observed by HYVIS. Atmos. Res., 32,115-124. Orikasa, R, and M. Murakami, 1997. A new version of hydrometeor videosonde for cirrus cloud observations. /. Meteor. Soc. Japan, 75,1033-1039. Personne, P., C. Duroure, C. Isaka, and H. Isaka, 1991. Geometrical characteristics of cirrus ice crystals. International Association of Meteorology and Atmospheric Physics Program and Abstracts. IAMAP, Villeneuve D'Ascq, France. Ranz, WE., and J.B. Wong, 1952. Impaction of dust and smoke particles. Ind. Eng. Chem., 44,1371-1381. Raschke, E., P. Flamant, Y. Fouquart, P. Hignett, H. Isaka, PR. Jonas, H. Sundquist, and P. Wendling, 1998. Cloud-radiation studies during the European cloud and radiation experiment (EUCREX). Surveys Geophys., 19,89-138. Raschke, H., J. Schmetz, J. Heintzenberg, R. Kandel, and R. Saunders, 1990. International Cirrus Experiment. ESA Bull., 14,113-119. Sassen, K., C.J. Grund, J.D. Spinhirne, M.M. Hardesty, and J.M. Alvarez, 1990. The 27-28 October 1986 FIRE IFO cirrus case study: a five lidar overview of cloud structure and evolution. Mon. Wea. Rev., 118, 2288-2311. Sassen, K., D.O'C. Starr, and T. Uttal, 1989. Mesoscale and microscale structure of cirrus clouds: three case studies. /. Atmos. Sci., 46, 371-396. Strom, J., and J. Heintzenberg, 1994. Water vapor, condensed water, and crystal concentration in orographically influenced cirrus clouds. /. Atmos. Sci., 51,2368-2383. Strom, J., B. Strauss, T. Anderson, F. Schroder, J. Heintzenberg, and P. Wendling, 1997. In situ observations of the microphysical properties of young cirrus clouds. /. Atmos. Sci., 54, 2542-2553.

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Twohy, C.H., A.J. Schanot, and W.A. Cooper, 1997. Measurement of condensed water content in liquid and ice clouds using an airborne counterflow virtual impactor. /. Atmos. Ocean. Tech., 14,197-202. Varley, D.J., 1978. Cirrus particle distribution study, Part I. Technical Report AFGL-TR78-0192, Air Force Geophysical Laboratory, Hanscom Air Force Base, MA. Weickmann, H., 1947. Die Eisphase in der Atmosphare. Royal Aircraft Establishment, Farnborough, UK. Welch, R.M., S.K. Cox, and J.M. Davis, 1980. Solar Radiation and Clouds. Meteorological Monogragh no. 39. American Meteorological Society. Wielicki, B. A., J.T. Suttles, A.J. Heymsfield, R.M. Welch, ID. Spinhirne, M.-L.C. Wu, D.O'C. Starr, L. Parker, and R.F. Arduini, 1990. The 27-28 October 1986 FIRE IFO cirrus case study: Comparison of radiative transfer theory with observations by satellite and aircraft. Mon. Wea. Rev., 118, 2356-2376.

5

Laboratory Studies of Cirrus Cloud Processes PAUL J. D E M O T T

A number of processes that play a role in the formation, evolution of microphysical properties, and radiative characteristics of cirrus clouds are amenable to investigation in a laboratory setting. These laboratory studies provide fundamental data for quantifying and validating theoretical concepts and help guide investigations involving direct and remote measurements of cirrus. Laboratory data also may be used for formulating parameterizations for numerical cloud models, especially where information is incomplete or full descriptions are not possible. This chapter reviews results from laboratory studies of ice formation, ice crystal growth, radiative transfer, and aerosol scavenging and transformation in the cirrus environment. Emphasis is placed on ice formation in cirrus conditions. The related topic of contrail formation is covered separately in this book. The formation mechanisms of lower stratospheric clouds are reviewed elsewhere (e.g., Tolbert 1994; Peter 1996; Carslaw et al. 1997; Koop et al. 1997a).

5.1. Ice Formation Processes in Cirrus 5.1.1. Overview Laboratory studies of cirrus ice formation are at a rapidly developing stage, so it is useful to provide significant background bases for current and needed studies. Key issues are aerosol composition, ice nucleation mechanisms, and the synergy between theory and laboratory measurements. Vali (1996), Baker (1997) and Martin (2000) discuss some of these issues in review papers. 102

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Upper tropospheric aerosols Upper tropospheric aerosol particles play an important catalytic role in the formation of cirrus. The nucleation process is important in determining the microphysical properties of cirrus. Numerical modeling studies (e.g., Jensen and Toon 1994; DeMott et al. 1994,1997; Heymsfield and Sabin 1989) indicate that variation in the factors that drive the nucleation of ice and variations in the physical and chemical characteristics of aerosol particle populations lead to the formation of cirrus with different microphysical characteristics. Knowledge of the physics and chemistry of aerosols in the upper troposphere and lower stratosphere has evolved at a rapid pace. A detailed accounting of this topic is beyond the scope of this chapter. For the purpose of the present discussion, it is sufficient to note that the aerosol from which cirrus nucleate may vary significantly from place to place. Differences in aerosol properties in time and space occur because particles can arrive to the upper troposphere in so many ways and from so many sources. For example, cumulus convection can loft boundary-layer air into the upper troposphere that is rich in particles derived from surface generation, combustion processes (over continents), and boundary-layer chemical processing. Many of these particles may be sulfates, but their composition may transform depending on the concentrations of trace gas species. For example, an abundance of ammonia in air could favor the formation of ammonium sulfate from an initial population of sulfuric acid particles. Convection also introduces large amounts of insoluble matter to the upper troposphere. Thus, although sulfates have sometimes been observed to dominate the aerosol (Sheridan et al. 1994), insoluble inorganic species can be found in a large proportion of aerosols on other occasions (Chen et al. 1998; Talbot et al. 1998; Buseck and Posfai 1999). The insoluble components of mixed particles can act as heterogeneous nucleants for crystallizing liquid to dry solute or liquid to ice under conditions that are quite different than for a pure solute particle. The ubiquitous nature of organic components of sulfates and other aerosol particles throughout the troposphere has been determined (Novakov et al. 1997; Murphy et al. 1998). These organics may alter chemical and cloud formation processes in ways that are not yet fully understood. Where cirrus clouds have been present in the upper troposphere, aerosols are collected, modified by chemical reactions on ice crystals, and redistributed through sedimentation to lower levels. The particles remaining after cloud dissipation may have quite different physical, chemical, and cloud-nucleating properties. This cloud "processing" may also leave large regions or layers of the atmosphere depleted of aerosol particles. The reduction of particle surface area for condensation of gases makes these locations favored areas for the nucleation of new particles, sulfuric acid in particular. This appears to be a primary mechanism for maintaining the upper tropospheric aerosol populations (e.g., Schroder and Strom 1997; Clarke et al. 1999). Other local- or regional-scale impacts on upper tropospheric aerosol properties are produced by the exchange of air with the lower stratosphere and the direct injection of particulates by jet aircraft. Lower stratospheric air is typically dominated by sulfuric acid aerosols and tends to contain less insoluble matter

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(Pueschel et al. 1992; Sheridan et al. 1994; Murphy et al. 1998). Aircraft exhaust has been implicated in enhancing black carbon concentrations in cirrus (Petzold et al. 1998; Strom and Ohlsson 1998). The role of exhaust particles as potential nuclei for cirrus formation is the subject of current study. The relation between aerosol composition and ice-nucleating properties is not well understood (see, e.g., Pruppacher and Klett 1997). Figure 5.1 provides a summary in schematic form of the various potential pathways to ice formation. Ice nucleation at cirrus conditions may occur homogeneously in liquid aerosol particles or heterogeneously on particles that may or may not already contain water as a component.

Figure 5.1. Hypothesized pathways to ice formation in cirrus clouds. The particle types and phase are indicated, and the size of particles is intended to indicate their relative growth or dilution. The vertical position indicates (higher) humidity, (lower) temperature, and the height of formation of the cirrus cloud as indicated by ice particle formation. The nucleation pathways are A, homogeneous freezing of solution droplets; B, homogeneous freezing limited by deliquescence requirement; Cl, homogeneous freezing limited by secondary phase crystallization; C2, heterogeneous freezing induced by secondary phase crystallization; D, heterogeneous freezing of solution droplets; El, deposition nucleation on an insoluble particle; E2, deposition nucleation on an anhydrous (dry) soluble particle; F, contact freezing nucleation.

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Homogeneous ice nudeation Homogeneous freezing nucleation, analogous to that which occurs in pure water droplets, may occur in concentrated solution (haze) droplets at below about -40° C (pathway A in fig. 5.1). This mechanism can occur at relative humidities that are below 100% with respect to water. The presence of solute has the effect of lowering the freezing rate compared to an equal-sized pure droplet, but the freezing rate also increases sharply with decreasing temperature. An increase in relative humidity with respect to water (RHW) leads to an increase in the equilibrium size of solution droplets, thus diluting the solute to a condition (depending on temperature) where freezing occurs. Other phase transition behaviors of aerosol particles complicate homogeneous freezing in cirrus conditions. For example, the transformation of a solid (anhydrous) soluble particle to a saline droplet occurs spontaneously at the deliquescence relative humidity. The temperature-dependent solubility characteristics of aerosols determine the humidity of deliquescence (Tang and Munkelwitz 1993). This RHW for deliquescence usually increases with decreasing temperature for salt particles, potentially imposing a limitation on freezing (pathway B in fig. 5.1). The deliquescence humidity also increases for smaller particle sizes (Chen 1994). Once a particle has become liquid, it must dry significantly below the deliquescence RHW in order to crystallize again as an anhydrous particle of the same composition. This complete crystallization, also known as efflorescence, is a nucleation phenomenon and so requires the solute to supersaturate. The particle in pathway A in figure 5.1 has not undergone efflorescence, but the particle in pathway B has. Consequently, the particle in B is limited from freezing until it deliquesces. When aerosols are already in a liquid state, chemical phase transitions may alter the compositional makeup of haze particles at lower temperatures. Consequently, the expected conditions where freezing will occur may be altered (pathway Cl in fig. 5.1). For example, (NH4)3H(SO4)2 (letovicite) may crystallize in NH4HSO4 (ammonium bisulfate) solutions. The freezing conditions of the remaining acidified solution may be quite different from the original bisulfate solution. The common basis for quantifying ice formation processes in cirrus for use in numerical models has been classical nucleation theory (e.g., Pruppacher and Klett 1997; Khvorostyanov and Sassen 1998). The limitations of classical theory and its application of macroscopic attributes to microscale ice embryo formation must be acknowledged at the outset of any discussion of its use. Nevertheless, the theory is intellectually appealing, and there is evidence that it can be applied to explain measurements of ice formation by homogeneous freezing in pure water droplets. The fundamental relation that describes the steady-state nucleation rate, 7hf (cm^s"1) of ice embryos in a liquid drop may be written as (see, e.g., Pruppacher and Klett 1997),

In equation 1, AFact is the activation energy for movement of water molecules from the solvent to the ice phase, AFg is the energy of formation of the critical

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embryo, k is Boltzmann's constant, T is temperature. The pre-exponential factor, C, is

where Nc is the monomer concentration (= 5 x 1014 for pure water), pw is the density of water, pj is the density of ice, h is Planck's constant, and ai/s is the interfacial energy of the ice-solution interface. The energy of formation in the spherical cap model of an ice embryo may be formulated as

where rg is the germ radius. Khvorostyanov and Sassen (1998) have derived

where the temperature-dependent "effective" latent heat of formation (Lef) replaces the average latent heat of freezing from previous classical treatments. T0 is the triple point of water (approximately the melting temperature), 5W is the water saturation ratio, and G = RT/(LefMw) in equation 4, Mw being the molecular weight of water and R the universal gas constant. Mackenzie et al. (1998) offered an alternative form of rg. Equations 1-4 are generalized here for any solution droplet composition. For particles in equilibrium with the vapor phase, the Kohler equation relates Sw to aerosol composition via the aerosol water activity. Thus, equations 1-4 and the Kohler equation provide a set of equations for calculating /hf as a function of ambient temperature, humidity, and aerosol size distribution. At infinite dilution, S^ tends to 1, which is the case for a pure water droplet. Expressions for the temperature dependencies of pw, pi? Lef, and AFact for pure water are found in Khvorostyanov and Sassen (1998), Jensen et al. (1994), and Pruppacher (1995). Solute particles may freeze at 5W < 1. The most obvious consequence of this is to suppress the melting point temperature, TQ, in equation 4. However, this simplistic view belies other dependencies that solutes may introduce. Two of the most problematic quantities in applying homogeneous nucleation theory to solutions are AFact and ai/s. These quantities are sometimes treated to depend on temperature alone (e.g., Khvorostyanov and Sassen 1998), but clearly they must depend also on solution composition (e.g., Luo et al. 1992; Tabazadeh et al. 1997). One approach to determining AFacl has been to equate it to the measurable energy for viscous flow (e.g., Jeffery and Austin 1997; Tabazadeh et al. 1997). In the viscous flow approximation, A.Fact always increases monotonically toward low temperature. Pruppacher (1995) proposed that, for pure water, this term decreases with decreasing temperature below -30°C, reflecting that transfer across the ice-water interface may involve increasingly larger clusters of water molecules for which the hydrogen bonds are broken only at the cluster periphery. In contrast, Jeffery and Austin (1997) point out that a correct derivation of the activation energy from water self-diffusivity data provides the lower

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values of AFact that were required by Pruppacher (1995) to bring theory into agreement with experiment for pure water. This issue will likely remain a point of contention among theoreticians. The determination of o~i/s by experimental techniques is difficult, and measurements even for pure water show a spread of as much as 25% over the temperature range from 0 to -40° C (Pruppacher and Klett 1997). In the context of the above equations, huge differences in nucleation rate can result from this uncertainty in oi/s. Indirect methods exist for estimating oi/s for aqueous solutions. One may apply Antonoffs rule to conject that oi/s is equal to the absolute difference of the individual surface tensions of ice and solution against air (see, e.g., Tabazadeh et al. 1997). Alternatively, oi/s is estimated to be the fusion heat required to change the hydrogen bonds from the oriented solid state to the aqueous state (e.g., Luo et al. 1992; Pruppacher and Klett 1997). At very low temperatures where crystal growth rates are much slower than embryo formation rates, it is possible to derive AFact from crystallization kinetics and then use this estimate to determine oi/s from nucleation rate measurements at warmer temperatures (see, e.g., Disselkamp et al. 1996). The more common scenario is that freezing rate measurements are used to determine AFact or oi/s, assuming that the other quantity can be estimated (see, e.g., Hagen et al. 1981; DeMott and Rogers 1990). This has always compromised somewhat the comparison of classical theory with experiments. Homogeneous nucleation is a stochastic process. Thus, the fraction, Fh{, of droplets with volume Vd that freeze homogeneously in a small time interval, At, is given by This expression for Fh{ serves as the basis for calculating /hf from laboratory measurements of the Poisson statistics of homogeneous freezing (Hagen et al. 1981; DeMott and Rogers 1990; Disselkamp et al. 1996; Kramer et al. 1996; Koop et al. 1997b; Shaw and Lamb 1999). Equation 5 also serves as the basis for making numerical model calculations of ice formation in cirrus, starting from a specified aerosol size distribution and chemical composition. Both /hf and Vd depend on aerosol properties. The droplet volume depends on the water uptake of aerosol particles, which is a function of their solute composition. Approximations may permit an analytical solution to be obtained for the fraction of the total aerosol nucleating ice that depends only on (model) grid point conditions and moment parameters of the aerosol size distribution. The validity of such simplifications, which allow details of the nucleation process to be incorporated into mesoscale and global scale models, are testable in the laboratory. Numerical studies of cirrus that included ice formation by homogeneous freezing of solution droplets have offered some tantalizing insights into the roles of aerosol properties and cloud forcing in determining cirrus properties. For example, for one assumed aerosol composition, the concentration of ice crystals is largely controlled by the balance between vapor production by cloud updraft and vapor depletion by ice crystal growth (e.g., Heymsfield and Sabin 1989; Sassen and Dodd 1989; Jensen and Toon 1994; DeMott et al. 1997). If updrafts are sustained until vapor depletion dominates, then higher concentrations of ice crystals are

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predicted to form at higher updrafts. Only extreme changes in particle size distribution, such as occur after volcanic eruptions (Jensen and Toon 1992), can temporarily alter the predicted relationship by more than some tens of percent. A potentially more important way that solution composition could alter cirrus is by changing the humidity required for cloud initiation (DeMott et al. 1997). Lowering the humidity required for formation might alter the water vapor balance toward favoring lower ice crystal concentrations, but larger ice crystals and more widespread cirrus. Nevertheless, these numerical studies were done without detailed information on the low temperature hydration and freezing behavior of different relevant compositions of solution droplets. It is likely that a range of sulf ate particle compositions exist in regions of the upper troposphere, depending on transport processes from source regions and the thermodynamic conditions along the transport pathway (Tabazadeh and Toon 1998). Detailed thermodynamic models of the phase and composition of soluble aerosol particle systems at low temperatures now exist (e.g., Clegg et al. 1998), but necessarily require extrapolation in the much of the cirrus temperature and humidity regime. Laboratory studies can provide the fundamental data required. One could also envision laboratory cloud chamber simulations being used to validate model predictions of the relation between cloud forcing and cloud properties. Heterogeneous ice nucleation There are at least four different mechanisms hypothesized to lead to heterogeneous ice nucleation by aerosol particles (Vali 1985). Direct deposition of ice to an insoluble surface is indicated as pathway El in figure 5.1. It is also possible that soluble but dry (anhydrous) sulfate particles may form ice at low temperatures in this same manner (Martin 1998; Tabazadeh and Toon 1998). This is indicated as pathway E2 in figure 5.1. Contact freezing nucleation may occur after a solid particle collides with a liquid haze particle (pathway F in fig. 5.1). In condensation freezing (pathway D in fig. 5.1), the soluble component of a mixed particle causes condensation, and the insoluble component catalyzes freezing instantaneously. The nucleation process is referred to as immersion freezing if the insoluble component catalyzes ice formation at a much later time (lower temperature or greater droplet dilution) following either collision or condensation. Figure 5.1 indicates that immersion freezing might also occur when a new crystalline phase forms within a haze droplet upon cooling (pathway C2).The importance of the deposition mechanism anywhere is an open question due to the low likelihood of finding completely insoluble particles. Most scrutiny has focused on the potential roles of condensation and immersion freezing nucleation. Nevertheless, knowledge of the importance of the different pathways in figure 5.1 is poor. The role of heterogeneous nucleation in cirrus is the subject of renewed attention in laboratory studies. Knowledge of the presence of insoluble particulates in the upper troposphere and advent of improved capabilities to measure heterogeneous ice nuclei concentrations and compositions there (e.g., DeMott et al. 1998; Rogers et al. 1998) provide motivation for new laboratory studies. Numerical simulations suggesting that heterogeneous nucleation could dominate in

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cirrus formed by the widespread, slow ascent of air (DeMott et al. 1997; Jensen and Toon 1997) also motivate laboratory studies. The theoretical basis for quantifying heterogeneous nucleation is much less certain than for homogeneous freezing. Theoretical descriptions require information on surface properties for innumerable substances that could act as ice nuclei, and these properties could depend on aerosol processing effects. For example, the free energy of formation for heterogeneous freezing nucleation may be written

where /(mi/n^) is a geometric factor (Pruppacher and Klett 1997) that depends in the simplest case (spherical cap embryo on a curved and uniform substrate) on the cosine of the contact angle between the ice embryo and substrate nucleus (mi/n = cos6i/n) and the ratio of the nucleus to ice embryo radius (x = rn/rg). Effective freezing nuclei have higher values of mi/n, and this value determines a nearly temperature-independent ice saturation ratio at which a nucleation rate of 1 event per particle per second occurs. For example, using equation 6 in the model of Tabazadeh et al. (1997), even a fairly ineffective freezing nucleus (e.g., mi/n = 0.1) of 100 nm size is calculated to instantly freeze a 400-nm sulfuric acid solution droplet once the ice saturation ratio exceeds 1.25 (ice relative humidity RHi = 125%). 5.1.2. Laboratory Methodologies for Studying Cirrus Ice Formation New data are needed on the chemical phase, water activity, and ice-phase transition conditions of bulk and dispersed phase (wet and dry aerosol) particulates at cirrus temperatures. These data will come from studies using a variety of methods. Methods for studying cirrus ice formation in the laboratory may be placed into various categories. At the most basic are studies of the freezing of relatively large volumes of solutions (e.g., Gable et al. 1950; Ohtake 1993; Chelf and Martin 1999). These studies provide the equilibrium freezing temperature as a function of composition for a solute-water system, a fundamental piece of information concerning ice nucleation. Relevant secondary data come from measurements of water vapor pressure over solutions at low temperature (e.g., Zhang et al. 1993; Massucci et al. 1996). A second category of experiments examines the behavior of small dry particles or solution droplets dispersed in air or in another medium. Subcategories of experiments on dispersed-phase particles focus on the behavior of particle populations or on the behavior of individual particles. Devices to study the freezing of populations of liquid droplets were some of the first to give inferences to the homogeneous and heterogeneous freezing behavior of small liquid aerosol particles at cirrus conditions. Populations of solution droplets have been observed optically while supported on a chilled surface or at the interface of two surfaces of differing density (Pruppacher and Neiberger 1963; Koop et al. 1998). Other experiments involved creating droplet emulsions

I 10

Cirrus

that were monitored, using calorimetric techniques, for ice formation during cooling and for melting conditions on warming (Rasmussen and Luyet 1970; Ganguly and Adiseshaiah 1992). The unknown effect of instrument surfaces or surface interaction with the mother phase in emulsions on nucleation is a concern in such studies. The concept of flow tubes is to expose freely suspended particles of known composition to a known temperature for a defined time. A large number of studies have used flow tubes to study the infrared spectroscopic changes of populations of aerosol particles in conditions representative of the upper troposphere and lower stratosphere. These studies seek to determine the nonequilibrium-phase transitions of deliquescence, efflorescence, chemical crystallization in drops (e.g., Cziczo et al. 1997; Onasch et al. 1999), and the freezing of water in particles of differing compositions (e.g., Bertram et al. 1996; Clapp et al. 1997; Cziczo and Abbatt 1999). Composition is fixed in such studies by flowing high concentrations of liquid aerosol particles rapidly through a constant temperature tube. The principle is that the water in the particles exceeds the gas phase water by such a large amount that the composition of the particles does not readjust to the ice saturation conditions in the tube during the residence time. Definition of the composition of particles at the point of freezing is another experimental issue. Composition is usually determined based on extrapolation of relationships between composition and the area under certain FTIR (Fourier transform infrared spectroscopy) spectroscopic bands. These relationships are determined from studies of thin films of known composition, usually conducted at temperatures that are warmer than cirrus (e.g., Anthony et al. 1995). Particle size measurements support composition determinations, but inferences by way of Mie theory require optical constant data as a function of composition at low temperature. Refractive indices as a function of temperature and composition in the stratospheric regime have been determined recently from infrared aerosol extinction spectra obtained in flow tube (Niedzela et al. 1998) and thin film studies (Tisdale et al. 1998). Improvements in defining particle composition have also been made by coupling tunable diode laser hygrometers to the same sample volume where FTIR measurements are made (Niedzela et al. 1998) or by using a second FTIR spectrometer to measure the composition of evaporated haze particles. In an ice-thermal diffusion chamber, the goal is for particles to adjust in size, in a natural manner, toward equilibrium with set temperature and humidity conditions. The relative humidity condition of ice nucleation is thereby measured and composition is determined by application of diffusional growth equations. Equilibrium conditions are achieved by varying the temperature of two parallel ice surfaces (e.g., Rogers 1988; Rogers et al. 1998). These devices may be oriented horizontally to develop a static gradient of temperature (warm over cold) and vapor density (high over low) into which aerosol particles are drawn. Alternately, aerosols flow through the systems in a horizontal or vertical orientation. A flow system permits continuous measurements and helps assures that vapor is not depleted by ice particle growth. Definition of the conditions to which particles are exposed is aided by focusing the aerosol into a lamina (e.g., by surrounding it with particle-free flows). Detection of ice formation is aided by the fact that,

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under most conditions, ice particles will grow rapidly to sizes that can be distinguished in some way (e.g., optically) from haze particles. This also yields information on ice particle growth rates. Nucleation studies can also be done in larger volume chambers. Aerosols can be observed over long time periods or during slow cooling at ice saturation in such devices (e.g., Disselkamp et al. 1996). Other cloud chambers are capable of processing aerosols through realistic thermodynamic trajectories and repeated cloud formation events (e.g., White et al. 1987; DeMott and Rogers 1990). Such methods could provide validation of other laboratory results for conditions that mimic the real atmosphere, yet they are easier to control and observe. In the area of single particle experiments, the modern development of great promise involves the isolation of aerosol particles from surfaces by optical, acoustic, or electrodynamic levitation (see review of Davis 1997). The electrodynamic levitation method has been used most commonly for phase change and growth studies (Tang and Munkelwitz 1994; Wyslouzil et al. 1994; Lamb et al. 1996; Carleton et al. 1997; Bacon et al. 1998; Xu et al. 1998). A particle is balanced in space horizontally by applying an alternating current to a ring electrode. The particle is balanced against gravity by applying a direct current to the end caps of the cylinder around the particle. The resulting electrostatic field confines the charged particle to a stable position in space. The growth of particles is determined from relationships among the DC current required to produce the levitating field, particle charge, and mass. Particle composition is calculated based on particle growth from a known initial composition. Changes in mass reflect nucleation or changes in particle composition. Observations of light scattering by, or infrared emission from, larger particles (5-100 urn) may be made to better define composition and phase transitions or to determine how particles depolarize light. A useful capability that has not been generally implemented with the levitation techniques is control on water vapor pressure. Anders et al. (1996) and Roth and Frohn (1998) describe a low-temperature optical levitation device that permits particle exposure to an ice-supersaturated airflow, but the precision of humidity control is not yet sufficient for accurate study. Swanson et al. (1999) describe a combination electrodynamic balance and ice-thermal diffusion chamber. This system has thus far been operated only at very low ice supersaturations. 5,1.3, Results of Laboratory Studies of Ice Formation in Cirrus Homogeneous ice nucleation Pruppacher (1995) summarized nearly 40 years of efforts to measure the homogeneous freezing nucleation rate of pure water by various methods. These included measurements of droplets cooled on surfaces or thermocouples, within (as emulsions) or at the interface of liquids, or suspended in the air. Some measurements on the freezing temperature of pure or highly dilute droplets free of surface contact or surfactants are plotted in figure 5.2 along with the theoretical nucleation rate curves proposed by Pruppacher (1995) and by Jeffery and Austin (1997). The data include measurements in slow (DeMott and Rogers 1990) and

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Cirrus

Figure 5.2. Homogeneous freezing nucleation rate of pure water versus temperature. The theoretical results of Pruppacher (1995) and Jeffery and Austin (1997) are given by the dashed and solid lines, respectively. Pruppacher's curve does not extend below -45°C because he deemed this to be a critical temperature below which pure liquid water could not exist. Selected data for freely suspended dilute or pure water droplets are from DeMott and Rogers (1990), given by x symbols with error bars, from Hagen et al. (1981), given by triangles with error bars, and for Kramer et al. (1996), given by open circles. The results of Huang and Bartell (1995), shown as diamonds, are for cubic ice formation in minute water clusters at 550 bar.

rapid (Hagen et al. 1981) expansion cloud chambers, as well as the first measurements made on levitated droplets (Kramer et al. 1996). It is possible to bring standard classical theory into good agreement with the existing experimental data. In one case, this requires an appeal to some proven and some hypothesized critical behaviors of water at -45°C (Pruppacher 1995) which, nevertheless, do not explain the observation of freezing (as cubic ice) of clusters of water molecules at temperatures around -70°C (Huang and Bartell 1995). Jeffery and Austin (1997) got classical theory to agree with the standard data and the very low temperature results by using a new analytical equation of state that accounts for the role of strong hydrogen bonds in determining the properties of water (Jeffery and Austin 1999). Some authors suggest that many of the results in figure 5.2 reflect heterogeneous nucleation and so are a high-temperature limit for homogeneous freezing conditions (e.g., Granasy 1995). Most early studies of the freezing of solutions at temperatures in the warmer part of the cirrus regime were done on populations of droplets, sometimes quite large ones, suspended in oil. In cases where heterogeneous nucleation was determined not to play a role, Pruppacher and Neiberger (1963) showed that 2000-um

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solution droplets froze at progressively lower temperatures as solute concentration increased. This tendency is expected theoretically. Nevertheless, the temperature depression of the freezing point compared to pure water droplets of equivalent sizes exceeded the equilibrium melting point depression by up to a few degrees at solution molalities up to 1 mole/kg. Hoffer (1961) noted a similar effect for different solutions with molality up to about 3 mole/kg. Pruppacher and Neiberger (1963) speculated that the extra amount of supercooling required for freezing was a reflection of the effects of ion size or ion charge on ordering of ice molecules in solutions. Nevertheless, no consistent picture has emerged from studies that have attempted to resolve the nature of the ionic hindrances to ice formation in solutions (Hoffer 1961; Pruppacher and Neiberger 1963; Ganguly and Adiseshiah 1992). During the 1970s, researchers with interests in cryobiological applications noted a more patterned behavior to the effects of solutes and other cryoprotective liquids on homogeneous freezing conditions. Working with emulsions of droplets of a few microns in size, Rasmussen and Luyet (1970), Rasmussen and Mackenzie (1972), and Mackenzie (1977) showed that both ionic and nonionic liquids displayed freezing-point depressions that increased in direct proportion to melting-point depressions measured in the same experiments. Figure 5.3 integrates some of the results from this group along with the emulsion data of Ganguly and Adeshaiah (1992) and data on the freezing of larger solution droplets from Hoffer (1961) and Pruppacher and Neiberger (1963). Individual solutions were found to obey the expression

where ATn and Arm are the depressions of the freezing (or nucleation) and melting point temperatures, respectively. The coefficient A, ranges from 1.4 to 2.2 for different solutions. Khvorostyanov and Sassen (1998) have suggested that some part of the reason that A, is typically so much greater than 1 may be due to the temperature dependence of the latent heat of freezing. Rasmussen (1982a,b) has pointed out previously that this relationship between nucleation and melting temperatures cannot be easily derived from classical nucleation theory if the expected dependencies of Oi/s and AFact on solution properties are included. Koop et al. (2000) recently proposed that the typical A, is a consequence of nucleation depending primarily on water activity by way of the hydrogen bonding structures required for freezing. This hypothesis does not explain the range of A, observed. Sassen and Dodd (1988,1989) proposed that a simple means of parameterizing the nucleation temperatures (e.g., the temperatures at which JhfVd ~ 1/s) of solution droplets for cirrus conditions was to define an effective freezing temperature (reff), given by This expression may be substituted for temperature (T) in. the classical theoretical equations for /hf or simply within a polynomial function that describes the results for 7hf shown in figure 5.2. Using A = 1.7, Sassen and Dodd (1989) used a microphysical model to estimate the relative humidity for cirrus formation (RHwnuc). RHwnuc could be described by

I 14

Cirrus

Figure 5.3. Summary of the relationship between the measured depression of the nucleation temperatures (AT1,,) of solution droplets below those of pure water droplets and the measured (in same experiments) or tabulated (from data on bulk solutions) melting point depressions. All data are from studies of the freezing of captive droplets ranging in size from 1 um (emulsions) to a few hundred microns. Particular solutes are denoted by squares (NH4C1), diamonds (KC1), triangles (LiCl), circles (NaCl), plus signs (KC1), and asterisks (CaCl2). Data for these solutes are from Rasmussen (1982a) and Rasmussen and Mackenzie (1972) (filled symbols), Pruppacher and Neiberger (1963) (open symbols), and Ganguly and Adiseshaiah (1992) (shaded symbols). The x symbols indicate data for a variety of other solutes examined by the authors listed and by Hoffer (1961). The solid lines indicate 1:1 and 2:1 relationships between the two temperature depressions. The dashed line is a fit to the numerous data points of Koop et al. (1998) for H2SO4/H2O droplets.

with coefficients a = -0.276, b = 5.36 x 10~3, and c = 0. DeMott et al. (1994,1997) also used equations 7 and 8 substituted either into a polynomial equation to describe /hf or into equation 1 to investigate the critical sensitivities and uncertainties in predicting homogeneous freezing in cirrus. Figure 5.4 explores the validity of this parametric approach to using laboratory data, and the parameterization of Koop et al. (2000), as compared to using classical theory. The nucleation rates versus temperature by the parametric method agree in form with classical theoretical treatments of homogenous freezing of H2SO4 solution droplets. The agreement of the Khvorostyanov and Sassen (1998) model with

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I 15

Figure 5.4. Comparison of methods for calculating the homogeneous freezing nucleation rate of 15 weight % (-93% relative humidity at equilibrium) sulfuric acid droplets versus temperature. All methods have an explicit or implicit basis in laboratory studies. The solid curves labeled A, = 1 and A = 1.7 were obtained by substituting Teff (equation 8) for temperature in a polynomial fit for JAcknowledgments Recent PARS cirrus cloud research has been funded by National and Austin, 1997). The filled square points are based on the theoretical model of Khvorostyanov and Sassen (1998) that extends the classical theory of Pruppacher (1995) to solutions. The solution droplet curve is to the left of the pure water curve. The thin, broken curves are from substituting Teff (k = 1,1.7) for temperature in solution-dependent quantities in the theoretical equations for homogeneous freezing of pure water given in Jensen et al. (1994). The triangles are based on the theoretical model of Tabazadeh et al. (2000) that was constrained by the measurements of Koop et al. (1998). The thick, dashed curve is the water activity-dependent parameterization proposed by Koop et al. (2000).

A, = 1 is interesting, but may be fortuitous because this theoretical model ignores the compositional dependencies in oi/s and AFact. The theoretical calculations based on Tabazadeh et al. (2000) include these dependencies but predict a different position and slope to the nucleation rate curve. The position of this curve is reasonably close to the position predicted by A, = 1.7 (suggested by fig. 5.3) and by the Koop et al. (2000) parameterization.The slope difference may indicate a deficiency of the parametric approach, or it may be an artifact of the manner in which Tabazadeh et al. determined ai/s (Antonoff's rule) and AFact (adjusted to obtain agreement of/ hf with the laboratory data of Koop et al. 1998). More laboratory data could help to resolve this issue and reduce the uncertainty in the temperature and composition at which a solution droplet is predicted to freeze. According to figure 5.4, this uncertainty is as large as several degrees Celsius. The relationship between Arm and ATn shown in figure 5.3 has not, until very recently, been investigated for soluble particles that are particularly relevant to

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Cirrus

ice formation in cirrus. A simplified consideration of the soluble components of upper tropospheric aerosols has led to the greatest recent experimental focus on the H2SO4/H2O/(NH4)2SO4 ternary liquid aerosol system. This system encompasses all compositions of sulfate aerosols, from H2SO4 through the 1:1 ratio of ammonia and sulfate ion (ammonium bisulfate) to the completely neutralized form ((NH4)2SO4). Figure 5.5 summarizes some measurements of ice formation in sulfuric acid aerosols. Various details are given in the figure caption. Experimental results are given as different threshold conditions for ice formation and are shown on thermodynamic-phase diagrams in temperature-composition and/or temperaturehumidity space. This jump from a discussion primarily of nucleation rates to one of freezing conditions is done to simplify and conceptualize the implications for cirrus cloud formation and to enable comparison of varied experimental techniques. Nevertheless, one must recognize that all the techniques have kinetic limitations that imply different sensitivities to nucleation rate. Therefore, the definition of threshold freezing conditions differs in each case. Additional fundamental kinetic limitations to ice formation may also exist that are not yet understood. The most apparent feature in figure 5.5 is the large variability in current results on where H2SO4/H2O particles freeze. The FTIR/flow tube measurements of Bertram et al. (1996) provided the first low-temperature measurements of freezing conditions of small (-200 nm), free-flowing sulfuric acid particles as a function of composition. The Bertram et al. data suggest X ~ 1 for their stated onset conditions. Koop et al. (1998) observed ice formation in populations of -10 um H2SO4 droplets placed on a chilled hydrophobic surface. These larger drops needed to supercool a great deal more compared to the freezing of small, freeflowing drops (e.g., A, = 1.9), as shown in figures 5.4 and 5.5. Measurements of levitated single droplets of up to 50 um diameter by Kramer (1998) support the Koop et al. results. Both data sets on larger drops are consistent with the freezing- versus melting-point depression relations for other solutions (figure 5.4) and with laboratory observations of how difficult it is to freeze stratospheric (>35 weight percent composition) H2SO4 aerosols (e.g., Song 1993; Anthony et al. 1995; Carleton et al. 1997; Koop et al. 1997b). Figure 5.5. Experimental results on the freezing conditions for sulfuric acid/water aerosols. Interpolations from one diagram to the other were made on the assumption of equilibrium and using low temperature vapor pressure data. Flow tube results of Bertram et al. (1996) for 400-nm (mean) diameter polydisperse aerosols are given by the filled circles. The data given by open circles are based on the droplet freezing device data of Koop et al. (1998) for 5-12 urn particles. The squares are based on studies of levitated 40-um particles by Kramer (1998). The filled diamonds are for approximately 100nm droplets from continuous flow diffusion chamber studies (Chen et al. 2000). The melting point curve (ice saturation), indicated as "T0 - AT^u," is based on Gable et al. (1950). Thfo is the homogeneous freezing temperature of pure water (235 K used). The curves indicated as "Thfo A!Tmelt" and "Thf0 - 2*A7meit" are equivalent to assuming A = 1 and 2, respectively, in equation 8 for 5-um droplets. The observed conditions for cirrus formation summarized by Heymsfield and Miloshevich (1995) are shown by the shaded line in panel b.

I 17

I 18

Cirrus

More recent measurements of small H2SO4 droplet freezing by Chen et al. (2000) are also included in figure 5.5. These measurements, made with a continuous flow diffusion chamber (CFD), agree with the large drop studies. The CFD measurements indicated that different fractions of particles nucleated ice at different sets of temperature and humidity conditions, when provided with a set residence time. The CFD results for 1 % of approximately 100-nm particles nucleating in about 12s are plotted in figure 5.5. Chen et al. (2000) used equations 7 and 8, the Kohler equation (to infer droplet composition and thereby Arm), and a polynomial for /hf of pure water to find that these data are consistent with an average value of A ~ 2.0. This information is not readily determined by comparison to the constant A, lines in figure 5.5, since those lines are plotted for a specific (large) droplet size. The nucleated fraction is not easily discerned in all types of studies. In flow tube studies, a transition of FTIR spectra showing some ice to one that no longer changes and is presumed to be all ice is observed. This transition can occur over many degrees Celsius (Bertram et al. 1996; Clapp et al. 1997; Cziczo and Abbatt 1999) and may reflect inhibition of complete freezing or simply the successive nucleation of larger fractions of a polydisperse particle population. Future studies should attempt to validate the actual percentages of particles of known size nucleating in all experiments. Nucleation rates should also be derived and presented. Some authors have already done so. Figure 5.5b also indicates the conditions for ice formation in continental cirrus clouds, based on Heymsfield and Miloshevich (1995). These authors inferred the onset conditions (RHwnuc) of cirrus and orographic wave clouds from the maximum RHW measured in clear air around clouds. Heymsfield and Miloshevich (1995) matched the measured RHwnuc to equation 9, finding a - 1.8892, b = 0.0281, and c - 1.3336 x 10~4. It is apparent that these conditions for the formation of ice in continental cirrus clouds are not satisfied by assuming that cirrus haze particles are composed of sulfuric acid that freezes by homogeneous nucleation. Sulfuric acid solution droplets require a degree of dilution for freezing that is only achieved above 90% relative humidity at all temperatures warmer than -60°C. Even with A = 1, the threshold freezing conditions of sulfuric acid aerosols require higher RHW than Heymsfield and Miloshevich's (1995) RHwnuc for cirrus formation. Complete freezing in a real updraft scenario might require even higher ambient RHW. More recently, Heymsfield et al. (1998) found no dependence of RHwnuc (-95%) on temperature in selected sampling around cirrus over oceans. These authors also found the Heymsfield and Milosevich (1995) parameterization to generally underestimate RHwnuc at temperatures below -55°C, independent of air mass source region. Both of these more recent observations may reflect the role of sulfuric acid aerosols in ice formation in some cirrus. A compilation of measurements of deliquescence, efflorescence, and freezing of ammonium sulfate aerosols is shown in figure 5.6. These results indicate the potential importance of the phase states of the ammoniated sulfates under different atmospheric conditions. There is good agreement (data not shown) obtained in levitation experiments (Xu et al. 1998) and flow tube studies (Cziczo and Abbatt 1999; Onasch et al. 1999) on the weak temperature and compositional

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dependence of the deliquescence line. These results on deliquescence are consistent with the calculations of thermodynamic models (Clegg et al. 1998). Likewise, good agreement on the compositions along the ice (saturation) equilibrium line has been obtained by different methods. Considerable disagreement exists between flow tube and levitation experimental results on conditions for efflorescence of liquid (NH4)2SO4 droplets (Onash et al. 1999). Nevertheless, this disagreement may be partly explained by the much longer observation time and lower nucleation rates observed in the levitation experiments. Figure 5.6 includes flow tube and diffusion chamber, and droplet freezing results of the ice formation conditions of ammonium sulfate aerosols. The CFD measurements of Chen et al. (2000) are for monodisperse, submicron-sized, liquid ammonium sulfate aerosol particles. The phase state of particles was not known in the static diffusion chamber measurements of Detwiler (1980), but they were probably liquid. Chen et al. (2000) determined an average value of A, = 1.75 ± 0.35 for their data. This value is close to that inferred from recent studies of freezing of micron-sized emulsified ammonium sulfate droplets (Bertram et al. 2000). Data from Bertram et al. (2000) can be shown to correlate with A, = 2.1. The flow tube results of Cziczo and Abbatt (1999) are for the onset or very first ice formation in polydisperse liquid particles. In contrast to the other studies, these results indicate that some (unknown) fraction of ammonium sulfate solution droplets can freeze in a very (solute) concentrated state in the atmosphere. Most interesting is the fact that the experimental freezing conditions agree well with the observed RHwnuc conditions needed for ice formation in continental cirrus (Heymsfield and Miloshevich 1995). This result suggests a case where A, < 1. Since X < 1 suggest enhancement of homogeneous freezing by the solute in small solution droplets, these results need further confirmation. Estimations of nucleation rates in the various studies are underway and should help in evaluating results. Chen et al. (2000) also noted that dried (NH4)2SO4 required higher RHW (by at least 5%) for ice formation to occur as compared to initially liquid aerosols. Dry solutes could nucleate ice formation by deposition nucleation or by first deliquescing and then freezing. The extrapolation of the deliquescence line below the eutectic temperature is educated conjecture, but deviation of this line to higher saturation ratios at low temperatures could explain the Chen et al. (2000) observations. The first measurements of the low-temperature phase states of ammonium bisulfate particles in an electrodynamic trap (Imre et al. 1997) were in substantial disagreement with thermodynamic model (Clegg et al. 1998) calculations of conditions for deliquescence and the equilibrium compositions at ice saturation (see Tabazadeh and Toon 1998). Experiments by Chelf and Martin (1999) and Yao et al. (1999) using larger solution volumes suggest that the levitation measurements require reevaluation. These authors performed measurements of solution composition upon freezing and measured the vapor pressures over NH4HSO4 solutions at low temperatures. These more recent and standard measurements agree well with the thermodynamic model of Clegg et al. (1998). It was demonstrated that under most tropospheric conditions, letovicite

120

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[(NH4)3H(SO4)2] is the first substance to crystallize from liquid bisulfate solutions. Imre et al. (1997) found a possible exception to this rule at around -31°C, where they noted the formation of the hydrate NH4HSO4-8H2O, but this result requires new validation in light of the other discrepancies with bulk solution studies. When letovicite does crystallize from NH4HSO4 solutions, the remaining solution maintains an excess of H+ ions (acidifies) and may only effloresce at very low humidity. FTIR studies conducted at room temperature were unable to demonstrate efflorescence of wet bisulfate aerosols down to 2% RHW (Cziczo et al. 1997). In contrast, Chen et al. (2000) noted indirect evidence of partial crystallization (as letovicite) in the process of drying NH4HSO4 aerosols. The reasons for this discrepancy are under study. Figure 5.7 shows the first experimental measurements of ice nucleation conditions for ammonium bisulfate aerosol particles. The Chen et al. (2000) results are from continuous flow diffusion chamber studies of submicron, liquid solution droplets while Koop et al. (1999) studied emulsified micron-sized droplets. Data points from the polynomial provided by Koop et al. (1999) to describe the median freezing temperature of droplets are plotted in figure 5.7 and correlate with A, = 2.3. Chen et al. (2000) inferred A, ~ 1.4 for bisulfate droplet freezing, but the uncertainty of the measurements did not allow for them to be distinguished from the freezing conditions of either ammonium sulfate or sulfuric acid. Bertram et al. (2000) likewise concluded that there was no significant difference in the average freezing conditions of various sulfate aerosols. Much work still remains on resolving the freezing behavior of droplets of specific compositions in cirrus conditions. Many other species such as nitrates may play an important role in ice formation in cirrus (e.g.,Tabazadeh and Toon 1998). The impact of HNO3 on enhancing water uptake in ternary solutions with sulfuric acid is well known (e.g., Molina et al. 1993; Lamb et al. 1996). The potential impacts of organic components on the growth and freezing of haze particles must also be considered.

Figure 5.6. Experimental results on freezing conditions for ammonium sulfate aerosols plotted on (a) temperature/composition and (b) temperature/water saturation ratio (= RHW/100) phase diagrams. The data given by the filled circles are the onset conditions for ice formation in the flow tube studies of Cziczo and Abbatt (1999). The open circles are based on the emulsion droplet-freezing data (Bertram et al., 1999). The diamonds are the conditions for nucleating 1 % of particles as ice in continuous flow diffusion chamber (CFD) studies (Chen et al. 2000). The square symbols are for ice nucleation of 1% of particles in the static diffusion chamber studies of Detwiler (1980). Particle sizes of around 200 nm (prior to water uptake) were used in diffusion chamber and flow tube studies, while drops of sizes 5-20 um were used in Bertram et al. (2000). Particles were monodisperse only in the CFD studies. The curve defining conditions for deliquescence and the equilibrium melting point curve are based on Clegg et al. (1998). These curves are extrapolated below their point of intersection ("eutectic"). The efflorescence curves (see text) in panel a are based on (1) Xu et al. (1998) (1) and (2) Cziczo and Abbatt (1999) (2). Other lines are as defined in figure 5.5.

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Figure 5.7. Experimental results on freezing conditions for ammonium bisulfate aerosols plotted on a temperature/water saturation ratio (= RHW/100) phase diagram. The data points (diamond) indicate conditions for 1 % of 200 nm (prior to water uptake) particles freezing in continuous flow diffusion chamber studies (Chen et al. 2000). The deliquescence line is plotted for letovicite because letovicite crystallized in bisulfate solution droplets when they were dried following generation by Chen et al. (2000). The open circle symbols are based on the results of emulsion (3-12 um droplets) freezing studies (Koop et al., 1999).

Heterogeneous nucleation of ice The discussion of laboratory results on heterogeneous ice nucleation given here will largely focus on cirrus clouds at temperatures below -35°C. This reflects the definition of cirrus, as ice clouds, given at the beginning of this book. It must be acknowledged that this omits some cirruslike clouds, at temperatures between -25 and -35°C, where heterogeneous ice nucleation processes are the only primary mechanisms for generating ice crystals. Laboratory studies have demonstrated that certain insoluble particulates will cause solution drops to freeze in more concentrated form than they do homogeneously (e.g., Hoffer 1961; Reischel and Vali 1975). Some results are adapted from Hoffer (1961) in figure 5.8. Hoffer observed approximately lOO-um pure water droplets freeze at -36.5°C.The freezing point lowering by solution droplets of MgCl2 plus Na2SO4 closely followed equation 7 with A, = 2. Pure water droplets

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Figure 5.8. Depression of the median heterogeneous freezing temperature of approximately 100-um droplets as a function of the composition (given as a fraction of saturated) of solutions of MgCl2 and Na2SO4. The ice nuclei used in droplets were illite (squares, median freezing T = -24°C), montmorillonite (triangles, median freezing T = -24°C), hallyosite (diamonds, median freezing T = -32.5°C), and kaolinite (crosses, median freezing T = -32.5°C). The median freezing temperature for pure water droplets was -36.5°C, and the homogeneous freezing point depressions of pure solution droplets are given by the circles. These latter values are shown to approximately agree with A, = 2. Adapted from Hoffer (1961).

seeded with different clay particles froze heterogeneously at the higher median temperatures indicated in the caption for figure 5.8. The separation of the data points for seeded solution droplets from those for unseeded droplets may be partly the consequence of plotting the median freezing temperatures of populations of droplets in figure 5.8. Heterogeneous freezing occurred over a broader range of temperatures than for freezing pure-solution droplets. Nevertheless, it is probably valid to note that the Arn-solute-concentration relationship for seeded solution droplets approximately parallels the one for homogeneous freezing. A careful examination of figure 5.8 indicates that heterogeneous freezing may become even rnore difficult as a droplet becomes saturated with solute. This inference is supported by the observations of Koop et al. (1995,1997b) and Biermann et al. (1996) on the sulfuric acid system. These authors have shown that various mierometeorites, metal oxides, silicates, and even Agl nuclei do not crystallize hydrate or ice formation in concentrated sulfuric acid drops at stratospheric

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temperatures. A reasonable conclusion from figure 5.8 would be that A,het < Xhom. It will be of interest to extend measurements of heterogeneous freezing to conditions of high solute concentration (>0.1-1 saturation of solute) that exceed those existing at the point where homogeneous freezing will occur. Limited data also indicate that soot particles will freeze water at low temperatures (DeMott 1990; Diehl and Mitra 1998; DeMott et al. 1999). The icenucleating properties of soot aerosols are of interest due to the contribution of combustion processes (jet fuel combustion in particular) to the upper tropospheric aerosol. DeMott (1990) nucleated micron-sized cloud droplets on soot particles produced from burning acetylene and observed ice formation from the suspended droplets during simulated adiabatic cooling. That study found that only a few percent of 80-120 nm soot particles froze micron-sized water droplets at temperatures down to -34°C. Freezing fraction was also found to directly relate to particle surface area, as is expected theoretically for a uniform surface. The observation that not all particles of one size froze at the same temperature is not explainable by theory, but is a frequent finding in studies of heterogeneous freezing. Diehl and Mitra (1998) observed the freezing of large droplets (-200-400 u,m) formed from a liquid suspension containing particles produced from burning jet fuel. In this case, more than one particle may have been placed within each droplet. Diehl and Mitra (1998) found that 100% of their droplets froze when suspended in a wind tunnel below about -28°C. A much lower freezing efficiency is obtained from the Diehl and Mitra data when the calculation is referenced to the total particle surface area within the "dirty" drops, more consistent with DeMott's (1990) results. DeMott et al. (1999) report the first experiments on freezing of small soot particles in cirrus conditions. They showed that polydisperse (240 nm average diameter) black carbon particles coated by sulfuric acid would act as heterogeneous freezing nuclei when the acid coating exceeded a few weight percent of particle mass and temperature was below -53°C. Numerical calculations indicate the potential importance of the heterogeneous freezing nucleation mechanism to cirrus formation conditions. Jensen and Toon (1997) used a classical theoretical approach to demonstrate that existing concentrations of soot particles acting as freezing nuclei should lower ice crystal concentrations in cirrus compared to the singular homogeneous freezing scenario. Jensen and Toon assumed a contact parameter of m^ = 0.8 in their analyses. Karcher et al. (1996) measured mi/n = 0.57 on a larger graphite surface. The laboratory data of DeMott (1990) suggest that some soot aerosols probably act with raj/n < 0.1. DeMott et al. (1997) used the empirical approach embodied in equation 8 to extrapolate the soot freezing fractions of DeMott (1990) to the case of H2SO4 solution droplets freezing at low temperatures. Despite the differences in the assumed ice-nucleating properties of soot particles, DeMott et al. (1997) showed the same functional effect of heterogeneous ice nuclei abundance on cirrus crystal concentrations as did Jensen and Toon (cf. Jensen and Toon 1997: fig. 4 with DeMott et al. 1997: fig. 7). Both numerical studies suggest that freezing nuclei would have the greatest impact on cirrus crystal concentrations for low updraft rates (<20cm/s) and in warmer cirrus. DeMott et al. (1997) also empha-

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sized that the other critical role of heterogeneous ice nuclei was to lower the threshold humidity for cirrus formation. In the absence of detailed information on the ice-nucleating properties of soot particles at temperature below -40°C, these are only qualitative inferences. Few data exist on heterogeneous ice-nucleation mechanisms besides freezing at low temperatures. A common misconception is that ice formation by deposition nucleation should ensue at very low ice supersaturations. Detwiler and Vonnegut (1981) measured the need for steadily increasing ice supersaturation with decreasing temperature in order to activate deposition nucleation on Agl particles. An ice supersaturation of 20% was needed at -60° C, even though Agl has mi/n = 0.96 for deposition. More common atmospheric nuclei might be expected to have much lower mi/n and thus would require exceedingly high ice supersaturations for ice formation by this mechanism. Although laboratory and modeling studies suggest the potentially important role of heterogeneous ice nuclei in cirrus, their role is critically tied to the abundance of insoluble particulates. As noted previously, different data sets differ in the observed abundance of insoluble particulates in the upper troposphere (Hagen et al. 1994; Sheridan et al. 1994; Chen et al. 1998; Murphy et al. 1998). The presence of insoluble cores within haze particles lofted to cirrus levels also will likely affect how readily such particles effloresce (e.g., Oatis et al. 1998; Han and Martin 1999). Ultimately, more may be learned about these issues by applying some of the laboratory techniques to the atmosphere after sufficient refinement.

5.2. Other Cirrus-related Laboratory Studies

5.2.1. Ice Crystal Morphology, Growth, and Evaporation in Cirrus The radiative effects of cirrus ice particles depend not only on their concentrations, but also on their subsequent growth or evaporation and their shapes. A number of laboratory studies have been performed to determine the growth habits, growth rates, and evaporation rates of ventilated or freely falling ice particles existing at temperatures higher than -30°C. These studies used an assortment of laboratory devices, including diffusion chambers, cloud chambers, and supercooled cloud tunnels (e.g., Ryan et al. 1976; Oraltay and Hallett 1989; Takahashi et al. 1991; Song and Lamb 1994a). Kobayashi (1965) conducted studies in the temperature regime from -40 to -90°C, but these were of epitaxial growth on large substrate surfaces at standard pressure. Gonda (1983) studied the growth of artificially nucleated crystals in free fall in a cold chamber (-40 to -140°C) at standard pressure. The increased diffusivity of water molecules in air at lower cirrus pressures should lead to faster crystal growth rates and could affect crystal habit and morphology. Bailey and Hallett (1998) map out growth rates and ice crystal morphology at low temperatures, reduced pressures, and variable ice saturation ratios for crystals held on drawn glass threads in a thermal diffusion chamber. Some of these results have been mentioned in a previous chapter. These experiments validate the pressure effect on growth rate. Bailey

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and Hallett (1998) have also found a high frequency of occurrence of crystals with nonhexagonal symmetry and scalene-hexagonal shapes in cirrus conditions. Crystal polycrystallinity has been found to increase toward lower temperatures at the low to moderate ice supersaturations often found in cirrus. Emphasis has been given to the study of levitated single ice crystals. Bacon et al. (1998) used electrodynamic isolation to investigate evaporation rates of frost crystal structures at temperatures from 0 to -30°C. The ratios of crystal dimensions along different growth axes increased as crystals evaporated. This result increased the likelihood of crystal fracture, suggesting that fracture is a potentially important secondary ice production process for complex ice crystals. One ice crystal could spawn many particles in regions of evaporation. Swanson et al. (1999) used the same levitation device to examine ice crystal growth rates at low ice supersaturations and temperatures as low as -30°C. Crystal growth and sublimation rates were in agreement with recent theoretical formulations. It can be expected that much data on ice crystal habit transitions, growth, and evaporation rates in the cirrus regime will be obtained through single particle studies of these types. A question of particular interest regarding cirrus clouds is the influence of ice crystal surfaces on chemical processing and the effects of surface chemistry on the lifetimes of cirrus crystals. Studies of HNO3 and HC1 uptake and desorption on ice at cirrus conditions have been performed using ion chfomatography of frost crystals grown in a diffusion chamber (e.g., Diehl et al. 1995,1998) arid FTIR spectroscopic probing of thin films (e.g., Zondlo et al. 1997; Warshawsky et al. 1999). Current results do not support inhibition of cirrus crystal evaporation because typical HNO3 partial pressures are too low to lead to liquid surface coverage. Ice crystal studies must be extended to lower temperatures, higher ice saturation ratios, and varied orientations of crystals to address processes ifi cirrus conditions. All ice crystal studies should ultimately investigate the effect that the underlying nucleation process may have on the initial form that ice crystals take. 5.2.2. Radiative Properties of Cirrus Ice Crystals Laboratory studies provide fundamental data on the interaction of radiation with cirrus clouds, validating theories and giving practical information for interpreting active and passive remote sensing data. A handful of laboratory studies have been performed to measure the scattering properties of cirrus ice crystals. Most of these have been performed in the warmer segment of the cirrus regime. The conduct of increasingly detailed theoretical calculations of scattering by complex cirrus crystals (see chapter 13) and the development of optical array nephelometers for directly measuring scattering phase function in cirrus clouds (e.g., Gayet et al. 1998; Lawson et al. 1998) have helped motivate new laboratory studies. Some groups have used cloud chambers that contained a light source (e.g., diode laser) and a means for focusing and collecting scattered light (Nikiforova et al. 1978; Volkovitskiy et al. 1980; Sassen and Liou 1979a,b; Rimmer and Saunders 1997; Saunders et al. 1998). Particle imaging nephelometers have also been used to measure the scattering properties of laboratory clouds (Lawson

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et al. 1998). These laboratory investigations have validated the optical phenomena expected theoretically for certain ice crystal habits, but not for others. Lawson et al. (1998) also noted the close reproduction of natural cirrus crystal habits to -42°C in laboratory clouds formed by controlled expansion. However, many of the expected halo phenomena for different crystal types were smoothed out in the phase function measurements (Lawson et al. 1998). Smooth phase functions may indicate the effect of surface roughness properties (Yang and Liou 1998). Could roughness be induced by the nature of the nucleation process? Issues for cloud chamber studies that require future consideration include the range of crystal sizes that can be investigated and understanding the influence of multiple scattering, background liquid droplets, and non-monodisperse ice-crystal size distributions on interpreting phase function measurements. Saunders et al. (1998) made some progress on these issues. Scattering and depolarization measurements are also being integrated with single particle (electrodynamic) isolation techniques (Roth and Frohn 1998; Swanson et al. 1999; Bacon and Swanson 2000). Chapter 13 discusses these measurements. The impact of the complex nucleation processes on scattering and depolarizing properties is a consideration for future investigations in the laboratory. 5.2.3. Collection and Transformation of Aerosols by Cirrus Nucleation processes are only one means for particles to be collected (scavenged) in cirrus. Ice crystal growth and cirrus cloud dynamics can be expected to lead to the redistribution of aerosol particles after nucleation. Additionally, cirrus crystals can scavenge atmospheric aerosols from the interstitial air. Some laboratory data have been obtained on this process in the warm temperature regime of cirrus. Bell and Saunders (1991, 1995) produced hexagonal plate ice crystals in a cloud chamber and allowed these to settle through an aerosol chamber at 27°C. These authors found high scavenging efficiencies (0.1-1) for supermicron aerosols by crystals smaller than 150 um. The noted decrease in scavenging efficiency with increased crystal size was not to the extent necessary to give agreement with extrapolations from theoretical calculations at larger crystal sizes (Martin et al. 1980). Song and Lamb (1994b) studied scavenging of submicron aerosol particles by columnar and plate crystals down to —14°C in a continuous flow cloud chamber. Their measurements agreed with theoretical calculations of scavenging efficiency for 100-400 um plates (Martin et al. 1980) and columns (Miller and Wang 1989). The measurements of Song and Lamb (1994b) suggest that actual scavenging efficiencies may exceed theoretical values for crystals smaller than 100 urn. Ice crystals smaller than 100 urn are commonly found in cirrus and contrails. The reaction of gas-phase chemical species on cirrus ice crystals or on the various phases of aerosols that may be present in the upper troposphere is a topic only recently explored. Laboratory studies of HNO3 uptake by cirrus crystals and the effect on crystal evaporation have been mentioned. Other species may also be taken up on cirrus, and the presence of one or another condensate could alter the reactivity of the particles for other species. These chemical reactions can lead

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to transformations of aerosols in and around cirrus clouds. This is a topic of laboratory investigation, particularly among the researchers who have studied reactions on polar stratospheric clouds. Due to aerosol and chemical scavenging processes, the aerosols remaining after evaporation of cirrus clouds may be greatly modified compared to the particles that were present before cloud processing. This processing of aerosols may affect their ice nucleation properties at later times. These complex issues deserve greater study.

5.3. Summary Numerous scientific problems related to understanding cirrus clouds are now being addressed through laboratory studies. This should continue to be an area of vigorous study in the future. Already, field and laboratory programs focusing on cirrus clouds and ice formation processes are in the planning stages. More and more, these efforts will involve participants from many disciplines. The need for validation of remote sensing measurements and model development should also persist.

Acknowledgments A large number of colleagues, referenced throughout this chapter, deserve thanks for responding to requests for information. Jon Abbatt, Matt Bailey, Allan Bertram, Yalei Chen, Daniel Cziczo, Thomas Koop, Sonia Kreidenweis, Scot Martin, David Rogers, Tony Prenni, Azadeh Tabazadeh, and Vitaly Khvorostyanov provided additional helpful discussions and specific material. Special thanks to Andrew Detwiler and Gabor Vali for their thorough reviews, and to the National Science Foundation (NSF ATM0071321) and the National Aeronautics and Space Administration (NAG 5-9308) for their support while I was writing this chapter.

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Lamb, D., A.M. Moyle, and W.H. Brune, 1996. The environmental control of individual aqueous particles in a cubic electrodynamic levitation system. Aerosol. Sci. Technol., 24,263-278. Lawson, R.P., AJ. Heymsfield, S.M. Aulenbach, and T.L. Jensen, 1998. Shapes, sizes and light scattering properties of ice crystals in cirrus and a persistent contrail during SUCCESS. Geophys. Res. Lett., 25,1331-1334. Luo, B.P., Th. Peter, and P.J. Crutzen, 1992. Maximum supercooling of H2SO4 acid aerosol droplets. Ber. Bunsenges. Phys. Chem., 96,334-338. Mackenzie, A.P., 1977. Non-equilibrium freezing behavior of aqueous systems. Phil. Trans. R. Soc. Lond. B., 278,167-189. Mackenzie, A.R., A. Laaksonen, E. Batris, and M. Kulmala, 1998. The Turnbull correlation and the freezing of stratospheric aerosol droplets. /. Geophys. Res. D., 103,

10875-10884. Martin, J.J., P.K. Wang, and H.R. Pruppacher, 1980. A theoretical determination of the efficiency with which aerosol particles are collected by simple ice crystal plates. /. Atmos. Sci., 37,1628-1638. Martin, S.T., 1998. Phase transformations of the ternary system (NH4)2SO4-H2SO4-H2O and the implications for cirrus cloud formation. Geophys. Res. Lett., 25,1657-1660. Martin, S.T., 2000. Phase transitions of aqueous atmospheric particles. Chem. Rev., 100, 3403-3453. Massucci, M., S.L. Clegg, and P. Brimblecombe, 1996. Equilibrium vapor pressure of H2O above aqueous H2SO4 at low temperature. /. Chem. Eng. Data, 41, 765-778. Miller, N.K., and P.K. Wang, 1989. Theoretical determination of the efficiency of aerosol particle collection by falling columnar ice crystals. /. Atmos. Sci., 46,1656-1663. Molina, M.J., R. Zhang, P.J. Woolridge, J.R. McMahon, J.E. Kim, Y.H. Chang, and K.D. Beyer, 1993. Physical chemistry of the H2SO4/HNO3/H2O system. Science, 261, 1418-1423. Murphy, D.M., D.S. Thomson, and M.J. Mahoney, 1998. In situ measurements of organics, meteoritic material, mercury, and other elements in aerosols at 5 to 19 kilometers. Science, 282,1664-1669. Niedzela, R.F., M.L. Norman, R.E. Miller, and D.R. Worsnop, 1998.Temperature- and composition-dependent infrared optical constants for sulfuric acid. Geophys. Res. Lett., 25, 4477-1480. Nikiforova, N.K., L.N. Pavlova, and V.P. Snykov, 1978. The Rassvet high-speed scattering phase function measuring system. Trudy. IEM., 83, 28-32. Novakov, T, D.A. Hegg, and P.V. Hobbs, 1997. Airborne measurements of carbonaceous aerosols on the East Coast of the United States. /. Geophys. Res., 102, 3002330030. Oatis, S., D. Imre, R. McGraw, and J. Xu, 1998. Heterogeneous nucleation of a common atmospheric aerosol: Ammonium sulfate. Geophys. Res. Lett., 25,4469-4472. Ohtake, T, 1993. Freezing points of H2SO4 aqueous solutions and formation of stratospheric ice clouds. Tellus, 45B, 138-144. Onasch, T.B., R.L. Siefert, S.D. Brooks, A.J. Prenni, B. Murray, M.A. Wilson, and M.A. Tolbert, 1999. Infrared spectroscopic study of the deliquescence and efflorescence of ammonium sulf ate aerosol as a function of temperature. /. Geophys. Res., 104, 21317-21326. Oraltay, R.G., and J. Hallett, 1989. Evaporation and melting of ice crystals: a laboratory study. Atmos. Res., 24,169-189. Peter, Th., 1996. Formation mechanisms of polar stratospheric clouds. In Nucleation and Atmospheric Aerosols 1996 (M. Kulmala and P.E. Wagner, eds.). Pergamon Press, New York, pp. 280-291.

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Petzold, A., J. Strom, S. Ohlsson, and P.P. Schroder, 1998. Elemental composition and morphology of ice-crystal residual particles in cirrus clouds and contrails. Atmos. Res., 49, 21-34. Pruppacher, H.R., 1995. A new look at homogeneous ice nucleation in supercooled water drops. /. Atmos. Sci., 52,1924-1933. Pruppacher, H.R., and J.D. Klett, 1997. Microphysics of Clouds and Precipitation, 2nd ed. Kluwer, Norwell, MA. Pruppacher, H.R., and M. Neiberger, 1963. The effect of water soluble substances on the supercooling of water drops. J. Atmos. Sci., 20, 376-385. Pueschel, R.F., D.F. Blake, K.G. Snetsinger, A.D.A. Hansen, S. Verma, and K. Kato, 1992. Black carbon (soot) aerosol in the lower stratosphere and upper troposphere. Geophys. Res. Lett., 19,1659-1662. Rasmussen, D.H., 1982a. Thermodynamic and nucleation phenomena: A set of experimental observations. /. Cryst. Growth, 56, 56-66. Rasmussen, D.H., 1982b. Ice formation in aqueous systems. /. Microscopy, 128, 167174. Rasmussen, D.H., and B. Luyet, 1970. Contribution to the establishment of the temperature-concentration curves of homogeneous nucleation in solutions of some cryoprotective agents. Biodynamica, 11, 33-44. Rasmussen, D.H., and A.P. Mackenzie, 1972. Effect of solute on ice-solution interfacial free energy; Calculation from measure homogeneous nucleation temperatures. In Water Structure at the Water Polymer Interface (H.H.G. Jellinek, ed.). Plenum Press, New York, pp. 126-145. Reischel, M.T., and G. Vali, 1975. Freezing nucleation in aqueous electrolytes. Tellus, 27, 414-427. Rimmer, J.S., and C.P.R. Saunders, 1997. Radiative scattering by artificially produced clouds of hexagonal plate ice crystals. Atmos. Res., 45,153-164. Rogers, D.C., 1988. Development of a continuous flow thermal gradient diffusion chamber for ice nucleation studies. Atmos. Res., 22,149-181. Rogers, D.C., P.J. DeMott, S.M. Kreidenweis, and Y. Chen, 1998. Measurements of ice nucleating aerosols during SUCCESS. Geophys. Res. Lett., 25,1383-1386. Roth, N., and A. Frohn, 1998. Size and polarization behavior of optically levitated frozen water droplets. Atmos. Environ., 32, 3139—3143. Ryan, B.F., E.R. Wishart, and D.E. Shaw, 1976. The growth rates and densities of ice crystals between -3°C and -21°C. /. Atmos. Sci., 33, 842-850. Sassen, K., and G.C. Dodd, 1988. Homogeneous nucleation rate for highly supercooled cirrus cloud droplets. /. Atmos. Sci., 45,1357-1369. Sassen, K., and G.C. Dodd, 1989. Haze particle nucleation simulations in cirrus clouds, and applications for numerical and lidar studies. /. Atmos. Sci., 46, 3005-3014. Sassen, K., and K.N. Liou, 1979a. Scattering of polarised laser light by water droplet, mixed phase and ice crystal clouds: Part I. Angular scattering patterns. /. Atmos. Sci., 36, 838-851. Sassen, K., and K.N. Liou, 1979b. Scattering of polarised laser light by water droplet, mixed phase and ice crystal clouds: Part II. Angular depolarizing and multiple scattering behavior. /. Atmos. Sci., 36, 852-861. Sassen, K., H. Zhao, and B-K. Yu, 1989. Backscatter laser depolarization studies of simulated stratospheric aerosols: crystallized sulfuric acid droplets. Applid Optics, 28, 3024-3029. Saunders, G, J. Rimmer, P. Jonas, J. Arathoon, and C. Liu, 1998. Preliminary laboratory studies of the optical scattering properties of the crystal clouds. Ann. Geophys., 16, 618-627.

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Wyslouzil, B., K.L. Carleton, D.M. Sonnenfroh, W.T. Rawlins, and S. Arnold, 1994. Observation of hydration of single, modified carbon aerosols. Geophys. Res. Lett, 19,2107-2110. Xu, I, D. Imre, R. McGraw, and I. Tang, 1998. Ammonium sulfate: Equilibrium and metastability phase diagrams from 40 to -50°C. /. Phys. Chem. B., 102, 7462-7469. Yang, P., and K.N. Liou, 1998. Single-scattering properties of complex ice crystals in terrestrial atmosphere. Contributions to Atmospheric Physics [Beitrage zur Physik der Atmosphare], 71,223-248. Yao, Y, M. Massucci, S.L. Clegg, and P.J. Brimblecombe, 1999. Equilibrium water partial pressures and salt solubilities in aqueous NH4HSO4 to low temperatures. /. Phys. Chem. A., 3678-3686. Zhang, R., P.J. Woolridge, J.P.D. Abbatt, and MJ. Molina, 1993. Physical chemistry of the H2SO4/H2O binary system at low temperatures: Stratospheric implications. J. Phys. Chem., 97, 7351-7358. Zondlo, M.A., S.B. Barone, and M.A. Tolbert, 1997. Uptake of HNO3 on ice under upper tropospheric conditions. Geophys. Res. Lett., 24,1391-1394.

6

Cirrus and Weather A Satellite Perspective

DONALD WYLIE

6.1. How Common Are Cirrus?

Cirrus were originally thought of as benign cloud forms that could be used for predicting the onset of foul weather, such as "mare's tails" and "anvil edges," but not of great concern because they do not produce any damaging winds or hydrometers. Our original view of cirrus was from the ground, so they were mostly ignored until aircraft started flying in them and making cirruslike contrails in the latter part of World War II. Cirrus limited visibility for the aircraft, and contrails made detection of aircraft from the ground easier. This led to the first studies of cirrus by the Air Force (Stone 1957). Had our first views of earth been from space, cirrus would have been an obvious cloud and often an obstruction to viewing everything else on the planet. Cirrus are difficult to see on visual satellite images, which is deceiving because they reflect enough solar radiation to obscure quantitative measurements of the land and water surfaces. Cirrus are more obvious in window channel infrared images, and they block any sensor that tries to look horizontally through them from either aircraft or satellites. The term "invisible cirrus" originated from an attempt to fly a horizontal viewing sensor on an aircraft for detecting approaching objects (missiles). The sensor was obscured because of its long path length through cirrus, while ground observers did not report the cirrus. Pilots were uncertain whether they were in a cloud or not. The frequency of cirrus reported from satellite data often surprises other scientists. Wylie and Menzel (1999) reported finding cirrus in 25-30% of GOES/VAS (Geostationary Operational Environmental Satellite/Visual spin 136

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scan radiometer Atmospheric Sounder) data over the continental United States. A similar satellite instrument flying globally, the HIRS (High Resolution Infrared Radiometer Sounder) on the National Oceanic and Atmospheric Administration (NOAA) satellites, reported cirrus 43% of the time (Wylie and Menzel 1994; Wylie and Menzel 1999). The horizontally viewing SAGE (Stratospheric Aerosol and Gas Experiment) is even more sensitive and reports cirrus in 50-70% of its data (Wang et al. 1996). These numbers should not have surprised people because the compilations of ground-based weather observations by Warren et al. (1988) show cirrus frequencies as high as 75% in Indonesia. The frequency of cirrus reports depends on the sensitivity and size of the field of view (FOV) of the sensor. There have been comparisons between three satellite global cirrus data sets. Wylie and Wang (1997) discuss the Wisconsin analysis of HIRS versus the SAGE. Liao et al. (1995a,b) discuss SAGE versus the International Satellite Cloud Climatology Project (ISCCP), and Jin et al. (1996) discuss the ISCCP versus the Wisconsin analysis of HIRS. The more sensitive sensor always reports more cirrus. The sensor with the largest FOV sensor also will report more cloud cover of all forms, including cirrus. The ISCCP is the least sensitive to cirrus and has the smallest FOV, so it reported the lowest frequency of cirrus. The HIRS is in the middle in sensitivity, FOV size, and reported cirrus frequency, and the SAGE has the greatest sensitivity, the largest FOV size, and consequently reports the highest cirrus frequency. 6.2. Correlations of Cirrus with Weather Patterns

The compendium on cirrus and cirrus forecasting by Stone (1957) is one of the best discussions of where cirrus are found in weather patterns. This is surprising because it was written well before satellite images of the earth were available. Stone had to use cirrus observations from aircraft and surface weather observers. Cirrus clouds are of secondary concern to these observers. Precipitating clouds and severe winds are more threatening and thus their first concern. Nephanalysis studies of satellite imagery in the 1960s echoed the relationship between jet streams and cirrus described by Stone. Cirrus are more obvious on infrared satellite images because of their top-of-the-atmosphere viewing perspective. There has been surprisingly little work on the relationship of cirrus to weather patterns since the 1960s. Menzel et al. (1992) made a statistical study correlating satellite reports of cirrus with wind patterns and radar echoes. It verified the concepts in Stone (1957) and gave statistical probabilities of cirrus. Weather forecasters have traditionally estimated cloud cover, including cirrus, as part of the preparation of their text forecasts. They know that the presence or absence of cloud cover can radically affect maximum and minimum surface temperature. They visually examined the weather patterns forecast by the numerical models and then mentally estimated the cloud cover. Clouds had to be added to the forecast mentally because forecast models did not explicitly forecast clouds. The models forecast lower troposphere (700mb) humidity and precipitable water, which are used for forecasting convective clouds and precipitation. But humidity forecasts for cirrus altitudes were seldom plotted,

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leaving the forecasters to guess cirrus clouds from the 500 or 300mb height patterns. Numerical models have experimented with generating cirrus clouds directly using moisture budgets and equations describing condensation and precipitation processes. Chapters 16-18 of this book describe these models in detail. The most exciting work is being done by the European Center for Medium Range Forecasting (ECMWF) because they have incorporated clouds into their global forecast model. This effort has moved numerical modeling of cirrus out of the experimental category to the daily forecast model, which is a bold step. 6.3. Where Do Cirrus Occur?

Cirrus generally occur where three types of generating mechanisms are present: 1) cumulonimbus convection, 2) baroclinic fronts and lows, and 3) orographic lifting. Figure 6.1 shows the global distribution of clouds above 6km from the HIRS satellite analysis of Wylie and Menzel (1999). Cirrus are most frequently found in the Intertropical Convergence Zone (ITCZ) in the tropics both over land and oceans (white band in fig. 6.1). Cirrus frequencies are near 100% in Indonesia and part of the African Congo during the boreal summer. The white band of high frequency cirrus in figure 6.1 moves north and south with the seasonal change in the ITCZ. The second most frequent location of cirrus is the mid-latitude storm belts, from 30° to 50° latitude. In the boreal winter (fig. 6.1), the North Atlantic and North Pacific Oceans have high frequencies of cirrus (>60% of the time) because of frontal weather systems. In the boreal summer, the cirrus frequency in the northern oceanic areas decreases as the frontal activity weakens. The cirrus frequency in the Antarctic Ocean increases with the intensification in frontal weather systems in the austral winter. Mountains also generate cirrus clouds from orographic lifting as air flows over them and in the ascending part of waves generated by the mountain crests. Cirrus frequencies of >50% were found in the Wisconsin HIRS analysis in the Himalayas of Asia in the boreal winter (fig. 6.1). The Wisconsin HIRS analysis underreported cirrus in high-altitude mountain areas (Jin et al. 1996). Cirrus frequencies are probably higher in the Rocky and Himalayan mountains than shown in figure 6.1. Randall et al. (1996) emphasized the high concentrations of cirrus in mountain ranges reported by the ISCCP as being the main locations of mid-latitude cirrus. However, the ISCCP data used in this study underreported cirrus in other areas (Jin et al. 1996). A gradient in lower cirrus frequency from the Rocky Mountains eastward to the central United States was reported. This gradient does not appear in other cirrus studies such as Menzel et al. (1992), Wylie et al. (1994), Wang et al. (1996), and Wylie and Menzel (1999). The SAGE data (Wang et al. 1996) did not find any cloud concentrations in any mountain range; however, they do not show cloud frequencies below 10km altitude. This implies that mountaingenerated cirrus are in the middle troposphere and seldom reach the upper troposphere.

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Figure 6.1. The frequency of high (above 6km) clouds detected by HIRS from 1989 to 1997. Boreal winter is the months of December, January, and February, and boreal summer is the months of June, July, and August.

As mentioned above, cirrus often owe their existence to cumulonimbus convection, especially in the tropics and the ITCZ. Cumulonimbus inject water vapor as well as ice particles into the upper troposphere. Without the humidity, cirrus would eventually precipitate or evaporate. The added water vapor leads to long bands of cirrus emanating from the eastern Pacific up into the United States. The 6.7-UMn infrared water channel image in figure 6.2 shows upper tropospheric water and some cirrus clouds flowing northeastward from the Yucatan of Mexico, across Florida, into the Atlantic Ocean. The latitudinal extent of cirrus in the tropics is far beyond the active convective cells often extending into the midlatitudes. These cirrus may be part of Hadley cell spreading of air from the convective anvils, which probably provides the moisture that allows the tropical cirrus to exist for long periods and float great distances from the areas of convection. The compendium of Stone (1957) discusses the most likely locations for cirrus, which are in the northward flowing side of Rossby wave troughs (fig. 6.3) from

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Figure 6.2. A 6.7-um infrared water channel image of North America from GOES 8 on December 14,1998. Light areas have upper tropospheric water vapor and white areas are cirrus clouds.

the trough axis to the ridge (across the eastern United States in fig. 6.3). The thickest cirrus are on the southeastern side of the jet stream core of maximum wind speed. Stone (1957) also noted that the jet stream core of maximum winds often defines a northern boundary of cirrus. This boundary is often obvious on satellite images. Cirrus often move through the ridge into the southward flowing part of the trough, as indicated in the upper left side of figure 6.3. The ridge cirrus are thin on its eastern edge and often occur with few clouds below it. The southward or equatorward part of the trough is known for having few clouds at any level in the troposphere. A statistical study of the relationship of cirrus clouds to upper tropospheric wind fields was reported in Menzel et al. (1992). This study was confined mostly to the continental United States because it used the GOES VAS geostationary satellite sounder to locate the clouds. It confirmed that the location of the cirrus is mostly south of the jet core (see fig. 6.4), but only where winds were accelerating. Of the all the cirrus detected by the GOES VAS system (« 30% of the VAS data), 23% of the cirrus were found south of the jet core and only 6% north of the core where winds were accelerating. Where winds were decelerating, the

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141

Figure 6.3. A schematic of the locations of cirrus in the synoptic ridge, trough, and jet pattern. (From Stone 1957: fig. 30.)

Figure 6.4. The locations of cirrus clouds in upper tropospheric wind patterns. The total of 49% is the fraction of the cirrus detected by GOES-VAS that were in 300mb winds >35m/s. Cirrus observations averaged 30% of the GOES-VAS data. (From Menzel et al. 1992: fig. 4.)

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Figure 6.5. Boundaries of the areas where cirrus were associated with radar echoes (solid line). (From Menzel et al. 1992: fig. 3.)

cirrus were evenly distributed north and south of the jet core, with 10% of it on each side of the jet core. The deceleration region is usually in the ridge of the Rossby wave (fig. 6.3). The jet core was defined as 300-mb winds >35m/s. Fortynine percent of the cirrus observations were in this category; the other 51% were in lighter winds. The comparison of cirrus to radar echoes by Menzel et al. (1992) noted that in summer, 52% of the cirrus were over or close to the radar echoes (see fig. 6.5). But in winter only 22% of the cirrus near radar echoes and the cirrus coverage was nearly the same as in the summer. The National Weather Service radar data used in this study showed only rain events, ignoring drizzle and lighter mist, because 1986 radar data used predated the more sensitive NEXRAD (Nextgeneration Radar) system. The rain events studied were presumed to be from cumulus convection. But the abundance of cirrus not associated with rain events led Menzel et al. (1992) to conclude that at least one-half of the cirrus over the continental United States resulted from middle and upper tropospheric dynamic motions other than convection.

6.4. Relationship to Numerical Model Fields Numerical models have climatological moisture and vertical motion fields that correspond to the locations of the cirrus shown in figure 6.1. An example of this relationship is shown in figure 6.6, where the latitudinal cross section of the ver-

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Figure 6.6. (Top) Boreal summer (June, July, and August) averaged vertical motion from the ECMWF model for 1980-87 from Schubert et al. (1990). (Bottom) Frequency of HIRS cloud observation of 500mb and higher from the NOAA HIRS satellite sensor, 1989-93 (Wylie and Menzel, 1994).

tical motion field from the ECMWF model (Schubert et al. 1990) is compared to a similar cross-section of high cloud frequency (above 500mb) from the Wylie and Menzel (1994) climatology. These two cross-sections came from different time periods; the ECMWF is from 1980-87, whereas the cloud climatology is from 1989-93. Nevertheless, a good correspondence can be seen between the latitudes of greater cloud frequencies and the vertical motion. The ITCZ has the highest average values of vertical motion and cloud frequency. The latitude of greatest sinking motion is the subtropical high pressure systems over oceans and deserts over land. They have the lowest cloud frequencies, as expected. Secondary maxima in rising motion and cloud frequency appear in higher latitude storm belts. Recently, the relative humidity fields from NOAA's National Center for Environmental Prediction (NCEP) were compared to the cirrus observations made from the HIRS (Wylie and Menzel 1999) for November 1-15, 1998. This is a

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global comparison using coincident HIRS and NCEP data. Relative humidity is analyzed every 50mb in height and every 12 h by NCEP. This is called the NCEP Final Analysis product. The relative humidity fields were examined in two ways for the differences between areas of high clouds and cloud-free areas (see table 6.1). The relative humidities with respect to liquid (RHiiquid) were used. In cloudfree areas, the RHiiquid at 300mb was used. Only cloud reports from 500mb to the top of the atmosphere were considered, and 300mb was the most common upper tropospheric cloud level. The results show huge differences between cloudy and clear areas. In the tropics and southern latitudes the differences were 19% (43-24) to 29% (48-19). A second comparison calculated a vertically averaged relative humidity called the upper tropospheric relative humidity (UTH) defined by Soden and Bretherton (1996). The UTH average is vertically weighted according to the height of temperature surfaces. Its original purpose was for comparing a water-sensitive satellite infrared channel at 6.7 urn to the upper level moisture in model fields. Most weight is usually given to the 300-400 mb levels, but the weighting function is designed to follow the vertical variance in the 6.7-um channel sensitivity with latitude and weather patterns. Eight days in November 1998 were used. The cloudy versus clear differences in UTH were 18% (table 6.1). The relative humidities and UTH were calculated for the liquid phase of water. Cirrus clouds are mostly composed of ice particles. Using the mean temperatures and pressures of these data the relative humidities with respect to ice (RHice) also are shown in table 6.1. UTH was calculated from NCEP Final Analysis profiles at the locations of the NOAA 11 HIRS data using the method described in Soden and Bretherton (1996). Cloud-level relative humidity also was taken from the NCEP analysis. In clear areas the 300-mb level relative humidity was used. The tropical RHwater of 46% equates to a 63% RHice (table 6.1), and the mid-latitude values of 59% and 63% RHwater are 83% and 85% RHice. The RHice values are higher than RH,iquid but still below saturation. 6.5. Concluding Remarks

Table 6.1 clearly shows that clouds occur where the relative humidities with respect to ice are below saturation in the model's fields. This problem occurs in Table 6. 1 . Upper tropospheric relative humidity (UTH) and NCEP relative humidity averages for cloudy and clear areas globally, November 1-15, 1998 %

Location 30-60°N 20°S-20°N (tropics) 30-60°S

No. of High HIRS observations Cloud

UTH (%)

'Cloud-Level

Clear

Cloud

Clear

RHwater (%) Cloud

Average temperature (K)

Average pressure (mb)

RHlce (%)

5088 8139

41 43

28 24

61 43

43 26

59 46

235.5 239.2

347 303

83 63

6066

48

19

64

45

63

239.8

390

85

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all global models because clouds form on scales of motion smaller than resolved in these models. Furthermore, the under-saturation problem (RHice = 63%) is largest in the tropics where cirrus frequencies are the highest. To NCEP's credit, its final analysis has recognizable differences between cloudy and clear regions averaging 13-29% in RH[iquid and 17-19% in UTH.This implies that numerical cirrus forecasts can be made even though saturation with respect to ice is not achieved over all of the model's grid cell. Cirrus clouds are one of the hardest cloud forms to numerically predict. The dynamics that produce them are weak and have only subtle differences from the dynamics that dissipate them. In the cold upper troposphere, cirrus particles can last for long periods of time (see chapter 17). Condensation also occurs where mixing ratios are very small. Getting these dynamics correct is a challenge for numerical models, but recent advances indicate it is a challenge that can be met. The use of numerical models for cirrus prediction is highly desirable because the use of weather patterns for subjective prediction is limited. The front and cyclone conceptual models of weather patterns were invented in the Norwegian and Austrian Schools of Meteorology for weather forecasting long before numerical models. They are still partially used today. However, conceptual models have a disadvantage because they assume weather patterns are similar. In reality, weather patterns have widely differing sizes, shapes, strengths, dimensions, and are affected by regional terrain and coast lines. These complications often cause weather forecasters to under- or over-forecast cloud cover. Finally, climate change can only be predicted if numerical models correctly predict the formation and dissipation of clouds. The radiation fields are vitally important to any prediction of climate, and clouds are the largest controlling factor of radiative heating/cooling in the atmosphere.

References Jin, Y., W.B. Rossow, and D.P. Wylie, 1996. Comparison of the climatologies of high-level clouds from HIRS and ISCCP. /. Climate, 9, 2850-2879. Liao, X., W.B. Rossow, and D. Rind, 1995a. Comparison between SAGE II and ISCCP high-level clouds, 1. Global and zonal mean cloud amounts. J. Geoph. Res., 100, 1121-1135. Liao, X., W.B. Rossow, and D. Rind, 1995b. Comparison between SAGE II and ISCCP high-level clouds, 2. Locating cloud tops. /. Geoph. Res., 100,1137-1147. Menzel, W.P., D.P. Wylie, and K.I. Strabala, 1992. Seasonal and diurnal changes in cirrus clouds as seen in four years of observations with the VAS. J. Appl. Meteor., 31,370-385. Randall, D.A., B. Albrecht, S. Cox, D. Johnson, P. Minnis, W. Rossow, and D. O'C. Starr, 1996. On FIRE at ten. Adv. Geophys., 38, 37-177. Schubert, S., C.-K. Park, W. Higgins, S. Moorth, and M. Suarez, 1990. An Atlas of ECMWF Analyses (1980-87): Part I—First momentum quantities. NASA Technical Memorandum 100747,258 pp. Stone, R.G., 1957. A compendium on cirrus and cirrus forecasting. Air Force Weather Service Technical Report, AWS TR 105-130. AWS. Soden, B.J., and P.P. Bretherton, 1994. Evaluation of water vapor distribution in general circulation models using satellite observations. J. Geophy. Res., 99, Dl, 1187-1210.

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Wang, PH., M.P. McCormick, P. Minnis, G.S. Kent, and K.M. Skeens, 1996. A 6-year climatology of cloud occurrence frequency from SAGE II observations (1985-1990). / Geophy. Res., 101,29407-29429. Warren, S.G., C.J. Hahn, J. London, R.M. Chervin, and R.L. Jenne, 1988. Global distribution of total cloud cover and cloud type amounts over oceans. NCAR/TN-317+STR. National Center for Atmospheric Research, Boulder, CO. Wylie, D.P, and P. Wang, 1997. Comparison of cloud frequency data from HIRS and SAGE II. J. Geophy. Res., 102, 29893-29900. Wylie, D.P, and W.P Menzel, 1999. Eight years of high cloud statistics using HIRS. /. Climate, 12,170-184. Wylie, D.P., W.P. Menzel, H.M. Woolf, and K.I. Strabala, 1994. Four years of global cirrus cloud statistics using HIRS. /. Climate, 7,1972-1986.

7

Satellite Remote Sensing of Cirrus

PATRICK M I N N I S

The determination of cirrus properties over large spatial and temporal scales will, in most instances, require the use of satellite data. Global coverage at resolutions as fine as several meters are attainable with instruments on Landsat, and temporal coverage at 1-min intervals is now available with the latest Geostationary Operational Environmental Satellite (GOES) imagers. Extracting information about cirrus clouds from these satellite data sets is often difficult because of variations in background, similarities to other cloud types, and the frequently semitransparent nature of cirrus clouds. From the surface, cirrus clouds are readily discerned by the human observer via the patterns of scattered visible radiation from the sun, moon, and stars. The relatively uniform background presented by the sky facilitates cloud detection and the familiar textures, structures, and apparent altitude of cirrus distinguish it from other cloud types. From satellites, cirrus can also be detected from scattered visible radiation, but the demands of accurate identification for different surface backgrounds over the entire diurnal cycle and quantification of the cirrus properties require the analysis of radiances scattered or emitted over a wide range of the electromagnetic spectrum. Many of these spectra and high-resolution satellite data can be used to understand certain aspects of cirrus clouds in particular situations. Intensive study of well-measured cases can yield a wealth of information about cirrus properties on fine scales (e.g., Minnis et al. 1990; Westphal et al. 1996). Production of a global climatology of cirrus clouds, however, requires compromises in spatial, temporal, and spectral coverage (e.g., Schiffer and Rossow 1983). This chapter summarizes both the state of the art and the potential for future passive remote sensing 147

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systems to aid the understanding of cirrus processes and to acquire sufficient statistics for constraining and refining weather and climate models. 7.1. Cirrus Properties

Theoretically, many different aspects of cirrus can be determined from passive sensing systems. A limited number of quantities are the focus of most efforts to describe cirrus clouds. These include the areal coverage, top and base altitude or pressure, thickness, top and base temperatures, optical depth, effective particle size and shape, vertical ice water path, and size, shape and spacing of the cloud cells. In many situations, accurate values for all of these parameters should be sufficient to describe a cirrus cloud and its potential to interact with the environment. Together, these quantities determine how much water must be frozen to form the cloud, the volume of space it occupies, and how it will affect the radiation fields. The normalized radiative properties of the cloud, its reflectance (or albedo), transmittance, and absorption, connect the optical properties with the radiative fluxes and intensities leaving the cloud in a given direction. As we learn more about cirrus and as models improve, however, more detailed properties such as the vertical and horizontal distributions of the ice crystals within the cloud may be required to meet future accuracy requirements. Ideally, each parameter should be evaluated at all times of day over all areas, but the spectral, temporal, and spatial sampling characteristics of current and future satellites are limited. Geostationary satellites view a given area at all hours of the day but are limited to a single viewing zenith angle and a portion of the Earth roughly covering 110° of latitude and longitude. Polar regions cannot be seen from these satellites. Sun-synchronous orbiters view a given area equatorward of the poles generally twice per day at the same times each day from different angles. Areas near the poles can be viewed up to 14 times per day. Precessing satellites can observe a given area at all times of day from a different angle during each overpass, but these satellites are often restricted in zonal coverage and require a relatively long time period (weeks to months) to cover the diurnal cycle. Thus, combinations of satellites in different types of orbits are needed to overcome the sampling deficiencies of any single satellite. The general approach for quantifying cirrus clouds consists of two stages: identification of the cloud and retrieval of its properties. Typically, the cloud is identified by comparing an observed radiance or set of radiances to the values expected for a cloudless scene. If the observed value is sufficiently different from the expected clear radiance, then the scene or imager pixel is designated as cloudy. Cloudy radiances are then compared with model-computed radiances to find the best matches in terms of the various cloud properties. The number of quantities that can be derived depends on the available channels and the independent information contained in them. For example, determination of cloud height requires spectra that are sensitive to cloud pressure or temperature or to some feature of the air mass above cloud such as the amount of Rayleigh scattering. Thus, remote sensing channels have been developed to take advantage of unique characteristics of the interaction of clouds with various spectra.

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7.2. Past and Current Techniques

Satellite remote sensing of cirrus began, in a fashion, around the beginning of the space age. Arking (1964) used an objective threshold technique to derive cloud coverage from 32-gray-level video images in the visible spectrum taken by the TIROS-VII (Television Infrared Observation Satellite) satellite. Although cirrus clouds were not explicitly identified, they were included in the derived cloud fraction. In an early effort to determine cirrus cloud properties, Conover (1965) used similar TIROS data to derive the albedos of selected cirrus clouds. Rasool (1964) made one of the earliest attempts to derive cloud heights and nighttime cloud amounts directly from TIROS-III data taken in the 8-12-jim infrared window. The limitations of using single-channel data for discriminating cirrus from other clouds were recognized early, resulting in the development of multispectral techniques to account for the semitransparency of many cirrus clouds and to derive their altitudes. Basically, cirrus retrieval methods have focused mostly on two distinct sets of infrared spectra. One, the CO2-slicing technique, uses closely spaced spectra in the CO2 absorption band near 15 (im to sound the atmosphere (Smith 1967; Chahine 1970). The other techniques primarily rely on thermal infrared measurements in the atmospheric windows between 8 and 12u,m and around 3.7 um with the addition of other channels, especially the visible channel (-0.65 urn), in particular situations. The CO2-slicing techniques also use one of the window channels. Images from the GOES-8 are used to illustrate the information content in these spectral bands. Figure 7.1 shows 4-km visible (0.65 um) and infrared window (10.8 um) images of the southeastern United States taken from the GOES-8 imager. A well-developed anticyclone has relatively thin cirrus clouds on its leading (eastern) edge over Virginia and North Carolina and also over central Alabama. Thicker cirrus caps most of the remaining storm area. The thin cirrus clouds have a relatively low visible reflectance (fig. 7.la), but appear bright (cold) in the infrared (fig. 7.1b). Thicker cirrus are bright in both channels. Low stratus over Oklahoma and stratocumulus off the coast are readily identified as bright or highly reflective in the visible image and relatively dark (warm) in the infrared. Except for the cirrus, skies are clear over the eastern United States. Snow is evident around the Great Lakes and over the northeastern United States. These types of images are most familiar as they are commonly used for presenting current weather conditions to the public. Less familiar are the sounding data. GOES-8 also has an 8-km sounder with 19 channels. Images from GOES-8 sounder channels 2, 3, 4, and 5 are shown in figure 7.2 for the same scene in figure 7.1. The CO2-slicing technique often uses the spectra in these channels, 14.4,14.0,13.7, and 13.4 um, respectively, with the 10.8-um data to derive cloud parameters. The images in figure 7.2 illustrate the information in these sounding channels. Channel 2 is sensitive only to the upper troposphere so that only the very highest clouds produce a signal in figure 7.2a. As the wavelength decreases, the radiance contains increasing information about the lower atmosphere and, eventually, the surface. The outline of the anticyclone is the primary feature in figure 7.2b (14.0um), in addition to a slight north-south

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GOES8 Ixnager Data March 8, 1999 (1545 UTC)

Figure 7.1. GOES-8 4-km imager views of the United States for 1545 UTC, March 8,199 (a) Visible channel, (b) 10.8-um channel

gray-scale or temperature gradient. The gradient becomes steeper in figure 7.2 (13.7 jim) with the appearance of some of the low clouds over the ocean. Th remaining low clouds become evident in figure 7.2d (13.4 urn). Thus, the sounde provides images that roughly correspond to some cumulative slice of the atmos phere at a particular pressure. The retrieval problem consists of convertin images like those in figures 7.1 and 7.2 to cloud properties

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Figure 7.2. GOES-8 8-km sounder views of the United States for 1545 UTC, March 8, 1999. (a) Channel 2,14.4 urn; (b) channel 3,14.0 urn; (c) channel 4,13.7 urn; (d) channel 5, 13.4 urn.

7.2.1. CO2-Slicing Method The quantities that can be determined with the CO2-slicing method are the cloudtop pressure, pc, and the cloud effective emissivity, Afe, where N refers to cloud fraction and e is the infrared emissivity. The quantity Ate is sometimes referred to as effective cloud fraction. It can be shown that the ratio of the cloud signals for two spectral bands at frequencies v± and v2 viewing the same scene is

where / is the radiance, the subscript clr refers to clear, T is the transmittance, ps is the surface pressure, and B[v, T(p)] is the Planck function for v at temperature T of pressure level p (Smith and Platt 1978). If the spectral bands are close together, the effective emittances are approximately the same. Thus, effective emittances cancel each other. The two observed radiances are given, and the clear radiances are computed as the average values for nearby clear pixels. Typically, a clear threshold is applied to the 10.8-um channel to determine which pixels are clear. The right side of equation 1 is computed using a temperature profile and a profile of atmospheric transmittance for each spectral band over a range of cloud pressures from the surface to the tropopause. The observed ratios are compared with those calculated from the models to find the best match yielding an estimate of cloud pressure for four different band ratios (14.4/14.0, 14.0/13.7, 14.0/13.4, and 13.7/13.4 or some similar combination).

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The effective emissivity is then computed for each spectral band ratio using the observed window channel radiance, the clear-sky window channel radiance, and the opaque cloud radiance based on the cloud pressure derived from equation 1 as

where the subscript w refers to the infrared window channel and B[vw, T(pc)] is the opaque cloud radiance. The final values of cloud pressure and effective emissivity are selected as those that best satisfy the radiative transfer equation for the four CO2 bands (Menzel et al. 1983). The cloud height and temperature can be determined from pc using the vertical profile of pressure and temperature for the scene. This technique can be applied to any satellite data that include a set of radiances at wavelengths similar to those used for the GOES-8 sounder. The CO2slicing method has been used to derive effective cloud amounts and pressures over a variety of temporal and spatial scales (e.g., Smith et al. 1974; Susskind et al. 1987;Wylie and Menzel 1989; Wylie et al. 1994) and is currently used to continuously monitor these cloud properties on an operational basis. This method was originally limited to sensors with relatively large fields of view (-50 km), so it was difficult to separate the cloud fraction of the pixel from the emissivity. As the size of the sounder field of view has decreased, the assumptions that the cloud fraction is unity and that the effective emissivity is the actual emissivity have become more viable (e.g., Wielicki and Parker 1992). This is especially true for the 1-km sounding channels on the moderate resolution imaging spectroradiometer (MODIS) on the Earth Observing System (EOS) satellites. Thus, CO2-slicing results from newer sounders will provide a better estimate of cloud fraction and emissivity than previously possible. For cirrus clouds, the cloud-top pressure can be determined to within 100 hPa or better depending on the thickness, density, and horizontal extent of the cloud. The technique, like many others, assumes that only a single layer of clouds is within a given pixel and is dependent on the meteorological profiles used in the retrievals. Thus, a field of view containing overlapped clouds or a mix of layers will yield a cloud pressure between the levels of the clouds in the scene. Errors in the sounding or in the clear-sky temperature will cause inaccuracies in the effective emissivities, especially for low clouds (e.g., Wielicki and Coakley 1981). Strong surface inversions and nearly isothermal atmospheres like those found in the polar regions can also introduce significant errors. Furthermore, this approach does not yield some of the cloud optical properties that can be determined using other methods. Nevertheless, the CO2-slicing technique remains especially valuable for determining the presence and height of cirrus clouds during all times of day in most atmospheric conditions.

7.2.2. Solar and Infrared-Window Techniques The other class of algorithms most commonly used for downlooking satellites uses an assortment of spectra that generally include the infrared window channel

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around 11 urn. The 11 -urn radiance is used to determine the cloud temperature Tc, while other channels provide information about the remaining properties. In a simple form that neglects attenuation by the atmosphere above the cirrus, the observed radiance at any wavelength, A,, is

where the subscript b refers the background radiance incident at cloud base, p^ is the reflectance of the cloud, S0 is the solar radiance, u,0 is the cosine of the solar zenith angle 00, and 6 is the viewing zenith angle. Wavelength is used here as the reference unit instead of frequency because solar channels are often used in these retrievals. If the solar component is negligible (X > 5.0 urn), equation 3 can be reduced, using the form of the observed equivalent blackbody temperature recorded by the sensor, as where B^ l is the inverse Planck function and T^\T is the clear-sky or background temperature. The effective infrared emissivity is

where D is the effective diameter of the ice crystals in the cloud, H is the crystal habit, and now TX represents the spectral optical depth. The effective emissivity includes both scattering and emission by the cloud and varies with the background and cloud temperatures (Minnis et al. 1998). The spectral optical depth is

where IWC is the ice water concentration, z is altitude, Az is the thickness of the cloud layer, and Cx.ext is the spectral extinction cross section of the crystals. Ice water path, the integral of IWC over the depth of the cloud, is useful for cloud process modeling because it defines how much water is frozen in a vertical column. Extinction optical depth is the sum of the absorption and scattering optical depths. The single-scattering albedo, which is the ratio of scattering to extinction, determines the relative amount of absorption and is proportional to the ice index of refraction. The scattering phase function determines the angular pattern of scattering. In general, the visible (0.65 um) optical depth, Tvis, is used as a reference, such that

where Q is the extinction efficiency. If the infrared component is negligible (A, < 3.5 um), then equation 3 reduces, after dividing by S0\i0, to

where p^ = PAC(TX> D, H, jj,0, 0, (|>), and <|) is the azimuth angle relative to the sun, and px/> = pxt(|Lio, 6, ())) and varies with location and surface type. For other

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wavelengths (3.5 < A, < 5.0 urn), both the solar and emitted components must be considered as in equations 4 and 7 to solve equation 3 for Tc. The cloud temperature is then used in conjunction with a sounding as in the CO2-slicing approach to estimate cloud height or pressure. Equations 3-7 imply that the cloud emissivity at one wavelength is related to those at other wavelengths. The key variable is cloud optical depth. Determination of the optical depth, explicitly or implicitly, from another channel allows an estimate of the window-channel emissivity. Empirical methods have been used to relate cloud solar reflectance either directly to emissivity (e.g., Shenk and Curran 1973; Reynolds and Vonder Haar 1977) or to visible optical depth and then to emissivity where the ratios of extinction efficiencies from equation 7 are -0.5 for A, = Hum (e.g.,Minnis et al. 1990; Spinhirne and Hart 1990).The empirical approaches have limited utility, however, because the dependencies on angles and crystal size and habit in equations 5 and 7 cannot be ascertained. To account for these other variables and establish a direct link to general circulation and cloud process models, ex and p^ are computed theoretically with a radiative transfer model (RTM) for a range of conditions. The results are matched to observations to obtain an optical depth and emissivity. Rossow et al. (1989) pioneered this technique by deriving Tvis from NOAA-5 scanning radiometer data using RTM results for a theoretical, plane-parallel cloud composed of liquid water droplets having an effective radius and variance of 10 urn and 0.15, respectively. The emissivity was computed simply as the absorption emissivity that neglects scattering and assumes an extinction ratio of 0.81 (Rossow and Lacis 1990). This method, with the extinction ratio changed to 0.50, served as the initial cloud retrieval technique for production of the International Satellite Cloud Climatology Project (ISCCP; Schiffer and Rossow 1983) "C" product, which comprises a 3-hourly, 280-km global data set of cloud amounts, heights, and optical depths. As the theoretical optical properties of realistically shaped crystals became available (e.g., Takano and Liou 1989), it was found that models based on spherically shaped particles for cirrus required larger optical depths compared to model clouds composed of randomly oriented hexagonal ice crystals (e.g., Minnis et al. 1993b). Thus, when used in retrievals, the cloud height is usually underestimated with a spherical-particle model compared to the hexagonal column model (Minnis et al. 1993a). Such results led to a reformulation of the ISCCP methodology to include optical depths for clouds with Tc < 260 K based on calculations with a polyhedral crystal model (Macke 1993). This new approach was used to derive the ISCCP "D" product (Rossow and Schiffer 1999). The hexagonal column model is used in a high-temporal resolution analysis of clouds for the Atmospheric Radiation Measurement (ARM) program (Minnis et al. 1995b). High cloud amounts (pc < 440 hPa) determined with the ISCCP C method applied to NOAA-11 advanced very high resolution radiometer (AVHRR) data for April 1990 were compared to coincident results from an analysis of highresolution infrared radiometer sounder (HIRS) data with the CO2-slicing method (Jin et al. 1996). These results are shown in figure 7.3 with the monthly mean daytime global high cloudiness from the ISCCP D product and the monthly mean high cloud coverage from March, April, and May 1971-81 (Warren et al. 1986,

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Figure 7.3. Comparison of satellite-derived, zonal mean high cloud amounts for April 1990 and surface-observed (SFC) mean high cloudiness for boreal spring 1971-81. HIRS and ISCCP-C values are adapted from Jin et al. (1996). ISCCP-D values are derived from ISCCP daytime D2 product. SFC data are ocean-land-weighted means of cirrus and cumulonimbus from Warren et al. (1986,1988).

1988). The surface-derived high cloud coverage is the sum of all cirrus types and cumulonimbus. All of the results show similar patterns but different magnitudes. The HIRS high cloud amounts are greater than almost all of the ISCCP and surface means, especially in the tropics. The ISCCP D averages exceed their C counterparts everywhere except in mid-latitudes. While some of the differences are due to sampling discrepancies; most of the difference in the tropics and subtropics arises due to the change from a 10-urn-radius spherical particle to the 30-um polyhedral crystal that raised the altitude of many cirrus clouds. Although some attempt was made to account for cloud overlap in the surface compilations, the satellite cirrus coverage always exceeds that from the surface observations. Jin et al. (1996) discuss the reasons for the ISCCP and HIRS differences. Because cirrus particles can take a wide variety of shapes and sizes, no single particle shape or set of optical properties will always produce an accurate optical depth retrieval (e.g., Spinhirne et al. 1996). If a shape is assumed, it is possible to derive the particle size and phase using a combination of visible and 11-um radiances with those measured at a mildly absorbing wavelength. The most commonly used wavelengths are those near 1.6,2.1,3.7-4.0,8.4, and 12 urn. While the theory and many of the methods for deriving particle size have been presented in some detail (Minnis et al. 1995a), a brief review is appropriate. During daytime, the solar radiance reflected by the clouds increases the apparent brightness temperature in the solar-infrared window more than that reflected by the surface. This difference typically distinguishes clouds from the surface, as illustrated in figure 7.4a, which shows the differences in temperature between the GOES-8 3.9 and 10.8-um channels. Because both channels are atmospheric windows, the brightness temperatures should be very close in the absence of solar reflectance and clouds. For a given optical depth, the magnitude of the 3.9-um

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Figure 7.4. Brightness temperature differences from GOES-8 4-km imager for 1545 UTC March 8, 1999. (a) Channel 2 (3.9um)-channel 4 (10.8um), range from black to white is -1-50K. (b) Channel 4 (10.8u,m)-channel 5 (12.0pm), range from black to white is 0—5 K.

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reflectance increases with decreasing particle size and is generally greater for liquid than for ice clouds (e.g., Minnis et al. 1998). Hence, because it has relatively large ice crystals, the snow evident in figure 7.la reflects minimal 3.9-um radiation and disappears in figure 7.4a.The ice and liquid water indices of refraction vary between 8 and 12 urn, so cloud emissivity differs with wavelength, resulting in brightness temperature differences across the infrared window for optically thin clouds. This effect is most evident in the thin cirrus clouds over the eastern United States in figure 7.4b. The driest clear areas over land and the optically thickest clouds have 11-12-um brightness temperature differences near zero. This temperature difference depends on tvis, Tc, and Ts as well as on phase and particle size and shape (e.g., Parol et al. 1991; Takano et al. 1992). It increases both with decreasing particle size (e.g., Minnis et al. 1998; Prabhakara et al. 1988) and with increasing temperature contrast, as illustrated in figure 7.5. To take advantage of these characteristics, Arking and Childs (1985) introduced a three-channel technique that used a combination of 0.73,3.7, and 11-um data with models that assumed a spherical particle shape and a constant cloud temperature for an ensemble of pixels. The methodology of Han et al. (1994) for retrieving liquid-water-cloud droplet sizes has been adapted to derive cirrus particle size using a hexagonal ice column model to interpret 0.65,0.87,3.7,10.8, and 12(jm radiances (e.g., Minnis et al. 1995a; Rao et al. 1995; Giraud et al. 1997). Some large data sets have been analyzed to produce the first climatologies of cirrus particle size and optical depth (e.g., Han et al. 1996; Minnis et al. 1997a) for daytime. Figure 7.6 shows the mean fractional coverage, Tc, and D for ice clouds during April 1987 derived by Minnis et al. (1997b). Overall, the zonal patterns in coverage are similar to those in figure 7.3 with a maximum slightly north of the equator, but the amounts are slightly less than found in the ISCCP C product. The use of an objective phase determination without consideration of the visible-infrared retrieval resulted in an underestimate of the cirrus coverage. Both ice cloud temperatures and particle sizes are at a minimum in the tropics. Particle size shows no dependence on surface type. The mean value of D, about 60 jim, is based on the hexagonal column model and is similar to that found by Han et al. (1996).

Figure 7.5. Brightness temperature differences between radiances at 10.8 and 12.6 um computed for cirrus clouds at 240 (thick lines) and 264 K (thin lines) with surface temperatures of 300 and 292 K, respectively, in a tropical atmosphere with 9 = 0°. The dotted, small dash, large dash, and solid lines correspond to effective radii of 3, 6,12, and 24}im, respectively. Adapted from Prabhakara et al. (1988).

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Figure 7.6. Ice cloud properties derived from NOAA-9 AVHRR data by Minnis et al. (1997) for April 1987 using every fifth day of data.

The techniques relying on the visible channel are limited to daytime and are unreliable over the poles. Techniques that are useful for all times of day are multispectral infrared methods that are applicable only to semitransparent cirrus. Inoue (1985) recognized the value of the 11-12-um temperature difference n_12) and developed a method to derive cirrus cloud temperature and emissivity based on an assumed relationship between the 11- and 12-um cirrus emissivity from NOAA-7 AVHRR data. Prabhakara et al. (1988) used spectral differences between 10.8- and 12.6-(im temperatures measured over oceans by the infrared interferometer spectrometer (IRIS) on Nimbus 4 to derive a thin cirrus index that shows a primary maximum over the tropical western Pacific and

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eastern Indian Ocean. Ou et al. (1993) developed an approach similar to that of Inoue (1985), but using 10.8- and 3.7-um data simultaneously, to derive Tc, T, and D at night. Lin and Coakley (1993) examined the use of 3.7,10.8, and 12.0-um AVHRR data together in regional aggregates of pixels to define a common value for Tc and D using spherical ice particles. The optical depth of each pixel can then be determined from the observed temperatures. Strabala et al. (1994) developed a trispectral threshold method to classify scenes in 11,12, and 8.4-um images as clear, thin water or ice cloud, mixed phase, and thick water or ice clouds. This approach has the potential for deriving microphysical properties also. W.L. Smith, Jr. et al. (1997) used the 3.9-, 10.8-, and 12.0-um GOES-8 channels to simultaneously derive Tc, D, and T for each pixel using GOES-8 data. Lidar data were used to verify that the technique produced accurate values of Tc for optically thin clouds. 7.2.3. Transmission Techniques Most remote sensing of cirrus from satellites uses reflected and emitted radiation. An entirely different approach to deriving cirrus properties involves the use of solar radiation transmitted through the Earth's limb such as the Stratospheric Aerosol and Gas Experiment (SAGE). Solar occultation sensors that view the sun's disk through the atmosphere as the satellite passes from night to day or vice versa measure the attenuation of solar radiance by the atmospheric components in the intervening air mass. Although most often used for aerosol or gas concentration monitoring, solar occultation has also been used to monitor clouds on a large scale using both shortwave (Wang et al. 1995 a) and infrared window spectra (e.g., Rinsland et al. 1998). These approaches are extremely limited in temporal and spatial coverage because of the sunrise or sunset and the direct view to the sun requirements, respectively. Thus, a long time period must be sampled for meaningful statistics. Occultation measurements are very sensitive to any cloudiness in the path (-250km), however, and can easily detect "invisible" or subvisual cirrus clouds near the tropopause that are not detected with the other techniques (Wang et al. 1996). Some information about the effective sizes of the particles in these clouds can also be determined using the relative extinction in the two wavelengths (Wang et al. 1995b) used by SAGE. Cloud layering and thickness data can also be derived for each occultation by measuring extinction at various points as the sensor field of view crosses the sun's disk (Wang et al. 1998). The SAGE analyses yield a much greater frequency of cirrus occurrence than CO2-slicing primarily because it is more sensitive to the very thin cirrus and has a larger field of view (Wylie and Wang 1997). A more complete discussion of the cirrus climatologies is found in chapter 9. 7.2.4. Additional Limitations and Validation One of the biggest limitations to current techniques is the frequent occurrence of multilevel clouds. Several methods have been developed, but none is sufficiently mature for general application. Baum et al. (1994) used HIRS CO2-slicing to determine the altitude of the upper-level cirrus and then used multispectral

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infrared data to derive the cloud properties. This approach may eventually be applied to the upcoming MODIS instrument on the EOS satellites and could improve nighttime retrievals significantly. It is somewhat similar to the method of Jin and Rossow (1997). Ou et al. (1996) developed a multispectral approach to determine which pixels contain multilayered clouds and then applied a retrieval method (Ou et al. 1993,1998) to derive the properties of the thin cirrus above the thick, low-level cloud. Another approach that is applicable only over oceans uses a combination of microwave soundings for liquid-water cloud temperature and liquid water path, infrared radiance for the upper-level cloud temperature, and visible reflectance for the combined cloud optical depth (Lin et al. 1998). This methodology can be used even when the cirrus cloud is optically thick, but it does not apply to precipitating clouds. Although the multispectral infrared methods can retrieve cirrus heights much better than single-channel methods, they are extremely sensitive to the temperature and water vapor profiles (Liou et al. 1990) and require accurate surface emissivity data (Strabala et al. 1994; W.L. Smith, Jr. et al. 1997). None of these algorithms has been used for global retrievals of cirrus height, optical depth, and particle size at night. Even if these methods can be applied operationally, they cannot be used to derive the cloud microphysics at night for thick clouds because the brightness temperatures differences become very small. Current phase-detection methods often rely on characteristics that overlap for particular ranges of ice (small) and water (large) particle sizes. Also, mixed-phase clouds are not uniquely detectable with any recent technology. Cloud base and thickness are currently only estimated with a few crude techniques (e.g., W.L. Smith, Jr. et al. 1993). These properties are important for weather and aviation as well as for the atmospheric and surface radiation budgets. No methods have yet been rigorously developed to determine ice crystal habit. None of the current algorithms using emitted and reflected radiation is sensitive to subvisual clouds. Current model-based retrievals rely on plane-parallel cloud models, but cirrus clouds are often horizontally and vertically inhomogeneous. The impact of using such models is unknown. New techniques, models, and measurements are needed to address all of these parameters. Validating all of the cirrus properties derived from satellite data is a challenging task. Cloud height and boundaries are most accurately measured with radar or lidar and can serve to verify the same quantities retrieved by the satellites (e.g., Minnis et al. 1993a). When combined with other instruments, radars can be used to derive cloud ice water path, particle size, and optical depth for comparison with satellite results (e.g., Mace et al. 1998). Sun photometers can be used to determine thin cloud optical depths that can be used for retrieval validation. In situ measurements are required to verify the derived cloud particle sizes and shapes (e.g., Ou et al. 1998; Young et al. 1998). These are more costly and present special logistical problems of scale differences between aircraft flight paths and satellite pixels. Nevertheless, in situ data are critical for knowing exactly what is in the cloud. Multiangle views are also useful for validating cloud optical depth and particle size retrievals (e.g., Minnis et al. 1993a). The retrieved values should be consistent independent of the viewing conditions. Other methods that compare cloud amounts to visual observations

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and other retrievals are also important components of the evaluation of cirrus remote sensing. 7.3. Future Methods

A substantial number of new satellites and remote sensing instrumentation are either in space or planned for launch before 2005. This new technology offers some hope for addressing shortcomings of the current systems. Sensors on new research satellites include the visible infrared scanner (VIRS) on the Tropical Rainfall Measuring Mission satellite, the polarisation and directionality of the Earth's reflectances (POLDER) scanner on ADEOS-1, and the along track scanning radiometer (ATSR) on ERS-2. The Clouds and the Earth's Radiant Energy System (CERES) project is using the VIRS 0.65,1.6, 3.7,10.8, and 12urn data to derive all of the cirrus properties except for cirrus in multilevel cases (Minnis et al. 1995a, 1999). Figure 7.7 shows a set of images taken over the southwestern United States from the VIRS 0.65, 10.8, and 1.6-um channels. Snow over the Rocky Mountains and Sierra Nevada is bright in both the visible and infrared imagery, but almost black in the 1.6-um image. Clear land areas, however, are the brightest features in figure 7.7c. The clouds, especially cirrus, are darker than the land, but not the snow. When used together with the 3.7-um data, the 1.6 reflectances will substantially aid the determination of cloud phase. The 1.6-um channel is being used in the VIRS retrievals in a manner similar to that proposed by Masuda and Takashima (1990) for the new AVHRR on the NOAA-15. Baran et al. (1997) used the 0.87- and 1.6-um channels on the ATSR-2 and its multiangle views to discern cloud particle size and to estimate particle shape. The multispectral, multiview data taken by POLDER are being intensively studied for improving cloud retrievals. Goloub et al. (1999) have developed a technique to determine phase from multiangle polarized measurements at 0.87 um. Chepfer et al. (1999, 2000) used POLDER multiview polarized reflectances to discern cloud phase and ice crystal shape and orientation. The wide range of MODIS channels will also enhance the application of older algorithms because of improved spatial resolution. The CO2-slicing technique can be applied to 1-km data simultaneously with other imager data. Thin cirrus clouds will be detected more easily during the daytime with the 1.38-um channel (e.g., Gao et al. 1993). Other spectra have been considered for cirrus retrievals but have not yet been measured with spaceborne instruments, although prototypes for such instrumentation have been developed. Cloud-top height estimates may be improved with oxygen-A absorption band radiances (e.g., Fischer and Grassl 1991). Selected spectra in the microwave (Evans and Stephens 1995) and in the submillimeter (Evans et al. 1998) ranges show considerable promise for better 24-h measurements of water path and large particle sizes in ice clouds. These spectra are also insensitive to liquid water so that the signal from the cirrus clouds can be isolated. Infrared interferometers may also yield new insight into cirrus microphysics (Smith et al. 1993). The interferometer spectra in figure 7.8 from the high resolution interferometer spectrometer (HIS) on the NASA ER-2 aircraft (Smith et al. 1998) reveal interesting features in the observed scenes. In the

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Figure 7.7. VIRS imagery over the southwestern United States, 1630 UTC, January 5,1998. (a) 0.65urn, (b) 10.8um, (c) 1.6 um.

window region between 800 and 1000 cnT1, the brightness temperatures decrease with decreasing wave number for the clear scene because of water vapor attenuation near 12.5 Jim (800cm"1). In contrast to the other clouds, the small-particle cirrus show a substantial decrease in temperature with decreasing wave number. These cirrus are very thin optically yet have noticeable effects on the spectra. Thus, both particle size and subvisual cirrus detection may be accomplished with interferometer data. The interferometer also has the advantage of simultaneously sounding of water vapor, CO2, clouds, and trace gases. Scanning and spacequalified versions of HIS are under development. Such instruments would add valuable information for extracting cirrus properties from satellites.

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Figure 7.8. Infrared spectra from the HIS taken during April 21,1996 between 2031 and 2256 UTC from the NASA ER-2 over the western United States. (Courtesy of D.E. DeSlover, University of Wisconsin).

Future monitoring systems will carry a wide array of instruments that can be used synergistically to provide a more complete quantification of cirrus clouds for climate and weather model verification and, possibly, initialization. Interpreting the vast quantities of new data, however, remains one of the greatest challenges for cirrus remote sensing.

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Masuda, K., andT.Takashima, 1990. Deriving cirrus information using the visible and nearIR channels of the future NOAA-AVHRR radiometer. Remote Sens. Environ., 31, 65-81. Menzel, W.P., W.L. Smith, and T.R. Stewart, 1983. Improved cloud motion wind vector and altitude assignment using VAS. / Appl. Meteor., 22, 377-384. Minnis, P., D.P. Garber, D.F. Young, R.F. Arduini, and Y. Takano, 1998. Parameterization of reflectance and effective emittance for satellite remote sensing of cloud properties. J. Atmos. ScL, 55,3313-3339. Minnis, P., P.W. Heck, and D.F. Young, 1993a. Inference of cirrus cloud properties from satellite-observed visible and infrared radiances. Part II: Verification of theoretical radiative properties. /. Atmos. Sci., 50,1305-1322. Minnis, P., P.W. Heck, S. Mayor, and D.F. Young, 1997a. A near-global analysis of cloud microphysical properties. In IRS '96: Current Problems in Atmospheric Radiation (W.L. Smith and K. Stamnes, eds.). Deepak Publishing, Hampton, VA, pp. 445448. Minnis, P., K.-N. Liou, and Y. Takano, 1993b. Inference of cirrus cloud properties from satellite-observed visible and infrared radiances. Part I: Parameterization of radiance fields. / Atmos. ScL, 50,11279-11304. Minnis, P., D.P. Kratz, J.A. Coakley, Jr., M.D. King, R. Arduini, D.P. Garber, P.W. Heck, S. Mayor, W.L. Smith, Jr., and D.F. Young, 1995a. Cloud optical property retrieval (Subsystem 4.3). In Clouds and the Earth's Radiant Energy System (CERES) Algorithm Theoretical Basis Document, vol. Ill: Cloud Analyses and Radiance Inversions (Subsystem 4), NASA RP 1376 (CERES Science Team, ed.). National Aeronautics and Space Administration, Hampton, VA, pp. 135-176. Minnis, P., W.L. Smith, Jr., D.P. Garber, J.K. Ayers, and D.R. Doelling, 1995b. Cloud properties derived from GOES-7 for the Spring 1994 ARM Intensive Observing Period using version 1.0.0 of the ARM satellite data analysis program. NASA RP 1366. NASA, Hampton, VA. Minnis, P., D.F. Young, B.A. Baum, P.W. Heck, and S. Mayor, 1997b. A near-global analysis of cloud microphysical properties using multispectral AVHRR data. In Proceedings oftheAMS 9th Conference on Atmospheric Radiation, Long Beach, CA, February 2-7, American Meterological Society, Boston, MA, pp. 443-446. Minnis, P., D.F. Young, K. Sassen, J.M. Alvarez, and C.J. Grund, 1990. The 27-28 October 1986 FIRE IFO case study: cirrus parameter relationships derived from satellite and lidar data. Mon. Wea. Rev., 118, 2402-2425. Minnis, P., D.F. Young, B.A. Wielicki, P.W. Heck, S. Sun-Mack, and T. Murray, 1999. Cloud properties derived from VIRS for CERES. In Proceedings oftheAMS 10th Conference on Atmospheric Radiation, Madison, WI, June 28-July 2, American Meteorological Society, Boston, MA. pp. 21-24. Ou, S.C., K. Liou, and B.A. Baum, 1996. Detection of multilayer cloud systems using AVHRR data: Verification based on FIRE II IFO composite measurements. J. Appl. Meteor., 35,178-191. Ou, S.C., K. Liou, and T.R. Caudill, 1998. Remote sounding of multilayer cirrus cloud systems using AVHRR data collected furing FIRE-II-IFO. J. Appl. Meteor., 37, 241-254. Ou, S.C., K. Liou, WM. Gooch, and Y. Takano, 1993. Remote sensing of cirrus cloud properties using Advanced Very-High Resolution Radiometer 3.7 and 10.9-um channels. Appl. Opt., 32,2171-2180. Parol, F, J.C. Buriez, G. Brognies, and Y. Fouquart, 1991. Information content of AVHRR channels 4 and 5 with respect to particle size. /. Appl. Meteor., 30, 973-984.

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Prabhakara, C, R.S. Fraser, G. Dalu, M.-L. Wu, and RJ. Curran, 1988. Thin cirrus cloudsseasonal distribution over oceans deduced from Nimus-4 IRIS. /. Appl. Meteor., 27, 379-399. Rao, N.X., S.C. Ou, and K.-N. Liou, 1995. Removal of solar component in AVHRR 3.7um radiances for the retrieval of cirrus cloud parameters. /. Appl. Meteor., 34,482^99. Rasool, S.I., 1964. Cloud heights and nighttime cloud cover from TIROS radiation data. J.Atmos.ScL, 21,152-156. Reynolds, D.W., and T.H. Vonder Haar, 1977. A bispectral method for cloud parameter determination. Mon. Wea. Rev., 105,446-457. Rinsland, C.P., M.R. Gunson, P. Wang, P., R.F. Arduini, B.A. Baum, P. Minnis, A. Goldman, M.C. Abrams, R. Zander, L. Mahieu, R.J. Salawitch, H.A. Michelsen, F.W. Irion, and M.J. Newchurch, 1998. ATMOS/ATLAS 3 infrared profile measurements of clouds in the tropical upper troposphere: cirrus microphysical properties and trace gas enhancements from rapid, deep convective transport. /. Quant. Spectres. Rad. Trans., 60, 891-901. Rossow, W.B., L.C. Garder, and A.A. Lacis, 1989. Global, seasonal cloud variations from satellite radiance measurements. II—Sensitivity of analysis. /. Climate, 2,419-458. Rossow, W.B., and A.A. Lacis, 1990. Global, seasonal cloud variations from satellite radiance measurements. II—Cloud properties and radiative effects. J. Climate, 3, 1204-1253. Rossow, W.B., and R.A. Schiffer, 1999. Advances in understanding clouds from ISCCP. Bull. Amer. Meteorol. Soc., 80,2261-2287. Schiffer, R.A., and W.B. Rossow, 1983. The International Satellite Cloud Climatology Program (ISCCP): The first project of the World Climate research Programme. Bull. Am. Meteor ol Soc., 64, 779-784. Shenk, WE., and R.J. Curran, 1973. A multispectral method for estimating cirrus cloud top heights. /. Appl. Meteor., 11,1213-1216. Smith, W.L., 1967. An iterative method for deducing tropospheric temperature and moisture profiles from satellite radiation measurements. Mon. Wea. Rev., 95, 17961802. Smith, W.L., S. Ackerman, H. Revercomb, H. Huang, D.H. DeSlover, W. Feltz, L. Gumley, and A. Collard, 1998. Infrared spectral absorption of nearly invisible cirrus clouds. Geophys. Res. Lett., 25,1136-1140. Smith, W.L., X.L. Ma, S.A. Ackerman, H.E. Revercomb, and R.O. Knuteson, 1993. Remote sensing cloud properties from high spectral resolution infrared observations. J. Atmos. ScL,50,1708-1720. Smith, W.L., and C.M.R. Platt, 1978. Intercomparison of radiosonde, ground-based laser, and satellite deduced cloud heights. /. Appl. Meteor., 17,1796-1802. Smith, W.L., H.M. Woolf, P.G.Abel, CM. Hayden, M. Chalfant, and N. Grody, 1974. Nimbus 5 sounder data processing system. Part I: Measurement characteristics and data reduction procedures. NOAA Tech. Memo. NESS 57. National Oceanic and Atmospheric Administration, Washington, DC. Smith, W.L., Jr.,P. Minnis, J.M.Alvarez,T.Uttal,J.M.Intrieri,T.P. Ackerman, and E.E.Clothiaux, 1993. Development of methods for inferring cloud thickness and cloud-base height from satellite radiance data. In The FIRE Cirrus Science Results 1993, NASA CP-3238. National Aeronautics and Space Administration, Hampton, VA, pp. 32-35. Smith, W.L., Jr., L. Nguyen, D.P. Garber, D.F. Young, P. Minnis, and J. Spinhirne, 1997. Comparison of cloud heights derived from satellite and ARM surface lidar data. Proc. 6th Ann. ARM Science Team Mtg., San Antonio, TX, Mar. 4-7,1996, 287-291. Spinhirne, J.D., and WD. Hart, 1990. Cirrus structure and radiative properties from airborne lidar and spectral radiometer measurements. Mon. Wea. Rev., 118,2329-2343.

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Spinhirne, J.D., W.D. Hart, and D.L. Hlavka, 1996. Cirrus infrared parameters and shortwave reflectance relations from observations. /. Atmos. ScL, 53,1438-1458. Strabala, K.I., S.A. Ackerman, and W.P. Menzel, 1994. Cloud properties inferred from 8-12 micron data. /. Appl. Meteor., 33,212-229. Susskind, J., D. Reuter, and M.T. Chahine, 1987. Cloud fields retrieved from analysis of HIRS/MSU sounding data./ Geophys. Res., 92,4035-4050. Takano, Y., and K.-N. Liou, 1989. Radiative transfer in cirrus clouds: I. Single scattering and optical properties of oriented hexagonal ice crystals. /. Atmos. ScL, 46,3-19. Takano, Y., K.-N. Liou, and P. Minnis, 1992. The effects of small ice crystals on cirrus infrared radiative properties. /. Atmos. ScL, 49,1487-1493. Wang, P.-H., M.P. McCormick, P. Minnis, G.S. Kent, O.K. Yue, and K.M. Skeens, 1995a. A method for estimating the vertical frequency of the SAGE II opaque cloud frequency. Geophys. Res. Lett., 22, 243-246. Wang, P.-H., P. Minnis, and G.K. Yue, 1995b. Extinction (1-um) properties of high-altitude clouds from solar occultation measurements (1985-1990): Evidence of volcanic aerosol effect. /. Geophys. Res., 100, 3181-3199. Wang, P.-H., P. Minnis, M.P. McCormick, G.S. Kent, and K.M. Skeens, 1996. A 6-year climatology of cloud occurrence frequency from SAGE II observations (1985-1990). J. Geophys. Res., 101,29407-29429. Wang, P.-H., P. Minnis, M.P. McCormick, G.S. Kent, G.K. Yue, D.F. Young, and K.M. Skeens, 1998. A study of the vertical structure of tropical (20°S-20°N) optically thin clouds from SAGE II observations. Atmos. Res., 47-48,599-614. Warren, S.G., CJ. Hahn, J. London, R.M. Chervin, and R.L. Jenne, 1986. Global distribution of total cloud cover and cloud type amounts over land. NCAR/TN-273+STR. National Center for Atmospheric Research, Boulder, CO. Warren, S.G., CJ. Hahn, J. London, R.M. Chervin, and R.L. Jenne, 1988. Global distribution of total cloud cover and cloud type amounts over ocean. NCAR/TN-317+STR. National Center for Atmospheric Research, Boulder, CO. Westphal, D.L., S. Kinne, J.M. Alvarez, S.G. Benjamin, W.L. Eberhard, AJ. Heymsfield, R.A. Kropfli, G.G. Mace, S.Y. Matrosov, S.H. Melfi, P. Minnis, P. Pilewskie, J.B. Snider, B.J. Soden, D.O'C. Starr, T. Uttal, and D.F. Young, 1996. Initialization and validation of a simulation of cirrus using FIRE-II data. J. Atmos. Sci., 53, 3397-3429. Wielicki, B.A., and J.A. Coakley, 1981. Cloud retrieval using infrared sounder data: Error analysis. /. Appl. Meteor., 20,157-169. Wielicki, B.A., and L. Parker, 1992. On the determination of cloud cover from satellite sensors: The effect of spatial resolution. /. Geophys. Res., 97,12799-12823. Wylie, D.P., and W.P. Menzel, 1989. Two years of cloud cover statistics using VAS. /. dim. Appl. Meteor., 2, 380-392. Wylie, D.P., W.P. Menzel, H.M. Woolf, and K.I. Strabala, 1994. Four years of global cirrus statistics using HIRS. /. Climate, 7,1972-1986. Wylie, D.P., and P.-H. Wang, 1997. Comparison of cloud frequency data from thje highresolution radiometer sounder and the Stratospheric Aerosol and Gas Experiment II. /. Geophys. Res., 102, 29893-29900. Young, D.F., P. Minnis, D. Baumgardner, and H. Gerber, 1998. Comparison of in situ and satellite-derived cloud properties during SUCCESS. Geophys. Res. Lett., 25, 1125-1128.

8

Ground-Based Remote Sensing of Cirrus Clouds

K E N N E T H SASSEN G E R A L D G. MACE

8.1. Researching Cirrus in the Modern Era

Cirrus clouds have only recently been recognized as having a significant influence on weather and climate through their impact on the radiative energy budget of the atmosphere. In addition, the unique difficulties presented by the study of cirrus put them on the "back burner" of atmospheric research for much of the twentieth century. Foremost, because they inhabit the frigid upper troposphere, their inaccessibility has hampered intensive research. Other factors have included a lack of in situ instrumentation to effectively sample the clouds and environment, and basic uncertainties in the underlying physics of ice cloud formation, growth, and maintenance. Cloud systems that produced precipitation, severe weather, or hazards to aviation were deemed more worthy of research support until the mid1980s. Beginning at this time, however, major field research programs such as the First ISCCP (International Satellite Cloud Climatology Program) Regional Experiment (FIRE; Cox et al. 1987), International Cirrus Experiment (ICE; Raschke et al. 1990), Experimental Cloud Lidar Pilot Study (ECLIPS; Platt et al. 1994), and the Atmospheric Radiation Measurement (ARM) Program (Stokes and Schwartz 1994) have concentrated on cirrus cloud research, relying heavily on ground-based remote sensing observations combined with research aircraft. What has caused this change in research emphasis is an appreciation for the potentially significant role that cirrus play in maintaining the radiation balance of the earth-atmosphere system (Liou 1986). As climate change issues were treated more seriously, it was recognized that the effects, or feedbacks, of extensive high-level ice clouds in response to global warming could be pivotal. 168

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This fortunately came at a time when new generations of meteorological instrumentation were becoming available. Beginning in the early 1970s, major advancements were made in the fields of numerical cloud modeling and cloud measurements using aircraft probes, satellite multispectral imaging, and remote sensing with lidar, short-wavelength radar, and radiometers, all greatly facilitating cirrus research. Each of these experimental approaches have their advantages and drawbacks, and it should also be noted that a successful cloud modeling effort relies on field data for establishing boundary conditions and providing case studies for validation. Although the technologies created for in situ aircraft measurements can clearly provide unique knowledge of cirrus cloud thermodynamic and microphysical properties (Dowling and Radke 1990), available probes may suffer from limitations in their response to the wide range of cirrus particles and actually sample a rather small volume of cloud during any mission. Nonetheless, such data provide the foundation for achieving a broad understanding of cirrus cloud microphysical content, as well as creating a snapshot of cloud conditions for model and remote sensor algorithm testing. However, as a consequence of the great expense of sampling cirrus with jet aircraft, such studies will be of limited application, devoted mainly to major field campaigns. At the other extreme, earth-orbiting satellite observations with their expansive view hold great promise for characterizing the global coverage of cirrus clouds. Unfortunately, cirrus are notoriously difficult to identify and characterize from satellites due to their quintessential property: by definition they are optically thin in both the visible and infrared (chapter 2), so it can be difficult with current methods to distinguish them from underlying clouds or terrain. The topic for this chapter is limited to the knowledge that can be gained from ground-based (or airborne) active remote sensors, which are often combined with radiometers to help resolve unknowns and limit uncertainties in derived data products. It is increasingly being recognized, as in the basic design of the ARM Cloud and Radiation Testbed (CART) sites (Stokes and Schwartz 1994), that combined active/passive cloud observations can produce strongly synergistic results. The basic advantages of active remote sensing are the relatively small expense involved in obtaining extended observations, the inherent ability to obtain accurate range-resolved data, and the application of a number of powerful techniques such as depolarization, Doppler, and quantitative data approaches that can be applied to derive important cloud variables. Passive remote sensors add important height-integrated cloud properties at even less effort and expense. Since the first FIRE Intensive Field Observations (IFO I) experiment in 1986, it has been recognized that lidar and radar are indispensable for monitoring the macrophysical and some microphysical properties of cirrus clouds (Sassen et al. 1990). Modern radar systems use advanced short-wavelength (0.3-1.Ocm) technologies to enhance the detection of the relatively diffuse cirrus ice clouds in the upper troposphere. This selection of radar wavelengths follows from fundamental Rayleigh scattering laws, which dictate that particle scattering follows the wavelength A-"4 rule, such that millimeter waves are best suited for detecting the relatively small cirrus crystals. The radar wavelengths are generally selected

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by the location of microwave transmission windows for water vapor and molecular oxygen in the K-band (7.5-11.1 mm) and W-band (2.5-3.7mm). Lidars are ideally suited to research cirrus because of the great sensitivity of light scattering to the presence of aerosols and hydrometeors and the variety of optical techniques that can be applied (Platt 1979; Carswell 1981; Grund and Eloranta 1990; Sassen 1991; Eberhard 1992; Platt et al. 1994). Lidar measurements of cirrus cloud height boundaries can be made to meter-height accuracy in the absence of range-limiting optical attenuation effects, which are fortunately relatively uncommon in cirrus. In this chapter we review the basics of remote sensing and signal processing, summarize the techniques for remotely determining cirrus cloud boundaries, microphysical content, and radiative properties, and then provide an application of these approaches in terms of the analysis of an intensively observed recent cirrus cloud case study. 8.2. Active Remote Sensing Fundamentals

The scattering interaction of electromagnetic waves with the simplest particle shape, the homogeneous sphere, is governed rigorously by Mie-Lorenz theory, which demonstrates that the strength and angular distribution of the scattering response is strongly a function of the particle radius, r, in relation to the incident wavelength, X (as expressed by the size parameter x = 2n r/X), as well as the particle refractive index. This has crucial consequences for the probing of cloud and precipitation particles using radar and lidar. Generally, at the centimeter wavelengths of traditional radars, the sizes of most hydrometeors are much smaller than the radar wavelength, such that backscattering and attenuation are proportional to the particle diameter d6 and d3, respectively. This is the domain of the Rayleigh approximation, which has traditionally proved highly useful to the radar meteorologist in interpreting radar signals. The scattering of visible light by hydrometeors, on the other hand, generally is confined to the geometrical optics domain, in which both backscattering and attenuation obey a d2 law. These basic rules have important implications for cirrus remote sensing. In contrast to spheres, only approximate theories apply to the scattering of the nonspherical particles that inhabit cirrus. For particles much smaller than the incident wavelength, the Rayleigh/Gans approximation effectively treats simple ice crystal shapes in terms of prolate and oblate ellipsoids (Schneider and Stephens 1995); it works because the Rayleigh interaction with ice particles is quite weak, so the exact shape is not crucially important (Liao and Sassen 1994). Resolving the particle major and minor axes into the incident polarization plane wave also shows that backscatter depolarization, although similarly weak, depends strongly on the particle axis ratio (Battan 1973; Sassen and Khvorostyanov 1998). In the geometric optics realm of light scattering, ice crystals disclose their backscattering behavior through the ray tracing method. For visible lasers, the depolarization of the incident wave can be computed for as many orders of internal reflections as deemed worthy to consider (Takano and Liou 1989). The depolarization of light results from the reorientation of the

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incident E vector during each internal reflection/refraction leading to backscattering, except at strongly absorbing wavelengths such as the mid-infrared (~10|Lim) CO2 laser, where internal energy is quickly absorbed (Eberhard 1992). Analogous to the strong interaction of light with ice crystals, backscatter laser depolarization is also strong (Sassen 1991, 2000), typically accounting for about one-third of the total returned energy. Because lidar and radar share their fundamental operating principles, a similar equation can be used to describe the relation between backscattered power, P, as a function of range, R, and the system constants and atmospheric target properties. This basic equation for polarization lidar applications for the case of isotropic scattering (Schotland et al. 1971) works well for many lidar/radar applications:

where the subscripts _L and || refer to the planes of polarization perpendicular and parallel to the incident polarization plane, P0 is the linearly polarized output power, c the speed of light, t the laser pulse length, Ar the receiver collecting area (or dish gain), |3 the backscattering coefficient per unit volume (in units of per length per steradian), r| the multiple scattering correction factor, and a is the extinction coefficient per unit volume (per length). (Note that the convention in radar practice reverses the symbols for the two scattering coefficients.) The integral is taken over the range of R = 0 to R. Finally, an important data quantity in the study of nonspherical particles is the linear depolarization ratio, 5, which can be expressed from the ratio of the polarized radar/lidar equations as: which reduces simply to the ratio of the backscattering coefficients, assuming that transmission is independent of polarization. (Scenarios can be envisioned where this is violated, such as scanning a lidar beam through a field of uniformly oriented ice crystals, see Sassen 2000.) Other indicators of backscatter depolarization are the circular (or elliptical) depolarization ratio, and various combined linear-circular depolarization ratios, using circularly polarized radar transmitters and dual dishes. Another powerful radar tool involving polarization is the measurement of differential reflectivity (ZDR), which uses the ratio of parallelpolarized backscattered powers in the vertical and horizontal polarization planes to sense hydrometeor shapes and orientations. Below, we divide the basics of signal analysis between lidar and radar for convenience. 8.2.1. Lidar Signal Processing The height-normalized relative returned signal for a lidar can be calculated using the single-scattering lidar equation expressed as

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where C is the system constant that includes all the operational parameters and constants in equation 1, pt(z) is the total volume backscatter coefficient including molecular pm, aerosol (3a, and cloud (3C constituents, and ot(z) is similarly the total volume extinction coefficient (Sassen et al. 1989a). S(z)z2 is then used to estimate PC(Z), assuming |3a(z) and oa(z) are negligibly small in comparison:

where

and the backscatter coefficient of air molecules is calculated using Rayleigh formula (Fernald et al. 1972), depending on the laser wavelength and the air density calculated from a local atmospheric sounding profile. As used here the factor TJ accounts for the effective overestimation of cloud extinction due to the strong forward-scattering peak found in typical cirrus cloud phase functions at lidar wavelengths. This forward-scattering peak causes a fraction of the scattered photons to remain within the propagating lidar pulse (i.e., as captive diffraction), and thus varies from 0.5 to 1.0. The backscatter-to-extinction ratio, k, equivalent to 4n times the normalized scattering phase function at 180°, is a measure of the relative backward strength of the scattering process. Measurements show that k varies between 0.01 and 0.06 per steradian in cirrus (Grund and Eloranta 1990; Sassen et al. 1990; Sauvage et al. 1999). The approach of specifying a pure molecular atmosphere boundary condition at some height z0 below cloud base, which corresponds to the range-normalized lidar signal minima S(z0)z02, is generally valid for cirrus because of the very clean conditions typical of the upper troposphere (see Sassen and Cho 1992). There have been many discussions in the literature regarding the inversion of the lidar equation and the accuracy and stability of the lidar retrieval solution (Davis 1969; Fernald et al. 1972; Platt 1979; Klett 1981,1985; Fernald 1984; Del Guasta 1998). Currently, the Klett single-component solution and the Fernald two-component solution are widely used. For dense clouds, accurate CT can be obtained with the former method, provided that k is constant through the cloud. For thin clouds, accurate (3 can be obtained with the Fernald method, but the accuracy of the extinction coefficient depends on the accuracy of k. Although the single wavelength lidar retrieval involves some uncertainty, it still yields meaningful results (Sassen et al. 1989a; Sassen and Cho 1992; Del Guasta et al. 1993; Pal et al. 1995). Obviously, the k value is of crucial importance because all derived lidar optical properties depend on its determination. Fortunately, more sophisticated spectroscopic lidar approaches yield quantitative information on optical attenuation. These methods use combined Raman elastic-backscatter lidar (Ansmann et al.

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1992) and high spectral resolution lidar (HSRL; Grund and Eloranta 1990). The Raman lidar method determines the extinction and backscatter profiles independently on the basis of the expected return from nitrogen, a well-mixed gas in the upper troposphere, with its density provided by coincident sounding profiles. The HSRL technique separately measures the molecular and particle backscatter components of lidar return based on the fact that molecular returns are Doppler-broadened due to kinetic motions, while the elastic returns from clouds and aerosols closely maintain the laser frequency. 8.2.2. Radar Signal Analysis Microwave radar systems, despite operating on similar principles, sense fundamentally different atmospheric properties than visible lidars. Although some extinction is caused by gases (principally water vapor and oxygen) at shorter radar wavelengths, backscattering from air molecules and most aerosols is too weak to be detected. The radar minimum detectable signal (MDS) is determined by radar system design (transmitter power and antenna gain), and the number of returns that are averaged. Identification of a "noise floor" is therefore crucial to interpreting returns that are above the MDS and subject to quantitative examination. The fundamental measured quantity of a radar system (which we assume has Doppler measurement capabilities) is the power density spectrum: this provides the backscattered energy from particles moving relative to the radar in some number of discrete velocity bins (see the example in fig. 8.1). Typically this information is reduced to the first three moments of the Doppler spectrum: the radar reflectivity (zeroth moment), the mean Doppler velocity (first moment), and the spectral width (second moment). The zeroth moment is referred to as the equivalent radar reflectivity factor, Ze, and represents the total power backscattered by the sum of particles per unit volume (Doviak and Zrnic 1993). It is straightforward to show that, assuming particle scattering can be approximated by Rayleigh theory, Ze is equivalent to the sixth moment of the particle size distribution. This dependence is at once an advantage and disadvantage of radar remote sensing. In one sense, the elegant description of the backscattered energy in terms of a simple parameter is more tractable than similar quantities that can be derived from lidar. However, because we are interested in either the area of the size distribution for radiative transfer studies or the volume of the size distribution to derive the cloud water mass, the sixth moment dependence presents difficulties that make interpreting Ze challenging. Obviously, Ze is quite sensitive to the existence of the largest particles in the crystal population. Figure 8.2 illustrates this sensitivity using a theoretical size distribution described by a first-order modified gamma function that can mimic cirrus particles. Particles with effective radii 80 urn < rsff < 200 um contribute most to the total reflectivity, with the peak contribution coming from particles near 150 urn. The interplay between the rapidly decreasing number of larger particles and Ze dictates the shape of the cumulative reflectivity curve. Most cirrus algorithms have as their central goal the conversion of the sixth moment of the size distribution into one of the other moments that have more physical relevance.

Figure 8.1. Power density spectra recorded by the millimeter cloud radar at the SGP ARM site in Oklahoma on September 26, 1997 at 2045:43 UTC, at heights of (a) 9375m, (b) 9465 m, and (c) 9555 m. The plots reveal the amount of backscattered microwave energy from particles moving at discrete radial speeds relative to the vertically pointing radar beam. Positive velocities are down ward.

Figure 8.2. Normalized cumulative moments of a typical cirrus particle size distribution. The heavy solid line shows the fractional contribution of the particle size distribution to the sixth moment (proportional to the radar reflectivity), the light solid line the third moment (ice water content), the heavy dashed line the second moment (extinction coefficient), and the light dashed line is the zeroth moment (total concentration of particles). The abscissa is expressed in terms of the effective radius, defined as the volume of the particle divided by the area of the particle. The figure demonstrates, for instance, that nearly 100% of the sixth moment (radar reflectivity) comes from the largest 20% of the particle size distribution. 174

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The second and third moments, also plotted in figure 8.2, indicate that any attempt to extrapolate from the sixth to some lower order moment must be done with care because a major contribution to the lower moments comes from portions of the size distribution that are not well sensed by radar. A further difficulty is that the central assumption relating the backscattered power with the sixth moment (namely, that the particles scatter according to Rayleigh theory) is often violated. This is of particular concern at W-band frequencies. Such issues have been addressed by Schneider and Stephens (1995), who showed that for most cirrus the assumption of prolate or oblate Rayleigh spheroids provides sufficient accuracy. 8.3. Measuring Cloud Boundaries and Structure

Since the early days of meteorological research, the importance of determining cloud height for classifying cloud type was recognized. Methods advanced from triangulation measurements to stereo photography and aircraft penetrations, eventually giving way to the use of remote sensors. The application of active remote sensing methods to this problem is of major importance to climaterelated research. Not only can lidar and radar define cloud boundaries under suitable conditions, but it is implicit that the vertical and temporal variations in backscattering reveal information on the internal structures of cirrus clouds (e.g., Sassen et al. 1989b), at resolutions down to about 75m for millimeter wave radar and 1.5m for Nd:YAG lidar. The importance of such simple cloud boundary characterizations cannot be overstated, especially in terms of creating proper cloud height climatologies. In addition to other critical information such as cloud phase, effective particle size, and various vertically integrated properties (see below), the heights (and temperatures) of cloud layers control, in a fundamental way, the radiation balance of the earth-atmosphere system. Nonetheless, there is clearly the danger that the derived cloud heights will be specific to the remote sensing system and/or detection algorithm used. A major source of uncertainty is the sensitivity and wavelength of the sensor, particularly in terms of lidar versus radar capabilities. With state-of-the-art sensitivities, however, lidar- and radar-detected cirrus cloud base altitudes will typically be quite similar (Sassen et al. 1989b; Intrieri et al. 1993) because the few relatively large ice particles resisting evaporation can be readily detected in either the Rayleigh or geometric optics domain: millimeter-wave radar may even have a slight advantage because of better signal processing technologies and the larger beam widths that favor the detection of diffuse targets. The probability of detecting cirrus cloud top, however, is typically stacked in favor of lidar, as long as the cloud optical thickness does not completely attenuate the backscattered return (Sassen 1984; Sassen et al. 1989b, 1998). This is a result of the fact that cirrus generally develop from the top-down, with the smallest newly formed particles dominant at cloud top. Visible lidars will sense the small cloud-top ice particles at about the same efficiency as any cirrus particle, but microwave radar with its d6 dependence will inevitably run out of signal as cirrus cloud top is approached.

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As described by Platt et al. (1994), during ECLIPS three basic methods were applied to the determination of cloud boundaries: the differential zero-crossing method, the threshold method, and a quantitative approach based on the clearair assumption. In the first method (Pal et al. 1992), the cloud base height, Zcb, is determined directly from the zero crossing of the signal slope dPIdZ. In practice, however, there are likely numerous other zero crossings that arise from inhomogeneities in the cloud, surrounding aerosols, and signal noise, such that arbitrary thresholds and careful tuning are necessary. The cloud top height, Zct, is determined by requiring that the backscatter signal P(Zct) is equal to P(Zcb), which under many cloudy conditions can underestimate the actual height. The threshold method defines cloud base as that altitude where a statistically significant signal increase above the background fluctuations occurs for a number of successive height intervals. Cloud top height is determined after calculating the standard deviation of noise above cloud top. The method of Sassen and Cho (1992) for thin or sub visual cirrus retrieval fits lidar data to the Rayleigh backscatter profile calculated from radiosonde data, under the assumption of negligible aerosol backscatter at some altitude in the upper troposphere just below the cirrus. The cloud base and top altitudes are retrieved automatically when cloud backscattering increases above the molecular level, although some threshold criterion is still specified to reject noncloud targets. This method retrieves cloud-base and cloud-top altitudes and cloud optical properties simultaneously and can be used for any cirrus case where the optical depth is small enough to measure the molecular backscatter returns above the cloud. Young (1995) also used a cloud-detection algorithm for thin clouds, with reference to a measured signal in cloud free regions. An alternative approach to determining cloud boundaries in radar and lidar data was offered by Clothiaux et al. (1995,1998). The basic concept is straightforward and extends from the observation that, on average, a cloud lidar or radar return is identified primarily from its temporal and vertical consistency. This is especially true in radar applications because no signal is received from clear air. However, with appropriate normalization, the general approach is still applicable for lidar. The initial step identifies the statistics of the noise background in a cloud-free region. Small regions of the data field are then treated similarly, and the probability that these data points contain only noise is determined by comparing the statistics of the two regions. Each data point is examined a number of times in the context of all surrounding points, and each of the probabilities are subsequently used to identify those points that have a low probability of containing only noise. An example of this approach applied to ARM CART micropulse lidar data (Spinhirne 1993) is shown in figure 8.3. In figure 8.3a, the cirrus sensed by the eye-safe lidar at night stand out above the noise and would be easily identified using thresholding techniques, but the daytime cirrus are nearly masked by the solar background noise at the 0.523-um laser wavelength. After applying the cloud masking algorithm, however, all the cirrus are identified above those pixels that have statistics similar to the noise. There is not yet a universal algorithm that is suitable for all situations and that has the ability to deal with signal quality and to differentiate between various

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Figure 8.3. Example of the statistical cloud mask algorithm of Clothiaux et al. (1995,1998), showing micropulse lidar data collected at the SGP ARM site on May 2,1994. In (a) the raw data shows cirrus during the night from 0600 to 1000 UTC and again during the day after 1200 UTC; (b) shows how the masking algorithm effectively separates signal from noise using the local statistics of the returned signal.

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targets such as clouds, virga, aerosols, or insects (a potentially significant problem with millimeter wave radars). As we shall see, such algorithms for multiple remote sensors are currently under development. 8.4. Deriving Cirrus Cloud Microphysical Properties

Improving our knowledge of the microphysical content of cirrus clouds contributes directly to a more realistic evaluation of their impact on radiation, climate, and climate change scenarios (see chapter 19). The data quantities of importance radiatively are the ice particle number size distribution, effective particle size, reff, orientation, local ice water content (IWC), and vertically integrated ice water path (IWP). Much was previously learned passively of cirrus ice crystal shape and orientation from halo/arc observations and ray-tracing model simulations, showing particles of a basic hexagonal habit. This research has increasingly been in the realm of active remote sensors. In contrast to lidar techniques, which have great difficulty in deriving quantitative cirrus cloud content information like IWC, millimeter-wave radars offer considerable promise. We begin with current research based on algorithms using calibrated radar (often in combination with other remote sensors), and then discuss the capabilities of lidar and radar polarization diversity techniques. As mentioned earlier, much has been learned of cirrus microphysical and radiative properties in the past few decades due to observational programs that used surface-based remote sensors and in situ aircraft probes. A number of algorithms have emerged from these studies that diagnose cirrus microphysical properties from various combinations of remote sensing observations. These algorithms can conveniently be grouped by the number of observational parameters used as inputs. Increasing the number of input parameters leads generally to an increase in the number of derived parameters, improved accuracy, or less dependence on assumptions, or some combination of these. Single-parameter techniques tend to be based on empirical data fits or cloud model outputs and generally produce a single microphysical parameter such as IWC. Examples of such algorithms are the schemes by Liao and Sassen (1994) and Sassen and Liao (1996), which treated K- and W-band radar frequencies. They used ice crystal data sets collected by aircraft and from the ground in polar regions, in combination with conjugate gradient-fast Fourier transform (CGFFT) scattering calculations to obtain regression relationships between radar reflectivity and IWC and optical and microwave extinction coefficients. A similar regression relationship was offered by Atlas et al. (1995), who examined an in situ data set collected during the FIRE I experiment. They also considered the standard error in the IWC-Ze relationship and argued that in most cases, the error is so large that little information can be gleaned from the regression analysis. However, recent calculations using a cloud model (fig. 8.4; Sassen and Khvorostyanov 1998) indicate that single-parameter regression equations may be applicable in particular regions of cirrus clouds. Most algorithms that use more than one input parameter generally assume that the particle size distribution conforms to some predetermined functional

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Figure 8.4. Comparison of IWC versus ice equivalent radar reflectivity factor, Z(, relations derived from empirical (solid lines; from Liao and Sassen 1994) and cloud model (lines with symbols) sources (after Sassen and Khvorostyanov 1998). The cloud model results are shown in terms of vertical profiles (note inserted heights for one profile) at four selected horizontal positions within the simulated cirrus domain. Note that the hysteresis affect results from the typical vertical evolution of cirrus cloud content, but where small newly formed particles are absent, the model predictions after 1 h of cloud growth converge with the empirical relations.

form (e.g., gamma size distribution), and the unknown parameters of this distribution can be derived from the input data. Cloud microphysical properties are then calculated from the derived distribution. Multiparameter algorithms can be further subdivided into those that use the moments of the Doppler radar spectrum (Matrosov et al. 1994), and those using the radar reflectivity and a vertically integrated measurement of some cloud property (Matrosov et al. 1992; Mace et al. 1998a). The use of the first or second moments of the Doppler spectra generally allows retrieval of cloud microphysical properties in each radar range gate by assuming that the Doppler velocity contains information regarding the terminal velocity of a particle (Matrosov et al. 1994). Since these observed moments represent some convolution of particle f allspeed, vertical air velocity, and turbulent motions, this assumption requires careful attention, especially in cirrus where terminal velocities are weak. Although retrieval techniques that use the full Doppler spectrum (fig. 8.1) have been developed and applied to water clouds, with some success, similar algorithms have not as yet been applied to cirrus clouds. Although infrequently applied to cirrus, multi-wavelength techniques have promise for sensing vertical profiles of reff. These methods rely on the principle

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that both backscattering and extinction can be quite sensitive to the relation between reff and the incident wavelength. In practice, the greatest sensitivity to particle size lies in the transition region between the Rayleigh and Mie-Lorenz (or geometric optics) scattering domains (i.e., for particles of a size close to the wavelength), either when the wavelengths are widely separated to take advantage of major scattering domain differences or when a strong wavelengthdependence in the particle refractive index can be exploited. For example, Intrieri et al. (1993) proposed a method to infer cirrus particle size by comparing theoretically expected backscatter coefficients to observed returns from 3.2cm and 8.6-mm radars, and 10.6-um lidar. The use of dual-wavelength millimeter wave radars also has promise, as has been shown in studies of tropical thunderstorm anvils (Sekelsky et al. 1999). As an example of a two-parameter algorithm, let us describe a modification of the Matrosov et al. (1992) approach that is being applied to the operational ARM data stream (Mace et al. 1998a), motivated by the particular mix of observations being collected there. Infrared radiance spectra, Rn, observed by the atmospheric emittance radiance interferometer (AERI; Smith et al. 1993) are combined with the Ze observed by the millimeter cloud radar (MMCR; Moran et al. 1998) to derive cirrus microphysical properties. Our initial goal is to derive layer-averaged cloud properties to evaluate the affects of optically thin cirrus on the radiation field at the surface and top of atmosphere (TOA). We assume the layer-averaged particle size distribution can be described in terms of the firstorder modified gamma distribution (Kosarev and Mazin 1991). By specifying the order of the distribution, the unknown parameters reduce to a constant of proportionality and a length parameter that can be derived in terms of the distribution mode. The fundamental relationship we use to relate these observations is similar to that of Matrasov et al. (1992); namely, where ea is the cloud emittance, co0 is the single scattering albedo, a is the extinction coefficient averaged over the layer, and A/z is the cirrus layer thickness. Fu and Liou (1993) provide polynomial-based parameterizations of co0 and a in terms of particle size and IWR By assuming the average particle size distribution can be reasonably approximated by a unimodal modified gamma distribution, we express Ze in terms of reff and IWR The retrieval then reduces to finding a specific gamma distribution function that yields the observed radar reflectivity, and, when inserted into a radiative transfer model, generates the observed downwelling radiance observed by the AERI. Further details of this technique can be found in Mace et al. (1998a,b). Finally, the utility of various polarization diversity techniques for inferring unique cirrus cloud microphysical properties can be summarized. Although, as previously mentioned, this lies predominantly in the realm of visible lidar studies, the prospect of scanning radar measurements should not be overlooked given the increased research emphasis in millimeter-wave technologies. For example, although it is still a significant barrier to attain the necessary polarization isolation and sensitivity to measure the extremely weak cirrus 8-values to identify

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particle shape, some targets such as snowfall and the melting layer bright band can generate easily measurable depolarization ratios (Battan 1973). Matrosov et al. (1996) have shown the utility of scanning radar measurements for detecting certain ice crystal orientations, such as horizontally oriented planar ice crystals in low-level clouds and precipitation, but it is unlikely that such methods can normally be applied to the usually inhomogeneous situation in cirrus layers. Methods using the differential polarization technique during radar elevation angle scans (Sassen et al. 1989b) also have value in inferring ice crystal shape and orientation. Regarding lidar depolarization studies, as recently reviewed in Sassen (1991, 2000), this optical technique offers a wealth of information regarding ice particle shape and orientation. It has been predicted through ray-tracing simulations that the lidar 8 value essentially depends, for simple crystal habits, on the particle aspect ratio (Takano and Liou 1989). Thus, in principle, lidar depolarization can be used to identify cirrus ice particle shape, but in reality this potential is often limited by the tendency for cirrus clouds to be composed of a diverse mixture of particles at any particular position. Mixing processes often cause regions of cirrus to assume a homogenized content leading to the frequently observed 8 of 0.35-0.45 in the absence of the oriented planar crystal anomaly observed in the zenith direction. Nonetheless, portions of cirrus clouds inevitably display significant 8-value variations that hint at relatively uniform crystal nucleation and growth conditions, such as in generating regions or fallstreaks. Such internal cloud structures are often also clearly disclosed by variations in laser or radar backscattering and Doppler velocity. Foremost among the polarization lidar applications is the ability to identify the anisotropic conditions associated with probing near-horizontally oriented plate ice crystals, although it remains to be determined how various orientations of column or other particles affect depolarization. The signature of the oriented plate crystal cloud is strong laser backscattering and near-zero 8-values. However, these effects vanish as the lidar is tipped off the zenith direction and so are easily identified and do not threaten the unique ability of polarization lidar to unambiguously discriminate between water and ice phase clouds. Ice particle orientation effects have significant implications for radiative transfer.

8.5. Radiative Properties

Although a simple radar algorithm to estimate cirrus cloud optical depth has been offered based on empirical data (Sassen and Liao 1996), in view of the fact that cloud levels containing small ice crystals will go undetected by most millimeter-wave radars (Sassen and Khvorostyanov 1998), this remains an uncertain application. We have already pointed out the great difficulties inherent in relating the Rayleigh-scattered signals to what is essentially an optical scattering problem. Figure 8.2 succinctly illustrates the fundamental difficulty. Information on the small end of the particle size distribution needs to be added to the radar reflectivity in order to infer optical properties. This is, in essence, what the radar plus infrared or Doppler velocity algorithms attempt to correct. However,

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regardless of the approach, the fact that lidar operates in the same spectral range involved in solar and terrestrial radiative transfer is a distinct advantage. The important optical parameters are vertical profiles of a, from which the visible cloud optical depth, T, is derived, the infrared cloud emittance, ea, and measures of the angular scattering pattern of the particles such as single-scattering albedo, co0, asymmetry factor, g, and the lidar k ratio. Also note that other terms often used in radiative parameterizations are reff and IWP, as discussed in the previous section on microphysics. It is important to reiterate that the key to understanding the climatic impact of cirrus clouds lies in the relation between their radiative effects in the solar versus terrestrial spectra in the mid-infrared atmospheric window. In other words, is their solar albedo effect more or less important than their greenhouse effect in maintaining the global radiative balance? Thus, of the greatest significance for climate research is the ability to measure i and ea. Relatively straightforward approaches have been established for estimating these radiometric quantities using passive measurements. One such example is the use of sun photometry for estimating i. The basic principle is simply a statement of the Beer-Lambert law that is solved for optical depth. This simple solution assumes that all photons that are scattered from the direct solar beam are removed from the direct beam. However, the directional scattering of solar radiation by typical ice crystals is strongly peaked in the forward direction. Shiobara and Asano (1994) examined this problem using Monte Carlo radiative transfer modeling and realistic cirrus scattering phase functions and derived a simple correction. Despite these relatively direct passive approaches, the most exploited and perhaps accurate approach is the combined lidar-infrared radiometer (LIRAD) technique. Before describing this technique in some detail below, it should be mentioned that in view of the importance of using an accurate k in the inversion of the lidar equation, lidars operating on the Raman or HSRL principles display the advantage of the direct assessment of optical extinction. The LIRAD technique for deriving cirrus properties was first described by Platt (1973). Cloud optical depth and emittance (as defined by Liou 1992) are derived using an iterative technique that corrects the downwelling radiance measured by the radiometer using the lidar backscatter profile (Platt 1979). First, an initial guess of k/2r\ is used to calculate the vertical profile of attenuationcorrected lidar backscatter coefficient, (3c(z)- This profile, in conjunction with atmospheric sounding data, is used to derive cirrus cloud heights and temperatures. The infrared absorption coefficient, aa(z), is calculated by assuming a relationship between (3c(z) and oa(z) of the form aa(z) = £,$c(z), using an initial guess of £. Next, a theoretical value of the cloud radiance 7at, is calculated from

where the blackbody radiance, 7b, is estimated using radiosonde temperatures, and 7SC is the cloud-emitted radiance that is scattered in and out of the radiometer beam, obtained from a cloud-scattering model. The cloud radiance, 7C, is

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derived by correcting the radiometer-measured 7m for emission of atmospheric gases using the equations 7C = (7m - 7srrbc - I)/Tbc and 7g = 7acTcrbc + 7icrbc + 7bc. 7bc and Tc represent the transmittances below the cloud and in-cloud, respectively. These transmittances and the radiances due to the emission of gases above 7ac, below, 7bc, and in the cloud 7ic are derived using a radiative transfer model, and 7sr describes the upwelling radiance reflected off the cloud into the radiometer beam. Once oa(z) is determined, the absorption optical depth, 6a, ea, and integrated backscatter coefficient, y(n), is calculated for each lidar profile using the equations

With y(7i) and ea estimated for each lidar profile, an equation of the form

is fit to the results to obtain the coefficients k/2r\ and 2r|a. The quantity a is defined as the ratio of the visible (i.e., lidar wavelength) extinction coefficient to the infrared absorption coefficient (over the radiometer bandwidth). The new /c/2r| value is then used to recalculate PC(Z), and this process is repeated until the value of |3c(z) varies insignificantly. Once the final value of k/2r\ is obtained, k is determined by estimating rj. Platt et al. (1998) estimated r| as a function of cloud temperature, but it can also be calculated based on the cloud type and lidar receiver field-of-view. The value of k is important because it is used in the calculation of x from the lidar backscatter coefficient following the equation

As an illustration of this method, figure 8.5 depicts preliminary results of infrared cloud emittance versus optical mid-cloud temperature, cloud thickness, and visible optical depth for typical mid-latitude cirrus observed from the University of Utah Facility for Atmospheric Remote Sensing (PARS; see Sassen 1997). These cirrus were observed over a 1-year period between April 1992 and March 1993 using a subset of the ongoing 12-year FARS data set. Our results for ea versus optical mid-cloud temperature are compared with those presented by Platt et al. (1998) for Southern Hemisphere mid-latitude and equatorial results in figure 8.5a.

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Figure 8.5. Comparison of (a) cloud emittance versus optical mid-cloud temperature for PARS mid-latitude cirrus (squares, with bars indicating standard deviations), and southern mid-latitude (triangles) and equatorial (diamonds) cirrus from Platt et al. (1998). Also shown are emittance versus (b) physical cloud thickness and (c) visible optical depth measured at Salt Lake City, Utah.

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Our initial results from FARS are similar to those from southern Australia. In general, ea tends to increase with increasing cloud temperature (a), cloud thickness (£), and T (c). These trends are interrelated to a large extent because, on average, increasingly warm or deep cloud layers will possess a greater optical depth. Clearly, cirrus clouds do not act anything like blackbodies, but are gray emitters. 8.6. A Multiple Remote Sensor Case Study

Here we present a cirrus cloud case study that occurred at the Southern Great Plains (SGP) ARM site in Oklahoma on September 26,1997 during an intensive observation period where data from several visiting instruments were collected to augment the operational ARM observations. Coordinated in situ data were also collected by the University of North Dakota Citation aircraft from 1800 to 2130 UTC. This cirrus constituted the remains of hurricane Nora that made landfall in the southwestern United States on September 24. The tropical system quickly disintegrated as it moved on shore, but the upper-level remains rapidly propagated northward through Arizona and Utah. FARS lidar data were coincidentally collected as this cirrus shield passed over Salt Lake City the previous day, and vivid optical displays were observed then, as later. The cirrus clouds subsequently curved anticyclonically around an upper tropospheric ridge axis and approached the ARM site in northwesterly flow by 1800 UTC on September 26. Figure 8.6a,c shows polarization diversity lidar (PDL; Sassen 1994) and CART MMCR height-time cross-sections collected as the thickening cirrus layer advected overhead. The lidar and radar vertical resolutions are 1.5 and 45m, respectively. As a first level of lidar/radar data intercomparison, the colored symbols indicate our latest cloud boundary algorithm determinations of cirrus cloud base and cloud-top altitudes (see also the comparison in fig. 8.7). Considering that the MMCR is probably one of the most sensitive radars existent, the derived cloud boundaries are in quite good agreement. The lidar cloud-top altitudes typically lie a few hundred meters above the radar-detected heights, except during the initial thin cirrus episode when the radar failed to detect the thin cirrus between the denser mesoscale uncinus-generating masses (e.g., at -1815 and 1910 UTC). On the other hand, from 2030 to 2045 UTC, strong lidar returns from the plunging lower cirrus streak restricted the PDL cloud-top heights due to the combined effects of strong optical attenuation and limited signal-handling dynamic range. Keeping in mind that these remote sensors are state of the art, the cloud boundaries and internal structures revealed by the patterns in backscattering are in (rare) correspondence. Figure 8.6b shows the PDL linear depolarization display of this cirrus, which exemplifies the behavior of halo/arc-producing cirrus, showing initially extensive areas of horizontally oriented planar ice crystals, as indicated by the 8 < 0.1. Having described a number of numerical methods to derive cirrus properties, we provide in figures 8.8 and 8.9 an intercomparison of data quantities for this case study using a number of remote sensors at the SGP CART site. Figure 8.8 compares the fields of IWC retrieved using the empirically based Liao and Sassen (1994) radar reflectivity and an emerging algorithm that uses the first three

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Figure 8.6. A polarization diversity lidar (PDL) and millimeter cloud radar (MMCR) case study of the cirrus cloud shield from Pacific hurricane Nora studied on September 26,1997 from the SGP CART site. The cirrus cloud top and base heights (above mean sea level; MSL) derived from our latest "universal" algorithm are shown by symbols in the lidar returned energy height-time display at top (a. in relative units) and the radar display at bottom (c. note inserted key of 10 log Ze). The middle display shows the corresponding PDL linear depolarization ratios (b. note inserted 6 key).

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Figure 8.7. Comparison of the derived radar and lidar cloud top and cloud base heights from the data given in figure 8.6, showing unusually good agreement.

moments of the radar spectrum. Although we hesitate to describe this algorithm in detail, the scheme assumes a crystal habit (polycrystals in this case) and essentially calculates a particle size distribution at each height that simultaneously satisfies the observed moments after being corrected for air motions. As can also be inferred from the IWP panel at bottom, the Doppler moments method produces much higher IWC values, perhaps due to the effects of particle aggregation (which increases particle fallspeeds) in the dense fallstreaks beginning at about 2000 UTC. Because the reflectivity-only method based on measured crystal masses is subject to uncertainties due to both small particles and aggregates, the reflectivity-radiance method may be the most reliable under these conditions. The intercomparisons in figure 8.9 shed light on the behavior and limitations of the various techniques used to derive cloud optical depth and emittance in this cirrus cloud. The result of applying the five diverse techniques to determine i indicate that, despite some differences caused partly by differences in the locations of the sensors at the CART site and the zenith versus solar positions (with respect to the MFRSR data), the same trends are clearly evident. Following a gradual T increase, the rapid vertical cloud development at about 2000 UTC (see fig. 8.6) generates a dramatic increase in i. All approaches yield a i approximately equal to 3.0 at those times (-2045 and 2130 UTC) that the PDL was unable to detect the actual cirrus cloud-top altitude. As shown in Kinne et al. (1992) and Sassen and Cho (1992), this i represents the usual limit lidar is able to penetrate through dense cirrus or altostratus clouds. The differences in results between the two methods used to infer ea in figure 8.9b are significant, especially in the initial thin cirrus stage, even when the

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Figure 8.8. Retrievals from the MMCR Ze data from the hurricane Nora cirrus (fig. 8.6), showing fields of ice water content (in terms of log IWC) derived from the Liao and Sassen (1994) algorithm and the Doppler moments method. At bottom is a comparison of the vertically integrated ice water path, derived from these methods plus the reflectivityradiance approach (Mace et al. 1998a).

LIRAD-derived optical mid-cloud temperatures are used in the radar/AERI analysis. A possible reason for the discrepancy is the dominance of small ice crystals in the high, cold cirrus, which could display absorption efficiencies lower than those usually considered in parameterizations. In figure 8.10 a scatterplot of i versus ea obtained from the LIRAD method is compared to a curve from Fu and Liou (1993) originally relating visible optical depth (at 0.55 um) to cloud emissivity, which was converted to emittance by dividing the absorption optical depth by a diffusivity factor of 1.66 (see Liou 1992).The modeled emittances were computed by inserting the radiative properties derived from the observed contents

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Figure 8.9. Comparison of various methods for retrieving (a) visible cloud optical depth and (b) infrared cloud emittance using the same cirrus cloud data set. At top are compared the T derived using the Sassen and Liao (1996) radar Ze algorithm, the reflectivityradiance method, our analysis of the CART Raman lidar (Goldsmith et al. 1998), the combined PDL and mid-infrared radiometer LIRAD technique, and the 0.860 |im channel of the CART multiple frequency rotating shadowband radiometer MFRSR. At bottom the £a derived from the LIRAD and reflectivity-radiance methods using 1- and 3-min data averages, respectively, are compared.

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Figure 8.10. Comparison of derived cloud emittance versus visible optical depth for the hurricane Nora cirrus case study and previous results from Fu and Liou (1993). Each symbol represents a 1-min average of lidar and radiometer data. The curve was computed using single-scattering properties derived from in situ observations of cirrus clouds as input into a broad-band radiative transfer model.

of 11 cirrus clouds, and assuming various cloud thicknesses, into a delta-fourstream radiative transfer model for nonhomogeneous atmospheres. The agreement of the average cirrus relationship with the case study data points shows that these two different methods of deriving cirrus radiative properties produce a similar trend, but suggest that this particular cirrus could be somewhat unusual. The LIRAD data yield maximum £a ~ 0.85, which is appropriate for a dense cirrus/altostratus cloud (e.g., Platt et al. 1998; Chapter 2). Figure 8.11 depicts a comparison of the CART observed downwelling solar fluxes at the surface with calculations from the radiative transfer algorithm of Toon et al. (1989) for the initial thin cirrus event prior to about 2000 UTC. For these flux calculations, the diagnosed cloud microphysical properties were used as input to the radiative parameterization of Fu and Liou (1993). In this figure,

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19 I

Figure 8.11. A comparison of the observed CART downwelling solar fluxes with those cal culated using the Toon et al. (1989) radiative transfer algorithm for the September 26,1997 Nora cirrus case study. The diamonds are observed values and the x symbols show data calculated using the microphysical properties obtained from the Z-radiance algorithm. The means and standard deviations of the observed and calculated flux fractions are given below the figure.

the fluxes are normalized to remain between 0 (100% of the clear sky flux removed from the downwelling solar) and 1 (no change to the downwelling solar) using an estimate of the clear sky flux following the technique of Long (1995). During much of this early portion, the observed flux was larger than the clear sky flux, indicating positive cloud forcing. This occurrence is not unusual for thin cirrus and arises from the predominant forward scattering of the direct beam and side scattering of solar energy that would not normally reach the pyranometer. Comparing fluxes is our current approach at validating the retrieval algorithm during periods when in situ aircraft are not available. Our reasoning is that if we are able to model the surface solar flux with sufficient accuracy, then the cloud properties derived from the data attain the level of accuracy needed to ascertain their influence on the radiation fields. However, this case illustrates a flaw with that approach; cirrus tend to be quite heterogeneous and their lateral structures influences the fluxes. Thus, plane-parallel radiative transfer calculations often do not faithfully represent an accurate comparison. This particular case did, however, have in situ data with which to compare. Figure 8.12 compares the averaged size distribution collected by the 2DC optical probe on the Citation aircraft with the retrieved size distribution. Because this algorithm returns layer-averaged quantities, it is difficult in a cirrus layer with

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Figure 8.12. Comparison of the cirrus particle size distribution measured by the Citation aircraft (bars) and the particle size distribution retrieved using the radar reflectivity and downwelling radiance (filled squares) algorithm. This comparison uses data averaged between 1800 and 2100UTC on September 26,1997 over the SGP ARM site.

substantial variability to make meaningful comparisons. Therefore, we averaged over a substantial period to make this comparison, which is similar to the procedure of Mace et al. (1998a), where the measured size spectra were compared to diagnosed spectra from the reflectivity-radiance algorithm. The middle portion of the size distribution (between roughly 200 and 600 um) shows excellent agreement, whereas the smaller sizes tend to be under predicted and the larger sizes over predicted. The greater number of small particles observed in certain cloud regions may be due to the bimodality of the size spectra, which is especially true because radars are insensitive to the small particle mode. Similar algorithms (e.g., Matrosov et al. 1992, 1994) would also have similar problems when encountering such cloud volumes.

8.7. Concluding Remarks We have attempted here to overview the current expertise of a variety of modern remote sensing systems to infer the microphysical, macrophysical, and radiative properties of cirrus clouds. There is little doubt that, in combination with complementary satellite, aircraft, and modeling approaches, ground-based remote sensors will continue to significantly advance our comprehension of the effects of cirrus clouds on climate. Indeed, the relative ease and moderate expense of such ground-based remote sensing programs promises a dual role: a steady progression of basic research findings of important cirrus cloud properties derived from the case study approach, and an availability of climatologically

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representative data sets of crucial importance to the improvement and validation of satellite and global circulation model results. As for our current state of knowledge, the retrieved microphysical and radiative properties from the cirrus cloud case study in section 8.6 have yielded a range of results according to the method used. Rather than asserting at this time which approach is the most correct, we instead simply state that such intercomparisons illustrate the need for the refinement of cirrus cloud retrieval algorithms. We also need to access the degrees of uncertainty in derived data quantities that can be tolerated for radiative transfer and climate research. No doubt our current capabilities for deriving the heights of cirrus cloud boundaries to the tens-of-meter scale is more than adequate, but what are the radiative consequences of a twofold uncertainty in optical depth, as in figure 8.9a, for example? At the same time, the users of retrieved data quantities, especially if they are routinely generated without rigorous data quality controls, should be cautioned that a variety of remote sensor maintenance and calibration issues can affect sensor performance and data reliability. In addition, there is always the danger that the algorithm is flawed or inappropriately applied. Terminology is crucially important in view of basic remote sensor limitations. For example, it is vital that a proper terminology be used to characterize the cloud boundary heights detected by lidar and radar systems. If there is the possibility that a particular lidar measurement has been unable to detect the actual cloud top, then terms such as "apparent" or "attenuated" cirrus cloud top height should be used. For radar, it is probably always wise to use the term "radar cloud top" height because cirrus cloud-top particles are generally the smallest and the hardest to detect at radar frequencies (Sassen and Khvorostyanov 1998). It is wise to become familiar with the device and the algorithm before blindly accepting the data products. Finally, we anticipate that incorporation of advancing microwave radar and laser spectroscopic technologies will further stimulate the application of active remote sensors for cirrus cloud research, both from the ground and from orbiting platforms. We are particularly encouraged by plans to deploy lidar and millimeter-wave radar systems on satellites. With this view from space, our comprehension of the properties of cirrus clouds on the global scale will increase dramatically. Acknowledgments Recent PARS remote sensing and cirrus cloud algorithm research has been funded by National Science Foundation grant ATM-9528287, National Aeronautics and Space Administration grants NAG-1-2083 and NAG-2-1106, and Department of Energy grants DE-FG0394ER61747, DE-FG02-90ER61071, and contract 350153-AQ5 from the Atmospheric Radiation Measurement program. We thank our students and staff, particularly J. M. Barnett, Z. Wang, and J. Shin, for their contributions. References Ansmann, A., U. Wandinger, M. Riebesell, C. Weitkamp, and W. Michaelis, 1992. Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar. Appl. Opt., 31,7113-7131.

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Atlas, D., S.Y. Matrosov, AJ. Heymsfield, M.-D. Chou, and D.B. Wolf, 1995. Radar and radiation properties of ice clouds. /. Appl. Meteor., 34,2329-2345. Battan, L.J., 1973. Radar Observation of the Atmosphere. University of Chicago Press, Chicago. Carswell, A.I., 1981. Laser measurements in clouds. In Clouds: Their Formation, Optical Properties and EffectsTt (P. Hobbs and A. Deepak, eds.). Academic Press, pp. 363-406. Clothiaux, E.E., G.G. Mace,T.P. Ackerman, T.J. Kane, J.D. Spinhirne, and V.S. Scott, 1998. An automated algorithm for detection of hydrometeor returns in micropulse lidar data. J. Atmos. Oceanic Technol., 15,1035-1042. Clothiaux, E.E., M.A. Miller, B.A. Albrecht, T.P. Ackerman, J. Verlinde, D.M. Babb, R.M. Peters, and W.J. Syrett, 1995. An evaluation of a 94-GHz radar for remote sensing of cloud properties. /. Atmos. Oceanic Technol., 12,201-229. Cox, S.K., D.S. McDougal, D.A. Randall, and R.A. Schiffer, 1987. FIRE-The First ISCCP Regional Experiment. Bull. Amer. Meteor, Soc., 13,114-118. Davis, P.A., 1969. The analysis of lidar signatures of cirrus clouds. Appl. Opt., 8,2099-2102. Del Guasta, M.D., 1998. Errors in the retrieval of thin-cloud optical parameters obtained with a two-boundary algorithm. Appl. Opt., 37,5522-5540. Del Guasta, M.D., M. Morandi, L. Stefanutti, J. Brechet, and J. Piquad, 1993. One year of cloud lidar data from Dumont D'Urville (Antarctica). I. General overview of geometrical and optical properties. / Geophys. Res., 98,18575-18587. Doviak, J.D., and D.S. Zrnic, 1993. Doppler Radar and Weather Observations, 2nd ed. Academic Press, San Diego, CA. Dowling, D.R., and L.F. Radke, 1990. A summary of the physical properties of cirrus clouds. /. Appl Meteor., 29, 970-978. Eberhard, W.L., 1992. Ice-cloud depolarization of backscatter for CO2 and other infrared lidars. Appl Opt., 31, 6485-6490. Fernald, F.G., 1984. Analysis of atmospheric lidar observations: some comments. Appl. Opt., 23,652-654. Fernald, EG., B.M. Herman, and J.A. Reagan, 1972. Determination of aerosol height distributions by lidar. /. Appl. Meteor., 11, 482-489. Fu, Q., and K.N. Liou, 1993. Parameterization of the radiative properties of cirrus clouds. /. Atmos. ScL, 50, 2008-2025. Goldsmith, J.E.M., F.H. Blair, S.E. Bisson, and D.D. Turner, 1998. Turn-key Raman lidar for profiling atmospheric water vapor, clouds, and aerosols. Appl. Opt., 37,4979-4989. Grund, C.J., and E.W. Eloranta, 1990. The 27-28 October 1986 FIRE IFO cirrus case study: Cloud optical properties determined by high spectral resolution lidar. Mon. Wea. Rev., 118,2344-2355. Intrieri, J.M., G.L. Stephens, W.L. Eberhard, and T. Uttal, 1993. A method for determination cirrus cloud particle size using lidar and radar backscatter technique. /. Appl. Meteor., 32,1074-1082. Kinne, S., T.P. Ackerman, AJ. Heymsfield, F.P.J. Valero, K. Sassen, and J.D. Spinhirne, 1992. Cirrus microphysics and radiative transfer: Cloud field study on 28 October 1986. Mon. Wea. Rev., 120, 661-684. Klett, J.D., 1981. Stable analytical inversion solution for processing lidar returns. Appl. Opt., 20,211-220. Klett, J.D., 1985. Lidar inversion with variable backscatter/extinction ratios. Appl. Opt.,24, 1638-1643. Kosarev, A.L., and I.P. Mazin, 1991. An empirical model of the physical structure of upper layer clouds. Atmos. Res., 26,213-228. Liao, L., and K. Sassen, 1994. Investigation of relationships between Ka-band radar reflectivity and ice and liquid water contents. Atmos. Res., 34,231-248.

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Liou, K.N., 1986. Influence of cirrus clouds on weather and climate processes: A global perspective. Mon. Wea. Rev., 114,1167-1199. Liou, K.N., 1992. Radiation and Cloud Processes in the Atmosphere: Theory, Observation, and Modeling. Oxford University Press, New York. Long, C.N., 1995. Surface radiative energy budget and cloud forcing: Results from TOGA COARE and techniques for identifying and calculating clear sky irradiance. PhD thesis, Pennsylvania State University, State College. Mace, G.G., T.P. Ackerman, P. Minnis, and D.F. Young, 1998a. Cirrus layer microphysical properties derived from surface-based millimeter radar and infrared interferometer data. /. Geophys. Res., 103,23207-23216. Mace, G.G., K. Sassen, S. Kinne, and T.P. Ackerman, 1998b. An examination of cirrus cloud characteristics using data from millimeter radar and lidar: The 24 April SUCCESS case study. Geophys. Res. Lett., 25,1133-1136. Matrosov, S.Y., B.W. Orr, R.A. Kropfli, and J.B. Snider, 1994. Retrieval of vertical profiles of cirrus cloud microphysical parameters from Doppler radar and infrared radiometer measurements. /. Appl. Meteor., 33,617-626. Matrosov, S.Y., R.F. Reinking, R.A. Kropfli, and B.W. Bartrom, 1996. Estimation of ice hydrometeor types and shapes from radar polarization measurements. /. Atmos. Oceanic Technol, 13, 85-96. Matrosov, S.Y.,T. Uttal, J.B. Snider, and R.A. Kropfli, 1992. Estimation of ice cloud parameters from ground-based infrared radiometer and radar measurement. J. Geophys. Res., 97,11567-11574. Moran, K.P., B.E. Mariner, M.J. Post, R.A. Kropfli, D.C. Welsh, and K.B. Widener, 1998. An unattended cloud-profiling radar for use in climate research. Bull. Amer. Meteor. Soc., 79, 443-455. Pal, S.R., A.I. Carswell, I. Gordon, and A. Fong, 1995. Lidar-derived cloud properties obtained during the ECLIPS program. / Appl. Meteor., 34,2388-2399. Pal, S.R., W. Steinbrecht, and A.I. Carswell, 1992. Automated method for lidar determination of cloud base height and vertical extent. Appl. Opt., 34,1488-1494. Platt, C.M.R., 1973. Lidar and radiometric observations of cirrus clouds. /. Atmos. Sci., 30, 1991-1204. Platt, C.M.R., 1979. Remote sensing of high clouds. I: Visible and infrared optical properties from lidar and radiometer measurements. J. Appl. Meteor., 18,1130-1143. Platt, C.M.R., S.A. Young, A.I. Carswell, S.R. Pal, M.P. McCormick, D.M. Winker, M. DelGuasta, L. Stefanutti, W.L. Eberhard, M. Hardesty, P.H. Flamant, R. Valentine, B. Forgan, G.G. Gmimestad, H. Jager, S.S. Khmelevstov, I. Kolev, B. Kaprieolev, D. Lu, K. Sassen, VS. Shamanaev, O. Uchina, Y. Mizuno, U. Wandinger, C. Weitkamp, A. Ansmann, and C. Woldridge, 1994. The experimental cloud lidar pilot study (ECLIPS) for cloud-radiation research. Bull. Amer. Meteor. Soc., 75,1635-1654. Platt, C.M.R., S.A. Young, P.J. Manson, G.R. Patterson, S.C. Marsden, R.T. Austin, and J. Churnside, 1998. The optical properties of equatorial cirrus from observations in the ARM pilot radiation observation experiment. /. Atmos. Sci., 55,1977-1996. Raschke, E.J., J. Schmetz, J. Heintenberg, R. Kandel, and R.W. Saunders, 1990. The International Cirrus Experiment (ICE)-A joint European effort. ESA J., 14, 193199. Sassen, K., 1984. Deep orographic cloud structure and composition derived from comprehensive remote sensing measurements. /. Climat. Appl. Meteor., 23,568-583. Sassen, K., 1991. The polarization lidar technique for cloud research: A review and current assessment. Bull. Amer. Meteor. Soc., 72,1848-1866. Sassen, K., 1994. Advances in polarization diversity lidar for cloud remote sensing. Proc. IEEE., 82,1907-1914.

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Sassen, K., 1997. Contrail-cirrus and their potential for regional climate change. Bull. Amer. Meteor. Soc., 78,1885-1903. Sassen, K., 2000. The lidar backscatter depolarization technique for cloud and aerosol research. In Light Scattering by Nonspherical Particles: Theory, Measurements, and Geophysical Applications, (M.L. Mischenko, J.W. Hovenier, and L.D. Travis, eds.). Academic Press, New York pp. 393^16. Sassen, K., and B.S. Cho, 1992. Subvisual-thin cirrus lidar dataset for satellite verification and climatological research. J. Appl. Meteor., 31,1275-1285. Sassen, K., M.K. Griffin, and G.C. Dodd, 1989a. Optical scattering and microphysical properties of subvisual cirrus clouds, and climatic implications. /. Appl. Meteor., 28, 91-98. Sassen, K., C.J. Grund, ID. Spinhirne, J.M. Alvarez, and M.J. Hardesty, 1990. The 27-28 October 1986 FIRE IFO cirrus case study: A five lidar overview of cloud structure and evolution. Mon. Wea. Rev., 118,2288-2312. Sassen, K., and V.I. Khvorostyanov, 1998. Radar probing of cirrus and contrails: Insights from 2D model simulations. Geophys. Res. Lett., 25, 975-978. Sassen, K., and L. Liao, 1996. Estimation of cloud content by W-band radar. /. Appl. Meteor., 35, 932-938. Sassen, K., G.G. Mace, J. Hallett, and M.R. Poellot, 1998. Corona-producing ice clouds: A case study of a cold cirrus layer. Appl. Opt., 37,1477-1485. Sassen, K., D. O'C. Starr, and T. Uttal, 1989b. Mesoscale and microscale structure of cirrus clouds: Three case studies. J. Atmos. Sci.,46,371-396. Sauvage, L., H. Chepfer, V. Trouillet, P.H. Flamant, G. Brogniez, J. Pelon, and F. Albers, 1999. Remote sensing of cirrus radiative parameters during EUCREX'94. Case study of 17 April 1994. Part I: Observations. Mon. Wea. Rev., 127,486-503. Schneider, T.L., and G.L. Stephens, 1995. Theoretical aspects of modeling backscattering by cirrus particles at millimeter wavelengths. /. Atmos. Sci., 52,4367^385. Schotland, R.M., K. Sassen, and R.J. Stone, 1971. Observations by lidar of linear depolarization ratios by hydrometeors. /. Appl. Meteor., 10,1011-1017. Sekelsky, S.M., W.L. Ecklund, J.M. Firda, K.S. Gage, and R.E. Mclntosh, 1999. Particle size estimation in ice-phase clouds using multifrequency radar reflectivity measurements at 95, 33, and 2.8 GHz. /. Appl. Meteor., 38, 5-28. Shiobara, M., and S. Asano, 1994. Estimation of cirrus optical thickness from sun photometer measurements. /. Appl. Meteor., 33, 672-681. Smith, W.L., X.L. Ma, S.A. Ackerman, H.E. Revercomb, and R.O. Knuteson, 1993. Remote sensing cloud properties from high spectral resolution infrared observations. /. Atmos. Sci., 50,1708-1720. Spinhirne, J.D., 1993. Micro pulse lidar. IEEE Trans., 31, 48-55. Stokes, G.M., and S.E. Schwartz, 1994. The Atmospheric Radiation Measurement (ARM) program: Programmatic background and design of the cloud and radiation testbed. Bull. Amer. Meteor. Soc., 75,1201-1221. Takano, Y, and K.N. Liou, 1989. Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals. /. Atmos. Sci., 46, 3-19. Toon, O.B., C.P. McKay, T.P. Ackerman, and K. Santhanam, 1989. Rapid calculation of radiative heating rates and photodissociation rates in inhomogeneous multiple scattering atmospheres. /. Geophys. Res., 94,16287-16301. Young, S. A., 1995. Analysis of lidar backscatter profiles in optically thin clouds. Appl. Opt., 34,7019-7031.

9

Molecular-Backscatter Lidar Profiling of the Volume-Scattering Coefficient in Cirrus

ALBERT ANSMANN

9.1. Background

Backscatter and polarization lidars have already been used extensively to investigate ice clouds (see chapters 2 and 10). A severe limitation is that trustworthy values of the volume-scattering coefficient, one of the most important parameters in the description of the impact of cirrus on climate, cannot be derived from data taken with these lidars. Even the retrieved cirrus backscattercoefficient profile is often questionable. A discussion of achievements and limitations of the lidar method can be found in the literature (e.g., Fernald et al. 1972; Klett 1981; Fernald 1984; Klett 1985; Sasano et al. 1985; Bissonnette 1986; Ansmann et al. 1992b; Kovalev 1995). The procedure, with all its subsequent modifications and improvements, suffers from the fact that two physical quantities, the particle backscatter coefficient and the particle extinction coefficient, must be determined from only one lidar signal. The uncertainties in the estimated optical parameters are especially large in cirrus, in which the relationship between particle extinction and backscattering can vary strongly in space and time. The situation improved significantly when the first molecular (Raman) backscatter lidar experiments demonstrated that accurate extinction profiling throughout the entire troposphere is possible (Ansmann et al. 1990,1992b). After the Pinatubo eruption, it was shown that even at stratospheric heights profiles of the volume-scattering coefficient can easily be obtained with a Raman lidar (Ansmann et al. 1991,1993a, 1997; Ferrare et al. 1992; Gross et al. 1995; Donavan und Carswell 1997). 197

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Two types of molecular-backscatter lidars for extinction measurements are available. The Raman lidar measures lidar return signals elastically backscattered by air molecules and particles and inelastically (Raman) backscattered by nitrogen and/or oxygen molecules (Cooney et al. 1969; Melfi 1972; Ansmann et al. 1992a; Whiteman et al. 1992; Reichardt et al. 1996). Interference-filter polychromators and double-grating monochromators (Arshinov et al. 1983; Wandinger et al. 1998) are used to separate the aerosol signal from the vibrational-rotational or pure rotational Raman signals, to reduce the sky background radiation, and, for the Raman channels, to block the strong elastic-backscatter radiation at the laser wavelength. The suppression has to be better than 10~8. The second type of a molecular-backscatter lidar is the High Spectral Resolution Lidar (HSRL). This lidar measures the spectral distribution of light elastically backscattered by particles and air molecules (Shipley et al. 1983; Sroga et al. 1983; Grund and Eloranta 1990,1991; She et al. 1992; Piironen and Eloranta 1994). The spectral width of Rayleigh-backscattered photons is increased due to Doppler shifts caused by the thermal motion of the molecules. The thermal motion of aerosol and cloud particles is much slower, and the backscatter spectrum is nearly unchanged. A pure molecular signal is measured by blocking the narrow aerosol peak (e.g., by use of an atomic vapor filter). A second channel detects the total backscatter. The molecular-backscatter coefficient can easily be calculated from the molecular density profile, which in turn is often sufficiently well known from the assumption of standard atmospheric temperature and pressure conditions. Thus, from the magnitude of the measured molecular signal relative to the calculated one, one may unambiguously determine the atmospheric extinction profile. Furthermore, the ratio of the aerosol return to the molecular return provides a direct measurement of the particle backscatter coefficient, which is also not possible with a simple one-channel aerosol backscatter lidar. Whereas the Rayleigh lidar is operational at day and night, the Raman lidar is used for nighttime cirrus observations only. The strength of Raman signals is a factor of 20 (rotational Raman lines) to 500 (vibrational-rotational Raman lines) weaker than the one of Rayleigh signals. However, by applying narrow bandpass filters or a doublegrating setup with a bandwidth of less than 0.2 nm, Raman lidar observations of cirrus are even possible at daytime, as our latest experience shows. Ground-based solar-blind lidars operating at laser wavelengths well below 300 nm are not appropriate for measurements in the upper troposphere because of strong absorption of laser radiation by ozone. In this chapter the basics of the common aerosol-backscatter lidar and the molecular-backscatter lidar techniques concerning the retrieval of cirrus backscatter and extinction properties are summarized and critically reviewed. The theoretical background (section 9.2) of both methods is described. In section 9.3, simulation results are presented which clearly demonstrate the unreliability of results obtained with common backscatter lidars. In contrast, cirrus observations taken with a Raman lidar are presented in section 9.4 to illustrate the usefulness of this technique.

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Method

9.2.1. Extinction-Coefficient Retrieval from Aerosol-Backscatter Lidar Signals The lidar equation for lidar return signals elastically backscattered by air molecules and aerosol particles, in its simplest form, can be written as:

where PR is the signal due to Rayleigh and particle scattering received from height R, P0 is the transmitted laser pulse energy, and $(R) (in km"1 sr"1) and a(R) (in knr1) are the coefficients for 180° backscatter and extinction, respectively. For the sake of simplicity, lidar parameters describing the efficiencies of the optical and detection units and the laser-beam-receiver-field-of-view overlap function are set to 1. Backscattering and extinction is caused by particles (index P) and molecules (index M):

Absorption effects can be neglected at typical laser wavelengths (e.g., 355 nm, 532nm, or 1064nm). The fundamental formalism used to determine the particle extinction and backscatter coefficients from elastic-backscatter signals is the Klett method. The technique, which originates from Hitschfeld and Bordan's radar application (Hitschfeld and Bordan 1954), is often referred to as the Klett method because Klett (1981) reformulated the formalism to make it convenient for the analysis of lidar observations. In this technique, the particle extinction and/or backscatter coefficient is obtained by solving a Bernoulli equation that is derived from the lidar equation 1 under the assumption of a constant relationship between particle extinction and backscattering:

The solution of the Bernoulli differential equation in terms of the backscatter coefficient can then be written as follows (Fernald 1984):

with

and

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SM = (871/3) sr is the Rayleigh extinction-to-backscattering ratio. The particle extinction coefficient is related to the solution for the backscatter coefficient by

According to equations 5 and 7, a reference or boundary value for the particle backscatter coefficient, {3P(-ft0)> at the reference height R0 has to be estimated, in addition to the lidar ratio SP. Fortunately, in the case of cirrus profiling, the influence of this boundary value on the solution of equation 5 is small because most of the time air is very clean in the free troposphere above 5 km. (3P(,R0) <^ (3M(^o) can be assumed at wavelengths <532nm outside cirrus without introducing large errors. As mentioned, the height profile of the Rayleigh backscattering (3M(^) needed in equations 5-7 to separate Rayleigh and particle contributions is usually determined from a standard-atmosphere model or, if available, from actual radiosonde data of pressure and temperature. Some further information must be added to understand the simulation results presented in the next section. Equation 5 can in principle be integrated by starting from the reference height, R0, which may be either the near end (R > R0, forward integration) or the remote end of the measuring range (R < R0, backward integration). Numerical stability, however, is only given in the backward integration case (Klett 1981). As shown in Ansmann et al. (1992b), an appropriate backscatter-weighted mean cirrus lidar ratio together with the cirrus optical depth may be determined by applying both forward and backward integration, if the backscatter reference values at heights below and above the cloud can be estimated properly. Such a situation is usually given in periods without significant amounts of volcanic aerosols in the stratosphere. The most critical input parameter in the Klett method is the cirrus lidar ratio. Depending on the ice-crystal characteristics (e.g., size, shape, orientation in space), the lidar ratio can vary over more than two orders of magnitude within a few meters. The extinction-to-backscatter ratio is about 5 and 15 sr for relatively small solid needles, plates, and columns (Takano and Liou 1989; Macke 1993; Macke et al. 1996) and can be as high as about 150 sr for hollow crystals (Macke 1993; Liou and Takano 1994; Takano and Liou 1995). In the case of specular reflection caused by falling, horizontally oriented ice crystals, the lidar ratio is close to 1 sr (Platt 1978; Macke et al. 1996). Such a situation can often be observed with a vertically pointing lidar (Ansmann et al. 1992b). Thus, the assumption of a range-independent lidar ratio (equation 4) is unrealistic. However, an alternative approach to the problem is not available. Because of the lack of information about the actual vertical distribution of the microphysical properties, any assumption about the range dependence of the cirrus lidar ratio is as doubtful as the one of equation 4. From these facts one must conclude that use of the Klett method to retrieve cirrus extinction profiles is senseless. This will be further emphasized in section 9.3.

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9.2.2. Extinction-Coefficient Determination from Molecular-Backscatter Lidar Signals The determination of the particle extinction coefficient from molecular-backscatter signals is rather straightforward. Lidar-ratio assumptions are not needed here, neither in the case of the extinction determination, nor in the case of the backscatter-coefficient retrieval. In contrast to the Klett method, these two scattering parameters can be derived independently of one another from the set of the aerosol and the molecular signals. The lidar ratio is directly measured in this way (Ansmann et al. 1992b). The advantage of the molecular-backscatter method is obvious from the respective lidar equation, which has the form

The coefficient (3Ra denotes Rayleigh or Raman backscattering. Particle backscattering does not appear in equation 9. The only particle-scattering effect on the signal strength is attenuation. a(R, AO) describes the extinction on the way up to the backscatter region; a(R, ARa) describes the extinction on the way back to the lidar. For the Rayleigh or the rotational Raman case ARa = AO can be used. However, in the case of a vibrational-rotational Raman signal, the shift of the wavelength from AO before to ARa after the scattering process must be considered. If, for example, an Nd: YAG laser wavelength of 532 nm is transmitted, the first Stokes vibration-rotation branch of nitrogen is centered at ARa = 607 nm. The molecular backscatter coefficient is calculated from the molecular number density, WRa, which is the nitrogen or oxygen number density for the Raman case and the air-molecule number density for the Rayleigh case, and the differential cross-section doRa/dQ(7i, AO) for the scattering process (Raman or Rayleigh) at the laser wavelength AO and the scattering angle 71:

is identical to |3M in equation 2, if equations 9 and 10 describe a Rayleigh signal. Starting from equations 9 and 10, the following equation for the particle extinction coefficient at wavelength AO is obtained (Ansmann et al. 1990):

The wavelength dependence of the extinction coefficient is described with the parameter k by the relation ctp(Ao)/aP(ARa) = (ARa/Ao)fc. k is close to zero for icecrystal scattering. With k = 0, the denominator in equation 11 becomes 2. According to equation 11, the particle extinction coefficient is obtained from the profile of the range-corrected signal P(R, ARa)/?2 after the correction of the decrease of air density with height [d/dR(\nNKa(R))] and Rayleigh extinction [OCM(^, AO), aM(R, ARa)]. Systematic errors caused by atmospheric input parameters can be

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neglected when aerosol layers or clouds in the upper troposphere are monitored (Ansmann et al. 1992b). The main error source is signal noise. As mentioned, in addition to the extinction coefficient, the particle backscatter coefficient can be calculated from the ratio of the aerosol (particle plus Rayleigh) backscatter signal to the molecular backscatter signal (Cooney et al. 1969; Melfi 1972; Ansmann et al. 1992b). Because signal ratios are used, atmospheric transmission effects on each signal are cancelled out so that the unattenuated (true) backscatter coeffcient is determined. When applying the Klett method the unattenuated backscatter coefficient can only be obtained if the transmission effect is properly corrected for (i.e., if the particle lidar ratio is properly estimated). 9.3. Simulation

To investigate the influence of systematic and statistical errors of vertical lidar observations, simulation studies are helpful. Because of the lack of simultaneous airborne measurements, model calculations often are the only way to analyze the limitations of lidar applications in detail. In figure 9.1, the simulated optical properties of a cirrus cloud cover between 8 and llkm are shown. The corresponding aerosol and N2 Raman signals, calculated with equations 1 and 9 from these cirrus-scattering profiles, are given in figure 9.2. Standard atmospheric conditions are assumed for Rayleigh scattering. For the sake of simplicity, a rangeindependent cirrus extinction coefficient is assumed. The backscatter coefficient, in contrast, varies strongly. Thin layers with a rather low particle extinctionto-backscatter ratio of 2 sr indicate regions with specular reflection. According to model calulations of cirrus scattering phase functions, the chosen lidar-ratio profile in figure 9.1 may represent a cloud with small hexagonal particles in the upper part (generating cells, lidar ratio around 10sr), growing crystals, which become complex in shape and partly hollow with decreasing height, (lidar ratio 30-80 sr) in the central part, and, again, small crystals caused by evaporation close to the cloud base height.

Figure 9.1. Simulated cirrus profiles of particle extinction (dotted curve) and backscatter coefficients (solid curve) at 532 nm and extinction-tobackscatter ratio. The profiles are used to calculate the lidar returns in figure 9.2.

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Figure 9.2. Simulated aerosol (Rayleigh + particle) backscatter signal (dotted line) at 532 nm and molecular (N2 Raman) backscatter signal at 607nm (solid line). Signals are calculated assuming standard atmospheric conditions for Rayleigh scattering and cirrus optical properties in figure 9.1. Signals are calculated for a laser pulse power of 300ml Common Raman lidar system parameters are assumed, 2% of the backscattered photons collected with a 1-m telescope are detected, 10,000 laser shots are averaged corresponding to a signal averaging time of 330s at a laser pulse repetition rate of 30 Hz. Range resolution is 15 m. Shot noise according to Poisson statistics is added to the signals. The particle extinction coefficients in the right-hand panels are calculated from elasticbackscatter signals (dotted line) and from the N2 Raman signals (solid line). The Raman signal profile is smoothed with a window length of 150m.

The solutions for the extinction coefficient calulated from the aerosol signals with the Klett method (equations 5-8) and from the molecular signals with equation 11 are shown in figure 9.2 as well (right-hand panel). Whereas the uncertainties in the molecular-backscatter lidar solutions are dominated by signal noise, the Klett solutions are mainly affected by systematic errors due to the assumed range-independent lidar ratio. Backward and forward integration modes of the Klett technique have been applied with correct reference backscatter values at 7850m (forward integration) and 11,250m height (backward integration). Under these favorable conditions the backscatter-weighted mean lidar ratio (here SP - 6sr), together with the optical depth of the cirrus layer, can be determined. Nevertheless, even in this most optimistic case the extinction profile is rather useless. If layers with specular reflection are absent, as is the case for a lidar operating at an elevation angle of, say, 80°, and lidar ratios are replaced by, say, 10 sr (8400 to 8800m) and 60 sr (9800 to 10,000m), the deviations are approximately reduced by a factor of 2. Klett solutions are then between 0.05km"1 and 0.5 km'1. However, caution must be exercised in the data evaluation if aerosol layers reach up to the cirrus level or volcanic stratospheric aerosols are present above the cloud layer so that reliable estimates for the boundary values are not available. In this case the Klett method fails completely. In view of all these shortcomings, the importance of the molecularbackscatter lidar method for atmospheric extinction observations becomes obvious. As mentioned, only the simulated signal noise affects the determined profile. In figure 9.2, this uncertainty can be further reduced by taking a larger

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signal-smoothing length. By increasing the smoothing window from 150m to 300 m, the error (standard deviation) decreases by 23/2 (Ansmann et al. 1992b) (i.e., approximately by a factor of 3). In real measurements, spatial and temporal signal averaging can introduce a significant systematic error (underestimation) of the mean extinction properties when the extinction coefficient varies strongly between 0 and >1 km"1 (Ansmann et al. 1992b). By averaging lidar return signals, transmission rather than extinction properties are averaged. Thus, only the extinction coefficients related to the mean cirrus transmission profile can be determined. The underestimation is negligible if the scattering properties are nearly constant, and is less than about 20% with respect to the mean extinction profile if the cirrus scattering coefficients are of the order of 0.5 km'1 or less and if these do not vary by more than 50%. Appropriate averaging periods and range cells can easily be determined from the highly resolved primary elastic-backscatter data. The averaging problem affects both the Klett and the Raman lidar solutions (Ansmann et al. 1992b). 9.4. Measurement

First routine cirrus profiling with a molecular-backscatter lidar was conducted during the International Cirrus Experiment 1989 (ICE 89; Ansmann et al. 1992b, 1993b). An example is shown in figure 9.3. At that time we used a powerful excimer laser transmitting pulses at 308 nm. Ozone absorption had to be corrected before equation 11 could be applied. A standard-atmosphere ozone profile was assumed in figure 9.3. The resulting influence on the extinction coef-

Figure 9.3. Cirrus extinction and backscatter coefficients and the corresponding extinction-to-backscatter ratio measured with a Raman lidar on September 20, 1989 during the International Cirrus Experiment 1989 (Ansmann et al. 1992b). Signal averaging time and signal-profile smoothing length are 9 min and 300 m, respectively. Laser wavelength is 308 nm. The dotted lines in the first two panels indicate Rayleigh extinction and backscattering profiles. Errors introduced by the uncertainty of ozone absorption (at 308 nm) on the lidar ratio are shown as dashed lines in the right-hand panel. The error bars indicate the standard deviation due to signal noise.

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ficient and the lidar ratio is, however, small, as can be seen in the lidar ratio plot. From our early Raman lidar observations, we got the strong feeling that backscatter and extinction properties of cirrus often have nothing to do with each other. Conclusions concerning the extinction profile cannot be drawn from the backscatter-coefficient profile. One of our latest cirrus measurements is given in figure 9.4. The state-of-theart lidar uses a powerful Nd: YAG laser, a 1-m telescope, and detects vibrationalrotational Raman signals at 387 nm (N2), 407 nm (H2O), and 607 nm (N2) with an interference-filter polychromator as well as pure rotational Raman signals between 529 and 533 nm (N2, O2) with a double-grating monochromator (Mattis et al. 1998; Wandinger et al. 1998). In addition to the molecular signals, elasticbackscatter lidar returns are measured at 355, 532 (parallel and cross-polarized components), and 1064nm. From the rotational Raman signals the temperature profile can be calculated; the ratio of the water-vapor and the nitrogen Raman signals yields the height profile of the water-vapor mixing ratio. In figure 9.4, the cirrus extinction coefficients at 355 and 532 nm determined from N2 Raman signal profiles at 387 and 607 nm, respectively, are shown together with the backscatter-coefficient profiles, derived from the aerosol-to-Raman signal profiles, and with the lidar-ratio profiles. To obtain extinction values at 532 nm throughout the geometrically and optically very thick ice cloud layer (optical depth of 1.6 to 1.8), 60,000 laser shots, equivalent to 30min, had to be averaged, and the resulting signal profiles had to be smoothed further with window lengths of 300 (<5300m), 600 (5300-7500m), and 1200m (>7500m). In this way, the relative statistical error is generally below 25% for the extinction and lidar-ratio values in figure 9.4. The backscatter coefficients are determined from signal-ratio profiles smoothed with 300 and 600m for heights below and above 8000m, respectively. Because the lidar was optimized for 532 nm at that time only, a complete extinction profile at 355 nm could not be obtained. The analysis of the primary lidar data indicated a stable cloud deck with nearly constant scattering conditions during the 30-min period shown. In such a case, the above-mentioned

Figure 9.4. Cirrus measurement with a state-of-the-art Raman lidar. The observation was taken on November 2,1998. Signal averaging time is 30min. Signal profiles are smoothed with window lengths between 300 and 600m (backscatter) and 300 and 1200m (extinction, lidar ratio). The error bars indicate the standard deviation due to signal noise.

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signal-averaging effect is believed to cause an underestimation of the mean extinction coefficients of <10%. As can be seen, the backscatter coefficients for the two wavelengths are equal in the lower part of the cloud and deviate from each other in the main cloud deck. In contrast, the extinction values were larger at 355 nm in the lower part of the cloud and equal at both wavelengths in the upper part. The reason for these differences is not clear. In the case of a small detection wavelength compared to the mean particle size, one would expect a wavelength-independent scattering behavior. The observed effect of decreasing extinction with wavelength in the lower part of the cloud may happen if the diameter of the evaporating particles is close to the laser wavelength. Alignment problems probably also contributed to the observed differences. The two beams may have pointed to slightly different directions and may have had different divergences. This can result in significantly different sampling volumes. A beam expander is used to reduce the divergence of each beam to about O.lmrad. At cloud base, the diameter of each beam is less than 0.2m. The overlap effect must always be taken into account when multibeam lidar observations of typically nonuniform clouds are discussed. Finally, multiple scattering is a general problem in the case of cirrus observations with lidar and has been extensively analyzed for elastically backscattered light since the early 1970s. Wandinger (1998) extended this work to molecularbackscatter lidar observations. Figure 9.5 summarizes the main findings. In cirrus, photons forward scattered by large ice crystals can remain in the receiver field of view and can be backscattered to the receiver. As a consequence, the apparent scattering coefficients (directly determined from the signal profiles) are smaller than the single-scattering values to be determined. The larger the particles, the more photons are scattered into the forward direction and the larger

Figure 9.5. Cirrus optical properties measured on June 1, 1992 (upper panels) and corresponding errors due to multiple scattering (lower panels; Wandinger 1998). Multiple scattering is ignored (solid curves) and corrected by use of scattering phase functions after Takano and Jayaweera (1985) for relatively small hexagonal plates (45 |im width, 18um length; dotted curves) and larger hexagonal columns (45 (im width, 112 um length; dashed curves).

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the multiple-scattering effect. The influence mainly depends on the distance of the lidar from the cloud, the cirrus optical depth, the size of the crystals, the laser beam divergence, and the receiver field of view (RFOV). Figure 9.5 shows a Raman lidar measurement together with calculations indicating the strength of the effect of multiple scattering. The beam divergence was O.lmrad and the RFOV was 0.4mrad in that experiment. Because the backscatter calculation is based on signal ratios, the effect is more or less cancelled out. The errors of the extinction coefficient and of the lidar ratio can be as high as 60% at the cloud base. The relative influence of multiple scattering decreases with increasing height (i.e., with increasing spread of the laser radiation or increasing effective beam divergence caused by light scattering). Another consequence is that the largest relative errors are expected in cases with subvisible or thin cirrus when the laser beam remains narrow throughout the cloud. Multiple scattering is not taken into account in figures 9.3 and 9.4. Thus the single-scattering coefficients (and the lidar ratios) may be about 20-50% larger than the apparent ones shown. After the correction of the effect in the way described in figure 9.5, the residual error is believed to be of the order of 10%. 9.5. Conclusion

The state-of-the-art lidar techniques for cirrus-scattering profiling have been reviewed. It has been shown that, in contrast to the widely used elasticbackscatter lidars, only molecular-backscatter lidars can provide reliable extinction profiles. Such observations are not only the basic requirement for a good characterization of cirrus transmission properties, but may also be used for a remote estimation of the ice-water content, which is proportional to the extinction coefficient multiplied by the surface-area-weighted mean or effective radius (size) of the ice crystals (Chylek 1978; Platt and Takashima 1987). However, a good estimate of the size parameter is needed here. The most important error sources are signal noise and systematic effects caused by multiple scattering and inappropriate signal averaging if cirrus extinction varies strongly during the averaging period. Keeping these influences in mind, the volume-scattering-coefficient profile in cirrus can be determined with a relative error of the order of 20-30%, a range resolution of 150-600m, and a temporal resolution of 5-30 min. Care must also be taken when comparing multibeam (multi-wavelength) observations. Slightly different beam directions and divergences can introduce significant differences in the solutions for the different wavelengths because of the small sampling volume. Laser-beam diameters are of the order of 0.1-0.2 m only if a beam expander is used. An optimum lidar for cirrus observations will be equipped with at least one molecular-backscatter channel in addition to two aerosol channels for the detection of parallel- and cross-polarized signal components. Although the advantage of a molecular-backscatter lidar is tremendous and well known in the lidar community, only a few systems are currently used for tropospheric aerosol and cloud measurements. In the case of the Raman lidar technique, which can easily be set up, this has to do with the fact that high-power lasers and relatively

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Cirrus

large telescopes are needed. A Raman lidar is much more expensive than a typical polarization lidar normally used in cirrus studies. However, assuming that high-quality extinction information is available, the simultaneous determination of height profiles of the depolarization ratio, the extinction and backscatter coefficients, and the lidar ratio yields a unique data set for a detailed study of cirrus scattering properties and may allow a much better description of the climate-relevant cirrus characteristics. In this context, a close link to the modeling community is demanded. Without accompanying simulations of cirrus-scattering properties with special emphasis on scattering angles between 0° and 5° and between 179° and 180° and for a large variety of hollow and solid crystals, a less ambiguous interpretation of the findings in terms of physical quantities seems to be impossible.

References

Ansmann, A., J. Bosenberg, G. Brogniez, S. Elouragini, P.H. Flamant, K. Klapheck, L. Menenger, H. Linne, W. Michaelis, M. Riebesell, C. Senff, P. Y. Thro, U. Wandinger, and C. Weitkamp, 1993b. Lidar network observations of cirrus morphological and scattering properties during the International Cirrus Experiment 1989: The 18 October 1989 case study and statistical analysis. /. Appl. Meteorol, 32,1608-1622. Ansmann, A., I. Mattis, U. Wandinger, F. Wagner, J. Reichardt, and T. Deshler, 1997. Evolution of the Pinatubo aerosol: Raman lidar observations of particle optical depth, effective radius, mass, and surface area over central Europe at 53.4° N. /. Atmos. ScL, 54,2630-2641. Ansmann, A., M. Riebesell, U. Wandinger, C. Weitkamp, E. Voss, W. Lahmann, and W. Michaelis, 1992a. Combined Raman elastic-backscatter lidar for vertical profiling of moisture, aerosol extinction, backscatter, and lidar ratio. Appl. Phys. B, 55,18-28. Ansmann, A., M. Riebesell, and C. Weitkamp, 1990. Measurements of atmospheric aerosol extinction profiles with a Raman lidar. Opt. Lett., 15, 746-748. Ansmann, A., U. Wandinger, M. Riebesell, C. Weitkamp, and W. Michaelis, 1992b. Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar. Appl. Opt., 31, 7113-7131. Ansmann, A., U. Wandinger, C. Schulze, C. Weitkamp, and W. Michaelis, 1991. Stratospheric aerosol measurements with a combined Raman elastic-backscatter lidar. in Proceedings, Optical Remote Sensing of the Atmosphere (Optical Society of America, ed.). OTUE17-1-OTUE17-3, OSA, Williamsburg, VA. Ansmann, A., U. Wandinger, and C. Weitkamp, 1993a. One-year observations of MountPinatubo aerosol with an advanced Raman lidar over Germany at 53.5° N. Geophys. Res. Lett., 20,711-714. Arshinov, Yu. F., S.M. Bobrovnikov, V.E. Zuev, and V.M. Mitev, 1983. Atmospheric temperature measurements using a pure rotational Raman lidar. Appl. Opt., 22, 2984-2990. Bissonnette, L.R., 1986. Sensitivity analysis of lidar inversion algorithm. Appl. Opt., 25, 2112-2125. Cooney, J.A., J. Orr, and C. Tomasetti, 1969. Measurements separating the gaseous and aerosol components of laser atmospheric backscatter. Nature, 224,1098-1099. Chylek, P., 1978. Extinction and liquid water content of fogs and clouds. J. Atmos. Sci., 35, 296-300.

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Donavan, D.P., and A.I. Carswell, 1997. Principal component analysis applied to multiwavelength lidar aerosol backscatter and extinction measurements. Appl. Opt., 36, 9406-9424. Fernald, EG., 1984. Analysis of atmospheric lidar observations: some comments. Appl. Opt., 23,652-653. Fernald, F.G., B.M. Herman, and J.A. Reagan, 1972. Determination of aerosol height distributions by lidar. /. Appl. Meteorol., 11,482-489. Ferrare, R.A., S.A. Mem, D.N. Whiteman, and K.D. Evans, 1992. Raman lidar measurements of Pinatubo aerosols over south-eastern Kansas during November-December 1991. Geophys. Res. Lett., 19,1599-1603. Gross, M.R., TJ. McGee, U.N. Singh, and P. Kimvilakani, 1995. Measurements of stratospheric aerosols with a combined elastic-Raman-backscatter lidar. Appl Opt., 34, 6915-6924. Grund, C.J., and E.W. Eloranta, 1990.The 27-28 October 1986 FIRE IFO cirrus case study: cloud optical properties determined by high spectral resolution lidar. Mon. Wea. Rev., 118,2344-2355. Grund, C.J., and E.W. Eloranta, 1991. The University of Wisconsin High Spectral Resolution Lidar. Opt. Eng., 30, 6-12. Hitschfeld, W, and J. Bordan, 1954. Errors inherent in the radar measurement of rainfall at attenuating wavelengths. J. Meteorol., 11,58-67. Klett, J.D., 1981. Stable analytical solution for processing lidar returns. Appl. Opt., 20, 211-220. Klett, J.D., 1985. Lidar inversion with variable backscatter/extinction ratios. Appl. Opt., 24, 1638-1643. Kovalev, V.A., 1995. Sensitivity of the lidar solution to errors of the aerosolbackscatter-toextinction ratio: influence of a monotonic change in the aerosol extinction coefficient. Appl. Opt., 34,3457-3462. Liou, K.N., and Y.Takano, 1994. Light scattering by nonspherical particles: Remote sensing and climatic implications. Atmos. Res., 31, 271-298. Macke, A., 1993. Scattering of light by polyhedral ice crystals. Appl. Opt., 32,2780-2788. Macke, A., J. Miiller, and E. Raschke, 1996. Single scattering properties of atmosphericice crystals. / Atmos. Sci., 53,2813-2825. Mattis, I., U. Wandinger, D. Miiller, A. Ansmann, and D. Althausen, 1998. Routine dualwavelength Raman lidar observations at Leipzig as part of an aerosol lidar network in Germany, in Proceedings of the 19th International Laser Radar Conference (U.N. Singh, S. Ismail, and G. Schwemmer, eds.). NASA/CP-1998-207671/PT1, National Aeronautics and Space Administration, Washington, DC, pp. 29-32. Melfi, S.H., 1972. Remote measurements of the atmosphere using Raman scattering. Appl. Opt., 11,1605-1610. Piironen, P., and E.W. Eloranta, 1994. Demonstration of a high spectral resolution lidar based on an iodine absorption filter. Opt. Lett., 19,234-236. Platt, C.M.R., 1978. Lidar backscatter from horizontal ice crystal plates. /. Appl. Meteorol, 17,482-488. Platt, C.M.R., and T. Takashima, 1987. Retrieval of water cloud properties from carbon dioxide lidar soundings. Appl. Opt., 26,1257-1263. Reichardt, J., U. Wandinger, M. Serwazi, and C. Weitkamp, 1996. Combined Raman lidar for aerosol, ozone, and moisture measurements. Opt. Eng., 5,1457-1465. Sasano, Y., E.V. Browell, and S. Ismail, 1985. Error caused by using a constant extinction/backscatter ratio in the lidar solution. Appl. Opt., 24,3929-3932. Shipley, S.T., D.H. Tracy, E.W. Eloranta, J.T. Trauger, J.T Sroga, F.L. Roesler, and J.A. Weinman, 1983. High spectral resolution lidar to measure optical scattering

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properties of atmospheric aerosols: 1: Theory and instrumentation. Appl. Opt., 22, 3717-3724. She, C.Y., R.J. Alvarez II, L.M. Caldwell, and D.A. Krueger, 1992. High-spectralresolution Rayleigh-Mie lidar measurement of aerosol and atmospheric profiles. Opt. Lett., 17,541-543. Sroga, J.T., E.W. Eloranta, S.T. Shipley, F.L. Roesler, and PJ. Tryon, 1983. High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 2: Calibration and data analysis. Appl. Opt., 22, 3725-3732. Takano, Y., and K. Jajaweera, 1985. Scattering phase matrix for hexagonal ice crystals computed from ray optics. Appl. Opt., 24,3254-3263. Takano, Y., and K.N. Liou, 1989. Solar radiative transfer in cirrus clouds. Part I: single scattering and optical properties of hexagonal ice crystals. /. Atmos. Sci., 46, 3-19. Takano, Y, and K.N. Liou, 1995. Radiative transfer in cirrus clouds. Part III: light scattering by irregular ice crystals. /. Atmos. Sci., 52, 818-837. Wandinger, U., 1998. Multiple-scattering influence on extinction- and backscattercoefficient measurements with Raman and high-spectral-resolution lidars. Appl. Opt., 37,417^27. Wandinger, U., I. Mattis, A. Ansmann, Y. Arshinov, S. Bobrovnikov, and I. Serikov, 1998. Tropospheric temperature profiling based on detection of Stokes and anti-Stokes rotational Raman lines at 532 nm. in Proceedings of the 19th International Laser Radar Conference (UN. Singh, S. Ismail, and G. Schwemmer, eds.). NASA/CP-1998207671/PT1, National Aeronautics and Space Administration, Washington, DC, pp. 297-299. Whiteman, D.N., S.H. Melfi, and R.A. Ferrare, 1992. Raman lidar system for the measurement of water vapor and aerosols in the Earth's atmosphere. Appl. Opt., 31, 3068-3082.

10

Structural and Optical Properties of Cirrus from LIRAD-type Observations C. M A R T I N R. PLATT

The problem of cirrus clouds, their formation and interactions with solar and infrared (IR) radiation, has been studied over the past two or three decades. Considerable progress has been made over that time through ground-based, satellite, and aircraft observations. This has led to the implementation of fairly sophisticated parameterizations in global circulation models (GCMs; e.g., Rotstayn 1997). However, many problems concerning cirrus properties and their formation remain (e.g., Lee and Somerville 1996; Lohmann and Roeckner 1996). The lidar/radiometer (LIRAD) method was originally formulated to obtain cirrus radiative properties from the ground, with the long-range aim of improving models of the earth's climate (Platt and Gambling 1971; Platt 1973). The method enables many repeated observations easily, once the initial equipment is assembled. The method is essentially a way of obtaining cloud height and depth (from which cloud temperature can be obtained from radiosonde data) simultaneously with a measurement of infrared radiance. This is accomplished in the atmospheric window (8-13 um), where water vapor or other gaseous absorption is small enough to allow measurement of cirrus cloud radiance without too much error. A cirrus IR emittance can then be calculated, given the cloud depth and temperature. This simple scheme can reveal other facets of the cirrus cloud, such as information on cloud microphysics and particle size. A second lidar channel for detecting depolarized radiation gives information on cloud phase, and even cloud ice crystal habit in the case of hexagonal plate crystals. This chapter describes LIRAD measurements taken over many years in both mid-latitude and tropical cirrus. The observations described by Platt (1973), 21 I

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Platt and Dilley (1981), and Platt et al. (1987,1998) are then compared to some LIRAD-type observations made by other workers in the field.

I O.I. The LIRAD Technique

10.1.1. Lidar Experimental and Analytical Methods The LIRAD method uses a calibrated lidar and narrow-beam spectral infrared radiometer placed in close proximity, with both axes aligned accurately to observe the same volume of cloud. The secret of the method is to use compatible field apertures in both instruments and to use a sensitive radiometer that is fast enough to record the rapid fluctuations in cloud emission that can occur (e.g., Platt and Dilley 1981). The lidar is calibrated carefully against a known molecular atmosphere. Typical lidar and radiometer characteristics are shown in table 10.1. Platt et al. (1998) also used a microwave radiometer that measures the integrated water vapor path, leading to considerable improvements in accounting for water vapor absorption. The LIRAD method involves two independent observations: the vertical profile of lidar backscatter and the infrared spectral radiance in a chosen narrow band of wavelengths. The lidar equations involve the isotropic backscatter coefficient, Bc(n,z), the volume extinction coefficient, ac(z), and isotropic backscatter to extinction ratio, k, which is defined by

Note that many lidar researchers use the backscatter coefficient, (3C (= #c(7C,z)/47r) sr"1 and the lidar ratio, S(= 4n/k) sr. The attenuated backscatter coefficient, B'c(ii,z) at altitude z is given by

Table I O.I. Typical LIRAD instrument characteristics (from Platt et al. 1998) Instrument

Parameter

Value

Lidar

Wavelengths Pulse energies Pulse widths Pulse repetition rate Telescope diameter Telescope field of view Detectors

1064 nm, 532 nm, 355 nm 360 ml, 190mJ,95mJ 8 ns, 6 ns, 5 ns 10 Hz (optimum) 40cm 2mrad (usual) 2x Thorn EMI 9816B photomultipliers (PMTs)

CSIRO Mark II radiometer

Wavelength Aperture Field of view Detector Minimum detectable radiance

10.84 ± 0.5 urn 4cm 4-20 mrad Unicam Golay cell 1.34xlO-1Wm-2sr'Hz-1/2

Structural and Optical Properties

213

where ZQ is cloud-base altitude and r\(z" - z0) is a multiple scattering factor. If it is assumed that T| and k are constant with altitude in the cloud, then equation 2 can be inverted to give

The volume extinction coefficient, ac, from equation 1 is then

Substituting for Bc(n,z) from equation 4 and integrating equation 2 through cloud depth gives the integrated attenuated backscatter, y'(rc), where zt is the cloud top altitude,

The quantity r| is, in fact, usually variable with cloud depth. Then the quantity outside the brackets in equation 5 becomes /c/2fj, TJ in equation 3 becomes rj, and the value inside the brackets becomes r\(zt - ZQ), (Platt 1979), notated hereafter as r\e. 10.1.2. Infrared Analysis Methods We define the volume absorption coefficient (at 10.84 ± 0.5 urn in these studies) as Ga(z). The absorption optical depth, 8a, of the cloud is then,

with an equivalent expression for the visible optical depth. In earlier papers, and in some of the diagrams, the symbol i was used for optical depth, but i has since been used for transmittance. The infrared absorption emittance, ea, is then e a =l-exp(-8 fl ).

(7)

In terms of ea, equation 5 can be written

where the quantity is defined by

Values of k/2 T| and 2ar\e can be retrieved by fitting a curve of the form of equation 8 to experimental data. An example of such a fit is shown in figure 10.1 for mid-latitude cirrus (Platt and Dilley 1981).

214

Cirrus

Figure I O.I. Plot of integrated attenuated backscatter versus infrared emittance, ea, showing the dependence on emittance and temperature (Platt and Dilley 1981).

The lidar integrated linear depolarization ratio, A, is given by

where the subscripts refer to perpendicular and parallel polarization. 10.1.3. Determination of the Infrared Quantities Ea and Ga Values of ea and aa are calculated from the measured passive infrared radiance. Before this can be done, the measured radiance at the ground (Ls) is corrected for the transmittance (T) of the atmosphere, due mainly to water vapor, for radiance Lsky emitted by water vapor in the atmosphere and for scattering effects within the cloud. These effects can be described by the two equations

where Lsc is a radiance component due to scattering within the cloud and Lr is a component due to upwelling radiation from below scattered into the downward beam. These two components compose about 5% and 10% of Lfl, respectively, and so can be separated and subtracted, as shown in equation 12 (Platt and Stephens 1980). The cloud emittance, ea, is calculated by comparing the observed absorption radiance, Lfl, with a computed value, LM, from the lidar backscatter profile. A ratio (£) between the IR absorption coefficient, aa(z), and the corrected lidar backscatter coefficient, Bc(n,z), is assumed for each cloud profile (Platt and Dilley 1981), and ^ is varied until La = Lat. The necessary assumption of a single value of £ through the cloud depth (for each profile; it can be varied between profiles, but

Structural and Optical Properties

215

there is no information to allow variation within one profile) does not cause much error in the calculation of emittance (Platt et al. 1987). The quantity a is equal to 1/fccj and is therefore also a single average value through each profile. As shown later in section 10.4, a is fairly constant for temperatures > -50°C.The blackbody spectral radiance at each level in the cloud is obtained from a radiometer calibration curve and radiosonde temperature data. 10.1.4. Water Vapor Absorption and Emission The chief absorber in the clear atmosphere at the radiometer filter wavelengths is water vapor with small contributions from carbon dioxide, ozone and aerosols. In a tropical atmosphere, with 4-6 cm of precipitable water, transmittance between a cirrus cloud and the ground can be <0.4. The dependence of atmospheric transmittance on water vapor radiance for the Pilot Radiation Observation Experiment (PROBE; Platt et al. 1998) is shown in figure 10.2. The computation used radiosonde humidity profiles and a range of continuum absorption coefficients. The tight relationship is due to rather constant conditions of temperature. The precipitable water at mid-latitudes is smaller, typically 1.5cm or less, with an equivalent transmittance of about 0.85. Continuous observations of total water path were available in PROBE from the National Oceanic and Atmospheric Administration Environmental Technology Laboratory microwave radiometer (Westwater et al. 1995).

Figure 10.2. Plot of the atmospheric transmittance versus sky radiance due to water vapor in a tropical atmosphere during PROBE. The number of points is increased by using several different absorption coefficients with each radiosonde profile (Platt et al. 1998).

216

Cirrus

Figure 10.3. Typical values of the multiple scattering factor, T\e. The cloud-base altitude (range) was 10km, the telescope aperture 1 mrad, and the cloud extinction coefficient 5km"1. An ice cloud scattering phase function was used (after Platt 1981). The values are either for different depths into a cloud or for clouds of different depths and optical depths.

10.1.5. Multiple Scattering The multiple scattering effects in a lidar beam have been investigated for both cirrus and low clouds (e.g., Platt 1981; Bissonnette et al. 1995). In cirrus clouds, the multiple scattering factor, r\e, has values typically <0.5, causing a considerable reduction in effective cloud extinction (Platt 1981). The value of T]e for cirrus clouds is also sensitive to the ice crystal scattering phase function (i.e., the ice crystal habit). Typical values of r\e for a cirrus scattering-phase function are shown in figure 10.3. Values increase with cloud depth or optical depth as multiple scattering is diffused increasingly from the lidar beam. Values of ff and r|e can be calculated accurately for a given cloud scatteringphase function with Monte Carlo techniques (e.g., Platt 1981). However, current lack of information on realistic scattering-phase functions in cirrus implies that uncertainties in r| are about ±30%. This affects the accuracy of retrieved values of visible extinction coefficient ac, k, and a. 10.2. LIRAD Results on Mid-Latitude Cirrus

The first LIRAD results were obtained in Australia with the University of Adelaide Ruby lidar (694 nm) and CSIRO Mark I IR radiometer (10.84 ± 0.5 urn), reported in Platt (1973). A plot of y'(rc) versus optical depth 8a from these observations is shown in figure 10.4, where the asymptotic value gives k/2r\. Values of the latter varied from 0.25 and 0.4 among different case studies. Observations between 1975 and 1981 were taken at Aspendale, 38°S, with the CSIRO Ruby lidar (694nm) and MARK II infrared radiometer (10.84 ± 0.5 urn). An investigation of deep cirrostratus clouds was made in 1972 at Adelaide and again in 1975 at Aspendale (Platt and Dilley 1979). These data yielded higher emittances than for isolated cirrus. A longer series of LIRAD observations was made at Aspendale over the winter of 1978 (Platt and Dilley 1981) and thejummer of 1979-80 (Platt et al. 1987). Values of cloud depth, efl, Y'(TC), and k/2r\ were obtained over a range of

Structural and Optical Properties

217

Figure 10.4. The first LIRAD results obtained, showing integrated attenuated backscatter plotted against infrared optical depth, 8a, for one cloud (after Platt 1973). Bars indicate uncertainty in a single value of5 fl .

cloud temperatures between -60°C and -20°C. The distribution of various emittance values is shown in figure 10.5. Forty-five percent of values are less than 0.2, a typical characteristic of cirrus clouds. Mean values of ea and 5a both showed dependence on cloud temperature. Although there were large standard deviations in values at any one temperature, average values exhibited a well-defined temperature dependence, as shown in figure 10.6a for ea. Similar values in a tropical atmosphere from a field experiment in Darwin, Northern territory, Australia (Platt et al. 1984), are shown in figure 10.6b. Values were lower at the lower tropical temperatures but were similar to mid-latitude values at the higher temperatures. The values of Y(K) (i-6-? k/2r\ as efl —> 1) varied with temperature, as indicated in figure 10.1. Values of k/2r\ in various temperature ranges are plotted in figure 10.7.The change of A:/2rf with temperature is most pronounced between -45°C and -35°C, a range where the nucleation of ice crystals changes from heterogeneous to homogeneous.

Figure 10.5. Percentage of total infrared emittance values in a given interval for a year of midlatitude cirrus observations (from data in Platt et al. 1987).

218

Cirrus

Figure 10.6. (a) Values of infrared emittance, ea, plotted against mid-cloud temperature for both winter and summer seasons and (b) for a tropical experiment (after Platt et al. 1987). The bars show the standard deviation in the measured values in a given temperature range. Estimated errors in en are <5%.

Certain lidar backscatter profiles, at temperatures between -35°C and -20°C, gave anomalously high values of y'(rc), as shown in figure 10.8, where a base curve is plotted around minimum values of y'(n). Above the curve are scattered values that are up to five times the normal values. These high values also exhibited anomalously low values of depolarization ratio, a property of backscatter from oriented ice crystals (e.g., Platt et al. 1978). Values of k!2r\ in the tropical case covered a small range between 0.32 and 0.35 for temperatures between -80°C and -40°C The quantity at|e, which is given by the shape of the y'(rc) versus ea curve, was found to increase with decreasing temperature. Now, a is a function of the mean particle size (Platt 1979), particularly for a particle radius less than about 20 um. Values of ar\e are discussed further below.

Figure 10.7. Values of effective backscatter to extinction ratio, fc/2r[ plotted against mid-cloud temperature for winter and summer seasons at Aspendale (after Platt et al. 1987).

Structural and Optical Properties

219

Figure 10.8. Values of integrated attenuated backscatter, Y'(rc)> plotted against ea for one cloud, showing some anomalous backscatter (after Platt et al. 1987).

10.3. LIRAD Observations of Equatorial Cirrus

Observations on equatorial cirrus were made as part of the Atmospheric Radiation Measurement (ARM) Pilot Radiation Observation Experiment (PROBE) at Kavieng, New Ireland, Papua New Guinea, 2°S of the equator in January-February 1993 (Platt et al. 1998). Characteristics of the lidar and radiometers used are shown in table 10.1. A new Nd-YAG laser at 532 nm was used, together with the Mark II radiometer. A narrow-beam filter radiometer, using a cooled detector (Platt et al. 1993), and with a superior performance to the CSIRO Mark II, was also available, but supplies of liquid nitrogen were too limited for extended observations. The NOAA Environmental Technology Laboratory operated a microwave radiometer and infrared interferometer (Westwater et al. 1995). The integrated water vapor path was measured by the microwave radiometer, which allowed for the correction of the effects of large water vapor variations on the radiance. Short-term variations in water vapor radiance (and thus also transmittance) were often as large as the retrieved cirrus radiance. Typical variations in water path are shown in figure 10.9. The total observed radiance in cloudless conditions (that is, Lsky in equation 11, and thus also T) was normalized to the water vapor path at times of the six-hourly radiosonde ascents. The retrieved cirrus radiance from equation 11 is seen to be only about 15% of the water vapor radiance. This process led also to values for the water vapor continuum absorption coefficient that were found to be similar to those given by Roberts et al. (1976) and Clough et al. (1989), with some modification of the values for tropical atmospheres as discussed by Westwater et al. (1995). Typical lidar profiles are shown in figure 10.10. The Mt. Pinatubo volcanic cloud can be seen above the semitransparent cirrus layer in figure lO.lOa. The cloud in figure 10.1Gb is more attenuating. Figure 10.11 shows infrared emittance, ea, plotted against mid-cloud temperature. LIRAD data from past experiments

220

Cirrus

Figure 10.9. Integrated water vapor path, fitted cloudless radiance (10.86 ± 0.5 um), and retrieved cloud radiance (uncorrected for atmospheric transmittance) for one period in ARM PROBE (Platt et al. 1998).

Figure 10.10. Typical (a) weak and (b) strong normalized lidar backscatter profiles from tropical cirrus in the ARM PROBE experiment (Platt et al. 1998).

Structural and Optical Properties

221

Figure 10.11. Values of infrared emittance, efl, versus mid-cloud temperature for the PROBE experiment, compared to mid-latitude results (Platt et al. 1998). Bars show the variability in ea. The estimated error is <5%. Data from Minnis et al. (1990) are discussed in section 10.4.

are included. The Kavieng PROBE values are higher than the other values, except in the case of tropical anvil cirrus measured at Darwin (Platt et al. 1984). These higher values are due in part to the deeper clouds observed at Kavieng compared to the synoptic cirrus layers observed over Darwin, as shown in figure 10.12. Equivalent values of k/2r\ are shown in figure 10.13, and the increase in this quantity with temperature is again evident. The Kavieng PROBE values appear to be lower than those at other locations, except for the summer Aspendale data. Values below -60°C continue to decrease with temperature. The PROBE data represent the greatest range of values yet obtained. The value k/2 T| increases linearly with temperature. Experimental values of k/2r( and aff and calculated values of k and a are shown in table 10.2. The values of k and a are different from those calculated in Platt et al. (1998) because values of the multiple scattering factor r[ have been updated recently (Platt et al. 2001). TTiis was based on the fact that the initial values of a found in PROBE (Platt et al. 1998) indicated a cloud particle diameter in the colder clouds of the order of 10 urn. Calculations of TJ based on this size then indicated higher values of multiple scattering factors rf than were used in PROBE, at least for the colder temperatures. Retrieved values of k in table 10.2 based on the new values of r\ are compared with the calculated ones shown in table 10.3. They are seen to cover a rather

222

Cirrus

Figure 10.12. Cloud depth at various temperatures measured in ARM PROBE at Kavieng compared to those at Darwin for synoptic type cirrus (Platt et al. 1998). Bars show standard deviations in measured cloud depth. Lidar vertical resolution is 7.5 m.

Figure 10.13. Values of k!2i\ (that is, k!2 t|) plotted against mid-cloud temperature for tropical clouds at Kavieng in the ARM PROBE compared with other experiments (Platt et al. 1998).

Structural and Optical Properties

k

_

223

_

Table 10.2. Values of —, k, 2ar|, a and De using indicated values of r\ (Platt et al. 2001)

2r|

Mid-cloud temperature (°C)

0.14 0.18 0.22 0.29

-70 -60 -50 -40

0.60 0.60 0.50 0.43

(0.09) (0.09) (0.12) (0.08)

0.17 0.22 0.22 0.25

(0.03) (0.03) (0.05) (0.05)

2.9 3.4 3.6 1.7

2.4 2.8 3.6 2.0

(0.3) (0.4) (0.9) (0.2)

15 (+25, -4) 12 (+7, -4) 7 (+8, -2) >100

Note: Values in parentheses arise from indicated uncertainties in r\.

similar range. Deduced values of a in table 10.2 are seen to be generally larger at the lower temperatures. Using theoretical values of a (Mitchell and Arnott 1994, Mitchell 2000) deduced values of effective diameter De are also shown in table 10.2. Values of De at temperatures of -50°C and less are seen to be of the order of lOum to 20 um, particles that are smaller than those generally found at higher temperatures. The presence of small particles in high, cold ice clouds has also been detected in situ by Heymsfield (1986) and by Platt et al. (1989) from aircraft lidar, radiometer, and in situ particle observations. Platt and Arking (1997) also deduced the presence of layers of small crystals in cold cirrus from multichannel scanning radiometer observations of reflected near-IR solar radiation and emitted IR radiation. Models of tropical cirrus by Jensen et al. (1996) indicate that cirrus with ice crystals smaller than 10 um can exist near the tropical tropopause. Strom et al. (1997) detected small particles in young cirrus clouds from aircraft observations. The significance of small particles in cold cirrus clouds is that the solar albedo will be increased and the infrared emittance decreased compared to clouds of larger particles. The importance of crystal size was pointed out by Stephens et al. (1990), who demonstrated that for mid-latitude clouds, the ice water feedback parameter for cirrus would change sign from positive to negative when the effective radius of cirrus particles decreased below 24 urn. For tropical clouds the critical radius might be smaller, but the principle would be the same. Based on the

Table 10.3. Some values of backscatter-to-extinction ratio, k, calculated from scattering theory (Platt et al. 1998)

k Crystal habit Solid bullet Hollow column Bullet rosette Solid column Capped column

Macke (1993)

Takano and Liou (1995)

0.10 0.11 0.11 0.16 0.22

0.08-0.10 0.33-0.51 0.90

224

Cirrus

recent formulation of Mitchell and Arnott (1994), the values of a found in PROBE for cloud temperatures less than -50°C would indicate effective radii in the region of 20 um or less. It is also significant in the PROBE data that visible optical depths could be quite high in these cold clouds (because of the high a values), leading to substantial negative feedback effects. These particles are also significant to remote sensing with millimeter radar because such radar will not detect cloud particles less than about 20 urn in size (e.g., Intrieri et al. 1993). Such small particles can be expected at the tops of midlatitude cirrus (Platt et al. 1989) as well as in cold tropical clouds. Cold tropical clouds near the tropopause observed in northern Australia with lidar and millimeter radar were also not sensed with the radar (Austin et al. 1998). 10.4. Comparison with Other Observations

Cloud properties obtained by LIRAD in Australia are compared here with similar data from other laboratories. Considerable data on cirrus radiative properties were collected in the First ISCCP Regional Experiment (FIRE). Spinhirne and Hart (1990), using lidar and IR radiometry from an ER-2 aircraft, obtained relations between albedo and emittance, showing the large range of IR emittances typical for cirrus. Grund and Eloranta (1990), using high spectral resolution lidar, were able to determine bulk values of the backscatter-to-extinction ratio, 1/S (= Pan/4n = k/4n) in cirrus. A plot of their data is shown in figure 10.14, indicating how 1/S changes with optical thickness. The centroid of the cirrus was observed to drop with time, indicating higher values of 1/S at the lower altitudes (not shown), in agreement with the results of Platt et al. (1998). Minnis et al. (1990) determined albedo-emittance relations from satellite and lidar data. They also determined emittance and absorption coefficient values that varied with temperature. The trend of their results is also shown in figure 10.11. Ackerman et al. (1990) used lidar and high spectral resolution infrared data to

Figure 10.14. Time history of the total cloud optical thickness (that is, optical depth) (lower full line) and bulk normalized backscatter phase function (i.e., 1/S) for a cirrus cloud from FIRE 1986 (after Grund and Eloranta, 1990).

Structural and Optical Properties

225

Figure 10.15. The lidar integrated attenuated backscatter (sr^1) plotted against emittance, efl, in the 10-um band measured with an interferometer in FIRE 1986. Filled triangles denote midcloud altitudes of less than 9 km; open triangles are for mid-cloud altitudes greater than 9 km (after Ackerman et al. 1990).

obtain information on particle size, showing regions of small particles. They also obtained a plot of integrated attenuated backscatter versus emittance, shown in figure 10.15. The colder clouds show the lower values, in agreement with Platt et al. (1998), and absolute amplitudes are comparable. Del Guasta et al. (1993) determined the visible extinction coefficient in many cases of Antarctic cirrus in the Experimental Cloud Lidar Pilot Study (ECLIPS), as shown in figure 10.16. Values increase appreciably for temperatures greater than -30°C. Spinhirne et al. (1996) found a relationship between infrared absorption coefficient and cloud temperature, with large scatter equivalent to that shown in figure 10.6a. Sassen and Cho (1992) found values of k that showed considerable

Figure 10.16. Values of the extinction coefficient retrieved from lidar backscatter profiles taken in the Antarctic. The box shows the expression for the solid line (after Del Guasta et al. 1993).

226

Cirrus

scatter but with a tendency for values to increase with temperature. Their values varied between 0.025, for very thin, "invisible" cirrus, and 0.69. Pal et al. (1995) determined values of visible optical depth from lidar that showed a fall-off in frequency with increasing cloud optical depth, in agreement with Platt et al. (1998), and with the equivalent fall-off in emittance shown in figure 10.5. 10.5. Lidar Linear Depolarization Ratio

The lidar linear depolarization ratio, A (equation 10), has been used since the 1970s (e.g., Schotland et al. 1971; Sassen 1977) to examine cloud phase. In the LIRAD technique, observations of depolarization are useful for the further interpretation of data. Water drops only depolarize the laser pulse radiation weakly, whereas ice crystals, with one exception, depolarize strongly. The exception is the oriented ice crystal plate, which also depolarizes weakly when illuminated perpendicular to its plane face. Multiple scattering in water clouds will also depolarize the radiation as optical depth increases. Figure 10.17 shows an increase in A toward lower temperatures. This trend is similar to that observed by Sassen and Cho (1992), indicating a change in either size or ice crystal habit. Values in equatorial cirrus clouds followed the same trends as mid-latitude clouds. Layers of plate crystals were also found in tropical clouds (Platt et al. 1998).

Figure 10.17. Collected values of lidar linear depolarization ratio in cirrus plotted against mid-cloud temperature (Platt et al. 1998).

Structural and Optical Properties 227 10.6. Conclusions

The LIRAD technique has lent itself well to obtaining statistics on the infrared and visible properties of cirrus clouds over many regions and temperatures. Trends in infrared emittance and absorption coefficient with temperature give the first comprehensive set of observational data for comparison with, and parameterizations of, general circulation models of the atmosphere (GCMs). The quantities k and a also show trends with temperature and can be used to obtain visible optical depth and (small) cloud particle size, respectively. The visible extinction coefficient,CTC(Z),also gives a measure of ice water content (Platt 1997). The addition of modern modeling and experimental techniques to LIRAD will lead to further exciting new developments. The availability of theoretical scattering-phase functions for a wide range of crystal types (e.g., Macke 1993; Takano and Liou 1995) can be used to obtain a better understanding of TJ and its variability. The measurement of cirrus scattering functions at intermediate angles with the tilt-scan radiometer above cloud top (Spinhirne et al. 1996) is also a useful initial step to obtaining realistic cirrus scattering-phase functions. Raman lidar is a development that allows the independent measurement of extinction in a cloud (Ansmann et al. 1992), thus leading to more accurate values of the quantity k and visible optical depth. Similar methods to separate cloud backscatter and optical depth are the high spectral resolution lidar (Grund and Eloranta 1990) and the Rayleigh backscatter cloud transmittance method (e.g., Young 1995). Sensitive millimeter radar that can detect many cirrus clouds is also now available. The radar/lidar ratio is very sensitive to cloud particle size (e.g., Intrieri et al. 1993), and profiles of effective radius through cirrus can now be obtained with combined instruments. Matrosov et al. (1994) have also retrieved cirrus particle sizes from Doppler millimeter radar and infrared radiometry. The above new multi-wavelength techniques combined with LIRAD will provide the next leap forward in our knowledge of cirrus clouds. Comprehensive remote sensing experiments are needed, along with aircraft in situ observations. Acknowledgments The LIRAD system of observation and analysis was developed at the Division of Atmospheric Research, CSIRO, Aspendale, Australia. I thank my colleagues at the division, particularly Mac Dilley, John Bennett, Stuart Young, Richard Austin, Graeme Patterson, Brian Turner, Reg Henry and Stephen Marsden, for their considerable assistance over the years. The tropical PROBE work was funded partially by the U.S. Department of Energy, Office of Health and Environmental Research, grant no. DE-FG02-92ER61373. References

Ackerman, S.A., W.L. Smith, J.D. Spinhirne, and H.E. Revercomb, 1990. The 27-28 October 1986 FIRE IFO cirrus case study: Spectral properties of cirrus clouds in the 8-12 um window. Mon. Wea. Rev., 118, 2377-2388.

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Ansmann, A., U. Wandinger, M. Riebesell, C. Weitkamp, and W. Michaelis, 1992. Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar. Appl. Opt., 31, 7113-7131. Austin, R.T., S.A. Young, C.M.R. Platt, G.R. Patterson, S. Marsden, S.M. Sekelsky, and R.E. Mclntosh, 1998. Retrieval of tropical cirrus cloud properties from ground-based lidar and millimeter-wave radar sensing at the maritime continent thunderstorm experiment, in Proceedings of the 7th Atmospheric Radiation Measurement (ARM) Program, San Antonio, Texas, March 3-7, 1997. U.S. Department of Energy, Washington, DC, pp. 389-393. Bissonnette, L.R., P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A.V. Starkov, M. Noormohammadian, U.G. Oppel, D.M. Winker, E.P Zege, I.L. Katsev, and I.N. Polonsky, 1995. LIDAR multiple scattering from clouds. Appl. Phys. B, 60, 355-362. Clough, S.A., EX. Kneizys, and R.W. Davies, 1989. Line shape and the water vapor continuum. Atmos. Res., 23, 229-241. Del Guasta, M., M. Morandi, L. Stefanutti, J. Brechet, and J. Piquad, 1993. One year of cloud lidar data from Dumont D'Urville (Antarctica). I. General overview of geometrical and optical properties./. Geophys. Res., 98,18575-18587. Grund, C.J., and E.W. Eloranta, 1990. The 27-28 October 1986 FIRE IFO cirrus case study: Cloud optical properties determined by high spectral resolution lidar. Mon. Wea. Rev., 118, 2344-2355. Heymsfield, A.J., 1986. Ice particles observed in a cirriform cloud at -83°C and implications for polar stratospheric clouds. /. Atmos. Sci., 43, 851-855. Intrieri, J.M., G.L. Stephens, W.L. Eberhard, and T. Uttal, 1993. A method for obtaining cirrus cloud particle sizes using lidar and radar backscatter technique. J. Appl. Meteor., 32,1074-1082. Jensen, E.J., O.B. Toon, H.B. Selkirk, J.D. Spinhirne, and M.R. Schoeberl, 1996. On the formation and persistence of subvisible cirrus clouds near the tropical tropopause. / Geophys. Res., 101, 21361-21375. Lee, W.-H., and R.C.J. Somerville, 1996. Effects of alternative cloud radiation parameterizations in a general circulation model. Ann. Geophys., 14,107-114. Lohmann, U., and E. Roeckner, 1996. Design and performance of a new cloud microphysics scheme developed for the ECHAM general circulation model. Climate Dynam., 13, 557-572. Macke, A., 1993. Scattering of light by polyhedral ice crystals. Appl. Opt., 32, 27802788. Matrosov, S.Y., B.W. Orr, R.A. Kropfli, and J.B. Snider, 1994. Retrieval of vertical profiles of cirrus cloud microphysical parameters from Doppler radar and infrared radiometer measurements. /. Appl. Meteor., 33, 617-626. Minnis, P., D.F. Young, K. Sassen, J.M. Alvarez, and CJ. Grund, 1990. The 27-28 October 1986 FIRE IFO Cirrus case Study: Cirrus parameter relationships derived from satellite and lidar data. Mon. Wea. Rev., 118, 2402-2425. Mitchell, D.L., and W.P. Arnott, 1994. A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds, II: dependence of absorption and extinction on ice crystal morphology. J. Atmos. Sci., 51, 817-832. Mitchell, D.L., 2000. Parameterization of the Mie Extinction and Absorption Coefficients for Water Clouds. /. Atmos. Sci., 57,1311-1326. Pal, S.R., A. I. Carswell, I. Gordon, and A. Fong, 1995. Lidar-derived cloud optical properties obtained during the ECLIPS program. /. Appl. Meteor., 34,2388-2399. Platt, C.M.R., 1973. Lidar and radiometric observations of cirrus clouds. /. Atmos. Sci., 30, 1191-1204.

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Platt, C.M.R., 1979. Remote sounding of high clouds. I: Calculation of visible and infrared optical properties from lidar and radiometer measurements. /. Appl. Meteor., 18, 1130-1143. Platt, C.M.R., 1981. Remote sounding of high clouds. Ill: Monte Carlo calculations of multiple scattered lidar returns. /. Atmos. Sci., 38,156-167. Platt, C.M.R., 1997. A parameterization of the visible extinction of ice clouds in terms of the ice/water content. J. Atmos. Sci., 54, 2083-2098. Platt, C.M.R., N.L. Abshire, and G.T. McNice, 1978. Some microphysical properties of an ice cloud from lidar observation of horizontally oriented crystals. /. Appl. Meteor., 17, 1220-1224. Platt, C.M.R., and A. Arking, 1997. A case study of cirrus layers with variable 3.74 urn reflection properties in the First FIRE Experiment, 2 November 1986. Theor. Appll. Climatol., 56,137-152. Platt, C.M.R., J.W. Bennett, S.A. Young, M.D. Fenwick, PJ. Manson, G.R. Patterson, and B. Petraitis, 1993. Narrow-beam fast filter radiometry and the use of the lidar/radiometer method in the Atmospheric Radiation Measurement Program, in Proceedings of the Third Atmospheric Radiation Measurement (ARM) Science Team Meeting, Norman, Oklahoma. March 1-4. U.S. Department of Energy, Washington, DC. pp. 293-297. Platt, C.M.R., and A.C. Dilley, 1979. Remote sounding of high clouds. II: Emissivity of cirrostratus. /. Appl. Meteor., 18,1144-1150. Platt, C.M.R., and A.C. Dilley, 1981. Remote sounding of high clouds. IV: Observed temperature variations in cirrus optical properties./. Atmos. Sci., 38, 1069-1082. Platt, C.M.R., A.C. Dilley, J.C. Scott, I.J. Barton, and G.L. Stephens, 1984. Remote sounding of high clouds, V: Infrared properties and structure of tropical thunderstorm anvils. J. dim. and Appl. Meteor., 23,1296-1308. Platt, C.M.R., and D.J. Gambling, 1971. Emissivity of high layer clouds by combined lidar and radiometric techniques. Quart. J. R. Met. Soc., 97, 322-325. Platt, C.M.R., J.C. Scott, and A.C. Dilley, 1987. Remote sounding of high clouds. VI: Optical properties of midlatitude and tropical cirrus. /. Atmos. Sci., 44,729-747. Platt, C.M.R., J.D. Spinhirne, and W.D. Hart, 1989. Optical and microphysical properties of a cold cirrus cloud: Evidence for regions of small ice particles. /. Geophys. Res., 94, 11151-11164. Platt, C.M.R., and G.L Stephens, 1980. The interpretation of remotely sensed high cloud emittances. /. Atmos. Sci., 37, 2314-2322. Platt, C.M.R., S.A. Young, PJ. Manson, G.R. Patterson, S.C. Marsden, R.T. Austin, and J. Churnside, 1998. The optical properties of equatorial cirrus from observations in the ARM Pilot Radiation Observation Experiment. /. Atmos. Sci., 55, 1977-1996. Platt, C.M.R., S.A. Young, R.T. Austin, G.R. Patterson, D.L. Mitchell, and S. Miller, 2001. LIRAD observations of tropical cirrus clouds in MCTEX, Part I: Optical properties, and detection of small particles in cold cirrus, in press. Roberts, R.E., E.A. Selby, and L.M. Biberman, 1976. Infrared continuum absorption by atmospheric water vapor in the 8-12urn window. Appl. Opt., 15, 2085-2090. Rotstayn, L.D., 1997. A physically based scheme for the treatment of stratiform clouds and precipitation in large-scale models. Part I. Description and evaluation of the microphysical processes. Q. J. R. Meteorol. Soc., 123,1227-1282. Sassen, K., 1977. Cloud phase discrimination with polarization diversity lidar. J. Rech. Atmos., 11, 179-190. Sassen, K., and B.S. Cho, 1992. Subvisual-thin cirrus lidar dataset for satellite verification and climatological research. /. Appl. Meteor., 31,1275-1286. Schotland, R.M., K. Sassen, and R. Stone, 1971. Observations by lidar of linear depolarization ratios for hydrometeors./. Appl. Meteor., 10, 1011-1017.

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Spinhirne, J.D., and W.D. Hart, 1990. Cirrus structure and radiative parameters from airborne lidar and spectral radiometer observations: The 28 October 1986 FIRE Study: Man. Wea. Rev., 118, 2329-2343. Spinhirne, J.D., W.D. Hart, and D.L. Hlavka, 1996. Cirrus infrared parameters and shortwave reflectance relations from observations. /. Atmos. Sci., 53,1438-1458. Stephens, G.L., S.-C. Tsay, P.W. Stackhouse, Jr., and P.J. Flatau, 1990. The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback. /. Atmos. ScL, 47,1742-1753. Strom, I, B. Strauss, T. Anderson, F. Schroder, J. Heintzenberg, and P. Wendling, 1997. In situ observations of the microphysical properties of young cirrus clouds. J. Atmos. Sci., 54,2542-2553. Takano, Y., and K.N. Liou, 1995. Radiative transfer in cirrus clouds. Part III: Light scattering by irregular ice crystals. /. Atmos. Sci., 52, 818-837. Westwater, E.R., J.H. Churnside, J.A. Shaw, J.B. Snider, K.S, Gage, Y. Han, W. Ecklund, A. Riddle, and A.C. Williams, 1995. Ground-based remote sensor observations during the PROBE experiment in the tropical western Pacific, in Proceedings of the International Science Symposium, vol. II. IEEE catalog no. 95CH35770, pp. 882-886. Young, S.A., 1995. Analysis of lidar backscatter profiles in optically thin clouds. Appl. Opt., 34, 7019-7031.

II Contrail Cirrus ULRICH SCHUMANN

A contrail (a term introduced for "condensation trail" in 1942 by British pilots) is a visible cloud forming behind aircraft, mainly due to water vapor emissions from the engines. Contrails were first observed behind propeller-driven aircraft in 1915 but form as well from the exhaust of jet engines in cold ambient air (Schumann 1996a). Contrails are visible indicators of cruising aircraft and may impact the Earth's climate. Aircraft exhaust may influence cloud formation either directly by forming contrails or indirectly by causing an aerosol of black carbon soot, volatile particles, and metallic particles which later impact the formation and properties of cirrus clouds in the same air mass at other places. Though the cover by contrails is small compared to the cover by natural cirrus clouds, the potential climatic importance of contrails is being studied intensively. A review of the results obtained so far has been prepared for an assessment on Aviation and the Global Atmosphere (IPCC 1999). It reveals considerable progress in understanding aviation-produced aerosols and cloudiness (Fahey and Schumann 1999). Contrail studies also aid in learning about cirrus formation because contrails are cirrus clouds that form under relatively well defined and reproducible conditions. This chapter reviews some of the progress in understanding contrail formation, occurrence, properties, and radiative impact and identifies some important unanswered questions.

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11.1. Contrail Formation Contrail formation can be accurately predicted for given atmospheric temperature and humidity conditions. Contrails form thermodynamically according to the Schmidt-Appleman criterion (Schmidt 1941; Appleman 1953) when the relative humidity (RH) in the plume of exhaust gases mixing with ambient air temporarily reaches or exceeds liquid saturation, so that liquid droplets form on cloudcondensation nuclei (CCN) and soon freeze to ice particles. Measurements have shown that liquid saturation is indeed necessary (see fig. 11.1) and that contrails do not form when the RH exceeds ice saturation (Jensen et al. 1998b; Karcher et al. 1998a; Schumann et al. 2000). The maximum RH reaches liquid saturation

Figure I I . I. Observations indicating that contrails form when the mixing of exhaust gases with ambient air leads to liquid saturation. The data are grouped according to cases with (a) observed contrails (b) observed onset of contrail formation, and (c) no contrails. The symbols represent measured temperature and water vapor partial pressure of ambient air near cruising aircraft of known type. The lines departing from the point of ambient conditions represent the mixing lines with slopes depending on the parameters given in the text. The curves represent saturation pressure for liquid (full) and ice (dashed) saturation. From Karcher et al. (1998a).

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when the ambient temperature is below a threshold temperature of typically -50° to -35°C, depending on ambient pressure and humidity and aircraft properties. This maximum is reached in the young plume (age <0.5 s) closely behind the aircraft. In the aging plume, kilometers behind the aircraft, the relative humidity decreases and approaches the humidity of the ambient air. Persistent contrail formation requires that the ambient atmosphere is ice-saturated (Brewer 1946; Jensen et al. 1998b). Aircraft exhaust may lead to cirrus clouds where no clouds would have formed otherwise. Ice-supersaturated air is often free of visible clouds because the supersaturation is too small for ice particle nucleation to occur (Heymsfield et al. 1998b; Gierens et al. 1999b). Persistent contrails may last for hours and grow into a spreading cirrus cloud. Although aircraft flying through ice-supersaturated air masses trigger contrail formation by the increase of humidity within their exhaust trails, the ice formed in long-lasting contrails originates almost completely from ambient water vapor (Knollenberg 1972). The threshold temperature for contrail formation in the Schmidt-Appleman criterion depends on ambient pressure, p, and ambient RH and on the parameters that determine the steepness, de/dT = EIH2o cp /?/[0.622 <2eff]> °f tne mixing line (fig. 11.1) of excess partial water pressure, e, versus excess temperature, T, in the plume (Schumann 1996a). The parameters include the emission index (El) of water mass per burnt fuel mass (EIH2o = 1-25 for typical jet fuels with 13.8% hydrogen mass fraction), the specific heat capacity of air, cp = 1004J/kgK~1, and the effective amount of heat, <2eff, released into the exhaust per unit fuel mass, where <2eff = (1 - TJ) Q depends on the specific heat of combustion of the fuel in the engine (Q = 43MJ/kg) and the overall efficiency, t|, of the aircraft propulsion system. The dependence on engine efficiency was noted by Schmidt (1941). The efficiency can be computed from r\ - (F V)/(mF Q) for given engine thrust, F, aircraft speed, V, engine fuel consumption rate, mF, and Q (Schumann 1996a). Propulsion engineers call mF/F the specific fuel consumption. Typical values of T| are in the range 0.2-0.4, its value grew from older low-bypass to modern highbypass engines. Some authors use "contrail factors" EIH2o/<2eff explicitly depending on the by-pass ratio of engines (Coleman 1996; Ferris 1996; Mazin 1996; Schrader 1997). The spatial scales and the lifetime of contrails depend on ambient humidity and the rate of mixing, (dNldt)IN. The dilution factor, N, measures the mass of air with which the exhaust from a unit mass of burnt fuel mixes. The mixing process depends on different mechanisms and proceeds at different rates in the early jet regime, the vortex regime, the vortex breakup regime, and the atmospheric dispersion regime (Gerz et al. 1998). The dispersion regime ends when the plume concentrations are diluted to ambient concentration levels within their natural range of variability. For modern large subsonic aircraft, the regimes typically extend to plume ages of 10s, 100s, 3min, and 3h, respectively. The dilution factor has been measured in a large set of field experiments (Schumann et al. 1998) and has been found to vary approximately with plume age, ?, as N = 7000 (t/to)0'8, t0 = 1 s, for t from 6ms to 104s. The three-dimensional vortex dynamics and the mixing processes have been studied in large-eddy simulations (e.g., Lewellen and Lewellen 1996; Gerz et al.

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1998), partly including cloud microphysical processes (Gierens 1996; Gierens and Jensen 1998; Jensen et al. 1998a). Details of the structure of contrails have been measured with Lidar methods (Freudenthaler et al. 1995; Sassen and Hsueh 1998; Sussmann 1999) and in situ techniques (Petzold et al. 1997; Strom and Ohlsson 1998b). At the end of the vortex regime, contrails are grown vertically to 150-300 m depth with little horizontal spreading. The vertical extent of contrails is smaller the more stable the stratification of the atmosphere. Horizontal growth in the dispersion regime is often dominated by wind shear that spreads a contrail to a band of several kilometers in width. Measured growth rates of width vary between 18 and 140m/min and of cross-section between 3500 and 25,000m2/min. Contrails older than 15min may extend more than 300-800 m vertical depth (Freudenthaler et al. 1995). The life cycle of contrails under the impact of complex atmospheric motions, evaporating and sedimenting particles, and radiative heat sources (Gierens and Jensen 1998; Jensen et al. 1998a) are still being investigated. I 1.2. Particle Formation in Contrails

The formation of contrail particles is a complex microphysical process, which we understand today far better than a few years ago (Miake-Lye et al. 1993). The number of ice particles that are formed behind an aircraft depend on ambient humidity and temperature, on the amount of emitted ions, soot particles, sulfur content of the fuel, fraction of fuel sulfur oxidized to sulfuric acid, the rate of homogeneous and heterogeneous freezing of supercooled solutions, the efficiency of SO2 heterogeneous oxidation, the effect of other condensable gases such as HNO3, and ambient aerosols (Yu and Turco 1998a). Figure 11.1 implies that contrail particles form first as liquid droplets. Many of the liquid droplets must freeze quickly in the jet plume at ages less than 0.1 s because otherwise they cannot grow large enough to form a visible contrail some 10m behind the engine as observed (Karcher et al. 1996; Schumann 1996b). For droplet formation by water condensation, cloud condensation nuclei (CCN) must be available. Ambient aerosol contains too few CCNs to explain the large number of ice particles (104-105/cm) required for the early visibility of contrails 10-30 m behind engine exit (Karcher 1996). In addition to entrained ambient aerosol, the CCN sources include soot particles and freshly nucleated sulfuric acid/water droplets (Karcher et al. 1996), parts of which form on chemi-ions emitted by the engines (Yu and Turco 1998b). The number of small particles in engine plumes has been measured with condensation-nucleus (CN) counters which count the number of particles grown in a saturated environment inside the instrument to optically detectable sizes. Such instruments detect particles larger than a threshold diameter of 3-20 nm. Using exhaust samples from heated or unheated inlets, the instruments determine the nonvolatile (soot) or total particle fractions. By reference to the excess concentration of conserved species such as CO2 in the plume, one can determine the El of particles (i.e., the number of particles emitted per unit mass of burnt fuel). Aerosol particle and ice crystal size distributions in the range of 150 nm to

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500 (am have been measured by optical particle spectrometers, replicators, and by counterflow virtual impactors selecting ice particles larger than about 5^im (Goodman et al. 1998; Lawson et al. 1998; Schroder et al. 2000). Soot size distributions have been determined by spectrometers for dry aerosols (Hagen et al. 1998; Petzold et al. 1999a; Pueschel et al. 1998). Detailed size spectra of aircraftinduced aerosol at diameters less than 150nm are becoming available now from measurements with cascades of CN counters. Size spectra were previously measured by counting the particles in various size intervals discriminated by electrical aerosol-size qualifiers (Hagen et al. 1996). When analyzing such measured size spectra (e.g., Konopka et al. 1997), one must be aware of the drying process between sample inlet and particle counters. Previous measurements may overestimate the contribution from ambient particles larger than 300 nm (before drying) or from particles contained in ice particles larger than 300 nm because of anisokinetic sampling inlets. So far, the measurements show that aircraft emit about 1015 soot particles larger than about 5 nm per kilogram of burnt fuel. Their concentration exceeds 106/cm3 near the engine exit plane. The term "soot" is used to denote all black or gray carbon-containing, nonvolatile products from incomplete combustion processes in the engine. Soot particles are composed of individual, nearly spherical particles (spherules), which have a mean radius between 10 and 30nm. Agglomerated soot particle sizes are typically 10-100 nm in diameter. Engines emit about 0.01-0.2 g soot/kg fuel (Petzold and Dopelheuer 1998). The fleet average is near 0.04g/kg (Petzold et al. 1999b). Graphitelike soot particles are hydrophobic. Soot particles from hydrocarbon flames are partially hydrated (Chughtai et al. 1996). The activation of soot particles that grow to droplets which then freeze is not yet fully understood (Karcher et al. 1996). Measurements in young exhaust plumes at cruise show less soot particles outside ice particles in plumes with contrails than in plumes without contrails, indicating that the emitted soot particles participate in the formation of ice particles (Schroder et al. 1998). Also, measurements of the refractive index of particles larger than 150nm suggest that soot enters water particles (Kuhn et al. 1998). Soot seems to be the dominant ice nucleus in the upper part of sinking contrails in the vortex regime, whereas the lower part seems to contain ice particles freshly formed mainly from ambient aerosol (Strom and Ohlsson 1998a). The number of ice particles found in aged contrails correlates with the amount of absorbing material measured and with air traffic density, indicating a relationship between ice particles in contrails and soot emissions (Strom and Ohlsson 1998b). Individual soot (and some metal) particles have been found in ice particles of aged contrails (Petzold and Schroder 1998; Twohy and Gandrud 1998; Petzold et al. 1998). Models suggest that contrails would also form without soot and sulfur emissions by activation from freezing of background particles (Jensen et al. 1998c; Karcher et al. 1998a). However, the resulting contrails would have fewer and larger particles and hence less direct radiative impact. It is unknown whether the soot aerosol induced by air traffic in the upper troposphere causes cirrus clouds with more or less ice particles (Jensen and Toon 1997). In addition to soot, measurements show that aircraft induce 1015-4 x 1017 volatile particles larger than about 5 nm in diameter per kilogram of burnt fuel

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into the young plume (Anderson et al. 1998; Karcher et al. 1998b).This number varies strongly with the detection limit of the CN counters used. Volatile particles originate from the emitted water vapor, the sulfuric acid (formed in burning sulfur-containing fuels; mean sulfur mass content near 500 ppm) and from the chemi-ions. Aerosol models (Karcher et al. 1998b; Yu et al. 1998) show that the measured volatile particles larger than 5nm originate from chemi-ions (as measured by Arnold et al. 1998a,b) because the force between charged particles enhances coagulation (Yu and Turco 1998b). The number of volatile particles measured in plumes behind different aircraft grows with the mass fraction of sulfur in the fuel used (Schumann et al. 1996; Anderson et al. 1998; Schroder et al. 1998), indicating that part of the fuel sulfur is converted to sulfuric acid, which participates in bimolecular homogeneous or heterogeneous nucleation and condensation and enhances particle growth. For one aircraft, chemical ion mass spectrometric measurements show that 0.4-2.5% of the fuel sulfur is converted to sulfuric acid (Curtius et al. 1998). Other indirect measurements suggest much larger conversion rates (Fahey and Schumann 1999). It appears that the conversion fraction depends on the fuel-sulfur content and on the engine type (Lukachko et al. 1998; Miake-Lye et al. 1998). Recent studies suggest that some volatile material is formed from emitted hydrocarbons (Karcher et al. 1998b). Because of sulfuric acid formation, the number of ice particles formed in contrails increases and the mean size decreases with fuel sulfur content, though weakly. Measurements indicate that the number of ice particles increases by a factor of 2 and the mean crystal size shrinks by about 20% for fuel sulfur content increasing from 0.02 to 3 g/kg (Petzold et al. 1997). Sulfuric aerosol seems to be the dominant ice-forming aerosol at temperatures far below the threshold temperature for contrail formation (Karcher 1998), but even strong changes in fuel sulfur have only a small (<0.4K) impact on the threshold temperature (Busen and Schumann 1995; Schumann et al. 1996). However, ice crystals formed in contrails scavenge vapors and particles, creating a sulfate aerosol accumulation mode that may contribute to ice nuclei, and this source of ice nuclei is amplified with higher sulfur emissions (Yu and Turco 1998a). It is expected that large and highly diluted sulfuric acid droplets or large-soot aerosols coated with sulfate material will have the strongest impact on cirrus ice formation (Jensen and Toon 1997). However, this relationship has not yet been determined experimentally. Also, it is not clear which air traffic parameter controls the amount of induced contrail cirrus best. Is it the fuel consumption, the number of aircraft, the number of particles emitted, or the number of ice particles formed in the plume after a few minutes? These questions need further investigations. Ice particles in young contrails (age 1-20 s) are small, about lum in diameter. Under high ambient humidity, they grow to larger ice particles. Ice particle size spectra within and at the edge of young contrails systematically differ from each other (Petzold et al. 1997). At the edges, the relative humidity with respect to ice can be larger, causing larger ice crystals to form. Large ice particles (300 urn and 2 mm in diameter) have been measured in several-minutes-old plumes in very humid air (Knollenberg 1972; Heymsfield et al. 1998a), and such particles sediment quickly.

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At least in some cases, the number of particles in contrails seems to be dictated mainly by the processes in the fresh plume. As a contrail spreads, the total number of particles (about 10n-1012 ice crystals/m length of contrail) was observed to stay fairly constant (Schroder et al. 2000; Spinhirne et al. 1998). However, this observation needs to be checked further. Clearly, some particles will eventually sediment out of the contrail. In ice-supersaturated air, aircraft induce particles also by vertical air motions enhancing the relative humidity (Gierens and Strom 1998). In such cases most of the surviving ice particles originate in the wake behind the downward-traveling vortex tube generated behind aircraft. The number of ice particles per unit flight path grows with the size of the aircraft (Gierens and Strom 1998). The fraction of surviving ice crystals can be much smaller (e.g., by a factor of 200) than the number of ice particles generated in the early jet phase of the contrail (Sussmann and Gierens 1999). Contrail ice particles may sediment and dehydrate the upper troposphere or may seed lower-level cloud formation (Knollenberg 1972). Sedimentation of ice crystals in strongly supersaturated air has been observed (Schumann 1994; Heymsfield et al. 1998a), but the significance of such precipitation is unknown. 11.3. Contrail Occurrence

Extensive contrail cirrus may form in ice-supersaturated air. Ice supersaturated regions are expected to be common in the upper troposphere but to occur rarely in the stratosphere, at least somewhat above the tropopause. In the upper troposphere, ice-saturated air masses can exist without forming clouds, as shown by the presence of persistent contrails outside cirrus clouds. Air masses become icesupersaturated when lifted, which occurs under suitable meteorological conditions (Kastner et al. 1999). An ice-saturated air mass may reach liquid saturation when lifted 300-400 m by ambient air motions. Ice-supersaturation has been measured by high-precision frost-point hygrometers in a few localized cases (Brewer 1946; Murphy et al. 1990; Heymsfield et al. 1998b). For example, in the upper troposphere over the North Atlantic, Ovarlez et al. (1999) measured RH exceeding 150% with respect to ice saturation at -60 to -50°C ambient temperature [i.e., higher than the ice nucleation limit deduced by Heymsfield et al. (1998b)], possibly because of different nucleation properties in maritime air masses. Gierens et al. (1999b) analyzed hygrometer data taken during the MOZAIC project onboard in-service airliners of type Airbus A340 (Helten et al. 1998; Marenco et al. 1998) and found that 13.5% of all the flights occurred in air masses that are ice-supersaturated but that liquid saturation is found rarely. The MOZAIC data agreed within 5-15% of liquid saturation with in-flight frost-point measurements (Helten et al. 1999), just sufficient for this kind of analysis. The frequency or area of coverage of Earth by contrails has been measured only in a few selected regions. At northern mid-latitudes, the contrail frequency peaks around February/March and has a minimum during July (Mazin 1996; Minnis et al. 1997). Persistent contrails were visible from surface stations over the continental United States for 12% of all observations. The observed contrail

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frequency is well correlated with the fuel consumption in the same region. Hence, contrail coverage is limited by the number of aircraft flights and not by the atmospheric conditions. Contrails occur within thin cirrus in approximately 80% of the observations (Minnis et al. 1997; Sassen 1997). In situ measurements of contrails inside and outside cirrus clouds indicate that contrail growth is only weakly, if at all, affected by preexisting cirrus clouds (Schroder et al. 1998a). Contrails often get wide and thick enough to induce radiative disturbances that are detectable in satellite data. Individual contrails have been traced in satellite pictures for up to 18h (Minnis et al. 1998). Figure 11.2 shows the unusual example of a spiral contrail formed from a circulating military aircraft. Radiosonde data (station Schleswig of 12 UT May 22, 1998) for that region and day indicate that the contrail formed above 9 km altitude (pressure <300 hPa, temperature <-47°C) where the wind blew at more than HOkm/h from 330°.

Figure 11.2. Spiral contrail observed in NOAA-14 AVHRR satellite data west of Denmark at 1236 UT, May 22,1998, with at least eight circles of about 60km diameter, and a shift of 195km between the first and the eighth circle at wind speed of HOkm/h, implying a contrail length of about 1500km and contrail age of 1.7-1.9h. (Picture processed by H. Mannstein.)

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The resultant contrail length of about 1500km for a typical aircraft speed of 800km/h and the shift of the circles by 195km with the wind of known speed imply a contrail age of about 1.7-1.9 h. Line-shaped contrails are often visible in multispectral advanced very high resolution radiometer (AVHRR) satellite data. Based on AVHRR channel 4 and 5 differences (near 11 and 12 jam) and a pattern recognition algorithm to differentiate line-shaped clouds from fuzzy cirrus clouds, Mannstein et al. (1999) evaluated the contrail cover over central Europe for 666 days of the years 1995-96 using nearly all noon passages of the NOAA-14 satellite. In the annual mean, line-shaped contrails at noon cover about 0.5% of the area over central Europe. This represents a lower bound for the actual contrail cover because the algorithm cannot identify non-line-shaped contrails. During night the cover is one-third this value in this region. The day/night cover ratio depends on the local day/night traffic ratio, which is different in different regions but amounts to 2.7 in the global average (Schmitt and Brunner 1997). Contrails persist in air masses that are cold and humid enough. From contrail observations these air masses have been estimated to cover 10-20% of the area over parts of Europe (Mannstein et al. 1999) and the United States (Carleton and Lamb 1986). This fraction is consistent with the frequency of icesupersaturation found in MOZAIC data (Gierens et al. 1999b). Hence, as air traffic increases, persistent contrail coverage might increase up to a limit of 10-20% in these regions. Estimates of the global cover of air masses that are cold and humid enough to carry contrails were obtained using meteorological data on temperature and humidity versus pressure altitude over the globe. Using consistently analyzed weather data of the ECMWF for this purpose together with the SchmidtAppleman criterion and a subgrid parameterization of cirrus formation conditions, this potential contrail cover is computed to be largest in the upper troposphere (16% global mean cover; Sausen et al. 1998). The actual contrail cover is computed from the product of the potential cover and the fuel consumption rate in the same region. The product is scaled to match the observed mean contrail cover in those regions where satellite observations exist. Sausen et al. (1998) scaled their cover to the 0.5% mean cover reported by Bakan et al. (1994) for a European/Atlantic region. The computed contrail cover for linear dependence on fuel emissions of 1992 and an overall propulsion efficiency r| = 0.3 reaches 5% over the eastern United States west of New York, with a zonal mean maximum of 0.6% at 50° N, and a global mean cover of 0.09%. The scaling used by Sausen et al. (1998) results in a mean cover of 1.8% in the region where Mannstein et al. (1999) report only 0.5% mean cover during day (Gierens et al. 1999a). Hence the scaling used by Sausen et al. (1998) may overestimate the actual global contrail cover. Observations show that persistent contrails can evolve into extended cirrus that are unrecognizable as aircraft-generated clouds (Schumann and Wendling 1990; Minnis et al. 1998). Aviation-induced aerosol may also affect cirrus clouds indirectly through changes in ice-forming particles and their concentrations. Satellite data suggest that the actual impact of aircraft on cirrus cover may be larger than the computed line-shaped contrail cover. Hence, more work is needed

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to determine the amount of global cover by contrails, which is about 0.1%, with an estimated uncertainty range from 0.02 to 0.2%. The impact of aircraft-induced aerosols and contrails and related cirrus changes is expected to grow with the amount of traffic. Some long-term cirrus observations from ground and from satellites (Liepert 1997; Wylie and Menzel 1999; Boucher 1999; see Fahey and Schumann 1999) indicate increases in cirrus amounts and cirrus frequencies in regions with heavy air traffic. Solar corona observations taken from astrophysical observatories suffer from contrails (Spannagl 1977). The radiance from the corona 40 seconds above the solar limb (0.265° from the sun's center), is typically 10~6-10~3 times smaller than the radiance from the center of the solar disk. Even at 0.5° angular distance from the sun's center, the radiance induced by forward-scattering ice crystals in a thin cirrus cloud with optical depth 0.3 exceeds 1 % of the radiance of the direct sun (Thomalla et al. 1983) and hence makes corona observations impossible. At the mountain observatory on the Wendelstein, Germany, in the northern Alps, the corona was observable on about 120 days/year from 1943 until 1961 (fig. 11.3). Thereafter, the frequency of observability declined substantially to less than 40 days/year by 1978. The number of clear-sky days and the number of solar hours at the same place did not change considerably, so the trends of the corona observations are not due to changing meteorology. Observations of the solar photosphere are less sensitive to cirrus cover and show a weaker trend than the corona observations. The personnel and the priority given to photosphere and corona observations at Wendelstein did not change until 1979. Similar trends in the number of corona days at the Pic du Midi, France, were possibly affected by changes in the personnel or priority of these observations. Data from Norikura, Japan, show no trend. The apparent decrease at Kislovodsk, Russia, until 1976 (Spannagl 1977) did not continue after 1978. The changes at the European stations appear to coincide with the onset of commercial jet traffic in the 1960s. The differences between the Japanese and European observations may be explained by different traffic densities (Spannagl 1977). Such observations are noteworthy but not conclusive. More work is needed to identify and verify or falsify any systematic relationship between air traffic and changes in cloud-related parameters. I 1A Properties of Persistent Contrail Particles

With respect to climatic impact, short-lived contrails are unimportant because of their small degree of cover (about 10~6 of the Earth surface; Ponater et al. 1996). The radiative effects of contrails depend mainly on the coverage and optical depth of persistent contrails. Lidar data reveal a solar optical depth of such contrails that varies typically between 0.05 and 0.5 (Kastner et al. 1993; Jager et al. 1998). The optical depth of contrails remains about constant during the first hour despite horizontal spreading. Occasionally, very thick contrails (order 700m) with optical thickness greater than 1.0 are found at larger temperatures (up to -30°C; Schumann and Wendling 1990; Gayet et al. 1996).The optical depth and the radiative effects of contrails depend on the size, number, and shape of particles, and on the ice water content (IWC).

Figure 11.3. Number of clear-sky days, solar hours, days suitable for solar photospheric observations, and days suitable for solar corona observations per year at Wendelstein (1841 m above sea level, Germany, northern Alps, 12°OF E, 47°42' N), and number of days suitable for corona observations per year for the observatories at Pic du Midi (2861m, Pyrennes, southern France, 8°42' E, 42°56' N), Kislovodsk (2130m, Russia, 42°40' E, 43°45' N, east of the Black Sea), and Norikura (2876m, Japan, 137°33'19" E, 36°06'49" N). Data for the period 1943-1976 are from Spannagl (1997). Data thereafter are from various sources (Deutscher Wetterdienst, Miinchen; Quarterly Bulletin on Solar Activity; yearbooks of the Wendelstein Observatory; Takashi Sakurai, Norikura Solar Observatory). Linear regressions are plotted in two panels with slopes and correlation coefficients, r2, as given. For all other curves, correlation coefficients would be <0.2.

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Contrail particle sizes increase with time in humid air. Ice crystals in young contrails are typically smaller (mean radius of 5-15 urn) than in cirrus clouds (mean radius >30-150um, depending on temperature; see fig. 11.4). In humid air, contrail particles may grow up to 2mm in size (Knollenberg 1972; Strauss et al. 1997). Such large crystals are within the natural variability of cirrus particle sizes. As a consequence, old, dispersed contrails appear to have similar particle sizes as surrounding cirrus (Duda and Spinhirne 1998; Minnis et al. 1998; Schroder et al. 2000). The number of ice crystals in contrails of 10-30min age (order 10-200/cm3) is much larger than in cirrus clouds (Sassen 1997; Schroder et al. 2000). Strong depolarization of lidar returns by contrails with growing particles that are a few minutes old indicate aspherical particle shapes (Freudenthaler et al. 1996; Sassen 1997). Using optical detectors and replicators, both complex ice particles (Goodman et al. 1998; Lawson et al. 1998; Liou et al. 1998; Meyers and Hallett 1998) and nearly spherical ice particles (Strauss et al. 1997; Schroder et al. 2000) were identified. Spherical particles seem to prevail at low ambient temperatures (<-55°C). At low temperatures the ice particles in the contrail core do not find enough water to grow. Hence, the particles in the core remain close to spherical, while the particles near the humid boundary of contrails may become

Figure 11.4. Ice particle size spectra (unit: cm 3) measured with optical particle spectrometers in contrails of different ages and in young cirrus clouds and dry aerosol size spectrum (dried aerosol spectrometer PCASP probes and optical FSSP-300 spectrometer data). Adapted from Schroder et al. (2000).

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large and very complex in shape, especially at high ambient temperature and humidity (Heymsfield et al. 1998a). The larger particles are of various shapes, with the largest particles being bullet rosettes (Lawson et al. 1998). No model exists yet to predict the shape of the particles forming. The IWC of contrails depends, as for cirrus clouds, on temperature, ambient humidity, time available for water deposition, vertical motion of the ambient air, precipitation, and possibly cooling of the ice particles by radiation (Knollenberg 1972). A simple model assumed that the IWC is one half of the amount of water available for ice formation between the limit of ice nucleation and ice saturation (Meerkotter et al. 1999). The limit for ice nucleation is the RH above which nuclei grow and form ice. Heymsfield et al. (1998b) found that the critical RH for ice nucleation decreases almost linearly from water saturation (100% RH) at temperatures above -39°C to 75% RH at and below -55°C. These assumptions result in a function of IWC that depends only on temperature. As a consequence of the saturation properties of water, the IWC grows approximately exponentially with temperature (fig. 11.5). The IWC values implied by this model are a little higher than those measured in cirrus clouds (see Meerkotter et al. 1999). This is reasonable because ice particles in cirrus clouds are larger and may sediment more quickly and over longer periods than in contrails. Figure 11.5 shows the few IWC data points that were measured within aged contrails (Gayet et al. 1996; Sassen 1997; Schroder et al. 2000), including data of the SUCCESS experiment (Heymsfield et al. 1998a). The IWC values vary between 0.7 and 18mg/m3. The data generally support the postulated temperature dependence of the IWC within reasonable limits. Deviations between the measured IWC values and any systematic trend are not surprising because of the difficulties in measuring IWC inside a contrail, which are due to the shortcomings of the various sensors and the representativity of such measurements in a contrail cloud, which is highly heterogeneous spatially. The plot does not include the large IWC values reported by Knollenberg (1972). Values of up to 135mg/m3 at -33.5°C ambient temperature in a contrail of 30min age exceed the amount of water vapor available for ice formation from liquid saturation at this temperature by a factor of 2. The large IWC values are hard to understand because they require that ice particles were formed in an air mass of 100% RH initially and were cooled (e.g., radiatively by about 5 K within the 30min of contrail age). Such a cooling rate (240K/day) can hardly be expected for the cirrus layer as a whole (Liou 1986), but large ice particles at the top of the cirrus and above lower level clouds may experience strong radiative cooling (Gierens 1994). The observations cannot be explained by rising air because the contrail was observed to descend and the data were taken 460m below the level of contrail initialization. If aircraft contrails cause deposition of all water vapor in excess of ice-saturation to form ice particles, the potential IWC can be computed from measured humidity values. Figure 11.5 shows the potential IWC computed from humidity data measured in the MOZAIC project (see above) and in the POLINAT project (Schumann et al. 2000). The mean values of the potential IWC values increase approximately exponentially with temperature:

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Figure I 1.5. Ice water content (IWC) versus ambient temperature. The dashed curve is a proposed contrail IWC model (Meerkotter et al. 1999). The isolated symbols denote individual IWC data measured in aged contrail cirrus by Schroder et al. (2000), by the Desert Research Institute as reported by Sassen (1997), Gayet et al. (1996), and in the SUCCESS experiment between 2314 and 2322UTC, May 12,1996 (see Heymsfield et al. 1998). The filled and open rhombic symbols with error bars denote the mean and the median value and the standard deviations of the potential IWC and temperature deduced from humidity and temperature measurements during the MOZAIC project within the intervals from -70° to -20°C in 10°C intervals (Helten et al. 1998; Gierens et al. 1999b). The filled and open triangles with error bars denote the same from the POLINAT data (Ovarlez et al. 1999; Schumann et al. 2000). The straight full line is the linear least square fit to the logarithmic mean values of the potential IWC values from MOZAIC.

This interpolation is close to the model proposed by Meerkotter et al. (1999) but does not show a change in trend near -39°C as would be expected if the RH of ice nucleation is 100% above and less than 100% below that temperature. Further IWC measurements in persistent contrails are needed to verify this relationship.

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I 1.5. Radiative Forcing by Contrails

Radiative forcing by contrails is computed using one-dimensional radiative transfer models suitable for geometrically and optically thin, plane-parallel homogeneous cirrus layers in a static atmosphere (Liou 1986; Fu and Liou 1993; Fortuin et al. 1995; Strauss et al. 1997; Raschke et al. 1998). The three-dimensional effect of narrow but thin contrails seems to be small (Schulz 1998), but some measurements below thick contrails indicate smaller long-wave forcing than expected for homogeneous cloud layers (Kuhn 1970). Cloud radiative forcing is denned as the change in net flux at some level in the atmosphere calculated in response to a perturbation in clouds for otherwise fixed atmospheric parameters. A positive net flux change represents an energy gain and hence a net heating of the Earth's system below the level considered. In most cases, contrails increase the Earth's system albedo and hence cause a negative radiative forcing in the shortwave (SW) range. Contrails have a lower temperature than the atmosphere below the contrails and hence induce a positive radiative forcing in the long-wave (LW) range. The net radiative forcing is the sum of the SW and LW contributions. In most cases, the net radiative forcing is positive at top of the atmosphere but negative at the Earth's surface, especially during daytime. The radiative forcing grows with the optical depth (or ice water path; IWP) and with the amount of contrail cover. A parameter study of radiative forcing by contrails was reported by Meerkotter et al. (1999). The radiative forcing at the top of the atmosphere for 100% contrail cover and either spheres or randomly oriented hexagons is plotted versus time of day in figure 11.6 for a contrail with a visible optical depth of 0.5. The particle size spectrum is assumed to be the same as measured by Strauss et al. (1997) with a volume-mean particle diameter of 16.4 um. Contrails heat most when covering a warm and bright surface. Contrails are most efficient in radiatively forcing the Earth's atmosphere in the tropics and over low-level clouds and are more efficient in summer than in winter. Contrails with smaller ice particles cause stronger heating than other cirrus with the same IWP because the albedo increases less strongly than the thermal absorption efficiency with decreasing crystal size. However, for very small crystals [i.e., for particle radius smaller than about 10um (depending on IWP)], a reduction in radius cools the atmosphere because the albedo increases more than the absorption efficiency. Contrails with spherical particles cause more heating than hexagonal ice particles (fig. 11.6). At the top of the atmosphere, for a global mean contrail cover of 0.1% and an average optical depth of 0.3, contrails have been computed to cause about 0.02 W/m2 daily mean radiative forcing in the global mean, with an estimated uncertainty factor of 4. As shown in figure 11.7c, the radiative forcing is larger regionally with maximum values of up to 0.7 W/m2 over parts of Europe and the United States (Minnis et al. 1999).The contrail cover and, even more so, the radiative forcing is relatively large compared to fuel consumption along the narrow long-distance flight routes in the upper troposphere. For given fuel consumption, the radiative forcing is larger over Europe than over the United States. The contrail forcing appears to be larger than the radiative forcing from past carbon

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Figure 11.6. Flux changes at top of atmosphere (TOA) and at the surface versus time of day for long-wave (LW), and net (SW + LW, short-wave and long-wave) fluxes for spherical and hexagonal (shown for TOA only) particles. Adapted from Meerkotter et al. (1999).

dioxide emissions from aircraft (IPCC 1999). The biggest uncertainties of computed contrail forcing values appear to result from the not-well-known contrail cover and optical depth values and unknown impact of aircraft emissions on natural cirrus. Contrails cause a small and slow heating of the troposphere. Strauss et al. (1997) used a one-dimensional radiative convective model to simulate the climatic conditions of a mid-European region. They found a steady-state mean temperature increase on the order of 0.05 K for a 0.5% increase in current contrail

Figure 11.7. (a) Air traffic as of 1992 in terms of vertically integrated annual mean fuel consumption [g(fuel)/m2 a"1] above 500 hPa according to the DLR-2 data set (Schmitt and Brunner, 1997). (b) Computed contrail cover for this traffic (Sausen et al. 1998), and (c) net radiative forcing at the top of atmosphere in the daily and annual average for this contrail cover and an assumed 0.55-|Lim optical depth of 0.3 (Minnis et al. 1999). The contours give the percentage relative to the maximum values of 11.14g/m2a~1, 5.45%, and 0.725 W/m2, in the panels from top to bottom, respectively.

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cloud cover—too small to be measurable. With a two-dimensional radiative convective model, a 1K increase was found in surface temperature over most of the Northern Hemisphere for an additional cirrus cover of 5% (Liou et al. 1990). Using a global circulation model, the potential effects of contrails on global climate were simulated by introducing additional cirrus cover with the same optical properties as natural cirrus in air traffic regions with large fuel consumption (Ponater et al. 1996). The induced temperature change was significant for an assumed 5% additional cirrus cloud cover in the main traffic regions. These studies demonstrate the importance of contrails in climate change but do not yet provide a reliable quantitative assessment. As illustrated in figure 11.6, contrails cool the surface during the day and heat the surface during the night and hence reduce the daily temperature amplitude. The net effect depends strongly on the daily variation of contrail cloud cover. A reduction of solar flux by 50W/m2, as measured by Sassen (1997), is to be expected locally in the shadow of thick contrails (T > 1). The surface LW forcing is small because of shielding of terrestrial radiation by water vapor in the atmosphere above the surface. Hence, the Earth's surface locally receives less solar energy in the shadow of contrails (Sassen 1997). This does not exclude a warming of the atmosphere-surface system driven by the net flux change at the top of the atmosphere. As shown by radiation-convection models, vertical heat exchange in the atmosphere may cause warming of the surface even when it gets less energy by radiation (Strauss et al. 1997). Besides the forcing by line-shaped contrail cirrus, the global radiation balance may also be perturbed if there is a significant indirect effect of aircraft-induced aerosol, water vapor, and contrails on the cover and properties (particle size distribution, number density, and composition) of natural cirrus clouds. In addition, there might be other indirect cloud-related effects, such as humidity changes, precipitation, and others still to be identified. The radiative forcing from these indirect effects are unknown. Preliminary studies (Wyser and Strom 1998; Meerkotter et al. 1999) show that aircraft-induced changes in the particle size of natural cirrus clouds may cause radiative forcing comparable to the direct forcing due to additional contrail cloud cover. This requires further studies. In the future, contrail cloudiness will increase more strongly than global aviation fuel consumption if air traffic increases mainly in the upper troposphere or if engines have larger overall efficiency, causing cooler exhaust for the same water concentration and hence contrails also at lower altitudes (an increase of the efficiency, t|, from 0.3 to 0.5 reduces the threshold level of contrail formation by 700m). The radiative forcing may increase even more when the contrail cover increases relatively more in the tropics. In a scenario for the year 2050 with a threefold increase in fuel consumption, a four- to fivefold increase in contrail cover and a sixfold increase in radiative forcing is expected (Gierens et al. 1999a). Higher cruise altitudes will increase contrail cover in the subtropics, and flying lower will increase contrail cover in polar regions (Sausen et al. 1998). Future research should help to reduce the main uncertainties: cover and mean optical depth of contrails over the globe and indirect impact of aircraftgenerated aerosols on cirrus cloudiness. For that purpose it would be interesting to know any differences between cirrus cloud properties in the Southern and

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Northern hemispheres at mid-latitudes, with large differences in aerosol loading near the tropopause (Kent et al. 1998). Also, it would be important to know how long and with which areal fraction persistent contrails cover a region and impact the daily temperature range.

Acknowledgments I am grateful to important contributions that I received in preparing the material used for this review, in particular from the authors, contributors, and reviewers of the related chapter 3 of the IPCC assessment, especially David W. Fancy, Klaus Gierens, Bernd Karcher, Ralf Meerkotter, Patrick Minnis, Robert Sausen, and O. Brian Toon. I thank Stefan Kinne for providing data from the SUCCESS experiments, Herman Smit and Alain Marenco for providing access to the MOZAIC data, Joelle Ovarlez for the frost-point temperature data measured during POLINAT, Richard Meyer and Hermann Mannstein for providing satellite data, and Franz P. Schroder, David R. Doelling, and Klaus Gierens for providing materials and figures prior to publication. I thank Otto Barnbantner, Heinz Earwig, Guido Kugelmann, Jean-Louis Leroy, Christian Spannagl, Takashi Sakurai, and Peter Wendling for help in collecting and understanding the data shown in figure 11.3. Finally, I thank David K. Lynch for inviting me to contribute to this book.

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Kuhn, P.M., 1970. Airborne observations of contrail effects on the thermal radiation budget. /. Atmos. Sci., 27, 937-942. Kuhn, M., A. Petzold, D. Baumgardner, and P.P. Schroder, 1998. Particle composition of a young condensation trail and of upper tropospheric aerosol. Geophys. Res. Lett., 25, 2679-2682. Lawson, R.P., A.J. Heymsfield, S.M. Aulenbach, and T.L. Jensen, 1998. Shapes, sizes and light scattering properties of ice crystals in cirrus and a persistent contrail during SUCCESS. Geophys. Res. Lett., 25,1331-1334. Lewellen, D.C., and W.S. Lewellen, 1996. Large eddy simulations of the vortex-pair breakup in aircraft wakes. AIAA Journal, 34,2337-2345. Liepert, E.G., 1997. Recent changes in solar radiation under cloudy conditions. Int. J. Climat., 17,1581-1593. Liou, K., 1986. Influence of cirrus clouds on weather and climate processes: A global perspective. Mon. Wea. Rev., 114,1167-1199. Liou, K.-N., S.C. Ou, and G. Koenig, 1990. An investigation of the climatic effect of contrail cirrus. In Air Traffic and the Environment: Background, Tendencies, and Potential Global Atmospheric Effects (U. Schumann, ed.). Springer-Verlag, Berlin, pp. 154-169. Liou, K.N., P. Yang, Y. Takano, K. Sassen, T. Charlock, and W. Arnott, 1998. On the radiative properties of contrail cirrus. Geophys. Res. Lett., 25,1161-1164. Lukachko, S.P., LA. Waitz, R.C. Miake-Lye, R.C. Brown, and M.R. Anderson, 1998. Production of sulfate aerosol precursors in the turbine and exhaust nozzle of an aircraft engine. /. Geophys. Res., 103,16159-16174. Mannstein, H., R. Meyer, and P. Wendling, 1999. Operational detection of contrails from NOAA-AVHRR-data. Int. J. Remote Sensing, 20,1641-1660. Marenco, A., V. Thouret, P. Nedelec, H. Smit, M. Helten, D. Kley, F. Karcher, P. Simon, K. Law, J. Pyle, G. Poschmann, R. von Wrede, C. Hume, and T. Cook, 1998. Measurement of ozone and water vapor by Airbus in-service aircraft: The MOZAIC airborne program, an overview. /. Geophys. Res., 103, 2563125642. Mazin, I.P., 1996. Aircraft condensation trails. Iz. Atmos. Oceanic Phys., 32,1-13. Meerkotter, R., U. Schumann, D.R. Doelling, P. Minnis,T. Nakajima, and Y.Tsushima, 1999. Radiative forcing by contrails. Ann. Geophys, 17,1080-1094. Meyers, M., and J. Hallett, 1998. Ice crystal morphology in aircraft contrails and cirrus. In Proceedings of the Conference on Cloud Physics, August 17-21, 1998, Everett, WA. American Meteorological Society, Boston, MA, p. 4. Miake-Lye, R.C, B.E. Anderson, W.R. Cofer, H.A. Wallio, G.D. Nowicki, J.O. Ballenthin, D.E. Hunton, W.B. Knighton, T.M. Miller, IV. Seeley, and A.A. Viggiano, 1998. SOX oxidation and volatile aerosol in aircraft exhaust plumes depend on fuel sulfur content. Geophys. Res. Lett., 25,1677-1680. Miake-Lye, R.C, M. Martinez-Sanchez, R.C. Brown, and C.E. Kolb, 1993. Plume and wake dynamics, mixing and chemistry behind an HSCT aircraft. / Aircraft, 30, 467479. Minnis, P., J.K. Ayers, and S.P. Weaver, 1997. Surface-based observations of contrail occurrence frequency over the U.S., April 1993-April 1994. NASA Reference publ. 1404. National Aeronautics and Space Administration, Washington, DC. Minnis, P., U. Schumann, D.R. Doelling, K.M. Gierens, and D.W. Fahey, 1999. Global distribution of contrail radiative forcing. Geophys. Res. Lett., 26,1853-1856. Minnis, P., D.F. Young, D.P. Garber, L. Nguyen, W.L. Smith, Jr., and R. Palikonda, 1998. Transformation of contrails into cirrus during SUCCESS. Geophys. Res. Lett., 25, 1157-1160.

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Murphy, D.M., K.K. Kelly, A.F. Tuck, and M.H. Proffitt, 1990. Ice saturation at the tropopause observed from the ER-2 aircraft. Geophys. Res. Lett., 17,353-356. Ovarlez, J., H. Ovarlez, R.-M. Philippe, and J. Capus, 1999. Water vapor measurements during POLINAT 2 experiment. In Final POLINAT-2 Report (U. Schumann, ed.). Air Pollution Research Report EUR 18877 EN, Luxembourg, Brussels, pp. 111120. Petzold, A., R. Busen, P.P. Schroder, R. Baumann, M. Kuhn, J. Strom, D.E. Hagen, P.D. Whitefield, D. Baumgardner, F. Arnold, S. Borrmann, and U. Schumann, 1997. Near field measurements on contrail properties from fuels with different sulfur content. /. Geophys. Res., 102,29867-29881. Petzold, A., and A. Dopelheuer, 1998. Reexamination of black carbon mass emission indices of a jet engine. Aerosol. Sci. and Techn., 29,355-356. Petzold, A., and P.P. Schroder, 1998. Jet engine exhaust aerosol characterization. Aerosol Sci. Tech., 28,62-76. Petzold, A., J. Strom, S. Ohlsson, and P.P. Schroder, 1998. Elemental composition and morphology of ice-crystal residual particles in cirrus clouds and contrails. Atmos. Res., 49,21-34. Petzold, A., J. Strom, P.P. Schroder, and B. Karcher, 1999a. Carbonaceous aerosol in jet engine exhaust: Emission characteristics and implications for heterogeneous chemistry. Atmos. Environ, 33,2689-2698. Petzold, A., A. Dopelheuer, C.A. Brock, and P.P. Schroder, 1999b. In situ observations and model calculations of black carbon emission by aircraft at cruise altitude. /. Geophys. Res., 104, 22171-22181. Ponater, M., S. Brinkop, R. Sausen, and U. Schumann, 1996. Simulating the global atmospheric response to aircraft water vapour emissions and contrails: A first approach using a GCM. Ann. Geophys., 14, 941-960. Pueschel, R.F., S. Verma, G.V. Ferry, S.D. Howard, S. Vay, S. A. Kinne, J. Goodman, and A. Strawa, 1998. Sulfuric acid and soot particle formation in aircraft exhaust. Geophys. Res. Lett., 25,1685-1588. Raschke, E., P. Flamant, Y. Fouquart, P. Hignett, H. Isaka, P.R. Jonas, H. Sundquist, and P. Wendling, 1998. Cloud-radiation studies during the European Cloud and Radiation Experiment (EUCREX). Surveys Geophys., 19, 89-138. Sassen, K., 1997. Contrail-cirrus and their potential for regional climate change. Bull. Amer. Meteor. Soc., 78,1885-1903. Sassen, K., and C.-Y. Hsueh, 1998. Contrail properties derived from highresolution polarization lidar studies during SUCCESS. Geophys. Res. Lett., 25,11651168. Sausen, R., K. Gierens, M. Ponater, and U. Schumann, 1998. A diagnostic study of the global distribution of contrails: Part I: Present day climate. Theor. Appl. Climatol., 61, 127-141. Schmidt, E., 1941. Die Entstehung von Eisnebel aus den Auspuffgasen von Flugmotoren. In Schriften der Deutschen Akademie der Luftfahrtforschung. Verlag R. Oldenbourg, Miinchen, Heft 44, pp. 1-15. Schmitt, A., and B. Brunner, 1997. Emissions from aviation and their development over time. In DLR-Mitteilung 97-04, Deutsches Zentrum fur Luft- und Raumfahrt, Koln, Germany, pp. 37-52. Schrader, M.L., 1997. Calculations of aircraft contrail formation critical temperatures. /. Appl Meteor., 36,1725-1728. Schroder, P., B. Karcher, C. Duroure, J. Strom, A. Petzold, J.-F. Gayet, B. Strauss, P. Wendling, and A. Thomas, 2000. On the transition of contrails into cirrus clouds. J. Atmos. Sci., 57,464-480.

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12

Subvisual Cirrus

DAVID K. LYNCH KENNETH SASSEN

Starting during World War II, pilots flying high over the tropics reported "a thin layer of cirrus 500ft above us". Yet as they ascended, they still observed more thin cirrus above them, leading to the colloquialism "cirrus evadus." With the corning of lidar in the early 1960s, rumors and unqualified reports of subvisual cirrus were replaced with validated detections, in situ sampling, and the first systematic studies (Uthe 1977; Barnes 1980,1982). Heymsfield (1986) described observations over Kwajalein Atoll in the western tropical Pacific Ocean, where pilots and lidars could clearly see the cloud but DMSP (U.S. Defense Meteorological Satellite Program) radiance measurements and ground observers could not. The term "subvisual" is a relatively recent appellation. Prior terminology included cirrus haze, semitransparent cirrus, subvisible cirrus veils, low density clouds, fields of ice aerosols, cirrus, anvil cirrus, and high altitude tropical (HAT) cirrus. Subvisual cirrus clouds (SVC) are widespread (Winker and Trepte 1998; see chapter 12, this volume) and virtually undetectable with existing passive sensors. Orbiting solar limb occupation systems such as the Stratospheric Aerosol and Gas Experiment (SAGE) can detect these clouds, but only by looking at them horizontally where the optical depths are significant. SVC appear to affect climate primarily by heating the planet, though to what extent this may happen is unknown. Much of what we know is based on work by Heymsfield (1986), Platt et al. (1987), Sassen et al. (1989, 1992), Flatau et al. (1990), Liou et al. (1990), Hutchinson et al. (1991,1993), Dalcher (1992), Sassen and Cho (1992), Takano et al. (1992), Lynch (1993), Schmidt et al. (1993), Schmidt and Lynch (1995), and Winker and Trepte (1998). 256

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12.1. Defining Properties

SVC are defined as any high clouds composed primarily of ice (WMO 1975) and whose vertical visible optical depth is 0.03 or less (Sassen and Cho 1992). Such clouds are usually found near the tropopause and are less than about 1 km thick vertically. SVC do not appear to be fundamentally different from ordinary, optically thicker cirrus. They do, however, differ from average cirrus by being colder (-5090°C), thinner (<0.03 optical depths at 0.694 urn), and having smaller particles (typically about <50um diameter). Thus, SVC occupy the extreme range of thin (i.e., bluish-colored) cirrus cloud properties, and most of their characteristics can be traced to the small amount of water vapor available in the region where SVC form (Jensen et al. 1996a,b; Rosenfeld et al. 1998).

12.2. Optical Properties

SVC are normally invisible to the naked eye because they have such a low contrast at most solar-scattering angles. They can, however, often be detected visually within a few degrees of the sun, particularly if the air is very clear and if the SVC display enough structure or motion to be distinguished from a uniform layer, or at sunset. SVC, by definition, always appear bluish when viewed from the ground, but they can sometimes be identified by the solar (or lunar) optical phenomena known to be generated by small particles (Sassen et al. 1989; Sassen 1991). These optical displays are the aureole and corona. As with any detection scheme, visual detection depends on color or brightness contrast, and SVC exhibit very low contrast at all wavelengths. In the visible part of the spectrum, ice absorbs little light, and therefore scattering is the dominant means of interacting with sunlight. A significant absorption exists near 3.1 um, but the most important absorption occurs between 8 and 13 um, where the bulk of the Earth's thermal radiation occurs and where, coincidentally, the atmosphere is relatively transparent.

12.3. Microphysical Properties

Practically all that is known about the composition of SVC comes from the limited high altitude aircraft studies of Heymsfield (1986). SVC particles are 1-50 um in diameter—very small compared to thicker, more easily detected cirrus (often >100um). On the basis of the passive remote sensing analysis of corona displays in SVC, particle diameters of between 10 and 30 um have been derived (Sassen 1991). The crystals may be any shape, although trigonal and hexagonal prisms with aspect ratios near unity are common. These properties lead to relatively large diffraction widths (1-35°) and relatively small asymmetry parameters (0.4-0.6) outside of strong absorption bands (Liou et al. 1998).

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12.4. Large-scale Properties

SVC are predominantly a tropical/subtropical phenomenon. In some parts of the Pacific and Indian oceans such as the Bay of Bengal, these clouds are almost ubiquitous. SVC are believed to be primarily the remnants of the deep convection found straddling the Intertropical Convergence Zone (ITCZ) between the two subtropical jet streams. These correspond to latitudes ±20-30° but vary seasonally. Subvisual cirrus associated with equatorial regions appear to have the largest extent and longest persistence and are observed frequently. Other occurrences of SVC are less common. Mid-latitude and probably polar SVC occur primarily in association with visible cirrus cloud fields—that is, in thin spots or along margins (Sassen and Cho 1992). Subvisual cirrus associated with the jet stream are likely to be "streak" clouds due to the shear forces involved. A common scenario in the southern United States is the advection of subtropical moisture above 200-300mb into the vicinity of the jet stream. Subvisual cirrus are also generated with the passage of fronts, particularly cold fronts (Schmidt 1991). SVC may appear where orographic lifting forces the formation of an optically thin cloud. There is a wide disparity in the observations reported, as reflected by the signature characteristics. There are two varieties of these clouds: streak clouds and vertically extensive clouds. The streak clouds tend to be elongated along the direction of the wind and of limited extent in the vertical and crosswind directions. Vertically extensive clouds have limited horizontal extent but have highly variable geometrical thickness. Other types of SVC can also occur. Convective cloud anvils are a source of optically thin clouds at high altitude. Whether these clouds are actually attached, subvisual cloud edges, or detached subvisual cloud remnants, is uncertain. 12.5. Occurrence and Climatology

The global- and annual-averaged occurrence of cirrus may be as high as 50% according to satellite measurements (chapter 6). The occurrence of cirrus, however, is geographically and seasonal variable to a large extent. While some places in world may be cirrus-free for months, others are under a veil for extended periods. There currently are no global SVC climatologies because such studies are done using passive satellite systems and such systems do not detect SVC. Region lidar climatologies of SVC do exist (chapter 2). However, SVC tend to occur with thicker cirrus, and therefore the climatologies of the two should be similar, at least at mid-latitudes (Schmidt and Lynch 1995). SVC are believed to be the most common near the tropical tropopause (Jensen et al. 1996a,b; Rosenfeld et al. 1998). However, the only global study to date has been the Lidar In-Space Technology Experiment (LITE, see Winker et al. 1996; Winker and Trepte 1998). LITE sampled very thin cirrus clouds and provided the first data showing their global distribution, which is concentrated in the tropics and subtropics (figure 12.1). However, the planet was too sparsely sampled both spatially and temporally to produce a true global climatology.

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Figure 12.1 (Adapted from Winker and Trepte 1998). The horizontal extent and altitude of subvisual (laminar) cirrus based on results from the Lidar In-Space Technology Experiment (LITE). The range of the NCEP tropopause heights along the LITE ground track at all longitudes during the mission are shown by the shaded area.

Regardless of specific origin, the formation of a SVC layer requires a highaltitude moisture flux and turbulent conditions or wave action to initiate crystal growth. The vertical motion induced by gravity waves is attractive as a mechanism to initiate formation of optically thin clouds, particularly when banded structures are observed. Top-down convection processes at the tropopause are also possible formation mechanisms, as is motion due to lateral shearing equatorward of the jet stream core (Browning and Pardoe 1973). The ITCZ and fronts are sources of gravity wave generation, while the jet core induces lateral shearing of similar magnitude to the Coriolis parameter on its flanks. Cloud formation is prevalent in all cases. A significant fraction of SVC sightings appear to be observations of cloud remnants. Orographically produced cloud remnants, material blown off anvil tops, and diffuse contrails in regions with a high volume of air traffic are all simple examples. The interaction of gravity waves with moisture fields near the tropopause that are saturated with respect to ice is highly likely to cause cloud formation. SVC often occur at or near the tropopause. The difference in height between the top of an SVC layer and the tropopause varies with latitude, as established by statistics compiled from airborne observations (Williams et al. 1985). The height difference is 1.1 ± 1.6km in Alaska, 2.2 ± 1.8km in New Mexico, and 3.5 ± 2.3km in the Marshall Islands. A likely reason for the latitude dependence is the change in the moist adiabatic lapse rate near the tropopause that occurs from tropical to polar regions. The pseudo-adiabat governs the height at which saturation with respect to ice occurs—hence the latitude dependence.

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12.6. Prediction

Almost any scheme that successfully predicts cirrus will also predict SVC because the latter is a subset of the former. However, a notable exception is in the equatorial lows, where SVC may be present for weeks or months in otherwise clear skies. Predicting SVC can be done in several ways, depending on the purpose of the prediction. Persistence prediction takes the existing cirrus field and propagates it based on wind conditions. It is useful for short periods of time, usually about a day unless clearly defined weather patterns are present. In that case the cirrus prediction can be correlated to the expected behavior of the air masses. Physical prediction is based on the physical properties of the atmosphere (temperature, humidity and wind profiles, turbulence, aerosol content, etc.) and computing their behavior. Such studies are difficult owing to uncertainties in the initial conditions in the model and the uncertainties in the spatiotemporal state and evolution of the physical properties of the atmosphere. Eventually, however, these are expected to give the best results. We are not aware of any operational prediction program aimed specifically at visual or subvisual cirrus clouds. 12.7. Detection

From the standpoint of a given detection system, any cirrus that cannot be detected is "subvisual." The minimum detectable optical depth varies from system to system and even from situation to situation for a given system (daytime, background radiance, etc.) There is a continuum of cirrus cloud optical depths ranging from zero to an upper limit of about 3.0 in most cirrus (Sassen 2001). Based on high-powered lidar measurements, the minimum visible optical depth for SVC is approximately 0.03 under good viewing conditions (Sassen and Cho 1992). Under poor viewing conditions such as hazy skies, uniform cirrus layers with much larger optical depths may go undetected. The inability to detect and compensate for SVC can have significant consequences on satellite systems when they derive parameters such as sea surface temperature through SVC. For example, an optical depth of i = 0.03 in the visible corresponds roughly to the same value at Hum. However, visible extinction is largely due to scattering, but at Hum absorption plays the key role.The transmission of such a cloud is about exp(-0.03) or 97%. An unmitigated signal loss of 3% at Hum corresponds to a temperature error of about 2K at 283K. More extensive studies show that the mean sensitivity in retrieved surface temperature is about A77T ~ 100 (Cornette and Shanks 1993). Such an error would be intolerable in most modern satellite remote sensing systems. Among active remote sensors, ground-based lidar is the most sensitive to SVC. Even millimeter-wave research radars, which can detect the larger particles in conventional cirrus, would have extreme difficulties in detecting the small particles typical of SVC. Although no passive satellite system using emitted infrared or reflected solar light can detect SVC at the present time (chapter 12), clouds that are subvisual

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vertically but extended horizontally enough to have larger horizontal optical depths can be detected at the limb with solar occultation devices. The most successful program to have done this is the Stratospheric Aerosol and Gas Experiment (SAGE I, II, III) projects. Wylie reviews the SAGE results in chapter 6. Passive detection of SVC should be possible, but so far the attempts have been disappointing, especially from operational systems. Improving passive detection systems to the point where they can detect and measure SVC is a goal that should be pursued vigorously. The upcoming PICASSO-CENA (Pathfinder Instruments for Cloud and Aerosol Space borne Observations—Climatologie Etundue des Nuages et des Aerosols) mission (Winker and Wielicki 2000) should greatly expand our ability to detect and characterize SVC from space. 12.8. Subvisual Cirrus Model

Shettle et al. (1988) and Shettle (1989) supplied a macrophysical SVC model in MODTRAN that used 4 urn radius spherical ice particles rather than the larger 64-um radius particles used in the MODTRAN model for ordinary cirrus. In this SVC model, the user specifies cloud base and height, extinction coefficient, K (km"1), at 0.55 urn, and the model takes precomputed extinction efficiencies and calculates the clouds' optical properties. This model is easy to use and gives tolerably good results in many situations. Table 12.1 shows our model of a thin cirrus cloud based on microphysical parameters. This model meets the generally accepted standards of SVC. Some of the parameters are related to others, and thus the model may appear somewhat redundant or overspecific. In fact, table 12.1 consists of guidelines rather than absolute requirements. While not necessarily representative of all possible SVC, the model possesses enough of their characteristics to form a foundation against which system and algorithm developers can test their detection approaches. 12.9. Recommendations

To better understand SVC, we suggest the following efforts: 1) More in situ measurements are needed to determine the microphysical content of the clouds. This will allow the direct calculation of the individual particle's optical properties and the means to determine the particle size distribution. Special attention should be paid to the small particle sizes (down to 1 um) because these could be the most numerous particles, probably have the largest cross-section per unit mass, and are the most difficult to detect with conventional particle counters. 2) Complete global satellite lidar climatology including seasonal variations is needed. 3) High-altitude multispectral visible and infrared observations should be conducted. Such programs will produce the passive signatures, which can be used to plan future sensors and detection algorithms. Such measurements should be part of coordinated multi-instrument campaigns like FIRE (First ISCCP Regional Experiment). 4) Better physical prognostication tools are needed.

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Table 12.1. Guidelines for subvisual cirrus models Composition Particle size (long dimension) Particle shape Number density Thickness (Az) Height Horizontal size Temperature Temperature range Optical thickness (T) Depolarization ratio Asymmetry parameter Ice water content

Nonspherical ice particles <50um Plates, columns, aspect ratios near unity <5 x 104/m3 <1 km 12-18 km (at or near tropopause) Mesoscale (20-2000 km) -40 to -90°C Nearly isothermal <0.03 at 0.5 um 0.5-0.8 0.4-0.6 <2 x lO^g/m3

Optical constants of crystalline (as opposed to amorphous) hexagonal ice should be used. Particle shapes must be defined by the user because each shape has a different asymmetry parameter, extinction efficiency, and emissivity. The approach to defining a SVC model is to first decide on the particle properties and then compute Qea, depolarization ratio, asymmetry parameter, and other properties needed for a radiative transfer model. Next solve for the number density n(r) (or N) by imposing the optical depth condition T < 0.03 at 0.5 jam [i.e., I = L$Qea(r)Gn(r)dr, where a is the geometrical cross-section of the particle]. Properties such as ice water content can then be calculated. Finally, the thickness and height (which defines temperature) are specified.

12.10. Summary Subvisual cirrus remain one of the most challenging aspects of cirrus research because they are difficult to detect and characterize. Although their spatial extent is still poorly understood, in view of their potential impact on climate, the ability to detect them will continue to be vital to many aspects of meteorology and remote sensing.

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Flatau, P.J., G.L. Stephens, and B.T. Draine, 1990. Radiative properties of visible and sub visible cirrus: Scattering in hexagonal ice crystals. In FIRE Science Results 1988 (D.S. McDougal and H.S. Wagner, eds.). NASA Conference Publication 3083. National Aeronautics and Space Administration, Washington, DC. Heymsfield, A.J., 1986. Ice particles observed in a cirriform cloud at -83°C and implications for polar stratospheric clouds. /. Atmos. Sci., 43, 851-855. Hutchinson, K.D., J. Mack, G. Logan, K.R. Hardy, and S. Westerman, 1993. The identification of optically-thin cirrus clouds by automated classification algorithms using nighttime, multi-spectral, multi-sensor meteorological satellite data. In Proceedings of Passive Infrared Remote Sensing of Clouds and the Atmosphere Conference 1934 (D. Lynch, ed.). Orlando, FL, pp. 240-243, SPIE, Bellingham, WA. Hutchinson, K.D., J. Mack, R. McDonald, and G. Logan, 1991. The positive identification of optically-thin cirrus in nighttime, multispectral meteorological satellite imagery by automated cloud detection and typing algorithms. In Proceedings of Cloud Impacts on DoD Operations and Systems, L.D. Grantham (Ed.) Los Angeles, CA. Jensen, E.J., O.B. Toon, L. Pfister, and H. Selkirk, 1996a. Dehydration of the upper troposphere by subvisual cirrus clouds near the tropical tropopause. Geophys. Res. Lett., 23, 825-828. Jensen, E.J., O.B. Toon, H. Selkirk, J.D. Spinhirne, and M.R. Schoeberl, 1996b. On the formation and persistence of subvisual cirrus clouds near the tropical tropopause. J. Geophys. Res., 101, 21361-21375. Liou, K.N., Y.Takano, S.C. Ou, A.J. Heymsfield, and W. Kreiss, 1990. Infrared transmission through cirrus clouds: a radiative model for target detection. Appl. Opt., 29, 18861896. Liou, K.N., P. Yang, Y. Takano, K. Sassen, T.P. Charlock, and W.P. Arnott, 1998. On the radiative properties of contrail cirrus. Geophys. Res. Lett., 25,1161-1164. Lynch, D.K., 1993. Subvisual cirrus: what it is and where you find it. In Proceedings of Passive Infrared Remote Sensing of Clouds and the Atmosphere Conference 1934 (D. Lynch, ed.). Orlando, FL, pp. 264-274. SPIE, Bellingham, WA. Platt, C.M.R., J.C Scott, and A.C. Dilley, 1987. Remote sounding of high clouds. Part VI: Optical properties of midlatitude and tropical cirrus. /. Atmos. Sci., 44, 729-747. Rosenfield, J.E., D.B. Considine, M.R. Schoeberl, and E.V. Browell, 1998. The impact of subvisual cirrus clouds near the tropopause on stratospheric water vapor. Geophys. Res. Lett., 49,1883-1886. Sassen, K., 1991. Corona producing cirrus cloud properties derived from polarization lidar and photographic analyses. Appl. Opt., 30, 3421-3428. Sassen, K., and B.S. Cho, 1992. Subvisual/thin cirrus lidar dataset for satellite verification and climatological research. J. Appl. Meteor., 31,1275-1285. Sassen, K., M.K. Griffin, and G.C. Dodd, 1989. Optical scattering and microphysical properties of subvisual cirrus clouds, and climatic implications. /. Appl. Meteor., 28, 91-98. Schmidt, E.O., 1991. Cloud properties as inferred from HIRS/2 multi-spectral data. PhD thesis. Georgia Institute of Technology, Atlanta, GA. Schmidt, E.O., J.M. Alvarez, M.A. Vaughn, and D.P. Wylie, 1993. A review of subvisual cirrus morphology. In Proceedings of Passive Infrared Remote Sensing of Clouds and the Atmosphere Conference 1934 (D. Lynch, ed.). Orlando, FL, pp. 230-239. Schmidt, E.O., and D.K. Lynch, 1995. Subvisual cirrus: associations to the dynamic atmosphere and radiative effects. In Proceedings of Passive Infrared Remote Sensing of Clouds and the Atmosphere 111, SPIE 2578 (D. Lynch, ed.). Sept. 25-28, Paris, pp. 68-75. Shettle, E.P., 1989. Models of aerosols, clouds and precipitation for atmospheric propagation studies. In Atmospheric Propagation in the UV, Visible, IR and MM-Wave regions

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and Related System Aspects. Advisory Group for Aerospace Research and Development, Paris meeting, Copenhagen, pp. 9-13. Shettle, E.P., EX. Kneizys, S.A. Clough, G.P. Anderson, L.W. Abreu, and J.H. Chetwynd, 1988. Cloud models in LOWTRAN and FASCODE. In Proceedings of the CIDOS88 Workshop (D.D. Grantham and J.W. Snow, eds.). pp. 199-206. Phillips Laboratory, Hansomb AFB. Takano, Y., K.N. Liou, and P. Minnis, 1992. The effects of small ice crystals on cirrus infrared radiative properties. /. Atmos. Sci., 49,1487-1493. Uthe, E., and P.B. Russell, 1977. Lidar Observations of Tropical High Altitude Cirrus Clouds. In Proceedings of the IAMAP Symposium on Radiation in the Atmosphere, Garmisch-Partenkirchen, Germany. Science Press, pp. 242-244. Williams, W.J., D.G. Murcray, and S. Proffitt, 1985. Characterization of the radiometric tropopause. In Proceedings of the IRIS Meeting on Targets, Backgrounds and Discrimination. Environmental Research Institute of Michigan, Ann Arbor, MI. Winker, D.M., R.H. Couch, and M.P. McCormick, 1996. An overview of LITE: NASA's Lidar In-space Technology Experiment. Proc. IEEE, 84,164-180. Winker, D.M., and C.R. Trepte, 1998. "Laminar cirrus observed near the tropical tropopause by LITE. Geophys. Res. Lett., 25, 3351-3354. Winker, D.M., and B. A Wielicki, 2000. The PICASSO-CENA Mission. In Sensors, Systems, and Next Generation Satellites (H. Fujisada, ed.), Proc. SPIE, vol. 3870,26-36. WMO, 1975. International Cloud Atlas. World Meterological Organization, Geneva.

13

Radiative Transfer in Cirrus Clouds Light Scattering and Spectral Information

K.N.

LIOU

Y. T A K A N O P. Y A N G Y. GU

The importance of cirrus clouds in climate has been recognized in the light of a number of intensive composite field observations: the First ISCCP Regional Experiment (FIRE) I in October-November 1986; FIRE II in NovemberDecember 1991; the European experiment on cirrus (ICE/EUCREX) in 1989; Subsonic Aircraft: Contrail and Cloud Effect Special Study (SUCCESS) in April 1996. Based on observations from the ground-based lidar and radar, airborne instrumentation, and satellites, cirrus clouds are typically located in the upper troposphere and lower stratosphere (Liou 1986). The formation, maintenance, and dissipation of cirrus clouds are directly associated with synoptic and mesoscale disturbances as well as related to deep cumulus outflows. Increases of high cloud cover have been reported at a number of urban airports in the United States based on surface observations spanning 40 years (Liou et al. 1990; Frankel et al. 1997). These increases have been attributed to the contrails and water vapor produced by jet airplane traffic. Satellite observations from NOAA polar-orbiting HighResolution Infrared Radiation Sounder (HIRS) using the CO2 slicing method (Wylie et al. 1994) also show that cirrus cloud cover substantially increased between 60° S and 60° N during a 4-year period from June 1989 to September 1993. Understanding the role of cirrus clouds in climate must begin with reliable modeling of their radiative properties for incorporation in climate models as well as determination of the global variability of their composition, structure, and optical properties. Development of the remote sensing methodologies for the detection and retrieval of the ubiquitous visible and subvisual cirrus clouds requires the basic scattering, absorption, and polarization data for ice crystals in conjunction with appropriate radiative transfer models. 265

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We present the fundamentals involving radiative transfer in cirrus clouds and review pertinent research. In section 13.1, an overview of the subject of light scattering by ice crystals is presented in which we discuss a unification of the geometric optics approach for large ice particles and the finite-difference time domain numerical solution for small ice particles, referred to as the unified theory. Section 13.2 presents radiative transfer in cirrus clouds involving two unique properties: orientation of nonspherical ice crystals and cloud inhomogeneity. In section 13.3, we examine and review the spectral information on cirrus clouds from the perspectives of theoretical radiative transfer simulations and available observations. Finally, a summary is given in section 13.4. 13.1. Light Scattering by Ice Crystals

The growth of ice crystals has been a subject of important research in the discipline of cloud physics pertaining to cloud formation and precipitation processes. From experiments conducted in cold chambers, it has been shown that the shape and size of an ice particle are closely related to temperature and supersaturation, but an ice particle generally has a basic hexagonal structure. If the ice crystal growth involves collision and coalescence, its shape can be extremely complex. Observations from the air based on the optical probes and replicator technique for mid-latitude, tropical, and contrail cirrus show that these clouds are largely composed of plates, solid and hollow columns, bullet rosettes, aggregates, and ice crystals having irregular surfaces, with sizes spanning from a few micrometers to thousand of micrometers. It is clear that ice crystals are much more complicated than spherical water droplets with respect to the transfer of radiation in the atmosphere. The scattering of light by spherical particles can be solved by the exact LorenzMie Theory and computations can be carried out for the size parameters that are practical for atmospheric applications. Solving the scattering of light by nonspherical ice crystals of different sizes and shapes has been a contemporary subject of continued research. Liou (1972) made the first effort to construct an ice cloud model taking into account such factors as the orientation of ice particles using the exact scattering solution for cylinders as a prototype. Figure 13.1 shows comparisons of the phase function between theoretical calculations for randomly oriented ice cylinders and laboratory measurements for hexagonal columns conducted by Huffman and Thursby (1969). Also shown for comparison purposes is the phase function result for ice spheres with a y size distribution having a mode radius of 4u,m. For the first time, it was pointed out that nonspherical particles scatter more light in the side-scattering directions (60-120° scattering angles) than their spherical counterparts. Information about the phase functions for ice crystals is critical to the development of remote sensing techniques to infer cirrus cloud optical depths and microphysical properties (Minnis et al. 1993; Mishchenko et al. 1996a). The geometric ray-tracing approach has long been used to identify the positions of fascinating halos and arcs (Humphreys 1954; Greenler 1980; Liou 1980; Lynch and Livingston 1995), and Jacobowitz (1971) made the first attempt to

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Figure 13.1. Comparisons of the phase function between the theoretical results for randomly oriented ice cylinders and the laboratory measurement for hexagonal columns. Also presented is the phase function for polydisperse ice spheres having a mode radius of 4 um. The phase functions for a visible wavelength of 0.55 um are normalized to 1 at the scattering angle of 10° for these comparisons (after Liou 1972).

determine the angular scattering pattern for infinitely long hexagonal columns based on this approach. A more comprehensive ray-tracing analysis to compute the phase functions for finite hexagonal columns and plates was undertaken by Wendling et al. (1979), Liou and Coleman (1980), and Coleman and Liou (1981). Further, a ray-tracing model for hexagonal ice crystals accounting for internal absorption and full polarization was developed by Cai and Liou (1982), in which the diffraction component for a hexagonal aperture was also included in association with the geometric optics method. Takano and Liou (1989a) innovated a geometric ray-tracing program that takes into account the ice crystal size distribution and the possibility of horizontal orientation. New features in the program included incorporation of the birefringent properties of ice and the 8 transmission in the 0° scattering angle produced by direct transmission through two parallel surfaces. This paper has been widely cited, and the representative phase functions for columns and plates presented in the text are commonly referred to as Takano and Liou's phase function. Use of the Monte Carlo method in conjunction with geometric ray-tracing has been presented in the work of Wendling et al. (1979), discussed above. Macke (1993) and Macke et al. (1996) developed a geometric ray-tracing technique in connection with a fractal approach for the

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ice particle geometry. Takano and Liou (1995) further innovated a hit-and-miss Monte Carlo method to trace photons in complex ice crystals, including absorption and polarization. Incorporation of some aspects of the ice crystal surface roughness in the context of geometric ray-tracing has been undertaken by Takano and Liou (1995), Muinonen et al. (1996), Macke et al. (1996), and Yang and Liou (1998). The method of geometric ray-tracing is based on the physical principle that the size of a particle is much larger than the incident wavelength, so that the light beam can be thought of as consisting of a bundle of separate rays that hits the particle. The width of the light beam is much larger than the wavelength and yet small compared with the particle's size. Each ray that hits the particle will undergo reflection and refraction and will pursue its own specific path along a straight line according to Snell's law at the surface. The energies associated with reflection and refraction are determined by the Fresnel coefficients (Born and Wolf 1975). Diffraction, in contrast, follows the Babinet principle, in which a scatterer can be replaced by an opening on an opaque screen perpendicular to the incident light that has the same geometric shape as the projected cross-section of the scatterer. The well-known Fraunhofer diffraction formula can be used to compute the diffraction component for hexagonal ice crystals. The energy carried by the diffracted and Fresnel rays is assumed to be the same as the energy intercepted by the scatterer's cross-section projected along the incident direction. The intensity of the far-field scattered light can be subsequently computed from the summation of the intensity contributed by each individual ray emerging in the same direction. It is generally assumed that the interference may be smoothed out when the particles are randomly oriented. It is evident that, in addition to the requirement of the localization principle, the conventional geometric ray-tracing technique assumes that the energy may be decomposed into equal extinction from diffraction and Fresnel rays; that is, the extinction efficiency = 2 regardless of particle size parameters. Moreover, computations of the far-field directly by ray-tracing will produce a discontinuous distribution of the scattered energy known as the 5 transmission (Takano and Liou 1989a). Yang and Liou (1995, 1996a) have undertaken an improved approach to circumvent the aforementioned shortcomings in the conventional geometric ray-tracing method that can only be applied to size parameters on the order of 50 or larger depending on the optical properties of the particle. In this approach, the energies determined from ray tracing at the particle surface are collected and mapped to the far field based on the exact electromagnetic wave theory in which full-phase interferences are accounted for. In this manner, the only approximation is in the calculations of the surface electric field. The improved approach allows the applicability of the geometric optics method for light-scattering calculations to ice particle size parameters on the order of about 15-20, as validated from the results computed from the finite-difference time domain (FDTD) method, introduced below. Recognizing the limitations of the geometric ray-tracing method, we have searched for an appropriate methodology that can be effectively used to solve the scattering of light by nonspherical ice crystals with small size parameters. In this quest, we found that several approaches can be used to solve the scattering

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of light by nonspherical particles, including the FDTD technique mentioned above, the discrete-dipole approximation (e.g., Draine and Plateau 1994), and the T-matrix or the extended boundary condition method for spheriods (e.g., Mishchenko et al. 1996b). The FDTD technique, pioneered by electrical engineers (Yee 1966; Umashankar and Talflove 1982; Talflove 1995) for the purpose of identifying irregular objects from backscattering radar returns, appears to be most suitable for the continuity of our light-scattering programs. This method is a numerical technique for the solution of the Maxwell equations using appropriate absorbing boundary conditions and has been demonstrated to be one of the most robust and accurate numerical methods involving small particles with arbitrary composition and geometry (Yang and Liou 1996b).The FDTD method begins with the discretization of the three-dimensional scatterer by a number of suitably selected rectangular cells at which the optical properties are defined. Discretizations are then carried out for the Maxwell curl equations by using the finite-difference approximation in both time and space. Scattering of the excited wave in the time domain can be simulated in a manner of timemarching iterations. Implementation of an efficient absorbing boundary condition is subsequently required to suppress spurious reflections within the finite domain. Further, to obtain the frequency response, one can use the discrete Fourier transform technique to obtain the frequency spectrum of the timedependent signals based on a Gaussian pulse. The far-field solutions can finally be derived from the near-field results using a surface- or volume-integration technique. Fundamental problems in the FDTD numerical approach include the staircasing effect in approximating the particle shape and the absorbing boundary condition used to truncate the computational domain. By comparing with the exact results computed from the Lorenz-Mie theory for spheres and circular cylinders, we have shown that the FDTD approach for light scattering can be applied to size parameters smaller than about 20 with acceptable accuracies and computer resources. It is unlikely that one specific method can be satisfactorily used to resolve the intricate scattering problems involving nonspherical ice crystals of all size parameters. However, by unifying the geometric optics and FDTD methods described above, we are now in a position to perform calculations of light scattering and absorption by ice crystals covering all sizes and shapes that commonly occur in the atmosphere. This approach is referred to as the unified theory for light scattering. In figure 13.2, this theory is illustrated in terms of the extinction efficiency as a function of size parameter for randomly oriented columns. The length-towidth ratio for the column is 6 and the incident wavelength used is 0.63 um. Because of the requirement of the computational time and accuracy, the FDTD results are presented for the size parameter from 1 to 30. The results computed from the improved geometric optics method cover the size parameter from 1 to 1000. Significant deviations occur when the size parameter is smaller than about 15. The inapplicability of the localization principle inherent in geometric ray tracing for the calculation of the electric field at the surface of the scatterer with a small size parameter is clearly illustrated in this comparison. As noted previously, the extinction coefficient = 2 regardless of the size parameter in the conventional geometric optics method. A series of systematic comparisons has

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Figure 13.2. The extinction efficiency as a function of size parameter for randomly oriented ice columns with the length (L)-to-width (a) ratio of 6. The extinction efficiency for the conventional geometric ray tracing = 2 regardless of the size. The solid curve and dots are results computed from the improved geometric optics approach and the finitedifference time domain technique. Because of the requirements of the computer time and accuracy, the latter technique is applicable to size parameters on the order of 30. By combining these two methods, referred to as the unified theory, light-scattering calculations can be carried out for any size and shape that can be defined numerically.

been carried out for the phase function, single-scattering albedo, and extinction cross-section computed by the improved geometric optics and FDTD methods for solid and hollow columns, plates, bullet rosettes, and aggregates. The geometric optics method can produce acceptable accuracies for the single-scattering parameters for these ice crystal shapes with size parameters on the order of 15-20. Further, we also find that the peaks in the 22° and 46° halos generated by the geometric ray tracing reduce substantially when the size parameter is smaller than about 60. Some of the cirrus clouds that do not produce halos and arcs could involve small ice crystals and/or deviation of large ice crystals from hexagonal geometries caused by the growth processes. Figure 13.3 illustrates various commonly observed ice crystal habits generated by computer and the associated phase functions using the 0.63-um wavelength. Eleven ice crystal types are displayed, including solid and hollow columns, single and double plates and a plate with attachments, a bullet rosette with four branches, an aggregate composed of eight columns, a snowflake, and an ice particle with rough surfaces defined by a two-dimensional Gaussian probability function. Also shown are an ice sphere and an ice spheroid whose phase functions are computed by the exact theory. The phase function for the sphere shows a maximum at the rainbow angle of about 138° and a broad minimum at the side-scattering directions 60-120°, whereas the spheroid displays a maximum pattern in this scattering angle range. Both phase functions deviate significantly from those of ice particles. The patterns for snowflake,

Figure 13.3. Eleven ice crystal habits commonly occurring in cirrus clouds generated by the computer program, along with the associated phase function patterns for the 0.63-um wavelength. The solid lines are results computed from the geometric ray tracing; the dashed lines in the upper Also panels are results generated form the finite-difference time domain technique in which the size size parameters parametersare areindicated indicatedintinthe thediagreams. diagrams. Also shown for comparisons are phase functions for spheroid and sphere.

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dendrite, and plate with attachments are produced by a fractal shape-generation program. The phase functions for randomly oriented ice particles whose size parameters are on the order of 100 are computed from a hit-and-miss Monte Carlo program. The phase function patterns for the hexagonal-based ice crystals such as solid column, single and double plates, bullet rosette, and column aggregate all display a strong 22° halo peak (two refractions through a 60° prism angle), a halo peak at 46° (two refractions through a 90° prism angle), and a maximum at about 160° (one and two internal reflections). The backscattering peak for these ice crystals is produced by external and internal reflections. The bullet also exhibits a peak at about 7°. For plates with small attachments and snowflake, the 22° and 46° halo peaks are also clearly shown. In the case of hallow column, the 46°, 160°, and backscattering maxima are absent due to the lack of scattering material. For simple and complicated dendrites, the 22° and 160° maxima vanish, but the backscattering is still strong due to internal reflection contributions. The results for small ice crystals computed from the FDTD method are displayed in the top four panels. The patterns for the column-based ice particles are similar in the forward diffraction as well as in other scattering angle regions. Phase function differences between large and small ice crystals are clearly illustrated. In figure 13.4 we show the phase function and degree of linear polarization for a representative cirrostratus ice crystal size distribution (Liou 1992) having a mean effective size (see below for definition) of about 42|um. Based on replicator and optical probe measurements (Heymsfield and Miloshevish 1993; Arnott et al. 1994), we use a cirrus cloud model composed of 50% bullet rosettes/aggregates, 30% hollow columns, and 20% plates. Four remote sensing wavelengths of 0.63, 1.6, 3.7, and 10 |im are used in the calculations. These wavelengths are typical of the image channels (e.g., the AVHRR on board NOAA satellites). The results for other image wavelengths, 0.86 um and 10.9 and llpm are similar to those for 0.63 and lOfim, respectively, for the phase function and polarization patterns. In the phase function, the 0.63 and 1.6 jam wavelengths display a peak at the 22° halo position. Because of the ice absorption, all the features associated with hexagonal ice crystals vanish at 3.7 and 10 urn, except the forward diffraction peak. The linear polarization patterns for single scattering show a number of maxima features at the 0.63 and 1.6fj,m wavelengths: a slight negative polarization at the 22° peak, a positive polarization at the 46° peak, and a strong negative polarization close to the backscattering. From about 60° to 140°, about 10% polarization is observed. The case of 10|im exhibits a maximum at about 90° produced principally by external reflection and limited internal reflections of light beam. The spectral single-scattering parameters for ice crystals in terms of asymmetry factor, single-scattering albedo, and extinction cross-section are presented in figure 13.5 using the cirrus cloud model defined previously for the wavelengths from 0.2 to 5 |im. We have selected three mean effective ice crystal sizes ranging from 10 um (contrail cirrus) to 42 (im (typical cirrostratus) to 124 |im (cirrus uncinus), defined by

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Figure 13.4. Phase function and linear polarization patterns for a typical cirrostratus with a mean effective ice crystal size of about 42 um composed of 50% bullet rosettes/ aggregates, 30% hollow columns, and 20% plates—a shape model based on replicator and optical probe measurements. Four remote sensing wavelengths are displayed. For size parameters less than 15, the finite-difference time domain method is used in the calculations. In the phase function, the vertical scale applies to the lowest curve; the upper curves are displayed upward by a factor of 10.

where n(D) is the ice crystal size distribution, and V and A denote the volume and projection area of an ice crystal, respectively. IWC is the ice water content, Pi is the bulk ice density, and At is the projection area per unit volume. This definition allows the consideration of irregular ice crystals in terms of the volume and projection area and is directly proportional to IWC. The averaged extinction cross-section is normalized in reference to the value at 0.5 um. In the visible and near IR wavelengths, the averaged size parameter is sufficiently large so that the extinction efficiency ~ to 2 on the basis of the optical theorem. The singlescattering albedo pattern mimics the variability of the imaginary refractive index for ice (see Liou 1992) with a large minimum located at about 3(im. The asymmetry factor remains about the same in the visible and near IR wavelengths for a given mean effective ice crystal size, except at about 3 |im, at which diffraction predominates and generates strong forward scattering. The single-scattering albedo decreases as the mean effective size increases, with the exception in the vicinity of 2.85 urn, referred to as the Christiansen effect. This effect occurs when the real part of the refractive index approaches 1, while the corresponding imaginary part is substantially large, resulting in the domination of absorption.

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Figure 13.5. Single-scattering albedo, asymmetry factor, and normalized extinction coefficient (in reference to the value at 0.5 urn) as functions of wavelength for three ice crystal size distributions with mean effective sizes of 10,42, and 124 urn and the shape model defined in figure 13.4.

13.2. Radiative Transfer in Cirrus Clouds

Because of the unique properties of ice crystals in cirrus clouds and their appearance, two specific features must be considered in the discussion of radiative transfer: ice crystal orientation, and finite and inhomogeneous nature of the cloud. 13.2.1. Radiative Transfer in Oriented Ice Particles The spatial orientation of hexagonal and irregular ice crystals in cirrus clouds is a significant factor in the transfer of radiation in the atmosphere. The fact that numerous halos and arcs have been observed demonstrates that specific orientation of ice particles must exist in some cirrus. Based on a laboratory experiment, Jayaweera and Mason (1965), in studying the behavior of freely falling cylinders in a viscous fluid, discovered that if the diameter-to-length ratio is less than 1, cylinders will fall with long axes horizontally oriented. Observations of the behaviors of columnar and plate crystals in cirrus clouds have shown that these particles fall with their major axes oriented in the direction parallel to the

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ground. Orientation of ice particles in cirrus clouds has been observed by numerous lidar measurements based on the depolarization technique (e.g., Platt et al. 1978; Sassen 1991) at the backscattering direction (i.e., zenith angle of 0°). The depolarization ratio of the backscattered return from horizontally oriented plates is close to zero, but this ratio increases significantly as the lidar scans a few degrees off the vertical. Specific orientation occurs when the ice particles have relatively large sizes and defined shapes such as columns and plates. However, if the ice crystals are irregular such as aggregates, preferred orientation is unlikely to occur. Furthermore, smaller ice crystals in cirrus clouds where substantial turbulence occurs would have the tendency to orient in three-dimensional space. Finally, it has been noted that ice particle orientation and alignment are closely modulated by the electric field in clouds. In the case of horizontally oriented ice crystals, their single-scattering parameters are dependent on the direction of incident light beam. Thus, the conventional formulation for the multiple-scattering problem requires modification. Liou (1980) formulated the basic equation for the transfer of solar radiation in an optically anisotropic medium. Stephens (1980) and Asano (1983) discussed the transfer of radiation through anisotropic ice clouds in which the phase function is expressed in terms of the incident angle. Takano and Liou (1989b) used the realistic scattering parameters and the Stokes vector for horizontally oriented ice crystals in association with the adding method for radiative transfer. Takano and Liou (1993) further presented the theoretical formulations and numerical calculations involving the transfer of polarized thermal infrared radiation in optically anisotropic media with a specific application to horizontally oriented ice particles. Below, we present a unified theoretical formulation that is applicable to both solar and thermal infrared radiative transfer including polarization for horizontally oriented ice crystals. The formulation presented below, after slight modifications, can also be directly applied to the random orientation condition. Consider a cirrus cloud composed of ice crystals oriented horizontally. In this case, the incoming light beam is symmetrical with respect to the azimuthal angle, 0, and is dependent on the cosine of the zenith angle, |i. We may define a differential normal optical depth such that di = -fiedz, where the vertical extinction coefficient Pb = pe (|i = 1) and z is the distance. Let the Stokes vector intensity, I, = (/, Q,U,V). It follows that the general equation governing the transfer of diffuse intensity can be expressed in the form

where the actual extinction coefficient normalized by the vertical extinction coefficient is defined by

For horizontally oriented particles, the extinction coefficient matrix can be expressed by (Martin 1974; Mishchenko 1991)

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where Ppol and pcpoi are polarization and copolarization components of the extinction coefficients with respect to the incident Stokes vector. For all practical purposes, we may use the scalar (3e for applications to ice crystal cases. The source function in the basic radiative transfer equation can be written as follows:

where the single-scattering albedo is defined by

with PS the scattering coefficient matrix, which has the similar form as the extinction coefficient matrix, F0 represents the Stokes vector for the incident solar irradiance, B(T) is the Planck intensity at a temperature T, Ie = (1, Qe, 0,0) with -Qe the linear polarization component associated with emission, and the scattering phase matrix

where the rotation matrix is given by

with i-i and i2 the angles that are determined from the spherical geometry. The phase matrix in general consists of 16 elements as follows:

In equation 4, the second and third terms on the right-hand side represent the contribution from the direct solar radiation and thermal emission from a medium having a temperature, T, which is azimuthally independent. Also note that

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k(Q = Ps/Pe- For wavelengths shorter than about 3.7 um, thermal emission within the Earth-atmosphere system can be neglected in comparison to radiation from the sun. For wavelengths longer than Sum, the reverse is true. Between 3.7 and 5 um, the relative importance of thermal emission and solar reflection for a cloud layer depends largely on the position of the sun and the cloud temperature. If the particles are randomly oriented in space in such a manner that each one of them has a plane of symmetry, the law of reciprocity can be applied so that the directions of the incident and scattered polarized beams can be reversed, with the final results being equal (Perrin 1942; van de Hulst 1957). Moreover, the (7, <2) components of the Stokes vector are invariant to the change in the incident Stokes parameters from (U, V) to (-£/, -V). It follows that the phase matrix reduces to six independent elements, as follows:

In this case, k(u) = 1, and p}s, p}e, and 03 are independent of \L. Figure 13.6 shows an example of the bidirectional reflectances for horizontally oriented (referred to as Parry) and randomly oriented (three-dimensional) columns using a representative cirrostratus ice crystal size distribution with an optical depth of 1 in the plane defined by the zenith (9) and relative azimuthal (()) - <|)o) angles. The wavelength and the cosine of the solar zenith angle used are 2.2 um and 0.5, respectively. Note that the domain for reflectances is from 60° to 180° scattering angles, which do not cover the commonly observed halos located at 22° and 46°. In the three-dimensional case, the maximum at 9 = 80° and close to the principal plane (j) - §0 = 0° is related to the limb brightening. Otherwise, the reflectance variations are relatively small in the linear scale. In the case of Parry columns, we see numerous reflection maxima. The chief ones are 1) the subsun located at 9 = 60° in the principal plane produced by external reflections, 2) the lower Parry arc located at 9 ~ 80° in the principal plane generated by two refractions, and 3) the antisolar peak located at 9 ~ 60° and (j) - §0 = 180° cause by one internal reflection. Much larger anisotropy occurs in this case as compared with the three-dimensional case. In realistic cirrus clouds, we would anticipate that some of the large and defined ice particles are horizontally oriented. If appropriate and specific radiometric measurements can be made, it would appear that the ice particle orientation properties could be inferred. As shown by Takano and Liou (1989b, 1993), polarization of the sunlight reflected from clouds can be used to differentiate the cloud thermodynamic phase (spherical water droplets and nonspherical ice crystals) and to infer the ice crystal size/shape. Information of polarization of the reflected sunlight has been used by astronomers to infer particle sizes and optical characteristics of the cloud deck of Venus (Lyot 1929). Hansen and Hovenier (1974) performed an extensive investigation of the particle shape, size, and refractive index of the Venus cloud by comparing the observed linear polarization with comprehensive multiple-

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Figure 13.6. Bidirectional reflectances at a wavelength of 2.2 um for ice columns randomly oriented in space (3-D) and oriented parallel to the ground (Parry columns) in the plane of zenith and azmuthal angles. For the Parry column case, three peak features are marked in the diagram.

scattering calculations involving spherical particles and Rayleigh molecules. Coffeen (1979) has measured the linear polarization pattern of sunlight reflected from optically thick cirrus clouds, the results of which have been interpreted by Takano and Liou (1989b) and Liou and Takano (1994) using the single-scattering results for hexagonal plates and columns, and later a combination of regular and irregular ice particles, as shown in the upper panel of figure 13.7. Polarization of sunlight reflected from cirrus clouds has been reported by Chepfer et al. (1998) during the European Cloud Radiation Experiment 1994 campaign based on airborne polarimeter measurements from the Polarization and Directionality of the Earth's Reflectances (POLDER) instrument. Two channels in this instrument at 0.443 and 0.864 u,m were used for polarization measurements. The lower panel of figure 13.7 shows the observed polarization defined by P = (Q2 + U2 + V2)1'2 for two cirrus cloud episodes. In the left and right diagrams, the scattering angle ranges are 75° to 165° and 90° to 180°, respectively, with the respective solar zenith angles depicted in the diagrams. After extensive trial-and-error analyses, we found that an optical depth of about 3 matches the observed data on the left diagram most closely. Radiative transfer calculations

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Figure 13.7. The upper panel shows linear polarization of sunlight reflected from cirrus clouds measured at the 2.22 um (Coffeen 1979). The lower panels display full polarization observed from the polarimeter at 0.864 um on board the POLDER in the scattering angle domain (Chepfer et al. 1998). The theoretical results are computed for hollow columns, plates, and ice particles with rough surfaces using the best-fit optical depth of 3 (see text for further explanations).

are subsequently performed using randomly oriented hollow columns, plates, and irregular ice particles. The plate case (L/2a = 8/80 um) appears to fit the observations in all scattering angle ranges, as displayed in the left diagram, except in the backscattering, in which the irregular ice particle case fits better. The polarization data presented on the right diagram illustrate a peak at about 104° (subsun feature) associated with the horizontal orientation of ice plates and columns. To provide adequate interpretation, full 16-phase matrix elements are needed in radiative transfer calculations. This is a research area requiring further delicate numerical analyses.

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13.2.2. Radiative Transfer in Finite Inhomogeneous Cirrus Clouds Satellite mapping of the optical depth in the mid-latitude and tropical regions has illustrated that cirrus clouds are frequently finite in nature and display substantial horizontal variabilities (Minnis et al. 1993; Baum et al. 1995; Ou et al. 1995). Vertical inhomogeneity of the ice crystal size distribution and ice water content is also demonstrated in replicator sounding observations (Heymsfield and Miloshevich 1993) and in the time series of backscattering coefficients derived from lidar returns (Spinhirne and Hart 1990; Sassen 1991). Thus, the potential effects of cloud geometry and inhomogeneity on the transfer of radiation must be studied to understand their impact on the radiative properties of the atmosphere as well as to properly interpret radiometric measurements from the ground, the air, and space. The importance of the spatial inhomgeneity and finiteness of clouds on the radiation field, especially in regard to the question of cloud absorption, has been discussed by Stephens and Tsay (1990), Liou (1992), and Liou and Rao (1996). Most of the approaches to three-dimensional radiative transfer use the Monte Carlo method (e.g., Cahalan et al. 1994; Chylek and Dobble 1995). For applications to cirrus clouds, Liou and Rao (1996) used the successive orders of scattering approach, which can be directly applied to specific geometry and inhomogeneous structure of a medium. One of the fundamental difficulties in the modeling of three-dimensional radiative transfer is the requirement for computer sources. Substantial computer time and storage are often required in the simulations to achieve reliable accuracies. In conjunction with our objective of investigating the effects of three-dimensional inhomogeneous cirrus on the radiative flux and heating rate profiles in the atmosphere, we have developed a modified diffusion approximation for radiative transfer using Cartesian coordinates. The conceptual and numerical approach to this difficult problem is presented below. The general equation governing the transfer of diffuse intensity, /, can be expressed in the form

where s is the position vector; Q is a unit vector representing the angular direction of scattering through the position vector; (3e is the extinction coefficient for cloud particles, which is a function of the position vector; and the source function which is produced by the single scattering of the direct solar irradiance, multiple scattering of the diffuse intensity, and emission of the cloud, can be written as follows:

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In equation 10,03 = Ps/pe is the single-scattering albedo with (3S the scattering coefficient; the phase function, P, is defined by the position and the incoming and outgoing solid angles Qf(Qo) and Q, respectively; FQ is the incident solar irradiance; Ts is the optical depth in the direction of the incident solar radiation; and B(T) is the Planck function of temperature T. Applicability of the source function in solar and thermal infrared regions is wavelength dependent, as discussed previously. By expanding the phase function and the intensity in terms of spherical harmonic functions and by taking four terms in the expansion in a manner presented in Liou and Ou (1979) and Liou (1992), the following three-dimensional inhomogeneous diffusion equation can be derived in the form

where all the variables are a function of the coordinate (;t,y,z); (3t = (3e (1 - G5g); cct = (3e(l - 05); Ft = Spj^o exp(-is)/47u for solar radiation, and Fl = 3(3e(l - 05)B(T) for thermal infrared radiation; g denotes the asymmetry factor; IQ is thefirstcom ponent of the intensity expansion; and the diffusion operator V2 = 32/3*2 + 32/3y2 + 32/3z2. Equation 11 is a general second-order elliptic equation in which the coefficients are variables. The solution requires the imposition of the boundary conditions such that the incident flux at each surface is equal to zero (or a constant). We solve the system of equations numerically by using the finite difference method. The three-point finite difference scheme is used to represent the secondorder partial differential terms in equation 11. The simultaneous over-relaxation method, which offers efficient convergence, is used to calculate /jj at each preset grid point. Once /o is determined, the diffuse intensity can then be obtained by

where h = 3(1 - 05g)/2; q = G5gF0/127i, Xi = x; x2 = y; x3 = z; £lz = u,, Qx = (1 - u2)1'2 coscj); and Qy = (1 - u,2)1/2sin<|). To increase the computational accuracy, we have applied the similarity principle for radiative transfer to each grid point such that p; = Pe (1 - 05/),G5' = 05(1 -/)/(! - (D/), and g' = (g -/)/(! -/).The fractional energ in the diffraction peak of the phase function, /, is taken to be G52/5, where G32 is the second moment in the phase function expansion. For thermal infrared radiation, the last term in equation 12 vanishes. Contrail cirrus are a typical example of finite clouds. Observations from lidar backscattering and depolarization also demonstrate that these clouds are highly inhomogeneous (K. Sassen, personal communication). At this point, a threedimensional extinction coefficient field for cirrus from observations is not available. For this reason, we constructed a hypothetical extinction coefficient field in the x - z plane, as shown in figure 13.8. For radiative transfer calculations, the extinction coefficients are assumed to be the same in the y-direction. The solar and emergent angles used are 10° and 40°, respectively, with the relative azimuthal angle of 140°. The reflectance pattern is presented in the x - y plane at the cloud top. Maximum values close to the edge are shown because of the position of the sun and larger extinction coefficients. Same patterns are displayed along the y-direction. By using a mean extinction coefficient in the x - z plane,

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Figure 13.8. The top panel illustrates an extinction coefficient field mimicking contrail in the x-y plane. The lower panel displays the bidirectional reflectances for inhomogeneous and homogeneous contrail fields in the x-y plane.

the reflectance pattern now corresponds to a homogeneous cloud. Except near the left edge, associated with the finite geometry, the pattern is uniform. This example demonstrates the significance and intricacy of the finite and inhomogeneous cloud structure with respect to its radiative properties. It is a subject that requires further numerical experimentations and carefully designed radiometric observations. 13.3. Spectral Information of Cirrus Clouds

We first examine the spectral information of cirrus clouds from the perspective of radiative transfer. We follow the line-by-line equivalent model developed by Liou et al. (1998) for this study. In brief, the model uses the correlated kdistribution (CKD) method to derive the equivalent absorption coefficients in the domain of the cumulative probability function, g, which replaces the wave

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number (see, e.g., Fu and Liou 1993) in connection with multiple-scattering calculations involving clouds and aerosols. The use of the g function circumvents the requirement of resolving the individual line structures, which are strongly dependent on pressure. The CKD method is exact in the limits of weak- and strongline approximations as well as for a single line and lines with periodic occurrence (Goody and Yung 1989; Fu and Liou 1993). Based on this method only a few integration points are required to achieve acceptable accuracies in the transmittance calculations for inhomogeneous atmospheres. The CKD method is attracitve because the computational speed is essential in many spectral radiative transfer calculations, particularly in conjunction with multiple scattering due to particulates. In the solar spectral interval from 2000 to 21,000cm"1 (0.5-5 um), H2O is the chief absorber with minor contributions from CO2 in the 2.0- and 2.7-um bands. The overlap between H2O and CO2 lines can be accounted for by means of the multiplication rule. Absorption due to O3 and O2 bands and Rayleigh scattering contributions is included in multiple-scattering calculations based on the conventional method. Figure 13.9 illustrates the spectral bidirectional reflectance and absorptance for the three cirrus types defined in figure 13.5. The calculation uses a solar zenith angle of 30°, an emergent angle of 0°, an ice water path (IWP) of 1 g/m2, and a spectral interval of 50cm"1 containing 30 g covering the spectrum from 0.2 to 5 Jim. The contribution of thermal emission for wavelengths longer than 3.7 um is not included. From the absorption spectrum, the H2O absorption bands located at 3.2, 2.7, 1.87,1.38, 1.1, 0.94, 0.82, and 0.72um are evident, as are the 4.3-um

Figure 13.9. Spectral bidirectional reflectance and absorptance for cirrus clouds with mean effective ice crystal sizes of 10, 42, and 124 um corresponding to figure 13.5 as functions of wavelength. Absorption bands due to ozone, water vapor, and carbon dioxide are identified.

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CO2 and O3 bands. The bidirectional reflectances have maxima in between the H2O absorption bands. Small ice crystals reflect more solar radiation. Sufficient ice crystal size information is shown in the near infrared spectrum. Note that to a good approximation, the visible optical depth TV = YWP(a + b/De), where a and b are certain coefficients. One of the unique instruments that measured the spectral radiances from the atmosphere and the surface is the infrared imaging spectrometer/radiometer associated with the Airborne Remote Earth Sensing System (ARES) Program on board the WB-57F high-altitude research aircraft. The ARES was operated as a 75-channel imaging spectrometer with a pushbroom mode having a 45-pixel array pointing in the nadir direction, taking data at the standard rates of 10, 20, 40, or 80 s. The ARES covers the wavelengths from 2 to 6.4 um, where transitions from solar reflection to thermal emission takes place. The optical elements of ARES provide a pixel instantaneous field of view of slightly more than 1 mrad that corresponds to about 15m ground resolution for a flight of 15km. On September 16,1995, several flights were conducted in cirrus cloudy conditions over the western Boston area (Ou et al. 1998). Figure 13.10 shows typical ARES 75channel spectra obtained over clear and cirrus cloudy areas. Several bands are noted in the spectra: the 2.7-um band produced by YI and v3 fundamental; the 3.2-um H2O band associated with 2v2; the 4.3-um CO2 band due to the v3 fundamental and P and R branches; and the H2O 6.3-um vibrational (v2)—rotational band. There are three windows located at the 2.2, 3.7, and 4.7 urn regions. Large measurement noise exists for channels 1-25 (1.9-2.7 urn), where the solar reflection contributions are dominant and the cirrus reflection is stronger than the surface reflection. For channels 26-75 (2.7-6.4 |im), the thermal emission of cirrus

Figure 13.10. Measured spectra for clear and cirrus cloudy conditions from the ARES program on board the WB-57 high-altitude research aircraft on September 16,1995 over the Boston area. The 75-channel spectra cover the wavelengths from 2 to 6.4 um, a transition from the contribution of solar reflection to thermal emission due to ice particles. The measurements for wavelengths shorter than 2.5 urn had calibration problems. (After Ou et al. 1998, with modification.)

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predominates. The relative contributions to upwelling radiances at the top of cirrus clouds for wavelengths between about 3 and 5 urn are largely dependent on the solar zenith angle and the cloud temperature. The effects of cirrus clouds are illustrated in the spectral intervals 2-2.5 jLim, 3-4 urn, and 4.5-5.5 um. Information on the temperature, optical depth, and mean effective ice crystal size of cirrus clouds in the 5-um region was explored by Ou et al. (1998). In the spectrum shorter than about 2urn, rich information on cirrus clouds has been studied by a number of researchers. Wielicki et al. (1993) investigated the possibility of using the 0.83 and 1.65 um radiances from LANDSAT to determine ice particle sizes. Gao and Kaufman (1995) presented an approach to detect thin cirrus using the 1.38- and 1.88-um water vapor bands from the airborne visible infrared imaging spectrometer (AVIRIS); the low-level water vapor absorption provides a dark background for high cirrus detection. Rolland and Liou (1998) showed that the cirrus optical depth and mean effective size can be determined from correlations of 0.63/1.6 and 0.63/2.2 um wavelengths following the approach described in King et al. (1997), which has been successfully applied to water clouds. The principle involves the optical properties of clouds with respect to the visible and near infrared window wavelengths. For the former, absorption is negligibly small and the reflectances are primarily dependent on the cloud optical depth. For the latter, some absorption exists such that the reflectances are largely controlled by the particle sizes. The reliable and correct phase functions for nonspherical ice crystals are critical for the development of correlation tables associated with retrieval purposes, particularly for thin cirrus clouds whose optical depths are inversely proportional to phase functions. In figure 13.9, information of the high-level cirrus is evident in a number of water vapor absorption bands. The 1.4-um band appears to be most useful for the cirrus cloud detection because of the combination of the strength of this absorption band and the amount of solar energy residing within the band. The solar spectral lines reflected from other planets have been observed and used to determine the composition of planetary atmospheres (Goody and Yung 1989). Such observations have not been made from satellites for the earth, however. Based on the spectral radiative transfer program described previously and using a IcnT1 resolution containing 10 equivalent absorption coefficients, we computed and studied the bidirectional reflectances in the 1.4-um H2O band covering 6600-7500 cm'1. In the calculations, we used two ice-crystal size distributions having the mean effective ice crystal sizes of 42 and 124 um with a shape composition of 50% aggregates/bullet rosettes, 30% hollow columns, and 20% plates. Figure 13.11 shows the results for clear and cirrus cloudy conditions in which the mid-latitude summer atmospheric water vapor profile is used. The cirrus cloud base is placed at 8km with an optical depth of 1. The line structure of water vapor absorption exhibits significant fluctuations. At about 71007400cm"1, reflectances from clear atmospheres are extremely small due to strong water vapor absorption. Multiple scattering due to ice crystals contributes to the strength of reflectances in the line-wing regions. It would be difficult to examine the full information content of cirrus clouds within the complexity of line

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structure. For this reason, we ordered the bidirectional line spectra for the clear condition according to their magnitudes in such a manner that a monotonic increasing function is displayed in the rearranged wave number domain. Subsequently, the bidirectional line spectra for cirrus cloudy conditions are followed in accord with this rearranged wave number domain. Low values represent that the reflectances are associated with line center, whereas high values correspond to line wings. In the lower panel of figure 13.11, the largest reflectance in the line wing is about 0.1 for the clear case corresponding to the surface albedo used. For the small optical depth of 0.1, reflectance increases in the center of the water vapor absorption lines produced by the scattering contribution of ice crystals. Pronounced scattering events occur for the optical depth of 0.5 and 1, as demonstrated in the rearranged spectra. Larger fluctuations shown in the optical depth of 1 are due to the fact that the scattering and absorption coefficients for ice do not align with the absorption coefficients for water vapor. To further inspect the information content of ice crystal size, cloud height, and solar zenith angle, we have carried out a number of analyses in terms of the cloud radiative forcing (CRF; i.e., the differences of the cloud and clear reflectances) defined by

Figure 13.11. The upper diagram shows the bidirectional reflectance in the 1.4-um water vapor band as a function of wave number from 6600 to 7500cm-1 for clear and cirrus cloudy atmospheres. A cirrostratus located at 8km with a thickness of 2 km in the mid-latitude summer atmosphere is used in the calculation. The surface albedo and the solar and emergent angles used are 0.1 and 60° and 0°, respectively. The lower diagram presents the bidirectional reflectance in the rearranged wavenumber domain according to the order of the clear reflectance values, a monotonic increasing curve, for a number of optical depths.

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We are specifically interested in thin cirrus and use an optical depth of 0.1 in the following presentation. First, we examine the effect of ice crystal size on the CRF spectrum assuming other pertinent variables remain unchanged. Two mean effective ice crystal sizes of 42 and 124 urn are used (fig. 13.12). The largest CRF difference appears in the line wings unaffected by the water vapor absorption in the rearranged wave number of 900 cnr1. Scattering and absorption by ice particles contribute to large deviations, and in these cases the reflectances are less than the surface albedo because of a small cloud optical depth. Second, we inspect the CRF spectrum due to the effect of cloud-base height using two values, 10 and 6km. Significant differences occur in the rearranged wave numbers smaller than 450cm"1 associated with the center of water vapor absorption line, as shown in the middle panel of figure 13.12. The reflectance signals here exclusively arise from the scattering of ice crystals. For the lower cloud, absorption of water vapor above the cloud substantially reduces its reflectance. Finally, we examine the effect of the position of the sun on the CRF spectrum using two solar zenith angles of 70° and 30°. The larger angle representing a lower sun position produces stronger reflectances in the entire rearranged wave number domain. In this case, the effective optical depth for the thin cloud is enhanced so that ice crystals can undergo more scattering.

Figure 13.12. Cloud radiative forcing (CRF) defined as the difference between the cloud and clear reflectances, in the rearranged wave number domain. The top, middle, and bottom diagrams illustrate the sensitivity of CRF with respect to the mean effective ice crystal size, the cloud base height, and the solar zenith angle, respectively. The optical depth used is 0.1, and all other parameters used are displayed in the diagrams.

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It is clear that substantial information on thin cirrus clouds can be observed from the 1.4 um spectrum. As noted above, analysis of the solar reflection spectra has been the only tool available for exploring the composition and structure of planetary atmospheres before entry probe. Unfortunately, measurements of the rich solar line spectra reflected from clouds in the Earth's atmosphere have not been attempted at this point. Advancement of remote sensing and climate research involving clouds in general and high cirrus in particular would significantly benefit from the development of a spectral instrument in the 1.4-|j,m region. In the analysis of the satellite infrared radiation interferometer spectrometer (IRIS) data, Prabhakara et al. (1993) illustrated that thin cirrus in the tropics can be identified in the 8-12-|im window region. The IRIS instrument was on board Nimbus III (Conrath et al. 1970) and IV (Kunde et al. 1974) and provided for the first time the infrared emission of the atmosphere from about 400 to 1600 cm'1 with a 5 cm'1 spectral resolution. Although the interferometer spectrometer experiment was not followed in the United States satellite program, three Fourier spectrometers in the spectral range 400-1600 cm"1 were included in the European METEOR satellites in the late 1970s. In the analysis of the emission spectra measured in clear and cirrus cloudy atmospheres, Spankuch and Dohler (1985) found that the presence of cirrus clouds significantly reduced the upwelling radiances in the entire spectral region, except in the center of the CO215-fim band. Smith et al. (1995) developed a high spectral resolution infrared spectrometer, referred to as HIS, intended for satellite applications. The HIS is a Michelson interferometer covering a spectral region from 3.5 to 19 um with high spectral resolution (A/AX > 2000). The spatial resolution of this instrument depends on its position and is about 2 km at the earth's surface below the ER-2 aircraft at 20km. Smith et al. (1995) showed that sufficient information on cirrus clouds exists in the HIS spectrum and suggested that the cirrus cloud structure and composition may be inferred. Further, Smith et al. (1998) displayed an interesting spectrum for a case involving a cold cirrus that was particularly evident in the 800-1000 cm'1 window region. Due to two fundamental obstacles, we have not been able to successfully carry out spectral radiative transfer simulations in the thermal infrared for cirrus cloudy conditions. First, the scattering and absorption properties of nonspherical ice particles are largely unknown. Takano et al. (1992) used the solution for spheroidal particles and showed that a better interpretation can be made for measurements made in a number of window wavelengths in terms of the brightness temperature difference correlation, as compared with Lorenz-Mie results for spheres. As discussed earlier, when the ice crystal size parameters are smaller than about 20, it is physically incorrect to use the geometric ray-tracing approach for light-scattering calculations. With the availability of the FDTD method for small particles, the morphology of ice crystals can be accounted for in the analysis. Second, to effectively incorporate the multiple scattering process involving ice particles in an atmosphere where absorption of various greenhouse gases dominates requires innovative approaches. With the advance of the CKD method described above, we are now in a position to conduct physically based and efficient radiative transfer calculations to interpret the measured infrared spectra

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and to explore methodologies for the retrieval of cirrus cloud structure and compositions. In reference to the clear and cold cirrus spectra presented in Smith et al. (1998), we use a spectral interval of 1 cm'1 with 30 correlated absorption coefficients in which the adding/doubling method for radiative transfer is used to perform calculations in the spectral region from 800 to 970 cm'1 in which we can neglect overlaps between H2O and CO2 lines and H2O and O3 lines for wave numbers smaller and larger than these two, respectively. Moreover, we incorporate the water vapor continuum parameterization developed by Clough et al. (1989) in the calculations. We define the cloud radiative forcing as follows: where BT denotes the brightness temperature. Using the slope of the spectrum and the mean value as shown in figure 13.13, we have developed a preliminary approach to infer the ice crystal size and cloud optical depth. The left-hand side of figure 13.13 displays the measured AB and the computed results of AB for three mean effective ice crystal size of 42, 12, and 5 urn. The cloud-base height and thickness are fixed at 10.53 and 0.915km, respectively, based on lidar observations in this case. The slope of the AB spectrum is shown to be a function of the mean effective ice crystal size. It is clear that the AB for the 12 urn mean size follows the observed AB most closely. The optical depth is not known a

Figure 13.13. HIS data measured during the SUCCESS experiment, April 21,1996, from 800 to 970cm'1 (Smith et al. 1998) in terms of the cloud radiative forcing, defined as the difference between the clear and cloudy brightness temperatures. The theoretical results in the diagram on the left are shown for three mean effective ice crystal sizes. The diagram on the right displays the averaged value as a function of optical depth (see text for further explanation).

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priori. To infer the optical depth we must construct a number of averaged AB values from the spectra as functions of the optical depth. The intercept from the measurements represented by the horizontal bar gives the best value of 1.14. Further analyses of the HIS data for cirrus and physical interpretations are needed to develop a physically based retrieval algorithm; the successful one would require appropriate validations using the co-located measurements of ice microphysics. 13.4. Summary

In this chapter, we have discussed and reviewed a number of fundamental issues concerned with the transfer of solar and thermal infrared radiation in cirrus clouds. These include light scattering and absorption by nonspherical ice crystals, radiative transfer in cirrus containing oriented ice crystals, and radiative transfer in finite and inhomogeneous clouds. The subject of light scattering by nonspherical ice crystals was briefly overviewed and the method of geometric ray tracing was introduced. Limitations of the geometic optics approach which requires the localization of light rays were discussed. This approach after modification that involves the exact mapping of the electric field at the near field to the far field can produce acceptable accuracies for size parameters greater than about 15-20. After researching an appropriate method to complement the geometric optics approach, we found that the finite-difference time domain technique for the numerical solution of light scattering by small nonspherical and inhomogeneous particles appears to be attractive from the standpoint of accuracy requirements and efficiency for size parameters less than about 20. Thus, by combining the aforementioned two methods, referred to as the unified theory for light scattering by ice crystals, we can now undertake reliable computations for the single-scattering properties of ice crystals covering all sizes and shapes definable by mathematical or numerical means. Representative phase function, linear polarization, and single-scattering properties for various ice crystal sizes and shapes and a cirrus cloud model were presented within the context of the information content of ice crystals. On the subject of radiative transfer, we reviewed the fundamentals associated with the orientation properties of ice particles due to the nature of nonsphericity. We outlined a formulation for the transfer of both solar and infrared radiation in terms of the Stokes vector in horizontally oriented ice crystals. In this case, the single-scattering properties of these types of ice particles are dependent on the direction of the incoming light beam, and the full four-by-four phase matrix is required in the discussion of the transfer process. A simple modification leads to the condition for random orientation in which only six independent phasefunction elements are needed. An example of bidirectional reflectances for randomly and horizontally oriented columns was presented to demonstrate that the latter case exhibits more anisotropy in the reflected pattern, a feature that could be important for the interpretation of satellite measurements involving cirrus clouds. Moreover, interpretation of the polarization of sunlight reflected

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from cirrus clouds measured from aircraft reveals noticeable information of the ice crystal shape and size. On the basis of satellite imageries and lidar backscattering returns, cirrus clouds appear inhomogeneous and finite in extent. Consequently, the issue of radiative transfer in inhomogeneous cirrus must be addressed and follow by assessing its relative importance in satellite applications and radiative transfer parameterizations. Although most approaches to this have used the Monte Carlo method in radiative transfer simulations, we have undertaken a more fundamental approach based on the successive order of scattering, which can account for special geometry and inhomogeneity. However, because of the computer resource requirements, particularly for applications to entire solar and infrared spectra, we have innovated a modified diffusion approximation for radiative transfer in which the 5 adjustment for the sharp diffraction peak in the phase function can be accounted for locally. We demonstrate a case study by generating an extinction coefficient field representing contrail cirrus and examine the reflectance differences between inhomogeneous and homogeneous conditions. Much work is needed in this area in order to achieve a comprehensive physical realization as to the implications to remote sensing and radiative heating/cooling rate calculations for climate models. Finally, we reviewed and presented the information content of the structure and compositions of cirrus clouds from the perspectives of theoretical radiative transfer simulations and available observations. Line-by-line equivalent radiative transfer calculations involving the gaseous absorption sorted by the correlated k-distribution method coupled by multiple scattering and absorption of ice particles were carried out for solar bands with respect to the optical depth and ice crystal size information. In particular, we found that the 1.4-u.m water vapor lines after rearrangement exhibit distinction features that can be used to retrieve cloud optical and microphysical properties. In this pursuit, we defined a term called the "cloud radiative forcing," the difference between the cloud and clear reflectances, and demonstrated that the ice crystal size, cloud position, and optical depth are displayed in various parts of the rearranged spectra and solar zenith angles. Moreover, we presented observational evidence of cirrus clouds in the spectrum of the ARES data covering 2 to 6.4 um, a transition of domination from solar reflection to thermal emission in which cirrus clouds generally have larger signals than clear conditions in the former, while the reverse is true for the latter. The information content of thin cirrus in the HIS spectrum from 800 to 970cm'1 was then introduced. We demonstrated that it is feasible to deduce the ice crystal size and infrared optical depth objectively from the spectrum by using its slope and mean value. It is clear in view of the preceding presentations that a number of issues associated with the role of cirrus clouds in remote sensing and in climate modeling are still unresolved and require in-depth and well-organized theoretical and observational investigations. Indeed, owing to the spatial and temporal variabilities of ice crystal sizes and shapes in cirrus clouds as well as their high location in the atmosphere, remote sensing of their microphysical and optical properties from space and determination of their radiative properties and parameterizations represent an unusual challenge in atmospheric sciences. A number of

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radiometer-spectrometers and polarimeters available for the aircraft platform mentioned above, as well as several proposed and planned satellite instruments, such as the Moderate Resolution Imaging Spectroradiometer (MODIS; King et al. 1992), the Multi-angle Imaging SpectroRadiometer (MISR; Diner et al. 1998), and the Earth Observing Scanning Polarimeter (EOSP; Hansen et al. 1995), will undoubtedly provide an excellent opportunity to meet this challenge.

Acknowledgments. Support of the research work contained in this paper includes National Science Foundation grant ATM-9907924, National Aeronautics and Space Administration grants NAG-5-9667 and NAG-5-7738, U.S. Air Force Office of Scientific Research grant F49620-98-1-0232, and Department of Energy grant DE-FG0398-ER62526. References Arnott, W.P., Y.Y. Dong, J. Hallett, and M.D. Poellot, 1994. Role of small ice crystals in radiative properties of cirrus: A case study, FIRE II, November 22,1991. /. Geophys. Res., 99,1371-1381. Asano, S., 1983. Transfer of solar radiation in optically anisotropic ice clouds. J. Meteor. Soc. Japan, 61,402-413. Baum B.A., T. Uttal, M. Poellot, T.P. Ackerman, J.M. Alvarez, J. Intrieri, D. O'C. Starr, J. Titlow, V. Tovinkere, and E. Clothiaux, 1995. Satellite remote sensing of multiple cloud layers. /. Atmos. Sci., 52,4210-4230. Born, M., and E. Wolf, 1975. Principles of Optics. Pergamon Press, New York. Cahalan, R., W. Ridgway, and W. Wiscombe, 1994. Independent pixel and Monte Carlo estimates of stratocumulus albedo. /. Atmos. Sci., 51, 3776-3790. Cai, Q.M., and K.N. Liou, 1982. Theory of polarized light scattering by hexagonal ice crystals. Appl. Opt., 21, 3569-3580. Chepfer, H., G. Brogniez, and Y. Fouquart, 1998. Cirrus cloud's microphysical properties deduced from POLDER observations. J. Quant. Spectrosc. Radial. Transfer, 60, 375390. Chylek, P., and J.S. Dobble, 1995. Radiative properties of finite inhomogeneous cirrus clouds: Monte Carlo simulation. /. Atmos. Sci., 52,3512-3522. Clough, S.A., F.X. Kneizys, and R.W. Davies, 1989. Line shape and the water vapor continuum. Atmos. Res., 23,229-241. Coffeen, D.L., 1979. Polarization and scattering characteristics in the atmosphere of Earth, Venus, and Jupiter. /. Opt. Soc. Am., 69,1051-1064. Coleman, R.F., and K.N. Liou, 1981. Light scattering by hexagonal ice crystals. /. Atmos. Sci., 38,1260-1271. Conrath, B.J., R.A. Hanel, V.G. Kunde, and C. Prabhakara, 1970. The infrared interferometer experiment on Nimbus 3. /. Geophys. Res., 75,5831-5857. Diner, D.J., et al. 1998. Multi-angle Imaging SpectroRadiometer (MISR) Instrument description and experiment overview. IEEE Trans. Geosci. Remote Sens. 36, 10721087. Draine, B.T., and P.J. Flatau, 1994. Discrete-dipole approximation for scattering calculations. /. Opt. Soc. Am. All, 1491-1499. Frankel, D., K.N. Liou, S.C. Ou, D.P. Wylie, and W.P Menzel, 1997. Observations of cirrus cloud extent and their impacts to climate. In Proceedings of the Ninth Confer-

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ence on Atmospheric Radiation, Long Beach, CA. American Meteorological Society, Boston, MA, pp. 414-417. Fu, Q., and K.N. Liou, 1993. Parameterization of the radiative properties of cirrus clouds. /. Atmos. ScL, 50,2008-2025. Gao, B.-C, and Y.J. Kaufman, 1995. Selection of the 1.375-um MODIS channel for remote sensing of cirrus clouds and stratospheric aerosols from space. J. Atmos. Sci., 52, 4231-4237. Goody, R.M., and Y.L. Yung, 1989. Atmospheric Radiation: Theoretical Basis. Oxford University Press, New York. Greenler, R., 1980. Rainbows, Halos, and Glories. Cambridge University Press, Cambridge. Hansen J.E., and J.W. Hovenier, 1974. Interpretation of the polarization of Venus. /. Atmos. ScL, 31,1137-1160. Hansen J. et al. 1995. Low-cost long-term monitoring of global climate forcings and feedbacks, dim. Change, 31,247-271. Heymsfield, A.J., and L.M. Miloshevich, 1993. Overview of microphysics and state parameter measurements from FIRE-II. In Proceedings of the Conference on FIRE Cirrus Science Results 1993, Breckenridge, Colorado. National Aeronautics and Space Administration, Washington, DC, pp. 1-4. Huffman, P.J., and W.R. Thursby, Jr., 1969. Light scattering by ice crystals. /. Atmos. Sci., 26,1073-1077. Humphreys, W.J., 1954. Physics of the Air. Dover. New York. Jacobowitz, H., 1971. A method for computing transfer of solar radiation through clouds of hexagonal ice crystals. J. Quant. Spectrosc. Radial. Transfer, 11, 691-695. Jayaweera, K., and B.J. Mason, 1965. The behavior of freely falling cylinders and cones in a viscous fluid. /. Fluid Mech., 22,709-720. King, M.D., Y.J. Kaufman, W.P. Menzel, and D. Tanre, 1992. Remote sensing of cloud, aerosol, and water vapor properties from the Moderate Resolution Imaging Spectroradiometer. IEEE Trans. Geosci. Remote Sens. 30,2-27. King, M.D., S.C., Tsay, S.E., Platnick, M., Wang, and K.N., Liou, 1997. Cloud retrieval algorithm for MODIS; Optical thickness, effective particle radius, and thermodynamic phase. MODIS Algorithm Theoretical Basis Document no. ATBD-MOD-05.MOD06Cloud Product. Goddard Space Flight Center, Greenbelt, Maryland. Kunde, V.G., B.J. Conrath, R.A. Hanel, W.C. Maguire, C. Prabhakara, and V.V. Solomonson, 1974. The Nimbus IV infrared spectroscopy experiment. 2. Comparison of observed and theoretical radiances from 425-1450cm'1. J. Geophys. Res., 79, 777784. Liou, K.N., 1972. Light scattering by ice clouds in the visible and infrared: A theoretical study. J. Atmos. ScL, 29, 524-536. Liou, K.N., 1980. An Introduction to Atmospheric Radiation. Academic Press, New York. Liou, K.N, 1986. Influence of cirrus clouds on weather and climate processes; A global perspective. Mon. Wea. Rev., 114,1167-1198. Liou, K.N., 1992. Radiation and Cloud Processes in the Atmosphere: Theory, Observation, and Modeling. Oxford University Press, New York. Liou, K.N, and R.H. Coleman, 1980. Light scattering by hexagonal columns and plates. In Light Scattering by Irregularly Shaped Particles (D.W. Schuerman, ed.). Plenum Press, New York, pp. 207-218. Liou K.N, and S.C. Ou, 1979. Infrared radiative transfer in finite cloud layers. /. Atmos. Sci., 36,1985-1996. Liou, K.N., S.C. Ou, and G. Koenig, 1990. An investigation on the climatic effect of contrail cirrus. In Air Traffic and the Environmental-Background, Tendencies and

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Potential Global Atmospheric Effects (U. Schumann, ed.). Springer-Verlag, Berlin, pp. 154-169. Liou, K.N., and N. Rao, 1996. Radiative transfer in cirrus clouds. Part IV: On cloud geometry, inhomogeneity, and absorption. /. Atmos. Sci., 53,3046-3065. Liou, K.N., and Y.Takano, 1994. Light scattering by nonspherical particles: Remote sensing and climatic implications. Atmos. Res., 31,271-298. Liou, K.N., P. Yang, Y.Takano, K. Sassen,T.P. Charlock, and W.P. Arnott, 1998. On the radiative properties of contrail cirrus. Geophys. Res. Lett, 25,1161-1164. Lynch, D.K., and W. Livingston, 1995. Color and Light in Nature. Cambridge University Press, Cambridge. Lyot, B., 1929. Recherches sur la polarisation de la lumiere des planetes et de quelques substances terrestres. Ann. Observ. Paris (Meudori), 8. [Available in English as NASA TTF-187,1964, National Aeronautics and Space Administration, Washington, DC.] Macke, A., 1993. Scattering of light by polyhedral ice crystals. Appl. Opt., 32,2780-2788. Macke, A., J. Mueller, and E. Rascke, 1996. Single scattering properties of atmospheric ice crystals./. Atmos. Sci., 53,2813-2825. Martin, P.G., 1974. Interstellar polarization from a medium with changing grain alignment. Astrophys. J., 187, 461-412. Minnis, P., K.N. Liou, and Y. Takano, 1993. Inference of cirrus cloud properties using satellite-observed visible and infrared radiances. Part I: Parameterization of radiance field. /. Atmos. Sci., 50,1279-1304. Mishchenko, M.I., 1991. Extinction and polarization of transmitted light by partially aligned nonspherical grains. Astrophys. J., 367,561-574. Mishchenko, M.I., W.B. Rossow, A. Macke, and A.A. Lacis, 1996a. Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape. /. Geophys. Res. 101,16973-16985. Mishchenko, M.I., L.D. Travis, and D.W. Mackowski, 1996b. T-matrix computations of light scattering by nonspherical particles: A review. /. Quant. Spectrosc. Radiat. Transfer. 55, 535-575. Muinonen, K.,T. Nousiainen, P. Fast, K. Lumme, and J.I. Peltoniemi, 1996. Light scattering by Gaussian random particles: Ray optics approximation. /. Quant. Spectrosc. Radiat. Transfer, 55, 577-613. Ou, S.C., K.N. Liou, Y. Takano, NX. Rao, Q. Fu, A.J. Heymsfield, L.M. Miloshevich, B. Baum, and S.A. Kinne, 1995. Remote sounding of cirrus cloud optical depths and ice crystal sizes from AVHRR data: Verification using FIRE II IFO measurements. J. Atmos. Sci., 52,4143^158. Ou S.C., K.N. Liou, P. Yang, P. Rolland, T.R. Caudill, J. Lisowski, and B. Morrison, 1998. Airborne retrieval of cirrus cloud optical and microphysical properties using Airborne Remote Earth Sensing System 5.1-5.3 and 3.7-fim channel data./. Geophy. Res., 103,23231-23242. Perrin, F, 1942. Polarization of light scattered by isotropic opalescent media. /. Chem. Phys., 10,415^27. Platt, C.M.R., N.L. Abshire, and G.T. McNice, 1978. Some microphysical properties of an ice cloud from lidar observations of horizontally oriented crystals. /. Appl. Meteor., 17,1220-1224. Prabhakara, C, D.P. Kratz, J.-M. Yoo, G. Dalu, and A. Vernekar, 1993. Optically thin cirrus clouds: Radiative impact on the warm pool. /. Quant. Spectrosc. Radiat. Transfer, 49, 467-483. Rolland, P., and K.N. Liou, 1998. Remote sensing of optical and microphysical properties of cirrus clouds using MODIS channels. In Proceedings of the Cirrus Topical Meeting, Baltimore, Maryland. Optical Society of America, pp. 17-19.

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Sassen, K., 1991. The polarization lidar technique for cloud research: A review and current assessment. Bull. Amer. Meteor. Soc., 72,1848-1886. Smith, W.L., S. Ackerman, H. Revercomb, H. Huang, D.H. DeSlover, W. Feltz, L. Gumley, and A. Collard, 1998. Infrared spectral absorption of nearly invisible cirrus clouds. Geophys. Res. Lett., 25,1137-1140. Smith, W.L., H.L. Revercomb, R.O. Knuteson, F.A. Best, R. Dedecker, H.B. Howell, and H.M. Woolf, 1995. Cirrus cloud properties derived from high spectral resolution infrared spectrometer during FIRE II. Part I: The High resolution Interferometer Sounder (HIS) Systems. / Atmos. Sci., 52,4238^245. Spankuch, D., and W. Dohler, 1985. Radiative properties of cirrus clouds in the middle ir derived from Fourier spectrometer measurements form space. Z. Meteor., 6, 314324. Spinhirne, J.D., and W.D. Hart, 1990. Cirrus structure and radiative parameters from airborne lidar and spectral radiometer observations: The 28 October 1986 FIRE study. Mon. Wea. Rev., 118, 2329-2343. Stephens, G.L., 1980. Radiative transfer in a linear lattice: Application to anisotropic ice crystals. /. Atmos. Sci., 37,2095-2104. Stephens, G.L., and S.-C. Tsay, 1990. On the cloud absorption anomaly. Q. J. R. Meteor. Soc., 116,671-704. Taflove, A., 1995. Computational Electromagnetics in the Finite-Difference Time Domain Method. Artech House. Boston. Takano, Y., and K.N. Liou, 1989a. Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals. /. Atmos. Sci., 46, 3-19. Takano, Y., and K.N. Liou, 1989b. Solar radiative transfer in cirrus clouds. Part II: Theory and computation of multiple scattering in an anisotropic medium. /. Atmos. Sci., 46, 20-36. Takano, Y, and K.N. Liou, 1993. Transfer of polarized infrared radiation in optically anisotropic media: Application to horizontally oriented crystals. /. Opt. Soc. Amer. A, 10,1243-1256. Takano, Y, and K.N. Liou, 1995. Radiative transfer in cirrus clouds. Part III: Light scattering by irregular ice crystals. /. Atmos. Sci., 52, 818-837. Takano, Y, K.N. Liou, and P. Minnis, 1992. The effects of small ice crystals on cirrus infrared radiative properties. /. Atmos. Sci., 49,1487-1493. Umashankar, K., and A. Taflove, 1982. A novel method to analyze electromagnetic scattering of complex objects. IEEE, Trans. Electromagn. Compat., EMC-24, 397-405. van de Hulst, H.C., 1957. Light Scattering by Small Particles. Wiley, New York. Wendling, P., R. Wendling, and H.K. Weickman, 1979. Scattering of solar radiation by hexagonal ice crystals. Appl. Opt., 18, 2663-2671. Wielicki, B.A., P. Minnis, R. Arduini, L. Parker, S.-C. Tsay, Y Takano, and K.N. Liou, 1993. Remote sensing estimates of cirrus particle size for tropical and midlatitude cirrus: Hexagonal crystals and ice spheres. In Proceedings of the Conference on FIRE Cirrus Science Results 1993, Breckenridge, Colorado. National Aeronautics and Space Administration, Washington, DC, pp. 201-204. Wylie, D.P., W.P. Menzel, H.M. Woolf, and K.I. Strabala, 1994. Four years of global cirrus cloud statistics using HIRS. /. Climate, 7,1972-1986. Yang P., and K.N. Liou, 1995. Light scattering by hexagonal ice crystals: comparison of finite-difference time domain and geometric optics models. J. Opt. Soc. Am. A, 12, 162-176. Yang, P., and K.N. Liou, 1996a. A geometric-optics-integral-equation method for light scattering by nonspherical ice crystals. Appl. Opt., 35, 6568-6584.

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Yang, P., and K.N. Liou, 1996b. Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space. /. Opt. Soc. Am. A., 13,2072-2085. Yang, P., and K.N. Liou, 1998. Single-scattering properties of complex ice crystals in terrestrial atmosphere. Contr. Atmos. Phy., 71,223-248. Yee, S.K., 1966. Numerical solution of initial boundary value problems involving Maxwell's equation in isotropic media. IEEE Trans. Antennas Propag., AP-14,302-307.

14

On Cirrus Modeling for General Circulation and Climate Models

HILDING SUNDQVIST

14.1 Cirrus Characteristics and Modeling Aspects Cirrus clouds are significant regulators of the earth's radiation budget. Cirrus generally have low ice water content, leading to partial transparency to radiation, and a variety of ice crystal types constitutes the cloud. As a consequence, cirrus have complex optical qualities, which are discussed in other chapters of this book. In this chapter, I discuss the appearance and behavior of the cirrus clouds per se and discuss approaches to include those features in numerical models by parameterization. The number of general circulation models (GCMs) containing physically based parameterizations of cloud processes with prognostic equations for water/ice content increased remarkably during the 1990s. Model simulations of the general circulation of the atmosphere have shown a pronounced sensitivity to modeled optical properties of cirrus (e.g., Ramanathan et al. 1983; Senior and Mitchell 1993; Mitchell 1994b; Fowler and Randall 1996a,b; Kristjansson et al. 1998). Most studies with GCMs and climate models have focused on features of radiation and energy budgets and the modulation of these budgets as a consequence of changes in cloudiness quality or other conditions. Much less attention has been paid to the characteristics and realism of the model cloudiness itself (e.g., Liou 1992). Only meager discussions are generally found on these topics from studies in this context. In most cases, zonally averaged and/or bird's-eyeview cloudiness are reported. The reason for this is the sparseness of observational data, which makes it difficult to conduct a detailed verification of the simulated cloud fields. Many papers on model experimentation on this topic do 297

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indeed contain statements that uncertainties in cloud behavior constitute a severe weakness of the simulations (Senior and Mitchell 1993; Mitchell 1994). It is also emphasized that substantial improvement in our understanding of the behavior of clouds (not least cirrus) is required for satisfactory confidence in simulations of different climate scenarios. The critical need for high-accuracy measurements of upper-tropospheric water vapor is emphasized for example, in a paper by Stephens et al. (1996) discussing satellite measurements of water vapor. Clouds also have an indirect effect on climatology because their appearance and disappearance (evaporation) modulate the distribution of water vapor in the atmosphere. This effect may be especially prominent in cirrus. At cirrus altitudes, the difference between the saturation humidity and the ice water content of cirrus is considerably smaller than the corresponding difference at lower levels with higher temperatures and warm clouds. Evaporation of cirrus in the upper troposphere may therefore change the relative humidity substantially in this region, so the cloud situation has an essential impact on the equilibrium moisture content there. Operational measurements of moisture at low temperatures have a relatively large uncertainty, and the humidity analyses used for operational numerical weather prediction are therefore strongly governed by the 6-h model predictions of humidity in the assimilation cycle. These analyses may then also constitute elements of the climate data record. Consequently, assumptions about the liquid-ice phase conditions and the model treatment of cirrus have a pronounced impact on our notion of the water content of the upper troposphere. This again emphasizes the need for studies that lead to an enhanced understanding of dynamic and microphysical processes of cirrus, and eventually to a reliable certainty in their simulation in GCMs and other models. It is likely that large portions of the extensive cirrus clouds over tropical and subtropical regions emanate from anvils at the top of convective clouds, which are condensate-rich sources of cirrus. The idea that the difference between the saturation humidity and the water content of cirrus is often relatively small leads to the inference that evaporation of merely a fraction of the cirrus cloud may be sufficient to saturate the environmental air. This may explain why cirrus can survive transport over long distances away from the convective sources. Hence, it is of great importance to understand the processes forming anvils. It is not just the complex optical qualities of cirrus that distinguish them from warm clouds, but also the microphysical features and processes of cirrus. The main mechanism for ice crystal growth is deposition. This in turn means that there is no direct mechanism for generation of precipitation, but the particles fall as they become too heavy to be suspended by the upwind. In this context we are naturally led to the question of the definition of a cloud. Here I define a cloud as consisting of particles whose fallspeed due to gravitation is smaller than the upwind that is suspending them. That is, matter so heavy that its net vertical velocity is downward is denned as precipitation. Applying this to cirrus means that the rate of precipitation from this type of cloud is tantamount to the rate of production of ice crystals with a size or weight causing a net downward velocity. For inclusion in GCMs, it is, in general, hardly feasible, and certainly not realistic, to treat the evolution of individual cloud crystals. Instead, the bulk amount of cloud

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ice has to be used as a dependent variable. It is pertinent to note that, irrespective of how a specific scheme of prognostic equations of the cirrus condensationcloud processes is designed, it is necessary to know, or adopt, the size distribution of the cloud particles. The ice crystals of cirrus appear in many different shapes as a function of the environmental state, such as temperature, humidity, and aerosol type and amount. These circumstances affect both the microphysical growth characteristics and the optical properties (Liou 1995). These aspects are treated in several chapters of this book. It is not the cirrus cloud alone, but also the precipitating ice crystal mass (virga) that determines the optical depth of the cirrus layers. An appropriate account of the evaporation of the precipitating mass is therefore required. There is not unanimous agreement on the definition of cirrus. Their particular quality is due to the low temperatures at which these clouds exist. Here I adopt the definition that cirrus consist solely of ice crystals and furthermore presume saturation with respect to ice and that the temperature is below Tcir = -38°C. An important question regarding cirrus is what density of ice crystals produce a detectable effect on radiation. This density (optical depth) limit, which is probably a function of size distribution and crystal habit, may be adopted as a useful definition of the existence of a cloud. This question of the density-radiation relationship is also of vital interest in verifying and validating model simulations of cirrus. Whether fractional cloud cover has to be considered is another question, closely related to the density-radiation question. The basic condition is determined by the resolution, ideally the three-dimensional one. It seems that the resolution used in GCM and climate models generally is so coarse that fractional cover has to be accounted for. In the following sections, I discuss more elaborately views and suggestions devoted to the deduction of a physically based parameterization of cirrus.

14.2. Parameterization of Cirrus

14.2.1. Basic Considerations To derive a scheme for model treatment of cirrus, I start from a relatively simplistic approach, which I can then broaden by gradually accounting for refined considerations. I also review some schemes that are currently applied in GCMs. It is pertinent to note that the present discussion deals with approaches suitable for use in GCMs. In cloud-resolving models (CRMs), the mode of approach may be somewhat different with respect to details. Studies with the aid of CRMs constitute important research efforts that may give vital insights into many detailed processes. Aspects of CRMs are mentioned here only when they are relevant for the present review. A cloud scheme presumes that at least cloud extension and ice water content are regarded as variables. Some of the basic questions in this context have been

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discussed in the previous section. There is still a crucial question specific for cirrus modeling: What conditions shall be applied to decide whether or not condensation can take place? To elaborate on the above points, I consider the thermodynamic equation and the tendency equations of water vapor, cloud ice content, and precipitating water content respectively, as follows

where Lvi is the latent heat of deposition, Aa is all tendencies except that due to release of latent heat, Q is the rate of release of latent heat or rate of production of condensate, EP is the rate of evaporation of precipitation, GP is the rate of generation of precipitation, m is the cloud ice water mixing ratio, raP is the precipitating (ice) water mixing ratio, VP is the fall velocity of bulk precipitating water mass, and p is the air density. The remaining quantities have their conventional meaning. I first suggest an approach that also demonstrates the main features connected with the deduction of a cirrus parameterization scheme. I review some different cirrus schemes, which are applied in GCMs. To make the budget relations clear, the tendency equation of precipitating matter is included. By definition, the rate of precipitation at a level z (downward flux of water mass) is mPpVP. Omitting the left-hand term and the first term on the right-hand side of equation 4 and integrating from a level z to the top of the cloud, where the flux is zero, we find

Hence, the rate of precipitation at an arbitrary level is obtained from the integral of GP from that level to the top. So, if we do not include a prognostic equation for the precipitating matter, the rate of precipitation is obtained from equation 5a; if rap is required (as it is for calculation of EP), we have to adopt a (typical) fall velocity of the precipitation in question and diagnostically calculate mP from

We reformulate equation 2 in terms of relative humidity, U, and saturationspecific humidity, qs, (i.e., q = Uqs), by applying the Clausius-Clapeyron relation and get

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where the last right-hand-side is inserted from equation 2.Then, eliminating dT/dt between equations 1 and 5, we obtain after rearrangement of the terms

where

and

For later reference, I introduce the notation Mq:

Equation 7 shows that condensation may occur without direct transport convergence of vapor, through temperature changes (AT < 0), which result from for example expansion or radiative flux divergence. A prominent term of equation 7 is qsdU/dt, which together with GP of equation 3, has to be formulated to close the system of equations 1-3 and 7. There are two circumstances under which dU/dt * 0. One appears in the beginning of the cirrus condensation during the existence of a supersaturation that is being relaxed toward an equilibrium value (near saturation). The other situation with a non-zero humidity tendency may generally be present when a fraction of the grid square (or box) is covered by the cloud; in that situation, only part of the grid square has a relative humidity that allows condensation, implying that the grid point value of U then may vary with time. I return to the q^dU/dt term but first discuss the formulation of the generation of precipitation, GP. 14.2.2. Microphysical Aspects As stated above, the cloud proper is the ice water mass that is carried by the upwind, w, against the gravitational mean fall speed, V, which is (disregarding the sign)

where N(D) is the size distribution of the cloud ice crystals, and M(D) is the mass of the crystal of size D. Strictly, the upper integration limit should be DP, the size beyond which the crystals are so heavy that they precipitate. But if N(D) is (essentially) made up of the cloud particles, then the contribution to the integral for D > Dp, is negligible. Then setting w - V in equation 8, the ice water mixing ratio, mci, of the cloud is obtained from

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provided that we know the integral in the numerator (i.e., the size distribution and the terminal fall speed of individual crystals). From other chapters of this book, I conclude that the integral on the right hand side of equation 9 is most likely a function of the ambient conditions, such as temperature, humidity, aerosol existence, and upwind. As we gain a confident insight into such relations, it will become possible to obtain a consistent relation between mci and, for instance, the equivalent radius, which is an important cloud optical property (Wyser 1998). Based on various observational data, several relations between mass and fall velocity have been formulated (e.g., Locatelli and Hobbs 1974). In their paper on ice-cloud parameterizing, Heymsfield and Donner (1990) use a corresponding relation, while Mitchell (1996) treated the terminal velocity of individual crystal types and their sizes. But those relations are applicable to the fall velocity of the precipitating part of the ice crystals and are not suitable to be applied in equation 9. In those relations, the mass is proportional to the fall velocity raised to a large power (exponent -5-10). When the fall velocity is deduced from the mass, this implies a pronounced sensitivity to small uncertainties in velocity (a percentage change in velocity becomes amplified by the factor exponent value in the corresponding change in mass). The mass-fall velocity relations given in Cotton and Anthes (1989), and based on the observational data of Hobbs et al. (1972), are valid for smaller crystal sizes and hence for cloud ice mass. Simplifying these latter relations by taking a representative number density, N, and fall velocity, V, of the cloud ice particles, we obtain a related ice water mixing ratio,

where the product k\k2 varies from about 5000kg~°5ms 1 for a cloud consisting of small partjcles to about 8000kg~°5m/s for a cloud having typically larger particles. Then, V is here replaced with w, which is obtained from the model calculations. With w varying between 0.1 m/s for small particles, and Im/s for large particles (e.g^in anvils), mci will have mixing ratio values between 5 x 10~5 and 2 x 10~3, for N ~ 5 x 104. This mci corresponds to the autoconversion threshold of cloud ice in Fowler et al. (1996). They point out that they have to use a lower value than recommended by Lin et al. (1983), because the GCM has a low resolution without consideration of fractional cloud cover. Considering md to be an amount toward which the cloud water content adjusts as a result of the microphysical processes, and presuming that we have a w-value available from the model calculations, a description of the release of precipitation is suggested as follows

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Considering that the amount of ice water that is greater than rac( precipitates, the exponent cix should be given a value >1. The time scale that is represented by the inverse of kci reflects the time it takes to adjust toward mci through precipitation of "overweight" mass. The length of this adjustment time may be taken as the time it takes until the precipitating mass has been removed from the cirrus cloud layer due to the flux at the base of the cloud. That is,

where A/zc, is the thickness of the cirrus cloud layer. Expression 12 implies that kci ~ 2 x 10~3 to 5 x IQ'4. Fowler et al. (1996a) adopted a temperature-dependent coefficient, 10-3exp[0.25(r- 273)]. 14.2.3. Evaporation of Precipitating Ice Crystals The precipitating matter will be subject to evaporation when it falls through subsaturated strata. The rate of evaporation is described by the same relation as the depositional growth. For an individual particle, the evaporation is proportional to a representative size measure, C, the subsaturation, (S - Us - U), and a function, K, of vapor diffusion and thermal conductivity coefficients. Adopting an equivalent diameter for the size, and assuming an exponential size distribution, integration over the entire spectrum yields a relation for E? at a level z:

where equation 5b is introduced to give the last equality, hence VP is the average fall speed of the precipitation; kE is a rate coefficient to be determined, and P = 0.5. With a ventilation effect, which is size dependent, included in K, we get P = 0.65 (Kessler 1969). The unit of EP here is per second (mixing ratio per unit time). The coefficient kE contains the square root of the number concentration per unit length, dimension (nT4), and K.The latter is a pronounced function of temperature, so kEis about 15 times larger at 248 K than at 220 K. We may estimate how far the precipitation falls before it is completely evaporated. We consider

Integrating equation 14 over a fall distance, hE, required to evaporate the mp(cloud base), we find

Taking P = 0.5, kE = 10~5, VP ~ 1 m/s, Pbase ~ 4mm/day, and a subsaturation of 40% (U = 0.6), we obtain hE = 2300m.

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14.2.4. Macrophysical and Meso-scale Aspects As concluded above, a formulation of the qsdU/dt term in equation 7 is needed to close our system. The problem is closely connected with processes of both microphysical scales and larger scales. There are two basic possibilities for condensation to take place. One is that the supersaturation is high enough for, what is termed homogeneous (Heymsfield and Miloshevich 1995), condensation to occur. The other possibility is that small ice crystals, advected or falling into a volume of air, act as freezing nuclei if the humidity is at, or above saturation. In the case of homogeneous condensation, Heymsfield and Miloshevich (1995) found a temperature-dependent threshold value of relative humidity, t/hom. For the second alternative, it is necessary to establish at what concentration the freezing nuclei become effective initiators of cirrus formation. Zurovac-Jevtic (1999a) reported that the resulting model cirrus situation is sensitive to the chosen lower limit in this context. To account for the Brownian-dif fusion contact nucleation process, Lohmann and Roeckner (1996) related the droplet number concentration to sulfate aerosol mass, which is empirically different over oceans and land as well as over the two hemispheres. Whether condensation commences due to one or the other of the two alternatives, it is necessary to state how a supersaturation is relaxed toward an equilibrium (near saturation) value. Assume an exponential adjustment of the relative humidity to saturation,

where Us = 1 is the relative humidity at saturation, T is a relaxation time, which we take to be on the order of a fraction of 1 h, and conceivably T is a function of current type and number density of aerosol (freezing nuclei). The above discussion applies to an in-cloud situation (i.e., 100% cloud cover). The matter of fractional cloudiness adds considerable complexity to the parameterization of condensation-cloud processes. As noted above, we need to find (empirically) a guiding resolution at which it is reasonable to assume that the cloud fully fills a (grid-box) volume of air. Fractional cloudiness means that only part of an air volume is saturated. Consequently, it is then necessary to describe how the available humidity, Mq (equation 7a) is partitioned between the condensation proper on one hand, and a general humidity change in the cloud-free part of the volume on the other (Sundqvist 1978,1993). So far, there are no physically based parameterizations derived for fractional cloudiness and rate of change of relative humidity in partially cloud-free air volumes. These questions appear to be the most difficult ones in this context. Strictly, fractional cloud cover is a diagnostic, nonphysical quantity, but Tiedtke (1993) and Rasch and Kristjansson (1998) introduced an intriguing application of a prognostic treatment of fractional cover. Wilson and Ballard (1998) also considered the matter of fractional cover. For the time being, the best we can do is to resort to empirical or statistical approaches. It is not unusual to find reports from field measurements that report strong spatial variations of cloud ice content on relatively short scales. It appears

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natural to apply the principle introduced by Sommeria and Deardorff (1977), which is based on a statistical distribution of points where condensation occurs inside a given volume. In the case of anvils, the situation probably is markedly different from cirrus formed through large-scale lifting and similar circumstances. The pronounced convergence of vapor at the top of convective cells also brings suitable freezing nuclei, implying that condensation can take place without particular supersaturation, provided the temperature is below TciT. Convective clouds and anvils are likely to be of subgrid scale. As a consequence, anvils may form even if the gridbox relative humidity is below saturation. Assuming that the fractional cover is calculated separately, a plausible requirement on the relative humidity for condensation to take place is that the environmental humidity together with the moisture brought up during a time step in that fractional area of the grid square be greater than the saturation value. This may then be expressed as follows

where b is the cloud cover and q0 is the environmental specific humidity in the cloud-free area, and Mq is defined in equation 7a. The grid square specific humidity when condensation takes place in a fraction b is

Eliminating q0 between equations 17a and 17b and expressing the condition in terms of relative humidity, we get

In summary, the above derivation then consists of the following closed set of equations (omitting the precipitating mass as a prognostic variable): the prognostic equations 1-3; the consistency relation (equation 7); and the parametric relations (equations 10-11,13,16 and 17c or a corresponding relation). In deducing those relations, the crucial quantities for cirrus parameterization are also identified. Those quantities are size distribution, fall velocities of particles, and particle number density. These are primarily temperature dependent. The quantities are components of the above approach, for which some (typical?) averages have been adopted. The scheme has the potential for refinements. As we gain more insight into the microphysical relations, the ice water mixing ratio, m, may be divided into different categories of particle shapes, whereby it becomes necessary to describe transfer processes between the categories. It is here pertinent to observe studies by Mitchell (1994a), Mitchell et al. (1996), and Khvorostyanov and Sassen (1998), for example, which aim at an improved understanding of size distributions, fall velocities, and ice water contents. Wyser (1998) and Wyser and Yang (1998) suggest microphysics parameterizations that are consistent both with regard to cloud physics and optical qualities.

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14.3. Modeling with Specific Parameterization of Cirrus

As stated above, there are a few NWP models and GCMs that treat an ice phase of hydrometeors in their condensation cloud schemes. Examples of such approaches are found in Senior and Mitchell (1993), Del Genio et al. (1996), Fowler and Randall (1996b), Fowler et al. (1996), Lohmann and Roeckner (1996), Rotstayn (1997), Rasch and Kristjansson (1998), Wilson and Ballard (1998), and Zurovac-Jevtic (1999a,b). Heymsfield and Donner (1990) presented the first specific ice cloud parameterizations intended for use in large-scale models. Some of the approaches have a specific treatment of cirrus clouds and/or pay particular attention to the model cloud behavior (Heymsfield and Donner 1990; Del Genio et al. 1996; Fowler et al. 1996b; Wilson and Ballard 1998; Zurovac-Jevtic 1999a,b), whereas others concentrate on the optical properties of the ice crystal clouds and associated effects (Senior and Mitchell 1993; Kristjansson et al. 1998). The approach suggested by Heymsfield and Donner (1990) is simplistic and straightforward. They demonstrate the characteristics of the scheme with the aid of theoretical calculations and comparisons with FIRE data (Cox et al. 1987). The scheme is based on essentially the model vertical velocity, from which the amount of condensate produced during lifting is calculated under the assumption that freezing nuclei are abundant. The rate of removal of ice mass due to precipitation is obtained from a bulk terminal velocity, which is a function of the ice mixing ratio. An elaborate investigation of sublimation and survival distances of ice particles in subsaturated environments is included. The approach suggested in section 14.2 has not yet been tested in a threedimensional model. A few tests have been carried out in a one-dimensional version. In a standard atmosphere with a vertical velocity forcing between 300mb and 200mb with maximum speed of 15cm/s, the resulting cirrus ice water path is 0.002 kg/m2 and the total ice water path (including the precipitating ice) is 0.006 kg/m2; the maximum ice water content is about 3 x 10~3 g/kg. In a case with a deep convective cloud with the anvil top at about 12.5 km altitude, T= -65°C and maximum vertical velocity in the anvil of about l.Sm/s1, the result is a cirrus ice water path of 0.35 kg/m2 and a total ice water path of 1.1 kg/m2; the maximum ice water content is about 0.4 g/kg. In their scheme for cloud microphysical processes, Fowler et al. (1996a) used prognostic variables for cloud liquid water, cloud ice, rain, and snow. It is assumed that sufficient nuclei always are present to initiate condensation and deposition. The sinks of cloud ice (i.e., the rate of generation of precipitation) are autoconversion and collection of ice by snow. The former mechanism is similar to expression 11, but with a fixed value on the threshold parameter, and as indicated a temperature dependent coefficient. It is important to note that the scheme includes a spreading of cirrus from detraining convective cells. In a subsequent paper, Fowler et al. (1996b) carried out comprehensive analyses of the simulated hydrometeor fields and an evaluation of the sensitivity to the assumptions of the scheme. Among other things, they found pronounced sensitivity to the value of the autoconversion threshold, which emphasizes the key role of size distribution and fall velocity as they govern this threshold value. A great deal may be learned

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from this type of well-planned model experiment, but at the same time it is an important reminder of the great and urgent need for adequate observational data, to which the model results eventually must be compared. Zurovac-Jevtic (1999a) focused on the cirrus parameterization part of an overall condensation-cloud scheme. The cirrus ice water content is diagnosed from time step to time step, under the assumption that the cloud ice amount has a relatively short time of adjustment to the ambient conditions. Hence, the tendency of m is available in this quasi-equilibrium assumption. The release of latent heat is given by expression 7, so to guarantee a balanced water budget, the rate of release of precipitation is obtained by solving for GP in equation 3. The approach is included in a high-resolution numerical weather prediction model and has been applied to a mid-latitude situation and to a tropical situation (Zurovac-Jevtic, 1999b), in both cases with some observational data for comparison. In the present form, it appears that the scheme does not sufficiently account for the temperature dependence of derived parameters because the relation between temperature and cloud ice amount, indicated in observational data (Heymsfield and Platt 1984), is not clearly simulated. Zurovac-Jevtic (1998b) found an important sensitivity to assumed size distributions in the scheme. 14.4. Verification Aspects

In efforts to develop cirrus parameterizations for GCM, it is my opinion that results from model integrations should be analyzed in the synoptic time scale— not as statistical features—over extended time periods to account for all relevant circulation conditions that may be expected to occur. To obtain a revealing and constructive evaluation of the performance of a cloud scheme, it is absolutely necessary that observational cirrus data are available. The above discussions have shown that, in addition to ice water content, cloud cover, temperature, humidity, such data should contain information on ice crystal habits, size distributions, fall velocities, and survival distances (depth of virga). The chapters of this book show that there are useful data sets available from field campaigns. Those data have their greatest value in connection with the derivation of parameterization schemes and first-test applications in full-fledged model integrations. It appears difficult to detect, catch, and measure small ice particles. This means that ice crystal size distributions suffer from uncertainties, which severely affect the derivation of the cloud characteristics. Enhanced certainty in this respect would also suggest what lower limit of water content should be used to define a cirrus cloud for modeling and verification purposes. To reliably verify and validate model simulations, data covering large areas are required. Such coverage is provided only by satellite measurements. The great coverage is obtained at the expense of the details and three-dimensionality of field measurements. Retrievals of cirrus cloud parameters, especially, still suffer from uncertainties and inaccuracies, so it is essential that studies be encouraged and supported to achieve improvements in this respect. In conclusion, a good deal of useful data already exist for use in connection with numerical weather prediction and GCM experiments. It is important that

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we find ways to promote the much needed improvement of information and cooperation between the measuring and observing community and the modeling community. Then the former may be given a better insight into the modeler's request for observation data, and the latter will learn about potentials and limitations in measurements and observations. References Cotton, W.R., and R.A. Anthes, 1989. Storm and Cloud Dynamics. Academic Press, New York, Cox, S.K., D. McDougal, D.A. Randall, and R.A. Schiffer, 1987. FIRE-The First ISCCP Regional Experiment. Bull Amer. Meteor. Soc., 68,114-118. Del Genio, A.D., M-S. Yao, W. Kovari, and K.K.-W, Lo, 1996. A prognostic cloud water parameterization for global climate models. / Climate, 9,270-304. Fowler, L.D., and D.A. Randall, 1996a. Liquid and ice cloud microphysics in the CSU General Circulation Model. Part II: Impact on cloudiness, the earth's radiation budget, and the general circulation of the atmosphere. /. Climate, 9,530-560. Fowler, L.D., and D.A. Randall, 1996b. Liquid and ice cloud microphysics in the CSU General Circulation Model. Part III: Sensitivity to modeling assumptions. /. Climate, 9,561-586. Fowler, L.D., D.A. Randall, and S.A. Rutledge, 1996. Liquid and ice cloud microphysics in the CSU General Circulation Model. Part I: Model description and simulated microphysical processes. /. Climate, 9,489-529. Heymsfield, A.J., and L.J. Donner, 1990. A scheme for parameterizing ice-cloud water content in general circulation models. /. Atmos. Sci., 47,1865-1877. Heymsfield, A.J., and L.M. Miloshevich, 1995. Relative humidity and temperature influence on cirrus formation and evolution: observations from wave clouds in FIRE II. /. Atmos. Sci., 52,4302-4326. Heymsfield, A.J., and C.M.R. Platt, 1984. A parameterization of the particle size spectrum of ice clouds in terms of the ambient temperature and ice water content. /. Atmos. Sci., 41,846-855. Hobbs, P.V., L.F. Radke, A.B. Fraser, J.D. Locatelli, C.E. Robertson, D.G. Atkinson, R.J. Farber, R.R. Weiss, and R.C. Easter, 1972. Field observations and theoretical studies of clouds and precipitation over the Cascade Mountains and their modifications by artificial seeding (1971-72). Research Report VII. Department of Atmospheric Science, University of Washington, Seattle. Kessler, E., 1969. On the Distribution and Continuity of Water Substance in Atmospheric Circulation. Meteorological Monographs 10. American Meteorological Society, Boston, MA. Khvorostyanov, V.I., and K. Sassen, 1998. Cirrus cloud simulation using explicit microphysics and radiation. Part I: Model description. /. Atmos. Sci., 55,1808-1821. Kristjansson, I.E., J.M. Edwards, and D.L. Mitchell, 1998, A new parameterization scheme for the optical properties of ice crystals for use in general circulation models of the atmosphere. Phy& Chem. Earth (in press). Lin, Y.-L., R,D. Farley, and H.D. Orville, 1983. Bulk parameterization of snow field in a cloud model. /. Climate Appl. Meteor., 22,1065-1092. Liou, K.N., 1992. Radiation and Cloud Processes in the Atmosphere. Oxford University Press, New York. Liou, K.N., 1995. Issues related to parameterization of the radiative properties of ice

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clouds in GCMs. In Workshop on Cloud Microphysics Parameterizations in Global Atmospheric Circulation Models. Kananaskis, Alberta, Canada, 23-25 May, 1995, WCRP-90. World Meteorological Organization, Geneva pp. 233-247. Locatelli, J.D., and P.V. Hobbs, 1974. Fall speeds and masses of solid precipitation particles. J. Geophys. Res., 79,2185-2197. Lohmann, U, and E. Roeckner, 1996. Design and performance of a new microphysics scheme developed for the ECHAM general circulation model. Climate Dynamics, 12, 557-572. Mitchell, D.L., 1994a. A model predicting the evolution of ice size spectra and radiative properties of cirrus clouds. Part I: Microphysics. /. Atmos. Sci., 51,797-816. Mitchell, D.L., 1996. Use of mass- and area-dimensional power laws for determining precipitation particle terminal velocities. /. Atmos. Sci., 53,1710-1723. Mitchell, D.L., S.K. Chai, Y. Liu, A.J. Heymsfield, and Y. Dong, 1996. Modeling cirrus clouds. Part I: Treatment of bimodal size spectra and case study analysis. /. Atmos. Sci., 53,2952-2966. Mitchell, J.F.B., 1994b. Modelling clouds in GCMs for climate change studies. In Report of International Workshop on Cloud- Radiation Interactions and Their Parameterization in Climate Models, Camp Springs, Maryland, 18-20 October 1993. WCRP-86. World Meteorological Organization, Geneva pp. 40-41. Ramanathan, V.E., EJ. Pitcher, R.C. Malone, and M.L. Blackmon, 1983. The response of a spectral general circulation model to refinements in radiative processes. /. Atmos. Sci., 40,605-630. Rasch, PI, and I.E. Kristjansson, 1998. A comparison of the CCM3 model climate usingdiagnosed and predicted condensate parameterizations. /. Climate, 11,1587-1614. Rotstayn, L.D., 1997. A physically based scheme for the treatment of clouds and precipitation in large-scale models. I: Description and evaluation of the microphysical processes. Quart. J. Roy. Meteor. Soc., 123,1227-1282. Senior, C.A., and J.F.B. Mitchell, 1993. Carbone dioxide and climate: The impact of cloud parameterization. /. Climate, 6,393-418. Sommeria, G., and J.W. Deardorff, 1977. Subgridscale condensation in models of nonprecipitating clouds. / Atmos. Sci., 34,344-355. Stephens, G.L., D.L. Jackson, and I. Wittmayer, 1996. Global observations of uppertropospheric water vapor derived from TOYS radiance data. J. Climate, 9, 305-326. Sundqvist, H., 1978. A parameterization scheme for non-convective condensation including prediction of cloud water content. Quart. J. Roy. Meteor. Soc., 104,677-690. Sundqvist, H., 1993. Parameterization of condensation and associated clouds in models for weather prediction and general circulation simulation. In Aerosol-Cloud-Climate Interactions (P.V. Hobbs, ed.). Academic Press, New York, pp. 175-203. Tiedtke, M., 1993. Representation of clouds in large-scale models. Mon. Wea. Rev., 121, 3040-3061, Wilson, D.R. and S.P. Ballard, 1996. A microphysical based precipitation scheme for the UK Meteorological Office unified model. Quart. J. Roy. Meteor. Soc., 125,1607-1636. Wyser, K., 1998. The effective radius in ice clouds. /. Climate, 11,1793-1802. Wyser, K., and P. Yang, 1998. Average ice crystal size and bulk short-wave singlescattering properties in cirrus clouds. Atmos. Res., 49,315-335. Zurovac-Jevtic, D., 1999a. Development of a cirrus parameterization scheme: Performance studies in HIRLAM. Mon. Wea. Rev., 127,47(M85. Zurovac-Jevtic, Dance, 1999b. Cirrus modeling in the Tropics, chapter of Ph.D. Thesis, Dynamic modeling of cirrus cloud characteristics. Department of Meteorology, Stockholm University, Sweden.

15

GCM Simulations of Cirrus for Climate Studies A N T H O N Y D. DEL G E N I O

15.1. The Challenge of Modeling Cirrus Clouds

One of the great challenges in predicting the rate and geographical pattern of climate change is to faithfully represent the feedback effects of various cloud types that arise via different mechanisms in different parts of the atmosphere. Cirrus clouds are a particularly uncertain component of general circulation model (GCM) simulations of long-term climate change for a variety of reasons, as detailed below. First, cirrus encompass a wide range of optical thicknesses and altitudes. At one extreme are the thin tropopause cirrus that barely affect the short-wave albedo while radiating to space at very cold temperatures, producing a net positive effect on the planetary radiation balance and causing local upper troposphere warming, thus stabilizing the lapse rate. At the other extreme are thick cumulus anvil cirrus whose bases descend to the freezing level; these clouds produce significant but opposing short-wave and long-wave effects on the planetary energy balance while cooling the surface via their reflection of sunlight. In fact, satellite climatologies show a continuum of optical thicknesses between these two extremes (Rossow and Schiffer 1991). In a climate change, the net effect of cirrus might either be a positive or a negative feedback, depending on the sign and magnitude of the cloud cover change in each cloud-type category and the direction and extent of changes in their optical properties (see Stephens et al. 1990). Second, the dynamic processes that create cirrus are poorly resolved and different in different parts of the globe. In the tropics, small-scale convective trans310

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port of water from the planetary boundary layer to the upper troposphere is the immediate source of a significant fraction of the condensate in mesoscale cirrus anvils (see Gamache and Houze 1983), and ultimately the source of much of the water vapor that condenses out in large-scale uplift to form thinner cirrus. However, many observed thin cirrus cannot directly be identified with a convective source, suggesting that in situ upper troposphere dynamics and regeneration processes within cirrus (see Starr and Cox 1985) are important. In mid-latitudes, although summertime continental convection is a source of cirrus, in general cirrus is associated with mesoscale frontal circulations in synoptic-scale baroclinic waves and jet streaks (see Starr and Wylie 1990; Mace et al. 1995). Third, prediction of cirrus formation depends on the accuracy of transports of small concentrations of water vapor to and within the upper troposphere. The Clausius-Clapeyron equation implies that upper troposphere water vapor concentrations are several orders of magnitude smaller than those in the lower troposphere. Global numerical models, especially climate models that typically have only 10-20 vertical layers, have difficulty resolving such vertical gradients of water vapor. Thus, even a small error in the upward water vapor transport by the "resolved" dynamics in such models can result in first-order errors in instantaneous upper-level humidity. As a result, global models often fluctuate between extremely dry and supersaturated conditions at high altitude, producing bimodal distributions of high-level cloud cover with peaks near 0 and 100% (see Slingo 1980). Fourth, the relative humidity at which cirrus clouds form varies depending on the nature and concentration of nucleating particles. At sufficiently cold temperatures (<-40°C), homogeneous nucleation at vapor conditions near saturation with respect to ice is believed to occur, but at subfreezing temperatures warmer than this, heterogeneous freezing of supercooled liquid water droplets, which requires vapor saturation with respect to liquid water to initiate, is the dominant mechanism (see Sassen and Dodd 1989). The identity and availability of suitable ice nuclei are not well understood, making it difficult to predict the onset of cirrus in specific situations. Finally, cirrus are more difficult to observe than other cloud types, and hence their parameterization is more poorly constrained by available data. Global climatologies for all cloud types are produced by the International Satellite Cloud Climatology Project (ISCCP; Rossow and Schiffer 1991) from nadir-viewing, passive remote sensing instruments. Below a visible optical thickness i ~ 0.3, however, such retrievals have difficulty determining the correct cloud-top altitude, and below a T-value of about 0.1 are generally incapable of even detecting the presence of cirrus (Liao et al. 1995). Uncertainty in cirrus optical property retrievals is exacerbated by the large variety of cirrus crystal shapes and therefore scattering phase functions, that exist. Unlike liquid water, which can be observed in cloud emission at microwave frequencies, ice is fairly transparent except for a scattering signature by the largest particles at high microwave frequencies, and a climatology of ice water path thus does not exist. The majority of research on cirrus clouds emphasizes their microphysical and radiative properties, and especially how these contrast with the characteristics of liquid-phase clouds. Although these are undoubtedly important, the radiative

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effect of water in the vapor phase differs far more from the radiative effects of water in the liquid and ice phases than the latter two differ from each other. Hence, the first-order problem for GCM parameterization is the formation of cirrus, a subject that is fraught with uncertainties. This chapter reflects that viewpoint. The chapter is organized as follows: section 15.2 illustrates the role that both thin and thick cirrus play in the current climate and the potential they have to alter the sensitivity of climate to an external forcing. Sections 15.3 and 15.4 present some of the issues facing modelers in the parameterization of thick and thin cirrus, respectively. Finally, section 15.5 describes needed observations and strategies for using GCMs in combination with cloud-resolving models (CRMs) to develop improved global simulations of cirrus. 15.2. The Role of Cirrus in the Current Climate and Climate Change

The community of high-cloud researchers is dominated by two extreme viewpoints. One group focuses on extremely thin cirrus that are difficult to observe, under the false assumptions that everything is known about thicker, more easily detected high clouds and that thick, high clouds are not areally extensive enough to be climatically significant. Another group focuses on the optically thick, high cloud that is associated with most precipitation, discounting the impact on dynamics of the diabatic heating due to thinner, high clouds. In reality, all highcloud types are important climatically, and outstanding questions remain about all types. Hartmann et al. (1992) combined the ISCCP and Earth Radiation Budget Experiment (ERBE) data sets to subdivide the atmosphere into a small number of cloud types with similar impacts on the radiation budget and similar variability. Their results indicate that high clouds with i > 9.38 dominate the short-wave forcing in the tropics, while clouds thinner and thicker than i = 9.38 have comparable effects on outgoing long-wave radiation that dominate those from low and middle cloud types. Chen et al. (2000) used ISCCP data in combination with climatological information on cloud thicknesses, water vapor, and temperature in a radiative transfer model to estimate the effects of different cloud types on the top-of-the-atmosphere (TOA), within-atmosphere, and surface radiation budgets. Table 15.1, adapted from their work, illustrates that although thin, high cloud occurs over a larger area of the globe, it does not necessarily dominate the radiative impact of high clouds as a whole; in fact, the relative importance of different high-cloud types changes with the altitude at which one considers the energy budget. Thin, high cloud (0.02 < i < 3.55) is the only type that has a net positive TOA radiative effect. Moderate optical thickness (3.55 < T < 22.63) and optically thick (i > 22.63) high clouds have a negative TOA effect, with the latter dominating globally because of different short-wave and long-wave degrees of compensation between cover and albedo effects. (Moderate high-cloud coverage exceeds that of thick, high cloud, but thick, high clouds have higher albedo; in contrast, both moderate and thick, high clouds have near-unit emissivity, so long-wave warming

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Table 15.1. Global radiative impact (W/m2) of different high-cloud types (defined by their visible optical thickness, see text) on the energy budget at different altitudes Top of atmosphere Short-wave Long-wave Thin (13%) Moderate (6%) Thick (3%)

-4.2 -7.9 -6.2

5.5 5.5 2.9

Atmosphere

Surface

Net Short-wave Long-wave Net Short-wave Long-wave 1.3 -2.4 -3.3

-0.6 -0.7 -0.4

4.4 3.8 2.2

3.8 3.1 1.8

-3.6 -7.2 -5.8

1.1 1.7 0.7

Net -2.5 -5.5 -5.1

Adapted from Chen et al. (2000). Global areal coverage is indicated next to each cloud type.

effects due to the greater cover of moderate high cloud dominate.) Within the atmosphere, all high-cloud types have a net warming impact because short-wave cloud absorption is small; thin cirrus have the largest effect because they have the greatest cloud cover. The surface effect of all high-cloud types is negative because albedo effects are similar to those at TOA, while long-wave effects at the surface are severely muted by the intervening water vapor (and to some extent by low cloud in less humid regions). Overall, the largest negative net surface effect is due to moderate high clouds, which have greater cover than thick clouds and higher albedo than thin, high clouds. It is not known whether cirrus clouds as a class combine to produce a negative or a positive feedback on long-term climate change. Existing climate models produce a bewildering variety of predictions (see Cess et al. 1996), considering that all models agree that in a warming climate, an enhanced hydrologic cycle will result in stronger, deeper upward transport of water by convection and largescale motions. Cess et al. show that in response to a prescribed ±2°C sea surface temperature (SST) perturbation, long-wave amplification factors (which are due almost entirely to cirrus) of direct radiative forcing range from 0.4 (strong negative feedback) to 1.8 (strong positive feedback) among recent versions of 16 GCMs. At one extreme is the National Center for Atmospheric Research Community Climate Model Version 2, which prescribes cirrus optical properties and predicts an overall decrease in cirrus with warming despite an upward shift in altitude; the former change dominates to produce negative long-wave feedback. At the other extreme is the Laboratoire de Meteorologie Dynamique GCM, which has variable cloud optical properties and simulates increases in both cirrus cover and emissivity with warming, giving positive long-wave cloud feedback. Short-wave contributions of cirrus are also variable, but are largely explainable according to whether a given GCM allows for variable optical properties and a convective source of cirrus anvil water. Those that do incorporate such physics generally predict a negative cirrus component of short-wave cloud feedback, while those that do not tend to simulate a positive cirrus short-wave feedback. The cirrus "wild card" in an actual climate change scenario is easily demonstrated with the Model IF version of the Goddard Institute for Space Studies (GISS) GCM (Del Genio et al. 1996; Yao and Del Genio 1999). The standard version of this model has a 3.1°C global sensitivity to a doubling of CO2 when coupled to a mixed layer ocean and run to equilibrium. A set of three sensitivity

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experiments illustrates the range of uncertainty caused by our poor knowledge of cirrus and the processes that form them: 1. Typical of most GCMs, the GISS GCM underpredicts thin cirrus coverage (0.1-6% depending on latitude, as opposed to 5-20% observed by Stratospheric Aerosol and Gas Experiment II, according to Liao et al. 1995). A crude upper limit on the climatic role of the missing thin cirrus can be estimated by invoking the following artificial parameterization: Assume 100% thin (visible optical thickness T = 0.1) cirrus coverage at the tropopause in the current climate. If a doubling of CO2 causes thin cirrus T to increase fractionally by the same amount as the tropopause humidity (27%), then the resulting additional warming is 1.3°C, giving a global sensitivity of 4.4°C. 2. Thick convective anvil cirrus are created in part by the detrainment of condensate from cumulus updrafts. How much of this condensate detrains depends on the evolution of the drop size distribution in the updraft, the strength of the updraft itself, and the extent of entrainment of drier environmental air, all of which are beyond the scope of current parameterizations. The GISS GCM assumes that all vapor condensed in cumulus updrafts above the 550 rnb level detrains; when detrainment is excluded, the global sensitivity rises by 0.6°C, to 3.7°C. Allowing some of the condensate formed below the 550mb level to be transported upward and detrain would presumably lower the sensitivity of the model instead, since these clouds are already optically thick. 3. Since cirrus properties are sensitive to the dynamic processes that form them, the cirrus cloud feedback depends on uncertainties in the response of the largescale dynamics to climate forcing as much as it does on parameterization uncertainties. We conducted two pairs of fixed SST perturbation (±2°C) perpetual July experiments (which overemphasize tropical feedbacks relative to CO2 doubling simulations) with identical versions of the cloud parameterization: One in which the SST change is applied uniformly, and another in which the tropical East Pacific is allowed to warm or cool by >2°C, and the tropical West Pacific by <2°C, thus reducing/intensifying the longitudinal SST gradient and Walker circulation in the warmer/cooler climate. The model produces vastly different climate sensitivities (0.49 vs. 1.12°C-m2/W in the uniform and altered gradient cases, respectively) because the different responses of the Walker cell supply different amounts of water vapor to the upper troposphere in the two runs (Del Genio et al. 1996).

15.3. Parameterization Issues for Thick Cumulus Anvil Cirrus

The previous section demonstrates that prediction of the physics controlling the cloud cover and optical thickness of cumulus anvil cirrus clouds is central to a plausible estimate of climate sensitivity. Anvils exist in a wide variety of sizes, thicknesses, and lifetimes. Figure 15.1 shows the distribution of anvil radiative properties observed during the Tropical Ocean Global Atmosphere/Coupled Ocean Atmosphere Response Experiment (TOGA/COARE); convective clusters were defined using the ISCCP DX data set and the cluster detection algorithm of Machado and Rossow (1993). It can be seen that small (100200km radius) clusters have a broad range of optical thicknesses (T ~ 10-50),

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Figure 15.1. Life cycle mean anvil visible optical thickness versus cluster size for all convective clusters of size >100km during the TOGA/COARE IOP detected with the Machado and Rossow (1993) algorithm (Ye 1999).

whereas intermediate optical thickness clusters range in size from 100km to almost 1000km. These properties are undoubtedly influenced by the extent of water transport by convective updrafts and eventual detrainment into the anvils themselves, but it is probably not possible to predict the strength of convective water transport in a GCM from first principles. Furthermore, there is an equally important source of anvil condensate from in situ mesoscale uplift and condensation. Unfortunately, the extent of detrainment versus local production of anvil ice varies widely depending on the nature of the convective system. Table 15.2 is a sampling of water budget estimates from observations and CRM simulations of convective events in different locations. Detrainment of condensate into anvils can be either an insignificant fraction of, or comparable to, the amount of precipitation that reaches the ground in different convective systems. Plausibly this is related to the Table 1 5.2. Some Observational and Modeling Estimates of Cumulus Detrainment, Normalized by Total Precipitation, in Tropical and Mid-latitude Convective Clusters Model, date, reference GATE, Sept. 12 (Gamache and Houze 1983) COPT81, May 27-28 (Roux and Ju 1990) OK PRE-STORM, June 10-11 (Callus and Johnson 1991) GATE, Sept. 12 CRM (Ferrier et al. 1996) COHMEX, June 29 CRM (Ferrier et al. 1996)

Detrained condensate 0.42-0.61 0.14 0.26 0.63-0.73 0.37

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strength of the convection itself: Weak updrafts are less capable of lofting the larger droplets that comprise much of the mass of condensed water than are strong updrafts, and so in general we might expect condensate detrainment (and hence anvil cirrus optical thickness and cover) to scale with convective strength. This presents a challenging problem for parameterization: The factors controlling updraft strength are not yet understood fundamentally, and it is not obvious that the essential relationships between updraft strength and cumulus microphysics can even be parameterized in a large-scale model. In addition, other environmental factors such as the ambient humidity structure may influence both the amount of condensate (and hence droplet size) and the degree to which entrainment dilution takes place. Nonetheless, there are at least some indications that convection strength affects cluster optical thickness. Figure 15.2 shows ISCCP optical thicknesses for 9 TOGA/COARE clusters that were also observed by a passive microwave instrument mounted on the ER-2 aircraft (McGaughey et al. 1996). The 85-GHz brightness temperature, which is sensitive to scattering by large ice particles and hence thought to be diagnostic of strong vertical motion lofting ice to high levels, correlates well (in a negative sense, since scattering depresses the brightness temperature) with visible optical thickness in all but one case. Furthermore, the highest optical thickness cluster (with the coldest brightness temperature) was associated with extensive lightning discharges and large (30dBZ) radar reflectivity in the mixed phase region of the cloud (Petersen et al. 1996), features that can only be explained if strong updrafts loft supercooled liquid water to high, cold levels in the cloud. Likewise, two of the less optically

Figure 15.2. ER-2 AMPR 85.5-GHz average brightness temperatures for convective cores sampled during 9 TOGA/COARE flights (McGaughey et al. 1996) versus ISCCP DX visible optical thickness averaged over the spatial extent and life cycle of associated anvils.

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thick clusters in the diagram were observed by Petersen et al. to occur during a period of suppressed lightning. Ye (1999) has investigated the pre-storm environmental factors contributing to the observed size and optical thickness differences among the TOGA/COARE clusters in figure 15.1 by defining subensembles of large size, small size/optically thin, and small size/optically thick clusters. Large size clusters tend to be favored by strong large-scale upward motion throughout the troposphere and moist low- to mid-level relative humidities, which destabilize the atmosphere and increase the probability that updrafts will maintain their buoyancy against entrainment dilution. Consistent with this, large storms exist in slightly more buoyant environments: Convective available potential energy (CAPE) for pseudo-adiabatically lifted surface parcels is slightly greater for the large size subensemble (3008 J/kg) than for the two small size subensembles (2687 J/kg). This is a promising result for parameterization development because GCMs predict large-scale vertical velocity and relative humidity and have been shown to be capable of simulating reasonable statistics of CAPE occurrence (Ye et al. 1998). On the other hand, large-size clusters are also favored in conditions of strong (>30 m/s) front-to-rear flow, which is not related in any obvious way to the large-scale zonal or meridional wind because of variations in cluster propagation speed and direction that are difficult to predict in a large-scale model. Unlike cluster size, cluster optical thickness has no obvious relationship to parcel buoyancy in the TOGA/COARE data set. Instead, optically thick anvils appear to be favored in situations of strong, low-level moisture convergence, which optimizes the source of condensate. Furthermore, there is a preference for optically thick anvils in situations of strong upper troposphere shear; specifically, an increase in front-to-rear flow with height above the 500-mb level allows cumulus condensate to flow back into a trailing anvil cloud, increasing its ice content, while a decrease in front-to-rear flow with height causes more condensate to fall into the advancing updraft, enhancing autoconversion and reducing detrainment. 15.4. Parameterization Issues for Thin Cirrus

Cirrus clouds that are sufficiently thin for their long-wave radiative warming effect to dominate present a different set of parameterization challenges. First among these is understanding why such cirrus exist. In mid-latitudes, thin cirrus are found in regions of upper-level rising motion in advance of the surface warm fronts of baroclinic waves and are also associated with mesoscale circulations in the vicinity of jet streak entrance and exit regions. In the tropics and the summer mid-latitudes, cirrus are also observed as the product of outflow from deep convective updrafts, usually adjacent to the outer, thinner portion of the cumulus anvil. These source types explain the geographical distribution of thin cirrus simulated by GCMs (fig. 15.3), with peaks in the Intertropical Convergence Zone and mid-latitude storm tracks, and are consistent with the latitudinal variation in thin cirrus occurrence observed by SAGE II (Liao et al. 1995).

3 18

Cirrus

Figure 15.3. October geographical distribution of thin (t < 1) cirrus occurrence (%) in the tropopause region (80-192 mb) simulated by the 2° x 2.5° x 18 L version of the GISS GCM. The contour interval is 10%.

However, the frequency of occurrence of thin cirrus, especially near the tropical tropopause, is much higher than that of convection, and individual thin cirrus clouds often have no obvious connection to a convective source. This type of detached cirrus may sustain itself for long periods of time via cloud-scale motions arising from radiative destabilization within the cloud, but the extent to which this occurs and the role played by such processes climatologically is unknown. Such cirrus are likely to be underrepresented in climate models: The radiative heating profile is sensitive to the cloud physical thickness, typically 0.5 km or less (Starr and Wylie 1990), but current climate GCMs tend to have upper troposphere layers at least twice this thick. Climatologically, the relative contributions to cirrus occurrence from direct convective outflow, large-scale upward motion, and internal cloud-scale regeneration have not been determined. One potential way to distinguish source mechanisms is via characteristic differences in cloud radiative properties and the environmental situations in which they occur. Figure 15.4 shows scatterplots of thin (T < 1) cirrus cloud cover and optical thickness as a function of relative humidity (RH) for the near-tropopause layers of a 2° x 2.5° x 18 L version of the GISS GCM. There are two distinct populations of clouds. For RH > 0.65 (the assumed threshold for stratiform cloud formation in the GCM), cloud cover increases systematically with RH up to 100% cover according to the parameterization proposed by Sundqvist (1978); the two different curves followed by most points in this region of the diagram reflect the fact that GCM stratiform clouds are assumed to fill the gridbox vertically when the layer is disturbed by a coexisting convective event but are assumed to spread out horizontally and have subgrid-scale physical thickness when the box is convectively stable. Superimposed on this is a second population of mostly small cloud cover cirrus occurring primarily (but not

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Figure 15.4. Scatterplot of individual layer thin (T < 1) cirrus (upper) cloud cover and (lower) visible optical thickness versus relative humidity with respect to ice for the GISS GCM cirrus distribution shown in figure 15.3.

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exclusively) in the presence of dry upper-level conditions. These cirrus are created directly from convective outflow into otherwise unfavorable environments for cirrus generation by the GCM's cumulus parameterization. Note that the two populations play qualitatively different climatic roles: The stratiform cirrus are a response to moist upper-level conditions and act as a sink of water vapor; the convective cirrus are a source of water vapor (after they sublime) for a previously very dry upper troposphere. Correct simulation of the balance between this source and sink, currently unverifiable with data, is a prerequisite for confidence in a GCM's prediction of water vapor feedback in a warming climate. Not surprisingly given the qualitatively different source mechanisms, the frequency distribution of cirrus optical thickness in figure 15.4 is bimodal.Thin cirrus produced by the stratiform cloud parameterization almost exclusively have T > 0.04, while thin cirrus produced by convective outflow span a broad range of optical thicknesses down to 0.001, with peak occurrence in the range 0.01 < i < 0.1. Beyerle et al. (1998) also observed a bimodal distribution of cirrus optical thickness in lidar observations of the tropical Atlantic; however, the thinner segment of their population peaks at lower T than that of the convective outflow population in the GCM. Whether the Beyerle et al. results are climatologically representative is not known. Vertical resolution is not the only problem for GCM cirrus simulation; horizontal resolution is also an issue because cirrus formation and maintenance occur largely on the cloud scale and the mesoscale. Cirrus sensitivity to unresolved dynamics (i.e., cumulus updrafts) may appear to be primarily a tropical problem, but this is not the case. In mid-latitudes, cirrus form typically in ageostrophic circulations associated with 50-km wide frontal uplift regions of baroclinic waves and upper troposphere jet streaks and tropopause folds (see Starr and Wylie 1990; Mace et al. 1995). Although climate GCMs do a surprisingly good job of portraying marginally resolved synoptic aspects of baroclinic waves, they cannot resolve the shears and temperature gradients in the frontal regions. The result is simulated fronts that are more upright than tilted, according to the SawyerEliassen equation, and cirrus occurrence only within the column that contains the surface front rather than spread over a broad region in advance of the front. GCMs that do not underpredict mid-latitude cirrus may often accomplish this artificially via a background vertical eddy diffusion of moisture not tied to any specific process. This may be either explicitly parameterized or an implicit consequence of inaccuracies in the GCM's finite-difference scheme or spectral representation of transport. Water vapor transport errors can also be reflected in choices made in the parameterization of cirrus microphysics. For example, a model with excessive ice crystal fallspeeds may be one whose grid-scale vertical transport of water vapor is too strong and which therefore overpredicts cirrus [see the original version of the United Kingdom Meteorological Office prognostic cloud water scheme developed by Smith (1990)], whereas a model that underestimates upward water fluxes and underpredicts cirrus may characteristically have very weak ice fallout [see the GISS prognostic scheme of Del Genio et al. (1996)]. Given the important role of cirrus in regulating outgoing long-wave radiation, it can be argued that the wide range of cirrus microphysics parameterizations in use in current GCMs is less indicative of uncertainties in the microphysics

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itself and more indicative of the need to compensate for errors in other parts of the GCM. One exception to this statement is the generally ignored problem of the scale dependence of parameterizations. Existing parameterizations of cirrus microphysical processes (see Heymsfield 1977) are valid on the scale of individual cirrus and are appropriate for use in CRMs, which resolve single clouds. Such parameterizations are sometimes adopted for use in GCMs with grid sizes of hundreds of kilometers, though. On this scale, there is substantial subgrid variability in ice water content (IWC), and to the extent that process parameterizations are nonlinear functions of IWC, they are inappropriate for use in a GCM. For example, the GCM gridbox mean IWC should generally be much smaller than the large local values in regions of cloud in which the majority of ice sedimentation occurs; use of a scheme valid on the cloud scale will cause ice to build unrealistically in the GCM. The same issue arises in simulating the radiative effects of cirrus: even if three-dimensional aspects of radiation are ignored, the gridbox mean albedo and emissivity are not simply related to the gridbox mean IWC because of subgrid IWC variability and the nonlinear relation between albedo/emissivity and optical thickness. Considine et al. (1997) have suggested that histograms of marine-stratus liquid water path are related to cloud cover in a straightforward manner that depends only on the mean cloud depth and the standard deviation of the lifting condensation levels for surface air parcels. Their simple model successfully predicts a distribution that peaks at the lowest value when skies are partly cloudy but at finite liquid water path values in overcast conditions. Cirrus would seem to be more complex—there is no well-defined lower boundary for parcel origin, and horizontal water fluxes should be more important than in the planetary boundary layer. Nonetheless, aircraft observations of cirrus IWC from 18 FIRE II flights analyzed by Smith and Del Genio (2001) exhibit exactly the same behavior (fig. 15.5). The only exception is a single flight (KA05) through nearly overcast skies whose histogram resembles that for partly cloudy situations; this cloud formed under anomalously highly stratified, weakly turbulent conditions that would plausibly suppress the vertical motions required to produce partial cloud clearing. These results tentatively suggest that universal subgrid distributions that depend on only a few parameters may be a feasible approach to the GCM scaledependence issue for radiation and microphysics. Cirrus can nucleate in three fundamentally different ways: Homogeneously, at temperatures T < -40°C; heterogeneously via direct deposition from vapor to ice on a suitable nucleus; and heterogeneously via freezing of previously condensed supercooled water droplets. For GCMs, this translates into uncertainty about whether to make liquid or ice cloud at temperatures above the homogeneous nucleation point but below freezing, and whether to assume saturation with respect to the ice or the liquid phase (or alternatively on the grid scale, a threshold RH referenced to one or the other phase) as the condition for initiating cirrus formation. This issue is only beginning to receive attention in the context of the impact of contrails on cirrus formation (see Jensen and Toon 1997). Less appreciated is the possible indirect effect of aerosols produced in the lower troposphere on cirrus. The indirect effect is generally thought of as purely a short-wave,

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Figure 15.5. FIRE II cirrus ice water content histograms for flights (upper) SA07 (cloud cover 100%), (middle) SA13 (51%), and (lower) KA05 (97%). Overlain are the predictions of a simple cirrus analog to the model of Considine et al. (1997; see also Smith and Del Genio 2001). low-stratus problem, but sulfur chemistry-climate models (see Lohmann and Feichter 1997) suggest that upper troposphere sulfate mixing ratios in northern mid-latitudes are comparable to tropical near-surface concentrations, and observations during SUCCESS suggest significant surface sources of upper troposphere sulfate as well (Dibb et al. 1998), raising the possibility of an indirect longwave effect on cirrus. In the GISS GCM, referencing cirrus initiation to ice rather than to water saturation makes a qualitative difference in the model's energy budget and circulation. Because ice saturation is easier to achieve, cirrus is more frequent, more ice is formed, especially at low latitudes where water vapor concentrations are highest, and less short-wave radiation is thus absorbed in the tropics. This in turn reduces the latitudinal radiative forcing imbalance that drives the general circulation. With a reduced need for poleward heat transport, mid-latitude synoptic storms weaken, producing less cirrus there, and absorbed short-wave radiation consequently increases instead in mid-latitudes. 15.5. Observation and Modeling Strategies for Improved Cirrus Parameterization Parameterization of the formation as well as of the microphysical and radiative properties of cirrus is more uncertain than for liquid-phase clouds because they

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are more difficult to observe, as described in section 15.1. The radiative impact of cirrus within a column of atmosphere is the integrated effect of a large number of parameters: coverage, height, physical thickness, particle size and shape, IWC, and subgrid variability of the cirrus itself; the same properties of any other cloud layers below the cirrus; environmental temperature and humidity profiles; and the surface albedo. Several of these quantities are rather poorly constrained by observations, at least climatologically. Thus, there are many combinations of the parameters within the realm of plausibility that produce similar radiative fluxes. For example, since thick anvil cirrus have approximately unit emissivity, one can change their IWC without changing the long-wave cloud forcing. Thus, three models, one with overly thick anvils and overly thin underlying stratus, another with thinner anvils and thicker stratus, and a third with thin anvils and thin stratus but small ice crystal sizes, can theoretically produce the same TOA radiation budget. As proof that such compensating errors actually occur, Rasch and Kristjannson (1998) showed that state-of-the-art climate GCMs differ wildly in their estimates of global ice water path. Table 15.3, adapted from their work, shows the ice and liquid water paths and the global TOA radiation budgets from three representative GCMs having prognostic cloud water schemes. Each model is within 10 W/m2 of ERBE-derived absorbed short-wave and outgoing long-wave radiation, and given the factor of two differences in available microwave liquid water path climatologies, each is within range of one of the existing estimates, yet the global ice water paths differ by almost an order of magnitude among the models. The absence of a reliable ice water path climatology makes such leeway possible in models. Lin and Rossow (1996) have indirectly estimated ice water path as a residual from ISCCP optical thicknesses, particle size assumptions, and microwave liquid water path estimates, but an approach based on more direct sensing of ice itself is desirable. Recent advances in submillimeter passive remote sensing (see Evans et al. 1998) offer hope that global estimates of ice water path may soon be feasible. Beyond this, active remote sensing techniques that provide cloud-base heights and thicknesses and allow radiative heating profiles through the atmosphere to be calculated would provide additional constraints, but only if such instruments can sample a sufficiently large

Table 15.3. Cloud water paths and top-of-the-atniosphere radiation budgets of three GCMs: GISS (Del Genio et al. 1996), CSU (Fowler et al. 1996), and CCM3 with the prognostic cloud water scheme of Rasch and Kristjannson (1998)

Ice water path (g/m2) Liquid water path (g/m2) Absorbed short-wave radiation (W/m2) Outgoing long-wave radiation (W/m2)

GISS

CSU

CCM3

150 90 238 235

18 44 228 230

20 32 237 237

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fraction of the globe in unbiased fashion for sufficiently long time periods to provide a representative climatology. Finally, more observational constraints on cirrus nucleating particles and environmental humidity conditions, well beyond the few case studies currently available, would help modelers more accurately simulate when cirrus should form. Cloud-resolving modeling of cirrus, as advocated by the GEWEX Cloud System Study (GCSS), also has the potential to contribute to improved parameterization. Three of the four GCSS working groups (WG) study cirrus in some fashion: WG2 focuses specifically on cirrus, and WG3 (extratropical layer clouds) and WG4 (deep convective systems) focus on the dynamic entities that are the sources of most cirrus clouds. The GCSS approach currently envisions a limited number of idealized and real-world case studies by CRMs in tandem with singlecolumn model (SCM) versions of GCM parameterizations as a vehicle for parameterization development. The limited scope of this approach is consistent with the status of GCSS as an unfunded program but is probably not sufficient to meet most parameterization goals. A more comprehensive strategy would add two components: 1. Simulation of a large number of cases by CRMs, covering the phase space of relevant parameters in different climate regimes, would define the probability density functions of subgrid-scale variations of relevant parameters needed to predict fractional cloudiness and to scale microphysical process and radiative parameterizations that are valid on the cloud scale up to the GCM grid scale. 2. SCMs forced by observed dynamic fluxes in theory can test the validity of cloud parameterizations, to the extent that the dynamic fluxes can be accurately specified. Because cloud simulation in a GCM depends also on the accuracy of the simulated dynamics, a separate project exploring the ability of climate GCMs to predict the synoptic evolution and associated mesoscale fluxes of water that determine when and where clouds form, starting from common analysisgenerated initial conditions, would complement current GCSS activities. In the context of a climate GCM, it is not necessary to simulate cirrus occurrence in specific weather events as much as it is necessary to simulate their statistics and relationships with characteristic dynamic structures. Lau and Crane (1995), for example, use ISCCP data in combination with a meteorological analysis to produce composite maps of the relationship of cirrus and other cloud types to features of synoptic-scale midlatitude and tropical storms. This suggests that systematic analysis of a climate GCM's simulation of weather and cirrus formation, composited over many weather events, would provide insights into model inadequacies. Unfortunately, extensive analysis of models is not yet embraced by funding agencies as being of equal value to acquisition of data, making the prospects for progress in this area remote.

Acknowledgments This research was supported by the National Aeronautics and Space Administration Tropical Rainfall Measuring Mission and the Department of Energy Atmospheric Radiation Measurement Program. I thank W. Kovari, Jr., for assistance with the figures.

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References Beyerle, G, H.-J. Schafer, R. Neuber, O. Schrems, and I.S. McDermid, 1998. Dual wavelength lidar observation of tropical high-altitude cirrus clouds during the ALBATROSS 1996 campaign. Geophys. Res. Lett., 25, 919-922. Cess, R.D., et al., 1996. Cloud feedback in atmospheric general circulation models: An update. /. Geophys. Res., 101,12791-12794. Chen, T., W.B. Rossow, and Y. Zhang, 2000. Radiative effects of cloud type variations. /. Climate, 13,264-286. Considine, G., J.A. Curry, and B. Wielicki, 1997. Modeling cloud fraction and horizontal variability in marine boundary layer clouds./. Geophys. Res., 102,13517-13525. Del Genio, A.D., M.-S. Yao, W. Kovari, and K.K.-W. Lo, 1996. A prognostic cloud water parameterization for global climate models. /. Climate, 9,270-304. Dibb, J.E., R.W. Talbot, and M.B. Loomis, 1998. Tropospheric sulfate distribution during SUCCESS: Contributions from jet exhaust and surface sources. Geophys. Res. Lett., 25,1375-1378. Evans, K.F., S.J. Walter, A.J. Heymsfield, and M.N. Deeter, 1998. Modeling of submillimeter passive remote sensing of cirrus clouds. /. Appl. Meteor., 37,184-205. Ferrier, B.S., J. Simpson, and W.-K. Tao, 1996. Factors responsible for precipitation efficiencies in midlatitude and tropical squall simulations. Mon. Wea. Rev., 124, 2100-2125. Fowler, L.D., D.A. Randall, and S.A. Rutledge, 1996. Liquid and ice cloud microphysics in the CSU general circulation model. Part I: Model description and simulated microphysical processes. /. Climate, 9,489-529. Gallus, W.A., Jr., and R.H. Johnson, 1991. Heat and moisture budgets of an intense midlatitude squall line. /. Atmos. Sci., 48,122-146. Gamache, J.F., and R.A. Houze, Jr., 1983. Water budget of a mesoscale convective system in the tropics. /. Atmos. Sci., 40,1835-1850. Hartmann, D.L., M.E. Ockert-Bell, and M.L. Michelsen, 1992. The effect of cloud type on Earth's energy balance: Global analysis. /. Climate, 5,1281-1304. Heymsfield, A.J., 1977. Precipitation development in stratiform ice clouds: A microphysical and dynamical study. /. Atmos. Sci., 34, 367-381. Jensen, E.J., and O.B. Toon, 1997. The potential impact of soot particles from aircraft exhaust on cirrus clouds. Geophys. Res. Lett., 24,249-252. Lau, N.-C, and M.W. Crane, 1995. A satellite view of the synoptic-scale organization of cloud properties in midlatitude and tropical circulation systems. Mon. Wea. Rev., 123, 1984-2006. Liao, X., W.B. Rossow, and D. Rind, 1995. Comparison between SAGE II and ISCCP high-level clouds: 1. Global and zonal mean cloud amounts. /. Geophys. Res., 100, 1121-1135. Lin, B., and W.B. Rossow, 1996. Seasonal variation of liquid and ice water path in nonprecipitating clouds over oceans. /. Climate, 9,2890-2902. Lohmann, U., and J. Feichter, 1997. Impact of sulfate aerosols on albedo and lifetime of clouds: A sensitivity study with the ECHAM4 GCM. /. Geophys. Res., 102, 13685-13700. Mace, G.G., D.O'C. Starr, T.P. Ackerman, and P. Minnis, 1995. Examination of coupling between an upper-tropospheric cloud system and synoptic-scale dynamics diagnosed from wind profiler and radiosonde data. /. Atmos. Sci., 52,4094-4127. Machado, L.A.T., and W.B. Rossow, 1993. Structural characteristics and radiative properties of tropical cloud clusters. Mon. Wea. Rev., 121,3234-3260.

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McGaughey, G., E.J. Zipser, R.W. Spencer, and R.E. Hood, 1996. High-resolution passive microwave observations of convective systems over the tropical Pacific Ocean. /. Appl. Meteor., 35,1921-1947. Petersen, W.A., S.A. Rutledge, and R.E. Orville, 1996. Cloud-to-ground lightning observations from TOGA/COARE: Selected results and lightning location algorithms. Mon. Wea. Rev., 124, 602-620. Rasch, P.J., and J.E. Kristjansson, 1998. A comparison of the CCM3 model climate using diagnosed and predicted condensate parameterizations. /. Climate, 11,1587-1614. Rossow, W.B., and R.A. Schiffer, 1991. ISCCP cloud data products. Bull. Amer. Meteor. Soc., 72,1-20. Roux, E, and S. Ju, 1990. Single-Doppler observations of a West-African squall line on 27-28 May 1981 during COPT 81: Kinematics, thermodynamics and water budget. Mon. Wea. Rev., 118,1826-1854. Sassen, K., and G.C. Dodd, 1989. Haze particle nucleation simulations in cirrus clouds and applications for numerical and lidar studies./. Atmos. Sci., 46,3005-3014. Slingo, J.M., 1980. A cloud parametrization scheme derived from GATE data for use with a numerical model. Quart. J. R. Met. Soc., 106,747-770. Smith, R.N.B., 1990. A scheme for predicting layer clouds and their water content in a general circulation model. Quart. J. Roy. Meteor. Soc., 116,435^60. Smith, S.A., and A.D. Del Genio, 2001. A simple model of cirrus horizontal inhomogeneity and cloud fraction. Quart. J. Roy. Meteor. Soc., in press. Starr, D.O'G, and S.K. Cox, 1985. Cirrus clouds. Part II: Numerical experiments on the formation and maintenance of cirrus. /. Atmos. Sci., 42,2663-2681. Starr, D.O'C, and D.P. Wylie, 1990. The 27-28 October 1986 FIRE cirrus case study: Meteorology and clouds. Mon. Wea. Rev., 118,2259-2287. Stephens, G.L., S.-C. Tsay, P.W. Stackhouse, Jr., and P.J. Flatau, 1990. The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback. / Atmos. Sci., 47,1742-1753. Sundqvist, H., 1978. A parameterization scheme for non-convective condensation including prediction of cloud water content. Quart. J. R. Met. Soc., 104,677-690. Yao, M.-S., and A.D. Del Genio, 1999. Effects of cloud parameterization on climate changes in the GISS GCM. /. Climate, 12,761-779. Ye, B., 1999. Cumulus anvil cloud properties, large-scale conditions, and climate change. PhD dissertation. Columbia University, New York. Ye, B., A.D. Del Genio, and K.K.-W. Lo, 1998. CAPE variations in the current climate and in a climate change. /. Climate, 11,1997-2015.

16

Ice Clouds in Numerical Weather Prediction Models Progress, Problems, and Prospects

C H R I S T I A N JAKOB

The properties of cirrus, as well as the role ice clouds play in the atmosphere, have been extensively described in the previous chapters. To represent the effects of cirrus in atmospheric models, several intimately linked processes need to be described. These processes include the generation and dissipation of ice clouds as well as their interaction with the radiative fluxes throughout the atmosphere. In this chapter the cloud parameterization aspects of this problem (i.e., the treatment of the generation and dissipation of ice clouds), are discussed in the context of global numerical weather prediction (NWP) models. Aspects of the radiative transfer in ice clouds can be found in chapter 13. The main focus of the current chapter is on the cloud parameterization used in the global forecast model of the European Centre for Medium-Range Weather Forecasts (ECMWF). This parameterization will serve as an example in highlighting the progress made, the problems encountered, and the prospects for improving the representation of ice clouds in atmospheric models. The principles of representing clouds in global NWP models are identical to those in general circulation models (GCMs) used for climate research (see chapter 15). Although ice clouds are the focus of this book, a substantial part of this chapter will be concerned with the overall treatment of clouds in numerical models of the atmosphere. In fact, many models used in NWP today distinguish ice clouds from mixed-phase and water clouds only as a function of temperature. Cloud parameterizations in GCMs have evolved rapidly over the last few years. Section 16.2 is a general overview of the progress made. Section 16.3 will describe the cloud parameterization that is currently used in the ECMWF forecast model as a specific example for a state-of-the-art cloud 327

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parameterization in NWP. General aspects of the simulation of ice clouds with this model will be presented. GCM simulations of the atmosphere are very sensitive to the treatment of clouds in general (Senior and Mitchell 1993; Rasch and Kristjansson 1998) and to assumptions about cloud ice in particular (Fowler et al. 1996; Jakob and Morcrette 1995). Section 16.4 gives an example of those sensitivities and the model design problems that can arise when model sensitivities exist in combination with a lack of observations, as noted for cloud ice by Stephens et al. (1998). As an example, the fallspeed of settling ice particles in the ECMWF model is systematically modified and the model climate response to those modifications assessed. The model climate undoubtedly affects the overall forecast performance of NWP models, particularly in the medium range (5-10 days). However, there is an additional requirement for a cloud parameterization when applied in those models—namely, the ability to predict the instantaneous distribution of clouds over the globe. There are two main reasons for demanding good knowledge about clouds at any given time. First, they are a forecast product, and one can envisage the direct use of model output for their prediction. Second, a large amount of data is gathered in cloudy regions by existing and planned satellite systems. A reasonable simulation of clouds in short-range forecasts is a prerequisite for the use of this data in global data assimilation systems. These "new" tasks for a cloud parameterization lead to additional requirements for the evaluation of NWP predicted cloud fields. Section 16.5 examines the prospects of using new data sources, such as radar and lidar measurements, for that purpose.

16.1. General Parameterization Issues

Arakawa (1975) summarized the reasons for parameterizing clouds in GCMs and the state of the then-existing parameterization schemes as follows: The importance of clouds in climate modelling cannot be overemphasized. Clouds, and their associated physical processes, influence the climate in the following ways: 1. By coupling dynamical and hydrological processes in the atmosphere through the heat of condensation and evaporation and redistributions of sensible and latent heat and momentum; 2. By coupling radiative and dynamical-hydrological processes in the atmosphere through the reflection, absorption, and emission of radiation; 3. By coupling hydrological processes in the atmosphere and in the ground through precipitation; and 4. By influencing the couplings between the atmosphere and the ground through modifications of the radiation and the turbulent transfers at the surface. Although these cloud-dominated processes have long been known to be important in determining climate, clouds have been very poorly formulated in climate models.

Today, the treatment of clouds in GCMs can probably still be described as crude. Nevertheless, state-of-the-art cloud parameterizations today are considerably more advanced than those in 1975. The difficulties in parameterizing clouds

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arise partly from a lack of understanding of the processes in individual clouds, and partly from problems in describing the distribution of an ensemble of clouds in a several-hundred square-kilometer gridbox based only on knowledge about the average dynamic and thermodynamic variables. It is the purpose of this section to briefly review the conceptual changes in the approach to cloud parameterization and to highlight the most recent developments relevant to ice clouds. One of the main tasks of cloud parameterizations is the description of the radiative of effects of clouds on both the atmosphere and the Earth's surface. To achieve this, several parameters such as the areal cloud cover in a gridbox, its vertical extent, the amount and phase of condensate, and the size and shape of the cloud particles need to be described. Out of this list, cloud parameterizations classically deal with the fractional cloud cover and the amount and phase of condensate. For all other parameters, simple assumptions are made whose details depend on the complexity of the treatment of clouds in the radiation schemes used in the respective model. To describe the latent heat effects connected to clouds and precipitation, a description of the condensation and evaporation processes within clouds, as well as the formation and dissipation of precipitation, are necessary. This requires some treatment of the microphysical processes occurring in clouds and precipitation. The process of moist convection, which obviously leads to cloud formation, is treated by a separate parameterization scheme in all global atmospheric models (e.g., Arakawa and Schubert 1974; Tiedtke 1989). These parameterizations are designed to describe the influence of moist convection on the heat and moisture budget of the model's gridboxes. Although a link to clouds obviously exists, the parameterization of that link continues to be a matter of lively debate (e.g.,Tiedtke 1993; Randall 1995). Early cloud parameterizations diagnosed both fractional coverage and condensate content from the large-scale conditions, such as relative humidity (e.g., Slingo 1987). Such a treatment can only provide the interaction of clouds with radiation, and the latent heat effects need to be treated with separate, simple condensation schemes. Condensation is assumed to occur whenever the gridbox mean relative humidity exceeds 100%, and the resulting condensate is precipitated out in the same model time-step. Introducing a convective cloud type whose area coverage is diagnosed from the convective precipitation rate and whose condensate content is prescribed provides a link to the convection schemes. The complete separation of convection, cloud, and condensation schemes, apart from being counterintuitive, leads to the undesirable effect that the clouds that interact with the radiative fluxes are not related to the actual condensation/ evaporation processes predicted by the model. Ice clouds in these early schemes either did not exist at all or the phase of the condensate was prescribed as a function of temperature. The link between the hydrological and radiative aspects of clouds was first established with the introduction of a prognostic equation for cloud condensate (Sundqvist 1978), where the condensation and evaporation processes directly modify the amount of condensate that is used in describing the radiative impact of the clouds. The cloud fraction is still treated as a diagnostic quantity

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depending mainly on the relative humidity in the gridbox. Most NWP centers today are using, or are about to use, a prognostic equation for cloud condensate in their operational global forecasting systems. An alternative approach is that of Smith (1990), in which the cloud variables (both fraction and condensate amount) are diagnosed assuming some knowledge about the distribution of moisture and temperature-related variables in a grid box. In both approaches convective clouds are separate entities whose treatment is similar to that in the diagnostic schemes. In early implementations of the prognostic condensate equation, the distinction of phase is still made based on temperature. More recent applications of the schemes include a separate equation for the evolution of cloud ice (e.g., Fowler et al. 1996, Rotstayn 1997). Tiedtke (1993) proposed an approach to cloud parameterization that includes prognostic equations for both cloud fraction and cloud condensate. One of the most important differences between Tiedtke's approach and the ones described above is the manner in which individual physical processes affect the clouds. Earlier cloud parameterizations predict clouds using the current value, or the rate of change, of grid-mean variables after all physical processes (e.g., vertical motion, convection, turbulence) have adjusted those variables. In other words, the clouds are based on the net integrated result of all physical processes. In Tiedtke's "process-oriented" approach, the clouds are the direct result of the physical processes. Here, the potential of each individual process to generate or dissipate clouds is assessed, and a change of cloud fraction and amount of condensate due to that process is evaluated. Figure 16.1 shows the conceptual difference between the two approaches in a schematic way. The process-oriented approach leads to a very strong coupling of all physical processes and their effects on clouds. Of all conceptual changes made in recent years, the most important one for ice clouds is the direct link of convection to clouds, which is now used in many cloud parameterizations (e.g., Ose 1993;Tiedtke 1993; Roeckner 1995; Del Genio et al. 1996; Fowler et al. 1996). The ice cloud types affected are those generated by active deep convection, which are frequently observed in the atmosphere in the form of anvil clouds and/or cirrus debris. The basic idea behind this coupling is illustrated in figure 16.2. In simplified terms, the convective parameterization describes the circulation of mass through convective-scale updrafts, which are driven to a large extent by the latent heat release due to condensation. The condensate formed in these updrafts is transferred into the model clouds at the levels where the convective updrafts terminate. In deep convection this leads to a large source of cloud ice in the upper troposphere, which strongly affects the radiative balance. It will be shown later that this source of cloud ice can be the most important one in an atmospheric model. 16.2. The ECMWF Cloud Parameterization

In the following sections the ECMWF model is used to highlight some critical aspects of the parameterization of ice clouds in NWP models. The cloud parameterization used in this model has been developed by Tiedtke (1993), with

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Figure 16.1. Schematic of the (top) integrating and (bottom) process-oriented approaches to cloud parameterization.

further changes discussed by Jakob (1994). The scheme is based on two prognostic equations for cloud fraction, a, and cloud condensate, / (the sum of water and ice):

and

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Figure 16.2. Schematic of the link of detrainment of condensate from convective updrafts to cloud production.

where Aaj represents advection, and Sait and Dal are the source and dissipation terms for cloud fraction and condensate, respectively. Sources for cloud fraction and condensate in the scheme arise from convection, boundary layer turbulence (for stratocumulus clouds), large-scale lifting, and diabatic cooling. The dissipation terms are determined by evaporation processes due to subsiding motions, including both large-scale and cumulus-induced subsidence, diabatic heating, turbulent erosion processes at both cloud top and cloud sides, and precipitation processes (condensate only). Through the direct link of clouds to all physical processes, the scheme falls into the class of the process-oriented schemes as

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described in the previous section. The distinction between the different phases of condensate is made solely as a function of temperature. Pure ice clouds exist for temperatures lower than -23°C, mixed-phase clouds occur between -23°C and 0°C, and pure water clouds are formed at temperatures above 0°C. The definition of an ice cloud in the ECMWF model would therefore be a cloud that exists at a temperature colder than -23 °C, quite different from the definition of cirrus used elsewhere in this book. Figure 16.3 shows the zonal mean ice water path (IWP) for June/July/August (JJA) 1987 and December/January/February (DJF) 1987-88 produced by the ECMWF model. The model has in each case been integrated for a 4-month period, beginning 1 month before the averaging period, with a horizontal resolution of T63 (= 250km), 31 model levels in the vertical, and time-varying seasurface temperatures (SST). For JJA, the geographical distribution of IWP exhibits two maxima, which are located in the Intertropical Convergence Zone (ITCZ) and at mid-latitudes of the Southern (winter) Hemisphere. The largest values of IWP in the model occur over the tropical oceans, reaching values >100g/m2. The values in the winter hemisphere reach 100 g/m2, whereas the summer hemisphere values are only half as large. In DJF, the mid-latitude maximum shifts to the Northern Hemisphere, although the values remain lower

Figure 16.3. Zonal mean distribution of ice water path produced by 4-months integrations of the ECMWF model at T63L31 resolution. The results shown are averages over the last 3 months of the integrations.

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than those in the Southern Hemiphere in JJA. The tropical IWP is lower than in JJA and the maximum is shifted south, consistent with the southward movement of the ITCZ. One of the biggest problems in global modeling is that there is little data to judge the quality of the simulation of IWP shown in figure 16.3, as highlighted by Stephens et al. (1998). Lin and Rossow (1996) have derived the only estimates of IWP on a global scale to date. They found values of 80-120 g/m2 for the winter mid-latitudes, 50-100 g/m2 for the tropics, and 50-100 g/m2 for the summer mid-latitudes. The model simulation appears to be in good agreement with those values; however, it should be assessed with great caution. First, agreement in zonal mean averages of a vertically integrated quantity might not be indicative of a good simulation of cloud ice, and second, the error margins are large in both model and observations. To assess which physical processes contribute to the cloud ice distributions shown above, zonal mean distributions of different source and sink terms for cloud ice (T < -23°C) have been calculated (fig. 16.4). The results shown represent vertical integrals for all layers with T < -23°C averaged over a model integration for July 1998. There are two sources of cloud ice: the detrainment from convection and the condensation processes due to large-scale motion and radiative cooling. The largest sources for cloud ice occur in the tropics. The dominant source is convection, which accounts for 90% of the total cloud ice production. The subtropics, particularly in the winter hemisphere, are regions of minimum ice production. At mid-latitudes two different pictures emerge. In the Northern Hemisphere (summer) southward of 80°N, convection still dominates ice generation. This is most likely due to the fact that in summer considerable amounts of ice are generated by convective events over the land areas. Also, due to the activity of the summer monsoons, the subtropical minimum is much less visible in this hemisphere. In the Southern Hemisphere (winter), the ice generation is dominated by nonconvective condensation processes mostly linked to ascending motion in model-resolved baroclinic systems. The two sinks of cloud ice are evaporation processes, due to large-scale or cumulus-induced subsidence and radiative heating, and the conversion to precipitation. The dominant sink term in all regions is clearly the conversion of cloud ice to precipitation. The apparent residual between sources in sinks is due to ice settling out of the bottom of the integration domain, which comprises only levels with temperatures lower than -23°C (pure ice clouds). Note that in figure 16.3, typical IWPs are an order of magnitude smaller than their sources and sinks. Hence, the IWP is not necessarily indicative of the strength of the hydrological cycle of the model. 16.3. Sensitivity to Ice Fallspeed

Atmospheric models are very sensitive to the treatment of cloud ice (e.g., Gregory and Morris, 1996). As an example, the sensitivity of the ECMWF model climate to assumptions about value of the terminal velocity of ice particles will be investigated. First, a brief overview over the fallout parameterization and its numerical implementation is given.

Figure 16.4. Zonal mean distribution of sources and sinks of cloud ice in the ECMWF model. The results represent an average for July 1998 taken from a T63L31 simulation of the month. Included are sources due to detrainment from convection (Detr.) and nonconvective condensation processes (Cond.) and sinks due to evaporation (Evap) and precipitation (CVSN).

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16.3.1. Ice Fallout Formulation and Its Numerical Treatment As in many GCMs, the fallspeed of cloud ice is parameterized in the ECMWF model as a function of ice content using the functional form

where a and b are constants, p is the air density, and / the specific ice content in units of kilograms per kilogram. The derived fallspeed is then used to calculate the tendency of cloud ice due to settling (sett) for a given model layer as the flux divergence of the ice flux as

Note that the positive sign of the right-hand-side of equation 4 occurs because vt is defined positive downward. A careful look at the physical meaning of equations 3 and 4 in an atmospheric model having a horizontal resolution of up to several hundred kilometers reveals several problems. First, the use of a single fallspeed implies that all ice particles in the gridbox are falling at that speed. This is an oversimplification because, in reality, a spectrum of ice particle sizes and terminal velocities exist. Second, there are numerical treatment considerations. Typical fallspeeds given by equation 3 reach values between 0.5 and Im/s, and in GCMs, model time-steps can be 30min to 1 h with vertical resolutions in the upper troposphere of 500m to 1 km. With a fallspeed of, say, Im/s, ice particles will settle through more than one model level in one model time step. Hence, the numerical treatment of equation 4 is far from trivial. Consequences of the first problem are highlighted by the following example. If a constant fallspeed, v, = v(0, is assumed, equation 4 reduces to a onedimensional advection equation. It can be shown for this equation that an explicit upstream numerical treatment,

yields an exact solution if viQAt = Az. In the case of two model layers with cloud ice contents of /£_! = /0 and l'k = Vk_2 = 0, the solution of equation 5 under the additional assumption that vi0At = Az yields for layers k and k - 1 is /£f = 0 and Ik* - k- Thus, the whole ice content is moved down one model layer. Although numerically exact, this solution reveals the simplicity of the physical assumption made because in reality an ice cloud does not move as a "block" because of the variety of fall velocities present. In the second problem, the long time steps encountered in GCM simulations prevent an explicit numerical treatment of equation 4 because the solution for v,-oAf » Az becomes numerically unstable. One possibility of achieving numerical stability is to solve equation 4 analytically, as proposed in Rotstayn (1997). Tiedtke (1993) has shown that if equation 2 can be rearranged in the form

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yielding the solution

It is evident that in case of equation 4 such a rearrangement is possible, whereby C = v/o/Jt-i/Az and D = v,0/Az. Using the same assumptions as above, solutions for the ice contents in layer k - 1 and k are /£f = 0.37/0 and /fAf ~ 0.63/0. This solution, although numerically inaccurate, leads to a physically more appealing result. Cloud that was initially confined to layer k -1 has spread downward without being completely removed from layer A;. This is entirely an artifact of the numerical treatment and should hence be treated with great care when interpreting model output. 16.3.2. Sensitivity to the Value of Terminal Velocity of Ice The operational ECMWF global model uses a formulation of ice settling following equation 4 with a numerical treatment as in equation 7. The fallspeed in that version is a function of the ice content as in equation 3. The constants are chosen as a = 3.29 and b = 0.16, following Heymsfield and Donner (1990). The integration of the model with that version is referred to as the control simulation. Six more model integrations were carried out, each using a fixed value of fallspeed of 0.1, 0.3, 0.5,1,1.5, and 2m/s, respectively. Figure 16.5 shows the 3-month average (JJA) of the global means of IWP, integral radiative flux divergence (= top of the atmosphere minus surface net radiative flux), and precipitation as a function of ice fallspeed. The horizontal lines represent the results of the control experiment. It is evident that with the reduction of fall speed, the IWP averaged over the globe increases from values around 40g/m2 for the largest assumed fall speed (2m/s) to 140 g/m2 for the smallest (0.1 m/s).This leads to a reduction of the global mean integral radiative flux divergence from 110W/m2 to 90W/m2 This decrease is achieved mainly through a decrease in outgoing long-wave radiation (OLR).The integral flux divergence of the solar component and the net surface long-wave radiation change only by small amounts (not shown). The reduction in the radiative cooling has an immediate effect on the atmosphere's response through latent heat release, which becomes obvious in figure 16.5c.The global mean precipitation is reduced from 3.25 mm/day to 2.7 mm/day. The main reduction is in convective precipitation, pointing to a much lower level of convective activity when using small ice fallspeeds. The geographical distribution of the changes outlined is shown in figure 16.6 for the most extreme case of fallspeed, v, = 0.1 m/s. The figure shows the change in IWP, OLR, and convective precipitation with respect to the control simulation. The largest changes occur in the tropics. This is not surprising because the tropics have been identified as the region of maximum ice production (see fig. 16.4) in the model. It is, however, noteworthy that the regions of maximum change in OLR do not coincide with the region of minimum OLR in the ITCZ (not shown) but occur downwind to both sides of the minimum value. This is most

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Figure 16.5. Three-months averages (JJA87) of the global means of (a) ice water/liquid water path, (b) integral radiative flux divergence, and (c) precipitation in aT63L31 version of the ECMWF model as a function of the assumed fallspeed for ice. Control model results are shown as horizontal lines. Precipitation is shown as total precipitation (TP) and is split into convective (CP) and large-scale (LSP) precipitation.

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Figure 16.5. (continued)

likely due to an increase of the residence time of cloud ice in the atmosphere caused by the decrease in the fallspeed of the ice. Hence, the advection process is now able to transport ice farther away from its source before it falls out. It has been shown that through the modification of assumed fallspeed of ice particles, the climate of the ECMWF model, particularly in the tropics, can be changed dramatically. It is obvious from the slope of the curves in figure 16.5a-c that the control model results are situated in a sensitive part of the parameter space, although not the most sensitive one. Hence, small changes to the fallspeed parameterization will substantially modify the model climate. Unfortunately, the accuracy of the available global observations is not sufficient to draw firm conclusions about the correct value of IWP in the sensitivity experiments. In the next section, recently available observations of ice cloud parameters, such as cloud fraction and ice content, are used to evaluate model performance. 16.4. New Data Sources for the Evaluation of Ice Cloud Parameterizations

The high sensitivity of atmospheric models to the treatment of ice clouds calls for a thorough model evaluation. Unfortunately, as mentioned before, few observations for such an evaluation exist. This is particularly true for global data sets on the long time-scales necessary to evaluate climate model predictions of ice clouds. Because NWP models have the advantage of predicting individual cloud

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Figure 16.6. June/July/August 1987 differences between the experiment assuming v, = 0.1 m/s and the control simulation for ice water path (g/m2; top), outgoing long-wave radiation (W/m2; middle), and convective precipitation (mm/day bottom).

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events, it is possible to evaluate these "cloud forecasts" directly, using data that are available only for a limited time or at few locations. The approach is to perform short-range forecasts with the NWP model and then to compare the results to instantaneous measurements of cloud parameters, such as cloud fraction (Mace et al. 1998a; Miller et al. 1999). Two examples, using a space-borne lidar system and a ground-based radar, are used to highlight this method. In September 1994 the LITE (McCormick et al. 1993; Winker et al. 1996) lidar system was installed on the space shuttle Discovery. Miller et al. (1999) derived cross-sections of the vertical distribution of cloud fraction from the LITE data and compared them to those predicted by the ECMWF model in the 24- to 30-h forecast range (fig. 16.7). This particular orbit includes a slice through the western Pacific warm pool, and it is therefore possible to evaluate model clouds that are most likely produced by the convection detrainment mechanism described earlier. It is evident that the model is able to simulate the deep,

Figure 16.7. Comparison of the vertical distribution of cloud fraction from LITE orbit 124 as predicted by the ECMWF model (top) with that derived from LITE (Miller et al. 1999) (bottom).

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anvil-like cloud structures between 0° N and 20° N. This comparison, together with the work of Mace et al. (1998a), is one of the first to evaluate the details of the vertical structure of model-generated cloud fields. Although important, the correct simulation of cloud fraction is a necessary but not a sufficient condition for capturing the main hydrological and radiative effects of modeled clouds. The amount of condensate present in the cloud must also be correctly simulated. In the context of the Atmospheric Radiation Measurement program (ARM; Stokes and Schwartz, 1994), millimeter-wave cloud radars (MMCR; Moran et al. 1998) have been installed at ARM's Southern Great Plains (SGP), Tropical Western Pacific, and North Slope of Alaska sites. Mace et al. (1998a) have used data from the radar at the SGP site to evaluate the ability of the ECMWF model to predict the vertical distribution of hydrometeors. They concluded that the model exhibits sufficient skill to allow more detailed investigations. Mace et al. (1998b) derived ice contents for isolated cirrus clouds from combined radar reflectivity and infrared interferometer data. Figure 16.8 shows a first evaluation of the ECMWF model's ability to simulate the ice content in those clouds. The figure shows the frequency distribution of ice content for clouds at temperatures lower than 219 K and higher than 227 K (note that all clouds in this study need to be colder than 250 K to be ice clouds) derived from observations and two versions of the ECMWF model. The chosen boundary tempera-

Figure 16.8. Frequency distributions of cloud ice in isolated cirrus (see Mace et al. 1998b for definition) over the ARM SGP site for two different temperature ranges. Shown are values derived from a combination of radar reflectivity and infrared interferometer data and from two versions of the ECMWF model.

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tures represent the 33% and 67% percentiles of the observed cloud distribution with respect to temperature. The observations were gathered between November 1996 and December 1997. The model data represent the periods November 1996-October 1997 and January-July 1998. Although the time periods over which the comparison is made are not identical, enough cases are used in all samples to allow at least a qualitative comparison. A marked difference in the shape of the observed distributions exists for the two temperature regimes. At low temperatures the distribution is fairly narrow and exhibits a large peak at low ice contents. Although similar in shape, the distribution at high temperatures is much broader, and the peak at low ice contents is less pronounced. Large ice contents are encountered more frequently at high temperatures. The model captures this difference in the distributions to a fair degree. However, both model versions severely overestimate the frequency of very low ice contents and underestimate the number of events with intermediate values. Despite these problems, the 1998 version of the model, which incorporates a change to the numerical treatment of falling cloud ice, constitutes an improvement over the 1997 version. Although only qualitative in nature, this comparison is a major step forward in model evaluation. For the first time, a long time series of point observations of cloud ice exist, and they can be compared to model results at least in a statistical way. The model-to-data comparisons presented above are far from comprehensive. They should only be considered as examples of the possible ways to evaluate short-range model cloud forecasts using the remotely sensed data. This approach will gain importance with the use of data provided by anticipated space-borne radar systems within the next 5-10 years. 16.6. Summary

Despite the considerable progress made in the last few years, the parameterization of clouds in general, and that of ice clouds in particular, remains one of the biggest challenges in global modeling. The large sensitivity that modeled atmospheres show to parameterization assumptions and the general lack of data necessary to evaluate the model simulations creates a serious problem for the modeling community. The use of new data acquired by both space-borne and ground-based active remote sensing instruments for the evaluation of ice cloud simulations in atmospheric models shows the optimistic prospects for eliminating some of the remaining uncertainties. It was the purpose of this chapter to outline these three aspects for global NWP models using the ECMWF model as an example. In the future, NWP will continue to play an important role in the quest to improve cloud simulations in global models. References

Arakawa, A., 1975. Modelling clouds and cloud processes for use in climate models. Global Atmospheric Research Program Publication Series, no. 16; The Physical Basis of Climate and Climate Modeling. 183-197.

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Arakawa, A., and W.H. Schubert, 1974. The interactions of a cumulus cloud ensemble with the large-scale environment. Part I. J. Atmos. Sci., 31, 674-701. Del Genio, A.D., M.-S. Yao, W. Kovari, and K.K.-W. Lo, 1996. A prognostic cloud water parameterization for global climate models. J. dim., 9,270-304. Fowler, L.D., D.A. Randall, and S.A. Rutledge, 1996. Liquid and ice cloud microphysics in the CSU general circulation model. Part I: Model description and simulated microphysical processes. /. dim., 9,489-529. Gregory, D., and D. Morris, 1996. The sensitivity of climate simulations to the specification of mixed phase clouds, dim. Dyn., 12, 641-651. Heymsfield, A.J., and L.J. Donner, 1990. A scheme for parameterizing ice-cloud water content in general circulation models. /. Atmos. Sci., 47,1865-1877. Jakob, G, 1994. The impact of the new cloud scheme on ECMWF's integrated forecasting system. In ECMWF Workshop on Modeling, Validation and Assimilation of Clouds, Oct. 31-Nov. 4, 1994. European Centre for Medium-Range Weather Forecasts, Reading, UK, pp. 277-294. Jakob, G, and J.-J. Morcrette, 1995. Sensitivity of the ECMWF model to the treatment of the ice phase. In Cloud Microphysics Parametrizations in Global Atmospheric Circulation Models, WMO/TD-no. 713. World Meteorological Organization, Geneva, pp. 37-46. Lin, B., and W.B. Rossow, 1996. Seasonal variation of liquid and ice water path in nonprecipitating clouds over oceans. /. dim., 9,2890-2902. Mace, G.G., C. Jakob, and K.P. Moran, 1998a. Validation of hydrometeor occurrence predicted by the ECMWF model using millimeter wave radar data. Geophys. Res. Lett., 25,1645-1648. Mace G.G., T.P. Ackerman, P. Minnis, and D.F. Young, 1998b. Cirrus layer microphysicsl properties derived from surface-based millimeter radar and infrared interferometer data./. Geophys. Res., 103, 23207-23216. McCormick, M.P., D.M. Winker, E.V. Browell, J.A. Coakley, C.S. Gardner, R.M. Hoff, G.S. Kent, S.H. Melfi, R.T. Menzies, C.M.R. Platt, D.A. Randall, and J.A. Reagan, 1993. Scientific investigations planned for the Lidar In-space Technology Experiment (LITE). Bull. Amer. Meteor. Soc., 74, 205-214. Miller, S.D., G.L. Stephens, and A.C.M. Beljaars, 1999. A validation survey of the ECMWF prognostic cloud scheme using LITE. Geophys. Res. Lett., 26,1417-1420. Moran, K.P., B.E. Mariner, M.J. Post, R.A. Kropfli, D.C. Welsh, and K.B. Widener, 1998. An unattended cloud profiling radar for use in climate research. Bull. Amer. Meteor. Soc. 79,443^55. Ose, T, 1993. An examination of the effects of explicit cloud water in the UCLA GCM. J. Meteor. Soc. Japan, 71, 93-109. Randall, D.A., 1995. Parameterizing fractional cloudiness produced by cumulus detrainment. In Cloud Microphysics Parameterizations in Global Atmospheric Circulation Models, WMO/TD-No. 713, World Meteorological Organization, Geneva pp. 1-16. Rasch, P.J., and J.E. Kristjansson, 1998. A comparison of the CCM3 model climate using diagnosed and predicted condensate parameterizations. /. dim., 11,1587-1614. Roeckner, E., 1995. Parameterization of cloud radiative properties in the ECHAM4 model. In Workshop on Cloud Microphysics Parameterizations in Global Atmospheric Circulation Models, WMO/TD-No. 713, World Meteorological Organization, Geneva pp. 105-116. Rotstayn, L.D., 1997. A physically based scheme for the treatment of stratiform clouds and precipitation in large-scale models. I: Description and evaluation of the microphysical processes. Quart. J. Roy. Meteor. Soc., 123,1227-1282.

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Senior, C.A., and J.F.B. Mitchell, 1993. Carbon dioxide and climate: The impact of cloud parameterization. /. dim., 6, 393^-18. Slingo, J.M., 1987. The development and verification of a cloud prediction scheme for the ECMWF model. Quart. J. Roy. Meteor. Soc., 113, 899-927. Smith, R.N.B., 1990. A scheme for predicting layer clouds and their water content in a general circulation model. Quart. J. Roy. Meteor. Soc., 116,435-460. Stephens, G.L., C. Jakob, and M. Miller, 1998. Atmospheric ice —a major gap in understanding the effects of clouds on climate. Global Energy and Water Cycle Experiment Newsletter, 8, no. 1. Stokes, G.M., and S.E. Schwartz, 1994. The Atmospheric Radiation Measurement (ARM) Program: Programmatic background and design of the Cloud and Radiation Test Bed. Bull. Amer. Meteor. Soc., 75,1201-1221. Sundqvist, H., 1978. A parameterization scheme for non-convective condensation including prediction of cloud water content. Quart. J. Roy. Meteor. Soc., 104, 677-690. Tiedtke, M., 1989. A comprehensive mass flux scheme for cumulus parameterization in large-scale models. Man. Wea. Rev., 117,1779-1800. Tiedtke, M., 1993. Representation of clouds in large-scale models. Mon. Wea. Rev., 121, 3040-3061. Winker, D.M., R.H. Couch, and M.P. Cormick, 1996. An overview of LITE: NASA's Lidar In-space Technology Experiment. Proc. IEEE, 84,164-180.

17

Dynamical Processes in Cirrus Clouds A Review of Observational Results

MARKUS QUANTE DAVID O'C. STARR

17.1. The Role of Dynamics and Related Experimental Studies

Local dynamical processes are a key factor determining the microphysical characteristics and typically heterogeneous macroscopic structure of cirrus cloud fields. The internal and background flow fields are correspondingly heterogeneous, albeit only weakly turbulent in most instances, as is discussed here. Nucleation processes and ice crystal growth and habit are intrinsically governed by the local temperature and humidity (saturation ratio) conditions that, in turn, are strongly regulated by the intensity and duration of local updrafts and downdrafts. The microphysical result of equivalent lift by a 50cm/s updraft over a cell width of 200m is quite different from that by a 0.5 cm/s updraft over a 2-km width, even though the overall mass fluxes are equivalent. The great degree of horizontal structure seen in fallstreaks emanating from cirrus likely reflects corresponding variability in microphysical properties, primarily ice crystal size, resulting from variability in the dynamical conditions in the ice-crystal-generating layer. The ice fallout process is a first-order effect in determining overall cloud ice water path. Entrainment of noncloudy environmental air and internal mixing processes are other dynamical aspects that likely play a significant role in cloud life cycle. Dynamical processes provide an important coupling between cirrus cloud microphysical and radiative processes, as described in chapter 18 and illustrated in figure 17.1. Cirrus cloud microphysical properties and macroscopic structure strongly affect the overall radiative properties of a cirrus cloud field and thus the important radiative effect of cirrus in the climate system. Knowledge of the dynamical 346

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Figure 17.1. Schematic illustrating the complex interactions within cirrus clouds among turbulence and other dynamical processes and microphysical and radiative processes.

processes influencing cloud macrophysical properties and microphysical structure is important to understanding the origin of these characteristics. Moreover, cloud-resolving models of cirrus cloud systems must be evaluated in these respects due to the importance of cloud dynamical processes in determining overall cloud properties. Dynamical processes in cirrus are linked to the state of the background flow field that, in general, is characterized by significant wind shear and a stable thermal stratification. Gravity waves are ubiquitous and occur over a range of scales. Upper tropospheric turbulence tends to occur intermittently in patches, likely a result of sporadic shear generation (Kelvin-Helmholtz instabilities) or breaking gravity waves. Turbulent mixing in stratified shear flows is a notoriously difficult subject, and advances in its description have been obtained only recently (e.g., Fernando 1991; Schumann and Gerz 1995; Vanneste and Haynes 2000). Additionally, cloud-scale turbulence in cirrus may be generated by heating and cooling effects associated with phase changes of water and radiative processes leading locally to convection. Only a limited set of detailed dynamical measurements in cirrus is available. The data were chiefly obtained during the FIRE (Starr 1987) and ICE/EUCREX (Raschke 1988; Raschke et al. 1998) field campaigns. Extended measurements of turbulence in cirrus were first reported by groups from the former USSR (Pinus and Litvinova 1980; Dmitriev et al. 1984,1986; Ermakov et al. 1984). Most of the data have been obtained at mid-latitudes in the Northern Hemisphere. Here we discuss results from analysis of the available in situ data. Results from studies using high-resolution Doppler radars (e.g., Auria and Campistron 1987; Palmer and Martner 1995; Fujiyoshi et al. 1999) are not considered here, but will likely become increasingly important.

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Concepts for analyzing and interpreting turbulence data are presented in section 17.2, and gravity waves are also discussed. Existing measurements are briefly reviewed in section 17.3. Results of published studies are surveyed and discussed in section 17.4, including mean flow characteristics, turbulent statistics and fluxes, and results from spectral and wavelet-transform analyses. Conclusions and recommendations are offered in section 17.5. 17.2. General Concepts

Turbulence in cirrus clouds is linked to the dynamical state of the ambient flow field in which the clouds are embedded. To distinguish cloud dynamical processes, it is important to properly account for the background flow, its variability, and associated processes when interpreting high-frequency turbulence measurements. Intermittent turbulence may occur in the absence of cloud or in association with, but quasi-independent of, cloud processes. Some ambiguity is often present. Here we provide a brief theoretical background on turbulence quantities and their importance. More elaborate discussions of atmospheric turbulence may be found in reviews by Panofsky and Dutton (1984) and Wyngaard (1992). Houze (1993) discusses turbulence and instabilities in his book on cloud dynamics. In general, it is important to distinguish between developed turbulence and waves and other coherent structures because of differences in their transport characteristics and resultant differences in the interactions with cloud processes. In a vertically sheared, stably stratified flow, typical of upper tropospheric conditions, several questions are of fundamental importance, including the effects of buoyancy on different scales of turbulence and on mixing in the turbulence regime and the production of turbulence by shear-turbulence interactions. In general, it is suggested that mixing in a sheared, stratified turbulent flow consists of a small number of powerful stirring events (e.g., Piccirillo and Van Atta 1997) confined to thin layers, total mixing across larger distances can be regarded as a discontinuous process in time occurring in a stepwise manner involving several turbulence events (Dewan 1981; Vanneste and Haynes 2000). If the sources of turbulence vanish, the turbulence decays rapidly or may even collapse under the influence of strong stratification (e.g., Etling 1993). If gravity (buoyancy) waves are present in the flow, wave-turbulence interactions are possible. Reviews of turbulence in stably stratified flows and related transitional phenomena are provided by Hopfinger (1987) and Thorpe (1987). 17.2.1. Turbulent Kinetic Energy In the simplified case of homogeneous turbulence where the effects of vertical shear and stratification dominate, the turbulent kinetic energy, .Ekin, evolves according to

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with Ekin = 1/2 (u'2 + v'2 + w'2} ; u', v', w', and 0' denote the fluctuating parts of the velocity components and potential temperature, respectively (prime indicates the deviation from an appropriate average; e.g., horizontal); U and V are the mean horizontal wind components, 90 is the mean potential temperature, and g is the acceleration due to gravity. Terms contributing to shear (mechanical) production of Ekin are denoted P, while B indicates the buoyancy consumption/production term, and e represents viscous dissipation. Although homogeneous turbulence is unlikely to occur over extended areas, the above relationship is useful to illustrate the interplay of shear production and buoyancy effects, which are believed to be the predominant factors in upper tropospheric turbulence associated with cirrus cloud systems. Turbulent kinetic energy (TKE) may be mechanically produced by extraction of kinetic energy from the mean flow in the presence of wind shear (i.e., Kelvin-Helmholtz instability) or by gravity wave-breaking. Buoyancy production of TKE occurs through radiative heating and latent heat release (phase changes of water) that influence the heat flux, w'Q'. For example, cloud-top radiative cooling can lead to sinking air motion (TKE production) and associated eddy generation, as seen in marine stratocumulus cloud layers. Conversely, enhanced infrared radiative cooling can occur in association with enhanced ice water content in a rising air parcel, leading to a negative eddy heat flux (TKE consumption). The rates of radiative and latent heating are generally of comparable magnitude in cirrus clouds, although the spatial patterns can be quite different given the history and far-field (nonlocal) factors that determine local radiative heating. In terms of local TKE production in a cirrus cloud, the radiative and latent heating fields may act in opposition or in concert depending on the local circumstances. In a statically stable environment, TKE is mainly consumed by work against the thermal stratification and by viscous dissipation. Because the buoyancy term acts only on the vertical velocity component of TKE, the flow tends to be anisotropic on scales where this term dominates. In general, the distribution of cloud-related sources and sporadic wave-breaking events leads to an overall intermittent distribution of TKE. Hence, horizontal wind shear and advection of TKE can also be significant factors. Thus, because of the intermittence of the generation mechanisms and subsequent decay, turbulence in the stably stratified cloudy atmosphere appears intrinsically heterogeneous especially in the vertical. It occurs in thin pancake-like patches, each following a more or less independent life-cycle. Flow parameters commonly used to assess the existence of atmospheric turbulence are the Brunt-Vaisala frequency, N, and the Richardson number, Ri, which are defined by the vertical gradient of potential temperature and the vertical shear of horizontal wind velocity as: and

350

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It is generally accepted that for Ri smaller than a critical value (Ricrn = 0.25), initial perturbations or disturbances will grow exponentially. However, this is a local criterion. Ri, as defined above, is often evaluated over extended vertical layers using, for example, standard radiosonde data. In this case, a value of bulk Ri greater than 0.25 does not ensure that Ri less than 0.25 does not exist somewhere in a sublayer within the extended layer. Thus, turbulence generation can occur in flows with bulk Ri larger than RiCTn, although it tends to decay with time because subsequent mixing will destroy the original discontinuity. Considerable turbulence exists if the Ozmidov scale, L0 = (e/7V3)1/2, which corresponds to a balance between inertial and buoyancy effects, is significantly larger than the Kolmogorov microscale, LK = (v3/e)1/4, which corresponds to the smallest scale in a flow at which dissipation takes place, and where v is the kinematic viscosity. In other words, there is room for the development of an extended inertial subrange. The Ozmidov scale is related to the buoyancy length scale, LB = oJN, by a factor of about 10-30 (LB = 10-30 L0; e.g., Bacmeister et al. 1996). Here, GW denotes the standard deviation of the vertical air velocity. Buoyancy prevents larger amplitude vertical motions from developing at vertical scales larger than LB (Lesieur 1990). Thus, in an environment generally characterized by Ri much greater than 0.25, except possibly within shallow, embedded subregions, sources of turbulence will occur only for limited times and in limited spatial areas, and the turbulence generated will tend to decay, especially in the vertical dimension. Thus, intermittent turbulence is expected in the upper troposphere and will predominately consist of quasi-two-dimensional motions, especially at larger (meso) scales. The signatures of an originally well-mixed or distorted field of passive tracers, such as cloud particles, may be left behind in a highly structured appearance. In oceanographic flows, this phenomenon is sometimes called "fossil" turbulence (Gibson 1987). Thus, highly structured cloud features, as might be revealed by lidar or millimeter-radar observations, do not necessarily indicate the structure and intensity of the corresponding flow field at that time. 17.2.2. Energy Spectra and Cascade Cirrus clouds range in horizontal scale from hundreds of meters to hundreds of kilometers. Turbulent flows may contain motions at all scales up to tens of kilometers, and coherent dynamical phenomena, such as gravity waves, also occur within this range. Turbulent energy that is inserted into an environment at a specific scale or over a limited subrange of scales can potentially cascade to smaller (downscale) and/or larger (upscale) scales. Upscale energy transport might originate from initially three-dimensional, smaller-scale turbulence, which, after its decay or collapse, builds up a quasi-two-dimensional mesoscale-turbulence regime (Gage 1979; Lilly 1983). Mixing processes are generally associated with a downscale cascade. Analysis of the spectral (scale) distribution of TKE can be very useful in characterizing and understanding the processes at work in the upper troposphere and in cirrus cloud systems. For example, fundamental cloud processes, such as ice crystal nucleation, may be dominated by effects of a

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specific subrange of the overall flow field given the inherent time constants associated with those processes. Observations of the mesoscale flow field in the upper troposphere have revealed a typical spectral slope of -5/3 for wavenumber energy spectra, E(k), of the horizontal wind components (e.g., Gage 1979; Nastrom and Gage 1985). Lilly's stratified turbulence theory leads to the following spectral relation for the mesoscale:

where ku is the largest wave number in the constant slope range of stratified turbulence and aL is Lilly's universal constant. Only a small percentage of the turbulent energy injected at a scale of the order of the buoyancy length scale, LB, is needed for the development of the stratified turbulence spectrum. A competing explanation of the observed spectra in the mesoscale region that also leads to a theoretical slope of -5/3, considers a saturated gravity-wave spectrum (van Zandt 1982; Sidi et al. 1988). There is no final agreement on the more appropriate interpretation of the available data. Both wave and turbulence processes seem to contribute to the observed mesoscale spectra. At intermediate scales, spectral slopes between -3 and -5/3 can be expected in a stably stratified flow. At the smallest scales, a -5/3 slope and a quasi-isotropic flow often mark the classical inertial subrange of Kolmogorov's turbulence theory, which provides the following relation:

where kB is the buoyancy wavenumber and a*: denotes Kolmogorov's universal constant. The intermediate scales are increasingly influenced by stratification, where turbulent energy is lost significantly as eddies work against buoyancy forces. In an extension of earlier work by Bolgiano (1962), Shur (1962), and Lumley (1964) that predicted fixed spectral slopes for the vertical air velocity spectra of either -11/5 or -3, Weinstock (1978) showed that no universal spectral slope exists for this buoyancy subrange. He derived a complex spectral relation that depends on the flux Richardson number and the local TKE. In a later study, Weinstock (1980) found a tendency for energy cascade processes to generate a spectral hump (peak) at length scales smaller than the "effective" source scale at which a gap (dip) would form. Here, the effective source scale is a length scale characterized by enhanced energy cascading to other scales. Thus, the occurrence of a peak in the energy distribution does not necessarily indicate that this is the predominant scale of the energy source, as the occurrence of significant spectral energy at a particular scale may only reflect the cascade of energy from other scales. Furthermore, a -5/3 slope for energy spectra of horizontal wind components in stably stratified flows does not always indicate inertial subrange turbulence. The spectral regimes mentioned above are illustrated in a schematic shown in figure 17.2. The transition from smaller-scale, three-dimensional turbulence to quasi-two-dimensional (mesoscale) turbulence typically occurs over scale lengths of the order of 2-10 km.

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Figure 17.2. Illustrative representation of power spectral density, S, as a function of the horizontal wave number, k, for the quasi-two-dimensional and the smaller scale threedimensional flow regimes. BSR indicates the buoyancy subrange, and ISR denotes the inertial subrange.

Thus, the interpretation of velocity spectra is not straightforward and many factors need to be considered. Some ambiguity is often present. 17.2.3. Gravity Waves Gravity waves are ubiquitous in the atmosphere (Stewart 1969) and may coexist and interact with turbulence or convective circulations. Gravity waves in the upper troposphere have been reported with wavelengths of a few kilometers up to several tens of kilometers. These scales are comparable to scales observed in cirrus cloud systems (Sassen et al. 1989). Thus, gravity-wave phenomena are often present within cirrus cloud systems and may potentially influence, or be influenced by, cirrus cloud processes. It is important to distinguish gravity waves and turbulence because of their different transport characteristics. The nature of gravity waves and their relation to turbulence is discussed by Dewan (1985), Weinstock (1987), Finnigan (1988), and Fritts and Werne (2000). Convective and dynamical instabilities associated with atmospheric waves are extensively reviewed by Fritts and Rastogi (1985). Gravity waves can arise from synoptic scale phenomena in the upper troposphere (e.g., Uccellini and Koch 1987; Starr et al. 1992), such as geostrophic adjustment processes, as well as from mesoscale processes such as the intrusion of deep convection. Lower tropospheric processes associated with frontal zones or even boundary layer convection can stimulate gravity waves that may propagate into the upper troposphere. The structure of cirrus is also influenced by orography and associated wave-generating processes. Cirrus are more frequent over mountainous regions (Wylie and Menzel 1994; Randall et al. 1996) and transverse (standing) wave patterns and longitudinal structures (streamers) are often observed for hundreds of kilometers downwind of mountain barriers.

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In measurements, it is often difficult to distinguish the signal due to gravity waves from that due to turbulence, convection, or other processes, especially for in situ observations as from aircraft. Linear gravity waves may be identified in time series data by a nearly 90° phase shift between vertical velocity and temperature which is assessable by cross-spectral analysis. However, the observed signal may be quite complex due to the superposition of various intermittent processes. Separation of the component signals is not straightforward. Moreover, the sample is often statistically inadequate, especially for the longer wavelength waves. The difficulty is further compounded by the tendency for gravity waves to occur intermittently in small groups of variable frequency whose alignment with the aircraft flight track is uncertain. Remote sensing observations are only now beginning to be explored for detection and quantification of wave signals in cirrus cloud systems. The possible contribution of gravity waves to mesoscale energy spectra and velocity variances of horizontal wind components has already been discussed and is believed to be significant in many cirrus cloud data sets. 17.3. Measurements and Studies

Observations of turbulence in cirrus have been made by specially instrumented aircraft using either five-hole pressure probes or wind vanes mounted on nose booms or radomes in combination with data from an inertial navigation system to derive the three velocity components. Fast-response temperature measurements have been obtained from Rosemount temperature sensors, and fastresponse humidity measurements have occasionally been made using Lyman-oc hygrometers. The basic principles of airborne turbulence measurements are outlined by Lenschow (1986). The uncertainties of in situ observations, especially in weak turbulence as often expected at cirrus level, are discussed by Quante et al. (1996) and Chan et al. (1998). Weak turbulence is especially challenging due to instrumental limitations. The difficulties in adequately determining the mean mesoscale vertical motion in cirrus from airborne measurements, which is typically a few centimeters per second, are described by Gultepe et al. (1990). Data sampling rates used during reported airborne measurements range between 1 Hz and 100 Hz. In most cases, a sampling rate of 1 Hz is not adequate to resolve inertial subrange turbulence. This affects the related estimation of dissipation rates and the determination of the flow isotropy. There are relatively few studies that report on analysis of turbulence in cirrus clouds. Most are presented as case studies. In an early investigation, Heymsfield (1975) explored the formation and maintenance of cirrus uncinus clouds and explained the observed phenomena/structure dynamically as a result of wind shear and convective activity. The measurements could not directly resolve smaller scale turbulence. The work by Pinus and Litvinova (1980), Dmitriev et al. (1984,1986), Ermakov et al. (1984), Sassen et al. (1989), Flatau et al. (1990), Smith et al. (1990), Gultepe and Rao (1993), Gultepe and Starr (1995) and Demoz et al. (1998) assess dynamics and turbulence in cirrus based on data with 1-Hz resolution and therefore resolving length scales down to about 150m. Studies by

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Table 1 7. 1 . Time and location of major observational programs for which turbulence measurements in cirrus have been evaluated Campaign Dedicated flights

Year/month (season)

FIRE

Spring-autumn 1978-1980 Oct.-Nov. 1981 Mar.-Apr. 1982 Oct. 1986

ICE

Sept.-Oct. 1987

ICE

Sept.-Oct. 1989

FIRE II

Nov.-Dec. 1991

EUCREX CART RCS

Sept.-Oct. 1993 April 1994

SUCCESS

April 1996

Dedicated flights

Location

Reference

European and far eastern part of former USSR Vologda, Northern part of former USSR Wisconsin, Minnesota, USA North Sea, German Bight, Germany North Sea, German Bight, Germany Coffeyville, Kansas, USA Prestwick, Scotland Lamont, Oklahoma, USA Lamont, Oklahoma, USA

Ermakov et al. (1984) Dmitriev et al. (1984, 1986) Flatau et al. (1990) Gultepe and Starr (1995) Quante (1989) Quante et al. (1990) Quante and Brown (1992) Gultepe et al. (1995) Smith and Jonas (1997)

Demoz et al. (1998)

Quante (1989), Quante et al. (1990), Quante and Brown (1992), Gultepe et al. (1995) and Smith and Jonas (1996) use high resolution data (sampling rates greater than 20 Hz to resolve spatial scales of less than 10m), capable of resolving inertial subrange turbulence. Dmitriev et al. (1986) and Quante and Brown (1992) compare turbulence in different types of cirrus clouds. Pinus and Litvinova (1980) and Ermakov et al. (1984) compare turbulence in cirrus to that in other types of stratiform clouds within the troposphere. The major observational programs for which turbulence measurements in cirrus have been evaluated along with relevant references are listed in table 17.1. Results from selected studies are described in the next section.

17.4. Survey of Results

With the exception of the studies by Dmitriev et al. (1984,1986) and Ermakov et al. (1984), who published mean statistical quantities and energy spectra averaged over many cases, studies of in situ turbulence measurements in cirrus have been mainly discussed in relation to the specific meteorological situation encountered. Here, we provide a survey of the available results rather than focusing on individual case studies. 17'.4.1. Mean Flow Characteristics Considerable vertical shear of horizontal wind velocity and/or direction, at least over portions of the cloud vertical extent, is reported in most studies. The most

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intense shear is found in jet stream cirrus, with magnitudes up to lOm/skm" 1 (e.g., Quante and Brown 1992; Demoz et al. 1998). In almost all cases, the overall thermal stratification of the cloud layer is stable where calculated bulk Richardson numbers were much larger than 1, in agreement with the results of Starr and Cox (1980) based on analysis of more than 3600 radiosonde ascents through upper tropospheric clouds. Example profiles of horizontal wind speed and Ri for different types of cirrus selected from ICE/EUCREX missions are shown in figure 17.3. Shear zones (speed and/or direction; the latter not shown) are evident in all cases. Typical values for the mean static stability expressed as potential temperature gradients here ranged from 4 K/km to 7 K/km, rarely dropping below 2K/km. In some cases, very stable layers were observed above cloud top with potential temperature gradients up to 10 K/km. Brunt-Vaisala frequencies ranged between 0.005/s as a lower limit and 0.5/s for the stable regions (Quante 1989; Smith and Jonas 1996). The Ri profile for the ICE-207 mission indicates the possibility of shear generation. Based on the overall stratification and bulk Ri of cirrus cloud layers, it might be concluded that shear generation of turbulence is somewhat uncommon and that convection is rare in cirrus clouds. However, cirrus cloud systems often contain mesoscale patches with a highly cellular appearance at small scales over some limited portion of their vertical extent (Sassen et al. 1990). Corresponding evidence for shallow embedded layers (-100 m) with approximately neutral (icepseudoadiabatic) stratification is not uncommon when high vertical resolution sonde data or airborne profiles are available (Gultepe and Starr 1995; Demoz

Figure 17.3. Profiles of horizontal wind velocity and Richardson number for different types of cirrus selected from ICE/EUCREX cases. The scale for the Richardson number has been cut off at Ri = 10. Cases are classified as jet stream cirrus (ICE 207), frontal cirrus (ICE 212), cirrus in upper-level trough (ICE 216), jet front cirrus (ICE 217), and convective cirrus associated with an occlusion (EUCREX 108). Only ICE 207 (base 7km; top 9.3km) and EUCREX 108 (base 6.5km; top llkm) not totally in cloud.

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et al. 1998). This indicates that small-scale convective processes are likely to be active. It might be assumed that shear instabilities are also likely in such layers. However, lidar and millimeter-radar observations do not usually show tilted cells in these shallow cirrus-generating layers as might be expected in the presence of vertical wind shear (e.g., Sassen et al. 1995). Evaluation of Ri at this scale has not been generally possible. Wind profiles from conventional sonde data typically do not adequately resolve the wind profile as significant vertical averaging must be used in processing the raw data to suppress noise. Moreover, typical airborne in situ sampling patterns usually emphasize vertical profiles via a series of extended horizontal flight legs at intervals of 500m or more in the vertical, as seen in figure 17.3, with rapid ascents/descents during turns between the selected flight levels. Spiraling ascents/descents have also been used. Proper separation of the wind field into its component parts is problematic during rapidly changing aircraft altitude, and the wind data are usually disregarded during these maneuvers. Thus, the required high vertical resolution wind profiles are not generally available. If shallow convective layers are commonly present within cirrus, they provide a source for gravity-wave generation in adjoining stable layers at a scale governed by the depth of the convective layer. Cell widths generally range from hundreds of meters to 1-2 km. Boundary layer studies indicate that such cells should exhibit an aspect ratio on the order of 5-7, which is consistent with the inference of shallow generating layers. Gravity-wave activity can also be stimulated at larger scales, governed by the stability (TV) and depth of the adjoining layers. Another interesting consequence of shallow, unsheared generating layers is that the vertical wind shear in the regions immediately bounding the convective layer would be larger than estimated from bulk (low vertical) resolution data, and thus the possibility for shear generation of turbulence may be underestimated there. Wave breaking may also be enhanced as a result. The source of such shallow apparently convective layers is uncertain. Modeling studies show that cloudrelated processes such as latent and radiative heating/cooling can tend to destabilize layers within and around a cloud layer. However, differential advection associated with larger scale dynamical processes or mesoscale stratified turbulence could also lead to the formation of such structures. Given that intermittent turbulence is commonly observed in cirrus clouds, it must be concluded that mechanical and/or buoyancy generation mechanisms are present. However, the overall stability and the shallowness of the apparent generating layers results in a turbulence field that is usually in a perpetual transition between sporadic generation of TKE and its damping or dying out by stratification, leaving sometimes a highly structured patchy ice cloud field behind (fossil turbulence). Buoyancy lengths derived from ICE/EUCREX data range from 5m to 50m for regions with low to high turbulence intensity, respectively. Maximum values observed for different types of cirrus are listed in table 17.2. The numerical values are calculated from high-pass filtered vertical air velocity time series and the Brunt-Vaisala frequency for the appropriate height interval. Cut-off wavelengths of 2 and 5 km have been used and result in almost the same values for LB when segments obviously influenced by gravity waves are excluded. The buoyancy

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Table 1 7.2. Maximum buoyancy length scales for different types of cirrus observed during ICE/EUCREX as deduced from rms values of the high pass-filtered (2 km and 5 km cutoff) vertical velocity and the layer mean Brunt- Vaisala frequency Buoyancy wavelength (m) Type of cirrus Jet stream Occlusion (convection) Jet front Frontal Upper-level trough

2km

5km

38 20 15 9 6

42 24 20 10 8

length scale marks the upper limit of a possible inertial subrange and is therefore an important quantity influencing the selection of an appropriate grid size in large eddy models used to simulate cirrus cloud processes. 17.4.2. Turbulence Statistics and Fluxes Examination of «', v', w', and 6' time series along horizontal flight legs flown through cirrus reveals an inhomogeneous appearance in nearly all cases. Thus, calculation of representative turbulence statistics is rather difficult. Figure 17.4 presents a vertical cross-section of a wind and temperature field together with

Figure 17.4. Vertical cross-section of wind (dashed lines; m/s) and temperature (solid lines; °C) fields in a jet stream cirrus observed on November 11, 1981 (from Dmitriev et al. 1984). Cross-hatched areas represent regions of dense cirrus; wavy lines mark zones of relatively intense turbulence (ov,w > 0.1 m/s).

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the location of turbulent zones in jet stream cirrus as observed by Dmitriev et al. (1984). Regions of dense cirrus are marked by cross-hatched areas. The wavy lines indicate sections along flight legs where more intense turbulence was encountered; the criterion was a local standard deviation of 0.1 m/s to be exceeded simultaneously by ov and ow. The turbulent zones are not necessarily found in the cloudy parts and are distributed intermittently within the flow, a typical phenomenon for cases with shear-induced turbulence. It is also of note that, although cloudy areas might be deemed to have a stable thermal stratification based on an assessment of lapse rate over the entire vertical extent of a cloudy region, shallow layers exhibiting unstable, or nearly so, thermal stratification are also evident (e.g., along -40°C isotherm and along the -47°C and -49°C isotherms in the left-most 50km of the analysis), consistent with the ideas discussed in section 17.4.1. Individual vertical air velocity time series are shown in figure 17.5. The examples chosen are from a jet stream cirrus case (fig. 17.5a) and a case with embedded convective cells (fig. 17.5b). The length of the flight legs was about 100km. The inhomogeneous and dissimilar appearance of the w time series is obvious. In the very stable layer just above cloud top (fig. 17.5a), a region of distinct wave motions is evident, and high-frequency turbulent fluctuations are minimal. The amplitude of the waves approaches Im/s. Yet, considerable turbulence was encountered on a flight leg flown only a few hundred meters below this level (fig. 17.5b). Velocity fluctuations there reached values up to ±2 m/s in the most

Figure 17.5. Time series of vertical air velocity as measured by the FALCON aircraft (100 Hz sampling) along flight legs in (a) jet stream cirrus, above cloud top at a flight altitude of 9.5km (upper curve) and in the cloud-top region at an altitude of 8.9km (lower curve) for mission ICE 207 (from Quante and Brown 1992) and in (b) cirrus associated with an occluded frontal system encountered during mission EUCREX 108 (courtesy of M. Quante).

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intense region and were mainly produced by a wave-breaking event. Less intense w-fluctuations, but still patches of considerable turbulence, are seen in figure 17.5b.This leg was flown in convectively active cirrus associated with an occluded upper layer front. The most intense turbulence reported in cirrus, with vertical air velocity fluctuations up to 5-6 m/s, have been measured in lee-wave lenticular cirrus (A. Heymsfield, personal communication, 1996). Velocity variance or the standard deviation of u', v', and w' can be used as indicators of turbulence intensity. However, reported values of these quantities are sensitive to the methods used to separate small-scale turbulence from trends, mesoscale variations and waves in the flow which might otherwise dominate the statistics. Researchers use different filters and filter limits (cut-offs). Also, the specific location of an analyzed segment along a flight path may have a strong impact on the results, as evident from the preceding discussion. Typical standard deviations of the horizontal velocity components for high-pass filtered data (2-km cutoff) vary from 0.1 m/s in the calmer regions found in all types of cirrus to 0.4m/s in turbulent zones within jet stream cirrus. Ratios of o^ to ou>v generally range from 0.1 to 0.4, indicating a high degree of anisotropy. However, higher ratios of about 0.7 may be found in jet stream cirrus and cirrus dominated by convective activity (e.g., Quante and Brown 1992; Gultepe and Starr 1995; Smith and Jonas 1996). The highest reported values of the variance ratios are found inside clouds. Dmitriev et al. (1986) calculated mean vertical profiles of velocity and temperature standard deviations from all their observations of cirrostratus clouds observed during several summer experiments. They found that vertical profiles of GV>W and o>, in general, behave similarly, with maximum values occurring around the center of the cloud layers. However, they also found that turbulence again increases above cloud top. This may indicate contamination of their statistics by wave activity, as similar results have not been reported by other groups. Some studies have examined the turbulent fluxes of heat and moisture. Sampling issues make the derivation of statistically significant mean values extremely difficult. Nevertheless, the variability of the correlation products can provide useful information. Time series of eddy potential heat fluxes at different altitudes within a cirrus cloud in a less stable environment, taken from Gultepe and Starr (1995), are shown in figure 17.6. In this case, the mean fluxes are close to zero. Again, specific segments of a flight leg can yield a different assessment. Notable deviations from the mean build up a pattern, which is suggestive of small-scale convection within a mesoscale updraft-downdraft couplet. Gultepe et al. (1995) evaluated sensible heat and latent heat fluxes for additional cirrus cases where the fluxes were separated into small and larger scale components, as well as into contributions from upward and downward moving air. The magnitude of the derived heat flux was comparable to that observed in marine stratocumulus clouds. Based on observations of a cirrus case during the 1986 FIRE campaign, Gultepe and Rao (1993) estimated components of the moisture and heat budgets for a cirrus cloud field. They concluded that advection was a dominant process in determining the budgets for that case. Turbulent heat and moisture fluxes were significant only in the lower levels of the cloud. However, the authors

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Cirrus

Figure 17.6. Example of time series of eddy potential heat flux for different altitudes in a cirrus observed on October 19,1986 during FIRE; triangles indicate upward air motion, downward motions are denoted by dots (from Gultepe and Starr 1995).

reported large error bars for the turbulence terms (about 50%) in the budget equations. 17.4.3. Spectral Characteristics Power-spectral analysis Power spectra of velocity components are calculated using fast Fourier transform (FFT) or maximum entropy methods. Spectra for u and v at longer wavelengths (a few kilometers to about 100km) tend to show a -5/3 slope, in accordance with the theory of stratified turbulence (section 17.2.2). Field experiments generally do not sample the longer scales adequately; flight legs of 100km, or less, are typical. However, extensive data collected on commercial airliners during the Global Atmospheric Sampling Program (GASP) contain an excellent sample for the larger scales. The GASP data analysis is described by Nastrom and Gage (1985). Additional information is given by Flatau et al. (1990). Results are shown in figure 17.7, where the power spectral density for the u component is compared for in-cloud (longer than 50s) flight segments and cloud-free air. The -5/3 behavior at longer wavelengths is apparent. The spectral peaks at 8 and 16km are due to the inertial navigation system of the aircraft, and a steeper slope is seen at smaller scales. The smaller scale inertial subrange is not resolved by these data. An important result is that the energy density is greater at all resolved scales for the in-cloud data in comparison to the clear-air observations. This indicates that the upper-level ice clouds were associated with sources of mesoscale variability

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Figure 17.7. Power spectral density of the w-velocity component versus wave number and wavelength. The analyzed aircraft data were gathered during the Global Atmospheric Sampling Program. The dotted line marks a spectral slope of -5/3 (spectral data provided by G. Nastrom).

(such as the jet stream, elevated frontal zones, or deep convection) and/or themselves contribute to enhancing the variability on these scales. In the transition region (scale lengths from 2km to about 10km) between the more three-dimensional regime at small scales and the quasi-two-dimensional turbulence regime at larger scales, spectra of M, v, and w often exhibit a great deal of structure. The many intermediate spectral peaks and slopes suggest a mixture of wave influence, local convective activity, and sporadic wave-breaking events. On some occasions, spectral slopes around -3 indicate the existence of a buoyancy subrange. Sassen et al. (1989) provide good examples from three case studies for the variability of spectral behavior in the transition range, revealing the ubiquitous mesoscale organization of the cloud systems. At shorter wavelengths (some hundred meters and less), spectral slopes again tend to approach a -5/3 roll-off, pointing toward the existence of an inertial subrange at smaller scales where a tendency toward isotropy in the flow is also found. Figure 17.8 shows spectra in the active developing turbulence of a wave-breaking event and in the region of less intense background turbulence nearby at the same height level. The w-spectrum is noticeably damped at the transitional frequencies for the less intense (decaying) turbulence. In the active turbulence-generation region (fig. 17.8a), the spectra show higher energy levels and indicate isotropy up to a wavelength of roughly 500m (-0.3 Hz). These relatively large quasi-isotropic eddies are found only occasionally in cirrus, mostly in situations with strong wind shear. In contrast, isotropy extends only to a scale of about 20m (~8Hz) in the less intense background turbulence region (fig. 17.8b). As a synopsis, a comparison of w-spectra for selected regions with highest turbulence intensity in different types of cirrus is shown in figure 17.9. The power spectral densities span about 2.5 orders of magnitude for the different cases at

362

Cirrus

Figure 17.8. Power spectra of the u, v, and w air velocity components measured by the FALCON aircraft during mission ICE 207 for a (a) wave-breaking event and (b) in background turbulence. For clarity, the power spectral densities (PSDs) have been averaged logarithmically over the spectral bins (courtesy of M. Quante).

the frequency of IHz, corresponding to a wavelength between 140m to 180m. By far, the highest energy level was found for the jet-stream cirrus case. In general, identification of dominant processes responsible for observed cloud structure from aircraft measurements alone is not an easy task. This is due to the limited coverage that does not yet allow an adequate depiction of the three-dimensional flow field nor a systematic characterization of the full life cycle of elements within mostly heterogeneous cirrus cloud fields. Figure 17.10 provides an example for spectra marking distinctly different dynamical regimes for

Figure 17.9. Power spectral density of vertical velocity for different types of cirrus encountered during ICE/EUCREX and ARM RCS. Only quasi-homogeneous segments (20-50 km long) with highest turbulence intensity for each case are shown; results are logarithmically averaged. (Courtesy of M. Quante; ARM data provided by G. Mace.)

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Figure 17.10. (a) Ice water content as measured by Particle Measurement System optical probes and the vertical air velocity component, w, along a flight leg at 8.3km height by the Hercules C-130 during mission ICE 207. (b) Power spectral densities of w for the indicated segments (courtesy of M. Quante; IWC data provided by PR. A. Brown of UK Meteorological Office.)

segments within the same cloud system with different ice water content (IWC) and size spectra (not shown). The corresponding IWC and w time series are also shown. For segment b (320-450s, about 19km), the spectral energy at all frequencies exceeds that for the other segments by about one order of magnitude where the origin of the strong turbulence is most likely again due to a breaking wave encountered during an approach into a more dense jet-stream cirrus field. The spectral slope for this segment is slightly steeper than -5/3, indicating that the turbulence cascade was not yet fully developed. The highest vertical velocity fluctuations are aligned with a local peak in IWC, suggesting that turbulence was strongly influencing the cloud development. The energy-containing frequency at about 0.075 Hz corresponds to a length scale of about 2km, the depth of the shear layer. Highest IWC is found in the region with moderate intensity turbulence that maintains a mixed layer—likely a result of previous mechanical generation events. Smith and Jonas (1996) found just the opposite behavior

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Table 1 7.3. Typical values (ranges) of the dissipation rate in cirrus and in clear air reported by different groups Dissipation rates (e) (m2/s3) In cirrus 0.9xlO-4...1.6xlO~4 1 x HT4 . . . 6 x ICT4

0.4 x HT4 . . . 2.5 x ID"4 (0.01 x 10-4) . . . 8 x 10-4 In clear air 1 x 10~5 <5 x 1Q-5 1 x 10-8 . . . 1.6 x 1Q-7

Location

Reference

Northern latitudes, former USSR Mid-latitudes, Eastern part of former USSR Mid-latitudes, W. Europe Mid-latitudes, USA

Dmitriev et al. (1984) Ermakov et al. (1984)

Lower stratosphere Upper troposphere Upper troposphere

Lilly et al. (1974) Gultepe and Starr (1995) Schumann et al. (1995)

Quante and Brown (1992) Gultepe and Starr (1995)

for a convectively active cirrus where downdrafts caused by cloud-top radiative cooling may have entrained dry air from above into the cloud and thereby thinning the cloud. Turbulence dissipation rates (e) can be deduced from power spectra, if an inertial subrange is clearly established. For this evaluation, the Kolmogorov spectral relation (section 17.2.2) is inverted. Gultepe and Starr (1995) alternatively used a structure function method to deduce e. Calculated dissipation rates in cirrus range from 0.5 x lO^m^s3 to 8 x !CT4m2/s3 for low to high turbulence intensity, respectively. In table 17.3, dissipation rates reported for cirrus cases are compared to those measured in clear air. On average, e is an order of magnitude larger in cirrus clouds than in cloud-free regions of the upper troposphere and lower stratosphere. Cross-spectral analysis To determine the existence of linear gravity waves in the cirrus flow field, crossspectral analysis has been applied to time series of vertical velocity and potential temperature by Quante and Brown (1992), Gultepe and Starr (1995), and Smith and Jonas (1996). In the presence of linear waves, w and T phase-spectra are expected to show a phase shift of 90° and a peak in the coherence spectrum at the relevant wavelength. It should be mentioned that reported wavelengths, deduced from the spectra of airborne in situ observations, only give an upper limit for the actual wavelengths, since the angle of the flight path with respect to the orientation of the wave field cannot be inferred from the measurements. In general, the phase speed and propagation direction differ from the mean wind velocity and wind direction in a sheared flow. In the ICE/EUCREX data analyzed by Quante and Brown (1992), gravity waves with wavelengths between about 2km and 20km were clearly identified. In two cases, wave trains with an exceptional short wavelength of about 1km were found. A breaking wave (Kelvin-Helmholtz instability) with a wavelength of 3.8km (about 2.4 times the mean shear layer depth) was detected in a jet-stream cirrus case. Smith and Jonas

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(1996) discuss the occurrence of short wavelength gravity waves (about 2km) in convective cirrus. They conclude that the waves were forced by convection from below. Gultepe and Starr (1995) also detected waves with a large range of wavelengths, 0.8-11 km, in cirrus, in which velocity shear played a minor role. They also reported on a large mesoscale wave structure with a wavelength of about 170km. Although this feature was clearly evident, the possible contribution by the so-called Schuler oscillation (characteristic for inertial navigation platforms) with a period of about 84min, is unknown, but might be significant. Since the w-amplitude was quite small (less than 3cm/s) compared to the horizontal wind components, this feature might have been a two-dimensional vortical structure. Overall, spectral analysis confirm that the flow field in cirrus clouds is commonly quite complicated with co-occurring turbulence at many scales and smallscale convective activity, gravity waves, and maybe two-dimensional mesoscale turbulence. 17.4.4. Wavelet Analysis The wavelet transform (e.g., Daubechies 1990,1992) has been applied to analyze turbulence data gathered in cirrus clouds to delineate coherent structures and waves that might be present and to assess the local scaling behavior (Quante and Yamada 1992; Smith and Jonas 1997; Demoz et al. 1998). This analysis method has previously been used in turbulence research with good success (e.g., Liandrat and Moret-Bailly 1990; Yamada and Ohkitani 1991; Farge 1992; Farge et al. 1996; Abry 1997; Farge et al. 1999). Wavelet transform analysis has great potential as a tool for advanced analysis of cloud dynamic processes in complex flows. Some basics of the technique are given here. The wavelet transform arose as an analysis tool capable of providing information about a signal simultaneously in time (or space) and frequency (or scale). It is used to decompose an arbitrary signal into elementary contributions at different scales as a function of location or time. This is not equivalently possible by traditional Fourier analysis. The wavelet transform coefficients, T(b,a), of the signal,/(jc), are defined by

The wavelets are generated from an analysis function, y, called "mother wavelet," by dilatations, a, and translations, b, (a,b) e 3l*+ x $:

There are a number of possible wavelet functions that can be used for the analysis of signals. If the admissibility condition (Daubechies 1992) for the function is fulfilled, the original signal can be recovered from the wavelet coefficients. An intentionally modified signal can also be generated from selected or manipulated coefficients.

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The results of wavelet analysis are usually visualized as a two-dimensional display (scalogram) in scale/frequency versus location/time. However, the wavelet coefficients can also be analyzed in other ways, including the calculation of higher order statistical moments (strongly wavelet dependent), correlation analysis, and the calculation of spectra. A wavelet scalogram for the vertical air velocity as measured during a transition from a turbulent burst to less intense background turbulence in the cloud-top region (8.9km) of a jet-stream cirrus is shown in figure 17.11. The original data are displayed in figure 17.5a. The analyzing function adopted for the continuous analysis here was a "Mexican hat" wavelet. Scale is linear with respect to geometric length, where a scale of 50 corresponds to a physical length of about 1.8km, and a scale of 10 corresponds to about 360m. The analyzed segment covers a horizontal distance of roughly 15km along the flight leg. The squared amplitude of the wavelet coefficients is shown where the logarithm of the amplitude is mapped onto a gray scale (0-255). Up to a position of 9km, branching structures cover the entire scale domain shown here where the location of small-scale fluctuations appears coupled to the occurrence of larger scale fluctuations with intervening more quiescent periods at all scales. This likely indicates an energy cascade from larger scales (breaking waves) to smaller scales. Maximum values were found at a scale around 50-60 (1.8-2.2km). The transition to the calmer region starts at a position of 9km, where the locations of events at smaller scales are less intense and more or less detached from the intermediate scales. The turbulence in this cirrus case is produced by wave-breaking events in the shear flow that decay to

Figure 17.11. Scalogram (scale vs. position) of wavelet transform coefficients for the vertical velocity component as measured at the transition of a turbulent burst to background conditions in a jet stream cirrus on September 29,1989 during the International Cirrus Experiment. The underlying time series of w is shown in figure 17.5a, lower curve. A scale of 50 corresponds to a wavelength of about 1.8km. See text for further discussion. (Courtesy of M. Quante.)

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Figure 17.12. Wavelet coefficients for a vertical velocity time series at the lower boundary (5.3km) of an ice cloud observed on April 21,1996 over Oklahoma. An octave of 0 corresponds to a length scale of about 1.2km (scale doubles for each unit increase in octave). The position along the flight leg is given in seconds (from Demoz et al. 1998).

background intensities in the stable stratification. The wavelet analysis is well suited to localize and quantify the associated flow features. The existence of gravity waves within a heterogeneous flow in a cirrus environment is revealed in the wavelet scalogram displayed in figure 17.12, taken from Demoz et al. (1998). The data were gathered by the NASA DC-8 on April 21,1996, over Oklahoma. A continuous complex "Morlet" wavelet was used, and the scalogram shows the amplitude of the real part of the transform coefficients in a frequency-time display. The zero octave corresponds to a length scale of 1.2km, and the length scale doubles with each octave/scale increment. In the second half of the leg, a relatively strong series of oscillations at a scale of about 30km (octave of 4.4) is evident. These show the upward and downward phases of a series of waves (i.e., a wave train) that was encountered. Other wave families are also apparent at intermediate scales of about 5 km (octave 2), and patches of relatively intense activity are seen at even smaller scales during this time. The flight leg was flown near cloud base and the latter more active portion was flown in cloud. The analysis enables a relatively clear delineation of a hierarchy of phenomena that were not so evident in an inspection of the original time series due to their superposition. Smith and Jonas (1997) applied a discrete wavelet transform to vertical velocity time series from the EUCREX '93 campaign. The 'Daubechies-20' wavelet was used to construct scalograms and spectra. By this method, convec-

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Figure 17.13. Power spectral density calculated from conditionally sampled wavelet coefficients for denser (ice crystal concentration > 10/L) and less dense cloudy segments along an entire flight pass in a frontal cirrus observed on October 17,1989 during the International Cirrus Experiment. A scale parameter of 11 corresponds to about 10m and a scale of 5 to about 1.3km in spatial dimensions. (Courtesy of M. Quante; microphysical data provided by P.R.A. Brown of UK Met. Office.)

tive elements and wave-produced turbulence could be localized in the complex flow. Wavelet analysis can also be used for conditional sampling. In figure 17.13, power spectra calculated from wavelet coefficients are compared. For the discrete wavelet transform, a "Meyer" wavelet was used because of its ability to resolve steep spectral slopes (Perrtier et al., 1995). The measurements were gathered by the MRF Hercules C-130 during the ICE 89 campaign in fast-moving frontal cirrus. The wavelet coefficients of the vertical velocity component for an entire flight leg were conditionally subsampled according to the cloud condition. The particle number concentration, as measured by particle measurement system (PMS) optical probes, was used to select in-cloud and out-of-cloud coefficients within the same background flow using a threshold of 10 particles/L. The resulting spectra show remarkably different behavior. In cloud, the spectra rolls off with a slope of about -5/3, indicating the existence of a developed turbulence cascade in the inertial subrange region. Out of cloud, a much steeper slope is found where the greater amplitudes at larger scales appear disconnected from small-scale features. It is supposed that cloud processes, such as latent and radiative heating/cooling, maintain the turbulence within the cloudy segments. The above examples illustrate that wavelet analysis is a powerful tool for analysis of turbulence measurements in cirrus. It needs to be further explored and applied to ascertain the statistical significance of the results and to assess the choice of appropriate analysis functions for the respective problem under investigation. 17.5. Conclusions

Analysis of available cirrus cloud observations reveals a complex and challenging dynamical environment. Although the reported turbulence can be classified

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as weak in most cases, the interactions with other cloud processes are significant nonetheless. Dynamical processes play a leading role in determining cloud structure, which is typically heterogeneous. Stronger turbulence is observed in regions with strong wind shear and in some convectively active cells. Turbulence occurs intermittently in patches and coexists, or probably nonlinearly interacts, with wavy motions on a variety of scales. The presence of waves in the flow field, with typical wavelengths ranging from 2 km to more than 40 km, is reported almost in all published studies. Waves may simultaneously occur on a number of scales. On larger scales (A > 2km), turbulence tends to be quasi-two-dimensional, while isotropic three-dimensional turbulence occurs on small scales (A, < 100m).Typical scales of energy containing eddies vary between a few tens of meters and some hundred meters. On some occasions, significant energy resides in eddies as large as 2 km. The amplitudes of co-existing wave and turbulent motions are often comparable and together with the generally weak intensities make for a challenging analysis problem. Turbulence and wave activity are noticeably more intense in cloudy regions, though the cause and effect of this relationship are not definitively established. Delineation between cloud processes and phenomena associated with the background flow is particularly challenging. Due to the intermittent and nonstationary character of the flow, representative turbulence statistics and TKE budgets are difficult to assess. Although a significant amount of in situ turbulence data has been analyzed, more quality observations in cirrus clouds are sorely needed. Additional observations would help establish the significance of present findings, which is an important concern given the existing ambiguities, and would also provide a better sample over the variety of cirrus cloud types and situations. In particular, observations in tropical and anvil cirrus clouds are highly desired. In some instances, a more detailed analysis of existing data by wavelet analysis in combination with a thorough analysis of microphysical and radiation measurements could provide significantly more insight into the processes at work. More studies are needed that combine in situ measurements of turbulence and ice particles with remote sensing data, as in Gultepe et al. (1995), to better relate results of the turbulence analysis to cloud microphysical parameters and macroscopic cloud structure. New observations should seek to take advantage of technological advances. For example, the measurements should be of the highest resolution and accuracy. Quality in situ water vapor measurements are needed. New experiments should also aim to provide a dense network (space and time) for vertical profiling of wind, potential temperature, and humidity to allow for better identification of dynamical regimes and their development during cloud life cycles. The use of dropsondes would be a valuable extension to earlier observational strategies. Global Positioning System tracking of sondes might yield the required vertical resolution of the horizontal wind field. A means to map the local threedimensional wind field would be extremely useful. Advantage should be taken of real-time, surface-based or airborne active remote sensing to provide a more interactive airborne in situ sampling strategy in response to the observed conditions. In general, more thought is needed on optimal sampling strategies for cirrus in light of the increased understanding of characteristic cloud structures

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that is being developed from extended surface-based remote sensing observations such as ARM. Cirrus are commonly observed to be quite heterogeneous and often exhibit multilayered structure. Besides the occurrence of multiple layers on the synoptic scale, as described by Starr and Wylie (1990), for example, remote sensing observations reveal that these individual layers are commonly composed of a series of sloping, shallow mesoscale strata in an interleaved pattern. The heterogeneous appearance of cirrus may be partly explained by the patchy occurrence of turbulence, limited vertical mixing, and the effects of cloud processes such as ice crystal sedimentation and the interplay of latent and radiative heating patterns with the local buoyancy field. Thus, turbulence generated by the cloud and its interaction with the background flow must be taken into account when addressing the life cycle of cirrus clouds. Coupling of the mesoscale flow features with the cloud-related dynamical processes is a challenging task for the largeeddy type of models due to the range of scales that must be included.

Acknowledgments M.Q. thanks P.R.A. Brown of the UK Meteorological Office and Dr. B. Guillemet of the University of Clermont Ferrand for their help during the evaluation of some of the aircraft data and Prof. G. Nastrom, St. Cloud State University, for providing spectral data from the GASP program. Valuable discussions with Profs. H. Isaka and P. Jonas, and D.S. with B. Demoz and I. Gultepe, on the topic are gratefully acknowledged. The support provided to M.Q. by Prof. Raschke of GKSS throughout the experimental and analysis phases is appreciated. Some of the work presented here was financially supported by the Climate and Environment Program of the European Union and the NASA Radiation Sciences Program.

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Raschke, E., 1988. The international satellite cloud climatology project, ISCCP, and its European regional experiment ICE (International Cirrus Experiment). Atmos. Res., 21,191-201. Raschke, E., P. Flamant, Y. Fouquart, P. Hignett, H. Isaka, PR. Jonas, H. Sundquist, and P. Wendling, 1998. Cloud-radiation studies during the European cloud and radiation experiment (EUCREX). Surv. Geophys., 19, 89-138. Sassen, K., D.O'C. Starr, and T. Uttal, 1989. Mesoscale and microscale structure of cirrus clouds: three case studies. /. Atmos. Sci., 46,371-396. Sassen, K., C.J. Grund, J.D. Spinhirne, M.M. Hardesty, and J.M. Alvarez, 1990. The 27-28 October 1986 FIRE IFO cirrus case study: A five lidar overview of cloud structure and evolution. Mon. Wea. Rev., 118, 2288-2311. Sassen, K., D.O'C. Starr, G.G. Mace, M.R. Poellot, S.H. Melfi, W.L. Eberhard, J.D. Spinhirne, E.W. Eloranta, D.E. Hagen, and J. Hallett, 1995. The 5-6 December 1991 FIRE IFO II Jet Stream Cirrus Case Study: The Influence of Volcanic Aerosols. /. Atmos. Sci., 52, 97-123. Schumann, U., and T. Gerz, 1995. Turbulent mixing in stably stratified shear flows. /. Appl. Meteor., 34,33-48. Schumann, U., P. Konopka, R. Baumann, R. Busen,T. Gerz, H. Schlager, P. Schulte, and H. Volkert, 1995. Estimate of diffusion parameters of aircraft exhaust plumes near the tropopause from nitric oxide and turbulence measurements. J. Geophys. Res., 100, 14147-14162. Shur, G.N., 1962. Experimental investigations of the energy spectrum of atmospheric turbulence. Tr. Tsentra. Aerolog. Observ., 43, 79-90. Sidi, C, J. Lefere, F. Daulaudier, and J. Barat, 1988. An improved atmospheric buoyancy wave spectrum model. /. Geophys. Res., 93,774-790. Smith, S.A., and PR. Jonas, 1996. Observations of turbulence in cirrus clouds. Atmos. Res., 43,1-29. Smith, S. A., and PR. Jonas, 1997. Wavelet analysis of turbulence in cirrus clouds. Ann. Geophysicae, 15,1447-1456. Smith, W.L., P.P. Hein, and S.K. Cox, 1990. The 27-28 October 1986 FIRE IFO cirrus case study: In situ observations of radiation and dynamic properties of a cirrus cloud layer. Mon. Wea. .Rev., 118, 2389-2401. Starr, D.O'C, 1987. A cirrus-cloud experiment: Intensive field observations planned for FIRE. Bull. Amer. Meteor. Soc., 68,119-124. Starr, D.O.'G, and S.K. Cox, 1980. Characteristics of middle and upper tropospheric clouds as deduced from rawinsonde data. Atmos. Sci. Paper no. 327, Colorado State University, Fort Collins. Starr, D.O'C., and DP. Wylie, 1990. The 27-28 October 1986 FIRE Cirrus Case Study: Meteorology and Clouds. Mon. Wea. Rev., 118, 2259-2287. Starr, D. O'C, C.L. Korb, G.K. Schwemmer, and C.Y. Weng, 1992. Observations of the height-dependent pressure perturbation structure of a strong mesoscale gravity wave. Mon. Wea. Rev., 120, 2808-2820. Stewart, R.W., 1969. Turbulence and waves in a stratified atmosphere. Radio Science, 4, 1269-1278. Thorpe, S.A., 1987. Transitional phenomena and the development of turbulence in stratified flows: a review. /. Geophys. Res., 92,5231-5248. Uccellini, L.W., and S.E. Koch, 1987. The synoptic setting and possible energy sources for mesoscale wave disturbances. Mon. Wea. Rev., 115, 721-729. Vanneste, J., and PH. Haynes, 2000. Intermittent mixing in strongly stratified fluids as a random walk. /. of Fluid Mech., 411,165-185.

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18

Dynamical Processes in Cirrus Clouds Concepts and Models

D A V I D O C. S T A R R MARKUS QUANTE

Advancement in the understanding of cirrus clouds and their life cycle comes through symbiotic use of models, observations, and related concepts (fig. 18.1). Models of cirrus clouds represent an integration of our knowledge of cirrus cloud properties and processes. They provide a capacity to extend knowledge and enhance understanding in ways that complement existing observational capabilities. Models can be used to develop new theories, such as parameterizations, and focus science issues and observational requirements and developments. For example, early model results of Starr and Cox (1985a) and Starr (1987b) predicted that fine cellular structure (~lkm or less) would be found in the upper part of extended stratiform cirrus clouds. This prediction was confirmed when high-frequency sensors were deployed both for active remote sensing (Sassen et al. 1990a, 1995) and later for in-situ measurements (Quante and Brown 1992; Gultepe et al. 1995; Quante et al. 1996). Sampling rates of 10Hz, or better, are now accepted as a minimum requirement for resolving cirrus cloud internal structure and circulation where 1-Hz or coarser measurements were previously used. Similarly, discrepancies between observed cloud radiative properties and calculations (theory) based on corresponding in-situ observations of cloud microphysical properties (Sassen et al. 1990b) led to the development of improved observing capabilities for small ice crystals (Arnott et al. 1994; Miloshevich and Heymsfield 1997; Lawson et al. 1998). Such sensors are now regarded as part of the standard complement when doing in-situ microphysical measurements in cirrus. At the same time, observations are absolutely essential in developing and evaluating cloud models. No cloud modeler wants to apply a model or theory too far beyond the limits of what can be observationally confirmed, at least in gross 375

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Figure 18.1. Interactions between concepts, models, and observations are crucial in advancing knowledge.

terms. The third aspect of this triad is concepts. Although models and observations can lead to predictions or diagnosis of unexpected relationships, they are each limited by the concepts that were used in their design and/or implementation. In the end, new concepts arising from analogy to other phenomena and/or from synergistic integration of existing knowledge can lead to new understanding, new models, new instruments, and new sampling strategies (fig. 18.1). Chapter 17 focuses on observations of internal cloud circulation and structure. In this chapter, we briefly review the evolution of concepts and models describing dynamical processes in cirrus clouds. We focus on the scale of individual clouds and mesoscale cloud systems, rather than on synoptic-scale cloud systems that are discussed in chapter 6. Last, an international activity seeking to spur the development and application of cirrus cloud models is described. This is the GEWEX (Global Energy and Water Cycle Experiment) Cloud System Study (GCSS; Browning et al. 1994) Working Group on Cirrus Cloud Systems that is currently engaged in systematic comparison and evaluation of cirrus cloud models.

18.1. Early Concepts Ludlam (1956) considered the circulations associated with common forms of fair weather cirrus clouds, such as cirrus uncinus. Although there were earlier perti-

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Figure 18.2. Schematic diagram of cirrus uncinus cloud indicating effects of vertical wind shear and static stability on cloud morphology (after Yagi 1969).

nent studies, we take this as our starting point. Ludlam described a head cell responsible for the generation of the long streamers of precipitation-sized ice particles (fig. 18.2). He understood that the "mare's tail" represented vertical propagation via the ice crystal fallspeed (gravitational settling) and that particle size could be inferred by analyzing the shape of the streamer (noting the wind profile). Ludlam recognized that substantial particle growth could (and did) occur in these streamers, unlike the case of rain falling from clouds in the lower troposphere. Thus, he understood that regions of supersaturation with respect to the ice phase could be maintained in the upper troposphere and, by inference, that ice saturation did not ensure nucleation of ice crystals. Streamers were much more apparent than the head cell to surface observers. Indeed, one gets the definite impression that identifying the head cells associated with individual streamers was more an act of faith than of unambiguous observation in most cases (e.g., Ludlam 1980). This is also our experience and aptly illustrates the importance of the concepts used in data interpretation. Ludlam described the cell heads as small, ~1 km or less, and speculated that they were convective in nature. This leads to the inference that relatively shallow layers, conditionally unstable to ice pseudoadiabatic processes, existed in the upper troposphere (fig. 18.2). Moreover, the process leading to the formation of such layers could continue over extended time periods, as layers of cirrus uncinus were observed to persist for many hours on some occasions. This was a lot to deduce from very simple measurements. The set of papers by Heymsfield (1975a,b,c) represents the next major advance in understanding cirrus cloud dynamics and the implications thereof. In some regards, this work supplies quantitative in-situ measurements and calculations to support many of the qualitative concepts proposed by Ludlam, and later, more quantitatively using stereographic techniques and soundings by Oddie (1959), Reuss (1963), Yagi et al. (1968), and Yagi (1969). Heymsfield (1975a) reported in-situ observations of updraft speeds and ice water contents in cirrus uncinus clouds, including the head region, as well as for cirrostratus cases. Heymsfield (1975b) developed concepts (e.g., fig. 18.3a), congruent with the observations, to explain the shape of the cirrus uncinus cloud, including the role of conditional

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Figure 18.3. Schematic diagram of cirrus uncinus cloud (A) showing characteristic shape, dimension, and operative process in situations with positive vertical wind shear and (B) with modification illustrating the development of new turrets along fallstreak driven by destabilization associated with evaporative cooling (after Heymsfield 1975b).

instability and updraft speed; ice crystal nucleation, growth, and fallspeed; and vertical wind shear. Of interest is the inclusion of new cell development from the streamer trail in this concept model (fig. 18.3b; see also Sassen et al. 1989). Ludlam also recognized that diabatic heating/cooling could potentially lead to generation of new cells; in other words, that the sublimation cooling within a sloped fallstreak could thermally destabilize that region relative to the underlying air where the shear-induced slope is essential to the development of the new

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cells. Heymsfield (1975c) provided detailed calculations of the development, evolution, and spatial-temporal distribution of the ice crystal population using a parcel model together with the conceptual model of the dynamical structure of the cloud. Heymsfield (1977) provided a substantial body of additional measurements of cirrus cloud ice water content and particle spectra for synoptic cirrostratus cloud systems over the northwestern United States. He also inferred the mesoscale (-10 km) vertical-motion forcing associated with these cloud systems using a conceptual model of the cloud water budget along with the in-situ observations of ice water content and particle spectra, radar observations, and calculations of particle fallspeed. This work played a major role in enabling the subsequent development of a dynamical model of cirrus clouds by Starr and Cox (1985a). In turn, these observations were enabled by the development of optical probes for measuring cirrus cloud particles from high-flying jet aircraft (Heymsfield and Knollenberg 1972). 18.2. Beginning of More Complete Models and Further Concepts

Starr and Cox (1985a) developed a two-dimensional (;c, z) model of cirrus clouds that explicitly resolved (predicted) dynamical processes on a grid mesh of 100 m resolution over a domain of 6 km in the horizontal and 4 km in the vertical. Formation of ice was diagnosed via an assumed equilibria condition in terms of saturation with respect to ice, where a relative humidity with respect to ice (RHice) of 120% was required to initiate ice formation from water vapor. Although ice particle spectra and development were not explicitly included (no particle growth equation as in Heymsfield 1975c), the effect of the particle size/habit distribution on the cloud ice water budget was included via an empirically based parameterization of the vertical flux of ice water due to gravitational sedimentation or fallspeed. A unique size/habit distribution was associated with each possible ice water content (IWC) and the effective fallspeed correspondingly inferred. Radiative processes, both in the infrared and solar spectrum, were also included in the model where local radiative heating/cooling was diagnosed based on the local vertical distribution of cloud ice. This model did not permit treatment of vertically sheared situations (cyclic/periodic lateral boundary conditions) but did incorporate a mechanism to specify an imposed domain-wide (mesoscale) verticalmotion forcing. Results from the Starr-Cox model played a major role in developing the scientific underpinning and design of the First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment (FIRE) field program in Wisconsin in 1986. In particular, the predominant dependence of horizontally averaged, vertically integrated, cirrus ice water path (IWP) on broad-scale dynamical forcing (Starr 1987a) necessitated an attempt to observe this forcing using rawinsondes in conjunction with in situ and remote sensing observations of cloud physical makeup. Starr and Cox (1985a) found that embedded cellular development was prevalent in their simulations of cirrostratus cloud layers, which was not surprising

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given that the initial thermal stratification of cloud generation layer was conditionally neutral with respect to ice pseudoadiabatic processes. These cells developed at horizontal scales of ~lkm or less, consistent with the depth of the cloud-generating layer, in association with dynamical features (updrafts). The circulations were not strong (initial updrafts of -0.5 m/s) and declined to smaller values later in the simulations (10-20cm/s), appreciably smaller than maximum updrafts (50 cm/s to Im/s) reported in cirrus uncinus and embedded cirrus cells by Heymsfield (1975a, 1977). Nonetheless, cellular structure and circulations persisted. Starr and Cox (1985b) found significant differences in IWP between simulations of midday and nighttime cirrus. These differences were more than twice what could simply be explained by differences in the direct effect of radiative tendency on temperature and thus RHice. As shown in figure 18.4, the daytime simulation exhibited greater cellularity late in the simulation and, indeed, reflected the persistence of individual cells in contrast to the more homogenous nighttime IWC field where cells developed and decayed on fairly short time scales (20-30 min). A simple analysis yields the conclusion that buoyancy production of vertical air motions (updrafts/downdrafts) is predominantly by thermal perturbations. Generation of vorticity is via the horizontal gradient of {(9/0) + qv + q], where 6 is potential temperature, qv is the water vapor specific humidity, q\ is the ice water specific humidity, and 0 is the horizontal average of 0. Maximum thermal perturbations in cells reported by Heymsfield (1977) are about 0.1 °C. The corresponding effect of a relatively large 5% humidity perturbation or a 5mg/m3 IWC perturbation are each more than an order of magnitude less in most situations. Thus, virtual temperature and mass-loading effects on cirrus internal circulations are generally of secondary importance. Moreover, perturbations in radiative heating/cooling associated with IWC cells are significant in magnitude in comparison to the existing thermal perturbations. These heating/cooling perturbations can occur deep in the cloud due to the relatively small optical thickness, unlike in the case of stratocumulus where the radiative effects occur predominantly near cloud top and base. Local radiative perturbations can either create or destroy thermal perturbations of about 0.1 °C over time periods of 20-40 min, comparable to cell lifetimes in the nighttime case. Thus, Starr and Cox concluded that, in addition to the direct effect on temperature and RHice and the overall effects on stability arising through the mean profile of radiative heating, local horizontal gradients of radiative heating/cooling have a pronounced effect on the circulation and structure within cirrus clouds, at least for the relatively warm cirrus cases they considered (-30 to -35°C). The day-night differences were attributed to the effects of positive correlation between local infrared radiative cooling enhancements and positive thermal anomalies associated with the production of cloud mass and circulation, which are offset in daytime by the similarly correlated effects of perturbations in solar warming. Subsequent studies of cold (-55 to -60° C) cirrus did not show this pronounced day-night difference (Starr 1987b) and were generally more cellular, possibly because the optical depths and IWPs were significantly smaller such that the circulation-damping effect of infrared radiative anomalies were correspondingly reduced.

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Figure 18.4. Comparison of ice water specific humidity fields (qt) after Ih in simulation of cirrostratus formed in a neutrally stratified layer (a) at night (infrared only), (b) during midday (infrared plus solar), and (c) for simulation of altocumulus (altostratus) under nearly identical conditions at night (after Starr and Cox 1985b). Contours at g, of 10~3,1, 10, and 20mg/kg in panels a and b, and 10~3,1, 50,100, and 150mg/kg in panel c.

In addition to the predominant role of broad-scale lifting in determining overall cirrus cloud properties, Starr and Cox (1985b) found that the effects of particle size/habit distribution were the second most important factor, as represented in their model via the ice water fallspeed. This is well illustrated by their comparison of a cirrus simulation to a simulation of an altocumulus (altostratus) cloud layer where the cloud water fallspeed is set to a small value (~lcm/s), reflecting the presence of only small cloud droplets. The vertical distributions of cloud water were markedly different between these simulations (fig. 18.5b,c). The altocumulus simulation resembled a stratocumulus layer where cloud water

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Figure 18.5. Comparison of (a) time-dependent, domain-averaged cloud water content for simulations of cirrostratus and altocumulus (altostratus) formed in a neutrally stratified layer at night, as in figure 18.4. Time sequence of cloud water content profiles shown in (b) and (c), respectively (after Starr and Cox 1985a and 1985b).

peaks high in the cloud layer. The cells were broader (fig. 18.4), and a significantly more energetic circulation was found with updrafts as large as 2 m/s. Differences in overall cloud water path were large (fig. 18.5a) and consistent with the cloud classification presented in chapter 2. Starr and Cox (1985a) also speculated on the possibility that cirrus cloudgenerating layers might be self-propagating in the vertical. New convective cloud-generating layers might arise at some distance below an initial cloudgenerating layer through the cumulative effects of moistening associated with the evaporation of crystals falling from the overlaying layer together with the tendency toward unstable thermal stratification arising from the vertical pattern of sublimation cooling. They indicate that this convective layer is expected to develop at a distance of about 500m below the "mother" cloud layer. Such structure is often revealed by modern active remote sensing observations of cirrus (e.g., Sassen et al. 1995).

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18.2.1. Further Concepts Derived from Analysis The 1990s emphasized field experiments and their analysis, as summarized in chapter 17. Of particular note are the series of experiments conducted by the FIRE (Starr 1987a) and ICE/EUCREX (International Cirrus Experiment; Raschke 1988; European Cloud and Radiation Experiment; Raschke et al. 1998) Programs. Based on their analysis of FIRE observations, Starr and Wylie (1990) developed a concept of top-down development of high cirrus cloud systems (from just below the tropopause), where the propagation was attributed to the effects of ice mass fallspeed and associated destabilization, and initial forcing was attributed to lifting associated with ageostrophic flow aloft. A concept of bottom-up development for middle-level cirruslike cloud layers formed through the effects of upglide along frontal surfaces and associated instability, leading to upward convective propagation of cloud top, was also advanced. Another important concept was put forth by Sassen et al. (1989). They reported a characteristic mesoscale structure of cirrus cloud systems that is similar in geometric appearance to that associated with the individual uncinus cells described by Ludlam (i.e., clusters of cells organized into active regions with horizontal dimension of 10-100 km, or more, with extensive mesoscale fallstreaks).They called these mesoscale uncinus complexes (MUCs). Analysis of in situ dynamical observations support this contention (e.g., Smith et al. 1990). Similar features were first seen by Plank et al. (1955) in pioneering radar observations. Further, the concept of two-dimensional (jc, y) turbulence, associated with kinetic energy cascades, was proposed as a means to explain dynamical observations in the upper troposphere (see discussion in chapter 17). It has been speculated that such a process might explain the dominant and persistent mesoscale structure found in cirrus cloud systems by providing a persistent, albeit weak, vertical-motion forcing mechanism on the requisite scales where other mechanisms, such as baroclinic instability, are not believed to be effective. It should also be noted in passing that derivation of the larger scale forcing (vertical air motion) is not an easy problem at subsynoptic scales (e.g., Mace et al. 1995). 18.2.2. Ideas on Anvils Another conceptual model should also be mentioned: cirrus outflow plumes from deep convection. Lilly (1989) noted that a mixed layer can probably be maintained through turbulence generated by a strong radiative heat flux curvature in dense cirrus anvil clouds. E. Eloranta (1990, personal communication) has made observations that accord with this idea. Lilly also described a cloud-layer lifting mechanism whereby an entire mesoscale cloud layer can be lifted through the buoyancy effects of radiative heating, leading to cooling of the cloud layer and acting to maintain it against the strongly dissipative effects of net radiative heating found in tropical regions and also in mid-latitude summertime situations where surface temperatures are warm. Nevertheless, the issue of cirrus anvil maintenance and propagation remains poorly understood because few observations pertinent to these theories exist.

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18.3. Current Models

A new generation of dynamical cirrus cloud models is being developed. In comparison to the Starr-Cox model, these models typically include more sophisticated treatments of radiative processes and unresolved (subgrid-scale) turbulence. However, the most important change has been to explicitly treat the nucleation and growth of the ice phase. In this regard, they are an outgrowth of the early parcel models of cirrus microphysical development reported by Sassen and Dodd (1989), Heymsfield and Sabin (1989), and others. Predictive equations for the growth rate of ice crystals of a specified habit are used for a set of ice crystal sizes or size bins. These "bin" models explicitly resolve the local ice crystal size distribution. The motivation for developing such models comes from a number of quarters including the perception that cirrus cloud microphysical properties may be significantly sensitive to the ambient aerosol population, which could be a significant climate issue with respect to the effects of volcanic eruptions (Sassen et al. 1995) and aviation (see chapter 11) on the aerosol composition of the upper troposphere. In essence, cloud radiative properties are sensitive to cloud microphysical makeup (Stephens et al. 1990; Mitchell and Arnott 1994). Moreover, proper account of size sorting via gravitational settling, a dominant feature of cirrus cloud systems (see chapter 4), requires such a treatment. Cirrus bin models have been reported by Jensen et al. (1994a), Lin (1997), Khvorostyanov and Sassen (1998a), and Gu and Liou (2000), and a new version of the CSU RAMS model has appeared (W. Cotton 1998, personal communication). In addition to efforts to validate such models using data from field experiments (e.g., Jensen et al. 1994b), these models have been used to investigate the evolution of cirrus anvil systems in the tropics (Lin and Ackerman 1998), the maintenance of high subvisual cirrus prevalent near the tropical tropopause (Jensen et al. 1996a,b), contrails (Khvorostyanov and Sassen 1998c), fundamental issues of nucleation and ice particle growth and implications for cirrus cloud development (e.g., Khvorostyanov and Sassen 1998b) including studies of lenticular (mountain wave) clouds (Jensen et al. 1998), and development of remote sensing algorithms (Sassen and Khvorostyanov 1998). In most cases, however, the emphasis of these studies is only now beginning to be applied at a scale where internal cirrus cloud dynamical processes will be well resolved (i.e., with fine grid scales; -20-100m). This is an important path because the details of the nucleation mechanism and the subsequent development are strongly controlled by the local supersaturation, temperature, and cooling rate (see chapter 5), and these are all largely a function of the intensity and duration of the local vertical circulation. For example, an uplift at 2cm/s may only trigger weak heterogeneous nucleation and produce relatively few ice crystals that grow quickly to large sizes, while a 50cm/s updraft may trigger a strong homogeneous nucleation process that produces copious numbers of ice crystals which consequently experience limited growth and remain relatively small. Clearly, two regions might experience an equivalent rate of broad-scale uplift yet contain very different spectra of smaller scale vertical motions with substantial resultant differences in overall microphysical makeup, and therefore, cloud radiative properties.

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However, bin models are computationally intensive. Thus, models using bulk treatments of cirrus cloud microphysical processes are still valuable because they can be economically applied over fine grids (~ 10-50 m) to study cloud dynamics (Gierens 1996; Gierens and Jensen 1998) or over large domains (100-1000 km) to study cloud system development (Levkov et al. 1992, 1998; Heckman and Cotton 1993; Westphal et al. 1996). In particular, the bulk model approach is usually used, due to computational limitations, when investigating processes that inherently require three spatial dimensions. The bulk microphysical schemes used in such models have become increasingly more sophisticated and now typically include treatment of nucleation processes and diagnosis of the local crystal number density as well as size distribution parameters (double-moment schemes). Further improvements may be expected through the findings of bin model studies. For example, Khvorostyanov and Sassen (1998b) found that the relaxation times for ice crystal growth are significant with respect to the integration time steps used in bulk microphysics cirrus cloud models. This has implications for possible improvements in the way the phase-change adjustment is handled in bulk models. It is expected that this generation of cirrus cloud models (bulk and bin) will be applied to more fully explore the role of cloud dynamics. As described below, a key model comparison activity is occurring within this community that will do much to facilitate such progress. It involves cirrus cloud models of all types. Cirrus Model Comparison Projects The GCSS Working Group on Cirrus Cloud Systems (WG2) has embarked on a systematic comparison of cirrus cloud models. Initially, two projects are underway, the results of which are available on the World Wide Web (http://eos913c.gsfc.nasa.gov/gcss_wg2/). The first project is a comparison of dynamical cirrus cloud models, often called cloud-resolving models (CRMs), and single column models (SCMs) that are single grid-column implementations of general circulation models (GCMs) used for numerical weather forecasting and climate simulation. This Idealized Cirrus Model Comparison (ICMC) Project (Starr et al. 2000) compares the results of simulations for idealized initial conditions and cloud forcing. The second project, the Cirrus Parcel Model Comparison (CPMC) Project (Lin et al. 2000) compares simulations of ice crystal nucleation and the development of ice particle spectra under environmental conditions corresponding to the same situations considered in the ICMC Project, but limited to a closed air parcel (i.e., no exchange of heat or water with its environment) and subject to an externally specified rate of lifting (adiabatic cooling) and a common specified aerosol population associated with cloud initiation via homogeneous nucleation. The purpose of these projects is to improve models of cirrus cloud systems and the validation thereof, as well as to stimulate their use in developing cirrus cloud parameterizations for implementation in larger scale models (GCMs) used for climate studies and numerical weather prediction. Future projects of WG2 will consider a series of well-observed cirrus cloud cases.

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The ICMC Project involves simulations of cirrus formed in a resting, icesupersaturated (RHice = 120% in upper half), and conditionally neutral (with respect to ice pseudoadiabatic processes) layer. This is done for two temperature domains: a "warm" cirrus case formed at -33 to -42°C (8-9 km in 45° N spring/fall atmosphere) and a "cold" cirrus case generated at -52 to -61.5°C (13-14 km in 30° N summer atmosphere). Cloud formation is forced by the imposition of an artificial cooling corresponding to what would occur in the event of uniform adiabatic uplift at 3cm/s (25°C/day) and initiated via a random field of small (less than 0.02°C) thermal perturbations. Thus, these cases correspond to uplift of a potentially convective layer. There is neither mean horizontal flow nor vertical wind shear. Thus, purely mechanical generation of turbulence by the mean flow does not occur. The forcing is turned off after 4 h of simulation, and decay of the cloud layer is then simulated for an additional 2h. Simulations are done with infrared radiative processes included and with no radiative processes. Solar radiative processes are not considered. Cases with a stable thermal stratification in the cloud generation layer are also done. Although this project is still in progress, one early result that is pertinent here is that a significant bifurcation is found between the results of models using bulk representations of microphysical processes (e.g., Starr and Cox 1985a) and those using an explicit size-resolved treatment of the development of the ice crystal population (e.g., Lin 1997). The former tend to diagnose a significant population of large ice crystals (hundreds of microns in length) that dominate the ice water field, whereas the latter tend to be dominated by copious, small ice crystals (tens of microns) with few large crystals. The former leads to a very active ice fallout process with strong sublimation cooling of the subcloud region. Together with the previously described radiative effects, this limits buoyancy production and results in relatively weak internal cloud circulations (updrafts of 10-30cm/s). In contrast, the bin models tend to develop a significantly more vigorous internal circulation (updrafts approaching Im/s). Ice water is carried upward in the generating cells because of the smaller fallspeeds associated with smaller crystals. Thus, cloud water and infrared cooling become concentrated higher in the cloud. This is analogous to the early comparison of a cirrus simulation to an altocumulus simulation by Starr and Cox (1985b) where the primary difference in model configuration was in the specification of ice water fallspeed—much smaller for the simulation of the liquid phase altocumulus cloud (~lcm/s) compared to the cirrus simulation (-40-60 cm/s). The differences are fairly dramatic not only in the intensity of the internal circulation but also in the shape of the ice water content and radiative cooling profiles. To illustrate, profiles of IWC are show in figure 18.6a for a simulation with a model using the Starr and Cox (1985a) parameterization of ice water fallspeed versus the same model where the ice water fallspeed is limited to values less than 20 cm/s (a value comparable to the average value seen in some bin models) but otherwise the same. Here again, we see the marked difference in vertical IWC profile, with peak values occurring low in the cloud layer for the Starr-Cox parameterization but high in the cloud for the reduced ice water fallspeed (v*) run where a large difference in overall IWP is also evident. The

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Figure 18.6. Comparison of simulations of cirrus cloud layer formed in a neutrally stratified layer at night. Vertical profiles at 120min shown for (a) horizontally averaged ice water content and (b) root-mean-square vertical air velocity. Thick lines denote simulation with Starr-Cox parameterization for ice water fallspeed, and thin lines denote simulation where ice water fallspeed is limited to values of 20 cm/s or less.

difference in cloud dynamics is even more dramatic where the root-meansquare vertical motions are nearly 20 times stronger in the reduced v* run (fig. 18.6b). Corresponding fields of IWC and winds are shown in figures 18.7 and 18.8, respectively, where the differences in structure and intensity are also quite evident. The reduced v* run exhibits more organization in the circulation field in addition to being appreciably more intense. These dynamical differences are less, but still significant, in similar test simulations of vertically sheared cloud layers. A few tentative conclusions may be drawn. First, significant disparity exists between different classes of cirrus cloud models, even in terms of relatively gross measures. The disagreements are generally much less between models of a similar type (in terms of approach to treatment of microphysical processes) but not insignificant. Second, as noted by Starr and Cox (1985b), the properties

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Figure 18.7. Comparison of simulations of cirrus cloud layer formed in a neutrally stratified layer at night. Ice water content fields shown at 120 min for (A) simulation with Starr-Cox parameterization for ice water fallspeed and (B) simulation where ice water fallspeed is limited to values of 20cm/s or less. Contours on logio scale where 3 and 4 correspond to 1 and 10mg/m3, respectively.

Figure 18.8. Comparison of simulations of cirrus cloud layer formed in neutrally stratified layer at night. Vertical air velocity field shown at 120 min for (A) simulation with StarrCox parameterization for ice water fallspeed and (B) simulation where ice water fallspeed is limited to values of 20 cm/s or less. Contours at ±5, ±10, and ±15 cm/s in panel (A) and at ±50, ±100, and ±150 cm/s in panel (B). Positive contours are lighter shade.

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of cirrus clouds result from the operation of microphysical, dynamical, and radiative processes in a highly coupled manner (e.g., see figure 17.1). These processes are strongly interdependent and interactive. Third, and maybe most interesting, these results suggest potential alternative approaches to assessing model performance. The conventional assumption has been that comparison of model-simulated ice water content fields, especially horizontally averaged IWP, to observations should be used to assess model performance. However, measurement of ice water content is fraught with difficulties and remains uncertain at an unacceptable level for this purpose (±20% at best and maybe closer to a factor of 2 for cold cirrus where small crystals dominate). Moreover, the error characteristics of various measurement systems have systematic height dependencies related to the sensing limitation and the strong vertical dependence of microphysical properties in actual cirrus. For example, in-situ probes may have difficulties with either small or large crystals where the relative dominance of such crystals varies strongly with height (Heymsfield et al. 1990; Arnott et al. 1994; Miloshevich and Heymsfield 1997; chapter 4, this volume). Similarly, millimeter-wavelength cloud radar is considerably more sensitive to large crystals than to small crystals. This sensitivity to the shape of the particle size distribution and the natural variability thereof, makes retrieval of IWC uncertain, even for retrievals that incorporate information from other remote sensing tools. Consider further that IWP is strongly controlled by imposed broadscale uplift. This is an even more difficult parameter to quantitatively derive from observations, especially when the forcing is weak, as is often the case for cirrus cloud systems and at scales where the models are typically run (~10km). Small adjustments, within observational uncertainty, in the imposed forcing yield significant changes in the resultant simulated IWP. As a result, assessments using observations of IWP should be regarded as semi-quantitative given the capability to tune the model result using reasonable adjustments in the imposed vertical motion. However, the preliminary WG2 ICMC Project results suggest that analysis of in situ dynamical observations, especially perturbations of vertical velocity, may provide a useful alternative means to assess the performance of the models. Although observations of mean vertical air velocity are uncertain, high-frequency measurement of vertical motion (and temperature) perturbations are quite good. The difficulty with this approach is that nature usually presents us with rather complex situations. As described in chapter 17, a variety of generation mechanisms may coexist in a typical cirrus cloud, including mechanical as well as buoyancy generation of turbulence, and a rich background of gravity wave activity. Moreover, these processes are typically episodic or intermittent, leading to a rather complex dynamical environment as illustrated in the analysis of Demoz et al. (1998) (see chapter 17). Nevertheless, an unpublished comparison of a simulation of the case analyzed by Demoz et al. (1998) that included interleaved layers of strong and weak vertical wind shear and stable and neutral layers, yielded remarkably good agreement in terms of the scale and intensity of the small circulation features in the cloud layer, though the strong signals attributed to traveling gravity waves were absent.

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Given the fundamental disparity as to microphysical development, the recent invigoration of research on nucleation processes (chapter 5) is very welcome and should be continued or expanded. Moreover, the motivation for the CPMC Project is evident. Early results from CPMC Project have led to identification of some model deficiencies, as is also the case with the ICMC Project. In addition, the preliminary results indicate that, although there are some notable discrepancies in the case of homogeneous nucleation, the account of heterogeneous nucleation is quite divergent among the models. This process may be particularly important in situations of weak forcing, as is often the case on the broad scale. If nothing else, the above discussion illustrates that systematic comparison of models may yield unexpected results with potentially significant implications for observation and analysis strategies. More thought needs to be given to the evaluation of models and the collection and analysis of data for this purpose. 18.4. Issues and Future Work

There has been much progress in developing dynamical models of cirrus cloud systems, especially with the size-resolved treatment of cirrus microphysical processes. Cirrus models have been applied to improve understanding of various forms of cirrus over the last few years, even contrails. This extension in our interest and application has been dramatic. We are well armed with a definitive set of concepts for understanding dynamic processes in cirrus clouds, some of which have stood the test of observations and become more refined as a result. That is not to say that further conceptual breakthroughs and developments, or debunking, cannot occur. In fact, this is an area where, in our view, progress is lagging behind the models and observational capabilities. There also remain notable areas where improvements in the models are needed and where additional developments or investigations are definitely warranted. The most glaring of these needs is for rigorous quantitative validation and evaluation of models using observations. New and creative ideas on how to do this are needed. We need to seek more sophisticated and achievable tests that take maximum advantage of our observational capabilities; the obvious or "most important" comparison may not be the best measure in this regard. An excellent avenue to possibly discover these ideas is through the detailed systematic comparative analysis of model output, such as in the ICMC Project. Aerosols and their impact on cirrus cloud development must be more rigorously established because of their potentially strong effects on all aspects of cirrus cloud makeup and properties, including cloud dynamical processes. Specifically, we need to confirm the validity of and/or improve present treatments of the role of aerosols, nucleation processes, and crystal growth. Although there is more general agreement about homogeneous nucleation, heterogeneous nucleation may also be important since predictions of cloud particle number density seem

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too large in comparison to observations, even though the latter have been revised upward by a significant amount in recent years. Recent observations suggest that aerosols of complex makeup are prevalent in the upper troposphere (Murphy et al. 1998). Further progress in laboratory work (see chapter 5) and in-situ observations is needed to support this requirement. Systematic efforts to compare and evaluate models, such as the CPMC Project, are also essential to identify key testable aspects and parameters, which may not be those that one would expect a priori. Because of the importance of local radiative effects in modulating internal cloud circulation, the internal radiative fields must be accurately represented in a dynamic cirrus cloud model. Yet even the overall solar absorptance of clouds is in question (Stephens and Tsay 1990; Harshvardhan et al. 1996; see also chapter 13, this volume), much less the internal structure of the radiative forcing. In particular, we need strong observational confirmation of the treatment of incloud solar absorption, and evaluation of three-dimensional radiative transfer effects at infrared and, especially, at solar wavelengths, including zenith angle dependencies. Without further information, modelers will tend to remain focused on nighttime (no solar) simulations as their most trusted results, which is at variance with the need for model validation using observations which are typically made during daytime, at least for the in situ observations. It has been proposed that two-dimensional (2-D) turbulence (chapter 17) plays a significant role in organizing cirrus cloud systems. This mechanism needs to be demonstrated in a credible fashion and quantitatively analyzed. In particular, we need modeling studies that incorporate 2-D (x, v) turbulence and cirrus cloud processes. To handle generation of 2-D turbulence and to investigate the relationship to cirrus cloud systems, a three-dimensional model of regional scale is required. Yet, a high-resolution model is desired to adequately treat cloud dynamical processes. Use of a large-eddy simulation (LES) cirrus model nested within a larger-scale regional model seems a promising approach (e.g., Heckman and Cotton 1993). Models capable of treating this problem now exist but need to demonstrate that the interfaces between the domains are well handled, as this can be a very challenging aspect. Similarly, we need to understand the interactions of cirrus cloud systems with propagating gravity waves over a range of scales. One of the most characteristic properties of the upper troposphere is the presence of vertical wind shear. In particular, cirrus clouds are associated with the jet stream, where strong shear is prevalent, though there is some evidence to suggest that shallow, embedded cirrus-generating layers may have little or no vertical wind shear in some cases, despite the overall situation. At this time, most reported cirrus modeling studies (cited here) are done in a 2-D framework, though the model may be reported as 3-D capable. To some extent, this has been dictated by computational limitations as the treatment of size-resolved microphysics and advanced radiation codes are computationally demanding. The 3-D studies have predominantly been done with regional-scale models with bulk microphysics, albeit with fairly sophisticated parametric treatments of size distribution (Heckman and Cotton 1993; Levkov et al. 1998). Though the effects of vertical wind shear are included, in-cloud dynamical processes are typically not well

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resolved in comparison to LES models. An issue that needs to be addressed is the applicability of 2-D dynamical models for cirrus cloud simulations in comparison to 3-D LES models, including size-resolved microphysics. This needs to be done for nonsheared and vertically sheared environments. The difficulty here is partly attributable to the rather large horizontal domain size required to perform a simulation of a sheared environment without undue influence by the boundary conditions, which are never perfect. Because of the climatic importance of tropical cirrus (see chapter 15) and the presumed important role of deep convection in producing these clouds (see chapter 16), studies of tropical cirrus clouds are desperately needed. Cirrus cloud production can be either directly through detrainment of ice and water vapor or indirectly through the later formation of cirrus from the vapor enhancement resulting from the decay of anvil cloud systems. Theories of cirrus anvil development and evolution have been proposed (described earlier), as have theories of the shield of subtropopause thin cirrus that is observed over the tropics (e.g., Jensen et al. 1996b). At present, these must be regarded as somewhat uncertain. Model simulations have not been terribly successful in resolving the basic physical mechanisms responsible for these clouds. The central need is for observations and model studies of tropical cirrus systems, especially in relationship to deep convective cloud systems and the broad-scale forcing. In particular, these observations need to resolve the structure and makeup of these clouds at fairly high resolution to test the existing models. The model studies should be fairly comprehensive (i.e., including both the deep convective and cirrus cloud components). Finally, improvements in the capability to observe cloud physical properties and the environmental conditions associated with cirrus cloud systems are still needed. The most obvious requirement is for reliable and accurate measurements of ice water content. Improvements in measurements of ambient humidity and aerosols are also sorely needed. In addition to the present capability for uplooking or down-looking remote sensing, side-scanning (e.g., ±20° from horizontal) airborne systems might give new, enlightening perspectives on cirrus clouds. For example, snapshot characterization of the IWC, dynamical, thermal, and humidity fields in a volume (aircraft motion for third dimension) would provide a most useful advancement. This is simply not achievable with present in-situ probes or fixed-view remote sensors. Such 3-D renderings would provide a fairly definitive test for our models, even if limited to only one or two of the essential parameters, such as IWC or winds.

Acknowledgments We acknowledge the many interactions with our colleagues and especially the FIRE and ICE/EUCREX Science Teams. In particular, we have benefited from many insightful discussions with Ken Sassen, University of Utah, on these issues. Andrew Lare helped in preparing the manuscript and figures. The support provided to M.Q. by Prof. Raschke of GKSS is greatly appreciated. Some of the work presented here was financially supported by the Climate and Environment Program of the European Union and the NASA Radiation Sciences Program, the latter under the capable leadership of Robert Curran and his predecessor, Tim Suttles, at NASA HQ.

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References Arnott, W.P., Y. Dong, J. Hallett, and M.R. Poellot, 1994. Role of small ice crystals in radiative properties of cirrus: A case study. FIRE II, November 22,1991. J. Geophys. Res., 99,1371-1381. Browning, K.A., A. Betts, P.R. Jonas, R. Kershaw, M. Manton, P.J. Mason, M. Miller, M.W. Moncrieff, H. Sundqvist, W.K. Tao, M. Tiedke, P.V. Hobbs, J. Mitchell, E. Raschke, R.E. Stewart, and J. Simpson, 1994. The GEWEX Cloud System Study (GCSS). Bull Amer. Meteor. Soc., 74, 387-399. Demoz, B.B., D.O'C Starr, K.R. Chan, and S.W. Bowen, 1998. Wavelet analysis of dynamical processes in cirrus. Geophys. Res. Lett., 25 (9), 1347-1350. Gierens, K.M., 1996. Numerical simulations of persistent contrails. /. Atmos. ScL, 53, 3333-3348. Gierens, K., and E. Jensen, 1998. A numerical study of the contrail-to-cirrus transition. Geophys. Res. Lett., 25,4341-4344. Gu, Y., and K.N. Liou, 2000. Interactions of radiation, microphysics, and turbulence in the evolution of cirrus clouds. /. Atmos. ScL, 57,2463-2479. Gultepe, I., D.O'C. Starr, A.J. Heymsfield, T. Uttal, T. Ackerman, and D.L. Westphal, 1995. Dynamical characteristics of cirrus clouds from aircraft and radar measurements in micro and meso-y scales. /. Atmos. Sci., 52,4060-4078. Harshvardhan, W. Ridgway, V. Ramaswamy, S.M. Freidenreich, and M. Batey, 1996. Solar absorption in cloudy atmospheres. Preprint Volume, Seventh Symposium on Global Change Studies, Atlanta, Georgia. American Meteorological Society, Boston, MA, pp. 127-134. Heckman, S.T., and W.R. Cotton, 1993. Mesoscale simulation of cirrus clouds—FIRE case study and sensitivity analysis. Mon. Wea. Rev., 121,2264-2284. Heymsfield, A.J., 1975a. Cirrus uncinus generating cells and the evolution of cirriform clouds. Part I: Aircraft observations of the growth of the ice phase. /. Atmos. Sci., 32, 799-808. Heymsfield, A.J., 1975b. Cirrus uncinus generating cells and the evolution of cirriform clouds. Part II: The structure and circulation of the cirrus uncinus generating head. /. Atmos. Sci., 4, 809-819. Heymsfield, A.J., 1975c. Cirrus uncinus generating cells and the evolution of cirriform clouds. Part II: Numerical computations of the growth of the ice phase. /. Atmos. Sci., 4,820-830. Heymsfield, A.J., 1977. Precipitation development in stratiform ice clouds: A microphysical and dynamical study. /. Atmos. Sci., 34, 367-381. Heymsfield, A.J., and R.G. Knollenberg, 1972. Properties of cirrus generating cells. J. Atmos. Sci., 29,1358-1366. Heymsfield, A.J., K.M. Miller, and J.D. Spinhirne, 1990. The 27-28 October 1986 FIRE cirrus case study: Cloud microstructure. Mon. Wea. Rev., 118,2313-2328. Heymsfield, A.J., and R.M. Sabin, 1989. Cirrus crystal nucleation by homogeneous freezing of solution droplets. /. Atmos. Sci., 46,2252-2264. Jensen, E.J., O.B. Toon, L. Pfister, and H. Selkirk, 1996a. Dehydration of the upper troposphere by subvisual cirrus clouds near the tropical tropopause. Geophys. Res. Lett., 23,825-828. Jensen, E.J., O.B. Toon, H. Selkirk, J.D. Spinhirne, and M.R. Schoeberl, 1996b. On the formation and persistence of subvisual cirrus clouds near the tropical tropopause. J. Geophys. Res., 101,21361-21375. Jensen, E.J., O.B. Toon, A. Tabazadeh, G.W. Sachse, B.E. Anderson, K.R. Chan, C.W. Twohy, B. Gandrud, S.M. Aulenbach, A.J. Heymsfield, J. Hallett, and B. Gary, 1998. Ice

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nucleation processes in upper tropospheric wave clouds during SUCCESS. Geophys. Res. Lett., 25,1363-1366. Jensen, E.J., O.B. Toon, D.L. Westphal, S. Kinne, and A.J Heymsfield, 1994a. Microphysical modeling of cirrus. Part I: Comparison with 1986 FIRE IFO measurements. /. Geophys. Res., 99-D5,10421-10442. Jensen, E.J., O.B. Toon, D.L. Westphal, S. Kinne, and A.J. Heymsfield, 1994b. Microphysical modeling of cirrus. Part II: Sensitivity studies. /. Geophys. Res., 99-D5, 1044310454. Khvorostyanov, V.I., and K. Sassen, 1998a. Cirrus cloud simulation with explicit microphysics and radiation: Part I. Model description. /. Atmos. ScL, 55, 18081821. Khvorostyanov, V.I., and K. Sassen, 1998b. Cirrus cloud simulation with explicit microphysics and radiation: Part II. Microphysics, vapor and ice mass budgets, and optical and radiative properties. /. Atmos. ScL, 55,1822-1845. Khvorostyanov, V., and K. Sassen, 1998c. Cloud model simulation of a contrail case study: Surface cooling against upper tropospheric warming. Geophys. Res. Lett., 25, 21452148. Lawson, R.P., A.J. Heymsfield, S.M. Aulenbach, and T.L. Jensen, 1998. Shapes, sizes and light scattering properties of ice crystals in cirrus and a persistent contrail during SUCCESS. Geophys. Res. Lett, 25,1331-1334. Levkov, L., B. Rockel, H. Kapitza, and E. Raschke, 1992. 3-D mesoscale numerical studies of cirrus and startus by their time and space evolution. Contr. Atmos. Phys., 65,35-58. Levkov, L., B. Rockel, H. Schiller, and L. Kornblueh, 1998. 3-D simulation of clouds with subgrid fluctuations of temperature and humidity. Impact of primary nucleation parameterizations on the formation and maintenance of cirrus. Atmos. Res., 47-48, 327-341. Lilly, O.K., 1989. Cirrus outflow dynamics. /. Atmos. ScL, 45,1594-1605. Lin, R.-R, 1997. A numerical study of the evolution of nocturnal cirrus by a twodimensional model with explicit microphysics. PhD dissertation. Pennsylvania State University, State College. Lin, R.-F., and T.P. Ackerman, 1998. Numerical simulations of cirrus anvils in nighttime conditions by a two-dimensional cloud resolving model with explicit microphysics. In Preprint Volume, Conference on Cloud Physics, Everett, Washington. American Meteorological Society, Boston, MA, pp. 57-59. Lin, R.-F, D.O'C. Starr, P.J. DeMott, R. Cotton, E. Jensen, and K. Sassen, 2000. Cirrus Parcel Model Comparison Project Phase 1. Proceedings, 13th International Conference on Clouds and Precipitation, 14-18 August 2000, Reno, Nevada, 1221-1224. Ludlam, F.H., 1956. The forms of ice clouds, II. Quart. J. Roy. Meteor. Soc., 74,39-56. Ludlam, F.H., 1980. Clouds and Storms. The Behavior and Effect of Water in the Atmosphere. Pennsylvania State University, State College. Mace, G.G., D.O'C. Starr, T.P. Ackerman, and P. Minnis, 1995. Examination of coupling between an upper tropospheric cloud system and synoptic-scale dynamics diagnosed from wind profiler and radiosonde data. /. Atmos. ScL, 52,4094-4127. Miloshevich, L.M., and A.J. Heymsfield, 1997. A balloon-borne continuous cloud particle replicator for measuring vertical profiles of cloud microphysical properties: Instrument design, performance and collection efficiency analysis. /. Atmos. Ocean Tech., 14, 753-768. Mitchell, D.L., and W.P. Arnott, 1994. A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part II: Dependence of absorption and extinction on ice crystal morphology. /. Atmos. ScL, 51,817-832.

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Murphy, D.M., D.S. Thompson, and M.J. Mahoney, 1998. In situ measurements of organics, meteoric material, mercury, and other elements in aerosols at 5 to 19 kilometers. Science, 282,1664-1669. Oddie, B.C.V., 1959. Some cirrus observations made by the Westminster Shiant Isles Expedition. Weather, 4,204-208. Plank, V.G., D. Atlas, and W.H. Paulsen, 1955. The nature and detectability of clouds and precipitation as determined by 1.25 centimeter radar. /. Meteor., 12,358-378. Quante, M., and P.R.A. Brown, 1992. Turbulence in different types of cirrus clouds. In Proceedings of the llth ICCP, 10-14 August, Montreal, Atmospheric Environment Service, Toronto, Canada vol. I, pp. 510-513. Quante, M., P.R.A. Brown, R. Baumann, B. Guillemet, and P. Hignett, 1996. Three aircraft intercomparison of dynamical and thermodynamical measurements during the PreEUCREX campaign. Contr. Atmos. Phys., 69,129-146. Raschke, E., 1988. The international satellite cloud climatology project, ISCCP, and its european regional experiment ICE (International Cirrus Experiment). Atmos. Res., 21,191-201. Raschke, E., P. Flamant, Y. Fouquart, P. Hignett, H. Isaka, PR. Jonas, H. Sundquist, and P. Wendling, 1998. Cloud-radiation studies during the European cloud and radiation experiment (EUCREX). Surveys Geophys., 19, 89-138. Reuss, J.H., 1963. Wolken-StereomeBbildreihen I: Cirren in vertikaler Windscherung. Contr. Phys. Atmos., 36,173-188. Sassen, K., D.O'C. Starr, and T. Uttal, 1989. Mesoscale and microscale structure of cirrus clouds: Three case studies. /. Atmos. Sci., 46,371-396. Sassen, K., and G.C. Dodd, 1989. Haze particle nucleation simulations in cirrus clouds, and applications for numerical modeling and lidar studies. J. Atmos. Sci., 46, 30053014. Sassen, K., C.J. Grund, J.D. Spinhirne, M. Hardesty, and J.M. Alvarez, 1990a. The 27-28 October 1986 FIRE cirrus case study: A five lidar overview of cloud structure and evolution. Mon. Wea. Rev., 118,2288-2311. Sassen, K., AJ. Heymsfield, and D.O'C. Starr, 1990b. Is there a cirrus small particle anomaly? In Preprint Volume, Conference on Cloud Physics, San Francisco, California. American Meteorological Society, Boston, MA, pp. J91-J95. Sassen, K., and V.I. Khvorostyanov, 1998. Radar probing of cirrus and contrails: Insights from 2D model simulations. Geophys. Res. Lett., 25, 975-978. Sassen, K., D.O'C. Starr, G.G. Mace, M.R. Poellot, S.H. Melfi, W.L. Eberhard, J.D. Spinhirne, E.W. Eloranta, D.E. Hagen, and J. Hallett, 1995. The 5-6 December 1991 FIRE IFO II jet stream cirrus case study: The influence of volcanic aerosols. /. Atmos. Sci., 52, 91-123. Smith, W.L. Jr., P.F. Hein, and S.K. Cox, 1990. The 27-28 October 1986 FIRE cirrus case study: In situ observations of radiation and dynamic properties of a cirrus cloud layer. Mon. Wea. Rev., 118,2389-2401. Starr, D.O'C., 1987a. A cirrus cloud experiment: Intensive field observations planned for FIRE. Bull. Amer. Meteoro. Soc., 68,119-124. Starr, D.O'C, 1987b. Effects of radiative processes in thin cirrus. /. Geophys. Res., 92, 3973-3978. Starr, D.O'C., and S.K. Cox, 1985a. Cirrus clouds, Part I: A cirrus cloud model. J. Atmos. Sci., 42,2663-2681. Starr, D.O'C, and S.K. Cox, 1985b. Cirrus clouds, Part II: Numerical experiments on the formation and maintenance of cirrus. /. Atmos. Sci., 42,2682-2694. Starr, D.O'C., and D.P. Wylie, 1990. The 27-28 October 1986 FIRE cirrus case study: Meteorology and clouds. Mon. Wea. Rev., 118,2259-2287.

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Starr, D.O'C, A. Benedetti, M. Boehm, P.R.A. Brown, K.M. Gierens, E. Girard, V. Giraud, C. Jakob, E. Jensen, V. Khvorostyanov, M. Koehler, A. Lare, R.-F. Lin, K.-I. Maruyama, M. Montero, W.-K. Tao, Y. Wang, and D. Wilson, 2000. Comparison of Cirrus Cloud Models: A Project of the GEWEX Cloud System Study (GCSS) Working Group on Cirrus Cloud Systems. Proceedings, 13th International Conference on Clouds and Precipitation, 14-18 August 2000, Reno, Nevada, l-b. Stephens, G.L., and S.-C. Tsay, 1990. On the cloud absorption anomaly. Quart. J. Roy. Meteor. Soc, 116, 671-704. Stephens, G.L., S.-C. Tsay, P.W. Stackhouse, and P.J. Flatau, 1990. The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback. /. Atmos. ScL, 47,1742-1753. Westphal, D.L., S. Kinne, P. Pilewskie, J.M. Alvarez, P. Minnis, D.F. Young, S.G. Benjamin, W.L. Eberhard, R.A. Kropfli, S.Y. Matrosov, J.B. Snyder, T.A. Uttal, A.J. Heymsfield, G.G. Mace, S.H. Melfi, D.O'C. Starr, and B.J. Soden, 1996. Initialization and validation of a simulation of cirrus using FIRE-II data. /. Atmos. Sci., 53,3397-3429. Yagi,T.,T. Harimaya, and C. Magono, 1968. On the shape and movement of cirrus uncinus clouds by the trigonometric method using stereophotographs-studies of cirrus clouds: Part II. /. Meteor. Soc. Japan, 46,266-271. Yagi, T, 1969. On the relation between the shape of cirrus clouds and the static stability of cloud level-studies of cirrus clouds: Part IV. /. Meteor. Soc. Japan, 47,59-64.

19

Microphysical Processes in Cirrus and Their Impact on Radiation A Mesoscale Modeling Perspective

VITALY I.

KHVOROSTYANOV

K E N N E T H SASSEN

19.1. Lessening the Uncertainties in Cirrus Radiative Effects

The impact of cloudiness on the global radiative budget and its climatic consequences have been widely discussed during the last three decades. It was gradually recognized that the climatic effect of cloudiness depends on its height: low- and middle-level cloudiness have a total cooling effect on the Earth climatic system, while the upper-level clouds, cirrus, may have mostly a warming effect (IPCC 1995). The net effect of cirrus (i.e., warming or cooling), is much less clear because neither their microphysical and optical properties, nor the processes that govern their formation, are well understood and parameterized in climate models. These uncertainties have stimulated several major field projects performed within the International Satellite Cloud Climatology Project (ISCCP; Rossow and Schiffer 1991) with subsequent data analysis reports [e.g., FIRE IFO-I (1990), FIRE IFO-II (1995), and EUCREX (Raschke et al. 1996)]. The relevant theoretical works, and even the simplest climate models, indicate that the climatic impact of cirrus depends on their microstructure: clouds composed of small crystals with effective radii less than about 16 um have a total cooling effect, but clouds of larger crystals have a warming effect (Stephens et al. 1990). It was shown that the total cloud forcing at the top of the atmosphere (TOA) is positive from a few to a few tens of watts per square meter for the large crystals and decreases with decreasing crystal radius (Fu and Liou 1993). Most of the previous theoretical studies of cirrus radiative properties, after choosing some model of microphysics and some values for the mass extinction and absorption 397

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coefficients, then prescribed them to the whole cloud, neglecting any vertical variations. Simulations with general circulation models (GCMs) showed that cirrus clouds with their optical properties parameterized in such a way (i.e., constant with height) have a total warming effect and positive feedbacks with respect to greenhouse gas-induced global warming (e.g., Ramanathan et al. 1983; Wetherald and Manabe 1988). Today, the estimation of the warming/cooling effect of cirrus has become even more complicated due to two factors. First, for many years the usual in situ probes allowed the measurement of ice crystals with radii only larger than 25-50 |Lim, so the smallest and most optically and radiatively active crystals were unresolved. Second, both experimental data (e.g., Sassen et al. 1989, 1995; Heymsfield and Miloshevich 1995; Heymsfield et al. 1990) and comprehensive studies of the cirrus life cycles with various numerical models (e.g., Starr and Cox 1985; Heckman and Cotton 1993; DeMott et al. 1994; Jensen et al. 1994; Mitchell 1994) showed that crystal radii generally increase downward in cirrus clouds. Thus, ice crystals of various sizes are contained in each vertical column. Because cirrus optical properties appear to vary fundamentally in the vertical, different cirrus layers could have different warming or cooling effects, and whether one characteristically dominates remains unclear. It is encouraging that advanced GCMs have begun to incorporate the prognostic equations for liquid and ice water contents and parameterizations for cloud microphysics and optical properties and applied them in particular to the assessment of cirrus radiative effects (e.g., Sundquist 1993; Kiehl and Zander 1995; Jacob and Morcrett 1995; Fowler et al. 1996). Nonetheless, such schemes can be improved based on cloud-resolving model findings. Khvorostyanov and Sassen (1998a,b) used a cloud model with explicit spectral microphysics to simulate the development of a cirrus case and its microphysical, optical, and radiative properties with account for the aforementioned effects of small crystals and the vertical inhomogeneity in optical coefficients. The three main findings of this study were: (1) due to the vertical inhomogeneity of the crystal mean radius, the mass extinction and absorption coefficients cannot be characterized by a mean value, but rather display variable vertical profiles; (2) with account for these profiles, the albedo effect becomes much stronger and near local noon overwhelms the greenhouse effect, so that the total effect is cooling near midday; and (3) a large amount of the supersaturation, comparable to the ice water content (IWC), remains uncondensed because the process of deposition in cirrus is rather slow. The condensation process is determined by a characteristic time, t/c, of supersaturation absorption, which, according to Khvorostyanov and Sassen's (1998a,b) model results, vary from 0.5 to 3h, in contrast to many liquid clouds, where it is 1-10 s, and condensation is practically instantaneous (Cotton and Anthes 1989; Pruppacher and Klett 1997). The results in Khvorostyanov and Sassen (1998a,b) were obtained for one particular cirrus case and their generality was unclear. For example, one could ask how the results depend on the initial temperature and humidity profiles and mechanisms of crystals nucleation, or how the time of day influences the radiative fluxes and the relation between the albedo and greenhouse effects. Thus,

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what can we expect as to the climatic impact of a variety of cirrus cloud systems? In this chapter we provide some initial insight into these important uncertainties by summarizing the results of three distinct cirrus cases with different initial inputs—two warm cases and one cold case. The sensitivity of cirrus properties is studied with respect to (1) two different mechanisms of heterogeneous nucleation (first warm case); (2) competition between homogeneous and heterogeneous nucleation, and the effects of long-wave (LW) and shortwave (SW) radiation on cloud properties (second warm case); (3) effect of temperature on microphysical and radiative properties (third case); and (4) the effect of different cirrus on radiative fluxes and cloud forcing, with radiative calculations over the 24-h diurnal cycle (cases 1-3). Based on these results, some recommendations for simple but reasonable parameterizations of the cirrus mass balance and optical properties are proposed that can be incorporated into cloud bulk models and GCMs. 19.2. Model Description

The cloud model relied on here can be run in 1D/2D/3D (one-dimensional, twodimensional, or three-dimensional) modes and has been applied to various cloud types (Khvorostyanov 1995). Its development for application to the specific conditions in cirrus clouds was described by Khvorostyanov and Sassen (1998a). Since then, two important model improvements have been made: an explicit evaluation of the size spectra of deliquescent aerosols (haze particles), and a new description of one of the most important processes in cirrus, homogeneous nucleation. Because the model has already been described in detail, we provide here only a brief description with emphasis on the new elements. The model generally contains seven basic kernels: (1) mesoscale dynamics; (2) transport of cloud condensation nuclei (CCN) and ice nuclei (IN); (3) formation of the size spectra of deliquescent submicron aerosol (haze particles); (4) homogeneous and heterogeneous nucleation of crystals; (5) cloud microphysics (kinetic equation for the crystal size spectra and for the droplet spectra if the liquid phase forms) and thermodynamics (temperature, humidity and supersaturation); (6) long-wave radiation; and (7) solar radiation. This approach allows detailed calculations of the phase transformations and dynamics, precipitation, and the optical and radiative characteristics of the simulated cirrus clouds, as outlined below. 19.2.1. Microphysics and Thermodynamics Because cirrus ice crystals are mostly axially symmetric, we approximate the crystals as spheroids with axes (r,, /, /) and describe the crystal size distributions over the one (major or minor) axis, r,-, which can be called the equivalent radius when we consider the volume equivalent sphere. The crystal shapes can be accounted for by specifying the axis ratio ^, = //r,-. In the general 3-D case, the kinetic equation for the crystal size distributions, /•(*, y, z, t, r,-), can be written in the form (e.g., Khvorostyanov and Sassen 1998a):

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Here x, y,_z are the coordinates, t is time, rt is the crystal radius, vfa) is terminal velocity, A is the operator of turbulent diffusion, and U = («, v, w) is the vector of the wind speed. The last four terms on the right-hand-side of equation 1 describe the microphysical processes: nucleation, deposition or sublimation, coagulation, and the multiplication of particles, respectively. These processes are evaluated, or parameterized, as described below. The second of these terms describes the growth or evaporation by vapor diffusion of the mass mt - (47C/3)plr^ with the growth rate, rh of the axes r, of a crystal:

where D is the water vapor diffusion coefficient; pfl and p; are the density of air and ice; F ~ 1, 8,: = q - qsi, the supersaturation over ice; q and qsi are the specific humidity and saturation humidity over ice; kfi = Ce/rh the electrical capacity factor; Ce is the crystal shape factor defined from the electrostatic analogy (Ce = r, for spheres), and Fkin and Fven are the kinetic and ventilation factors (Pruppacher and Klett 1997). Fields of the potential temperature, 6, and humidity, q, are calculated with the usual equations accounting for the wind and turbulent transport, phase transitions, radiative heating rates. The integral deposition/sublimation rate, ec(, can be expressed via a size distribution function and the growth rate of a crystal using equation 2 (see Khvorostyanov and Sassen 1998a):

where Nf and r, are the crystal concentration and mean radius, and ifc is the characteristic supersaturation absorption time for crystals. This "condensation time" was analyzed with respect to supersaturation relaxation by Kachurin (1953), Twomey (1959), Sedunov (1965, 1974), Mazin (1968), and more recently by Khvorostyanov and Curry (1999a) for liquid clouds, and probably for the first time in detail by Khvorostyanov and Sassen (1998b) for crystalline cirrus clouds. Because the supersaturation term is present in equations 1-3, the integraldifferential supersaturation equation is solved in this model at every time step. 19.2.2. Ice Nucleation The term (dfi/dt)nud in equation 1 describes nucleation of ice crystals, which is divided into the two main modes of homogeneous and heterogeneous freezing, or Jc = Jhcom + /?et.

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Homogeneous nucleation rate A further development of the classical theory of homogeneous nucleation as described in Khvorostyanov and Sassen (1998c) is used in this model. The nucleation rate, Jk (cm3/s) is determined via (Pruppacher and Klett 1997):

where AFacf is the activation energy for diffusion across the liquid-ice boundary; AFg is the critical energy of ice germ formation; pw is the density of water; k and h are the Boltzmann's and Planck's constants, respectively; ai/s is the surface tension at the ice and water (or solution) interface; Nc is the number of molecules in contact with a unit area of ice; and T is the droplet temperature. Integrating the condition of equilibrium for the three-phase system, i.e., water vapor plus an aqueous solution (haze particle) containing an ice germ (Pruppacher and Klett 1997), simple analytical expressions for the critical germ radius, rg, and AFg with account for the solution and curvature effects were derived in Khvorostyanov and Sassen (1998c):

where Sw is the saturation ratio over water; T0 is the triple point (273. 15 K); G(T) = RuTIMwLmef(T), a dimensionless parameter (G ~ 0.6 at T = -50°C); Mw is the molecular weight of water; Ru is the universal gas constant; and Lmef(T) is the effective melting heat obtained after integration over T. A similar expression for rg was used by Tabazadeh et al. (1997), but with water activity, aw, in the denominator instead of our Sw. The term aw accounts for solution effects, and because we also accounted for curvature effects, the combination of these two allowed us to simplify the equation for rg and express it directly via Sw. The T-dependencies of Lm, AFact, and o;/s were found by DeMott et al. (1994), Jensen et al. (1994), Pruppacher and Klett (1997), Jeffery and Austin (1997), Tabazadeh et al. (1997), and Khvorostyanov and Sassen (1998c) from experimental and theoretical results. Below, we use the equation fits from Khvorostyanov and Sassen (1998c). Equation 6 for rg contains two particular cases of classical homogeneous nucleation theory. First, at T —» T0 (slightly below 0°C), it is simplified to rg - 2a;/5/(JRvrpilnS'w), the expression of Kelvin (1870; see Pruppacher and Klett 1997) for the homogeneous nucleation of a crystal (or droplet) directly from the vapor. Second, for pure water droplets at Sw = 1, equation 6 transforms into rg = 2oi/i/[Lmpjln(r0/r)], the classical expression of J. J. Thompson (1882; see Pruppacher and Klett 1997) for nucleation by the freezing of supercooled water. Thus, our new equation 6 unifies these two cases and, being derived from general principles, represents a generalization of the classical homogeneous nucleation

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theory for three-phase systems. Along with equation 5 for Jk, they provide the description of homogeneous freezing for haze particles in cirrus (Sw < 1), droplets of pure water (Sw = 1), and the high supersaturations (Sw » 1), as might be found at the initial stage of contrail formation. Being simple, they are in a good agreement with previous models and measurements of/ fa ( J) over a wide T-range (see Khvorostyanov and Sassen 1998c) and can be used in cloud models. Size spectra of deliquescent aerosol (haze particles) To save computer resources, our representation of the spectra of deliquescent haze, f(rh}, is based on the simple yet accurate analytical aerosol model that includes hygroscopic growth developed in Khvorostyanov and Curry (1999b). We assume that the size spectrum of a dry aerosol can be described by the Junge size distribution, fs(rs} ~ r'^ with index u,, normalized to the total concentration, N, in the region rmin = 0.1 um < rs < rmax = lum, which represents the major contribution to the crystal nucleation rate. The soluble mass, ras, is parameterized in the form ms = em(4/3)7cps(vf(1+p) (Sedunov 1974), where em is the soluble fraction of a nucleus, and the parameter P depends on the chemical composition and physical properties of an aerosol: for example, ms ~ rs3 for p = 0.5, and ms ~ rs2 for P = 0. Although P generally varies with radius, we assume for simplicity a constant value for the submicron aerosol fraction, and consider in more detail the most important case for P = 0.5. Under these assumptions, the wet spectrum //,(/>,) for the case of subsaturation was derived as (Khvorostyanov and Curry 1999b):

Here #s/a is Kelvin's curvature parameter at the solution-air interface; b depends on chemical composition; jiwet is the power index for the wet aerosol; and the index R determines explicitly the relative humidity dependence of the size spectrum:

where Ox is the osmotic coefficient; v is the number of ions in solution; Ms is the molecular weight of the soluble fraction, and p^ is its density; as = I for p = 0.5. The distribution (equation 7) is a superposition of two power laws by radii with indices u.wet and (u,wet + 1). The parameter R - 1 for p = 0.5 and (j, = 4 (a typical value for the Junge index); thus the particle sizes in the whole spectrum grow with increasing humidity as (1 - Sw)~l (see Khvorostyanov and Curry 1999b). Equations 7-8 allow the calculation of the haze particle size spectra with various chemical compositions and em. Typical parameters for substances that serve as nuclei in cirrus are as follows. For ammonium sulfate, v<E>5 = 2 at Sw > 0.85-0.95, Ms = 132, ps = 1.77 g/cm3, and b = 0.505 if £m = 1 (fully soluble nuclei), and b = 0.25 for em = 0.5 (for 50% soluble material). For sulfuric acid, Ms = 98, p, = 1.83g/cm3, and, assuming O5 ~ 1, then b = 1.01. The integral nucleation rate is calculated by

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integration of the individual rate, 7fa, in equation 5 with the haze size spectrum of equation 7. Heterogeneous nucleation rate Parameterizations of this process are usually based on various results of laboratory and field measurements (see reviews in DeMott et al. 1994; Pruppacher and Klett 1997). Because a unified theory of heterogeneous nucleation does not exist, we have tested two methods in the model. The first is based on Fletcher's (1962) dependence of the IN temperature activation spectrum, 7V/(7) = aF- exp[+6X?o - T)] with the standard values aF = lO^/L1, bF = 0.6/K (hereafter "T-type activation"), and incorporation of the Sassen (1992) height-dependency correction, exp(-A5z), (where As = 0.75/km) in the nucleation rate (see Khvorostyanov and Sassen 1998a). The second method uses the parameterization of Meyers et al. (1992) based on cloud chamber experiments: Nt = exp(a + 68,), with a = -0.639 and b = 0.1296 if 8, is in percent (hereafter "8-type activation"). 19.2.3. Solution Algorithm The system of equations for thermodynamics and microphysics is solved by the splitting method as described in Khvorostyanov and Sassen (1998a). The fields of T, q, and ^(r,) at one model time step, Af, are calculated (split) in six substeps: the first three account for the transport along the jc, y, and z axes (the only two substeps in a 2-D model), the fourth for the adjustment of the fields (condensation/evaporation), the fifth for the coagulation processes, and the sixth substep for the nucleation of new crystals. During the fourth substep, the growth/ evaporation of crystals by deposition/sublimation is calculated after a transition to the equation for supersaturation with respect to ice, 8,. After the removal of space variables, it can be written for the three-phase system containing water vapor, crystals, and droplets (if the liquid phase forms), as described in Khvorostyanov and Sassen (1998a). In this study, we consider processes without vigorous updrafts or the liquid phase. So, we can write the supersaturation equation for the pure crystalline cloud as

where T/C is the ice crystal supersaturation relaxation time, (37/3f)rad is the radiative heating rate, and ja is the adiabatic temperature gradient. The first term on the right-hand side describes relaxation (decrease) of supersaturation due to absorption by hydrometeors, and the second term describes generation of supersaturation due to positive vertical velocity and radiative cooling. Because supersaturation is a small difference between two large values (q and qsi), an approach based on the evaluation of supersaturation seems more precise than the calculation of humidity directly. It might sometimes be useful to rewrite this equation in the form:

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where 5, = 8,-/
where jw is the wet adiabatic gradient; cp is the specific heat capacity; Le is the sublimation heat; and "the effective radiative velocity," wrad = -(7/yfl)(377dr)rad is introduced (Khvorostyanov and Curry 1999a), which allows the simple comparison of dynamic and radiative effects. For example, LW cooling of -lOK/day corresponds to wiad = 1.2cm/s. The tables of 8eq and ifc, which may vary from a few seconds to >1000h for various Nh rh and various cloud types, are given in Khvorostyanov and Sassen (1998b). During the fifth substep, the growth by the accretion of crystals is calculated according to stochastic collection equations (Cotton and Anthes 1989), and during the sixth and final substep ice nucleation is calculated. Having the distribution functions, fh many characteristics can be calculated as the integrals (moments) over the size spectra at each grid point and time step, such as ice water content (IWC), Nt, mean and effective radii, radar and lidar reflectivities, absorption and extinction coefficients, optical thickness and emissivity, and the integral terminal velocities. The model also allows for the detailed evaluation of the supersaturation budget (generation and absorption rates) along with the crystal mass budget: the gravitational flux of crystals (precipitation rate), the regular flux due

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to vertical velocities, the turbulent flux, and the total budget of crystal mass (see examples in Khvorostyanov and Sassen 1998b). 19.2.4. Dynamics The mesoscale dynamics (M, w) in the 2-D model version are calculated in the vertical x-z plane with use of equations for the vorticity, t|, and Poisson equation for the streamfunction, \j/. 19.2.5. Long-wave and Solar Radiation The radiative fluxes, heating rates, and cloud forcing are calculated in the twostream approximation with 31 wavelengths in the SW and 4 bands in the LW spectra (Khvorostyanov and Sassen 1998a). The mass absorption, ccmabs, and scattering, omsc, coefficients are calculated at each grid point using analytical formulae based on anomalous diffraction theory (ADT; van de Hulst 1957, Stephens et al. 1990; Mitchell and Arnott 1994). First, calculated size spectra are approximated by y-distributions in the radiative units of the model, then the simple but accurate formulae for
where and m^ and KX are the real and imaginary parts of the refractive index of ice, and the effective radius, reff, is related to F, as reff = (/?, + 3)/(p,- +1) F,. Equations 13 and 14 show that the optical coefficients in cirrus are not constant with height but may strongly decrease downward with increasing crystal radii. It will be shown that this influences cirrus radiative properties and could cause a wide variation in the measured "mean" absorption coefficients. 19.2.6. Model Configuration for Cirrus The computational domain in the model version designed to simulate cirrus consists of three variable domains in the vertical depending on the height of the cirrus layer. In the three cases described below, we use (1) a lower layer of 7 levels with vertical resolution of 0.7-2 km from the surface, zs, to the lower boundary of the middle domain, zbot, with height z = 5-12 km; (2) a main domain including cloud of 31 levels from zbot = 5-12 km to ztop = 11-14 km with 100-200 m resolution; and (3) an upper layer of 15 levels from ztop to 24-30 km with 1-1.5 km resolution. This structure allows the simulation of high-level clouds with sufficient

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vertical resolution, as well as the calculation of the LW and SW radiative fluxes down to the surface and above the cloud up to 24-30 km, and an estimation of the outgoing LW and reflected solar radiation at the TOA. The number of horizontal gridpoints in the 2-D model version used here is 33, at the resolutions described below. The time step is 10s for dynamics and transport of heat, humidity, and crystals and 0.1-10 s for microphysics; radiative codes were called every 30s.

19.3. Cirrus Simulation Results: Three Case Studies

In this section, three cases of simulated midlatitude cirrus clouds are considered: (1) a relatively warm cirrus in a thick (-3.5 km), saturated layer with generic initial model profiles; (2) cirrus in a thinner (1.5km) saturated layer displaying the similar generic initial profiles distributed within the GEWEX (Global Energy and Water Exchange Experiment) Cloud System Study (Starr 1997); and (3) a case treating radiosonde profiles from a cold (-70°C) and high (14km) cirrus layer observed at the Atmospheric Radiation Measurement (ARM) Clouds and Radiation Testbed (CART) site in Oklahoma, USA, on April 19,1994 (Sassen et al. 1998). Several model runs were performed for each case, with varying schemes of nucleation, radiation, and other features described below, but using the same initial profiles. This approach allows us to begin the assessment of the sensitivity of cirrus cloud structure, content, and radiative properties to such diverse factors. 19.3.1. Cirrus Case 1 To simulate a common type of mid-latitude cirrus cloud, the model was initialized analogous to Starr and Cox (1985), with generic profiles of temperature and humidity similar to those observed during the FIRE and EUCREX field campaigns. The initial profile of T corresponds to a relatively stable atmosphere from -23°C at height zbot = 6km to -57°C at 10.5km, with a slightly more unstable layer from 7.0 to 9.2km. Initial relative humidity with respect to ice (RHI) was supersaturated in the latter layer with a maximum value of 5%. Horizontal grid steps of x = 3km and a horizontal domain of 96km were modeled. To simulate the effects of an upper-level trough, a horizontally and vertically inhomogeneous synoptic-scale vertical velocity field constant in time was superimposed on the mesoscale velocity field generated by the model. Its maximum of 5 cm/s is at x = 33 km, z = 8.3 km, and decreases to 1-2 cm/s at the boundaries. Although these initial model inputs are the same as those used in Khvorostyanov and Sassen (1998b), in this case we performed two different model runs using the T-type and 6-type heterogeneous nucleation mechanisms to evaluate how these model processes acted in the absence of homogeneous nucleation. Cirrus meso- and microstructures The cloud structure after Ih of simulation for these two basic cases is presented in figure 19.1. The main region of updrafts (fig. 19.1a) is located in the

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Figure 19.1. Cirrus case 1 meso- and microstructure after 1 h of simulation with (a-g) Ttype and (h-j) 6-type heterogeneous nucleation (see text). Shown are (a) vertical velocities, (b,h) crystal number density, (c,i) ice water content, (d) crystal mean radius, (e) VAPOR.EXCESS, (f) supersaturation relaxation time, and (g,j) REL.IWC.

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horizontal domain at x = 15-45 km and at heights 7.0-9.0 km, where mesoscale updrafts are reinforced by the large-scale ascent. This accelerates the processes of crystal growth and latent heat release, increasing the local buoyancy. The microphysical properties for the T-type nucleation are shown in figure 19.1a-g. The simulated TV, (fig. 19.1b) exhibits some slight cellular structure with maximum concentrations of about 200/L at a z of about 9.0km, which is optimal for nucleation because of the combination of the coldest temperature and stillelevated RHI.The maximum IWC (fig. 19.1c) at 1 h reaches 18-20mg/m3 at about 1-1.5 km below the level of maximum Nh which coincides with the region of the strongest synoptic-scale updrafts in the upper level trough (x - 15-45 km). The perturbations caused by the mesoscale velocities are much weaker. The crystal mean radius (fig. 19.1d) has a minimum (5-10 um) in the upper layer at about 9 km, where the heterogeneous nucleation continuously adds small crystals at the maximum rate. Crystal radii increase downward to 40-45 um in the layer with positive supersaturation at z = 7-8 km, and to 50 um at 6-7 km, where evaporation begins to take place. With 5-type nucleation, the general spatial structure of the cirrus after 1 h is similar, with a maximum nucleation rate near z = 9km, but TV,- is about 100 times smaller and does not exceed 2/L (fig. 19.1h) and IWC is about 50 times less, not exceeding 0.4mg/m3 (fig. 19.1i).Thus, the nucleation and condensation processes are much slower in this case. After 2-3 h, the properties of the clouds with T- and 8-types of nucleation become more similar, as described below. In either case, it is appropriate to call the layer around 9.0km height the "crystal generation layer," while the layer beneath at about 8.2km can be called the "IWC generation layer" or "deposition layer," and the layer below about 7km "the evaporation layer." Crystal generation is highest in the upper layer because of the rapid nucleation rate at the coldest temperatures, and crystal growth is the fastest in the layer below, where the mean vertical velocities and supersaturations are the largest. This modeled structure coincides with the schematization derived from observations of Heymsfield and Miloshevich (1995). Slow condensation in cirrus and ice budget The detailed analysis of the supersaturation budget performed by Khvorostyanov and Sassen (1998b) showed that the rate of supersaturation production during the initial 30-60 min is substantially greater than the IWC condensed during these times. The rest of the produced supersaturation is not condensed but is present in the cloud in the form of vapor, and even after 1 h, 8, * 0, as might be expected in a bulk model or GCM or in a liquid cloud, but is 5-10% in a thick layer. Thus, the condensation process in cirrus (which transforms generated 8, into IWC) is a rather slow process. The following three important quantities characterize the noninstantaneous nature of the deposition process: the supersaturation relaxation time, tfc, defined in equation 4, the excess of uncondensed vapor (supersaturation), VAPOR.EXCESS, and the relative amount of the condensed ice or percent of condensed ice, REL.IWC, defined as:

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VAPOR.EXCESS (mg/m3) represents the amount of uncondensed vapor available for deposition and could be transformed into ice (as is usually done in bulk cloud models or GCMs), but is still uncondensed in this microphysical model. REL.IWC (percent) is the ratio of the IWC condensed by the model, to the maximum amount of ice that could be condensed in a bulk model if the condition q = qsi (or 8, = 0) was assumed. Figure 19.1e shows that VAPOR.EXCESS with T-nucleation after Ih in the whole cloud is 6-20 mg/m3 (i.e., comparable or greater than the IWC). The minimum values of ifc are 20-30min in the center (fig. 19.If) and grow to 120-180 min and more toward the periphery. These are characteristic times of the deposition process that determine the e-folding decrease of the generated supersaturation and deposition rate, ec(. Thus, the condensation process is slow in cirrus clouds, and the amount of the condensed ice is only 20-50% after 1 h (fig. 19.Ig). So the instantaneous bulk condensation may overestimate IWC, and hence optical thickness, emissivity, and so on, by two to five times. The situation is even more dramatic with the 5-type nucleation. After Ih, REL.IWC < 1-2% in the entire cloud (fig. 19.1J), and the remaining 98-99% is uncondensed because Nt < 1-2/L, ft ~ 30 um, and ifc > 16 h. Only after 3h does Nt reach 10-15/L at z - 8.5km, fi ~ 40-60 um, and T/C > 1.6h, such that IWC is about 10-20mg/m3, but still REL.IWC is 1-2% at 9km and linearly grows downward to a maximum of 40-60% at 7 km. Thus, the amount of condensed ice strongly depends on the mechanisms of nucleation, or more fundamentally, on the nucleation rate. Optical and radiative properties The properties for the case presented here correspond to the microphysical properties with T-type nucleation in figure 19.1. Such important cloud properties, which influence their radiative properties (radiative fluxes, heating/cooling rates, optical thickness, etc.), are the mass absorption amabs and extinction omext coefficients and the single-scattering albedo. Numerous experiments and discussions devoted to these coefficients have derived a wide range of values, from 100 to 3500cm2/g (see, e.g., Stephens et al. 1990; Liou 1992; Khvorostyanov and Sassen 1998b), and until recently the reason for this variability was unclear. The use of the microphysical model provides an explanation for this variability in view of the existence of characteristic vertical microphysical profiles. These are presented in figure 19.2, which shows that, in spite of the different IWC at various horizontal locations, the profiles of the mass coefficients are close to some "universal" ones with maxima of 1600-1800 cm2/g for omext and 700-800 cm2/g for amabs in the uppermost crystal-generating layer with the smallest crystals, while the values strongly decrease downward to omext of 200-400 cm2/g and ccmabs of 100-200 cm2/g in the lower half of the cloud. This may explain the previously observed variability in these coefficients, since different local values could be measured by an aircraft at various heights, or during

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Figure 19.2. Vertical profiles of the mass absorption a^bs and extinction o^xt coefficients (cm2/g) at four horizontal locations, x (see fig. 19.1) for case 1 with T-type nucleation.

surface-based measurements, different vertical layers of cirrus with different ocmabs could contribute predominantly to the measured signal. Note that more precise evaluation of the omext and amabs horizontal variabilities can be done with finer model horizontal resolution. When evaluating the radiative properties of clouds, previous numerical studies and GCMs have generally used some prescribed values of amabs and crmext that were constant with height for the entire cloud. To check the accuracy of such an approximation, we compared radiative fluxes and heating rates calculated by two methods. Method A uses the coefficients calculated in each grid point in this model (i.e., with the computed size spectra), as with the profiles shown in figure 19.2. Method B is closer to that used in GCMs: for LW radiation, a value constant with height of ccmabs = 600cm2/g is used with emissivity expressed via the ice water path (IWP), and, for SW radiation, a parameterization of optical thickness is used Here a constant effective radius of 30 um was chosen, as in some GCMs. The difference between methods A and B is only in the optical properties, while IWC remain the same. The comparison of methods A and B in figure 19.3 is for the two horizontal positions of the corresponding 2-D fields in figure 19.1 (x = 9km and 33km), and the two vertical profiles of the optical coefficients in figure 19.2. It shows that the difference between methods A and B for the LW radiative fluxes is 35-50 W/m2, which is much larger than the radiative forcing at TOA that might be induced by the increase of CO2 by the year 2100, or about 4.5 W/m2 (IPCC 1995). The difference in LW heating rates is even more dramatic. Method B exhibits a picture

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41

Figure 19.3. Vertical profiles of the radiative fluxes and heating rates for the long-wave radiation (upper row) and short-wave radiation (lower row) calculated with method A (calculated height-dependent optical coefficients) and method B (constant-with-height optical coefficients).

considered to be the classical one for cirrus (i.e., strong heating in the lower half of the cloud up to 8 K/day, and strong cooling in the upper half up to -20 K/day). Method A with calculated ocmabs does not exhibit any heating, but a slight cooling at all layers with maximum of -2 to -4 K/day in the upper layer. Thus, the use of the constant-with-height optical coefficients may lead to a strong overestimation of the static instability of the atmosphere caused by cirrus clouds. The difference in the fluxes between the two methods for solar radiation (lower row) is even larger, 50-100W/m2, whereas the difference in the heating rates is smaller than that between x = 9 and 33km. In some previous GCM studies where cirrus radiative properties were evaluated similar to method B (e.g., Ramanathan et al. 1983), it was found that cirrus produce positive feedbacks with respect to CO2-induced global warming because the strong heating at cirrus bottom and cooling at top leads to the instability of the upper troposphere and increased convective activity. Stephens et al. (1990) found that some critical ref ~ 16 um exists, such that the sign of feedbacks changes

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at crystal radii, r ~ re{. As we can now see, a more detailed account of cirrus vertical structure produces a more stable upper troposphere, and the magnitude or sign of this feedback (or critical ref) may change if it were possible to perform new GCM experiments using a more appropriate treatment of cirrus optical properties. Cloud forcing and total heating rates One of the most informative characteristics of cirrus climatic effect is the cloud forcing, which is defined here as C/)|S,, = F^dst -F^st, where the indices l,s, and t mean LW, SW, and total components, "net" is the net flux defined to be positive downward, and "cloud" means the whole domain is covered by cloud. It was shown in previous studies with vertically constant optical coefficients that, averaged over 24 h, the TOA cirrus cloud forcing is generally positive (e.g., Fu and Liou 1993), meaning that cirrus would always warm the troposphere. To estimate the possible radiative and climatic effects of the type of cirrus shown in figure 19.1 during different times of day, we made the assumption that this cloud would exist for 24 h with the same properties (cirrus lifetimes are from a few hours to more than 24 h; if it exists only n hours, the results below should be multiplied by «/24). We then horizontally averaged vertical profiles of IWC, mean radius, and optical properties after the Ih simulation shown in figure 19.1 and calculated the diurnal march of the cloud forcing at altitudes from the surface to 24km using methods A and B. The results in figure 19.4 show that the total LW + SW cirrus cloud forcing, Ct, is negative at all altitudes during almost the whole daytime because the albedo effect exceeds the greenhouse effect due to the abundance of relatively small crystals in the upper cloud region. The minima C, - -60W/m2 at TOA and -90 W/m2 are at the surface near noon. Ct is positive with a TOA maximum of 20 W/m2 during the night and changes sign after sunrise and before sunset. These results are similar using methods A and B, although method B overestimates the total albedo effect during the day by about 20 W/m2, and the total greenhouse effect by 30-60 W/m2 during the night. Thus, the cirrus radiative/climatic effect should not simply be regarded as causing warming, as is often assumed, but depends on the time of day, with cooling during the day and warming at night. Cloud forcing averaged over 24 h for both methods A and B (fig. 19.5), shows that with method A the SW forcing is negative at about -40 W/m2, and LW forcing is positive and increases from 15 W/m2 at the surface to 35 W/m2 at TOA. The total forcing is -20 W/m2 at the surface and increases almost linearly upward, reaching -5 W/m2 above the tropopause. Method B overestimates SW cooling by 15-20 W/m2 and LW warming by 15-35 W/m2, so the total cloud forcing exhibits similar (-20 W/m2) cooling at the surface, but much stronger warming at TOA, or 15 W/m2. This last result is in agreement with other theoretical calculations, although we see that the assumption of height-invariant optical coefficients (method B) may essentially (by 20 W/m2) overestimate the cirrus heating effect at TOA. The radiative heating rates averaged over 24 h (fig. 19.6) again show that method B overestimates the effects of cirrus: maximum LW cooling is -1 I/day at 8.2km (less -3K/day with method A), and maximum LW heating is 4/day at

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Figure 19.4. Diurnal march of the total (short-wave + longwave) cirrus cloud forcing calculated with methods (a) A and (b) B with the horizontally averaged microphysical fields shown in figure 19.1 using T-type nucleation.

Figure 19.5. Vertical profiles of 24-h averaged components of the cirrus total cloud forcing, C,, calculated with methods (a) A and (b) B for case 1, using the T-type nucleation. Rectangles denote the height at which Ct changes the sign.

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Figure 19.6. Vertical profiles of 24-h averaged long-wave, short-wave, and total heating

rates calculated with methods (a) A and (b) B.

6.5km (no LW heating in the lower layer with method A). Thus, the diurnally averaged heating rates again show that method B may overestimate convective instability of the upper troposphere, amount of cirrus, upward motion of the tropopause, and the other greenhouse gas-induced effects. Obviously, in addition to the cirrus and atmospheric profiles, values of cloud forcing should also depend on season and latitude. The described results were obtained for the latitude of Salt Lake City (40.8° N), Utah, in mid-April. Before drawing more conclusions for our climatic system, similar calculations must be performed for other latitudes and seasons. 19.3.2. Cirrus Case 2 The initial atmospheric state profiles offered by Starr (1997) are similar to those used in the first example, except that the perturbation of the initial humidity profile was larger but in a much thinner layer from 8.0 to 9.2km, and the maximum 8, = 20% occurs at z = 8.5km and linearly decreased to 5; = -60% at z ^ 10km and at z < 7km. The main cloud domain was from 5 to llkm with a vertical step 200m, such that the 5-7-km layer was subsaturated with RHI = 40%. The temperature was -20°C at 5km and linearly decreased to -55°C at llkm with a slightly more unstable, 1-km thick layer, around 8km. A constant with height and time upward vertical velocity of 3cm/s was superimposed on the mesoscale model-generated vertical velocities, with no external wind shear. Horizontal steps were 0.5km in a domain of 16km. Impact of nucleation scheme on cirrus evolution We performed five 3-h model runs to test the sensitivity of the model and cirrus properties to the mechanisms of crystal nucleation and radiative processes: (1) heterogeneous nucleation only of the 5-type with no radiation; (2) homogeneous

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nucleation only with no radiation; (3) both nucleations processes with no radiation; (4) heterogeneous 8-type plus LW radiation; and (5) both nucleation processes plus both LW and SW radiation. A comparison of the temporal evolution of the maximum values of cloud microphysical properties and vertical velocity with different nucleation mechanisms is shown in figure 19.7. With heterogeneous nucleation only (fig. 19.7a), the crystals form from the beginning in the rather thick layer with 6/ > 0 and their generation continues for 3 h; TV, reaches a maximum of 30/L after 1 h and then declines to 20/L; IWC reaches a maximum 11 mg/m3 after 1.5 h, and the maximum mean crystal radius varies between 70 and 90 urn. After 1.5-2h, a stabilization of the cloud is seen, and further changes are rather small, such that a balance exists between supersaturation production, crystal generation, and growth and precipitation. With homogeneous nucleation only (fig. 19.7b), which may imitate a basic lack of IN in the upper troposphere, the crystal nucleation starts much later, after 80 min, when Sw driven by the vertical velocities exceeds some threshold value above 90% required for homogeneous nucleation. However, at 90min, TV, reaches a 180/L maximum, which is six times greater than with heterogeneous nucleation. Then the supersaturation depletion due to crystal absorption exceeds supersaturation generation, Sw decreases and falls below the threshold, and further nucleation is prohibited for some time. Because the crystals grow and precipitate from the upper layer, while supersaturation generation continues, eventually the threshold value of Sw is reached again, and the next nucleation impulse takes place. This occurs at 170 min (fig. 19.7) in the upper cirrus layer at about 9.5km. Thus, in contrast to the heterogeneous nucleation case,

Figure 19.7. Comparison of the temporal evolution of the maximum values of cirrus microphysical properties in cirrus case 2 with (a) heterogeneous nucleation only and (b) homogeneous nucleation only, including crystal concentration, Nt, ice water content, mean radius, and vertical velocity.

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homogeneous nucleation proceeds as an impulselike process as a threshold value of Sw is attained. Such an impulselike nucleation behavior was obtained by Sassen and Dodd (1989) in a parcel model using a constant updraft velocity, but with a periodicity of a several minutes due to the large w of about 1 m/s and the assumed wind shear rate. In our case, the nucleation events are separated by 90min. Impact of nucleation and radiation on cirrus vertical structure Vertical profiles of the horizontally averaged cloud properties after 3 h are presented in figure 19.8. The IWC profiles (fig. 19.8a) are similar for the two nucleation cases, with maxima of 11-15 mg/m3 at z = 7.5-8.1km; in the homogeneous case the cloud is located 0.7-1.Okm lower and is about 0.5 km thinner. The TV, profiles (fig. 19.8b) differ more strongly: with the S-type heterogeneous nucleation, a maximum of 20/L is located near 9.5km, and TV, decreases downward to vanish at about 6 km. This upper maximum is caused by the 8, maximum from 9.5 to 10km (fig. 19.8d), where it is generated by constant updrafts and cannot be compensated for by the vapor absorption by small crystals with radii 5-10 um (fig. 19.8c). As a result, this layer has a large condensation time of 2-3h (fig. 19.8e). Lower at 8-9 km, where the crystal sizes increase and 8, and the heterogeneous nucleation rate decrease, ifc declines to about 90min. Due to the impulselike homogeneous nucleation process, the TV, profile at 3 h exhibits two maxima (fig. 19.8b): "old" crystals with 60-u.m mean radius at z = 7.5 km, and new, approximately 10-(im crystals at 9.5 km. In cases with a deficit of IN and/or stronger updrafts, such steplike homogeneous nucleation episodes could explain the sometimes observed layered vertical cirrus structure, with the layer age increasing downward. The supersaturation over ice (fig. 19.8d) becomes negative below 8km, such that the upper half of the cloud is supersaturated and the lower half is subsaturated. A somewhat paradoxical fact is that the maximum IWC is located not at the height with maximum 8,, but 1.5-2 km lower near the 8/ = 0 level, and reflects the cumulative character of condensation in cirrus (i.e., slow deposition during precipitation down to 8, = 0). The lower 2-3-km portion of the cloud is evaporating, but only very slowly as ifc increases from about Ih at 7.5-8.0 km to >3h below 7km (thus IWC decreases downward to 5.5km). We can then define the lower cirrus boundary according to, for example, where IWC = 0, but not by virtue of zero supersaturation. The relative amount of condensed ice is even lower than in case 1 (fig. 19.8f) because JV,- is lower, ifc is larger, and the condensation slower. Thus, after 3 h of heterogeneous nucleation, the relative amount of condensed ice near cloud top is only 5-10%, increases steadily up to 60-100% near the IWCmax at 8km, but becomes negative below with minima of -100% (-170% with homogeneous nucleation) at 0.5km below the saturated region at 7.5km, and finally -10-50% lower in the evaporation regime. So, subsaturation is two to four times larger than the IWC. Surprisingly, if this IWC was evaporated using the bulk model approach (instantaneous evaporation), the cloud thickness would be two to three times (1.5-2 km) thinner.

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Figure 19.8. Effects of nucleation (homogeneous or heterogeneous only) and radiation (with and without long-wave effects) on cirrus microphysics in cirrus case 2 after 3h. Shown are vertical profiles of (a) liquid water content, (b) crystal concentration, (c) crystal mean radius, (d) Supersaturations over ice and water, (e) supersaturation relaxation time, and (f) relative amount of condensed ice.

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Because rm increases from 10 um near cloud top to 50-70 um near cloud bottom, the mass absorption and scattering coefficients exhibit profiles similar to the first example. The optical thickness, ivis, of 0.4-0.45 is two to three times less than in case 1 with a T-type heterogeneous nucleation. When both nucleation mechanisms are allowed, heterogeneous nucleation suppresses the growth of supersaturation in these weak updrafts, and the threshold of homogeneous nucleation is not reached. Inclusion of both LW and SW radiation interaction causes rather weak variations of cirrus properties by 5-10% after 3 h. The albedo of the cloud itself is 5-7%, maximum LW cooling is -4K/day, and solar heating is 2 K/day, so the radiative-effective velocities do not exceed 0.3-0.5 cm/s, and the overall radiative effect on the cloud is small. The crystal size spectra shown in fig. 19.9 clearly reflect the differences in the nucleation mechanisms. For the heterogeneous case, the modal radius, rm, from 25 um at 9 km (the continuous generating layer) monotonically increases to 5070 urn at 6-7 km, and its maximum decreases downward. For the homogeneous impulselike nucleation, we see a mixture of the older crystals with rm of about 60 um with a maximum increasing downward, and a recently formed small crystal fraction with rm of about 10 um at 9.2km with signs of bimodality a bit lower due to this secondary nucleation. These features determine cloud optical properties.

Figure 19.9. Crystal size spectra from our cirrus case 2 at time 5 h: (a) heterogeneous nucleation of 8-type and (b) homogeneous nucleation on haze particles of ammonium sulfate.

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Cloud forcing and heating rates The diurnal cycle of cloud forcing for this case with heterogeneous nucleation (fig. 19.10) is similar to case 1: negative during most of the day with minima of -50 to -70W/m2 near noon, and positive during the night with a 20W/m2 maximum with method A; the amplitude of the forcing is 20W/m2 larger with method B. The total forcing averaged over 24 h (fig. 19.11) is negative at the surface (-20 and -25W/m2 with methods A and B), and positive (7 versus 35 W/m2 with methods A and B) at TOA. Therefore, this cirrus cloud cools the surface and heats the upper tropospheric column, in qualitative agreement with some other results (e.g., Fu and Liou 1993), although method B fundamentally (by five times) overestimates the total TOA warming and the thickness of the upper heated layer: Ct becomes positive only above 7km with method A and above 2.5km with B. The diurnally averaged radiative heating rates (fig. 19.11c, d) again show strong differences between methods A and B. The maxima are similar to those in case 1: -2.5K/day in the LW, l.OK/day for the SW, and -1.5K/day total at z = 8.5km. (Note that the temperature jump at z = 5km is an artifact caused by the permanent cooling of the middle domain by vertical velocities of 3cm/s for 3h.) Method B predicts a cooling rate about five times greater along with the occurrence of strong heating in the lower cirrus, which is an artifact of the unjustified constancy with height of the absorption coefficients. 19.3.3. Cirrus Case 3 To initialize the model for this unusual (for mid-latitudes) type of cold and high cirrus layer, we used the sounding data obtained from the Oklahoma ARM CART site on April 19,1994 near the time of aircraft and surface-based remote sensing measurements (Sassen et al. 1998). The local sounding revealed a weak subtropical jet stream with a maximum wind speed of 26m/s just below the

Figure 19.10. Diurnal march of the total (short-wave + long-wave) cirrus cloud forcing calculated for cirrus case 2 with methods (a) A and (b) B with the horizontally averaged microphysical profiles shown in fig. 19.8 (analogous to fig. 19.4).

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Figure 19.11. Vertical profiles of the 24-h averaged components of the cirrus total cloud forcing, C,, calculated for cirrus case 2 with methods (a) A and (b) B, and of the total heating rates with (c) A and (d) B. Rectangles denote the height where C, changes sign: cooling below and warming above (analogous to fig. 19.5).

14.1km tropopause. Although the moisture was increasing through advection, it was still rather low at a relative humidity with respect to water (RHW) of about 40% at cirrus altitude, which corresponds at this low cloud-top temperature (71°C) to a slight supersaturation over ice of 5-10%. Horizontal model steps of 0.5km were used in a domain of 16km. Nucleation mode Several model runs were performed with differing nucleation mechanisms, concentrations of haze particles, and dynamic forcing to achieve quantitative agreement with the detailed set of experimental results (Sassen et al. 1998). The in situ

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microphysical probes showed relatively minute, ambiguously shaped crystals, and it was hypothesized that these crystals could have grown from haze droplets of sulfuric acid derived from the lower stratosphere. This is confirmed by our extensive model sensitivity tests. The most appropriate scenario of crystal nucleation was chosen after testing three different mechanisms. The heterogeneous 8-type nucleation gave crystal concentrations lower than those observed (see case 2), and the low RHW prohibited homogeneous nucleation of dry ammonium sulfate nuclei. Thus we assumed that homogeneous nucleation took place on the submicron haze droplets of sulfuric acid that could be activated at rather low RHW. In contrast to cases 1 and 2, where the concentrations of CCN and IN were chosen decreasing upward (meaning that their influx was from the lower troposphere), the concentration of cloud-forming particles was taken in this case as decreasing downward from the tropopause (and observed cloud top) by e times on the scale of about 1 km, which may correspond to the penetration of sulfuric acid droplets from the lower stratosphere. A parabolic profile for the large-scale vertical velocity of 2-5 cm/s was chosen, which corresponds to the convergence in an upperlevel trough. Evolution of microphysics A height-time display of the horizontally averaged microphysical properties from this cirrus is shown in figure 19.12. After the initial nucleation of pristine crystals, their growth is very slow due to the low temperature: for the same 8,, the growth rate of a crystal is proportional to the vapor density that decreases exponentially with T. Thus, in this case, it takes 4-5 h for the crystal mean radius to exceed lOum.The cloud boundaries were at 12.5 and 13.8 km. The terminal velocities of these crystals are small; they precipitate very slowly, and the mean radius vertical profiles exhibit only slight variations, with a small increase downward. The NI has a maximum closer to the cloud top due to the upward-increasing acid droplet concentration and lowering temperature that favors nucleation. The IWC does not exceed 0.5mg/m3 with a maximum near the central portion. The crystal size spectra (fig. 19.13) are monomodal with modal radii of about 8-11 um. These calculated microphysical properties are in a good agreement with those observed by Sassen et al. (1998), who described this cloud as rare, corona-producing cirrus that must have been composed of such small-sized crystals. Radiative heating and cloud forcing The vertical variations of the optical coefficients are much less compared to the previous cases (ocabs ~ 400-600 cm2/g, osc ~ 1300-1800 cm2/g) because of the more homogeneous profiles of r,. The visible optical thickness computed after 5 h is only 0.026. However, this thin cloud causes a rather strong modulation of the heating rates. In contrast to the previous cases, the LW heating rate is positive in the whole cloud, with a maximum of 1.4K/day (figs. 19.14 and 19.15). The LW cooling rate in the subcloud layer has 2 minima of -2 to -3 K/day at the surface and at 7.5km, and a maximum of -0.5 K/day at 5km. When added to positive

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Figure 19.12. Time-height evolution of horizontally averaged cold cirrus microphysical characteristics for cirrus case 3, modeled after the April 19,1994 CART cirrus case study.

Figure 19.13. Calculated crystal size spectra after 5 h simulation time at various heights for cirrus case 3.

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Figure 19.14. Height-time display of the diurnal cycle of (a) the total heating rate and (b) cloud forcing for the cold case 3 cirrus.

solar heating with a maximum of 1.5/day at 5km, it produces an interesting layered structure in total radiative heating: around noon there are two maxima of cooling at -2.5/day in the lower 3-km layer and -2.0/day near 10km, and two maxima of total heating near 5-6 km (caused by solar heating) and 13km (caused by cirrus effects). The 24-h averaged picture (fig. 19.15a) shows the total heating of the cloudless troposphere and the heating of 1-1.5 K/day at the cirrus layer. So, such cold, high, and often long-lived cirrus may cause rather strong radiative heating of the upper troposphere. The diurnal cycle of cloud forcing (fig. 19.14b) is similar to the previous cases: negative during the day and positive at night, although its values are much smaller due to the small optical thickness. The averaged forcing (fig. 19.15b) is -1.2 W/m2 at the surface and 1.5 W/m2 at TOA, so this thin cirrus, as in case 2, also cools the surface and heats the whole tropospheric column. Note that this effect is similar to that obtained for contrails with even smaller crystals of 3-4 um (Khvorostyanov and Sassen 1998d), and to case 2 noted above.

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Figure 19.15. Vertical profiles of the 24-h averaged (a) total heating rate and (b) cloud forcing for the cold cirrus case 3.

These results indicate that the following atmospheric conditions may lead to the formation of such a cold mid-latitude cirrus as was observed on April 19, 1994, presumably formed on sulfuric acid haze droplets: (1) persistent areas of uplift in the upper troposphere that increase RHW; (2) a high-altitude tropopause that brings together the source of (tropospheric) moisture and (stratospheric) cloud-forming particles; and (3) a mechanism of troposphere/ stratosphere exchange that contributes to the formation of such cirrus clouds. 19.4. Summary and Conclusions

A 2-D version of a 1-D/2-D/3-D cloud model with explicit microphysics and radiation, previously used to simulate cirrus clouds (Khvorostyanov and Sassen 1998a), has been modified for a more accurate and complete account of several processes in cirrus. New elements include a simple analytical parameterization of the size spectra of deliquescent submicron haze particles of various chemical compositions (Khvorostyanov and Curry 1999b), a further development of homogeneous nucleation theory (Khvorostyanov and Sassen 1998c), and the

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two-step radiative computations over the diurnal cycle in order to simulate cirrus radiative effects and estimate their possible impact on climate. The three different cases simulated here correspond to diverse mid-latitude conditions: two cases with idealized initial profiles for a relatively warm and stable atmosphere based on thick and thin cirrus clouds, and a case with an observed high and cold cirrus (Sassen et al. 1998) using sounding data from the Oklahoma ARM CART site. These simulations are presumed appropriate for occurrences of developing cirrus clouds generated in a stable atmosphere by relatively slow, synoptic-scale ascent present (e.g., within an upper-level short wave trough). The main results are summarized below. The ice crystal nucleation mechanism as seen from the nearly 40 runs performed during this study can be schematized as follows. First, a layer supersaturated with respect to ice is created due to the advection of moisture or the cooling from upward vertical velocities, or both. Then homogeneous and/or heterogeneous nucleation initiates cloud formation at a relative humidity somewhat below water saturation from minute haze particles (see also Sassen and Dodd 1988, 1989; Heymsfield and Sabin 1989; DeMott et al. 1994; Jensen et al. 1994). The activity and interaction of the nucleation modes depend on the chemical composition of the haze particles. If they consist of ammonium sulfate, deliquescence and homogeneous nucleation requires some temperature-dependent threshold humidity of >0.8, or >0.4 if the aerosol has been previously deliquesced. However, if the cooling rate is slow enough (w < 20cm/s), heterogeneous nucleation with IN concentration on the order of a few tens per cubic centimeter may cause the depletion of the saturation ratio, and the homogeneous nucleation threshold may not be attained. If the haze particles consist of sulfuric acid with a lower threshold humidity, the two nucleation modes may potentially proceed simultaneously. Finally, if IN are scarce and heterogeneous nucleation is restricted, homogeneous nucleation may occur periodically in rather thin layers in a steplike manner following the initial nucleation, as suggested by Sassen and Dodd (1989) for constant updrafts. Subsequently, the crystals precipitate and thus allow for the growth of supersaturation in updrafts until the threshold humidity value is once again achieved. The periodicity of homogeneous nucleation may be as low as 2-3 h in weak updrafts, which may explain some layered cirrus structures. The vertical cirrus cloud structure also depends on the nucleation mechanism. With all types of nucleation, its rate increases upward with decreasing temperature, and a crystal-generating layer occurs in the upper portion of the ice supersaturated layer. The crystal concentration is at a maximum here, and as the small crystals then precipitate through the underlying supersaturated, or deposition layer, they grow and maximize the IWC. Finally, the crystals precipitate into the subsaturated layer and gradually evaporate in the evaporation layer, decreasing the crystal concentration and IWC and temporarily increasing the mean radius. These model results are in general agreement with the schematization based on observational data from Heymsfield and Miloshevich (1995). In cases with homogeneous nucleation only, the crystal concentration profiles may be bimodal or multimodal in height. The slowness of the condensation process in cirrus clouds is one of the main features that distinguish them from the liquid clouds. It is determined by the

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characteristic time of supersaturation absorption by crystals, ifc ~ (47tDAr(r,)~1. Because in liquid clouds this time is typically 1-10 s for droplet concentrations of 200-400/cm3 and mean radii of 5-10 um, the condensation process is fast, and supersaturation is usually less than 0.01-0.1%. In contrast, we show that the condensation time in cold ice clouds varies from 0.5 to >5 h and depends on the nucleation mechanism. In the cases simulated even after a few hours of cloud development, there is typically a residual vapor supersaturation with respect to ice on the order of 5-10%, while the percentage of condensed ice varies from only 10 to 60% of the amount that could potentially be converted to ice during this time using the bulk approach, and IWC is comparable to or significantly less than the amount of uncondensed excess vapor. In the lower evaporating layer, the percentage of evaporated IWC is described in similar terms. Many bulk cloud models and GCMs condense the entire vapor excess or evaporate the IWC in a few time steps (i.e., 5-10min), or in a characteristic model time of about Ih, but this procedure can substantially over- or underestimate the IWC, optical thickness, latent heat, and so on. The treatment of condensation in cloud and climate models can be revised where it is too rapid, as described in the next section. Cirrus optical properties (mass absorption amabs and scattering omsc coefficients) from this model vary widely with cloud height and time. Earlier experimental studies have produced a wide range of values for the LW coefficients, ocTOabs of 100-3500 cm2/g. GCM and cloud models often use some "average" values, typically amabs = 600-1500 cm2/g. Simultaneous calculations of cirrus microphysical and optical properties with our model show the probable reason for this wide range: since ocmabs ~ ref~] and ref(z) grows downward, ocmabs decreases toward the cloud bottom. Thus, a single representative value of amabs is inappropriate. There is generally a 3-D field of ocmabs that depends on the precise cloud microstructure, and so determines the fields of optical thickness, emissivity, fluxes, and cooling/heating rates. Similar 3-D fields of the amsc coefficient determine the optical properties in the solar spectrum. However, according to the simulated vertical structure of cirrus, the coefficients have typical vertical profiles with a maximum in the upper part of the cloud containing the smallest crystals of amabs = 800-1000 cm2/g and owsc = 1500-2000 cm2/g, with much lower values in the main cloud containing larger crystals of ccmabs = 100-150 cm2/g and Gmsc = 200-300 cm2/g. Many GCMs still use the cirrus optical coefficients that are constant with height because of problems with resolving vertical structure. This may be extremely important for climate and climate change studies. A special comparison of the radiative fluxes and heating rates calculated with the optical coefficients produced by this model (method A) and with those typically used in GCMs (method B), has shown that the use of the latter can lead to a significant increase in the LW and SW upward and downward radiative fluxes (by 30-100 W/m2), and in the cooling rate in the upper part and the heating in the lower part of the cloud. This may cause an unjustifiable increase in the static instability and cirrus cloud convective activity in the upper troposphere. An improved parameterization of the dependence of these coefficients on cloud microstructure, as suggested in the next section, would create a more stable atmosphere and influence cloudradiation feedbacks. In particular, the positive feedbacks between cirrus clouds

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and global warming induced by greenhouse gases obtained in some GCMs might be different in magnitude or even in sign. For the first time in our simulations, calculation of the diurnal cycle of radiative fluxes and cloud forcing have shown that the total cloud forcing, C, (LW + SW), is negative during most of the daytime (i.e., the albedo effect exceeds the greenhouse effect as a result of an abundance of small crystals in the upper cloud region), and that C, is obviously positive at night. The total 24-h averaged forcing (assuming that the same cirrus exists over this time or may form with equal probability at any time of the day) is negative at the surface: -20 W/m2 for cases 1 and 2 with 2-3-km thick cirrus, and -1.2 W/m2 for the high, cold, thin cirrus in case 3. These cirrus clouds then cool the surface using either method A or B. At the top of the atmosphere, however, the forcing with method A is slightly negative (-5 W/m2) for case 1 and slightly positive for case 2 (7 W/m2), while with method B it is positive and large: 20 W/m2 and 35 W/m2, respectively. Hence, method B tends to overestimate cloud forcing and cirrus warming at the TOA by 20-30 W/m2. The overall thermodynamic consequences of such counteracting radiative cirrus effects in the lower and upper troposphere can be estimated only with the help of more advanced GCMs that can account for the interplay of microphysical and optical properties. 19.5. Recommendations for Parameterizations

19.5.1. Threshold Humidity for Cirrus Formation GCMs and weather forecast models often use the conception of the threshold humidity, RHWth, for the onset of large-scale condensation. The value of RHWth can be determined with use of equation 6. Since rg should be positive, we have (TQ/T)SWG > 1, so equation 6 imposes a condition of minimum threshold saturation ratio, SWjth for homogeneous nucleation, which decreases with T (e.g., SWith = 0.70-0.75 at T ~ -55 to -37°C) and resembles the thresholds found with a parcel model in Sassen and Dodd (1989) and the aircraft data in Heymsfield and Miloshevich (1995). Thus, equation 18 determines the minimum of Sw required to initiate any ice nucleation. Due to gridbox averaging in GCMs, the effective threshold 5W;th might be slightly lower, but equation 18 is still a useful starting estimate. 19.5.2. Ice Mass Budget Because most bulk cloud models and GCMs transform the entire vapor excess in a few time steps (i.e., 5-10min) to relax the residual supersaturation to zero, this may overestimate the IWC by a factor of two to four or more. Based on our model results, the following recommendations of increasing complexity can be suggested: 1) decrease the amount of ice condensed in 1-3 h by a factor of two to four to test sensitivity to the ice condensation rate; 2) introduce some

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characteristic deposition time, ifc (typically 0.5-1 h), to calculate the equilibrium supersaturation §eq defined by equation 12, and then subtract 5eq from the "bulk" condensed IWC -q- qsi (i.e., correct as IWC = q - qsi - 8eq); and 3) use Nt, and fi as the prognostic or diagnostic variables to calculate the deposition time, thus producing a deposition/sublimation rate of e = (q - qs}lifc instead of £ = -(dqjdt), as in some GCMs. This should improve the predicted cirrus cloud content. 19.5.3. Optical Properties Method A accounts for the vertical profiles of amabs, omext, and IWC. The traditional method used in GCMs includes e, and TX, which can be written as the integrals from the cloud bottom zb to cloud top zt:

where amabs[r,(z)] represents the optical coefficient depending on mean radius, which depends on height. Vertical profiles of ocmabs(z), amext(z) can be related to the profile of r,(z) or ref(z) based on ADT or other methods (e.g., Stephens et al. 1990; Ebert and Curry 1992; Fu and Liou 1993; Mitchell and Arnott 1994; Khvorostyanov and Sassen 1998a). If the IWC and ft(z) profiles are prognostic or diagnostic variables in a GCM, e and i can be directly calculated from equations 19a,b. If, however, these profiles are unknown, then using the typical experimental vertical structure of developed mid-latitude cirrus (e.g., Sassen et al. 1989) and our model results, we can parameterize IWC and rt(z} as parabolic profiles:

where H = zb - zt is cloud depth, values with index "max" are the maximum values reached at zmax, a and b are the parameters that determine the location of the vertical maximum, and CN = [(a + b)la]a[(a + b)lb\b is a normalizing constant. For parameterizations (equation 20), maximum values are located at a relative height ZmJH. For the developed cirrus we can choose a = 1/4, b = 1, such that maxima are located at zmax = 0.2 H (in the lower quarter of the cloud) and CN = 1.87. For cirrus with maximum IWC in the middle cloud part we can choose in a = 1, b = 1, then zmax = 0.5//, CN - 4. Equations 19-20 using method A can be recommended for GCMs because they account for the cirrus vertical structure. Method B assumes some constant-with-height average ocmabs(z), amext(z).Then e and i can be expressed from equations 19a and 19b via IWP and the heightaveraged amabs(z), amext(z) (see equations 16 and 17). However, the results presented above show that the application of these equations, which are currently used in many GCM and cloud models, may lead to substantial errors. Thus we recommend for the calculation of cirrus radiative properties the use of equations 19 and 20, using vertical profiles of the coefficients.

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19.6. Problems and Future Tasks

The application of cloud-resolving models for cirrus studies and the improvement of parameterizations for GCMs requires the solution of the following three important problems: development of microphysical theories for both homogeneous and heterogeneous nucleation; more precise calculations of the ice and vapor mass budgets with account for residual supersaturation; and generalization of the kinetic equations. The first problem includes obtaining new data on the fundamental properties of the water substance that govern nucleation at low temperatures (-40 to -60°C), a better understanding of the basic physics of homogeneous nucleation at even colder temperatures, and the development of a microphysical theory for heterogeneous nucleation that also treats the effects of solutions on IN activation similar to recent homogeneous nucleation models. The second task involves either incorporation of the supersaturation equation in cloud models or appropriate parameterizations for adjusting the residual supersaturation. The final basic problem of cloud modeling is that the kinetic equation used here and in the other cloud models with explicit microphysics is valid only in the "high-frequency approximation," in which the characteristic time of turbulence, IL, of 5-10min is substantially smaller than t/c (see reviews of the theories of stochastic condensation in Cotton and Anthes 1989; Pruppacher and Klett 1997; Khvorostyanov and Curry 1999a).This is approximately valid for the three cases considered here but may not be valid for cirrus layers and contrails with higher Nt and smaller T/C. Thus, a generalization of the kinetic equation for stochastic condensation is required for arbitrary relations of IL and ifc such as those derived in Khvorostyanov and Curry (1999a). This allows more precise numerical solutions and analytical solutions of the y-distribution type with simple expressions for its indices, p, via meteorological parameters, instead of relying on empirical parameterizations. However, more general equations include additional covariances of the turbulent fluctuations of the /', 8,', and u', which can be evaluated only with use of experimental data for different situations in cirrus. Evaluation of these covariances and verification of the kinetic equations, along with the development of numerical methods for their solution, are among the top priorities for cloud numerical modeling using the explicit microphysics method. Finally, we state some problems and tasks that seem to require a more concentrated effort to resolve, in order to achieve a more accurate assessment of cirrus cloud climatic effects, including 1) the improvement of humidity measurements at low temperatures/high altitudes and estimations of supersaturation over ice in cirrus; 2) more realistic measurements of small (5-50 u.m) ice crystals; 3) measurements of the vertical and horizontal variability of CCN and IN in upper troposphere; 4) an intercomparison program of cloud-resolving models (bulk and explicit microphysics, using various parameterizations of radiative effects); and 5) modeling efforts directed toward both tropical and polar cirrus, with comparison to mid-latitudes. Only after such advances are realized will we be in a position to accurately evaluate whether cirrus clouds represent a positive or negative feedback to global warming.

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Acknowledgments This research has been supported by grant DE-FG03-94ER61747 from the Department of Energy Atmospheric Radiation Measurement program, and by National Science Foundation grant ATM-9528287. We thank David Starr for useful discussions and providing the GCSS atmospheric profiles. References Cotton, W.R., and R.A. Anthes, 1989. Storm and Cloud Dynamics. Academic Press, New York. DeMott, P.J., M.P. Meyers, and W.R. Cotton, 1994. Parameterization and impact of ice initiation processes relevant to numerical model simulation of cirrus clouds. /. Atmos. ScL, 51,77-90. Ebert, E.E., and J.A. Curry, 1992. A parameterization of ice cloud optical properties for climate models. /. Geophys. Res., 97,3831-3836. FIRE IFO-I, 1990. First ISCCP Regional Experiment, Intensive Field Observational Period-I. Mon. Wea. Rev. (special issue), 118. FIRE IFO-II, 1995. First ISCCP Regional Experiment, Intensive Field Observational Period-II. J. Atmos. Sci. (special issue), 52,4041-4385. Fletcher, N.H., 1962. The Physics ofRainclouds. Cambridge University Press, Cambridge, MA. Fowler, L.D., D.A. Randall, and S.A. Rutledge, 1996. Liquid and ice cloud microphysics in the CSU general circulation model. Part I: Model description and simulated microphysical processes. /. Climate, 9,489-529. Fu, Q., and K.N. Liou, 1993. Parameterization of the radiative properties of cirrus clouds. /. Atmos. Sci., 50,2008-2025. Heckman, S.T., and W.R. Cotton, 1993. Mesoscale numerical simulation of cirrus clouds— FIRE case study and sensitivity analysis. Mon. Wea. Rev., 21, 2264-2284. Heymsfield, A.J., K.M. Miller, and ID. Spinhirne, 1990. The 27-28 October 1986 FIRE IFO Cirrus Case Study: Cloud microstructure. Mon. Wea. Rev., 118, 2313-2328. Heymsfield, A.J., and R.M. Sabin, 1989. Cirrus crystal nucleation by homogeneous freezing of solution droplets. /. Atmos. Sci., 46, 2252-2264. Heymsfield, A.J., and L.M. Miloshevich, 1995. Relative humidity and temperature influences on cirrus formation and evolution: Observations from wave clouds and FIREII. /. Atmos. Sci., 52, 4302^303. IPCC, 1995. Intergovermnmental Panel on Climate Change: Radiative Forcing of Climate Change and Evaluation of the IPCC IS92 Emission Scenarios. Cambridge University Press. Jacob, C, and J.-J. Morcrett, 1995. Sensitivity of the ECMWF model to the treatment of the ice phase. In Workshop on Cloud Microphysics Parametizations in Global Atmospheric Circulation Models. Kananaskis, Alberta, Canada, May 1995. WCRP-90, WMO, Geneva, pp. 37-46. Jeffery, C.A., and P.H. Austin, 1997. Homogeneous nucleation of supercooled water: Results from a new equation of state. /. Geophys. Res., 102,25269-25279. Jensen, E.J., O.B. Toon, D.L. Westphal, S. Kinne, and AJ. Heymsfield, 1994. Microphysical modeling of cirrus, 1. Comparison with 1986 FIRE IFO measurements. /. Geophys. Res., 99,10421-10442. Kachurin, L.G., 1953. On the vapor supersaturation and droplet growth in the liquid clouds. Sov. Meteorol. Hydrol., 8, 23-26. Khvorostyanov, V.I., 1995. Mesoscale processes of cloud formation, cloud-radiation interaction and their modeling with explicit cloud microphysics. Atmos. Res., 39,1-67.

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Khvorostyanov, V.I., and J.A. Curry, 1999a. Towards the theory of stochastic condensation in clouds. Part I: A general kinetic equation, and Part II. Analytical solutions of gamma distribution type. /. Atmos. Sci., 56, 3985-3996, and 3997^013. Khvorostyanov, V.I., and J.A. Curry, 1999b. A simple analytical model of aerosol properties with account for hygroscopic growth. Part I: Equilibrium size spectra and CCN activity spectra, and Part II: Scattering and absorption coefficients /. Geophys. Res., 104,2163-2184. Khvorostyanov, V.I., and K. Sassen, 1998a. Cirrus cloud simulation using explicit microphysics and radiation. Part I: Model description. /. Atmos. Sci., 55,1808-1821. Khvorostyanov, V.I., and K. Sassen, 1998b. Cirrus cloud simulation using explicit microphysics and radiation. Part II: Microphysics, vapor and ice mass budgets, and optical and radiative properties. /. Atmos. Sci., 55,1822-1845. Khvorostyanov, V.I., and K. Sassen, 1998c. Towards the theory of homogeneous nucleation and its parameterization for cloud models. Geophys. Res. Lett., 25, 3155-3158. Khvorostyanov, V.I., and K. Sassen, 1998d. Cloud model simulation of a contrail case study: Surface cooling against upper tropospheric warming. Geophys. Res. Lett., 25, 2145-2148. Kiehl, IT, and C.S. Zander, 1995. A prognostic ice water scheme for anvil clouds. In Workshop on Cloud Microphysics Parameterizations in Global Atmospheric Circulation Models, Kananaskis, Alberta, Canada, May 1995. WCRP-90, WMO, Geneva, pp. 167-188. Liou, K.N., 1992. Radiation and Cloud Processes in the Atmosphere. Oxford University Press, New York. Mazin, I.P., 1968. The stochastic condensation and its effect on the formation of cloud drop size distribution. In Proceedings of the International Conference on Cloud Physics, Toronto, pp. 67-71. Meyers, M.P., P.J. DeMott, and W.R. Cotton, 1992. New primary ice-nucleation parameterizations in an explicit cloud model. /. Appl. Meteor., 31,708-721. Mitchell, D.L., 1994. A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part I: Microphysics. J. Atmos. Sci., 51, 797816. Mitchell, D.L., and W.P. Arnott, 1994. A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part II: Dependence of absorption and extinction on ice crystal morphology. /. Atmos. Sci., 51, 817-832. Pruppacher, H.R., and J.D. Klett, 1997. Microphysics of Clouds and Precipitation, 2nd ed., Kluwer, Dordrecht. Ramanathan, V, E.J. Pitcher, R.C. Malone, and M.L. Blackmon, 1983. The response of a spectral general circulation model to refinements in radiative properties. / Atmos. Sci., 40, 605-630. Raschke, E.F., G. Albers, Brogniez, et al., 1996. European Cloud and Radiation Experiment (EUCREX). Final Report, EV5V-CT92-0130. GKSS Research Center, Geesthacht, Germany. Rossow, W.B., and R.A. Schiffer, 1991. ISCCP cloud data products. Bull. Amer. Meteor. Soc., 72,2-20. Sassen, K., 1992. Ice nuclei availability in the higher tropospheric: implications of a remote sensing cloud phase climatology. In: Nucleation and Atmospheric Aerosols (N. Fukuta and P. Wagner, eds.). Deepak Publishing, Hampton, Virgina pp. 287-290. Sassen, K., and G.C. Dodd, 1988. Homogeneous nucleation rate for highly supercooled cirrus cloud droplets. / Atmos. Sci., 45,1357-1369. Sassen, K., and G.C. Dodd, 1989. Haze particle nucleation simulation in cirrus clouds, and application for numerical and lidar studies. / Atmos. Sci., 46, 3005-3014.

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Sassen, K., G.G. Mace, J. Hallett, and M.R. Poellot, 1998. Corona-producing ice clouds: A case study of a cold midlatitude cirrus layer. Appl. Opt., 37,1477-1485. Sassen, K., G.G. Mace, M.R. Poellot, S J. Melfi, W.L. Eberhard., J.D. Spinhirne, E.W. Eloranta, D.E. Hagen, and J. Hallett, 1995. The 5-6 December 1991 FIRE IFO II jet stream cirrus case study: Possible influences of volcanic aerosols. /. Atmos. Sci., 52, 97-123. Sassen, K., D. O'C. Starr, and T. Uttal, 1989. Mesoscale and microscale structure of cirrus clouds: Three case studies. /. Atmos. Sci., 46,371-396. Sedunov, Y.S., 1965. The fine structure of the clouds and its role in formation of the cloud droplet spectra. Izv. Acad. Sci. USSR, Atmos. Oceanic. Phys., 1,722-731. Sedunov, Y.S., 1974. Physics of Drop Formation in the Atmosphere. Wiley, New York. Starr, D. O'C., 1997. Cirrus Clouds Models Intercomparison Project, http://eos913.gsfc. nasa.gov/gcss_wg2. Starr, D. O'C., and S.K. Cox, 1985. Cirrus clouds. Part I: A cirrus cloud model, and Part II: Numerical experiment on the formation and maintenance of cirrus. /. Atmos. Sci., 42, 2663-2681 and 2682-2694. Stephens, G.L., S.C.Tsay, P.W. Stackhouse, and P.J. Flatau, 1990. The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback. J. Atmos Sci., 47,1742-1753. Sundquist, H., 1993. Inclusion of ice phase of hydrometeors in cloud parameterizations for mesoscale and large-scale models. Contr. Atmos. Phys., 66,137-147. Tabazadeh, A., E.J. Jensen, and O.B.Toon, 1997. A model description for cirrus cloud nucleation from homogeneous freezing of sulfate aerosols. /. Geophys. Res., 102, 23845-23850. Twomey, S., 1959. The nuclei of natural cloud formation. II. The supersaturation in natural clouds and the variation of cloud droplet concentration. Geoph. Pura Appl., 43, 243-249. van de Hulst, H., 1957. Light Scattering by Small Particles. Dover New York. Wetherald, R.T., and S. Manabe, 1988. Cloud feedback processes in a general circulation model. /. Atmos. Sci., 45,1397-1415.

20

Cirrus, Climate, and Global Change

GRAEME L. STEPHENS

20.1. Introduction Understanding the climate of Earth and the way climate varies in time requires a quantitative understanding of the way water cycles back and forth between the atmosphere and at the Earth's surface. The exchanges of water between the surface and atmosphere establish the hydrological cycle, and it is the influence of this cycle on the energy budget of Earth that is central not only to understanding present climate but also to the prediction of climate change. Processes relating to the smallest of the reservoirs of water—namely, the atmospheric branch of the hydrological cycle—play an especially critical role in climate change. Water in vapor phase is the critical greenhouse gas (e.g., Chahine 1992) providing much studied feedbacks on climate forcing (Lindzen 1990; Rind et al. 1991; Stephens and Greenwald 1991; Inamdar and Ramanathan 1998; Hall and Manabe 1999). Water in the form of condensed, precipitation-sized particles is an important source of energy fueling circulation systems and is the fundamental supply of fresh water to life on Earth. Liquid water cloud droplets significantly modulate the radiative budget of the planet (e.g., Wielicki et al. 1995). Water that exists as ice particles suspended in the atmosphere is perhaps the smallest of the water reservoirs of the atmosphere, yet these ice crystals when distributed as part of large-scale cirrus clouds exert a disproportionate influence on the energy and water budgets of the planet. This chapter briefly speculates on the important ways cirrus clouds affect the Earth's climate. The topics discussed are central to what is referred to as the cloud-climate problem, which might be schematically represented in terms of 433

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I. Given cirrus, what is the radiative heating? II. Given heating, what of cirrus? Figure 20.1. The cloud-climate problem deals with couplings that occur through the relationship of the vertical distribution of clouds (ice and water) and their impact on the atmospheric circulation via effects of clouds on heating and moistening the atmosphere and heating the surface.

the coupled processes represented in figure 20.1. The two most critical scientific questions associated with the cloud-climate problem are also stated in figure 20.1. Answers to these questions require a clearer understanding of how the large-scale circulation of the atmosphere governs cloud formation and evolution, how these clouds heat and moisten the atmosphere, and how this heating and moistening effect in turn feeds back to influence the dynamical and thermodynamical properties of the atmosphere. Progress in the cirrus cloud-climate problem specifically requires that we understand 1) the different controls of the large-scale circulation on the formation of cirrus, either directly such as through large-scale ascent typical of midlatitude cirrus or indirectly through the effects of the circulation on convection and detrainment of ice more typical of tropical cirrus; 2) how the larger-scale and local-scale thermodynamic properties affect both the microphysics of cirrus and in turn the radiative properties of these clouds; and 3) how the radiative properties and microphysical properties of cirrus in turn affect the larger-scale environmental thermodynamic and dynamic properties of the atmosphere through their influence on radiative transfer and the water budget of the upper troposphere. 20.2. Effects of Cirrus on Water Vapor

As mentioned above, the mechanisms that produce widespread cirrus clouds in one way or another connect to the dynamical state of the atmosphere and the

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association between this state and the availability of upper tropospheric moisture. For example, Newell et al. (1996) using a combination of vertical motion diagnosed by European Centre for Medium Range Weather Forecasts (ECMWF) MLS water vapor, and airborne lidar observations of cirrus demonstrated that cirrus primarily occur in regions of large-scale ascent and near 100% relative humidity. They further found no evidence in the 12 cases studied of cirrus penetrating the tropopause. The role of cirrus in the de-hydration of the lower stratosphere and subsequent effects on stratospheric chemistry remains a topic of ongoing research (e.g., Hoffman and Oltmans 1992; Mote et al. 1996; Rosenfield et al. 1998). While the formation of cirrus depends on the amount and distribution of water vapor, this vertical distribution of water vapor in turn is sensitive to the presence of ice crystals, the nature of the microphysical properties of these ice crystals, and the associated way these crystals fall in the atmosphere. This sensitivity, demonstrated in a number of studies (e.g., Donner et al. 1997; Stephens et al. 1998), is emphasized in figure 20.2. Shown in figure 20.2a are two different vertical distributions of cloud presented as a 3-month average for the December-JanuaryFebruary 1987-88 season over the West and Central Pacific (15° N to 5° S, 130° to 180° E) taken from T63L31 integrations of the global ECMWF model. The two curves refer to different integrations using two different versions of the cloud scheme in that model, one allowing the ice crystals of upper tropospheric clouds to fall farther than the second scheme. The effect of fallspeed on the vertical distribution of water vapor is presented in figure 20.2b along with profiles of relative humidity derived from TOGA/ COARE observations of Lin and Johnson (1996) in figure 20.2c. The difference between the two model profiles are substantial. The decrease in relative humidity just above 200 hPa in the prognostic scheme and the increase in relative humidity in a thick layer between 300 and 700 hPa are due to the strong coupling of the clouds to the convection in that particular scheme. Instead of evaporating all detrained condensate, the ice crystals are able to precipitate into lower layers, providing a source of water vapor on evaporation, substantially increasing the relative humidity in this broad layer. This result illustrates an important point: the water vapor budget of the climatically sensitive region of the upper troposphere is greatly influenced by the amount of condensate (in the form of ice) and the vertical distribution of this condensate. Present satellite methods (e.g., Lin and Rossow 1997), although crude, provide some guidance in evaluating ice contents predicted by global models. However, improved observations of the ice water content of clouds and the vertical distribution of these clouds are required to verify whether the cloud prognostic schemes that contain more advanced representations of physics are more realistic in their prediction of cirrus clouds and of the effects of these clouds on water vapor. 20.3. Effects of Cirrus on Radiation

Satellite-based observational programs such ERBE (Earth Radiation Budget Experiment) (Barkstrom 1984), CERES (Wielicki et al. 1996), and ISCCP

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Figure 20.2. (a) A profile of cloud amount and (b) relative humidity averaged over December-January-February 1987-88 and averaged over the region of the tropical pacific (15° N to 5° S, 130° to 180° E). (c) Radiosonde observations from TOGA COARE (Lin and Johnson 1996).

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(Rossow and Schiffer 1991) have furthered our understanding of the effects of clouds, particularly on the top-of-atmosphere (TOA) radiation budget. Nonetheless, progress toward understanding the effects of clouds on radiative heating within the atmosphere and at the surface has been slow. Figure 20.3 emphasizes this point, showing the net clear and cloudy sky TOA flux differences as observed in July 1988 by ERBE and as predicted in a current GCM climate model (Randall et al. 1989). The net effect of clouds on the TOA radiation balance arises through compensating effects of clouds on the individual long- and short-wave fluxes (e.g., Harrison et al. 1995). However, an entirely different picture emerges when the radiation budgets of the atmosphere and surface are considered (fig. 20.3c, d). The lack of global observations at the surface forces us to resort to use of output from global general circulation models to produce the results shown. According to the results from one such model (fig. 20.3c), clouds radiatively heat the atmosphere at low latitudes and radiatively cool the surface by an almost equivalent amount. Clouds vertically redistribute the absorbed energy of the atmospheric column, depositing radiative energy in the atmosphere in cloud layers largely at the expense of energy absorbed at the surface—a redistribution that is entirely concealed in the view provided by TOA fluxes alone. Figure 20.4 offers a different perspective on the effects of clouds on both the surface and atmospheric radiation budgets and on how clouds redistribute the radiative heating within the atmospheric column. The figure presents the zonally averaged, clear minus cloudy-sky flux differences and highlights a number of points that warrant discussion. First, clouds heat the atmosphere at lower latitudes and cool the atmosphere higher latitudes—a response that requires enhanced transport of heat meridionally compared to the clear sky (Wang and Rossow 1998).This low-latitude atmospheric heating and high-latitude atmospheric cooling occurs largely through infrared radiative transfer processes. To first order, this heating is governed by the vertical structure of cloud layers (fig. 20.5), and it is the tropical cirrus clouds, in particular, that produce the low-latitude heating maximum depicted in figure 20.3c. Second, the effects of clouds on the surface budget is, more or less, the reciprocal of that in the atmosphere, at least at lower latitudes. Clouds tend to cool the surface in this region of the globe and heat the surface at higher latitudes. The former is controlled by shortwave radiative transfer, whereas the latter is controlled by infrared effects. The consequences of these results are 1. If atmospheric radiative heating is an important element of the cirrus cloudclimate feedback problem, and if this heating is determined to first order by the height and thickness of the cloud layers, then the processes that determine the bulk layered structure of cirrus (such as large-scale forcing and convection) may thus be viewed as primarily important to the cirrus cloud-climate feed back problem. 2. If the surface cooling at low latitudes is largely a solar radiative transfer process, then the properties that determine how much solar energy is transmitted to the surface (such as the cloud microphysics and optical properties) are also important ingredients of the cirrus cloud-climate feedback problems.

Top-of-the-atmosphere Net Cloud Radiative Forcing (W rrr2)

Figure 20.3. The difference between cloudy and clear-sky net radiative fluxes in (W/m2) (a) at the top of the atmosphere (TOA) from ERBE, (b) at the TOA from global circulation model (GCM) simulations, (c) at the surface from the GCM, and (d) within the atmosphere from the GCM.

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Figure. 20.4. GCM model derived clear minus cloud radiative fluxes within the atmosphere (upper) and at the surface (lower). The former represents the additional radiative flux convergence of the entire atmospheric column over and above that of the clear sky.

3. The properties that influence the atmospheric heating are presumably important to processes that occur on a different time scale (in the atmosphere and fast) than those properties that affect the surface (such as in the ocean and slow). Is it meaningful to separate the different cirrus properties in this way. Are the most important feedbacks those associated with fast processes or those associated with slow processes?

20.4. Feedbacks

The class of processes considered important to the cloud-climate feedback problem include processes that determine where and why clouds form and the association of these processes to large-scale circulation and processes that

Figure. 20.5. The vertical structure of clouds cannot be determined from the radiation emitted and reflected at the top of the atmosphere (TOA), which is nearly the same in the three cases above. Vertical profiles of cloud radiative heating rate (K/day) are significantly different because the location and thickness of cloud layers (shaded) are different (adapted from Slingo and Slingo 1988). The net column flux divergence is given for each case. Comparing to figure 20.3, the clear-sky divergence is about -80W/m2, producing column heating of +45 W/m2 (left panel), +12W/m2 (center panel), and +3 W/m2 (right panel) relative to clear skies.

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determine how much heating and cooling is produced by clouds and the processes that determine how the atmosphere (and oceans) change due to this heating and cooling. These processes represent a wide range of space and time scales, involving mechanisms that act primarily on the local or cloud-scale to mechanisms that occur on the grosser synoptic to global scales. 20.4.1. Cloud Process Feedbacks The nature of local-scale cloud process feedbacks is illustrated by the work of Jakob and colleagues (chapter 14, this volume), who examined the effects of the vertical overlap of clouds on precipitation production. Figure 20.6 presents the zonal-mean precipitation derived from three one-step integrations of the ECMWF global model using a subgrid precipitation scheme that assumes one of the three different vertical overlap assumptions indicated. Of the three schemes, the random overlap assumption spreads the cloud out over the gridbox more than in the other schemes. This enhanced spreading out minimizes the precipitation that falls from clouds above into cloudy layers below, reducing the total amount of precipitation through both a reduction in the supply of falling ice crystals to clouds below and an increase of evaporation of precipitation falling into clear layers. 20.4.2. Large-scale Feedbacks A number of other modeling studies have explored the feedbacks between the effects of clouds on the heating of the atmosphere resulting from an imposed

Figure 20.6. Zonal mean large-scale precipitation rate for the first time step of a T63L31 integration with the subgrid precipitation model using maximum-random (solid), maximum (dashed), and random (dotted) cloud overlap.

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change in the vertical distribution of radiative heating. The general characteristics of this cirrus cloud-convection feedback are portrayed in figure 20.7. For example, Slingo and Slingo (1988) introduced a new cloud-diagnostic parameterization in the NCAR global circulation model that resulted in an increase in upper tropospheric clouds and reduced radiative cooling at these levels. Liang and Wang (1997) performed similar sensitivity experiments in which changes in radiative heating occurred as a result of changes in the assumptions used to account for overlapping cloud layers. Although the changes led to an overall decrease in cloudiness, the proportion of high cloud to low cloud was increased, resulting in a response on the circulation similar to that reported by Slingo and Slingo. Cloud changes in the Fowler and Randall (1994) study occurred when they introduced a new cloud scheme capable of predicting the different classes of water. In this case, upper-level cloudiness was reduced, but the optical prop-

Figure 20.7. (a) The radiation-convection feedback associated with changing upper-level cloudiness and the profile of radiative heating. The negative feedback is so strong in global circulation models that small changes of upper-level cloud and associated heating lead to reductions in global precipitation by 20% (e.g., Liang and Wang 1997). (b) The same feedback operating in reverse in a coupled ocean-atmosphere model (adapted from Arakawa 1997).

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erties of the clouds, now predicted by the new scheme, produced an increased absorption and heating in the upper layers and a model response similar to that reported in the other studies and demonstrated a critical sensitivity of the general circulation to the distribution and amount of ice in layered upper tropospheric clouds. Simple changes in parameterization of the production of ice content led to profound changes in radiative heating (Fowler and Randall 1994). In each case, the amount of upper-level cloud (through changing cloud amount and/or ice content) is a key quantity. Increased stabilization of the atmosphere produced significant reductions in global precipitation and, in turn, provided a feedback to the upper-level cloudiness. The fourth modeling study is that of Ma et al. (1994) and involves a coupled atmosphere-ocean model. The same feedback operates in this model, although in the opposite direction to those described above. The characteristics of this feedback are shown in figure 20.Ib (from Arakawa 1997). In this case, the cloudiness is changed in such a way as to produce a decreased radiative heating by clouds (through a decrease in emissivity), leading to (relative) cooling aloft, destabilizing the atmosphere and increasing convection, resulting in stronger evaporation and colder sea surface temperatures (SSTs). These studies, along with other similar studies (e.g., Wang and Rossow 1998), provide clear examples of the sensitivity of current models to changes in the vertical distribution of clouds and radiative properties of clouds. As exemplified in the Ma et al. (1994) study, we expect that these sensitivities will become even more acute, and cloud processes will play a more central role as we move forward into the era of coupled models (Arakawa 1997). The explicit relationship between ice mass (a predicted quantity in new prognostic schemes in global circulation models) and the radiative properties of ice clouds (a parameterization currently in models that varies from almost entirely empirical to largely physical with parameters estimated subjectively) needs to be tested by observations. Unfortunately, the necessary observations do not exist on the global scale. 20.5. Evaluating Model Predictions of Cirrus Clouds: A Global Perspective from Space

Figure 20.8 outlines the evaluation strategy currently pursued under the GEWEX Cloud System Study (GCSS) Program (Browning 1993). The approach aims to integrate measurements with cloud-resolving models as a way of testing and ultimately developing new parameterizations for use in both numerical weather prediction (NWP) and climate prediction models. An important step in this processes is to evaluate the cloudiness in NWP models and assimilation systems because the NWP assimilation system provides the large-scale forcing used to initialize cloud-resolving models, which are then compared to field measurements. Field measurements, either collected routinely as part of systematic programs such the U.S. Department of Energy Atmospheric Radiation Measurement program (ARM; Stokes and Schwartz 1994), or available from intensive experimental programs, can test the global cloud data derived from satellite observations as well as test our understanding of isolated key processes.

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Figure 20.8. The GCSS strategy includes use of global data to test numerical weather predictions and combines satellite and field data to verify cloud process models applied to specific case studies. This strategy of evaluating a hierarchy of process models using satellite, intensive field observations, and data collected routinely will lead to a better understanding and thus more refined parameterizations of cloud processes.

The combination of global and field measurement data will lead to a better understanding of key cloud processes and thus ultimately to better representations of these processes in NWP and climate models. At present our ability to evaluate cloud properties predicted either by global models or predicted by cloud-resolving models is either too qualitative to provide strict tests of models, as is the case of satellite observations, or too limited to test our ability to predict clouds associated with a prescribed, large-scale forcing. The limitation of current satellite data in assessing cloud properties is underscored in figure 20.9. This figure shows two 18-h forecasts of the distribution of ice water path for a mid-latitude frontal cloud system and the resulting fields of outgoing longwave radiation (OLR) associated with these predictions (Jakob and Rizzi 1996). Each forecast uses a slightly different version of the cloud physics in the ECMWF forecast model that produces different ice contents and ice crystal particle sizes. One forecast (physics 1) produces smaller ice water paths and smaller particle sizes, giving rise to larger optical depths and hence reduced OLR than that in the second forecast (physics 2). This is a direct and telling illustration of the lack of one-to-one correspondence between ice water path and optical depth. Because of this ambiguity, optical depth information derived from satellite radiance data cannot be used as a way of evaluating cloud ice content in models. The ambiguity between TOA radiative fluxes and ice water path has also noted in the model analyses study of Rasch and Kristjansson (1998). What is crucially needed for model verification are global measurements of ice content.

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Figure 20.9. The ice water path-optical depth conundrum. Shown are the predicted ice water paths and associated estimates of the outgoing long-wave radiation determined from two 18-h forecasts using the ECMWF model of a mid-latitude frontal system. The different assumptions about the way ice crystals fall lead to the differences shown.

20.6. Summary

This chapter has briefly addressed the important ways cirrus clouds affect the Earth's climate and identified two key scientific questions associated with the cirrus cloud-climate problem: 1) To what extent does the large-scale circulation affect the formation of cirrus, either directly such as through large-scale ascent, or indirectly through the effects of the circulation on convection and detrainment

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of ice? 2) To what extent do (cirrus) clouds, as a result of their radiative and microphysical properties, affect the larger-scale environmental thermodynamic and dynamic properties of the atmosphere through their influence on radiative transfer and the water budget of the upper troposphere? Our ability to address these questions in quantitative detail is largely hindered by a substantial lack of observations. Total column-integrated estimates of optical depth and cloud-top heights (all that is currently available from satellite observations) unfortunately do not resolve the key processes that are considered important to climate and climate feedbacks. Optical depth information alone is insufficient to test understanding of feedbacks between clouds and heating they produce. As a minimum, we need simultaneous profiles of optical depth and water/ice content. Particle size information, if available, can also be used to test other cloud physical processes such as precipitation formation, evaporation, and ice fallout. Although the observational basis of our knowledge is limited, we can infer that 1) layered ice clouds modulate both the solar radiation reflected to space and thus received at the surface as well as the long-wave radiation absorbed in the atmosphere and thus the radiative heating of the atmosphere — an effect likely to be important in cirrus clouds-climate feedback mechanisms. 2) Layered clouds are a stage in the circulation of water from high cumulus towers into the upper troposphere. Water vapor in the upper troposphere and lower stratosphere is important not only to our understanding of the greenhouse effect (Lindzen 1990; Rind et al. 1991) but perhaps also to the chemistry of the lower stratosphere. The influence of cirrus on the water vapor in these regions of the atmosphere, however, is not quantitatively understood. The observational basis for our understanding, although rudimentary at this time, will receive a much-needed boost with the launch of CloudSat (Stephens et al. 2000) and PICASO-CENA missions currently being developed under the NASA Earth System Science Pathfinder program (ESSP).

Acknowledgments This chapter contains elements of research supported by the U.S. Department of Energy/ARM, DE-FG03-94ER61748, and under the National Aeronautics and Space Administration NAG5-6637.

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Slingo A., and J. Slingo, 1988. Response of a general circulation model to cloud longwave radiative forcing: Part I. Introduction and initial experiments. Quart. J. Roy. Meteorol. Soc., 114,1027-1062. Stephens, G.L., and T. Greenwald, 1991. The Earth's radiation budget and its relation to atmospheric hydrology 1: Observations of the clear-sky greenhouse effect. J. Geophys. Res., 96,15311-15324. Stephens, G.L., C. Jakob, and M. Miller, 1998. Atmospheric ice: A major gap in understanding the effects of clouds on climate. GEWEX Newslett., 8(1), February 1998. Stephens, G.L., D. Vane, and S. Walter, 2000. CloudSat: A new dimension to the global observation of clouds. In workshop on cloud processes and cloud feedbacks in largescale models, ECMWF, Reading, UK, 9-13 Nov. 1999, World Climate Research Program (WCRP-110),WMO/TD No 993,143-160. Stokes, G.M., and S.E. Schwartz, 1994. The Atmospheric Radiation Measurement (ARM) Program; programmatic background and design of the cloud and radiation test bed. Bull. Amer. Sci., 75,1201-1221. Wang, I, and W.B. Rossow, 1998. Effects of cloud vertical structure on atmospheric circulation in the GISS GCM. J. Climate, 11,3010-3029. wielicki, B.A., 1996. Clouds and the Earth's Radiant Energy System (CERES): An Earth observing experiment. Bull. Amer. Meteorol. Soc., 77, 853-872. Wielicki, B., R.D. Cess, M.D. King, D.A. Randall, and E. Harrison, 1995. Mission to planet Earth; Role of clouds and radiation in climate. Bull. Amer. Meteor. Soc., 76,2125-2153.

21

Cirrus The Future

DAVID K . L Y N C H K E N N E T H SASSEN ANTHONY DEL GENIO ANDREW J. HEYMSFIELD PATRICK R. M I N N I S C. M A R T I N R. PLATT MARKUS QUANTE ULRICH SCHUMANN HILDING SUNDQVIST

Sometime we see a cloud that's dragonish A vapour sometime like a bear or lion, A tower'd citadel, a pendent rock, A forked mountain, or blue promontory, With trees upon't, that nod unto the world, And mock our eyes with air: thou hast seen these signs; They are black vesper's pageants . . . That which is now a horse, even with a thought The rack dislimns, and makes it indistinct, As water is in water. Shakespeare, Antony and Cleopatra

The preceding 20 chapters reveal cirrus in considerable depth. Just as important, however, is what is not revealed. There are many things that we do not know or understand about cirrus. In this final chapter we present the outstanding scientific issues facing the cirrus research community. Our goal here is to produce a guide for students, scientists, policy makers, and funding organizations who wish to quickly grasp the direction and future needs of cirrus research. The impact of cirrus clouds on climate and how they interact with a climate perturbed by human enterprise is only dimly perceived. Do cirrus clouds, on a regional or global scale, act to cool or warm our planet? By reflecting incoming solar radiation to space, they can cool. Yet as an opacity source in the 10-um window, they 449

450

Cirrus

can radiate downward and warm the Earth. Which process dominates, and under what conditions does warming overtake cooling? Does the atmosphere react to cirrus globally or regionally (i.e., can cirrus increase pole-equator temperature differences or mute them)? Are there other mechanisms at work that defeat or amplify temperature changes by cirrus? We do not yet know. Programs such as SUCCESS, ICE, CRYSTAL, INCA, and FIRE/SHEBA will do much to answer questions about contrails and cirrus variability from one part of the world to another. They also will go a long way toward understanding one of the most difficult problems in meteorology: how convection and turbulence are related to cirrus formation and maintenance. In the meantime, existing capabilities are underused. For example, remote sensing techniques for estimating ice water path now exist but have not been assigned enough priority to achieve the necessary breakthroughs. Considerable progress could also be made in data analysis. As in other fields, analyzing existing data has a lower funding priority than designing and building new hardware and flight systems. Three fields of inquiry need more attention before we can claim a sufficient understanding of cirrus: physical properties, radiative properties, and modeling. These fields are interconnected in often subtle ways. 21.1. Physical Properties

Much of what we do not know about cirrus involves the range of properties and their evolution in time. Cirrus are not one but many types of clouds, a situation that has come about because "cirrus" is a morphological category, not a physical one. Different parts of the same clouds will change in different ways in response to changing environmental conditions, often on time scales of minutes or hours. The precise form of crystal growth is influenced by too many parameters to be reproduced analytically in the foreseeable future. Temperature, humidity, supersaturation, ventilation, existing morphology, and perhaps even trace impurities in the air and nuclei all affect an ice crystal's shape. Shape and size (and orientation) as well as refractive index determine a crystal's radiative properties. The radiative properties determine whether or not a cirrus cloud warms or cools the Earth. Radiative properties even feedback to the cloud itself and influence its evolution. How are cirrus crystals produced? Is homogeneous nucleation the only means? What is the nature of updrafts and vertical motions associated with cirrus formation? What is the microphysical structure of cirrus in the vertical? What role does aggregation play in the evolution of crystals? Many of these questions can be addressed in the laboratory, but others require in situ studies. More effort should be made to parameterize experimental growth properties and then introduce the results into cloud and climate-modeling codes. Better in situ (aircraft, balloons, dropsondes) probes are essential for detecting and characterizing small ice particles (<10|j,m across) and for directly measuring ice water content. These probes are necessary for determining optical properties such as phase function and asymmetry parameter, which are vital to modeling codes. A number of new in situ particle-size measuring instruments are

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45 I

undergoing field tests, and these promising devices could translate into major advances, especially when used in aircraft that can reach the tropopause. Remotely piloted vehicles capable of prolonged stays in cirrus could also provide a cost-effective means of gathering detailed information about cirrus. Many fundamental properties of cirrus clouds can be evaluated from the ground, leading to the creation of site-specific climatologies. This situation can only improve as more advanced (i.e., Raman and high spectral resolution) lidars, lidar-radiometer (LIRAD) combinations, and millimeter-wave Doppler radars are applied to the regular investigation of cirrus clouds to yield more accurate optical extinction and cloud microphysics. For example, by adding a Raman backscatter channel for nitrogen molecules, more reliable measurements of cirrus extinction (and optical depth) can be made; the LIRAD approach combines shortwave (lidar) and infrared radiometer data to measure optical depth accurately; and radar offers the potential for deriving quantitative cirrus microphysical properties using Rayleigh theory. Better cloud-property retrieval algorithms based on multiple active and passive remote sensors will also increase the accuracy of derived cirrus cloud optical and microphysical properties, which are crucial for comprehending their effects on the radiation balance of the earth-atmosphere system. Improving our knowledge of the full gamut of cirrus cloud properties will contribute to our ability to effectively simulate these remote clouds in numerical models, from which a gradual improvement in weather forecasting, general circulation, and climate prediction models can be expected. Dynamic features and effects of turbulence and cloud-scale vertical motions influence the physical properties of clouds, which in turn affect the clouds' radiative properties. Thus, dynamics should be considered in studies addressing the explicit life cycle of cirrus. Not only are microphysical characteristics important for the cloud-radiation interaction, so too are where, when, and how long cirrus persist. This is because the availability of sufficient water vapor is highly dependent on mixing and advection. Cloud-resolving models need to include the complex interaction between cloud-scale dynamics and larger scale dynamic persist. These links need to be established from observations and experiments. There are two aspects to the problem. The first involves instrumentation and sampling strategies. The influence of turbulence and vertical motions on the development of cirrus must be better quantified and related to the effects of cloud microphysical changes. Optimized sampling strategies must be developed that make use of combined remote sensing and in situ observations to locate the in situ measurements within the three-dimensional cloud field. The goal should be the delineation between cloud-induced phenomena and those associated with the surrounding environment. Multi-aircraft experiments should obtain simultaneous measurements at different heights in neighboring cloud areas to resolve the dynamics of cloud-generating cells in contrast to the more passive parts of the clouds. New experiments should also provide a dense network (space and time) for vertical profiling of wind, potential temperature, and humidity to allow better identification of dynamic regimes and their development during cloud life cycles. The use of dropsondes would be a valuable extension to earlier observational strategies. Global Positioning System (GPS) tracking of sondes might yield the

452

Cirrus

required vertical resolution of the horizontal wind field. A means to map the local three-dimensional wind field would be extremely useful. Real-time, surface-based or airborne active remote sensing should provide a more interactive airborne in situ sampling strategy in response to the observed conditions. The second aspect involves analysis. Although a significant amount of in situ turbulence data has been analyzed, more quality observations in cirrus clouds are sorely needed. Additional observations would help establish the significance of present findings, an important concern given the existing ambiguities. They would also provide a better sample over the variety of cirrus cloud types and situations. In particular, observations in tropical and anvil cirrus clouds are badly needed. In some instances, a more detailed analysis of existing data by wavelet analysis in combination with a thorough analysis of microphysical and radiation measurements could provide significantly more insight into the processes at work. More studies are needed that combine in situ measurements of turbulence and ice particles with remote sensing data to better comprehend cloud microphysical parameters and macroscopic cloud structure. Contrails are a special form of cirrus about which there are many unanswered questions: How do persistent contrails evolve with time, and what are their microphysical, morphological, and radiative properties? Which are the most important aircraft parameters controlling the properties of persistent contrails: the number of aircraft cruising; the amount of fuel consumed; the number of condensation nuclei and ice nuclei induced by aircraft; soot, sulfuric acid droplets, and mixed aerosols induced by aircraft; or turbulent mixing induced by aircraft? Which are the most important environmental parameters controlling the properties of persistent contrails: ambient temperature, relative humidity, rising or sinking air motions, wind shear, turbulence, solar and terrestrial radiation, ambient aerosol properties, or preexisting cirrus clouds? Which air masses are conditioned to form persistent contrails, how thick and wide are such air masses, how are these air masses distributed over the globe, and how are these air masses related to largescale dynamics of the atmosphere? What is the contrail cloud cover over regions other than over Europe and the United States? Is mean contrail cover increasing, and how is this increase related to air traffic properties? What will be the future change in contrail cover? How does the future change in contrail cover depend on parameters of future air traffic and future climate? How do aircraft change background aerosol with respect to cloud-forming properties? What is the impact of aircraft-induced aerosol changes on the microphysical properties, optical properties, areal coverage, and frequency of occurrence of cirrus clouds? Is the mean cirrus cover increasings and which part of this increase is due to aircraft? What are the consequences of cirrus changes for radiative forcing, for the hydrological cycle, for air chemistry, and climate? Is there an observable relationship between aircraft-produced aerosol and cirrus properties? How can one model the contrail-aerosol-cirrus cloud relationships? What is the most efficient strategy to reduce aircraft impact on cirrus clouds? Measurements should be performed to identify the relationship between aerosols and cirrus properties, for example, by measuring in different air masses with low and high aerosol concentrations. Models should be developed to account for the indirect effects of aerosols on cirrus properties for global climate studies. Finally, remote sensing

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should be applied to identify contrail cover, trends in contrail and cirrus cloudiness, and changes in radiative properties of cirrus clouds. 21.2. Radiative Properties

Although many models predict that cirrus should warm the Earth, they can assume the opposite effect as the optical depth increases. Pivotal factors include cloud height, optical depth, and mean crystal size. Ice clouds possess different solar reflection characteristics from water clouds. Yet cirrus are composed of a mixture of a variety of ice crystal habits and sizes, where one habit may predominate, depending on temperature and saturation. The solar reflection can change depending on the ice crystal habit. These differences have wide implications for climate research. What is required to solve the problem of cirrus-radiation interaction is a two-pronged approach of modeling of ice crystal scattering and carefully designed observational programs. The asymmetry parameter determines the relative amount of sunlight scattered downward to Earth and upward to space. Recent modeling using different ideal ice crystal shapes has given varying ice crystal scattering phase functions that yield different asymmetry parameters. Ice crystal models have also been run for distorted crystals, thus changing the asymmetry parameters. Such work is crucial to our understanding of energy balance and should be expanded in combination with experimental verification. The concerted modeling approach should be supplemented by comprehensive aircraft experiments that measure ice crystal shape, irregularity and size, fluxes of solar and infrared radiation, and lidar backscatter intensities. New instruments that are operating will measure asymmetry parameter directly; this will lead to significant advances in understanding how cirrus reflect solar radiation. The experiments should be repeated at many different cirrus temperatures. Lidar backscatter-to-extinction ratios are also affected by ice crystal habit and deformation. Methods for using lidar backscatter to derive the scattering phase function and asymmetry factor would allow resolution of the radiation-cloud interaction problem. Deriving cloud physical and optical properties in all conditions remains a challenge for cirrus remote sensing, especially from satellites. With better estimates of cirrus optical depth, effective particle sizes, and shapes in all conditions, it will be possible to improve our estimates of ice water path, a quantity fundamentally important in general circulation models. Although substantial improvements were made in the 1990s, much more research is needed to accurately determine the parameters that tie the hydrological and radiative processes together in the upper troposphere. Because reflected solar radiation contains more information about the clouds than emitted radiation, refined techniques are needed for retrieving cirrus properties at night. However, measurements and calculation of infrared properties, for instance by LIRAD, can be related to visible optical depth theoretically. Consistent day-night retrievals of all of the cirrus parameters will enhance our ability to fully understand the radiative and dynamic processes governing cirrus growth and dissipation. Methods need to be

454

Cirrus

developed for identifying cirrus in multilayered cloud fields and isolating their effects during both day and night. Algorithms for systematically using multiangle satellite data, either on a single instrument or on two satellites, should be developed to monitor cirrus properties, especially cloud particle shape, more accurately than possible with current approaches. Satellites with a nearly direct backscatter view would be particularly valuable for estimating particle shape. The physical thickness of cirrus is an especially elusive quantity for operational cloud monitoring from satellites. Advances in determining cloud thickness will be valuable for a variety of applications, including the computation of atmospheric and surface radiative heating. Future satellite sensors will contain much of the information needed for deriving cirrus properties, but development of a variety of innovative and practical techniques is essential if the host of data from those instruments are to be converted into useful scientific products. To obtain the global view of the climatic importance of cirrus clouds, measurements from earth-orbiting satellites are a necessity. Although passive, multispectral satellite measurements have shown promise for studying high clouds, and the latest generation of radiometers have recently been launched into orbit, major advances can only be expected after active remote sensing space-borne measurements are added to complement the passive data streams. The physical thickness of cirrus is an especially elusive quantity for operational cloud monitoring from satellites. Advances in determining cloud thickness will be valuable for a variety of applications, including the computation of atmospheric and surface radiative heating. The ability to measure cloud thickness directly from space on a global scale using lidar and radar is of vital importance in understanding and monitoring the global radiation budget. 21.3. Modeling Cirrus span a wide range of optical thicknesses that encompass both positive and negative net cloud forcing. The processes responsible for their formation, maintenance, and dissipation are not yet adequately understood. Therefore, the role of cirrus in climate change is potentially significant but currently impossible to quantify, even as to the sign of their net feedback. Crucial areas for future investigation include 1) the dynamic scales of motion that are primarily responsible for the transport of water vapor to the upper troposphere that results in cirrus formation; 2) the vapor saturation conditions required to form cirrus at different temperatures and in different dynamic regimes; 3) the global importance of cirrus contrail formation and the potential indirect effect on cirrus of aerosols lofted from the planetary boundary layer into the upper troposphere; 4) factors controlling the small-scale variability statistics of cirrus and their impact on largescale representations of cirrus radiative effects and microphysical processes; 5) environmental factors determining the strength of convective condensate transport and detrainment into mesoscale cirrus anvils; 6) a global assessment of the relative fractions of supercooled liquid water and ice in the atmosphere as a function of temperature, dynamics, cloud age, and so on, which in turn requires the development and implementation of remote sensing techniques that can measure

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ice water path; and 7) similarities and differences between mid-latitude and tropical cirrus and between cirrus and winter or polar low-level ice clouds. Therefore we should promote a close cooperation between the measuring and observing community, on one hand, and the modeling community on the other. The former may be given a better insight into the modeler's request for observational data, while the latter will learn about potentials and limitations in measurements and observations. 21.4. Conclusion

The outlook for making major strides in our understanding of those cirrus cloud properties of importance to climate research is promising in terms of improved in situ probes, satellite and ground-based remote sensing techniques, and numerical modeling. However, some of the problems are so complex that one may ask whether a solution to them is possible at all. For example, given a complete physical description of a parcel of air, it is still difficult to predict the size and shapes of the crystals that actually form. For many other questions, the methods exist at least in principle, but focused research programs for applying them to provide the answers in reasonable time scales are missing. Fortunately, plans are currently being finalized to orbit both a lidar (PICASSO) and 95-GHz radar (CloudSat) and other sensors in formation, along with the latest generation of Earthorbiting satellites, to profile clouds and aerosols on a global scale. These new satellites represent the first step into a deeper realm of monitoring the clouds, including the tenuous upper tropospheric cirrus. We hope that the importance and beauty of cirrus clouds, as described in this book, will attract further scientists and research programs to promote progress in understanding.

Acknowledgments This work was supported by The Aerospace Corporation's Independent Research and Development Program.

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Appendix

Chapter 2 Plates: Cirrus Case Studies

plate 2.1.Reprresentative fisheye photographs of the clouds desribed in the FARS cirrus case studies,corresponding to plates 2.2 (a),2.4-

2.9 b-g, and 2,11b. the day of the month,and houre and minute in UTC is at lower right .althought plates 2.1-211 are responsible here in black and white, the original photograph are coloure

Plate 2.2. PARS ruby lidar returned energy gray scale and color linear depolarization ratio (8, see key at lower right) displays of the classic cirrus fibratus observed on October 14-15,1998. The solid and dashed lines in the panel at top right give the local temperature and dewpoint temperature profiles: note that radiosonde dewpoints are not considered reliable for temperatures <-40°C.

Plate 2.3. PARS ruby lidar returned energy gray scale and color linear depolarization ratio for the cirrostratus and fibratus studied on the evening of October 17,1992.

Plate 2.4. PARS ruby lidar returned energy gray scale and color linear depolarization ratio for the fibratus and spissatus studied on January 17,1997.

Plate 2.5. PARS ruby lidar displays of the cirrostratus/spissatus transition on March 25,1992.

Plate 2.6. Ruby lidar displays of a halo-producing cirrostratus cloud studied from PARS on April 25,1997.

Plate 2.7. Ruby lidar displays of a cold corona-producing cirrostratus cloud studied from PARS on December 10,1992.

Plate 2.8. Polarization diversity lidar (0.532 urn) backscattering and depolarization displays of a multilayered, standing lenticular cirrus wave cloud studied from PARS on January 11,1999.

Plate 2.9. Polarization diversity lidar (0.532) um) displays of the cirrostratus to altostratus transitions obtained at Faras on March 29, 1999, as in plate 2.8.3

Plate 2.10. Ruby lidar displays of a cirrostratus altocumulogenitus cloud sampled at PARS on October 6,1992.

Plate 2.11. PARS ruby lidar displays of descending cirrus fibratus and altocumulus cirrogenitus clouds from January 9,1996.

Index

Abercrombie, Ralph, 5 absorptance, solar, 380,391 absorption gaseous, 211 water vapor, 211 coefficient, 215,219,225,227,397,398, 405,409,421,426 vertical profiles, 401, 426 accretion, 404 activation energy, 401 active sensors. See lidar, radar adsorbed layer, 52 Advanced Very High Resolution Radiometer (AVHRR), 272 AERI. See Atmospheric Emittance Radiance Interferometer aerosol particles ammonium bisulfate, 105,116,119, 121-122 ammonium sulfate, 103,118-121 back scatter lidar, 199 carbonaceous, 104,124 composition, 103-104, 402 deliquescence of, 105,110,118,120-122 effects, 384, 386,390 efflorescence of, 105,110-118-121

from aircraft exhaust, 103-104 interactions with cirrus, 127-128 letovicite, 121-122 organic, 103,121 scavenging of, 102,127-128 secondary phase transitions in, 104-105, 110,121 size spectra, parameterization, 402 sources of, 103 sulfuric acid, 103,109,114-118,121, 123-124,421,424 upper tropospheric, 103, 357, 362,369 aggregates, 270, 272 air pressure, 46,47,52,53 air traffic, 246 airborne (aircraft) measurements, 14,169, 185,191,211,223,224,227,233, 265,289,322,353,450 Airborne Remote Earth Sensing System (ARES), 284,291 Airborne Visible Infrared Imaging Spectrometer (AVIRIS), 285 aircraft. See airborne albedo, 153,224 cloud, 418 effect, 397,398, 412,427 469

470

Index

albedo (cont.) emittance, relations, 224 solar, 223 algorithms, 178-180,187-193 multiparameter, 178-179 multi-wavelength, 179-180 single-parameter, 178 two-parameter, 5,180 altocumulus, 17,18,24, 33-35 altostratus, 17, 31-33 ammonium sulfate, 402,418,421 Anaxagorus of Clazomenae, 1 Antarctic, 53 anvil (cirrus), 8,18-19,23,78,259,298, 302,305,306, 310-317,323, 451 cloud retrieval, 451 multi-angle satellite data, 453 Appleman criterion, 232 ARES. See Airborne Remote Earth Sensing System ARM. See Atmospheric Radiation Measurement asymmetry parameter (factor), 257, 274, 451 atmosphere, tropical, 215,217 Atmospheric Emittance Radiance Interferometer (AERI), 180,188 (See ••) Atmospheric Radiation Measurement (ARM) program of the US DOE, 154,443 attenuation, 170,175 autoconversion threshold, 302, 306 aureole, 257 AVHRR. See Advanced Very High Resolution Radiometer AVIRIS. See Airborne Visible Infrared Imaging Spectrometer backscattering, 170-173 (See also scattering) anomalous, 218,219 attenuated coefficient, 212 backscatter-to-extinction cloud, 227 coefficient, 172 integrated, attenuated, 213,217,218, 219, 225 lidar coefficient, 214 lidar profile, 214 power, 171

ratio, 172,212,223,224,225,227,453 ratio, effective, 218, 221, 222, 223 ratio, retrieved, values, 221 rayleigh, cloud, transmittance, 227 balloon borne instruments, 83 basal plane, 52 Beer-Lambert law, 182 bidirectional reflectance, 277, 278, 282, 283, 286 blackbody, spectral, radiance, 215 boundary layer, 54 brightness temperature, 289 Brownian motion, 61, 62 Brunt-Vaisala frequency, 349, 355, 356, 357 buoyancy, 348, 350, 351 length scale, 350,351, 356,357 production, 349, 356 subrange, 351,352, 361 C60,54 calibration, molecular, atmosphere, 212 CAPE. See convective available potential energy carbon dioxide, 215 CART. See Cloud and Radiation Testbed CAT. See clear air turbulence CCN. See cloud condensation nuclei CERES. See Clouds and the Earth's Radiant Energy System chemi-ion, 234 Christiansen effect, 273 cirrocumulus, 6 cirrostratus, 6, 78, 273, 286, 287, 375, 377, 379 cirrus altitude, 148,151-154 and relative humidity, 105,109-110,114, 117-118,120,122 antarctic, 225 anvils, 383, 392 (See also anvils] cirrostratus, 375, 377, 379 classification, 4-9 climatology, 5,11-40,258,451 cold, 223 composition, 3, 6,450 contrails, 231-255, 384-385 coverage, 148,149 definition, 6 with regard to detectable radiation effect, 299 with regard to temperature, 299

Index

emittance, 31-33, 36,187-190,180,211, 214 equatorial, 219,226 evadus, 256 field experiments, 79 formation of, 19-20,95,105,109-125 frequency, 138 frontal, 355,362,368,383 history, 3-10 horizontally oriented plates in, 23-24 ice water content of, 298 ice water content related to vertical velocity, 298, 302 ice water feedback parameter, 223 influence on climate, 175-178 infrared and visible, properties, 226 inhomogeneous, 280 invisible. See also subvisual cirrus, 226 isolated, 216 jet stream, 355, 357,358, 362,364, 366 laboratory studies of, 102-135 lenticular, 384 life cycle, 346,362,369, 370, 375-392 location, 138 macrophysical properties, 25-27 mesoscale uncinus complex (MUC), 22-23, 383 mid latitude, 211,224 names, 5, 6-8 observational data of, for verification, 307 requirement of with respect to parameters, 307 requirement of with respect to coverage, 307 occurrence, 138 parameterization of, included in modeling, 306-307 physically based parameterization of, 299, 304 optical depth, 18-19 prediction, 5,341 properties, other, 6,78,211 radiative properties, 211,224 semi transparent layer, 219 size distribution, 89, 90, 91 spissatus, 18,22-23 subvisual, 159,160, 256-264,384, 392 synoptic, 222 temperature, 148,153,155,157,158,160 thickness, 153,159,160,454 tropical, 78-101, 211, 220

471

types, 7,16-17, 36-37 uncinus, 20,22,376-378 warming/cooling effect of, 397,412,419, 423 CKD. See correlated k distribution Clausius-Clapyeron equation, 46 clear air turbulence (CAT), 347 climate, 175-178,248,433^48 climatology, 5,147,154 PARS, 183-185 ISCCP, 154 surface observations, 154,155 cloud albedo, single-scattering, 153 base altitude, 213,216 cold high ice, 223 composition, 235 concepts, 328-330 condensation nuclei (CCN), 55,56,68, 71,399,429 deep cirrostratus, 216 definition of, 298 depth, 211,216,222 emissivity, 152,154,158,160,212 evaluation of, 339-343 extinction, 153,154,159, 216 fibratus, 22-23 forecasts, 5,341 formation, 232 fraction parameterizations, 329-333 number, 235 in NWP, 327-345 link to convection parameterization, 330 microphysics, 178, 211, 398, 399 mammatta in cirrus, 23 mid latitude, 226 models, 398, 399, 429 multi-level, 159-160 optical depth, 148,153,154,160,226 particle habit, 148,153,154,157,160, 161 particle orientation, 161 particle phase, 155,157,160,161 particle size, 148,153,154,159-161, 211, 227 particles, 224,234,240 persistence, 233 properties, 178-185 radiative forcing. See cloud forcing radiative properties, 178,181-185 regional effects, 245

472

Index

cloud (cont.) scattering effects, 214 shape, 242 size, 242 spectrum, 242 temperature, 217-219,221-225 thermodynamics, 399 threshold, 233phase, 226 transmission, 159 tropical, 78-101,222, 223, 226 water, 226 cloud boundaries and structure, 175-178 methods of determining cloud boundaries, 176 methods of determining cloud height, 175 sources of uncertainty, 175 cloud chambers, 111-112,125-126,403 cloud feedback, 439 cloud-climate (feedback) problem, 434, 439,441 process related feedbacks, 441 large scale feedbacks, 441 cloud forcing, 245,286-289,312-313,397, 412,419,423,424 cloud radar use in GCM evaluation, 342 Cloud and Radiation Testbed (CART), 169,187 cloud radiative forcing. See cloud forcing Clouds and the Earth's Radiant Energy System (CERES), 435 CloudSat, 446, 455 cloudscope, 55, 58, 59, 67, 82 CO2 slicing, 149,151,152,154,159,161 CO2, 58 coagulation, 400 coherent structures, 365 conceptual model of cirrus formation, 95 condensation conditions or possibilities for, 300,304, 305 conditional instability, 379,380,386 conduction & conductivity, 46,49,50 continuous replica, 66 covariances, 429 contrails, 6,19, 23,56,102,231-255,265, 282,451-452 climate effect, 248 convection, 347, 353,355, 356,359,361, 365, 368

convective available potential energy (CAPE), 317 corona, 24,240,257 correlated k distribution (CKD) method, 282,283 coverage, 239 CPI probe, 83 critical energy of germ formation, 401 radius of ice germ, 401 cross, sectional area, 92 crystal. See ice crystal CRYSTAL, 450 cumulus detrainment, 314-317 CVI probe, 83 Defense Meteorological Satellite System (DMSP), 256 Definitions cirrus, 6 with regard to detectable radiation effect, 299 with regard to temperature, 299 cloud, 298 cirrocumulus, 6 cirrostratus, 6 subvisual cirrus, 6, 257 LIRAD, 451 precipitation, 298 dehydration, 435 deliquescence, 105,110,118,120-122 delta transmission, 267 depolarization, 170-171,181, 226, 242 (See also polarization) backscatter, 170-171 lidar, 21-22,181 linear depolarization ratio, 171 ratio, integrated, 214 ratio, linear, 226 deposition crystal growth by, 400,415,421 layer, 408 Descartes, Rene, 1-2 detrainment, 330, 341 diameter, effective, 223 diffraction, 257,268 diffusion chamber, 53,110-111,116-119,121, 125-126 growth of ice crystals by vapor, 107, 110-111,125-127

Index

transport, 46 diffusivity, 46,49 dilution, 233 Discours de la methode, 1-2 dislocation, 54 dissipation rate, 364 diurnal cycle, of cloud forcing, 412,419,423,424 heating rates, 412,420,423,424 DMSP. See Defense Meteorological Satellite System Doppler radar, 347 dorite, 53 downshear, 68 drag coefficient, 63 Drebbel, Cornelis, 4 Droplet concentration, 426 haze of sulfuric acid, 421,424 nucleation from vapor, 401 size spectra, 399 supersaturation relaxation time, 426 dropsondes, 451 dynamical measurements, 347 processes, 77, 346-374, 375-396 sources, 310-311, 314, 317-318, 320, 324 Earth Observing Scanning Polarimeter (EOSP), 292 Earth Radiation Budget Experiment (ERBE), 312-313,323,435,437 ECLIPS. See Experimental Cloud Lidar Pilot Study ECMWE See European Center for Medium Range Weather Forecasts eddy, 61 effective freezing temperature, 113,115 efflorescence, 105,110,118-121 electrodynamic balance. See levitation ellipsometry, 51 ellipticity, 62 emissivity (& emittance), 51,63,65,152, 154,158,160, 212,225, 226,410, 428 emittance (See also emissivity) infrared, 218,219,221,223,227 infrared, percentage, in, intervals, 217 emulsions, freezing of, 109-111,113-114, 121-122 energy cascade, 351,368

473

-containing range, 363, 369 dissipation, 349,364 interfacial, 105-107 of activation, 105-107 of formation of ice embryos, 106,109 spectrum, 351,354,360, 361 entrainment, 346, 347, 392 EOSP. See Earth Observing Scanning Polarimeter ERBE. See Earth Radiation Budget Experiment EUCREX. See European Cloud Radiation Experiment Eulerian measurement, 67 European Center for Medium Range Weather Forecasts (ECMWF), 435, 444 European Cloud Radiation Experiment (EUCREX), 265,278, 383 evadus, 256 evaporation, 52, 58, 59 of cirrus in the upper troposphere, 298 of precipitating ice crystals, 303 of precipitation, 300 parameterization of, 303 evaporation layer, 408,416, 426 experiment, arm, pilot, radiation, (probe), 219 experiment, tropical, 218 Experimental Cloud Lidar Pilot Study, 225 extinction, 65 cloud, 153,154,159 coefficient, 92, 216, 225, 227, 274, 397, 398, 405,409, 421,426 efficiency, 270 visible-to-infrared absorption, ratio, 223, 224, 227 visible-to-infrared absorption, ratio, effective, 221, 223 facet(s), 49, 54, 55,58,70 Facility for Atmospheric Remote Sensing (PARS), 20,183-185 fallspeed, ice water, 301,376, 379, 381,384, 386-387 fall velocity, 55,61,300,302, 305,435 PARS. See Facility for Atmospheric Remote Sensing FDTD. See finite-difference time domain feedbacks, 313-314,439,441. Also See cloud feedbacks

474

Index

feedbacks (cont.) global warming, 398,411,412,429 Ferrald two-component solution, 172 field research programs, 168 finite-difference time domain (FDTD) method, 268-271 FIRE. See First ISCCP Regional Experiment First ISCCP Regional Experiment (FIRE), 79,224,261,265,321-322, 379,383 flow asymmetry, 61 flow tubes, 110,116,118-119,121 Fludd, Robert, 4 forcing. See cloud, forcing formvar, 42 Fourier transform infrared spectroscopy (FTIR), 110,116,118,121,126 fractional cloud cover, 299 relation to grid-box relative humidity, 304,305 prognostic treatment of, 304 Fraunhofer diffraction, 268 freezing, 234 apparatus for study of, 109-111 heterogeneous, 108-109,122-125 homogeneous, 104-108,111-122 of emulsions, 109-111,113-114,121122 point, depression of, 113-123 temperature (effective), 113,115 frost, 46 FSSP probe, 82 Gage-Lilly theory, 351 Galileo, 4 GCM. See General Circulation Model GCSS. See GEWEX Cloud System Study general circulation, 322 General Circulation Model (GCM), 310-326,398,410,427 sensitivity of model climate to ice cloud microphysics, 334-339 geometric ray tracing, 65,266,267 germanium, 54 GEWEX Cloud System Study (GCSS), 324,376,385,443 GEWEX. See Global Energy and Water Cycle Experiment Global Positioning System (GPS), 451 GPS. See Global Positioning System gravity wave(s), 68, 69,71,259, 347, 350,

352, 353,356, 357, 364,365,367, 389,391 breaking, 349,356,359,361, 366 spectrum, 351 greenhouse effect, 397,398,412,427 growth, 45,46,53 habit. See ice crystal(s) habit halos, 4,23-24,270,277,278 22 degree, 4,62 haze and haze particles, 56,402,421,424 HAT. See high altitude tropical cirrus heat flux, 359 diffusion, 68,69 transport, 46 high altitude tropical cirrus (HAT), 256 high frequency approximation, 429 High Resolution Infrared Radiation Sounder (HIRS), 265 High Spectral Resolution Infrared Spectrometer (HIS), 288, 289,291 high spectral resolution lidar (HSRL), 173,198,224, 227 Hildebrandsson, 5 HIRS. See High Resolution Infrared Radiation Sounder HIS. See High Spectral Resolution Infrared Spectrometer Howard, Luke, 4—5 HSRL. See high spectral resolution lidar humidity. See relative humidity Hurricane Nora, 185 hydrological cycle, 433 hydrometeor videosonde, 83 HYVIS. See hydrometeor videosonde ICE. See International Cirrus Experiment ice layer particles, 240 saturation, 239 ice crystal(s), 41-77,102-135 axes, 400 breakup, 58 chemical uptake by, 126-127 columns and plates, 267 concentration, 407,415,416,422, 425 cubic, 52,53, 54 defect, 53,55,58 dendrite, 52,54,58,62 density, 49,61

Index depolarisation, properties, 226 diamond dust, 47, 49,70,71 diffusional growth of, 107,110-111, 125-127 electrical capacity factor, 400 evaporation of, 125-128 fall speed, 336-339,435 four fold symmetry, 54 generation layer, 408,425 germ, 401 growth, 41,45,46,49,51,53,60 rate, 71,400,421,450 mechanism of, 298 habit(s), 42-43, 52-54,56,58,62,66,68, 70,125-126,211,223,226,257,267, 270,272,453 laboratory studies of, 102-135 mass, 400 mean effective ice crystal size, 269, 272-274,283,286-289 mean radius, 407,408,415,421 multiple, 58 nucleation, 217,400,401,403,414,416, 421, 425,426,429 nuclei, 399,421,429 number density, 302-305 orientation, 61, 62 phase function, 216 polycrystal, 53,55,58 pristine, 54,68 radiative properties of, 126-127, 265-296 scattering by, 126-127, 265-296 shape, 399,400, 421 single, 58 size distribution, 299, 301, 303, 305, 306-307 skeletal, 54 small, 223 symmetry, 43,52,54 terminal velocity of ice parameterization of, 336-337 GCM climate sensitivity to, 337339 vertical velocity and ice formation, 107-108,118,124 ice water content (IWC), 88, 89,93,94, 95, 243,363,379, 380,382,386, 387, 389,392 sources of in GCM, 334-335 evaluation of GCM simulation of, 342-343

475

ice water path, 148,153,160,161,323, 333-334,380, 382,387, 389,444 impulse-like nucleation, 416,426 incas. See anvil indirect effect, 321-322 inertial subrange, 350, 351,352,354,357, 360,361, 368 infrared forcing, 63 Infrared Interferometer Spectrometer (IRIS), 288 infrared radiation, 65 interferometer, 161-163 intermittency, 347,349,353, 369 International Cirrus Experiment (ICE), 265,450 International Satellite Cloud Climatology Project (ISCCP), 261,265,310-313, 323,379,435,450 Intertropical convergence zone (ITCZ), 258,259 inversion, 66 ISCCP. See International Satellite Cloud Climatology Project isotropy, 349,351, 353,359,361,369 ITCZ. See Intertropical convergence zone IWC. See ice water content Jetstream, 141 Kelvin's critical radius, equation, 401 Kelvin-Helmholtz instability, 347,349,364 kinetic equation for size spectra, 399,400, 429 kinetic Interference, 51 Klett single-component solution, 172 Kohler, 55 Kolmogorov's theory, 351 Kolmogorov constant, 351 Kolmogorov microscale, 350 Kwajelain, 256 Laboratory, 5 apparatus, 109-111,125-128 studies, 102-135 Lagrangian observation, 66 Lamarck, Jean-Bap tiste, 4-5 large eddy model, 357,370 large scale forcing, 437,445 laser, nd:yag, 219 laser, pulse, radiation, depolarisation, 226 latent heat, 46 freezing, 106

476

Index

latent heat (cont.) release, 349 lenticular cloud, 68 levitation, 111, 119,126-127 lidar, 5,16,31,169-173,175,181,185,187, 197-210,211-230 and contrails, 242 attenuation, 175 backscatter, profile, 212, 218,220 calibrated, 212 depolarization, 181 first, 5 high spectral resolution, 198,224,227 lidar ratio, 200 molecular-backscatter, 197 Raman, 172-173,198,226,451 resolution, 175,185 ruby, 216 signal processing, 171-173 use in GCM evaluation, 341 usual limit, 187 vertical, resolution, 222 Lidar-Infrared Radiometer (LIRAD), 182, 188,190,211-230, 451,453 observations, Adelaide, 216 observations, Aspendale, 216 results, 217 typical instrument characteristics, 212 Lidar In Space Experiment (LITE), 258-259 liquid saturation, 232 LIRAD. See Lidar-Infrared Radiometer LITE. See Lidar In Space Experiment LN2, 58 Lorenz-Mie theory. See Mie theory Mariotte, Edme, 4 mass budget, in cirrus, 408,416,427 mean effective ice crystal size, 269, 272-274, 283,286-289 mean free path, 54 melting heat, 401 melting point depression of, 106,110,113-118,120, 122 relation to freezing point, 113-122 microphysical processes, 397 microphysics explicit, 398,429 evolution of, 408,415,421 microscopy, 51

microwave, 67 Mie theory, 66,170,180,266,269,288 Mie-Lorenz theory. See Mie theory minimum deviation, 4 MISR. See Multi-angle Imaging Spectroradiometer mixing, 233, 346, 347,348,350, 370 models and modeling, 297-309,310-326, 397^32,433^48,454 aerosols composition, 108,118-119, 234 cirrus, 375-392 cloud resolving, 385 bin microphysics, 384-386 bulk microphysics, 384-386 large eddy, 391-392 parcel, 379,385 single column, 385 cirrus formation, 95 cirrus, results relaxation scale, phase, 385 day-night differences, 380 cell scale/structure, 375, 377,379,380 validation and evaluation, 389-390 nucleation, 377,384,390 measurement requirements, 375, 378, 384, 392 climate, 398,410, 427 cloud, 398, 399, 429 general circulation models (GCMs), 310-324, 398, 410, 427 ice nucleation, 103,105-109,113-115, 124-125 microphysical cloud, 399 numerical weather prediction (NWP) models, 327-345,443,444 numerical, 398 subvisual cirrus, 261-262 Moderate Resolution Imaging Spectroradiometer (MODIS), 292 MODIS. See Moderate Resolution Imaging Spectroradiometer MODTRAN, 261 moisture flux, 359 molecular-backscatter lidar, 197 molecularly smooth surface, 48,52 Monte Carlo method, 216,268,280,291 morphology, 58 MUC. See mesoscale uncinus complex Multi-angle Imaging Spectroradiometer (MISR), 292

Index

multiple scattering factor, 213,221,223, 227 multiple scattering, 206,216,221,223,226, 227 multi-wavelength, techniques, 227 negative feedback effects, 224 Nevzorov probe, 83 nucleation, 54,68,103,236, 311,321-322, 400,414,416,421,425,429 and aerosol particle composition, 103, 104-111,113-124 and temperature, 111-125 and vertical velocity (updraft), 107-108, 118,124 classical theory of, 105-107,112, 114-115,124 heterogeneous, 108-109,122-125,403 homogeneous, 104-108,111-122,401 impulse-like, 416,426 instruments, 109-111 mechanisms of, 104-109 on aerosols, 17,33,36 on haze particles, 17,19, 36 parameterization of, 105-107,113-115, 124-125 rate of, 105-107,112,114-115,124 number density, 302-305 Numerical Weather Prediction (NWP) models, 327-345,443,444 noctilucent clouds, 47 NWP. See Numerical Weather Prediction OLR. See outgoing longwave radiation optical effects, 68,69,71 optical depth (thickness), 18-19,63,65, 213,224, 226, 227, 240,278, 279, 286,287,289,290,310-316, 318-320,410, 418,421, 428,444, 446 optical depth, infrared, 213, 216, 217 optical properties (coefficients), 63,410, 421,426,428 orographic clouds (See also gravity waves), 19,68,258,259 outgoing longwave radiation (OLR), 444 oxygen-A, 161 Ozmidov scale, 350 ozone, 215 parameterization issues, 314-322 parameterization aerosol size spectra, 402

477

cirrus emissivity, 428 cirrus optical thickness, 428 crystal diffusion growth, 400 crystal size spectra, 429 GCM, 211 ice water content, 427,428 of cirrus included in modeling, 306307 of generation of precipitation, 302 of macrophysical and meso-scale aspects, 304 of microphysical aspects, 301 physically based of cirrus, 299 supersaturation, 403,404 threshold humidity, 427 particle(s) back scatter coefficient, 199 extinction coefficient, 200 size distribution, 89,90, 91 size, 218,223,225 small, 223,225 passive sensors, 169,182 (See also atmospheric emittance radiance interferometer) phase function, 267,271,273 phase matrix, 276, 277 PICASSO-CENA, 261,455,446 Pilot Radiation Observation Experiment (PROBE), 221, 222,224 plume, 233 PMS probes, 66 Polarization and Directionality of the Earth's Reflectances (POLDER), 278,279 polarization, 161,171,273,278,279 (See also depolarization) differential reflectivity, 171 polar stratospheric clouds, 47 POLDER. See Polarization and Directionality of the Earth's Reflectances pollen, 61-62 potential temperature, 349,355,364 power spectral density, 360,361, 362,363 precipitation definition of, 298 generation of, 298,300, 301 parameterization of evaporation of, 303 parameterization of generation of, 302 rate of, at an arbitrary level, 300 principal cloud types, 8

478

Index

probes ID, C probe, 82 2D probes, 81 CPI probe, 83 dropsondes, 451 FSSP probe, 82 hydrometeor videosonde, 83 Nevzorov probe, 8 PMS probes, 66 PROBE. See Pilot Radiation Observation Experiment radar, 15-16,67,160,168-196 Doppler, 227,451 millimeter, 224,227 minimum detectable signal, 173 power density spectrum, 173 resolution, 175,185 signal analysis, 173-175 radar/lidar, ratio, 227 radiance, 152,159,284 absorption, 214 cirrus, retrieved, 219 cloudless, 220 infrared, 211 measured at the ground, 214 passive infrared, 214 retrieved cloud, 220 scattering in cloud, 214 sky, 215 upwelling, from, ground, 214 radiation, 49, 50, 63,77 budget, 397,437 depolarised, 211 infrared, 211 solar, 211 temperature, 49 radiative effects, 310,312-313 fluxes, 411,426 forcing, 245,397,412,419,423 heating/cooling, 347, 349,356, 364,368, 411,412,420,423, 424,434,437,439 transfer, 265-296 radiometer calibration, curve, 215 CSIRO Mark IIR, 216 filter, wavelengths, 215 infrared spectral, 212 Mark II, 216, 219 microwave, 212,219 multichannel, scanning, 223

narrow beam filter, 219 Raman lidar method, 172-173 ray tracing, 266,267 Rayleigh number, 51 Rayleigh scattering and theory, 169-170, 180,451 (See also lidar, passive sensors) reflectance, 153,154,160 refractive index, 63,65 relative amount of condensed ice, 408, 409,416,426 relative humidity, 144,239, 435 and cirrus formation, 105,109-110,114, 117-118,120,122 relaxation of supersaturation, 398,400, 404,428 remotely piloted vehicles, 451 Renou, 5 replica & replicator, 42,43, 59, 63,70 replicator, 82,83 retrieval, 63 Reynolds number, 46,61,62 Richardson number, 349,351,355 critical, 350 bulk, 350,355 riming, 58 Rossby wave, 67 Santorio, Santorio, 4 SAGE. See Stratospheric Gas and Aerosol Experiment satellite, 66 ADEOS, 161 ERS-2,161 GOES, 5,147,149-152 Landsat, 147 NOAA, 154,158,161 remote sensing, 147-167 sampling, 148 TIROS, 5,149 instruments ATSR-2,161 AVHRR, 154,158,159,161 CERES, 161 HIRS, 154 IRIS, 158 MODIS, 152,160,161 POLDER, 161 SAGE, 159 VIRS, 161,162 satellite observations, 14-15,136,147-167, 224,435,444,446

Index

saturated vapor density & pressure, 4748 saturation ratio, 401,416 threshold of nucleation, 427 scattering, 67,169-172 (See also backscattering) by hydrometeors, 170 coefficients, 397,398, 405,409,421, 426 phase function, 216,226 phase, function, ice, crystal, 216 single-scattering lidar equation, 171 theory, backscatter, to, extinction, ratio, from, 223 Schmidt-Appleman criterion, 232 Scoresby, 18,20,52, 54 screw dislocation, 54 secondary ice crystal formation, 126 SHEBA. See Surface Heat Budget of the Arctic Ocean silver halide, 54 single scattering albedo, 274 (See also albedo) size parameter, 268-273 size spectra, of aerosol, 402 droplets, 399 crystals, 399, 404, 418, 422,429 size sorting, 384 slowness of condensation in cirrus, 407, 409, 425 sodium chloride, 45,46 solar albedo, 64 solar observations, 240 solar occultation, 159 soot, 232 spectra/spectral, 282-284, 289 spectral analysis, 360 ff splitting method of solution, 403 stacking faults, 52, 53 stereoscopic techniques, 377 stochastic condensation, 429 Stokes vector, 275 strain, 48 stratification. See conditional instability stratocumulus, 380,381 stratosphere, 435, 446 Stratospheric Gas and Aerosol Experiment II (SAGE II), 256,261, 314,317 subgrid variability, 321-322 sublimation, 400

479

Subsonic Aircraft: Contrail and Cloud Effect Special Study (SUCCESS), 265,289, 322,450 subvisual cirrus (SVC), 6,20, 256-264 SUCCESS. See Subsonic Aircraft: Contrail and Cloud Effect Special Study sulfur & sulfuric acid, 234, 402,421 relaxation toward equilibrium, 301 sun photometer, 160 supercooled liquid water (SLW) clouds, 48 (See also altocumulus) in cirrus, 17 and cirrus formation, 17,33-34 from cirrus, 34-35 supercooled water, 48 supersaturation, 47,55,56,68, 69,71,400, 408,409, 416,417 equation, 403 equilibrium, 404,428 generation time, 404 relaxation time, 398, 400, 404, 416, 428 relaxation toward equilibrium, 301 residual in cirrus, 398, 426, 429 vertical profiles, 417 Surface Heat Budget of the Arctic Ocean (SHEBA), 450 surface migration, 52 surface tension, 401 SVC. See subvisual cirrus Television and InfraRed Observations Satellite (TIROS), 5 temperature brightness, 289 cloud, 217-219,221-225 difference, 155-157 excess, deficit, 48 radiosonde, 215 tropical, 217 terminal velocity, 46,49, 61,63 (See also fall speed, fall velocity) parameterization of, 336-337 GCM climate sensitivity to, 337-339 theory of ice nucleation, 105-107,112, 114-115,124 thermal conductivity, 47 thermal infrared, 63 thermal perturbations, 380,386 thermodynamic modeling of liquid aerosols, 108,118-119 thermodynamics, 232 thermometer, 4

480

Index

thin cirrus (See also subvisual cirrus), 310-313,317-322 Thompson's critical radius, equation, 401 threshold humidity, 427 TIROS. See Television and InfraRed Observations Satellite TOA. See Top of Atmosphere TOGA/COARE. See Tropical Ocean/Global Atmosphere Coupled Ocean/Atmosphere Response Experiment Top-of Atmosphere (TOA) fluxes (See also outgoing longwave radiation), 437, 444 radiative budget, 437 transmittance, 213 atmospheric, 214,215,220 tropical cirrus, 78-101 Tropical Ocean/Global Atmosphere Coupled Ocean/Atmosphere Response Experiment (TOGA/COARE), 314-317,435 tropopause, 27,71,257,259 two parameter classification, 5 turbulence, 68, 347,429,451 stratified, 383,391 heat and vapor diffusion, 68 clear air turbulence (CAT), 347 decaying turbulence, 349, 350, 361 fossile, 350, 356 intensity, 361, 362, 363 measurements, 347,353,354,368 quasi-two-dimensional, 351, 352, 361, 365,369 spectrum. See energy spectrum stratified, 351, 360,383, 391 turbulent fluxes, 357,359 turbulent kinetic energy (TKE), 348,349, 350,351,356, 369 undersaturation, 58 unified theory for light scattering, 269 updraft, 55,67,377,380,382,384,386-387, 389 upper tropospheric humidity, 144 ventilation, 46,50 Venturi, Giovanni, 4 verification aspects cirrus data for, 307 vertical microphysical profiles, 87

vertical motion, 60 Video Ice Particle Sampler (VIPS), 82 VIPS. See Video Ice Particle Sampler volatility, 235 volume, absorption coefficient, 213 volume, extinction coefficient, 212 volume-scattering coefficient, 197 velocity fluctuations, 357,358 velocity variance, 353,358,359 warming/cooling effect of cirrus, 397,412, 419,423 water absorption, 283-288 drops, 226 greenhouse gas, 433,446 ice crystal effects, 434 path total, 215 precipitable, 215 transport, 311,314-315,320,324 water vapor, 211,215 diffusion, 69 diffusivity, 47, 68 excess (uncondensed) in cloud, 407,409, 426 path, integrated, 212,219,220 radiance, 214,215 wavelength infrared, 149,151,159 microwave, 160,161 submillimeter, 161 visible, 149 wavelet analysis, 365,366, 367,368,369 weather, 28-30,136-146,327-345 Weibull distribution, 67 wind components, 349,351,353, 354,356, 357,361 wind profile, 355,356 wind shear, 317,347-349,354,355,356, 361,369, 391-392 window region, 284,288 WMO. See World Meteorological Organization World Meteorological Organization (WMO), 6, 8, 9,256 WW II, 256 X-ray, 53 Young, Thomas, 4