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Preface Rivers have been the focus of human activity since the early civilizations. Even in modern times a large number of activities of the engineers such as water supply, irrigation, water quality control, power generation, flood control, river regulation, navigation and recreation are centered around rivers. Hence considerable interest has been evinced in the society about various aspects of rivers such as their formation, hydraulics and sediment transport, erosion and sedimentation, and effect of natural and human interferences on rivers. Books have been written on rivers by geologists, geomorphologists, hydraulic engineers, hydrologists and geographers. Even though all of them have attempted to understand the behaviour of rivers that have carved their channels through the material deposited by them, the emphasis of each one of them is different from that of the other depending on his background, objectives of writing the book and the targeted readership. Yet fewer attempts seem to have been made to synthesize the contributions of these scientists into a coherent text that takes a balanced view of the subject of river morphology. To fill this gap is the objective in writing this book. Hence, the text covers history of fluvial hydraulics and geomorphology, drainage basin characteristics, erosion, fluvial morphology, hydraulics of alluvial and gravel-bed rivers, river bed and channel changes, fluvial palaeo hydrology, analytical and numerical modeling of fluvial processes, morphology of some Indian rivers, rivers and environment, and data needs for morphological studies. The text can be used for teaching a course on river morphology to graduate and undergraduate students in civil engineering and geology, and as a reference material for engineers engaged in planning and management of rivers. My interest and involvement in the study of alluvial rivers and associated problems started with late Prof. E.W. Lane, and Profs. M.L. Albertson, D.B. Simons and E.V. Richardson of the Colorado State University, Fort Collins (U.S.A.). Over four decades of teaching and research in fluvial hydraulics, and association with colleagues at the University of Roorkee (now I.I.T. Roorkee) India, have helped me in looking at rivers in a much broader perspective. My association with Central Water and Power Research Station at Pune over the last decade further enriched my association with the rivers problems. While preparing the manuscript of the book, valuable assistance has been rendered by my former colleagues Profs. K.G. Ranga Raju and U.C. Kothyari who have gone through the draft of the book and given valuable suggestions for its improvement; most of these have been incorporated. I am indebted to Profs. Rajiv Sinha of I.I.T. Kanpur, Brahma Parkash and Pradeep Kumar of I.I.T. Roorkee, and V.S. Kale of the University of Poona for making their publications available to me. I
vi
Preface
am thankful to Dr. Z.S. Tarapore and subsequent directors of CWPRS for allowing me to work at the research station for the past thirteen years. I am particularly thankful to M.S. Shitole, Joint Director, D.N. Deshmukh, J.D. Prayag, R.A. Oak, Hradaya Prakash, Pradeep Kumar, Mukund Deshpande, Y.N. Karanjikar and others whose assistance has been valuable in finalizing the manuscript of the book. Lastly, I am thankful to my wife Vidya and daughter Rashmi for the patience shown by them while I was preparing the manuscript. December 2005 R-1 Sankul Condominium Near Deenanath Hospital Evandavane, Pune-411004
R. J. Garde
List of Symbols a1,a2,a3 A Ab Af Au
coefficients/exponents area of cross-section, area of basin area at bankful stage, area corresponding to bed area of fan area of basin of order u
Au Aw b B BI C Ca CD CL
mean area of basin of order u area of corresponding to wall exponent width of rectangular channel Brice braiding index Chezy’s coefficient, suspended sediment concentration at a point, climate index reference suspended sediment concentration drag coefficient lift coefficient
CB , C d* d, d50 d16, d50, d84, d90 da di dmax D DC Dd Dmax E ER f
bed material concentration in ppm by wt., total load concentration dimensionless sediment size median size of bed material, rain drop size sediment size such that 16,50,84,90 percent material is finer than this size respectively arithmetic mean size any size fraction maximum size of sediment depth of flow (WD=A) depth at the centre drainage density maximum depth kinetic energy of storm entrenchment ratio Darcy-Weisbach resistance coefficient
viii
River Morphology
f¢ f ¢¢ f1 F Fb Fbo FD Fe FL
friction factor corresponding to grain roughness friction factor corresponding to form roughness Lacey’s silt factor stream frequency Blench’s bed factor value of Fb when bed load is negligible drag force erosion factor lift force
Fr
Froude number (= U/ gD )
Fs g G Ge G¥ DG hb hs H i I I30 j ks K Ko l L ls Lu
Blench’s side factor gravitational acceleration transport rate of any section equilibrium transport rate sediment transport rate at infinity change in G head loss in bend saltation height average height at ripple or dunes, bars; relief index intensity of rain fall maximum 30 minute intensity during storm index roughness parameter erodibility index, diffusion coefficient, wave number (= 2pD/L) theoretical diffusion coefficient length, distance, length of aggradation average length of ripples or dunes, length of stream up to drainage divide saltation length total length of streams of order u
Lu
mean length of streams of order u exponent percent of silt-clay in perimeter, Kramer’s uniformity coefficient, dimensionless velocity bed or water wave meander belt meander length meander width (MB-W)
m M Mb ML MW
ix
List of Symbols
n nb ns Nu nw pi P Pmax q qb qBv qc qs qT qTv
index, exponent, Manning’s n Manning’s n with respect to bed Strickler’s n number of streams of order u Manning’s n with respect to wall per cent perimeter, annual rainfall average monthly maximum precipitation discharge per unit width bed load transport rate in weight/width volumetric bed load transport rate per unit width critical water discharge per unit width suspended load transport rate per unit width total sediment transport rate in volume per unit width total volumetric sediment transport rate per unit width
q*
dimensionless discharge (= q/ gd 3 )
q¢ Q, Qw
lateral inflow per unit length on both sides water discharge
Q1
= Qb/d2 gd
Q2
= Qb S/d2 gd
Q3
= Qb/d2 gd S
Q2.33 Qb QB Qma Qmaf Qr QS QT r rc ri, ro R RA Rb
flood discharge of return period 2.33 years bankful discharge bed-load discharge mean annual discharge mean annual flood discharge runoff rate per unit area suspended load discharge total sediment transport rate in weight or volume radius centre line radius of bend inner and outer radius of bend hydraulic radius, annul run off, run off parameter area ratio hydraulic radius corresponding to bed, bifurcation ratio
x
River Morphology
Rb¢, Rb¢¢ Re RL Rm
Rb with respect to grain and form roughness respectively Reynolds number length ratio of Horton mean radius of meander bends
Ro*2
= Dg s d 3 /r f n 2
Rs RW R* S, So S¢ S¢¢ Sa Sf Si SW
bifurcation ratio for slope hydraulic radius corresponding to walls particle Reynolds number u* d/v slope, bed slope, slope at x = o slope corresponding to grain roughness slope corresponding to form roughness annual erosion rate in cm (absolute) energy slope, fan slope sinuosity water surface slope
S
average catchment slope
Su SDR SE tp
average slope of segments of order u sediment delivery ratio super-elevation time to peak
T TE u
number of years, also dimensionless excess shear {= ( t' - t 0 c ) / t 0 c } trap efficiency of reservoirs local velocity in x direction, order of stream
u¢2
ud udcr
r.m.s. value of velocity function in x direction velocity at the top of particle critical velocity at particle level
u*
shear velocity (= t 0 / r f )
u*¢ u*¢¢ U Ucr Ug UW v
shear velocity corresponding to grain roughness shear velocity corresponding to form roughness average velocity average critical velocity average velocity of particle moving as bed load average velocity of bed form or wave local velocity in y direction
xi
List of Symbols
v¢2
vq vmax vr Vcp w w¢ 2 W Wav Wb Wo Ws x y Y1 z Z
Zo a a1, a2, a3 b gs, gf d d¢ Dgs Îm Îs h q k k0 l m n x
r.m.s. value of velocity fluctuations in y direction velocity in q direction maximum velocity at any vertical velocity in r direction average velocity in the vertical local velocity in z direction, mean width of rib r.m.s. value of velocity fluctuations in z direction average width (WD = A); weight of the particle average unit weight over T years bankful width unit weight value of sediment water surface width distance in x direction, a dimensionless coefficient distance from the wall hydraulic mean depth (=A/Ws) lateral distance from the origin, actual slope of suspended sediment distribution curve, elevation of bed at given x and t; side slope of channel (Z hor.: 1 vert.) theoretical value of suspended distribution curve; bed elevation at x = 0 energy correction coefficient exponents es /em ratio of sediment transfer coefficient to the momentum transfer coefficient specific weights of sediment and fluid lag distance thickness of laminar sub-layer difference in specific weights of sediment and fluid momentum transfer coefficient sediment transfer coefficient dimensionless distance in the vertical angle Karman constant (actual) Karman constant (clear water) porosity, wave length dynamic viscosity of fluid kinematic viscosity of fluid sheltering coefficient
xii rf rs s sg t to t0c tr, tq t* t*c j jB, jS, jT y y¢ w w0
River Morphology
mass density of fluid mass density of sediment arithmetic standard deviation geometric standard deviation shear stress average shear stress on the bed critical shear stress for sediment components of shear stress on the bed along r and q direction dimensionless shear stress dimensionless critical shear stress angle of repose dimensionless bed-load, suspended load and total load transport rate respectively = Dgsd35/t0 = Dgsd35/t0¢ fall velocity fall velocity under ideal conditions
Subscripts and superscripts Subscripts * dimensionless quantity c pertaining to critical condition pertaining to section 1, 2. 1, 2 Superscripts ' corresponding to grain roughness '' corresponding to form roughness
Glossary of Some Terms in River Morphology Below is given meaning of some terms occurring in the text. (adapted from Easterbrook 1969) Abrasion: wearing away of particle due to friction Aggradation: rise in bed level of the stream over large length Alluvium: unconsolidated sediment deposited by river; sediment deposited in river bed, floodplains, lakes, alluvial fans etc. Alluvial fan: cone shaped accumulation of debris or sediment deposited by the stream as it descends from steep slope to a plain where the material deposits in the form of a fan Avalanche: mass of snow sliding down the mountain Avulsion: shifting of a river course Base level: the level below which a land surface cannot be reduced by running water Bed-load: material moved on or near the bed due to tractive force of the flow Bed-forms: features developed on the bed of the river due to interaction between flowing water and river bed sediments Bed-load: material moved on or near the bed due to tractive force of the flow Bed material load: material transported by the stream which has the stream bed or banks as its origin Beheaded stream: lower portion of the stream from which water has been diverted due to stream piracy Braided stream: a stream divided into a number of channels by island formation, which may join and bifurcate again and again Cirque: a deep steep walled recess in a mountain caused by erosion due to glaciers Colluvium: unconsolidated deposits, usually at the foot hills or cliff, brought down by gravity Creep: slow down-slope movement of rock fragments and soil Crevasse: a fissure formed in glacial ice due to various strains Degradation: general lowering of stream bed over large length due to deficiency of sediment load as compared to its sediment transport capacity Delta: a triangular shaped alluvial deposit formed when a stream enters lake or sea Diastrophism: the process or processes by which the crust of the earth’s surface is deformed
xiv
River Morphology
Divide: a ridge between the streams; a line of separation between drainage basins Drainage basin: the area drained by a system of rivers Eolian: deposits which are due to transporting action of the wind Ephemeral stream: the stream which flows only in direct response to precipitation; it receives no water from ground water Escarpment: relatively steep slope or cliff separating gently sloping tracts Eustatic: pertaining to simultaneous world wide changes in sea level Floodplain: relatively flat land strip on one or both sides of a stream built by sediment deposits during flooding. It is sometimes called active flood plain Fluvial: produced by the action of rivers Geomorphic cycle: erosion cycle during which land forms are evolved which change from youth to maturity to old, each of which is characterized by distinctive features Geologic structure: it includes not only folding, faulting and uplift of the crust but also includes other factors related to the physical and chemical characteristics of rocks, relative resistance to weathering, dip, strike, jointing, stratification etc. Glacial drift: material transported by glaciers Glacial trough: U-shaped valley produced by glacial erosion Hanging valley: a tributary valley whose floor is higher than that of the main valley at the junction due to degradation of the main valley Incised meander or entrenched meander: a deep sinuous valley cut by a rejuvenated stream Levee: natural or man-made embankment above the general level of floodplain which confines the stream channel Loess: fine sized particles deposited by wind Mass-wasting: the down-slope movement of rock debris under the influence of gravity Meander scar: crescent-shaped cut in a valley side made by lateral planation of the outer part of a meander Meandering stream: a stream that follows sinuous or crooked path Misfit stream: a stream whose meanders are either too small or too large, compared to valley width Monadnock: a residual hill or mountain standing above a peneplain Oxbow: a crescent-shaped lake formed in an abandoned river bend by a meander cutoff Palaeosol: a buried soil Peneplain: a landscape of low relief formed by long continued erosion Periglacial: region beyond the margin of a glacier Piracy: diversion of one stream by the other Pleistocene: the last Ice Age
Glossary of Some Terms in River Morphology
xv
Regimes of flow: characteristics of bed and water surface produced by water flowing on a loose alluvial bed Rejuvenation: activation of erosion of a stream by uplift, climatic changes or change in base level Relief: the difference between high and low points of the land surface Saltation load: material bouncing along the bed or moved directly or indirectly by the impact of bouncing particles Scour: local lowering of the bed of the stream usually due to presence of a hydraulic structure in the stream Suspended load: that part of the sediment load carried by the stream that is kept in suspension by turbulent fluctuations Talus: an accumulation of loose rock mass at the base of a cliff Terrace: a flat or gently sloping surface bordered by an escarpment, it is composed of alluvium or bed rock. It is flooded so rarely that it does not grow by sediment deposition Underfit stream: a stream which is too small for the valley through which it flows
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Contents Preface
v
List of Symbols
vii
Glossary
xiii
1. INTRODUCTION 1.1 Introduction 1.2 Some Problems in River Morphology 1.3 Historical Developments in Fluvial Hydraulics 1.4 Historical Developments in Geomorphology 1.5 Scope References
1 1 2 4 7 9 10
2. DRAINAGE BASINS AND CHANNEL NETWORKS 2.1 Introduction 2.2 Drainage Patterns and Texture 2.3 Stream Order 2.4 Horton’s Laws of Stream Numbers and Stream Lengths 2.5 Areas of Drainage Basins 2.6 Basin Shape 2.7 Lithology 2.8 Vegetation 2.9 Drainage Densities and Stream Frequency 2.10 Relief Aspects 2.11 Drainage Basin Characteristics and Hydrology 2.12 Random Walk Model 2.13 Concluding Remarks References
11 11 12 14 16 19 21 21 22 24 26 29 29 31 31
3. SOIL EROSION AND SEDIMENT YIELD 3.1 Introduction 3.2 Global Erosion Rates
34 34 35
xviii
River Morphology
3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10
Types of Erosion Factors Affecting Erosion Mechanics of Sheet Erosion Equations for Predicting Soil Loss from Agricultural Lands Measurement of Sediment Yield Sediment Delivery Ratio Process Based Modelling of Erosion Erosion Rates from Indian Catchments References
39 41 44 48 50 56 60 64 67
4. FLUVIAL MORPHOLOGY 4.1 Geomorphology and Fluvial Morphology 4.2 Geomorphic Cycle (or Cycle of Erosion) 4.3 Rejuvenation of Erosion Cycle 4.4 Criticism of Geomorphic Cycle 4.5 Noncyclic Concept of Landscape Evolution 4.6 Geological Time Scale 4.7 Glaciation 4.8 Fluvial Morphology 4.9 Topography Produced by Streams 4.10 Variables in River Morphology 4.11 Neotectonics and Earthquakes References
71 71 72 74 74 76 77 80 82 94 104 105 107
5. HYDRAULICS OF ALLUVIAL STREAMS 5.1 Introduction 5.2 Incipient Motion 5.3 Modes of Sediment Transport 5.4 Bed-Forms in Unidirectional Flow 5.5 Resistance to Flow in Alluvial Streams 5.6 Bed-Load Transport 5.7 Suspended Load Transport 5.8 Total Load Transport References
110 110 110 120 124 137 145 150 158 164
6. HYDRAULIC GEOMETRY AND PLAN FORMS OF ALLUVIAL RIVERS 6.1 Introduction 6.2 Stable Channels Carrying Sediment 6.3 Hydraulic Geometry of Alluvial Streams 6.4 Empirical Relationships for Hydraulic Geometry
169 169 170 176 180
xix
Contents
6.5 6.6 6.7 6.8 6.9 6.10
Non-Dimensional Relations for Hydraulic Geometry Flow Around Bends with Rigid and Alluvial Beds Shear Direction Near Curved Stream Bed and Bed Topography Braided Rivers Meandering Stability Analysis and Criteria for Plan-Forms References
186 189 194 198 202 212 223
7. GRAVEL-BED RIVERS 7.1 Introduction 7.2 Data for Gravel-Bed Rivers 7.3 Bed Material 7.4 Pavement 7.5 Hydraulic Geometry 7.6 Bed Features in Gravel-Bed Rivers 7.7 Resistance to Flow in Gravel-Bed Rivers 7.8 Sediment Transport in Gravel-Bed Rivers References
229 229 230 230 233 233 237 241 246 253
8. FLUVIAL PALAEO HYDROLOGY 8.1 Introduction 8.2 Objectives of Palaeo Hydrologic Studies 8.3 Basis of Analysis 8.4 Climatic Changes: Past and Future 8.5 Palaeo Hydrologic Estimates of Discharge and Velocity 8.6 Palaeo Hydrologic Studies in India 8.7 Fluvial Palaeo Hydrologic Studies in India References
256 256 257 258 260 262 267 271 273
9. BED LEVEL VARIATION IN STREAMS 9.1 Introduction Degradation 9.2 Types of Degradation 9.3 Downstream Progression Degradation 9.4 Upstream Progression Degradation 9.5 Effects of Degradation 9.6 Prediction of Depth of Degradation 9.7 Control of Degradation Local Scour Around Bridge Piers 9.8 Factors Affecting Scour
275 275 277 277 282 285 285 286 286 286 288
xx
River Morphology
9.9 9.10 9.11 9.12 9.13 9.14 9.15 9.16 9.17 9.18
Equations for Predicting Scour Depth Verification of Equations for Scour Depth Scour in Gravelly Material Scour in Cohesive Soils Protection of Scour Around Bridge Piers Aggradation Occurrence of Aggradation Reservoir Sedimentation Sediment Inflow and Trap Efficiency Movement and Sediment Deposition in Reservoirs Modeling of Sediment Deposition Methods for Preserving and Restoring Reservoir Capacity References
291 293 295 296 296 296 297 301 302 304 306 310 311
10. RIVER CHANNEL CHANGES 10.1 Introduction 10.2 Avulsion 10.3 Stream Capture 10.4 Erosion at Bends 10.5 Natural and Artificial Cut-Offs 10.6 Channel Pattern Changes 10.7 Longitudinal Grain Sorting References
315 315 315 321 323 326 329 331 334
11. ANALYTICAL MODELS OF RIVER MORPHOLOGY 11.1 Introduction 11.2 Basic One-Dimensional Equations 11.3 Analysis of Water Surfaces and Bed Waves 11.4 Analytical Models 11.5 Some Applications of Linear Models References
337 337 338 342 343 346 357
12. NUMERICAL MODELS FOR MORPHOLOGICAL STUDIES 12.1 Introduction 12.2 One-Dimensional Equations 12.3 Numerical Schemes of Solution 12.4 Classification of One-Dimensional Models 12.5 Convergence and Stability 12.6 Boundary Conditions
359 359 360 362 363 366 367
xxi
Contents
12.7 12.8 12.9 12.10 12.11
Channel Cross-Sections and Method of Erosion or Deposition Modeling of Armouring HEC – 6 CRARIMA Applications of HEC – 6 References
368 369 372 376 378 383
13. MORPHOLOGY OF SOME INDIAN RIVERS 13.1 River Systems in North India Kosi 13.2 Introduction 13.3 Catchment Characteristics and Geology 13.4 Geotectonics 13.5 Hydrology 13.6 Sediment Size and Slope 13.7 Morphology of the Kosi 13.8 Management of the Kosi 13.9 Present Day Problems of the Kosi Brahmaputra 13.10 Introduction 13.11 River Characteristics 13.12 Seismicity and Landslides 13.13 Climate and Hydrology 13.14 Resistance to Flow and Sediment Transport 13.15 Plan-Forms 13.16 Flooding and Flood Protection 13.17 Drainage of Hinter Lands 13.18 River Bed Changes in Brahmaputra 13.19 Development Plans 13.20 Role of Dredging References
386 386 388 388 391 392 393 395 396 398 402 402 402 407 410 411 414 416 419 420 422 423 424 424
14. RIVERS AND ENVIRONMENT 14.1 Introduction 14.2 Actions Causing Disturbance in Stream System and Their Impacts 14.3 Environmental Effects of Hydraulic Structures 14.4 Dams and Reservoirs 14.5 Water Quality in Reservoirs 14.6 Thermal and Hydro-Power Plants
427 427 429 429 430 433 436
xxii
River Morphology
14.7 14.8 14.9 14.10
Recreation Stream Pollution River Action Plans Stream Restoration References 15. DATA REQUIREMENTS FOR MORPHOLOGICAL STUDIES 15.1 Introduction 15.2 Maps, Air-Photos, Satellite Imageries 15.3 Lithology and Tectonics 15.4 Vegetal Cover 15.5 Geomorphic Map 15.6 Basin Characteristics and Morphometry 15.7 Sea-Level Fluctuations, Climatic and Other Changes 15.8 Cross-Sections, Longitudinal Section and Plan-Form 15.9 Bed and Bank Material 15.10 Hydrologic Data 15.11 Sediment Load Data 15.12 Stratigraphic Studies 15.13 Water Quality Related Data 15.14 Catalogue of Information on Morphological Studies References
437 437 438 439 440 442 442 442 445 446 446 449 450 451 453 454 455 456 458 459 459
Appendix A
462
Author Index
463
Subject Index
473
C H A P T E R
1
Introduction 1.1
INTRODUCTION
A river carries water, sediment and solute from the drainage area to the sea and is thus of interest to hydraulic engineers, geomorphologists and sedimentologists. This is important to engineers because water is used for a variety of purposes by humanity; water courses are used as navigation channels, and also erosion, transportation and deposition of sediment cause a number of problems in the river and in the catchment that must be solved pragmatically. The direct effect of transportation of sediment and water from the geologist’s and geomorphologist’s point of view is that the structure and form of the river and adjoining areas are continually changed due to erosion and sedimentation. The rates of this change are variable. While geologists and geomorphologists are concerned about changes taking place in 103 to 106 years or more, engineers are concerned with changes in a river during a relatively short period, say 10–20 years to probably 50–100 years. These channel changes can be in the form of size, shape, composition of bed material, slope and plan-form. The engineer’s primary objective is to understand the basic mechanisms of erosion, transportation and deposition of sediment by flow in the river and develop qualitative and quantitative methods for prediction of river behaviour. The approach followed by engineers is called fluvial hydraulics or river dynamics and this approach has been developed during the past 200–300 years. The other approach taken by geologists and geomorphologists is primarily qualitative even though, in recent years some quantitative methods have been used. Morphology is defined as the science of structure or form. Hence according to Worcester (1948) geomorphology is the science of landforms; it is the interpretive description of the relief features of the earth. It thus describes the surface of the lithosphere, explains its origin and interprets its history. To understand geomorphology one should know in detail the composition and structure of the rocks of the earth and the processes which act on it. Geomorphology recognises that the earth’s surface has changed in the past and is changing at present due to internal and external processes. The internal processes are those, which originate within the earth itself and include diastrophism and volcanism. External processes shaping the earth’s surface include running water, weathering, waves and shore currents, glaciers, avalanches, and plant, animal and human
2
River Morphology
activities. It may be mentioned that most of the changes taking place in the earth’s surface are slow, even though a few may be catastrophic. Conventional texts in geomorphology would deal in detail about the internal and external processes which cause changes in the landform and then deal with the topography produced by streams in humid regions, by winds in arid and semiarid regions, glaciers, shore processes, ground water, volcanoes etc. Geomorphology is sometimes called physiography. This latter term, as used particularly in Europe, includes climatology, meteorology, oceanography and mathematical geography. Inasmuch as these are not addressed in this book, the term geomorphology is preferred to physiography. The word “fluvial” means produced by river action. Hence fluvial morphology means the science of landforms as produced by river action. It can also be called river morphology; it is a branch of geomorphology and it would deal with form of the streams and adjoining areas as brought about by erosion, transportation and deposition of sediment by the running water. Both river morphology and geomorphology are descriptive sciences based mainly on careful observation and interpretation of natural phenomena. In the last century hydraulic engineers, hydrologists and geographers have also made contributions to river morphology.
1.2
SOME PROBLEMS IN RIVER MORPHOLOGY
Since the dawn of civilization, mankind has used rivers for supporting and sustaining life. This has been done by harnessing and controlling rivers for the benefit of people. In doing so the regime or stability of the river is invariably disturbed. In discussing these problems caused by disturbance in the stability of rivers, it is desirable to define what geomorphologists call a graded stream (Mackin 1948). A graded stream, poised stream, balanced stream or a stream in equilibrium is defined by Mackin as the one in which channel dimensions and slope are so adjusted over a period of time that it carries incoming sediment load and water without appreciable erosion or deposition. In geologic time frame no river can be graded because of the natural tendency of land mass and rivers to erode gradually towards sea level. In a true dynamic sense also no river can be in true equilibrium since the discharge changes continuously. However, it may be mentioned that the changes related to geomorphic erosion are very slow and hence if one considers a time period of a few years to some decades, most of the streams can be considered to be in equilibrium, except a few rivers such as the Kosi, the Brahmaputra and the Yellow river which are truly unstable. This equilibrium of the stream is disturbed by natural or man-made interferences in one or more of the conditions that maintain the equilibrium. A few of these instances are discussed below. i. When a large dam is constructed across the river to store water for irrigation, water supply, flood control, generation of water power, navigation or recreation, the sediment transport capacity upstream of the dam is reduced thereby causing aggradation in the main reservoir and also in the tributaries on the upstream. This has many undesirable effects including depletion of reservoir capacity and flooding of the upstream areas. In some cases such as the Imperial dam on the Colorado river and Bhakra dam on the Sutlej in India sediment deposition has been found to occur 70-80 km upstream of the dam. The water released from the reservoir is almost sediment free and hence it picks up sediment from the bed and banks of the stream causing degradation over long reaches of the stream. It
Introduction
ii.
iii.
iv.
v.
vi.
vii.
viii.
3
may also lead to channel widening or change in the planform of the river. Needless to emphasise, degradation has many undesirable effects. It has long been recognized that water transport is comparatively much cheaper than road or rail transport and hence many streams such as the Danube, the Volga, the Rhine, the Mississippi, the Yangtze, the Ganga, the Brahmaputra and the Nile have been used for navigation since ancient times. Making the river navigable year around involves construction of dams, locks, channel widening, channel straightening and channel contraction using spurs or jetties and bank stabilization. It may also involve dredging and releasing additional water during low flows. These changes affect the stability of the river and hence executions of such changes need consideration from hydraulic and morphologic points of view. Barrages, canal head works, sediment excluders and extractors in irrigation canals are constructed for withdrawing relatively sediment free water for irrigation and water supply purposes. This disturbs the equilibrium of the stream causing aggradation in the downstream reaches. Similarly, aggradation takes place when rivers are used for dumping mining wastes hoping that the stream will safely carry the dumped material downstream. However, the stream can carry this excess load only with increased slope, which is achieved by aggradation. This happened, for example, on the Yuba river in California (U.S.A.) during gold-rush period in the latter half of the 19th century. Similarly, when sand and gravel are mined from the river bed to meet the ever increasing demand of the construction industry, the river downstream is found to degrade creating many problems in that reach. Such degradation in the river causes similar effects in the tributaries and sub-tributaries on the downstream side. In order to have equitable distribution of water throughout the country large scale transfer of water from one basin to the other is either contemplated or is being executed. This is likely to disturb the equilibrium of the streams because the balance between water distribution and sediment load distribution is likely to be disturbed. Construction of flood control works such as embankments, reservoirs, channel straightening, meander cut-offs and channel improvement also tend to disturb the equilibrium of the stream and needs careful study. Large scale dredging carried out along the river for navigation purposes also disturbs the sediment balance and hence the stream equilibrium. There are other less obvious factors that affect the stability of the stream, i.e., they affect channel slope, plan-form, cross-section, and alignment. Some of these are the following: Change in drainage basin characteristics due to change in land use such as deforestation, reforestation, agricultural land development, road construction, urbanization, and building of dams and check-dams disturb the river equilibrium by changing runoff and sediment load and trigger changes in the channel characteristics. Ruhe (1971) has described the case where straightening of a channel had repercussions throughout the basin. In the Willow river (Crawford County, Iowa, USA) straightening led to channel deepening and widening. In addition, new deeply entrenched gullies extended for many kilometres up the tributary system and developed hill slides, disrupting agricultural lands and public roads.
4
River Morphology
When urbanization takes place large-scale changes are induced in the catchment, its hydrological characteristics and the sediment yield. Because of breaking of new grounds, removing of vegetation, and use of construction equipment, the runoff and storm flow increases and hence land erosion is accelerated. As a result the sediment load of the streams is often increased dramatically. Wolman and Schick (1967) recorded up to 50,000 tons/km2/yr sediment load at one site, as compared to 80-200 tons/km2/yr under normal conditions. After the urban area is developed, infiltration is reduced and ground water levels may be lowered. Untreated waste including sewage may be discharged into the streams causing pollution, which in turn, may be lethal for the aquatic life and detrimental to the use of the water in downstream reaches for drinking and recreational purposes. Due to urbanization there is an encroachment on the flood plain and hence channels are confined resulting in higher flood levels. ix. Long term changes in the climate or hydrologic regime lead to significant changes in discharge, type of sediment load and its quality which lead to change in channel dimensions, change in river course and/or change in plan-form or meander characteristics. In extreme case the river can cease to exist. x. Earthquakes and active tectonic movement such as subsidence or upheaval are found to influence the river stability. Earthquake of magnitude greater than 4 on Richter scale can trigger a number of landslides through out the region and earthquake of magnitude 8 or larger is capable of triggering tens of thousands of land slides throughout the region that extends to more than 400 km from the fault (Wilson and Keefer 1985). Heavy rainfall following such landslides can bring enormous amount of material in the stream and can change its regime. Gee (1951) has reported the damage caused by 15 August 1950 earthquake in Brahmaputra valley that was of 8.6 intensity on Richter scale. He found that 75 percent of hills in 4 3000 km2 area were mutilated by landslides. Small and large rivers became blocked by material that fell in them and some even ceased to flow. Flood following the earthquake burst these dams and large quantity of sediment and rock material was carried downstream. The rivers Dibang and Subansiri twice changed their courses. The Brahmaputra got considerably silted up near Dibrugarh, and the bed level rose by a few metres; it took several years for the excess sediment to move downstream. In engineering literature little attention has been paid to active neo-tectonic movement as a factor influencing river morphology. The rates of surficial deformation in certain region may vary from less than 10 mm/yr to more than 10 mm/yr for seismic deformation. When considered over a few decades such deformation can affect valley slope enough to affect the river morphology. If at a particular section along the river there is uplift there is aggradation on upstream and downstream side while in between there is degradation.
1.3
HISTORICAL DEVELOPMENTS IN FLUVIAL HYDRAULICS (GARDE 1995)
Even though mankind has been living with sediment problems for the past several centuries, relatively little progress was made in our knowledge about sediment movement up to 16th century A.D. Earlier civilizations in the valleys of the Indus, the Tigris, the Euphrates, the Nile and the Yellow rivers were
5
Introduction
using canals for supplying water for irrigation through unlined channels. These canals either took off from a weir or they were inundation canals. The common problem with these canals was silting and hence frequent sediment removal was necessary. Locating the canals on the outer side of the bend of a stream to reduce sediment entry into canal seems to have been practised. The Chinese had made considerable progress in controlling large rivers, flood diversion, and similar other problems. The Romans had made progress in water supply and sewerage. The Greeks knew about the fall velocity of different sediment particles. During 1600–1800 A.D. relatively more progress was made in understanding the physics of flow in open channels. The basic equations governing the flow, viz. the continuity equation and the equations of motion were developed during this period. d¢ Alembert (1717–1783) gave the differential equation for continuity of flow which was generalized by Leonard Euler (1707–1783). It was also during this period that the equations of motion, commonly known as Euler’s equations were established. The French engineer Chezy (1718–1798) gave the resistance equation U = C RS where U is the average velocity, R the hydraulic radius, S the channel slope and C is Chezy coefficient. Some basic ideas about river hydraulics were initiated by Dominico Guglielmini (1655–1710) and Paul Frizi; both wrote books on rivers. Du Buat (1734–1809) gave scouring velocities for materials of different sizes. Much more progress was made during 19th century. Bouniceau, Grass, Lechalas, Suchier and Deacon conducted studies and critical velocities for different sized materials were recommended. Brahm showed that the critical velocity is proportional to (submerged particle weight)1/6. D.F. duBoys (1847-1924) gave a simple model for bed-load transport and reached the conclusion that qB ~ to (to – toc) were qB is the rate of bed-load transport, and to and toc are the average bed shear stress and critical shear stress for given size of bed material respectively. During this period two new resistance equations, which are now commonly used, were proposed. These are Darcy-Weisbach equation:
hf =
fL U2 D 2g
Manning’s equation
U=
1 2 / 3 1/ 2 R S n
and ...(1.1)
Here hf is the head loss in length L of pipe diameter D, R is the hydraulic radius, S is the slope and f and n are friction factor and Manning’s roughness coefficient respectively. In the latter half of 19th century O. Fargue (1827–1910) who was closely associated with the developmental work of the river Garonne, gave what are popularly known as “Fargue’s rules” of river behaviour. Finally equations of motion for laminar flow and turbulent flow, commonly known as Navier-Stokes equations and Reynolds equations were developed. Similarly Sternberg gave his law for the reduction of sediment size along the river by the combined action of grinding and sorting. It was also at the fag end of 19th century that Kennedy proposed the method for design of stable channels based on canal data from India that was later modified by Lacey and others. The first half of the twentieth century witnessed all round progress in fluvial hydraulics. G.K. Gilbert (1843–1918) performed extensive laboratory experiments and studied modes of sediment
6
River Morphology
transport, and observed various bed-forms. Different investigators later used the hydraulic data collected by Gilbert to study resistance and sediment transport in channels. As regards channel resistance, Strickler analysed Swiss river data and for plane beds with coarse material proposed the equation n = d 150/ 6 /21
...(1.2)
where d50 is expressed in metres. Exner tried to explain formation of bed undulations using the equations of motion. During this period a number of investigators conducted experiments in the laboratory and developed empirical equations for critical shear stress (i.e., shear stress at which sediment of a given size just starts moving) as a function of sediment size d and the difference in specific weight between sediment and water Dgs. However, the credit for developing the rational criterion for incipient motion that is based on sound principles of fluid mechanics goes to A.F. Shields (1908–1974). Using sediments of different relative densities and sizes, he obtained a unique curve between toc/Dgs d and t oc / r f .d / n . Here toc is critical shear stress for sediment of size d and n is the kinematic viscosity of fluid. The term
t oc / r f = u*c is known as critical shear velocity.
In a similar manner a number of empirical equations were developed by different investigators relating rate of bed-load transport to (to – toc), (q – qc) or (U – Uc) where q is the discharge per unit width, U is the average velocity of flow, and quantities with subscript c refer to their values at incipient motion conditions. However, these equations were of limited use. In 1948 E. Meyer-Peter and R. Müller proposed an empirical equation for bed-load transport which is based on a wide range of sediment sizes and flow conditions and which is used often even today. A. Kalinske and H.A. Einstein developed bedload equations using statistical nature of sediment movement. Simultaneously progress was made in developing the theory of suspended sediment transport. The German meteorologist Schmidt gave the equation w o C + Îs
dC =0 dy
...(1.3)
for distribution of suspended sediment in the vertical. Here C is the concentration of sediment of fall velocity wo at a distance y from the bed and Îs is sediment transfer coefficient. This equation was integrated independently by Rouse and by Ippen using equation for velocity distribution obtained by Karman and Prandtl, and the integrated form was verified by Vanoni and Ismail. Simultaneously, bedload and suspended load samplers were developed and tested in Europe and U.S.A., which greatly helped in collecting valuable data on sediment transport by rivers. As regards the resistance to flow, Karman and Prandtl’s equations for velocity distribution for turbulent flow in pipes were adapted to open channel flow and velocity distribution laws for hydrodynamically smooth and rough surfaces were established. Einstein (1904–1963) suggested a method for separating grain resistance and form resistance of bed undulations while Einstein and Barbarossa proposed a method for predicting resistance to flow in alluvial streams. Lastly on the basis of a large volume of data from stable mobile bed alluvial channels and building on the advances made by Kennedy, Lindley, King and others, G. Lacey (1887–1980) proposed a method of channel design according to which for given Q and bed material size, the channel depth, width and
Introduction
7
slope are uniquely fixed. Also data were collected about the geometry of alluvial rivers and equations have been developed to predict width and depth as a function of bankful discharge and sediment size. The last half of the twentieth century has seen considerable progress in fluvial hydraulics. The characteristics of different bed-forms have been studied and criteria for their prediction established. A number of equations have been developed to predict the resistance and sediment transport rates of uniform and non-uniform sediments. Kennedy, Engelund, Hansen and Fredsoe, have studied stability of mobile bed subjected to small disturbances to explain the formation of dunes, antidunes and plane bed. Similarly, Hansen, Callander, Parker, Hayaski and Ozaki, Engelund and Skovgaard and others have carried out stability analysis to determine the conditions under which streams meander. And finally, with the availability of high speed computers the equations of motion in alluvial streams have been solved to develop methods of prediction of bed levels in unsteady non-uniform flows such as silting of reservoirs, aggradation caused by increase in sediment load or decrease in discharge and degradation caused by increase in flow. Simultaneously field data are being collected to test various softwares developed for solving such problems. Also experimental data are being collected to study some basic problems such as armouring and pickup function. There has also seen considerable activity in understanding the hydraulics of gravel-bed rivers, their hydraulic geometry and sediment transport and scour.
1.4
HISTORICAL DEVELOPMENTS IN GEOMORPHOLOGY (Tinkler, 1985)
From the Greek writings one can extract three basic principles regarding the rational investigations of landforms; these are (i) the concept of infinite time, (ii) reality of denudation i.e., loss of mass or material from the landscape and (iii) acceptance of the principle of conservation of mass. Herodotus (485– 425 B.C.) recognized the importance of yearly increments of silt and clay deposition by the Nile. He also anticipated the idea of changing sea levels that is of great significance in geomorphology. Aristotle (384 – 322 B.C.) thought that rainfall might produce a temporary torrent, but doubted that it could maintain flow in a river. Strabo (54 B.C.–25 A.D.) noted examples of local sinking and rise of the land. He also mentioned about the effect of ebbs and tides on the growth of delta. Both Strabo and Seneca (B.C.– 65 A.D.) recognized the role played by volcanic activity and earthquakes on the landforms. During the many centuries that followed the decline of the Roman Empire, there was little or no progress of scientific thought in Europe; however, some learning process continued in Arabia. During 941–982 A.D. there is reference to erosion and transportation of sediment by the streams and wind and weathering in the four-volume tretise on discourses of the Brothers of Purity. Little progress was made in Europe between the first century and beginning of the 16th century. During the fifteenth, sixteenth and seventeenth centuries landforms were explained by the philosophy of catastrophism, according to which the features of the earth were created as a result of violent catastrophic actions. Leonardo da Vinci (1452–1519 A.D.) had very advanced ideas about geologic thinking for his time. He recognized that streams cut the valleys and that the streams carried sediment from one part of the earth and deposited at other places. The Frenchman Baffon (1707–1788) thought
8
River Morphology
that erosion by streams would eventually reduce the land to the sea level. He was also the first to suggest that the age of the earth was not to be measured in terms of a few thousand years. Another Frenchman Guetthard (1715–1786) also discussed about the degradation of mountains by streams and emphasized that not all the material removed by the stream would immediately be carried to the sea but a part would also deposit on the flood plains. The Swiss De Saussure (1740–1799) recognized the ability of glaciers to carry out erosional work. James Hutton (1726–1797) who entered the university at the age of 14 to study humanities was more interested in chemistry and geology. Finally, he was educated as a physician. However, instead of practising medicine he gradually switched over to agriculture and travelled through Southern England during which time he developed his interest in geology. Hutton is known for propounding the concept that “the present is the key to the past”, thus establishing the doctrine of uniformitarianism. His writings clearly express the concept of a river system and its geomorphic significance. Some other important concepts introduced by Hutton are: i. A vast portion of the present rocks is composed of bodies, animals, vegetables and minerals of more ancient formation. ii. All present rocks are going to decay and their material going to deposit in the sea. iii. The morphological process requires indefinitely long geological time. iv. There is a conceptual possibility of relative change between land and sea levels leading to upheaval. Hutton’s friend John Playfair (1748–1819) who was Professor of Mathematics and Philosophy at Edinburgh was in contact with Hutton, Joseph Black, and Adam Smith. After the death of Hutton in 1797 Playfair published “Illustrations of Huttonian Theory of Earth” in 1802 for he had realized how confused and repetitive were the writings of Hutton; Playfair’s work was smaller, cheaper, and precise with great clarity and beauty of expression. Playfair presented Hutton’s ideas and conclusions clearly. Playfair also proclaimed the ability of glaciers to erode their valleys deeply. Sir Charles Lyell (1797–1875) wrote a number of textbooks to spread the geologic knowledge. He was somewhat doubtful about the immense ability of running water to carve the valleys. It was during 19th century that there was recognition of an ice age during which much of North Europe was covered with ice sheets. Playfair had sensed the possibility of large boulders being transported by glaciers. Louis Agassiz (1807-1873), Venetz of Switzerland in 1821, Bernardi of Germany in 1832 and Jean de Charpentier in 1836 supported this concept of glaciation in Europe. In the later part of 19th century books were written to describe the principles of landform development. These were by Peschel, Richthofen and A. Penck. The basic foundation of geomorphology was laid in America in the later half of 19th century by Major J.W. Powell (1834-1902), G.K. Gilbert (1843-1918) and C.E. Dutton (1841-1912). Powell’s studies of Unita Mountains emphasized the importance of geologic structure in the classification of landforms. He also introduced the concept of the limiting level to which the land-level would reduce and called it the base level. Col. George Greenwood earlier used this concept in Europe in 1857. Powell recognized that the process of erosion, if carried undisturbed on land, would reduce it eventually to a level little above sea level. He was able to correctly interpret that various unconformities in rocks in the Grand Canyon, Colorado (U.S.A.) correspond to ancient periods of land erosion.
Introduction
9
G.K. Gilbert’s contribution in experimental work carried out in California has already been described. He was a pioneer in studying hydraulic mining and its effect on stream morphology. His other contributions include recognizing the importance of lateral planation by streams in the development of valleys and his explanation of Henry Mountains of Utah (U.S.A.) as the result of erosion of intrusive bodies. Dutton gave a penetrating analysis of individual landforms. Gilbert and Dutton are given credit for initiating the concept of erosional unloading of the earth’s crest technically known as isostasy. W.M. Davis (1850–1934) had greater impact on the development of geomorphology than any one else. Of all the contributions to geomorphology, Davis is remembered for introducing the concept of geomorphic cycle. According to this concept in the evolution of landscapes there is a systematic sequence that enables one to recognize the stages of development of landforms. This sequence is called by him as youth, maturity and old age. These landsforms are explainable in terms of differences in geologic structure, geomorphic processes and the stage of development. In the development of the idea of geomorphic cycle Davis had assumed that there is a relatively rapid uplift due to diastrophism which is followed by a relatively long period of standstill which permits the erosion cycle to run its course. W. Penck and his followers questioned Davis’ idea of geomorphic cycle during 1920’s and 30’s. In spite of these objections the Davisian geomorphic cycle is still considered a reasonable model primarily because of the absence of a plausible reasonable alternative.
Recent Contributions Since the end of the Second World War a large number of aspects about river morphology have been or are being studied. These include channel geometry, mathematical modelling, effect of neo-tectonics and mass movements on channels, fluvial systems, experimental fluvial morphology, palaeo climatic and palaeo hydrologic effects and gravel-bed rivers. Scientists working at U.S. Geological Survey have studied short-term morphology of river channels; they include W.B. Langbein, L.B. Leopold and M.G. Wolman. S.A. Schumm, M.P. Mosley and W.E. Weaver studied fluvial systems and performed experiments in the laboratory to study river morphology. J.R.L. Allen from U.K. has done extensive work on the character and classification of bed forms and sedimentary structures with respect to deltas, meanders and floodplains. Many investigators including K.J. Gregory, J. Lewin, V.R. Baker and L. Starkel have studied Palaeo climatic and palaeo hydrologic effects on river channels. Geographers in U.K. have given impetus to the research in gravel-bed rivers and this work is now continued in Canada, U.S.A. and New Zealand.
1.5
SCOPE
The text takes a balanced view of the contributions made by engineers, geologists, geomorphologists and geographers to fluvial morphology. Introduction, morphologic problems, and history of fluvial hydraulics and geomorphology are discussed in the first chapter. The second chapter is devoted to the discussion about drainage basin and channel networks. The third chapter deals with erosion from the catchment in humid regions where erosion due to water action predominates. The fourth chapter presents basic concepts from geomorphology such as geomorphic cycle, stages of landform and rivers and discusses the erosional and depositional features developed by rivers. Chapter five deals with the hydraulics of alluvial rivers while chapter six deals with the hydraulic geometry and plan-forms in alluvial streams. The seventh chapter
10
River Morphology
deals with gravel-bed rivers. Chapter eight deals with fluvial paleo hydrology while chapters nine and ten are devoted to changes in bed level and plan-form. Chapters eleven and twelve deal with analytical and numerical models used in studying the transient flows in rivers. Chapter thirteen is devoted to the discussion of morphology of the Kosi and the Brahmaputra rivers in India. Chapter fourteen deals with rivers and environment, and the fifteenth chapter dicusses the data requirements for morphological studies.
References Garde, R.J. (1995) History of Fluvial Hydraulics. New Age International (P) Ltd., Publishers, New Delhi. Gee, G.P. (1951) The Assam Earthquake of 1950. Jour. Bombay Natural History Society, Vol. 50, pp. 629–638. Mackin, J.H. (1948) Concept of the Graded River. Bul. Geological Society of America, Vol. 59, pp. 463–512. Ouchi, S. (1985) Response of Alluvial Rivers to Slow Active Tectonic Movement. Bul. Geological Society of America, Vol. 96, Apr, pp. 504–513. Ruhe, R.V. (1971) Stream Region and Man’s Manipulation - in Environmental Geomorphology (Ed. D.R. Coates). Publication in Geomorphology, State University of New York, Binghamton, U.S.A. Thornbury, W.D. (1969) Principles of Geomorphology. John Wiley and Sons Inc., New York, 2nd Ed. Chapter 1. Tinkler, K.J. (1985) A Short History of Geomorphology. Croom Helm (P) Ltd., U.K., 1st Edition. Wilson, R.C. and Keefer, D.K. (1985) Predicting Areal Limits of Earthquake–Induced Land Sliding. In Evaluating Earthquake Hazards in the Los Angeles Region (Ed. Ziony, J.I.). USGS Professional Paper 1360, pp 317–345 Wolman, M.G. and Schick A.P. (1967) Effects of Construction on Fluvial Sediment Urban and Sub-urban Areas of Maryland. Water Resources Research, Vol. 3, pp. 451–464. Worcester, P.G. (1948) A Text Book of Geomorphology. D. Van Nostrand Co. Inc., New York, U.S.A., 2nd Edition.
C H A P T E R
2
Drainage Basins and Channel Networks 2.1
INTRODUCTION
Drainage basin is an area drained by the stream and its tributaries. It is bounded by a divide. Drainage basin is also sometimes called watershed or catchment area. It can be thought of as an open system that receives energy or input from the atmosphere and sun over the basin and loses energy or output through the water and sediment mainly through the basin mouth or outlet (Strahler 1964). The present form of any drainage basin is the result of the processes that have operated in the past on the material available locally. These processes at the basin level are the precipitation and runoff, sediment yield and rate of erosion. However, these processes in the past may not be the same in their relative importance as the ones that operate in the drainage basin at present. The importance of studying the drainage basin characteristics derives from the need of studying forms of channels and channel networks as they are related to physical characteristics of the drainage basin, and also from the need of relating physical characteristics of the basin to flow characteristics and sediment yield. The drainage pattern is the arrangement and length of small, medium and large streams in the basin. Two aspects of the development of drainage basins have been studied. In earlier years, the drainage pattern development in relation to the structure and lithology of the underlying rocks was studied. This was essentially qualitative in nature. In the recent times drainage patterns have been treated more as geometric patterns and attempts have been made to derive relationships for them (Horton 1945). The drainage pattern acquired at any time is the result of the combined effect of lithology, precipitation pattern and climate, and their variation with respect to space and time. Since the sediment eroded from the drainage basin along with water causing erosion, flows through the tributaries and the main stream, the drainage net is intimately associated with the hydraulic geometry of the stream channels and their longitudinal profile. As suggested by Schumm (1977) the drainage basin is primarily a sediment production area where climate, diastrophism and land use act as the upstream controls.
12
River Morphology
Glock (1932) assumed that the drainage pattern is initiated on an essentially smooth plane due to the uplift. According to him the drainage pattern goes through the following developmental stages: initiation, elongation (headward growth of the main stream), elaboration (filling in of the previously undissected areas by small tributaries), maximum extension (the maximum development of the drainage pattern) and abstraction (loss of tributaries as the elevation is reduced through time). This sequence takes a long time in geologic sense. During this sequence the sediment yield first increases to a maximum and then decreases. However, such erosional development cannot be observed. Hence several drainage basins in different stages of development are studied at a given time. Thus what is to be observed in time domain is studied in space domain assuming the process to be ergodic. The topographic characteristics of the drainage basin can be visualised either for the basin or for the drainage network. The most important topographic characteristics for the basin are its area, length, shape and relief. The corresponding characteristics for the drainage network are area tributary to stream channels, drainage density, stream length, network shape or drainage pattern, and network relief.
2.2
DRAINAGE PATTERNS AND TEXTURE
Drainage pattern is the general arrangement of channels in a drainage basin. Drainage patterns reflect the influence of such factors as initial slope, inequalities in rock hardness, structural controls, recent diastrophism, and recent geomorphic and geologic history of the drainage basin. Because drainage patterns are influenced by many factors, they are quite useful in the interpretation of geomorphic features and their study represents one of the more practical approaches to the understanding of the structural and lithologic controls on landform evolution. Looking at them in the most general manner, one can classify drainage patterns into the following categories: Figure 2.1 (a) shows dendritic or branch-like pattern that is probably the most common drainage pattern. This is characterised by irregular branching of tributary streams in many directions and at almost any angle usually less than 90o. Dendritic patterns develop on rocks of uniform resistance and indicate a complete lack of structural control. This pattern is more likely to be found on nearly horizontal sedimentary rocks or on areas of massive igneous rocks. They may also be seen on complex metamorphosed rocks. Trellised or lattice-like pattern shown in Fig. 2.1 (b) displays a system of sub-parallel streams, usually along the strike of the rock formations or between parallel or nearly parallel topographic features recently deposited by wind or ice. Radial pattern shown in Fig. 2.1 (c) is usually found on the flanks of domes or volcanoes and various other types of isolated conical and sub conical hills. Parallel drainage pattern shown in Fig. 2.1 (d) is usually found in regions of pronounced slope or structural controls that lead to regular spacing of parallel or near parallel streams. Rectangular drainage pattern shown in Fig. 2.1 (e) has the main stream and its tributaries displaying right-angled bends. This is common in areas where joints and faults intersect at right angle. The streams are thus adjusted to the underlying structure. Deranged drainage pattern, see Fig. 2.1 (f) indicates a complete lack of structural or bed rock control. Here the preglacial drainage has been affected by glaciation and new drainage has not had enough time to develop any significant degree of integration. It is marked by irregular stream courses that flow into and out of lakes and swamps and have only a few short tributaries.
13
Drainage Basins and Channel Networks
a) Dendritic pattern
c) Radial or concentric pattern
b) Trellis Trelliedororlattice latticelike likepattern pattern
d) Parallel pattern
e) Rectangular pattern
f) Deranged pattern
g) Centripetal pattern
h) Highly violent pattern
Fig. 2.1 Various drainage pattern
Centripetal pattern shown in Fig. 2.1 (g) is encountered locally. Here the drainage lines converge into a central depression. These are found on sinkholes, craters and other basin like depressions. Highly violent pattern shown in Fig. 2.1 (h) is characteristic of areas of complex geology. The complex drainage patterns observed in nature are a result of differing lithology, regional slopes, presence of joints and faults, and geologic activities such as glaciation, volcanism and limestone solution. Zernitz (1932), Howard (1967) and Thornbury (1969) have given full description of commonly occurring drainage patterns and their interpretation.
Drainage Texture An important geomorphic concept about the drainage pattern is the drainage texture by which one means relative spacing of drainage lines. Drainage texture is commonly expressed as fine, medium or coarse. Climate affects the drainage texture both directly and indirectly. The amount and type of precipitation influence directly the quantity and character of runoff. In areas where the precipitation
14
River Morphology
occurs primarily in the form of thunder showers, a larger percentage of rainfall will result in runoff immediately and hence, other factors remaining the same, there will be more surface drainage lines. The climate affects the drainage texture indirectly by its control on the amount and types of vegetation present which, in turn, influences the amount and rate of surface runoff. With similar conditions of lithology and geologic structure, semiarid regions have finer drainage structure than humid regions, even though major streams may be more widely spaced in semiarid than in humid regions. It is also noticed that drainage lines are more numerous over impermeable materials than over permeable areas. The initial relief also affects drainage structure; drainage lines develop in larger number upon an irregular surface than on the one that lacks conspicuous relief. Bad-land topography promotes fine drainage structure. Impermeable clays and shales, sparse vegetation and existence of thundershowers are responsible for very fine drainage structure. Coarse drainage structure is in particular found on sand and gravel outwash plains. Gravel plains have fewer drainage lines on them than adjacent till plains underlain by relatively impermeable clay till. The drainage structure can be qualitatively related to a parameter known as drainage density (see section 2.9) first defined by Horton (1932) as total length of streams per unit of drainage area. Drainage density varies from about 0.93 km/km2 on steep impervious areas to nearly zero for highly permeable basins. It varies from about 2.0 to 0.60 km/km2 in humid regions. As indicated by Smith (1950) and Strahler (1957), coarse drainage structure corresponds to drainage density less than 5.0 km/km2, medium drainage structure to drainage density value between 5 and 15 km/km 2 and fine drainage structure to drainage density between 15 and 150 km/km2.
2.3
STREAM ORDER
A stream net or river net is the interrelated drainage pattern formed by a set of streams in a certain area. A junction is the point where two channels meet. A link is any unbroken stretch of the river between two junctions; this is then known as the interior link. If it is between the source and first junction, it is called the exterior link. Quantitative analysis of the stream network really started with Horton (1945). This analysis has been developed to facilitate comparison between different drainage basins, to help obtain relations between various aspects of drainage patterns, and to define certain useful properties of drainage basins in significant terms. According to Horton (1945) the main stream in the river net should be denoted by the same order number all the way from its mouth to its headwaters. Thus, at every junction where the order changes, one of the lower order streams is renumbered to the higher order and the process repeated. Thus in Fig. 2.2 (a) the main stream is shown as the fourth order stream right back to its source. The third order streams which are tributary to the fourth order stream are also extended back to their farthest source as the third order streams and so on. The streams joining the third order stream are second order stream and they can be extended backward. It can be immediately realized that a certain amount of subjectivity is involved in the ordering of streams according to Horton’s method. In Strahler’s (1952) system, see Fig. 2.2 (b), the headwater streams that receive no tributary are called first order streams. Two first order streams unite to give a second order stream. Two second order streams unite to give a third order stream and so on. When two streams of different order unite, the combined stream retains the order of the higher order stream. A combination of two streams of lower
15
Drainage Basins and Channel Networks
a) Horton (1945)
b) Strahler (1952)
c) Scheideggar (1965)
d) Shreve (1967)
Fig. 2.2
Systems of stream ordering
order, say (u – 1), with a stream of given order u increases the order of the latter by one integer, that is (u + 1). The result of this system of ordering is that it does not reflect any increments except approximately doubling the discharge if one assumes that streams of the same order in the same drainage basin carry approximately equal discharges. Scheideggar (1965) defines the order x after two streams of order u1 and u2 by
d
x = log2 2 u1 ´ 2 u2
i
...(2.1)
His system of ordering is shown in Fig. 2.2 (c). Shreve (1967) has suggested a system of ordering streams in which, the order numbers of two streams contributing to the junction are added to arrive at the order number below the junction, see Fig. 2.2 (d). Thus each exterior link or head tributary has a magnitude 1. If links of magnitude u1 and u2 join, then the resultant downstream link has the order (u1 + u2). If we assume that the first order streams are approximately of the same magnitude and that the discharge is neither lost nor gained from any source other than the tributaries (which is not completely true) then Shreve number is roughly proportional to the discharge in the segment of the stream. It may be mentioned that Strahler’s system of ordering has been more commonly used than the other methods and the same is utilised herein. The analysis of drainage basin considering stream orders is often known as morphometry. The morphometric analysis of drainage basins carried out by Horton (1945), Strahler (1952), Rzhanitsyn (1960) and others is based on the premise that for the given conditions of lithology, climate, rainfall, and other relevant parameters in the basin, the river net, the slope and the surface relief tend to reach a steady state in which the morphology is adjusted to transmit the sediment and excess flow produced. If there are any major climatic or hydrologic changes in the region, the steady state
16
River Morphology
morphologic characteristics will naturally be modified. In other words, the river net is the definite response of the drainage basin to the complex physical processes taking place over the drainage basin.
2.4
HORTONS LAWS OF STREAM NUMBERS AND STREAM LENGTHS
Consider a river net in a drainage basin in which the highest order of the stream is K. Let u represent the order of any segment and Nu represent the number of streams of the order u. It has been found by Horton and other investigators that if log (Nu) is plotted against u for any river net the data fall on a single straight line with Nu decreasing for increasing u, see Fig. 2.3. Hence the relation between Nu and u can be expressed as 4
- Daddy's creek - Alleghney river - Sher river (India)
3
log Nu
Rb = 4.34 2 Rb = 4.12 1 Rb = 4.07 0
0
1
2
3
u
4
5
6
7
Fig. 2.3 Variation of log Nu with u (Horton’s ordering system)
Also or
log Nu = a – bu log N(u + 1) = a – b (u + 1) log
Nu = b from which one gets N( u +1)
...(2.2) ...(2.3)
Nu = 10b = Rb N( u +1)
Here a and b are constants. The constant Rb is known as the bifurcation ratio. It is defined as the number of streams of order u divided by number of streams of order (u – 1). Since Nk = 1 N(k – 1)/Nk = Rb or N(k – 1) = Rb N(k – 2) = N(k – 1) ´ Rb = Rb2 Nu = Rb(k – u)
...(2.4)
17
Drainage Basins and Channel Networks
It may be mentioned that for small drainage basins the relation between log Nu and u has been found to be slightly concave upwards thus deviating from the linear relationship expressed by Eq. (2.2); however the deviation becomes smaller as u increases, see Smart (1967). Horton (1945) found that the value of Rb varied from 2 to 4 for the river nets investigated by him, whereas Strahler (1964) found this range to be from 3 to 5 for the drainage basins in which geologic structures do not distort the drainage pattern. Mittal et al. (1974) found Rb to lie between 4.4 and 5.0 for sixty-two third order drainage basins in Garhwal, Himalaya (India), where lithologic conditions were represented by limestones, quartzites, phyllites, sand-shales and alluvium. This value ranged between 3.5 and 4.5 for sixth and seventh order sub basins of the Narmada, see NIH (1995). It has been found by some investigators that the bifurcation ratio Rb is not independent of the order of stream, and hence in a particular drainage basin Rb should be calculated between streams of 1 order lag with those of 2 order lag in order to reduce the difficulties introduced by order and the size of area analysed. Schumm (1956) recommends the use of weighted Rb designated as WRb WRb =
d
S Rb ( u , u + 1) Nu + N u + 1 SN
i
where Nu is the number of streams of u th order. The principle embodied in Eqs. (2.2) and (2.3) is commonly known as Horton’s Law of Stream Numbers which states that “The number of streams of different order in a given drainage basin tends closely to approximate an inverse geometric series in which the first term is unity and the ratio is the bifurcation ratio”. (Horton 1945). The fact that the bifurcation ratio remains fairly constant is interpreted to mean that the drainage basins in homogenous materials tend to show geometric similarity. Strahler (1964) has emphasized that there is a close relationship between the shape of the drainage basin, bifurcation ratio and the shape of the unit hydrograph. A very elongated basin will have a very high value of Rb (of the order of 15 or so) and will give a sustained unit graph with low peak. On the other hand a near circular drainage basin will have a low Rb value (around 2.4 or so) and would yield a unit graph with high peak and small base length. It can be seen from Eq. (2.4) that n
åN
u
i =1
= RbK - 1 + RbK - 2 + RbK - 3
d
U| || + ..... + 1V || |W
= N1 + N2 + N3 + ..... N k
i
= RbK - 1 ( Rb - 1 ) .....
...(2.5)
If one measures the total length of streams of a given order u in a drainage basin and designates it Lu, the mean length of the streams of order u, Lu will be
18 10
5
10
6
10
4
10
5
10
3
10
4
10
2
10
3
10
1
10
2
10
0
10
1
10
–1
10
0
10
–2
}u
Nu and }u km
2
Nu
øu
Sessquehanna river basin (U.S.A.) 6
Fig. 2.4
2
4 6 u Order
8
10 10
Lukm
River Morphology
–1
Variation of Nu, Au , Lu with u
Lu = Lu/Nu
...(2.6)
If in any given basin log Lu is plotted against u one gets log Lu increasing linearly with u, thus yielding a straight line, see Fig. 2.4. This means that Lu / Lu – 1 = constant RL
...(2.7)
where RL is known as the Horton’s length ratio. It follows from Eq. (2.7) that L2 = L1 RL, L3 = L2 RL = L1 RL2 and
...(2.8)
Lu = L1 RLu - 1
The principle embodied in Eqs. (2.7) and (2.8) is known as Horton’s Second Law of Stream Lengths, which states that “The average lengths of the streams of each of the different orders in a drainage basin tend closely to approximate a direct geometric series in which the first term is the average length of streams of first order”. (Horton 1945). Morisawa (1962) has found that RL values ranged from 2 to 3 in Applachian Plateau Province (U.S.A.), while its value ranged between 1.50 and 2.40 for four sub basins of Narmada. These two laws of drainage composition have been substantiated by several investigators irrespective of whether Horton’s or Strahler’s method of stream ordering is used. They include Chorely (1957), Morisawa (1962) and Gregory (1966). The total length of streams of order u will be Lu Nu. Substituting the value of Nu from Eq. (2.4) and using Eq. (2.8) one gets
19
Drainage Basins and Channel Networks
Lu = Total length of streams of order u = Nu Lu = L1 RL(u – 1) Rb(k – u) Hence total length of the streams of Kth order basin will be K
åL
u =
L1 Rbk - 1 + L1 RL RbK - 2 + L1 RL2 RbK - 3 + ... L1 RLK Rb- 2 + L1 RLK - 1
1
R| R F R I F R I S|1 + R + GH R JK + GH R JK T 2
=
L1 RbK -1
L
L
L
b
b
b
3
FR I + ... + G J HR K
K -2
L b
FR I +G J HR K L b
K -1
U| V| W
...(2.9)
Substituting RL/Rb = RLB one can simplify the above equation to the form K
å 1
K -1 Lu = L1 Rb
dR dR
K LBI K LB
i - 1i -1
...(2.9)
Another length parameter introduced by Horton (1945) is the length of overland flow Lo which is the length of flow path, projected to the horizontal, of non channel flow from the point of drainage divide to the point on the adjacent stream channel. Length of overland flow is one of the most important variables affecting the hydrologic and physiographic development of the drainage basin. During evolution of the drainage basin Lo is approximately equal to half the reciprocal of the drainage density.
2.5
AREAS OF DRAINAGE BASINS
Basin area is hydrologically important because it directly affects the size of the storm hydrograph, and the magnitude of mean and peak flows. Amount of sediment eroded from the drainage basin is also related to the basin area. In fact, since almost every watershed characteristic is correlated with area, the area is the most important parameter in the description of form and processes of the drainage basin. The area Au of a basin of given order u is defined as the total area projected upon a horizontal plane, which contributes overland flow to the channel segment of a given order and all the tributaries of the lower order. Thus area of the basin of the third order, A3 will be the sum of areas of first and second order basins, plus all additional areas, known as inter-basin areas, contributing directly to channels of order higher than the first. Thus A2 = S N1 A1 + S N1 Ao2 where Ao2 is the inter-basin area contributing to second order segments. In general one can write Au = {S N1 A1 + SN1 A2 + SN1 A3 + ... S N1 Au – 1}
...(2.10)
+ {SN1 Ao1 + S N1 Ao2 + ... SN1 Aou } Law of areas has been inferred by Horton (1945) and stated by Schumm (1956), according to which the mean basin areas of stream of each order tend closely to approximate a direct geometric sequence in which the first term is the mean area of the first order basin. Hence if log Au is plotted against u, a straight line is obtained as shown in Fig. 2.4. From this one can deduce that
20
River Morphology
Au = A1 RAu- 1
...(2.11)
where Au is the mean area of basin of order u, A1 is mean area of first order basins, and RA is known as the area ratio. Some attempts have been made to relate stream lengths to basin areas. It is argued that according to the laws of stream lengths and basin areas, both these parameters are related to the stream order. Hence a relation of the type L ~ An should relate basin length to the basin area. On the basis of over 300 measurements made by Langbein (1947), Hack (1957) found that this relation is of the type L = 1.16 A0.60
...(2.12)
L km
where L is the stream length in km measured up to the drainage divide and A is basin area in km2. For geometrically similar basins one would expect L ~ A0.50. Since according to Hack L ~ A0.60, it means that drainage basin changes its shape in the downstream direction; it tends to become longer and narrower as it changes. Figure 2.5 shows variation of L with A for different regions as well as the enveloping curves.
10
3
10
2
10
1
10
0
10
–1
1. 2. 3. 4. 5. 6. 7. 8.
W. Malaysia Deron W. USA Uganda Wales Australia Nebraska (USA) E. USA
Envelope curves
10
3
10
2
10
1
10
0
10
1
10
2
10
3
2
A km
Fig. 2.5 Variation of total stream length with basin area
Müller (see Gregory and Walling (1976)) defines three lengths to describe the stream length. These are the length of the stream channel Le, the length of valley Lv and shortest distance between the mouth and the source of stream Lm. Hack has also shown that Au = A1 RAu - 1
u ( RLB - 1) ( RLB - 1)
...(2.13)
21
Drainage Basins and Channel Networks
2.6
BASIN SHAPE
Basin shape affects the hydrologic characteristics of the basin, namely hydrograph shape. As mentioned earlier a long narrow basin having high bifurcation ratio gives a low but sustained peak whereas round basins with low bifurcation ratio would give a sharply peaked hydrograph. Several shape factors have been suggested to describe the shape of the basins, some of which are listed below: Table 2.1 S.No.
Notation
Definition
Form factors for basins Reference
Form factor Rf Basin area Au/(Basin length)2 Circularity Basin area Au/Area of circle ratio C with the same perimeter
Horton (1932) Miller (1953)
3.
Elongation ratio E
Schumm (1956)
4.
Lamniscate ratio K
1. 2.
(Diameter of a circle with area of basin)/(Maximum basin length) (Basin length)2/4 (basin area)
Chorely et al. (1957)
Comments Reciprocal of this is used by Corps of Engineers (U.S.A.) in Hydrograph analysis C = 0.6 to 0.7 for homogeneous basins of 1st and 2nd order. For non-homogenous basin C = 0.4 to 0.50 E = 0.6 to 1.0; lower value for areas with strong relief and steep slope —
The circularity and elongation ratios can be of practical utility in predicting certain hydrological characteristics of the drainage basin. Elongation ratio has been used in the studies of sediment eroded from the basins. In general drainage basins tend to become more elongated with strong relief and steep slopes. Available data indicate that the drainage basin gets relatively elongated as its size increases.
2.7
LITHOLOGY
The lithology and rock structure in the basin play an important role in influencing the hydrologic, erosional and other characteristics of the basin. The rock type and soil mantle affect the infiltration capacity. Permeable soil or rock allows water to percolate into the ground which later may be discharged into the stream. Hence the surface runoff is reduced. Basins with bed rock or soil which is relatively impermeable produce high volume of surface runoff and very little ground water flow. Rock type governs the character and rate weathering, the weathering products obtained and hence the nature of sediment and solutes supplied to the stream. The nature and effect of vegetation is also partly governed by rock type, which in turn governs the sediment supply. Hence sediment load vs water discharge relationship would depend on rock type. Similarly alluvial fan area vs drainage area relationship also depends on rock type. The rock type also influences the shape of the valley and stream because it controls resistance to erosion and also the runoff as discussed above. Morisawa (1968) found that valleys cut in unconsolidated beach sands and gravels were V-shaped, while those cut in silts and muds were flat bottomed. In the same manner Brush and Hack have found that the correlation between channel gradient S and its length L depends on the lithology and rock type. If S = a Lb the slope decreased with increase in L for all the rock types i.e., b was negative, but the rate of decrease varied with rock type. Lastly,
22
River Morphology
lithology and rock structure also affect the morphometry and geometry of the drainage basins. A flatlying resistant bed will cause increase in stream length and decrease in stream slope. Where the sediments are folded, stream cutting across resistant strata will be short and steep with small drainage areas. Similarly drainage pattern is also influenced by lithology. For flat and homogenous rock surface drainage net tends to form at random and streams flowing in all directions i.e. dendritic pattern. In the case of jointed or folded rocks streams tend to erode the channel along a weakness. If joints are the weakness, their orientation determines the stream pattern. In tilted or folded strata streams tend to develop along linear bands of outcropping weak rock. Therefore, a full understanding of lithology is essential for the study of river morphology.
2.8
VEGETATION
Vegetation including grass, shrubs, and forests plays an important role in the hydrologic cycle and catchment erosion. Hence, its effect is of prime importance to those working on river morphology and river dynamics. Studies by various investigators have shown that water and sediment yield, flood peaks and the time of their occurrence, and the velocity of travel of the flow peak are strongly influenced by the nature and extent of vegetation. When the pressure on the land, because of increase in the population and human activity, was not heavy, there were marginal changes in the forests, and minor disturbances in their coverage were soon made up naturally. However, because of increase in the population and industrial growth and consequent increase in food, space and energy requirements of nations, there has been indiscriminate deforestation in some parts of the world. In the early eighties, most of the tropical forests were estimated as being altered by man at around 12 million hectares per year, see Bruijnzeel (1990). Many investigators consider this as an underestimate. Deforestation includes cutting of trees for fuel, timber and other industrial uses, deforestation caused by great and small forest fires, shifting of zoom cultivation, construction activity related to logging such as creation of access roads, skid tracks and landings, clearing areas for habitation and developing industry, surface mining and similar activities. Generally speaking, a forest subjected to some of the above mentioned disturbances may recover to its previous state if left alone for a sufficiently long period. However, this is not the case when the forest is converted to permanent agriculture such as grazing, cropping or extractive tree crops. The effects of partial or complete removal of forest on climate, water yield and its seasonal distribution and on sediment production have been studied by many investigators. Below are given the salient features of these effects, (see Bruijnzeel (1990)). Rainfall and Water Yield 1. Tropical forests reflect about 12 percent of the incident short wave radiation while agricultural crops reflect 15 to 20 percent. Hence a different partitioning of energy between warming up of the boundary layer and evaporation is to be expected when tropical forests are converted to grass lands or agricultural crops. 2. As a result of extensive studies during the past four decades, it is found that the extent of forests has definite effect on rainfall. 3. It has been found that in humid tropics removal of natural forests cover may result in considerable initial increase in water yield, the increase depending on the amount of rain received.
Drainage Basins and Channel Networks
23
4. The initial increase in water yield, after removal of the forest cover, gradually decreases with the passage of years and may return to pre cut flows in about eight years in case of natural regrowth.
Stream Flow Regime 1. Geological, topographical and vegetative cover play an important role on floods and hence isolation of effect of vegetation becomes rather difficult. 2. If geology is favourable, cutting vegetation shifts infiltration flow to surface flow and therefore peaks will enhance. 3. Also in the absence of retarding effect, the peak is likely to occur earlier. 4. Change in evapo-transpiration and infiltration opportunities associated with change in forest cover will govern the dry season flows. If infiltration opportunities after forest removal have decreased to the extent that the increase in amount of water leaving the area as stream flow exceeds the gain in base flow associated with reduced evapo-transpiration, then the dry season flow is reduced. If on the other hand, the surface infiltration characteristics are maintained over most of the area by deliberate soil conservation practices or by some other method, then the effect of reduced evapo-transpiration after clearing will show up as increased base flow or dry seasonal flow.
Sediment Production and Yield When dealing with the effect of change in forest cover on erosion and sedimentation it is helpful to distinguish between surface erosion (i.e., splash, sheet and rill erosion), gully erosion, and mass movements because the ability of vegetation cover to control the various forms of erosion is rather different. It is well known that only part of the material eroded from hill side will enter drainage network, the rest may move into temporary storage such as depressions, foot slopes, small alluvial fans or in small tributaries, behind debris basins or flood plains. The stored material may be released during large storms or caught by vegetation, or form stable topographic elements. Since these storage opportunities tend to increase with increase in area, sediment delivery ratio, which is defined as the amount of sediment passing a given section during a given time divided by amount of sediment eroded from upstream in the same time, is found to decrease with increase in catchment area. It may be years before sediment stored in temporary storages is released and its effect felt several kilometers downstream from the region of erosion. Sediment yield, which is rate of sediment passing a given section, is discussed in detail, in Chapter–III. This was found to be the case on the Brahmaputra river in Assam (India) after 1950 strong earthquake, see Goswami (1985). During August 1950 earthquake, apparently one of the most severe ever recorded, massive landslides occurred which temporarily blocked many major tributaries. Bursting of these dams after several days not only produced devastating floods downstream, but also brought down enormous volume of sediment thereby raising the beds of these rivers considerably. The mean annual suspended load and water discharge between 1955–1963 were 750 000 m3 and 16 530 m3/s as against 130 000 m3 and 14 850 m3/s during 1969–1976. Also during the former period the river reach upstream of Pandu was aggrading, whilst it was degrading during 1969–1976.
24
River Morphology
Surface and Gully Erosion Studies by Wiersum (1984) have indicated that erosion is minimum (0.10 to 0.60 tonnes/km 2/year) in those areas where soil surface is adequately protected by a well developed litter and herb layer. When this layer is destroyed or removed, erosion rates rise dramatically to 500 to 5000 tonnes/km2/year. Hence protection from tree stands lays not so much in the ability of tree canopy to break the power of rain drops but rather in developing and maintaining a litter layer. When rills are formed and they grow into gullies, their lateral and head ward extension through scouring, undercutting and subsequent collapse of walls cause a large increase in sediment production.
Mass Wasting Some of the highest reported natural erosion rates from rain-forested areas have been related to intense mass wasting under conditions of steep topography, tectonic activity, and intense rainfall. In mass wasting, steep slopes in combination with geological and climatic factors are more important than land use. Prasad (1975) after ten years of observations of seismic activity, rainfall and occurrence of land slides in eastern Nepal concluded that intense precipitation and associated saturation of soil were apparently more important than seismic shocks. Starkel (1972) has opined that the role of vegetation in preventing shallow slope failures (less than 3 m) is very important; Manandhar and Khanal (1988) have confirmed this in south of Khatmandu. As regards the influence of tall vegetation on slope stability, the net effect is considered positive, the major factor being the mechanical reinforcement of the soil by tree roots.
2.9
DRAINAGE DENSITIES AND STREAM FREQUENCY
Drainage density is defined as the total length of streams in a basin divided by its area. Hence the drainage density Dd is given by Dd =
å å K
N
1
1
Lu/A
...(2.14)
and will have dimension of km–1. Here N is the number of streams of order u and K is the order of the river basin. Greater drainage density means more channels per unit area or more closeness of channel spacing. Drainage density varies over a wide range from 2 km–1 to 800 km–1 or even more depending on the character of subsoil material, vegetation and relief. Climate is equally important in determining the drainage density since it controls discharge and indirectly the vegetation. Table 2.2 illustrates the effect of these factors, namely lithology, climate and vegetation on the drainage density. Drainage density does not seem to change regularly with stream order within basins. Investigations by Morisawa (1968) indicate that drainage density of the whole basin tends to approximate the mean drainage density of the 1st order basins in the watershed. Langbein appreciated the significance of drainage density as a factor determining the time of travel of water. Since water and sediment flow through the stream channels, annual sediment yield from the catchment is found to increase with increase in drainage as sediment yield ~ Dd0.1 (Garde and Kothyari 1987). Osborn has found that mean annual flood Q2.33 is proportional to Dd2.0 . Gregory and Walling (1976) have plotted total stream length against drainage area for a large number of catchments and found that L ~ A0.378 up to 100 km2 area and beyond that the exponent of A somewhat increases, see Fig. 2.5. Hence one can conclude that L/A i.e. Dd would decrease as A increases.
25
Drainage Basins and Channel Networks
Table 2.2 Effect of lithology, climate and vegetation on drainage density [Adapted from Selby 1967, NIH 1993] Location
Lithology
Climate
Vegetation
Humid, Continental
Deciduous forest
D d km–1
Pennsilvania (U.S.A.)
Horizontal resistant sand stone
2–2.5
Colorado (U.S.A.)
Granite, gneiss and schist
Humid, montane
Montane forest
2.5–5.6
Maryland (U.S.A.)
Shale
Humid, Continental
Coniferous and deciduous forest
4.4
Volcanic Plateau (New Zealand)
Pumice and ignimbrite
Temperate, maritime
Scrub and grass
5.4
South Auckland (New Zealand)
Graywacke overlain by volcanic ash
Temperate, maritime
Formerly green forest, now pasture grass
15.7
South Dakota (U.S.A.)
Clay and shale
Semiarid
Sparse bunch grasses or none
50–160
Arizona (U.S.A.)
Horizontally bedded shale
Hot desert
None
106–220
New Jersey (U.S.A.)
Clay and sand fill
Humid continental
None
344-825
Bihar (India)
Alluvium to Granite, Gneiss
Humid
59 per cent agriculture and 41 percent forest etc.
0.377
Obtaining drainage density can be a tricky problem because a lot would depend on the scale of the map used. Hence uniform scale needs to be used in the comparison of drainage densities of different basins. Carlson and Langbein (1960) have recommended a more rapid method of estimation of the drainage density. Draw a line of known length L on the contour map and count the number of streams n which intersect this line. A minimum of 50 contour crossings is advocated to provide an adequate sample. Then drainage density equals 1.41 n/L. Strahler (1964) considered the drainage density Dd to be a variable dependent on runoff rate per unit area Qr, erosion proportionately factor K (which is mass rate of erosion per unit area per unit eroding force), relief H, mass density of fluid rf, dynamic viscosity m, and g. \
Dd = f (Qr, K H, rf , m, g) The above equation can be written in dimensionless form as
FG H
Dd H = f KQr ,
Qr r f H Qr2 , gH m
IJ K
The first term (Dd H) is known as the ruggedness number, (Qr K) is known as Horton number, which expresses the relative intensity of erosion processes in the drainage basin, (Qr rf H/m) is Reynolds number and (Qr2/g H) is Froude number. Schumm (1956) has introduced a parameter called constant of channel maintenance C that represents the area in km2 necessary to develop and maintain one kilometer of drainage channel. If Au is plotted against Su1 Lu it is found that the two are related linearly as
26
River Morphology
Au = a + C Su1 Lu
...(2.15)
C being the constant of channel maintenance. A basin with relatively impermeable strata requires a smaller drainage area to maintain a permanent channel as compared to the basin with permeable strata. The constant of channel maintenance is taken as a measure of erodibility of the basin. Horton (1932) defines the stream frequency F as the number of stream segments of all orders within a given basin of order K, divided by the basin area; or F = Su1 Nu /Ak
...(2.16)
From the analysis of worldwide data Peltier (1962) found that for areas of comparable average slope, stream frequency is greater in semi-arid regions; it is least in the arid regions and intermediate in humid regions. High drainage densities or stream frequencies are a reflection of increased channel development and hence should give high sediment yield, which is really the case. Melton (1958) has analysed in detail the relationship between stream frequency and drainage density both of which measure the texture of the drainage net, yet each treats the different aspect of it. According to him it is possible to construct two hypothetical drainage basins having the same drainage density but different stream frequency, and vice versa. However, in nature there is a good correlation between the two. From the analysis of 156 drainage basins covering a wide range of climatic and lithological conditions, Melton found the following relation F = 0.434 Dd2 –2
where F is in km and Dd is in km
2.10
...(2.17)
–1
RELIEF ASPECTS
The relief is the difference in elevation between given points. Maximum basin relief is the difference in elevation between the basin mouth and the highest point on the basin perimeter. Alternative definition of maximum relief is the basin relief along the longest dimension of the basin parallel to the principal drainage line. Relief ratio Rk is the ratio of maximum basin relief to the horizontal distance along the longest dimension of basin parallel to the principal drainage line (Schumm 1956). Melton (1958) defines the relative relief as the maximum relief H divided by the basin perimeter P while Maxwell defines the relative relief as H divided to basin diameter. Use of the perimeter as the horizontal length dimension solves the difficulty of locating a suitable axial line in the basin. Two other parameters involving maximum relief have been defined by Strahler (1957). The ruggedness number is the product of maximum relief H and the drainage density Dd i.e. (H Dd). The geometry number is defined as (H Dd /S) where S is the ground slope. Both these parameters are dimensionless. Observed values of ruggedness number vary from 0.05 to about 1. Strahler (1964) found that the geometry number varies over a relatively narrow range viz. 0.40 to 1.0. Schumm (1954) found that for six small drainage basins in Colorado Plateau Province (U.S.A.) the relief ratio Rh correlated well with annual sediment loss giving a relationship of the form log (annual sediment loss) ~ Rh
27
Drainage Basins and Channel Networks
Admittedly, relief ratio strongly influences the sediment loss since the force exerted on the surface is directly related to Rh. However, climatic factors such as rainfall and vegetal cover also affect sediment loss. Schumm’s data shown in Fig. 2.6 are taken from catchments in the same region; hence climatic conditions were similar even though the lithology changed somewhat.
10
0
3
Schumm's data
Shale
Annual sediment loss Ha.m/km
2
8 6
2
Friable sandstone
ak
roc
k
4
10
4
8 0
0.1
sis
8 1
Re
Conglomerate sandstone
–1
tan
t to
we
2
5
0.2
0.3
0.4
0.5
0.6
Rh
Fig. 2.6 Relation between annual sediment loss and Rh (Schumm 1954)
Hypsometric Curves Let “a” be the horizontal projected area of a drainage basin at an elevation h (see Fig. 2.7) and A be the total projected area. Then one can prepare a curve between relative height h/H and relative area a/A as shown in the Figure 2.7. Such a curve is known as hypsometric curve. The analysis of large drainage basins using such curves was first done by Langbein (1947) and later used by Strahler and others. The hypsometric curve, in general, will change with time because of the gradual erosion of areas at higher levels and hence the relative position of the hypsometric curve on a/H vs h/H graph gives an idea about the stage of development of the basin landscape. Figure 2.7 shows young and mature stages of topography. This figure also shows monadnock phase in which the resistant rock in the basin may form prominent hills at isolated places giving a distorted hypsometric curve. Sometimes the integral
z 1
f (x) dx where f (x) = h/H and x = a/A is used as an index of evolution of the topography of the basin.
o
This integral represents the rock mass that is still to be eroded. Young phase would correspond to a high value of the integral while mature phase would correspond to a relatively small value. Strahler (1964) has indicated that most of the hypsometric curves can be represented by an equation of the form
28
River Morphology
y Divide
Entire basin area A
1.0
Original land surface Young
0.8 Mature (Equilibrium)
0.6 Area a
h H 0.4 Monadnock (Prominent hills) (x, y)
Summit plane
H
0.2 h
y
a 0 Base plane Fig. 2.7
0
0.2
0.4
0.6
0.8
1.0
a/A
Hypsometric curve
F d - x a IJ y=G H x d - aK
z
...(2.18)
Here y and x are as shown in Fig 2.7. The exponent z increases as the topography becomes more mature. Hypsometric curves are also related to hydrologic characteristics of the drainage basin. Thus distribution of elevation in a drainage basin is closely related to the amount of flood storage available, the effect of which is to make the rising limb of hydrograph less steep, increase the time lag and make the peak lower and less pronounced. Knowledge of hypsometric curve is also useful in better estimates of rainfall, snowfall and evaporation in the basin.
Channel Slopes A composite stream profile in a drainage basin can be prepared in the following way. For each first order streams vertical drop and horizontal length of the segment is determined. From these data mean drop and mean horizontal length are determined. This procedure is followed for streams of all orders. The triangles for each order are connected in sequence to produce a composite profile. Since each segment slope is governed by the average discharge and average sediment load, a segmented profile looks logical even though we tend to draw a continuous curve through these points. If S u is the average slope of the segments of order u, Horton (1945) expressed variation of S u by the law of stream slopes according to which Su = S1 RsK - u where Rs is ratio similar to bifurcation ratio and can be called slope ratio.
...(2.19)
29
Drainage Basins and Channel Networks
2.11
DRAINAGE BASIN CHARACTERISTICS AND HYDROLOGY
Many times a need is felt to have hydrologic data at sites where gauging station data are not available. Since there is a lack of data about precipitation (input) and stream flow (output), there is great difficulty in testing input-output models unless severe simplifying assumptions are made. Hence, scientists have worked on the premise that fluvial activity and form of the land must be related. This was reflected in Strahler’s dimensional analysis presented earlier where runoff per unit area was related to erosion, relief and drainage density. Bodhaine and Thomas (see Osborn 1980) obtained the following expression for mean annual flood Q Q = 0.638 A0.889 L– 0.037 R1.135 G
...(2.20)
where L is ratio of lake area to catchment area expressed in percent, G is the geologic factor and R is the average annual runoff. A number of studies conducted in the U.S.A. and other countries have shown that basic drainage parameters such as stream length, basin length, basin relief area, drainage density, and slope are adequate to obtain correlations with different flows from the basin. The ungauged flows for which the methods have been developed are 7 day low flows of 2-yr and 20-yr return periods Q2 and Q20 respectively, average annual flow Qaa, two year and 50 year peak flows Q2p and Q50p and sediment flow Qs. One flow is considered to be functionally related to another flow of same type of different return period. Thus Q2p = f (Q50p)
...(2.21)
For low flows this general relationship is Q1L = f (Q2L)–n
...(2.22)
where n is positive. Some of the successful geomorphic parameters used are (L1 . H) (LT . H), (LT H0.5) and (Dd . L1) L1, where L1 is the length of first order perennial streams, H is the relief, LT is the total length of streams and Dd is the drainage density (Osborn, 1971). It may be noted that all these parameters are dimensional. Work done on the geomorphological instantaneous unit hydrograph has been summarised by Rodriguez-Iturbe (1993). GIUH is defined as the probability density function for the time of arrival of a randomly chosen drop to the gauging site and is related to Horton’s Rb, RL, RA, average velocity of the stream flow v and length of the channel of highest order LW. The peak flow qp and time to peak tp are given as qp = 1.31 RL0.43 ULW– 1 tp
FR I = 0.44 G J HR K B
...(2.23)
0.55
–1
RL–0.38 LWU
...(2.24)
A
Here qp is in hr–1, U in m/s, tp in hr and LW in km.
2.12
RANDOM WALK MODEL
The precipitation falling on a uniformly sloping plain develops an incipient set of rills near the watershed divide; these are generally oriented downhill. As the rills deepen with time, cross grading
30
River Morphology
Uniform spacing at origin
Fig. 2.8
Random walk model for stream network
begins owing to overflow of shallow rills. The direction that the cross grading takes place and the micro piracy of the incipient rills are postulated to be a matter of chance until the rills deepen sufficiently. This randomness in the first stages of development of stream has led to formulation of random walk model for drainage network. To illustrate the basic ideas behind random walk model assume a row of equally spaced points on the boundary of the drainage basin say at 1.5 cm apart; eight such points are shown in Fig. 2.8. They can be considered as source of first order streams. Assume each point can move to the right, left or in the forward direction through a fixed distance so that the motion is downhill. As a result, a series of staggering paths will be generated and junctions may occur after which the joint path will be extended as a single unit, see Leopold and Langbein (1962), Shreve (1966 and 1967). Such artificial networks have properties and relationships closely approximating Horton’s laws. As a consequence, it has been suggested that some of these relationships are attributes common to all systems of randomly developed networks and are not really laws of orderly stream development. Of course it does not follow that stream networks are generated at random, even though random walk models approximate to them in many aspects. Some may even argue that streams do not develop from head downwards but do so from mouth upwards. Leopold and Langbein found that for such a random walk model constructed, Lu + 1/Lu came out to be 2.8, a figure which lies between 2.5 and 3.7 the range obtained by Horton (1945). Similarly, from random walk model it is found that Lu ~ A0.64 which agrees well with Hack’s relation L = 1.16 A0.60 as given in Eq. (2.13). One may argue that the development of drainage network is not so much a matter of chance but it is influenced by lithology, climate, vegetation and antecedent conditions. The present streams may reflect the effects of sequences of beds that have been eradicated by erosion during geologic past. Since random walk model ignores all these factors one must view such a model with caution.
31
Drainage Basins and Channel Networks
2.13
CONCLUDING REMARKS
At the end it is pertinent to mention that most of the generalities developed in this chapter have been obtained from the data on small basins in weak rocks in U.S.A. Such basins adjust rapidly to the changing conditions. Therefore one may assume that some present property or properties are controlling the stream geometry and slope which can be measured and statistical relations obtained. If variation in lithology is great and erosional history complex, the drainage net analysis may become more involved (Sparks 1972).
References Bruijnzeel, L.A.(1990) Hydrology of Moist Tropical Forests and Effects of Conservation. A State of Knowledge Review. Division of Water Sciences, IHP, UNESCO, Paris (France). 224 p. Carlson, C.W. and Langbein, W.B. (1960). Rapid Approximation of Drainage Density: Line Intersection Method. USGS Water Resources Division, Bull. 11, February 10. Chorely, R.J. (1957). Illustrating the Laws of Morphometry. Geo. Mag. Vol. 94. Chorely, R.J., Malm, D.E.G. and Pogorzelski, H.A. (1957) A New Standard for Estimating Basin Shape, Am. Jour. Sci., Vol. 255, pp. 138– 141. Garde, R.J. and Kothyari, U.C. (1987) Sediment Yield Estimation. JIP, CBIP, India, Vol. 44, No. 3. Garde, R.J. and Kothyari, U.C. (1990) Flood Estimation in Indian Catchments. Jour. of Hydrology, Elsevier Science Publications, Amsterdam, Netherlands, Vol. 113, pp. 135–146. Goswami, D.C. (1985) Brahmaputra River, Assam, India: Physiography, Basin Denudation and Channel Aggradation. WR Research, Vol. 21. Gregory, K.J. (1966) Dry Valleys and Composition of the Drainage Net. Jour. Hydro. Vol. 4, pp. 327–340. Gregory, K.J. and Walling, D.E. (1976) Drainage Basin Form and Processes:A Geomorphological Approach. Edward Arnold (Publishers) Ltd., London, Paper-Back Edition, 458 p. Glock, W.S. (1932) Available Relief as a Factor of Control in the Profile of Land Form. Jour. Geol., Vol. 40, pp. 74–83. Hack, J.T. (1957) Studies of Longitudinal Stream Profiles in Virginia and Maryland. USGS Professional Paper 294 – B,. 53 p. Horton, R.E. (1932) Drainage Basin Characteristics. Trans. AGU, Vol. 13, pp. 350–361. Horton, R.E. (1945) Erosional Development of Stream Their Drainage Basins:Hydrological Approach to Quantitative Morphology. Bull. Geol. Soc. Am. Vol. 50, pp. 275–370. Howard, A.D. (1967) Drainage Analysis in Geologic Interpretation:A Summation. Am. Soc. Petroleum Geologists Bull. Vol. 51, pp. 2246–2259. Langbein, W.B. et al. (1947) Topographic Characteristics of Drainage Basins. USGS Water Supply Paper 968C. Leopold, L.B. and Langbein, W.B. (1962) the Concept of Entropy in Landscape Evolution. Theoretical Papers in Hydrologic and Geomorphic Sciences. USGS Professional Paper 500A. 20 p. Manandhar, I.N. and Khanal, N.R. (1988) Study of Landscape Processes with Special Reference to Landslides in Lele Watershed, Central Nepal. Unpublished Report, Dept. of Geology, Tribhuvan University, Khatmandu (Nepal). Melton, M.A. (1958) Geometrical Properties of Mature Drainage Systems and Their Representation in an E4 Phase. Jour. Geol. Vol. 66, pp. 35–54.
32
River Morphology
Miller, V.C. (1953) A Quantitative Geomorphic Study of Drainage Basin Characteristics in the Clinch Mountain Area, Verginia and Tennessee, Project NR 389-042, Tech. Rept. No. 3, Columbia University, New York (U.S.A.). Mittal, R.S., Parkash, B. and Bajpai, I.P. (1974) Drainage Basin Morphometric Study of the Part of Garhwal Himalaya. Himalayan Geology, Wadia Institute of Himalayan Geology. Morisawa, M.E. (1962) Quantitative Geomorphology of Some Watersheds in Appalachian Plateau. Geol. Soc. Am. Bull. Vol. 73, No. 9, pp. 1025–1046. Morisawa, M.E. (1968) Streams–Their Dynamics and Morphology. Earth and Planetary Science Series, McGraw Hill Book Company, N.Y. 175 pp National Institute of Hydrology (1993) Geomorphological Characteristics of Punpun Basin of Ganga River System, Roorkee (India), CS (AR) - 125. National Institute of Hydrology (1995) Fluvial Geomorphological Characteristics of Four Sub-basins of Upper Narmada, Roorkee (India), CS(AR) - 159. Osborn, J.F. (1980) Drainage Basin Characteristics Applied to Hydraulic Design and Water Resources Management, Chapter 8, In Geomorphology and Engineering (Ed. Coates, D.R.), George Allen and Unwin, London, 1980, pp. 141– 172. Peltier, L.C. (1962) Area Sampling for Terrain Analysis. Prof. Geogr. Vol. 14, pp. 24–28. Prasad, R.C. (1975) The Landslide and Erosion Problems with Special Reference to the Kosi Catchment. Proc. of the Seminar on Landslides and Toe Erosion Problems with Special Reference to Himalayan Region. Gangtok, Sikkim. Rodriguez - Iturbe, I. (1993) The Geomorphological Unit Hydrograph, Chapter 3 in Channel Network Hydrology (Ed. Beven, K. and Kirkby, M.J.), John Willey and sons, New York, pp. 43–68. Rzhanitsyn, N.A. (1960) Morphological and Hydrological Regularities of the Structure of the River Net. Published by Gidrameterizdat, Leningrad (Translated into English by P.B. Kimgold, USDA, ARS, U.S.A.) Scheideggar, A.E. (1965) The Algebra of Stream Order Numbers, USGS Prof. Paper 5258, pp. 187–189. Schumm, S.A. (1954) The Relation of Drainage Basin Relief to Sediment Loss. International Union of Geodesy and Geophysics; 10th General Assembly, Rome, IASH Publ. 36, Vol. 1, pp. 216–219. Schumm, S.A. (1956) Evolution of Drainage Systems and Slopes in Badlands at Perth Amboy, New Jersey, Geol. Soc. Am. Bulletin. 67, pp. 597–646. Schumm, S.A. (1977) The Fluvial System. Wiley Interscience Publication. John Wiley and Sons., New York. 338 p. Selby, M.J. (1967) Morphometry of Drainage Basins in Areas of Pumice Lithology. Proc. 5th New Zealand Geography Conference, New Zealand Geogr. Soc., Auckland (N.Z.), pp. 169–174. Shreve, R.L. (1966) Statistical Laws of Stream Numbers. Jour. Geo. Vol. 74, pp. 17–37. Shreve, R.L. (1967) Infinite Topological Random Channel Networks. Jour. Geol. Vol. 75, No. 2, pp. 178–186. Smart, J.S. (1967) A Comment on Horton’s Law of Stream Numbers. WR Research, Vol. 3, pp. 773–776. Smith, K.G. (1950) Standards for Grading Texture of Erosional Topography. Am. Jour. Sci. Vol. 248, pp. 655–658. Sparks, B.W. (1972) Geomorphology, Longman Group Ltd., London, Chapter 6, 2nd Ed. Strahler, A.N. (1952) Dynamic Basins of Geomorphology, Bull. Geol. Soc. Am., Vol. 63, pp. 923–938. Strahler, A.N. (1957) Quantitative Analysis of Watershed Geomorphology. Trans. AGU, Vol. 38, pp. 913–920. Strahler, A.N. (1964) Quantitative Geomorphology of Drainage Basins and Channel Networks. Section 4-II in Handbook of Applied Hydrology (Ed. V.T. Chow ) McGraw Hill Book Company Ltd., New York, pp. 4–39 to 4–76.
Drainage Basins and Channel Networks
33
Thornbury, W.D. (1969) Principles of Geomorphology. Wiley International Edition, John Wiley and Sons, Inc., 2nd Edition. Wiersum, K.F. (1984) Surface Erosion under Various Tropical Agroforestry Systems, in Proceedings Symposium on Effects of Forest. Land use on Erosion and Slope Stability (Eds C.L. D’Loughlin and A.J. Pearce.). IUFRO, Vienna and East-West Centre, Honolulu, (Hawaii). Zernitz, E.R. (1932) Drainage Patterns and Their Significance. Jour. of Geol., Vol. 40, pp. 498–521.
C H A P T E R
3
Soil Erosion and Sediment Yield 3.1
INTRODUCTION
Soil can be eroded from its present state by the action of water, wind and glaciers; however in the context of the theme of this book, attention is concentrated on soil erosion by water, which is by far the most important in humid and semi-humid areas. Soil erosion by water is the process of detachment of soil particles by the impact of rainfall and runoff, and its transport down the slope. Erosion from mountainous areas and agricultural lands is the major source of sediment transported by the streams and that deposited in reservoirs, flood plains, and deltas. Sediment load is also generated by erosion of bed and banks of the streams, by the mass movements of sediment such as land slides, rockslides and mud flows, and because of construction activity related to roads, buildings and dams. Part of the sediment from the above-mentioned sources, which is carried by the stream, is stored in the valley bottom and on flood plains and released later. Hence, erosion of sediment is discontinuous with time and it displays a high degree of spatial variability. Since part of the sediment eroded from an area can deposit in the lower reaches, the rate of erosion is usually greater than the rate at which sediment is carried downstream at any section; the latter is knows as the sediment yield. It may be mentioned that since landscape formation and changes in it are due to differential erosion and deposition of sediment, erosion, sediment yield and landscape formation are closely interrelated; therefore study of soil erosion and sediment yield assumes great importance in river morphology. Excessive erosion rates in the catchments of the rivers Kosi and Brahmaputra in India are responsible for the severe migration of the Kosi and change of river regime of the Brahmaputra. Similar problems are also encountered in China on the Yellow river. Reservoirs constructed on streams carrying sediment lose their capacity due to deposition of sediment in the reservoir. On an average Indian reservoirs are losing their storage capacity between 0.05 to 5.0 percent per year. In Pakistan, Mangla reservoir, which was planned to last 100 years, is now expected to last only 57 years due to excessive sediment deposition (El-Swaify et al. 1982). Dendy (1968) opined that if the present rates of sedimentation continue a large per cent of small reservoirs would lose about fifty percent capacity in the next three decades.
35
Soil Erosion and Sediment Yield
Soil erosion is found to reduce crop productivity and large tracts of land are made unproductive every year. Brown (1984) estimated that about 23 billion tons of soil from croplands in the world is being lost every year. Accordingly to UNEP (1980), about 20 million-hectare areas in the world become uneconomical for cropping each year due to soil erosion and erosion induced degradation.
3.2
GLOBAL EROSION RATES
Sediment going out of the catchment every year i.e., sediment yield gives a valuable idea about rates of erosion and soil loss from the drainage basin. This information is also very useful in studying the sediment problems and river behaviour. The sediment yield is made of suspended load and bed-load. Except when the depth is small and material is coarse, it is rather difficult to measure the bed-load. Hence most of available data on erosion rates only include suspended load, which is normally expressed in tons/km2/year or tons/year. The mean annual suspended sediment yield expressed as tons/km2/year varies over a very wide range. Low sediment yield is generally associated with lowland areas or areas underlain by rocks that are highly resistant to weathering and erosion, e.g., 1.0 ton/km2/year for many rivers in Poland, and 1.7 tons/km2/year for a river draining the Southern Table Lands and Highlands of New South Wales, see Walling (1988). Some of the high values of sediment yield obtained are from highly erodible loess region. Table 3.1 adapted from Walling (1988) lists some of the high sediment yield values. Table 3.1 Maximum values of specific suspended sediment yield (Walling 1988) Country
River
China Dali Taiwan Kenya North Island New Zealand
Huangfuchuan 187 Tsengwen Perkerra Waiapu Waingaromia
Drainage area km2
Suspended sediment yield tons/km2/year
3199 21 700 1000 1310 1378 175
55 500 — 28 000 19 520 19 970 17 340
High values of suspended sediment yield can be attributed to various factors such as underlying geology, topography, climatic conditions, high erodibility of soils and land use. Steep slopes and high intensity of rainfall can also cause high values of sediment yield. Holeman (1968) has given valuable information on the sediment yield of major rivers of the world. Table 3.2 gives such data for some rivers in the world, which discharge more than 104 tons of sediment each year into the sea. Some idea about erosion rates observed in various continents would also be helpful in knowing which regions contribute the highest and the lowest sediment load to the oceans. Table 3.3 is based on the synthesis of data given by Strakov, and Milliman and Meade (1983). Table 3.3 indicates that the highest sediment load is fed to the oceans every year by Asia and the next in line would be South America and North and Central America. On the basis of whatever data that were then available some investigators have produced maps of global suspended sediment yield. One such map prepared by Walling (1988) is shown in Fig. 3.1. From the analysis of such data estimates are
36
River Morphology
Table 3.2 S.No
1.
Some rivers of the world discharging more than 104 tons/year sediment to the sea (Holeman, Ref. p. 68 (1982)
River
Yellow
Location
Total drainage area 103 km2
China
Average annual sediment load
Average water discharge 103 m3/s
103 tons
tons/km2
666
2080 000
2945
1.50
2.
Ganga
India
945
1600 000
1563
11.80
3.
Brahmaputra
Bangladesh
658
800 000
1445
12.20
4.
Yangtze
China
1920
550 000
547
21.80
5.
Indus
Pakistan
957
480 000
508
5.60
6.
Ching (tributary of Yellow)
China
56
450 000
8008
0.057
7.
Amazon
Brazil
5709
400 000
67
181.40
8.
Mississippi
U.S.A.
3185
344 000
109
17.90
9.
Irrawaddy
Mynamar
425
330 000
914
15.60
10.
Missouri
U.S.A. (Missouri)
1354
240 000
176
2.00
11.
Lo (tributary of Yellow)
China
26
210 000
7890
—
12.
Kosi
India
61
190 000
3117
1.80
13.
Mekong
Thailand
786
187 000
484
11.10
14.
Colorado
U.S.A.
630
149 000
422
0.16
15.
Red
Vietnam
118
143 000
1207
3.90
16.
Nile
Egypt
2944
122 000
39
2.80
Table 3.3 Continent
Mean erosion rates in different continents Area 10 6 km2
Erosion rate tons/km2/year
Africa
29.81
35 - 72
Asia
44.89
208 - 229
Australia
7.86
43
North and Central America
20.44
84 - 113
South America
17.9
100 - 148
9.7
50 - 75
Europe
made of the total suspended sediment load transported to the ocean every year. Some of the estimates of mean annual sediment load are given in Table 3.4. The earlier data base was meagre whereas in the estimates made in 80 have been based on data from over 2000 rivers spread over all the continents. Hence, these recent estimates are likely to be more accurate than the older ones.
Soil Erosion and Sediment Yield
Sediment Yield 2 1 t.km yr 1000 750 500 250 100 50 Deserts and permanent ice
Fig. 3.1 Suspended sediment yield on global basis (Walling 1988)
37
38
River Morphology
Table 3.4 Some estimates of the yearly-suspended sediment transport to oceans Author
Year
Estimated mean annual load in 10 6 tons
Keunen
1950
32 500
Pechinov
1959
24 200
Fournier
1960
51 100
Mackenzie & Garrels
1966
8300
Holeman
1968
15 700
USSR National Committee for IHD
1974
15 000
Walling and Webb
1983
15 000
According to the concept of geomorphic cycle, material is continually eroded from higher elevation areas and brought down to the low-lying areas and sea thereby reducing the slope of the terrain. Natural agents such as rainfall and runoff, wind and glaciers cause this erosion. Geologists have made estimates of such erosion. The time required to reduce the uplifted land surface to a gently undulating plain was estimated by Davis to be 20–200 million years. Geomorphologists use four types of evidences to estimate the rate of loss of material from the land. These are: (i) Method based on estimates of suspended and dissolved material transported by rivers; this is obtained by sampling the sediment load and discharge measurements. (ii) Measurement of sediment accumulated in reservoirs. (iii) Measurement of surface processes on slopes including rates of soil creep, surface wash and landslides. (iv) Comparison of known geological or radiocarbon dates with landform changes identified as subsequent to them. Because of the different techniques used and also because of the fact that erosion 2000
Normal Relief
Steep relief
1000 Steep relief
200 100 Normal relief
50
10
1.5
20
R
S
P
2.5
Ground loss (mm/1000 yr)
500
G
R S P G
Fig. 3.2 Ranges of rates of lowering of land surfaces (Young 1969)
39
Soil Erosion and Sediment Yield
rates are governed by rock type, climate, vegetation, basin area, relative relief and steepness of slope the reported erosion rates in different environments are not rigorously comparable. Young (1969) has examined the then-available data on erosion rates and found it necessary to divide the results into two classes of relief: normal relief including plains moderately dissected areas and gentle to moderate slopes, and steep relief including mountainous areas and individual steep slopes. His results are shown in Fig. 3.2. All data have been converted into mm/1000 years and are plotted on logarithmic scale. For large variations the extreme limits are shown on the ordinate and on abscissa the method used for measurement is indicated viz. R river load, S reservoir sedimentation, P surface process measurements and G geological evidence. His analysis gives an average erosion rate of 500 mm/1000 years for steep relief and 46 mm/1000 years for normal relief. He has also mentioned that with respect to rock type there are no marked differences in rates of erosion between igneous and metamorphic rocks, siliceous sedimentaries and lime stones; unconsolidated rocks are eroded 10–1000 times faster than consolidated rocks. Schumm (1963) suggests that denudation rate of about 900 mm/1000 years be considered as an average maximum rate for drainage basins of the order of 4000 km2. On the basis of suspended sediment yield of the Kosi as reported by Khosla (1953), Schumm obtains nearly the same rate as quoted above. On the other hand, he reports data by Zeuner, Gilluly, Stone and Gutenberg, which indicate that the present maximum rates of uplift or orogeny are far in excess of rates of denudation in many areas. These are 76 m/10 000 years in California, 30 m/10 000 years in Russia, 45 m/10 000 years in Japan and 100 m/10 000 years in the Gulf area. Even though average uplift rates may be 1/3 or 1/4 of the maximum rates and further it is not known that uplift will continue at this rate, it does indicate that timeindependent landforms may not be obtained in some cases because the rates of denudation and uplift are so different.
3.3
TYPES OF EROSION
Major types of soil erosion due to the action of water include sheet erosion, rill and inter-rill erosion, concentrated flow erosion on gully erosion, and stream channel erosion. Sheet erosion is the erosion of land surface caused by the impact of raindrops and transport of soil by overland flow. Sheet erosion is more or less uniform removal of soil without development of water channels. Rill and inter-rill erosion caused by surface runoff results in numerous small-eroded channels across the landscape. Rills are
Fig. 3.3 Formation of gullies
40
River Morphology
defined as eroded channels so small that tillage operations obliterate them every year. Both sheet erosion and rill erosion are widespread over a field and according to Foster (1988) can exceed 20 000 tons/km2 in severe cases. The topography of most fields causes surface runoff in a few major natural waterways before leaving the fields. Erosion that occurs in these areas is called concentrated flow erosion; the impact of this erosion is localized in and around the waterways. When eroded channels in concentrated flow areas become so large that they cannot be easily crossed they are called gullies. Gullies are steep sided water channels, which carry ephemeral flow during storms. Formation of gullies is shown in Fig. 3.3. Gullies are associated with accelerated erosion and hence with landscape instability. Gullies may not normally develop from rills; their development is a complex process, which is not fully understood. Some observations indicate that small depressions caused by weakening of vegetal cover get enlarged; several such depressions coalesce and form a channel, which develops into a gully. Some gully action is found to occur due to subsidence of pipes or tunnels formed underground due to subsurface flow. This normally happens in high sodium soils. In a few cases gully action has been initiated where linear landslides leave deep steep sided scars, which may be occupied by running water in subsequent storms (Morgan 1979). Discontinuous gullies represent youthful stage while fused gullies are an early mature stage of development. The sediment removed from the landscape due to formation, widening or deepening of gullies is known as gully erosion (Heede 1975, and Piest et al. 1975). Very little is known about rates of gully erosion. It may be added that ephemeral streams are those streams, which do not flow continuously. They respond only to the occurrence of precipitation. Other times they are almost dry. Perennial streams are those streams which flow continuously, their water supply coming from rainfall, snow melt and ground water. Stream channel erosion includes stream bank erosion, valley trenching, streambed lowering and flood plain scour. It can also include the material carried by streams such as that from mine wastes and construction activities (such as dams, tunnels and roads) along the banks of the channel. In general, sheet erosion is the prime offender in humid regions, whereas in more arid parts where the rainfall is experienced in short high intensity storms, channel erosion is more predominant. Material derived from sheet erosion source is fine-grained material swept from fields and carried in suspension to and through the conveyance system. Channel type erosion is a source of coarser material and this material is obtained from the areas, which are already a part of the transportation system. In general sheet erosion forms a major part of total erosion from a given area. Thus Roehl (1963) found that in 4300 km2 of well scattered area in South Eastern U.S.A. sheet erosion accounted for 66 to 100 percent of the total erosion. Mass movement includes large-scale erosion due to tectonic activity, landslides, creep rock flow or mud flows; the eroded material is ultimately fed to the stream thereby increasing the sediment concentration substantially. Gross Ventre landslide South of Yellow Stone Park U.S.A., which occurred in 1925, produced 50 Mm3 rock materials forming a 68 m high dam in the valley. The lake formed by this dam was 8.0 km long. Rockslide at Frank (B.C. Canada) in 1903 brought down 35 Mm 3 rock debris. Such landslides are a common occurrence in the valleys of Himalaya in India. Relative importance of sheet erosion, gully erosion, channel erosion, mass movement, and accelerated erosion due to construction of roads etc. varies from one catchment to the other since it depends on various factors. Robinson (1977) has given data on sediment sources and their total contribution to the sediment in streams in U.S.A., (see Table 3.5).
41
Soil Erosion and Sediment Yield
Table 3.5 Sediment sources and their total contribution to sediment in streams in U.S.A. (Robinson 1977) Sediment source
Total sediment in 106 tons/years
Agricultural lands
680
Percent of total 40
Stream bank erosion
450
26
Pasture and range land
210
12
Forest lands
130
7
Other federal lands
115
6
Urban
73
4
Roads
51
3
Mining
18
1
Other
14
1
3.4
FACTORS AFFECTING EROSION
Factors affecting erosion are briefly discussed below.
Rainfall and Temperature Rainfall is the most important factor affecting erosion because of its power to detach the soil particles and its ability to produce runoff, which causes erosion and transportation of the eroded material. Erosion can be produced by a short duration high intensity storm during which the infiltration capacity is exceeded. Prolonged low intensity storms can also cause erosion. In the case of erosion due to water, the antecedent conditions of the soil with regard to soil moisture play an important role. If the soil is already well soaked by previous storm a low intensity short duration storm can also cause significant erosion. For each area one would expect a critical or threshold value of rainfall intensity above which significant erosion would take place. Depending on geologic conditions this value varies from 10 mm/hr to 30 mm/ hr. The erosive ability of rainfall depends upon its intensity and duration and velocity and diameter of the rain drops. For the same mean annual precipitation the annual erosion would depend on how this precipitation is distributed over the year. Fournier (1949) found that the ratio (maximum monthly rainfall/annual rainfall) is a better rainfall parameter for the study of erosion. Garde and Kothyari (1987) have utilised this parameter in their analysis of erosion from the Indian catchments. Temperature plays an important role in the process of weathering, especially mechanical weathering, which leads to the disintegration of rocks. Alternate freezing and thawing, and alternate heating and cooling are the processes involved in this disintegration. Rainfall is responsible for chemical weathering as well as for transportation and deposition of the eroded material. Considering the importance of rainfall and temperature in the process of erosion it is natural that mean annual temperature and mean annual rainfall be used as the criteria for classifying modes of weathering and transportation as done by Leopold, Wolman and Miller (1964), (see Fig. 3.4). For any given temperature the erosion rate first increases with increase in precipitation, reaches a maximum and then significantly reduces. This reduction is due to the growth of vegetation which protects the soil surface from direct impact of rain drops, increases infiltration and gives direct protection from erosion due to foliage lying on the ground. This is shown in Fig. 3.5.
42
River Morphology
Mean annual temp. °C
30
Mechanical Chemical weathering weathering mass movement wind running water 20 running water Mechanical and chemical weathering running water 10 mass movement Mechanical weathering mass movement running water
0
10
20
Wind 0
20 40 60 80 100 120 140 160 180 200 Mean annual rainfall, cm.
Fig. 3.4 Hypothetical morphogenic regions 160 Mean annual temp. 10°C
Effective precipitation cm
140 120 100
Forest
80 60
Grassland
40 Desert shrub
20 0
0
100
200
300
400
2
Sediment yield tons/Km . yr
Fig. 3.5
Sediment yield as related to precipitation and vegetation (Leopold et al. 1964)
Soil Characteristics The erodibility of soil depends on its texture, aggregate stability, shear strength, infiltration capacity, and organic and chemical contents. Coarser the particles smaller will be their erodibility. Similarly greater the relative density less will be the erodibility. The clay content combines with organic matter and forms clods of soil. The stability of the clods determines the resistance to erosion. The shear strength parameter is more useful in the study of mass movements such as landslides. The erodibility index of the soil designated as K is used in the Universal Soil Loss Equation USLE for agricultural lands discussed in section 3.6. It can be determined for the known values of per cent of silt and clay, per cent of sand (0.10 mm to 0.20 mm), percent of organic matter, soil structure and permeability. Figure 3.6 shows the monograph for determining the value of K for the known characteristics as given by Wischmeir et al. (1971). If all the details of soil are not available one can use the following average values given in Table 3.6.
43
Soil Erosion and Sediment Yield
Table 3.6
Average value of erodibility Factor K
Soil
Range of K
Soil loams
0.40 to 0.70
Clay loams
0.30 to 0.40
Sandy loams
0.10 to 0.30
Gravely loams
0.03 to 0.10
0.7
0 %OM = 0
10
Silt + very fine sand
30
80 60
0.5 0.4 0.3
40 40
50 60 70 80
1 Very fine granular 2 Fine granular 3 Coarse granular 4 Blocky massive 1234 Soil strucuture
0.6
20
0.2
0.7
0.1
0.6
0
Percent sand (0.1 0.2 mm) 0
90 100
Example given 65% Silt + V.F. sand 20% Sand (0.1 = 0.2 mm) 3% Organic matter Soil structure Fine granular Permeability slow to moderate
Soil erodibility factor K
20
1 2 3 4
0.5 0.4 0.3 0.2 0.1 0
6 5 4 3 2 1 Permeability
6 Very slow 5 Slow 4 Slow to mod 3 Moderate 2 Mode-rapid 1 Rapid
K = 0.38
Fig. 3.6 Monograph for computing soil erodibility factor K in Universal Soil Loss Equation (Weischmeir et al. 1971)
Slope Geometry Erosion is found to increase with increase in slope and length of the slope; this is due to corresponding increase in the velocity and volume of surface runoff. Erosion rate per unit area can be expressed as
Erosion ~ S m Ln Area
...(3.1)
where the values of m and n are found to be different by different investigators. Values of m and n obtained by various investigators as given by Morgan (1979) are listed in Table 3.7. It can be seen that m and n are functions of process of erosion, magnitude of slope, steepness, length and vegetal cover.
Vegetation Vegetation or plant cover reduces erosion of soil, its effectiveness depending on the height and continuity of canopy, density of ground cover and the root density. For a given temperature, as the precipitation increases the sediment yield in tons/km2 increases and reaches a maximum value. If the
44
River Morphology
Table 3.7 Values of m and n in Eq. 3.1(Robinson 1977) Investigator
m
n
Zingg Hudson and Jackson Hovarth and Erodi
1.40 2.0 1.60 to 0.70
0.60 — —
Quinn, Morgan and Smith Kirkby
0.70 to 1.0 1.0 to 2.0 1.3 to 2.0 —
— — 0.3 – 0.7 1.0 – 2.0
Conditions/Comments From five experimental stations in U.S.A. From experimental stations in Zimbabwe m decreased with increase in slope in laboratory studies m increased as grass cover decreased For soil creep and splash erosion For erosion by overland flow For erosion with rilling
canopy is near the ground it dissipates the kinetic energy of rain. Canopy on the ground also increases roughness and reduces the velocity of surface flow. Roots play an important role in reducing erosion rate. Roots create easy passages for water to infiltrate thereby increasing the infiltration rate and reducing the surface runoff. Small roots also bind the soil mass thereby increasing its resistance to erosion. Generally forests are the most effective in reducing erosion because of their canopy; dense grass is equally effective. Experimental evidence indicates that the erosion-cover relationship is non-linear. As vegetal cover increases from zero there is a rapid decreases in soil loss; however beyond 60 percent cover, further increase in vegetal cover reduces the soil loss marginally. Table 3.8 shows the erosion-cover relationship generalised after Elwell (1980) and Elwell and Stocking (1974). It can be seen from Table 3.8 that for adequate erosion protection at least 60–70 percent of the ground should be covered by vegetation. Table 3.8 Relationship between percent vegetal cover and percent reduction in soil loss 20 32
400
10 60
5 70
20°C
It may be mentioned that there is an interaction between rainfall and vegetation in controlling erosion rates. Langbein and Schumm (1958) have found that vegetation bulk in kg/m2 varies as the annual precipitation raised to a power greater than unity. With increasing precipitation the vegetation changes from desert shrubs to grassland to forest. As a result, when vegetation intensity becomes adequate it inhibits erosion. Hence, on a regional scale initially erosion rate increases with increase in annual precipitation, reaches a maximum and then decreases with further increase in precipitation. Schumm (1977) expressed the effect of mean annual temperature and annual precipitation on sediment yield as shown in Fig. 3.7. It can be seen that as the annual temperature increases the peak of the sediment yield occurs at higher value of annual precipitation. This is so because at higher
40 10
15°C
60 5
5°C 10°C
80 1.5
2
100 0.5
Mean annual sed. yield tons/km
Mean seasonal vegetal cover % Soil loss as a % of bare plot soil loss
300 200 100 0
0
40
80
120
160
Mean annual precipitation cm
Fig. 3.7 Variation of sediment yield with mean annual precipitation and temperature (Schumm 1977)
45
Soil Erosion and Sediment Yield
temperature there is greater evapo-transpiration; hence less amount of precipitation is available for causing runoff. As a result, peak rate of sediment yield shifts to the right. However, studies by Walling and Kleo for 1296 measuring stations all over the world, by Sharma and Chatterji for small reservoirs in Rajasthan (India), by Dunne in Kenya, by Griffiths in New Zealand, and by Duglas in Australia do not support the universality of Fig. 3.7. (Tiwari 1993).
3.5
MECHANICS OF SHEET EROSION
As the rainfall occurs the overland flow normally occurs at shallow depth for a short distance without forming any small depressions or furrows called rills. The pre-rill flow is many times called inter-rill flow and associated erosion is known as inter-rill erosion. In this area the depth of flow and the corresponding shear on the surface are very small. Here the dominating factor influencing the surface erosion is rainfall impact. On the other hand, once the flow enters the rills and is concentrated, the depth of flow is large. Therefore erosion in rill-flow is related to the runoff characteristics; this erosion is sometimes called rill-erosion. It may be mentioned that rills are not a permanent feature. Rills formed from one storm are often obliterated before the next storm of sufficient intensity, which can cause rilling. Most rill systems are discontinuous i.e., they have no connection with the main stream. Rills are usually initiated at a critical distance down the slope where overland flow becomes canalised. It may also be emphasized that rill erosion accounts for majority of erosion from the hillside. Mutchler and Young (1975) found that on a 4.5 m slope plots in U.S.A., over eight percent of material was transported in rills. Relative importance of rill erosion depends on the rill spacing. Smaller the spacing between rills greater will be the rill erosion. Four processes associated with inter-rill and rill erosion can be identified as: Soil detachment by rainfall; Soil transport by rainfall; Soil detachment by runoff; Soil transport by runoff. Mutchler and Young (1975) have summarised the mechanism of soil detachment by raindrops. Raindrop sizes usually range from 7.0 mm to fine mist size and in any rainfall there are raindrops of various sizes. A normal or Gaussian distribution based on the raindrop volumes is usually assumed. Hence median raindrop diameter d is that diameter for which equal amounts of volume are contained in larger and smaller drops than d. Laws and Parsons (1943) have found a relationship between intensity of rainfall I in mm/hour and d in mm as d = 1.24 I 0.182
...(3.2)
The raindrops attain a terminal fall velocity, which depends on their size, air density and temperature. Terminal fall velocity can be obtained from CD versus Reynolds number diagram for a sphere, given in all textbooks on Fluid Mechanics. The terminal fall velocity for 5 mm drop will be about 9.0 m/s and it will be 1.0 m/s for 0.25 mm drop. Presence of strong wind has two effects on terminal fall velocity. Firstly it can increase the velocity of drops striking the land surface and secondly it causes raindrops to strike the surface at an angle to the vertical. The ability of rain to cause soil erosion is attributed to its rate and the distribution of drop size, both of which affect the energy load of a rainstorm. The erosivity of a rainstorm is attributed to its kinetic energy or momentum; both these
46
River Morphology
parameters can be related to rainfall intensity or total amount of rainfall. Rose (1960), Williams (1969) and Kinnell (1973) have related the erosivity rate to momentum of rainfall. Williams and Kinnell have given the following equations for momentum M: log M = 0.711 log I – 1.461 M = 0.0213 I – 1.62
UV W
...(3.3)
Here M is in dynes cm –2 s –1 and I is in mm/hour. The kinetic energy of the rainfall is a major factor initiating soil detachment. Kinetic energy of rainfall can be either measured or can be computed if one knows the rain drop size distribution and corresponding terminal fall velocities. Investigators have used the following three forms of equations to relate kinetic energy E of rainfall expended per unit quantity of rainfall to the rainfall intensity I. E = a + b log ( I ) E = c + (b - a I E=bI-a
-1
U| )V |W
...(3.4)
Where a, b, c are empirical constants. Wischmeir and Smith (1958) gave the following equation E = 13.32 + 9.78 log I
...(3.5)
2
where E is in J/m .mm and I is the rainfall intensity in mm/hour. Hudson (1965) has given the following equation E = 29.8 –
127.5 I
...(3.6)
There are a large number of equations developed for E which are based on data from different regions such as Nigeria, Zimbabwe and U.S.A. It may be mentioned that for a given choice of equation for E, the kinetic energy for a storm having non-uniform rainfall intensity is computed by (i) dividing the storm into small time increments in which the rainfall intensity can be assumed to the uniform; (ii) determining the rainfall intensity in mm/hour for each time increment; (iii) computing Ei for each intensity Ii using the chosen relationship between E and I; (iv) determining E = SEi. When the raindrop hits the soil surface there is a splash of water and its shape is as shown in Fig. 3.8. The splash shape parameters, which define its geometry, are crater width W, splash height H, splash angle b, sheet angle a and sheet radius r. These quantities change with respect to time and their variation with time as recorded by a high-speed camera is also shown in Fig. 3.8. The erosive action of raindrop is effective very early after the impact and in the vicinity of the centre of impact. Evidence indicates that the raindrop impact is most erosive where a thin layer of water about one fifth the drop diameter is present. If the surface water depth is about three drop diameters, it protects the soil from raindrop impact. As the splash height reduces and the crater width increases a horizontal flow velocity away from the splash is caused. This velocity among other parameters also depends on the ratio of water depth to drop diameter and is maximum when this ratio is 0.33, this horizontal component of velocity greatly increases the potential of this surface flow to transport detached soil particles.
47
Soil Erosion and Sediment Yield
b
r Sheet radius
H
a
W
a and b in°
90 80
Sheet angle a
70 60
Splash angle b
H and W in cm
50 0 4
0.01
0.02
0.03
Crater width W
3
Splash height H
2 1 0
0
0.01
0.02
0.03
Time after Impact s
Fig. 3.8 Changes in splash parameters with time
It must also be mentioned that as the raindrop hits a thin water layer surface, a large number of smaller water droplets are produced. Mutchler (1971) found that one drop of 5.67 mm diameter on 0.10 mm water depth on a smooth glass produced as many as 4000 droplets which would eventually hit the soil surface, generate turbulence and throw additional material in suspension. Raindrop impact effects are present in rills also; but because of relatively larger water depth compared to the size of drops, the impact effect is not so pronounced.
Erosivity Indices In developing equations for predicting sheet erosion some investigators have developed erosivity indices, which depend on rainfall intensity, kinetic energy and other characteristics of rainfall. Some of these indices are described below: Wischmeier and Smith (1958) use the rainfall parameter R = EI 30 where E is the total kinetic energy of the storm and I30 is the maximum 30 minute intensity of rainfall during the storm. They found that soil loss correlates well with EI30. The term I30 is computed as twice the greatest amount of rain falling in any 30 consecutive minutes; E is calculated using Eq. (3.5). The parameter R is used in Universal Soil Loss Equation (see below). Fournier (1960) developed an erosivity index for river basins on the basis of relationship between suspended load in rivers and climatic data and relief characteristics. The index called climate index C is defined as C = p2/P where p is the rainfall amount in wettest month and P is the annual rainfall. This index was subsequently modified by FAO (1977) as follows: 2 C1 = S12 1 p i /P
48
River Morphology
where pi is rainfall in ith month. It is also found that the index C1 is linearly related to the index R i.e. EI30 as R = a + b C1
...(3.7)
where a and b vary widely from region to region having different climatic conditions.
3.6
EQUATIONS FOR PREDICTING SOIL LOSS FROM AGRICULTURAL LANDS
Since about 1940 considerable research on soil erosion from agricultural lands has been carried out in U.S.A. and other countries. Often laboratory and field plots have been used to obtain experimental data for predicting and evaluating soil erosion. Laboratory plots are of area about 1.0 m2 or less and many times rainfall simulators are used on them. These are used to study basic erosion phases that are difficult to study on larger plots, for example, surface sealing, aggregate stability, raindrop detachment, and splash transport. In such experiments one must be careful in minimising the edge effects in such plots. The plots used in the development of Universal Soil Loss Equation are large enough to represent the complete process of rill and inter-rill erosion. These are of such size that their sediment delivery ratio is very high. There are various empirical equations, which give the rate of sheet erosion. However, because of their empirical nature the equations would be strictly valid in the region where they are developed. Hence only the functional relationships are mentioned to emphasize the variables to which soil erosion has been related. According to Ellison (1945) the soil dislodged E1 in weight per unit area per unit time can be expressed as E1 = K wo4.33 d1.07 I0.65
...(3.8)
where wo is the terminal fall velocity, d is the raindrop diameter, I is the intensity of rainfall, and K is a constant. Musgrave and his associates in the Soil Conservation Service in U.S.A. made observations and analysed rates of sheet erosion. As a result an empirical equation of the form Ei ~ F Ri So1.35 L10.35 P1.75
...(3.9)
was proposed in which Ei is the soil loss in weight per unit area per year, F is the soil factor based the erodibility of soil and other physical factors, Ri is the factor which is related to the land use, So is the steepness of slope in percent, L1 is the length of the slope and P is the maximum 30 minute rainfall expected in the locality with a 2 years return period. The constant of proportionality in this equation depends on the units used to describe these variables.
Universal Soil Loss Equation (USLE) Soil erosion rates from cultivated lands in U.S.A. are predicted by using the Universal Soil Loss Equation (USLE) developed by Wischmeier and Smith (1962, 1965) on the basis of statistical analysis of a large number of plot-years of data from 47 locations in 24 states. The equation takes into account the effect of rainfall, soil characteristics, slope and length factor for the land, and crop and management practices on soil erosion. This equation is an improvement over the earlier methods in that the abovementioned factors have been quantified and used in the equation. The Universal Soil Loss Equation is E =RKLSCP
...(3.10)
49
Soil Erosion and Sediment Yield
where E is the computed soil loss either in tons/acre year or tons/ha year. R is the rainfall factor in hundred of foot-ton-inches per acre-hour-year or in MJ. mm/ha h yr. It is the combined erosivity due to rainfall and runoff. It is the average number of erosion index units in a year of rain. K is the soil erodibility factor in tons-acre-hours per hundreds of foot-ton-inches-acres or tons-hahour-ha-MJ-mm. (see Fig. 3.6) L is the slope length factor S is the slope steepness factor C is the cropping management factor P is the erosion control practice factor Erosion index is a measure of erosive force of the rainfall and is computed as the product of the total kinetic energy of the rainstorm and its maximum 30 minutes intensity. This is summed for a period of record and divided by the number of years to get its average value. This product correlates well with the soil erosion. Wischmeier and Smith (1965) have prepared a map of U.S.A. indicating Iso-R value lines; R-value varies from 0 to 600 in U.S.A. Soil erodibility factor K has been discussed earlier. It is defined as the erosion rate per unit of erosion index on 72.6 feet long and nine percent slope of cultivated soil. K values give an integrated effect of the characteristics of the soil which influence its permeability and ability to resist detachment and transport by rainfall and runoff. In central and eastern U.S.A. K values range from 0.03 to 0.70. The slope length factor L accounts for the fact that as the length of slope increases, there is increased runoff. It is defined as the ratio of soil loss for a given slope length to the soil loss from 72.6 feet length, other factors remaining the same. If l is the slope length it is found that the soil loss ~ l1.3 to 1.6 and hence soil loss per unit length will be approximately proportional to l0.50. Slope steepness factor S takes into account the increase in the velocity of runoff as slope increases. Taking nine percent slope as standard, S is defined as the ratio of soil loss for a given slope to that from a nine percent slope. If So is the slope steepness in percent, S is related to So as S = 0.0076 + 0.0053 So + 0.000 776 So2
...(3.11)
Hence the combined effect of slope length and slope steepness in USLE is given as LS = l0.50 (0.0076 + 0.0053 So + 0.000 776 So2 )
...(3.12)
Cropping management factor C accounts for the crop rotation, used tillage method, crop residue treatment, productivity level and other cultural practices. Its value is the ratio of soil loss from a field with given cropping and management practices to the soil loss from the fallow conditions used to evaluate the K factor. The C factor for individual crops varies with the stage of crop growth and has been evaluated. Erosion control practice factor P accounts for the effect of conservation practices such as contouring strip cropping, and terracing on the resulting erosion (see Blakely et al. (1955) and Meyer and Mannering (1967)). Its value is the ratio of soil loss with one of these practices to the soil loss with straight row farming. Earlier USLE is revised and updated by the Agricultural Research Service and some universities in U.S.A., (see Foster (1988)). This is done i. to incorporate recently collected data for conservation tillage and range lands into the equation; ii. to improve the applicability of USLE to other climatic regions;
50
River Morphology
iii. to improve the performance of USLE for conditions where no data exist; and iv. to estimate values of the factor C. Attempts are also made to use USLE to estimate soil loss from isolated storm events. Other improvement being attempted is to evaluate sediment yield by using USLE equation. However this would require use of the concept of sediment delivery ratio. At present effect of topographic features on sediment delivery ratio is not known; hence this method of estimating sediment yield is not accurate. The Universal Soil Loss Equation is used for a number of purposes. Commonly it is used to find out the soil loss under a given condition. If an acceptable value of soil loss E is chosen the slope length L required to bring down the soil loss to the chosen value can be calculated. In this way appropriate terrace spacing can be determined. Alternatively the value of C can be predicted and appropriate cropping practice is specified. It may however be mentioned that the data on which USLE is based are from east of Rocky Mountains in U.S.A. Hence values of C pertain to this region only. As mentioned by Morgan (1979), Hudson and Roose have applied this equation in Zimbabwe and Ivory Coast respectively. Morgan (1979) has pointed out that there is considerable interdependence between the variables used in USLE and some are counted twice. For example, rainfall affects both R and C factors, and terracing the L and P factors. It is also pointed out that one important factor to which soil loss is closely related namely runoff has not been included in USLE. This has been overcome by Foster, Meyer, and Onstad who have suggested replacement of rainfall factor R by R1, which depends on R, the storm runoff Q in inches and qp the storm peak runoff in in/hr. R1 is given by R1 = 0.50 R + 15 Q qp1/3
...(3.13)
However this needs further verification. McCool and Rendard (1990) have reported the efforts made in U.S.A. to revise USLE to estimate more accurately the soil loss from both crop and range land areas. The modified equation is known as Revised Universal Soil Loss Equation (RUSLE). All the factors R, K, LS, C and P have received attention. McCool and Rendard have discussed major changes incorporated in RUSLE. Thus R-values are related to (El15). Further R equivalent approach is used to reflect the combined effect of drain and snowmelt.
3.7
MEASUREMENT OF SEDIMENT YIELD
Sediment yield is the amount of sediment passing through a given section in unit time. It can be expressed in tons/km2/yr. Two most common methods of determining sediment yield from river basins are by measurement of suspended load, and from reservoir sedimentation surveys. These methods and associated problems are briefly discussed below:
Suspended Sediment Measurements Determining the average suspended sediment concentration and multiplying it by the discharge can measure suspended sediment. Average suspended sediment concentration in a vertical can be obtained by first taking a number of samples at different locations in the vertical and then taking the average. However, since this is time-consuming and expensive, the following procedures are adopted. A single sample at water surface or 0.6 times the depth below water surface is taken. Sampling at water surface is easier and can give reasonably good results if suspended sediment is very fine. For slightly coarser materials, an empirical coefficient can be used to get average concentration from the
51
Soil Erosion and Sediment Yield
known surface concentration. However, it may be mentioned that the coefficient would really depend on suspended sediment size and flow conditions. Sampling at 0.60 depths has been used in India and some parts of U.S.A. in the hope that it gives the average concentration, presumably because the mean velocity occurs approximately at this level. Analysis of wide range of data indicates that, for reasonable accuracy, one-point measurements should be made between 0.6 and 0.8 depths, the larger value being suitable for coarser sediment. A better method would be to take concentrations at 0.2D and 0.8D and obtain the average concentration as C=
F3C H8
0 .2 D
5 + C0 .8 D 8
I K
...(3.14)
as suggested by Straub. The three point method involves measurement of concentration at surface, mid depth and bottom; the mean concentration can then be obtained either by giving equal weightage to all the three samples or by giving a weightage of two to the mid-depth sample and one to the other two samples. If the stream cross-section is non-rectangular the average concentration in the vertical will be different for different verticals; hence sampling verticals have to be chosen. The following methods are available: i. single vertical at the midstream; ii. single vertical at the point of greatest depth; iii. verticals at 1/4, 1/2, 3/4 width; iv. verticals at 1/6, 1/2, 5/6 width; v. four or more verticals spaced equally across the stream; vi. verticals at middles of sections of equal discharge. The final choice of the number of verticals depends on the availability of man power, funds, crosssectional shape and accuracy desired. The suspended load carried by the stream can then be determined from Qs =
å
N
1
qi Ci
...(3.15)
where N is the number of verticals, qi is discharge at the centre of each vertical and Ci is the average concentration. A brief comment about the frequency of sampling is in order. In reality, samples must be collected at such a frequency which is satisfactory both from the point of view of accuracy needed and the expenses involved. Variations of sediment load occur due to variations in storm characteristics; size, shape, geological and topographical features of the drainage area, and characteristics of the stream. Out of these, the size of the drainage area appears to be the single most important factor. For smaller drainage areas water and sediment discharges are greatly dependent on local storm characteristics. For larger drainage areas, where the runoff accrues from different storms and sub-watersheds, the variation in water and sediment discharge with time is smaller. Therefore, as a rule, larger the drainage area smaller can be the frequency; however during a flood when discharge and sediment concentration vary rapidly, frequent sampling is required. For example, in the case of the Coon Creek, Wisconsin (U.S.A.), having a drainage area of 200 km2, it was found that 90 percent of the total sediment load for 15 months was
52
River Morphology
discharged within ten days or 2.2 percent of the time, (see TCPSM (1969)). Sampling frequencies vary widely depending on agency conducting the sampling, purpose of collection of data, nature of stream and funds available. Sampling interval during low flows can vary from a day to a week. During the rising stage of a flood, intervals varying from 30 minutes to 12 hours have been utilised. After collecting such data the suspended load Qs is related to the corresponding water discharge Q; or alternately suspended load per unit width qs is related to discharge per unit width q. Several field engineers have reported a relationship between qs and q in the form qs = a qb
...(3.16)
where b is found to vary between 1.9 and 2.2 and can be taken as 2.0 as an approximation. However, Leopold and Maddock (1953) found that b varies between 2.0 and 3.0 for many American rivers. The value of ‘a’ would depend on the units used. The usual practice is to develop such a relationship from data for a few years and then use it to compute suspended load for other years where only water discharge variation is known. Certain limitations of qs vs q relation need to be discussed. The qs vs q relations do not take into account such factors as sediment size, river slope, watershed characteristics, and pattern of discharge variation. Experience has shown that such relationships can be different for the rising and falling stages of the streams. In fact, these can be different for different seasons for the same stream. Significant variations can also be obtained because the peak of sediment discharge and that of water discharge may not coincide. For these reasons qs vs q or Qs vs Q relation can only be an approximate guide to the amount of suspended load and should be used with caution. To the suspended load must be added the bed-load carried by stream to get the total load. As mentioned earlier except in the case of shallow streams flowing through relatively coarse material, it is rather difficult to measure the bed-load. Lane and Borland (1951) cite the following classification of Maddock, in which percentage of unmeasured load (i.e. bed-load plus unmeasured suspended load) is related to the concentration of measured suspended load, type of bed material and the texture of suspended material, see Table 3.9. Table 3.9 Maddock’s classification to determine unmeasured load Concentration of measured suspended sediment in ppm
Type of material forming the channel
Texture of the suspended sediment
Less than 1000 Less than 1000 1000 to 7500 1000 to 7500 Over 7500 Over 7500
Sand Gravel, rock or consolidated clay Sand Gravel, rock or consolidated clay Sand Gravel, rock or consolidated clay
Similar to bed material Small amount of sand Similar to bed material 25 percent sand or clay Similar to bed material 25 percent sand or less
Unmeasured load as a percentage 25 to 150 5 to 12 10 to 35 5 to 12 10 to 15 2 to 8
The average values of qS /qT as obtained from actual measurements or otherwise are available for some natural streams. Here qT is the total load. These are listed in Table 3.10. Dekov and Mozzherin (1984) found the ratio of bed-load to suspended load for large streams to be 0.08 for rivers in plain and 0.23 for mountain rivers.
53
Soil Erosion and Sediment Yield
Table 3.10 River Mississippi river at mouth Colorado river at Yuma Niobrara river near Cody Niobrara river near Valentine Snake river near Burge Five mile creek near Riverton Middle Loup river near Dunning Biose river near Twin Springs Moore Creek above Granite Creek
Typical values of qS / qT for natural streams in U.S.A. Sediment size in mm
Average qS / qT
0.14 0.10 0.30 0.27 0.29 0.24 0.33 0.10 0.25
0.90 0.80 0.49 0.47 0.67 0.81 0.53 0.65 0.75
Tricart (1962) has highlighted the dangers in determining the average erosion rates caused by the temporal and spatial variation in erosion. His main argument is that there are different types of discontinuities in the time domain. We have already seen that Qs vs Q relation is not truly unique. Time lags between flow and sediment are much greater for less mobile material such as coarse sand, gravel and boulders than for colloids, silts and clays, because while the former move slowly and intermittently as bed-load the latter move as suspended load and with nearly the same velocity as the flow. Then there are seasonal discontinuities, which cease more or less for long periods but recur nearly every year. Sporadic phenomena are caused by floods of large return periods. Catastrophic phenomena caused by landslides and earthquakes bring in a very large amount of sediment over a short period and only once in a while. Since the material in transport moves at different speeds, is stopped and is stored in location dictated by geomorphic evolution, the temporal discontinuities and spatial discontinuities are closely interlinked. On micro scale, the erosion-taking place from hill slopes caused by rainfall may not be uniform over the whole slope because of spatial changes in vegetation, roughness and erodibility of the material. Then as the material moves to the foot of the slope, coarse material may get deposited due to reduction in slope. This is also assisted due to reduction in flow caused by the high permeability of the fan. Further, material brought down by avalanches, land slides and source chutes is also discontinuous and sporadic in variation. Lastly, in the main river sediment is trapped by vegetation, on flood plain, in the riverbed, and at places where currents are weak. It may take years before the material is mobilised again and deposited elsewhere. This seems to be too complex a phenomenon to utilise deterministic model and hence Tricart thought that a statistical approach needs to be used.
Reservoir Surveys When a large capacity dam is constructed across a stream, a backwater is caused on the upstream side of the dam, which reduces the energy gradient, and velocity of flow. This effect is felt for several kilometers in the upstream direction. As a result, the ability of the stream to transport sediment load is progressively reduced from beginning of backwater curve towards the dam and the excess sediment gets deposited. If the reservoir capacity to the annual inflow ratio is about or greater than unity, most of the sediment gets deposited upstream of the dam and only a small percent of finer material may pass over the dam and through the sluices. Since such deposition over a period of years reduces the valuable capacity of the reservoir to store water, reservoirs are periodically surveyed to determine the amount of
54
River Morphology
sediment deposited in the reservoir. Hence such surveys provide valuable data on sediment load carried by the stream. There are two general methods of conducting reservoir surveys. These are the range-line survey, and contour survey. The general procedure of carrying out reservoir surveys has changed little in the past four or five decades; however significant advances have taken place in the equipment available for carrying out the surveys. Choice of the method depends on availability and character of previous mapping or survey records, the size of reservoir, degree of accuracy needed, and scope of study objectives. The range-line method is more widely used for medium and large reservoirs. In this method a number of cross sections of the reservoir are surveyed before the reservoir is first filled and then periodically resurveyed. These cross sections are called ranges. From known data for the consecutive surveys at each range line, one can determine area of sediment deposition, from which total volume of sediment deposited on the upstream side of the dam can be determined. Contour method is used for small reservoirs, which are occasionally empty, or at low stage. The contour method uses essentially the topographic mapping procedures. To apply this method first a good contour map of the reservoir is prepared before its filling. Similar contour map can be obtained periodically many times by aerial survey. The contour interval is 1.5 m to 0.5 m. From such consecutive contour maps the sediment volume deposited during certain period can be ascertained. New techniques of reservoir surveys are being used at present and these are discussed by Bruk (1985). Now a days reservoir surveys are carried out using Global Positioning System (GPS). GPS (GARMIN 2000 and Chatterjee et al. 2001) is a satellite-based navigation system made up of a network of 24 satellites placed into orbit by U.S. Department of Defence; this system is now available for civilian use. It works in any weather condition, 24 hours a day. These satellites circle the earth twice a day in a precise orbit and transmit signal information to the earth. Using signal information from three or more satellites at the same time, the receivers on the earth use triangulation techniques to calculate the exact location of the reservoir. The GPS receivers have a number of potential errors, but if Differential Global Positioning System (DGPS), is used by having two identical receivers, they provide an accurate means of surveying. The basic principle of DGPS is that errors calculated by two receivers in a local area will have common errors. Here one GPS receiver at the base station is located on the surveyed point, and the second one called the rover station is located on the motorised boat, which collects bathymetric data for reservoirs. The reference station GPS receiver knows the position of its antenna and can determine the errors in satellite signals. The error between measured and calculated is the total error. The range errors for each satellite are formatted into messages and the modular encodes these data. In an amplified form these data are radiated through antenna to roving GPS Station for real time position correction. Hence, when the two receivers are operated concurrently, by comparing and processing of signals of both the stations, the position of roving station can be obtained with adequate accuracy. The depth measuring unit consists of sonic sounding equipment, which comprises recorder, transmitting and recovering transducers and a power supply. This equipment needs frequent calibration. With such equipment depths can be measured with an error less than one percent. Once the volume of sediment deposited in a given period is known, it can be converted into corresponding weight if the average unit weight of sediment Wav over a period of T years is known. Miller (1953) has given the following equation for Wav.
55
Soil Erosion and Sediment Yield
Wav = Wo + 0.434K
LM T ln (T - 1)OP NT - 1 Q
...(3.17)
where Wav and Wo are the average unit weight and initial unit weight in kN/m3 of the deposited sediment in T years and the coefficient K depends on the sediment size and method of reservoir operation. Values of K as recommended by Lane and Koelzer are given in Table 3.11. Table 3.11 Recommended values of K in Eq. 3.17 (U.S. Govt. and IIHR 1943) S. No.
1. 2. 3. 4.
Reservoir operation
Deposited sediment Boulders, gravel sand Silt Clays
Sediment always submerged or nearly submerged Normally a moderate reservoir draw down Normally considerable reservoir Reservoir normally empty
0 0 0 0
0.90 0.42 0.16 0
2.51 1.68 0.94 0
Knowing the percentages of the individual fractions in the deposited sediment Wo can be determined as Wo = S iN= 1 Woi pi/100. In the same way weighted K value can be determined and used in Eq. (3.17). To determine initial unit weight Table 3.12 can be used: Table 3.12
Initial unit weights of sediment
Material
kN/m3
Clays Silts Sands Gravel Boulders
7.5 9.5 16 20 22
As has been already mentioned, some material flows over and through the dam; therefore sediment deposited in the reservoir during a given time will be less than sediment flowing into the reservoir during the same time. This ratio expressed in percent is commonly known as the trap efficiency Te of the reservoir, which will vary between 0 and 100 percent. If the trap efficiency of the reservoir is known, yearly quantity of sediment deposited in the reservoir can be converted into sediment yield using the relation:
FG Annual quantity of sedimentIJ H deposited in the reservoir K Sediment yield = (Trap efficiency/100)
...(3.18)
56
River Morphology
In general, the trap efficiency of a reservoir depends on the ratio of storage capacity to annual inflow, age of the reservoir, shape of the reservoir, method of reservoir operation, sediment size and its distribution and type and location of outlets. There is no general method available for the determination of trap efficiency, which takes into account all these factors. What is being used at present is the trap efficiency versus (capacity/inflow) ratio curve proposed by Brune (1953) on the basis of record of 44 normally ponded reservoirs in U.S.A., (see Fig. 3.9). On the same figure are also plotted some data from reservoirs in China, India and South Africa. At present this curve is used in most of the countries for normally ponded reservoirs.
Trap efficiency, To (%)
100
80 60
Envelopes
40
Reservoirs in China Reservoirs in USA Reservoirs in S. Africa Reservoirs in India
20 0 0.001
0.01
0.1
1.0
10.0
Capacity/Inflow Fig. 3.9 Trap efficiency of normally ponded reservoirs
Sediment Yield Computations Theoretically one can use the equations for bed-load and suspended load computations given in Chapter V and determine the bed material load carried by the stream at a given discharge, which will be the sum of bed-load and suspended load. To this should be added an estimated quantity of wash load i.e., material that is washed into the stream from the drainage basin and which is usually finer than the material found in the bed and banks of the stream. If such calculations are made for various discharges, one can prepare the sediment discharge vs water discharge curve from which average annual sediment discharge can be computed. However, it may be pointed out that what is obtained from such calculations is really the sediment transport capacity; and it may be quite different from measured sediment yield especially in the upper reaches of the river. Hence this method is inferior to the other two methods discussed above.
3.8
SEDIMENT DELIVERY RATIO
As mentioned earlier, sediment delivery ratio is defined as the ratio between amount of sediment load passing a given section during a certain period and the total amount of erosion from the upstream catchment during the same period. It can be either expressed as a mere ratio or as a percentage. For plots of area less than 1.0 km2, the sediment delivery ratio SDR is almost 100 percent, and it decreases as the
57
Soil Erosion and Sediment Yield
catchment area increases. SDR for a particular basin is influenced by a wide range of geomorphological and environmental factors including the nature, extent and location of sediment sources, relief and slope characteristics, drainage pattern and channel conditions, vegetation cover, land use, and soil structure. Basin area is probably the most important variable with which SDR is related. As the catchment area increases, the catchment slope as well as the channel gradient decreases and hence there is an increasing opportunity for sediment deposition on flood plain and in channels. Therefore, SDR decreases as A increases. Other variables used to study variation of SDR are basin relief, annual runoff and gully density. Figure 3.10 shows the band of scatter of variation of SDR with A for some regions in U.S.A. and former U.S.S.R. This figure also shows the curve proposed by Soil Conservation Service of U.S.A. It may be mentioned that for some catchments in China, SDR is found to be 100 percent even up to catchment area of 1000 km2. This may probably be due to very fine material such as loess that is eroded and transported without any deposition.
SDR
100
10
1.0
Curve proposed by SCS, U.S.A.
Central and eastern U.S.A. Corn waste lands W. Iawa, U.S.A. Blackland Prairle, Texsas, U.S.A. Mule creek, Iowa, U.S.A. South-Eastern Piedmant, U.S.A. Missouri basin loess hills, U.S.A. Pasture waste lands, Iowa, U.S.A. USSR 0.01
0.10
1.0 A km
Enveloping lines
2
10
100
1000
Fig. 3.10 Relation between SDR and A
It needs to be mentioned that there are some serious difficulties in the estimation of SDR, (see Walling (1988)). Firstly, correct estimation of gross erosion must be made. This is done by estimating sheet erosion based on soil loss equation and correcting it to take into account the channel and gully erosion. This procedure has a certain amount of uncertainty. Another problem in the determination of SDR is the temporal discontinuity that may be involved in the sediment delivery as pointed out by Tricart. Sediment eroded at one location may be temporarily stored and subsequently remobilised many times before reaching the outlet of the basin. The third difficulty in relating sediment yield downstream to the soil erosion upstream is from the fact that the sediment transported by a river represents the material derived from a number of sources other than upland erosion, e.g., channel and gully erosion and mass movement etc. Their estimation is very difficult. A study by FAO (1979) has compared the sediment yield with estimate of contemporary soil erosion rates from a number of African river basins having catchment areas between 150 km2 and 157 400 km2. This comparison indicates that the soil erosion rates are about one order of magnitude greater than the reported sediment yields. One of the equations, which take into account three variables in estimating SDR, is that by Roehl (1962) which is based on the data from south eastern U.S.A. It is
58
River Morphology
SDR =
a
f
231.7 Steepness A 0 . 23 B 2 . 79
0 . 51
...(3.19)
where steepness is defined as the ratio of the maximum difference in elevation in m and basin length along the main waterway in m, A is the catchment area in km2, and B is the bifurcation ratio. Bifurcation ratio is the weighted mean ratio of a number of streams of given order to the number of streams in the next higher order (see Chapter II). For the average value of B = 4.37 for Roehl’s data one gets SDR =
a
f
3.792 Steepness A 0 . 23
0 .51
...(3.20)
Walling (1988) lists a few more equations developed for different states in U.S.A. and China. A more rational and probably a more rigorous approach to defining and investigating the sediment delivery characteristics of the drainage basin is provided by the sediment budget concept, originally advocated by Dietrich and Dunne (1978) and developed by Lehre (1982) and others. Here various sediment sources within the basin are defined and the sediment mobilised from these sources is routed to and through the channel system by considering various sinks. A typical representation of such a budget for the Coon Creek in U.S.A. for the period 1938–1975 is shown in Fig. 3.11. Walling (1988) has represented similar data for the Lone Tree Creek (California), and the Oka river in U.S.S.R. It was found that in all the cases the proportion of the eroded sediment delivered to the basin outlet is very small. However, it may be mentioned that presently the availability of techniques for quantifying the various sources and sinks involved in budgeting the sediment is very limited, and as such mean SDR vs A curve is often used to obtain erosion rate from observed sediment yield. Sources
Sinks
76.7% Upland sheet and till erosion
55.7% Colluvial deposits
11.9%
Upland gully erosion 11.4% Channel erosion
Area = 360 km
Fig. 3.11
77.0% Upland valleys 4.9% Upper main valley 25.6% Lower main valley
2
6.7%
Sediment budget for the Coon Creek, Wisconsin (USA) (Area 360 km 2)
Since there is always a gain or loss of sediment storage in the system, the input from slopes and catchment rarely equals the sediment yield. The sediment storages in the catchment include slope storage (i.e., colluvium) and stream valley storage (i.e., alluvium). Colluvium when transported by gravity or by water may partly remain colluvium, or become alluvium, or become sediment yield i.e.
59
Soil Erosion and Sediment Yield
Sediment Sediment Sediment loss gain loss
Sediment gain
Sediment Sediment Sediment Sediment loss gain loss gain
Sediment Sediment loss gain
efflux. Similarly alluvium can be eroded from the channel or flood plain and redeposited as alluvium or become sediment yield. Limiting the discussion about valley storage, the most important process in valley storage gain is vertical accretion from overbank stream flow; other important storage zones are alluvial fans of small tributaries and colluvial deposits from adjacent slopes. In sediment budget a steady state would imply input equals output, and upland erosion equals sediment yield. Since steady state is a very rare, one would like to study gain or loss of sediment from the valley as a function of time, and relate the nature of variation to the external factors, which influence the gain, or loss of storage; Trimble (1995) has done this and identified five conceptual models of valley storage fluxes, which are shown in Fig. 3.12 and briefly described below. Model-1 (Quasi-steady)
+
Vertical accretion Steady-state Lateral erosion
100 yrs
Model-1 (Vertical accretion with lateral erosion)
Vertical accretion
+
Vertical erosion 100 yrs
Lateral erosion
Model-3 (Valley trenching)
+ 100 yrs
Model-4 (Urban stream)
+ Paving of channels 20 yrs
Moderate control Uncontrolled
+
Mass movements
Flushing
Colluvium accretion
Model-5 (High energy instability, mountains and arid streams)
20-100 yrs
Fig. 3.12 Conceptual models of valley storage fluxes (Trimble 1995)
Model-1 (Quasi steady state) is applicable to humid regions where adequate vegetation can develop and stabilise the landscape. There will be very little upland erosion and hence very little sediment load. Lateral erosion of one bank would cause lateral deposition on the opposite bank. The perturbations in the vertical accretion of floodplain would be a few centimetres per millennium at most. This situation existed in eastern U.S.A. before European settlement.
60
River Morphology
Model-2 (Perturbation of humid area quasi steady state) is applicable in humid area where sediment load in excess of transport capacity is generated by strong climatic or natural forces (e.g., mining or large construction activity). This causes vertical accretion of floodplain and the channel. When the activity in the upland area stops, this deposited sediment is gradually eroded and transported downstream. This removal of deposited sediment shows exponential decrease. If the sediment supply from the upland is low, lateral erosion of channel may take place later. Model–3 (Valley trenching and arroyo cutting) is applicable when the climate or human induced perturbations cause an incremental increase in discharge greater than incremental increase in sediment discharge. This can result in trenching or gullying. The example of this model is found in semi arid south western U.S.A. In such areas the fragile grasslands were overgrazed, the vegetation was thinned drastically and the soil compacted resulting in greater stream flows and arroyo cutting. In Model–4 (Urban streams), a brief rapid increase in erosion occurs while urbanisation in underway, but when it is stabilised due to increasing imperviousness of the area the runoff increases and erosion decreases. This initiates arroyo cutting. In order to save valuable land, if arroyos are stabilised by paving the Model-4 results, otherwise Model-3 results. Model-5 (High energy instability, mounting and arid streams) is applicable to streams with a very narrow floodplain and very steep valley sides. The sediment budget in this case is much more episodic than cyclic in nature. Net storage gain can come from vertical accretion coming from fans of small tributaries and mass movement from valley sides. Sediment loss comes from large events, which flush sediment downstream. This model shows a period of accretion followed by flushing events, and the process is repeated at uneven time intervals. Identifying the sediment budget model enhances our understanding of the fluvial processes working in the system and throws light on the magnitude and time scales of sediment storage fluxes under the given environmental conditions and natural and man made perturbations.
3.9
PROCESS BASED MODELLING OF EROSION
Even though USLE summarises a vast body of regionally derived data and expresses it in the equation form, the researchers are aware of its empirical nature and its limitation that it is not universally applicable. Further, it is also recognised that USLE does not explicitly represent the processes involved in soil erosion. As a result USLE gives only an average annual soil loss. Therefore, several attempts have been made to develop methodology for prediction of erosion by modelling the basic processes involved. These are discussed by Rose (1988).
Overland Flow Consider flow on a planar land surface on a slope. Let L be the length of slope. Then the sediment flux flowing out of a unit width is qs = q C
...(3.21) 3
where qs is in mass of sediment/time, width, q is volume rate of water in m /s m, and C is the sediment concentration in oven dry mass of sediment per volume of suspension. One must now obtain expression for overland flow q. One can write
61
Soil Erosion and Sediment Yield
R =P–I
...(3.22)
where R is the excess rainfall, P is the precipitation and I is the rate of infiltration all being function of time. If Q represents runoff per unit area Q = q/(L)
...(3.23)
One can then see that R =Q ...(3.24) However, if L is large and R varies with time, it will be seen that changes in Q will lag behind those in R. Thus in general R ¹ Q. It can be shown that R » Q + Kp
¶Q ¶t
...(3.25)
where Kp depends on length, slope and roughness of the plane, Q, and on whether the overland flow is laminar or turbulent. The flux q(x) at any distance is given by q(x) = Qx
...(3.26)
Erosion and Deposition Processes The following three processes affect the sediment concentration: 1. Rainfall detachment in which raindrops splash sediment from the soil surface into the water of overland flow. 2. Sediment deposition, which is the result of sediment settling out under the action of gravity; and 3. Entrainment of sediment from the soil surface in which sediment is picked up from rills, interrills and in sheet flow. Rate of raindrop detachment e is expressed as e = a Ce P
...(3.27)
2
where e is in kg/m s, a is the measure of detachability of soil by rainfall rate P and Ce is the fraction of soil surface exposed to the rain drops. The rate of sediment deposition di for a given size class i of fall velocity wi is expressed as di = wi Ci
...(3.28)
where Ci is the sediment concentration of size class i. The rate of sediment entrainment can be related to excess stream power over its critical value. Let the rate of sediment entrainment for a given size class be gi. Then conservation of mass principle applied to a given size class i yields ¶ ¶ (qCi) + (DCi) = ei + gi – di ¶x ¶t
...(3.29)
where D is the depth of overland flow at any time. Making certain approximations, Eq. (3.29) can be reduced to ordinary first order differential equation, which can be solved to yield C(L, t) =
FG ac p IJ S H QI K e
I i = 1 (g i)
+ r f gSKC g (1 – x*/L)
...(3.30)
62
River Morphology
FG H
for L > xi . Here I is the number of sediment class ranges, gi = 1 +
IJ K
wi rf is mass density of water, S is Q
the land slope, K = (1 + 0.2677h), where h is the efficiency of net sediment entrainment and transport, Cr is the fraction of soil surface unprotected from entrainment by overland flow, and x* is the distance down slope from the top of the plane beyond which sediment entrainment commences. The accumulated mass of sediment Ms from a plane of width W is thus given by Ms = WL
z
t
R C(L, t)QDt
...(3.31)
0
where tR is the duration of runoff. Equation (3.30) can be written as C (L, t) = A + B
...(3.32)
where A is the net contribution to sediment concentration of rainfall detachment over deposition, and B is the net contribution of entrainment over deposition. Assuming A to be negligible and taking time average values of x*, Q and h, as x* , Q and h, C (L) can be expressed as
F H
C(L) = 2700ShCr 1 -
x* L
I K
...(3.33)
Dynamic Simulation Models A more elaborate model is given by Negev (1969), which is commonly known as Stanford Sediment Model. In this model, the rainfall impinging on the land surface is divided into two parts, that falling on the impervious surfaces and that falling on the pervious surfaces. The sediment supply from impervious surface is determined by a power function relationship taking hourly rainfall as the independent variable. Rain falling on the soil is assumed to loosen the material by raindrop splash. This loosened material, called soil splash is then considered as potential sediment for the stream. If overland flow occurs, as computed by Stanford Watershed Model, then all the soil splash material in previous storages is transported together with the current soil splash material. Overland flow is also used to compute the rate of rill and gully erosion using power function relationship. Rill and gully erosion is then divided into inter load and bed material storage. The input to this model consists of hourly and daily recorded rainfall, daily recorded flow and sediment load, hourly overland flow, a translation histogram for routing the sediment through the stream system, information on the sediment rating curve for use in adjusting the material assigned to inter load and bed material load from rill and gully process, and set of parameters and exponents for use in the various power functions by which the sediment erosion processes are estimated. These are adjusted during the runs to calibrate the model. Use of this model to the Napa river, St. Helena, California (U.S.A.) and the river Clyde in Scotland has given good results. Other dynamic models developed include the one developed by Simons et al., (1975). The various processes modelled in this program include, interception, infiltration, overland flow from rainfall excess, sediment detachment due to raindrop impact, sheet erosion by overland flow, channel erosion and the routing of water and sediment through the channel system. The sediment detachment is calculated during a specific time increment as a function of rainfall intensity and provision is made for
63
Soil Erosion and Sediment Yield Storm characteristics
Basin characteristics
Sizewise soil detachment by raindrop impact with provision for amounting
Water routing Overland flow data Overland flow routing Overland flow bed material routing Channel flow data
Overland flow bed material routing
Bed material load hydrograph
Antecedent characteristics
Loose soil storage
Soil detachment by overland flow considering sizewise transport capacity and supply of loose soil
Loose soil storage
Overland flow wash load routing
Soil detachment by channel erosion
Loose soil erosion
Total sediment yield
Channel flow wash load routing
Wash load hydrograph
Fig. 3.13 Flow chart for water and sediment routing model developed at Colorado State University (Simons et al. 1975)
calculating the detachment of different size fractions and for the development of surface armouring. Sediment supply for the transport depends on the initial depth of loose soil remaining from the previous storms, the amount of soil detachment by rain drop impact and the amount of soil detached by surface runoff. Sediment transported by overland flow is calculated using Meyer-Peter and Müller’s formula for bed-load transport. Similar procedure is used to route the wash load and the bed material load through the channel system using continuity equation to determine occurrence of aggradation or degradation. Figure 3.13 shows flow chart for this model. It may be mentioned that in recent times several such models have been developed. Morgan et al. (1990) describe the European Soil Erosion Model (EUROSEM) developed as a collaborative project by seven European countries. Two more models can be briefly discussed. Kothyari et al. (1997) have developed a method for estimation of temporal variation of sediment yield for a single storm in small catchments. The method is based on numerical solution of kinematic wave equation for simulation of overland flow, continuity equation for sediment and expressions for sediment detachment and transport. The model is calibrated and verified using twelve experimental catchments ranging in size from 0.002 km2 to 92.5 km2. For single storm events sediment yield varied from 0.003 tons to 800 tons. Julien and Rojas (2002) have discussed a physically based model simulating hydrologic response of a watershed to distributed rainfall field, considering time-dependent processes such as precipitation, interception, infiltration, surface runoff and channel routing, and upland erosion, transport and sedimentation, the model predicts, flood and sediment load variations with time. The model was applied to 21 km2 Goodwin Creek catchment in U.S.A.
64
River Morphology
Stochastic Models Lack of detailed long duration record of erosion rates has hampered the application of various stochastic and time series modelling procedures to the erosion process. Yet some attempts have been made in the application of Autoregressive Moving Average (ARMA) Models to the records of Suspended Sediment concentration. Sharma et al. (1979) describe the use of a simple system model of this type to model the monthly and daily sediment yield of several catchments in Ontario, Canada. The model used to describe daily erosion rates explained 95 percent of the variation in the erosion process of the Thames river at Ingersol, while the monthly model accounted for more than 81 percent of short-term values of sediment concentration recorded during individual storm events.
3.10
EROSION RATES FROM INDIAN CATCHMENTS
In India the approaches used for prediction of erosion rates have been essentially empirical involving regression method. This is primarily so because of the lack of availability of extensive data needed for use of physically based and simulation models. Earlier Khosla (1953) analysed the then available data from Indian reservoirs and reservoirs from abroad and found that the annual sediment yield in Mm3 is proportional to A0.72 where A is the catchment area in km2. However, Garde and Kothyari (1987) found large variations from this relationship when it was tested with recently collected Indian data. Dhruva Narayan et al. (1983) used the data from seventeen catchments in India and obtained the following relations for annual sediment yield T1 in metric tons. T1 = 5.5 + 1.1 Q
...(3.34)
where Q is the annual runoff in M ham. This equation was further modified to T1 = 5.3 + 12.7 QW1
...(3.35)
where W1 = T1/A, A being in M ha. Average value of W1 was found to be 1.25 M tons/M ha. Another relationship proposed by them involved use of EI30. T1 = (0.342 ´ 10 –6)A0.84 (EI30)1.65
...(3.36)
where EI30 is the product of average annual value of the sum of maximum 30 minute rainfall intensity in cm/hr and kinetic energy value E given by E = 210 + 89 log I30
...(3.37)
E being in tons/ha m. However, these equations need to be verified with additional data before these can be used with confidence. By far the most detailed analysis of Indian data has been carried out by Garde and Kothyari (1987, 1990). They analysed the average annual sediment yield data from 50 catchments in India having areas varying from 43 km2 to 83 880 km2. These data were obtained from the surveys of small, medium and large reservoirs with sedimentation period of at least ten years. Analysis of data indicated that the average annual erosion rate Sa in cm is a function of average annual rainfall P in cm, the average 1 n S AiSi, the drainage density D in km –1, the ratio (Pmax /P) where Pmax A1 is the average monthly maximum rainfall in cm, and the erosion factor Fe which gives an integrated effect of vegetation on erosion. The erosion factor Fe was defined as
catchment slope defined as S =
65
Soil Erosion and Sediment Yield
Fe =
1 [0.8 AA + 0.6 AG + 0.3 AF + 0.1 AW] A
...(3.38)
where AA is the arable area, AG scrub and grass covered area, AF is protected forest area, and AW is the waste land area all in km2. A map showing lines of constant Fe values was prepared from available data and this is shown as Fig. 3.14. The range of variables used by Garde and Kothyari are given below: – 108.3 cm P 63.77 cm – 381.11 cm Pmax 9.0 cm – 1.00 S 0.001 – 0.200 Fe 0.28 2 2 –1 D 0.002 km – 0.31 km–1 A 43 km – 82 880 km The regression analysis of the data gave the following equation for Sa Sa = 0.02 P0.60 Fe1.70 S 0.25 Dd0.10 (Pmax/P)0.19
...(3.39)
This relationship was then used on ungauged catchments for which all other data except Sa values were available. Sa was then computed from which sediment yield was expressed in tons/km2/year. Thus using data from 154 catchments an iso-erosion rate map was prepared which is shown in Fig. 3.15. It can be seen that the erosion rates in India vary from about 350 tons/km2/year to 2500 tons/km2/year. High erosion rates in North eastern region, parts of U.P., Bihar and Punjab, and in certain areas in Andhra Pradesh are partly due to high rainfall in these regions and partly due to geologic conditions and land usages. Considering that out of the variables affecting the erosion rate, only the annual rainfall changes from year to year, the following equation was proposed by Garde and Kothyari (1987) for the estimation of annual erosion rates. Pa = 0.02 Pam Fe1.70 S – 0.25 Dd0.10(Pmax/P)0.19
...(3.40)
where Pa is the annual precipitation in cm. Here m is the exponent, which was found to be related to coefficient of variation of annual precipitation. It may be seen from comparing Eqs. (3.39) and (3.40) that P0.6 =
1 n
å
n i
Paim
where n is the number of years. Analysis of rainfall data from 100 rainfall stations indicated that as coefficient of variation changed from 0.1 to 0.70, m, value of the exponent increased from 0.600 to 0.607. This variation is shown in the following table: Cv 0.10 0.20 0.30 0.40 0.50 0.70 m in Eq. (3.40) 0.600 0.601 0.602 0.603 0.605 0.607 Thus for annual sediment yield computation Eq. 3.40 with table for m can be utilised. For future year wise prediction of sediment yield, one must generate annual rainfall series for known P and Cv and then compute the sediment yield. The annual series in India are found to follow normal distribution. It may be mentioned that with the passage of time land use pattern as well as extent of forest and other vegetation is bound to change and hence Fig. 3.11 need to be modified at regular time intervals and so also Fig. 3.12. However Eqs. (3.39) and (3.40) will not change.
66
River Morphology
0.55
0.55
0.55 0.6 0.6
0.55
0.6
0.5 0.55
Nep
al
0.5
n Bhuta
0.6 0.6
0.6
0.4
0.4
0.55 Bangladesh
0.6 0.4
0.5
0.5
0.5
0.55
0.55
0.45
0.54
0.54 0.45
Notations Igneous intrusive rocks Sedimentary unconsolidated (Recent alluviums) Metamorphic (Schists)
0.55
Sedimentary consolidated Unclassified crystallines Khondalite 0.45
Other igneous and metamorphic rocks
0.5
Iso-erosion factor lines Geologic boundaries Sri Lanka
Fig. 3.14 Lines of constant Fe superimposed on the geological map of India (Garde and Kothyari 1987)
Soil Erosion and Sediment Yield
Fig. 3.15 Iso-erosion rate lines in tons/km2 yr (Garde and Kothyari 1987)
67
68
River Morphology
References Blakely, B.D., Coyle, J.J. and Steele, J.G. (1955) Erosion on Cultivated Land. Soil- The 1957 USDA Year Book of Agriculture. Brown, L.R. (1984) Conserving Soils. In State of the World 1984, (Ed. Brown L.R.) Norton, New York. Bruk, S. (1985) Methods of Computing Sedimentation in Lakes and Reservoirs. A Contribution to the IHP-II Project, A. 2.6.1. Panel, UNESCO, Paris, pp. 224. Brune, G.M. (1953) Trap Efficiency of Reservoirs. Trans. AGU, Vol. 34, No. 3, July, pp. 407-418. Chatterjee, P.K., Bathija, T.S. and Sangeet, S. (2001) Methods of Reservoir Sedimentation surveys. Proc. Of C.B.I.P. Seminar on Reservoir Sedimentation, Ooty, Tamil Nadu, India, pp. 33-41. Dekov, A.P. and Mozzherin, V.I. (1984) Eroziya I Stok Nanosov na Zemle. Izadatolstvo Karzanskogo Universiteta. Dendy, F.E. (1968) Sedimentation in Nation’s Reservoirs. Jour. Soil and Water Conservation, Vol. 23, No. 4. Dietrich, W.B. and Dunne, T. (1978) Sediment Budget for a Small Catchment in Mountain Terrain. Zeitschrift fur Geomorphologie. Supplementband, 29, pp. 191-206. Dhruva Narayana and Ram Babu (1983) Estimates of soil Erosion from India. JIDD, Proc. ASCE, Vol. 109, No. 4. Ellison, W.D. (1945) Some Effects of Rainfall and Surface on Erosion and Infiltration. Trans. AGU, Vol. 26, No. 3. El-Swaify, S.A., Dangler, E.W. and Armstrong, C.L., (1982) Soil Erosion by Water in the Tropics. University of Hawaii Research Extension Series No. 024. Elwell, H.A. (1980) Design of Safe Rotational Systems. Department of Conservation and Extension, Harare (Zimbabwe). Elwell, H.A. and Stocking M.A. (1974) Rainfall Parameter and a Cover Model to Predict Runoff and Soil Loss from Grazing Trails in the Rhodesian Sandveld. Proc. of the Grassland Society of South Africa, Vol. 9. FAO, U.N. (1977) Assessing Soil Degradation. Soils Bulletin 34, Rome, Italy. FAO, U.N. (1979) A Provisional Methodology of Soil Degradation Assessment, Rome, Italy. Foster, G.R. (1988) Modelling Soil Erosion and Sediment Yield. In Soil Erosion Research Methods (Ed. Lal R.) Soil Water Conservation Society, Ankeny, Iowa (U.S.A.), pp. 97-118. Fournier, F. (1949) Les Facteurs Climatiques de l ‘Erosion du Sol. Assoc. Geo’graphes Francais, Bull. Vol. 203. Fournier, F. (1960) Climat et Erosion: la Relation entre l ‘Erosion du Sol par l ‘Eau et les Precipitations Atmospheriques. Presses Universitaires de France, Paris. Garde, R.J. and Dattatri, J. (1961) Investigation of the Total Sediment discharge of Alluvial Streams. Roorkee University of Research Journal (India), Vol. No. pp. 65-78. Garde, R.J. and Kothyari U.C. (1987) Sediment Yield Estimation. Journal of Irrigation and Power (India), CBIP, Vol. 44, No. 3. Garde, R.J. and Kothyari U.C. (1990) Erosion Prediction Models for Large Catchments. International Symposium on Water Erosion, Sedimentation and Resources Conservation. CSWCRTI, Dehradun, Oct. pp 89-102 GARMIN (2000) G.P.S. Guide for Beginners. Garmin Intl. Inc. Olathe, Kansas (U.S.A.) Heede, B.H. (1975) Stages of Development of Gullies in the West. Proc. of the Sediment Yield Workshop, USDA, Oxford (Mississippi), ARS-S-40. Holeman, J.N. (1968) The Sediment Yield of Major Rivers of the World. W.R. Research, Vol. 4, pp. 737-747. Hudson, N.W. (1965) The Influence of Rainfall on Mechanics of Soil Erosion with Particular Reference to Northern Rhodesia. M.S. Thesis, University of Cape Town, South Africa. Janda, T. Dunne and Swanson, D.N. General Tech. Report PNW 141, Forest Service USDA Portland, Oregon, U.S.A.
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Julien, P. and Rojas, R. (2002) Computer Modeling of Upland Erosion. Proc. Of 12 APD Intl. Congress, Singapore, Vol. 1, pp. 475-483. Kinnell, P.I.A. (1973) The Problem of Assessing the Erosive Power of Rainfall from Meteorological Observations. Proc. Soil Science Society of America, Vol. 37, pp. 617-621. Khosla, A.N. (1953) Silting of Reservoirs. CBIP Publication No. 51, New Delhi (India). Kothyari, U.C., Tiwari, A.K. and Singh, R. (1997) Estimation of Temporal Variation of Sediment Yield from Small Catchments through the Kinematic Method. Jour. Of Hydrology, Vol. 203, pp. 39-57. Kuenen, P.H. (1950) Marine Geology. John Wiley and Sons, Inc., New York. Lane, E.W. and Borland, W.M. (1951) Estimating Bed Load. Trans. AGU, Vol. 32, No. 1, February. Langbein, W.B. and Schumm, S.A. (1958) Yield of Sediment in Relation to Mean Annual Precipitation. Trans. AGU, Vol. 39. Laws, J.O. and Parsons, D.A. (1943) The Relation of Raindrop Size to Intensity. Trans. AGU., Vol. 24. Lehre, A.K. (1982) Sediment Budget in a Small Coast Range Drainage Basin in North Central California. In Sediment Budget and Routing in Forest Drainage Basins (Ed Swanson, R.J.) Leopold, L.B. and Wolman, M.G. and Miller, J.P. (1964) Fluvial Processes in Geomorphology. W.H. Freeman and Co., San Francisco, U.S.A. Leopold, L.B. and Maddock, T. (1953) The Hydraulic Geometry of Steam Channel and Some Physiographic Implications. USGS Professional Paper 252. Mackenzie, F.T. and Garrel, R.M. (1966) Chemical Mass Balance Between Rivers and Oceans. Am. Jour. Sci., Vol. 264, pp. 507-525. McCool, D.K. and Rendard, K.G. (1990) The Revised Universal Soil Loss Equation. Proc. of Int. Symposium on Water Erosion Sedimentation and Resource conservation, Dehradun (India), Oct., pp. 60-70. Meyer, L.D. and Mannering, J.V. (1967) Tillage and Land Modification for Water Erosion Control. ASAE-ASASCSA Tillage Conference Proc. pp. 58-62. Miller, C.R. (1953) Determination of Unit Weight of Sediment for Use in Sediment Volume Computations. USBR, Denver, U.S.A.. Milliman, J.D. and Meade, R.H. (1983) Worldwide Delivery of River Sediments to Oceans. Jour. Geology Vol. 91, pp. 1-21. Morgan, R.P.C. (1979) Soil Erosion. Longman Group Ltd., London. Morgan, R.P.C., Quinton, J.N. and Rikson, R.J. (1990) Structure of Soil Erosion Prediction Model for the European Community. International Symposium on Water Erosion, Sedimentation and Resource Conservation - CSWCRTI, Dehradun, Oct., pp. 49-59. Mutchler, C.K. (1971) Splash Production by Water Drop Impact. Water Resources Research, Vol. 7. Mutchler, C.K. and Young, R.A. (1975) Soil Detachment by Raindrops. Proc. of the Sediment Yield Workshop, USDA, Oxford (Mississippi), U.S.A., ARS-S-40, pp. 113-117. Negev, M. (1969) A Sediment Model on Digital Computer. Stanford University, U.S.A., Civil Engg. Deptt., Tech. Rep. No. 76. Pechinov, D. (1959) Vodna Eroziya I To’rd Ottok. Priroda, Vol. 8, pp. 49-52. Piest R.F., Bradford, J.M. and Spomer, R.G. (1975) Mechanism of Erosion and Sediment Movement from Gullies. Proc. of the Sediment Yield Workshop. USDA, Oxford, Mississippi, ARS-S-40, pp. 162-176. Robinson, A.R. (1977) Relationship Between Soil Erosion and Sediment Delivery. Symposium on Erosion and Solid Matter Transport in Inland Waters, IASH, No. 122, July, pp. 159-167. Roehl, J.E. (1963) Sediment Source Areas, Delivery Areas and Influencing Morphological Factors. IASH Publication No. 59.
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Rose, C.W. (1960) Soil Detachment Caused by Rainfall. Soil Science, Vol. 89, pp. 28-35. Rose, C.W. (1988) Research Progress on Soil Erosion Processes and a Basis for Soil Conservation Practices. In Soil Erosion Research Methods (Ed. R. Lal. ) Soil and Water Conservation Society, Ankeny, Iowa, U.S.A., pp. 119-140. Schumm, S.A. (1963) Disparity Between Present Rates of Denudation and Orogeny. U.S. Geological Survey, Professional Pape 454-H, pp. 13 Schumm, S.A. (1977) The Fluvial System A Wiley Interscience Publication, John Wiley and Sons Inc. Sharma, T.C., Hines, W.G.S. and Dickinson, W.T. (1979) Input-Output Model for Runoff Sediment Yield Processes. J. of Hydrology, Vol. 40. Simons, D.B., Li, R.M. and Stevens, M.A. (1975) Development of Models for Predicting Water and Sediment Routing and Sediment Yield from Storms on Small Watersheds. CSU Report No. CER-74-75, DBS-RMLMAS-24. TCPSM (1969) Sediment Measurement Techniques: A Fluvial Sediment Task Force Committee on the Preparation of Sediment Manual Report, JHD, Proc. ASCE. Vol. 95, No. HY-5, September. Tiwari, A.K. (1993) Temporal variation of Sediment Yield from Small Catchments. Ph.D Thesis, University of Roorkee. Tricart, J. (1962) Les Discontinuities dan les Phenomenes d’ Erosion. Int. Assoc. Sci. Hydro., Vol. 59. Trimble, S.W. (1995) Catchment Sediment Budgets and Change. In chaning River channels (Eds. Gruznell, A and Petts, G.) John Wiley and Sons, Chicester, pp. 210-215. U.N.E.P. (1980) Annual Review. United Nations Environmental Program, Nairobi, Kenya. U.S. Govt. and IIHR (1943) A Study of Measurement and Analysis of Sediment Loads in Streams. Density of Sediments Deposited in Reservoirs, Rep. No. 9. U.S.S.R. National Committee for I.H.D. (1974) Mirovoi Vodnyi Balans I Vodnye Resursy Zemli. Gidrometerozat, Leningrad. Van Rijn, L.C. (1982) Sediment Transport, Part II: Suspended Load Transport. JHE, Proc. ASCE, Vol. 110, No. 11, November, pp. 1613-1641. Walling, D.E. (1988) Measuring Sediment Yield from River Basin In Soil Erosion Research Methods (Ed) R.Lal. Soil and Water Conservation Society, Ankeny, Iowa, U.S.A., pp. 39-74. Walling, D.E. and Webb, B.W. (1983) Patterns of Sediment Yield. In Background to Palaeohydrology (Ed Gregory K.J.) John Wiley and Sons, Chichester, U.K., pp. 69-100. Williams, M.A. (1969) Prediction of Rainfall Splash Erosion in the Seasonaly Wet Tropics. Nature, Vol. 222, pp. 763-765. Wischmeier, W.H. and Smith, D.D. (1958) Rainfall Energy and its Relationship to Soil Loss. Trans. AGU, Vol. 39, pp. 285-291. Wischmeier, W.H. and Smith, D.D. (1962) Soil Loss Estimation as a Tool in Water Management Planning. Int. Assoc. For Sci. Hydro. Pub. No.59, pp. 148-159. Wischmeier, W.H. and Smith, D.D. (1978) Predicting Rainfall Erosion Losses: A Guide to Conservation Planning. USDA Agricultural Handbook No. 537, pp. 58. Wischmeier, W.H., Jhonson, C.B. and Cross, B.V. (1971) A Soil Erodibility Monograph for Farmland and Construction Sites. Jour. Soil and Water Conservation, Vol. 26, pp. 189-192. Young, A. (1969) Present Rate of Land Erosion. Nature, Vol. 224, pp. 851-852.
C H A P T E R
4
Fluvial Morphology 4.1
GEOMORPHOLOGY AND FLUVIAL MORPHOLOGY
The name geomorphology originates from the Greek terms geo meaning earth, morphe meaning form and logos meaning discourse. Hence, geomorphology is the science of the origin and evolution of topographic features caused by physical and chemical processes operating at or near the earth’s surface. The landforms may result or may be modified by denudational processes, depositional processes or a combination of the two. Denudational or degradational processes are sometimes called exogenous processes while the depositional processes are known as endogenous processes. Together they are known as geomorphic processes. Among the agents and processes which shape the configuration of earth’s surface, the important ones are: (i) Running water, (ii) Glaciers, (iii) Ground water, (iv) Waves and currents, (v) Wind, (vi) Weathering, (vii) Volcanism and (viii) Diastrophism. Running water is that part of rainfall or snows melt which flows on earth’s surface after infiltration requirement is satisfied; this is known as surface runoff. It collects in streams, which continually erode the land and deposit the material elsewhere. Landforms produced by glaciers are markedly different because glaciers move slowly and are capable of carrying large quantities of coarse material with them. Groundwater, while in contact with rocks, promotes solution and other types of chemical weathering. This leads to unique landforms, especially in the areas of rapidly soluble rocks, such as limestone. Waves beating against the shorelines of seas and large lakes modify shorelines by their erosive action and subsequent deposition of the eroded material elsewhere. In arid and semi-arid regions and in regions having abundant supply of loose sand, wind is an effective agent of erosion and deposition. Weathering action loosens the rocks and breaks them into smaller pieces, which can be transported by different agencies. Mechanical weathering produces angular hill-slopes whereas chemical weathering promotes smooth rounded slopes. Volcanic eruptions produce distinctive landforms such as volcanic cones and lava flows. A sudden change in land surface or part of it due to tensile or compressive forces is known as diastrophism. It can be seen that volcanism and diastrophism are endogenous processes. Since the word fluvial means produced by rivers, the term fluvial morphology can be defined as a science dealing with forms as those produced by river action. Fluvial morphology is of great interest to
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hydraulic engineers, geologists, geo-morphologists, geographers and environmental engineers, since many of the complex problems they have to deal with are due to the form of the streams created by the erosion, transportation and deposition of sediment carried by them. Even though several scientists have contributed to the development of the science of geomorphology, W.M. Davis in the early 20th century was primarily responsible for synthesising many of the earlier developments and presenting them in the form of a unified system for the study of landforms. Certain basic concepts developed by geo-morphologists are of significance to hydraulic engineers and these are discussed here in brief.
4.2
GEOMORPHIC CYCLE (OR CYCLE OF EROSION)
The basic idea underlying the concept of geomorphic cycle or the cycle of erosion is that the topography of a stable region evolves through a continuous sequence of landforms having distinctive characteristics at successive stages of development. The process starts with the initial uplift of landmass through diastrophism. This initial uplift is tacitly assumed to take place without appreciable erosion. Since in most regions the current uplift rates are much greater than the denudation rates, the above assumption is a reasonable one. Later the cycle of erosion proceeds under prolonged tectonic stability producing various types of topography, which are characteristic of the various lengths of time for which the water has acted on it; the material is continually eroded from the land surface and deposited in the sea. The elevation of the land surface is thus gradually lowered and land surface flattened until after a very long time the whole surface is reduced to a gently sloping plain called peneplain. This is the end of the cycle and an upheaval will start a new cycle (Davis 1909, Lane 1955). Davis introduced the word peneplain to describe landscapes that have undergone long continued weathering and erosion in humid climate. In the geographical context the word plain connotes a surface of very low relief. Realising that the ultimate base level is the limit of sub-aerial erosion, which like a mathematical limit, may be approached asymptotically but never reached, Davis prefixed the word “plain” by the Latin word “pene” meaning almost. This peneplain is a surface of regional extent, resulting from long continued fluvial erosion. Another concept introduced by the geo-morphologists and which is useful in discussion of fluvial morphology in general and the cycle of erosion in particular is that of base level first formulated by Powell in 1875. In fact he wrote (Esterbrook 1969), “We may consider the level of sea to be a grand base level, below which the dry lands cannot be eroded; but we may also have, for local and temporary purposes, other base levels of erosion, which are the levels of the beds of the principal streams which carry away the products of erosion. The base level would in fact, be an imaginary surface inclining slightly in all parts towards the lower end of principal stream”. Powell’s definition of base level, thus includes three basic ideas; namely (i) The ultimate limit of sub-aerial erosion of the continent is the base level of the sea. (ii) Locally resistant rocks in the path of the stream, lakes in the stream path, or other obstacles can produce temporary base level. (iii) Tributaries may not erode below that of the main stream, and since mainstream will always have some slope, the base level need not always be a flat surface.
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Thus, sea level may be considered as a general, permanent base level which fluctuates from time to time but which remains normally within a range of a few metres. Local base levels such as rock outcrops and lakes are temporary; changes in base level cause changes in the mainstream, tributaries and subtributaries. The geomorphic cycle is subdivided into parts of unequal duration, each part being characterised by the degree and the variety of relief and by the rate of change, as well as by the amount of change that has been accomplished since the initiation of the cycle. The various stages in the geomorphic cycle are described in terms of age beginning with youth, which passes into maturity and then into old age. The topographic features of the first stage are spoken of as young or youthful, later ones as mature and those of the last stage as old, with further subdivisions when desirable such as, for example, early and late maturity. It may also be mentioned that each of these stages need not be of the same duration. Davis considered youth a relatively brief phase and thought old age involved a tremendously longer period of time than either of the two stages. It should also be noted that the blending of types of topographies is the rule rather than an exception. Thus in a region of general youthful characteristics, some streams and valleys may be mature. Similarly in mature plateaus there will be some youthful streams actively engaged in deepening their valleys. The span of time involved in a complete transformation of landscape may run into millions of years. Consequently during a period of scientific observation the changes in topography may be unnoticeable.
Youthful Topography Youthful topography is characterised by comparatively few streams but usually they have high gradients. Drainage may be poor with lakes and swamps on the divides between the streams. Streams flow in deep walled canyons or V-shaped valleys; these will be shallow or deep depending on the height of the region above sea level. Usually streams are actively engaged in cutting their valleys deeper. Youthful topography also possesses rapids and falls. There will be general lack of development of flood plain except along trunk streams.
Mature Topography When the region advances from youth to maturity in the cycle of erosion, the drainage is better developed with the number of streams increasing. The streams cut their valleys to lowermost levels, their tributaries are well established and lakes, swamps and rapids disappear. Meanders may exist. Since streams start eroding laterally, valleys are flat but the widths of the valley floors do not greatly exceed the width of the meander belt. If streams flow through homogenous rocks, tree-like drainage pattern known as dendritic pattern is developed during maturity of topography. In the regions of folded beds the drainage pattern is rectangular i.e. tributaries meet their main streams at right angles.
Old Topography In old topography, all main streams have very flat slope and are meandering back and forth over their flood plains. Valleys are extremely broad and slope gently both laterally and longitudinally; valley widths are considerably greater than the widths of meander belts. Their velocities are low and transporting power for sediment very limited. The whole landscape is gently rolling. Occasionally erosional remnants stand above the general land surface. Lakes, swamps and marshes may be present but they are on flood plains and not in inter-stream tracts as in youth. The topography tends towards the
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ultimate form namely peneplain which is a large land area of low relief that has been reduced to nearly base level by the combined action of weathering and streams. As a rule, surfaces of peneplains are not flat but gently rolling with low hills standing island-like erosion remnants in the general surface of lands (Worcester 1948). Geomorphic cycle discussed above is for humid region. An arid region is deficient in rainfall and also in vegetation. The groundwater table is also low. As a result deep subsurface chemical weathering is light, but surface chemical weathering does take place. Strong winds that blow carry dust from wherever it is found. As a result of these differences, the landforms obtained in the youth, mature and old ages in arid region are different from those in humid region. Worcester (1948) has discussed these in detail.
4.3
REJUVENATION OF EROSION CYCLE
Once initiated the erosion cycle does not always proceed to completion without interruption. Worldwide changes in sea level, tectonic uplifts of the earth’s crust and climatic changes are the three principal causes of rejuvenation. Changes in sea level are brought about by subsidence of portions of ocean basins. The lowering of base level will cause streams to cut into the valley and form incised channels whereas rise of sea levels will force streams to deposit their sediment load in channels and aggrade. Tectonic down warping or uplifting of land produces the same effects as lowering or rising of sea level. Changes in morphology due to change in climate are discussed in detail by Schumm (1969). Climatic changes affect the precipitation, which in turn affects the vegetation and surface runoff. The latter two, in turn, change the discharge in the stream, erosion pattern and sediment load. Thus climatic changes induce significant changes in drainage pattern and stream behaviour. In general, typical topography formed due to rejuvenation includes uplifted peneplains, incised meanders, stream terraces and hanging valleys. If rejuvenation takes place in this manner, the first erosion cycle remains incomplete and a new one starts. It may happen that before the new cycle completes, rejuvenation may be effected. It is, therefore, believed that partial erosion cycles may be more common than the complete ones.
4.4
CRITICISM OF GEOMORPHIC CYCLE
For the purpose of exposition, Davis made several simplifying assumptions, which have become the target of critical comment (Rice 1977); one of the most important was the separation of uplift and erosion into two distinct episodes. He thereby envisaged initial uplift taking place without appreciable erosion and then erosion under prolonged tectonic stability. However, current rates of uplift so exceed those for denudation that it is clear erosion does not normally constitute a limit of continued surface elevation. It is also argued, as partly discussed under rejuvenation, that stability is unlikely to stay long enough to permit reduction of an upland area to peneplain because of persistent tectonic activity. It is thus argued that the only stage in the Davisian cycle not represented on the earth’s surface at the present day is the peneplain. It is also worth recalling that periodicity of major climatic oscillations during the Pleistocene epoch (see Sect. 4.6) seem to have been of the order of 105 years. On the basis of known denudation rates the length of time required for an erosion cycle to run its full course cannot be less than 106 years. This
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means that any area will almost certainly have experienced many climatic fluctuations in the course of a single cycle with consequent changes in erosional processes. Penck (Penck 1924, Bloom 1978) differed fundamentally from Davis. Even though he accepted the idea that landscapes could be reduced to the end forms of low relief, he maintained that these end forms never became the initial forms of new episode of dissection. According to him the uplift was not rapid and then zero as Davis supposed, but always began slowly, reached a maximum and then waned gradually to a stop. During the long stage of initial slow uplift, all prior forms were destroyed, and a new surface of low relief, adjusted to a balance between uplift and degradation developed. This initial surface of low relief was called Primärrumpf by Penck. He argued that the rate of crustal movement varies greatly from time to time. Hence according to him, depending on whether rate of uplift is equal to, less than or greater than down cutting, the slope profile will be straight, convex upwards or concave upwards. No erosional sequence of forms was allowed by Penck’s scheme, because each morphologic assemblage was related to certain tectonic condition. Penck also denied any climatic control of geomorphic processes other than glaciations, believing that tectonics alone determined landform assemblages. For many years, the ideas of Penck received little support from English speaking geomorphologists. However, these have attracted attention since then and found them thought provoking even though at times contradictory. King (1962) a geo-morphologist from South Africa, formulated his ideas in a predominantly semiarid region where very little geological deformation had taken place in recent times. King believes in the supremacy of cyclic erosion in the development of continental landscapes and argues that the chief defect of Davisian concept is the absence of parallel slope retreat. King’s concept of changes in valley slope is that the chief means of landscape change is the migration of valley side slopes away from the rivers without significant change of angle as shown in Fig. 4.1 (a). On the other hand, Davis concluded that during youthful stream incision, valley sides would be steep. Once rapid valley deepening has ceased, the slope processes almost solely influence the form leading to a gradual decline in the angle, (see Fig. 4.1 (b)). Stream incision Almost parallel slope receding a King Stream incision Slope reducing b Davis Fig. 4.1 Valley slope evolution according to King and Davis
Both King and Davis argue that their models of landscape evolution could be adapted to a wide variety of climatic environment with only minor modifications. However, in 1909 Davis was convinced
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of the need to formulate a separate cycle for arid region because of (i) absence of the normal base level control in areas without perennial streams draining to the coast; (ii) increasing importance of wind action; and (iii) belief that a unique combination of the processes might lead to slope retreat without angular decline. Since then many writers such as Peltier have proposed variety of the original Davisian cycle, believed to be more appropriate to specific climatic zones. It is shown that climatic zone in which the cycle of erosion has been deemed to be significantly different from those outlined by Davis and King is the humid tropics, where chemical weathering significantly affects the development of landforms. Another climatic zone for which a distinctive cycle of erosion has been proposed is peri-glacial.
4.5
NON-CYCLIC CONCEPT OF LANDSCAPE EVOLUTION
Reactions against the limitations of the Davisian cycle of erosion have led to reassessments more radical than those discussed so far. Hack (1960) views landscape as the product of competition between the resistance of crustal materials to erosion and the forces of denudation. He argues that the orderliness of stream organization first discerned by Horton (1945) will naturally lead to regularity in the overall pattern of relief. Within a single climatic region where stream and slope profiles are both controlled by the nature of bedrock, similar geologic conditions should produce similar topography. Thus Hack put forward the concept of non-cyclic approach in the form of dynamic equilibrium. He does not probably question the existence of a very long period of land form evolution, but argues that its details are now lost beyond reconstruction; hence he is more concerned about the relationship between form and processes and adopts an attitude of ignorance towards land form history. Thus, Hacks’s argument implies that landforms adapt easily to changing environmental controls; however if this logic were stretched too far it would preclude, for instance, the identification of formerly glaciated areas. It may be mentioned (Craig 1982) that during the past the geo-morphologists have developed mathematical models for slope erosion. Three models can be mentioned in this respect. The first is ¶Z ¶Z =–b ¶t ¶x
...(4.1)
where Z is the elevation, t is the time, x is the distance from the divide and b is a positive constant called recession coefficient. Thus the rate of denudation is proportional to the slope. Where the denudation is proportional to convex curvature, the equation used is ¶Z ¶2 Z =a ¶t ¶x 2
...(4.2)
where a is called debris diffusion coefficient. These two equations have been brought together by Hirano (see Craig 1982) in a form, which describes the combined effects of weathering (Eq. 4.1) and creep (Eq. 4.2). The equation is ¶2 Z ¶Z ¶Z =a +b 2 ¶t ¶x ¶x
...(4.3)
There is considerable difficulty in determining which equation should be used for a particular situation and hence only a few areas are subjected to this type of analysis.
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Hence, in spite of all the limitations of Davisian erosion cycle, it is still considered as the best because no other viable alternative meeting all the objections to Davisian cycle is available.
4.6
GEOLOGICAL TIME SCALE
Historical or stratigraphical geology is mainly concerned with the description and classification of rocks with a view to arranging them in chronological order in which they were laid down on the surface of the earth. Of the three groups of rocks – sedimentary, igneous and metamorphic – only the sedimentary rocks are amenable to such an arrangement since they have been deposited layer by layer and contain the remains of organisms which flourished while they were formed. The time scales used by the hydraulic engineer and the geologist are quite different. The hydraulic engineer uses seconds or days as the unit of time when dealing with transport rates of water or sediment. When he is dealing with the morphological changes such as aggradation or degradation of the riverbed he is concerned with bed level changes occurring in a few years or a few decades at the most. As against this in stratigraphy the unit time used is million years. Thus Lord Kelvin (Rice 1977) assumed that earth started as a molten body, and applying the theory of cooling to this mass he estimated that to attain the present day temperature the earth must have taken 20 to 40 million years. For arranging the various geologic formations in the order of increasing antiquity, the geologist uses various means at his disposal. The first is the fundamental principle of superposition in which the upper beds in an un-inverted succession are dated as younger than the lower ones. The second means is the palaentological dating depending on the fossil content of the formation. Each formation encloses a fossil assemblage, which is characteristic and different from that of the underlying or over lying formations. The animal and vegetable organisms of each geological age bear special characters not found in those of other ages. It needs to be emphasised that the fossils present in a series of formations are not only a function of the period when the formation was laid down but are also a function of (i) the geological period when rocks were formed; (ii) the zoological or botanical provinces in which the locality was situated; and (iii) the physical conditions prevalent at the time, e.g. depth, salinity, muddiness of water, temperature, character of sea bottom and currents. The geological formations are named in such a manner that they indicate the stage of development of the organisms. Thus the Azoic era is completely devoid of organisms, while Proterozoic era shows traces of the most primitive life. The Palaeozoic era contains the remains of ancient plants and animals, and so on to the recent time. The third means used for determining the age of formation is the lithology. Each lithology unit may comprise a number of individual beds having more or less the same characters, when it is spoken of as a formation, and given a local or specific name to distinguish it from a similar formation of different age or belonging to a different area. Lithology is many times useful in the determination of chronology. With the discovery of radioactive elements uranium and thorium at the end of 19th and beginning of 20th century a more powerful means was available for determining the chronology of rocks and other formations. It was found that uranium and thorium emit alpha and beta radiations; alpha radiation consists of positively charged helium nuclei with two positive charges while beta radiation consists of negatively charged electrons. Depending on the nature of radioactive elements half the atoms of the element will disintegrate in this manner in a period known as half-life of the element concerned. As a result of such emission of alpha and beta radiation a new element or daughter element is formed. If the quantity of the parent element to the daughter element is known at any time, the period during which the
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radioactive decay has taken place can be calculated. Uranium and thorium, as a result of radioactive decay are finally converted to lead Pb206, Pb207, or Pb208 isotopes. The isotopic analysis of the minerals is carried out using the technique of mass spectroscopy. Using radioactive dating techniques, it is estimated that the age of crustal material of the earth is about 4,500 million years while the age of lunar rock ranges from 3,000 to 4,500 million years. Table 4.1 gives the era, group, system or formation or rocks, and the chief fossils found in these formations. Even though geologists are interested in all the eras from Quaternary to Azoic or Archaen, geo-morphologists consider Quaternary and Tertiary periods as of primary significance to them; this is so because it is believed that the majority of landforms are about a million years old, and the remaining not more than 20 to 30 million years old. Hence, from the geo-morphologist’s point of view it becomes crucial that the dating between Quaternary and Tertiary periods is done carefully. This aspect has been discussed in detail by Rice (1977) and the following discussion is based on his comments. The dating of Cenozoic era has become complicated because of various reasons. Earlier stratigraphic column was constructed on the basis of marine sediments and faunas raised above the modern sea level. Such continuous marine successions are rare in the late Cenozoic age, and the contemporary terrestrial beds tend to be fragmentary, of short duration and local. The second difficulty arises because of the relatively brief duration of Cenozoic era because of which the biological evolution during this period was not adequate to delimit the era. Then there were at least eight or probably even more environmental changes during this period, which have complicated building up of the chronological sequence. Lastly, as regards methods of estimating the age of the formation, K/Ar dating is most suitable for Cenozoic era; however because of the very small amount of Ar present in the formations the accuracy of the method is doubtful. Sufficient light has been thrown on the chronology of Cenozoic era by obtaining cores of materials deposited on the beds of deep seas. These deposits contain fossils of marine organisms such as foraminiferal, globorotalia menardii and diatoms in large numbers. Since these organisms have different environmental requirements, their fossils give information on the changing temperature of seawater. The change in the ratio O18/O16 of the isotopes of oxygen in the shells also indicates the temperature changes. Shells formed in the cold climate are relatively richer in O18. Such evidences have helped in fixing the chronology of later Cenozoic era. Some investigators argue that the most distinctive characteristic of Pleistocene epoch is the development of large continental ice sheets in Europe and North America. Hence the beginning of Pleistocene should be equated with dramatic fall in temperature. However, glaciation in different parts of the world leads to a very large variation in the onset of Pleistocene. Therefore many argue that it is unwise to relate glaciation to Pleistocene. Similar uncertainty prevails in fixing the Pleistocene–Holocene boundary. The term Holocene was originally intended to designate the post glaciation period. However, the melting of ice sheets being transgressive of time, the post glaciation period in one region could be glaciation period in another region. Therefore, this criterion was difficult to use. Hence the boundary between Pleistocene and Holocene is fixed arbitrarily. The most accepted boundary is that first proposed by Scandinavian workers using pollen analysis. Using this technique the period of rapid warming indicating the onset of Holocene has been fixed at about 10,000 years ago. It is necessary to emphasize that during the Pleistocene era some areas were covered by ice sheets while some were not. In glaciated areas the attention was focussed on till sheets laid down one over the
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Fluvial Morphology
Table 4.1 Geological time scale [Adapted from Wadia (1961), and Krishnan (1982)] Era
Period
Epoch
Duration
M years
Years before present
Chief fossils
M years (Ma) Cenozoic
Quaternary
Tertiary
Mesozoic
Palaezoic
Proterozoic Azoic
Secondary
Holocene (present) Pleistocene (Glacial) Pliocene Miocene Oligocene Eocene
0.01
0.01
1
1
7 17 13 27
8 25 38 65
Cretaceons
75
140
Giant reptiles and ammonites disappear at the end. Flowering plants become numerous
Jurassic
60
200
Triassic Permian Carboni-ferous
40 50 60
240 290 350
Ammonites abundant. First birds, flowering plants and sea urchins Ammonites, reptiles, amphibia abundant. Arid climate
Devonian Silurian
60
410
Ordovician
35
445
Cambrion
60 100
505 605
Primary
Precambrian Archaen
Precambrian Archaen
2500 3600
Living animals Man appears; many animals dies off during glaciation Mamals, mollusca, and flowering plants dominate. Divisian largely based on proportion of living to extinct species of mollusca and the presence of mammal species
Trilobites disappear at the end Many non-flowering plants, first reptiles appear Abundance of corals, branchiopoda, first amphibious and lung-fishes Graptolites disappear at the end; first fishes; probably first land plants Abundance of trilobites and graptolites Abundance of trilobites Soft bodied animals and plants Lifeless
other as a result of multiple glacial advances. Equal attention was given to the pollen analysis of biogenic materials entrapped within the tills. Similarly a thorough study was made of non-marine molluscs and beetles. However, it has been found that the record of terrestrial sediments in glaciated regions is small and is confined to the later part of Pleistocene era. In the unglaciated regions, at a limited number of places pollen analysis has been used. Some deep core samples have also been obtained from the desert areas where earlier lakes existed. Another technique used to determine the chronology of continental land surfaces in Pleistocene era is the carbon C14 dating which is very useful for dating of Pleistocene and Holocene eras because of short half-life of 5730 years of C14. This method depends on the fact that the atmosphere and the hydrosphere represent reservoirs of radioactive carbon C14, which are tapped by animals and plants to build up their structures and tissues. The source of radioactive carbon lies in the cosmic ray bombardment of nitrogen in the atmosphere, which converts it into C14. Carbon has three isotopes C12, C13 and C14 and it is present in the atmosphere
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River Morphology
in the form of CO2. Out of the three isotopes C14 is the only unstable isotope with half-life of 5730 years. In historical times a balance was reached between new C14 received from cosmic radiation and that disintegrated due to radioactive decay. Since living organisms absorb CO2, each organism absorbs a fixed proportion of C14 of the total carbon absorbed during the lifetime. After the death of the living organism, the replenishment of C14 ceases and C14 content declines due to radioactive decay. The ratio of radioactive to the total carbon present at any time is, therefore, a measure of the age of the organic materials such as bones, tusks, grains, wood, hide, peat etc. The method is suitable for dating up to 50,000 years.
4.7
GLACIATION
Glacier is a slow moving mass of ice formed by accumulation of snow in mountain valleys and other places. Area of the continents that is covered by ice at present is close to 15 M km2, the largest part of which is concentrated in Antarctica (12.5 M km2) and in Greenland (1.7 M km2). Glaciers today, except at high altitudes and in high latitudes, are of minor importance in shaping landforms; but those that existed during the Pleistocene epoch have left their imprints on many millions of square kilometres of the earth’s surface. About 10 M km2 of the North America, 5 M km2 of Europe, 4 M km2 of Siberia and large parts of the Himalayas were glaciated. Pleistocene epoch consisted of four major glacial ages separated by interglacial ages of probably far greater duration than the glacial ones. The latest glaciation has left the most obvious imprints on the topography. Glaciers are classified into ice caps, valley glaciers, ice-streams and glacier ice. Glaciers that are continuous sheets of snow from which ice may move in all directions are known as ice caps. Glaciers that are confined to courses, which direct their movement, are called valley-glaciers and ice-streams. Glacier, which spreads in cake-like sheets over level ground at the base of glaciated areas, is known as glacier ice.
Glaciation in India (Wadia 1961, Krishnan 1982) Majority of the present Himalayan glaciers are three to five km in lengths, however there are some giant glaciers of forty km or more in length such as the Milam and Gangotri glaciers of Kumon and Zemu glacier draining Kanchanjunga group of peaks in Sikkim. The latest glaciers of the Indian subcontinent are those of Karakoram discharging into the Indus river; these are Hispar and Batura of the Hunza valley, and Biafo and Baltora of the Shigar, a tributary of the Indus. These are about 50 km in length and 130 to 330 m in thickness. These are the latest survivors of the last Ice Age of the Himalayas. Presence of terminal moraines covered, many times by grass, seen in Pir Panjal moraines at the snouts of existing glaciers at low level hills of Punjab lead to the conclusion that at least this part of India experienced glacial age in Pleistocene epoch. Parts of India lying to the south of Himalayas experienced cold pluvial epochs during this period. The evidence leading to this conclusion is derived from the fauna and flora of the hills and mountains in India and Sri Lanka. According to Wadia (1961) indications of extensive glaciation in the immediate past and in the present glaciers are: (i) presence of enormous heaps of terminal moraine covered by grass and trees; (ii) presence of ice transported blocks; and (iii) smoothed or striated hummocky rock surfaces. According to geologists the Kashmir area of the Himalayas underwent four distinct glaciations separated by the interglacial warm periods; the last of the glaciations occurred about ten to twenty thousand years back.
Fluvial Morphology
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Glacial Movement and Erosion Glaciers move slowly showing erratic and sudden advances of their fronts. Glaciers reduce in size by the combined action of melting and evaporation/sublimation, a process known as ablation. Glaciers may also get nourishment and thus increase in size. Depending on whether a glacier gets nourishment or not the glacier is called an active or inactive glacier. Active glacier will have an advancing front whereas an inactive glacier will have a receding front. Abundant striations, polished and grooved rock surfaces give evidence of effective glacial erosion. The bottom topography of bedrock floor may show irregularity and over deepening which cannot possibly be explained by any other way than to assume that they are due to local glacial scouring. One of the simplest ways of assessing the rate of erosion due to glaciers is by the measurement of sediment being carried by melt water issuing from glacier snout. On the basis of observations by Reid, Thorarinson and Corbel from Muir, Hoffellsjokul and St. Sorlin glaciers respectively, Rice (1977) suggests that the mean erosion rate by active glacier lies in the range of 1 to 5 mm/year which is seen to be much higher than most of the figures for stream erosion. Glacial erosion includes two processes, namely plucking and abrasion. Plucking occurs when moving ice freezes on to the bed rock and pulls out blocks which are then carried away. Abrasion is due to grinding effect. Grooves formed on the bottom can be 2 m deep and 100 m long, even though grooves up to 30 m deep and ten km long have also been observed. Large blocks of un-weathered rock found in both glacial and fluvio-glacial deposits are mainly due to plucking.
Erosional and Depositional Landforms Ice streams flowing in high mountainous areas have modified their valleys to such a great extent that their forms are distinctly different from the valleys caused by fluvial erosion. Some of the most important erosional landforms produced by glacial erosion are cirques, glacial troughs and hanging valleys. CIRQUES: Cirque is a French word-meaning amphitheatre like basin, not completely enclosed. It is the most distinctive, common landform caused by glacial erosion in mountain high lands. It is a steep sided semi-circular basin found at valley heads; but it may not Head connect in its downstream part with a valley. The name is applied wall Threshold to shallow basins which mark the steps of snow banks which Basin never grow into glaciers. A typical cirque consists of a steep head wall on the upstream side, followed by a deep basin and then a Fig. 4.2 Cirque gradually sloping up surface known as threshold, see Fig. 4.2. The longitudinal profile of cirques approximately follows the equation of the form y = (1 – x) e – x and is almost independent of rock type. Conditions which favour maximum cirque development are: (i) rather wide spacing of prelacies valleys so as to permit expansion without intersection of adjacent cirques at an early stage; (ii) adequate snowfall which can form large snow fields and glaciers, but not heavy enough to form ice-caps; and (iii) fairly homogenous rocks which permit cirque extension equally well in any direction. GLACIAL TROUGHS: Next in importance to cirques is the most distinctive topographic feature in glaciated mountains, namely glacial trough. It is the valley, which is modified, in its cross-sectional shape and the longitudinal profile due to glaciers. Most glacial troughs were originally stream cut
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River Morphology
valleys. Glacial trough heads at the lower edge of the cirque threshold; however, there is a drop from cirque threshold to the floor of glacial trough. The longitudinal profile of the glacial trough is irregular and ungraded; the profiles are seldom smooth and concave upward type. Instead, they have a series of glacial steps, which are more pronounced in the upper reaches than in the lower. Glacial steps have been attributed to differential glacial abrasion in contracting and expanding sections of the valley, effect of varying rock hardness and to preglacial irregularities. Presence of jointed rocks can also lead to glacial steps. The cross-sectional profile of a glacial trough is significantly different from that of an unglaciated valley in mountainous area. While many glacial troughs are U-shaped, stream formed valleys in mountains are usually V-shaped. Davis has suggested that the cross profile of a glacial trough follows a catenary curve. The difference in the cross profiles of glacial troughs are often related to the difference in the thickness of glacier, valley lithology, structure of rocks in which the trough is cut, and the number of times the valley is glaciated. Some portion of the glacial troughs may exhibit flat floors, which are attributed to the deposition subsequent to the trough development. The material deposited may be due to aggradation caused by deposition of outwash material by glacial recession or post-glacial alluvial deposit. HANGING VALLEYS: The tributaries usually join the river valley accordantly i.e., there is no difference in bed elevation of the main river valley and that of the tributary. However, glacial troughs often have tributary troughs or valleys joining the main trough discordantly, producing elevation drops at the junction. This is known as the hanging valley. Some valleys in Kashmir and in Sikkim exhibit hanging valleys of this type (see Wadia 1961, Krishnan 1982). However, it may be emphasised that hanging valleys cannot be interpreted as evidence of past glaciation because they can be formed due to reasons other than glaciation; for example a hanging valley can be formed if the main stream is degrading rapidly and the tributary is intermittent. Glacial deposits are usually heterogeneous and lack stratification. These deposits are of three types, namely end moraine, lateral moraine, and ground moraine, depending on whether the deposition took place at the end of, at the side of, or beneath an ice stream. Only some glaciers build end moraine; this depends on whether the ice front maintains itself in one position for a sufficiently long time. Then if the ice-fed stream emerging from the glacier is capable of transporting the end moraine, it wouldn’t deposit. Lateral moraines form along the sides of an ice stream mainly from the materials, which are contributed from the valley sides above the glacier by weathering and mass movement. Lateral moraines are usually patchy and may or may not be found on both sides. Ground moraine is more closely associated with ice caps than with ice streams. The streams flowing on, within or beneath the glacier deposit the material eroded and transported by the glaciers and ice streams. This material is known as glacio-fluviatile. The most common landforms in this material are valley trains, eskars, kame terraces, and outwash fans or deltas. These are described by Thornbury (1969).
4.8
FLUVIAL MORPHOLOGY
Fluvial morphology deals with streams and stream systems as produced by the action of flowing water. The features produced on the land surface by flowing water can be aptly called fluvial landscapes. As the erosion cycle proceeds the morphology of streams also changes and the streams pass through the three stages of development as the earth’s surface namely youth, maturity and old age. Although the
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Fluvial Morphology
stage reached by the stream usually corresponds to that of the surrounding topography, this is not necessarily the case. Usually the stream is less youthful in character near its mouth than in the vicinity of its head waters (Hack 1960). If one considers a newly uplifted land mass as the starting point and traces the successive changes, which occur with time, the first stage of the stream will be youth. Here streams have relatively steep slopes and they are engaged in cutting their channels downwards. Lateral erosion and valley widening is extremely small. The cross section of the stream will be V-shaped with no or little flood plain. A youthful valley is shown in Fig. 4.3. Streams in youth may not have cut down enough resistant rock mass to attain a gradual profile; hence rapids and falls may exist along its course because sufficient time has not passed, since they were uplifted, for the stream to cut down and eliminate them. There are frequent changes in the slope of the stream caused by the differences in hardness of the strata over which they flow. Johnson (1932) suggests that early youth ends when lakes are eliminated and middle youth ends when falls and rapids are eliminated.
Fig. 4.3 Youthful valley
Late youth ends and early maturity starts when the rate of down cutting decreases and the rate of lateral erosion increases; establishment of grade also marks the passage from youth to maturity. Early maturity ends and late maturity begins when the valley width equals the width of the belt covered by the meanders of the stream. V-shaped valleys and rapids and waterfalls disappear which are characteristic of youthful age of stream. Figure 4.4 shows a mature valley. In the old stage there is pronounced meandering activity as a result of which width of flood plain exceeds several times the width of the meander belt. Oxbow lakes and swamps are usually present as a result of cut-offs developed naturally. Natural levees, which form banks confining stream channels, may be built up until the channel is some metres above the general level of the flood plain. Typical old stage is shown in Fig. 4.5.
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River Morphology Meander belt = Valley – floor width
Youth
Mature
Old
Fig. 4.4 Cross-valley profiles for various stages of stream
Fig. 4.5
Old-age stream
It sometimes happens that during the cycle of erosion certain changes occur which cause streams to incise their channels with greater vigour. This renewed down cutting is known as rejuvenation. Three principles causes for rejuvenation are: (i) World wide changes in seal level, (ii)Tectonic changes and (iii) Climatic changes.
Equilibrium in Natural Streams Geo-morphologists as well as engineers have used the concept of equilibrium in streams. A stream in equilibrium is called a graded stream or a poised stream. Mackin (1948) has given the following definition of a graded stream: “A graded stream is one in which, over a period of years, slope is delicately adjusted to provide, with available discharge and with prevailing channel characteristics, just the velocity required for the transportation of load supplied from the drainage basin. The graded stream is a system in equilibrium; its diagnostic characteristic is that any change in any of the controlling factors will cause a displacement of the equilibrium in a direction that will tend to absorb the effect of the change”.
Fluvial Morphology
85
Thus, the four variables related to the concept of a graded stream are slope, discharge, channel characteristics and sediment load. In a natural stream, the discharge is continuously changing due to precipitation, infiltration, evaporation and withdrawals. Although stream tends to pick up sediment or deposit it until load equals capacity, because of rapid variations in flow it cannot do so. Hence, in very short times the stream cannot be in equilibrium. Similarly, since the tendency of the streams is to lower the land surface to the sea level, over very long periods the stream cannot be in equilibrium. Thus, neither in very short not very long periods can a natural stream be considered to be in true equilibrium (Lane 1955). Yet, for all practical engineering purposes, most of the alluvial streams are in equilibrium over periods of the order of a few decades. In such streams, the bed may go down during high flows and fill back during low flows; yet the net amount of change is not sufficiently large to be detected by quantitative measurements. Most of the alluvial streams which are not affected by human interferences can be said to be graded or in equilibrium. Construction of dams, withdrawal or addition of clear water, addition of sediment load, contraction of stream and cutting off the bends are some the ways in which the equilibrium of the stream is disturbed by human activities.
Characteristics of Graded Streams To get better appreciation of the stream morphology the characteristics of graded streams are briefly enumerated here. Firstly the slope of a graded stream, in general, decreases in the downstream direction yielding a concave profile. Secondly, partly as a consequence of decreasing slope in the downstream direction, the stream drops the coarser material that it cannot transport, a phenomenon known as sorting; and partly due to abrasion, the bed material of an alluvial stream becomes finer in the downstream direction. Thirdly in humid regions as more and more tributaries join the main stream; the discharge increases in the downstream direction. However, if the stream passes through arid region, the discharge can actually decrease in downstream direction as in the case of the Euphrates in Iraq. This is primarily due to seepage and evaporation. In addition, the upper part of the drainage basin is the main source of sediment even though the runoff from this part of the catchments may be small. The runoff from the rest of the basin is large but it carries relatively less sediment. This leads to decrease in the average concentration of sediment in the downstream direction necessitating a smaller slope. Lastly, because of finer material, streams usually have relatively narrow channels i.e. larger width to depth ratio, in the downstream direction. As a result the stream has greater hydraulic efficiency and flows with a smaller slope. A graded stream may show aggradational tendency, albeit temporary, under the following conditions (Cotton 1941): 1. If dissection of upland region is in progress and a vast number of smaller new valleys and ravines come into existence in the stage of youth. To carry relatively higher load stream may increase slope by aggradation. 2. If the river after it is graded flows in a wider channel than it has hitherto had in youth, loss of depth in the stream may rebuilt in a reduction of velocity and transporting power that it needs steeper slope to carry the load. 3. As a river develops increasingly large curves by lateral corrasion, its length increases and slope decreases and hence carrying power decreases resulting in aggradation. 4. Decrease in water volume due to infiltration, evaporation or withdrawal can cause increase in slope due to aggradation.
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River Morphology
Variation of Sediment Size It is important for a river morphologist to know how the sediment characteristics change along the stream. The most important characteristic of sediment is its median size. It is found that in most of the streams there is reduction in size of sediment due to wearing or abrasion, fragmentation, weathering, dissolution and hydraulic sorting. Hydraulic sorting takes place in a stream because the sediment transport ability of the stream reduces in the downstream direction. It is difficult to know the relative importance of these processes in the reduction of sediment size. Hence, it is easier to model the reduction in size by assuming that, as done by Sternberg in 1875 (Rohan 1967), the reduction in weight of the particle dW is proportional to its weight W and the distance travelled dL. Hence dW = – CW dL
...(4.4)
where C is the constant of proportionality. Integration of this equation with the initial condition W = Wo when L = 0 yields W = Wo e – CL
...(4.5) 3
3
Further since for spherical particle W ~ d and Wo ~ do , one gets d3 = do3 e – CL or
d = do e– a1L
...(4.6)
c is known as the abrasion coefficient. Here d is the sediment size. This equation known as 3 Sternberg’s law is found to be valid on the Rhine in Germany. In Japan it is found to be valid for sediments coarser than 4.0 mm in size. Shulits (1941) has stated that a1 ~ (particle velocity)1/4. Values of a1 are found to vary between 0.006 km –1 and 0.11 km –1; however, it is not possible to predict its value at present. If dW is assumed to be proportional to surface area of the particle and dL, and one uses the initial condition W = Wo when L = 0, the following equation is obtained from Eq. (4.4).
a1 =
F W = GW H
1 3 o
I JK
c - 1L 3
3
...(4.7)
Lastly another formula known as Schaffernak’s formula (see Rohan 1967) is also some times used in describ
