SOIL CONSERVATION SERVICE CURVE NUMBER (SCS-CN) METHODOLOGY

Water Science and Technology Library

VOLUME42

Editor-in-Chief

V. P. Singh, Louisiana State University, Baton Rouge, U.S.A.

Editorial Advisory Board

M. Anderson, Bristol, U.K. L. Bengtsson, Lund, Sweden

J. F. Cruise, Huntsville, U.S.A. U. C. Kothyari, Roorkee, India S.E. Serrano, Lexington, U.S.A.

D. Stephenson, Johannesburg, South Africa W.G. Strupczewski, Warsaw, Poland

The titles published in this series are listed at the end of this volume.

SOIL CONSERVATION SERVICE CURVE NUMBER

(SCS-CN) METHODOLOGY

by

SURENDRA KUMAR MISHRA Hydrologic Design Division,

National Institute of Hydrology, Roorkee, Uttaranchal, India

and

VIJAY P. SINGH Department of Civil and Environmental Engineering,

Louisiana State University, Baton Rouge, U.S.A.

SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN 978-90-481-6225-3 ISBN 978-94-017-0147-1 (eBook) DOI 10.1007/978-94-017-0147-1

Printed an acid-free paper

AII Rights Reserved © 2003 Springer Science+Business Media Dordrecht

Originally published by Kluwer Academic Publishers in 2003 Softcover reprint ofthe hardcover Ist edition 2003

No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording

or otherwise, without written permis sion from the Publisher, with the exception of any material supplied specificalIy for the purpose of being entered

and executed on a computer system, for exclusive use by the purchaser of the work.

Dedicated

to

our families:

SKM: Rekha, Shivangi and Surabhi

VPS: Anita, Vinay and Arti

CONTENTS

Preface List of Symbols

1 INTRODUCTION 1.1 Rainfall-Runoff Modeling

1.2 Catchment Characteristics 1.2.1 Catchment Length, Width, and Slope 1.2.2 Catchment Area 1.2.3 Catchment Shape 1.2.4 Catchment Relief 1.2.5 Linear Measures 1.2.6 Drainage Patterns

1.3 Precipitation 1.3.1 Quantitative Description of Rainfall 1.3 .2 Temporal and Spatial Variation of Rainfall 1.3.3 Average Rainfall over an Area 1.3.4 Rainfall Storm Analysis

1.4 Interception 1.5 Surface Detention and Depression Storage 1.6 Evaporation

1.6.1 Water Budget Method 1.6.2 Mass Transfer Method 1.6.3 Energy Budget Method 1.6.4 Combination Method 1.6.5 Pan Evaporation 1.6.6 Evapotranspiration

1. 7 Infiltration 1. 7.1 Mechanism of Water Retention by Soil 1. 7.2 Retention Curves 1. 7.3 Darcy's Law 1. 7.4 Transport of Soil Moisture I. 7.5 Measurement of Infiltration 1. 7.6 Conceptual Infiltration Models 1. 7. 7 Infiltration Indices

1.8 Runoff 1.8.1 Modes of Runoff Generation 1.8.2 Runoff Concentration 1.8.3 Time of Concentration 1.8.4 Lag Time 1.8.5 How in Stream Channels 1.8.6 Rating Curve 1.8.7 Antecedent Moisture

1.9 Determination of Runoff Hydrograph 1.9.1 Unit Hydrograph (UH) 1. 9.2 Channel and Reservoir Routing

vii

xiii XV

1 1 2 2 3 3 3 3 4 4 4 5 6 8

31 32 33 33 34 36 37 39 40 44 45 46 47 47 50 51 56 58 58 60 61 63 65 65 66 67 67 71

1.10 Scope of the SCS-CN Concept in Hydrology 1.10.1 Computation of Infiltration and DSRO

Volumes 1.1 0.2 Computation of Infiltration Rates 1.10.3 Time-Distributed Event-Based

Hydrologic Simulation 1.10.4 Long-Term Hydrologic Simulation 1.1 0.5 Transport of Urban Pollutants 1.10.6 Sediment Yield

1.11 Organization of the Book

2. SCS-CN METHOD 2.1 Historical Background

2.1.1 Experimental Watersheds and Infiltration Studies

2.1.2 Development of Rainfall-Runoff Methods 2.2 SCS-CN Method 2.3 Factors Affecting CN

2.3.1 Soil Type 2.3.2 Land Use 2.3.3 Hydrologic Condition 2.3.4 Agricultural Management Practices 2.3.5 Antecedent Moisture Condition 2.3.6 Initial Abstraction and Climate 2.3.7 Rainfall Intensity and Duration

and Turbidity 2.4 Determination of Curve Number

2.4.1 Development of CN for Complexes 2.4.2 Rationale of Curve Number

2.5 Use of NEH -4 Tables for SCS-CN Application 2.6 Sensitivity Analysis

2.6.1 First-Order Sensitivity Analysis 2.6.2 Conventional Analysis

2. 7 Advantages and Limitations of the SCS-CN Method 2.8 SCS-CN Application to Distributed Watershed Modeling

2. 8.1 A vail ability of Data 2.8.2 Moglen Method 2.8.3 Advantages and Limitations of

the Moglen Method 2.8.4 Modified Moglen Method 2.8.5 Features of the Modified Moglen Method 2.8.6 Advantages and Limitations of the

Modified Moglen Method

3. ANALYTICAL DERIVATION OF THE SCS-CN METHOD 3.1 Early Rainfall-Runoff Methods 3.2 Analytical Derivation of the Mockus and Other Methods

3.2.1 Derivation of Mockus Method

Vlll

79

79 79

80 82 82 83 83

84 84

84 85 85 88 89 93 99

100 101 104

105 105 108 108 108 114 115 118 129 130 130 131

136 136 143

145

147 147 149 149

3.2.2 Derivation of Zoch Model 3.2.3 Derivation of Depression and

Interception Storage Models 3.3 Generalization of the SCS-CN Method

3. 3.1 Generalization of the Mockus Method 3.3.2 Statistical Derivation of the SCS-CN

Method 3.3.3 SCS-CN Derivation From the First-Order

Hypothesis 3.3.4 Derivation of SCS-CN Proportional

Equality 3.3.5 Non-Linear Derivation of SCS-CN Method 3.3.6 SCS-CN Derivation Including Initial

Abstraction 3.3.7 Development of an Initial Abstraction

Model 3.4 Implication of Generalization of the Mockus Method

3.4.1 Modification of the SCS-CN Method 3.4.2 General Form of SCS-CN Model

3.5 Characteristics of the SCS-CN and Mockus Methods 3.5.1 Mockus Method 3.5.2 SCS-CN Method 3.5.3 Numerical Comparison of Methods 3.5.4 Models Performance on Field Data

3.6 Functional Behaviour of the Existing and Modified SCS-CN Methods

3.6.1 Existing SCS-CN Method 3.6.2 Modified SCS-CN Method

3. 7 Significance of the Proportional Equality 3.7.1 Soil Porosity 3. 7.2 Proportional Equality 3.7.3 Significance ofCN 3.7.4 Another Interpretation of S-CN Mapping

Relation 3.8 Antecedent Moisture Conditions

3.8.1 Variation of CN With AMC 3.8.2 CN Derivation From Rainfall-Runoff Data

3.9 SCS-CN Concept as an Alternative to Power Law

4. DETERMINATION OF'S' USING VOLUMETRIC CONCEPT 4.1 Analytical Derivation

4.1.1 Equivalence Between SCS-CN Proportionality and C= S, Concepts

4.1.2 Effect of Antecedent Moisture Condition 4.1.3 Effect of Initial Abstraction 4.1.4 Effect of Fe 4.1.5 Effect of Storm Duration, Rainfall

Intensity, and Turbidity

ix

151

152 153 153

154

159

160 161

163

165 167 167 167 168 168 169 170 173

179 179 184 186 187 187 188

190 191 194 196 200

205 205

206 207 209 215

221

4.1.6 Effect of Agricultural Management Practices

4.2 Verification of Existing AMC Criteria 4.3 Determination of S

4.3.1 Homogeneous Gauged Watersheds 4.3.2 Heterogeneous Gauged Watersheds 4.3.3 Ungauged Watersheds

4.4 Use ofNEH-4 Tables 4.4.1 Workability of Model4 4.4.2 Inverse Computation of Fe From NEH-4

CN-Values 4.4.3 Verification of AMCCriteria For Fe-Values 4.4.4 Applicability of NEH-4 Tables to Existing

and General Models 4.4.5 Condensation ofNEH-4 Table

4.5 Advantages and Limitations of the Modified Model

5. DETERMINATION OF'S' USING PHYSICAL PRINCIPLES 5.1 Fokker-Planck Equation Of Infiltration 5.2 Description of S

5.2.1 Use of S, And Kh 5.2.2 Use of Kh-8 And \lf-8 Relations 5.2.3 Use of Intrinsic Sorptivity 5.2.4 Vertical Infiltration 5.2.5 Kinematic Wave

5.3 SIP Relations for the Modified Model 5.3.1 Effect of Fe On Si 5.3.2 Effect of M On Si 5.3.3 Effect of A On Si 5.3.3 Effect of P On Si

5.4 Determination of D, From Universal Soil Loss Equation

6. INFILTRATION AND RUNOFF HYDROGRAPH SIMULATION 6.1 SCS-CN-Based Infiltration and Runoff Models 6.2 Application Of Infiltration and Runoff Models

6.2.1 Infiltration Data 6.2.2 Ars Watersheds 6.2.3 Error Criteria for Simulation 6.2.4 Model Application to Infiltration Data 6.2.5 Model Application to Rainfall-Runoff

Data

7. LONG-TERM HYDROLOGIC SIMULATION 7 .I SCS-CN-Based Hydrologic Models

7.1.1 Williams-Laseur Model 7.1.2 Hawkins Model 7 .1.3 Pandit and Gopalakrishnan Model 7 .1.4 Mishra et al. Model

X

224 225 226 226 227 228 229 229

232 235

235 239 243

244 245 251 251 252 262 263 265 265 267 268 273 274 274

278 278 282 282 282 283 284

291

323 324 324 329 333 334

7.2 Simulation Using the Modified SCS-CN Model 336 7.2.1 Rainfall-Excess Computation 336 7.2.2 Soil Moisture Budgeting 336 7 .2.3 Computation of Evapotranspiration 337 7.2.4 Catchment Routing 338 7.2.5 Baseflow Computation 338

7.3 Application of the Modified SCS-CN Model 346 7.3.1 Parameter Estimation 346 7.3.2 Model Calibration and Validation 347 7.3.3 Volumetric Statistic 348 7.3.4 Effect of Storm Duration on Model

Parameters 353 7.3.5 Sensitivity Analysis 354

7.4 Application of the Variations of the Modified SCS-CN Model 356

8. TRANSPORT OF URBAN POLLUTANTS 360 8.1 Heavy Metals 361 8.2 Metal Partitioning 362 8.3 Metal Transport 364

8.3.1 Rating Curves In Open Channel Hydraulics 364 8.3.2 Governing Flow and Metal Transport

Equations of Equivalent Mass Depth of Flow 367 8.3.4 Relation Between Concentration and

Equivalent Mass Depth 368 8,4 SCS-CN Analogy for Metal Partitioning 369 8.5 Application of Wave Analogy 374

8.5.1 Experimental Watershed 374 8.5.2 Development of Looped Mass Rating

Curves 374 8.5.3 Process of Mixing of Metals With Rainfall 379 8.5.4 Development of Normal Mass Rating

Curves 381 8.5.5 Wave Analysis 389 8.5.6 Determination of Potential Mass Depth of

Flow 395 8.5.7 Limitations of Wave Analogy 396

8.6 Application of the SCS-CN Analogy To Metal Partitioning in the Rainfall-Runoff Environment 400

8.6.1 Derivation of l<c! And PCN 400 8.6.2 Relations Between 'If and Chemical

Characteristics of Rainfall 405 8.6.3 Relation Between Ir and 'If 406 8.6.4 Relation Between ADP and 'If 407

8. 7 Application of the SCS-CN Analogy To Metal Partitioning in the Snowmelt Environment 408

8.7.1 Snowmelt Water Quality Data 408 8.7.2 Metal Partitioning in Snowmelt Medium 413 8. 7.3 Relation of PCN And l<c! With the Medium

xi

Characteristics 414 8.7.4 PCN- and K.t-Based Ranking Of Metals 418

8.8 Application of the SCS-CN Analogy To Metal Partitioning in the Riverflow Environment 418

8.8.1 Don River Flow and Water Quality Data 418 8.8.2 Metal Partitioning in River Flow System 419 8.8.3 Relation Between Partitioning

Parameters and Medium Characteristics 422 8.9 P/CN-Based Characterization of Media 423 8.10 Determination of Annual Pollutant Loads 424

8.10.1 NPDES Permit 424 8.10.2 Dry- and Wet-Weather Conditions 425 8.10.3 Methodology for Estimation of

Annual Loads 425 8.1 0.4 Application Results 428

8.11 Summary 434

9. SEDIMENT YIELD 436 9.1 Computation of Sediment Yield 437 9.2 Analytical Derivation 439

9.2.1 Coupling of SCS-CN Method With USLE 440 9.3 Application 446

9.3.1 Study Areas 446 9.3.2 Discussion of Results 447

Appendix A: SCS-CN Theory for S Including Ia 457

Appendix B: Marquardt Algorithm 463

Appendix C: Analytical Derivation For Wave Characteristics 468

Appendix D: Universal Soil Loss Equation 479

References 481

Author Index 500

Subject Index 505

xii

PREFACE

The Soil Conservation Service (SCS) curve number (CN) method is one of the most popular methods for computing the runoff volume from a rainstorm. It is popular because it is simple, easy to understand and apply, and stable, and accounts for most of the runoff producing watershed characteristics, such as soil type, land use, hydrologic condition, and antecedent moisture condition. The SCS-CN method was originally developed for its use on small agricultural watersheds and has since been extended and applied to rural, forest and urban watersheds. Since the inception of the method, it has been applied to a wide range of environments. In recent years, the method has received much attention in the hydrologic literature.

The SCS-CN method was first published in 1956 in Section-4 of the National Engineering Handbook of Soil Conservation Service (now called the Natural Resources Conservation Service), U. S. Department of Agriculture. The publication has since been revised several times. However, the contents of the methodology have been nonetheless more or less the same. Being an agency methodology, the method has not passed through the process of a peer review and is, in general, accepted in the form it exists. Despite several limitations of the method and even questionable credibility at times, it has been in continuous use for the simple reason that it works fairly well at the field level.

Recent contributions have significantly enhanced the understanding of the SCS­CN method and consequently its application potential. In the simplest form, the fundamental proportionality concept of the method relates the two orthogonal hydrological processes of surface water and ground water and the other hypothesis relates to the atmospheric process. Qualitatively, the method broadly integrates all the three major processes of the hydrologic cycle; and therefore it can form one of the fundamental concepts of hydrology. Thus, there is a need to have another look at the SCS-CN method and highlight its potential for applications to perform hydrological tasks other than those originally intended. This text book is aimed at presenting an up-to-date account of the SCS-CN method and clarify its potential for practical applications.

The subject matter of the book is divided into nine chapters. Chapter 1 presents a brief introduction of rainfall-runoff modeling and presents elements of catchment, precipitation, interception, surface detention and depression storage, evaporation, infiltration, runoff, and the runoff hydrograph. The chapter is concluded with a discussion of the scope of the SCS-CN concept in hydrology. Providing a historical background of the SCS-CN method, Chapter 2 discusses the factors affecting the curve number (CN), the determination of CN, the use of NEH-4 tables, sensitivity analysis, advantages and limitations of the SCS-CN method, and application to distributed watershed modeling.

An analytical derivation of the SCS-CN method is presented in Chapter 3. It focuses on an analytical derivation of the Mockus and other methods, generalization of the Mockus method, implication of the generalized Mockus method, characteristics of the SCS­CN and Mockus methods, functional behavior of the existing and modified SCS-CN methods, significance of the proportional equality, antecedent moisture conditions, and the SCS-CN concept as an alternative to power law. Chapter 4 discusses a determination of'S' using the volumetric concept encompassing an analytical derivation, verification of the existing AMC criteria, determination of S, use of NEH-4 tables and advantages and limitations of the modified model.

xiii

Chapter 5 deals with determination of 'S' using physical principles, involving Fokker-Planck equation of infiltration, description of S, SIP relations for the modified model and determination of D, from universal soil loss equation. Simulation of infiltration and runoff hydrographs is dealt with in Chapter 6, with particular emphasis on SCS-CN-based infiltration and runoff models and application of infiltration and runoff models. Chapter 7 presents long-term hydrologic simulation. It presents hydrologic models of Williams and LaSeur, Hawkins, Pandit and Gopalkrishnan, and Mishra and others. Then, it discusses rainfall-excess computation, soil moisture budgeting, catchment routing, and baseflow computation. The chapter is concluded with a discussion of the application of the modified SCS-CN method and variations thereof.

Chapter 8 dwells upon transport of pollutants in urban watersheds. It discusses heavy metals, metal partitioning, metal transport, SCS-CN analogy for metal partitioning, application of wave analogy, application of SCS-CN analogy to metal partitioning in rainfall-runoff environment, snowmelt environment and riverflow environment, PCN-based characterization of media, and determination of annual pollutant loads. The last Chapter 9 deals with sediment yield. It presents an analytical derivation of an SCS-CN based sediment yield model and discusses its coupling with the Universal Soil Loss Equation. The chapter is concluded with a discussion of its application to several watersheds.

It is hoped that this book will be useful to agricultural scientists, agricultural and civil engineers, environmental engineers, forest and range scientists, as well as watershed managers. It will also be useful to college students and faculty members engaged in environment and water related studies.

This book would not have been possible were it not for the efforts and contributions of the USDA-SCS scientists and engineers who conceived the basic ideas in the first place and wrote the NEH-Section 4. The authors are therefore deeply grateful to the USDA-SCS. The authors also had many fruitful and enlightening discussions with their students, colleagues and friends working in the area of agricultural hydrology and watershed management and are thankful to them for these discussions. Finally, the authors would like to express their gratitude to their families for their support and understanding throughout this book project. Without their support the book would not come to fruition and it is therefore dedicated to them.

xiv

S. K. Mishra National Institute of Hydrology Roorkee, Uttaranchal, India

V. P. Singh Louisiana State University Baton Rouge, Louisiana, U.S. A.

A'

List of Symbols

coefficient of K-e, regression equations, and Singh and Yu model; coefficient of w-e relation; catchment or plot area, a parameter of the Green-Ampt model, a hydrologic soil group; albedo;

A" a constant of the Philip equation; ABFI antecedent baseflow index; AMC antecedent moisture condition; AMC I AMC corresponding to dry condition; AMC II AMC corresponding to normal condition; AMC IIIAMC corresponding to wet condition; API antecedent precipitation index; AT total catchment area; Aw total wetted area of the catchment; b parameter of the Mockus (1949) method,

a parameter rainfall depth-duration and regressions equations, an exponent of the modified Kostiakov model;

B a parameter of the Green-Ampt model, top width of the channel, a hydrologic soil group;

B' Bowen ratio; BD bulk density; c wave celerity,

A

c c

CEC CH ck CN

CN CN0

CNt Cr CT d

a coefficient of equation (1.72);

dimensionless wave celerity; runoff factor, a coefficient of the Meyer equation, a parameter of the Green-Ampt model, an empirical parameter, Chezy coefficient, Courant number, weir coefficient, a hydrologic soil group; ratio of cation-exchange capacity of clay to the % clay; a nondimensional quantity in Jensen-Raise method; kinematic wave celerity; curve number;

an average value of CN; curve number at time t = 0; curve number at time t; a coefficient related to catchment storage in equation (1.77); temperature coefficient; drainage density,

XV

D

DCIA DRH D. e

E

Ep ER ERH

Brooks-Corey pore-size distribution index; moisture diffusivity, duration of unit hydro graph, cell Reynold's number, a hydrologic soil group; directly connected impervious area; direct runoff hydrograph; soil depth above impeding layer; void ratio, an exponential; potential evaporation rate or volume, error; vapour pressure of the overlying air; mass transfer evaporation; net evaporation rate; saturation vapour pressure of the air at the mean monthly air temperature; pan evaporation; effective rainfall; effective rainfall hyetograph; saturation vapour pressure; saturation vapour pressure at the mean maximum and minimum

temperatures, respective! y; infiltration rate; minimum infiltration rate; initial infiltration rate; a function of horizontal wind speed; cumulative infiltration; cumulative dynamic portion of total infiltration; cumulative static portion of total infiltration; gravitational acceleration; some function; specific gravity of the medium; gauge height or flow depth; total potential head; Brooks-Corey bubling pressure head; capillary potential at the wetting front; Green-Ampt effective wetting front suction; matric suction; reference gauge height; instantaneous unit hydrograph; rainfall intensity, an imaginary unit; inflow, net inflow of water infiltrated into the ground, heat index in Tomthwaite formula, percent imperviousness; initial abstraction;

xvi

ie effective rainfall intensity; Ii and Ii_1indices for jth and (j-l)th days, respectively, in equation (1.82); i0 uniform rainfall intensity; IUH instantaneous unit hydrograph; j an integer; J annual temperature efficiency index; k hydraulic conductivity,

K

n

N

NEH-4 0 Oc o. p

p

p P. pC PD PDd Pe

coefficient of rainfall depth-duration-frequency relation; ratio of evaporating foliage surface to its horizontal projection, storage coefficient, a recession factor in equation (1.82); compactness ratio; form ratio; hydraulic conductivity;

average hydraulic conductivity; hydraulic conductivity at 80 ;

saturated hydraulic conductivity; pan coefficient; total water loss, length of the spillway crest; heat of vaporization; length from outlet to the centroid of the watershed; interception loss; exponent of K-8 and rainfall intensity-duration relations, exponent of w-e power relation, antecedent moisture; a nondimensional number; soil porosity, Manning's roughness, number of reservoirs in Nash model; an integer, an empirical parameter; National Engineering Handbook, Section 4; outflow; controlled reservoir outflow; uncontrolled reservoir outflow; hydraulic pressure, atmospheric pressure, ratio of mean daytime hours for a given month to the total daytime

hours; cumulative rainfall depth;

an average value of cumulative rainfall depth; annual rainfall; percent clay; particle density; number of people per hectare; cumulative effective rainfall depth;

xvii

PET pOM pS p5 q Q Q Q.

r. RH r, s

Sabs

s~N scs sd SH si s~ SMI So

So

s~ Sr

Sr(atm)

s, ST Sv

potential evapotranspiration; percent organic matter; percent sand; 5-d antecedent rainfall; discharge; cumulative direct surface runoff;

an average value of the cumulative direct surface runoff; annual runoff, net energy advected into the water body; long wave radiation loss by the water body; energy expended in the evaporation process, equilibrium flow rate; extra-terrestrial radiation; sensible heat transferred from water body to the atmosphere by

convection and conduction; incoming energy; reference discharge per unit width; energy expenditure; peak flow; global radiation; increase in energy stored in the water body; incremental direct runoff; radius of the capillary tube; hydraulic radius of the channel cross-section; aerodynamic resistance to vapor and heat transfer; relative humidity; bulk surface resistance, a function of leaf area index; potential maximum retention, storage space available in the soil column for water retention; absolute potential maximum retention;

variance of CN;

Soil Conservation Service; depression storage; S-hydrograph; interception storage depth;

variance of A.; soil moisture index; potential storage space available in the soil column for water

retention; channel bed slope;

variance of Q;

degree of saturation; atmospheric degree of saturation; soil sorptivity; total storage space available for water loss; storage capacity of vegetation for the projected area of the canopy;

xviii

SVL s2

X

t

soil-vegetation-land use complex;

variance of x;

time coordinate, storm duration;

non-dimensional time coordinate; time of concentration, a time parameter; effective storm duration; time to ponding; time of rise; time period, mean daily temperature;

T. overlying air temperature; Tb time-base of an infiltration decay curve; T L and t1 time lag; Tmax and Tmin maximum and minimum temperatures, respectively; TN temperature of the Nth month; T, storm duration,

v

Yo

v. Va(atm)

v

Vw

Vw(evap)

w

x y y

z, and z a

water surface temperature; intercept of temperature axis; time lags; daily consumptive use factor; unit hydrograph; Darcy velocity, uniform flow velocity; mean flow velocity; volume of air; volume of atmospheric air; total volume of soil column, reservoir storage; volume of voids; volume of solids, equivalent depth of depression storage; volume of water; volume of evaporated water; wind speed, an index of rainfall abstractions; wind speed at 1 m height; independent variable of regression equation, space coordinate; xi and xi ith and jth variables of x; an average value of variable x; dependent variable of regression equation; slope of the watershed;

space coordinates, " stands for non-dimensional; angle of contact of the meniscus, infiltration decay factor

xix

E

a coefficient of the modified Kostiakov model; a coefficient of equation (1.69), decay constant of depression storage;

dimensionless frequency factor;

logarithmic decrement; a partial differential operator; slope of the curve of saturated vapour pressure against temperature, change in the variable; a measure of accuracy, weighting factor in Muskingum equation; total potential head; hydrostatic pressure immediately below the interface; hydrostatic pressure at free water surface; an index of rainfall abstractions; psychrometric constant; Gamma function; heat of vaporization, hydraulic length of the watershed; mean overland flow length; initial abstraction coefficient;

an average value of the initial abstraction coefficient; dynamic viscosity; moisture content; perturbation of 8 about 80 ;

8 at any time level; initial moisture content; 8 at saturation; moisture content at time, t = T intrinsic sorpti vity; water or fluid density; air density; negative pressure; Green-Ampt effective wetting front suction; negative pressure at 80 ;

average negative pressure;

h at any time level; surface tension;

& dimensionless wave number; Q non-dimensional wave arnlitude; X characteristic depth. Subscripts I, II, III correspond to AMC I, AMC II, and AMC III, respectively; Subscripts A, B, C, D correspond to hydrologic soil group A, B, C, D, respectively; Superscript * represents normalised values of the variable.

XX