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 xiii List of Symbols XV 1 INTRODUCTION 1 1.1 Rainfall-Runoff Modeling 1 1.2 Catchment Characteristics 2 1.2.1 Catchment Length, Width, and Slope 2 1.2.2 Catchment Area 3 1.2.3 Catchment Shape 3 1.2.4 Catchment Relief 3 1.2.5 Linear Measures 3 1.2.6 Drainage Patterns 4 1.3 Precipitation 4 1.3.1 Quantitative Description of Rainfall 4 1.3 .2 Temporal and Spatial Variation of Rainfall 5 1.3.3 Average Rainfall over an Area 6 1.3.4 Rainfall Storm Analysis 8 1.4 Interception 31 1.5 Surface Detention and Depression Storage 32 1.6 Evaporation 33 1.6.1 Water Budget Method 33 1.6.2 Mass Transfer Method 34 1.6.3 Energy Budget Method 36 1.6.4 Combination Method 37 1.6.5 Pan Evaporation 39 1.6.6 Evapotranspiration 40 1. 7 Infiltration 44 1. 7.1 Mechanism of Water Retention by Soil 45 1. 7.2 Retention Curves 46 1. 7.3 Darcy's Law 47 1. 7.4 Transport of Soil Moisture 47 I. 7.5 Measurement of Infiltration 50 1. 7.6 Conceptual Infiltration Models 51 1. 7. 7 Infiltration Indices 56 1.8 Runoff 58 1.8.1 Modes of Runoff Generation 58 1.8.2 Runoff Concentration 60 1.8.3 Time of Concentration 61 1.8.4 Lag Time 63 1.8.5 How in Stream Channels 65 1.8.6 Rating Curve 65 1.8.7 Antecedent Moisture 66 1.9 Determination of Runoff Hydrograph 67 1.9.1 Unit Hydrograph (UH) 67 1. 9.2 Channel and Reservoir Routing 71 vii 1.10 Scope of the SCS-CN Concept in Hydrology 79 1.10.1 Computation of Infiltration and DSRO Volumes 79 1.1 0.2 Computation of Infiltration Rates 79 1.10.3 Time-Distributed Event-Based Hydrologic Simulation 80 1.10.4 Long-Term Hydrologic Simulation 82 1.1 0.5 Transport of Urban Pollutants 82 1.10.6 Sediment Yield 83 1.11 Organization of the Book 83 2. SCS-CN METHOD 84 2.1 Historical Background 84 2.1.1 Experimental Watersheds and Infiltration Studies 84 2.1.2 Development of Rainfall-Runoff Methods 85 2.2 SCS-CN Method 85 2.3 Factors Affecting CN 88 2.3.1 Soil Type 89 2.3.2 Land Use 93 2.3.3 Hydrologic Condition 99 2.3.4 Agricultural Management Practices 100 2.3.5 Antecedent Moisture Condition 101 2.3.6 Initial Abstraction and Climate 104 2.3.7 Rainfall Intensity and Duration and Turbidity 105 2.4 Determination of Curve Number 105 2.4.1 Development of CN for Complexes 108 2.4.2 Rationale of Curve Number 108 2.5 Use of NEH -4 Tables for SCS-CN Application 108 2.6 Sensitivity Analysis 114 2.6.1 First-Order Sensitivity Analysis 115 2.6.2 Conventional Analysis 118 2. 7 Advantages and Limitations of the SCS-CN Method 129 2.8 SCS-CN Application to Distributed Watershed Modeling 130 2. 8.1 A vail ability of Data 130 2.8.2 Moglen Method 131 2.8.3 Advantages and Limitations of the Moglen Method 136 2.8.4 Modified Moglen Method 136 2.8.5 Features of the Modified Moglen Method 143 2.8.6 Advantages and Limitations of the Modified Moglen Method 145 3. ANALYTICAL DERIVATION OF THE SCS-CN METHOD 147 3.1 Early Rainfall-Runoff Methods 147 3.2 Analytical Derivation of the Mockus and Other Methods 149 3.2.1 Derivation of Mockus Method 149 Vlll 3.2.2 Derivation of Zoch Model 151 3.2.3 Derivation of Depression and Interception Storage Models 152 3.3 Generalization of the SCS-CN Method 153 3. 3.1 Generalization of the Mockus Method 153 3.3.2 Statistical Derivation of the SCS-CN Method 154 3.3.3 SCS-CN Derivation From the First-Order Hypothesis 159 3.3.4 Derivation of SCS-CN Proportional Equality 160 3.3.5 Non-Linear Derivation of SCS-CN Method 161 3.3.6 SCS-CN Derivation Including Initial Abstraction 163 3.3.7 Development of an Initial Abstraction Model 165 3.4 Implication of Generalization of the Mockus Method 167 3.4.1 Modification of the SCS-CN Method 167 3.4.2 General Form of SCS-CN Model 167 3.5 Characteristics of the SCS-CN and Mockus Methods 168 3.5.1 Mockus Method 168 3.5.2 SCS-CN Method 169 3.5.3 Numerical Comparison of Methods 170 3.5.4 Models Performance on Field Data 173 3.6 Functional Behaviour of the Existing and Modified SCS-CN Methods 179 3.6.1 Existing SCS-CN Method 179 3.6.2 Modified SCS-CN Method 184 3. 7 Significance of the Proportional Equality 186 3.7.1 Soil Porosity 187 3. 7.2 Proportional Equality 187 3.7.3 Significance ofCN 188 3.7.4 Another Interpretation of S-CN Mapping Relation 190 3.8 Antecedent Moisture Conditions 191 3.8.1 Variation of CN With AMC 194 3.8.2 CN Derivation From Rainfall-Runoff Data 196 3.9 SCS-CN Concept as an Alternative to Power Law 200 4. DETERMINATION OF'S' USING VOLUMETRIC CONCEPT 205 4.1 Analytical Derivation 205 4.1.1 Equivalence Between SCS-CN Proportionality and C= S, Concepts 206 4.1.2 Effect of Antecedent Moisture Condition 207 4.1.3 Effect of Initial Abstraction 209 4.1.4 Effect of Fe 215 4.1.5 Effect of Storm Duration, Rainfall Intensity, and Turbidity 221 ix 4.1.6 Effect of Agricultural Management Practices 224 4.2 Verification of Existing AMC Criteria 225 4.3 Determination of S 226 4.3.1 Homogeneous Gauged Watersheds 226 4.3.2 Heterogeneous Gauged Watersheds 227 4.3.3 Ungauged Watersheds 228 4.4 Use ofNEH-4 Tables 229 4.4.1 Workability of Model4 229 4.4.2 Inverse Computation of Fe From NEH-4 CN-Values 232 4.4.3 Verification of AMCCriteria For Fe-Values 235 4.4.4 Applicability of NEH-4 Tables to Existing and General Models 235 4.4.5 Condensation ofNEH-4 Table 239 4.5 Advantages and Limitations of the Modified Model 243 5. DETERMINATION OF'S' USING PHYSICAL PRINCIPLES 244 5.1 Fokker-Planck Equation Of Infiltration 245 5.2 Description of S 251 5.2.1 Use of S, And Kh 251 5.2.2 Use of Kh-8 And \lf-8 Relations 252 5.2.3 Use of Intrinsic Sorptivity 262 5.2.4 Vertical Infiltration 263 5.2.5 Kinematic Wave 265 5.3 SIP Relations for the Modified Model 265 5.3.1 Effect of Fe On Si 267 5.3.2 Effect of M On Si 268 5.3.3 Effect of A On Si 273 5.3.3 Effect of P On Si 274 5.4 Determination of D, From Universal Soil Loss Equation 274 6. INFILTRATION AND RUNOFF HYDROGRAPH SIMULATION 278 6.1 SCS-CN-Based Infiltration and Runoff Models 278 6.2 Application Of Infiltration and Runoff Models 282 6.2.1 Infiltration Data 282 6.2.2 Ars Watersheds 282 6.2.3 Error Criteria for Simulation 283 6.2.4 Model Application to Infiltration Data 284 6.2.5 Model Application to Rainfall-Runoff Data 291 7. LONG-TERM HYDROLOGIC SIMULATION 323 7 .I SCS-CN-Based Hydrologic Models 324 7.1.1 Williams-Laseur Model 324 7.1.2 Hawkins Model 329 7 .1.3 Pandit and Gopalakrishnan Model 333 7 .1.4 Mishra et al. Model 334 X 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