Rainfall-Runoff Modelling Rainfall-Runoff Modelling The Primer SECOND EDITION Keith Beven Lancaster University, UK This edition first published 2012 © 2012 by John Wiley & Sons, Ltd Wiley-Blackwell is an imprint of John Wiley & Sons, formed by the merger of Wiley’s global Scientific, Technical and Medical business with Blackwell Publishing. Registered office: John Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK Editorial offices: 9600 Garsington Road, Oxford, OX4 2DQ, UK The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK 111 River Street, Hoboken, NJ 07030-5774, USA For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com/wiley-blackwell. The right of the author to be identified as the author of this work has been asserted in accordance with the UK Copyright, Designs and Patents Act 1988. 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Library of Congress Cataloging-in-Publication Data Beven, K. J. Rainfall-runoff modelling : the primer / Keith Beven. – 2nd ed. p. cm. Includes bibliographical references and index. ISBN 978-0-470-71459-1 (cloth) 1. Runoff–Mathematical models. 2. Rain and rainfall–Mathematical models. I. Title. GB980.B48 2011 551.488–dc23 2011028243 A catalogue record for this book is available from the British Library. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Set in 10/12pt Times by Thomson Digital, Noida, India First Impression 2012 For the next generation of hydrological modellers Contents Preface to the Second Edition xiii About the Author xvii List of Figures xix 1 Down to Basics: Runoff Processes and the Modelling Process 1 1.1 Why Model? 1 1.2 How to Use This Book 3 1.3 The Modelling Process 3 1.4 Perceptual Models of Catchment Hydrology 6 1.5 Flow Processes and Geochemical Characteristics 13 1.6 Runoff Generation and Runoff Routing 15 1.7 The Problem of Choosing a Conceptual Model 16 1.8 Model Calibration and Validation Issues 18 1.9 Key Points from Chapter 1 21 Box 1.1 The Legacy of Robert Elmer Horton (1875–1945) 22 2 Evolution of Rainfall–Runoff Models: Survival of the Fittest? 25 2.1 The Starting Point: The Rational Method 25 2.2 Practical Prediction: Runoff Coefficients and Time Transformations 26 2.3 Variations on the Unit Hydrograph 33 2.4 Early Digital Computer Models: The Stanford Watershed Model and Its Descendants 36 2.5 Distributed Process Description Based Models 40 2.6 Simplified Distributed Models Based on Distribution Functions 42 2.7 Recent Developments: What is the Current State of the Art? 43 2.8 Where to Find More on the History and Variety of Rainfall–Runoff Models 43 2.9 Key Points from Chapter 2 44 Box 2.1 Linearity, Nonlinearity and Nonstationarity 45 Box 2.2 The Xinanjiang, ARNO or VIC Model 46 Box 2.3 Control Volumes and Differential Equations 49 viii Contents 3 Data for Rainfall–Runoff Modelling 51 3.1 Rainfall Data 51 3.2 Discharge Data 55 3.3 Meteorological Data and the Estimation of Interception and Evapotranspiration 56 3.4 Meteorological Data and The Estimation of Snowmelt 60 3.5 Distributing Meteorological Data within a Catchment 61 3.6 Other Hydrological Variables 61 3.7 Digital Elevation Data 61 3.8 Geographical Information and Data Management Systems 66 3.9 Remote-sensing Data 67 3.10 Tracer Data for Understanding Catchment Responses 69 3.11 Linking Model Components and Data Series 70 3.12 Key Points from Chapter 3 71 Box 3.1 The Penman–Monteith Combination Equation for Estimating Evapotranspiration Rates 72 Box 3.2 Estimating Interception Losses 76 Box 3.3 Estimating Snowmelt by the Degree-Day Method 79 4 Predicting Hydrographs Using Models Based on Data 83 4.1 Data Availability and Empirical Modelling 83 4.2 Doing Hydrology Backwards 84 4.3 Transfer Function Models 87 4.4 Case Study: DBM Modelling of the CI6 Catchment at Llyn Briane, Wales 93 4.5 Physical Derivation of Transfer Functions 95 4.6 Other Methods of Developing Inductive Rainfall–Runoff Models from Observations 99 4.7 Key Points from Chapter 4 106 Box 4.1 Linear Transfer Function Models 107 Box 4.2 Use of Transfer Functions to Infer Effective Rainfalls 112 Box 4.3 Time Variable Estimation of Transfer Function Parameters and Derivation of Catchment Nonlinearity 113 5 Predicting Hydrographs Using Distributed Models Based on Process Descriptions 119 5.1 The Physical Basis of Distributed Models 119 5.2 Physically Based Rainfall–Runoff Models at the Catchment Scale 128 5.3 Case Study: Modelling Flow Processes at Reynolds Creek, Idaho 135 5.4 Case Study: Blind Validation Test of the SHE Model on the Slapton Wood Catchment 138 5.5 Simplified Distributed Models 140 5.6 Case Study: Distributed Modelling of Runoff Generation at Walnut Gulch, Arizona 148 5.7 Case Study: Modelling the R-5 Catchment at Chickasha, Oklahoma 151 5.8 Good Practice in the Application of Distributed Models 154 5.9 Discussion of Distributed Models Based on Continuum Differential Equations 155 5.10 Key Points from Chapter 5 157 Box 5.1 Descriptive Equations for Subsurface Flows 158 Contents ix Box 5.2 Estimating Infiltration Rates at the Soil Surface 160 Box 5.3 Solution of Partial Differential Equations: Some Basic Concepts 166 Box 5.4 Soil Moisture Characteristic Functions for Use in the Richards Equation 171 Box 5.5 Pedotransfer Functions 175 Box 5.6 Descriptive Equations for Surface Flows 177 Box 5.7 Derivation of the Kinematic Wave Equation 181 6 Hydrological Similarity, Distribution Functions and Semi-Distributed Rainfall–Runoff Models 185 6.1 Hydrological Similarity and Hydrological Response Units 185 6.2 The Probability Distributed Moisture (PDM) and Grid to Grid (G2G) Models 187 6.3 TOPMODEL 190 6.4 Case Study: Application of TOPMODEL to the Saeternbekken Catchment, Norway 198 6.5 TOPKAPI 203 6.6 Semi-Distributed Hydrological Response Unit (HRU) Models 204 6.7 Some Comments on the HRU Approach 207 6.8 Key Points from Chapter 6 208 Box 6.1 The Theory Underlying TOPMODEL 210 Box 6.2 The Soil and Water Assessment Tool (SWAT) Model 219 Box 6.3 The SCS Curve Number Model Revisited 224 7 Parameter Estimation and Predictive Uncertainty 231 7.1 Model Calibration or Conditioning 231 7.2 Parameter Response Surfaces and Sensitivity Analysis 233 7.3 Performance Measures and Likelihood Measures 239 7.4 Automatic Optimisation Techniques 241 7.5 Recognising Uncertainty in Models and Data: Forward Uncertainty Estimation 243 7.6 Types of Uncertainty Interval 244 7.7 Model Calibration Using Bayesian Statistical Methods 245 7.8 Dealing with Input Uncertainty in a Bayesian Framework 247 7.9 Model Calibration Using Set Theoretic Methods 249 7.10 Recognising Equifinality: The GLUE Method 252 7.11 Case Study: An Application of the GLUE Methodology in Modelling the Saeternbekken MINIFELT Catchment, Norway 258 7.12 Case Study: Application of GLUE Limits of Acceptability Approach to Evaluation in Modelling the Brue Catchment, Somerset, England 261 7.13 Other Applications of GLUE in Rainfall–Runoff Modelling 265 7.14 Comparison of GLUE and Bayesian Approaches to Uncertainty Estimation 266 7.15 Predictive Uncertainty, Risk and Decisions 267 7.16 Dynamic Parameters and Model Structural Error 268 7.17 Quality Control and Disinformation in Rainfall–Runoff Modelling 269 7.18 The Value of Data in Model Conditioning 274 7.19 Key Points from Chapter 7 274 Box 7.1 Likelihood Measures for use in Evaluating Models 276 Box 7.2 Combining Likelihood Measures 283 Box 7.3 Defining the Shape of a Response or Likelihood Surface 284 x Contents 8 Beyond the Primer: Models for Changing Risk 289 8.1 The Role of Rainfall–Runoff Models in Managing Future Risk 289 8.2 Short-Term Future Risk: Flood Forecasting 290 8.3 Data Requirements for Flood Forecasting 291 8.4 Rainfall–Runoff Modelling for Flood Forecasting 293 8.5 Case Study: Flood Forecasting in the River Eden Catchment, Cumbria, England 297 8.6 Rainfall–Runoff Modelling for Flood Frequency Estimation 299 8.7 Case Study: Modelling the Flood Frequency Characteristics on the Skalka Catchment, Czech Republic 302 8.8 Changing Risk: Catchment Change 305 8.9 Changing Risk: Climate Change 307 8.10 Key Points from Chapter 8 309 Box 8.1 Adaptive Gain Parameter Estimation for Real-Time Forecasting 311 9 Beyond the Primer: Next Generation Hydrological Models 313 9.1 Why are New Modelling Techniques Needed? 313 9.2 Representative Elementary Watershed Concepts 315 9.3 How are the REW Concepts Different from Other Hydrological