Deterministic Methods in Systems Hydrology - Chapter 1

IHE DELFT LECTURE NOTE SERIES Deterministic Methods in Systems Hydrology JAMES C.I. DOOGE J. PHILIP O’KANE A.A. BALKEMA PUBLISHERS / LISSE / ABINGDON / EXTON (PA) / TOKYO - 1 - Cover Design: Typesetting: Charon Tec Pvtt. Ltd, Chennai. India. PrintedintheNetherlands @2003 Swets4. Zeitlinger B.V.,Lisse All rights reserved. No part of this publication or the information contained herein may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, by photocopying, recording or otherwise, eithout written prior permission from the publishers. Although all care is taken to ensure the integrity and quality of this publication and the information herein, noresponsibility is assumed by the publishers nor the author for any damage to property or persons as a result of operation or use of this publication and/or the information contained rerein. Published by: A.A. Balkema Publishers, amember of Swets & Zeitlinger Publishers www.balkema.nl and www.szp.swetz.nl ISBN 90 5809 391 3 hardbound edition ISBN 90 5809 392 2 paperback edition To the memory of Eamonn Nash - 2 - TableofContents PREFACE XIII 1 THE SYSTEMS VIEWPOINT 1 11 Nature of systems approach 1 1.2 Systems terminology 3 1.3 Linear time-invariant systems 7 1.4 Discrete forms of convolution equation 13 1.5 Suggestions for further reading 15 2 NATURE OF HYDROLOGICAL SYSTEMS 17 2.1 The hydrological cycle as a system 17 2.2 Unit hydrograph methods 20 2.3 Identification of hydrological systems 26 2.4 Simulation of hydrological systems 28 3 SOME SYSTEMS MATHEMATICS 35 3.1 Matrix methods 35 3.2 Optimisation 37 3.3 Orthogonal functions 41 3.4 Application to systems analysis 45 3.5 Fourier and Laplace transforms 47 3.6 Differential equations 53 3.7 References on systems mathematics 55 4 BLACK-BOX ANALYSIS OF DIRECT STORM RUNOFF 59 4.1 The problem of system identification 59 4.2 Outline of numerical experimentation 61 4.3 Direct algebraic methods of identification 64 4.4 Optimisation methods of unit hydrograph derivation 67 4.5 Unit hydrograph derivation through z-transforms 71 4.6 Unit hydrograph derivation by harmonic analysis 74 4.7 Unit hydrograph derivation by Meixner analysis 76 4.8 Overall comparison of identification methods 78 5 LINEAR CONCEPTUAL MODELS OF DIRECT RUNOFF 81 5.1 Synthetic unit hydrographs 81 5.2 Comparison of conceptual models 85 5.3 Cascades of linear reservoirs 88 5.4 Limiting forms of cascade models 94 6 FITTING THE MODEL TO TUE DATA 101 6.1 Use of moment matching 101 6.2 Effect of data errors on conceptual models 103 6.3 Fitting one-parameter models 105 6.4 Fitting two- and three-parameter models 110 6.5 Regional analysis of data 118 - 3 - 7 SIMPLE MODELS OF SUBSURFACE FLOW 127 7.1 Flow through porous media 127 7.2 Steady percolation and steady capillary rise 133 7.3 Formulae for ponded infiltration 137 7.4 Simple conceptual models of infiltration 148 7.5 Effect of the water table 152 7.6 Groundwater storage and outflow 155 8 NON-LINEAR DETERMINISTIC MODELS 163 8.1 Non-linearity in hydrology 163 8.2 The problem of overland flow 169 8.3 Linearisation of non-linear systems 178 8.4 Non-ling black-box analysis 188 8.5 Concept of uniform non-linearity 192 PROBLEM SET 201 Runoff prediction System identification 201 System identification 201 Unit hydrograph derivation 202 Conceptual models 204 Comparing models 205 ACKNOWLEDGEMENTS 207 ENCOMIUM 209 REFERENCES 211 Appendix A - PICOMO: A Program for the Identification of Conceptual 225 Appendix B - Inverse Problems are III-Posed 261 Appendix C - The Non-Linearity of the Unsaturated Zone 273 Appendix D – Unsteady Flow in Open Channels 287 INDEX 303 - 4 - ... - tailieumienphi.vn