Deterministic methods in systems hydrology

326 Pages·2003·3.281 MB·English

by  O'Kane, J. P., Dooge, James

DETERMINISTICMETHODSINSYSTEMSHYDROLOGY
IHE DELFT LECTURE NOTE SERIES
Deterministic Methods in
Systems Hydrology
JAMES C.I. DOOGE
J. PHILIP O’KANE
A.A.BALKEMAPUBLISHERS/lisse/abingdon/exton(pa)/tokyo
Dooge, James.
Deterministic methods in systems hydrology / J.C.I. Dooge, J.P.J. O'Kane.
p. cm. -- (IHE lecture note series)
Includes bibliographical references.
ISBN 90-5809-391-3 --ISBN (invalid) 90-5809-392-2 (pbk.)
1. Hydrology--Mathematical models. 2. Hydrologic models. I. Dooge, James. II.
O'Kane, J. P., 1943- III. Title. IV. Series.
GB656.2.M33D66 2003
551.49'01'5118--dc21
2003042844
Typesetting: CharonTecPvt.Ltd,Chennai,India.
Printed in the Netherlands by Wilco, Amersfoort
©2003Swets&ZeitlingerB.V.,Lisse
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ISBN9058093913 hardboundedition
ISBN9058093922 paperbackedition
To the memory of Eamonn Nash

VII
Table of Contents
PREFACE XIII
1 THESYSTEMSVIEWPOINT 1
1.1 Natureofsystemsapproach 1
1.2 Systemsterminology 3
1.3 Lineartime-invariantsystems 7
1.4 Discreteformsofconvolutionequation 13
1.5 Suggestionsforfurtherreading 15
2 NATUREOFHYDROLOGICALSYSTEMS 17
2.1 Thehydrologicalcycleasasystem 17
2.2 Unithydrographmethods 20
2.3 Identificationofhydrologicalsystems 26
2.4 Simulationofhydrologicalsystems 28
3 SOMESYSTEMSMATHEMATICS 35
3.1 Matrixmethods 35
3.2 Optimisation 37
3.3 Orthogonalfunctions 41
3.4 Applicationtosystemsanalysis 45
3.5 FourierandLaplacetransforms 47
3.6 Differentialequations 53
3.7 Referencesonsystemsmathematics 55
4 BLACK-BOXANALYSISOFDIRECTSTORMRUNOFF 59
4.1 Theproblemofsystemidentification 59
4.2 Outlineofnumericalexperimentation 61
4.3 Directalgebraicmethodsofidentification 64
4.4 Optimisationmethodsofunithydrographderivation 67
4.5 Unithydrographderivationthroughz-transforms 71
4.6 Unithydrographderivationbyharmonicanalysis 74
4.7 UnithydrographderivationbyMeixneranalysis 76
4.8 Overallcomparisonofidentificationmethods 78
VIII Deterministicmethodsinsystemshydrology
5 LINEARCONCEPTUALMODELSOFDIRECTRUNOFF 81
5.1 Syntheticunithydrographs 81
5.2 Comparisonofconceptualmodels 85
5.3 Cascadesoflinearreservoirs 88
5.4 Limitingformsofcascademodels 94
6 FITTINGTHEMODELTOTHEDATA 101
6.1 Useofmomentmatching 101
6.2 Effectofdataerrorsonconceptualmodels 103
6.3 Fittingone-parametermodels 105
6.4 Fittingtwo-andthree-parametermodels 110
6.5 Regionalanalysisofdata 118
7 SIMPLEMODELSOFSUBSURFACEFLOW 127
7.1 Flowthroughporousmedia 127
7.2 Steadypercolationandsteadycapillaryrise 133
7.3 Formulaeforpondedinfiltration 137
7.4 Simpleconceptualmodelsofinfiltration 148
7.5 Effectofthewatertable 152
7.6 Groundwaterstorageandoutflow 155
8 NON-LINEARDETERMINISTICMODELS 163
8.1 Non-linearityinhydrology 163
8.2 Theproblemofoverlandflow 169
8.3 Linearisationofnon-linearsystems 178
8.4 Non-linearblack-boxanalysis 188
8.5 Conceptofuniformnon-linearity 192
PROBLEMSET 201
Runoffprediction 201
Systemidentification 201
Unithydrographderivation 202
Conceptualmodels 204
Comparingmodels 205
ACKNOWLEDGEMENTS 207
ENCOMIUM 209
REFERENCES 211
AppendixA—PICOMO:AProgramfortheIdentificationofConceptualModels 225
AppendixB—InverseProblemsareIII-Posed 261
AppendixC—TheNon-LinearityoftheUnsaturatedZone 273
AppendixD—UnsteadyFlowinOpenChannels 287
INDEX 303
IX
List of Figures
1.1 Theconceptofsystemoperation. 3
2.1 Thehydrologicalcycle. 18
2.2 Blockdiagramofthehydrologicalcycle. 18
2.3 Simplifiedcatchmentmodel. 19
2.4 Modelsofhydrologicalprocesses. 20
2.5 Superpositionofunithydrographs. 21
2.6 Hydrographresponse. 23
2.7 Effectiveprecipitation. 25
2.8 Classicalmethodsofunithydrographderivation. 26
2.9 Typicalregressionmodel. 30
2.10 Coaxialcorrelationdiagram(Becker,1996). 31
2.11 StanfordModelMarkIV. 33
2.12 Schematicdiagramoftheoverallmodelofthehydrologicalcycle. 34
4.1 Shapeofunithydrographinnumericalexperimentation. 62
4.2 Inputshapes. 62
4.3 Therelationshipbetweenoptimisationmethods. 69
4.4 Theprocedureintransformmethods. 71
5.1 Developmentofsyntheticunithydrographs. 84
5.2 Comparisonofconceptualmodelswith2parameters. 87
5.3 Limitingformsofunimodalcascade. 93
5.4 SimulationofGUH(GeomorphicUnitHydrograph). 93
5.5 LimitingformforU-shapedinflow. 98
6.1 One-parameterconceptualmodels. 107
6.2 Shapefactorcomparisonofconceptualmodels. 111
6.3 Themodelinclusiongraph. 115
6.4 ThemodelinclusiongraphwiththeRMSerrorsfortheBigMuddy 117
Riverdata(A).
6.5 ThemodelinclusiongraphwiththeRMSerrorsfortheAshbrook 117
Catchmentdata(B).
6.6 Thegeneralsyntheticscheme. 119
6.7 Shapefactorplottingofregionaldata. 120
6.8 Typicalunithydrographparameters. 121