Statistical modelling in hydrology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester u.a.
Wiley
1994
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 412 S. graph. Darst. |
| ISBN: | 0471950165 |
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| 245 | 1 | 0 | |a Statistical modelling in hydrology |c Robin T. Clarke |
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Titel: Statistical modelling in hydrology
Autor: Clarke, Robin T.
Jahr: 1994
Contents
Preface xiii
Chapter 1 Some applications of statistical models in hydrology 1
1.1 Hydrological variability 1
1.2 Statistical models 5
1.3 Statistical models using explanatory variables 6
1.4 The random component e, 7
1.5 Parsimony in statistical model building 7
1.6 Some hydrological uses of statistical models 8
1.6.1 Estimating floods with ?-year return period 9
1.6.2 Extending streamflow records 9
1.6.3 Information transfer to sites without flow records 10
1.6.4 Simulation of flow sequences for water resource planning
and operation 10
1.6.5 Modelling rainfall sequences for soil moisture simulation 11
1.6.6 Short-term forecasting of flood levels and discharges 11
1.6.7 Exploration of characteristics of very large bodies of data,
to define small subsets useful as explanatory variables 11
1.6.8 Identification of possible instrument errors, and faulty
readings, where large quantities of hydrological
data are recorded automatically 12
1.7 Computational facilities for efficient fitting of statistical models 12
1.8 GENSTAT and MATLAB conventions used in this book 13
1.9 Customised packages for hydrological analysis 14
1.10 Expert systems 14
1.11 Geographical information systems 15
1.12 Future developments 15
References 16
Chapter 2 Exploring and summarising hydrological data sets 17
2.1 Measures of position and dispersion 17
2.2 Graphical procedures in data reduction 18
2.2.1 The box-and-whisker plot 18
viu Contents
2.2.2 Histograms 19
2.2.3 Cumulative frequency diagrams 22
2.2.4 Flow duration curves 25
2.2.5 Double mass curves 26
2.2.6 Contour plots 26
2.3 More general numerical summaries of data sets 27
2.4 Exploring relations between variables 29
2.4.1 Plotting using lagged variables 33
2.5 Alternative descriptors of a data sample: /-moments 34
2.6 The importance of graphical studies of residuals 36
References 36
Exercises and extensions ^(,
Chapter 3 Fitting distributions 39
3.1 The null model 39
3.2 The likelihood function 4O
3.3 Fitting log-normal distributions by maximum likelihood 42
3.3.1 The two-parameter log-normal distribution 43
3.3.2 The three-parameter log-normal distribution 47
3.4 Estimation by the method of moments 49
3.5 Fitting gamma distributions by maximum likelihood 50
3.5.1 The two-parameter gamma distribution 50
3.5.2 The three-parameter gamma distribution 54
3.6 Using the likelihood function to choose between the gamma and
log-normal distributions 55
3.7 Fitting the Gumbel distribution by maximum likelihood. 58
3.8 The Weibull distribution 63
3.9 The generalised extreme value distribution 67
3.10 The Wakeby distribution 7j
3.11 The precision of maximum-likelihood estimates 73
3.12 Confidence intervals for G-year floods: or more generally, quantiles 75
3.12.1 Confidence intervals using the central limit theorem 75
3.12.2 Likelihood-based confidence intervals 76
3.13 Assessing goodness of fit 70
3.13.1 Cumulative plots 70
3.13.2 Envelope curves 8q
3.14 Concluding remarks o-
References „,
Exercises and extensions ,,
Chapter 4 Linear relationships with explanatory variables 86
4.1 Principles of regression analysis o¿
4.2 Hydrological applications of linear regression analysis 87
4.2.1 The Thomas-Fiering model for the simulation of monthly
flow sequences 07
Contents ix
4.2.2 Representation of a flow rating curve by a polynomial 88
4.2.3 Fitting of sediment rating curves, giving sediment
concentration in terms of discharge 88
4.2.4 Estimating missing values in flow records 88
4.2.5 Régionalisation of mean annual floods 88
4.2.6 Calculation of unit hydrograph ordinates from storm runoff
( ) and effective rainfall (?) sequences 89
4.2.7 Models representing certain non-linear systems 89
4.2.8 Fitting surfaces 89
4.2.9 Quality control of hydrometeorological data 90
4.3 The basics of linear regression 91
4.4 Special case: simple linear regression 95
4.4.1 Example: linear regression between annual floods at two sites,
records of different lengths 95
4.4.2 Example: regression of annual runoff on annual rainfall:
Plynlimon experimental catchments 100
4.4.3 Example: comparison of linear regressions 106
4.4.4 Comparison of regressions using the dummy-variable
procedure 114
4.5 Weighted linear regression 119
4.6 Example: multiple linear regression 127
4.7 Multiple regression subject to linear constraints: the Muskingum method
of flood routing 133
4.8 Generalised linear regression models: residuals {e,} with known
variance-covariance matrix V 140
4.9 Influence, consistency and leverage 141
4.9.1 Leverage 143
4.9.2 Standardised residuals 144
4.9.3 Deletion residuals and Cook statistics 145
4.10 Checks on normality of residuals in regression 146
4.11 Transformations in regression analysis 150
4.12 Information transfer and extension of flow records 152
4.13 'Updating' regression analyses using additional data 153
4.14 Ridge regression 154
References ' 55
Exercises and extensions 155
Chapter 5 Non-linear statistical models 164
5.1 Non-linearity as a characteristic of parametric structure 164
5.2 Transformations to linear form 167
5.3 Fitting the Green-Ampt equation to data from an infiltrometer:
an example of a transformation which fails 167
5.4 Fitting the wind velocity profile: a linearising transformation which
succeeds (sometimes) 173
5.5 Non-linear fitting procedures for some standard models 183
5.5.1 Example: fitting the Horton infiltration law 185
x Contents
5.5.2 Example: fitting a line plus exponential to digester data 194
5.5.3 Fitting non-linear models to stomatal conductances 201
5.5.4 Using a logistic curve to describe soil moisture characteristic 202
5.6 Fitting standard non-linear curves to grouped data: tests for parallelism 205
References 207
Exercises and extensions 207
Chapter 6 Generalised linear models 209
6.1 Linear models and their generalisation 209
6.1.1 The variance function, scaled deviance, and deviance of
generalised linear models 210
6.2 Logistic regression 213
6.2.1 Example: surface runoff studies using minitraps 213
6.2.2 Estimation of logistic regression parameters by maximum
likelihood 217
6.2.3 Testing for the significance of logistic regression 221
6.2.4 The information matrix, and Wald tests 223
6.2.5 Interpretation of the coefficients ß, in logistic regression 224
6.2.6 Other applications of logistic regression 226
6.3 Regression with constant coefficient of variation: an extension of the
Thomas-Fiering model 229
6.3.1 Generalised linear model with gamma-distributed errors and 231
log link function
6.3.2 Estimation of the dispersion parameter ? 234
6.3.3 Generation of gamma-distributed pseudo-random variâtes 235
6.4 Other forms of generalised linear model 237
6.4.1 A generalised linear model with the response variable
Poisson distributed: occurrence of peak flows on Rio
Itajaí-Açú at Apiuna 237
6.4.2 An alternative method for modelling heterogeneous variance
in linear regression: monthly flows from Rio Lava Tudo
at Fazenda Mineira 240
6.5 Diagnostic methods for generalised linear models 250
6.6 Concluding remarks 251
References 252
Exercises and extensions 252
Chapter 7 Multivariate models 254
7.1 Models with multiple response variables 254
7.2 Missing data 256
7.2.1 Sequences with parts of years missing: use of censored data
in flood estimation 257
7.2.2 Data sequences with entire years missing: the Beale-Little
algorithm 261
7.2.3 A numerical example of the Beale-Little algorithm: annual
flood data from four sites (Rio do Sul, Ibirama, Apiuna,
Indaial) on the Rio Itajaí-Açú 264
Contents xi
7.2.4 Data sequences with entire years missing: the EM algorithm 267
7.2.5 Box-Cox power transformations in the multivariate case 268
7.2.6 Likelihood-based confidence limits for quantiles: a shorter
series {y,} extended by means of a longer series [.x,},
correlated with it 282
7.2.7 A note on the bivariate gamma distribution 286
7.3 Multi-site modelling of monthly flows: some general observations 287
7.3.1 The multi-site Thomas-Fiering model: multivariate multiple
regression 289
7.3.2 Criticism of the model 294
7.3.3 Test that a correlation matrix is of diagonal form 296
7.3.4 The use of transformations when simulating flow sequences 297
7.3.5 Modelling monthly flow for the Apiuna and Indaial sites
(continued) 297
7.3.6 Multi-site models for monthly flows from basins with
intermittent flows 299
7.3.7 Estimating suspended sediment load: the case of two variâtes
at one site 300
7.4 Some other possible multivariate distributions 300
References 301
Exercises and extensions 302
Chapter 8 Rainfall-runoff models
8.1 The nature of 'lumped conceptual models' of river basin response to
rainfall 3O3
8.2 Examples of lumped conceptual models of river basin response to
rainfall 307
8.2.1 The Dawdy-O'Donnell model 307
8.2.2 The Nash-Sutcliffe layer model 309
8.2.3 The Institute of Hydrology lumped model 310
8.2.4 The IPH2 Model 317
8.2.5 The Sugawara tank model 319
8.3 'Lumped' and 'distributed' models 320
8.4 When can lumped models be used, and when must distributed models
be used? 323
8.5 A simple lumped-parameter model using artificial data 325
8.6 Measures of discrepancy between observations and fitted values 331
8.7 'Automatic' optimisation of parameters 337
8.8 Split-record tests 33^
8.9 Some general observations on rainfall-runoff modelling 340
8.10 A generalised distributed-parameter model 341
8.11 Some observations on models for sediment yield and water quality 343
8.12 The generalised likelihood uncertainty estimation procedure 344
References ^
Exercises and extensions
xii Contents
Chapter 9 The Modelling of Spatial Processes 352
9.1 The nature of spatial variation 352
9.2 The variogram 356
9.3 Calculation of the variogram for Potiribu data on saturated hydraulic
conductivity ? 356
9.4 Some isotropie variogram models 367
9.5 Optimal interpolation using the variogram 373
9.6 Universal kriging 378
References 380
Chapter 10 Some possible future developments in statistical modelling 381
10.1 Omissions 381
10.2 Some aspects of statistical modelling in hydrology which need
further research 382
10.2.1 Régionalisation 382
10.2.2 Regional water balance studies 384
References 386
Appendix Some results in probability and statistical theory 387
A. 1 The fundamentals of probability theory 387
A.2 Deductions from the axioms of probability 389
A.2.1 The probability of a union of two events A and ? that are
not mutually exclusive 389
A.2.2 The theorem of total probability 390
A.3 Some particular probability density functions 391
A.4 Moments of probability density functions 393
A.5 Distributions of functions of random variables 395
A.6 Moments of functions of random variables 396
A.7 Moments of bivariate distributions 396
A.8 Conditional distributions and their means 397
A.9 The bivariate normal distribution 398
A. 10 The multi variate normal distribution 399
A.ll Moments of functions of two or more random variables 399
A. 12 Maximum-likelihood estimation of µ, S for the multivariate normal
?(µ, S) 400
References 400
Bibliography 401
Index 409 |
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| indexdate | 2024-12-06T09:03:21Z |
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| isbn | 0471950165 |
| language | English |
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| spelling | Clarke, Robin T. Verfasser aut Statistical modelling in hydrology Robin T. Clarke Chichester u.a. Wiley 1994 XII, 412 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hydrologie - Modèles mathématiques Hydrologie - Modèles mathématiques ram Hydrologie gtt Statistische modellen gtt Mathematisches Modell Hydrology Mathematical models Hydrologie (DE-588)4026309-5 gnd rswk-swf Statistisches Modell (DE-588)4121722-6 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Hydrologie (DE-588)4026309-5 s Statistik (DE-588)4056995-0 s DE-604 Statistisches Modell (DE-588)4121722-6 s DE-188 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006684339&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Clarke, Robin T. Statistical modelling in hydrology Hydrologie - Modèles mathématiques Hydrologie - Modèles mathématiques ram Hydrologie gtt Statistische modellen gtt Mathematisches Modell Hydrology Mathematical models Hydrologie (DE-588)4026309-5 gnd Statistisches Modell (DE-588)4121722-6 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4026309-5 (DE-588)4121722-6 (DE-588)4056995-0 |
| title | Statistical modelling in hydrology |
| title_auth | Statistical modelling in hydrology |
| title_exact_search | Statistical modelling in hydrology |
| title_full | Statistical modelling in hydrology Robin T. Clarke |
| title_fullStr | Statistical modelling in hydrology Robin T. Clarke |
| title_full_unstemmed | Statistical modelling in hydrology Robin T. Clarke |
| title_short | Statistical modelling in hydrology |
| title_sort | statistical modelling in hydrology |
| topic | Hydrologie - Modèles mathématiques Hydrologie - Modèles mathématiques ram Hydrologie gtt Statistische modellen gtt Mathematisches Modell Hydrology Mathematical models Hydrologie (DE-588)4026309-5 gnd Statistisches Modell (DE-588)4121722-6 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Hydrologie - Modèles mathématiques Hydrologie Statistische modellen Mathematisches Modell Hydrology Mathematical models Statistisches Modell Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006684339&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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