Chaos in Hydrology: Bridging Determinism and Stochasticity
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer
[2017]
|
| Subjects: | |
| Online Access: | BTU01 FFW01 TUM01 UBG01 UBT01 UPA01 Volltext Inhaltsverzeichnis |
| Physical Description: | 1 Online Ressource (XXX, 394 p. 62 illus., 25 illus. in color) |
| ISBN: | 9789048125524 |
| DOI: | 10.1007/978-90-481-2552-4 |
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Record in the Search Index
| _version_ | 1804176868606214144 |
|---|---|
| adam_text | Titel: Chaos in hydrology
Autor: Sivakumar, Bellie
Jahr: 2017
Contents
Part I Hydrologie Systems and Modeling
1 Introduction............................................. 3
1.1 Definition of Hydrology.............................. 3
1.2 Hydrologie Cycle................................... 4
1.3 Scientific Development of Hydrology........................................6
1.4 Concept of Hydrologie System..................................................9
1.5 Hydrologie System Model........................................................11
1.6 Hydrologie Model Classification................................................13
1.6.1 Physical Models..........................................................13
1.6.2 Abstract Models..........................................................14
1.6.3 Remarks......................................................................15
1.7 Hydrologie Data and Time Series Modeling..............................15
1.8 Physical Basis of Time Series Modeling....................................17
1.9 Scope and Organization of the Book........................................19
References..............................................................................................21
2 Characteristics of Hydrologie Systems................................................29
2.1 Introduction..............................................................................29
2.2 Complexity................................................................................30
2.3 Correlation and Connection......................................................32
2.4 Trend........................................................................................34
2.5 Periodicity, Cyclicity, and Seasonality......................................34
2.6 Intermittency..............................................................................36
2.7 Stationarity and Nonstationarity................................................36
2.8 Linearity and Nonlinearity........................................................38
2.9 Determinism and Randomness..................................................39
2.10 Scale, Scaling, and Scale-invariance..........................................41
2.11 Self-organization and Self-organized Criticality........................43
2.12 Threshold..................................................................................44
2.13 Emergence................................................................................46
2.14 Feedback....................................................................................47
xiii
xiv Contents
2.15 Sensitivity to Initial Conditions..................................................48
2.16 The Class of Nonlinear Determinism and Chaos........................49
2.17 Summary..................................................................................50
References..............................................................................................50
3 Stochastic Time Series Methods..........................................................63
3.1 Introduction..............................................................................63
3.2 Brief History of Development of Stochastic Methods................65
3.3 Hydrologie Time Series and Classification................................66
3.4 Relevant Statistical Characteristics and Estimators....................67
3.4.1 Mean..........................................................................68
3.4.2 Variance....................................................................68
3.4.3 Coefficient of Variation..............................................69
3.4.4 Skewness Coefficient..................................................69
3.4.5 Autocorrelation Function............................................69
3.4.6 Power Spectrum..........................................................70
3.5 Parametric Methods..................................................................71
3.5.1 Autoregressive (AR) Models......................................71
3.5.2 Moving Average (MA) Models..................................73
3.5.3 Autoregressive Moving Average (ARMA) Models ... 73
3.5.4 Gamma Autoregressive (GAR) Models......................75
3.5.5 Periodic Models: PAR, PARMA, and PGAR
Models........................................................................76
3.5.6 Extension of AR, ARMA, PAR, and PARMA
Models to Multiple Variables....................................79
3.5.7 Disaggregation Models..............................................80
3.5.8 Markov Chain Models................................................82
3.5.9 Point Process Models..................................................84
3.5.10 Other Models..............................................................87
3.5.11 Remarks......................................................................88
3.6 Nonparametric Methods............................................................88
3.6.1 Bootstrap and Block Bootstrap..................................89
3.6.2 Kemel Density Estimate............................................90
3.6.3 k-Nearest Neighbor Resampling (KNNR)..................92
3.6.4 k-Nearest Neighbors with Local Polynomial
Regression..................................................................94
3.6.5 Others........................................................................95
3.7 Summaty..................................................................................96
References..............................................................................................96
4 Modern Nonlinear Time Series Methods............................................Ill
4.1 Introduction..............................................................................Ill
4.2 Nonlinear Stochastic Methods....................................................112
4.3 Data-based Mechanistic Models................................................113
4.4 Artificial Neural Networks........................................................115
Contents xv
4.5 Support Vector Machines..........................................................118
4.6 Wavelets....................................................................................120
4.7 Evolutionary Computing............................................................123
4.8 Fuzzy Logic..............................................................................126
4.9 Entropy-based Models..............................................................128
4.10 Nonlinear Dynamics and Chaos................................................129
4.11 Summary..................................................................................130
References..............................................................................................131
Part II Nonlinear Dynamics and Chaos
5 Fundamentals of Chaos Theory..........................................................149
5.1 Introduction..............................................................................149
5.2 Definition of Chaos....................................................................150
5.3 Brief History of the Development of Chaos Theory..................151
5.4 Dynamical Systems and Stability Analysis................................153
5.5 Attractors..................................................................................154
5.6 Bifurcations..............................................................................156
5.7 Interaction and Interdependence................................................157
5.8 Sensitivity to Initial Conditions..................................................158
5.9 State Space and Phase Space....................................................159
5.10 Fractal and Fractal Dimension..................................................161
5.11 Examples of Chaotic Dynamic Equations..................................161
5.11.1 Logistic Map..............................................................162
5.11.2 Henon Map................................................................164
5.11.3 Lorenz System............................................................164
5.11.4 Rössler System..........................................................167
5.12 Summary..................................................................................168
References..............................................................................................169
6 Chaos Identification and Prediction Methods....................................173
6.1 Introduction....................................... 173
6.2 Linear Tools and Limitations....................................................175
6.3 Phase Space Reconstruction......................................................177
6.4 Correlation Dimension Method..................................................179
6.4.1 Basic Concept............................................................179
6.4.2 The Grassberger-Procaccia (G-P) Algorithm..............180
6.4.3 Identification of Number of System Variables............181
6.4.4 An Example................................................................181
6.4.5 Improvements to the G-P Algorithm..........................182
6.5 False Nearest Neighbor (FNN) Algorithm................................183
6.6 Lyapunov Exponent Method......................................................184
6.7 Kolmogorov Entropy Method....................................................186
xvi Contents
6.8 Surrogate Data Method..............................................................187
6.9 Poincaré Maps..........................................................................189
6.10 Close Returns Plot....................................................................189
6.11 Nonlinear Prediction..................................................................191
6.11.1 Local Approximation Prediction................................191
6.11.2 Inverse Approach to Chaos Identification..................192
6.12 Summary..................................................................................193
References..............................................................................................194
7 Issues in Chaos Identification and Prediction....................................199
7.1 Introduction..............................................................................199
7.2 Delay Time................................................................................200
7.2.1 Delay Time Selection................................................201
7.2.2 Delay Window Selection............................................203
7.2.3 Remarks......................................................................204
7.3 Data Size..................................................................................205
7.3.1 Effects of Data Size....................................................206
7.3.2 Minimum Data Size....................................................207
7.4 Data Noise................................................................................211
7.4.1 Effects of Noise..........................................................212
7.4.2 Noise Level Determination........................................214
7.4.3 Noise Reduction........................................................216
7.4.4 Coupled Noise Level Determination
and Reduction: An Example......................................219
7.5 Zeros in Data............................................................................222
7.6 Other Issues..............................................................................223
7.7 Summary..................................................................................223
References..............................................................................................224
Part III Applications of Chaos Theory in Hydrology
8 Overview . ............................................................................................231
8.1 Introduction..............................................................................231
8.2 Early Stage (1980s-1990s)........................................................232
8.3 Change of Course (2000-2006)................................................236
8.4 Looking at Global-scale challenges (2007-)..............................237
8.5 Summary..................................................................................239
References..............................................................................................239
9 Applications to Rainfall Data..............................................................245
9.1 Introduction..............................................................................245
9.2 Identification and Prediction......................................................246
9.2.1 Chaos Analysis of Rainfall: An Example—Göta
River Basin................................................................250
Contents xvii
9.3 Scaling and Disaggregaüon/Downscaling..................................252
9.3.1 Chaotic Scale-invariance: An Example—Leaf
River Basin................................................................252
9.3.2 Chaotic Disaggregation: An Example—Leaf River
Basin..........................................................................255
9.3.3 Others........................................................................260
9.4 Spatial Variability and Classification..........................................261
9.5 Others (Data Size, Noise Reduction, Zeros)..............................263
9.6 Summary..................................................................................263
References..............................................................................................264
10 Applications to River Flow Data........................................................267
10.1 Introduction..............................................................................267
10.2 Identification and Prediction......................................................268
10.2.1 Chaos Analysis in River Flow:
An Example—Coaracy Nunes/Araguari
River Basin................................................................272
10.3 Scaling and Disaggregation........................................................276
10.3.1 Chaos and Scaling......................................................276
10.3.2 Chaotic Disaggregation of River Flow........................279
10.4 Spatial Variability and Classification..........................................285
10.5 Others........................................................................................291
10.6 Summary..................................................................................292
References..............................................................................................292
11 Applications to Other Hydrologie Data..............................................297
11.1 Introduction..............................................................................297
11.2 Rainfall-runoff...........................................................................298
11.3 Lake Volume and Level............................................................301
11.4 Sediment Transport....................................................................302
11.5 Groundwater..............................................................................310
11.5.1 Solute Transport........................................................311
11.5.2 Arsenic Contamination..............................................315
11.6 Others........................................................................................316
11.7 Summary..................................................................................317
References..............................................................................................318
12 Studies on Hydrologie Data Issues......................................................321
12.1 Introduction..............................................................................321
12.2 Delay Time................................................................................322
12.3 Data Size..................................................................................325
12.4 Data Noise................................................................................329
12.5 Zeros in Data............................................................................332
12.6 Others........................................................................................335
12.7 Summary..................................................................................336
References..............................................................................................336
xviii Contents
Part IV A Look Ahead
13 Current Status......................................................................................343
13.1 Introduction..............................................................................343
13.2 Reliable Identification................................................................344
13.3 Encouraging Predictions............................................................346
13.4 Successful Extensions................................................................347
13.5 Limitations and Concerns..........................................................349
13.6 Discussions and Debates............................................................351
13.7 Summary..................................................................................352
References..............................................................................................352
14 The Future............................................................................................357
14.1 Introduction..............................................................................357
14.2 Parameter Estimation................................................................358
14.3 Model Simplification..................................................................359
14.4 Integration of Concepts..............................................................362
14.5 Catchment Classification Framework........................................363
14.6 Multi-variable Analysis..............................................................365
14.7 Reconstruction of System Equations..........................................366
14.8 Downscaling of Global Climate Model Outputs........................367
14.9 Linking Theory, Data, and Physics............................................368
14.10 Summary..................................................................................369
References..............................................................................................370
15 Final Thoughts: Philosophy and Pragmatism....................................375
15.1 Introduction..............................................................................375
15.2 Philosophy................................................................................376
15.3 Pragmatism................................................................................378
15.4 Closing Remarks........................................................................380
References..............................................................................................381
Index...................................................... 383
|
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| spelling | Sivakumar, Bellie Verfasser aut Chaos in Hydrology Bridging Determinism and Stochasticity Bellie Sivakumar Dordrecht Springer [2017] © 2017 1 Online Ressource (XXX, 394 p. 62 illus., 25 illus. in color) txt rdacontent c rdamedia cr rdacarrier Earth sciences Hydrology Hydrogeology Geotechnical engineering System theory Civil engineering Earth Sciences Hydrology/Water Resources Civil Engineering Complex Systems Geotechnical Engineering & Applied Earth Sciences Statistical Physics and Dynamical Systems Geowissenschaften Erscheint auch als Druckausgabe 978-90-481-2551-7 https://doi.org/10.1007/978-90-481-2552-4 Verlag URL des Erstveröffentlichers Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029342795&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sivakumar, Bellie Chaos in Hydrology Bridging Determinism and Stochasticity Earth sciences Hydrology Hydrogeology Geotechnical engineering System theory Civil engineering Earth Sciences Hydrology/Water Resources Civil Engineering Complex Systems Geotechnical Engineering & Applied Earth Sciences Statistical Physics and Dynamical Systems Geowissenschaften |
| title | Chaos in Hydrology Bridging Determinism and Stochasticity |
| title_auth | Chaos in Hydrology Bridging Determinism and Stochasticity |
| title_exact_search | Chaos in Hydrology Bridging Determinism and Stochasticity |
| title_full | Chaos in Hydrology Bridging Determinism and Stochasticity Bellie Sivakumar |
| title_fullStr | Chaos in Hydrology Bridging Determinism and Stochasticity Bellie Sivakumar |
| title_full_unstemmed | Chaos in Hydrology Bridging Determinism and Stochasticity Bellie Sivakumar |
| title_short | Chaos in Hydrology |
| title_sort | chaos in hydrology bridging determinism and stochasticity |
| title_sub | Bridging Determinism and Stochasticity |
| topic | Earth sciences Hydrology Hydrogeology Geotechnical engineering System theory Civil engineering Earth Sciences Hydrology/Water Resources Civil Engineering Complex Systems Geotechnical Engineering & Applied Earth Sciences Statistical Physics and Dynamical Systems Geowissenschaften |
| topic_facet | Earth sciences Hydrology Hydrogeology Geotechnical engineering System theory Civil engineering Earth Sciences Hydrology/Water Resources Civil Engineering Complex Systems Geotechnical Engineering & Applied Earth Sciences Statistical Physics and Dynamical Systems Geowissenschaften |
| url | https://doi.org/10.1007/978-90-481-2552-4 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029342795&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT sivakumarbellie chaosinhydrologybridgingdeterminismandstochasticity |