Advances in Data-Based Approaches for Hydrologic Modeling and Forecasting

CONTENTS......Page 10
PREFACE......Page 6
LIST OF CONTRIBUTORS......Page 18
1.1. Background and Motivation......Page 23
1.2. Organization......Page 26
References......Page 32
CHAPTER 2 STOCHASTIC METHODS FOR MODELING PRECIPITATION AND STREAM FLOW......Page 39
2.1. Introduction......Page 40
2.2.1. Continuous Precipitation Models......Page 41
2.2.2.1. Markov Chain Models......Page 43
2.2.2.2. Alternating Renewal Models......Page 45
2.2.2.3. Models for Precipitation Amount......Page 46
2.2.3.1. Kernel Density Estimators......Page 47
2.2.3.2. K-NN Bootstrap Models......Page 52
2.2.4. Precipitation Disaggregation Models......Page 53
2.3.1. Continuous Time to Hourly Simulation......Page 54
2.3.2. Weekly, Monthly, and Seasonal Streamflow Simulation at aSingle Site......Page 55
2.3.3. Annual Streamflow Simulation at a Single Site......Page 57
2.3.4. Multisite Streamflow Simulation......Page 58
2.3.5. Temporal and Spatial Disaggregation Models......Page 59
2.3.6.1. Single Site......Page 61
2.4. Extensions of K-NN Resampling Approach......Page 63
2.5. Summary and Future Directions......Page 65
References......Page 69
CHAPTER 3 MODEL CALIBRATION IN WATERSHED HYDROLOGY......Page 75
3.1. Introduction......Page 76
3.2. Approaches to Parameter Estimation for Watershed Models......Page 78
3.2.1. Model Calibration......Page 80
3.2.1.1. Overview of the Manual Calibration Approach......Page 83
3.2.1.2. Overview of Automated Calibration Approaches......Page 84
3.3. Single-criterion Automated Calibration Methods......Page 85
3.3.1. A Historical Perspective......Page 86
3.3.2. The Shuffled Complex Evolution–University of Arizona (SCE–UA) Algorithm......Page 89
3.3.3. Limitations of Single-criterion Methods......Page 92
3.4. Multi-criteria Automated Calibration Methods......Page 93
3.4.1. Simultaneous Multi-criteria Calibration Approach......Page 94
3.4.2. Stepwise Multi-criteria Calibration Approach......Page 98
3.4.3. Multi-criteria Constraining Approach......Page 101
3.5. Automated Calibration of Spatially Distributed Watershed Models......Page 103
3.6. Treatment of Parameter Uncertainty......Page 109
3.6.1. Random Walk Metropolis (RWM) Algorithm......Page 110
3.6.2. DiffeRential Evolution Adaptive Metropolis (DREAM)......Page 112
3.6.3. Sequential Data Assimilation......Page 115
3.8. Summary and Conclusions......Page 117
References......Page 121
CHAPTER 4 SCALING AND FRACTALS IN HYDROLOGY......Page 129
4.1. Introduction......Page 130
4.2. Fractal and Scale-invariant Sets......Page 131
4.2.1. Fractal Sets and their Fractal Dimensions......Page 132
4.2.2. Scale-invariant Sets and their Generation......Page 134
4.3. Scale Invariance for Random Processes......Page 137
4.3.1. Self-similar Processes......Page 138
4.3.2. Scalar Multifractal Processes......Page 140
4.3.3. Multifractal Fields and Vector-valued Processes......Page 144
4.4.1. Relationship Between Scale-invariant and Stationary Processes......Page 146
4.4.2. Scale-invariant Processes as Renormalization Limits......Page 148
4.4.3.1. Self-similar Processes......Page 150
4.4.3.2. Multifractal Processes......Page 153
4.4.4. Scale-invariant Processes from Fractional Integration of α-stable Measures......Page 160
4.4.4.1. H-sssi Processes......Page 161
Fractional Brownian Motion......Page 162
4.4.4.2. Multifractal Processes......Page 163
4.4.5. Processes with Limited Scale Invariance......Page 165
Bounded Cascades......Page 167
Extended Self-Similarity......Page 168
Segmented Multifractality......Page 169
4.5.1. H-sssi Processes......Page 170
Second Moments of X(t) and its Increments......Page 171
Spectral Density......Page 172
4.5.2. Moment Scaling of Multifractal Processes......Page 173
Existence and Moment Divergence......Page 175
Dressed Distributions......Page 176
Dressed Moments......Page 178
4.5.4.1. A Large Deviation Result......Page 181
4.5.4.2. Implications on the Bare Cascades and Extension to the Dressed Cascades......Page 182
4.5.4.3. Cascade Extremes......Page 183
(i) Asymptotic Scaling Properties of the Return-period Values......Page 184
(ii) Analytical Approximation of Non-asymptotic Return-period Values......Page 186
(iii) Extremes from the Maximum in One Cascade Realization......Page 189
4.5.4.4. Origin of the Term “Multifractality”......Page 190
4.6.1. Forecasting......Page 191
Causally Filtered White Noise Method......Page 192
Hidden Markov Process Method......Page 194
4.6.2. Downscaling......Page 197
Conditional Simulation with Data of Types 1 and 2......Page 199
Conditional Analysis with Data of Type 3......Page 200
4.7. Inference of Scaling from Data......Page 203
4.7.1. Estimation of K(q), q > 0, for Stationary Multifractal Measures......Page 204
Performance of the Nonparametric Estimator \ZK (q)......Page 205
Alternative Nonparametric Estimators......Page 207
Parametric Estimation and Bias Correction......Page 210
Wavelet Tranform Modulus Maxima (WTMM) Estimators......Page 212
Alternative Methods......Page 214
4.7.3. Estimation of K(q), q > 0, for Multi-affine Processes by the Gradient Amplitude Method......Page 217
4.7.4. Estimation of Universal Parameters by the Double Trace Moment Method......Page 219
4.8.1. Rainfall......Page 221
Scaling in Time......Page 222
Scaling in Space......Page 224
Scaling in Space-Time......Page 225
Dependence of Scaling on Rainstorm Characteristics......Page 227
Deviations from Multifractal Scaling......Page 228
4.8.2. Fluvial Topography and River Networks......Page 230
General Scale-invariance Condition for River Basin Topography......Page 232
River Courses......Page 235
River Networks......Page 236
Width Function......Page 238
River Profiles and Topography......Page 240
4.8.3. Floods......Page 242
Temporal Scaling of Q(t)......Page 243
Scaling of the Annual Floods with Area......Page 245
Multifractal Interpretation of the Scaling of Annual Floods with Area......Page 248
4.8.4. Flow Through Porous Media......Page 250
4.9. Concluding Remarks......Page 255
References......Page 256
CHAPTER 5 REMOTE SENSING FOR PRECIPITATION AND HYDROLOGIC APPLICATIONS......Page 267
5.1. Introduction......Page 268
5.2. Precipitation Nowcasting from Space-based Platforms......Page 272
5.3. Data Uses in Precipitation Forecasting......Page 276
5.4.1. Soil Moisture......Page 278
5.4.2. Flood Forecasting and Water Management......Page 281
5.5. Conclusions and Outlook......Page 284
References......Page 285
CHAPTER 6 NEARLY TWO DECADES OF NEURAL NETWORK HYDROLOGIC MODELING......Page 289
6.1. The Long and Winding Road......Page 290
6.2. From Little Acorns Grow Mighty Oaks......Page 297
6.3. Establishing the Field (1990–2000)......Page 302
6.4. Evaluating the Field (2000–2001)......Page 304
Q1. Can NN be made to reveal any physics?......Page 306
Q2. Can an optimal training set be identified?......Page 308
Q3. Can NN improve on time series analysis?......Page 310
Q4. Can NN training be made more adaptive?......Page 312
Q5. Are NN good extrapolators?......Page 314
6.5. Enlarging the Field (2001–Present)......Page 320
6.5.1. Traditional Regression-type Applications......Page 322
6.5.2. The Merging of Technologies......Page 324
6.5.2.1. Neuro-fuzzy Products......Page 325
6.5.2.2. Neuroevolution Products......Page 327
6.5.3. Modular and Ensemble Modeling......Page 330
6.5.4. Neuro-hybrid Modeling......Page 337
6.5.4.1. Error Correction/Forecast Updating......Page 339
6.5.4.2. Embedded Products......Page 341
6.5.4.3. Neuroemulation Products......Page 344
6.6. Taking Positive Steps to Deliver the Goods......Page 347
6.6.1. Building a Collective Intelligence......Page 349
6.6.2. Deciphering of Internal Components......Page 352
6.6.3. Estimating Confidence and Uncertainty......Page 354
6.7. Final Thoughts: Searching for a ‘Killer App’......Page 356
References......Page 359
CHAPTER 7 EVOLUTIONARY COMPUTING IN HYDROLOGY......Page 369
7.1. Introduction......Page 370
7.2.1. Evolution Principle......Page 371
7.2.2. Evolutionary Computing Techniques......Page 372
7.3. Evolutionary Computing in Hydrology: An Overview......Page 373
7.4. Genetic Programming and its Scope in Hydrology......Page 374
7.4.1. Modeling the Observations: GP as a Modeling Tool......Page 377
7.4.2. Modeling the Model Error: GP as a Data Assimilation Tool......Page 380
7.4.3. Modeling the Model: GP as a Model Emulator Tool......Page 383
7.4.3.1. Model Order Reduction using GP Models as Spatial Interpolators......Page 384
7.4.3.2. GP as a Representative Model for Model Emulation......Page 385
7.5. Important Issues Pertaining to Genetic Computing......Page 387
7.6. Conclusions......Page 388
References......Page 389
8.1. From Fourier to Wavelets......Page 393
8.2. The Continuous Wavelet Transform......Page 395
8.3.1. Discrete Wavelet Transform......Page 399
8.3.2. Orthogonal Wavelet Bases and Orthogonal Wavelet Expansions......Page 405
8.4. Signal Energy Repartition in the Wavelet Frame......Page 407
8.5. Statistical Entropy in the Wavelet Frame......Page 413
8.6. Wavelet Analysis of the Time-scale Relationship Between Two Signals......Page 416
8.7. Wavelet Cross-spectrum and Coherence......Page 420
8.8. Applications of Wavelet Transforms in Hydrology and Earth Sciences......Page 422
Acknowledgments......Page 427
References......Page 428
CHAPTER 9 NONLINEAR DYNAMICS AND CHAOS IN HYDROLOGY......Page 433
9.1. Introduction......Page 434
9.2.1. Autocorrelation Function and Power Spectrum......Page 437
9.2.2. Phase Space Reconstruction......Page 438
9.2.3. Correlation Dimension Method......Page 442
9.2.4. Nonlinear Prediction Method and Inverse Approach......Page 443
9.2.5. Some Other Methods......Page 445
9.3. Chaos Theory in Hydrology: A Review......Page 447
9.3.1. Rainfall......Page 448
9.3.2. River Flow......Page 451
9.3.3. Rainfall-Runoff......Page 458
9.3.4. Lake Volume......Page 459
9.3.5. Sediment Transport......Page 461
9.3.6. Groundwater......Page 462
9.3.7.1. Scale and Scale Invariance......Page 464
9.3.7.2. Parameter Estimation......Page 465
9.3.7.3. Catchment Classification......Page 466
9.3.7.4. Sundry......Page 467
9.4. Chaos Theory in Hydrology: Current Status and Challenges......Page 468
9.5. Closing Remarks: Chaos Theory as a Bridge Between Deterministic and Stochastic Theories......Page 474
References......Page 478
10.1. Summary of Findings......Page 485
10.2. Data vs. Physics......Page 490
10.3. Integration of Different Approaches......Page 492
10.4. Communication......Page 494
10.5. Conclusion......Page 496
References......Page 497
INDEX......Page 501