Table Of ContentStatistical Downscaling
for Hydrological and
Environmental Applications
Statistical Downscaling
for Hydrological and
Environmental Applications
Taesam Lee and Vijay P. Singh
CRC Press
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Contents
Preface.......................................................................................................................xi
List of Abbreviations..............................................................................................xiii
Authors .....................................................................................................................xv
Chapter 1 Introduction ..........................................................................................1
1.1 Why Statistical Downscaling? ...................................................1
1.2 Climate Models .........................................................................1
1.3 Statistical Downscaling .............................................................2
1.4 Selection of Model Scheme .......................................................3
1.5 Structure of Chapters .................................................................6
1.6 Summary and Conclusion .........................................................7
Chapter 2 Statistical Background .........................................................................9
2.1 Probability and Statistics ...........................................................9
2.1.1 Probabilistic Theory .....................................................9
2.1.1.1 Probability Density Function and
Cumulative Distribution Function ................9
2.1.1.2 Descriptors of Random Variables .................9
2.1.2 Discrete Probability Distributions ..............................10
2.1.2.1 Bernoulli Distribution .................................11
2.1.2.2 Binomial Distribution .................................11
2.1.3 Continuous Probability Distributions .........................12
2.1.3.1 Normal Distribution and Lognormal
Distributions ...............................................12
2.1.3.2 Exponential and Gamma Distributions ......13
2.1.3.3 Generalized Extreme Value and
Gumbel Distribution ...................................15
2.1.4 Parameter Estimation for Probability Distributions ...16
2.1.4.1 Method of Moments ....................................16
2.1.4.2 Maximum Likelihood Estimation ..............16
2.1.5 Histogram and Empirical Distribution .......................19
2.2 Multivariate Random Variables ...............................................22
2.2.1 Multivariate Normal Distribution and Its
Conditional Distribution .............................................22
2.2.2 Covariance and Correlation........................................24
2.3 Random Simulation .................................................................24
2.3.1 Monte Carlo Simulation and Uniform Random
Number .......................................................................24
2.3.2 Simulation of Probability Distributions .....................26
2.4 Metaheuristic Algorithm .........................................................27
vii
viii Contents
2.4.1 Harmony Search ........................................................27
2.5 Summary and Conclusion .......................................................31
Chapter 3 Data and Format Description .............................................................33
3.1 GCM Data ...............................................................................33
3.2 Reanalysis Data .......................................................................34
3.3 RCM Data ................................................................................34
3.4 Summary and Conclusion .......................................................38
Chapter 4 Bias Correction ...................................................................................39
4.1 Why Bias Correction?..............................................................39
4.2 Occurrence Adjustment for Precipitation Data .......................39
4.3 Empirical Adjustment (Delta Method) ....................................41
4.4 Quantile Mapping ....................................................................43
4.4.1 General Quantile Mapping .........................................43
4.4.2 Nonparametric Quantile Mapping .............................46
4.4.3 Quantile Delta Mapping .............................................47
4.5 Summary and Comparison ......................................................50
Chapter 5 Regression Downscalings...................................................................53
5.1 Linear Regression Based Downscaling ...................................53
5.1.1 Simple Linear Regression ..........................................53
5.1.1.1 Significance Test .........................................55
5.1.2 Multiple Linear Regression ........................................58
5.2 Predictor Selection...................................................................70
5.2.1 Stepwise Regression ...................................................70
5.2.2 Least Absolute Shrinkage and Selection Operator ........74
5.3 Nonlinear Regression Modeling ..............................................87
5.3.1 Artificial Neural Network ..........................................87
5.4 Summary and Conclusion .......................................................92
Chapter 6 Weather Generator Downscaling .......................................................95
6.1 Mathematical Background ......................................................95
6.1.1 Autoregressive Models ...............................................95
6.1.2 Multivariate Autoregressive Model ............................95
6.1.3 Markov Chain .............................................................98
6.2 Weather Generator .................................................................100
6.2.1 Model Fitting ............................................................101
6.2.1.1 Precipitation ..............................................101
6.2.1.2 Weather Variables (T , T , SR) .............101
max min
6.2.2 Simulation of Weather Variables ..............................107
6.2.2.1 Precipitation ..............................................107
Contents ix
6.2.2.2 Weather Variables (T , T , SR) .............107
max min
6.2.3 Implementation of Downscaling ..............................109
6.3 Nonparametric Weather Generator .......................................111
6.3.1 Simulation under Current Climate ...........................112
6.3.2 Simulation under Future Climate Scenarios ............115
6.4 Summary and Conclusion .....................................................115
Chapter 7 Weather-Type Downscaling .............................................................117
7.1 Classification of Weather Types ............................................117
7.1.1 Empirical Weather Type ...........................................117
7.1.2 Objective Weather Type ...........................................117
7.2 Generation of Daily Rainfall Sequences ...............................121
7.3 Future Climate with Weather-Type Downscaling .................123
7.4 Summary and Conclusion .....................................................123
Chapter 8 Temporal Downscaling ....................................................................125
8.1 Background ............................................................................125
8.1.1 K-Nearest Neighbor Resampling ..............................125
8.2 Daily to Hourly Downscaling ................................................127
8.3 Summary and Conclusion .....................................................135
Chapter 9 Spatial Downscaling.........................................................................137
9.1 Mathematical Background ....................................................137
9.1.1 Bilinear Interpolation ...............................................137
9.1.2 Nearest Neighbor Interpolation ................................137
9.2 Bias Correction and Spatial Downscaling ............................138
9.3 Bias Correction and Constructed Analogues .......................143
9.4 Bias Correction and Stochastic Analogue .............................146
9.5 Summary and Comparison ....................................................152
References .............................................................................................................155
Index ......................................................................................................................159
