| Preface | p. v |
| Introduction | p. 1 |
| History | p. 1 |
| The Lay-Out | p. 3 |
| Concepts and Definitions | p. 3 |
| The problem: What is downscaling and why downscaling | p. 3 |
| What is downscaling? | p. 3 |
| Why downscaling? | p. 8 |
| Notations | p. 10 |
| Definitions | p. 12 |
| Anomalies in ESD | p. 18 |
| Further Reading | p. 19 |
| Examples | p. 19 |
| Exercises | p. 20 |
| Downscaling Strategies | p. 22 |
| Different Approaches | p. 22 |
| Dynamical downscaling | p. 22 |
| Philosophy Behind ESD | p. 24 |
| Considerations | p. 26 |
| A physics-inspired view | p. 32 |
| A purely statistical view | p. 34 |
| What is "Skillful Scale"? | p. 34 |
| Further Reading | p. 39 |
| Dynamical versus empirical-statistical downscaling | p. 39 |
| Examples | p. 41 |
| Geostrophic balance | p. 41 |
| Basic preprocessing | p. 41 |
| Exercises | p. 44 |
| Predictors and Preprocessing | p. 45 |
| Choosing Predictors | p. 45 |
| Circulation Indices | p. 46 |
| Stationarity | p. 48 |
| The North Atlantic Oscillation (NAO) | p. 49 |
| Autocorrelation and degrees of freedom | p. 49 |
| Empirical orthogonal functions | p. 50 |
| Varieties of EOF analysis | p. 57 |
| Rotated EOFs | p. 57 |
| Complex and frequency-domain EOFs | p. 58 |
| Complex EOFs | p. 58 |
| Frequency-domain EOFs | p. 59 |
| Extended EOFs | p. 59 |
| Mixed-field and common EOFs | p. 59 |
| EOF in ESD | p. 60 |
| Further Reading | p. 61 |
| Examples | p. 62 |
| Basic EOF analysis | p. 62 |
| Mixed-field EOFs | p. 62 |
| Extended EOFs | p. 63 |
| Exercises | p. 64 |
| Linear Techniques | p. 67 |
| Introduction | p. 67 |
| Linear Multivariate Methods | p. 69 |
| Regression | p. 70 |
| Multivariate regression models | p. 71 |
| Canonical Correlation Analysis | p. 73 |
| Classical CCA | p. 73 |
| Linear relationships from the model based on CCA | p. 75 |
| Singular Vectors | p. 76 |
| Further Reading | p. 78 |
| Examples | p. 78 |
| CCA | p. 80 |
| Exercises | p. 84 |
| Nonlinear Techniques | p. 85 |
| Introduction | p. 85 |
| The Analog Model | p. 85 |
| Caveats | p. 86 |
| Classification Methods | p. 90 |
| Cluster analysis | p. 91 |
| Neural Nets | p. 93 |
| Further Reading | p. 93 |
| Examples | p. 96 |
| Analog model (Fig. 5.8) | p. 96 |
| Clustering | p. 97 |
| Exercises | p. 97 |
| Predictions and Diagnostics | p. 98 |
| Common Notations and Definitions | p. 98 |
| Predictions | p. 99 |
| Trends | p. 100 |
| Test for trends | p. 101 |
| Trend-testing based on Spearman rank coefficient | p. 101 |
| Mann-Kendall rank correlation statistics | p. 101 |
| Trend testing based on student's t-test | p. 102 |
| Diagnostics | p. 102 |
| Statistical Inference | p. 103 |
| Confidence intervals for rejection | p. 103 |
| Student's t-test | p. 104 |
| F-statistics | p. 104 |
| Quality Control | p. 105 |
| Model Skill | p. 108 |
| Evaluation Techniques | p. 108 |
| Anomalous correlation | p. 109 |
| The R[superscript 2] score | p. 109 |
| Root-mean-square-error | p. 110 |
| Representative statistical distributions | p. 111 |
| Cross-Validation | p. 111 |
| Further Reading | p. 113 |
| Examples (Fig. 6.7) | p. 113 |
| Illustration of cross-validation | p. 113 |
| Using ESD to validate cyclone counts | p. 114 |
| ESD to reconstruct historical climate records | p. 116 |
| The objDS-function | p. 116 |
| Prediction pattern | p. 118 |
| Simple trend-fit | p. 120 |
| Scatter plot and correlation | p. 120 |
| Exercises | p. 120 |
| Shortcomings and Limitations | p. 122 |
| Level of Variability | p. 124 |
| Model Stationarity | p. 125 |
| "Perfect model" simulation | p. 126 |
| "Historical" simulation | p. 126 |
| Minimizing risk of nonstationarity | p. 127 |
| Consistency | p. 128 |
| Take-home messages | p. 130 |
| Examples | p. 131 |
| Exercises | p. 133 |
| Reducing Uncertainties | p. 134 |
| Cascading Uncertainties | p. 134 |
| De-Trending in the Calibration | p. 136 |
| Using Different Predictands | p. 138 |
| Optimal Number of Predictors | p. 138 |
| Trends versus Time Slices | p. 139 |
| Domain Choices | p. 141 |
| Spatial Coherence | p. 142 |
| Projection of EOFs | p. 144 |
| The Common EOF Frame | p. 144 |
| Adjustment and bias corrections | p. 146 |
| Further Reading | p. 146 |
| The Example Illustrating Huth's Paradox | p. 148 |
| Exercises | p. 148 |
| Downscaling Extremes and PDFs | p. 149 |
| Outliers and Extremes | p. 149 |
| Robustness and Resistance | p. 150 |
| Estimators | p. 151 |
| Probability Density Functions | p. 151 |
| What is probability distribution and why use it? | p. 151 |
| Normal/Gaussian distribution | p. 152 |
| The exponential distribution | p. 153 |
| Gamma distribution | p. 154 |
| Extreme Values | p. 156 |
| iid-test | p. 158 |
| Downscaling Extreme Indices | p. 160 |
| Generalized linear models | p. 160 |
| Maximum likelihood estimation | p. 161 |
| Downscaling PDFs | p. 162 |
| Downscaling PDFs for temperature | p. 163 |
| Downscaling PDFs for daily precipitation | p. 163 |
| Further Reading | p. 168 |
| Examples | p. 169 |
| iid-test | p. 169 |
| Downscaling PDFs for normal distribution | p. 169 |
| Downscaling PDFs exponential distribution | p. 170 |
| Exercises | p. 172 |
| Weather Generator | p. 173 |
| Weather Generator | p. 174 |
| Richardson Type WG for Precipitation | p. 175 |
| Downscaling Based on WG | p. 176 |
| Examples | p. 177 |
| Coin-flipping | p. 177 |
| Exercises | p. 177 |
| Implementing ESD | p. 179 |
| Numerical Tools | p. 179 |
| R | p. 179 |
| clim.pact | p. 179 |
| Rclim | p. 181 |
| SDSM | p. 181 |
| ClimateExplorer | p. 181 |
| ENSEMBLE-S2D | p. 181 |
| Gridding the Results | p. 182 |
| Kriging | p. 182 |
| Residual kriging | p. 182 |
| GIS-packages | p. 186 |
| Acknowledgments | p. 188 |
| Appendix | p. 189 |
| References | p. 201 |
| Index | p. 213 |
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