Note: Intro -- Extremes in a Changing Climate -- Foreword -- Preface -- Contents -- Contributors -- Chapter 1: Statistical Indices for the Diagnosing and Detecting Changes in Extremes -- 1.1 Introduction -- 1.2 Indices of Extremes for Weather and Climate Variables -- 1.3 Detection and Attribution of Changes in Climate Extremes -- 1.3.1 Changes in Extreme Temperatures -- 1.3.2 Anthropogenic Influence on Annual Maximum 1- or 5-Day Precipitation -- 1.3.3 Event Attribution -- 1.4 Summary -- References -- Chapter 2: Statistical Methods for Nonstationary Extremes -- 2.1 Introduction -- 2.2 Statistical Methods -- 2.2.1 Block Maxima -- 2.2.2 Excesses Over High Threshold -- 2.2.3 Point Process Approach -- 2.2.4 Parameter Estimation -- 2.2.4.1 Maximum Likelihood -- 2.2.4.2 Model Selection -- 2.2.4.3 Diagnostics -- 2.3 Examples -- 2.3.1 Trend in Block Maxima -- 2.3.1.1 Annual Peak Flow at Mercer Creek, WA -- 2.3.1.2 Winter Maximum Daily Precipitation at Manjimup, Western Australia -- 2.3.2 Trend in Point Process -- 2.3.2.1 Poisson-GP Model for Manjimup Winter Daily Precipitation -- 2.3.2.2 Point Process Applied to Manjimup Winter Daily Precipitation -- 2.4 Discussion -- References -- Chapter 3: Bayesian Methods for Non-stationary Extreme Value Analysis -- 3.1 Introduction -- 3.2 What Is Bayesian Inference? -- 3.2.1 Basics of Bayesian Inference -- 3.2.1.1 Notation -- 3.2.1.2 Likelihood -- 3.2.1.3 Prior Distribution -- 3.2.1.4 Posterior Distribution -- 3.2.2 MCMC Samplers -- 3.2.2.1 General Principles -- 3.2.2.2 A General-Purpose Sampler: The Metropolis-Hastings Algorithm -- 3.2.2.3 Monitoring Convergence -- 3.2.2.4 Building Efficient Samplers -- 3.2.3 Using the Posterior Distribution for Inference and Prediction -- 3.2.3.1 Posterior-Based Inference -- 3.2.3.2 The Predictive Distribution -- 3.2.3.3 Model Comparison and Bayesian Model Averaging. , 3.3 Local Inference of Non-stationary Models -- 3.3.1 Introducing Non-stationarity Using Covariate Modeling -- 3.3.2 Inference -- 3.3.3 Example: Extreme Rainfalls -- 3.3.3.1 Trend Model -- 3.3.3.2 Step-Change Model -- 3.3.3.3 Model Comparison and Model Averaging -- 3.3.3.4 Identifiability Issues -- 3.4 Regional Inference of Non-stationary Models -- 3.4.1 Motivation: Looking at Local Results at a Regional Scale -- 3.4.2 Notation -- 3.4.3 The Notion of Regional Parameters -- 3.4.4 Inference -- 3.4.4.1 The Spatial Independence Case -- 3.4.4.2 Accounting for Spatial Dependence -- 3.4.4.3 Inference with Spatially Dependent Data -- 3.4.5 Example: Extreme Rainfalls -- 3.5 Hierarchical Modeling -- 3.5.1 Principles of Hierarchical Modeling -- 3.5.1.1 Motivation -- 3.5.1.2 A Simple Example -- 3.5.2 Regional Hierarchical Modeling -- 3.5.2.1 Regional, Local and Stochastic Parameters -- 3.5.2.2 Inference -- 3.5.3 Case Study -- 3.5.3.1 Model Specification -- 3.5.3.2 Estimation -- 3.5.3.3 Prediction -- 3.5.4 Towards a Complete Spatiotemporal Modeling of Extreme Values -- 3.6 Conclusion -- 3.6.1 Benefits of the Bayesian Inference for Describing, Understanding and Predicting Extremes -- 3.6.2 Challenges and Future Research -- A.1 Appendix -- A.1.1 The Chib Method for Computing Marginal Likelihoods -- References -- Chapter 4: Return Periods and Return Levels Under Climate Change -- 4.1 Introduction -- 4.1.1 Return Periods and Return Levels Under Stationarity -- 4.1.2 Statistical Models for the Distribution's Tail -- 4.1.3 Interpretations of Return Periods Under Stationarity -- 4.1.4 Outline -- 4.2 Communicating Risk Under Non-stationarity -- 4.2.1 Communicating Changing Risk -- 4.2.2 Return Periods and Return Levels Under Non-stationarity -- 4.2.2.1 Return Period as Expected Waiting Time -- 4.2.2.2 Return Period as Expected Number of Events. , 4.3 Illustrative Example: Red River at Halstad -- 4.3.1 The Stationary Model -- 4.3.2 A Nonstationary Model -- 4.3.2.1 Communicating Changing Risk -- 4.3.2.2 Return Period as Expected Waiting Time -- 4.3.2.3 Return Period as Expected Number of Events -- 4.3.3 Other Possible Non-stationary Models -- 4.4 Discussion -- A Appendix -- A.1 Expansion of (4.2) -- A.2 Implicit Delta Method -- References -- Chapter 5: Multivariate Extreme Value Methods -- 5.1 Introduction -- 5.2 Copulas -- 5.2.1 Basic Features -- 5.2.2 Multivariate Association Measures -- 5.2.3 Asymptotic Dependence -- 5.2.4 Simulation -- 5.3 Multivariate Extreme Value Models -- 5.3.1 Extreme Value Copulas -- 5.3.2 Special Construction of MEV Distributions -- 5.4 Multivariate Return Periods and Design -- 5.4.1 Multivariate Return Periods -- 5.4.2 Multivariate Quantiles -- 5.4.3 Multivariate Design Events -- 5.4.3.1 Component-Wise Excess Design Realization -- 5.4.3.2 Most-Likely Design Realization -- 5.4.3.3 Further Notes About Design -- 5.5 Discussion and Perspectives -- References -- Chapter 6: Methods of Tail Dependence Estimation -- 6.1 Introduction -- 6.2 Tail Dependence: Basic Definitions -- 6.3 Copulas and Tail Dependence -- 6.3.1 Gaussian Copula -- 6.3.2 t-Copula -- 6.3.3 Gumbel-Hougaard Copula -- 6.4 Nonparametric Tail Dependence Methods -- 6.5 Extreme Value Threshold -- 6.6 Case Studies -- 6.7 Summary and Conclusions -- References -- Chapter 7: Stochastic Models of Climate Extremes: Theory and Observations -- 7.1 Introduction -- 7.1.1 Extreme Events: Definition, Relevance, and Sampling -- 7.1.2 Common Methods to Study Extreme Events -- 7.1.3 Novel Stochastic Approaches to Study Extreme Events -- 7.2 Theory -- 7.2.1 Stochastic Dynamics in a Nutshell -- 7.2.1.1 Interpretation of SDEs -- 7.2.1.2 SDE Versus Fokker-Planck Equation -- 7.2.2 Stochastic Dynamics of Climate Variability. , 7.2.3 Stochastic Models of Gaussian Variability: Hasselmann's Paradigm and the Red Climate Spectrum -- 7.2.4 Stochastic Models of Non-Gaussian Variability: A Null Hypothesis for the Statistics of Extreme Events -- 7.2.4.1 Skewness-Kurtosis Link -- 7.2.4.2 PDF and Power-Law Tails -- 7.2.4.3 Synthesis -- 7.3 Observations and Applications -- 7.3.1 Oceanic Examples -- 7.3.1.1 Sea Surface Temperature -- 7.3.1.2 Sea Surface Height -- 7.3.2 Atmospheric Examples -- 7.3.3 Other Applications -- 7.4 Conclusions -- 7.4.1 Where Do We Stand? -- 7.4.2 Outstanding Issues and Challenges -- References -- Chapter 8: Methods of Projecting Future Changes in Extremes -- 8.1 Extreme Indices -- 8.2 Extreme Value Theory Methods -- 8.3 Multi-Variate Climate and Weather Extremes -- 8.4 Summary -- References -- Chapter 9: Climate Variability and Weather Extremes: Model-Simulated and Historical Data -- 9.1 Introduction -- 9.2 Observed and Simulated Climate Variability and Weather Extremes -- 9.2.1 Boreal Winter (JFM) -- 9.2.1.1 Climatology and Variability -- 9.2.1.2 Regional Impacts of Climate Variability -- 9.2.1.3 Long-Term (Decadal Scale) Changes -- 9.2.2 Austral Winter (JAS) -- 9.2.2.1 Climatology and Variability -- 9.2.2.2 Regional Impacts of Climate Variability -- 9.2.2.3 Long-Term (Decadal Scale) Changes -- 9.3 Impact of CO2 Doubling and Uniform SST Increase -- 9.3.1 Boreal Winter (JFM) -- 9.3.1.1 Impact on the Mean Climate and Weather Variability -- 9.3.1.2 Impact on Climate Variability -- 9.3.2 Austral Winter (JAS) -- 9.3.2.1 Impact on Mean Climate and Weather Variability -- 9.3.2.2 Impact on Climate Variability -- 9.4 Summary and Discussion -- A.1 Appendices -- A.1.1 Appendix A -- A.1.1.1 The GEOS-5 Model and Experiments -- A.1.1.2 MERRA and Other Observations -- A.1.2 Appendix B -- A.1.2.1 Some Examples of Fits to the GEV Distribution -- References. , Chapter 10: Uncertainties in Observed Changes in Climate Extremes -- 10.1 Overview of Fundamental Issues Underlying Uncertainty -- 10.2 Specific Sources of Uncertainty -- 10.2.1 Chaotic Climate System -- 10.2.2 Measurements: Climate Station Inhomogeneities -- 10.2.3 Measurements: Sampling of Physical System -- 10.3 Methods for Quantification of Uncertainty -- 10.3.1 Monte Carlo Experiments -- 10.3.2 Standard Statistical Tools -- 10.3.3 Climate Model Ensemble Experiments -- 10.4 Applications -- 10.4.1 Extreme Precipitation Trends in the U.S. -- 10.4.2 Heat and Cold Wave Trends -- 10.4.3 The Hurricane Problem -- 10.4.4 The Tornado Problem -- 10.5 Concluding Remarks -- References -- Chapter 11: Uncertainties in Projections of Future Changes in Extremes -- 11.1 Introduction -- 11.2 Step 1. Identify Precipitation Metrics of Interest -- 11.3 Step 2. Select a Representative Climate Projections Ensemble -- 11.4 Step 3. Assess Projected Changes in Typical Precipitation Conditions -- 11.5 Step 4. Assess Projected Changes in Extreme Precipitation Conditions -- 11.6 Preliminary for Step 5: Low-Frequency Climate Variability and Its effect on Interpreting Projected Changes in Local Extremes -- 11.7 Step 5. Relate Variance in Projected Changes to Global Uncertainties -- 11.8 Step 6: Assess Changes Given Global/Local Interactions -- 11.9 Summary -- References -- Chapter 12: Global Data Sets for Analysis of Climate Extremes -- 12.1 Introduction -- 12.2 Data Issues Impacting the Analysis of Extremes -- 12.3 Climate Observing Networks -- 12.4 Data Sets for Examining Climate Extremes -- 12.5 Concluding Remarks -- References -- Chapter 13: Nonstationarity in Extremes and Engineering Design -- 13.1 Introduction -- 13.1.1 Setting the Scene -- 13.1.2 Recent Extremes, Their Impact and Questions They Raised -- 13.1.2.1 Boscastle Flood, Cornwall, UK - 16 August 2004. , 13.1.2.2 Hurricane Katrina, New Orleans, USA - August 2005.