Statistical Postprocessing of Ensemble Forecasts

Statistical Postprocessing of Ensemble Forecasts brings together chapters contributed by international subject-matter experts describing the current state of the art in the statistical postprocessing of ensemble forecasts. The book illustrates the use of these methods in several important applications including weather, hydrological and climate forecasts, and renewable energy forecasting. After an introductory section on ensemble forecasts and prediction systems, the second section of the book is devoted to exposition of the methods available for statistical postprocessing of ensemble forecasts: univariate and multivariate ensemble postprocessing are first reviewed by Wilks (Chapters 3), then Schefzik and Möller (Chapter 4), and the more specialized perspective necessary for postprocessing forecasts for extremes is presented by Friederichs, Wahl, and Buschow (Chapter 5). The second section concludes with a discussion of forecast verification methods devised specifically for evaluation of ensemble forecasts (Chapter 6 by Thorarinsdottir and Schuhen). The third section of this book is devoted to applications of ensemble postprocessing. Practical aspects of ensemble postprocessing are first detailed in Chapter 7 (Hamill), including an extended and illustrative case study. Chapters 8 (Hemri), 9 (Pinson and Messner), and 10 (Van Schaeybroeck and Vannitsem) discuss ensemble postprocessing specifically for hydrological applications, postprocessing in support of renewable energy applications, and postprocessing of long-range forecasts from months to decades. Finally, Chapter 11 (Messner) provides a guide to the ensemble-postprocessing software available in the R programming language, which should greatly help readers implement many of the ideas presented in this book. Edited by three experts with strong and complementary expertise in statistical postprocessing of ensemble forecasts, this book assesses the new and rapidly developing field of ensemble forecast postprocessing as an extension of the use of statistical corrections to traditional deterministic forecasts. Statistical Postprocessing of Ensemble Forecasts is an essential resource for researchers, operational practitioners, and students in weather, seasonal, and climate forecasting, as well as users of such forecasts in fields involving renewable energy, conventional energy, hydrology, environmental engineering, and agriculture. Consolidates, for the first time, the methodologies and applications of ensemble forecasts in one succinct place Provides real-world examples of methods used to formulate forecasts Presents the tools needed to make the best use of multiple model forecasts in a timely and efficient manner Statistical Postprocessing of Ensemble Forecasts Copyright Contributors Preface Uncertain Forecasts From Deterministic Dynamics Sensitivity to Initial Conditions, or ``Chaos ́ ́ Uncertainty and Probability in ``Deterministic ́ ́ Predictions Ensemble Forecasting Postprocessing Individual Dynamical Forecasts Postprocessing Ensemble Forecasts: Overview of This Book References Ensemble Forecasting and the Need for Calibration The Dynamical Weather Prediction Problem Historical Background Observations The Equations of Motion for the Atmosphere Computation of the Initial Conditions (Analysis) The Chaotic Nature of the Atmosphere From Single to Ensemble Forecasts Forecast Reliability and Accuracy Are Ensemble Forecasts More Valuable than a Single Forecast? Sources of Forecast Errors Characteristics of the Operational Global Ensemble Systems The Value of a Reforecast Suite A Look Into the Future Summary: The Key Messages of This Chapter References Univariate Ensemble Postprocessing Introduction Nonhomogeneous Regressions, and Other Regression Methods Nonhomogeneous Gaussian Regression (NGR) Nonhomogeneous Regressions With More Flexible Predictive Distributions Truncated Nonhomogeneous Regressions Censored Nonhomogeneous Regressions Logistic Regression Bayesian Model Averaging, and Other ``Ensemble Dressing ́ ́ Methods Bayesian Model Averaging (BMA) Other Ensemble Dressing Methods Fully Bayesian Ensemble Postprocessing Approaches Nonparametric Ensemble Postprocessing Methods Rank Histogram Recalibration Quantile Regression Ensemble Dressing Individual Ensemble-Member Adjustments ``Statistical Learning ́ ́ Methods for Ensemble Postprocessing Comparisons Among Methods References Ensemble Postprocessing Methods Incorporating Dependence Structures Introduction Dependence Modeling Via Copulas Copulas and Sklar's Theorem Parametric, in Particular Gaussian, Copulas Empirical Copulas Parametric Multivariate Approaches Intervariable Dependencies Spatial Dependencies Temporal Dependencies Nonparametric Multivariate Approaches Empirical Copula-Based Ensemble Postprocessing Ensemble Copula Coupling (ECC) Schaake Shuffle-Based Approaches Univariate Approaches Accounting for Dependencies Spatial Dependencies Temporal Dependencies Discussion References Postprocessing for Extreme Events Introduction Extreme-Value Theory Generalized Extreme-Value Distribution Peak-Over-Threshold Approach Nonstationary Extremes Postprocessing of Univariate Extremes: Precipitation Data and Ensemble Forecasts Approaches and Verification Variable Selection Comparison of Postprocessing Approaches Extreme-Value Theory for Multivariate and Spatial Extremes Extremal Dependence and Multivariate Extreme-Value Distributions Spatial Max-Stable Processes Postprocessing for Spatial Extremes: Wind Gusts Postprocessing for Marginal Distribution The Spatial Dependence Structure Conclusions Appendix References Verification: Assessment of Calibration and Accuracy Introduction Calibration Univariate Calibration Multivariate Calibration Example: Comparing Multivariate Ranking Methods Accuracy Univariate Assessment Simulation Study: Comparing Univariate Scoring Rules Assessing Extreme Events Example: Proper and Nonproper Verification of Extremes Multivariate Assessment Divergence Functions Testing Equal Predictive Performance Understanding Model Performance Summary References Practical Aspects of Statistical Postprocessing Introduction The Bias-Variance Tradeoff Training-Data Issues for Statistical Postprocessing Challenges in Developing Ideal Predictor Training Data Challenges in Gathering/Developing Ideal Predictand Training Data Proposed Remedies for Practical Issues in Statistical Postprocessing Improving the Approaches for Generating Reforecasts Circumventing Common Challenges Posed by Shorter Training Data Sets Substandard Analysis Data Case Study: Postprocessing to Generate High Resolution Probability-of-Precipitation From Global Multimodel Ensembles Collaborating on Software and Test Data to Accelerate Postprocessing Improvement Recommendations and Conclusions References Further Reading Applications of Postprocessing for Hydrological Forecasts Introduction Univariate Hydrological Postprocessing Skewness and the Assumption of Gaussianity Univariate Hydrological Ensemble Postprocessing Postprocessing of Hydrological Forecasts Versus Postprocessing of Meteorological Input Multivariate Hydrological Postprocessing Temporal Dependencies Spatial Dependencies Spatio-Temporal Dependencies Outlook References Application of Postprocessing for Renewable Energy Introduction Preliminaries: Relevant Forecasting Products and Notation Conversion of Meteorological Variables to Power Data and Empirical Features Local Polynomial Regression as a Basis Time-Varying Estimation to Accommodate Nonstationarity From Least Squares Estimation to Fitting of Principal Curves Calibrated Predictive Densities of Power Generation Calibration Prior to Conversion Kernel dressing of wind speed Inverse power curve transformation Calibration After Conversion Nonhomogeneous regression of wind power Adaptive kernel dressing Direct Calibration of Wind Power Conclusions and Perspectives Appendix: Simulated Data for the Conversion of Wind to Power References Postprocessing of Long-Range Forecasts Introduction Challenges of Long-Range Forecasts A Statistical Framework for Postprocessing Statistical Hypotheses Reliability of Long-Range Forecasts Multimodel Combination or Consolidation The Use of Multimodels for Probabilistic Forecasts Drift and Trend Correction Techniques Ensemble Postprocessing Techniques Application of Postprocessing in an Idealized Model Setting Experimental Setup Postprocessing Single-Model Ensembles Multimodel Ensemble Forecasts Application Using an Operational Long-Range Forecasting System Conclusions Appendix: The Idealized Model References Ensemble Postprocessing With R Introduction Deterministic Postprocessing Data Model Fitting Prediction Verification Univariate Postprocessing of Temperature Data Model Fitting Nonhomogeneous Gaussian regression BMA and other ensemble dressing approaches Prediction Verification Postprocessing of Precipitation Data Model Fitting Nonhomogeneous regression Bayesian model averaging Logistic regression Prediction Verification Multivariate Postprocessing of Temperature and Precipitation Data Model Fitting Prediction Verification Summary and Discussion Appendices Appendix A: Code for Some Functions Used in This Chapter Appendix B: Available R Packages for Ensemble Postprocessing Available data sets and data processing Ensemble postprocessing models Verification References Author Index A B C D E F G H I J K L M N O P R S T U V W X Y Z Subject Index A B C D E F G 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