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

The topic of predictability in weather and climate has advanced significantly in recent years, both in understanding the phenomena that affect weather and climate and in techniques used to model and forecast them. This book, first published in 2006, brings together some of the world's leading experts on predicting weather and climate. It addresses predictability from the theoretical to the practical, on timescales from days to decades. Topics such as the predictability of weather phenomena, coupled ocean-atmosphere systems and anthropogenic climate change are among those included. Ensemble systems for forecasting predictability are discussed extensively. Ed Lorenz, father of chaos theory, makes a contribution to theoretical analysis with a previously unpublished paper. This well-balanced volume will be a valuable resource for many years. High-calibre chapter authors and extensive subject coverage make it valuable to people with an interest in weather and climate forecasting and environmental science, from graduate students to researchers.

This handy reference introduces the subject of forecastverification and provides a review of the basic concepts,discussing different types of data that may be forecast. Each chapter covers a different type of predicted quantity(predictand), then looks at some of the relationships betweeneconomic value and skill scores, before moving on to review the keyconcepts and summarise aspects of forecast verification thatreceive the most attention in other disciplines. The book concludes with a discussion on the most importanttopics in the field that are the subject of current research orthat would benefit from future research. An easy to read guide of current techniques with real life casestudies An up-to-date and practical introduction to the differenttechniques and an examination of their strengths andweaknesses Practical advice given by some of the world?s leadingforecasting experts Case studies and illustrations of actual verification and itsinterpretation Comprehensive glossary and consistent statistical andmathematical definition of commonly used terms

The Gap Between Weather and Climate Forecasting: Sub-seasonal to Seasonal Prediction is an ideal reference for researchers and practitioners across the range of disciplines involved in the science, modeling, forecasting and application of this new frontier in sub-seasonal to seasonal (S2S) prediction. It provides an accessible, yet rigorous, introduction to the scientific principles and sources of predictability through the unique challenges of numerical simulation and forecasting with state-of-science modeling codes and supercomputers. Additional coverage includes the prospects for developing applications to trigger early action decisions to lessen weather catastrophes, minimize costly damage, and optimize operator decisions. The book consists of a set of contributed chapters solicited from experts and leaders in the fields of S2S predictability science, numerical modeling, operational forecasting, and developing application sectors. The introduction and conclusion, written by the co-editors, provides historical perspective, unique synthesis and prospects, and emerging opportunities in this exciting, complex and interdisciplinary field. - Contains contributed chapters from leaders and experts in sub-seasonal to seasonal science, forecasting and applications - Provides a one-stop shop for graduate students, academic and applied researchers, and practitioners in an emerging and interdisciplinary field - Offers a synthesis of the state of S2S science through the use of concrete examples, enabling potential users of S2S forecasts to quickly grasp the potential for application in their own decision-making - Includes a broad set of topics, illustrated with graphic examples, that highlight interdisciplinary linkages

This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.

Hydrometeorological prediction involves the forecasting of the state and variation of hydrometeorological elements -- including precipitation, temperature, humidity, soil moisture, river discharge, groundwater, etc.-- at different space and time scales. Such forecasts form an important scientific basis for informing public of natural hazards such as cyclones, heat waves, frosts, droughts and floods. Traditionally, and at most currently operational centers, hydrometeorological forecasts are deterministic, “single-valued” outlooks: i.e., the weather and hydrological models provide a single best guess of the magnitude and timing of the impending events. These forecasts suffer the obvious drawback of lacking uncertainty information that would help decision-makers assess the risks of forecast use. Recently, hydrometeorological ensemble forecast approaches have begun to be developed and used by operational collection of hydrometeorological services. In contrast to deterministic forecasts, ensemble forecasts are a multiple forecasts of the same events. The ensemble forecasts are generated by perturbing uncertain factors such as model forcings, initial conditions, and/or model physics. Ensemble techniques are attractive because they not only offer an estimate of the most probable future state of the hydrometeorological system, but also quantify the predictive uncertainty of a catastrophic hydrometeorological event occurring. The Hydrological Ensemble Prediction Experiment (HEPEX), initiated in 2004, has signaled a new era of collaboration toward the development of hydrometeorological ensemble forecasts. By bringing meteorologists, hydrologists and hydrometeorological forecast users together, HEPEX aims to improve operational hydrometeorological forecast approaches to a standard that can be used with confidence by emergencies and water resources managers. HEPEX advocates a hydrometeorological ensemble prediction system (HEPS) framework that consists of several basic building blocks. These components include:(a) an approach (typically statistical) for addressing uncertainty in meteorological inputs and generating statistically consistent space/time meteorological inputs for hydrological applications; (b) a land data assimilation approach for leveraging observation to reduce uncertainties in the initial and boundary conditions of the hydrological system; (c) approaches that address uncertainty in model parameters (also called ‘calibration’); (d) a hydrologic model or other approach for converting meteorological inputs into hydrological outputs; and finally (e) approaches for characterizing hydrological model output uncertainty. Also integral to HEPS is a verification system that can be used to evaluate the performance of all of its components. HEPS frameworks are being increasingly adopted by operational hydrometeorological agencies around the world to support risk management related to flash flooding, river and coastal flooding, drought, and water management. Real benefits of ensemble forecasts have been demonstrated in water emergence management decision making, optimization of reservoir operation, and other applications.

Statistical Methods in the Atmospheric Sciences, Third Edition, explains the latest statistical methods used to describe, analyze, test, and forecast atmospheric data. This revised and expanded text is intended to help students understand and communicate what their data sets have to say, or to make sense of the scientific literature in meteorology, climatology, and related disciplines. In this new edition, what was a single chapter on multivariate statistics has been expanded to a full six chapters on this important topic. Other chapters have also been revised and cover exploratory data analysis, probability distributions, hypothesis testing, statistical weather forecasting, forecast verification, and time series analysis. There is now an expanded treatment of resampling tests and key analysis techniques, an updated discussion on ensemble forecasting, and a detailed chapter on forecast verification. In addition, the book includes new sections on maximum likelihood and on statistical simulation and contains current references to original research. Students will benefit from pedagogical features including worked examples, end-of-chapter exercises with separate solutions, and numerous illustrations and equations. This book will be of interest to researchers and students in the atmospheric sciences, including meteorology, climatology, and other geophysical disciplines. - Accessible presentation and explanation of techniques for atmospheric data summarization, analysis, testing and forecasting - Many worked examples - End-of-chapter exercises, with answers provided