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Über dieses Buch

This richly illustrated book describes statistical extreme value theory for the quantification of natural hazards, such as strong winds, floods and rainfall, and discusses an interdisciplinary approach to allow the theoretical methods to be applied. The approach consists of a number of steps: data selection and correction, non-stationary theory (to account for trends due to climate change), and selecting appropriate estimation techniques based on both decision-theoretic features (e.g., Bayesian theory), empirical robustness and a valid treatment of uncertainties. It also examines and critically reviews alternative approaches based on stochastic and dynamic numerical models, as well as recently emerging data analysis issues and presents large-scale, multidisciplinary, state-of-the-art case studies.

Intended for all those with a basic knowledge of statistical methods interested in the quantification of natural hazards, the book is also a valuable resource for engineers conducting risk analyses in collaboration with scientists from other fields (such as hydrologists, meteorologists, climatologists).



Chapter 1. Extreme Events and History: For a Better Consideration of Natural Hazards

This preface aims to remind us of the fundamental importance, for our modern but fragile societies, of the difficult study of historical data on natural hazards. Forgetting is a regular feature of our decisions, and the preservation of the memory of natural disasters depends heavily on our ability to quantify their effects. The author, a climate historian, recalls here some fundamental aspects of this discipline and its necessary connection to statistical approaches to risk analysis.
Emmanuel Garnier

Chapter 2. Introduction

This introduction recalls the considerable socio-economic challenges associated with extreme natural hazards. The possibilities of statistical quantification of past hazards and extrapolation, offered by extreme value theory, make it an essential tool to improve risk mitigation. The objectives of this book, answering the questions of engineers, decision-makers, researchers, professors, and students, are briefly presented.
Nicolas Bousquet, Pietro Bernardara

Standard Extreme Value Theory


Chapter 3. Probabilistic Modeling and Statistical Quantification of Natural Hazards

This chapter presents the main useful concepts of the statistical approach to extreme values, such as return periods or levels, as well as a general methodology for conducting a statistical study. It also introduces alternative approaches, statistical or not, that can be valuable in dealing with extreme natural hazards.
Pietro Bernardara, Nicolas Bousquet

Chapter 4. Fundamental Concepts of Probability and Statistics

This chapter recalls the fundamental concepts and results of probability theory and statistical theory. These are essential to understand and use the tools of extreme value theory in an appropriate way. From the notions of randomness, probability distributions to random processes, from classical estimators to regression models, this chapter aims to facilitate the technical understanding of the rest of this book.
Nicolas Bousquet

Chapter 5. Collecting and Analyzing Data

This chapter focuses on the first steps of a statistical study of extreme values based on real hazard data. Illustrated by numerous examples, the qualitative and quantitative characteristics of these data are analyzed in order to come as close as possible to the theoretical conditions of application—in particular the notion of asymptotism—and to statistically characterize their nature (regular, truncated, censored...). This chapter is, therefore, an essential prerequisite for the concrete application of the theoretical tools presented in the following chapters.
Marc Andreewsky, Nicolas Bousquet

Chapter 6. Univariate Extreme Value Theory: Practice and Limitations

This chapter presents the classic theory of univariate extreme values and its application to various natural hazards described in the previous chapters. The limitations of this approach are discussed, which pave the way for the second part of this book.
Anne Dutfoy

Elements of Extensive Statistical Analysis


Chapter 7. Regional Extreme Value Analysis

This chapter focuses on the occurrence of extreme natural hazards in non-instrumented locations, whose neighborhood contains sites for which measured data are available. The spatial regionalization approach developed here, which is based on the detection of regions that are homogeneous in terms of risk, allows to propose a localized quantification of these events.
Jérôme Weiss, Marc Andreewsky

Chapter 8. Extreme Values of Non-stationary Time Series

This chapter considers the problem of quantifying extreme natural hazards in non-stationary situations, namely outside the traditional framework. For certain hazards, this framework makes it possible to take into account the influence of climate change. Two main approaches are considered: the first deals with the incorporation and selection of trends in the parameters of the laws of extremes, while the second, nonparametric, considers trend variations over the first two moments of the extreme distribution.
Sylvie Parey, Thi-Thu-Huong Hoang

Chapter 9. Multivariate Extreme Value Theory: Practice and Limits

This chapter presents the most recent developments in extreme value theory in cases of joint, or multivariate, hazards. This type of phenomenon is increasingly being studied, as it can be more destructive than a single hazard. Introducing, in particular, the notion of copula, this chapter takes up the notations and main concepts introduced in Chap. 6.
Anne Dutfoy

Chapter 10. Stochastic and Physics-Based Simulation of Extreme Situations

This chapter addresses two alternative approaches to extreme situations, which may be useful when the lack of extreme observations severely limits the relevance of a purely statistical approach. The first methodology is based on stochastic modeling of the regular phenomenon, for example, via autoregressive processes. Capturing this phenomenon allows extrapolation to extreme values based on theoretical properties of stochastic processes. The second approach is based on the use, by Monte Carlo-based methods, of numerical simulation models implementing the physical equations representing the phenomenon under study. This second approach, which is originally used in structural reliability, requires the development of specific simulation techniques that focus on very low-probability events; it appears to be more and more appropriate as expert knowledge of the phenomena increases.
Sylvie Parey, Thi-Thu-Huong Hoang, Nicolas Bousquet

Chapter 11. Bayesian Extreme Value Theory

This chapter provides an introduction to Bayesian statistical theory and a broad review of its application to extreme values. The Bayesian methodology differs greatly from the traditional approaches considered in the other chapters. Indeed, it requires the construction of so-called prior measures for the parameters of extreme value models and defines estimation through the minimization of a cost function adapted to the event. While Bayesian calculations (as those based on Monte Carlo Markov Chains) remain superficially discussed, this chapter focuses on modeling features, which allow expert opinion and historical knowledge to be integrated into the estimation of quantities of interest. In this respect, the Bayesian approach constitutes a methodology of increasing use, allowing the mixed treatment of aleatoric and epidemic uncertainties and adapted to the specific needs of engineers.
Nicolas Bousquet

Chapter 12. Perspectives

This chapter provides a brief summary of the latest results obtained in extreme value theory, and offers many suggestions for the reader interested in using these tools in a context where, in particular, statisticians and engineers cannot ignore the Big Data paradigm and the industrialization of machine learning tools, now essential components of modern artificial intelligence. Parallels are also made with other disciplines interested in extreme statistics.
Marc Andreewsky, Pietro Bernardara, Nicolas Bousquet, Anne Dutfoy, Sylvie Parey

Detailed Case Studies on Natural Hazards


Chapter 13. Predicting Extreme Ocean Swells

This chapter illustrates the conduct of a classic univariate extreme statistical study on severe ocean swell forecasting.
Pietro Bernardara

Chapter 14. Predicting Storm Surges

In this chapter, we present a second example of statistical estimation of extreme quantiles: millennial quantiles for storm surges at Brest (France), based on hourly sea-level measurements. We run sensitivity tests on parameter values, on the choice of analytic models for distributions, and on the statistical estimation methods chosen. Uncertainty in estimates and associated confidence intervals are also calculated and compared.
Marc Andreewsky

Chapter 15. Forecasting Extreme Winds

This chapter considers the modeling and forecasting of extreme wind values. This one-dimensional problem is dealt with in depth and provides a third example of the deployment of the “classic” methodology for the treatment of natural extreme values.
Sylvie Parey

Chapter 16. Conjunction of Rainfall in Neighboring Watersheds

This chapter presents, in great detail, a statistical study of extreme values in a bivariate setting, where the hazards considered together are rains in nearby watersheds. This type of natural hazard can cause destructive flooding. The different steps of the treatment methodology are clarified, and particular care is paid to checking the conditions of the relevance of the theory.
Nicolas Roche, Anne Dutfoy

Chapter 17. Conjunction of a Flood and a Storm

The case study in this chapter involves the conjunction of two climate hazards: a flood (high river flow) and a storm (strong wind), which we label Flow and Wind Speed for simplicity. A combination of the two is likely to jeopardize industrial installations. The aim of the study is to calculate the probability of the conjunction of these extreme events and produce daily probability and annual frequency plots of such events.
Alain Sibler, Anne Dutfoy

Chapter 18. SCHADEX: An Alternative to Extreme Value Statistics in Hydrology

This chapter presents, in detail, a methodology used by EDF in many hydrological studies, which offers an alternative to the use of extreme value distributions. Based on multi-exponential weather patterns and hydrological models, this approach has proven to be robust and demonstrates that the response provided by statistical theory is not necessarily the most appropriate in practice. The existence of this approach demonstrates the need to continue the research of suitable statistical models, and the comparison of real data with models derived from theory.
Emmanuel Paquet


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