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Extremes in a Changing Climate pp 115–162Cite as

Multivariate Extreme Value Methods

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Part of the book series: Water Science and Technology Library ((WSTL,volume 65))

Abstract

Multivariate extremes occur in several hydrologic and water resources problems. Despite their practical relevance, the real-life decision making as well as the number of designs based on an explicit treatment of multivariate variables is yet limited as compared to univariate analysis. A first problem arising when working in a multidimensional context is the lack of a “natural” definition of extreme values: essentially, this is due to the fact that different concepts of multivariate order and failure regions are possible. Also, in modeling multivariate extremes, central is the issue of dependence between the variables involved: again, several approaches are possible. A further practical problem is represented by the construction of multivariate Extreme Value models suitable for applications: the task is indeed difficult from a mathematical point of view. In addition, the calculation of multivariate Return Periods, quantiles, and design events, which represent quantities of utmost interest in applications, is rather tricky. In this Chapter we show how the use of Copulas may help in dealing with (and, possibly, solving) these problems.

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Acknowledgements

The Authors thank C. Sempi (Università del Salento, Lecce, Italy) and F. Durante (Università di Bozen–Bolzano, Bolzano, Italy) for invaluable helpful discussions and suggestions, and M. Pini (Università di Pavia, Pavia, Italy) for software recommendations. The excellent and constructive review of an anonymous Referee is also gratefully acknowledged. [G.S.] The research was partially supported by the Italian M.I.U.R. via the project “Metodi stocastici in finanza matematica”. The support of “Centro Mediterraneo Cambiamenti Climatici” (CMCC – Lecce, Italy) is acknowledged.

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Authors and Affiliations

  1. Dipartimento di Matematica e Fisica “E. De Giorgi”, Università del Salento, Provinciale Lecce-Arnesano, 193, I-73100, Lecce, Italy

    Gianfausto Salvadori

  2. Department of Hydraulic, Environmental, Roads and Surveying Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133, Milano, Italy

    Carlo De Michele

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  1. Gianfausto Salvadori
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Correspondence to Gianfausto Salvadori .

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  1. , Dept. of Civil and Env. Engineering, University of California, Irvine, Engineering Gateway E/4130, Irvine, 92697, California, USA

    Amir AghaKouchak

  2. NOAA's National Climatic Data Center, Patton Avenue 151, Asheville, 28801-5001, North Carolina, USA

    David Easterling

  3. , Dept. of Civil and Env. Engineering, University of California, Irvine, Engineering Gateway E/4130, Irvine, 92697, California, USA

    Kuolin Hsu

  4. NASA/Goddard Space Flight Center, Greenbelt Road 8800, Greenbelt, 20771, USA

    Siegfried Schubert

  5. , Dept. Civil & Environmental Engineering, University of California, Irvine, Engineering Gateway E/4130, Irvine, 92697, California, USA

    Soroosh Sorooshian

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Salvadori, G., De Michele, C. (2013). Multivariate Extreme Value Methods. In: AghaKouchak, A., Easterling, D., Hsu, K., Schubert, S., Sorooshian, S. (eds) Extremes in a Changing Climate. Water Science and Technology Library, vol 65. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4479-0_5

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