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Use of a Gaussian copula for multivariate extreme value analysis: some case studies in hydrology

Résumé : L'analyse probabiliste multivariée permet de prendre en compte plusieurs composantes d'un même phénomène. Cet article présente quatre cas d'application d'une copule Gaussienne en hydrologie, pour l'analyse régionale de la significativité de tests locaux, l'analyse d'un risque régional de défaillance, l'étude de courbes débit-durée-fréquence et leur utilisation pour la construction d'hydrogrammes de crue de référence, et l'étude d'une loi régionale des valeurs extrêmes avec prise en compte des dépendances spatiales. Certaines limites de cette copule sont enfin mises en évidence. / Risk assessment requires a description of the probabilistic properties of hydrological variables. In a number of cases, this description is made on a single variable, whereas most hydrological events are intrinsically multivariate. In this context, copulas have recently received attention in order to derive a multivariate frequency analysis. After a reminder of the general results in the field of multivariate extreme value theory, the paper gives a description of a very simple copula, the Gaussian copula. Four case studies demonstrate its usefulness in the contexts of field significance determination, regional risk analysis, discharge-duration-frequency (QdF) models with design hydrograph derivation and regional frequency analysis. The limitations and potential errors related to this statistical tool are also highlighted.
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Benjamin Renard, M. Lang. Use of a Gaussian copula for multivariate extreme value analysis: some case studies in hydrology. Advances in Water Resources, Elsevier, 2007, 30, p. 897 - p. 912. ⟨10.1016/j.advwatres.2006.08.001⟩. ⟨hal-00453788⟩

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