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

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 toot are also highlighted. (c) 2006 Elsevier Ltd. All rights reserved.