Abstract
Abstract. Multivariate Extreme Value models are a fundamental tool in order to assess potentially dangerous events. Exploiting recent theoretical developments in the theory of Copulas, new multiparameter models can be easily constructed. In this paper we suggest several strategies in order to estimate the parameters of the selected copula, according to different criteria: these may use a single station approach, or a cluster strategy, or exploit all the pair-wise relationships between the available gauge stations. An application to flood data is also illustrated and discussed.
Highlights
IntroductionMultivariate extremes occur in several hydrologic problems (like, e.g., space-time precipitation and floods (Singh, 1986; Pons, 1992; Wilks, 1998; Kim et al, 2003; Herr and Krzysztofowicz, 2005; Keef et al, 2009), or hydraulic conductivity in porous media – Journel and Alabert, 1988; Russo, 2009), as well as in many environmental problems (like, e.g., water quality and pollution (Grenney and Heyse, 1985), or sea levels – Butler et al, 2007)
Generalizations of Kendall’s τ (Nelsen, 1996), Spearman’s ρ (Schmid and Schmidt, 2007a,b), and Blomqvist’s β (Durante et al, 2007; Schmid and Schmidt, 2007c) to the d-variate case (d > 2) were only recently introduced – see below. These extensions may be of practical importance: on the one hand, they provide useful tools to quantify the dependence within clusters; on the other hand, they can be used to estimate the parameters of the multivariate model at play
In order to properly assess the risk, MEV models are fundamental in all areas of geophysics
Summary
Multivariate extremes occur in several hydrologic problems (like, e.g., space-time precipitation and floods (Singh, 1986; Pons, 1992; Wilks, 1998; Kim et al, 2003; Herr and Krzysztofowicz, 2005; Keef et al, 2009), or hydraulic conductivity in porous media – Journel and Alabert, 1988; Russo, 2009), as well as in many environmental problems (like, e.g., water quality and pollution (Grenney and Heyse, 1985), or sea levels – Butler et al, 2007). Generalizations of Kendall’s τ (Nelsen, 1996), Spearman’s ρ (Schmid and Schmidt, 2007a,b), and Blomqvist’s β (Durante et al, 2007; Schmid and Schmidt, 2007c) to the d-variate case (d > 2) were only recently introduced – see below These extensions may be of practical importance: on the one hand, they provide useful tools to quantify the dependence within clusters; on the other hand, they can be used to estimate the parameters of the multivariate model at play (see later). At present the application of these measures in actual case studies is still quite limited Another important issue is represented by the construction of Multivariate Extreme Value (hereafter, MEV) models involving a significant number of parameters.
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