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Applications of Copula in hydrological extreme analysis

Yue‐Ping Xu, Jia Li, Fei Cao, Qi Hua Ran

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Abstract

The dependences between multiple variables were analyzed aiming at some abnormal crossing phenomena of rainfall depths for different durations in hydrological extreme analysis.The relationship between multivariate joint density distributions and their marginal distributions was described through Copula.Gumbel-Hougaard Copula was used to model the dependences of rainfall depths for different durations.Results showed that rainfall depths obtained by Gumbel-Hougaard Copula were smaller than those obtained by conventional frequency analysis.Gumbel-Hougaard Copula can well describe the multivariate relationship and improve the abnormal crossing phenomena,so it can give more reasonable results and be further applied to hydrological extreme analysis.

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What this paper is about

The dependences between multiple variables were analyzed aiming at some abnormal crossing phenomena of rainfall depths for different durations in hydrological extreme analysis.The relationship between multivariate joint density distributions and their marginal distributions was described through Copula.Gumbel-Hougaard Copula was used to model the dependences of rainfall depths for different durations.Results showed that rainfall depths obtained by Gumbel-Hougaard Copula were smaller than those obtained by conventional frequency analysis.Gumbel-Hougaard Copula can well describe the multivariate relationship and improve the abnormal crossing phenomena,so it can give more reasonable results and be further applied to hydrological extreme analysis.

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Available abstract

The dependences between multiple variables were analyzed aiming at some abnormal crossing phenomena of rainfall depths for different durations in hydrological extreme analysis.The relationship between multivariate joint density distributions and their marginal distributions was described through Copula.Gumbel-Hougaard Copula was used to model the dependences of rainfall depths for different durations.Results showed that rainfall depths obtained by Gumbel-Hougaard Copula were smaller than those obtained by conventional frequency analysis.Gumbel-Hougaard Copula can well describe the multivariate relationship and improve the abnormal crossing phenomena,so it can give more reasonable results and be further applied to hydrological extreme analysis.

Key concepts: Gumbel distribution, Copula (linguistics), Multivariate statistics, Marginal distribution, Joint probability distribution, Extreme value theory, Econometrics, Statistics

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