Flood Double Frequency Analysis: 2D-Archimedean Copulas vs Bivariate Probability Distributions

Abstract

Floods are multidimensional phenomena which are conventionally studied considering the pairwise dependence between peak flow and flood volume or peak flow and duration. In this paper, the flood phenomenon is analysed based on the peak flow-flood volume dependence. The paper presents a comparison between two methodologies for the double frequency analysis using a bivariate probability distribution and the copulas approach. The comparison is performed with data from a case study example of the Ashuapmushuan river basin in Quebec, Canada. In the presented example the bivariate Extreme Value distribution type I (Gumbel) is used for comparison with the bivariate Gumbel-Hougaard Archimedean copula. For the parameters estimation of the the latter, the Kendall method and the maximum likelihood method are employed. Based on the derived results of the analysed example, it can be concluded that for engineering purposes, the copulas approach, regardless of the method of its parameter estimation, provides a simple and accurate approach for the frequency analysis of floods and the estimation of the design variables thereof. The Kendall estimation parameter method, as simpler method, is easier to apply.