Bivariate copulas functions for flood frequency analysis

Abstract

Bivariate flood frequency analysis offers improved understanding of the complex flood process and useful information in preparing flood mitigation measures. However, difficulties arise from limited bivariate distribution functions to jointly model major flood variables that are inter-correlated and each has different univariate marginal distribution. To overcome these difficulties, a Copula based methodology is presented in this study. Copula is functions that link univariate distribution functions to form bivariate distribution functions. Five Copula families namely Clayton, Gumbel, Frank, Gaussian and t Copulas were evaluated for modeling the joint dependence between peak flow-flood duration. The performance of four parameter estimation methods, namely inversion of Kendall's tau, inversion of Spearman's rho, maximum likelihood approach and inference function for margins for chosen copula's families are investigated. The analysis used 35 years hourly discharge data of Johor River from which the annual maximum were derived. Generalized Pareto and Generalized Extreme Value distribution were found to be the best to fit the flood variables based on the Kolmogorov-Smirnov goodness-of-fit test. Clayton Copula was chosen as the best fitted Copula function based on the Akaike Information Criterion goodness-of-fit test. It is found that, different methods of parameter estimation will give the same result on determining the best fit copula family. On performing a simulation based on a Cramer-von Mises as a test statistics to assess the performance of Copula distributions in modeling joint dependence structure of flood variables, it is found that Clayton Copula are well representing the flood variables. Thus, it is concluded that, the Clayton Copula based joint distribution function was found to be effective in preserving the dependency structure of flood variables. Thus, it is concluded that, the Clayton Copula based joint distribution function was found to be effective in preserving the dependency structure of flood variables.