Modelling of extreme rainfall using copula

Abstract

A copula-based analysis is usually performed in hydrology for the purpose of water management and flood prevention by analyzing the hydrological attributes, such as rainfall volume and duration. The primary goal of this study is to fit the rainfall volume and duration into copulas. The analysis was conducted on six selected rainfall stations in Malaysia with hourly rainfall data. The correlation between volume and duration is measured by Kendalls correlation coefficient. Clayton, Gumbel-Hougard (GH), Frank and Joe copulas of Archimedean family are used and the parameter of the copulas is estimated using Maximum Likelihood Estimation (MLE). Akaikes Information Criterion (AIC), three graphical methods, and Goodness-of-Fit (GOF) tests are used to find the best parameter estimation of copulas. The three graphical methods used are the conditional distribution function of Y|X, the distribution function of the copula, and a nonparametric estimate of the distribution of the copula approach. The GOF tests are The Kolmogorov-Smirnov (K-S) and Chi-Square (χ2) tests. Results estimate that Frank copula is found to be suitable to represent the rainfall volume and duration for all stations.