Bivariate copula for flood frequency analysis in Johor river basin

Abstract

Flooding is a multi-attribute event that is described by many factors such as peak flow and flood volume. It is extremely vital to consider both the flood volume and the flood peak while studying the flood frequency analysis as the univariate analysis cannot accurately portray the flood issue and suffers from an underestimation and an overestimation problem. Traditional univariate and multivariate modeling techniques have several mathematical shortcomings including the inability to distinguish between the marginal and joint behavior of the variables under study. Therefore, the copula function was introduced to tackle the above restriction. Six copula models will be applied in this study to find the best bivariate distribution between the flood variables in Johor River Basin, Malaysia, including Gaussian, Student-t, Clayton, Gumbel, Frank, and Joe. Before that, several marginal distributions were fitted to select the most appropriate distribution for flood variables. It was found that the Pearson Type-III fits both the flood peak flow and the flood volume best. The evaluation of the best univariate marginal distribution and the copula model will be based on Akaike Information Criterion (AIC). Our findings suggested that Frank Copula is more suited to represent the relationship between peak flow and flood volume as it portrays the lowest AIC values of -69.41 and highest log-likelihood values of 35.7, where both values outperform the other proposed copula models. However, future research which considers all three flood variables which are peak flow, volume, and duration should be conducted to attain a more reliable result.