Trivariate copula for flood frequency analysis in Johor river basin

Abstract

flood variables are generally random in nature and mutually correlated, consist of peak flow, flood duration and flood volume. flood frequency analysis defines the severity of a flood event by finding out their mutual dependence structure of flood variables. copula is presented for flood frequency analysis through this study. copula is a bivariate statistical method for constructing dependency structure and joint probabilistic distribution. copula relaxes the restriction of traditional flood frequency analysis by selecting marginal from different families of probability distribution functions for flood variables. thus, the trivariate copula function is developed in order to assess flood frequency. the analysis used 34 years hourly discharge data from year 1965 until year 2010 from johor river basin from which the annual maximum were derived. on evaluation of various probability distributions for representation of flood variables, it is found that the peak flow can be fitted as generalized pareto (gp) distribution while flood duration and flood volume are well represented as generalized extreme value (gev). the joint distribution is modeled using five trivariate copulas namely clayton, gumbel, frank, gaussian and student-t copulas. based on the performance measure and simulation, it is found that clayton copula is the best copula to represent the trivariate dependency structure of flood properties as compared to copulas. the obtained copula based joint distributions are used to calculate the return period of flood risks. the study concludes that the trivariate copula based methodology is a suitable choice for effective risk assessment of flood frequency analysis as it is able to consider the entire characteristics of flood variables.