Bivariate flood distribution analysis under parametric copula framework: a case study for Kelantan River basin in Malaysia

Abstract

Flood is becoming an intensive hydro-climatic issue at the Kelantan River basin in Malaysia. Univariate frequency analysis would be unreliable due to multidimensional behaviour of flood, which often demands multivariate flow exceedance probabilities. The joint distribution analysis of multiple interacting flood characteristics, i.e. flood peak, volume and duration, is very useful for understanding critical hydrologic behaviour at a river basin scale. In this paper, a copula-based methodology is incorporated for multivariate flood frequency analysis for the 50-year annual basis flood characteristics of Kelantan River basin at Guillemard bridge station in Malaysia. Investigation reveals that the Lognormal (2P), Johnson SB-4P and Gamma-3P are selected as marginal distributions for the flood peak flow, volume and duration series. Several bivariate families such as mono-parametric, bi-parametric (i.e. mixed version) and rotated version of Archimedean copulas and also the elliptical copula are introduced to cover a large dependence pattern of flood characteristics. The dependence parameter of bivariate copulas is estimated by the method of moments (MOM) based on the inversion of Kendall’s tau and maximum pseudo-likelihood estimator. To analytically validate and recognize most parsimonious copulas, GOF test and Cramer–von Mises distance statistics (Sn) with the parametric bootstrap method are employed. The Gaussian copula is identified as the most justifiable model for joint modelling of the flood peak–volume and peak–duration combination for MOM-based parameter estimation procedure. Similarly, the Frank copula is selected as the best-fitted structure for modelling peak–duration combination based on MPL estimators, but the MOM estimator recognized Gaussian copula as most suitable for peak–volume pair. Furthermore, the best-fitted copulas are used for obtaining the joint and conditional return periods of the flood characteristics.