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1 2020

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

Latif Shahid, Mustafa Firuza

Acta Geophysica

2020

Vol. 68, no. 3

821--859

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 food, which often demands multivariate fow exceedance probabilities. The joint distribution analysis of multiple interacting food characteristics, i.e. food 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 food frequency analysis for the 50-year annual basis food 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 food peak fow, 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 food 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 identifed as the most justifable model for joint modelling of the food peak–volume and peak–duration combination for MOM-based parameter estimation procedure. Similarly, the Frank copula is selected as the best-ftted 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-ftted copulas are used for obtaining the joint and conditional return periods of the food characteristics