Bivariate joint distribution analysis of the flood characteristics under semiparametric copula distribution framework for the Kelantan River basin in Malaysia

Abstract Flood is becoming the severe hydrologic issue at the Kelantan River basin in Malaysia. The joint distribution analysis among multiple interacting flood characteristics, i.e., flood peak discharge flow, volume, and duration series usually provide a comprehensive understanding of the hydrologic risk assessments through visualizing the multivariate exceedance probability or return periods. The traditional copulas-based methodology is frequently employed under parametric settings where parametric family functions are often employed to model univariate marginal distribution before capturing their dependence structure. Actually, no universal rules and literature are imposed to model any flood vectors through any fixed or predefined density function, which would follow the different distribution and needs to model by fitting most parsimonious function. Also, the copula function already relaxes the restriction of selecting marginal distributions from the same distribution families. Therefore, incorporation of non-parametric kernel density estimations or KDE would be much stable and less biased smoothing alternatives than the parametric approach. In this literature, the semi-parametric copula-based methodology is incorporated, where the flood marginals are modelled under the kernel functions and applied as a case study for 50 years annual maximum (AM) flood samples of the Kelantan River basin at the Gulliemard Bridge gauge station in Malaysia. The Archimedean families copulas (i.e., Frank, Gumbel and Clayton) and Elliptical copula (i.e., Gaussian copula) are tested, and thus best-fitted copulas are employed to model the bivariate joint distribution among flood characteristics, and which further employed to derive joint and conditional return periods.