A nonparametric copula distribution framework for bivariate joint distribution analysis of flood characteristics for the Kelantan River basin in Malaysia

The joint distribution analysis of multidimensional flood characteristics i.e., flood peak flow, volume and duration, often facilitates a comprehensive understanding in the hydrologic risk assessments. Copula-based methodology are frequently incorporated via parametric approach to model dependence structure of parametric based univariate marginal distributions. But, if the targeted copulas and univariate marginal distributions belongs to some specific parametric families, it might be problematic, if the underlying assumption are violated. Also, no universal rules and literatures are imposed to model any hydrologic vectors and their joint dependence structure through any fixed or pre-defined distributions. In this literature, a nonparametric copula simulation are incorporated and applied as a case study for 50 years annual maximum flood samples of the Kelantan River basin at the Gulliemard bridge station in Malaysia. In this study, a combination of both parametric and nonparametric marginal distribution separately conjoined by a nonparametric copulas framework, which is based on the Beta kernel function. The Beta kernel copula function are incorporated to estimate bivariate copula density which further used to derived joint cumulative density of flood peak-volume, volume-duration and peak-duration pairs and their associated joint as well as conditional return periods.