Deriving Design Flood Hydrographs Based on Copula Function: A Case Study in Pakistan

Flood events are characterized by flood peaks and volumes that can be mutually constructed using a copula function. The Indus basin system of Pakistan is periodically threatened by floods during monsoon seasons and thus causes huge losses to infrastructure as well as the community and economy. The design flood hydrograph (DFH) of suitable magnitude and degree is imperative for sheltering dams against the flood risk. The hydrological pair of flood peak and volume is required to be defined using a multivariate analysis method. In this paper, the joint probability function of the hydrological pair is employed to derive the DFH in the Indus basin system of Pakistan. Firstly, we compared the fitting performance of different probability distributions (PDs) as a marginal distribution. Next, we compared the Archimedean family of copulas to construct the bivariate joint distribution of flood peak and volume. Later, the equal frequency combination (EFC) method and most likely combination (MLC) method using “OR” joint return period (JRP_or), was involved to derive the design flood quantiles. Finally, we derived the DFH using the two combination methods based on Gumbel–Hougaard copula for different return periods. We presented the combination methods for updating the shape of the DFH in Pakistan. Our study will contribute towards the improvement of design standards of dams and environmental recovery in Pakistan.