Reservoirs operation alters the natural flow regime at downstream site and thus has a great impact on the design flood values. The general framework of flood regional composition and Equivalent Frequency Regional Composition (EFRC) method are currently used to calculate design floods at downstream site while considering the impact of the upstream reservoirs. However, this EFRC method deems perfect correlation between peak floods that occurred at one sub-basin and downstream site, which implicitly assumes that the rainfall and the land surface process are uniformly distributed for various sub-basins. In this study, the Conditional Expectation Regional Composition (CERC) method and Most Likely Regional Composition (MLRC) method based on copula function are proposed and developed under the flood regional composition framework. The proposed methods (i.e., CERC and MLRC) are tested and compared with the EFRC method in the Shuibuya-Geheyan-Gaobazhou cascade reservoirs located at Qingjiang River basin, a tributary of Yangtze River in China. Design flood values of the Gaobazhou reservoir site are estimated under the impact of upstream cascade reservoirs, respectively. Results show that design peak discharges at the Gaobazhou dam site have been significantly reduced due to the impact of upstream reservoir regulation. The EFRC method, not taking the actual dependence of floods occurred at various sub-basins into account; as a consequence, it yields an under-or overestimation of the risk that is associated with a given event in hydrological design. The proposed methods with stronger statistical basis can better capture the actual spatial correlation of flood events occurred at various sub-basins, and the estimated design flood values are more reasonable than the currently used EFRC method. The MLRC method is recommended for design flood estimation in the cascade reservoirs since its composition is unique and easy to implement.

Design flood estimation is very important for hydraulic structure design, reservoir operation, and water resources management. During the last few decades, severe flash floods have caused substantial human, agricultural, and economic damages in Pakistan during the Monsoon seasons. However, despite phenomenal losses, the flood characteristics are rarely investigated. In this paper, flood frequency analysis (FFA) on four major rivers over Pakistan is performed to probe probability distributions (PDs)at the right-tail flood events. For this purpose, (i) we employed ten different probability distributions associating with an L-moments method for constructing FFA models across Pakistan; (ii) we evaluated the best-fit distribution by using goodness-of-fit test and statistical criteria; and finally; (iii) we devised a Monte Carlo simulation to systematically evaluate the robustness of a selected distribution’s fitting performance by using a synthetic data series of different sizes. Our results indicated that generalized Pareto and Weibull emerged as the most viable options for quantifying hydrological quantiles for most of the river basins in Pakistan. Our main findings would provide rich information as references for flood risk assessment and water resource management 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.