Bivariate hydrologic risk analysis based on a coupled entropy-copula method for the Xiangxi River in the Three Gorges Reservoir area, China

In this study, a bivariate hydrologic risk framework is proposed based on a coupled entropy-copula method. In the proposed risk analysis framework, bivariate flood frequency would be analyzed for different flood variable pairs (i.e., flood peak-volume, flood peak-duration, flood volume-duration). The marginal distributions of flood peak, volume, and duration are quantified through both parametric (i.e., gamma, general extreme value (GEV), and lognormal distributions) and nonparametric (i.e., entropy) approaches. The joint probabilities of flood peak-volume, peak-duration, and volume-duration are established through copulas. The bivariate hydrologic risk is then derived based on the joint return period to reflect the interactive effects of flood variables on the final hydrologic risk values. The proposed method is applied to the risk analysis for the Xiangxi River in the Three Gorges Reservoir area, China. The results indicate the entropy method performs best in quantifying the distribution of flood duration. Bivariate hydrologic risk would then be generated to characterize the impacts of flood volume and duration on the occurrence of a flood. The results suggest that the bivariate risk for flood peak-volume would not decrease significantly for the flood volume less than 1000 m3/s. Moreover, a flood in the Xiangxi River may last at least 5 days without significant decrease of the bivariate risk for flood peak-duration.