Bivariate hydrologic risk analysis for the Xiangxi River in Three Gorges Reservoir Area, China

Abstract

Background: Hydrological extremes such as floods generally have multidimensional attributes with complex dependence structures. This leads to the urgent demand of hydrological risk analysis within a multivariate context. In this study, the bivariate hydrologic risk framework is proposed based on the bivariate 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), and the bivariate hydrologic risk is then derived based on the joint return period of a flood variable pair. The distribution of one flood variable conditional on another flood variable can also be obtained through the copula method.

Results: The proposed method is applied to the risk analysis for the Xiangxi River in the Three Gorges Reservoir area, China, based on 50 years streamflow measurements. The results indicate that the bivariate risk for flood peak flow-duration would keep constant for some time and then decrease as the increase of the flood duration. The bivariate risk for flood peak-volume holds a similar trend with the bivariate risk of flood peak-duration. The probability density functions (PDFs) of the flood volume and duration conditional on flood peak can also be generated through the best fitted copula function.

Conclusion: The results indicate that the distributions of flood volume would be highly influenced by the flood peak flows, in which the flood volume would be expected to increase as the increase of flood return period. Conversely, the distribution of the flood duration would not change significantly with the variation in the flood peak return period. The obtained conclusions from the bivariate hydrologic analysis can provide decision support for flood control and mitigation.