Multivariate flood risk analysis for Wei River

In this study, bivariate hydrologic risk analysis was conducted based on the daily streamflow discharge at the Xianyang station on the Wei River. This bivariate hydrologic risk analysis was conducted based on copula methods, in which the bivariate hydrologic frequency was firstly quantified through copulas, and the bivariate hydrologic risk analysis was then characterized based on the joint return period of flood pairs. The maximum likelihood estimation (MLE) and the method-of-moments-like (MOM) estimator were compared in estimating the unknown parameters in copula. The results showed that the Gumbel–Hougaard copula was most appropriate for modelling the dependence for all three flood pairs, in which the parameter of the copula for flood peak–volume was estimated by MLE and the parameters of the copulas for flood peak–duration and volume–duration were needed to be obtained by MOM. The bivariate hydrologic risk values are then obtained based on the AND-joint return period. The results show that the bivariate hydrologic values will not decrease until the corresponding volume for a flood is larger than 1.0 × 104 m3/s. For the bivariate hydrologic risk for flood peak–duration, the value will decrease quickly when the duration is longer than 5 days. Such bivariate hydrologic risk analysis can provide decision support for hydraulic facility design as well as actual flood control and mitigation.