Bivariate Seasonal Design Flood Estimation Based on Copulas

Seasonal design floods reflecting seasonal variation information are very important for reservoir operation and management. The seasonal design flood estimation method currently used in China is based on univariate frequency analysis and assumes that the seasonal and annual design frequencies are equal, which neither satisfies flood prevention standards nor considers the interdependence between different seasonal floods. The Danjiangkou reservoir located in the Han River basin, the first pilot basin of most regulated water resources management policy in China, was selected as a case study. After dividing the entire flood season into subseasons, a dependent structure of summer and autumn floods was established by copula functions. Three bivariate flood quantile selection methods, namely the equivalent frequency combination (EFC) method, conditional expectation combination (CEC) method, and conditional most likely combination (CMLC) method, were performed to estimate unique seasonal design floods to meet the needs in engineering and compared with the univariate design values. The evaluation criteria and a boundary identification method were used to assess the rationality of these combination methods. Compared with the CEC and EFC methods, the CMLC method has smaller root-mean square error (RMSE) and bias values by 12.9–34.8% and 22.6–36.4%, respectively. The CMLC and EFC methods are within the feasible regions, whereas the CEC estimators are beyond the feasible range. The results of economic analysis show that the CMLC method can enhance the floodwater use rate from 79.7 to 82.8% for the wet year and from 91.8 to 93.7% for the dry year in comparison with the EFC method. The CMLC method is more rational in physical realism and recommended for estimating seasonal design floods in the Danjiangkou reservoir, which would provide rich information as references for flood risk assessment, reservoir scheduling, and management.