Research on the Joint Distribution of Flood Magnitude and Occurrence Time Based on Copula Function

 To overcome the limitation of traditional staged design flood calculation that only considers the magnitude but neglects the probability of occurrence time, this study takes the measured data from 1951 to 2022 and historical surveyed floods of Longtan Reservoir as samples, and constructs a joint distribution model of the annual maximum 15-day flood volume and occurrence time. Firstly, the P-III distribution and Von Mises distribution with good fitting effects are adopted as the marginal distributions of flood magnitude and occurrence time respectively. Then, the Copula function theory is introduced, and the Clayton Copula function is selected as the most suitable one to describe the joint distribution of the annual maximum 15-day flood volume and time. The results show that there is a strong positive dependence between the annual maximum 15-day flood volume and occurrence time of Longtan Reservoir, with a Kendall rank correlation coefficient of 0.7918; the annual maximum flood events are highly concentrated in the main flood season from May to August, and the larger the flood volume, the more concentrated the occurrence time is in the core period of the main flood season, and the probability of extremely large floods occurring in the non-flood season is almost zero. This model breaks through the independent assumption of traditional staged flood calculation and can provide a more comprehensive and reliable probabilistic basis for the staged design flood calculation and flood control dispatching scheme optimization of Longtan Reservoir.