The Return Period Analysis of Heavy Rainfall Disasters Based on Copula Joint Statistical Modeling

Abstract In the last few years, with the frequent occurrence of extreme weather across the globe, it has become clear that a comprehensive understanding of the patterns and main characteristics of disaster occurrence is essential, and the willingness to study these variables has become more urgent than ever. This paper analyses the multivariate and spatial distribution characteristics of heavy precipitation disasters and proposes a method for estimating the degree of disaster-causing risk using a joint statistical model. This paper tests the model's validity with hourly precipitation data from 122 national meteorological stations in Shandong from 1990 to 2023. Based on heavy precipitation events in the past thirty years, different marginal distribution functions fit the duration of heavy precipitation and precipitation amount. The joint probability distribution model of two related variables is established based on the Copula joint distribution to analyze the change rule of heavy precipitation recurrence period in different periods and to analyze the characteristics of heavy precipitation causing disasters in Shandong Province on this basis. Compared with the disaster return period calculated by relying on univariate variables, the Copula function can more reasonably simulate the natural occurrence of the degree of disaster. This method can more scientifically describe the risk of disasters caused by heavy precipitation in different scenarios, especially the characteristics of disasters caused by short-term heavy precipitation, which can provide an adequate scientific basis for disaster prevention and mitigation planning and disaster risk management.