Calculating Combined Hazard Thresholds for Rainfall-Induced Hazards Based on Copula Functions

Against the background of global climate change and rapid urbanization, the frequency of extreme hydrological events has increased markedly, and hydrological and geological hazards induced by extreme heavy rainfall have occurred frequently. Considering the joint occurrence characteristics of heavy rainfall hazards, statistical methods are used in this study to develop a mathematical model for calculating hazard–risk combinations and disaster-triggering thresholds that integrates copula functions and the Kendall return period. First, a bivariate joint-distribution probability model is established using copula functions. Then, the Kendall return period under the same recurrence level is calculated to infer combined hazard thresholds for multiple disaster-causing factors. Taking rainfall-induced flash floods and landslides as examples, combined hazard thresholds are calculated. Rainfall and discharge measured at the Heyuan hydrological station in the period from 2001 to 2020 are taken as a case study. The results show that (1) the optimal bivariate copula function for annual maximum 1-day rainfall and annual maximum discharge is the Clayton Copula; (2) similarly, the optimal bivariate combined probability function for rainfall-induced landslides is the Gumbel Copula; and (3) the combined hazard thresholds of multiple disaster-causing factors for rainfall-induced flash floods and landslides differ substantially from the thresholds based on single disaster-causing factors. Taking the return period of 100 years as an example, the univariate thresholds of discharge and rainfall are 8530.38 m3/s and 217.82 mm, while the combined thresholds decrease to 5793.10 m3/s and 175.22 mm. Meanwhile, the univariate thresholds of rainfall and landslide probability are 195.02 mm and 0.82, but the combined thresholds decrease to 170.81 mm and 0.78, respectively. In other words, conventional single-factor threshold calculation methods can severely underestimate the actual hazard level, and coupling among multiple factors can induce a significant disaster superposition and amplification effect. This study reveals the risk-coupling mechanism of heavy rainfall hazards and provides technical support for the accurate identification, prediction, and early warning of rainfall-induced flash floods and landslides under climate change.