Investigation of the functional relationship between antecedent rainfall and the probability of debris flow occurrence in Jiangjia Gully, China

Abstract

Abstract. A larger antecedent effective precipitation (AEP) indicates a higher probability of a debris flow (Pdf) being triggered by subsequent rainfall. There are a number of scientific topics surrounding this qualitative conclusion that can be raised, including what kinds of variation rules do they follow, and whether there is a boundary limit. To answer these questions, Jiangjia Gully in Dongchuan, Yunnan province, China, was chosen as the study area, and a numerical calculation, rainfall scenario simulation, and Monte Carlo integration method were used to calculate the occurrence probability of debris flow under different AEP conditions and derive the functional relationship between Pdf and AEP. The relationship between Pdf and AEP can be quantified by a piecewise function, and Pdf reaches a maximum value of 18.96 % after the AEP exceeds 110 mm, indicating that debris flow in nature has an extremely small probability compared to the rainfall frequency. Data from 1094 rainfall events and 37 historical debris flow events were collected to verify the reasonability of the functional relationship. The results indicate that the first two stages of the piecewise function are highly correlated with the observation results. Our study confirms the correctness of the qualitative description of the relationship between AEP and Pdf, clarifies that debris flow is a small probability event compared to rainfall frequency, and quantitatively reveals the evolution law of debris flow occurrence probability with AEP, which can provide a clear reference for the early warning of debris flows.