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

Abstract. A larger antecedent effective precipitation (AEP) indicates a higher probability of a debris flow (Pdf) being triggered by subsequent rainfall. Scientific topics surrounding this qualitative conclusion that can be raised include what kinds of variation rules they follow and whether there is a boundary limit. To answer these questions, Jiangjia Gully in Dongchuan, Yunnan Province, China, is chosen as the study area, and numerical calculation, a rainfall scenario simulation, and the Monte Carlo integration method have been 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. Pdf is equal to 15.88 %, even when AEP reaches 85 mm, indicating that debris flow by nature has an extremely small probability compared to the rainfall frequency. Data from 1094 rainfall events and 37 historical debris flow events are collected to verify the reasonability of the functional relationship. The results indicate that the piecewise functions 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. All the above discoveries can provide a clear reference for the early warning of debris flows.