An effective antecedent precipitation model derived from the power-law relationship between landslide occurrence and rainfall level

Antecedent rainfall is an important predisposing factor in triggering landslides because it reduces soil suction and increases the pore-water pressure in soils. The existing approaches to quantify the antecedent rainfall were derived from empirical methods used to develop rainfall–runoff models in which the daily decays of rainfall within a given period preceding a given day are considered as independent processes. In this study, a methodology accounting for the effective antecedent rainfall that influences landslide occurrence is developed from a power-law relationship between the frequency of landslide occurrence and the landslide-triggering rainfall level. In this model, the decay rate of the daily rainfall is related to a scaling exponent defined by the power-law relationship, the decay process of daily rainfall within a given period preceding a given day is not independent but is interrelated, and the impact of rainfall in the preceding k days on soil moisture is associated with the precipitation from the preceding (k − 1) days.