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

• A new method to quantify antecedent rainfall affecting landslides is proposed.
• This method is derived from the power-law relation of rainfall–landslide.
• The decay of daily rainfall in a period preceding a given day is interrelated.
• Loss of water due to drainage and evaporation is reflected in the decay factor.

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.