Comparison of statistical methods and multi-time validation for the determination of the shallow landslide rainfall thresholds

Shallow landslides are unforeseeable phenomena often resulting in critical conditions in terms of people’s safety and damage. The main purpose of this paper is the comparison of different statistical methods used to determine the rainfall thresholds for the shallow landslide occurrence. Rainfall data over a 46-year period were collected for one rain gauge located in a test area of northwest Italy (Riviera Spezzina; RS). In the RS, intense rainfalls often induce shallow landslides causing damage and sometimes casualties. The rainfall events occurred in the 1967–2006 period were classified as events inducing shallow landslides (SLEs1967–2006) and events that did not trigger shallow landslides (NSLEs1967–2006). Thresholds for various percentiles of SLEs1967–2006 were computed by identifying the lower limit above which shallow landslides occurred. Another set of thresholds, corresponding to different probabilities of occurrence, was determined using SLEs1967–2006 and NSLEs1967–2006. The least-squares linear fit (LSF) and the quantile regression (QR) techniques were employed in the former approach, while the logistic regression (LR) was applied in the latter. The thresholds were validated with the same data used for their definition and with the data recorded in the 2008–2014 period. Contingency tables were created and contingencies and skill scores were computed. The 10% probability threshold obtained using the LR method is characterized by the best values of at least two skill scores for both periods considered; therefore, it may be considered the “best” threshold for the RS. The results of this work can help the choice of the best statistical method to determine the shallow landslide rainfall thresholds.