Definition of Rainfall Thresholds for Landslides Using Unbalanced Datasets: Two Case Studies in Shaanxi Province, China

The Lueyang and Xunyang counties in the Shaanxi province (China) are highly susceptible to rainfall-induced landslides. Rainfall thresholds are the most used tool to predict the occurrence of rainfall-induced landslides over large areas. However, the definition of robust thresholds may be difficult for unbalanced datasets, for which the number of non-landslide observations is much higher than the number of landslide observations. This study aims at defining adequate rainfall thresholds for the two study areas using landslide datasets that are strongly unbalanced in terms of occurrences vs. non-occurrences. Two types of rainfall thresholds are determined using a frequentist method at several non-exceedance and exceedance probabilities, separately considering rainfall events responsible for landslides (positive thresholds) and rainfall events not responsible for landslides (negative thresholds). The comparison between the two sets of thresholds shows that the method based on non-triggering events allows defining rainfall thresholds characterized by lower uncertainties and a better performance than the ones defined considering the triggering events, in both the study areas. In particular, the best-performing thresholds are the negative threshold defined at 15% exceedance probability for the Lueyang county and the negative threshold defined at 20% exceedance probability for the Xunyang county.