Landslide predictions through combined rainfall threshold models

Based on a minimum amount of rainfall that when reached or exceeded can trigger landslides, rainfall thresholds are used to predict potential landslide occurrence and are essential parts of many landslide early warning systems. Despite the extensive literature on the definition and use of rainfall thresholds, little attention has been given to examining and comparing the mathematical methods that can be used to define thresholds as lower bounds of clouds of empirical rainfall conditions known to have triggered landslides. When multiple thresholds are available, it is unclear how to combine them. Here, we address both issues. We test and compare four mathematical methods to define event cumulated rainfall-rainfall duration, ED thresholds using 2259 measurements of rainfall duration (D, in hours) and cumulated rainfall (E, in mm) that resulted in mostly shallow landslides in Italy between January 2002 and December 2012. The methods cover a broad spectrum of data driven approaches, including a frequentist least square method, a frequentist quantile regression method, a Bayesian quantile regression method, and a machine-learning symbolic regression method. We apply and compare the methods for three non-exceedance probability levels, p = 0.01, 0.05, 0.10, and we propose a voting strategy to combine the predictions into a single, dichotomous-i.e. 'sharp'-non-probabilistic landslide prediction that we apply to the available dataset of rainfall measurements.