Rainfall threshold ensemble for landslide prediction under data uncertainty

Based on a minimum amount of rainfall that can trigger landslides when reached or exceeded, rainfall thresholds are used to predict the occurrence of rainfall-induced landslides and are an essential part of many landslide early warning systems worldwide.The most common information used to define empirical rainfall thresholds is rainfall duration, cumulative rainfall and landslide occurrence time, all of which are derived from data sets with uncertainties, which are particularly important to consider when thresholds are used in early warning systems.The landslide information is usually obtained from a variety of sources, including newspapers, blogs, landslide databases, scientific journals, technical documents, event and firefighter reports, and the association between the geographical location and time of occurrence of the landslides and the rainfall records is made by expert judgement based on heuristic criteria. Inaccuracies in the location and/or time of occurrence of the landslide and lack of systematic mapping are the main sources of uncertainty.Assuming that a power law is a good descriptor of the dependence of cumulative rainfall on rainfall duration, in this work we focus our interest on a strategy to mitigate the epistemic uncertainties associated with the data that affect the model parameters: we propose an ensemble approach based on four different models to estimate the exceedance probability of landslide occurrence, which we combine through a voting scheme.Methods include a frequentist ordinary least square regression method, a frequentist quantile regression method, a Bayesian quantile regression method, and a machine learning symbolic regression method.The thresholds obtained by the four methods are equivalent to the opinions of four independent experts who were asked to give their advice on the minimum amount of cumulative rainfall required for a potential landslide to occur for a given duration of rainfall.We measure the level of agreement among the experts by counting the number of predictions that are above, below or in the range of uncertainty of the four thresholds. Finally, we take the most voted prediction as representative of the rainfall condition and the level of agreement/disagreement as an indication of the uncertainty in our prediction.This approach provides a novel and robust framework for considering uncertainty in rainfall thresholds and offers practical insights to enhance decision-making in landslide risk management.