Functional Regression for Space-Time Prediction of Precipitation-Induced Shallow Landslides in South Tyrol, Italy

Abstract

Landslides are geomorphic hazards in mountainous terrains across the globe, driven by a complex interplay of static and dynamic controls. Data-driven approaches have been employed to assess landslide occurrence at regional scales by analyzing the spatial aspects and time-varying conditions separately. However, the joint assessment of landslides in space and time remains challenging. This study aims to predict the occurrence of precipitation-induced shallow landslides in space and time within the Italian province of South Tyrol (7,400 km²). We introduce a functional predictor framework where precipitation is represented as a continuous time series, in contrast to conventional approaches that treat precipitation as a scalar predictor. Using hourly precipitation data and past landslide occurrences from 2012 to 2021, we implemented a functional generalized additive model to derive statistical relationships between landslide occurrence, various static scalar factors, and the preceding hourly precipitation as a functional predictor. We evaluated the resulting predictions through several cross-validation routines, yielding performance scores frequently exceeding 0.90. To demonstrate the model predictive capabilities, we performed a hindcast for a storm event in the Passeier Valley on 4–5 August 2016, capturing the observed landslide locations and illustrating the hourly evolution of the predicted probabilities. Compared to standard early warning approaches, this framework eliminates the need to predefine fixed time windows for precipitation aggregation while inherently accounting for lagged effects. By integrating static and dynamic controls, this research advances the prediction of landslides in space and time for large areas, addressing seasonal effects and underlying data limitations.