# Explainable Machine Learning for Mapping Rainfall-Induced Landslide Thresholds in Italy
## 4 Discussion
### Analysis of the Spatial Distribution of Rainfall Thresholds  
To provide a flexible framework for landslide early warning applications with varying risk management requirements, this study generated threshold maps at three probability levels (50%, 70%, and 90%). These multiple probability thresholds are designed to accommodate different operational needs: the 50% threshold offers high sensitivity for areas requiring maximum protection such as densely populated regions or critical infrastructure, the 70% threshold provides a balanced approach for general warning purposes, while the 90% threshold serves as a conservative reference for regions prioritizing the reduction of false alarms. Across the Italian territory, these multi-level thresholds exhibit significant spatial heterogeneity in rainfall requirements for landslide triggering. Under landslide occurrence probabilities of 50% and 70%, areas on both sides of the Apennine Mountains (e.g., Marche, Tuscany) required higher rainfall thresholds to trigger landslides. This phenomenon may be attributed to their relatively gentle terrain slopes (average slope gradients < 25\({}^{\circ}\)) and moderate annual rainfall (approximately 675-845 mm/yr). Gentle slopes likely prolong the time required for soil saturation by slowing surface runoff and promoting rainwater infiltration, necessitating stronger cumulative rainfall to destabilize slopes. In contrast, regions such as Liguria, Umbria, and southern Calabria exhibited lower thresholds, characterized by steeper terrain (average slope gradients > 35\({}^{\circ}\)) and frequent high-intensity rainfall events that rapidly reduce soil shear strength. At the 90% probability threshold, a notable convergence emerged in regional precipitation thresholds, accompanied by a significant attenuation of spatial heterogeneity. This phenomenon can be primarily attributed to two synergistic mechanisms: (1) From a modeling paradigm perspective, machine learning algorithms demonstrate diminished sensitivity to regional covariates under high-probability regimes. This inherent model behavior prioritizes robust generalization capabilities over spatial specificity, adopting conservative estimations to mitigate overfitting risks while maintaining prediction reliability under stringent confidence requirements. (2) Physically, extreme precipitation events approaching the 90% probability level create hydrogeomorphic conditions that override typical regional discriminators. Under such intense rainfall scenarios, the critical thresholds for soil saturation and slope instability become predominantly governed by hydrological determinants rather than localized terrain or pedological properties. This homogenization effect arises from the nonlinear threshold behavior characteristic of geotechnical systems, where the overwhelming hydraulic forcing during extreme events effectively neutralizes baseline spatial variability in soil permeability and slope stability indices. Previous studies [12; 64; 65] documented comparatively low precipitation thresholds in Sicily. In contrast, our study found that only the northern mountainous regions exhibited consistently lower thresholds across all probability quantiles, while the southern regions showed higher thresholds. This methodological divergence may arise from two principal considerations. First, despite their superior spatial continuity, the satellite-derived precipitation products adopted in this research exhibit less precise quantification of orographic precipitation than the rain gauge networks utilized in antecedent studies. Second, the machine-learning-driven predictive framework emphasizes the extraction of statistically significant patterns from global-scale multidimensional feature spaces, potentially inducing discrepant outcomes in localized geographical contexts (e.g., southern Sicily) relative to conventional regional modeling paradigms. Furthermore, it is plausible that the dataset for this region contains instances of extreme rainfall events within a relatively small spatial domain.