# Explainable Machine Learning for Mapping Rainfall-Induced Landslide Thresholds in Italy
## 3 Results
### Spatial Analysis of Rainfall Thresholds for Landslide Triggering  
To analyze the spatial distribution characteristics of rainfall thresholds for landslide triggering in Italy, this study first refined the constructed dataset of landslide-triggering rainfall events. A statistical analysis of rainfall duration revealed that events lasting between 1 and 5 days account for 82% of the total dataset (Figure 8). Given this distribution pattern, the analysis focuses on 1-5-day rainfall events (a total of 4564 events) to ensure the representativeness of the sample.  
Figure 6: SHAP partial dependence plots: (**a**) total rainfall, (**b**) rainfall intensity, (**c**) soil moisture, (**d**) elevation, (**e**) distance to river.  
Next, we loaded the pre-trained XGBoost model and reintroduced the filtered positive samples of 1-5-day rainfall events. Unlike previous analyses, during the adjustment process, we initially set both rainfall intensity and total rainfall to zero. Then, we gradually increased the total rainfall of each positive sample in increments of 0.1 mm until it reached 1.5 times its original value. Based on the relationship rainfall intensity = total rainfall/rain days, we simultaneously adjusted rainfall intensity while keeping all other features constant. The corresponding total rainfall values were recorded when the model's predicted probability reached 50%, 70%, and 90%. This method aims to simulate potential rainfall scenarios for each possible feature combination within the study region.  
As illustrated in Figure 9, we examined landslide-prone regions across Italy and randomly selected one representative site from each of four high-risk areas: Lombardy (LOM), Liguria (LIG), Marche (MAR), and Sicilia (SIC). All four cases demonstrated a gradual increase in landslide probability with rising total rainfall but exhibited variability in specific rainfall thresholds across regions.  
Figure 8: Distribution of rainfall event durations.  
Figure 7: Predicted landslide probability distribution by XGBoost model: (**a**) total rainfall—rain days, and (**b**) rainfall intensity—rain days.  
Based on the geographic coordinates and corresponding total rainfall data at 50%, 70%, and 90% probability levels for 1-5-day rainfall events, spatially interpolated minimum triggering rainfall threshold maps were generated using ordinary kriging in ArcGIS 10.8. The kriging interpolation utilized a spherical semivariogram model, with an output cell size set to 0.05 decimal degrees, a variable search radius approach, and 12 neighboring points for local estimation. The results revealed pronounced spatial heterogeneity in rainfall-triggered landslide thresholds across Italy. At the 50% and 70% probability levels (Figure 10a,b), regions requiring higher rainfall thresholds to trigger landslides were primarily concentrated along the Apennine Mountains, where annual precipitation was moderate, and the terrain was relatively gentle. In contrast, lower thresholds were prevalent in western and central Italy (e.g., Umbria, Liguria), the northern Alpine foothills, and southern regions (e.g., Calabria, Campania), where landslide susceptibility to rainfall was notably higher. At the 90% probability level (Figure 10c), rainfall thresholds increased substantially nationwide, with spatial variability diminishing as most regions converged toward uniformly high thresholds. This pattern underscored a key trend: threshold variability was most pronounced at 50% probability (exhibiting substantial inter-regional differences), moderately reduced at 70%, and nearly homogenized at 90%. These spatial distributions aligned with regional geophysical characteristics--lower thresholds in southern Italy corresponded to weathered soils and steep slopes, whereas higher thresholds in the Apennines reflected stable geological substrates and more gradual terrain.  
Figure 9: Spatial distribution of sampling points and regional case studies: (**a**) Italy-wide sampling map, (**b**) Lombardy (LOM), (**c**) Liguria (LIG), (**d**) Marche (MAR), and (**e**) Sicily (SIC).