## 4 Regional Scale Analysis
### Hazard Indicators
For the permafrost degradation index, the PermaNET project was used as a reference in this research, which uses one of the statistical permafrost distribution models developed. The explanatory variables are the mean annual air temperature, potential solar radiation, and mean annual precipitation. These were calculated for the entire Alps and were used to derive estimates of the probability of rock glaciers being intact or of the rock face temperature being below 0 \({}^{\circ}\)C. The values of the final raster file ranged from 0 to 255 and were divided into five equal classes. 6. The capacity of forests and vegetation to protect from landslides events was classified into four classes. The protection forests identified from the ROCKtheALPS project have the lowest hazard index, while the other woods from the Corine Land Cover database were classified as a medium hazard. Finally, the areas that are not covered by wood have the highest hazard value. 7. For the existing gravitational processes, the classification is based on [88]. This classification could be further developed depending on the availability of data (for example, different hazard values could be assigned to events depending on whether they are (i) active/reactivated/suspended landslides, (ii) dormant landslides, (iii) inactive/stabilized landslides, or (iv) areas affected by widespread shallow landslides). The available database for the Valle d'Aosta did not have this level of detail, and therefore, the raster was classified in a qualitative way. 8. Precipitation data are based on rainfall data of the region. The map of the spatial distribution of precipitation was obtained from the data measured by the rain gauges of some stations, and an extension to the whole territory was made using an interpolation algorithm (Interpolating Point Data) that creates a continuous surface from discrete points when it is impossible to take measurements throughout all the territory taken into consideration. The raster derived from the interpolation was classified into five classes through a quantile classification. 9. The hazard index related to the lithology and geological setting was differentiated for the three types of landslide phenomena: for each map, different values for the three macrocategories were used (a--landslides bodies, alluvial deposits, glacial deposits, and slope debris; b--sedimentary rocks; c--igneous and metamorphic rocks). The final index is obtained by summing the three results. What is important to underline is the fact that areas with hazard values of 4 and 5 (high and very high) are quite widespread and distributed among all indices. The indicator that includes more territory in the \"very high hazard\" category (H5) is the sixth one, \"vegetation and protection forests\". This is due to the fact that the Valle d'Aosta region has forests in the lowest part of the mountain ranges. Vegetation thins out, leaving space for exposed rock, which is assigned the highest score, occupying an area of 2523 km\({}^{2}\), equal to 77% of the regional territory. Another index that classifies most of the territory in class 5 is the second one, \"slope aspect\", with 1282 km\({}^{2}\) in H5, equal to 39%. The explanation for this lies in the morphology of the Valle d'Aosta, formed by an almost horizontal valley and consequently by many slopes facing south. Other indicators assessing a large part of the territory subject to high hazard are the first, \"acclivity\" and the last one, \"lithology and geological setting\", with, respectively, 1663 km\({}^{2}\) (51%) and 1428 km (44%) in class H4. This is because a large part of the region has steep slopes, between 20\({}^{\circ}\) and 30\({}^{\circ}\) in most of the territory. As far as lithology is concerned, a high hazard is evident since the variety of phenomena occurring (falls and topples, earth and mud flows, rotational and translational slides) take into account many lithological types that have been therefore included in the classification.