## 3 Materials and Methods  
### Valle d'Aosta Case Study  
As previously mentioned, the area used as a case study to apply the developed methodology was the Valle d'Aosta region; it is located in the Italian Western Alps on the border with France and Switzerland and is undoubtedly an interesting testing ground for glacial risk research since it is home to the highest mountains in the Alps: more than 20 peaks over 4000 m, including Mont Blanc, Monte Rosa, Matterhorn, and Gran Paradiso (Figure 1). In addition, Valle d'Aosta is a particularly exposed territory due to its conformation, the richness of glaciers located on often very steep slopes, with inhabited valley floors relatively close to the glaciers. The territory presents historical and current cases of different types of glacial hazards, such as the collapse of seracs from cold hanging glaciers, collapse of parts of temperate glaciers, and flash releases of water from glacial lakes present on the surface or contained inside the glaciers (endoglacial lakes). These glacial phenomena indirectly influence the dynamics of the current slopes due to the postponed effect of the pressure release of the glacial masses following their retreat. In particular, the types of gravitational movements in the Valle d'Aosta sector are varied, as are the dimensions of these events. They range from single collapses that accumulate at the base of rock faces to imposing phenomena of deep gravitational deformation that affect entire slopes. Other frequent manifestations are those of gravitational sliding, both planar and rotational, while extremely important manifestations from the diffusion and frequency point of view are the fluidification processes at the expense of the surface layer.  
From the data analysis included in the \"Inventario dei Fenomeni Franosi in Italia--IFFI\" Project (Inventory of Landslide Events in Italy), carried out by ISPRA and autonomous provinces [77], it results that an area comprising 16% of the whole territory is covered by and/or involved landslides. This statistic is already quite high; however, the inventory maps landslides in two ways: some are mapped over areas (about 30%), while most are just  
Figure 1: Map highlighting the location of the Valle d’Aosta region and its main characteristics: natural (glaciers, protected areas, and parks) and anthropic (roads, skiing facilities, and main cities). Data obtained from regional geoporals and databases of the Autonomous Region of Valle d’Aosta.  
point elements in the dataset. This means that the area affected by landslides that have occurred in the past in Valle d'Aosta (covering 16% of the regional territory) is underestimated because point data cannot be counted in this calculation.  
In addition, significant tourist flows, both in winter and summer, characterize the region: in 2015, Valle d'Aosta hosted 3,238,559 people of whom 1,283,293 were foreigners. Tourist districts, with both summer and winter facilities (skiing structures, hiking trails, etc.), and residences represent an important economic value for the area that may be threatened by landslides. Furthermore, with 27 areas declared Sites of Community Interest (SCIs) and 5 Special Protection Areas (SPAs), Valle d'Aosta is the European region with the highest concentration of protected areas. Thirteen percent of its surface area is occupied by parks, nature reserves, and oases. The largest protected area is the Gran Paradiso National Park (about 710 km\({}^{2}\)), followed by the Mont Avic Regional Park (about 57 km\({}^{2}\)), while nature reserves account for a further 0.023%. More than a quarter of the region territory is also covered by Special Protection Areas for wild birds. For this complex connection among glacier areas, touristic attraction, natural values, and economic values, the Valle d'Aosta region was specifically considered a significant test area for the proposed methodology.