## 3 Results
### Validation of the Results  
In the literature, there are only a few examples of measured velocity values of rapid landslides [10,11]; indeed; they are usually all modelled. This issue is even more complex when working at a regional scale. Therefore, in order to verify the reliability of the velocity values obtained with the spatialisation of the Heim Energy Line method [27], a validation procedure was performed using the Gravitational Process Path (GPP) model [17]. This is an extension of SAGA GIS that simulates the process path, the runout length, and the deposition area of gravitational phenomena using a digital elevation model (DEM). The  
Figure 5: Velocity values of a shallow landslide obtained by a Matlab code based on the Heim method. The continuous black line corresponds to the landslide boundary, and the black point to the release reference point according to the IFFI inventory. Figure 6: Velocity values of a rockfall obtained by a Matlab code based on the Heim method. The continuous black line corresponds to the landslide boundary, and the black point to the release reference point according to the IFFI inventory. GPP model combines several sub-models, which makes the model applicable to different processes such as rockfalls, debris flows, and snow avalanches. A further advantage of this model is that it requires a small amount of input data, allowing applications at a regional scale [46] as well as at a slope scale [7]. Regarding rockfalls and debris flows, the approaches typically used are \"Random Walk\" to determine the process path, the \"one-parameter friction model\" to calculate the runout distance of rockfalls, and the \"Perla, Cheng, McClung (PCM) model [47] in the case of debris flows [17]. The GPP model requires as input data a DEM and a release area raster. The Random Walk approach involves as input a slope threshold, below which the divergent flow is modelled, and two parameters that control the flow. The one-parameter friction model requires the definition of the following parameters: a free fall threshold representing the minimum angle between the starting cell and the current one to model the free fall, the energy reduction after the impact, a friction parameter, and the type of movement (sliding or rolling). The PCM model is a two-parameter friction model according to which the movement depends mainly on a sliding friction coefficient and a mass-to-drag ratio. The aforementioned parameters have been calibrated according to the value ranges found in the literature for the study area [48; 49]. The application of the model allows for obtaining three products: the \"Process Area\", which shows the number of passages of the material, \"Stopping Positions\", which highlight the arrival point of the landslide material, and \"Maximum Velocity\", which provides the maximum velocity values for each cell. This procedure was performed on selected samples of landslide polygons. Specifically, ten rockfalls and ten shallow landslides were analysed; Figures 7 and 8 show the velocity values obtained from the GPP model for a shallow landslide and a rockfall, respectively. These values can be compared with the velocities obtained by the proposed methodology shown in Figures 5 and 6. Other examples are shown in Figure 9. The comparison between the outputs highlights that the GPP results, even if with the same geometry, can be characterised by a greater extension. This is due to the different input data used by the two models. In fact, the proposed method works using a DEM corresponding to the landslide polygon, while the GPP model, requiring as input data a DEM of the whole region and the release area of the landslides, simulates the landslide path from the release area considering the entire territory. Figure 7: Velocity values of the shallow landslide, shown in Figure 5, obtained by the GPP model. The continuous black line corresponds to the landslide boundary, and the black point to the release reference point according to the IFFI inventory.