## 2 Materials and Methods
### Vulnerability and Damage Modelling  
For the development of the vulnerability unit, information about the portfolio exposure is required. First, the land-use type is needed; we used the Theia data at a 100-m resolution. Theia defined 23 land-use types; the data was re-categorized into 4 categories (Table 3). We assume the land use to be constant for the horizon 2050, as well as the number of buildings. The land-use data were overlaid with the DFCI meshes.  
Secondly, building location data were obtained from the vector building dataset BD TOPO IGN(r). In this study, we only focused on the individual residential building, for which we have more detailed insurance data. For the damage model, we assume that when a fire crosses three departments with different building densities and insured values, that the three are proportionally damaged (Figure 3).  
In terms of insured damages, wildfires may have important consequences for the buildings. They can totally damage the infrastructure. Nevertheless, wildfire damage is not covered within the Nat Cat scheme, and events destroying residential assets are extremely rare in France. In French newspapers, there is information about the costs for firemen, but not for the insured losses. Thus, the wildfire-related insured damages are not available. In order to bridge the gap, we used confidential CCR portfolio data aggregated at the department scale. The leaflet R package was used to map the data. We consider, in the model, that if the fire touches a house it is totally destroyed within the damage function. As there are no data on fire-related claims, we considered the insured values as the claims. This is contrary to Australia or the USA, where buildings are destroyed and the destruction functions are then calibrated [11]. The price of a m\({}^{2}\) of building per department was downloaded ([[https://www.meilleursagents.com/prix-immobilier/](https://www.meilleursagents.com/prix-immobilier/)]([https://www.meilleursagents.com/prix-immobilier/](https://www.meilleursagents.com/prix-immobilier/)) (accessed on 1 December 2021)). The fictive model applies the maximal historical burnt surface of each DFCI mesh since 1973 to the existing urban areas. Then, we count the number of damaged assets, \(i_{house}\), to which we apply the costs of a square meter of house per department, _PEM2_, and the insured values of the house and furniture at the department scale, _Peffur_.  
\[Fori_{house}=\sum P\epsilon M2+\ P\epsilon fur\]  
Third, the Wildland-Urban Interface (WUI), developed by the USA, describes areas where wildfires and urban areas interact, generating a potential loss of properties and life [10; 39]. The WUI types intermix, and interface areas were applied to the entire French scale at the DFCI mesh of 20 \(\times\) 20 km.  
Figure 3: When a fire (in red) touches, proportionally, the department within the DFCI mesh, the density of the houses is applied, and we obtain the number of houses burnt and the damage costs.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**New Classification** & **THEIA Land Use Types** \\ \hline Urban & Dense buildings; diffuse buildings; industrial and commercial areas; roads \\ Agriculture & Colza; cereals; protein crops; soybeans; sunflowers; maize; rice; \\  & tubers/roots; grasslands; orchards; vineyards; \\ Forest & Wilderness deciduous forest; coniferous forest; grasslands; \\  & woody moors; \\ Other surfaces & Mineral; beaches; dunes; glaciers/snow; water; \\ \hline \hline \end{tabular}
\end{table}
Table 3: New classification of the THEIA land-use data.  
Concerning the damage model, we assume the application of the maximal surface of burnt areas of each DFCI mesh on the urban surface of the same mesh; then, by using the departmental insured values, we are able to calculate the potential damages.