## 3 Methods
### Burned Area Detection Procedure  
The procedure for identifying burned areas was designed taking inspiration from a two-phase methodology [25; 26]. The procedure explores the entire multitemporal profile of the spectral indices to detect abrupt changes produced by wildfire disturbance. It is based on a set of empirical thresholds of spectral indices applied to the multitemporal profiles, mainly performed on a pixel base and then refined using object-based image analysis (OBIA). Each of the three considered spectral indices (NBR, BAIS2, and BAIS2\(\alpha\)) is used in combination with its respective difference spectral index (i.e., dNBR, dBAIS2, and dBAIS2\(\alpha\)), in order to retrieve burned pixels and a set of supplementary information (Table 1). The first procedure step (Step A) identifies core burned areas using a multitemporal pixel-based algorithm founded on spectral-temporal rule combination analysis. The algorithm first computes the difference in spectral indices from each pair of consecutive observations and later detects the temporal occurrence of the maximum relative difference within the multitemporal profile. If the found maximum relative difference, likely corresponding to the difference in spectral index value between pre-fire and post-fire observations, exceeds the threshold value d\({}_{\mathrm{C}}\) (difference index value for the core area), and the corresponding post-fire observation in the time of the spectral index exceeds the threshold value V\({}_{\mathrm{C}}\) (index value for the core area) (Figure 2), the pixel is classified as a burned area. In the second step (Step B), the pixels identified as burned areas were clustered together to form clumps of adjacent pixels. Afterward, sieve filtering is applied to the classified product in order to remove clumps smaller than the predefined threshold S\({}_{\mathrm{min}}\) (minimum clump size) (Figure 3), providing a set of seed regions representing core burned areas. The threshold values applied for the three different spectral indices are reported in Table 2. Threshold values were defined based on a preliminary analysis of sample images. To ensure consistency among the three spectral indices, threshold values were equalized by means of linear regression. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Information** & **Unit** & **Description** \\ \hline Pre-fire date & Day & Sensing date of the last S2 valid observation before wildfire occurrence \\ Post-fire date & Day & Sensing date of the S2 observation used to identify wildfire \\ Day span & Day & Arithmetic difference between post-fire and pre-fire dates \\ SI & dimensionless & Spectral index value calculated for the post-fire date \\ (e.g. NBR, BAIS2, BAIS2\(\alpha\)) & dimensionless & Difference spectral index value calculated from the arithmetic \\ (e.g. NBR, BAIS2, BAIS2\(\alpha\)) & difference between post-fire and pre-fire values \\ LAI & m\({}^{2}\)/m\({}^{2}\) & Leaf area index (LAI) calculated for the pre-fire date \\ dLAI & m\({}^{2}\)/m\({}^{2}\) & Difference LAI value calculated from arithmetic difference between \\  & & pre-fire and post-fire LAI values \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Supplementary information retrieved for each identified burned pixel. Figure 3: (**a**) Spatial distribution of the identified burned areas during Step A; (**b**) spatial distribution of the identified burned areas during Step B; (**c**) spatial distribution of the identified burned areas during Step C; (**d**) spatial distribution of the identified burned areas during Step D; (**e**) spatial distribution of the EFFIS, “MODIS burned areas” and Copernicus EMS rapid mapping activations (background: Sentinel-2B image acquired on 12 July 2017); (**f**) spatial distribution of the final map of identified burned areas (background: Sentinel-2B image acquired on 12 July 2017). Figure 2: Single pixel multitemporal profile showing the fire spectral index and the burned area identification parameters. Spectral-temporal rules are implemented to find the maximum relative difference.