# Automatic Methodology for Forest Fire Mapping with SuperDove Imagery
## 2 Materials and Methods
### Methodology for Burn-Area and Severity Mapping  
Figure 2 shows the outline of the methodology applied to obtain the burned-area map, as well as the severity of the fire. First, the preprocessing of the time series is carried out. As already mentioned, the data provider already provides atmospherically corrected and orthorectified images. Therefore, at this stage, only the final mosaic of the pre- and post-fire images is carried out, as well as the adjustment of the digital levels. Next, the different vegetation indices are calculated for the pre- and post-fire images, as well as the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Equation** & **Reference** \\ \hline Enhanced Vegetation Index (EVI) & \(EVI=25*\frac{NIR-RED}{(NIR+6*RED-75*BLUE)+1}\) & [42] \\ Global Environmental Monitoring Index (GEMI) & \(GEMI=\left(n*(1-0.25*n)-\frac{RED-0.125}{1-RED}\right)\), & [43] \\ Green Normalized Difference Vegetation Index (GNDVI) & \(\frac{2*(NIR^{2}-RED^{2})+1.5*NIR+0.5*RED}{NIR+RED+0.5}\) & [44] \\ Modified Simple Ratio (MSR) & \(MSR=\frac{RDVI-1}{\sqrt{RDVI+1}}\), donde \(RDVI=\frac{NIR}{RED}\) & [45] \\ Normalized Difference Vegetation Index (NDVI) & \(NDVI=\frac{NIR-RED}{NIR+RED}\) & [46] \\ Simple Ratio (SR) & \(SR=\frac{NIR}{RED}\) & [47] \\ Soil-Adjusted Vegetation Index (SAVI) & \(SAVI=\frac{1.5*(NIR-RED)}{NIR+RED+0.5}\) & [48] \\ Wide Dynamic Range & \(WDRVI=\frac{a*NIR-RED}{a*NIR+RED}\), where \(a\) goes from & [49] \\ Vegetation Index (WDRVI) & 0.1 to 0.2 & \\ Yellow Normalized Difference Vegetation Index (YNDVI) & \(YNDVI=\frac{NIR-YELLOW}{NIR+YELLOW}\) & [50] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Formulations and references for the different vegetation indices used in this work. Figure 1: Pre-fire (first column) and post-fire (second column) images for the four selected events: (**a,b**) north Attica; (**c,d**) Portbou; (**e,f**) Euboea; (**g,h**) Sierra de los Guájares. differences between indices. As detailed in Section 3.1, an evaluation was conducted to assess the differences in each vegetation index before and after the fire. The objective was to identify the most appropriate indices for detecting burned areas and mapping fire severity. As a result of this evaluation, two indices were selected, and their pixel-by-pixel values were used as two-dimensional vectors for the clustering algorithm. To determine which pixels correspond to a burned area, bisecting K-means clustering is executed, and thus a standard threshold interval is avoided. Bisecting K-means is a clustering algorithm that is a hybrid between divisive hierarchical clustering and K-means clustering [51; 52]. It employs a strategic iterative process to enhance precision. Initially, it considers the entire data set as a single cluster. This cluster is then divided into two distinct sub-clusters using the conventional K-means algorithm. Subsequently, the algorithm identifies the sub-cluster with the highest sum of squared errors (SSE) and selects it for further division. This iterative process of splitting continues until the algorithm achieves the predetermined number of clusters. By consistently bisecting the clusters and prioritizing those with the highest error, the bisecting K-means algorithm aims to boost the accuracy of clustering and ensure that data are grouped in a more meaningful manner. This algorithm provides some advantages over standard K-means. It provides a hierarchical structure to the clusters, which may be more informative than the flat clusters produced by standard K-means, and seems appropriate for the problem we address. Additionally, it is considered faster than normal K-means as it splits one group at a time, which can be more efficient. Finally, this method is particularly useful when dealing with large data sets and when a hierarchical cluster structure is desired. The two clusters correspond to burned and un-burned pixels. Finally, a severity map is synthesized by running the K-means clustering algorithm [52], but only on the pixels filtered through the burned-area mask.