## 3 Data and Methods
### Attribution of Weight to the Factors  
To calculate the weight of each factor, we used the AHP as a multi-criteria method. The AHP can estimate the significance of each factor given the pairwise comparisons among each one of the seven factors [29]. In our model, each factor belongs to one major category that influences fire risk. Particularly, slope, DEM, aspect, and TWI reflect the impact of topography and to some extent fuel condition on fire risk. The distance from roads and settlements captures the impact of human activity on fire ignition. Finally, land cover depicts the alternations of fire risk, due to fuel availability and fuel type. In order to estimate the pairwise comparisons, we consulted past studies and expert opinions. We considered the land cover to be the most important factor for this estimation [24; 25; 27]. Moreover, human activity plays a key role in fire risk identification, since in most cases, humans are the main cause of fires [13]. Therefore, the distance from roads and settlements has a serious impact on fire risk. The most important topographic factor is TWI, since it has a direct correlation with soil humidity, whereas the rest topographic factors contribute less to the overall fire risk. The final distribution of pairwise comparisons is presented in Table 8. Afterwards, the weights were calculated using the mathematical procedure established by [PERSON] [49]. The final weights of each factor are also shown in Table 8.  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  &
\begin{tabular}{c} **Land** \\ **Cover** \\ \end{tabular} & **Altitude** & **Aspect** & **Slope** & **TWI** & **DfR** & **DfS** & **Weight** \\ \hline Land cover & 1 & 3 & 3 & 3 & 3 & 2 & 2 & 0.27 \\ Altitude & 0.33 & 1 & 3 & 2 & 0.5 & 0.33 & 0.33 & 0.09 \\ Aspect & 0.33 & 0.33 & 1 & 0.5 & 0.25 & 0.33 & 0.33 & 0.05 \\ Slope & 0.33 & 0.5 & 2 & 1 & 0.5 & 0.33 & 0.33 & 0.07 \\ TWI & 0.33 & 2 & 4 & 2 & 1 & 0.33 & 0.33 & 0.12 \\ DfR & 0.5 & 3 & 3 & 3 & 3 & 1 & 3 & 0.23 \\ DfS & 0.5 & 3 & 3 & 3 & 3 & 0.33 & 1 & 0.17 \\ \hline SUM & 3.32 & 12.83 & 19 & 14.5 & 11.25 & 4.65 & 7.32 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Pairwise comparisons of fire risk factors along with the assigned weight.  
Figure 11: (**a**) Rasterized buffer zones of the distance from settlements. (**b**) Fire risk classification of the area around settlement locations.  
To verify the consistency of our comparison estimations, we calculated the consistency ratio (CR) by applying the following equations [30],  
\[\text{CI}=(\lambda\text{max}-\text{n})/(\text{n}-1) \tag{1}\]  
\[\text{CR}=\text{CI}/\text{RI} \tag{2}\]  
The \(\lambda\)max in Equation (1) is the perturbated eigenvalue of the matrix constructed by the pairwise comparisons, as depicted in Table 8. n is the order of the matrix, n = 7. The consistency index (CI) in Equation (1) measures the difference between \(\lambda\)max and the exact eigenvalue, n. The CR in Equation (2) is calculated from the random consistency index (RI) [50], as shown in Table 9.  
According to Table 9, RI = 1.32 for seven factors. Subsequently, concerning our pairwise estimations, CR = 0.07. Since CR < 0.1, the estimations of the pairwise matrix were consistent.  
The fire risk maps were calculated by the weighted sum of all factors  
\[\text{Fire Risk}=0.27*\text{LC}+0.09*\text{Altitude}+0.05*\text{ Aspect}+0.07*\text{Slope}+0.12*\text{TWI}+0.23*\text{DfR}+0.17*\text{DfS} \tag{3}\]