## 3 Results
### Hazard Unit
#### 3.2.2 Fire Occurrence  
In order to model the fire occurrence, we tested three machine learning-based methods and one GIS-based approach. Figure 8: Comparison of the squared deviation for the neutral network based on the Prométhée database from 1973 to 2005 concerning the burnt surface. Figure 7: Burnt surface simulated with Burr’s law (**a**), and compared to the observed data from the Prométhée database (**b**). First, we tried the decision tree. At the least, the learning base will contain 50% of the lines. We still obtained a high number of false negatives and badly classified results compared to the other machine learning methods (Figure 9). We could use a deeper tree, but the result wouldn't change much, and the tree would have too many leaves to be interpretable. The main variables are practically always the same, no matter which sample we take. The confusion matrix associated to the tree based on the learning base reveals 22.03% badly classified results; 40.01% false positives and 12.38% false negatives. The results are similar for the validation base, with 24.50% being badly classified, 43.56% false positives and 13.48% false negatives. Based on this method, the false negatives are too important and the results are insufficient. Next, we tested the Support Vector Machine (SVM). The objective was to split linearly the true and false results within the space of meteorological indexes (of dimension 14). The function svm of the package e1071 allows the realization of SVM by choosing among four nodal functions: linear, polynomial, radial or sigmoid. After different tests, the radial nodal function provides better results. Figure 10 provides the error rate on the learning base, and tests for a variation of the \(\gamma\) parameter. Among the three presented methods and related results, the three are similar in terms of performance. The more interesting rates to consider in the context of fire occurrence are the false negative and badly classified results, at around 14% (i.e., the number of fires that the model has not predicted). We assume that the models have good performance (Figure 10). Figure 10: Error rates according to the parameter \(\gamma\) for a radial nodal. Figure 9: Extract of the decision tree developed for the study. Then, in the continuity of the tests, we tested the random forest method. The implementation of the random forest of the learning base does not highlight false negatives and positives from phenomena of overlearning. Nevertheless, the random forest provides similar results from a dozen trees; the rate of bad classification was around 25% for a random forest predicting the occurrence of fires larger than 10 ha, the FWI, and the Q50 of the daily minimal temperature. We also tried to estimate the prediction of a burnt area of more than 10 ha; the best model was a random forest (Figure 11). The results are coherent and applicable to the historical datasets and for the 2050 future climate. We observe that the results of the projection are different according to the method of projection, as the models are calibrated on the Promethee area, and are projected to the entire country (Figure 12). Each model has at least 20% badly classified results and 40% false positives. Figure 11: The figure compares (**a**) the modelled prediction of fires of 10 ha for the summer of 2005 using a random forest, and observations from the same year (**b**). Figure 12: Comparison of the results from the three machine learning tools regarding the probability of at least one fire within the 2 km DFCI mesh during summer 2050 RCP 4.5. **(a)** The decision tree projection is the more moderated model; we observed the exposure of Landes, Rhône valley and Vosges. **(b)** The random forest’s projection highlights the Mediterranean and Corse areas’ exposure, with an increasing exposure of the Rhône valley, Landes, Bretagne, Nord-Pas-de-Calais and Pays-de-Loire; this model seems to be the more coherent one.