Modelling forest fire hazard
(1) Quentin Jolivet - Master 2 AIMAF, University of Rouen
(2) Roxane Marchal - Modelling, R&D Department, CCR
INTRODUCTION
The work carried out by Gualdi et al, 2022 [1] has highlighted France’s exposure to forest fires with future climate change. The most exposed areas are Corsica and the south-east of France (Mediterranean region). In 2022, 72,000 hectares burned in France as a result of approximately 290 fires[2].
Historically, France set up a forest fire prevention system with prevention plans created in 1987, infrastructures (fire roads, retention basins, etc.) and brushwood clearing operations. From an insurance point of view, damage to property caused by this hazard is covered by comprehensive home insurance but is not included in the Nat Cat compensation scheme.
In fact, 95% of fires are man-made and 80% of fires start within 50m of homes[3]. CCR is interested in modelling this hazard in the light of increasing temperature, wind and drought intensities that can lead to the outbreak of wildfires. The modelling of anthropogenic factors is more complex and only the conditions conducive to fire outbreaks are estimated.
The study is geographically focused on the most exposed departments, i.e. those in the Mediterranean Arc. The paper presents the work done to build a hazard module to model the probability of occurrence and spread of fires.
METHODOLOGY
The hazard model is initially based on data collection. Firstly, meteorological opendata (temperatures, precipitation, wind speed and direction) were downloaded from the DRIAS portal in NetCDF format and the time step is daily. The NetCDF format allows for the storage of large amounts of multidimensional data that covers spatial footprint and duration. The Forest Weather Index (FWI) provided daily by Météo-France was used as it is calculated from five variables including drought and air humidity. For France, the FWI values range from 0 to 20 points. Then, OSO THEIA land cover data and ESA Copernicus satellite imagery data concerning the zoning of burnt areas during historical events were retrieved to develop the model and validate it.
The probability of occurrence model
In the hazard model only fires over areas greater than 4 ha were treated to limit the over-representation of small fires. Criminal fires were not considered. Each DFCI (Défense des forêts contre les incendies) tile with 2 km resolution is assigned meteorological data by applying the nearest neighbour method. Starting from a point E, which represents the place where a fire historically started, we find the SAFRAN grid cell to which it belongs by calculating the lengths between point E and the different centres of the grid cells. The minimum length informs us of the corresponding square. The occurrence model is based on a logistic model that is binary: fire (1), no fire (0). The location effect is taken into account by a weight grid based on historical data since 1981. The greater the number of historical fires, the greater the weight assigned to this zone.
The climatic and geographical variables were therefore combined in a “fire score”, giving greater importance to periods of hot weather (i.e. above 25°C), FWI above 9 and low precipitation (below 0.2 mm). These thresholds were defined according to the quantile analysis.
To optimise computation times, the model only runs for 150 days per year, i.e. the last months of spring, the three months of summer and the first month of autumn.
The score is then weighted by the number of historical fires from 1981 in the same grid cell:
The propagation model
The propagation model is based on a percolation model, i.e. a model that evolves from one step to the next. The percolation model takes the point designated by the occurrence model as its starting point. Then it returns a list of all the points that have burned according to land use. Subsequently, it is checked that the recovered points do not belong to the list of burnt points, as they cannot be reignited. Then the probabilities are tested to see if the selected points ignite or not. The wind variable is included here because it little by little modifies the probability of transmission. If there is no wind or if the wind speed is higher than 140 km/h, the probability is unchanged (Figure 1).
In the presence of wind, the probability of transfer is altered. For example, if one considers strictly horizontal wind from west to east, the probabilities of fire starting for the points located north and south of the burning point are unchanged. On the other hand, the point in the east will have a higher probability of fire starting than in non-windy weather, and the point in the west will have a lower probability
The influence of temperature
The consideration of this variable was included to assess the correlation between burnt area and temperature. Temperature is the only weather-related variable that plays a role in the onset and spread of a fire.
Different temperature classes have been created and average burnt areas are assigned for each class. The increase is exponential. Figure 2 shows the change in the Napierian logarithm of the average area burnt by a fire as a function of the maximum temperature reached that day. The red line is the linear regression applied to the logarithm of the average burnt area as a function of the class of temperature.
# forest fires
# probability of occurrence
# hazard
Figure 1 - Modification of the probabilities with the integration of the ‘wind’ variable.
Figure 2 - Napierian logarithm of the average burnt area as a function of temperature.
Figure 3 - Return period (in years) of a fire of higher intensity than a burnt area (in ha), by department.
Figure 4 - Prediction model for the year 2017. In blue, the fires that actually occurred in 2017, in pink the fires predicted by the model.
THE PARTNERS
The University of Rouen is known for its AIMAF Master’s degree in Actuarial and Mathematical Engineering in Insurance and Finance, which offers training in statistical, numerical, and computing methods used in the finance and insurance sectors.
RESULTS
The departments of the Mediterranean Arc are not all exposed in the same way. The return period/fire area curves by department highlight the greater exposure of the departments of Var (83), Corsica (2A and 2B) and Bouches-du-Rhône (13). On the contrary, the departments of Hautes-Alpes (05), Drôme (26) and Lozère (48) are less exposed with smaller and less frequent burnt areas (Figure 3). The occurrence model was calibrated on the Prometheus data history by comparing predicted and actual fires. 278 fires occurred in 2017, and the model predicts 257 (Figure 4). The fires predicted by the probabilistic model cannot exactly match the historical data, especially due to the uncertainties regarding accidental fire outbreaks. However, highly exposed departments are well represented. The departments of Corsica and Bouches-duRhône are included. The integration of the temperature variable makes it possible to assess the correlation between burnt surfaces and temperature. Figure 5 shows the distribution of burnt areas over the history data. The distribution law of the discrete areas seems to be geometric (red curve).
By taking temperature into account, a decrease in the frequency of occurrence of small fires by 4 or 5 ha is observed. At 0°C, more than 85% of fires are less than 15 ha in size. In contrast, for an extreme temperature of 40°C, only 25% have an area of less than 15 ha. Similarly, a clear increase in the number of large fires as a function of temperature is considered. The propagation model was validated using the historical burnt areas downloaded from ESA Copernicus. Figure 6 on the next page is an output of the propagation model with the effect of wind being considered, for different speeds and integration of the prevailing wind direction.
CONCLUSION
This new Cat model contributes to the improvement of the understanding of natural risks that may occur in France. It allows to define the probabilities of fire outbreaks and the propagation of the latter according to meteorological and spatial data. The ability to define insured losses in a forward-looking manner allows for the development of discussions on the possible integration of this risk into the Nat Cat scheme. Beyond the insurance management of this risk, this study can be integrated into fire prevention policies./
Figure 5 - Histogram of burnt area since 1981 by class without considering temperature.
Figure 6 - Results of the propagation model (in red) and comparison with the actual burnt area (in black). Consideration of the prevailing west-east wind in the Olmeta-di-Tuda sector (Corsica) fire of 2017.
REFERENCES
1. Gualdi, B.; Binet-Stéphan, E.; Bahabi, A.; Marchal, R.; Moncoulon, D. Modelling Fire Risk Exposure for France Using Machine Learning. Appl. Sci. 2022, 12, 1635. https://doi.org/10.3390/ app12031635
2. Feedback on the 2022 forest fire season, https://www.interieur. gouv.fr/actualites/communiques/ retour-dexperience-sur-saisondes-feux-de-forets-2022-carolinecayeux-recoit accessed in November 2022
3. Bouisset C., L’urbanisation anarchique, facteur aggravant des incendies dans les Landes, The Conversation, 2022, consulté le 30/08/2022 https:// theconversation.com/ lurbanisation-anarchique-facteuraggravant-des-incendies-dans-leslandes-188619
CITATION
Jolivet et al, Modelling forest fires. In CCR 2022 Scientific Report; CCR, Paris, France, 2022, pp. 50-53