Modeling fire size of wildfires

The extent of fires, their periodicity and their impact on terrestrial communities is always a concern. Wildfires play an important role in shaping landscapes and as a source of CO2 and particulate matter. Modeling the spatial variability of wildfire extent is an important subject in order to understand and to predict future trends on their effect in landscape changes.

The most common approaches have been through point pattern analysis or by Markov random fields. Those methods have made possible to build risk maps, but for many forest managers knowing the fire size besides the location of the fire is very useful.

In this work researchers use spatial marked point processes to model the fire size of the forest fires. Their modeling approach incorporates spatial covariates as they are useful to model spatial variability and to gain insight about factors related to the presence of forest fires. Such information may be of great utility to predict the spreading of ongoing fires and also to prevent wildfire outburst by controlling risk factors.

Playing with statistics

Landscape patterns are determined by the frequency, intensity and extent of disturbances. Fire is one of the main disturbances affecting Mediterranean landscapes. Understanding the relationship between landscape and climatic characteristics with the spatial distribution of wildfire ignition sites and their final size or burned area is of great importance to design land use management rules and to implement policies leading to better landscape management.

Modeling the spatial incidence of wildfires and the fire size is important because of the need to understand how global warming and climate change may affect the landscape in the future years, as well as to understand which factors are related to spatial incidence and the size of the area burned. Previous studies have dealt with the problem of producing risk maps, considering risk as the probability that a wildfire ignites at some location  inside a study area using statistical methods. Despite their usefulness, most of the studies have not considered the burned area caused by each wildfire.

In this paper scienstits model the spatial distribution of the area burned by wildfires occurring in the province of Castellón, Spain, during the years 2001–2006, taking into account the fire size associated with wildfire occurrences as a variable of interest (Aragó et al., 2016). The goal was to find and fit statistical models, using Bayesian statistics, which could be useful to analyze the fire size and to identify which factors are relevant for explaining the spatial variation of fire size as a marked response variable in wildfire incidence. This approach allows to account for the effects of the risk factors on the spatial distribution of wildfire patterns.

Fig. 1 shows the locations of the fires occurring in the province of Castellón during the years 2001–2006. The circles in this figure show the size class in hectares for each fire. The figure shows the clustering behavior of fires with small size and the more uniform spatial pattern of wildfires due to spatial interaction among them (Aragó et al., 2016).

Fig. 1. Location of forest fires occurring in the province of Castellón, Spain, during the years 2001–2006. Circles are indicative of the size class for each fire. The classes are 0–1 ha, >1–6, <6–11, and so on. The last class includes fires whose burned area was above 21 ha.

The spread of wildfires to neighboring areas and hence its final size are usually related to factors such as local weather as well as to physical and biological factors, likely related to moisture and fuel quality and conditions. Researchers use spatially varying covariates aiming to explain part of the spatial variation of the observed final wildfire sizes. Four continuous covariates (slope, aspect, elevation and distance to the nearest road) and two categorical covariates (land use and year of occurrence) were included in the modeling process.

For each recorded wildfire, the associated information included the geographic coordinates of the centroid of the fire at its final size, the year, elevation, slope, aspect, land use, distance to the nearest road to the wildfire’s centroid, isothermality, soil permeability and final size. Here, the final size will be only considered as a mark, and given that no digital map for the other variables was available for the study area, they were discarded from the analysis. However, land use was included, elevation, slope, aspect and distance to the nearest road as covariates because digital maps of those variables were available for the province of Castellón.

Translating the results

Fig. 2 shows the empirical distribution of the fire size for the whole data set (left plot) and for the wildfires (right plot). The asymmetric shape of the distribution is characteristic of the distribution of the area burned by wildfires, with a high number of wildfires with small to moderate fire size and a small quantity of large fires at the extreme of the distribution.

Fig. 2. Frequency histogram of the fire size by wildfires in Castellón for the years 2001–2006 for the whole data set (left plot) and for those fires with fire sizes above 10 ha (right plot). The shaded bars correspond to the same frequency class. Note the change in the frequency scale.

Fig. 7 shows that the distribution of the fire size is concentrated in areas where the vegetation cover corresponded to active and abandoned crop fields (AC and AF), as well as in areas covered with grasslands and shrublands (NG and SL), although a significant part of the wildfires in Castellón ignited in areas covered by coniferous forests (CF).

Fig. 3. Distribution of the fire size by land use (left) and by distance to the nearest road (right) in Castellón for the years 2001–2006.

Looking at Fig. 1, one may notice that the ignition locations show a clustered behavior and that members of such clusters tend to be wildfires of small size. This implies that fire size is more likely influenced by local conditions such as fuel moisture and wind speed, or by the easiness of access to people in areas where the conditions to set a fire either intentional or accidental are similar around populated areas that result in a similar chance for wildfires to reach large sizes.

The coefficient posterior means for the significant terms indicate that provided the rest of the covariates are held constant, the area burned for the human caused wildfires is 5.8 times higher than the area burned for wildfires ignited by natural causes.

The effect of distance to road on the size of the area burned is almost negligible. However, an increase in the distance to road results in a 1% increase in the expected fire size for a wildfire, possibly because fires igniting close to roads are easier to detect and suppress before they spread over a wider area. This suggests that large wildfires tend to occur in remote areas where firefighting activities take a longer time to reach those remote areas.

Finally, the prediction map was presented for the expected fire size as well as the standard deviation associated for those predictions resulting from the best model (Fig. 8).

Fig. 4. Predicted mean fire size for the province of Castellón (left) and posterior standard deviation map (right).

What do we get out of all this?

INLA-SPDE was presented as a computationally efficient and statistically powerful approach to fit Bayesian models, which is considered as an alternative to computing demanding methods such as Markov Chain Monte carlo.

The analysis indicates that wildfire fire size is strongly associated with land use, with higher areas expected in areas where abandoned fields and shrublands are dominant. The proposed Bayesian hierarchical spatiotemporal models are extremely powerful and flexible, and can be easily improved by the inclusion of more covariates.

A by-product from the fitted model is the prediction map, which may be used for planning activities related to wildfire prevention and control. Other use of the prediction maps may be the assessment of the quantity of particulate matter and CO2 contributed to the atmosphere by each wildfire. This issue is important for health planning and for climate change modeling.

Source: Carlos Díaz-Avalos, Pablo Juan , Laura Serra-Saurina Modeling fire size of wildfires in Castellon (Spain), using spatiotemporal marked point processes. Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México; Department of Mathematics, Universidad Jaume I, Spain; Center for Research in Occupational Health (CiSAL), Department of Experimental and Health Sciences, Pompeu Fabra University, Barcelona, Spain

Main photo credit: José Ángel Arranz Sanz, General Director of the Natural Environment, Junta de Castilla y León.

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