Detecting and modeling multi-scale space-time structures: the case of wildfire occurrences

Gabriel, Edith; Opitz, Thomas; Bonneu, Florent

Journal de la société française de statistique, Tome 158 (2017) no. 3, pp. 86-105.

Les feux de forêt, qu’ils soient d’origine naturelle ou malveillante, représentent d’importants risques économiques et écologiques. La structure relative aux éclosions de feux est complexe, avec de fortes variations spatiales et temporelles, souvent dirigées par de nombreuses covariables telles que l’occupation des sols, le climat et la météo. Dans cet article, nous nous intéressons à l’éclosion de feux recensés quotidiennement depuis 1981 dans les Bouches-du-Rhône, région très touristique marquée par un climat méditérannéen, et pour lesquels nous connaissons la surface brûlée associée. Nous adoptons une approche basée sur les processus ponctuels afin d’étudier les variations spatio-temporelles à grande échelle et les interactions à petite échelle. Après un aperçu sur la litterature existante, nous explorons l’influence des covariables climatiques (comme la température, les précipitations) et de l’occupation des sols sur la probabilité d’occurrence d’un feu. Les questions statistiques sont soulevées par la structure multi-échelles des données, qui sont de plus définies sur des supports variés, comme des grilles très fines pour l’occupation des sols, des grilles grossières pour la localisation des feux qui engendrent de l’incertitude de positionnement, et des séries météorologiques observées en des sites irrégulièrement répartis. Nous ajustons à ces données un modèle de Cox log-gaussien incluant l’information des covariables et des effets spatio-temporels via la méthode INLA (Integrated Nested Laplace Approximation) et nous analysons la structure d’interaction résiduelle via la fonction $K$ spatio-temporelle inhomogène. Nous mettons en évidence et modélisons en particulier les effets inhibiteurs localement présents dans l’espace et dans le temps induits par de très grandes surfaces brûlées.

Wildfires due to natural origin or arson come along with important economic and ecological risks. Typically, the structure of relative risk of fire events is highly complex, shows strong variation over space and time and is driven by numerous covariates like land use, climate and weather. We here adopt a point process approach to study space-time large-scale variations and local interaction behavior in a data set reporting geolocalized fire events and burnt surfaces on a daily basis in the Bouches-du-Rhône county in Southern France, marked by a Mediterranean climate and high touristic activity. After a review of the existing literature, we explore the influence of land use and climatic covariates like temperature and precipitation on the probability of event occurrence. Statistical challenges arise from the multi-scale structure of data defined over various supports like fine grids for land use covariates, coarse grids for fire position leading to positional uncertainty, and meteorogical series observed at irregularly spaced measurement sites. We fit a log-Gaussian Cox process including covariate information and nonparametric spatial and temporal effects to our data through the technique of Integrated Nested Laplace Approximation, and we analyze the residual interaction structure through the space-time $K$-function adapted to the setting of second-order intensity reweighted stationarity. Specifically, we also study inhibitive effects that arise locally in time and space after fire events with relatively large burnt surfaces.

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