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

Résumé

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.