Probabilistic modeling of multiple spatial hazards: application to agricultural droughts, hydrological droughts and fire weather.

In France, year 2022 witnessed severe drought conditions, with very low flows in rivers starting already during the spring season and widespread wildfire occurrences in summer. In recent years, similar occurrences of consecutive droughts and wildfire hazards have been observed in other climatic regions of the world, including Greece, Portugal, Canary Islands, Canada, California, Australia, etc. These hazards can induce numerous strong socioeconomic impacts in areas such as agriculture, silviculture, energy, ecology, drinking water, civil protection, tourism, etc., and form a complex system of multiple drivers and risks interacting over space and time. Both the individual and the joint probabilities of occurrence of these multiple hazards driving the risks are expected to evolve with climate change. 

Characterizing the severity of such multiple hazards in probabilistic terms is challenging due to the multivariate nature of the problem, and the fact that each hazard has spatial structure and heterogeneity. In this presentation, we develop a relatively parsimonious stochastic model and estimation procedure to describe the joint space-time variability of three indices: (1) the Soil Wetness Index (SWI), used to characterize agricultural droughts (i.e. soil dryness); (2) River streamflow (Q), used to characterize hydrological droughts; (3) the Fire Weather Index (FWI), used to characterize fire-prone weather conditions. All indices are used at a monthly time step over the 1958-2023 period. SWI and FWI are derived from the SAFRAN atmospheric reanalysis and are available over Metropolitan France on a regular 8*8 km spatial grid (8597 pixels). Streamflow Q is measured at 232 streamgauging stations. 

The statistical model is based on a causal diagram where we postulate that agricultural drought (SWI) is a precursor for both hydrological drought (Q) and fire-prone conditions (FWI). The space-time distribution of SWI is therefore modeled first using a dimensionality-reduction method to provide a parsimonious description of the space-time variability of SWI. The distribution of Q is then modeled conditionally on the average value taken by SWI on each river catchment, using a generalized additive model for location, scale and shape (GAMLSS) regression. Similarly, the distribution of FWI is modeled conditionally on the value taken by SWI on the same pixel with a GAMLSS regression.

Despite its simplicity, the stochastic model is shown to appropriately reproduce several key properties of the three studied hazards, in particular their joint probability of occurrence, their long-term trends and the distribution of the spatial extent or the duration of multi-hazard events. Future work will apply the model to future projections in order to estimate how these properties evolve under climate change. We finish by discussing the relevance of the proposed approach when extrapolated to extreme levels and whether or not this simple approach is adapted to other types of multiple hazards, such as heat + humidity or storm surge + flooding.