Spatio-temporal modeling of avalanche frequencies in the French Alps

Avalanches threaten mountainous regions, and probabilistic long term hazard evaluation is a useful tool for land use planning and the definition of appropriate mitigation measures. This communication focuses on avalanches counts in the French Alps, and investigates their fluctuations in space and time within a Bayesian hierarchical modeling framework. We have at our disposal a 60 year data set covering the whole French Alps. The considered time scale is the winter. The elementary spatial scale is the township. It is small enough to allow information transfer between neighboring paths and large enough to avoid errors in paths localization. Data are standardized with a variable integrating the number of surveyed paths. A hierarchical Poisson-lognormal model appears well-adapted to depict the observation process with such discrete data. The spatial and temporal effects are assumed independent, and they are considered in the latent layer of the model. The temporal trend is modeled with a cubic spline whereas different spatial dependence sub-models are tested. The latter ones work on different types of supports (continuous field and discrete grid), and at different embedded spatial scales. Model inference and predictive sampling are carried out using Markov Chain Monte Carlo simulation methods. The spatial structure explains the larger part of the relative risks. The spatial dependence is visible at the scale of townships, but with a short range. At the larger scale of the massifs, the spatial dependence is weaker. The regional coherence of the results with the number of avalanche releases suggests that we may also search for other spatially structured variables implicated in the magnitude of avalanches that could help transfer information from one path to another. (C) 2010 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Spatial Statistics 2011