Hierarchical Bayesian modelling for spatial analysis of the number of avalanche occurrences at the scale of the township

The quantification of avalanche frequencies is necessary to compute snow avalanche return periods. In France, more than 5000 selected avalanche paths have been surveyed by forest rangers since the beginning of the 20th century. Few avalanches occur every year, but a spatial analysis makes it possible to overcome the sparseness of local data. An intermediate scale such as the township avoids errors in path localization and allows information to be transferred between neighboring paths.A statistical model inspired by spatial epidemiology is proposed. It associates a discrete Poisson model at the township scale and a latent autocorrelated field with neighboring relationships based on township boundaries. Spatial heterogeneity in avalanche frequencies is quantified and local noise is distinguished from the spatial structure. Model inference and predictive sampling are advantageously carried out in a hierarchical Bayesian modelling framework using Markov Chain Monte Carlo simulation methods.The illustrative example concerns the department of Savoie with 124 townships and 18,755 avalanches. The number of paths surveyed per township is used for data standardisation. Surprisingly, the spatial structure explains approximately 60% of the total variability of avalanche frequencies. Predictive values at the scale of the township range from 0.01 avalanches per year and path to 1.4 avalanches per year and path. Model validation, modelling hypotheses and possible extensions are discussed.