Spatio-temporal modeling of avalanche frequencies in the French Alps
Résumé
Over a large area as the whole French Alps, we relax the common assumption of separability between space and time of avalanche counts. Based on climate studies which exhibit zones characterized by distinct climatic behaviors, we assume that our 63-years series of avalanche counts can be divided into several clusters presenting a spatial pattern. On the latent layer of a hierarchical negative binomial-lognormal structure, we assume the existence of clusters characterized by independent temporal evolutions, modeled using smoothing splines. The clusters arise as the result of a multinomial probit regression, whith spatial coordinates as regressors. Bayesian inference of our case study is performed thanks to a Gibbs sampler. The number of clusters is assessed using cross validation, and is evaluated to 2 or 3. Details results for the 3-cluster model show that one cluster is located in the east of the region, whereas the 2 other clusters are located together in the west. We highlight three contrasted temporal trends for the three clusters. They result from regional climate change effect interacting with a strong altitudinal control. Some data with poor quality may somehow blur the results. For further interpretation, additional climate or topographic data could be brought into the analysis.