A spatio-temporal modelling framework for assessing the fluctuations of avalanche occurrence resulting from climate change: application to 60 years of data in the northern French Alps

Based on a previous township-scale model, a spatio-temporal framework is proposed to study the fluctuations of avalanche occurrence possibly resulting from climate change. The regional annual component is isolated from the total variability using a two-factor nonlinear analysis of variance. Moreover, relying on a Conditional AutoRegressive sub-model for the spatial effects, the structured time trend is distinguished from the random noise with different time series sub-models including autocorrelative, periodic and change-point models. The hierarchical structure obtained takes into account the uncertainty related to the estimation of the annual component for the quantification of the time trend. Bayesian inference is performed using Monte Carlo simulations. This allows a comparison of the different time series models and the prediction of future activity in an explicit unsteady context. Application to the northern French Alps illustrates the information provided by the model's different components, mainly the spatial and temporal terms as well as the spatio-temporal fluctuation of the relative risk. For instance, it shows no strong modifications in mean avalanche activity or in the number of winters of low or high activity over the last 60 years. This suggests that climate change has recently had little impact on the avalanching rhythm in this region. However, significant temporal patterns are highlighted: a complex combination of abrupt changes and pseudo-periodic cycles of approximately 15 years. For anticipating the future response of snow avalanches to climate change, correlating them with fluctuations of the constraining climatic factors is now necessary.