Inverse problem in avalanche dynamics models

Avalanche dynamics models are increasingly used to estimate the features of extremely rare events for avalanche zoning. They employ a frictional coefficient, which reflects something close to snow viscosity. As this coefficient is more conceptual than physical, it cannot be measured and must be fitted by matching avalanche dynamics model results and field data. However, most of the time, the historical record is not long enough to fit this coefficient for extremely rare events. Here we propose a deterministic inversion method to obtain the probability density function of this coefficient. The method has been applied to two avalanche paths in the French Alps, each with a sustained avalanche activity over the last century. For applications the Voellmy avalanche dynamics model has been used with no loss of generality. It is shown that the friction coefficient is a random variable whose marginal probability distribution varies rapidly and exhibits two or more peaks.