Avalanches: a probabilistic approach to modelling

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Abstract
A probabilistic approach to modelling avalanche origin and dynamics is developed. An avalanche process is considered as a single event. As a basis, the physically established deterministic models describing the processes of avalanche origin and motion are used. On the other hand, input data and/or parameters of these models are treated as random variables. The study is restricted only with respect to the dynamic stage of the avalanche process. It is assumed that the initial volume of snow, entrained into the motion, and the coefficients of dry and turbulent friction of the avalanche body are random variables. The other input data are deterministic. Three kinds of distribution laws for random variables are examined: uniform, normal and exponential. Several hundred numerical tests, carried out for the selected avalanche path No. 22 in the Khibiny region, Russia, allowed construction of the distribution functions for the output parameters of the dynamic model. These parameters are the front velocity, the height and the volume of the avalanche body at fixed points of the avalanche path. No very strong dependence of distribution functions on the kind of distribution laws was found. The model and empirical distribution functions are very close to one another for run-out distances and sufficiently close for depths and volumes of snow deposits.

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