Statistical and geometrical definition of snow avalanche runout

Abstract

Two mathematical models for calculating the extreme avalanche runout from a fixed reference point on the path are presented and contrasted. The models are: (1) estimates of confidence limits on regression analyses of topographic parameters and (2) calculation of confidence limits on runout estimates from extreme value statistics. Using the extreme value statistics model to define runout, and polynomial fits to avalanche path profiles, a geometrical model for avalanche terrain was constructed. Taken together, these models redefine the traditional zoning problem by dividing it into ( 1) an estimation of runout distance, requiring an engineering decision on the choice of confidence limit, and (2) a dynamic problem requiring speed estimates along the incline between the start and stop positions, with the geometry specified by the geometrical model between these positions.