Extreme avalanche runout: a comparison of empirical models

The prediction of snow avalanche runout distances and the probability of exceeding the predicted positions is the first and most important step required before making decisions about placement of facilities or control structures in snow avalanche prone terrain. There are two main prediction methods for calculating runout distances: (1) procedures linked to the selection of friction coefficients in avalanche dynamic models, and (2) empirical, statistical prediction based on terrain parameters for a set of extreme runout distances for the mountain range in question. Within the second method there are presently two competing empirical approaches to prediction: (i) ordinary least squares regression analysis related to angles measured for the path profile in question, and (ii) extreme value prediction of runout based on a Gumbel distribution of a dimensionless terrain parameter. In this paper a comparison of the two empirical methods with emphasis on the slope steepness in the runout zone is provided. The comparison is important, since the choice of method does affect the probability of the runout position being exceeded, particularly far into the runout zone where facilities are most likely to be located. The analysis shows that comparison of the models hinges on slope steepness in the runout zone and differences in calculating exceedance probabilities from the distributions used in the analysis (Gumbel distribution and Gaussian). The method based on the dimensionless Gumbel parameter provides more conservative predictions for flat terrain in the runout zone, and the regression - least squares method is more conservative for steep terrain in the runout zone. In addition, the Gumbel method is shown to be compatible with the characteristics of runout zone slope steepness shown by field data: there is very little dependence of runout distance on runout zone slope steepness.