Probabilistic Estimates of Extreme Snow Avalanche Runout Distance

The estimation of runout distances for long return period avalanches is vital in zoning schemes for mountainous countries. There are two broad methods to estimate snow avalanche runout distance. One involves the use of a physical model to calculate speeds along the incline, with runout distance determined when the speed drops to zero. The second method, which is used here, is based on empirical or statistical models from databases of extreme runout for a given mountain range or area. The second method has been used for more than 40 years with diverse datasets collected from North America and Europe. The primary reason for choosing the method used here is that it is independent of physical models such as avalanche dynamics, which allows comparisons between methods. In this paper, data from diverse datasets are analyzed to explain the relation between them to give an overall view of the meaning of the data. Runout is formulated from nine different datasets and 738 values of extreme runout, mostly with average return periods of about 100 years. Each dataset was initially fit to 65 probability density functions (pdf) using five goodness-of-fit tests. Detailed discussion and analysis are presented for a set of extreme value distributions (Gumbel, Frechet, Weibull). Two distributions had exemplary results in terms of goodness of fit: the generalized logistic (GLO) and the generalized extreme value (GEV) distributions. Considerations included both the goodness-of-fit and the heaviness of the tail, of which the latter is important in engineering decisions. The results showed that, generally, the GLO has a heavier tail. Our paper is the first to compare median extreme runout distances, the first to compare exceedance probability of extreme runout, and the first to analyze many probability distributions for a diverse set of datasets rigorously using five goodness-of-fit tests. Previous papers contained analysis mostly for the Gumbel distribution using only one goodness-of-fit test. Given that climate change is in effect, consideration of stationarity of the distributions is considered. Based on studies of climate change and avalanches, thus far, it has been suggested that stationarity should be a reasonable assumption for the extreme avalanche data considered.