Effects of triggering mechanism on snow avalanche slope angles and slab depths from field data

Abstract

Field data from snow avalanche fracture lines for slope angle and slab depth (measured perpendicular to the weak layer) were analyzed for different triggering mechanisms. For slope angle, the results showed that the same probability density function (pdf) (of log-logistic type) and range (25°–55°) apply independent of triggering mechanism. For slab depth, the same pdf (generalized extreme value) applies independent of triggering mechanism. For both slope angle and slab depth, the data skewness differentiated between triggering mechanism and increased with applied triggering load. For slope angle, skewness is lowest for natural triggering by snow loads and highest for triggering from human intervention. For slab depth, the skewness is lowest for natural triggering and highest for a mix of triggers including explosive control with skier triggering being intermediate. The results reveal the effects of triggering mechanism which are important for risk analyses and to guide avalanche forecasting.

Appendix: Comparison with the previous analyses for D

In this Appendix, a review of previous results relating D to probability theory is given.

Bair et al. (2008) also made an analysis of D from thousands of avalanches in ski areas in the USA. Bair et al. (2008) fit their data sets to 4 pdfs and concluded that the data follow either a two parameter Fréchet or GEV pdf. Since values of D < 30.5 cm were excluded, their study consisted of truncated distributions. Thus, their results cannot be compared directly to those here. For my three data sets, truncation at D = 30.5 cm implies an exclusion of approximately the first quartile of the data. It is not possible to make accurate assessments about pdfs with more than 20 % of the data (the left tail) excluded (Gaume et al. 2012). Gaume et al. (2012) also fit data to a GEV pdf from ski areas in France using truncated data sets, but they provided no goodness-of-fit criteria nor information on triggering mechanism so I have not included a comparison here.

All three of my data sets had a serious lack of fit for both P–P and Q–Q plots for the Fréchet distribution, and most of the goodness-of-fit criteria failed. For the Fréchet distribution, the skewness is undefined if the shape parameter is less than 3 since, in that case, the third moment does not exist (Benjamin and Cornell 1970). For my three data sets, the Fréchet shape parameter ranges from 1.9 to 2.1. I conclude that my three un-truncated data sets do not fit the two parameter Fréchet pdf which is claimed by Bair et al. (2008) to represent D for avalanches.

I truncated the largest data set here (191 values) at D = 30.5, 40 and 50 cm. In general, truncation increases the skewness. The shape parameter for either the Fréchet or GEV distributions depends only on the skewness. The shape parameter ranged from 1.9 (un-truncated) to 3.4 (D ≥ 0.50 m) (Fréchet) and from 5.6 (un-truncated) to 2.4 (D ≥ 0.50 m) (GEV; shape parameter: 1/k). The shape parameters obtained by Bair et al. (2008) ranged from 3.3 to 4.1 (Fréchet) and 3.1 to 1.9 (GEV) corresponding to truncation of my data set. Thus, it is likely that the fit and shape parameters found by Bair et al. (2008) are partly due to data truncation, manipulation and theoretical assumptions instead of avalanche behavior. Bair et al. (2008) assumed the location parameter was equal to zero for the Fréchet distribution, and this assumption can have drastic effects on the results. I fit my largest data set (191 values) to both the 3 parameter Fréchet distribution (nonzero location parameter) and the 2 parameter one used by Bair et al. (2008). The shape parameter changed from 1.9 (2 parameter pdf) to 4.8 (3 parameter pdf). For the latter, a good fit was found for all five goodness-of-fit tests (but not as good as for the GEV pdf), whereas there was lack of fit for the 2 parameter pdf proposed by Bair et al. (2008).