Probability models to convert snowpack stability into the number of dry-snow avalanches in North Japan

Abstract

Forecasting avalanches by numerically simulating snowpack stability is currently challenging. This study proposes probability models that convert the natural snowpack stability index estimated by the physical-based snowpack model into the probability of the number of dry-snow avalanches per day. For this purpose, three types of probability models formulated by Poisson, Negative Binomial, and Zero-Inflated Poisson distributions were developed, assuming that the avalanche occurrences follow a nonhomogeneous Poisson process. In these models, the expected number of avalanches per day increases exponentially with larger unstable snowpack areas where the stability index is below a threshold. Bayesian inference has optimized the models to fit the historical avalanches from the winter of 1958/1959 to the winter of 2011/2012 in December, January, and February in north Japan and Niigata regions. The optimized models largely replicated the probability density function of the number of historical avalanches and their exponential increase with increasing unstable snowpack areas. The posterior predictive checks and the widely applicable information criteria both indicated that the model formulated by Negative Binomial distribution best reproduced the number of historical avalanches. However, the models underestimated the number of avalanches in recent decades due to the nonhomogeneity in the statistical sensitivity of avalanche occurrences to the snowpack instability. We also demonstrated some practical applications of the models, such as predicting avalanche occurrences and reproducing the annual number of avalanches.