Extreme avalanche cycles: Return levels and probability distributions depending on snow and meteorological conditions

Guillaume Evin,Pascal Dkengne Sielenou,Nicolas Eckert,Philippe Naveau,Pascal Hagenmuller,Samuel Morin

doi:10.1016/j.wace.2021.100344

Abstract

Remarkable episodes of avalanche events, so-called snow avalanche cycles, are recurring threats to people and infrastructures in mountainous areas. This study focuses on the hazard assessment of snow avalanche cycles defined by daily occurrence numbers exceeding the 2-year return level. To this aim, extreme value distributions are tailored to account for discrete observations and potential covariates. A comprehensive statistical framework is provided including model fitting, model selection and evaluation, and derivation of quantities of interest such as return levels. In each of the 23 massifs of the French Alps, two discrete generalized Pareto (dGP) models are applied to extreme avalanche cycles extracted from 60 years of daily avalanche activity observations from 1958 to 2018, an unconditional version and a conditional version incorporating snow and meteorological covariates. In the conditional dGP model, the scale parameter is allowed to depend on snow and meteorological conditions from a local reanalysis, leading the corresponding distributions to outperform their unconditional counterparts in about half of the French Alps massifs. Unconditional dGP models provide valuable estimates of high return levels of avalanche numbers. In particular, it is shown that the number of avalanches per path which can be expected on average every 100 and 300 years for the French Alps is approximately equal to 0.25 (roughly one avalanche for four paths) and 0.32 (one avalanche for three paths). As exemplified with the January 2018 Eleanor winter storm, conditional dGP models refine the statistical description of the largest avalanche cycles by providing the information conditional to specific meteorological and snow conditions, with potential applications to avalanche forecasting and climate change impact studies. The same framework could be put to work in other mountain areas and for analyzing extreme counts of various other damaging phenomena.

Highlights

In the Alpine environment, snow avalanches are an everyday threat resulting in casualties as well as direct and indirect economic losses
Model selection We evaluate the predictive performance of the discrete generalized Pareto (dGP) models by comparing the fitted probabilistic distribution to observed remarkable avalanche cycles et, using the log-score (Gneiting and Raftery, 2007), defined as: LOG_SCORE(G, y) = − log g(y), where y is the observation, G is the predictive cumulative distribution function and g is its corresponding probability density function
We see that the fitted dGP distribution provides smoother decaying frequencies than observed frequencies, which are necessarily restricted to few numbers, but overall, model fit to data appears as fair as confirmed by the Kolmogorov–Smirnov GOF test (p-value=0.97)

Summary

Introduction

In the Alpine environment, snow avalanches are an everyday threat resulting in casualties as well as direct and indirect economic losses. A correct assessment of the statistical characteristics of the most extreme events is critical due to their potential catastrophic consequences (Schweizer et al, 2009). To this aim, the concept of avalanche cycle is often used to highlight a remarkable cluster of avalanche events at a given spatial scale (the mountain range, the district, etc.) and over a short period of time (typically a few days), and being able to characterize the severity of avalanche cycles in terms of probabilities is valuable

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Methods

Results