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.

雪崩事件的显着事件，即所谓的雪崩周期，正在对山区的人民和基础设施造成反复威胁。本研究侧重于由超过 2 年回归水平的每日发生次数定义的雪崩循环的危害评估。为了这个目的，极值分布被定制以解释离散观察和潜在协变量。提供了一个全面的统计框架，包括模型拟合、模型选择和评估以及收益水平等感兴趣数量的推导。在法国阿尔卑斯山的 23 个地块中的每一个中，两个离散的广义帕累托 (dGP) 模型应用于从 1958 年到 2018 年 60 年的每日雪崩活动观测中提取的极端雪崩周期，一个无条件版本和一个包含雪和气象协变量的条件版本。在条件 dGP 模型中，允许尺度参数取决于局部再分析的雪和气象条件，导致相应分布在大约一半的法国阿尔卑斯山地块中优于无条件分布。无条件 dGP 模型对雪崩数的高回报水平提供了有价值的估计。特别是，它表明法国阿尔卑斯山平均每 100 年和 300 年可预期的每条路径雪崩数量大约等于 0.25（大约 4 条路径发生 1 次雪崩）和 0.32（3 条路径发生 1 次雪崩） . 以 2018 年 1 月的埃莉诺冬季风暴为例，条件 dGP 模型通过提供以特定气象和雪况为条件的信息，对最大雪崩周期的统计描述进行了改进，在雪崩预测和气候变化影响研究中具有潜在的应用价值。相同的框架可以用于其他山区，并用于分析各种其他破坏性现象的极端数量。