Spatial variability of snowpack properties adds uncertainty in the evaluation of avalanche hazard. We propose a combined mechanical–statistical approach to study how spatial variation of slab depth affects the skier-triggering probability and possible release size. First, we generate multiple slab depth maps on a plane fictional slope based on Gaussian Random Fields (GRF) for a specific set of mean, variance and correlation length. For each GRF, we derive analytically the Skier Propagation Index (SPI). We then simulate multiple skier tracks and computed the probability based on the number of skier hits where SPI is below 1. Finally, we use a depth-averaged material point method to evaluate the possible avalanche size for given slab depth variations. The results of this analysis show that large correlation lengths and small variances lead to a lower probability of skier-triggering as it reduces the size and the number of areas with low slab depth. Then, we show the effect of skiing style and skier group size on skier-triggering probability. Spatial variability also affects the possible avalanche size by adding stress fluctuation causing early or late tensile failure. Finally, we demonstrate with our models the well-known relationship between the probability and the size in avalanche forecasting.

积雪特性的空间变化增加了雪崩危险评估的不确定性。我们提出了一种机械统计相结合的方法来研究板深度的空间变化如何影响滑雪者触发概率和可能的释放尺寸。首先，我们基于高斯随机场（GRF）在平面虚构坡度上生成多个板深度图，用于一组特定的均值、方差和相关长度。对于每个 GRF，我们通过分析得出滑雪者传播指数 (SPI)。然后，我们模拟多个滑雪者轨道，并根据 SPI 低于 1 的滑雪者撞击次数计算概率。最后，我们使用深度平均材料点方法来评估给定板深度变化的可能雪崩大小。该分析的结果表明，较大的相关长度和较小的方差会导致滑雪者触发的概率较低，因为它减少了低板深度区域的尺寸和数量。然后，我们展示了滑雪风格和滑雪者群体规模对滑雪者触发概率的影响。空间变异也会通过增加应力波动而影响可能的雪崩大小，从而导致早期或晚期拉伸破坏。最后，我们用我们的模型证明了雪崩预测中概率和大小之间众所周知的关系。