Size Frequency Distributions for Snow Avalanches

We examine crown size frequencies for two extensive datasets of observations made during operational avalanche control: 10,300 events at Mammoth Mountain, California and 219,000 events from the Westwide Avalanche Network (WAN) which includes ski areas and highway operations. We compare a dozen distributions, and we address observer bias by employing ratio estimates, smoothing functions, and exclusion rules. Knowing that avalanche professionals often do not record small events, we examine both datasets with no exclusions and with a 60 cm exclusion rule. The WAN data are best fit by a power law distribution using the 60 cm exclusion rule. The power law distribution with 60 cm exclusion also fits the Mammoth data, although these data are best fit by a hyperbolic tangent distribution under both the 60 cm exclusion rule and without exclusion. Our findings support past literature showing that power laws provide a good fit for size-frequency relationships across different regions. Power law distributions indicate scale invariance across several orders of magnitude and are consistent with self organized critical systems. Independent of the choice of distribution, we advocate the implementation of probabilistic avalanche forecasts that convey uncertainty to the end-user, unlike deterministic forecasts. We propose the use of cumulative distribution functions (CDFs) as the dependent variables in numerical avalanche forecast models. CDFs allow normalized output for a region or specific path. A user can infer the magnitude of avalanche events for each avalanche path or area of interest from the CDF. We attempt to create a basis for such an implementation in avalanche forecasting.