A Two-Threshold Model for Scaling Laws of Non-Interacting Snow Avalanches

TL;DR

This paper introduces a two-threshold cellular automaton model to explain the power-law distribution of snow avalanche sizes, linking failure thresholds to material properties and reproducing observed scaling behaviors.

Contribution

The study presents a novel two-threshold automaton model that captures the scaling laws of snow avalanches and related landslides, highlighting the role of material cohesion anisotropy.

Findings

Avalanche sizes follow a power-law distribution.

Model reproduces observed exponents for different avalanche types.

Threshold ratio controls the scaling behavior.

Abstract

The sizes of snow slab failure that trigger snow avalanches are power-law distributed. Such a power-law probability distribution function has also been proposed to characterize different landslide types. In order to understand this scaling for gravity driven systems, we introduce a two-threshold 2-d cellular automaton, in which failure occurs irreversibly. Taking snow slab avalanches as a model system, we find that the sizes of the largest avalanches just preceeding the lattice system breakdown are power law distributed. By tuning the maximum value of the ratio of the two failure thresholds our model reproduces the range of power law exponents observed for land-, rock- or snow avalanches. We suggest this control parameter represents the material cohesion anisotropy.