Parameterization of the snow fracture energy to model the onset of crack propagation in snowpack models

Abstract. Snowpack models are widely used to complement field observations in avalanche risk forecasting. They help estimate key indicators related to dry-snow slab avalanche triggering processes, such as failure initiation and crack propagation. In recent decades, several models have been developed to predict crack propagation propensity, typically characterized by the critical crack length (the cut length beyond which an initial crack self-propagates), measurable in the field using the Propagation Saw Test (PST). However, these models often depend on poorly constrained parameters, particularly, the weak layer fracture energy w_f. In this work, we relate the fracture energy to snow properties that can be measured directly or simulated by detailed snowpack models. To this end, we first exploit microstructural knowledge and data by computing the min-cut on about 300 three-dimensional snow microstructure images. The min-cut represents the smallest ice interface that would need to be fractured to separate two opposing sides of the structure, thus providing a quantitative proxy of fracture energy at the microscale. We fitted a relation between the min-cut and snow properties that can be measured or simulated, namely density and grain morphology. The min-cut is then linearly related to the fracture energy w_f using measurements from Richter et al. (2019), which track weak layers across multiple seasons and sites using PST and observed profiles. We retrieved w_f by inverting the state-of-the-art slab model WEAC (Weißgraeber and Rosendahl, 2023), based on manual measurements and snowpack simulations from the Crocus model. After calibration, w_f is evaluated in two slab models of different complexity for their ability to reproduce observed critical crack lengths, using both observed data and Crocus outputs. Although the correlation between min-cut and w_f remains moderate (i.e. R of 0.5 at most), likely due to measurement and modeling uncertainties, the parameterization demonstrate a clear added-value over the use of a constant w_f in reproducing realistic critical crack lengths (i.e. R = 0.59 and RMSE of 12.5 cm against R = 0.39 and RMSE = 14.5 cm). Moreover, the proposed parameterization performs well for identifying and monitoring weak layers over the course of the season. Its consistent performance across slab models and strong results using Crocus outputs highlight its potential for operational dry-snow slab avalanche hazard monitoring.