Back analysis of ice avalanches using depth-averaged modelling

As climate change continues, many glaciers around the world are warming and melting. Among these glaciers, those located in steep mountains are susceptible to instabilities, increasing the risk of a sudden release of ice. This release of ice may turn into a granular flow as the ice fractures while rolling downhill, sometimes over long distances, posing significant risks to infrastructures and mountain communities at lower altitudes. As the frequency of ice avalanches is expected to increase in the coming decades, it is crucial to understand and estimate their runout distances and the geometry of the final deposit to assess potential threats.
In this study, we simulated 15 past, well-documented ice avalanches with known volumes of detached ice and estimated release and deposition areas. The selected avalanches cover a wide range of volumes, from 40,000 to 85 million cubic meters, and are mainly located in the Alps, with two additional events in the Aru range in China. These avalanches are composed of ice, whereas flows mixed with snow, rocks, or water exhibit a different flow rheology. To simulate the ice avalanches, we used a depth-averaged flow model with the Voellmy rheology. This method is commonly used to reproduce large geophysical flows such as landslides and snow avalanches. For each event, multiple simulations were performed to define the parameter set that reproduces the observed avalanche's runout and geometry. Among these parameters, cohesion is determined based on weather conditions, and the Voellmy friction parameters, dry and turbulent friction, are systematically adjusted. 
From the performed simulations, we found a strong relationship between the volume of the ice avalanche and dry friction, with dry friction decreasing as volume increases. Moreover, turbulent friction is found to depend mainly on flow volume and dry friction, but is also influenced by other factors, such as topography and temperature at the time of the event. These results also provide insight into the internal dynamics of ice avalanches, which align with the few cases for which velocities were estimated. Based on the estimated parameters, we propose a scaling law to simulate an ice avalanche relying on the released ice volume. This study aims to provide an initial set of parameters for estimating the runout and final deposit of ice avalanches, contributing to forecasting and mitigating the risks associated with potential ice avalanches.