A comparison of fracture-physics-based calving models including hydrofracturing

The dynamic mass loss due to ice-flow from the Antarctic and Greenland ice sheets into oceans is one of the greatest sources of uncertainty in predicting future sea level rise. The fracture and detachment of icebergs, that is, calving controls the dynamic mass loss from ice sheets, and is intricately linked to climate dynamics through processes such as hydrofracturing, which can potentially contribute to rapid sea level rise over the coming centuries. Therefore, it is important that we improve our understanding and representation of calving in numerical ice sheet models. Fracture-physics-based calving models generally assume that calving occurs when the combination of surface and basal crevasses penetrates the entire ice thickness of a glacier or an ice shelf. These models can be categorized into three groups: zero-stress, linear elastic fracture mechanics (LEFM), and continuum damage mechanics (CDM) models. In this presentation, we compare a CDM model for time-dependent creep fracture against zero-stress and LEFM models for instantaneous elastic fracture of glacier ice. Specifically, we compare the penetration depths of dry and water-filled surface crevasses in grounded marine-terminating glaciers predicted by each model in relation to ice thickness, water depth in the surface crevasse, and seawater depth at the ice terminus. The CDM model agrees with the LEFM model for isolated crevasses when the seawater depth is small compared to ice thickness, and with the zero-stress model for a field of closely-spaced crevasses when the stress field is nearly uniform. Importantly, the CDM model disagrees with both LEFM and zero-stress models for hydrofracture-driven calving of a near-floatation glacier. This is because in the latter models water pressure in crevasses is simply added with the far-field stress to obtain the net crack-driving stress based on the linear superposition principle, which is invalid for the nonlinear viscous ice rheology. Using a full-Stokes finite element model, we show that a fully water-filled crevasse in a near-floatation grounded glacier will not propagate due to viscous stress redistribution. To conclude, we recommend that calving schemes including hydrofracture of crevasses be reformulated in Stokes-flow-based ice sheet models without relying on the superposition principle.