A Nye's Zero Stress Damage Model for Full Stokes Glacier Flow

Iceberg calving, which accounts for approximately half of ice shelf mass lost to the ocean, can be difficult to incorporate into models of glacier flow that approximate ice as a viscous fluid. Potentially complex calving criterion much be chosen and advection of pre-existing damage with the flowing ice must be considered. Here, we implemented a 2D full Stokes flowline model in the open-source finite element solver FEniCS. Because the damage generation process is not well understood on the scale of glaciers, we chose to implement Nye's zero stress criteria for our model. In our implementation, ice is completely broken once the greatest effective principle stress exceeds zero and is intact beneath the threshold. To include advection of damage, we used the material point method. In this method, damage is seeded on a large number of particles that advect with the velocity of ice. Material properties, like damage, can be projected from the material points to the finite element grid and vice versa using standard interpolation methods. Initial tests were performed using constant basal friction and surface mass balance on geometries with regions of both prograde and retrograde slopes. Preliminary results show that the calving front retreats at rates of approximately 200 meters per year and these rates that are sensitive to ice cliff height and bed geometry. Our model gives retreat behavior consistent with both the marine ice sheet instability and marine ice cliff instability and could be applied to glaciers of interest, such as Thwaites Glacier, to examine their stability.