Upper and Lower Bounds on the Stability of Calving Glaciers

Iceberg calving is responsible for nearly half of the mass lost from ice sheets to the oceans. However, a lack of a well-parameterized calving model leaves most numerical ice sheet models incomplete. Previous studies have sought to parameterize iceberg calving assuming that calving occurs when a surface crevasse intersects with a basal one. Although a variety of models have successfully reproduced patterns of glacier retreat, they are frequently tuned by adding melt water into surface crevasses until glacier behavior matches observations, which is puzzling because calving also occurs during winter when no melt water is available. Here we examine crevasse propagation using a 2D full-Stokes finite element model along the center flow of an idealized glacier terminating in ocean to see when water-free surface crevasses intersect with water-filled basal crevasses on a lubricated bed. Crevasse propagation is computed using the Nye zero-stress-model, assuming they have a negligible effect on the stress field of the glacier. We find that for a given water depth, simulated glaciers evolve to a state where either basal and surface crevasses intersect or the glacier begins to float. This allows us to map out a stability threshold that predicts for a given water depth if certain ice thicknesses will result in full thickness failure. Assuming seeds for crevasses are present everywhere, this threshold poses an upper limit on ice thickness: as the thickness decreases full thickness penetration is increasingly likely. Comparing our theoretical stability threshold with observational data deduced from Operation IceBridge, we find that most tidewater glaciers have water depth and ice thickness combinations fall in a narrow region above our predicted threshold and below buoyancy. The agreement between observations and our simulations suggests that glaciers evolve until they approach a critical stability threshold where small perturbations can trigger calving events. The stability diagram provides a simple relationship between ice thickness and water depth that can be implemented in numerical ice sheet models to simulate iceberg calving. Furthermore our results allow us to predict not only the conditions when ice tongues are likely to form and when the terminus is likely to remain grounded, but also a distribution of iceberg sizes.