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Portions of ice sheets grounded deep beneath sea level can disintegrate if tall ice cliffs at the ice-ocean boundary start to collapse under their own weight. This process, called marine ice cliff instability, could lead to catastrophic retreat of sections of West Antarctica on decadal-to-century time scales. Here we use a model that resolves flow and failure of ice to show that dynamic thinning can slow or stabilize cliff retreat, but when ice thickness increases rapidly upstream from the ice cliff, there is a transition to catastrophic collapse. However, even if vulnerable locations like Thwaites Glacier start to collapse, small resistive forces from sea-ice and calved debris can slow down or arrest retreat, reducing the potential for sustained ice sheet collapse. 

Projections of the growth and demise of ice sheets and glaciers require physical models of the processes governing flow and fracture of ice. The flow of glacier ice has been treated using increasingly sophisticated models. By contrast, fracture, the process ultimately responsible for half of the mass lost from ice sheets through iceberg calving, is often included using ad hoc parameterizations. In this study we seek to bridge this gap by introducing a model where ice obeys a power law rheology appropriate for intact ice below a yield strength. Above the yield strength, we introduce a separate rheology appropriate for the flow of heavily fractured ice, where ice deformation occurs more readily along faults and fractures. We show that, provided the motion of fractured ice is sufficiently rapid compared to that of intact ice, the behavior of glaciers depends solely on the rheology of intact ice and the yield strength of ice and is insensitive to the precise rheology of fractured ice. Moreover, assuming that glacier ice is unyielded allows us to bound the long‐term average rate of terminus advance, providing a first principles estimate of rates of retreat associated with the marine ice cliff instability. We illustrate model behavior using idealized geometries and climate forcing and show that the model not only exhibits realistic patterns of advance and retreat but also has the potential to exhibit hysteresis. This hysteresis could provide an explanation for the sudden onset of rapid retreat observed in marine‐terminating glaciers.

 

Quantifying the impact of submarine melting on calving is central to understanding the response of marine‐terminating glaciers to ocean forcing. Modeling and observational studies suggest the potential for submarine melting to amplify calving (the calving multiplier effect), but there is little consensus as to under what conditions this occurs. Here, by viewing a marine‐terminating glacier as an elastic beam, we propose an analytical basis for understanding the presence or absence of the calving multiplier effect. We show that as a terminus becomes undercut it becomes more susceptible to both serac failure (calving only of ice that is undercut, driven by vertical imbalance) and rotational failure (full‐thickness calving of ice behind the grounding line, driven by rotational imbalance). By deriving analytical stress thresholds for these two forms of calving, we suggest that the dominant of the two calving styles is determined principally by the shape of melt‐undercutting. Uniform undercutting extending from the bed to the waterline promotes serac failure and no multiplier effect, while glaciers experiencing linear undercutting that is greatest at the bed and zero at the waterline are more likely to experience rotational failure and a multiplier effect. Our study offers a quantitative framework for understanding where and when the calving multiplier effect occurs, and, therefore, a route to parameterizing the effect in ice sheet‐scale models.