ABSTRACT. Accurate modeling of calving glaciers relies on knowledge of many processes (ice flow, surface/submarine melting, calving, mélange interaction) and glacier-specific factors (air temperature, ocean circulation, precipitation rate, glacier geometry) that remain challenging to assess. Iceberg calving, especially, is important to glacier mass loss and difficult to resolve in currently-available models. Given these challenges facing even the most sophisticated models, there is value in simple, computationally-efficient models that can capture first-order effects. In this study we derive a simple model, extending Nye's perfect plastic approximation to include a yield surface at the calving front. With one climate-related input-either an upstream glacier thinning rate or glacier-wide accumulation-this model is able to simulate the advance and retreat of marine-terminating glaciers on annual to decadal scales. Our model requires knowledge of only two glacier-specific factors: glacier bed topography and basal shear strength, both reasonably constrained by laboratory and field observations. We apply the model to a case study of Columbia Glacier, Alaska and show that, despite its simplicity, the model succeeds in reproducing observed centerline profiles and rates of terminus retreat up to 2007.

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.

The representation of iceberg calving in numerical models is a key source of uncertainty in century-scale sea-level rise projections. Parameters central to model representations of calving, including the tensile strength of glacier ice, remain poorly constrained. Grain-size and sample-size dependence make it difficult to reconcile laboratory and in situ estimates of ice tensile strength. Further, assumptions of various numerical models obscure comparison of the ‘strength’ parameter with a physically observable value. Here, we address the problem of fracture during calving using an analogous natural laboratory: a viscoelastic analysis of observed surface deformation and associated stresses in the 2015 collapse of eastern Skaftá cauldron, Vatnajökull ice cap, Iceland. We find that the ice within the cauldron could have experienced instantaneous elastic stress on the order of several MPa. We observe surface crevasses at the cauldron edges and center, but find that large areas of ice remain intact despite high stress. Our findings suggest a tensile strength of glacier ice on the order of 1 MPa, consistent with laboratory estimates but exceeding previous glacier-specific estimates.

The Greenland Ice Sheet discharges ice to the ocean through hundreds of outlet glaciers. Recent acceleration of Greenland outlet glaciers has been linked to both oceanic and atmospheric drivers. Here, we leverage temporally dense observations, regional climate model output, and newly developed time series analysis tools to assess the most important forcings causing ice flow variability at one of the largest Greenland outlet glaciers, Helheim Glacier, from 2009 to 2017. We find that ice speed correlates most strongly with catchment-integrated runoff at seasonal to interannual scales, while multi-annual flow variability correlates most strongly with multi-annual terminus variability. The disparate time scales and the influence of subglacial topography on Helheim Glacier’s dynamics highlight different regimes that can inform modeling and forecasting of its future. Notably, our results suggest that the recent terminus history observed at Helheim is a response to, rather than the cause of, upstream changes.