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- ItemA simple stress-based cliff-calving law(Göttingen : Copernicus GmbH, 2019) Schlemm, T.; Levermann, A.Over large coastal regions in Greenland and Antarctica the ice sheet calves directly into the ocean. In contrast to ice-shelf calving, an increase in calving from grounded glaciers contributes directly to sea-level rise. Ice cliffs with a glacier freeboard larger than ≈100 m are currently not observed, but it has been shown that such ice cliffs are increasingly unstable with increasing ice thickness. This cliff calving can constitute a self-amplifying ice loss mechanism that may significantly alter sea-level projections both of Greenland and Antarctica. Here we seek to derive a minimalist stress-based parametrization for cliff calving from grounded glaciers whose freeboards exceed the 100 m stability limit derived in previous studies. This will be an extension of existing calving laws for tidewater glaciers to higher ice cliffs.
To this end we compute the stress field for a glacier with a simplified two-dimensional geometry from the two-dimensional Stokes equation. First we assume a constant yield stress to derive the failure region at the glacier front from the stress field within the glacier. Secondly, we assume a constant response time of ice failure due to exceedance of the yield stress. With this strongly constraining but very simple set of assumptions we propose a cliff-calving law where the calving rate follows a power-law dependence on the freeboard of the ice with exponents between 2 and 3, depending on the relative water depth at the calving front. The critical freeboard below which the ice front is stable decreases with increasing relative water depth of the calving front. For a dry water front it is, for example, 75 m. The purpose of this study is not to provide a comprehensive calving law but to derive a particularly simple equation with a transparent and minimalist set of assumptions.
- ItemParameterization for subgrid-scale motion of ice-shelf calving fronts(München : European Geopyhsical Union, 2011) Albrecht, T.; Martin, M.; Haseloff, M.; Winkelmann, R.; Levermann, A.In order to explore the response of the Greenland ice sheet (GIS) to climate change on long (centennial to multi-millennial) time scales, a regional energy-moisture balance model has been developed. This model simulates seasonal variations of temperature and precipitation over Greenland and explicitly accounts for elevation and albedo feedbacks. From these fields, the annual mean surface temperature and surface mass balance can be determined and used to force an ice sheet model. The melt component of the surface mass balance is computed here using both a positive degree day approach and a more physically-based alternative that includes insolation and albedo explicitly. As a validation of the climate model, we first simulated temperature and precipitation over Greenland for the prescribed, present-day topography. Our simulated climatology compares well to observations and does not differ significantly from that of a simple parameterization used in many previous simulations. Furthermore, the calculated surface mass balance using both melt schemes falls within the range of recent regional climate model results. For a prescribed, ice-free state, the differences in simulated climatology between the regional energy-moisture balance model and the simple parameterization become significant, with our model showing much stronger summer warming. When coupled to a three-dimensional ice sheet model and initialized with present-day conditions, the two melt schemes both allow realistic simulations of the present-day GIS.