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The Cryosphere An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/tc-2018-205
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/tc-2018-205
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 11 Oct 2018

Research article | 11 Oct 2018

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal The Cryosphere (TC).

A simple stress-based cliff-calving law

Tanja Schlemm1,2 and Anders Levermann1,2,3 Tanja Schlemm and Anders Levermann
  • 1Potsdam Institute for Climate Impact Research, Potsdam, Germany
  • 2Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
  • 3Lamont-Doherty Earth Observatory, Columbia University, New York, USA

Abstract. 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 cliff calving directly contributes to sea-level rise and a monotonously increasing calving rate with ice thickeness 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 minimalistic stress-based parameterization for cliff calving. 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 ice sheet. 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 assumption 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, 75m. The purpose of this study is not to provide a comprehensive calving law, but to derive a particularly simple equation with a transparent and minimalistic set of assumptions.

Tanja Schlemm and Anders Levermann
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Status: open (until 08 Jan 2019)
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Tanja Schlemm and Anders Levermann
Tanja Schlemm and Anders Levermann
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Latest update: 15 Dec 2018
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Short summary
We provide a simple stress-based parameterization for cliff calving of ice sheets. According to the resulting increasing dependence of the calving rate on ice thickness the parameterization might lead to a runaway ice loss in large parts of Greenland and Antarctica.
We provide a simple stress-based parameterization for cliff calving of ice sheets. According to...
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