A simple stress-based cliff-calving law
<p>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 <span class="...
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doaj-ec3a3a0f67f44ac7b0357256121cd5472020-11-25T01:04:44ZengCopernicus PublicationsThe Cryosphere1994-04161994-04242019-09-01132475248810.5194/tc-13-2475-2019A simple stress-based cliff-calving lawT. Schlemm0T. Schlemm1A. Levermann2A. Levermann3A. Levermann4Potsdam Institute for Climate Impact Research, Potsdam, GermanyInstitute of Physics and Astronomy, University of Potsdam, Potsdam, GermanyPotsdam Institute for Climate Impact Research, Potsdam, GermanyInstitute of Physics and Astronomy, University of Potsdam, Potsdam, GermanyLamont-Doherty Earth Observatory, Columbia University, New York, USA<p>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 <span class="inline-formula">≈100</span> 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 <span class="inline-formula">100</span> m stability limit derived in previous studies. This will be an extension of existing calving laws for tidewater glaciers to higher ice cliffs.</p> <p>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, <span class="inline-formula">75</span> 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.</p>https://www.the-cryosphere.net/13/2475/2019/tc-13-2475-2019.pdf |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
T. Schlemm T. Schlemm A. Levermann A. Levermann A. Levermann |
spellingShingle |
T. Schlemm T. Schlemm A. Levermann A. Levermann A. Levermann A simple stress-based cliff-calving law The Cryosphere |
author_facet |
T. Schlemm T. Schlemm A. Levermann A. Levermann A. Levermann |
author_sort |
T. Schlemm |
title |
A simple stress-based cliff-calving law |
title_short |
A simple stress-based cliff-calving law |
title_full |
A simple stress-based cliff-calving law |
title_fullStr |
A simple stress-based cliff-calving law |
title_full_unstemmed |
A simple stress-based cliff-calving law |
title_sort |
simple stress-based cliff-calving law |
publisher |
Copernicus Publications |
series |
The Cryosphere |
issn |
1994-0416 1994-0424 |
publishDate |
2019-09-01 |
description |
<p>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 <span class="inline-formula">≈100</span> 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 <span class="inline-formula">100</span> m stability limit derived in previous studies. This will be an extension of existing calving laws for tidewater glaciers to higher ice cliffs.</p>
<p>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, <span class="inline-formula">75</span> 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.</p> |
url |
https://www.the-cryosphere.net/13/2475/2019/tc-13-2475-2019.pdf |
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