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The Cryosphere An interactive open-access journal of the European Geosciences Union
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Volume 10, issue 4
The Cryosphere, 10, 1799–1807, 2016
https://doi.org/10.5194/tc-10-1799-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
The Cryosphere, 10, 1799–1807, 2016
https://doi.org/10.5194/tc-10-1799-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 18 Aug 2016

Research article | 18 Aug 2016

A simple equation for the melt elevation feedback of ice sheets

Anders Levermann1,2,3 and Ricarda Winkelmann1,3 Anders Levermann and Ricarda Winkelmann
  • 1Potsdam Institute for Climate Impact Research, Potsdam, Germany
  • 2LDEO, Columbia University, NY, USA
  • 3Institute of Physics, Potsdam University, Potsdam, Germany

Abstract. In recent decades, the Greenland Ice Sheet has been losing mass and has thereby contributed to global sea-level rise. The rate of ice loss is highly relevant for coastal protection worldwide. The ice loss is likely to increase under future warming. Beyond a critical temperature threshold, a meltdown of the Greenland Ice Sheet is induced by the self-enforcing feedback between its lowering surface elevation and its increasing surface mass loss: the more ice that is lost, the lower the ice surface and the warmer the surface air temperature, which fosters further melting and ice loss. The computation of this rate so far relies on complex numerical models which are the appropriate tools for capturing the complexity of the problem. By contrast we aim here at gaining a conceptual understanding by deriving a purposefully simple equation for the self-enforcing feedback which is then used to estimate the melt time for different levels of warming using three observable characteristics of the ice sheet itself and its surroundings. The analysis is purely conceptual in nature. It is missing important processes like ice dynamics for it to be useful for applications to sea-level rise on centennial timescales, but if the volume loss is dominated by the feedback, the resulting logarithmic equation unifies existing numerical simulations and shows that the melt time depends strongly on the level of warming with a critical slowdown near the threshold: the median time to lose 10 % of the present-day ice volume varies between about 3500 years for a temperature level of 0.5 °C above the threshold and 500 years for 5 °C. Unless future observations show a significantly higher melting sensitivity than currently observed, a complete meltdown is unlikely within the next 2000 years without significant ice-dynamical contributions.

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In recent decades, the Greenland Ice Sheet has been losing mass and has thereby contributed to global sea-level rise. Here we derive the basic equations for the melt elevation feedback that can lead to self-amplifying melt of the Greenland Ice Sheet and ice sheets in general. The theory unifies the results of complex models when the feedback dominates the dynamics and it allows us to estimate the melt time of ice sheets from data in cases where ice dynamic loss can be neglected.
In recent decades, the Greenland Ice Sheet has been losing mass and has thereby contributed to...
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