A comparison of different ways of dealing with isostasy: examples from modelling the Antarctic ice sheet during the last glacial cycle

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Abstract
The bedrock isostatic response exerts a strong control on ice-sheet dynamics and is therefore always taken into account in ice-sheet models. This paper reviews the various methods normally used in the ice-sheet modelling community to deal with the bedrock response and compares these with a more sophisticated full-Earth model. Each of these bedrock treatments, five in total, is coupled with a three-dimensional thermomechanical ice-sheet model under the same forcing conditions to simulate the Antarctic ice sheet during the last glacial cycle. The outputs of the simulations are compared on the basis of the time-dependent behaviour for the total ice volume and the mean bedrock elevation during the cycle and of the present rate of uplift over Antarctica. This comparison confirms the necessity of accounting for the elastic bending of the lithosphere in order to yield realistic bedrock patterns. It furthermore demonstrates the deficiencies inherent to the diffusion equation in modelling the complex deformation within the mantle. Nevertheless, when characteristic parameters are varied within their range of uncertainty, differences within one single method are often of the same order as those between the various methods. This overview finally attempts to point out the main advantages and drawbacks of each of these methods and to determine which one is most appropriate depending on the specific modelling requirements.

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