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Discussion papers | Copyright
https://doi.org/10.5194/gmd-2017-312
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Development and technical paper 07 Feb 2018

Development and technical paper | 07 Feb 2018

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This discussion paper is a preprint. A revision of the manuscript is under review for the journal Geoscientific Model Development (GMD).

Dynamically coupling Full Stokes and Shallow Shelf Approximation for marine ice sheet flow using Elmer/Ice (v8.3)

Eef C. H. van Dongen1,2,3,4, Nina Kirchner2,5, Martin B. van Gijzen3, Roderik S. W. van de Wal4, Thomas Zwinger6, Gong Cheng5,7, Per Lötstedt5,7, and Lina von Sydow5,7 Eef C. H. van Dongen et al.
  • 1Laboratory of Hydraulics, Hydrology and Glaciology, ETHZ, Zurich, Switzerland
  • 2Department of Physical Geography, Stockholm University, Stockholm, Sweden
  • 3Department of Applied Mathematical Analysis, Delft University of Technology, Delft, The Netherlands
  • 4Institute for Marine and Atmospheric Research Utrecht, Utrecht University, The Netherlands
  • 5Bolin Centre for Climate Research, Stockholm University, Stockholm, Sweden
  • 6CSC-IT Center for Science, Espoo, Finland
  • 7Division of Scientific Computing, Department of Information Technology, Uppsala University, Uppsala, Sweden

Abstract. Ice flow forced by gravity is governed by the Full Stokes (FS) equations, which are computationally expensive to solve due to their non-linearity introduced by the rheology. Therefore, approximations to the FS equations are used, especially when modelling an ice sheet complex (ice sheet, ice shelf and/or ice stream) on the order of 1000 years or longer. The Shallow Ice Approximation (SIA) and Shallow Shelf Approximation (SSA) are commonly used but are accurate only in certain parts of an ice sheet. Here, we report on a novel way of iteratively coupling FS and SSA that has been implemented in Elmer/Ice and applied to conceptual marine ice sheets. The FS-SSA coupling appears to be very accurate; the relative error in velocity compared to FS is below 0.5% for diagnostic and below 5% for prognostic runs. Results for grounding line dynamics obtained with the FS-SSA coupling are similar to results obtained from a FS model in an experiment with a periodical temperature forcing over 3000 years inducing grounding line advance and retreat. The rapid convergence of the FS-SSA coupling shows a large potential in reducing computation time, such that modelling an ice sheet complex for thousands of years should become feasible in the near future. Despite inefficient matrix assembly in the current implementation, computation time is reduced significantly, i.e. by 32%, when the coupling is applied to a 3D ice shelf. In the future, the FS-SSA coupling can be extended to include a SIA-FS coupling of ISCAL (Ice Sheet Coupled Approximation Level)-type.

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Short summary
Ice flow forced by gravity is governed by the Full Stokes (FS) equations, which are computationally expensive to solve. Therefore, approximations to the FS equations are used, especially when modelling an ice sheet on long time spans. Here, we report on a combination of an approximation with the FS equations, allowing to simulate the dynamics of ice sheets over long time spans without introducing artifacts caused by application of approximations in parts of the domain where they are not valid.
Ice flow forced by gravity is governed by the Full Stokes (FS) equations, which are...
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