Extended enthalpy formulations in the Ice-sheet and Sea-level System Model (ISSM) version 4.17: discontinuous conductivity and anisotropic streamline upwind Petrov–Galerkin (SUPG) method
The thermal state of an ice sheet is an important control on its past and future evolution. Some parts of the ice sheet may be polythermal, leading to discontinuous properties at the cold–temperate transition surface (CTS). These discontinuities require a careful treatment in ice sheet models (ISMs)...
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ftdoajarticles:oai:doaj.org/article:6afe2a7b03234a28911a67f67c444ceb 2023-05-15T16:39:42+02:00 Extended enthalpy formulations in the Ice-sheet and Sea-level System Model (ISSM) version 4.17: discontinuous conductivity and anisotropic streamline upwind Petrov–Galerkin (SUPG) method M. Rückamp A. Humbert T. Kleiner M. Morlighem H. Seroussi 2020-09-01T00:00:00Z https://doi.org/10.5194/gmd-13-4491-2020 https://doaj.org/article/6afe2a7b03234a28911a67f67c444ceb EN eng Copernicus Publications https://gmd.copernicus.org/articles/13/4491/2020/gmd-13-4491-2020.pdf https://doaj.org/toc/1991-959X https://doaj.org/toc/1991-9603 doi:10.5194/gmd-13-4491-2020 1991-959X 1991-9603 https://doaj.org/article/6afe2a7b03234a28911a67f67c444ceb Geoscientific Model Development, Vol 13, Pp 4491-4501 (2020) Geology QE1-996.5 article 2020 ftdoajarticles https://doi.org/10.5194/gmd-13-4491-2020 2022-12-31T07:43:59Z The thermal state of an ice sheet is an important control on its past and future evolution. Some parts of the ice sheet may be polythermal, leading to discontinuous properties at the cold–temperate transition surface (CTS). These discontinuities require a careful treatment in ice sheet models (ISMs). Additionally, the highly anisotropic geometry of the 3D elements in ice sheet modelling poses a problem for stabilization approaches in advection-dominated problems. Here, we present extended enthalpy formulations within the finite-element Ice-Sheet and Sea-Level System model (ISSM) that show a better performance than earlier implementations. In a first polythermal-slab experiment, we found that the treatment of the discontinuous conductivities at the CTS with a geometric mean produces more accurate results compared to the arithmetic or harmonic mean. This improvement is particularly efficient when applied to coarse vertical resolutions. In a second ice dome experiment, we find that the numerical solution is sensitive to the choice of stabilization parameters in the well-established streamline upwind Petrov–Galerkin (SUPG) method. As standard literature values for the SUPG stabilization parameter do not account for the highly anisotropic geometry of the 3D elements in ice sheet modelling, we propose a novel anisotropic SUPG (ASUPG) formulation. This formulation circumvents the problem of high aspect ratio by treating the horizontal and vertical directions separately in the stabilization coefficients. The ASUPG method provides accurate results for the thermodynamic equation on geometries with very small aspect ratios like ice sheets. Article in Journal/Newspaper Ice Sheet Directory of Open Access Journals: DOAJ Articles Geoscientific Model Development 13 9 4491 4501 |
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Open Polar |
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Directory of Open Access Journals: DOAJ Articles |
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ftdoajarticles |
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English |
topic |
Geology QE1-996.5 |
spellingShingle |
Geology QE1-996.5 M. Rückamp A. Humbert T. Kleiner M. Morlighem H. Seroussi Extended enthalpy formulations in the Ice-sheet and Sea-level System Model (ISSM) version 4.17: discontinuous conductivity and anisotropic streamline upwind Petrov–Galerkin (SUPG) method |
topic_facet |
Geology QE1-996.5 |
description |
The thermal state of an ice sheet is an important control on its past and future evolution. Some parts of the ice sheet may be polythermal, leading to discontinuous properties at the cold–temperate transition surface (CTS). These discontinuities require a careful treatment in ice sheet models (ISMs). Additionally, the highly anisotropic geometry of the 3D elements in ice sheet modelling poses a problem for stabilization approaches in advection-dominated problems. Here, we present extended enthalpy formulations within the finite-element Ice-Sheet and Sea-Level System model (ISSM) that show a better performance than earlier implementations. In a first polythermal-slab experiment, we found that the treatment of the discontinuous conductivities at the CTS with a geometric mean produces more accurate results compared to the arithmetic or harmonic mean. This improvement is particularly efficient when applied to coarse vertical resolutions. In a second ice dome experiment, we find that the numerical solution is sensitive to the choice of stabilization parameters in the well-established streamline upwind Petrov–Galerkin (SUPG) method. As standard literature values for the SUPG stabilization parameter do not account for the highly anisotropic geometry of the 3D elements in ice sheet modelling, we propose a novel anisotropic SUPG (ASUPG) formulation. This formulation circumvents the problem of high aspect ratio by treating the horizontal and vertical directions separately in the stabilization coefficients. The ASUPG method provides accurate results for the thermodynamic equation on geometries with very small aspect ratios like ice sheets. |
format |
Article in Journal/Newspaper |
author |
M. Rückamp A. Humbert T. Kleiner M. Morlighem H. Seroussi |
author_facet |
M. Rückamp A. Humbert T. Kleiner M. Morlighem H. Seroussi |
author_sort |
M. Rückamp |
title |
Extended enthalpy formulations in the Ice-sheet and Sea-level System Model (ISSM) version 4.17: discontinuous conductivity and anisotropic streamline upwind Petrov–Galerkin (SUPG) method |
title_short |
Extended enthalpy formulations in the Ice-sheet and Sea-level System Model (ISSM) version 4.17: discontinuous conductivity and anisotropic streamline upwind Petrov–Galerkin (SUPG) method |
title_full |
Extended enthalpy formulations in the Ice-sheet and Sea-level System Model (ISSM) version 4.17: discontinuous conductivity and anisotropic streamline upwind Petrov–Galerkin (SUPG) method |
title_fullStr |
Extended enthalpy formulations in the Ice-sheet and Sea-level System Model (ISSM) version 4.17: discontinuous conductivity and anisotropic streamline upwind Petrov–Galerkin (SUPG) method |
title_full_unstemmed |
Extended enthalpy formulations in the Ice-sheet and Sea-level System Model (ISSM) version 4.17: discontinuous conductivity and anisotropic streamline upwind Petrov–Galerkin (SUPG) method |
title_sort |
extended enthalpy formulations in the ice-sheet and sea-level system model (issm) version 4.17: discontinuous conductivity and anisotropic streamline upwind petrov–galerkin (supg) method |
publisher |
Copernicus Publications |
publishDate |
2020 |
url |
https://doi.org/10.5194/gmd-13-4491-2020 https://doaj.org/article/6afe2a7b03234a28911a67f67c444ceb |
genre |
Ice Sheet |
genre_facet |
Ice Sheet |
op_source |
Geoscientific Model Development, Vol 13, Pp 4491-4501 (2020) |
op_relation |
https://gmd.copernicus.org/articles/13/4491/2020/gmd-13-4491-2020.pdf https://doaj.org/toc/1991-959X https://doaj.org/toc/1991-9603 doi:10.5194/gmd-13-4491-2020 1991-959X 1991-9603 https://doaj.org/article/6afe2a7b03234a28911a67f67c444ceb |
op_doi |
https://doi.org/10.5194/gmd-13-4491-2020 |
container_title |
Geoscientific Model Development |
container_volume |
13 |
container_issue |
9 |
container_start_page |
4491 |
op_container_end_page |
4501 |
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1766030031526559744 |