A comparison of the performance of depth-integrated ice-dynamics solvers
In the last decade, the number of ice-sheet models has increased substantially, in line with the growth of the glaciological community. These models use solvers based on different approximations of ice dynamics. In particular, several depth-integrated dynamics approximations have emerged as fast sol...
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ftcopernicus:oai:publications.copernicus.org:tcd96650 2023-05-15T16:30:07+02:00 A comparison of the performance of depth-integrated ice-dynamics solvers Robinson, Alexander Goldberg, Daniel Lipscomb, William H. 2021-09-07 application/pdf https://doi.org/10.5194/tc-2021-239 https://tc.copernicus.org/preprints/tc-2021-239/ eng eng doi:10.5194/tc-2021-239 https://tc.copernicus.org/preprints/tc-2021-239/ eISSN: 1994-0424 Text 2021 ftcopernicus https://doi.org/10.5194/tc-2021-239 2021-09-13T16:22:27Z In the last decade, the number of ice-sheet models has increased substantially, in line with the growth of the glaciological community. These models use solvers based on different approximations of ice dynamics. In particular, several depth-integrated dynamics approximations have emerged as fast solvers capable of resolving the relevant physics of ice sheets at the continen- tal scale. However, the numerical stability of these schemes has not been studied systematically to evaluate their effectiveness in practice. Here we focus on three such solvers, the so-called Hybrid, L1L2-SIA and DIVA solvers, as well as the well-known SIA and SSA solvers as boundary cases. We investigate the numerical stability of these solvers as a function of grid resolution and the state of the ice sheet. Under simplified conditions with constant viscosity, the maximum stable timestep of the Hybrid solver, like the SIA solver, has a quadratic dependence on grid resolution. In contrast, the DIVA solver has a maximum timestep that is independent of resolution, like the SSA solver. Analysis indicates that the L1L2-SIA solver should behave similarly, but in practice, the complexity of its implementation can make it difficult to maintain stability. In realistic simulations of the Greenland ice sheet with a non-linear rheology, the DIVA and SSA solvers maintain superior numerical stability, while the SIA, Hybrid and L1L2-SIA solvers show markedly poorer performance. At a grid resolution of ∆ x = 4 km, the DIVA solver runs approximately 15 times faster than the Hybrid and L1L2-SIA solvers. Our analysis shows that as resolution increases, the ice-dynamics solver can act as a bottleneck to model performance. The DIVA solver emerges as a clear outlier in terms of both model performance and its representation of the ice-flow physics itself. Text Greenland Ice Sheet Copernicus Publications: E-Journals Greenland |
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Open Polar |
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Copernicus Publications: E-Journals |
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ftcopernicus |
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English |
description |
In the last decade, the number of ice-sheet models has increased substantially, in line with the growth of the glaciological community. These models use solvers based on different approximations of ice dynamics. In particular, several depth-integrated dynamics approximations have emerged as fast solvers capable of resolving the relevant physics of ice sheets at the continen- tal scale. However, the numerical stability of these schemes has not been studied systematically to evaluate their effectiveness in practice. Here we focus on three such solvers, the so-called Hybrid, L1L2-SIA and DIVA solvers, as well as the well-known SIA and SSA solvers as boundary cases. We investigate the numerical stability of these solvers as a function of grid resolution and the state of the ice sheet. Under simplified conditions with constant viscosity, the maximum stable timestep of the Hybrid solver, like the SIA solver, has a quadratic dependence on grid resolution. In contrast, the DIVA solver has a maximum timestep that is independent of resolution, like the SSA solver. Analysis indicates that the L1L2-SIA solver should behave similarly, but in practice, the complexity of its implementation can make it difficult to maintain stability. In realistic simulations of the Greenland ice sheet with a non-linear rheology, the DIVA and SSA solvers maintain superior numerical stability, while the SIA, Hybrid and L1L2-SIA solvers show markedly poorer performance. At a grid resolution of ∆ x = 4 km, the DIVA solver runs approximately 15 times faster than the Hybrid and L1L2-SIA solvers. Our analysis shows that as resolution increases, the ice-dynamics solver can act as a bottleneck to model performance. The DIVA solver emerges as a clear outlier in terms of both model performance and its representation of the ice-flow physics itself. |
format |
Text |
author |
Robinson, Alexander Goldberg, Daniel Lipscomb, William H. |
spellingShingle |
Robinson, Alexander Goldberg, Daniel Lipscomb, William H. A comparison of the performance of depth-integrated ice-dynamics solvers |
author_facet |
Robinson, Alexander Goldberg, Daniel Lipscomb, William H. |
author_sort |
Robinson, Alexander |
title |
A comparison of the performance of depth-integrated ice-dynamics solvers |
title_short |
A comparison of the performance of depth-integrated ice-dynamics solvers |
title_full |
A comparison of the performance of depth-integrated ice-dynamics solvers |
title_fullStr |
A comparison of the performance of depth-integrated ice-dynamics solvers |
title_full_unstemmed |
A comparison of the performance of depth-integrated ice-dynamics solvers |
title_sort |
comparison of the performance of depth-integrated ice-dynamics solvers |
publishDate |
2021 |
url |
https://doi.org/10.5194/tc-2021-239 https://tc.copernicus.org/preprints/tc-2021-239/ |
geographic |
Greenland |
geographic_facet |
Greenland |
genre |
Greenland Ice Sheet |
genre_facet |
Greenland Ice Sheet |
op_source |
eISSN: 1994-0424 |
op_relation |
doi:10.5194/tc-2021-239 https://tc.copernicus.org/preprints/tc-2021-239/ |
op_doi |
https://doi.org/10.5194/tc-2021-239 |
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1766019830158196736 |