Adjoint accuracy for the full Stokes ice flow model: limits to the transmission of basal friction variability to the surface
This work focuses on the numerical assessment of the accuracy of an adjoint-based gradient in the perspective of variational data assimilation and parameter identification in glaciology. Using noisy synthetic data, we quantify the ability to identify the friction coefficient for such methods with a...
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Copernicus Publications
2014
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ftnonlinearchiv:oai:noa.gwlb.de:cop_mods_00020107 2023-05-15T18:32:33+02:00 Adjoint accuracy for the full Stokes ice flow model: limits to the transmission of basal friction variability to the surface Martin, N. Monnier, J. 2014-04 electronic https://doi.org/10.5194/tc-8-721-2014 https://noa.gwlb.de/receive/cop_mods_00020107 https://noa.gwlb.de/servlets/MCRFileNodeServlet/cop_derivate_00020062/tc-8-721-2014.pdf https://tc.copernicus.org/articles/8/721/2014/tc-8-721-2014.pdf eng eng Copernicus Publications The Cryosphere -- ˜Theœ Cryosphere -- http://www.bibliothek.uni-regensburg.de/ezeit/?2393169 -- http://www.the-cryosphere.net/ -- 1994-0424 https://doi.org/10.5194/tc-8-721-2014 https://noa.gwlb.de/receive/cop_mods_00020107 https://noa.gwlb.de/servlets/MCRFileNodeServlet/cop_derivate_00020062/tc-8-721-2014.pdf https://tc.copernicus.org/articles/8/721/2014/tc-8-721-2014.pdf uneingeschränkt info:eu-repo/semantics/openAccess article Verlagsveröffentlichung article Text doc-type:article 2014 ftnonlinearchiv https://doi.org/10.5194/tc-8-721-2014 2022-02-08T22:52:17Z This work focuses on the numerical assessment of the accuracy of an adjoint-based gradient in the perspective of variational data assimilation and parameter identification in glaciology. Using noisy synthetic data, we quantify the ability to identify the friction coefficient for such methods with a non-linear friction law. The exact adjoint problem is solved, based on second-order numerical schemes, and a comparison with the so-called "self-adjoint" approximation, neglecting the viscosity dependence on the velocity (leading to an incorrect gradient), common in glaciology, is carried out. For data with a noise of 1%, a lower bound of identifiable wavelengths of 10 ice thicknesses in the friction coefficient is established, when using the exact adjoint method, while the "self-adjoint" method is limited, even for lower noise, to a minimum of 20 ice thickness wavelengths. The second-order exact gradient method therefore provides robustness and reliability for the parameter identification process. In another respect, the derivation of the adjoint model using algorithmic differentiation leads to the formulation of a generalization of the "self-adjoint" approximation towards an incomplete adjoint method, adjustable in precision and computational burden. Article in Journal/Newspaper The Cryosphere Niedersächsisches Online-Archiv NOA The Cryosphere 8 2 721 741 |
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article Verlagsveröffentlichung |
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article Verlagsveröffentlichung Martin, N. Monnier, J. Adjoint accuracy for the full Stokes ice flow model: limits to the transmission of basal friction variability to the surface |
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article Verlagsveröffentlichung |
description |
This work focuses on the numerical assessment of the accuracy of an adjoint-based gradient in the perspective of variational data assimilation and parameter identification in glaciology. Using noisy synthetic data, we quantify the ability to identify the friction coefficient for such methods with a non-linear friction law. The exact adjoint problem is solved, based on second-order numerical schemes, and a comparison with the so-called "self-adjoint" approximation, neglecting the viscosity dependence on the velocity (leading to an incorrect gradient), common in glaciology, is carried out. For data with a noise of 1%, a lower bound of identifiable wavelengths of 10 ice thicknesses in the friction coefficient is established, when using the exact adjoint method, while the "self-adjoint" method is limited, even for lower noise, to a minimum of 20 ice thickness wavelengths. The second-order exact gradient method therefore provides robustness and reliability for the parameter identification process. In another respect, the derivation of the adjoint model using algorithmic differentiation leads to the formulation of a generalization of the "self-adjoint" approximation towards an incomplete adjoint method, adjustable in precision and computational burden. |
format |
Article in Journal/Newspaper |
author |
Martin, N. Monnier, J. |
author_facet |
Martin, N. Monnier, J. |
author_sort |
Martin, N. |
title |
Adjoint accuracy for the full Stokes ice flow model: limits to the transmission of basal friction variability to the surface |
title_short |
Adjoint accuracy for the full Stokes ice flow model: limits to the transmission of basal friction variability to the surface |
title_full |
Adjoint accuracy for the full Stokes ice flow model: limits to the transmission of basal friction variability to the surface |
title_fullStr |
Adjoint accuracy for the full Stokes ice flow model: limits to the transmission of basal friction variability to the surface |
title_full_unstemmed |
Adjoint accuracy for the full Stokes ice flow model: limits to the transmission of basal friction variability to the surface |
title_sort |
adjoint accuracy for the full stokes ice flow model: limits to the transmission of basal friction variability to the surface |
publisher |
Copernicus Publications |
publishDate |
2014 |
url |
https://doi.org/10.5194/tc-8-721-2014 https://noa.gwlb.de/receive/cop_mods_00020107 https://noa.gwlb.de/servlets/MCRFileNodeServlet/cop_derivate_00020062/tc-8-721-2014.pdf https://tc.copernicus.org/articles/8/721/2014/tc-8-721-2014.pdf |
genre |
The Cryosphere |
genre_facet |
The Cryosphere |
op_relation |
The Cryosphere -- ˜Theœ Cryosphere -- http://www.bibliothek.uni-regensburg.de/ezeit/?2393169 -- http://www.the-cryosphere.net/ -- 1994-0424 https://doi.org/10.5194/tc-8-721-2014 https://noa.gwlb.de/receive/cop_mods_00020107 https://noa.gwlb.de/servlets/MCRFileNodeServlet/cop_derivate_00020062/tc-8-721-2014.pdf https://tc.copernicus.org/articles/8/721/2014/tc-8-721-2014.pdf |
op_rights |
uneingeschränkt info:eu-repo/semantics/openAccess |
op_doi |
https://doi.org/10.5194/tc-8-721-2014 |
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The Cryosphere |
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8 |
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2 |
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721 |
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741 |
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