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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2014
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ftdoajarticles:oai:doaj.org/article:af1e090006d04535bc5261b314a71961 2023-05-15T18:32:31+02:00 Adjoint accuracy for the full Stokes ice flow model: limits to the transmission of basal friction variability to the surface N. Martin J. Monnier 2014-04-01T00:00:00Z https://doi.org/10.5194/tc-8-721-2014 https://doaj.org/article/af1e090006d04535bc5261b314a71961 EN eng Copernicus Publications http://www.the-cryosphere.net/8/721/2014/tc-8-721-2014.pdf https://doaj.org/toc/1994-0416 https://doaj.org/toc/1994-0424 1994-0416 1994-0424 doi:10.5194/tc-8-721-2014 https://doaj.org/article/af1e090006d04535bc5261b314a71961 The Cryosphere, Vol 8, Iss 2, Pp 721-741 (2014) Environmental sciences GE1-350 Geology QE1-996.5 article 2014 ftdoajarticles https://doi.org/10.5194/tc-8-721-2014 2022-12-30T22:08:35Z 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 Directory of Open Access Journals: DOAJ Articles The Cryosphere 8 2 721 741 |
institution |
Open Polar |
collection |
Directory of Open Access Journals: DOAJ Articles |
op_collection_id |
ftdoajarticles |
language |
English |
topic |
Environmental sciences GE1-350 Geology QE1-996.5 |
spellingShingle |
Environmental sciences GE1-350 Geology QE1-996.5 N. Martin J. Monnier Adjoint accuracy for the full Stokes ice flow model: limits to the transmission of basal friction variability to the surface |
topic_facet |
Environmental sciences GE1-350 Geology QE1-996.5 |
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 |
N. Martin J. Monnier |
author_facet |
N. Martin J. Monnier |
author_sort |
N. Martin |
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://doaj.org/article/af1e090006d04535bc5261b314a71961 |
genre |
The Cryosphere |
genre_facet |
The Cryosphere |
op_source |
The Cryosphere, Vol 8, Iss 2, Pp 721-741 (2014) |
op_relation |
http://www.the-cryosphere.net/8/721/2014/tc-8-721-2014.pdf https://doaj.org/toc/1994-0416 https://doaj.org/toc/1994-0424 1994-0416 1994-0424 doi:10.5194/tc-8-721-2014 https://doaj.org/article/af1e090006d04535bc5261b314a71961 |
op_doi |
https://doi.org/10.5194/tc-8-721-2014 |
container_title |
The Cryosphere |
container_volume |
8 |
container_issue |
2 |
container_start_page |
721 |
op_container_end_page |
741 |
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1766216634635124736 |