Adjoint accuracy for the full-Stokes ice flow model: limits to the transmission of basal friction variability to the surface
International audience 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 f...
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ftunivtoulouse2:oai:HAL:hal-00957142v2 2024-05-19T07:49:25+00:00 Adjoint accuracy for the full-Stokes ice flow model: limits to the transmission of basal friction variability to the surface Martin, Nathan Monnier, Jerome Institut National des Sciences Appliquées - Toulouse (INSA Toulouse) Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT) Institut de Mathématiques de Toulouse UMR5219 (IMT) Université Toulouse Capitole (UT Capitole) Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse) Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J) Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3) Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS) 2014-04-24 https://hal.science/hal-00957142 https://hal.science/hal-00957142v2/document https://hal.science/hal-00957142v2/file/tc-2013-120.pdf https://doi.org/10.5194/tc-8-721-2014 en eng HAL CCSD Copernicus info:eu-repo/semantics/altIdentifier/doi/10.5194/tc-8-721-2014 hal-00957142 https://hal.science/hal-00957142 https://hal.science/hal-00957142v2/document https://hal.science/hal-00957142v2/file/tc-2013-120.pdf doi:10.5194/tc-8-721-2014 info:eu-repo/semantics/OpenAccess ISSN: 1994-0424 EISSN: 1994-0416 The Cryosphere https://hal.science/hal-00957142 The Cryosphere, 2014, 8, pp.721-741. ⟨10.5194/tc-8-721-2014⟩ http://www.the-cryosphere.net/8/721/2014/tc-8-721-2014.html friction identification fourier analysis adjoint method [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph] [SDU.STU.GL]Sciences of the Universe [physics]/Earth Sciences/Glaciology [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] info:eu-repo/semantics/article Journal articles 2014 ftunivtoulouse2 https://doi.org/10.5194/tc-8-721-2014 2024-04-29T00:03:22Z International audience 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 dependency to 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 thicknesses wavelengths. The second order exact gradient method therefore provides robustness and reliability for the parameter identification process. In other respect, the derivation of the adjoint model using algorithmic differentiation leads to formulate a generalization of the ''self-adjoint'' approximation towards an incomplete adjoint method, adjustable in precision and computational burden. Article in Journal/Newspaper The Cryosphere Université Toulouse 2 - Jean Jaurès: HAL The Cryosphere 8 2 721 741 |
institution |
Open Polar |
collection |
Université Toulouse 2 - Jean Jaurès: HAL |
op_collection_id |
ftunivtoulouse2 |
language |
English |
topic |
friction identification fourier analysis adjoint method [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph] [SDU.STU.GL]Sciences of the Universe [physics]/Earth Sciences/Glaciology [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] |
spellingShingle |
friction identification fourier analysis adjoint method [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph] [SDU.STU.GL]Sciences of the Universe [physics]/Earth Sciences/Glaciology [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Martin, Nathan Monnier, Jerome Adjoint accuracy for the full-Stokes ice flow model: limits to the transmission of basal friction variability to the surface |
topic_facet |
friction identification fourier analysis adjoint method [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph] [SDU.STU.GL]Sciences of the Universe [physics]/Earth Sciences/Glaciology [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] |
description |
International audience 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 dependency to 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 thicknesses wavelengths. The second order exact gradient method therefore provides robustness and reliability for the parameter identification process. In other respect, the derivation of the adjoint model using algorithmic differentiation leads to formulate a generalization of the ''self-adjoint'' approximation towards an incomplete adjoint method, adjustable in precision and computational burden. |
author2 |
Institut National des Sciences Appliquées - Toulouse (INSA Toulouse) Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT) Institut de Mathématiques de Toulouse UMR5219 (IMT) Université Toulouse Capitole (UT Capitole) Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse) Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J) Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3) Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS) |
format |
Article in Journal/Newspaper |
author |
Martin, Nathan Monnier, Jerome |
author_facet |
Martin, Nathan Monnier, Jerome |
author_sort |
Martin, Nathan |
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 |
HAL CCSD |
publishDate |
2014 |
url |
https://hal.science/hal-00957142 https://hal.science/hal-00957142v2/document https://hal.science/hal-00957142v2/file/tc-2013-120.pdf https://doi.org/10.5194/tc-8-721-2014 |
genre |
The Cryosphere |
genre_facet |
The Cryosphere |
op_source |
ISSN: 1994-0424 EISSN: 1994-0416 The Cryosphere https://hal.science/hal-00957142 The Cryosphere, 2014, 8, pp.721-741. ⟨10.5194/tc-8-721-2014⟩ http://www.the-cryosphere.net/8/721/2014/tc-8-721-2014.html |
op_relation |
info:eu-repo/semantics/altIdentifier/doi/10.5194/tc-8-721-2014 hal-00957142 https://hal.science/hal-00957142 https://hal.science/hal-00957142v2/document https://hal.science/hal-00957142v2/file/tc-2013-120.pdf doi:10.5194/tc-8-721-2014 |
op_rights |
info:eu-repo/semantics/OpenAccess |
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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1799467916241928192 |