Sensitivity of ice sheet surface velocity and elevation to variations in basal friction and topography in the full Stokes and shallow-shelf approximation frameworks using adjoint equations
Predictions of future mass loss from ice sheets are afflicted with uncertainty, caused, among others, by insufficient understanding of spatiotemporally variable processes at the inaccessible base of ice sheets for which few direct observations exist and of which basal friction is a prime example. He...
Published in: | The Cryosphere |
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Uppsala universitet, Avdelningen för beräkningsvetenskap
2021
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Online Access: | http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-440412 https://doi.org/10.5194/tc-15-715-2021 |
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ftuppsalauniv:oai:DiVA.org:uu-440412 2024-02-11T10:04:51+01:00 Sensitivity of ice sheet surface velocity and elevation to variations in basal friction and topography in the full Stokes and shallow-shelf approximation frameworks using adjoint equations Cheng, Gong Kirchner, Nina Lötstedt, Per 2021 application/pdf http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-440412 https://doi.org/10.5194/tc-15-715-2021 eng eng Uppsala universitet, Avdelningen för beräkningsvetenskap Uppsala universitet, Numerisk analys Stockholm Univ, Dept Phys Geog, S-10691 Stockholm, Sweden.;Stockholm Univ, Bolin Ctr Climate Res, S-10691 Stockholm, Sweden. COPERNICUS GESELLSCHAFT MBH The Cryosphere, 1994-0416, 2021, 15:2, s. 715-742 orcid:0000-0001-9171-6714 orcid:0000-0002-6371-5527 orcid:0000-0003-2143-3078 http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-440412 doi:10.5194/tc-15-715-2021 ISI:000619837600002 info:eu-repo/semantics/openAccess Physical Geography Naturgeografi Computational Mathematics Beräkningsmatematik Article in journal info:eu-repo/semantics/article text 2021 ftuppsalauniv https://doi.org/10.5194/tc-15-715-2021 2024-01-17T23:32:02Z Predictions of future mass loss from ice sheets are afflicted with uncertainty, caused, among others, by insufficient understanding of spatiotemporally variable processes at the inaccessible base of ice sheets for which few direct observations exist and of which basal friction is a prime example. Here, we present a general numerical framework for studying the relationship between bed and surface properties of ice sheets and glaciers. Specifically, we use an inverse modeling approach and the associated time-dependent adjoint equations, derived in the framework of a full Stokes model and a shallow-shelf/shelfy-stream approximation model, respectively, to determine the sensitivity of grounded ice sheet surface velocities and elevation to time-dependent perturbations in basal friction and basal topography. Analytical and numerical examples are presented showing the importance of including the time-dependent kinematic free surface equation for the elevation and its adjoint, in particular for observations of the elevation. A closed form of the analytical solutions to the adjoint equations is given for a two-dimensional vertical ice in steady state under the shallow-shelf approximation. There is a delay in time between a seasonal perturbation at the ice base and the observation of the change in elevation. A perturbation at the base in the topography has a direct effect in space at the surface above the perturbation, and a perturbation in the friction is propagated directly to the surface in time. Article in Journal/Newspaper Ice Sheet The Cryosphere Uppsala University: Publications (DiVA) The Cryosphere 15 2 715 742 |
institution |
Open Polar |
collection |
Uppsala University: Publications (DiVA) |
op_collection_id |
ftuppsalauniv |
language |
English |
topic |
Physical Geography Naturgeografi Computational Mathematics Beräkningsmatematik |
spellingShingle |
Physical Geography Naturgeografi Computational Mathematics Beräkningsmatematik Cheng, Gong Kirchner, Nina Lötstedt, Per Sensitivity of ice sheet surface velocity and elevation to variations in basal friction and topography in the full Stokes and shallow-shelf approximation frameworks using adjoint equations |
topic_facet |
Physical Geography Naturgeografi Computational Mathematics Beräkningsmatematik |
description |
Predictions of future mass loss from ice sheets are afflicted with uncertainty, caused, among others, by insufficient understanding of spatiotemporally variable processes at the inaccessible base of ice sheets for which few direct observations exist and of which basal friction is a prime example. Here, we present a general numerical framework for studying the relationship between bed and surface properties of ice sheets and glaciers. Specifically, we use an inverse modeling approach and the associated time-dependent adjoint equations, derived in the framework of a full Stokes model and a shallow-shelf/shelfy-stream approximation model, respectively, to determine the sensitivity of grounded ice sheet surface velocities and elevation to time-dependent perturbations in basal friction and basal topography. Analytical and numerical examples are presented showing the importance of including the time-dependent kinematic free surface equation for the elevation and its adjoint, in particular for observations of the elevation. A closed form of the analytical solutions to the adjoint equations is given for a two-dimensional vertical ice in steady state under the shallow-shelf approximation. There is a delay in time between a seasonal perturbation at the ice base and the observation of the change in elevation. A perturbation at the base in the topography has a direct effect in space at the surface above the perturbation, and a perturbation in the friction is propagated directly to the surface in time. |
format |
Article in Journal/Newspaper |
author |
Cheng, Gong Kirchner, Nina Lötstedt, Per |
author_facet |
Cheng, Gong Kirchner, Nina Lötstedt, Per |
author_sort |
Cheng, Gong |
title |
Sensitivity of ice sheet surface velocity and elevation to variations in basal friction and topography in the full Stokes and shallow-shelf approximation frameworks using adjoint equations |
title_short |
Sensitivity of ice sheet surface velocity and elevation to variations in basal friction and topography in the full Stokes and shallow-shelf approximation frameworks using adjoint equations |
title_full |
Sensitivity of ice sheet surface velocity and elevation to variations in basal friction and topography in the full Stokes and shallow-shelf approximation frameworks using adjoint equations |
title_fullStr |
Sensitivity of ice sheet surface velocity and elevation to variations in basal friction and topography in the full Stokes and shallow-shelf approximation frameworks using adjoint equations |
title_full_unstemmed |
Sensitivity of ice sheet surface velocity and elevation to variations in basal friction and topography in the full Stokes and shallow-shelf approximation frameworks using adjoint equations |
title_sort |
sensitivity of ice sheet surface velocity and elevation to variations in basal friction and topography in the full stokes and shallow-shelf approximation frameworks using adjoint equations |
publisher |
Uppsala universitet, Avdelningen för beräkningsvetenskap |
publishDate |
2021 |
url |
http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-440412 https://doi.org/10.5194/tc-15-715-2021 |
genre |
Ice Sheet The Cryosphere |
genre_facet |
Ice Sheet The Cryosphere |
op_relation |
The Cryosphere, 1994-0416, 2021, 15:2, s. 715-742 orcid:0000-0001-9171-6714 orcid:0000-0002-6371-5527 orcid:0000-0003-2143-3078 http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-440412 doi:10.5194/tc-15-715-2021 ISI:000619837600002 |
op_rights |
info:eu-repo/semantics/openAccess |
op_doi |
https://doi.org/10.5194/tc-15-715-2021 |
container_title |
The Cryosphere |
container_volume |
15 |
container_issue |
2 |
container_start_page |
715 |
op_container_end_page |
742 |
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1790601609135259648 |