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...
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ftdoajarticles:oai:doaj.org/article:6d54207a3a0b4041bccc3fb87dc654ba 2023-05-15T16:40:41+02:00 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 G. Cheng N. Kirchner P. Lötstedt 2021-02-01T00:00:00Z https://doi.org/10.5194/tc-15-715-2021 https://doaj.org/article/6d54207a3a0b4041bccc3fb87dc654ba EN eng Copernicus Publications https://tc.copernicus.org/articles/15/715/2021/tc-15-715-2021.pdf https://doaj.org/toc/1994-0416 https://doaj.org/toc/1994-0424 doi:10.5194/tc-15-715-2021 1994-0416 1994-0424 https://doaj.org/article/6d54207a3a0b4041bccc3fb87dc654ba The Cryosphere, Vol 15, Pp 715-742 (2021) Environmental sciences GE1-350 Geology QE1-996.5 article 2021 ftdoajarticles https://doi.org/10.5194/tc-15-715-2021 2022-12-31T10:52:05Z 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 Directory of Open Access Journals: DOAJ Articles The Cryosphere 15 2 715 742 |
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 G. Cheng N. Kirchner P. Lötstedt 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 |
Environmental sciences GE1-350 Geology QE1-996.5 |
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 |
G. Cheng N. Kirchner P. Lötstedt |
author_facet |
G. Cheng N. Kirchner P. Lötstedt |
author_sort |
G. Cheng |
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 |
Copernicus Publications |
publishDate |
2021 |
url |
https://doi.org/10.5194/tc-15-715-2021 https://doaj.org/article/6d54207a3a0b4041bccc3fb87dc654ba |
genre |
Ice Sheet The Cryosphere |
genre_facet |
Ice Sheet The Cryosphere |
op_source |
The Cryosphere, Vol 15, Pp 715-742 (2021) |
op_relation |
https://tc.copernicus.org/articles/15/715/2021/tc-15-715-2021.pdf https://doaj.org/toc/1994-0416 https://doaj.org/toc/1994-0424 doi:10.5194/tc-15-715-2021 1994-0416 1994-0424 https://doaj.org/article/6d54207a3a0b4041bccc3fb87dc654ba |
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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1766031085024575488 |