Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation
New analytical solutions describing the effects of small-amplitude perturbations in boundary data on flow in the shallow-ice-stream approximation are presented. These solutions are valid for a non-linear Weertman-type sliding law and for Newtonian ice rheology. Comparison is made with corresponding...
Published in: | The Cryosphere |
---|---|
Main Author: | |
Format: | Article in Journal/Newspaper |
Language: | English |
Published: |
European Geosciences Union
2008
|
Subjects: | |
Online Access: | http://nora.nerc.ac.uk/id/eprint/6799/ https://nora.nerc.ac.uk/id/eprint/6799/1/tc-2-77-2008.pdf https://doi.org/10.5194/tc-2-77-2008 |
id |
ftnerc:oai:nora.nerc.ac.uk:6799 |
---|---|
record_format |
openpolar |
spelling |
ftnerc:oai:nora.nerc.ac.uk:6799 2023-05-15T16:39:55+02:00 Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation Gudmundsson, G.H. 2008 text http://nora.nerc.ac.uk/id/eprint/6799/ https://nora.nerc.ac.uk/id/eprint/6799/1/tc-2-77-2008.pdf https://doi.org/10.5194/tc-2-77-2008 en eng European Geosciences Union https://nora.nerc.ac.uk/id/eprint/6799/1/tc-2-77-2008.pdf Gudmundsson, G.H. orcid:0000-0003-4236-5369 . 2008 Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation. Cryosphere, 2 (2). 77-93. https://doi.org/10.5194/tc-2-77-2008 <https://doi.org/10.5194/tc-2-77-2008> Glaciology Publication - Article PeerReviewed 2008 ftnerc https://doi.org/10.5194/tc-2-77-2008 2023-02-04T19:24:30Z New analytical solutions describing the effects of small-amplitude perturbations in boundary data on flow in the shallow-ice-stream approximation are presented. These solutions are valid for a non-linear Weertman-type sliding law and for Newtonian ice rheology. Comparison is made with corresponding solutions of the shallow-ice-sheet approximation, and with solutions of the full Stokes equations. The shallow-ice-stream approximation is commonly used to describe large-scale ice stream flow over a weak bed, while the shallow-ice-sheet approximation forms the basis of most current large-scale ice sheet models. It is found that the shallow-ice-stream approximation overestimates the effects of bed topography perturbations on surface profile for wavelengths less than about 5 to 10 ice thicknesses, the exact number depending on values of surface slope and slip ratio. For high slip ratios, the shallow-ice-stream approximation gives a very simple description of the relationship between bed and surface topography, with the corresponding transfer amplitudes being close to unity for any given wavelength. The shallow-ice-stream estimates for the timescales that govern the transient response of ice streams to external perturbations are considerably more accurate than those based on the shallow-ice-sheet approximation. In particular, in contrast to the shallow-ice-sheet approximation, the shallow-ice-stream approximation correctly reproduces the short-wavelength limit of the kinematic phase speed given by solving a linearised version of the full Stokes system. In accordance with the full Stokes solutions, the shallow-ice-sheet approximation predicts surface fields to react weakly to spatial variations in basal slipperiness with wavelengths less than about 10 to 20 ice thicknesses. Article in Journal/Newspaper Ice Sheet Natural Environment Research Council: NERC Open Research Archive Weertman ENVELOPE(-67.753,-67.753,-66.972,-66.972) The Cryosphere 2 2 77 93 |
institution |
Open Polar |
collection |
Natural Environment Research Council: NERC Open Research Archive |
op_collection_id |
ftnerc |
language |
English |
topic |
Glaciology |
spellingShingle |
Glaciology Gudmundsson, G.H. Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation |
topic_facet |
Glaciology |
description |
New analytical solutions describing the effects of small-amplitude perturbations in boundary data on flow in the shallow-ice-stream approximation are presented. These solutions are valid for a non-linear Weertman-type sliding law and for Newtonian ice rheology. Comparison is made with corresponding solutions of the shallow-ice-sheet approximation, and with solutions of the full Stokes equations. The shallow-ice-stream approximation is commonly used to describe large-scale ice stream flow over a weak bed, while the shallow-ice-sheet approximation forms the basis of most current large-scale ice sheet models. It is found that the shallow-ice-stream approximation overestimates the effects of bed topography perturbations on surface profile for wavelengths less than about 5 to 10 ice thicknesses, the exact number depending on values of surface slope and slip ratio. For high slip ratios, the shallow-ice-stream approximation gives a very simple description of the relationship between bed and surface topography, with the corresponding transfer amplitudes being close to unity for any given wavelength. The shallow-ice-stream estimates for the timescales that govern the transient response of ice streams to external perturbations are considerably more accurate than those based on the shallow-ice-sheet approximation. In particular, in contrast to the shallow-ice-sheet approximation, the shallow-ice-stream approximation correctly reproduces the short-wavelength limit of the kinematic phase speed given by solving a linearised version of the full Stokes system. In accordance with the full Stokes solutions, the shallow-ice-sheet approximation predicts surface fields to react weakly to spatial variations in basal slipperiness with wavelengths less than about 10 to 20 ice thicknesses. |
format |
Article in Journal/Newspaper |
author |
Gudmundsson, G.H. |
author_facet |
Gudmundsson, G.H. |
author_sort |
Gudmundsson, G.H. |
title |
Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation |
title_short |
Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation |
title_full |
Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation |
title_fullStr |
Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation |
title_full_unstemmed |
Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation |
title_sort |
analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation |
publisher |
European Geosciences Union |
publishDate |
2008 |
url |
http://nora.nerc.ac.uk/id/eprint/6799/ https://nora.nerc.ac.uk/id/eprint/6799/1/tc-2-77-2008.pdf https://doi.org/10.5194/tc-2-77-2008 |
long_lat |
ENVELOPE(-67.753,-67.753,-66.972,-66.972) |
geographic |
Weertman |
geographic_facet |
Weertman |
genre |
Ice Sheet |
genre_facet |
Ice Sheet |
op_relation |
https://nora.nerc.ac.uk/id/eprint/6799/1/tc-2-77-2008.pdf Gudmundsson, G.H. orcid:0000-0003-4236-5369 . 2008 Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation. Cryosphere, 2 (2). 77-93. https://doi.org/10.5194/tc-2-77-2008 <https://doi.org/10.5194/tc-2-77-2008> |
op_doi |
https://doi.org/10.5194/tc-2-77-2008 |
container_title |
The Cryosphere |
container_volume |
2 |
container_issue |
2 |
container_start_page |
77 |
op_container_end_page |
93 |
_version_ |
1766030265202769920 |