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...

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Published in:The Cryosphere
Main Author: Gudmundsson, Hilmar
Format: Article in Journal/Newspaper
Language:English
Published: Coperincus 2008
Subjects:
Online Access:https://nrl.northumbria.ac.uk/id/eprint/37816/
https://doi.org/10.5194/tc-2-77-2008
https://nrl.northumbria.ac.uk/id/eprint/37816/1/tc-2-77-2008.pdf
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spelling ftunivnorthumb:oai:nrl.northumbria.ac.uk:37816 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, Hilmar 2008-07-16 text https://nrl.northumbria.ac.uk/id/eprint/37816/ https://doi.org/10.5194/tc-2-77-2008 https://nrl.northumbria.ac.uk/id/eprint/37816/1/tc-2-77-2008.pdf en eng Coperincus https://nrl.northumbria.ac.uk/id/eprint/37816/1/tc-2-77-2008.pdf Gudmundsson, Hilmar (2008) Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation. The Cryosphere, 2. pp. 77-93. ISSN 1994-0424 cc_by CC-BY F800 Physical and Terrestrial Geographical and Environmental Sciences Article PeerReviewed 2008 ftunivnorthumb https://doi.org/10.5194/tc-2-77-2008 2022-09-25T06:09:06Z 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 The Cryosphere Northumbria University, Newcastle: Northumbria Research Link (NRL) Weertman ENVELOPE(-67.753,-67.753,-66.972,-66.972) The Cryosphere 2 2 77 93
institution Open Polar
collection Northumbria University, Newcastle: Northumbria Research Link (NRL)
op_collection_id ftunivnorthumb
language English
topic F800 Physical and Terrestrial Geographical and Environmental Sciences
spellingShingle F800 Physical and Terrestrial Geographical and Environmental Sciences
Gudmundsson, Hilmar
Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation
topic_facet F800 Physical and Terrestrial Geographical and Environmental Sciences
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, Hilmar
author_facet Gudmundsson, Hilmar
author_sort Gudmundsson, Hilmar
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 Coperincus
publishDate 2008
url https://nrl.northumbria.ac.uk/id/eprint/37816/
https://doi.org/10.5194/tc-2-77-2008
https://nrl.northumbria.ac.uk/id/eprint/37816/1/tc-2-77-2008.pdf
long_lat ENVELOPE(-67.753,-67.753,-66.972,-66.972)
geographic Weertman
geographic_facet Weertman
genre Ice Sheet
The Cryosphere
genre_facet Ice Sheet
The Cryosphere
op_relation https://nrl.northumbria.ac.uk/id/eprint/37816/1/tc-2-77-2008.pdf
Gudmundsson, Hilmar (2008) Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation. The Cryosphere, 2. pp. 77-93. ISSN 1994-0424
op_rights cc_by
op_rightsnorm CC-BY
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
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