Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation

Gudmundsson, G.H. ORCID: https://orcid.org/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

Before downloading, please read NORA policies.

Preview

Text
tc-2-77-2008.pdf - Published Version
Download (1MB) | Preview

Abstract/Summary

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.

Item Type:	Publication - Article
Digital Object Identifier (DOI):	https://doi.org/10.5194/tc-2-77-2008
Programmes:	BAS Programmes > Global Science in the Antarctic Context (2005-2009) > Glacial Retreat in Antarctica and Deglaciation of the Earth System
ISSN:	1994-0416
Additional Information. Not used in RCUK Gateway to Research.:	Open access article made available under a CC-BY Creative Commons Attribution license.
Additional Keywords:	Ice streams, Flow
NORA Subject Terms:	Glaciology
Date made live:	24 Mar 2009 13:57 +0 (UTC)
URI:	https://nora.nerc.ac.uk/id/eprint/6799

Item Type:

Publication - Article

Digital Object Identifier (DOI):

https://doi.org/10.5194/tc-2-77-2008

Programmes:

BAS Programmes > Global Science in the Antarctic Context (2005-2009) > Glacial Retreat in Antarctica and Deglaciation of the Earth System

ISSN:

1994-0416

Additional Information. Not used in RCUK Gateway to Research.:

Open access article made available under a CC-BY Creative Commons Attribution license.

Additional Keywords:

Ice streams, Flow