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The Cryosphere An interactive open-access journal of the European Geosciences Union
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https://doi.org/10.5194/tc-2020-108
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/tc-2020-108
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 13 May 2020

Submitted as: research article | 13 May 2020

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This preprint is currently under review for the journal TC.

Sensitivity of ice sheet surface velocity and elevation to variations in basal friction and topography in the Full Stokes and Shallow Shelf Approximation frameworks

Gong Cheng1, Nina Kirchner2,3, and Per Lötstedt1 Gong Cheng et al.
  • 1Department of Information Technology, Uppsala University, P. O. Box 337, 75105 Uppsala, Sweden
  • 2Department of Physical Geography, Stockholm University, 10691 Stockholm, Sweden
  • 3Bolin Centre for Climate Research, Stockholm University, 10691 Stockholm, Sweden

Abstract. Predictions of future mass loss from ice sheets are afflicted with uncertainty, caused, among others, by insufficient understanding of spatio-temporally 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 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 ice sheet surface velocities and elevation to 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 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. Perturbations with long wavelength and low frequency will propagate to the surface while those of short wavelength and high frequency are damped.

Gong Cheng et al.

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Gong Cheng et al.

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Latest update: 04 Jul 2020
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Short summary
We present an inverse modeling approach to improve the understanding of spatio-temporally variable processes at the inaccessible base of an ice sheet by determining the sensitivity of direct surface observations to perturbations of basal conditions. Time dependency is proved to be important in these types of problems. The effect of perturbations is analyzed based on analytical and numerical solutions.
We present an inverse modeling approach to improve the understanding of spatio-temporally...
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