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The Cryosphere An interactive open-access journal of the European Geosciences Union
https://doi.org/10.5194/tc-2017-6
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
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31 Jan 2017
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A revision of this discussion paper is under review for the journal The Cryosphere (TC).
Reply to Basal buoyancy and fast-moving glaciers: in defense of analytic force balance by C. J. van der Veen (2016)
Terence J. Hughes 1Earth Sciences and Climate Change, University of Maine, 404 North Sixth Street, Fort Pierre, South Dakota 57532, USA
*retired
Abstract. Two approaches to ice-sheet modeling are available. Analytical modeling is the traditional approach. It solves the force (momentum), mass, and energy balances to obtain three-dimensional solutions over time, beginning with the Navier-Stokes equations for the force balance. Geometrical modeling employs simple geometry to solve the force and mass balance in one dimension along ice flow. It is useful primarily to provide the first-order physical basis of ice-sheet modeling for students with little background in mathematics (Hughes, 2012). The geometric approach uses changes in ice-bed coupling along flow to calculate changes in ice elevation and thickness, using floating fraction φ along a flowline or flowband, where φ = 0 for sheet flow, 0 < φ < 1 for stream flow, and φ = 1 for shelf flow. This leads to confusion in reconciling the two approaches (Van der Veen, 2016). An attempt is made at reconciliation.

Citation: Hughes, T. J.: Reply to Basal buoyancy and fast-moving glaciers: in defense of analytic force balance by C. J. van der Veen (2016), The Cryosphere Discuss., https://doi.org/10.5194/tc-2017-6, in review, 2017.
Terence J. Hughes
Terence J. Hughes
Terence J. Hughes

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Short summary
Two approaches to ice-sheet modeling are available. Analytical modeling is the traditional approach. It solves the force (momentum), mass, and energy balances to obtain three-dimensional solutions over time. Geometrical modeling employs simple geometry to solve the force and mass balance in one dimension along ice flow. It is useful primarily to provide the first-order physical basis of ice-sheet modeling for students with little background in mathematics. The two approaches are compared.
Two approaches to ice-sheet modeling are available. Analytical modeling is the traditional...
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