Journal cover Journal topic
The Cryosphere An interactive open-access journal of the European Geosciences Union
The Cryosphere, 11, 2283-2303, 2017
https://doi.org/10.5194/tc-11-2283-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
05 Oct 2017
Boundary layer models for calving marine outlet glaciers
Christian Schoof1, Andrew D. Davis2, and Tiberiu V. Popa1 1Department of Earth, Ocean and Atmospheric Sciences, University of British Columbia, 2020–2207 Main Mall, Vancouver, BC, V6T 1Z4, Canada
2Department of Aeronautical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
Abstract. We consider the flow of marine-terminating outlet glaciers that are laterally confined in a channel of prescribed width. In that case, the drag exerted by the channel side walls on a floating ice shelf can reduce extensional stress at the grounding line. If ice flux through the grounding line increases with both ice thickness and extensional stress, then a longer shelf can reduce ice flux by decreasing extensional stress. Consequently, calving has an effect on flux through the grounding line by regulating the length of the shelf. In the absence of a shelf, it plays a similar role by controlling the above-flotation height of the calving cliff. Using two calving laws, one due to Nick et al. (2010) based on a model for crevasse propagation due to hydrofracture and the other simply asserting that calving occurs where the glacier ice becomes afloat, we pose and analyse a flowline model for a marine-terminating glacier by two methods: direct numerical solution and matched asymptotic expansions. The latter leads to a boundary layer formulation that predicts flux through the grounding line as a function of depth to bedrock, channel width, basal drag coefficient, and a calving parameter. By contrast with unbuttressed marine ice sheets, we find that flux can decrease with increasing depth to bedrock at the grounding line, reversing the usual stability criterion for steady grounding line location. Stable steady states can then have grounding lines located on retrograde slopes. We show how this anomalous behaviour relates to the strength of lateral versus basal drag on the grounded portion of the glacier and to the specifics of the calving law used.

Citation: Schoof, C., Davis, A. D., and Popa, T. V.: Boundary layer models for calving marine outlet glaciers, The Cryosphere, 11, 2283-2303, https://doi.org/10.5194/tc-11-2283-2017, 2017.
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We show mathematically and computationally how discharge of ice from ocean-terminating glaciers is controlled by a combination of different forces acting on ice near the grounding line of a glacier and how that combination of forces is affected by the process of iceberg formation, which limits the length of floating ice tongues extending in front of the glacier. We show that a deeper fjord may lead to a longer ice tongue providing greater drag on the glacier, slowing the rate of ice discharge.
We show mathematically and computationally how discharge of ice from ocean-terminating glaciers...
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