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    An Improved Analytical Solution for the Temperature Profile of Ice Sheets

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    Rezvanbehbahani_2019.pdf (2.678Mb)
    Issue Date
    2019-02-01
    Author
    Rezvanbehbahani, Soroush
    van der Veen, C. J.
    Stearns, Leigh A.
    Publisher
    Wiley
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Rights
    ©2019. American Geophysical Union. All Rights Reserved.
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    Abstract
    The one‐dimensional steady state analytical solution of the energy conservation equation obtained by Robin (1955, https://doi.org/10.3189/002214355793702028) is frequently used in glaciology. This solution assumes a linear change in surface velocity from a minimum value equal to minus the mass balance at the surface to zero at the bed. Here we show that this assumption of a linear velocity profile leads to large errors in the calculated temperature profile and especially in basal temperature. By prescribing a nonlinear power function of elevation above the bed for the vertical velocity profile arising from use of the Shallow Ice Approximation, we derive a new analytical solution for temperature. We show that the solution produces temperature profiles identical to numerical temperature solutions with the Shallow Ice Approximation vertical velocity near ice divides. We quantify the importance of strain heating and demonstrate that integrating the strain heating and adding it to the geothermal heat flux at the bed is a reasonable approximation for the interior regions. Our analytical solution does not include horizontal advection components, so we compare our solution with numerical solutions of a two‐dimensional advection‐diffusion model and assess the applicability and errors of the analytical solution away from the ice divide. We show that several parameters and assumptions impact the spatial extent of applicability of the new solution including surface mass balance rate and surface temperature lapse rate. We delineate regions of Greenland and Antarctica within which the analytical solution at any depth is likely within 2 K of the actual temperatures with horizontal advection.
    Description
    An edited version of this paper was published by AGU. Copyright 2019 American Geophysical Union.
    URI
    http://hdl.handle.net/1808/31448
    DOI
    https://doi.org/10.1029/2018JF004774
    Collections
    • Geography & Atmospheric Science Scholarly Works [199]
    Citation
    Rezvanbehbahani, S., vanderVeen, C. J., & Stearns, L. A. (2019). An improved analytical solution for the temperature profile of ice sheets. Journal of Geophysical Research: Earth Surface, 124, 271–286. https://doi.org/10.1029/2018JF004774

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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