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| Titel |
Accuracy of the zeroth- and second-order shallow-ice approximation – numerical and theoretical results |
| VerfasserIn |
J. Ahlkrona, N. Kirchner, P. Lötstedt |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1991-959X
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| Digitales Dokument |
URL |
| Erschienen |
In: Geoscientific Model Development ; 6, no. 6 ; Nr. 6, no. 6 (2013-12-19), S.2135-2152 |
| Datensatznummer |
250085025
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| Publikation (Nr.) |
 copernicus.org/gmd-6-2135-2013.pdf |
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| Zusammenfassung |
| In ice sheet modelling, the shallow-ice approximation (SIA) and
second-order shallow-ice approximation (SOSIA) schemes are
approaches to approximate the solution of the full Stokes equations
governing ice sheet dynamics. This is done by writing the solution
to the full Stokes equations as an asymptotic expansion in the
aspect ratio ε, i.e. the quotient between a characteristic
height and a characteristic length of the ice sheet. SIA retains the
zeroth-order terms and SOSIA the zeroth-, first-, and second-order
terms in the expansion. Here, we evaluate the order of accuracy of
SIA and SOSIA by numerically solving a two-dimensional model problem
for different values of ε, and comparing the solutions with
afinite element solution to the full Stokes equations obtained from
Elmer/Ice. The SIA and SOSIA solutions are also derived analytically
for the model problem. For decreasing ε, the computed
errors in SIA and SOSIA decrease, but not always in the expected
way. Moreover, they depend critically on a parameter introduced to
avoid singularities in Glen's flow law in the ice model. This is
because the assumptions behind the SIA and SOSIA neglect a thick,
high-viscosity boundary layer near the ice surface. The sensitivity
to the parameter is explained by the analytical solutions. As a verification
of the comparison technique, the SIA and SOSIA solutions for a fluid with
Newtonian rheology are compared to the solutions by Elmer/Ice, with results
agreeing very well with theory. |
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