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| Titel |
Quantification of error sources in the 2D mountain flow numerical test case and convergence studies with the limited area model COSMO-CLM |
| VerfasserIn |
Andreas Will, Jack Ogaja |
| Konferenz |
EGU General Assembly 2014
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 16 (2014) |
| Datensatznummer |
250100932
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| Publikation (Nr.) |
 EGU/EGU2014-16957.pdf |
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| Zusammenfassung |
| We investigated the absolute discretisation errors and the convergence properties of the
schemes implemented in the limited area model COSMO by application of the 2D mountain
flow test case. For standard linear hydrostatic configurations (10m height of the hill and 10km
half width) a complex error convergence was found for the horizontal and the vertical
velocity by comparison with high resolution reference case. This cannot be explained by the
formal order of convergence of the vertical and/or horizontal discretisation implemented in
the model. A theoretical analysis of the error sources was conducted for different
configurations of the damping at the model boundaries and for different mountain profiles. It
revealed maximum errors due to damping at the lateral and/or upper boundaries
and/or linearization for configurations known from literature (U = 10m-s, damping
configuration as used for operational applications). It is found that keeping the
error sources named above sufficiently small for a convergence study (relative error
below 10-3) leads to small hills (h = 1m) and velocities (U -¤ 10m-s) and thus to
high accuracy requirements (Δw < 10-6) for the simulation. Ín linear regime the
convergence can be investigated with respect to the analytical solution. In weakly linear
to nonlinear regime the convergence with respect to a high resolution reference
simulation can be investigated only. The analysis of the discretisation errors of the test
case shows that different configurations are recommended for the investigation
of the horizontal and vertical discretisation error convergence. In non-hydrostatic
regime the relative horizontal discretisation error is increased in comparison with the
hydrostatic regime. Thus, the horizontal schemes can be investigated best in the
non-hydrostatic regime, at vertical resolution of approx. 100m or higher (due to first order
accuracy of the vertical discretisation). The vertical discretisation convergence can be
investigated best in linear hydrostatic regime at a horizontal resolution of approx.
250m or higher. We analysed the discretisation errors for uniform horizontal and
stretched vertical grids and identified the model resolutions at which the unavoidable
linear error term (resulting from grid stretching) is dominating and those where the
second order error term of vertical discretisation is dominating. Furthermore the
corresponding horizontal and vertical resolutions have been identified for which the
discretisation errors have same order of magnitude. The results of the theoretical
analysis will be presented together with test case results for different configurations
exhibiting the theoretical findings for the schemes implemented in the COSMO
model. |
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