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| Titel |
A test of numerical instability and stiffness in the parametrizations of the ARPÉGE and ALADIN models |
| VerfasserIn |
M. Tudor |
| 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. 4 ; Nr. 6, no. 4 (2013-07-05), S.901-913 |
| Datensatznummer |
250017855
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| Publikation (Nr.) |
 copernicus.org/gmd-6-901-2013.pdf |
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| Zusammenfassung |
| Meteorological numerical weather prediction (NWP) models solve a system of
partial differential equations in time and space. Semi-lagrangian advection
schemes allow for long time steps. These longer time steps can result in
instabilities occurring in the model physics. A system of differential
equations in which some solution components decay more rapidly than others is
stiff. In this case it is stability rather than accuracy that restricts the
time step. The vertical diffusion parametrization can cause fast
non-meteorological oscillations around the slowly evolving true solution
(fibrillations). These are treated with an anti-fibrillation scheme, but
small oscillations remain in operational weather forecasts using ARPÉGE
and ALADIN models. In this paper, a simple test is designed to reveal if the
formulation of particular a physical parametrization is a stiff problem or
potentially numerically unstable in combination with any other part of the
model. When the test is applied to a stable scheme, the solution remains
stable. However, applying the test to a potentially unstable scheme yields a
solution with fibrillations of substantial amplitude. The parametrizations of
the NWP model ARPÉGE were tested one by one to see which one may be the
source of unstable model behaviour. The test identified the set of
equations in the stratiform precipitation scheme (a diagnostic Kessler-type
scheme) as a stiff problem, particularly the combination of terms arising due
to the evaporation of snow. |
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