A test of numerical instability and stiffness in the parametrizations of the ARPÉGE and ALADIN models
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 equat...
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2013-07-01
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| Series: | Geoscientific Model Development |
| Online Access: | http://www.geosci-model-dev.net/6/901/2013/gmd-6-901-2013.pdf |
| _version_ | 1818163236432773120 |
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| author | M. Tudor |
| author_facet | M. Tudor |
| author_sort | M. Tudor |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T16:46:21Z |
| format | Article |
| id | doaj.art-985fb2838c96477d87afe6229a2e1454 |
| institution | Directory Open Access Journal |
| issn | 1991-959X 1991-9603 |
| language | English |
| last_indexed | 2024-12-11T16:46:21Z |
| publishDate | 2013-07-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Geoscientific Model Development |
| spelling | doaj.art-985fb2838c96477d87afe6229a2e14542022-12-22T00:58:12ZengCopernicus PublicationsGeoscientific Model Development1991-959X1991-96032013-07-016490191310.5194/gmd-6-901-2013A test of numerical instability and stiffness in the parametrizations of the ARPÉGE and ALADIN modelsM. TudorMeteorological 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.http://www.geosci-model-dev.net/6/901/2013/gmd-6-901-2013.pdf |
| spellingShingle | M. Tudor A test of numerical instability and stiffness in the parametrizations of the ARPÉGE and ALADIN models Geoscientific Model Development |
| title | A test of numerical instability and stiffness in the parametrizations of the ARPÉGE and ALADIN models |
| title_full | A test of numerical instability and stiffness in the parametrizations of the ARPÉGE and ALADIN models |
| title_fullStr | A test of numerical instability and stiffness in the parametrizations of the ARPÉGE and ALADIN models |
| title_full_unstemmed | A test of numerical instability and stiffness in the parametrizations of the ARPÉGE and ALADIN models |
| title_short | A test of numerical instability and stiffness in the parametrizations of the ARPÉGE and ALADIN models |
| title_sort | test of numerical instability and stiffness in the parametrizations of the arpege and aladin models |
| url | http://www.geosci-model-dev.net/6/901/2013/gmd-6-901-2013.pdf |
| work_keys_str_mv | AT mtudor atestofnumericalinstabilityandstiffnessintheparametrizationsofthearpegeandaladinmodels AT mtudor testofnumericalinstabilityandstiffnessintheparametrizationsofthearpegeandaladinmodels |