Geosci. Model Dev. Discuss., 5, 4233-4268, 2012
© Author(s) 2012. This work is distributed
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This discussion paper has been under review for the journal Geoscientific Model Development (GMD). Please refer to the corresponding final paper in GMD.
A test of numerical instability and stiffness in the parametrizations of the ARPÉGE and ALADIN models
M. Tudor
Croatian Meteorological and Hydrological Service, Zagreb, Grič 3, Croatia

Abstract. Meteorological numerical weather prediction (NWP) models solve a system of partial differential equations in time and space. Semi-lagrangian advection scheme in the model dynamics allows 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 an operational weather forecasts using ARPÉGE and ALADIN models. It is needed to test of the complete model formulation, as implemented in the operational forecast. In this paper, a simple test is designed. The test reveals if the formulation of particular 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. But, applying the test to a potentially unstable scheme yields a solution with fibrillations of substantial amplitude. The parametrizations of a NWP model ARPÉGE were tested one by one to see which one may be the source of unstable model behaviour. The test has identified the stratiform precipitation scheme (a diagnostic Kessler type scheme) as a stiff problem, particularly the term that describes the evaporation of snow.

Citation: Tudor, M.: A test of numerical instability and stiffness in the parametrizations of the ARPÉGE and ALADIN models, Geosci. Model Dev. Discuss., 5, 4233-4268, doi:10.5194/gmdd-5-4233-2012, 2012.
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