Stabilization of non-linear vertical diffusion schemes in the context of NWP models
Stabilisation des schémas non-linéaires de diffusion verticale dans le contexte des modèles de prévision numérique du temps
Bénard P. ; Marki, A. ; Neytchev, P.N. ; Prtenjak, M.T.
Année de publication
2000
The stability of the nonlinear vertical diffusion equation such as <br>commonly used for parameterizing the turbulence in NWP models is <br>examined. As a starting point, this paper adopts the idea of Girard and <br>Delage and shows how their results can be modified when the problem is <br>examined in a less restrictive framework, typical of practical NWP <br>applications. In Girard and Delage's work, an optimal compromise between<br> stability and accuracy was proposed to eliminate the fibrillations <br>resulting from the instability, by applying a time decentering in the <br>diffusion operator for the points likely to be unstable according to a <br>local linear analysis of the stability. This key idea is pursued here, <br>but two important changes are examined: (i) an exact method for the <br>relaxation of the identity between thermal and dynamical exchange <br>coefficients, and (ii) the introduction of a modification to the <br>Richardson number for simulating the destabilization of the top of the <br>PBL in shallow convection conditions. Compared to an approximate <br>solution proposed by Girard and Delage for the first change, the one <br>proposed here is more accurate and possesses a formal justification. For<br> the second one, it is shown that the only consequence is that the <br>stability now depends on the largest value of the modified/not modified <br>Richardson number. A formulation of the temporal decentering consistent <br>with these changes is then proposed and evaluated.</div>
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