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
commonly used for parameterizing the turbulence in NWP models is
examined. As a starting point, this paper adopts the idea of Girard and
Delage and shows how their results can be modified when the problem is
examined in a less restrictive framework, typical of practical NWP
applications. In Girard and Delage's work, an optimal compromise between
stability and accuracy was proposed to eliminate the fibrillations
resulting from the instability, by applying a time decentering in the
diffusion operator for the points likely to be unstable according to a
local linear analysis of the stability. This key idea is pursued here,
but two important changes are examined: (i) an exact method for the
relaxation of the identity between thermal and dynamical exchange
coefficients, and (ii) the introduction of a modification to the
Richardson number for simulating the destabilization of the top of the
PBL in shallow convection conditions. Compared to an approximate
solution proposed by Girard and Delage for the first change, the one
proposed here is more accurate and possesses a formal justification. For
the second one, it is shown that the only consequence is that the
stability now depends on the largest value of the modified/not modified
Richardson number. A formulation of the temporal decentering consistent
with these changes is then proposed and evaluated.</div>
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