Stability analysis of turbulent heat exchange over the heterogeneous environmental interface in climate models

Dragutin Mihailović, Vladimir Kostić, Gordan Mimić and Ljiljana Cvetković

Applied Mathematics and Computation, 2015, vol. 265, issue C, 79-90

Abstract: Based on a short review of the different parameterization schemes for sub-grid scale surface fluxes in climate and other atmospheric models of different scales, the flux aggregation effect over a heterogeneous grid-box leading to the occurrence of Schmidt’s paradox is considered. To investigate this effect in the sub-grid scale parameterization, we have introduced a dynamical system approach, where the horizontal energy exchange is taken into account and is represented by a matrix of coupling parameters. Since it is, in general, very difficult to specify the quantities in that matrix, a sufficient condition for the asymptotic stability that can be applied for any coupling matrix is derived. Two theorems that consider the flux aggregation effect over a heterogeneous grid-box are proved. Finally, we have showed how, by their application, Schmidt’s paradox can be overcome. It is demonstrated through a numerical example of turbulent energy exchange over the grid-box including the part of the Prospect park, New York, USA.

Keywords: Climate modeling; Heterogeneous grid-box; Flux aggregation; Schmidt’s paradox; Asymptotic stability; Environmental interface (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:265:y:2015:i:c:p:79-90

DOI: 10.1016/j.amc.2015.04.121

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