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

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  • Mihailović, Dragutin
  • Kostić, Vladimir
  • Mimić, Gordan
  • Cvetković, Ljiljana

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.

Suggested Citation

  • Mihailović, Dragutin & Kostić, Vladimir & Mimić, Gordan & Cvetković, Ljiljana, 2015. "Stability analysis of turbulent heat exchange over the heterogeneous environmental interface in climate models," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 79-90.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:79-90
    DOI: 10.1016/j.amc.2015.04.121
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    References listed on IDEAS

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    1. Judith Curry, 2011. "Reasoning about climate uncertainty," Climatic Change, Springer, vol. 108(4), pages 723-732, October.
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