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On Bulk Models of Shallow Cumulus Convection

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  • 1 Laboratoire de Météorologie Dynamique du CNRS, IPSL, Université Pierre et Marie Curie, Paris, France
  • 2 Department of Atmospheric Sciences, University of California, Los Angeles, Los Angeles, California
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Abstract

Two-layer bulk models of the cloudy boundary layer are investigated, focusing on the consistency issues between common assumptions on the turbulent mixing and the thermodynamic profiles. Simplifications of the vertical structure of the conserved variables are shown to lead to inconsistent steady states. First, linear profiles in the cloud layer are incompatible with the common parameterizations of the turbulent mixing. Second, this approximation is inconsistent with simple models of an infinitely thin inversion layer. Simple mass-flux parameterizations of the turbulence are shown to produce reasonable profiles inside the cloud layer without solving the problem of the inversion. The cloud − environment difference and the vertical gradient of the conserved variables appear as interesting test variables for such models, as well as their ability to match the free-tropospheric boundary conditions. The latter certainly requires a unified approach for the cloud and inversion layers.

Corresponding author address: Gilles Bellon, Laboratoire de Météorologie Dynamique, Université Pierre et Marie Curie, case 99, 4 place Jussieu, 75252, Paris Cedex 5, France. Email: Gilles.Bellon@lmd.jussieu.fr

Abstract

Two-layer bulk models of the cloudy boundary layer are investigated, focusing on the consistency issues between common assumptions on the turbulent mixing and the thermodynamic profiles. Simplifications of the vertical structure of the conserved variables are shown to lead to inconsistent steady states. First, linear profiles in the cloud layer are incompatible with the common parameterizations of the turbulent mixing. Second, this approximation is inconsistent with simple models of an infinitely thin inversion layer. Simple mass-flux parameterizations of the turbulence are shown to produce reasonable profiles inside the cloud layer without solving the problem of the inversion. The cloud − environment difference and the vertical gradient of the conserved variables appear as interesting test variables for such models, as well as their ability to match the free-tropospheric boundary conditions. The latter certainly requires a unified approach for the cloud and inversion layers.

Corresponding author address: Gilles Bellon, Laboratoire de Météorologie Dynamique, Université Pierre et Marie Curie, case 99, 4 place Jussieu, 75252, Paris Cedex 5, France. Email: Gilles.Bellon@lmd.jussieu.fr

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