A Convective Cloud Model for Use in a Cumulus Parameterization Scheme

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  • 1 Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, Indiana
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Abstract

A quasi-one-dimensional steady-state cloud model that is based on integrating the two-dimensional equation for the azimuthal vorticity over the cloud radius is described. The equations are reduced to one dimension in the vertical direction by assuming that the streamfunction is oscillatory and a function of r only allowing this model to incorporate the nonhydrostatic pressure gradient force. It also includes an empirical buoyancy correction to account for vertical wind shear; the correction is based on application of the Klemp-Wilhelmson convective cloud model to a variety of buoyancy and wind-shear environments. In addition, the model includes consideration of rainwater, freezing of condensate, and a moist penetrative downdraft. The downdraft includes consideration of the nonhydrostatic pressure gradient, rainwater loading, and buoyancy; below cloud base, it is unsaturated.

The results from the model for cases with and without vertical wind shear are compared to the Schlesinger three-dimensional cloud model results for the same environmental conditions. The amount and vertical variation of the vertical mass flux, heat flux, and water vapor flux calculated by the quasi-one-dimensional model are comparable to the same produced by the Schlesinger model. Finally, implications of these results in regard to using this model in cumulus parameterization are given.

Abstract

A quasi-one-dimensional steady-state cloud model that is based on integrating the two-dimensional equation for the azimuthal vorticity over the cloud radius is described. The equations are reduced to one dimension in the vertical direction by assuming that the streamfunction is oscillatory and a function of r only allowing this model to incorporate the nonhydrostatic pressure gradient force. It also includes an empirical buoyancy correction to account for vertical wind shear; the correction is based on application of the Klemp-Wilhelmson convective cloud model to a variety of buoyancy and wind-shear environments. In addition, the model includes consideration of rainwater, freezing of condensate, and a moist penetrative downdraft. The downdraft includes consideration of the nonhydrostatic pressure gradient, rainwater loading, and buoyancy; below cloud base, it is unsaturated.

The results from the model for cases with and without vertical wind shear are compared to the Schlesinger three-dimensional cloud model results for the same environmental conditions. The amount and vertical variation of the vertical mass flux, heat flux, and water vapor flux calculated by the quasi-one-dimensional model are comparable to the same produced by the Schlesinger model. Finally, implications of these results in regard to using this model in cumulus parameterization are given.

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