The Representation of Cumulus Cloud Effects in the Large-Scale Vorticity Equation

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Abstract
A formulation is proposed to represent the effects of cumulus clouds in the large-scale vorticity equation. Cumulus clouds are found to modify the large-scale vorticity field through two processes: 1) the vertical advection of mean vorticity by the cumulus vertical cloud mass flux and 2) the twisting of horizontal vorticity into the vertical direction due to the inhomogeneous spatial distribution of the cloud population. Under the assumption that the divergence of mean horizontal eddy flux of vorticity can be neglected, the net effect of cumulus clouds can be completely specified in terms of the total cloud mass flux alone. No detailed knowledge of the dynamic fields of cumulus clouds is needed. GATE A/B-scale heat, moisture and vorticity budgets have been analyzed for a 1-day period (0000–2400 GMT 9 September) during Phase III to verify the validity of the theoretical formulation. The agreement between the theoretically predicted and the observed cloud effects appears very encouraging. Another important conclusion of this study is that the cloud vorticity when averaged over a cloud cross-sectional area is of the same order of magnitude as the large-scale mean vorticity, despite the smallness of the horizontal scale of cumulus clouds. This has some important implications on the analysis of mesoscale dynamic fields using observational data.

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