Abstract
The effects of cumulus convection on the large-scale vorticity budget are studied. The feasibility of parameterizing the cumulus effects is examined by relating the eddy correlation terms in the large-scale vorticity equation to the properties of cumulus ensembles. By introducing a spectral representation of a cumulus ensemble, a general expression for the cumulus effects is obtained. The expression reduces to a simple form when the fractional area coverage of cumulus clouds is very small and the mean cloud vorticity has the same order of magnitude as the mean vorticity of the environment. This approximate expression interprets the cumulus effects in terms of the detrainment of excess vorticity from the cumulus clouds, and of the vertical advection, the twisting and the stretching of the large-scale vorticity by cumulusinduced subsidence.
The approximate expression is combined with a spectral model of a cumulus ensemble, using the budget equations for mass, moist static energy, water substance and vorticity of sub-ensembles. The model is then used to estimate the cumulus effects over the Marshall Islands area and the calculated, vertical profile is compared with the observed profile of the residual of the large-scale vorticity budget (the apparent vorticity source). Cases with and without downdrafts are tested. The calculations without downdrafts produce excessively large vorticity source immediately above the cloud base and above the 300mb level. The inclusion of downdrafts and of lateral detrainment in the sub-ensemble budget equations significantly improves the results, especially below 700mb.
