Extensions to a similarity hypothesis for shallow cumulus convection

Grant and Brown (Quart. J. Roy. Meteorol. Soc., 125, 1913-1936) proposed a similarity hypothesis for shallow cumulus convection and evaluated it using large-eddy simulation results. Here, results from an additional independen t simulation are used to provide further support for the basic theory. At t he same time, some extensions to the theory are proposed. It is shown that the effects of non-zero fluxes at cloud base can be conveniently accounted for by a simple representation of the transport of scalar variance into the convecting layer. The effects of having more complex mean profile shapes w ithin the layer (and hence changes in the gradient production of variance) are also investigated.