Dimensional analysis of a convecting atmosphere in equilibrium with external forcing

It has recently been suggested by Renno and Ingersoll that certain properties of a convecting atmosphere in equilibrium with external forcing can be predicted by considering the convecting atmosphere as a heat engine. Their argument is modified to express the forcing of convection in terms of a specified cooling of the convective layer. It is found that convective available potential energy and mean convective vertical velocity are independent of the forcing, while the fractional area of the convection increases in proportion with the forcing. These predictions are consistent with recent numerical results from cloud-ensemble models. Finally, it is shown by a formal dimensional analysis that these conclusions are independent of the details of the thermodynamic formulation.