Further Studies of the Parameterization of the Influence of Cumulus Convection on Large-Scale Flow

The parameterization scheme devised by the author in a previous study has been extended to include both deep cumulus convection and shallow convection and a more rigorous derivation is given. In this scheme, the amounts and the vertical distributions of the latent heat released and the sensible heat transported by the deep cumulus are expressed solely in terms of the temperature difference between the cloud and the environment and the convergence of moisture produced by the large-scale flow. It is shown that the often stressed heating by compression in the descending region is automatically taken into consideration in this formulation. A comparison between the calculated results and the observational data of Reed and Recker for the composite easterly wave show that they are in good agreement in the regions of low-level convergence. A separate scheme is devised from the energy equations to represent the transports of heat and moisture by the shallow convection maintained by the thermal boundary layer.