Scaling analysis and experience with numerical models (e.g., E89) strongly suggest that subcloud layers are nearly in thermodynamic equilibrium, with heat fluxes from the surface nearly balancing convective and small-scale turbulent fluxes of entropy through the subcloud layer top. Assuming such a balance leads to a restraint (4) on equilibrium convective updraft mass flux, which shows that it is proportional to the surface enthalpy flux and the large-scale ascent rate just above the subcloud layer. A closed convective representation also requires a relationship between downdraft and updraft mass fluxes, and a link between tendencies of temperature in the lower and upper troposphere; both of these require a cloud model. (A cloud model is also required to predict the moistening of the free troposphere by convection.) But for the purposes of a simple model, we assume that the convective updraft and downdraft mass fluxes are proportional, with the proportionality related to a (variable) bulk precipitation efficiency, as in (7). The specification of both the convective updraft and downdraft mass fluxes allows for the prediction of lower-tropospheric saturation entropy (i.e., temperature), and the subcloud-layer entropy is diagnosed by assuming that it is equal to the lower tropospheric saturation entropy in regions of convection.
Use of such a subcloud equilibrium-based convection scheme was shown by Emanuel (1993) to yield realistic phase speeds and amplification rates of large-scale equatorial disturbances, provided small lags in the convective mass flux response were used. Here we have shown that this type of convection scheme also works very well in a simple model of tropical cyclones, with an expected sensitivity to the dependence of the bulk precipitation efficiency on environmental parameters such as relative humidity. These results support the conclusion of Raymond (1995) that thermodynamic quasi-equilibrium of the subcloud layer may provide an important and useful closure condition in the representation of the ensemble effects of cumulus convection.
Acknowledgments. This research was supported by the National Science Foundation under Grant ATM-9216906. The author thanks Alan Betts, David Raymond and an anonymous reviewer for their helpful remarks.