Remarks on Arakawa-Schubert's Quasi-Equilibrium theory

The original formulation of the cumulus parameterization scheme by Arakawa and Schubert (1974) contains an inconsistency related to the quasi-equilibrium assumption. The convective adjustment time scale, Tau-Adj, must be multiplied by the fractional area covered by convection, sigma, in order for their formulation to be consistent with the quasi-equilibrium idea. This problem with the Arakawa-Schubert model lies at the root of an inconsitency recently discovered by Yano (1999). This inconsistency leads to the incorrect conclusion that the cloud-work-function (or CAPE) is nearly zero in convecting atmospheres. Near zero CAPE in the tropical atmosphere provides the foundation for many theories of atmospheric circulation in the tropics. Arguments are presented against this notion of an atmosphere nearly neutral to moist convection.