The closure assumption of the Arakawa-Schubert (1974) cumulus parameterization takes the form of a balance between the generation of moist convective instability by large-scale processes and its destruction by clouds. This assumption can be justified by consideration of the kinetic energy budget of a cumulus subensemble. First, the kinetic energy generation and dissipation per unit cloud-base mass flux should approximately balance over time scales of the order of the large-scale processes. Second, the dissipation per unit cloud-base mass flux and, therefore, the kinetic energy generation per unit cloud-base mass flux (the cloud-work function) for a given subensemble should not depend substantially on the large-scale conditions. The cloud-work function quasi-equilibrium follows consequently and the unknown cloud-base mass flux is determined by an integral equation.
Observational evidence for the cloud-work function quasi-equilibrium is presented. Cloud-work functions are calculated from a variety of data sets in the tropics and subtropics including the GATE, AMTEX, VIMHEX and composited typhoon data. The results show that the cloud-work functions fall into a well-defined narrow range for each subensemble although the thermodynamical vertical structures for each data set are quite different.