Closure assumptions in the cumulus parameterization problem

While concentrating on the thermodynamical aspects of parameterizing deep cumulus clouds, some of the existing schemes are reviewed with an emphasis on their closure assumptions. It is shown that the closure assumptions in these schemes are some combination of four types. It is emphasized that observations should be used more extensively than in the past to directly verify and improve closure assumptions and to assess the limit of parameterizability. As an example, results from an analysis of the macroscopic behavior of moist convection are presented. The results suggest that cumulus clouds are basically parameterizable, in spite of the existence of mesoscale organization.