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Journal of the Meteorological Society of Japan. Ser. II
Vol. 64A (1986) p. 107-131



 The problem of cumulus parameterization is a closure problem, in which we seek a limited number of equations that govern the statistics of a system with huge dimensions. A great deal of uncertainty still exists in the choice of appropriate closure assumptions for this 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 our 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.

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