Cumulus parameterization and rainfall rates, Pt. 2

In the various formulations of Kuo-type (1965, 1974) cumulus parameterization schemes, the moistening and heating by the cumulus are made proportional to the humidity and temperature differences between a model cloud and its environment. The constants of proportionality which differentiate the various versions of Kuo's schemes are based on different closure assumptions. The proportion of available moisture supply that goes into the moistening by cumulus convection usually determines these constants. It is possible to calculate diagnostically the observed (or what might be called the exact) measures of these constants of proportionality. This makes it possible to define an ultimate Kuo scheme where the vertical integrals of the heating and moistening are exactly known but the vertical distributions are limited by the aforementioned structure functions. This ultimate Kuo scheme is not a prognostic scheme, but it serves as a benchmark in defining how far this type of scheme can be used in the prognostic sense. By using the final validated GATE B-scale data sets, a comparison is made between the observed vertical distributions of the apparent heat source and the apparent moisture sink (obtained from direct substitutions of observed data), with the ultimate Kuo scheme to assess its scope. Comparison of the 1965, 1974 Kuo-type schemes is then done with the ultimate Kuo scheme to address their limitations. A proposal for a mesoscale convergence parameter, eta , and a moistening parameter, b, is made to overcome some of the limitations of the above schemes. A multiple regression search of large-scale parameters, using 72 map times of data, is conducted to determine these parameters via least-square minimization of errors. These are next used to determine the vertical structure of moistening and heating, for a semiprognostic formulation. The results show that, by using the vertical average of the large-scale upward vertical motion and the lower tropospheric relative vorticity in the multiple regression, it is possible to attain an accuracy close to that prescribed by the ultimate Kuo scheme. Detailed results of the vertical distributions of the heating and moistening and the rainfall rates for the entire third phase of GATE are presented.