Cumulus Parameterization and Rainfall Rates II

Abstract

In the various formulations of Kuo (1965, 1974) type 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 that differentiate the various versions of the 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 diagnostically calculate the observed (or what might be called the exact) measures of these constants of proportionality. This enables one 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 one can progress with this type of scheme in the prognostic sense. Using the final validated GATE B-scale data sets a comparison is made between the observed vertical distributions of the apparent heat source and apparent moisture sink (obtained from direct substitutions of observed data) with the ultimate Kuo scheme to assess its scope. Comparison of Kuo (1965, 1974) type schemes is next carried out with the ultimate Kuo scheme to address their limitations. A proposal for a mesoscale convergence parameter ? and a moistening parameter b is made to overcome some of the limitations of the above schemes. Here a multiple regression search of large-scale parameters, using 72 map times of data, is carried out 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 semi-prognostic 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 on the vertical distributions of the heating and moistening and the rainfall rates for the entire third phase of GATE are presented in this paper.