Cumulus Parameterization and Rainfall Rates II

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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... 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...

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