Inclusion of Rainwater Budget and Convective Downdrafts in the Arakawa–Schubert Cumulus Parameterization

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Abstract
A combined updraft–downdraft model that includes the mass, rainwater, and vertical momentum budget equations for both updrafts and downdrafts is incorporated into the Arakawa–Schubert (A–S) cumulus parameterization. The model assumes that the rainwater generated in an updraft falls partly inside and partly outside the updraft. Two types of stationary solutions are identified for the coupled rainwater budget and vertical momentum equations: solutions for small tilting angles and solutions for large tilting angles. The balance of terms in the rainwater budget equation is quite different between these solutions, and solutions for small tilting angles are unstable, while solutions for large tilting angles are stable. The cause of the instability is interpreted, considering the effect of rain drag on the vertical transport of rainwater. The motivation for an optimum choice of the tilting angle for use in the revised parameterization is discussed. The results of semiprognostic and single-column prognostic tests of the revised A–S parameterization using the GATE Phase III data show drastic improvement in predicting the humidity field through the inclusion of downdraft effects. An updraft model with a simplified rainwater budget equation, which is used in the authors’ current GCM applications of the revised parameterization, is also presented.

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