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Modeling of convective rainfall rates is a central problem in tropical meteorology. Toward numerical weather prediction efforts the semi-prognostic approach (i.e., a one time-step prediction of rainfall rates) provides a relevant test of cumulus parameterization methods. In this paper we compare five currently available cumulus parameterization schemes using the semi-prognostic approach. The calculated rainfall rates are compared with observed estimates provided in the recent publication of Hudlow and Patterson (1979). Among these the scheme proposed by Kuo (1974) provides the least root-mean-square error between the calculated and the observed estimates, slightly better than that of Arakawa and Schubert (1974), which was used by Lord (1978a). The simplicity of the approach holds promise for numerical weather prediction. Unlike some of the other schemes this method is not sensitive to and does not require computation of internal parameters such as profiles of cloud mass flux updrafts and downdrafts, detrainment of cloud matter and entrainment of environmental air. The present paper does not address the prognostic evolution and verification of the vertical distribution of temperature, humidity or momentum. These will be compared for the different methods in more detail separately.

AbstractIn this paper, we consider three disparate classes of cumulus parameterization schemes, applied to cases of severe midlatitude convective storms observed during SESAME-1979. Objective analysis of the observed data was carded out and verifying heat and moisture budgets were computed. For the three types of schemes–Arakawa-Schubert, KreitzbM-Perkey, and Kuo–the underlying closure assumptions and cloud models are tested within the generalized framework of dynamic control, static control, and feedback. Using the semiprognostic approach, single time step predictions of the heating and drying rates due to convection are obtained for the three schemes and are compared with those diagnosed from the observed budgets. The results presented should have important implications for models with a resolution of more than 1 80 km.The vertical distributions of warming and drying are fairly well reproduced by the Arakawa-Schubert scheme, however, excessive amounts are predicted in most of the lower troposphere and insufficient drying is predicted just near the surface. This was ameliorated by incorporating moist convective-scale downdrafts into the parameterization. Although the downdraft mass flux is highly sensitive to some arbitrary parameters, the inclusion of downdrafts is shown to be crucial to predict the feedback correctly in the midlatitude environment. A test of the quasi-equilibrium assumption for these severe storm cases showed that it was valid (as had previously been demonstrated for the tropics). For the Kreitzberg-Perkey scheme, the most severe limitations were found to be a lack of dependence on large-scale destabilizing effects in the dynamic control and the assumption that clouds instantly decay and mix with their environment in the feedback. For the Kuo-type schemes, tests of its dynamic control demonstrated the need to include mesoscale moisture convergence in order to correctly predict the vertically integrated heating and drying rates, unless the resolved scale is fairly small and the moistening parameter is set to zero. Tests with the feedback-wherein the vertical distribution of heating and drying is dictated by the differences between cloud and environmental thermodynamic properties-revealed serious shortcomings. In particular, this scheme is unable to predict heating maxima for atmospheric layers exhibiting high static stability. Such stable layers are frequently noted in the midlatitude environment of severe convective storms.