Semi-prognostic tests of a new cumulus parameterization scheme for mesoscale modeling

A new cumulus parameterization scheme is developed, discussed, and tested. 3 sizes of clouds: small, medium and large are allowed by this scheme; they crudely represent a spectrum of clouds and all 3 sizes of cloud may exist at any given time. All clouds are based on a quasi-one-dimensional cloud model that has been shown to deliver mass, moisture and heat fluxes comparable to those calculated by a 3-dimensional convective cloud model at the mature stage of a modeled convective storm. The radus of the largest cloud is twice that of the medium-sized cloud which is, in turn, twice that of the smallest cloud. The largest cloud may also have a saturated downdraft that can penetrate to the ground. In order to close the relation between the cloud and grid scales, 3 closure relations are imposed. Together, they yield a unique solution of the cloud population at any given time. In the first 2 constraints, both the convective and grid scale mass and moisture budgets are linked. Of the possible cloud sets that satisfy both the mass and moisture constraints, we choose the one that produces the fastest rate of heating from integrating the individual cloud heating rates over the possible cloud sets and over the cloud depths. The scheme is tested semi-prognostically with Sesame V storm-scale analyses during a period in which the precipitation was almost exclusively convective in nature (2000 GMT to 2300 GMT on 20 May 1979). The comparison between observed grid scale and cumulus parameterization diagnosed heating and drying rates is quite good. This is true for both individual grid points and the convectively active area as a whole.