The horizontal scale of individual cumulus cloud is of the order of 0.1-10 Km. Therefore, models whose grid sizes are of the same order can directly resolve the cumulus clouds without the need of cumulus parameterization. On the other hand, grid spacing of synoptic forecast models are much greater than the sizes of individual cumulus clouds. Therefore, it becomes totally impracticable to resolve them in any numerical model of large-scale circulation. Instead, the collective influence of clouds within a larger area is formulated or parameterized in terms of the large scale environmental variables. This is called the cumulus paratemetization. The goal is to predict the changes in the large scale variables due to cumulus convection. Some of the well known schemes are the simple dry convective adjustment scheme, moist convective adjustment scheme, Kuo-type schemes (Kuo, 1965, 1974), and, the mass flux type schemes (Arakawa and Schubert, 1974). There are several schemes available at present for the parameterization of cumulus convection. The basic feature that differentiates them is the closure assumption upon which the schemes are based. Majority of the schemes use a mass flux type approach to parameterize the effects of cumulus convection and, they are based on the Arakawa-Schubert scheme in some form (i.e., Tiedtke, 1989), Simplified Arakawa-Schubert scheme (SAS) developed by Grell (1993), and the Relaxed Arakawa-Schubert scheme (RAS) proposed by Moorthi and Suarez (1992). The Kuo-type scheme uses convective instability and moisture convergence as a measure to parameterize cumulus convection, while Betts and Miller (1986) uses a mixing line approach for driving actual lapse rate toward moist adiabat. Some of the schemes use available buoyant energy or Convective Available Potential Energy (CAPE) for the closure (i.e., Fristch and Chappell, 1980), while others are based on a presumed equilibrium between surface enthalpy fluxes and input of low entropy air into the subcloud layer by convective updrafts (i.e., Emanuel, 1995). The real test of a physical parameterization scheme can be seen only in an operational NWP environment and, not in some isolated test cases. A typical cumulonimbus cloud is shown here in the picture.

REFERENCE

Betts, A.K. and M.J. Miller, 1986: A new convective adjustment scheme. Part I: Observational & theoretical basis. QJRMS, 112, 677-691.

Emanuel, K.A., 1995: The behavior of a simple hurricane model using a convective scheme based on subcloud-layer entropy equilibrium. Vol. 52, 3959-3968.

Fritsch, J.M. & C. Chappell, 1980: Numerical simulation of convectively driven pressure systems. Part I: Convective parameterization. J. Atmos. Sc., 37, 1722-1733.

Grell, G. A., 1993: Prognostic evaluation of assumptions used by cumulus parameterization. Mon. Wea. Rev., 121, 764-787.

Kuo, H.L., 1974: Further studies of the parameterization of the influence of cumulus convection on large scale flow. J. Atmos. Sci., 31, 1232-1240.

Kuo, H.L., 1965: On formation and intensification of tropical cyclones through latent heat release by cumulus convection. J. Atmos. Sci., 22, 40-63.

Moorthi S. and M.J. Suarez, 1992: Relaxed Arakawa-Schubert: A parameterization of moist convection for general circulation models. Mon. Wea. Rev., 120, 978-1002.

Tiedtke, M., 1989: A comprehensive mass flux scheme for cumulus parameterization in large-scale models. Mon. Wea. Rev., 117, 1799-1800.