Cumulus convection, as a meso-scale phenomenon, results in the release of latent heat and vertical drift of energy that by part could affect the large scale field of energy, humidity, and momentum of the atmosphere. Since the current numerical models are unable to resolve the singular cumulus convective clouds that are important from a meteorological point of view, it is used to apply some sort of approximation of them in their models. The method of approximating is called parameterization and closure problem. The fundamental idea of these methods is, to approximate the small and meso-scale part of variables by their large scale part. Furthermore we know the large scale part of fields tends to damp the small and meso-scale parts including cumulus convection activities.
The cumulus convection parameterization schemes (CPSs) are divided into schemes for large-scale models and schemes for mesoscale models. In this division, the mesoscale models are referred to models with grid spacing between 10-50 km and a time step in the order of several minutes, while the large-scale models have grid spacing larger than 50 km and a time step greater than several minutes. In this study, CPSs that are used in large and meso-scale models are generally and chronologically reviewed from the beginning of 1960 up to recent schemes. Wellknown large-scale schemes are the convective adjustment schemes and Kuo-type schemes which use moisture convergence to determine the location and intensity of convection. In the convective adjustment, it is assumed that under some constraints, a critical state for the large-scale thermodynamical field is adjusted to a new stable state and in Kuo-type schemes, convection is dependent on the moisture supply by large-scale flow convergence and boundary-layer turbulence. In developing schemes for mesoscale models, three approaches have been taken (Molinari, 1993): the traditional, the fully explicit and the hybrid approaches. CPSs which are still needed in contemporary numerical weather prediction models to simulate convection rely on a realistic cloud model as one of their crucial parts. The cloud model is a fundamental determinant of vertical mass flux, heating and drying profiles, and precipitation rate.
Although there was considerable progress in the modeling of cumulus convection systems, because of the complexity of the problem, especially in meso-scale models, it remains as an open problem in modeling of the atmosphere and a hot field of research for meteorologists.