A new convective adjustment scheme. Part I: Observational and theoretical basis

Cumulus parametrization started with simple attempts to represent the subgrid-scale effects of convective clouds. Manabe et al. (1965) proposed adjustment towards a moist adiabatic structure in the presence of conditional instability, and Kuo (1965, 1974) proposed a simple cloud model to redistribute the heating and moistening effects of precipitating clouds in the presence of grid-scale moisture convergence. The work of Ooyama (1971) and Arakawa and Schubert (1974) initiated a great deal of research attempting to parametrize cloud ensembles using a cloud spectrum and a simple cloud model (see review by Frank (1983)). One of the key objectives of the GATE experiment (Betts 1974) was to study organized deep convection in the tropics to test and develop convective parametrizations for numerical models. GATE diagnostic studies have documented the complexity of tropical mesoscale convection (Houze and Betts 1981): from the importance of mesoscale updraughts and downdraughts as well as convective-scale processes down to the effects of the cloud microphysical processes of freezing, melting and water loading. One might conclude from these phenomenological studies that cloud models of much greater complexity might be needed to parametrize cumulus convection (Frank 1983). Little progress has been made in this direction, however, because it is clearly impossible to attempt to integrate at each grid-point in a global model, a cloudscale model of much realism. This paper returns to a simpler approach to parametrization: the primary objective of the proposed parametrization scheme (Betts 1983b) is to ensure that the local vertical temperature and moisture structures in the large-scale model, which in nature are strongly constrained by convection, be realistic. The concept of a quasi-equilibrium between the cloud field and the large-scale forcing (introduced by Betts (1973) for shallow convection and by Arakawa and Schubert (1974) for deep clouds) has been well established, at least on larger space and time scales (Lord and Arakawa 1980; Lord 1982). This means that convective regions have characteristic temperature and moisture structures which can be documented observationally, and used as the basis of a convective adjustment procedure. Betts (1973) and Albrecht et al. (1979) modelled shallow convection using this approach. The main limitation of the moist adiabatic convective adjustment suggested by Manabe et al. (1965) for deep convection is that the tropical atmosphere does not approach a moist adiabatic equilibrium structure in the presence of deep convection. In the scheme proposed here we shall relax simultaneously the temperature and moisture structures towards observed quasi-equilibrium structures. This ensures that on the grid scale a global model always maintains a realistic vertical temperature and moisture structure in