LINEAR-STABILITY AND SINGLE-COLUMN ANALYSES OF SEVERAL CUMULUS PARAMETRIZATION CATEGORIES IN A SHALLOW-WATER MODEL

Using a mass-flux based approach, the thermodynamic cumulus parametriz ation problem is reformulated in a simple atmospheric model, which is an analogue of the shallow-water equations. The objective is to invest igate basic effects of elementary representations of several parametri zation categories. In particular, a linear stability analysis and a si ngle-column experiment are performed to infer the characteristics of e ach parametrization as regards its ability to simulate the large-scale organization or coherence of tropical convection. The moisture-conver gence closure (MC) scheme, which assumes that the ensemble of cumulus convection is controlled by the low-level moisture convergence as in K uo-type schemes, predicts the largest growth at the smallest scale. He nce, although it ensures the generation of a coherent propagating stru cture, its scale always corresponds to the grid size. Furthermore, the MC tends to produce a catastrophic positive feedback of moist convect ion to the large-scale convergence. In contrast, the statistical equil ibrium scheme, which assumes an instantaneous adjustment of the large- scale environment to a quasi-equilibrium state, such as Arakawa-Schube rt and moist convective adjustment schemes, asymptotes to a constant g rowth rate at small scales. Hence, this type of parametrization tends to generate a field like white noise with no large-scale coherence. Th e lagged-adjustment (LA) schemes, which have a short time-lag for the cumulus growth, as in the Betts-Miller scheme, feature a finite scale selection in the linear growth rate. This ensures a smooth large-scale coherence that is independent of the grid size, and is consistent wit h the scale-separation principle. A new type of parametrization is als o tested. This convective life-cycle (CLC) scheme represents the life cycle of a common type of convective system made up of deep precipitat ing convection and a subsequent mesoscale response. It uses a buoyancy -based closure. The growth-rate curve is similar to the other LA schem es, but the behaviour in the zero-dimensional (single-column) version of the model is qualitatively different. Although the CLC scheme does not automatically satisfy the scale separation principle, its grid-siz e dependence can be treated by a re-normalization principle. The resul ts are used to interpret some reported general-circulation-model resul ts regarding the impact of different parametrization schemes on the tr opical atmosphere at large scales.