Linear stability and single-column analyses of several cumulus parametrization categories in a shallow-water model

Abstract

Using a mass-flux based approach, the thermodynamic cumulus parametrization problem is reformulated in a simple atmospheric model, which is an analogue of the shallow-water equations. The objective is to investigate basic effects of elementary representations of several parametrization categories. In particular, a linear stability analysis and a single-column experiment are performed to infer the characteristics of each parametrization as regards its ability to simulate the large-scale organization or coherence of tropical convection. The moisture-convergence closure (MC) scheme, which assumes that the ensemble of cumulus convection is controlled by the low-level moisture convergence as in Kuo-type scheme, predicts the largest growth at the smallest scale. Hence, although it ensures the generation of a coherent propagating structure, its scale always corresponds to the grid size. Furthermore, the MC tends to produce a catastrophic positive feedback of moist convection to the large-scale convergence. In contrast, the statistical equilibrium scheme, which assumes an instantaneous adjustment of the large-scale environment to a quasi-equilibrium state, such as Arakawa-Schubert and moist convective adjustment schemes, asymptotes to a constant growth rate at small scales. Hence, this type of parametrization tends to generate a field like white noise with no large-scale coherence. The 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 with the scale-separation principle. A new type of parametrization is also tested. This convective life-cycle (CLC) scheme represnets the life cycle of a common type of convective system made up of deep precipitating convection and a subsequent mesoscale response. It uses a buoyancy-based closure. The growth-rate curve is similar to the other LA schemes, but the behaviour in the zero-dimensional (single-column) version of the model is qualitatively different. Although the CLC scheme does not automatically saisfy the scale-separation principle, its grid-size dependence can be treated by a re-normalization principle. The result are used to interpret some reported general-circulation-model results regarding the impact of different parametrization schemes on the tropical atmosphere at large scales.