An Ubiquitous Property of Simple Wave-CISK Models and Its Implications

Abstract

Models of wave-CISK are developed that possess a prescribed form for the vertical profile of the diabatic heating due to a cumulus cloud ensemble, and either an explicit or an implicit moisture budget constraint. A comparison is undertaken of the models that do not have an explicit moisture budget constraint but differ in that the amplitude of the cloud-induced diabatic heating is related to the vertical velocity field at different height levels in the lower troposphere. The comparison reveals the essential equivalence of these models. The neutral eigenmodes demark the transition between stability and instability, and the one associated with the lowest amplitude for the diabatic heating is independent of the height of the forcing level. The only difference between these models is shown to be in the interpretation and specification of the diabatic heating amplitude. It is further shown that the same neutral eigenmode pertains at the instability-stability boundary for a wave-CISK model with an explicit moisture budget constraint. The results obtained in this case are used to assess the potential for CISK in the tropics by examining the efficiency that the cloud ensemble must exhibit to sustain neutral modes. Finally, the imposition of an Artificial rigid-lid upper boundary condition is shown to prevent the occurrence of the aforementioned mode and there is a concomitant stabilizing effect upon the flow.