LARGE-SCALE CONVECTIVE INSTABILITY REVISITED

Linear convective instability is revisited to demonstrate the structurally different growth rates of disturbances in balanced and unbalanced models where diabatic heating is parameterized to be proportional to the vertical mass flux, and Ekman-type lower boundary conditions are introduced. The heating parameterization leads to an ''effective static stability,'' which is negative when the vertical cumulus mass flux exceeds the total mass flux. This results in large-scale convective overturning. The appropriate horizontal scale is the usual Rossby deformation radius modified by the parameter root gamma-1, where gamma is the ratio of cumulus to total mass flux. The unbalanced flow instability varies from zero growth to (sigma = 0) at finite horizontal scale (corresponding to twice the modified deformation radius L = 2R) to infinitely large values (sigma --> infinity) at smallest scales (L --> 0). The growth of the related balanced model commences at the same scale (L = 2R) but attains infinitely large values on approaching the scale of the modified deformation radius L = R. This short-wave cutoff appears as a result of the changing vertical mass flux-heating profile associated with the Ekman boundary condition. Growth rates, horizontal length scales, and associated mass flux profiles are qualitatively supported by observations. A feature of the solution is its dependence on vertical structure. Specifically, for each imposed vertical structure there are two solutions: one unbalanced corresponding to the cloud scale, and one balanced corresponding to the scale of the modified deformation radius. It is the thesis of this paper that the latter (large scale) solution represents a viable mechanism for the initial growth of either cloud clusters or tropical cyclones in nature.