The moist stability of a midlatitude zonal flow with a conditionally unstable layer in the presence of an Ekman layer is investigated. The vertical velocity employed in a simplified Kuo's parameterization is sustained by baroclinic wave forcing, diabatic heating and Ekman pumping. A general dispersion relation and eigenfunction are derived analytically for a class of flows with various vertical heating profiles.

The moist unstable mode may be regarded as a baroclinic wave modified by the bulk effect of the convective heating, for which the fundamental dependences of the baroclinic growth rate on the Burger number and vertical shear remain qualitatively valid. Waves longer than the Rossby radius of deformation are not appreciably affected, while the shorter waves are significantly destablized by the convective heating. The growth rates and wavelengths of the most unstable modes are nonlinear functions of the averaged specific humidity of the moist layer, and there is an optimum specific humidity that minimizes the preferred wavelength, this value being proportional to the static stability for a representative heating profile. The quasi-geostrophic constraints and baroclinity appear to be decisive factors that suppress short waves and lead to a finite preferred wavelength.

The destabilizing effect of the convection heating is considerably enhanced by the reduction of the static stability. Among the other influential parameters that affect the growth rate, relatively lower cloud top and a deep moist layer have a profound effect on the stability. Because of the cooperative interactions between favorable factors, the simultaneous occurrence of several of the mechanisms listed above may produce explosive-like growth. The relatively shallow convection and the Ekman layer will slow down the wave propagation speed.

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