A theoretical framework is developed for the evolution of baroclinic waves with latent heat release parameterized in terms of vertical velocity. Both wave-CISK and large-scale rain approaches are
included. The new quasi-geostrophic framework covers
evolution from general initial conditions on zonal flows with vertical shear, planetary vorticity gradient, a lower boundary and a tropopause.
The formulation is given completely in terms of potential vorticity, enabling partition of perturbations into Rossby-wave components, just as for the dry problem. Both modal and non-modal development can be understood to a good approximation in terms of propagation and interaction between these components alone. The key change with moisture is that growing normal modes are described in terms of four counter-propagating Rossby wave (CRW) components rather than two. ``Moist CRWs'' exist above and below the maximum in latent heating, in addition to the upper and lower level CRWs of dry theory. Four classifications of baroclinic development are defined by quantifying the strength of interaction between the four components and identifying the dominant pairs: ranging from essentially dry-instability to instability in the limit of strong heating far from
boundaries, with ``type-C cyclogenesis'' and ``diabatic Rossby waves'' being intermediate types. General initial conditions must also include ``passively-advected residual PV'', as in the dry problem.
H de Vries, J Methven, THA Frame, BJ Hoskins. Baroclinic waves with parameterized effects of moisture interpreted using Rossby wave components
accepted, J. Atmos. Sci., 2010