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The effects of cumulus heating and the possibility of CISK in extratropical latitudes are explored by combining the Eady model of baroclinic instability with wave-CISK. For perturbations about a state of rest, there is no intrinsic time scale, however the equations can be solved for geopotential tendency. It was found that CISK disturbances could not grow unless the heating exceeded a threshold value. This value is reduced when the boundary layer moisture content is increased, the static stability decreased, or the heating distributed lower in the troposphere. Perturbations about a baroclinic basic state, for small heating rates resemble a baroclinic wave with heating acting mainly to reduce the effective static stability, resulting in faster growth and shorter wavelengths. However, as the heating is increased, the instability gradually takes on the characteristics of the pure CISK disturbance. The transition level shows the same dependencies on model parameters as for the threshold in the CISK calculation, but occurs at a somewhat lower level. Comparison of model results with observations of three comma clouds and three polar lows seemed to suggest that two of the comma clouds originated as baroclinic waves which owed their short wavelengths to the effective reduction in stability caused by cumulus heating, while two of the polar lows seemed to have resulted from CISK. The remaining disturbances, one polar low and one comma cloud, appeared to correspond to values in the transition region.
Craig et al. (Sat,) studied this question.