Some further theoretical results concerning conditional instability of the second kind (CISK) are derived from Bratseth's model and verified for a more general non-Boussinesq model with a z-dependent heating function. In particular, the minimum threshold moisture content required for the instability, is shown to depend only upon environmental stratification and the vertical distribution of latent heat, while the preferred marginally unstable wavelength, in addition to being dependent on the stratification and the heating distribution, is also proportional to the inverse of the Coriolis parameter. A CISK index, which is defined as the ratio of a characteristic boundary layer specific humidity to the minimum threshold specific humidity of CISK, is used for assessing the relative potential for the CISK development in the Atlantic and the Pacific polar oceanic air masses, compared with that in a tropical oceanic air mass.

The limitation arising from use of a constant heating profile in the interpretation of the short wave cut-off is demonstrated. The criterion for short wave blow-up is analogous to that of convective instability. The necessary and sufficient condition for the presence of short wave cut-off and wave selection is that the threshold moisture content at the shortest wave exceeds the minimum threshold moisture content. The treatment of the unconditional heating intensity is also discussed.

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