A minimal model of a moist equatorial atmosphere is presented in which the precipitation rate is assumed to depend on just the vertically averaged saturation deficit and the convective available potential energy. When wind-induced surface heat exchange (WISHE) and cloud-radiation interactions are turned off, there are no growing modes. Gravity waves with wavenumbers smaller than a certain limit respond to a reduced static stability due to latent heat release, and therefore propagate more slowly than dry modes, while those with larger wavenumbers respond to the normal dry static stability. In addition, there exists a stationary mode that decays slowly with time. For realistic parameter values, the effect of reduced static stability on gravity waves is limited to wavelengths greater than the circumference of the earth. WISHE and cloud-radiation interactions both destabilize the stationary mode, but not the gravity waves.
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Fuchs et al. (2002) studied this question.
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