A Moisture-Stratiform Instability for Convectively Coupled Waves

A simple model of two vertical modes is constructed and analyzed to reveal the basic instability mechanisms of convectively coupled waves. The main novelty of this model is a convective parameterization based on the quasi-equilibrium concept and simplified for a model of two vertical modes. It hypothesizes 1) the approximate invariance of the difference between saturation moist static energy in the lower half of the troposphere and moist static energy in the subcloud layer, regardless of free troposphere humidity, and 2) that variations in the depth of convection are determined by moisture-deficit variations in the midtroposphere. Physical arguments for such a treatment are presented. For realistic model parameters chosen based on cloud system resolving model simulations (CSRMs) of an earlier study, the model produces unstable waves at wavelengths and with structures that compare well with the CSRM simulations and observations. A moisture–stratiform instability and a direct–stratiform instability are identified as the main instability mechanisms in the model. The former relies on the effect of midtroposphere humidity on the depth of convection. The latter relies on the climatological mean convective heating profile being top heavy, and it is identified to be the same as the stratiform instability mechanism proposed by B. E. Mapes. The moisture–stratiform instability appears to be the main instability mechanism for the convectively coupled wave development in the CSRM simulations. The finite response time of convection has a damping effect on the waves that is stronger at high wavenumbers. The net moistening effect of the second-mode convective heating also damps the waves, but more strongly at low wavenumbers. These effects help to shape the growth rate curve so that the most unstable waves are of a few thousand kilometers in scale.