Models for Stratiform Instability and Convectively Coupled Waves

A simplified intermediate model for analyzing and parameterizing convectively coupled tropical waves is introduced here. This model has two baroclinic modes of vertical structure: a direct heating mode and a stratiform mode. The key essential parameter in these models is the area fraction occupied by deep convection, c . The unstable convectively coupled waves that emerge from perturbation of a radiative convective equilibrium are discussed in detail through linearized stability analysis. Without any mean flow, for an overall cooling rate of 1 K day 1 as the area fraction parameter increases from c 0.0010 to c 0.0014 the waves pass from a regime with stable moist convective damping to a regime of ''stratiform'' instability with convectively coupled waves propagating at speeds of roughly 15 m s 1 ; instabilities for a band of wavelengths in the supercluster regime, O(1000)-O( Thus, these convectively coupled waves in the model reproduce several key features of convectively coupled waves in the troposphere processed from recent observational data by Wheeler and Kiladis. As the parameter c is increased further to values such as c 0.01, the band of unstable waves increases and spreads toward a mesoscale wavelength of O(100) km while the same wave structure and quantitative features mentioned above are retained for O(1000) km.