q 2001 American Meteorological Society 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, sc. 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 day21 as the area fraction parameter increases from sc 5 0.0010 to sc 5 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 s21; instabilities for a band of wavelengths in the supercluster regime, O(1000)–O(2000) km; and a vertical structure with a ‘‘wave tilt’ ’ where the temperature structure in the upper troposphere lags behind that in the lower troposphere. 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 sc is increased further to values such as sc 5 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