Equatorial convectively coupled waves in a simple muticlod model

Linear stability results for the multicloud model recently developed by the authors on an equatorial beta plane are presented here. The linearized equations, about a realistic radiative-convective equilibrium (RCE) are projected in the meridional direction via a Galerkin truncation procedure based on the parabolic cylinder functions. In a suitable parameter regime, the multicloud model exhibits convectively coupled Kelvin, M = 0 eastward (Yanai), and M = 1 westward inertia-gravity waves, unstable at the synoptic scales in agreement with the outgoing longwave radiation (OLR) spectral peaks observed by Wheeler and Kiladis. The horizontal wave structure and vertical wavenumber of the unstable waves qualitatively match those of the rotating equatorial shallow water waves but with a reduced phase speed, as in the observations. More importantly, they exhibit the same self-similar front-to-rear vertical tilt in the zonal winds, temperature, and heating fields as observed by Kiladis and colleagues. Similar to the case without rotation (from earlier work) a wave life cycle is identified, once again demonstrating the crucial role, played by congestus clouds and moisture, of preconditioning and moistening prior to deep convection and of triggering and maintaining the instability. When the troposphere is excessively dry, the convective wave instability fades out and an instability of low-frequency modes moving in both eastward and westward directions takes place. The eigenstructure of the low-frequency modes projects heavily on the congestus and moisture components and exhibits a quadruple vortex configuration reminiscent of Rossby waves with strong meridional convergence of warm and moist air toward the equatorial belt, suggesting a moistening and preconditioning role resembling the congestus standing mode seen in the case without rotation.