Convectively coupled gravity and moisture modes in a simple atmospheric model

Recent observational work shows that three factors control the formation of deep convection over tropical oceans; the saturation fraction of the troposphere, surface moist entropy fluxes, and the strength of convective inhibition. A linearized, two-dimensional, non-rotating model of the tropical atmosphere is presented here which incorporates all of these factors into its convective closure in a simplified fashion. Two types of large-scale unstable modes develop in this model, a slowly propagating 'moisture mode' which is driven primarily by saturation fraction anomalies, and a convectively coupled 'gravity mode' which is governed by anomalies in convective inhibition caused by buoyancy variations just above the top of the planetary boundary layer. The gravity mode maps onto the equatorial Kelvin wave in the earth's atmosphere and the predicted propagation speed for this mode is close to the observed phase speed of convectively coupled equatorial Kelvin waves. For reasonable parameter values the growth rate peaks at zonal wavenumbers at which Kelvin waves exhibit the greatest spectral energy. The computed vertical structure matches that of observed Kelvin waves, but is produced by a simple sinusoidal vertical heating profile with half-wavelength equal to the depth of the troposphere.