Model multi-cloud parameterizations for convectively coupled waves: Detailed nonlinear wave evolution

Recent observational analysis reveals the central role of three cloud types, congestus, stratiform, and deep-convective cumulus clouds, in the dynamics of large scale convectively coupled Kelvin waves, westward propagating 2-day waves, and the Madden–Julian oscillation. Recently, a systematic model convective parametrization highlighting the dynamic role of the three cloud types has been developed by the authors involving two baroclinic modes of vertical structure: a deep-convective heating mode and a second mode with low level heating and cooling corresponding, respectively, to congestus and stratiform clouds. The model includes a systematic moisture equation where the lower troposphere moisture increases through detrainment of shallow cumulus clouds, evaporation of stratiform rain, and moisture convergence and decreases through deep-convective precipitation and also a nonlinear switch which favors either deep or congestus convection depending on the relative dryness of the middle troposphere. The detailed nonlinear evolution of large scale convectively coupled waves in the model parametrization is studied here in a chaotic intermittent regime of the nonlinear dynamics associated with weaker mean radiative cooling where such waves are isolated in space and time. This regime is utilized to elucidate in a clean fashion several novel features of the model parametrization. In particular, four stages of nonlinear wave evolution occur: in the preconditioning and birth stages, the role of congestus moistening and second baroclinic convergence are crucial while in the dying stage of the large scale convectively coupled wave, the role of the nonlinear switch, and the drying of the troposphere are essential. In the mature phase, the large scale features of the convectively coupled waves resemble those in observations of convectively coupled Kelvin waves including the propagation speed, wave tilt, temperature, heating, and velocity structure.