A simple multi-cloud convective parametrization for tropical superclusters

We propose a convective parametrization model for tropical superclusters utilizing three cloud types, namely, deep convective, stratiform, and congestus clouds. The simplicity of the model resides in a crude vertical resolution of the primitive equations via a Galerkin projection onto the first and second baroclinic vertical modes supplemented with an active thin boundary layer. While the first baroclinic temperature equation is forced by the deep convective heating, the stratiform clouds heat the upper troposphere and the congestus clouds heat the lower troposphere by forcing accordingly the second baroclinic mode. The two shallow water systems are supplemented by a systematic derivation of an equation for the vertically averaged water vapor content and a boundary layer theta-e equation. A variable switch parameter Lambda depending on the moistness and dryness of the middle troposphere permits to consistently shut off or favor deep convection or congestus heating. A mean background moisture profile is imposed on the moisture distribution resulting in a moisture stratification which, consistently with observations, slows down the moisture-loaded-convectively coupled gravity waves. More importantly, both the first baroclinic and the second baroclinic velocity divergences are present within the moisture equation. Computer simulations yield intermittent convectively coupled gravity waves, traveling at speeds of about 10 to 15 m/s with many features resembling tropical superclusters (as in Majda et al. JAS 2004), evolving in a background of ubiquitous shallow convection. Moreover, right before they die the deep convective waves which appear and die on the time scale of the surface evaporative forcing, eject in both directions (first) baroclinic dry gravity waves moving at speeds of roughly 50 m/s leaving a significant trough of low moisture content yielding an amplification of the congestus heating, through the switch parameter Lambda, which in turn excites second baroclinic dry gravity waves moving at roughly 25 m/s which serve as a trigger for deep convection at the locations where the troposphere is moist enough to sustain it; probably through the second baroclinic divergence present within the moisture equation.