Convectively coupled waves in a simple multi-cloud model on a beta-plane

Despite the recent advances in super-computing, the current general circulation models (GCM) represent poorly the large scale variability associated with tropical convection. Multi-cloud model-convective parametrizations with a crude vertical resolution reduced to the first two baroclinic modes, using three cloud types (congestus, deep, and stratiform), introduced recently by the authors (JAS, 2006), have revealed to be very successful in representing key features of organized convection and convectively coupled tropical waves. The key instability mechanism is due to moisture and to the interactions between the three cloud types. When CAPE is positive and the middle atmosphere is dry, a moisture switch (or tigger) inhibits deep convection and promotes low level congestus heating. Congestus heating in turn induces low-level moisture convergence through the second baroclinic mode, which moistens and preconditions the middle troposphere to sustain (deep) convection beyond the freezing level. Stratiform anvils are represented by upper-tropospheric heating, which lags behind the direct/deep convection by a few hours (Mapes 2000). Linear analysis and nonlinear simulations performed in the case without rotation exhibit moist gravity wave packets moving at about 17 m/s with planetary scale envelopes moving often in the opposite direction at about 6 m/s and having many of the self-similar features of convectively coupled waves, reminiscent of the Madden-Julian oscillation. Here we present, for the first time, linear stability analysis on a beta plane, revealing convectively coupled equatorial (Kelvin, n = 0 inetrio-gravity/Yanai, n = 1 westward inertio-gravity/2 day) waves which are unstable in zonal wavenumber bands, within the synoptic scales, qualitatively matching the corresponding spectral peaks observed by Wheeler and Kiladis (1999). Despite their meridional differences, the waves have a self-similar vertical structure in agreement with the observations.