Wheeler-Kiladis Convectively-Coupled waves in a simple multicloud model on a beta-plane

Organized convection in the tropics involves a hierarchy of spatial and temporal scales ranging from the individual clouds of a few kilometres and a few hours to the mesoscale cloud clusters and superclusters and their intraseasonal/planetary scale wave envelopes, known as the Madden-Julian oscillation (Nakazawa, 1988). Interactions between large scale dynamics (and thermodynamics) and small scale convective processes are believed to play a crucial role in the generation and maintenance of these organized features. The analysis of Wheeler and Kiladis (1999) and Heartel and Kiladis (2004) showed that the dynamical fields and the power spectral peaks of the synoptic scale superclusters--identified as the convectively coupled waves, are closely related to the first few equatorially-trapped linear waves of Matsuno, but with a significantly reduced equivalent depth, namely, the Kelvin waves, the n=0 gravity (Yanai) waves, the n=1 westward gravity waves (known as the 2day waves), the mixed Rossby-gravity waves, and the Rossby waves. Despite recent research efforts and significant progress in computing capabilities, current GCM's often simulate poorly the dynamics and structure of convectively coupled waves, particularly the MJO, due to an inadequate treatment of organized convection by the convective parameterizations currently in use (Moncrieff).
K. and Majda have recently introduced a simple multi-cloud model parameterization for tropical convection, which takes into account some intrinsic characteristics of organized convection, such as its trimodal nature (Lin and Johnson, 1999) and the role played by moisture and congestus preconditioning and low-level convergence of moisture prior to deep convection as well as the role of the statiform anvils in the wake of the wave. As such, despite crude simplifications, the model reveals to be capable in reproducing many key features of convectively coupled waves and their planetary scale organization, through non-linear energy exchange across scales. In this talk we shall present some linear results in the case with rotation (on a beta-plane) revealing the persistence of convectively Kelvin, Yanai, and 2day waves, in the model, reminiscent of the convectively coupled waves of Wheeler and Kiladis. For instance, they all have the same self-similar vertical structure, with the famous front to rear vertical tilt in temperature, wind, heating, and moisture, observed by Kiladis and his co-authors. They also have instability bands, in the zonal wavenumber domain, and propagation speeds qualitatively matching the spectral peaks of Wheeler and Kiladis.(Joint work with Andrew J. Majda)