A general theoretical framework for understanding essential dynamics of Madden–Julian oscillation

Motivated by observed structure of Madden–Julian oscillation (MJO), a general theoretical model framework is advanced for understanding fundamental aspects of MJO dynamics. The model extends the Matsuno–Gill theory by incorporating (a) moisture feedback to precipitation, (b) a trio-interaction among equatorial waves, boundary layer (BL) dynamics, and precipitation, and (c) a simplified Betts–Miller (B–M) cumulus parameterization. The general model with B–M scheme yields a frictionally coupled dynamic moisture mode, which produces an equatorial planetary-scale, unstable system moving eastward slowly with coupled Kelvin–Rossby wave structure and BL moisture convergence leading major convection. The moisture feedback in B–M scheme reinforces the coupling between precipitation heating and Rossby waves and enhances the Rossby wave component in the MJO mode, thereby slowing down eastward propagation and resulting in a more realistic horizontal structure. It is, however, the BL frictional convergence feedback that couples equatorial Kelvin and Rossby waves with convective heating and selects a preferred eastward propagation. The eastward propagation speed in the model is inversely related to the relative intensity of the equatorial “Rossby” westerly versus “Kelvin” easterly associated with the MJO. The cumulus parameterization scheme may affect propagation speed through changing MJO horizontal structure. The SST or basic-state moist static energy has a fundamental control on MJO propagation speed and intensification/decay. Model sensitivity to BL and cumulus scheme parameters and ramifications of the model results to general circulation modeling are discussed.