A trio-interaction theory for Madden–Julian oscillation

The Madden–Julian oscillation (MJO) is the dominant mode of tropical atmospheric intraseasonal variability and a primary source of predictability for global sub-seasonal prediction. Understanding the origin and perpetuation of the MJO has eluded scientists for decades. The present paper starts with a brief review of progresses in theoretical studies of the MJO and a discussion of the essential MJO characteristics that a theory should explain. A general theoretical model framework is then described in an attempt to integrate the major existing theoretical models: the frictionally coupled Kelvin–Rossby wave, the moisture mode, the frictionally coupled dynamic moisture mode, the MJO skeleton, and the gravity wave interference, which are shown to be special cases of the general MJO model. The last part of the present paper focuses on a special form of trio-interaction theory in terms of the general model with a simplified Betts–Miller (B-M) cumulus parameterization scheme. This trio-interaction theory extends the Matsuno–Gill theory by incorporating a trio-interaction among convection, moisture, and wave-boundary layer (BL) dynamics. The model is shown to produce robust large-scale characteristics of the observed MJO, including the coupled Kelvin–Rossby wave structure, slow eastward propagation (~5 m/s) over warm pool, the planetary (zonal) scale circulation, the BL low-pressure and moisture convergence preceding major convection, and amplification/decay over warm/cold sea surface temperature (SST) regions. The BL moisture convergence feedback plays a central role in coupling equatorial Kelvin and Rossby waves with convective heating, selecting a preferred eastward propagation, and generating instability. The moisture feedback can enhance Rossby wave component, thereby substantially slowing down eastward propagation. With the trio-interaction theory, a number of fundamental issues of MJO dynamics are addressed: why the MJO possesses a mixed Kelvin–Rossby wave structure and how the Kelvin and Rossby waves, which propagate in opposite directions, could couple together with convection and select eastward propagation; what makes the MJO move eastward slowly in the eastern hemisphere, resulting in the 30–60-day periodicity; why MJO amplifies over the warm pool ocean and decays rapidly across the dateline. Limitation and ramifications of the model results to general circulation modeling of MJO are discussed.