Trio-Interacton Theory for Madden–Julian Oscillation

Understanding the origin and propagation of the Madden-Julian Oscillation (MJO) has eluded scientists for decades. We first present a brief review of progresses in theoretical studies of the MJO and discuss what are the essential MJO characteristics that a rudimentary theory should explain. We then describe a general theoretical model framework for mathematical description of the essential dynamics of MJO: The trio-interaction among (convective and radiative) heating, moisture, and (wave and boundary layer) dynamics. This general trio-interaction model can be used to derive all major existing theoretical models, for instance, the frictionally coupled moist Kelvin-Rossby wave, the moisture mode, the MJO skeleton, radiative feedback model, and the gravity wave interference. Using a special form of the trio-interaction model with a simplified Betts-Miller (B-M) cumulus parameterization scheme, we show that the trio-interaction mode with positive-only heating reproduces 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 roles of the frictional convergence feedback, moisture feedback, and equatorial wave feedback and the radiative heating effects on MJO dynamics are elaborated. 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 reduces the growth rate but enhance Rossby wave component, thereby substantially slowing down eastward propagation. The wave feedback can change the horizontal structure, thereby affecting MJO propagation speed and dispersion relationship. But the wave feedback effects are different with and without radiative heating. Radiative heating can generate instability and cause eastward propagation in the presence of the wave feedback. The trio-interaction theory also reveals an intrinsic relationship between the zonal asymmetry in the MJO structure and the MJO propagation speed, which are supported by observations and climate model simulations. Different convective parametrizations can produce different east-west structural asymmetry, thus different MJO propagation. The ramification of the model results to general circulation modeling of MJO and the model limitation are discussed.