Distilling the mechanism for the Madden–Julian Oscillation into a simple translating structure

This article presents a minimal model of the Madden–Julian Oscillation (MJO), isolating a robust mechanism that leads to the observed characteristic pattern and eastward propagation. A localized heat source at the Equator leads to a Gill‐like pattern in the geopotential, with moist air converging toward the heat source. Over a fairly wide range of parameters, the moisture convergence is found to be slightly to the east of the heat source, with moist air advected in from the east along the Kelvin lobe meeting slightly drier air advected meridionally around the Rossby lobes. The associated condensation then gives rise to a heat source that also is east of the original one, thus causing the pattern itself to propagate east with dryer regions both to the east and west of the region of precipitation. The speed of the propagation is limited by the ability of the moisture advection to move the condensational heat source; it thus scales with the fluid speed which is induced by the convective heat source, and so with the strength of the convective heating, and not with a gravity wave speed. The propagation speed also increases with the nominal offset between the centre of the pattern and the subsequent moistening and condensation. In the real world this distance, as well as the level and coherence of condensation, are determined not only by the location of moisture convergence but also by the complex physics of convection in the tropical environment. Thus, even though the underlying MJO mechanism is itself not complicated, its reproduction will depend rather sensitively on model parameters in simulations with comprehensive numerical models.