Geoffrey K Vallis

This paper 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 due to condensation at the equator leads to a Gill-like pattern in the geopotential, which in turn induces moisture convergence and further condensation. Over a wide range of parameters the moisture convergence is found to be slightly to the east of the heat source. This convergence leads to condensation and hence a heat source that also is east of the original one, thus causing the pattern itself to propagate east. The speed of the ensuing eastward propagation is limited by the ability of the moisture convergence to remain east of the moving condensation heat source. If the pattern moves too quickly, the moisture convergence cannot keep up; the propagation then slows and/or the pattern itself may dissolve. The speed of propagation thus scales with the fluid speed that is induced by the condensation itself, and thus in turn with the strength of the condensational heating, and not with a gravity wave speed. The speed also increases with the distance between the initial heating source and the subsequent condensation. In the real world this distance is determined not only by the location of moisture convergence but also by the complex physics of convection in a conditionally unstable environment, and thus cannot be accurately determined in any simple model. Thus, even though the underlying MJO mechanism is not complicated its reproduction will necessarily depend rather sensitively on model parameters in numerical simulations.