Convective Organization and the MJO


Vallis, G. K. 2021. Distilling the Mechanism for the Madden-Julian Oscillation into a Simple Translating Structure EarthArXiv, https://doi.org/10.31223/X5089K
PDF file (2MB).

Vallis, G. K., 2021. Convective Organization and Eastward Propagating Equatorial Disturbances in a Simple Excitable System. Quart. J. Roy. Met. Soc. https://doi.org/10.1002/qj.3792.
PDF File (2 MB)



Movies:

These movies make most sense if you have read the first manuscript...

A a self-sustaining eastward progressing disturbance in the moist shallow water equations on the equatorial beta plane.

An excitable system with large damping, and no rotation. The disturbance eventually dies.

An excitable system with small damping, with no rotation. The disturbance leads to self-sustained motion.

Plain Language Description

The Madden-Julian Oscillation is the largest and most important component of tropical variability on intra-seasonal times-scales, yet it has defied understanding for over 40 years. More than once its explanation has been described as the holy grail of atmospheric science. Here, we describe and illustrate a mechanism that robustly explains many of its features by using a simple model of moist fluid dynamics in conjunction with ideas from the theory of excitable systems, which is usually used to describe systems of neurons, chemical reactions and cellular automata. Convection aggregates at the equator but, because the system as a whole is unstable, convection is triggered nearby and the system propagates. The rotation of the Earth gives the propagation a preferred direction, eastwards, as observed.

Paper Abstract

We describe and illustrate a mechanism whereby convective aggregation and eastward propagating equatorial disturbances, similar in some respects to the Madden--Julian oscillation, arise. We construct a simple, explicit system consisting only of the shallow water equations plus a humidity variable; moisture enters via evaporation from a wet surface, is transported by the flow and removed by condensation, so providing a mass source to the height field. For a broad range of parameters the system is excitable and self-sustaining, even if linearly stable, with condensation producing convergence and gravity waves that, acting together, trigger more condensation. On the equatorial beta-plane the convection first aggregates near the equator, generating patterns related to those in the Matsuno--Gill problem. However, the pattern is unsteady and more convection is triggered on its eastern edge, leading to a precipitating disturbance that progresses eastward. The pattern is confined to a region within a few deformation radii of the equator because here the convection can best create the convergence needed to organize into a self-sustaining pattern. Formation of the disturbance preferentially occurs where the surface is warmer and sufficient time (a few tens of days) must pass before conditions arise that enable the disturbance to reform, as is characteristic both of excitable systems and the MJO itself. The speed of the disturbance depends on the efficiency of evaporation and the heat released by condensation, and is typically a few meters per second, much less than the Kelvin wave speed.