Convective Organization and Eastward Propagating Equatorial Disturbances in a Simple Excitable System

TL;DR

This paper presents a simple, explicit model demonstrating how convective aggregation and eastward equatorial disturbances, similar to the Madden-Julian oscillation, can self-organize and propagate eastward under certain conditions.

Contribution

It introduces a minimal system combining shallow water equations and humidity to explain the formation and propagation of equatorial disturbances, highlighting the role of excitation and self-sustaining convection.

Findings

Disturbances propagate eastward at a few meters per second.

Pattern confinement near the equator depends on deformation radii.

Formation of disturbances requires warm surface conditions and time for reorganization.

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 effect is enhanced by westward prevailing winds that increase the evaporation east of the disturbance. The pattern is confined to a region within a few deformation radii of 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.