A Simple Model of El Niño and the Southern Oscillation

Abstract

A model of tropical ocean-atmosphere interaction is used to study the El Niño?Southern Oscillation phenomenon. The model ocean consists of the single baroclinic mode of a two-layer ocean. The thermodynamics of the upper layer are highly parameterized; sea-surface temperature is assigned one of two values, warm or cool, according to whether the interface is shallower or deeper than an externally specified depth. The model atmosphere consists of two wind patches of zonal stress that are idealizations of the annual cycle of the equatorial trades, τs, and of Bjerknes' Walker circulation, τw. When the eastern ocean is in its cool state both patches drive the ocean; when it is warm τw is switched off. Solutions compare favorably with observations in several ways. Most importantly, for reasonable choices of parameters solutions oscillate at the long time scales associated with the Southern Oscillation. The response of the ocean to τw introduces positive feedback into the system, with the result that the system can adjust to one or the other of two equilibrium states: a state with τw switched on, and another with it switched off. The annual wind τs is the ?trigger? that switches τw off or on, and thereby prevents the system from ever reaching either equilibrium state. When τw switches on, equatorial Kelvin waves swiftly propagate from the wind patch into the eastern ocean, and raise the interface there to a shallow level. Rossby waves, also generated by the wind, subsequently reflect from the western boundary as a second set of equatorial Kelvin waves. The arrival of this second set in the eastern ocean begins a gradual deepening of the interface there toward its equilibrium value. It is this overshoot together with slow relaxation of the interface in the eastern ocean that allows the model to oscillate at long time scales. Essentially, the ocean must be sufficiently relaxed toward an equilibrium gate before τs can act to switch τw Off or on.