From Atmospheric Circulation to Global Change,

Edited by the Institute of Atmospheric Physics, Chinese Academy of Sciences,

China Meteorological Press, , 525-546

A Theory for El Nino Cycle

Department of Meteorology, School of Ocean and Earth Science and Technology, University of Hawaii

A theoretical model for the coupled tropical ocean and atmosphere is derived from physical principles. The model characterizes the temporal evolution of the El Nino cycle as a second order nonlinear dynamic system. With an annual mean basic state, the model has, for a rather restricted range of air-sea coupling strength, a unique limit cycle solution which is a stable attractor representing a regular interannual oscillation of the coupled ocean and atmosphere. The oscillation is characterized by a delicate phase lead of thermocline displacement to SST, which agrees well with observation. This phase lead results from a nonlinear interaction between SST and thermocline variations and plays a critical role in providing a negative feedback to turn a warming to a cooling or vice versa, sustaining the oscillation.

When the basic state varies annually, the limit cycle develops a strange attractor and the interannual oscillations exhibit deterministic chaos. We show that the basic state is most unstable (stable) in northern spring(fall). The season-dependent development of the coupled model causes a phase "lock" of the ENSO cycle with annual cycle - the transition phases of the oscillation tend to occur during most unstable season - which, in turn, causes the irregularities in the oscillation period and amplitude.

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