Conceptual models of El Niño and the Southern Oscillation

We present a few simple models which are intended to encapsulate some of the basic mechanisms of the El Nino/Southern Oscillation phenomenon. We consider one- and two-dimensional, continuous and low order models, with and without external stochastic forcing. In the low order models, even in the absence of stochastic forcing, chaos and aperiodic ENSO events can occur. This behavior is, however, rather sensitive to the choice of parameters and to the precise difference formulation used. Some of the detailed behavior of very low order models can also be unrealistic. However, the presence of multiple solutions is robust and insensitive to the differencing assumptions. One notable result of these models is that El Nino events partially phase-locked to the seasonal cycle can be produced both by by variations in trade-wind intensity and by imposed annual cycles in the temperature forcing. A continuous model which reduces to a chaotic low-order model in the limit of very coarse finite differencing is presented. Multiple, analytically derivable solutions exist which, however, are stable to infinitesimal perturbations. Larger perturbations or stochastic forcing can cause irregular oscillations between the two stationary states and El Nino like events, even in the absence of equatorial waves. Adding gravity waves produces somewhat more oscillatory behavior. Sustained oscillations leading to El Nino-like events are easy to produce with the addition of a seasonal cycle and some random noise. El Nino events are then found as occasional amplifications of the seasonal cycle. The difference between El Nino “events” and irregular amplifications of the seasonal cycle is then rather arbitrary. A common feature in all models is an oscillation between two equilibria due to an instability, either linear or to finite size perturbations, of the coupled ocean atmosphere system. The robustness of this suggests it may be a feature of the real system. The timing within events is governed by the detailed dynamics allowed in the particular model, but oscillatory behavior is readily obtained simply by allowing sufficiently strong, but not too strong, coupling between model atmosphere and ocean, plus perhaps some noise.