JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 93, NO. Cll, PAGES 13,979-13,991, NOVEMBER 15, 1988 Conceptual Models of E1Nifio and the Southern Oscillation G. K. VALLIS Scripps Institution of Oceanography, La Jolla, California We present a few simplemodels which are intendedto encapsulate some of the basic mechanisms of the E1Nifio/Southern Oscillation phenomenon. We consider one- and two-dimensional, continu- ous and low order models,with and without externalstochastic forcing. In the low order models, evenin 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. Someof the detailedbehaviorof very low order modelscan also be unrealistic. However, the presence of multiple solutions is robustand insensitive to the differencing assumptions. One notableresult of thesemodels is that E1 Nifio eventspartially phase-locked to the seasonal cycle can be produced both by by variations in trade-wind intensity and by imposed annualcycles 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 E1Nifio like events, even in the absence of equatorial waves.Adding gravitywaves produces somewhat moreoscillatory behav- ior. Sustained oscillations leadingto E1Nifio-like events are easyto produce with the addition of a seasonal cycleand somerandom noise. E1Nifio events are then found as occasional amplifications of the seasonal cycle. The difference between E1Nifio "events" and irregular amplifications of the seasonal cycleis then rather arbitrary. A common featurein all modelsis an oscillation between two equilibria due to an instability, eitherlinear 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 eventsis governed by the detailed dynamics allowed in the particularmodel, but oscillatory behavior is readily obtained simplyby allowingsufficiently strong, but not too strong, coupling between model atmosphere and ocean, plus perhaps somenoise. 1. INTRODUCTION Interest in the E1 Nifio/SouthernOscillation (ENSO) phe- nomenonhas been high for some time. Indeed, much of a recentedition of the Journal of Geophysical Research (vol- ume 92, issue C13) was devoted to observations and conse- quences of it. One obvious reason for this is the importance of the events both for tropical oceanography itself and for local fisheries, as well as for the possible influence of the tropical seasurface temperature field on the globalclimate. Another reasonis that it appearsthat it is now becoming possible to explain, at least in outline, the causes of the phe- nomenon. The coupling between atmosphere and ocean in- duces a positive feedback, which coupled with simpleideas of equatorial oceanic dynamics (stemming from the use of the shallow water equations) enables explanations to be of- fered which have a striking simplicity. (Of course,such explanations are not necessarily right.) Thus variousmod- els have been rather successful in explainingsome of the grosser featuresof the events [McWilliams and Gent, 1978; Cane andZebiak, 1985; McCreary andAnderson, 1984;Philan- der et al., 1984; Lau, 1981; Vallis, 1986; Schopf and Suarez, 1987]. The simplest of all these modelsis perhaps that of Vallis [1986], henceforth V86. Analyticstabilityarguments are available, and the model can be studied in detail. How- ever, the very simplicity of the model brings drawbacks. The model is so simplethat it clearlycannot be compared directlywith observations. Further,someof its behavioris Copyright 1988 by the American Geophysical Union. Paper number 88JC03029. 0148-0227/88/88JC-3029505.00 13,979 unrealistic (seesection 3 below). The question arises, is the behaviorof sucha model completely artifactual, or do the principal mechanisms exist in more complex models?It is the purpose of this paper to try to use the simpleideasand principalmechanisms thoughtimportantfor the ENSO cy- cle in modelsas simpleas possible, but without producing artifactual behavior. Let us first briefly review the main features of the ENSO phenomenon. We shalloftenreferto E1 Nifio "events", (and evenE1 Nifios)but without prejudice. Thussuch a terminol- ogy will not precludethe possibility that theseare merely manifestations of a sustained oscillation. 1. E1Nifio is the occurrence of an anomalously warm pool of water in the eastern equatorial Pacific Ocean. The event lasts for a few months. 2. Concurrent with the ocean warming,an atmospheric event occurs,namely a notable weakening of the trade winds. As one indicator, the sealevel pressure difference between Darwin and Tahiti is correlated with the oceanic events. 3. The event occurs aperiodically, with intervalsof be- tween 2 and 11 years,but typically they are 2 to 5 yearsapart. Therehavebeen nine or so events since 1945, when reliable records began, with largeevents in 1957, 1965, 1972, and 1982. There is evidence for E1 Nifio events for over400 years[Quinn et al., 1987]. 4. The event is phase locked to the seasonal cycle, normally reaching its maximum amplitude around Christmas time. However, large variations canoccur, notably in 1982-1983. 5. Similar events, if they occurat all, are much weaker in the Atlantic and Indian oceans.