2262 MONTHLY WEATHER REVIEW VOLUME II5A Model El Nifio-Southern Oscillation* STEPHEN E. ZEBIAK AND MARK A. CANELamont-Doherty Geological Observatory of Columbia University, Pa/isades, IVY 10964(Manuscript received I December 1986, in final form 23 March 1987) ABSTRACT A coupled atmosphere-ocean model is developed and used to study ~he ENSO (El Nifio/Southern Oscillation)phenomenon. With no anomalous external fordn~ the coupled model reproduces certain key features of theobserved phenomenon, including the recurrence of warm events at irregular intervals with a preference for threeto four year~ It is shown that the mean sea surface temperature, wind and ocean current fields determine thecharacteristic spatial structure of ENSO anomalies. The tendency for phase-locking of anomalies is explainedin terms of a variation in coupling strength associated with the annual cycle in the mean fields. Sensitivitystudies reveal that both the amplitude and the time scale of the oscillation are sensitive to several parametersthat affect the strength of the atmosphere-ocean coupling. Stronger coupling implies larger oscillations with alonger time scale. A critical element of the model oscillation is the variability in the equatorial heat content ofthe upper ocean. Equatorial heat content increases prior m warm events and decreases sharply during the event~A theory for this variability and the associated transitions between non-El Nifio and El Nifio states is presented.Implications of the model results for the prediction of El Nifio events are discussed.1. Introduction The collection of atmospheric and oceanic phenomena known as El Nifio and the Southern Oscillation(ENSO) have been the subject of intense interest andstudy over the past several years, especially in the wakeof the dramatic episode of 1982/83. Observationalstudies have identified the global dimensions of theclimate variations associated with the Southern Oscillation, and their close association with changes in thesurface temperature and current structure of the tropical Pacific Ocean. Many modeling studies have beenundertaken, each attempting to reproduce some majorfeature .or features of the observations and thus toidentify the set of interactions that can account for thispreferred mode ofinterannual variability in the oceanatmosphere system. Meteorological studies, using bothcomplex and simple models, point to the importanceof tropical Pacific sea surface temperature (SST)anomalies in producing observed atmospheric anomalies during ENSO (e.g., Rowntree, 1972; Wells, 1979;Keshavamurty, 1983; Shukla and Wallace, 1983; Zebiak, 1982, 1986; Gill and Rasmusson, 1983; Webster,1981; Lau, 1981). Oceanographic studies show that theobserved tropical Pacific SST and sea level anomaliesduring ENSO result primarily from the influence ofsurface wind stress anomalies (e.g., Busalacehi andO'Brien, 1981'; Cane, 1984; Philander and Siegel, 1985).The combined results identify the interactive nature * Contr/bution Number 4192 of the Lamont-Doherty GeologicalObservatory of Columbia Univerdty,of the phenomenon and show the need for a modelthat allows for such interaction. Although much of the.behavior of each component of the system can be reproduced with existing models by specifying the stateof the other, little has been said about the behavior ofthe coupled system. For example, questions concerninginitiation, duration, termination and irregular recurrence of ENSO events remain unanswered. To date there have been only a few attempts atstudying the coupled problem. MeWilliams and Gent(1978) and Lau ( 1981) have examined highly idealizedmodels and demonstrated the possibility of low-frequency variability in the coupled system that is absentin the individual components. MeCreary (1983) andMcCreary and Anderson (1984) present models withexplicit ocean dynamics but highly idealized atmospheres. They also find interannual variability undercertain assumptions. Vallis (1986) has shown that thepresence of nonlinearities in an othenvise idealizedcoupled model can lead to aperiodic Oscillations. Philander et al. (1984) examine a model with explicitlinear dynamics for both the atmosphere and the ocean.They find a coupled instability that leads to the growthof large-scale atmospheric and oceanic anomalies. Thedevelopment is arguably similar to the growth ofanomalies during ENSO, although the linearizafionsof the model do not permit equilibration and the subsequent decay of anomalies. In a more recent study,Philander (1985) presents a model which, with differentassumptions concerning air-sea coupling, simulates thedecay phase of ENSO. As pointed out by the author,the two versions of the model are in6ompatible becauseof the highly parameterized form of the coupling. Thusc 1987 American Meteorological SocietyOCTOBER 1987 STEPHEN E. ZEBIAK AND MARK A. CANE 2263the two cannot be combined in their present form todescribe the full ENSO cycle. Anderson and McCreary (1985) use a more sophisticated nonlinear ocean model with explicit dynamicsand thermodynamics, and they couple it to a linearatmosphere model, attempting to describe the evolution of the total SST and wind fields. They find interannual variability of the coupled system, though thespatial and temporal characteristics of the anomaliesdiffer somewhat from the real system. This may berelated to the difference in background states; that is,the model climatology differs considerably from theobserved mean state. The nonlinear coupled model ofSchopf and Suarez (private communication) producesa somewhat different climatology and correspondinglygives different interannual variability. Rennick and Haney (1986) and Hirst (1986) analyzein detail linear, free (i.e., unbounded) modes of thecoupled system. Again, low-frequency oscillatorymodes are found under a number of different assumptions. A major limitation of these studies is the absenceof oceanic boundaries. The boundaries are known toaffect the oceanic response qualitatively at low frequency. All of these results indicate that interannual variability can result from interaction between the tropicalocean and atmosphere. However, many specific questions regarding ENSO remain unanswered. For example, why does the system continue to oscillate oninterannual time s~ales, rather than seeking a moreuniform annually periodic state? What determines thepreferred period of 3-4 years, and what are the probablesources of aperiodicity? What accounts for the characteristic temporal and spatial patterns of ENSOanomalies? Here we attempt to address some of thesequestions and to build on the earlier studies of ENSO,using a coupled model of the tropical Pacific Oceanand atmosphere. The atmospheric component of thecoupled model has been described in Zebiak (1986;hereafter referred to as Z). It was shown to produceequatorial wind and convergence anomalies similar toobservations when forced by observed ENSO SSTanomalies, despite certain systematic discrepancies inthe off-equatorial response. The oceanic component ofthe model has been described in Zebiak (1984). Themodel was shown to reproduce key features of the observed SST anomalies during ENSO, when forced usingobserved tropical wind anomalies. The present coupledmodel differs from others in its treatment of the thermodynamics in the atmosphere and ocean, especiallythrough the inclusion of a moisture feedback processin the atmosphere and a thermodynamically active(though simplified) surface layer in the ocean. The remainder of this paper is organized as follows.The model components are reviewed in section 2, andthe results from an extended (90 year) coupled run arepresented in section 3. Section 4 examines certainmodel parameter sensitivities. The role of the annualcycle is analyzed in section 5, and in section 6, wepresent a theory for the ENSO cycle, based on the coupled model results. A summary and concluding remarks follow in section 7.2. Model description The model components have been presented in detail previously and will only be summarized here. (Thefull governing equations are given in the Appendix.)Both components describe perturbations about themean climatological state, with the climatology specified from observations. The Climate Analysis Centerdataset (see Rasmusson and Carpenter, 1982) was usedfor this purpose.a. Atmosphere The dynamics follow Gill (1980), i.e., steady-state,linear shallow-water equations on an equatorial betaplane. Linear dissipation in the form of Rayleigh friction and Newtonian cooling is used. The circulation isforced by a heating anomaly .that depends partly onlocal heating associated with SST anomalies an_d partlyon the low-level moisture convergence (parameterizedin terms of the surface wind convergence). Several observational studies (e.g., Cornejo-Garrido and Stone,1977; Ramage, 1977), as well as GCM calculations,have demonstrated the important contribution ofmoisture convergence to the overall tropical heat balance. The convergence feedback is incorporated into themodel using an iterative procedure in which the heatingat each iteration depends on the convergence field fromthe previous iteration. The scheme is analyzed in detailin Z. The feedback is nonlinear because the moisturerelated heating is operative only when the total windfield is convergent, and this depends not only on thecalculated convergence anomaly, but also on the specified mean convergence [see Eq. (A3)]. As shown inZ, the important effect of the feedback is to focus theatmospheric response to SST anomalies into or nearthe regions of mean convergence, in particular, the Intertropical Convergence Zone (ITCZ) and the SouthPacific Convergence Zone (SPCZ). Such focusing isconspicuous in the observed wind anomalies duringENSO (see Rasmusson and Carpenter, 1982).b. Ocean The model ocean basin is rectangular and extendsfrom 124-E to 80-W and from 29-N to 29-S. Thedynamics of the model begin with the linear reducedgravity model [Eqs. (A4)-(A7)] that has been used successfully in simulating thermocline depth anomaliesand surface pressure changes during E1 Nifio events(Busalacchi and O'Brien, 1981; Cane, 1984; Busalacchiand Cane, 1985). Such models produce only depthaveraged baroclinic currents, but the surface current isusually dominated by the frictional (Ekman) corn2264 MONTHLY WEATHER REVIEW VOLUME 115ponent. Therefore, a shallow frictional layer of constantdepth (50 m) is added to simulate the surface intensification of wind-driven currents in the real ocean. Thedynamics of this layer are also kept linear, but only byusing Rayleigh friction to stand in for nonlinear influences at the equator [Eqs. (A8)-(A9)]. As is commonin reduced-gravity models, the surface layer pressuregradient varies only with the thermocline depth. Thisassumption neglects the influence of any temperaturechanges occurring in the surface layer alone (i.e.,changes uncorrelated with those below). This influenceis usually, but not universally, negligible; hence its neglect cannot be justified rigorously. Mean surface currents were generated by spinningup the model with monthly mean climatological winds.These currents were then specified in the anomaly calculations. The thermodynamics describe the evolution of temperature anomalies in the model surface layer. Thegoverning equation includes three-dimensional temperature advection by both the specified mean currentsand the calculated anomalous currents. The assumedsurface heat flux anomaly is proportional to the localSST anomaly, acting always to adjust the temperaturefield toward its climatological mean state, which isspecified from observations. This parameterization is clearly oversimplified andis probably incorrect in some local regions, but nonetheless it agrees with the general results of observationalstudies (Ramage and Hori, 1981; Weare, 1983). Using the above formulations, the thermodynamicequation has the following form (where barred quantities represent mean fields and unbarred quantitiesrepresent anomalies):OT - 'ill' VT- I!1- V(~"- T) - M(v~s + ws) - M(~)Ot x~z-M(-,+w3rz-a,r, (1)where u~ and ws represent horizontal surface currentsand upwelling, respectively, and the function M(x) isdefined by M(x) = (2) x>0.This function accounts for the fact that surface temperature is affected by vertical advection only in thepresence of upwelling. The anomalous vertical temperature gradient, Tz, is defined by rz = (r- re)/H~, (3)where H1 is the surface layer depth, and Te measurestemperature anomalies entrained into the surface layer.The model parameterizes subsurface temperatureanomalies in terms ofthermocline motions, whi.ch canbe equated to the model upper-layer thickness variations. The parameterization arises by assuming a fixedvertical temperature profile for the thermocline structure and simply displacing this profile up and downwith the thermocline depth [as determined by the shallow-water dynamics, i.e., Eqs. (A4)-(A6)] This temperature profile is estimated from observations and fitto a simple functional form [Eq. (A13)]. We find thatthis form crudely approximates observed temperaturechanges below the mixed layer in the equatorial regionas a function of longitude and season. In particular,since the mean thermocline depth is shallow in the eastPacific, the subsurface temperature field is more sensitive to anomalous thermocline displacements there,in accord with observations. We emphasize that this isan empirical relationship. While it appears to accountfor much of the observed temperature variability belowthe surface layer, it cannot distinguish between thevarious processes contributing to that variability in thereal ocean. In Zebiak (1984) it was shown that this ocean modelsimulates the mean features of the observed SSTanomalies when forced by ENSO composite windanomalies and that the full complexity of(l) is requiredto achieve this.c. Coupling The ocean component is forced by surface windstress anomalies. A standard bulk formula is used togenerate stress anomalies from the combination of surface wind anomalies produced by the atmospheremodel and the background mean winds. The oceandynamics time step is 10 days. The atmosphere model is steady-state and was previously run with specified monthly mean SST anomalies to simulate monthly mean wind anomalies. Inthe present context, the wind field must be determinedat 10-day increments. There are several possible approaches. On one extreme, the model could be usedexactly as before, calculating the steady response to theSST anomaly field at each time step. This implicitlyassumes that the atmosphere adjusts very rapidly [0(23) days] to changes in boundary forcing and cannot bejustified. On the other extreme, time dependence couldbe added explicitly to the model. This would be computationally costly, since a time step of order 2 h wouldbe required for inertial gravity waves. Moreover, it isunnecessary because the important limiting time scaleis the longer one associated with the equilibration ofthe heating field, i.e., the moisture convergence feedback process. We adopt a third alternative: allowingtime dependence only in the moisture convergencecomponent of the heating. With this scheme, thechange in heating is computed at each time step, andthe assumed background convergence is the total convergence at the previous time step, rather than just themean convergence (as in the steady-state model). Because of the nonlinearity of the heating parameterization, this 'time-marching procedure allows the development of small-scale anomalies that can persist andbecome unrelated to subsequent SST anomaly patterns.OCTOBER 1987 STEPHEN E. ZEBIAK AND MARK A. CANE 2265We have found that the simplest and most effectiveway to prevent this is to recalculate the heating periodically using the steady model formulation, based onthe current SST anomaly field. (This strategy is similarto the periodic restarts often used with the leapfrogscheme to suppress splitting of the solution.) In themodel run to be presented in section 3, the recalculation was done once per month. The result of using adifferent criterion is discussed in section 4. In additionto the above, a maximum of three feedback iterationsis performed at each time step. This affects only thevery small-scale features of the response (see Z) andnot the larger-scale features that characterize the ENSOsignal. The net result is similar to applying spatialsmoothing and requires less computation. To summarize, the calculation of the atmosphericheating has been split into two parts. The portion related directly to SST operates the same as in Z andgives a wind response in equilibrium with the SST fieldon a time scale of I0 days. The portion of the heatingrelated to internal moisture convergence feedback operates in a time-stepping sense, and so forces a windfield adjustment on a somewhat longer time scale (oforder 1 month or more).3. Results: Standard case The followin~ is a description of a 90-year run ofthe coupled model. The run was initiated with an imposed westerly wind anomaly of the form Ua ~ (2 m s-l) exp[-(y/20-)2] (4)in the region 145-E to 170-W. The anomaly was heldfixed for a period of four months (from December untilApril of the first year) and then removed. Thereafterthere is no external forcing. All parameter values forthe model are as specified in the previous uncoupledcalculations of Zebiak (1984, 1986) and are listed inthe Appendix. Figure 1 shows a time record of area-averaged SSTanomalies for the regions 5-N-5-S, 90--150-W, and5-N-5-S, 150-W-160-E, designated as NINO3 andNINO4, respectively. A striking result is the recurrenceof warm events, deriving solely from self-interactionsof the coupled system. After the first, rather weak warmevent in year 0 (which results from the imposed initialcondition), the system exhibits quasi-regular oscillations with a favored period of 3-4 years. The oscillations appear at times to be very regular in amplitudeand structure, while at other times they are noticeablynonuniform, with variable amplitude and inter-eventspacing. Once initiated, however, the development ofthe major warm episodes is very closely tied to theannual cycle. They tend to peak either in June oraround the end of the year and have a total durationof between 14 and 18 months. The larger events exceed2-C in the east (and 3-C at the eastern boundary).During the mature phase of warm events, the largestSST anomalies occur in the east, with decreasing amplitude toward the west (NINO3 > NINO4). Also, theanomalies tend to peak first in the east and later in thecentral region. Figure 2, taken from Rasmusson and Carpenter(1982), shows a comparable time series computed fromobservations spanning the period 1921-76. Many similar characteristics are evident. For example, the oscillations are irregular but exhibit a strong preference fora 3-4 year period. Major warm events have a duration ~.lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll ;B, .xx, ..m, .A ..' IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIlllllllllllllll'20 5 I0 15 20 ::)5 30 ~lllllllllllllllllllllllllllllllllllllll[llllllllllllllllllllJ_:>lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll 30 35 40 45 50 55 60 '~11111111111111111111111111111111111111111111111111 IIIIIIII111 ..... .A ..A.A ..A A b 'k/'"-' .x:,,,:, -.w' ,x~q .~>11 III I II II I I I J Jl II I I I I I IIIII 60 65 70 75 80 85 90 TIME (yrs) I~G. l. Area-averaged SST anomalies for the 90-year model simulation. The solidline isNINO3 (5-N-5-S, 90--150-W), and the dotted line is NINO4 (5-N-5-S,150-W- 160-E).2266 MONTHLY WEATHER REVIEW VOLUME II5 4 3 2-I 1931 1932 1935 1934 1955 I 1938 1939 1940 4I :3 2 I,o~ o -I -2- .~- -4~ .~ , 1956 5 4m :5 2 Io~ 0" -I -~- -~- -~ - - I~?1 197~ 197~ I~?~ FiG. 2. Observed SST anomalies i~ the eastern Pacific (solid li~-)and the central Pacific (dotted line) (after Rasmusson and Cal~nter,1982).of somewhat more than a year and develop in a systematic fashion, with maximum amplification of central Pacific anomalies in (northern) summer and peaking of anomalies around the end of the year. The largestanomalies occur in the eastern Pacific and typicallyrange between 2- and 4-C for major ENSO events. A notable difference between the model results andthe observations is the lack of an initial coastal warmingin the model, such as is often, but not always, observedprior to the major central Pacific warming. The oceanmodel was unable to reproduce this feature even whenforced by composite ENSO winds, so the result is hardlysurprising here. The success of the simulation apartfrom this feature suggests that the details of the temperature field very near the east coast are not fundamental to the evolution of the larger-scale anomalies. Figure 3 shows a time series of area-averaged windanomalies for the 90-year simulation. Two indices,representing equatorial zonal wind anomalies in thewestern Pacific (5-N-5-S, 135-E-180-) and the eastern central Pacific (5-N-5-S, 180--140-W), areshown. The former is designated TW 1 and the lfitterTW2. The primary temporal characteristics are verysimilar to those of the temperature indices, althoughthe wind indices exhibit more high-frequency variability. During major warm events, the two indices varyin a similar fashion, indicating a very large scale coherent wind forcing, whereas during periods withoutmajor warm events the two indices are often out ofphase, indicating smaller scale wind patterns with lessnet influence on the ocean. As in the atmospheric calculation using prescribed SST anomalies, the westernPacific'zonal wind anomalies are weaker than observedand switch from westerly to easterly later than observed. A more detailed picture of the evolution of SST andwind anomalies during a warm event is given in Figs.4-11, which trace the development in three-month intervals between the end of year 30 and year 32. Tl/eperiod is characterized by one of the larger warm eventsof the 90-year simulation (see Fig. 1). The sequence begins in December of year 30 (Fig.4), at which time there are no appreciable anomaliesin either SST or wind. By March(31)~ (Fig. 5) a regionof warm SST anomaly has developed in the equatorialzone east of 170-W, with a maximum near 130-W.Associated with this are small westerly wind anomaliesin the region 130- to 160-W. The warm event is wellunderway by June(31) (Fig. 6), with SST anomaliesexceedihg 1 -C in the eastern equatorial Pacific andsizeable, (~ 1 m s-l) westerly wind anomalies in thecentral Pacific. As indicated above, the warming in theeastern ocean tends to occur uniformly, rather thaninitially at the coast. Most, but not all, observed eventsexhibit the earlier coastal anomaly. We believe this discrepancy is due, at least in part, to the lack of adequateresolution of the ocean model near the eastern boundary. This would lead to an underestimation 'of the response to both local and remote forcing. The observed tendency for expansion and amplification of both SST and wind anomalies in the fall ofan ENSO year also occurs in the model. By September(31) (Fig. 7), warm anomalies extend as far westwardas 160-E, and eastern Pacific anomalies exceed 2-C. ~ Hereafter, the number given in parentheses after a month is theyear of the 90-year simulation.OCTOBER 1987 STEPHEN E. ZEBIAK AND MARK A. CANE~'L_[ll I III II III III III I.I III I I Ill III Ill II I.i-'..lll III III II III I [11 I I1~ I~. -'"' 'o A. h,,',N,,,,~,,,,~,,,',~,,,,,,,,, X,,,,~,,,?,-I,,,,,,,,,,~22672~ll..l.'~lllllllllllllllllllJ:'lllllllllllllllllllllllllllllllllll_l_, "'~,,, ;.~,,,, ,'~/-1 ,';-,':, ,.'i,,,, ,'~ ,-'i ,',,,,,,, ,'~, ;,',',,,,, ,~., ,',,, 40 45 50 ,55 60 - ."'~.I/- ~ ~ '%'~/ "' '.- ".%7~ '".X~' '' _, F,,,,,~,.',,,,,, ,,,,,,,,,,,,,,,,',,,,,'~,,,;~,,,,,,,,,,,,,,,~ 60 65 70 75 80 85 so TIME (yrs) FIG. 3. Area-averaged zonal wind anomalies (m s-I) for the 90-year model simulation.The solid line is TWl (5-N-5-S, 135E--180-), and the dotted line is TW2 (5-N-5-S,180--140-W).Large westerly wind anomalies cover the whole equatorial central Pacific, with equatorward flow across thenormal position of the ITCZ. The easterly anomaliesin the eastern Pacific are not realistic. They also appeared in the uncoupled calculation using observedSST anomalies (see discussion in Z). In agreement withthe composites, a region of small negative SST anomalyand easterly wind anomaly has developed in the western Pacific at this time. The peak temperature anomalies occur in December(31) (Fig. 8), with a maximum at the coast and another one near 140-W. By December the SST anomalies also have expanded meridionally, compared withthe preceding patterns. These features are realistic, except that the coastal maximum is exaggerated. Thiswas also the case for the uncoupled ocean model. Boththe model and the composites show westerly windanomalies of about 2 m s-~ in the central Pacific atthis time. However, observations also show the development of easterly anomalies in the western Pacific.This feature does not develop in the model either atthis time or in the immediately ensuing months. Thesomewhat delayed termination of the model warmevent can be traced to this. By March(32) (Fig. 9), temperature anomalies havebegun to decrease, especially at the east coast. A single140--~ k~_O/I ~ - ':::'.':"-'0.25~ I I I 180- 140-WJiooNL(b) ~ ~ I - I, . ~ - .~FIO-S ~, I- I I I I 140-E 180- 140-W- - lOON b) I I I I I I I EOl- ' -~ ~' ' ' 'I I 0- S~- *IO0-W I I I I I I I ~40-E 180- 140'W IO0-WFIO. 4. (a) SST anomalies and (b) wind anomalies inDecember of year 30 of the model simulation.FIG. 5. As in Fig. 4, except for March of year 31.2268 MONTHLY WEATHER REVIEW VOLUME II5loon ~(O~,~O'''''') 140*E' L) ' ' /180' ~40*W IO0-W ~400Emo- ~4o- w ~oo- wiooN~b) ~~--$FIG. 6. As in Fig. 4, except for June of year 31.FIG. 8. As in Fig. 4, except for December of year 31.maximum now exists in the eastern central Pacific.The pattern is quite similar to the composite event forthis time, although the amplitude of the warm anomalyis about a factor of two larger than the composite. Verylarge westerly wind anomalies persist in the central Pacific, with increasing easterly anomalies farther to theeast. In June(32) (Fig. 10), the eastern ocean is still warm,though temperatures are decreasing rapidly. The westefiy wind anomalies have decreased and receded westward, and stronger eastefiies are evident in the east.By this time, the composites show cold SST anomaliesand poleward wind anomalies in the eastern ocean. During the summer of year 32 a dramatic changeoccurs in both widds and SST, amounting to a rapidtermination of the warm event. By September(32) (Fig.11), the equatorial eastern and central ocean is cold,and the winds are primarily meridional and directedpoleward. The temperature pattern is not unlike thatof the composite for this time, which also shows anequatorial tongue of cold anomaly extending acrossmuch of the basin. All of the major warm events in the model evolvein a similar fashion. Some of the smaller amplitudeanomalies develop differently and do not conform tothe canonical scenario. This may be true in reality aswell. Only the large anomalies have been studied intensively, and moreover, the focus has been on thecommon features of the events rather than their individual characteristics. An important element of the coupled system oscillation is the oceanic heat exchange in the equatorialregion. Figure 12 displays the model thermocline depthanomaly h(x, t) along the equator between years 30and 45 of the coupled run. This variable may be interpreted as a measure of the heat content of the upperocean. The major warm episodes (beginning in years31 and 41) are characterized by anomalously high heatcontent in the east and low heat content in the westfor a period of nearly a year. This occurs approximatelyin phase with the strong and sustained westerly windanomalies in the central Pacific (Fig. 13). Superimposed on the east-west exchanges of heat isa fluctuation in the zonal mean heat content of theequatorial region. The periods preceding major warmevents are characterized by above-normal heat contentat all longitudes (early in years 31 and 41), and theperiods immediately following warm events show a ' '\ ' ' ' (~ ~ I ~OON~,)-)' , -'5 / ~40'E 180- ~40'w ~-wiOoN~b). ~ ~ 140-e" , I ~ ~.....u-~u-- .~, . ' z. --///./// ~_~ ~~';- : -/.'-z.'/~~ / /.7 .r x ~ ~ ~ ~. / t 1 _\ ~ ~ ~ ~ ~ ~-, ' 1 " ," '" Y'"',"-'", 180' 140'W IO0*W140*e 180' 140-w iooOw140*El~o. 7. As in Fig. 4, except for September of year 31. FIG. 9. As in Fig. 4, except for March of year 32.OCTOBER 1987 STEPHEN E. ZEBIAK AND MARK A. CANE 2269 o I(~) ' o~'t,,,ON[- .::::.'. ],o~ o--'~ 140-E , "-~o.s ~"-7""'~ ~ /180~ 140-W IO0-W o [(b)' ' 'I0 EO[- .: :.~o-s~-'~' 2 ~4o0-~ /' '/ 'f \ '~ "'" 180- 140-W IO0-WFIG. 10. As in Fig. 4, except for June of year 32.41corresponding deficit of heat content (late in years 32 40and 42). It is important to note that the rise in netequatorial heat content precedes the development ofequatorial westerlies and positive SST anomalies in the ~9eastern ocean; that is, it precedes the ENSO event. Thissuggests that such a rise in equatorial heat content maybe a precondition for ENSO. We will return to this '~point in section 6. Also, note that the fluctuations in ~ 38heat content under consideration here are strictly adiabatic; they arise from variatio, ns in the upper-layer Lt.Ithickness induced by wind stress forcing alone. ~; ~7As seen from the preceding results, the signature of ~model warm events is a large-scale pattern of equatorialwesterly wind anomalies in the central Pacific andequatorial SST anomalies that extend across most of ~6the basin and decrease in amplitude from east to west.This characteristic structure derives from the effects ofthe mean SST, wind and current fields. The climato- 35logical mean state includes easterly trade winds blowingacross the eastern and central ocean. The easterly stressinduces equatorial upwelling and sets up a sizeablezonal tilt to the thermocline, such that the cold, subthermocline water is far removed from the surface inthe west, and very near the surface in the east. Becauseof the proximity of the main thermocline to the surface,FIG. 11. As in Fig. 4, except for September of year 32. ~ i 33 - ~ _L-> ,c,-~-~-.~.. 30 ~4o-[-' ~4o-w BG. 12. M~el ~em~Une d~ ~om~y at ~e ~tor ~ny~ 30 and y~ 45 of the 90-ye~ fimulafion. Positive anom~ies~e in~mt~ ~ mud ~nes, and ne~five anom~es ~ in~mt~~th ~h~ Un~. The contour inte~ is 10 m. Anom~es ~mter~n +20 m ~ ~ppl~; anom~es ~ater than -20 m ~e Mtched.2270 MONTHLY WEATHER REVIEW VOLUME 115444342414O39Ld ;.'573634b,33:;5231 ,3O 140-E 180 140'~/V iO0~W F~G. 13. Equatorial zonal wind stress anomalies between year 30and year 45 of the model simulation. Positive (westerly) anomaliesare indicated with solid lines, and negative (easterly) anomalies areindicated with dashed lines. Large westerly anomalies (~0.15 dyn/cm-2) are stippled.a given anomaly in upper-layer depth results in a subsurface temperature anomaly that is largest in the eastand smaller toward the west. In the presence of meanupwelling, a similar anomaly pattern is readily established in the surface layer as well. Thus, due to themean state of the tropical ocean, there is a natural tendency to produce SST anomalies that are largest in theeast and decreasing toward the west. In the case of alarge-scale positive SST anomaly pattern of this type,the atmospheric response includes equatorial westerlyanomalies that span nearly the entire region of SSTanomalies (see Z, and references cited there). The influence of the westerly wind anomalies is (a) to deepenthe eastern ocean thermocline, (b) to supress equatorialupwelling, and (c) to set up eastward current anomalies,.all of which tend to reinforce the temperature anomalypattern Thus, the feedbacl~ between the two media ispositive, leading to the sustained growth of large-scaleanomalies in their characteristic spatial modes. This ishow the model warm events develop. The developmentis not unlike that found in the linear model of Philanderet al. (1984), except for the preferred spatial structure.One aspect of the observations not found in the modelis the tendency for gradual eastward migration of atmospheric anomalies during the course of the warmevent (Rasmusson and Gill, 1983). We find that thisis better captured by the atmosphere component alonewhen forced with observed SST anomalies. The lackof such a feature in the coupled model is at least partlydue to the tendency of the ocean component to understate temperature anomalies in the western Pacific. Figure 13 shows that the model behavior during inter-event periods differs from that during warm events.The inter-event periods are characterized by easterlyanomalies that tend to develop in the eastern oceanand propagate rapidly westward. They are well correlated with similarly propagating anomalies in SST (notshown). There is little evidence of such features in observations. These rather small-scale, coupled anomaliescan develop and persist in the model because a portionof the atmospheric heating is related directly to localSST anomalies, regardless of spatial or temporal scales.In the real system, the local response to small-scale,transient features is probably diminished by the effectsof moisture and temperature advection in the boundarylayer. At times during the model simulation, westerlyanomalies appear in a fashion similar to the onset ofa Warm event, but the development quickly terminates(Fig. 13, years 38 and 44). The difference between these~two situations seems to be the presence of easterlyanomalies in the eastern Pacific. In the aborted eventcases, easterly anomalies exist in the east at the timethe westerly anomalies appear farther west. As thewesterlies grow, the. eastefiies do so as well, and shortlythereafter the development ceases. Preceding warmevents, on the other hand, there are no significant easterly anomalies in the east, either before the appearanceOCTOBER1987 STEPHEN E. ZEBIAK AND MARK A. CANE 2271of westerly anomalies or during their growth. The development of easterly anomalies can in turn be tracedto the time of year the would be warm event is gettingestablished. In each case of a terminated event, theinitial growth occurs in the early part of the year (January-March). The substantial warm events, on theother hand, start later (April-June). This suggests thatthe annual cycle exerts considerable influence over thedevelopment of ENSO events. Section 5 addresses therole of the annual cycle in greater detail. It was found that the processes contributing to SSTvariability in the coupled model are essentially the sameas was found with the ocean model alone when forcedwith observed winds. In the coastal upwelling zone, themean upwelling advection is dominant, with smallercontributions from the remaining terms (all acting inthe same sense). In the eastern equatorial Pacific, zonaladvection and anomalous upwelling also contributeimportantly to the development, especially during themature phase of the warm events. For the western andcentral equatorial region, the net effect of vertical advection is negligible, and zonal advection is dominant.4. Model sensitivities In this section we examine the sensitivity of themodel to some of its parameterizations. Since a complete treatment of model sensitivities cannot feasiblybe presented here, we will discuss only a selected setof experiments that illustrate the principal variationsin model behavior we have found. A more extensivetreatment is provided in Zebiak (1984). Each of thesensitivity experiments is a 25-year run, starting fromthe same initial conditions. The initial conditions aretaken from the beginning of year 31 of the 90-year run(the wind and SST anomalies at this time are shownin Fig..4). It should be noted, however, that the resultsare not sensitive to the initial conditions. Characteristicchanges in model behavior, where present, appearconsistently for widely varying initial states. For brevity,the results are shown only in terms of the NINO3 SSTanomaly index. We are thus focusing on the temporalcharacteristics and amplitudes of large-scale anomalies.a. Atmospheric parameterizations Two experiments were done with variations in theatmospheric heating parameterization. In the first experiment, the coefficient of the heating term proportional to SST anomalies [i.e., a in Eq. (A3a)] was increased by 10%. The NINO3 index from this run andfrom the standard run are shown together in Fig. 14a.Despite the modest increase in heating strength, thereis a large increase in the characteristic amplitude ofanomalies. Other properties of the earlier solution,however, are preserved; i.e., there are still irregular oscillations with a preferred time scale of 3-4 years. Thissuggests that the sensitivity of the oscillation amplitudeis much greater than that of the oscillation time scale.en 4 .0 5 I0 15 20 25 TIME (yeors)0 5 I0 15 20 25 TIME (yeors) FIG. 14. (a) NINO3 for the 25-year period starting at year 31 ofthe standard (90-year) run (heavy line) and corresponding curve fora test run starting from the same initial conditions with the atmospheric heating parameter a increased by 10% (thin line). (b) Similarcomparison between the standard run and a test run with the atmospheric convergence feedback parameter B increased by 7%.Other experiments with both increased and decreasedvalues of a confirm this. The results also illustrate thedegree to which the atmosphere-ocean coupling canamplify anomalies that might occur in either the atmosphere or the ocean alone. For prescribed SSTanomalies, a 10% increase in a could produce, at most,a 20% increase in wind stress anomalies. In the coupledmodel, however, it produces roughly a 100% increase. In the second experiment, the coefficient of thecomponent of heating proportional to low-level moisture convergence [i.e.,/5 in Eq. (A3b)] was increasedby 7%. The results (Fig. 14b) show that the generalcharacteristics of the solution are unchanged. Thisseems somewhat surprising, given the fact that the netlatent heating depends sensitively on/5 (as shown inZ). However, the sensitivity to/5 is scale-selective, withpredominantly the smaller scales being affected as/gincreases. Apparently, the net impact on the largerscale structure is minimal.b. Oceanic parameterizations The experiments of this type include the following: (i) a decrease of 30% in surface layer thermal dissipation (the decay time is increased from 125 days to160 days); (ii) an increase of 20% in the drag coefficient (usedin the bulk formula that relates model winds to windstress); (iii) an increase of 30% in all mean current speeds; (iv) a decrease of 13% in the oceanic equivalentdepth (from 86 to 75 cm);2272 MON'~HLY WEATHER REVIEW VOLUME 115 (v) an increase of 16% in the oceanic equivalentdepth (from 86 to 100 cm); (vi) a decrease of 30% in subsurface layer momentum dissipation (the decay time is increased from 30months to 42 months).The results of the six cases are shown in Figs. 15a-f,respectively. Judging from cases (i)-(iv), it is clear thatthe sensitivites to thermal dissipation, drag coefficient,mean currents and equivalent depth are all large. Ineach of these cases both the amplitude and the timescale of the oscillations increase. What is remarkableis the degree to which these different parameter changes(and others) produce the same result. Cases (i)-(iii) arevirtually indistinguishable in their characteristics, andcase (iv) differs only in being, more nearly periodic.The parameter changes in these experiments all act toincrease SST anomalies for fixed atmospheric anomalies. Reduced thermal dissipation deafly allows largerSST anomalies. A larger drag coefficient producesgreater wind-stress forcing for the ocean, resulting inlarger anomalies of all types. Stronger mean upwellingyields larger SST anomalies in response to thermoclinedisplacements. Finally, a smaller equivalent depth (fora fixed wind stress) produces larger thermocline variations and thus larger subsurface temperature anomalies. In the upwelling regions this again translates intolarger SST anomalies. In the coupled model, all of theseeffects induce an atmospheric response that furtherreinforces them; i.e., they increase the strength of theatmosphere-ocean coupling. Thus, the results indicatethat an increase in coupling strength, regardless of howit is achieved, results in oscillations with larger amplitude and period. Experiment (v) offers one example ofa parameter change in the opposite sense, that is, onewhich amounts to decreasing the coupling strength.The result in this case is smaller oscillations with ashorter period. Other cases of decreased couplingst. rength (not shown) are similar. Experiment (vi) illustrates a case of low sensitivity.As seen from Fig. 15f, a sizeable decrease in backgroundocean dissipation produces no change in the characteristics of the s61ution. In other experiments withmuch larger dissipation (decay times of order 1 year),the amplitude of the oscillations is noticeably reduced,but the preferred period remains the same.~- 4/ (a)l_=o0 5 I0 15 20 25 TIME (years)0 5 I0 15 20 25 TIME (years)~- 4/ ' (b)l0 5 I0 15 20 25 TIME (years)0 5 I0 15 20 25 TIME (years)0 5 I0 15 20 25 TIME (years)~ 4- (f)z~-2 0 .5 I0 15 20 25 TIME (ye0rs) I~G. 15. Comparison of standard ruff (heavy line in each case) and test runs (thin line) with (a) oceanicsurface-layer thermal dissipation decreased by 30%, (b) drag coefficient increased by 20%, (c) mean currentsincreased by 30%, (d) oceanic equivalent depth decreased by 13%, (e) oceanic equivalent depth increased by16%, and (f) subsurface layer momentum dissipation decreased by 30%.OCTOBER 1987 'STEPHEN E. ZEBIAK AND MARK A. CANE 2273 O I0 15 20 25 TIME (years)FIG. 16. Comparison of standard run (heavy line) and a .test run (thin line) with alternate coupling procedure (see text).c. Coupling procedure The coupling procedure described in section 2 involves recalculating the total atmospheric anomaliesonce a month and computing incremental changesotherwise. The recalculation prevents the eventualgrowth of unphysical small-scale features in the modelwinds. We have also examined a somewhat differentprocedure: recalculation of the wind anomalies onlyat those times when the temperature anomalies (asmeasured by NINO3) are very small. This proceduregives a less frequent recalculation (once per month ismore than is needed), but since the recalculation isnow linked to the ENSO cycle itself, it avoids introducing a separate time scale into the system. The resultsare shown in Fig. 16. The characteristic amplitude ofoscillations increases, and the favored period increasesfrom 3 years to 4 years. Along the lines of the previousdiscussion, this alternate procedure appears to increasethe coupling strength somewhat. In either case, however, the characteristics of the variability lie within realistic limits.5. Influence of the annual cycle Both real and model warm events are clearly tied tothe annual cycle, tending to amplify sharply during the(northern) summer, reach peak amplitude around theend of the year, and diminish during the following year.In order to examine the annual cycle influence in themodel, a set of experiments was done in which theannual cycle was turned off at various points duringthe evolution of a warm event. For each experiment,initial conditions were taken from January of year 31of the standard run (a warm event year), and the annualcycle was turned off at a given subsequent month byholding the mean fields fixed from then on. Four casesare shown, corresponding to suppressing the annualcycle in April(O), August(O), December(O), and July(l),where year 0 represents the warm event year. Figure 17a shows the evolution of NINO3 from thestandard run and from the April(O) experiment. Withthe background fields held in their April configurations,the growth of the warm event is retarded considerably.The amplitude increases more slowly, reaches a maximum several months later, and then decreases sharply.When the annual cycle is suppressed in August(O),the result is very different (Fig. 17b). The amplitudecontinues to rise sharply for many months into year1, peaking later and at a larger value than with theannual cycle included. The subsequent decline is similar to that during the summer period for the annualcycle case. In the standard run, the warm event has reachedmaximum amplitude and is subsiding by December(O).The result of maintaining December conditions fromthen on is shown in Fig. 17c. There is an immediateand steady decline into the middle of year 1, as opposedto a hesitation in the decline during the early part ofyear I if the annual cycle is maintained. The later development of negative anomalies, on the other hand,is suppressed relative to the annual cycle case. If July conditions are maintained from July(+ 1) onward (Fig. 17d), then compared to the standard case,the growth of negative anomalies continues longer andleads to larger anomalies during year(+2). This is analogous to the situation for the growth of positive anomalies in the August(O) experiment. The results demonstrate that the annual cycle influences the development of anomalies significantly. TheAugust(O) and July(l) experiments indicate that the(northern) summer period is most favorable for rapidgrowth of both positive and negative anomalies. Theremainder of the cases indicate that the spring periodis least favorable for anomaly growth and that the falland winter periods are intermediate. In terms of thediscussion in section 4, we can interpret the results as $ I 0-I-20 4~ $ 2 I 0-I-2 0(o)6 12 18 24 30(c)I I I I6 12 18 24 30 TIME (months) (b)6 12 18 24 30(d)I I I I6 12 18 24 $0 TIME (months) FIG. 17. Comparison of NINO3 for the 30-month period startingfrom January of year 31 of the standard run (heavy solid lines) and(a) test run with April conditions maintained after month 4, (b) testrun with August conditions maintained after month 8, (c) test runwith December conditions maintained after month 12, and (d) testrun with July conditions maintained after month 19. Test runs areshown by the dashed lines.2274 MONTHLY WEATHER REVIEW VOLUME 115an indication that the effective coupling strength ismodulated by the seasonal variations in mean fields.This interpretation also accounts for the manner inwhich ENSO anomalies are phase-locked to the annualcycle in the full model. Typically, small anomalies thatare present in the spring of an ENSO year amplify rapidly during the summer and fall, reaching large amplitude. During the winter period, the coupling strengthbegins to decrease significantly and becomes insufficient to maintain the large anomalies against themechanisms of dissipation (the most significant ofwhich is the thermal damping of the oceanic surfacelayer), and thus the anomalies begin to decrease. Aftera hesitation during the spring, an increase in couplingstrength during the following summer hastens the demise of the warm event and the growth of negativeanomalies. An examination of the seasonal variations in themean 'fields can explain the influence on couplingstrength. In the spring season (February-April), themean equatorial tradewinds are weak (Horel, 1982),as are the associated equatorial upwelling and easternPacific SST gradients. All of these act to diminish thegrowth of anomalies. A given wind an~omaly producesa relatively small stress anomaly because the mean windspeed is small. A given subsurface temperature anomalyis less readily transferred to the surface because theupwelling is weak. A given current anomaly is less effective in generating temperature anomalies becausethe mean temperature gradients are weak. On the otherhand, during summer and fall the mean winds, meanupwelling and mean SST gradients are all large, andthis period is favorable for anomaly growth. The winterseason is intermediate between these two extremes. Despite the fact that spring is the season of minimumgrowth rate, it is noteworthy that all the major warmevents first appear during this season. This is the timeof maximum SST in the eastern Pacific and the timewhen the ITCZ briefly extends southward to the equator. With mean convergence, the atmospheric feedbackmechanism is operative, and there can be considerablelocal response to SST anomalies. For this reason thespring may be a particularly favorable time for coupledanomalies to become organized. This idea has beenput forward previously by Philander (1985). The results suggest that, even without the annualcycle, the tendency for interannual oscillation persists.The April(O) and August(O) experiments, for example,eventually give a termination of the warm event andsubsequent development of negative anomalies, just asin the case with the annual cycle included (althoughat.a later time). Another experiment, illustrated in Fig.18, examines this issue further. In this experiment, theannual cycle was suppressed in July(0), and the calculation carried on for 25 years. The solution settlesinto a periodic oscillation with period 47 months. Extended runs using mean conditions from other months(not shown) give somewhat different periods and dif0 5 I0 15 20 25 TIME (years)FiG. 18. Comparison of standard run (heavy line) and test run(thin line) with July conditions maintained after July of year 0.ferent amplitudes. It is clear that, although the annualcycle strongly affects the evolution of anomalies (andin particular, the evolution of warm events), it is notessential to the system's tendency for interannual oscillation. Results to date suggest to us that the annualcycle contributes to the aperiodicity of the full model,though we have at present done insufficient calculationsto say with confidence that the annual cycle is requiredto give aperiodicity within the realistic range of modelparameters.6. Elements of the model oscillation One of the most robust characteristics of the modelsimulations is the tendency for oscillation on interannual .time scales. The oscillatory behavior persistsover a considerable range of parameter values and withor without the influence of the annual cycle. Since thereis no anomalous external forcing, this must result fromsome internal characteristics of the coupled system.However, the previous calculations have not Clearlyidentified the causes of the oscillation or what sets itstime scale. They have shown only that the time scale(and amplitude) of the oscillation is affected by a subtlecomposite of many different physical parameters.During the E1 Nifio, or warm event phase of the oscillation, the development clearly depends on a positivefeedback between large-scale atmospheric and oceanicanomalies. The feedback allows sustained anomaliesin both the atmosphere and the ocean that would notpersist in either medium alone. The same argumentcould be made with regard to anomalies of the oppositesign during non-E1 Nifio periods. But what causes thetransitions between these two states? As discussed inthe previous section, the annual cycle can stop thegrowth of anomalies at a particular time if its effectsare included in the model. In its absence, there are yetother mechanisms of equilibration. For example, theocean thermodynamics can produce surface temperatures no greater than the warmest temperature of themean state, as temperature variations result solely fromadvective processes, and the heat flux anomalies alwaysact in a dissipative manner. These effects insure thatanomalies do not grow to arbitrarily large amplitudebut do not explain why the system oscillates, as opposedto settling into a nonzero equilibrium state (or an anOCTOBER I987 STEPHEN E. ZEBIAK AND MARK A. CANE 2275nually periodic state with nonzero mean). Some otherfactor or factors must be responsible for this. In section 3 we showed that the integrated heat content along the equator varies with a phase that is different from that of the larger east-west fluctuationsthat characterize warm events (see Fig. 12). The integrated heat content tends to be high prior to the development of a warm event and is low in the aftermathof an event. We describe here some experiments thatdemonstrate the importance of this effect. The upper ocean heat content is measured by themodel upper layer depth, which approximates thethermocline depth in the real ocean. This variable affects the surface layer thermodynamics only throughthe parameterized subsurface temperature [Eq. (A 13)].In the following experiments the subsurface temperature was made more or less sensitive to changes in thearea-averaged heat content anomaly for the entireequatorial band between 5-N and 5-S. This region encompasses the equatorial upwelling zone, where subsurface anomalies can be expected to affect surfacetemperature. In the first experiment, subsurface temperature anomalies were made completely insensitiveto changes in the average heat content of the region.This amounts to replacing the variable h in (A 13) withthe expression h - h*, where h* is the average of hover the region of interest. Note that this does not alterthe temperature variations associated with the zonalslope of the equatorial thermocline; i.e., it does notsuppress the dominant ENSO signal. It does, however,suppress the temperature signal associated with anyuniform raising or lowering of the thermocline in thisregion. Initial conditions were again taken from thebeginning of year 31 of the standard run. Figure 19ashows the evolution of NINO3 over 25 years in theexperimental run, together with the same index fromthe standard run. The result of suppressing the effectsof changes in integrated heat content is dramatic: thesystem no longer oscillates, but rather moves immediately toward a new climatology with only annualvariability. The new climatology represents an El Nifiolike state, with relatively warm eastern ocean temperatures and weak equatorial trades. If the experiment isstarted at a time when h* is negative rather than positive(as in this case), the solution moves correspondinglytoward a climatology with colder SST and strongertrades. In either case, there is no intemnnual oscillation;the ENSO cycle does not survive. In a second experiment, exactly half of the actualfluctuation in h* was allowed to influence temperature;i.e., the variable h in (A13) was replaced by the expression h - 0.5h*. The result is shown in Fig. 19b. Thereis now an interannual oscillation with. amplitude similar to the original run, but with a characteristic periodof 5-6 years, nearly twice as long as before. Finally, the temperature effect associated with h*was enhanced by a factor of three [the variable h in(A13) was replaced by the expression h + 2h*]. As0 5 I0 15 20 25 TIME (years)0 5 I0 15 20 25 TIME (years) 0 5 I0 I 20 25 TIME (years) FIG. 19. Comparison of standard run (heavy line) and test run(thin line) with (a) effects of variations in equatorial heat contentsuppressed (see text), (b) effects of variations in equatorial heat contentreduced by 50%, and (c) effects of variations in equatorial heat contentincreased by 200%.shown in Fig. 19c, the result is an oscillation that, again,is similar to before in amplitude, but now exhibits amuch shorter period of 1-2 years. The results show empirically that the oscillatorycharacter of the coupled system depends on the effectof variations in net equatorial heat content. Withoutthis effect, there is no oscillation. If the effect is partiallysuppressed, the transitions between cold and warmstates are retarded. If the effect is enhanced, the transitions are hastened. Fluctuations in net heat contentsimilar to those of the coupled model are produced bythe linear ocean dynamics alone; in response to basinscale low-frequency periodic wind forcing (Cane andSarachik, 1981). In this forced case, the same phaselead of h* occurs; that is, h* is positive prior to thewesterly wind phase of the cycle and negative followingthis phase. In addition, the response is such that thechanges in thermocline depth in the eastern part of thebasin lead the changes in the winds by a fraction of theoscillation period. This property holds for all periodssignificantly greater than the Kelvin wave crossing period, (i.e., for periods of order a year or more), withthe precise degree of phase shift depending on frequency (among other factors).2276 MONTHLY WEATHER REVIEW VOLUME II5 In the coupled model, the winds are not specified,but rather are calculated from the SST field. The SSTfield, however, is affected strongly by thermocline motions in the eastern part of the basin (where there isvigorous upwelling and the mean position of the thermocline is close to the surface), and thus the winds arestrongly coupled to thermocline motions there. Moreover, the coupling is such that changes in wind stresstend to lag changes in thermocline depth. This is because it takes finite time for. upwelling effects to createsurface temperature anomalies from subsurface anomalies, and for the mean surface currents to spread theanomalies over a region large enough to influence theatmosphere significantly. The phase lag between windstress and thermocline is in precisely the same senseas is required by the equatorial ocean dynamics forlow-frequency oscillatory modes. We propose that it isbecause of this possible matching of phase relationsthat oscillations of the coupled system are possible. If there were a simple, linear relationship betweenthermocline depth and wind stress, the theory wouldpredict perfectly regular oscillations of the coupled system (though in general they would be exponentiallyincreasing or decreasing in amplitude). Of course, thisis not the case in the full model. Many processes comeinto play in relating thermocline motions to surfacewind stress, and others act somewhat independently,e.g., zonal temperature advection in the oceanic surfacelayer and moisture convergence effects in the atmosphere. The thermocline influence itself is a nonlinearfunction in the full model. Furthermore, all of theseprocesses are subject to seasonal variability associatedwith the annual cycle. Apart from providing negativefeedbacks at large amplitude which limit the growth ofanomalies, these effects tend to obscure othenvise uniform phase relations that would exist in a simpler, linear system. It is because of this that the nonlinear oscillations of the full model can exhibit variability inamplitude and period. Despite this, there is clearly apreference for 3-4 year periods. According to the present theory, this reflects a characteristic, if Somewhatvariable, time delay between dynamical changes in theeastern ocean and associated large-scale fluctuations inequatorial wind stress.7. Summary and conclusions 'We have presented a coupled model that is used tosimulate and study ENSO. The coupled model calculates perturbations about a (monthly) climatologicalmean state that is specified from observations. Withoutanomalous external forcing, the coupled model produces recurring warm events that are irregular in bothamplitude and spacing, but favor a 3-4 year period, asobserved. The events develop systematically, with thelargest growth occurring during the (northern) summerand fall and termination during the following springand summer. The signature of model warm events includes equatorial westerly wind anomalies in the centralPacific and large SST anomalies in the eastern Pacific.These features are in general agreement with observations. In the model, the characteristic spatial patternsresult from the configuration of the mean wind, currentand temperature fields. The phase-locking occurs bemuse the seasonal variations in these mean fields effectively modulate the coupling strength between atmospheric and oceanic anomalies. Despite the model's successes, it is limited in its ability to simulate the real system. A detailed comparisonwith observations shows discrepancies in both the atmospheric and oceanic simulations. We expect thatthe model can rather easily be improved in some respects and that better simulations will be possible withmore sophisticated models. Experiments with the model show that both the amplitude and the time scale of the cycle are sensitive tocertain parameters. All parameter changes whichamounted to increasing (decreasing) the strength of theatmosphere-oc'ean coupling tended to produce larger(smaller) amplitudes and longer (shorter) periods. Inno case, however, was interannual variability eliminated. This is true even in experiments with the annualcycle removed. The mechanism of low-frequency oscillation in the model is highly robust. A critical element of the model oscillation is thevariation in net heat content of the near-equatorialocean. There is a buildup in heat content prior to theonset of a warm episode and a rapid decrease in heatcontent during the course of the event. Though thissignal is small relative to the east-west fluctuations thatcharacterize the extremes of the cycle, it is not unimportant. In experiments where the effects of this fluctuation were artificially suppressed, the ENSO cyclewas eliminated. Similar fluctuations should be evidentin the real ocean if the model is correctly simulatingthe ENSO cycle. The variations in equatorial heat content are characteristic of bounded equatorial ocean dynamics forlow-frequency oscillatory forcing, and a concomitantof these fluctuations is a systematic phase lag betweenwind stress and thermocline motions in the easternpart of the basin. We have suggested that, within acertain parameter range, the physics of the coupledmodel allows such a phase relation between these fields,and that this is why interannual oscillations occur inthe coupled system. More work will be required to substantiate and possibly refine this theory. We havepointed to three elements that we believe are essentialto the interannual oscillations observed in the coupledmodel. First, there is a positive feedback between largescale atmospheric and oceanic anomalies. In otherwords, the background state of the coupled system isunstable to E1 Nifio-like perturbations. Second, thereare nonlinear mechanisms of equilibration that preventthe anomalies from growing to arbitrarily large amplitude. Dominant among these are the limits imposedOCTOBER1987 STEPHEN E. ZEBIAK AND MARK A. CANE 2277by the mean thermal structure of the ocean (in particular, the structure of the thermocline). These effectsare important in determining the characteristic amplitude range of anomalies. Finally, due to the natureof the atmosphere-ocean coupling, there is a systematic, though somewhat variable, time delay betweendynamical changes in the eastern ocean and associatedlarge-scale fluctuations in equatorial wind stress. Dueto the unique characteristics of equatorial ocean dynamics, this gives rise to a continuing succession oftransitions between non-El Nifio and E1 Nifio stateson interannual time scales. The transitions are a resultof the linear shallow-water dynamics and not other,less familiar aspects of the model. The presence ofnonlinear processes in the model additionally allowsthe possibility of aperiodicity. If the model is correctly simulating the real ENSOcycle, then the results have a number of implications.First, a necessary precondition for the onset of a warmepisode is above-normal equatorial heat content. Thisis not a sufficient condition, so it cannot take the placeof a forecast model. However, it can identify favorableperiods and can exclude others. Second, all the mechanisms essential to the ENSO cycle are containedwithin the tropical Pacific region alone. This does notpreclude the possibility of teleconnections to other regions. Finally, we need not appeal to random forcingof unknown origin in order to account for the aperiodicity of ENSO; it can result from strictly deterministicprocesses. All of these bear favorably on the prospectsfor prediction of El Nifio. Along these lines, we havefound that the same model as presented here has skillin forecasting ENSO at lead times of 1-2 years (Caneet al., 1986). This, we believe, adds further weight tothe argument that ENSO is largely controlled by deterministic processes in the tropical Pacific atmosphere-ocean system. Acknowledgments. We are deeply appreciative of thesupport for this work provided by Adrian Gill. Ourthanks to the many colleagues, notably including thereviewers of an earlier version, whose comments andcriticisms have contributed to an improved manuscript.Thanks to Karen Streech and Naomi Katz for invaluable help in preparing the manuscript. This work hasbeen supported by grants NAGW-916 from NASA andNA-84-AA-D-00031 of the U.S. TOGA Project Officeof NOAA.APPENDIXGoverning Equations of the Coupled Model The governing equations for the atmosphere (at iteration n) are as follows (see Zebiak, 1986): +eua" - lgoyDa" = -(P"/Po)x (A 1) eva" + floyUa" = -(lf /Po)~, (A2) ~(Pn/100) '~- Ca2[(I, lan)x "- (Van)y] ~--- --0s -- 01 n-I (A3) Os = (aT) exp[~- 30-C)/16.7-C1 (A3a) 0t" =/5[M(~+ c") - M(Z)I, (A3b)where M(x) = 0,x, x>X ~< 0.0 (A3c) In (A3a), ~(x, y, t) is the prescribed monthly meanSST, and T is the anomalous SST. In (A3b), Z(x, y, t)is the prescribed monthly mean surface wind convergence, and cn is the anomalous convergence at iterationn, defined by Cn ~-- --(I,~an)x -- (l)an)y. (A3d) The governing equations for the ocean (see Zebiak,1984) are fit -- flOYD ~-~ -g'hx + r(X)/pH- ru (A4) tSoyu = -g'hy + -Y)/pH- rv (A5) ht + H(ux + vy) = -rh, (A6)where u = H-~(H~u~ + H2u2). (AT)The subscripts 1 and 2 refer to the surface layer andunderlying layer, respectively. The equations governing the shear between layers 1and 2 are rs Us - lgoYDs = r(~)/pHi (A8) rsVs + l~oyus = r-')/pH~, (A9)where us --- Ill - u2. Equations (A4)-(A9) allow the surface current u~ tobe determined. From this, th& entrainment velocity iscalculated: Ws = HI [(Ul)x q- (VlM. (AIO)The temperature equation for the surface layer is, then,OTOt --UI- V(~'~- T)- fi~. VT- M(~s + w,)- M(~) X~z-M(~s+Ws)T-re oqr, (All) H~where ill(x, y, t) and Os(x, y, 0 are the mean horizontalcurrents and upwelling, respectively, ~x, y, t) is theprescribed mean SST, and T~(x) is the prescribed meanvertical temperature gradient. The entrainment temperature anomaly, Te, is defined by Te = 3'rsub + (1 -- 3')T. (A12)Tsub has the form_ fT~tanh[b~(h+h)]-tanh(b~h), h>0 lT2tanh[b2(~- h)] - tanh(b2h), h < 0, (A.13)where ~(x) is the prescribed mean upper layer depth.2278 MONTHLY WEATHER REVIEW VOLUME 115Parameter values used for the coupled simulation areas follows: e=(2days)-~, ca=60ms-~, a=0.031m2s-3/-C, /5= 1.6X 104m2s-2, r = (2.5 years)-~, c-~(g'H)m=2.9ms-~, H= 150m, Hi = 50m, rs=(2 daYS)-~, ors=(125 days)-~, 'y = 0.75, T~ -- 28-C, T2 = -40-C, b~=(80m)-~, b2=(33m)-LREFERENCESAnderson, D. L. T., and J. P. McCreary, 1985: Slowly propagating disturbances in a coupled ocean-atmosphere model. J. Phys. Atmos. Sci., 42, 615-629.Busalaeehi, A., and J. J. O'Brien, 1981: Interannual variability of the equatorial Pacific in the 1960's. J. Geophys. Res., 86, 10 901 10 907. , and M. A. Cane, 1985: Hindcasts of sea level variations during 1982/3 El Nifio. J. Phys..Oceanogr., 15, 213-221.Cane, M. A., 1984: Modeling sea level during El Nifio. J. Phys. Oceanogr., 14, 1864-1874. , and E. S. 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