6EquatorialCurrents:Observationsand Theory

Ants LeetmaaJulian P. McCreary, Jr.Dennis W. Moore

6.1 Introduction

Historically, our knowledge of the circulation patternsin the tropics was derived from compilations of ship-drift data and so was restricted to a description of thesurface currents. Although information of this type iscrude, a picture of the spatial and temporal structureof the surface flow field was deduced over the years,and it has been little improved upon in the modern eraof instrumentation. By contrast, almost all of the in-formation about subsurface equatorial flows has beenacquired recently. It is remarkable that one of the majorocean currents, the Pacific Equatorial Undercurrent,was not discovered until 1952.

For many reasons, progress in understanding equa-torial circulations has been slow. The equatorial re-gions are vast and remote. The swift currents and highvertical shears put special demands on instrumenta-tion. The geostrophic approximation, which is so use-ful at mid-latitudes, breaks down close to the equatorand cannot be relied on to give accurate informationabout the currents. Finally, the flows seem much moretime dependent than at mid-latitudes. Hence, on thebasis of individual cruises, haphazardly taken in timeand space, it is difficult to develop a consistent pictureof the circulation patterns.

The variability of equatorial circulations has onlyrecently been appreciated. This is partly because a greatdeal of the information about equatorial circulationscomes from the central Pacific, where historically themean appears to dominate the transient circulation;recent NORPAX (North Pacific Experiment) observa-tions (Wyrtki, McLain, and Patzert, 1977; Patzert, Bar-nett, Sessions, and Kilonsky, 1978), however, suggestthat the variability can be quite large even there. Inother regions such as the western or eastern Pacific orthe Indian Ocean, the fluctuating components are aslarge as or larger than the means.

The goal of this chapter is to give a short overviewof the outstanding features of the equatorial ocean cir-culation patterns, the dominant spatial and temporalstructures of the Pacific equatorial wind field (as anexample of the kinds of driving mechanisms that needto be considered), and a summary of some of the the-oretical ideas that have been developed to explain theocean circulation and its relation to the wind field. Noattempt is made to be comprehensive because in recentyears there have been numerous excellent reviews ofequatorial phenomena and theories for them. Theseinclude articles by Knauss (1963), Tsuchiya (1970), Rot-schi (1970), Philander (1973), Gill (1975a), and Mooreand Philander (1977). A collection of papers discussingvarious topics of equatorial oceanography is containedin the proceedings of the FINE (1978) workshop, held

i84A. Leetmaa, J. P. McCreary, Jr., and D. W. Moore

at Scripps Institution of Oceanography during the sum-mer of 1977. A comprehensive discussion of analytictechniques for studying forced baroclinic ocean mo-tions in the equatorial regions is presented in a three-part paper by Cane and Sarachik (1976, 1977, 1979). Indiscussing the theories, we shall stress the importantphysical ideas of each model (avoiding whenever pos-sible the use of mathematics), put them in historicalperspective, and relate them to the observations. Theobjective here is to identify the observations for whichwe have physical theories, and thereby indicate wherefurther work is needed.

The importance of knowing the detailed time andspatial structure of the wind field is emphasizedthroughout this chapter. The reason is that in the trop-ics, the characteristic response times for baroclinicoceanic processes are much shorter than they are atmid-latitude and are much closer to the time scalescharacterizing the wind variations. Therefore the baro-clinic response to atmospheric forcing is expected tobe much stronger than at mid-latitude. The implicationis that in order to arrive at a satisfactory explanationof the oceanic features, the temporal and spatial struc-ture of the atmospheric forcing must be known accu-rately.

6.2 Observations

6.2.1 The OceanThe surface currents are characterized by zonal bandsin which the flow is alternately eastward or westward(Knauss, 1963). The eastward flows are referred to ascountercurrents because they flow counter to the di-rection of the easterly trade winds. The westward flowsare referred to as North and South Equatorial Currents.In the Atlantic and the Pacific, the North EquatorialCountercurrent (NECC) is approximately located be-tween 5 and 10°N with westward flow to the north ofthis region in the North Equatorial Current (NEC) andwestward flow to the south of it in the South EquatorialCurrent (SEC). There is also evidence for a South Equa-torial Countercurrent (SECC) in both oceans between5 and 10°S (Reid, 1964b; Tsuchiya, 1970; Merle,1977); these flows are not as well developed, however,as the NECC. Both the intensity and location of thevarious currents vary seasonally (Knauss, 1963; Merle,1977). The SEC and NECC are strongest during Julyand August. In the northern winter and spring the SECgenerally vanishes and the NECC is weak; in the east-ern Pacific there is some evidence that during this timethe NECC is discontinuous at some longitudes or isentirely absent (Tsuchiya, 1974). In the northern sum-mer the Pacific NECC assumes its northernmost po-sition, whereas in the northern winter the current liesclosest to the equator. The data base is insufficient toshow an analogous migration of the Atlantic NECC.

The structure of the surface currents in the IndianOcean differs markedly from those in the other twooceans (African Pilot, 1967). In the Indian Ocean theSEC usually lies totally south of 4S. The predomi-nantly eastward flow in the Indian Ocean is almosttotally confined between the equator and the SEC.North of the equator the flow direction varies season-ally. During the northeast monsoon it is to the west.

The different circulation pattern in the Indian Oceanis no doubt related to the nature of the wind field. Inthe Atlantic and the Pacific, the southeast and thenortheast trades are well developed over most of theocean throughout the year. The mean stress is gener-ally greater than the annual or semiannual components.In the Indian Ocean south of about 100S, the southeasttrades are reasonably steady. North of 10°S, the meanwinds are weak and the stress field is dominated bythe strong, regular forcing of the southwest and north-east monsoons.

The earliest measurements that indicated that thecurrents at depth might behave differently from thoseat the surface were made in 1886 by Buchanan (1888;see discussion by Montgomery and Stroup, 1962). Us-ing drogues, he found that the subsurface flow on theequator in the Atlantic at 14°W was toward thesoutheast, while the surface flow had a slight westwardset. These unusual measurements were thought not tobe representative until after the discovery of the Equa-torial Undercurrent in the Pacific in 1952 (Cromwell,Montgomery, and Stroup, 1954). The Equatorial Un-dercurrent has been found to be a subsurface eastwardflow that is about 100-200 m thick and 200-300 kmwide. It is centered approximately on the equator. Itscore lies just beneath the base of the mixed layer in thetop of the equatorial thermocline. Undercurrents arefound in all three oceans. The one in the Indian Ocean,however, appears to be present primarily during thenortheast monsoon, and most observations of it havebeen made during the spring. A thorough discussion ofearly evidence for the Equatorial Undercurrent in allthree oceans is given in Montgomery (1962); see alsoPhilander (1973).

Evidence for additional subsurface countercurrentsin the Pacific is discussed in detail by Tsuchiya (1975).He finds narrow subsurface countercurrents in the Pa-cific Ocean symmetrically located about the equator.The jets occur at a depth of 200-300 m, and are asso-ciated with the poleward limits of the thermostad (asubsurface, relatively homogeneous layer of equatorial14°C water). In the eastern Pacific, they are locatedroughly at 5°N and 5°S and are distinct from the surfacecountercurrents as well as from the Equatorial Under-current itself. Further to the west, the jets move closerto the equator (Taft and Kovala, 1979) and have beenobserved to merge with the Equatorial Undercurrent(Hisard, Merle, and Voituriez, 1970). The jets appear in

I85Equatorial Currents

virtually all central and eastern Pacific Ocean hydro-graphic sections, and thus appear to be permanent fea-tures of the equatorial current system there. There isalso evidence that similar currents exist in the AtlanticOcean as well (Tsuchiya, 1975; Cochrane, Kelly, andOiling, 1979).

Although something is known about the temporalfluctuations of the surface currents from ship-drift ob-servations, little systematic information exists aboutthe time and space variations at any frequency. Therecent survey article by Wunsch (1978b) discusses theobservational evidence for equatorial motions with pe-riods from a few days to several months. Fluctuationshave been observed with periods of 4 to 5.5 days(Wunsch and Gill, 1976; Weisberg, Miller, Horigan, andKnauss, 1980; Weisberg, Horigan, and Colin, 1979)Harvey and Patzert (1976) present evidence that sug-gests waves with a period of about 25 days. Featureswith a similar time scale and wavelength of about1000 km are observed in the satellite infrared imagesof the equatorial front by Legeckis (1977b). In the At-lantic, Duiiing et al. (1975) found evidence for a mean-dering of the Equatorial Undercurrent with a "period"of 2-3 weeks and a "wavelength" of 3200 km duringGATE (GARP Atlantic Tropical Experiment).

Neumann, Beatty, and Escowitz (1975) and Katz etal. (1977) have shown that the east-west slope of thethermocline in the Atlantic varies on a seasonal timescale. This variation appears to be in phase withchanges in the zonal component of the wind stress.When the trades are strongest the tilt of the thermo-cline is the greatest, and when the stress is at a mini-mum so is the slope. Meyers (1979), in a similar anal-ysis for the Pacific, finds strong annual and interannualvariations in the depth of the 14° isotherm. This iso-therm was chosen because it is representative of move-ments of the thermocline as a whole. The east-westslope was a minimum in May and June and a maximumduring October and November. The easterly windstress is weakest in March-May; there is some phasechange, however, in the annual component with lon-gitude. Hence there appears to be a time lag betweenthe minimum east-west slope and the minimum wind.The exact relation between the winds and the varia-tions in the slope was difficult to deduce because thevariations about the mean slope are small and becausesmaller spatial scales than the basin width were pres-ent in the slope of the 140 isotherm. These smallerscales appear to propagate westward. In the IndianOcean the mean east-west stress is small. In the tran-sition between the monsoons, however, westerly windsappear along most of the equator. Associated withthese is an eastward oceanic jet and simultaneously arise in the sea level off Sumatra and a rise of the ther-mocline off East Africa (Wyrtki, 1973a). The oceanicresponse appears to occur coincidently with the winds.

6.2.2 The Wind FieldTo date, most theoretical treatments of equatorialflows consider the applied wind stress to be some sim-ple functions of time and latitude, whereas even themost general meteorological description of the tradesindicates that there is considerable spatial and tem-poral structure (Riehl, 1954). In recent years, there havebeen several thorough analyses of the stress field overthe ocean as derived from historical merchant-vesselreports. In the Pacific, this analysis was done for thewhole ocean by Wyrtki and Meyers (1975) and for theeastern part by Hastenrath and Lamb (1977). The latterauthors and Bunker (1976) also analyzed the winds overthe tropical Atlantic. From these studies, it is possibleto look in detail at the long-period temporal fluctua-tions and the large-scale spatial structure of the stressfield. For the sake of brevity, we shall limit our dis-cussion to the Pacific data. Some similar features areevident in the Atlantic, while the Indian Ocean windfield is dominated by the monsoon circulation.

Values of the zonal stress within 4 of the Pacificequator are shown in figure 6.1. These curves are de-rived from the mean monthly values of Wyrtki and

Figure 6.I The monthly variation in the mean zonal stressbetween 4N and 4°S. In figures 6.la-6.1k, the solid curvesdisplay the average stress for blocks of 10° of longitude cen-tered at the indicated values. The dashed curves show theproportion that is fitted by the annual and semiannual com-ponents. Figure 6.11 shows the amplitude of the mean, annual,and semiannual components as a function of longitude. Theamplitude of the mean component has been reduced by afactor of five, i.e., at 145°W it is about 0.5 dyncm -2 .

i86A. Leetmaa, J. P. McCreary, Jr., and D. W. Moore

5

Meyers (1975), which are tabulated for areas of 2 oflatitude by 100 of longitude. The monthly values of theequatorial zonal stress with the yearly mean removedare shown in figures 6.1a-6.1k. As can be seen, theannual and semiannual components account for almostall of the annual variation. The amplitudes and phasesof these components are tabulated in table 6.1 Thephase of the annual component decreases rapidly, al-though irregularly, to the east. The phase of the semi-annual component also decreases to the east, but moreslowly. The amplitudes of the mean, annual, and semi-annual components as a function of longitude areshown in figure 6.11. The mean stress over most of thePacific is about a factor of five larger than the annualand semiannual components. The amplitude of eachcomponent varies strongly in the zonal direction. Thuswe expect that models driven by zonally uniform stressdistributions may not be adequate for describing theoceanic response to the wind.

Meyers 11979) presents evidence that the longitudi-nal structure of the wind field must be properly ac-counted for. He finds significant energy at the semian-nual period in the eastern Pacific Ocean even thoughthere is little energy in the wind stress there at thatperiod. A study of the EASTROPAC data supports hisfindings. Figure 6.2 shows the average rate of changeof the depth of the 200 isotherm (m/60 days) between1IN and 1lS at four different longitudes. As can be seen,there is a pronounced semiannual variation, and thechanges occur almost simultaneously at each longi-tude. The large amplitude of the changes (-50 m/60days) is surprising considering the small amplitude ofthe semiannual component of the stress at these lon-gitudes (0.02-0.03 dyncm- 2 ). We suggest that thesefluctuations are caused by baroclinic waves that havepropagated eastward from a region where the semian-nual component of the stress is much larger. Meyersreached the same conclusion.

So far we have considered only winds in the vicinityof the equator and have ignored the transient changesin the stress, and the curl of the stress, that are relatedto seasonal movements of the Intertropical Conver-gence Zone (ITCZ). To investigate these effects, themonthly values of the stress averaged between 100 and120°W were examined. To emphasize the meridionalstructure, the weak monthly mean stress at the equator(-0.1 dyncm-2 ) was subtracted from the monthlymean value of the stress at each latitude. Resultingmonthly values are shown in figure 6.3. The annualmovement of the ITCZ has little effect close to theequator, with the largest amplitude of the variation inthe stress occurring at about 9°N. There the amplitudeis about 0.5 dyn cm-2. The variation south of the equa-tor is considerably less. But it is evident that the annualvariation in wind-stress curl can be very large and mustbe taken into account in the models.

Table 6.1 Amplitude and Phase of Annual and SemiannualComponents of Zonal Stressa

Annual Semiannual

Amplitude Amplitude(dyn cm-2 ) Phase (dyn cm-2 ) Phase

165°E 0.11 308° 0.05 77°

175°E 0.03 263° 0.03 46 °

175°W 0.04 239° 0.06 39 °

165°W 0.06 224° 0.07 34°

155°W 0.06 153° 0.07 13°

145°W 0.08 122° 0.10 356 °

135°W 0.05 113° 0.11 331 °

125°W 0.09 72° 0.10 337 °

115°W 0.08 55° 0.06 333 °

105°W 0.07 34° 0.03 287°

95°W 0.04 342 ° 0.02 291 °

a. Amplitude = a2 + b2, phase = tan-'(bla), and

= To + a cos 12 t + bl sin 2 t + a2 cos- t + b2 sin t.2 T2_ 6 -6

50In

ao

ID

E

0o

-50

Figure 6.2 The rate at which the depth of the 20°C isothermwas observed to change during the EASTROPAC expeditionin 1967 and early 1968.

I87Equatorial Currents

I I I I I I I I I I I I IJ F M A M J J A S O N D

X

I I . AI I I .I I I 0 1

O 1A Ax 98o Wo 105° "

A 112° "

a 118 "

N110

70

30

0o

30

70

110S

-.6 -.4 -.2 0

dyn/cm 2

Figure 6.3 Profiles of zonal wind stressillustrating the annual cycle. To emphstructure, the weak monthly mean valstress (the average of figures 6. i and 6. lthe monthly mean value at each latitud.... ,,,.,......_,· ........_..._,.,...___.

the depth-integrated value of the meridional velocityusually does not vanish, the suggestion of Montgomeryand Palmen (1940) does not represent a proper expla-nation for the North Equatorial Countercurrent.

Sverdrup (1947) suggested that the North EquatorialCountercurrent was not only a consequence of thezonal wind stress but also was related to the curl of thewind stress and continuity requirements. He assumedin his model that the currents were steady and van-ished at a deep level. The equations were integratedfrom this depth to the sea surface; hence the solutiongave no information about the vertical structure of themotion field. The apparent success of Sverdrup's theoryin the eastern Pacific is often cited as observationalendorsement of its widespread use in large-scale ocean-circulation theory.

In light of the earlier discussion about the large var-iability in the position and amplitude of the NECC,and the considerable monthly variation in the windsin this region, it is surprising that this steady theoryshould be applicable there. In fact, Sverdrup (1947) andReid (1948), instead of using the mean wind stress in|1ovir ----L--^- rrterfein 1ev 3 LI~- hT-,ho ~ - -rnoa r r

.2 .4 .6 tneir cumputatluns, useu lilc uil;oier-lNUVllln val-ues. They also used October-November oceanographicdata to compute vertically integrated pressure. Implicit

from 100 to 120°W, in their theory, then, was the assumption that thelasize the meridionaltasize the meridional oceanic response to the fluctuating winds was suffi-lue of the equatorialwas subtracted from ciently rapid that the ocean was almost always in equi-

e. librium with the instantaneous winds (i.e., quasi-

6.3 Theories

6.3.1 Integrated TheoriesThe earliest theoretical attempts sought an explanationfor the North Equatorial Countercurrent. This currentdefies intuition since it flows opposite to the prevailingwinds. Montgomery and Palm6n (1940) suggested thatthe easterly wind stress in the equatorial zone is bal-anced by the vertically integrated zonal pressure gra-dient. They presented supporting observational evi-dence in the Atlantic. One interesting result was theirdemonstration that the baroclinic pressure gradientsgenerally were confined to the top few hundred metersof the water column. As an explanation for the NorthEquatorial Countercurrent, they hypothesized that inthe doldrums, i.e., in the vicinity of the ITCZ, wherethe magnitude of the zonal stress is greatly reduced,the pressure gradient would maintain the value that ithad on either side of this region and hence no longerbe balanced by the wind stress. As a result, an eastwardflow would develop, which they suggested would beretarded by lateral friction. Charts of dynamic topog-raphy (Tsuchiya, 1968) indicate that the zonal pressuregradient in this region is, in fact, less than it is fartherto the north and south. Furthermore, since 1° or 2° offthe equator Coriolis terms cannot be neglected and

steady).Therefore, it is of some interest to redo the compu-

tations of Sverdrup and Reid using the values for themonthly mean stress field from Wyrtki and Meyers(1975) and to compare the results with oceanographicdata from different times of the year to see whetherSverdrup balance really is quasi-steady. The monthlyvalues of the zonal Sverdrup transport are shown infigure 6.4. The October and November curves lookquite similar to those of Sverdrup. The overall spatialand temporal evolution of the currents throughout theyear resembles the picture that has been derived forthe surface flow field from ship-drift observations. It ispossible to check to see whether the historical inte-grated geostrophic transports follow a similar patternof change.

During 1967 and the first part of 1968, hydrographicsections at four different longitudes between 100 and120°W were occupied across the equator at seven dif-ferent times. The geostrophic velocity computationsrelative to 500 db for these sections are given by Love(1972). Using these figures, the geostrophic transportfor 2° bands of latitude from 2 to 12°N was computedby a planimetric integration. The minimum contourinterval for the velocities was 5 cms-1; this intervalintroduces an uncertainty of about 3 x 109 kgs - into

I88A. Leetmaa, J. P. McCreary, Jr., and D. W. Moore

I

10N

O0

10'N

0'

10'N

0'

Figure 6.4 Upper panel depicts monthly Sverdrup transport.Lower two panels show geostrophic transports observed dur-

each transport computation (2.5 cms - x 500 m x2° x 1 gcm-3 ). The results of these integrations for thesections at 119°W and 112°W are shown in figure 6.4.The tendency at both sections is for the transport inthe south equatorial current to be strongest during thesummer. The NECC lies close to the equator early inthe year and moves northward during the summer andsouthward again during late fall. The transport patternsat both sections during the first part of 1967 and 1968are quite similar. This agreement could be coincidenceor indicate that these fluctuations perhaps have a reg-ular annual cycle. The observed geostrophic transportpatterns are visually similar to the theoretical pattern;there clearly are quantitative differences, however.

The important conclusion from this study is that itcannot be said whether the Sverdrup relation providesan accurate description of the currents in the easterntropical Pacific. Sverdrup and Reid were probably for-tunate in that their results seemed to agree so wellwith observations. The real problem with testing Sver-drup theory, in light of what we now know about bar-otropic and baroclinic adjustment, is associated withthe assumed level of no motion. For an ocean with afree-slip flat bottom, Sverdrup balance should hold forthe integrated flows and pressures, as long as the in-tegral goes all the way to the bottom and barotropicadjustment has had time to occur (approximately a fewdays). If the integration extends only over the surfacelayers (upper 500 or 1000 m, say), however, then theintegrated quantities depend on both the barotropicand baroclinic components, and a quasi-steady theorywill apply only if the dominant baroclinic modes havealso reached equilibrium. In general for the annualcycle, there is no reason this should be true since baro-

ing the EASTROPAC expedition.

clinic adjustment even near the equator takes at leasta few months. Clearly what is needed is an understand-ing of baroclinic adjustment processes.

6.3.2 Baroclinic TheoriesThe discovery of the Equatorial Undercurrent in thePacific in 1952 (Cromwell, Montgomery, and Stroup,1954) triggered a great deal of equatorial modeling ac-tivity in the latter part of that decade. Almost all ofthese early models include baroclinic effects in a crudeway by assuming the surface layer is essentially de-coupled from the deep ocean below (Yoshida, 1959;Stommel, 1960; Charney, 1960). Another assumptioncommon to these models is that all fields except thepressure are assumed to be independent of x, the east-west coordinate; the zonal pressure gradient Op/Ox istaken to be a constant related to the zonal wind stressthat is driving the motion.

The simplest and most elegant of these models isthat of Stommel (1960). This model is the first suc-cessful extension of classical Ekman theory to theequator. Stommel's model equations balance the Cor-iolis force with vertical diffusion of momentum (theEkman balance) while retaining horizontal pressuregradients. It is the zonal pressure gradient which allowshim to avoid the equatorial singularity of previous Ek-man theory, and which provides a source of eastwardmomentum to drive the undercurrent. The wind forc-ing is put into the ocean as a surface stress, and a zero-stress condition is imposed at the bottom of the layer.The vertical structure of the zonal velocity at the equa-tor is parabolic, with surface flow in the direction ofthe wind and subsurface flow (undercurrent) in theopposite direction. In addition, the model develops ameridional circulation very similar to that hypothe-

I89Equatorial Currents

sized by Cromwell to account for the distribution oftracers in the equatorial Pacific (Cromwell, 1953). Fig-ure 6.5, by Stommel (1960), illustrates the circulationpattern developed by his model. There is surface di-vergence of fluid from the equator, subsurface conver-gence, and equatorial upwelling. A major drawback ofthis theory is that the response is too closely related tothe choice of eddy viscosity v. Let U and L representthe velocity and depth scales of the flow and T measurethe equatorial zonal wind stress. Let H be the depth ofthe layer and 8 be the meridional derivative of theCoriolis parameter. Then in the Stommel model

U HTUV

and L = 2gH_2 ·

It is not possible to select a value for v which simul-taneously sets a realistic magnitude as well as widthscale for the flow. In particular, if v is adjusted so thatthe current has a reasonable speed, then it is far toonarrow.

Charney's (1960) nonlinear model differs fundamen-tally from Stommel's in that he requires a no-slip bot-tom boundary condition. Because of this stringent con-dition, the linear model cannot produce any flowcounter to wind, and so it is clearly the presence ofnonlinearities that allows the model to generate anundercurrent. Chamey computed the zonal and verti-cal velocity only on the equator. Later, Chamey andSpiegel (1971) extended the model off the equator todetermine the flow field in a meridional section andalso obtained the same general pattern of meridionalcirculation as that proposed by Cromwell. They ex-plained the existence of an undercurrent in bothmodels in the following qualitative manner [first sug-gested by Fofonoff and Montgomery (1955)]. Fluid con-verging toward the equator conserves absolute vortic-ity. As a result, planetary vorticity is converted torelative vorticity, and this conversion provides an ad-ditional source of eastward momentum to drive the

Figure 6.5 Schematic three-dimensional diagram of the flowfield in the neighborhood of the equator, not showing thevertical component of velocity, which can in principle bedetermined from continuity. (After Stommel, 1960.)

undercurrent. These studies show that nonlinearitiesare likely to play an important role in equatorial dy-namics. On the other hand, the nonlinear solutions areeven more sensitive to the choice of v than Stommel'slinear one. For example, when v decreases from 17 to14 cm2 s- l, the speed of the Equatorial Undercurrentmore than doubles, and the e-folding width of the jetnarrows significantly.

Other workers subsequently considered similar layermodels and explored the importance of terms in theequations of motion that were ignored in the earlierstudies (Philander, 1973; Cane, 1979b). Despite theirsuccesses, the layer models have obvious limitations.The assumption of anx-independent flow field is ques-tionable, the decoupling of the lower layer is highlyartificial, and the solutions are extremely dependenton the choice of mixing coefficients. Finally, the ob-servations themselves suggest the most serious draw-back. Although an undercurrent has been observed inthe mixed layer (see for example Hisard, Merle, andVoituriez, 1970), the strongest eastward flow is almostalways found in the thermocline below the surfacemixed layer. Therefore, an undercurrent model thattreats the effects of stratification in a more realisticway is required. It took another decade for such a modelto be developed, and the development proceeded froman entirely different direction, namely, from attemptsto understand time-dependent processes in the equa-torial region.

Initial interest in equatorial waves was largely the-oretical, and grew out of attempts to extend the theoryof midlatitude gravity and Rossby waves to the equator.Longuet-Higgins (1964, 1965, 1968a) undertook a de-tailed investigation of planetary waves on a rotatingsphere (cf. chapters 10 and 11). At about the same time,Blandford (1966) and Matsuno (1966) both used equa-torial -plane models (i.e., the Coriolis parameter isapproximated by f = py to describe free baroclinicwaves. [Groves (1955) had earlier derived the same -plane equatorially trapped solutions as Blandford andMatsuno, but he was considering barotropic tides.] Allof these studies are linear and inviscid, and considerperturbations on a background state consisting of astably stratified ocean at rest. Normal modes for thevertical structure of the fields are derived just as Fjeld-stad (1933) originally did for internal waves. The eigen-values for the vertical separation problem are usuallypresented as equivalent depths h' for the resulting nor-mal modes. In general, for a finite depth ocean, thereis one barotropic mode for which the equivalent depthis nearly equal to the actual depth of the ocean, andthe corresponding eigenfunction describing the depthdependence of the horizontal velocities and pressureperturbation is nearly depth independent. There is alsoa denumerably infinite set of baroclinic equivalent

I9oA. Leetmaa, J. P. McCreary, Jr., and D. W. Moore

depths. The vertical structures of the baroclinic eigen-functions depend on the details of the background den-sity distribution. For each equivalent depth h', there isa corresponding phase speed c defined by c2 = gh'.

With this separation, the horizontal and time de-pendence of each vertical mode of the system can nowbe investigated independently of the z-dependence. Ifc is the phase speed for the mode in question, then freeoscillations at frequency co can exist in a latitudinalband, lY I YT. In the equatorial p-plane model, theturning latitude is given by

Yr = 2 )+ (6.2)

and is strongly dependent on co. For the first baroclinicmode, c is typically about 250 cm s- l. Then at the an-nual cycle, YT = 6250 km; at the 5-day period YT =

640 kmin, a much smaller trapping scale. [For a completediscussion of free equatorial trapped waves see Mooreand Philander (1977) and chapter 10.]

Moore (1968) investigated the effects of oceanicboundaries on free waves at frequencies correspondingto strong equatorial trapping (near-minimum YT for agiven value of c). He showed that a Kelvin wave atfrequency hitting an eastern boundary will generallyreflect some of its energy back in the form of equato-rially trapped Rossby waves, and the rest of the energypropagates poleward as coastally trapped Kelvin waves.These results were later extended to the case of anincoming Kelvin wave of step-function form by An-derson and Rowlands (1976a).

The first observational evidence-in Pacific sea-levelvariations-for the existence of strongly equatoriallytrapped baroclinic waves in the ocean was presentedby Wunsch and Gill (1976). Spectral peaks correspond-ing to periods in the range 2-7 days were explained interms of equatorially trapped inertial-gravity waveswith vanishing east-west group velocity. The variationin the strength of the spectral peaks from islands atdifferent latitudes was consistent with the expectedlatitudinal structure of the theoretical wave modes (seefigure 10.11). Additional observational evidence forequatorially trapped waves was provided by Harvey andPatzert (1976) from deep mooring data in the easternequatorial Pacific. Weisberg, Miller, Horigan, andKnauss (1980) and Weisberg, Horigan, and Colin (1979)did the same using Atlantic GATE data and later Gulfof Guinea observations.

An interesting property of the low-frequency large-scale baroclinic waves (nearly nondispersive Rossbywaves) is that their phase speed increases markedly themore trapped they are to the equator. The swiftestwave, the equatorial Kelvin wave, is also the moststrongly trapped. This property suggests that the forced

baroclinic response of the equatorial ocean need notremain locally confined to the forcing region, but canradiate swiftly away. That is to say, baroclinic effectsmay be remotely as well as locally forced.

In 1969, Lighthill published a seminal paper entitled"Dynamic Response of the Indian Ocean to the Onsetof the Southwest Monsoon." He was motivated by theidea that the Somali Current might be remotely forcedby winds in the interior of the Indian Ocean. He cou-pled the wind stress to the model ocean in a novel way,not as a surface condition, but rather as a body forceuniformly distributed throughout an upper mixedlayer. This approach avoids the details of the frictionalprocesses by which the stress actually enters the oceanand allows the use of the inviscid normal modes tostudy the oceanic response to variable wind forcing.The model ocean is forced by an impulsive wind-stressdistribution concentrated away from the coast in thecenter of the Indian Ocean. In addition to the locallyforced response, long-wavelength nondispersive Rossbywaves are generated at the edge of the forcing regionand propagate westward to the coast. They are reflectedthere as short-wavelength dispersive Rossby waves thatremain trapped to the coast. He interpreted the coastalresponse as the onset of the Somali Current.

One of the most prominent features of the equatorialoceans is the presence of a strong near-surface pycno-cline. Observations show that changes in the pycno-cline depth can be large and occur very rapidly. It issensible to model this motion as simply as possible,with either a one-and-a-half-layer model (a single uppermoving layer overlying a slightly denser inert layer) orwith a two-layer model; in both cases the layer inter-face plays the role of the pycnocline. Wind stress entersthe ocean as a body force in the surface layer, and sosuch models are analogous to the Lighthill model if itis limited to a single baroclinic mode. Not surprisingly,a large number of these models, both linear and non-linear, have been used in the past decade to investigatea variety of equatorial adjustment problems.

O'Brien and Hurlburt (1974) used a two-layer modelto study the interior response of the equatorial IndianOcean to change in zonal wind stress. The model pro-duces an eastward equatorial jet with many of the ob-served features documented by Wyrtki (1973a). Themeridional structure of the accelerating jet producedin the O'Brien and Hurlburt model is basically thesame as the structure of the surface flow given in Yosh-ida's (1959) undercurrent paper and has been called theYoshida jet. See Moore and Philander (1977) for a de-tailed description of the spin-up of the Yoshida jet fromrest for a single inviscid baroclinic mode.

The idea that the Somali Current might be remotelyforced. stimulated a number of additional studies. An-derson and Rowlands (1976b) used a one-and-a-half-

I9IEquatorial Currents

____

layer analytical model to investigate the relative impor-tance of local and remote forcing. They concluded thatlocal forcing is initially dominant but that remotelyforced effects will ultimately become important. Hurl-burt and Thompson (1976) used a two-layer modelforced by a basin-wide northward stress T to show thatnonlinear advective effects rapidly become importantin the developing boundary flow. Cox (1976) addressedthe same problem using a more sophisticated 12-levelnumerical model. His findings corroborate the conclu-sions of the simpler models.

Hickey (1975) and Wyrtki (1975b) suggested that ElNiiio occurs in conjunction with a relaxation of thesoutheast trades in the central and western EquatorialPacific. Hurlburt, Kindle, and O'Brien (1976) appliedsubstantially the same model as O'Brien and Hurlburt(1974) to simulate the onset of El Nifio. They spun-upthe model with a uniform westward wind for 50 days,and then turned off the wind. Major features of theresponse included an eastward-traveling Kelvin waveoriginating at the western boundary, westward-travel-ing nondispersive Rossby waves originating at the east-ern boundary, and poleward-traveling Kelvin wavesalong the eastern boundary. The thickening of thewarm layer near the eastern boundary in response tothe relaxation of the winds demonstrated the plausi-bility of Wyrtki's hypothesis. Although the model ofHurlburt, Kindle, and O'Brien was nonlinear, the re-sponse was completely dominated by linear dynamics.The only discernible nonlinear effect was the steep-ening front of the poleward-propagating coastal Kelvinwave.

McCreary (1976) used a one-and-a-half-layer linearmodel in a similar study of El Nifio. He followed theinitial response of the eastern ocean to various zonallyuniform distributions of wind stress. Important con-clusions are the following. Changes in the meridionalwind field cannot cause an El Nifio event. Changes inthe zonal wind field outside the equatorial band(roughly +5° of latitude) are not important in generat-ing El Nifio. Finally, model results suggest that themeridional profile of the wind field can significantlyaffect the resulting flow field. For example, the south-ward motion of the ITCZ can force southward cross-equatorial transport of water in the eastern Pacific. Itis interesting that in this model the deepening of thepycnocline in the eastern Pacific is initiated by theweakening of the local zonal winds, and is stopped bythe arrival of an equatorially trapped Kelvin wave fromthe western ocean.

McCreary (1977, 1978), realizing that the changes inthe Pacific wind field during E1l Nifio are not zonallyuniform, but rather are confined in the central andwestern ocean, extended the model of the 1976 studyso that a wind-stress patch of limited longitudinal ex-

tent could be imposed. Figure 6.6 shows the adjustmentof the model thermocline topography after a weakeningof the westward trade winds by an amount+0.5 dyn cm-2 . The dotted lines in the upper left panelof the figure delineate the region of weakened tradewinds; the wind-stress change is a maximum in thecentral portion and weakens markedly in the surround-ing areas. After 35 days, a downwelling signal rapidlyradiates from the region of the wind patch as a packetof equatorially trapped Kelvin waves and already theequatorial thermocline (and also sea level) begins totilt to generate a zonal pressure gradient that balancesthe wind there. In the region of strongest wind curl,the thermocline begins to move closer to the surface,and this upwelling signal propagates westward as apacket of Rossby waves. After 69 days, the packet ofKelvin waves has already reflected from, and spreadalong, the eastern boundary. As time passes, this down-welling signal propagates back into the ocean interioras a packet of Rossby waves, and more and more upper-layer water piles up in the eastern ocean. As shown inthe lower two panels, the source of the water is a broadarea of the western and central ocean where the ther-mocline is uplifted; in some regions the thermoclinerises over 65 m. Note that in this case it is the arrivalof the Kelvin wave that causes the initial deepening ofthe pycnocline in the eastern ocean. The figure alsofurther demonstrates the importance of knowing thehorizontal structure of the wind field; the rapid tiltingof the equatorial thermocline, and the form of the ex-traequatorial upwelling are a direct result of the par-ticular structure chosen here.

Moore et al. (1978) suggested that the equatorial up-welling in the eastern Atlantic and coastal upwellingin the Gulf of Guinea might be a remote response toan increase in the strength of the westward wind stressin the western Atlantic. The variation of Oplx in thewestern Atlantic reported by Katz et al. (1977) wasinterpreted as the response to such an increase.O'Brien, Adamec, and Moore (1978) and Adamec andO'Brien (1978) used the same basic adjustment modelas had been applied earlier to the Indian and PacificOceans to study Atlantic adjustment. The ocean ge-ometry is rectangular with a rectangular notch cut outof the northeast comer of the basin to simulate WestAfrica. The model calculations showed that an increasein strength of the westward wind stress in the westernAtlantic generates an equatorial-upwelling responsethat propagates eastward, leaving behind a thermoclinetilt to balance the stress. When it hits the coast, theupwelling signal propagates away from the equatoralong the boundary and travels westward along thecoast of the Gulf of Guinea.

The important role that equatorially trapped wavesplay in all these models has stimulated several studies

I92A. Leetmaa, J. P. McCreary, Jr., and D. W. Moore

_ .___ _____ ______

I I I I I I I I I I I10000 5000

Figure 6.6 Time development of the thermocline depthanomaly to a longitudinally confined zonal wind stress. Thedotted lines in the upper left panel indicate the region of the

of the interaction of the waves with the mean zonalcurrents. Hallock (1977) used a two-and-a-half-layermodel forced by meridional surface winds to investi-gate the Equatorial Undercurrent meanders observedduring GATE. A meridional stress " with a zonalwavelength of 2400 km is turned on gradually in a fewdays and then held steady. Part of the response is anequatorially trapped Yanai wave of about 16-day period.The characteristics of this Yanai wave were somewhat,but not drastically, modified by including mean surfacecurrents in the upper layer and a mean undercurrentin the second layer. Thus it was suggested that theGATE observations of Equatorial Undercurrent mean-ders might be explained in terms of passive advectionof the Equatorial Undercurrent by a wind-generatedYanai wave. McPhaden and Knox (1979) and Philander(1979) used one-and-a-half-layer models to study themodifications of other free waves in the presence ofvarious meridional profiles of zonal mean currents.McPhaden and Knox concentrate on the equatorial Kel-vin and inertial-gravity waves (including the Yanaiwave), and conclude that the zonal velocity associatedwith a given mode can be strongly modified by thebackground currents. Philander also considers equato-rial Rossby waves and suggests that these waves maybe influenced strongly by the presence of the EquatorialUndercurrent.

-2000

-000

1000Iafter 28days 2000

10000 5000

wind. The solid lines in each panel indicate the presence ofan eastern ocean boundary. Horizontal distances are in kilo-meters. (After McCreary, 1977.)

Philander (1976) used a two-and-a-half-layer modelto show that background zonal currents also allowunstable waves and predicted a possible instability ofthe surface currents in the tropical Pacific. The mostunstable waves which propagate westward have awavelength of about 1000 km and a period of approxi-mately 25 days. The satellite observations of Legeckis(1977b) seem consistent with the instability scales Phi-lander predicted. A later numerical study by Cox (1980)confirmed a suggestion of Philander's that oscillationsgenerated by such surface-current instabilities couldpropagate zonally for large distances while propagatingvertically into the deep ocean. The results indicate thatthe Harvey and Patzert (1976) observations in the east-ern Pacific near the sea floor could, in fact, be suchremote effects of surface-current instabilities generatedfarther to the west.

It is now apparent that simple layer models havebeen remarkably successful in reproducing many of theobvious features of time-dependent equatorial oceancirculation. These models are intrinsically limited,however, in their ability to describe the vertical struc-ture of the ocean, and recently theoreticians have be-gun to study more sophisticated models that allow forhigh vertical resolution. There are several reasons forthis interest. In 1975, Luyten and Swallow (1976) dis-covered high-vertical-wavenumber equatorially trap-ped multiple jets in the Indian Ocean, and in 1978similar structures were observed in the Pacific (C. Erik-

I93Equatorial Currents

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sen, personal communication). In addition to this ob-servational impetus, general theoretical questions arisein trying to understand in greater detail just how thewind stress enters the ocean. For example, how validis the assumption that the wind enters as a body forcedistributed over a surface mixed layer? Finally, thereis the perennial interest in understanding the dynamicsof the Equatorial Undercurrent.

In order to model the multiple jets, Wunsch (1977)considered an inviscid continuously stratified model,which he took to be horizontally unbounded and infi-nitely deep. (At the end of his study he also reportedeffects introduced by a western ocean boundary.) Sincethe model was inviscid, it was not possible to introducethe wind stress as a surface boundary condition. In-stead, Wunsch assumed that a thin wind-driven surfaceboundary layer pumped the deeper ocean with a surfacedistribution of vertical velocity. For convenience, hechose for the form of the distribution a westward-prop-agating sinusoidal wave. To specify the solution, herequired it to match this vertical velocity distributionat the ocean surface and also to exhibit upward phasepropagation everywhere in the upper ocean (a radiationcondition). Although the north-south scale of the im-posed surface w-field was broad, the significant re-sponse was strongly equatorially trapped and showedan oscillatory structure in the vertical, just as in theobservations.

In an effort to understand better how wind stressenters the equatorial ocean and to explore further thevertical structures that might be possible in stratifiedviscid equatorial oceans, Moore (unpublished) has stud-ied the simplest linear model that includes the effectsof continuous stratification and vertical mixing on anequatorial ,8-plane. The buoyancy frequency N is takenas constant, constant eddy coefficients for vertical mix-ing of heat K and momentum v are used, and, for con-venience, unit Prandtl number is assumed (v = K). Theocean is laterally unbounded and infinitely deep. Thesimplest problem to treat is the analog of the Yoshidajet, in which the system is driven by a uniform zonalwind stress r started impulsively at t = 0. The problemas posed has a natural or canonical scaling. This meansthat for suitable choices of velocity scale U, time scaleT, horizontal length scale L, and depth scale H, theresulting nondimensional equations contain no param-eters. The scales are

L = (vN2/i 3)1 2,

T = (2N2) - ' /5,(6.3)

H = (2N)t,

U = r(,Nv3 )- '5 .

Note that equations (6.3) are much less dependent onv than are equations (6.1), essentially because here thedepth scale is no longer an externally set constant!This weak dependency on v is a characteristic advan-tage that all stratified models have over their homo-geneous counterparts. For N = 2 x 10- 3

S- 1

, = 20cm2 s, and r = 1 dyn cm-2, the typical values are L =60 km, T = 8 days, H = 40 m, and U = 2 m s-. Figures6.7A-6.7C show (y,z)-profiles of the zonal velocity uat times t = 0.25, 1.0, and 5.0 in Moore's model (theequator is at the right). The ranges are 0 - y - 5 positiveto the left and 0 - z < 10 positive down. Right on theequator in this x -independent model, the zonal velocityis simply governed by downward diffusion of momen-tum: ut = vuzz. The contour plot at time t = 0.25 showsthat initially this balance is nearly true everywhere. Atlater times, the Coriolis effects have a distinct influ-ence on the solution. The equatorial jet is well de-veloped by t = 1. The solution serves to illustratetypical time and space scales of equatorial processes,as well as to point out their dependence on modelparameters. Moreover, the model clearly suggests thatthe diffusion of zonal momentum into the deep oceanmay play an important role in equatorial dynamics.However, in this x-independent and bottomless modelthe jet continues to intensify and deepen indefinitely.The only way to reach a steady state is to require anon-slip bottom on the ocean or to allow zonal pressuregradients, either by adding zonal structure to the windfield or by introducing boundary effects.

In the past 2 years, several fully three-dimensionaland continuously stratified ocean models have beenused to study wind-driven equatorial ocean circulation.The numerical models of Semtner and Holland (1980)and Philander and Pacanowski (1980a,b) are nonlinear.The analytical model of McCreary (1980) is linear; it canbe regarded as an extension of the Lighthill model thatallows the diffusion of heat and momentum into thedeeper ocean, and also as an extension of the Stommelmodel into a stratified ocean. All three modelsare remarkably successful in reproducing many of theobserved features of the Equatorial Undercurrent. Forexample, figure 6.8 [taken from McCreary (1980)]shows the flow field in the center of the ocean basin(10,000 km wide), where the zonal wind stress reachesa maximum (-0.5 dyncm-2 ). The model EquatorialUndercurrent is situated in the main thermocline be-neath a surface mixed layer (75 m). The width anddepth scales, as well as the speed, of the zonal flow arerealistic. In addition, the pattern of meridional circu-lation resembles quite well the classic pattern sug-gested by Cromwell (1953); note that there is a strongconvergence of fluid slightly above the core of theEquatorial Undercurrent, strong surface upwelling, andweaker downwelling below the core. The presence of

I94A. Leetmaa, J. P. McCreary, Jr., and D. W. Moore

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Figure 6.8 Vertical sections of zonal velocity (left panel) andmeridional circulation (right panel) at the center of theocean basin. The contour interval is 20 cms-'; dotted con-tours are -+10 cms - 1. Calibration arrows in the lower leftcomer of the right panel have amplitudes 0.005 cms - 1 and10 cm sl, respectively. (After McCreary, 1980.)

zonal baroclinic pressure gradients and the diffusion ofmomentum into the deep ocean are crucial for thedevelopment of this undercurrent. In fact, at the equa-tor the balance of terms is simply Px = (vuz)z. Just asin the x-independent model discussed in the precedingparagraph, stratification weakens considerably the de-pendence of the solution on v. It is this property thatallows a realistic undercurrent to be generated for awide range of choices of v. The success of the linearmodel suggests that nonlinearities are not essential formaintaining the Equatorial Undercurrent. They appar-ently act only to modify the linear dynamics, not todestroy it.

5.0 Z

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0

Figure 6.7 (y, z)-contour plots of zonal velocity u in x-inde-pendent stratified spin-up on an equatorial ,3-plane, includingthe effects of vertical mixing. (A) t = 0.25. Diffusion effectsare dominant. (B) t = 1.0. Equatorial jet starts to develop. (C)t = 5.0. Jet continues to deepen.

6.4 Discussion

Observations of the equatorial oceans during the past30 years have shown the existence of surprisinglystrong subsurface currents and greatly increased ourknowledge of the mean structure and time variabilityof the surface flows. Zonal currents, both surface andsubsurface, tend to occur as narrow jets severalhundred kilometers wide, several hundred meters deep,and thousands of kilometers long. The observationsalso suggest that many tropical ocean events are re-motely forced. A prime example is the phenomenon ofEl Nifio, where wind changes in the central and west-ern Pacific are associated with strong changes in thethermal structure of the eastern Pacific.

Perhaps because the signal-to-noise ratio is so large,theroeticians have had remarkable success in providingexplanations for many equatorial phenomena. All themodels suggest that stratification is an essential ingre-dient in equatorial dynamics. Width, depth, and timescales of model response are all intimately related to

I95Equatorial Currents

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the background buoyancy frequency distribution [e.g.,see equation (6.3)]. The presence of stratification alsoallows the existence of swiftly propagating equatoriallytrapped baroclinic waves. These waves have been usedto account for remotely forced events as well as themeandering of equatorial currents.

Additional experimental and theoretical work needsto be done. It is now known that the tropical oceanresponds readily and coherently to large-scale low-fre-quency changes in the wind field. Moreover, the natureof the response depends critically on the spatial distri-bution of the wind field. It is important, then, to mon-itor the detailed structure of the wind field on theseasonal, annual, and interannual time scales. For thefirst time, such observations may be practical due torapidly improving satellite technology. Long time se-ries of the variability of the tropical ocean flow fieldmust also be obtained. Equatorial observations madein 1979 as part of the Global Weather Experimentshould add substantial new knowledge about the cir-culation in all three equatorial oceans. However, theduration of this experiment is too short; it will provideat most a single realization of the annual cycle.

A major advance in our understanding of equatorialdynamics occurred when simple layer models began tobe studied. These models were successful because theirsolutions could be easily and convincingly comparedwith observations; the layer interface is interpretableas the motion of the pycnocline. The recent use ofequatorial models with high vertical resolution sug-gests that other advances may soon be forthcoming.Such models can produce a much more detailed pictureof the flow field, and so can be quantitatively comparedto a greater degree with the observations. Obviousproblems to which these models should be applied in-clude the existence of the thermostad and the associ-ated subsurface countercurrents and the presence ofmultiple jet structures at the equator. In addition, evenmore sophisticated models that include realistic sur-face mixed layers need to be developed.

I96A. Leetmaa, J. P. McCreary, Jr., and D. W. Moore

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