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Deep- Research I 52 (2005) 179–188 www.elsevier.com/locate/dsr

A note on the validity ofthe Sverdrup balance in the Atlantic North Equatorial Countercurrent

Ariane Verdya,Ã, Markus Jochumb

aMIT / WHOI Joint Program in , Massachusetts Institute of Technology, Cambridge MA 02139, USA bDepartment of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge MA 02139, USA

Received 9 September 2003; received in revised form 10 May 2004; accepted 18 May 2004

Abstract

An general circulation model ofthe tropical is used to study the vertically integrated vorticity equation for the annual mean flow in the Atlantic North Equatorial Countercurrent (NECC). It is found that the nonlinear terms play an important role in the vorticity budget, in the western part ofthe basin. Sverdrup balance does not hold in the region ofthe North retroflection, where advection ofrelative vorticity by the mean flow and by the eddies is important. In the eastern part ofthe basin, these nonlinearities are negligible and the flow appears to be in Sverdrup balance. In the model, the cut-off location occurs at 32W: The results suggest that in the western part ofthe basin, observations relying on hydrographic data neglect two important contributions to the vorticity balance: advection ofplanetary vorticity by the deep meridional flow and advection ofrelative vorticity. r 2004 Elsevier Ltd. All rights reserved.

Keywords: Equatorial oceanography; Tropical Atlantic; Sverdrup balance; Vorticity

1. Introduction 1997) and it is a major path for the warm water return flow ofthe global meridional overturning The Atlantic North Equatorial Countercurrent circulation (Fratantoni et al., 2000; Jochum and (NECC) is one ofthe major Atlantic currents and Malanotte-Rizzoli, 2001). Therefore, understand- a core component ofthe climate system. Its ing the NECC dynamics is a prerequisite for the position coincides with the location ofthe analysis ofglobal and tropical Atlantic climate. Atlantic’s warmest waters (Enfield and Mayer, Sverdrup (1947) explained the Pacific NECC as the result ofa balance between vortex stretching induced by the wind and advection ofplanetary ÃCorresponding author. Tel.: +1 617 253 9345; fax: +1 617 253 6208. vorticity. His original paper is still one of E-mail address: [email protected] (A. Verdy). the pillars ofphysical oceanography and the

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‘‘Sverdrup balance’’ is used to analyze ocean American and African coastlines and a constant circulation almost everywhere outside the equa- depth of3000 m. The flat bottom is not a realistic torial regions and the western boundary currents. representation ofthe Atlantic seafloor, especially Most recently, Yu et al. (2000) used the Sverdrup in the region ofthe mid-Atlantic ridge; never- balance to analyze the Pacific NECC. theless, due to the strong tropical stratification, the In spite ofthe successes ofthe Sverdrup balance, impact oftopography on surfacecirculation is it has been difficult to demonstrate its validity negligible (Philander, 1990). This argument is experimentally (Leetmaa et al., 1981; Wunsch and supported by the success ofreduced gravity Roemmich, 1985; Kessler et al., 2003). More models in modelling tropical ocean circulation specifically, a recent study by Jochum and (Murtugudde et al., 1996). The model was spun up Malanotte-Rizzoli (2003) shows that the Atlantic for 20 years and the following 4 years are analyzed NECC is barotropically unstable, implying that in this study. The short spin up time is justified by the advection ofrelative vorticity is larger than the the fast adjustment of the tropical circulation (Liu advection ofplanetary vorticity ( Pedlosky, 1979). and Philander, 1995). This violates the major assumption ofthe Sverdr- In the region considered here (0–12N), the 1 up balance, that advection ofrelative vorticity is resolution is 4 in latitude, and in longitude it 1 negligible. ranges from 4 near the coast ofBrazil to 1 The vorticity balance ofthe Atlantic NECC has towards the eastern part ofthe basin. There are 30 been analyzed by Garzoli and Katz (1983) between vertical layers with a 10 m resolution in the top 46W and 10W: From historical wind and 100 m. The model is forced by climatological wind hydrographic data they concluded that the NECC stress from Hellerman and Rosenstein (1983). is in Sverdrup balance in the interior ofthe basin, is kept constant at a value of35 psu; from 42Wto22W: Outside this range the viscosity and diffusivity vary between 200 and vorticity budget could not be closed. Garzoli and 2000 m2=s; depending on the spatial resolution. Katz (1983) suspected that nonlinearities and The configuration ofthe model is described in lateral diffusion might be important near the more detail in Jochum and Malanotte-Rizzoli western and eastern boundaries. (2003). The present study is a continuation oftheir Comparisons ofthe circulation in the model work. Since the observational data base in the with the observed circulation in the tropical Atlantic is still not sufficient to determine the Atlantic (Jochum and Malanotte-Rizzoli, 2003; complete vorticity balance in the NECC, we used a Jochum et al., 2004) suggest that, although it is numerical model ofthe tropical Atlantic ocean idealized, the model reproduces the current instead. After a brief model description in Section strength and mesoscale variability observed in 2, the vorticity balance is analyzed in Section 3. the western and central tropical Atlantic. The Section 4 summarizes the results and discusses how simulated zonal velocity at 38W in April is shown the nonlinear dynamics affect the validity of the in Fig. 1. One can see the NECC centered at 6N; Sverdrup balance and influence our understanding the at 3N and the oftropical ocean circulation. Equatorial Undercurrent (EUC) just north ofthe equator. In Fig. 2, the model zonal transport at 38Wis 2. Model description compared with observations from Katz (1993). The transport is evaluated in the top 500 m, The (version MOM2b) between 3N and 9N: Katz (1993) calculated with simplified geometry is used to study the the geostrophic transport, relative to the 500-db circulation in the tropical Atlantic, specifically the level, from estimates of dynamic height derived North Brazil Current/North Equatorial Counter- from inverted echo sounder measurements of current (NBC/NECC) retroflection region. The acoustic travel time. For consistency the model basin extends from 25Sto30N; with idealized transport is also expressed relative to the 500-db ARTICLE IN PRESS

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Fig. 1. The zonal velocity across 38W in April (in cm/s). The eastward NECC can be seen at 6N; the westward South Equatorial Current at 3N; the EUC just north ofthe equator, and the westward Ekman flow everywhere in the upper 20 m. level, although it is not significantly different when 3. Vorticity balance expressed relative to the bottom. The model overestimates by approximately 5 Sv, but captures 3.1. Vertically integrated vorticity equation the seasonal cycle ofthe zonal transport, with maximum transport during the fall at around The vorticity equation is derived in Pedlosky 30 Sv and minimum transport during spring. (1979); here, we merely state its final form The geostrophic transport is eastward throughout Z Z the year, but weakened from February to May. ð~u ÁrÞz dz þ ð~u0 ÁrÞz0 dz þ bV During that period the northeast trade winds Z 1 curlz ~t drive a westward surface flow, which counters ¼ curlz F~dz þ ; ð1Þ and overwhelms the geostrophic flow, causing r0 r0 the reversal ofthe NECC; the rest ofthe year, the where the primed quantities are the deviations Ekman flow is eastward and adds to the from a 4-year mean. V represents meridional geostrophic flow (Richardson et al., 1992). transport, z is the relative vorticity, curlz is the This compensation between the geostrophic vertical component ofthe curl operator; ~t is the NECC and Ekman transports can be seen in surface , r0 is the reference density of Fig. 1. , and F~ is the horizontal friction, para- Interestingly, the simulated transport exhibits 2 metrized as Ahrh~u: The steady, linear and non- interannual variability, in spite ofthe climatologi- viscous approximation to Eq. (1), assuming a flat cal wind forcing. The year to year variation in the bottom and a rigid lid, yields the familiar Sverdrup maximum transport is approximately 5 Sv in the balance, in which case the vorticity input by the model and 7 Sv in the observations (Katz, 1993). wind is compensated by the meridional advection This implies that a substantial part ofthe observed ofplanetary vorticity interannual variability could be explained by curl ~t rather than by changes in the bV ¼ z : (2) wind field. r0 ARTICLE IN PRESS

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Fig. 2. Monthly averages ofzonal geostrophic transport between 3 N and 9N in the upper 500 m at 38W (in Sv), for the model (top) and the observations (bottom, reproduced from Katz, 1993). Longer ticks on the x-axis mark the beginning ofthe calendar year.

However, at times the NECC is nonlinear and vorticity budget, which was not possible with the turbulent, and one might wonder whether it is observations of Garzoli and Katz (1983). reasonable to neglect the advection ofrelative vorticity in that region. A snapshot ofthe present 3.2. Model results model (Fig. 3) illustrates that, at a given time, it is not obvious how to establish the position ofthe The position ofthe core ofthe NECC shifts mean current. The NECC appears as an accumu- between 4:5N (summer) and 8N (winter; see Fig. lation ofeddies. Here, we set out to understand 4a), as a result ofthe migration ofthe Inter- and quantify the nonlinear contributions to the Tropical Convergence Zone (Garzoli and Richard- ARTICLE IN PRESS

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Fig. 3. Snapshot ofthe velocity in the tropical Atlantic at 100 m depth. The NECC appears as an accumulation ofeddies. son, 1989). To capture the NECC throughout the negative due to a flow from the NECC to the year, we analyze the vorticity equation between EUC, in the western part ofthe basin below the 4N and 10N: The frictional western boundary . In those regions the nonlinearities layer, west of45–50 W; is excluded. Also, the neglected in the Sverdrup balance must be eastern part ofthe current, flowing in the Gulfof considered to close the vorticity budget. Guinea, is not considered since the dynamics in Nonlinear advective terms account almost that region are made more complex by the entirely for the departures from Sverdrup balance, presence ofthe zonal boundary. as can be seen in Fig. 5, which shows the terms of The wind stress curl is positive in most ofthe Eq. (1) as a function of longitude. Friction is region ofthe NECC; thus Sverdrup’s theory negligible everywhere except close to the western predicts northward transport in the interior of boundary. The vorticity equation is balanced the gyre. This prediction is tested against the withinqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the total uncertainty ofthe mean values simulated fields by comparing the two terms ofEq. P ( 1 ðx xÞ2 where N is the number ofdata (2). Fig. 4b shows the model’s meridional advec- N2 tion ofplanetary vorticity and the vortex stretch- points for the variable x). ing induced by the wind stress curl, zonally In the western part ofthe basin, the dominant averaged between 45W and 20W: This region balance is between advection ofplanetary vorticity excludes the NBC. There is a good agreement with and advection ofrelative vorticity (by the mean Sverdrup’s theory north of10 N; while in the flow and by the eddies). The contributions to the region ofthe NECC (4–10 N), the advection of nonlinear advection are zonal advection ofrelative @ planetary vorticity does not balance the input of vorticity by the mean flow (u @x z), meridional vorticity by the winds. In the region ofthe NECC advection ofrelative vorticity by the mean flow @ the magnitude ofthe meridional flow appears to be (v @y z), zonal advection ofrelative vorticity by the 0 @ 0 larger than what can be accounted for by the wind eddies (u @x z ) and meridional advection ofrelative 0 @ 0 stress curl. Between 5 Nand10N; there is vorticity by the eddies (v @y z ). The four compo- northward transport associated with the tropical nents are examined separately in order to assess gyre. South of5 N; the meridional transport is their relative importance and spatial distribution. ARTICLE IN PRESS

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(a)

(b)

Fig. 4. (a) Annual mean zonal velocity at 30W; illustrating the mean position ofthe core ofthe NECC. Contours show the southernmost and northernmost latitudes ofthe NECC core, occurring in the summer (dotted line) and winter (dash-dot line). (b) Both terms ofthe Sverdrup balance, averaged over the interior ofthe basin (45–20 W): input ofvorticity by the winds (solid line) and meridional advection ofplanetary vorticity (dashed line).

Near the western boundary, the mean meridional the NBC, and the interior ofthe gyre. Those flow is large and it is the northward advection of regions are aligned with the coastline rather than @v negative relative vorticity (@x o0) by the mean flow meridionally. We find that advection of which compensates for the northward advection of vorticity is opposed to the mean advection in the positive planetary vorticity. In the NBC/NECC western as well as where the retroflection, the zonal mean advection ofrelative NBC retroflects, but that these two types vorticity is the important nonlinear term. Just east ofadvection are the same direction in the ofthe retroflection, the eddy field is strong and interior ofthe gyre. Between 44 W and 32W; zonal eddy advection becomes important. zonal mean advection is the main nonlinear term Fig. 6 shows the spatial distribution ofthe in the region 4–7N; whereas meridional mean advection terms. They are plotted separately advection and meridional eddy advection dom- between 4N and 7N; and between 7Nand inate in the region 7–10N: East of32 W; non- 10N; in order to highlight the different regions of linear terms are negligible and the flow is in the western boundary current, the retroflection of Sverdrup balance. ARTICLE IN PRESS

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Fig. 5. Input ofvorticity by the winds (black line) and meridional advection ofplanetary vorticity (green line), and nonlinear advection terms (red line) averaged between 4N and 10N: The blue line indicates the residual, which is mainly due to the uncertainty ofthe mean fields. The frictional term is significant only very near the western boundary and is not shown on this plot.

(a)

(b)

Fig. 6. Nonlinear advection terms (a) averaged between 7N and 10N; (b) averaged between 4N and 7N: Red line: total advection; green line: advection ofmean relative vorticity by the mean flow; blue line: advection ofeddy relative vorticity by the eddies (in 1010 m=s2). The eastern part ofthe basin, where nonlinearities are negligible, is not shown.

3.3. Comparison with observations that the NECC, between 3N and 9N; was in Sverdrup balance in the interior ofthe basin (from Our results differ from those of Garzoli and 42Wto22W). The difference lies in the extent of Katz (1983), who concluded based on observations the region in which Sverdrup balance does not ARTICLE IN PRESS

186 A. Verdy, M. Jochum / Deep-Sea Research I 52 (2005) 179–188 hold: west of42 WinGarzoli and Katz (1983), below the . In the observations as but west of32 W in the present model. There are well as in our model, the seasonal thermocline several possible reasons for this difference. The has a mean depth ofapproximately 100 m. In our first and obvious one is that the model is not a model the transports below 100 m, although perfect representation of the ocean. Mainly smaller than the surface values, are not negligible; because ofthe idealized coastlines, but maybe also in the western part ofthe basin, the deep because ofthe variable grid spacing in the zonal meridional transports can contribute up to 50% direction, there is some uncertainty on the location to the total meridional transport. Thus, due where Sverdrup balance breaks down. to observational constraints Garzoli and Katz Other possible causes ofdiscrepancy lie in the (1983) could not account for two contributions resolution and availability ofobservational data- to the vorticity equation: the nonlinear advection sets. Firstly, using historical hydrographic ofrelative vorticity, and the deep meridional data leads to smoothing ofspatial gradients, due advection ofplanetary vorticity. In our model, to the coarse resolution ofthe data. Advective the deep meridional advection and the nonlinea- nonlinear terms will therefore be underestimated. rities have opposite signs below the thermocline Secondly, since velocity fields were not available (Fig. 7). The partial cancellation ofthese from the observational study, the vorticity equa- two contributions could explain why Garzoli and tion had to be written in terms ofthe seasonal Katz (1983), but not the present authors, found 1 thermocline depth, for a 1 2 layer ocean. The the flow between 42 W and 32 Wtobein implicit assumption is that the ocean is at rest Sverdrup balance.

(a) (b)

Fig. 7. Meridional advection ofplanetary vorticity (solid line) and nonlinear advection (dashed line) in the geostrophic interior (below the Ekman layer). Left panel is at 35W=7N; where Sverdrup balance does not hold; right panel at 25W=7N; where the Sverdrup balance is satisfied. The thermocline is about 100 m deep. In both cases the nonlinear terms and the transport below the thermocline have opposite signs, although their magnitude is less where the Sverdrup balance appears to be valid. ARTICLE IN PRESS

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4. Discussion (Cane et al., 1986) supported this assumption. The present results suggest that, at least in the tropical A high resolution model ofthe tropical Atlantic Atlantic, nonlinear dynamics may need to be is used to investigate the vorticity balance ofthe accounted for to understand the ocean circulation. Atlantic NECC. The present study focuses on the Another interesting result is that the eddy advec- nonlinear dynamics, which were not resolved in tion ofrelative vorticity is a significant contributor the observational study of Garzoli and Katz to the vorticity balance almost everywhere west of (1983). In the numerical model used here, it is 32W: This not only makes it difficult to develop a found that nonlinear advection of relative vorti- theoretical framework for the NECC, but is also a city, by the mean flow and by the eddies, is needed challenge to any observational study. to close the vorticity budget in the western part of The present results have implications for the the basin. Since the model flow fields are similar to study ofclimate as well. The NECC distributes the the observations, this result suggests that the warmest water ofthe Atlantic ocean, which in turn Sverdrup balance is not valid in the western part determines the strength and location oftropical ofthe real NECC either. The model, ofcourse, precipitation (Lindzen and Nigam, 1987). There- cannot predict exactly where the Sverdrup balance fore, an understanding of the heat transport by the breaks down, but our results strongly suggest that NECC is necessary to predict interannual climate it is invalid in a larger area than previously changes in the tropical Atlantic. Foltz et al. (2003) thought. To determine the exact location it will showed with PIRATA data that mer- be essential to get more observations, especially idional advection ofheat is a significant part ofthe between 44W and 32W: An analysis ofthe heat budget at 8N/38W; here it is shown that this vorticity balance using more recent datasets will meridional advection may depend not on local give valuable information regarding the extent of wind, but rather on the difficult to determine the area within which the Sverdrup balance holds. nonlinear processes. There are several other factors that could contribute to departures from the Sverdrup balance which have not been addressed here. One Acknowledgements ofthem is the interannual variability ofthe winds; by relying on climatological forcing we filter out The authors acknowledge the support ofPaola extreme years during which the Sverdrup balance Malanotte-Rizzoli and John Marshall. They are might not hold. Another factor is the spatial grateful to Silvia Garzoli and one anonymous resolution ofthe wind observations, which leads to reviewer for comments that helped to improve the a smoothing out ofstrong gradients. For the manuscript. This research was funded by NASA Pacific, Kessler et al. (2003) found that the use of Grant NAG5-7194 and NOAA Grant wind fields based on QuickScat has a profound NA16GP1576 at MIT. The computations were impact on the vorticity balance since it better performed at the NCAR facilities in Colorado and resolves the sharp gradients in the wind field. the results were analyzed with Ferret software. Therefore the validity of the Sverdrup balance in the eastern basin could still be challenged. References In conclusion, our results suggest that the nonlinear dynamics may dominate the flow not Cane, M.A., Dolan, S.C., Zebiak, S.E., 1986. Experimental only near the western boundary, but also in large forecasts of the 1982/83 El Nin˜o. Nature 321, 827–832. parts ofthe interior ofthe tropical Atlantic. This Enfield, D.B., Mayer, D.A., 1997. Tropical Atlantic SST has implications for our general understanding of variability and its relation to ENSO. Journal ofGeophysical the tropical ocean circulation. It is commonly Research 102, 929–945. Foltz, G.R., Grodsky, S.A., Carton, J.A., McPhaden, M.J., assumed that the tropical are governed by 2003. Seasonal mixed layer heat budget ofthe tropical linear dynamics, partly because the early successes Atlantic ocean. Journal ofGeophysical Research 108, 3146, in El Nin˜o forecasting with linear ocean models doi: 10.1029/2002 JC 001584. ARTICLE IN PRESS

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