ARTICLE IN PRESS Deep-Sea 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 Oceanography, 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 ocean general circulation model ofthe tropical Atlantic Ocean 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 Brazil Current 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 0967-0637/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.dsr.2004.05.014 ARTICLE IN PRESS 180 A. Verdy, M. Jochum / Deep-Sea Research I 52 (2005) 179–188 ‘‘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, Salinity 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 South Equatorial Current 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 Princeton Ocean Model (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 A. Verdy, M. Jochum / Deep-Sea Research I 52 (2005) 179–188 181 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 wind stress, r0 is the reference density of Fig. 1. seawater, 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 ocean dynamics rather than by changes in the bV ¼ z : (2) wind field. r0 ARTICLE IN PRESS 182 A. Verdy, M. Jochum / Deep-Sea Research I 52 (2005) 179–188 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.