The Atlantic Subtropical Front/Current Systems of Azores and St. Helena

Home , Azores Current, Brazil Current, Caribbean Current, Labrador Current, South Atlantic Current

VOLUME 37 JOURNAL OF PHYSICAL OCEANOGRAPHY NOVEMBER 2007

MANUELA F. JULIANO AND MÁRIO L. G. R. ALVES Laboratory of Marine Environment and Technology, University of the Azores, Praia da Vitória, Azores, Portugal

(Manuscript received 28 September 2004, in final form 9 January 2007)

ABSTRACT

A large-scale climatic ocean circulation model was used to study the Atlantic Ocean circulation. This inverse model is an extension of the ␤-spiral formulation presented in papers by Stommel and Schott with a more complete version of the vorticity equation, including relative vorticity in addition to planetary vorticity. Also, a more complete database for hydrological measurements in the Atlantic Ocean was used, including not only the National Oceanographic Data Center database but also World Ocean Circulation Experiment data and cruises near the Azores, Angola, and Guinea-Bissau. A detailed analysis of the Northern Hemisphere Azores Current and Front shows that this new database and the model results were able to capture all major features reported previously. In the Southern Hemisphere, the authors have identified fully and described the subtropical front that is the counterpart to the Azores Current, which they call the St. Helena Current and Front. Both current systems of both hemispheres have similar intensities, depth penetration, volume transports, and zonal flow. Both have associated subsurface adjacent countercurrent flows, and their main cores flow at similar latitudes (ϳ34°N for the Azores Current and 34°S for the St. Helena Current). It is argued that both current systems and associated fronts are the poleward 18°C Mode Water discontinuities of the two Atlantic subtropical gyres and that both originate at the corresponding hemisphere western boundary current systems from which they penetrate into the open ocean interior. Thus, both currents should have a similar forcing source, and their origin should not be linked to any geographical peculiarities.

1. Introduction A large anticyclonic gyre is found in the subtropical The atmospheric and oceanic circulations each show region of both hemispheres. In the Atlantic Ocean the a significant meridional symmetry in both hemispheres subtropical gyre of the Northern Hemisphere is delim- of the globe. In the ocean this symmetry can be noted ited to the south by the North Equatorial Current, to through the existence of western boundary currents, the west by the Caribbean Sea, the “Loop” Current, the eastern boundary currents, and open-ocean systems in Florida Current, and the Gulf Stream, to the north by both hemispheres. Despite these similarities, there are the North Atlantic Current, and to the east by eastern also a few differences, due either to continental geog- boundary current system. The Southern Hemisphere raphy peculiarities like the coastline tilting differences subtropical gyre is delimited by the South Equatorial between the Gulf Stream and the Brazil Current zones Current, the Brazil Current, the South Atlantic Current (see, e.g., Da Silveira et al. 1999) or to the existence of and Subantarctic Front (SAF), and the Benguela Cur- the interhemispheric meridional overturning circula- rent. The North Atlantic subtropical gyre is zonally tion that contributes to larger transports in the Gulf crossed by the Azores Current, which appears to be the Stream than in the Brazil Current. In the Southern poleward boundary of the 18°C Subtropical Mode Wa- Hemisphere, the absence of geographic barriers gives ter (Alves and Colin de Verdière 1999; Jia 2000). In the rise to the Antarctic Circumpolar Current, which has South Atlantic Ocean, previous studies (Gordon et al. no Northern Hemisphere counterpart. 1992; Tsuchiya et al. 1994; Belkin 1994; Belkin and Gor- don 1996; Provost et al. 1999) identified a subtropical zonal feature but did not note its similarity and corre- Corresponding author address: Manuela F. Juliano, LAMTec- spondence to the Azores Current in the North Atlantic. Laboratory of Marine Environment and Technology, University of the Azores, Apartado 64, Edifícios da Marina, 9760-412 Praia Therefore there had appeared to be an asymmetry be- da Vitória, Azores, Portugal. tween the North and South Atlantic gyres that could E-mail: [email protected] not be explained by asymmetry in atmospheric circula-

DOI: 10.1175/2007JPO3150.1

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JPO3121 2574 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 37 tion, because both hemispheres are dominated by anti- dressed, and the Jia (2000) arguments are revisited. In cyclonic zones: the Azores anticyclone in the Northern section 5, some conclusions are presented. Hemisphere and the St. Helena anticyclone in the Southern Hemisphere. To explain the apparent asym- 2. Data metry, Thompson (1971) suggested a combined effect of the Coriolis parameter and the gradient of topogra- For our Atlantic Ocean climatological description phy as being mainly responsible for the absence or (80°S–80°N, 100°W–35°E), we have used hydrological weakening of these zonal eastward currents in the data (temperature T and salinity S) as a function of Southern Hemisphere. We note also that even the well- pressure, longitude, latitude, and time that were ob- observed Azores Front/Current system has been poorly tained through historical databases: NODC, Global reproduced by general circulation numerical models, Temperature Salinity Profile Project (GTSPP), and possibly because of the weakness of the meridional WOCE. To these databases we have also added data density gradient in the models (Jia 2000). Also, the nec- from oceanographic cruises carried out in the region of essary condition for the existence of baroclinic instabil- the Azores,1 Angola,2 and Guinea-Bissau.3 The result- ity, one of the primary mechanisms now known to be ing database covered the period from 1940 to 1999. The responsible for the major variability of this system entire dataset was submitted to procedure for quality (Alves 1996; Beckmann et al. 1994a), is not verified in and validation control (the same as described in the these general circulation models, even when horizontal World Ocean Database 1998; Conkright et al. 1999), resolution is increased (Beckmann et al. 1994b). followed by objective interpolation using an algorithm, The upgrade of historical National Oceanographic described by Papoulis (1991), with a correlation radius Data Center (NODC) databases with data of higher of 500 km (Alves et al. 1994; Juliano 2003). In this way, resolution and quality [e.g., World Ocean Circulation optimized fields of temperature and salinity were ob- Experiment (WOCE)] for the South Atlantic and the tained, evenly distributed in five three-dimensional ma- implementation of an innovative method for large-scale trices for the Atlantic Ocean—one for each season and circulation determination now permits a much more one for the annual average. For the seasonal time complete description of the counterpart of the Azores blocks, the following aggregation was used: trimester 1 Current in the Southern Hemisphere. We have given it consisted of January–March; trimester 2 covered April– the name St. Helena Current. This name was chosen by June; trimester 3 was for July–September; and trimester analogy with the Azores Current because of the prox- 4 consisted of October–December. All of these matri- imity to St. Helena Island and because the atmospheric ces have 89 vertical levels unevenly distributed between 5 and 6000 dbar, as listed in Table 1, with a horizontal St. Helena anticyclone in the Southern Hemisphere is resolution of 0.5° ϫ 0.5° (latitude ϫ longitude) covering the counterpart of the northern Azores anticyclone. the Atlantic Ocean. This current has also been called the North Subtropical As an example of this procedure, Fig. 1 shows the Front (Belkin 1994; Belkin and Gordon 1996; Provost position of each validated data point at the surface and et al. 1999), the Brazil Current Front (Tsuchiya et al. for the annual average of the horizontal distributions of 1994), and the Benguela/South Atlantic Front (Gordon temperature and salinity. It is clear that there is much et al. 1992). more data for the Northern Hemisphere than for the The St. Helena Current appears to be a zonal cur- Southern Hemisphere and that, closer to the shore, the rent, flowing eastward with horizontal and vertical structure similar to the Azores Current. Ours appears to be a complete description of it and the first to rec- 1 Circulaça˜ o Oceaˆ nica e Dinaˆ mica Frontal na Regia˜ o dos ognize its similarity with the Azores Current and Front. Açores (CODFRA) project (JNICT-PMCT/C/MAR/941/90); The Azores and St. Helena Current/Front systems will Frente/Corrente dos Açores (FCA) cruises and the Frontogeńese both be described and compared herein. e Instabilidade Baroclıńica na Regiaõ dos Açores (FIBRA) A brief description of the data used is given in section project (STRIDE-STRDB/C/MAR/230/92), Simulaçaõ Nume´rica da Variabilidade e Clima da Frente–Corrente dos Açores 2, and in section 3 the large-scale ocean circulation (CVFCA) project (Praxis/3/3.2/EMG/1956/95) and Canary Is- model used is briefly described. In section 4 a compari- lands Azores Gibraltar Observations (CANIGO) project (MAST son is made between the well-known Azores Current/ III-MAS3-CT96–0060). 2 Front system and that of the less well known “St. Hel- Instituto de Investigaçaõ das Pescas e do Mar (IPIMAR) Re- port, cruise N/E “Capricórnio,” in Angola, October–December ena Current.” We emphasize similarities between the 1995 (in Portuguese). currents and note some differences. The cause for ex- 3 IPIMAR Report, cruise N/E “Capricórnio,” in Guinea- istence of these current/front systems is briefly ad- Bissau, May–June 1995 (in Portuguese).

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TABLE 1. Standard levels and depths (dbar).

Level Depth Level Depth Level Depth Level Depth Level Depth 1 5 19 95 37 270 55 750 73 2600 2 10 20 100 38 280 56 800 74 2800 3 15 21 110 39 290 57 850 75 3000 4 20 22 120 40 300 58 900 76 3200 5 25 23 130 41 320 59 950 77 3400 6 30 24 140 42 340 60 1000 78 3600 7 35 25 150 43 360 61 1100 79 3800 8 40 26 160 44 380 62 1200 80 4000 9 45 27 170 45 400 63 1300 81 4200 10 50 28 180 46 420 64 1400 82 4400 11 55 29 190 47 440 65 1500 83 4600 12 60 30 200 48 460 66 1600 84 4800 13 65 31 210 49 480 67 1700 85 5000 14 70 32 220 50 500 68 1800 86 5250 15 75 33 230 51 550 69 1900 87 5500 16 80 34 240 52 600 70 2000 88 5750 17 85 35 250 53 650 71 2200 89 6000 18 90 36 260 54 700 72 2400

sampling density increases. In the analysis of the sea- 3. The ocean circulation model sonal distribution (not represented), there is a clear a. Introduction increase in the sampling density during the summer months for each of the hemispheres. In the Northern There have been countless efforts to determine the Hemisphere the data coverage has very high density, general oceanic circulation based on the momentum even in the middle of the ocean, whereas in the South- equations following approaches valid for the large- ern Hemisphere there are fewer data—in particular, in the interior of the sub-Antarctic areas. After perform- ing objective horizontal mapping of temperature and salinity fields, one can also obtain the associated mean- square error (MSE) estimate. Figure 2 shows the horizontal MSE distribution associated with both the annual average of temperature and salinity at a depth of 5 dbar. It is clear that the in situ temperature MSE is lower than 0.05 everywhere, except in a small spot in the Southern Ocean. Salinity MSE is greater than that of temperature, but its largest values, above 0.05, occur essentially in the same southern Atlantic interior area as for the temperature MSE maximum. Figure 3 again shows the same MSE fields, but through a meridional cross section of the Atlantic, located at 30°W, and for the annual ensemble. The largest MSE is found to be smaller than 0.15, both for the temperature and salinity and, close to the bottom, only in certain spot areas, where sampling is difficult. Although the Northern Hemisphere appears to be the best sampled, there is nonetheless enough data in the South Atlantic to pro- ceed with a circulation calculation for the entire area. Once the five T and S time average matrices, from surface to bottom and for the entire Atlantic, were obtained, the computation of potential density was per- FIG. 1. Geographical locations of validated temperature and formed. salinity data at 5 dbar and for the annual ensemble.

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FIG. 2. Surface horizontal distribution (at 5 dbar) of the MSE associated with the (left) temperature and (right) salinity fields and for the annual ensemble. scale, beginning with in situ measurements of the hy- eral, the more complete the data sample is as to space drological field (Veronis 1987; Wunsch 1996). The most and time, the better the ocean circulation will be de- significant knowledge of large-scale ocean circulation duced. has been derived from observations of temperature and In this study we developed and applied a modified salinity. These quantities are simple to measure and, as version of the ␤-spiral method (Stommel and Schott compared with the directly measured velocity field, the 1977; Schott and Stommel 1978). The inclusion of mo- climatological signature they contain is not much con- mentum boundary conditions at the surface and at the taminated by the energetic movements induced by me- bottom and a vorticity equation that contains the non- soscale waves and eddies, which have much smaller linear relative vorticity advection terms, as well as the temporal and spatial scales. advection of planetary vorticity, are the major modifi- Because of the subjective and incomplete nature of cations to the traditional model. To our knowledge, the dynamical method with an arbitrary reference-level consideration of the nonlinear terms is novel. The non- velocity to compute the geostrophic flow, a great effort linear terms are important, but not crucial, for this sub- has been made to eliminate the indetermination of the tropical analysis. However, because the Atlantic is tack- velocity at the reference level (Stommel and Schott led as a whole, they are of central importance in those 1977; Wunsch 1978, 1996; Veronis 1987; Stommel and areas where strong currents occur and at the equator, Veronis 1981; Bogden et al. 1993). where the geostrophic hypothesis cannot be consid- There are also the diagnostic models (see Marchuck ered. The equatorial problem will be explored in a and Sarkisyan 1988) that use the combination of dy- forthcoming paper. namic arguments with the information within the in situ data available to compute the parameters of the circu- b. Formulations lation. The goal in these models is to estimate the circulation field (in particular, the three-dimensional ve- The starting point for the ocean circulation model ␤ locity field) and to test the dynamic concepts (especially presented in this paper is the spiral of Stommel and the role of turbulent heat mixing, salt, and potential Schott (1977) as presented by Wunsch (1996): vorticity balances). 2 2 All of these model outputs have in common a critical Ѩ h Ѩ h ␤ ͑u ϩ u ͒ͩ ͪ ϩ ͑␷ ϩ ␷ ͒ͩ Ϫ ͪ ϭ 0, ͑1͒ dependence on the input hydrological dataset. In gen- gr 0 ѨzѨx gr 0 ѨzѨy f

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ϭ ␷ ϭ ␨ where u (u, ) uH, is the vertical component of relative vorticity given by

Ѩ␷ Ѩu ␨ ϭ Ϫ , ͑5͒ Ѩx Ѩy

and L is the characteristic horizontal spatial scale of the movement whose velocity has a typical scale U. The resulting dynamical state is a linearized balance of vorticity that, in terms of planetary-scale flows, relates the vortex tube stretching of the planetary vorticity with the meridional advection of the meridional gradient of planetary vorticity represented by the Sverdrup balance in (2) (e.g., Pedlosky 1996). However, the ocean is, in fact, a turbulent system and ocean circulation is a large-scale phenomenon that is not stationary. It changes continuously over a wide range of frequencies and wavenumbers. A synoptic pic- ture of the ocean circulation should reveal areas of currents with small scales and intense gradients almost everywhere, with the mesoscale variability dominating. This is true either at the western boundary areas (Le Traon and Morrow 2001) or in the open ocean where intense and narrow currents may also reveal intermit- FIG. 3. Vertical distribution of the MSE for (a) temperature and (b) salinity at a meridional section along 30°W and for the annual tent mesoscale eddy activity. Mesoscale eddies lose ensemble. their energy to the smaller-scale processes through dis- sipation, but they also interact with each other, fuse ␤ together, and grow, revealing the quasigeostrophic tur- which is the -spiral equation. Here, ugr(x, y, z) and ␷ bulence nature of such flow patterns (McWilliams gr(x, y, z) are the zonal and meridional components 1989). They can also return energy to the mean flow of the relative geostrophic velocity, u0(x, y, z0) and ␷ and induce deep-water circulation (Holland et al. 1982; 0(x, y, z0) are the integration constants, which depend ϭ ␳ Lozier 1997; Alves and Colin de Verdière 1999). on z0 reference-level choice, z h(x, y, ) is the depth of an isopycnal surface ␳, f is the Coriolis parameter, For the planetary-scale circulation models, it is im- and ␤ is its meridional rate of change. In section 3c, a portant to know the average and collective effect that modified ␤-spiral model equation will be considered by these eddies of smaller scales can have in the flow and using a different vorticity approach instead of the Sver- in the large-scale vorticity balance. Such impact can drup relation alter the Sverdrup relation (Pedlosky 1996). Hence, we will consider modifications of the large-scale flow by Ѩw ␤␷ ϭ f ͑2͒ the mesoscale. Ѩz Let Leddy and Ueddy be the typical mesoscale ranges, that is assumed in deriving (1). so that c. Modified vorticity equation Ueddy ϭ O͑1͒. ͑6͒ ␤ 2 For large-scale oceanography, the advective terms Leddy are generally considered to be negligible when com- After combining the large scale with the average effect pared with the Coriolis acceleration; that is, the advec- of the mesoscale, we have (Pedlosky 1996) tion of relative vorticity is small when compared with ␨͒ ͑ ١ :the advection of planetary vorticity · u Ueddy UeddyLeddy ϭ ͩ ͪ . ͑7͒ uf͒ ␤L2 UL͑ · ١ UU ١f ϭ O͑U␤͒ or ͑3͒ eddy · ١␨ ϭ Oͩ ͪ K u · u L2 ϭ If we consider as typical scales of the flow Leddy 50 U ϭ ϭ Ϫ1 ␤ ϭ ϫ Ϫ13 ␧ ϭ K 1, ͑4͒ km, L 1000 km, U 1cms , and 2.1 10 ␤ 2 Ϫ1 Ϫ1 ϭ Ϫ1 L cm s ,aUeddy 5cms yields order 1 for the term

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on the right-hand side of (7). Thus, the advection of This new model has a richer dynamics than the origi- relative vorticity cannot be ignored. So, instead of the nal ␤ spiral in (1). Now the mesoscale turbulence rec- Sverdrup relation, we consider the following vorticity tification process is allowed to impact the large-scale equation: dynamics. If u and ␷ were known, then (13) would be a dif- Ѩw Ѩ␨ Ѩ␨ 0 0 ١͑␨ ϩ ͒ ϭ ϩ ␷ ϩ ␤ ͑ ͒ ferential equation for h (because ␨ would also be ϭ f Ѩ u · f u Ѩ ͩѨ ͪ 8 z x y known). However, we have only the potential density including relative vorticity advection. This vorticity field. Using our climatological description (section 2), ␳ equation includes the rectified effect of mesoscale tur- each isopycnic surface h(x, y, ) can be calculated at ␷ bulence on the large-scale flow. Integrating in the ver- each grid point. With ugr and gr calculated with the ␷ tical direction, we obtain thermal wind relations, we will attempt to find u0 and 0 in such a way that (13) is satisfied as closely as possible. 0 So, our mathematical problem is to solve an overde- ͒ ͑ ͒ ١͑␨ ϩ ͔͒ ϭ ͑ Ϫ ͓ ͵ u · f dz f wS wB , 9 ϪH termined system of m linear equations with two un- ␷ ϩ ␷ ϭ knowns u0 and 0 in the form of u0Ai1 0Ai2 Ci, where H(x, y) is the bottom topography and wS and wB which will include an (m ϩ 1) modified equation for the are the vertical velocity at the surface and at the bot- ocean top and bottom boundaries (see the appendix for tom, respectively, these being the upper and lower more details). boundary conditions of the model. At the surface (z ϭ 0) we assume that 4. Results and discussion k ␶ a. Nonequatorial Atlantic ͪ ͩ ϫ ١ · w ͑x, y,0͒ ϭ w ϭ S E ␳ f 0 Using the ocean circulation model presented in (13), 1 Ѩ␶ y Ѩ␶ x ␶ x the Atlantic Ocean annual mean surface current (at 5 ϭ ͩ Ϫ ͪ ϩ ␤, ͑10͒ ␳ Ѩ Ѩ 2 dbar) was generated. Figure 4a depicts the obtained 0 f x y ␳ f 0 circulation patterns. For comparison, Fig. 4b shows the ␶ ␶ ␤ where x and y are the horizontal components of wind linear -spiral case in (1). Both models reproduce all stress at the surface in the x and y directions, respec- the well-known ocean circulation features and systems, ␤ tively, and wE is the Ekman pumping. but the linear -spiral case shows smoother and slightly At the bottom (z ϭϪH) we will have slower patterns than are seen with the nonlinear approach. For reference, the acronyms defined in the fol- ѨH ѨH ͑ Ϫ ͒ ϭϪ Ϫ ␷ lowing paragraphs appear also in Table 2. wB x, y, H u͑zϭϪH͒ Ѩ ͑zϭϪH͒ Ѩ x y The North Atlantic Ocean’s subtropical gyre is gen- A erated by wind circulation and thermodynamics in the ϩ ͱ V ␨ ͑ ͒ ϭϪ ͒, 11 North Atlantic. It is delimited by the westward-flowing 2f ͑z H North Equatorial Current (NEC) with its axis located

where AV is the vertical turbulent viscosity coefficient around 10°–15°N, the Caribbean Current, the “Loop” in the bottom Ekman layer (Pedlosky 1987). Current (inside the Gulf of Mexico), the Florida Cur- rent around Florida, the Gulf Stream (GS), the east- d. The new ocean circulation model ward-flowing North Atlantic Current (NAC), and the Canary Current (CC) along the northwest African Using now the vorticity equation in (8) to eliminate w Coast. The eastward-flowing Azores Current (AzC) and using the relations (south of Azores) is a very prominent zonal current ͑ ͒ ϭ ͑ ͒ ϩ ͑ ͒ within the gyre. u x, y, z ugr x, y, z u0 x, y, z0 and The South Atlantic Ocean’s subtropical gyre is de- ␷͑ ͒ ϭ ␷ ͑ ͒ ϩ ␷ ͑ ͒ ͑ ͒ x, y, z gr x, y, z 0 x, y, z0 , 12 limited by the westward-flowing South Equatorial Cur- the model equation is rent (SEC) centered close to the equator, the Brazil Current (BzC) (flowing southwestward), the eastward- Ѩ2h 1 Ѩ␨ flowing South Atlantic Current (SAC), and the Ben- ͑u ϩ u ͒ͩ Ϫ ͪ ϩ ͑␷ ϩ ␷ ͒ gr 0 ѨzѨx f Ѩx gr 0 guela Current (BeC). The eastward-flowing St. Helena Current (StHC) is also a prominent zonal current 2 Ѩ h 1 Ѩ␨ ␤ within the gyre. ϫ ͩ Ϫ Ϫ ͪ ϭ 0. ͑13͒ ѨzѨy f Ѩy f The North Atlantic Ocean’s subpolar gyre is modi-

Unauthenticated | Downloaded 10/10/21 03:18 PM UTC NOVEMBER 2007 J U L I A N O A N D ALVES 2579 fied by the meridional overturning circulation that in- clonic meanders on the northern side of its main axis cludes deep-water formation in the Nordic seas and the and anticyclonic meanders on the southern side. De- Labrador Sea. Its extension as a cyclonic gyre is some- spite the fact that we are considering climatologic av- times difficult to define. It includes the northeastward- erages, this reflects the turbulent mesoscale nature of flowing NAC, the East and West Greenland Currents the real AzC system. This is in good agreement with (EGC and WGC), and the Labrador Current (LC). Klein and Siedler (1989), Schmitz and McCartney In the Southern Hemisphere, the signature of the (1993), Maillard and Käse (1989), Stramma and Siedler Antarctic Circumpolar Current (ACC) is very clear, (1988), Müller and Siedler (1992), Alves et al. (1994), flowing eastward in an almost zonal path (between 50° and Gould (1985). In the eastern Azores–Canary basin, and 70°S on the South American side and around 50°S the AzC splits into three main branches veering toward on the African side). Between the ACC and StHC, the the southeast. The first is located immediately east of eastward-flowing signature of the SAC is evident. the Mid-Atlantic Ridge (MAR) at approximately The model skills were evaluated through both its 32°W, the second is at 25°W, and the third forms the qualitative and quantitative results for the different At- Canary Current near the western coast of Africa. The lantic systems that have already been described in the location and intensity of these branches show seasonal past. In particular, the Gulf Stream system (Juliano variations (Juliano 2003) but are in good agreement 2003) shows an excellent correspondence between with Stramma and Siedler (1988). The CC connects the present results and those previously established. This AzC to the North Equatorial Current, resulting in the has given us the confidence to accept as reliable the closure of the eastern side part of the loop of the North circulation patterns obtained in lesser-known areas. Atlantic subtropical gyre. The following will provide a further validation check In Fig. 6a we present, as an example, the vertical of the ␤-spiral-derived currents through comparison of cross section of the mean eastward velocity component the AzC with previous studies, and a close parallelism (m sϪ1) in the North Atlantic at 30°W. It shows that the will be established with the StHC. An enlarged view of nucleus of the AzC is centered at 34°N and its maxi- the annual mean surface absolute circulation in the sub- mum intensity is at the surface. Its baroclinic structure, tropical North and South Atlantic, using the nonlinear on average, does not go deeper than 1000 dbar. Its model version in (13), is shown in Fig. 5. Despite the volume transport is estimated to be 8.0 Sv (1 Sv ϵ 106 existence of clear differences between the two hemi- m3 sϪ1), in good agreement with Klein and Siedler spheric zones, there are also remarkable similarities, (1989), Ollitrault (1995), Bigg (1990), Alves (1996), and these similarities will be pointed out in subsequent Alves and Colin de Verdière (1999), Jia (2000), and sections. Juliano (2003). In the southern region of the section, it is possible to identify part of the NEC flowing westward b. Azores Front/Current system (AzFC) (at approximately 23°N). On the northern limit, north For the North Atlantic subtropics (Fig. 5a) around of 43°N, we can find the southern part of the NAC, (40°N, 50°W), we clearly identify the bifurcation of flowing northeastward. Coupled to the northern side of the Gulf Stream into two main systems: the North At- the main AzC jet, it is possible to identify the shallow lantic Current in the northern part of the domain, surface mean eastward signature of the “corridor” of spreading northeastward, and the zonal Azores Current the pinched-off anticyclones (centered at ϳ40°N) that in the central area. The latter is connected to its source are formed in the AzC system (see also Fig. 22 in Alves region through a cyclonic meander with its center at and Colin de Verdière 1999). There is also clearly a around (35°N, 47.5°W). This meander appears with a westward mean current just adjacent to the northern permanent signature, throughout the year, although side of the AzC with a subsurface maximum of about some seasonal variations are to be noted in the connec- 0.01 m sϪ1 and located below the 500-dbar depth. This tion details between the AzC and the GS (Juliano countercurrent, designated by Alves (1996) and Alves 2003). These results are in agreement with Le Traon and Colin de Verdière (1999) as the Azores Counter- and De Mey (1994) and Alves and Colin de Verdière current (AzCC) and present in some results of high- (1999). resolution numerical models (Jia 2000), exists all year The AzC appears to be a permanent eastward flow, long, reaching a maximum intensity in the spring (Alves reaching to the Gulf of Cadiz. With an annual mean and Colin de Verdière 1999; Juliano 2003). Klein and velocity at the surface of about 6 cm sϪ1, it is centered Siedler (1989) and Stramma and Isemer (1988) have around 34°N and has a meridional extension of ap- detected a similar signal located between 200- and proximately 5° in latitude. It meanders all along its tra- 800-m depth, but this current has only been explicitly jectory, revealing a tendency for the formation of cy- mentioned by Onken (1993). However, none of these

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Ϫ FIG. 4. (a) Surface annual mean field of the horizontal absolute velocity (m s 1) in the Atlantic Ocean. Its calculation was achieved by solving the model equation in (13). (b) As in (a), but for the linear ␤-spiral case [(1)]. Note that the same features are presented in both model results but the linear ␤-spiral case is much smoother.

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FIG.4.(Continued)

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TABLE 2. List of the acronyms for currents shown in Fig. 4a. of relatively warm and salty water that fills the 50-m top layer and obstructs its detection by thermal IR satel- ACC Antarctic Circumpolar Current AzC Azores Current lite images (Gould 1985; Alves et al. 1994; Alves BeC Benguela Current 1996; M. Alves et al. 1995, unpublished manuscript). BzC Brazil Current In wintertime, this thermocline is replaced by a well- CC Canary Current developed mixed layer that can attain a thickness of EGC East Greenland Current 250 m (Levitus 1982; Alves 1996). In principle, this GS Gulf Stream LC Labrador Current would allow surface detection using thermal IR; how- MC Malvinas Current ever, because of the persistent cloud cover typical of NAC North Atlantic Current this region in winter, detection with passive radiom- NEC North Equatorial Current eters is difficult (Gould 1985). The same kind of prob- SAC South Atlantic Current lem is not encountered with sea surface height from SEC South Equatorial Current StHC St. Helena Current satellite altimetry (Alves 1996). The AzFC is also re- WGC West Greenland Current ported to be a region of very intense biological activity (Kahru et al. 1991; M. Alves et al. 1995, unpublished manuscript). latter researchers carried out a seasonal analysis or Alves (1996) and Alves and Colin de Verdière (1999) pointed out any explanation for its subsurface intensi- have shown through an intensive study of the AzFC fication. Later Cromwell et al. (1996), through the use wave mean flow interaction that 1) observed mesoscale of hydrography and European Remote Sensing Satel- patterns are largely determined by baroclinic instability lite-1 altimetry data, mentioned a surface countercur- processes, 2) the AzC jet and its mesoscale turbulence rent north of the main jet that was announced as ret- show a strong meridional asymmetry in agreement with roflection of the main jet. Alves and Colin de Verdière Le Traon and De Mey (1994) and Kielmann and Käse (1999), following an intensive study of mesoscale non- (1987) due to the great slope verified in its thermocline, linear instability of the AzC region, have shown more where the authors propose a mechanism that explains it recently that the AzCC is induced by the anticyclonic through simple Ertel potential vorticity arguments, and eddies formed on its north side and by the deformation 3) the rectification of the meridionally asymmetric of the meanders that were generated by the baroclinic mesoscale turbulence is able to create a westward- instability of the main jet, without resorting to the wind flowing countercurrent along the northern boundary of forcing mechanism proposed by Onken (1993). the AzFC main jet. They also show that the turbulent To understand these annual mean patterns, it is im- transport of Ertel’s potential vorticity induces this portant to keep in mind that the synoptic data (e.g., countercurrent at the surface, whereas the Coriolis oceanographic cruises) show that the AzC can attain 30 force acting on the ageostrophic meridional circulation Sv in the eastern basin circa 32°W (Pingree and Sinha is responsible for the existence of this countercurrent at 1998) and a surface speed of about 30 cm sϪ1, decreas- depth. This ageostrophic meridional circulation is bipo- ing to approximately 1 cm sϪ1 at 700 dbar (Ollitrault lar; that is, there is upwelling at the axis of the main jet 1995). Of course, the time-average transport and speed and downwelling at each of the sides. are much smaller because the mean meridional AzC Despite all of these results, the mechanisms that are signature is larger than the synoptic one as a result of responsible for AzFC origin are not yet totally estab- AzC meandering and also as a result of existing recir- lished. The AzFC is positioned well south of the region culation branches mainly to the south of it. of the zero mean wind stress curl and where Ekman The AzC is related to a thermohaline front, the pumping leads to a southward transport, implying that AzFC, which includes an intense meander and meso- its zonal orientation cannot be totally explained by scale eddy generation capacity. The AzFC is seen as the Sverdrup dynamics (Jia 2000). Käse and Krauss (1996) frontier separating the Subtropical Mode Water (18°C) hypothesized, using time series of surface wind stress (in the south) from the Subtropical Mode Water (13°C) data, that, despite the wind stress curl being signifi- (in the north), especially at its westernmost part (Pol- cantly negative in the latitude corridor between 35° and lard et al. 1996). Its main body is filled with North 50°N, it undergoes large annual and interannual fluc- Atlantic Central Water (NACW), and the Mediterra- tuations. They argued that, under these conditions, nean Water (MW) fills its lower extension (Harvey and nonlinear inertial effects could control dynamics in the Arhan 1988; Alves 1996; Juliano 2003). During the Gulf Stream extension, resulting in separation of the summer, the AzFC’s surface signature is masked by GS into the NAC and AzC. They also suggested that a the presence of a well-developed seasonal thermocline relative minimum of the wind stress curl exists in the

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Ϫ FIG. 5. Annual mean absolute horizontal velocity distribution (m s 1) at the surface using the nonlinear model formulation (a) in the northeast Atlantic and (b) in the South Atlantic. inner region of the North Atlantic subtropical gyre, cre- again the strength of our calculation and estimation ating conditions for formation of quasi-zonal flows that method. extend to the eastern North Atlantic. Jia (2000) presents a complementary explanation for c. St. Helena Front/Current system (StHFC) the formation and persistence of the AzC jet. Based on In the South Atlantic subtropical zone (Fig. 5b), the observations and numerical models, she suggests that two main South American western boundary currents transformation of water masses associated with the are the BzC flowing poleward and the Malvinas Cur- Mediterranean Sea water entrainment and flow into the rent (MC) flowing equatorward. The BzC is associated Atlantic in the Gulf of Cadiz may create a “point vor- with the circulation of the South Atlantic subtropical tex” and induce the formation of the AzC. These re- gyre and carries warm and relatively salty waters origi- sults are also supported by Özgökmen et al. (2001). nating in the subtropical region (Maamaatuaiahutapu Our results are valid for the whole range of longi- et al. 1992; Garzoli 1993). The MC, originating in the tudes of the AzFC and are in harmony with those ob- Antarctic Circumpolar Current, carries cold and less tained by the abovementioned authors. This confirms salty water from its source (Garzoli 1993). When the

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FIG. 6. The annual mean absolute eastward velocity at (a) 30°W for the Northern Hemisphere and (b) 17.5°W for the Southern Hemisphere. The contour interval is 0.005 m sϪ1, and positive values (eastward) are shaded. The AzC appears in (a) between 32° and 35°N (centered at 34°N) and penetrates down to 1000 dbar. The StHC appears in (b) between 32° and 36.5°S (centered at 34°S) and penetrates down to 1000 dbar.

MC encounters the BzC at the latitudes of about 35°– Stramma and Peterson (1990, who did not identify the 40°S (Garzoli 1993; Garzoli and Giulivi 1994) off the two separate current branches although they recognize coast of Argentina and Uruguay, they deflect eastward that the SAC does not coincide with the Subtropical toward the open ocean (Confluence Principal Investi- Front (STF) all along its path, the SAC is clearly dis- gators 1990; Boebel et al. 1999). The combined flow of tinct from the ACC and corresponds to the seaward the two currents of contrasting properties produces an propagation of the Gulf Stream, the NAC (e.g., Krauss intense and complex frontal structure, known as the 1986). Brazil–Malvinas confluence zone (e.g., Gordon and The northern branch (starting point represented by Greengrove 1986; Confluence Principal Investigators the character A), at approximately 35°S, is the result of 1990), which is located in the 35°–40°S area centered at the first retroflection of the BzC (Juliano 2003). It co- 55°W (Fig. 5b). incides in this region with the position of the Brazil In the lower part of Fig. 5b, south of 45°S, one can Front/Current. A close inspection of Fig. 5b shows that, identify the northern branch of the ACC, flowing east- although some recirculation occurs toward the Brazil ward with a zonal trajectory. This branch, with its Current, the majority of its flow deflects eastward, to- nucleus centered at 47.5°S, is the SAF. ward the open ocean (at ϳ35°S) (Tsuchiya et al. 1994). A further analysis of Fig. 5b shows that, from the It then takes a quasi-zonal path all across the South Brazil–Malvinas confluence zone, there are two main Atlantic basin, where it is probably the current identi- eastward-flowing branches (Belkin and Gordon 1996; fied by Gordon et al. (1992) as the Benguela/South Provost et al. 1999). The one farther south (represented Atlantic Current front. This current has a well-defined by the character B at its starting point) is a result of the baroclinic structure and flows zonally eastward all second retroflection of the BzC (Juliano 2003), turning across the eastern South Atlantic basin. At approxi- slightly northeastward up to approximately (40°S, mately (35°S, 10°E), it deflects northeastward, feeding 45°W) and then flowing eastward along this latitude. the Benguela Current (much like the Azores Current This branch constitutes the origin of the SAC. As in feeding the CC). This main zonal current constitutes

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what we are calling the StHC. We argue that it is now observed both in the horizontal distribution at the sur- possible to detect the full structure of the StHC both face (Fig. 5b) and at depth in the western basin at 40°, horizontally and vertically because we are using a much 35°, and 30°W (Fig. 8). more complete hydrological database and a greater At 35°W (Fig. 8b), the SAC core appears displaced spatial resolution than were used in the previous cited southward of 40°S, which is again in good agreement studies. The StHC is present in both linear and nonlin- with Stramma and Peterson (1990). At middepth, the ear formulations (Figs. 4a,b). SAC shows a wider signature that reveals interaction For the vertical structure of the StHC at 17.5°W (Fig. with the StHC and with the upper branch of the ACC 6b), its signature is clearly separate (centered at 34°S) (47.5°S), which is associated with the SAF. The second from the SAC (centered at 42°S). On the other hand, at positive core of ACC, centered at 50°S, is associated 17.5°W the SAC and ACC appear completely merged. with the Polar Front. Farther east, the StHC core starts North of the StHC, the SEC flows westward with maxi- to separate from the SAC, keeping its latitudinal posi- mum speeds at depths oscillating between 200 and 600 tion (Fig. 8c). The StHC becomes more distinct toward dbar. the east. At 30°W the southern edge of the SAC merges Figure 7 shows the annual mean vertical distributions with the northern edge of the ACC, making the SAC Ϫ3 of potential temperature (°C), salinity, ␴␪ (kg m ) and difficult to identify clearly. This is the result of a south- the eastward (positive) component of the absolute ve- ward displacement of the STF (Stramma and Peterson locity (m sϪ1) along a meridional section at 45°W. This 1990; Juliano 2003) and a northward SAF displacement section was chosen because it lies approximately in the (Juliano 2003). This is also confirmed by Schmid et al. region of origin for both currents (SAC and StHC) and (2000) and Davis et al. (1996) using Lagrangian floats. because it can be used for comparison with previous They suggested that there should be an interaction be- works (e.g., Stramma and Peterson 1990). Here, there tween the SAC and the ACC in the region 35°–20°W are two clearly identifiable current cores. The SAC and that, in this latter position, both currents merge core is centered at 39°S and has maximum speed at together into a single one (see Fig. 5b). To Schmid et al. the surface. Its vertical structure extends to below (2000) the structure of this interaction is still an open 1000 dbar, as in Stramma and Peterson (1990). Accord- issue. On the other hand, we see that at 30°W, the StHC core is well separated from the SAC core, with a well- ing to Fig. 7, the very strong near-surface salinity gra- defined baroclinic structure spreading down to 600 dbar dients acting in opposition to the temperature distribu- (Fig. 8c). Its central latitude from the surface to 600 tion partially explain the relative weakness of this dbar is 33°S. Another important issue is the presence, current maximum, also in agreement with Stramma and just south of the StHC, of a subsurface countercurrent Peterson (1990). Centered at 47.5°S is the northern centered approximately at 37°S at the 200-dbar level. branch of ACC, associated with the SAF. It shows a This countercurrent, which we call the St. Helena significant barotropic structure, in harmony with previ- Countercurrent (StHCC), is associated with the pres- ous results (Le Traon and Morrow 2001). A counter- ence of the 13°C Mode Water layer (STMW3 in Pro- current centered at 45°S clearly separates the SAC vost et al. 1999) that becomes even thicker toward the and ACC cores. It constitutes the southern recircula- east (Juliano 2003) (see Fig. 10a). Both the StHC and tion resulting from the confluence and is again in good the StHCC keep this pattern farther toward the east to agreement with Stramma and Peterson (1990). At 33°S, 10°W (Fig. 6b). At 5°W (Fig. 9), part of the SAC flow another eastward-flowing current core, well defined is displaced northward [which fits in with Stramma and and distinct from SAC, is observed. It corresponds to Peterson (1990)], getting closer to the StHC core. the StHC. This surface-intensified current has a baro- Around the Greenwich meridian, the StHC deflects clinic structure and a meridional width of approxi- slightly to southeast, and it keeps this trajectory to near mately 4°. When analyzing the vertical distribution of 10°E, at which point it veers northwestward and finally ␴ ␪ along this section (Fig. 7c), it is clear that an isopyc- merges with the BeC (Fig. 5b). nal gradient is positioned in the region of the StHC core (34°–35°S). East of 45°W (Fig. 5b), the StHC and the SAC pro- d. Comparison of the Azores and St. Helena ceed eastward along parallel paths. The StHC interacts Front/Current systems with the SAC up to approximately 30°W (Fig. 5b), at The diffuse equatorward eastern boundary currents which point the SAC moves slightly to the south of its and the fast, intense, poleward western boundary cur- mean position, joining the upper branch of ACC, while rents are linked by the open-ocean currents, which can the StHC keeps flowing zonally. These interactions are be intense and narrow currents and are where meso-

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FIG. 7. Vertical distributions along a meridional section at 45°W of annual mean (a) potential temperature Ϫ3 (contour interval is 1°C), (b) salinity (contour interval is 0.1), (c) ␴␪ (contour interval is 0.1 kg m ), and (d) eastward absolute velocity (contour interval is 0.005 m sϪ1, and the eastward positive values are shaded). scale eddies develop (Le Traon and Morrow 2001). the Gulf Stream], as well as exchanges between the This general scheme defines an interhemispheric sym- oceans via meridional overturning circulation (e.g., metry for the large-scale currents, present in the three Schmitz 1995). In a study of South Atlantic mode wa- oceans, which can be modified by regional particulars, ters, Provost et al. (1999) noticed the existence of a such as atmospheric forcing, the local bathymetry, north subtropical front that corresponds to our StHC, coastline tilting [see, e.g., Da Silveira et al. (1999) for but they did not elaborate. differences observed between the Brazil Current and We can now say that an increased database and reso-

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FIG. 8. The annual mean absolute eastward velocity at (a) 40°, (b) 35°, and (c) 30°W for the Southern Hemisphere. Contour interval is 0.005 m sϪ1, and the eastward positive values are shaded.

lution, together with a new circulation description, have they are situated approximately in the central part of made it possible to describe fully the counterpart of the the trajectory of the two currents. The resemblance be- AzC in the South Atlantic, which we have called the St. tween the two zonal mean components (AzC and Helena Current, by analogy with the Azores Current. StHC) in location, intensity, transport, depth attained, Similarity between the StHC and the AzC is evident and meridional width is evident. not only in their horizontal structure (location, meridi- As mentioned previously (in section 4b), the AzFC is onal width, and intensity) (cf. Figs. 5a and 5b), but also seen as a boundary separating the 18°C (south) and the in their vertical structure and volume transport (cf., 13°C (north) Subtropical Mode Waters. These struc- e.g., Figs. 6a and 6b). Such similarity extends also to tures are obvious in Fig. 10, with respect to the AzC. location and volume transport of their respective coun- For the StHC region, the resemblance and symmetry tercurrent systems (AzCC and StHCC). Another clear are remarkable. With respect to the vertical distribu- similarity is their origin. Both start from the corre- tion of the average temperature, we observe the pres- sponding western boundary currents of each hemi- ence of the same 13° and 18°C Mode Waters [also ob- sphere and interact with the NAC (AzC) and the SAC served by Tsuchiya et al. (1994) and Provost et al. (StHC) (Figs. 5a,b). Also, their thermohaline proper- (1999)] south and north of the StHC core, despite its ties mirror each other. The most significant difference smaller vertical thickness. The main difference is in the is that the SAC remains closer to the StHC than its depth of the 13°C water when compared with the AzC. North Atlantic equivalents. Also, because the South Pollard et al. (1996) showed that the AzCC coincides Atlantic is wider than the North Atlantic at these lati- with the southern limb of the anticyclonic circulation of tudes, it is clear why the AzC has a shorter extent than the 13°C Subpolar Mode Water. The main body of the the does the StHC. StHC is filled with South Atlantic Central Water, To illustrate further this interhemispheric mirror re- whereas, for the AzC, it is the North Atlantic Central semblance between the two current systems, some Water that plays this role (Figs. 10a,b). The StHC lower zonal means have been further calculated for the an- limit is filled with Antarctic Intermediate Water (AIW; nual mean distributions (Fig. 10). The temperature (°C) cold and diluted water) that contrasts with the MW (hot and salinity cross sections of zonal averages between and salty water), for the AzC case. Because the AIW 25° and 15°W for the Southern Hemisphere and be- and the MW have similar densities it explains why sym- tween 35° and 25°W for the Northern Hemisphere were metry is preserved even with such thermohaline differ- overlaid with the main zonal mean cores of StHC and ences. AzC, respectively. These sections were chosen because The zonal average cross section of the zonal current

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latitudes 35°–15°W. Symmetry is observed for the distribution of velocity and density in the two hemispheres. Differences appear at higher latitudes, mostly due to regional geographic differences. The presence of geographic boundaries in the polar regions of the Northern Hemisphere promotes the formation of a cyclonic circulation, the North Atlantic subpolar gyre, with no Southern Hemisphere counterpart. This aspect changes the relative structure of the South Atlantic Current and the North Atlantic Current. Whereas the NAC spreads northeastward, the SAC, because of the Antarctic Circumpolar Current, is concentrated in a narrow meridional zone attached to the ACC. How- ever, for the StHC and the AzC structures, the similarity is evident.

5. Conclusions The comprehensive hydrological database for the At- lantic Ocean used in this study, with greater geographical detail than has been used previously, has allowed us to reproduce the previously described ocean systems and to describe fully the Northern Subtropical Front (Brazil Current/Front), which we have called the St. FIG. 9. The annual mean absolute eastward velocity at 5°W for Helena Current, and to show its similarity with the Ϫ the Southern Hemisphere. Contour interval is 0.005 m s 1, and Azores Current. the eastward positive values are shaded. To be specific, we show unambiguously that the eastward-flowing St. Helena Current and the associated Ϫ1 Ϫ3 component (m s ), with ␴␪ (kg m ) superimposed, westward-flowing St. Helena Countercurrent emerge in between longitudes 30° and 5°W for the Southern exactly the same symmetric position to the equator as Hemisphere and between 40° and 20°W for the North- that of their counterparts, the eastward-flowing Azores ern Hemisphere (chosen to cover the largest part of the Current and the associated westward-flowing Azores path of StHC and AzC), reveals the mirror nature of Countercurrent. both current systems (Fig. 11a). Overlapping Fig. 11a Why has the current that we call the St. Helena Cur- (blue numbers) are the estimates for the volume trans- rent received so little notice? The first reason has to do port (Sv) of the two currents and their countercurrents, with the southern limit of the South Atlantic subtropi- in both hemispheres (positive eastward). Once again, cal gyre. This limit has usually been identified as the we emphasize the obvious similarities between the two South Atlantic Current (Stramma and Peterson 1990). flows, not only for the two currents with 8.0 Sv for Gordon et al. (1992), Tsuchiya et al. (1994), Belkin the StHC and 7.5 Sv for the AzC, but also for their (1994), Belkin and Gordon (1996), and Provost et al. westward countercurrents with Ϫ0.2 Sv for StHCC and (1999) noticed the signature of the St. Helena Current Ϫ0.9 Sv for the AzCC (above 700 dbar). We note, how- but did not recognize its correspondence with the ever, that despite its similarities the StHCC maximum is Azores Current. The transition between subtropical shallower (ϳ150 dbar) than that of the AzC (ϳ500 and polar water is not a continuous and smooth one. It dbar) and has a smaller volume transport. This may appears to be made of discontinuous jumps as shown in indicate an interaction between the SAC and StHC Tsuchiya et al. (1994). The first two of these jumps are mesoscale features; in the case of AzC, its mesoscale the AzFC and the StHFC, respectively, in the North activity is freer to develop without interaction with the and South Atlantic, and the second and biggest two NAC. jumps are the NAC and SAC, in the North and South To conclude and to illustrate better the interhemi- Atlantic, respectively. spheric similarity of both subtropical gyres, a meridi- Second, the AzC as been associated with Gibraltar onal cross section of velocity of the Atlantic Ocean is Strait and the Mediterranean outflow (e.g., Jia 2000; shown (Fig. 11b), based on the zonal average for the Özgökmen et al. 2001), which has no counterpart in the

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FIG. 10. Annual and zonal mean vertical distribution of (a) temperature (°C) and (b) salinity (left) between 25° and 15°Winthe Southern Hemisphere and (right) between 35° and 25°W in the Northern Hemisphere and for the latitude range shown. Superimposed onto these thermohaline fields in each hemisphere are the StHC and AzC cores only. AIW and MW water masses are colored in (b) using the salinity signature. Volume transports are also indicated for each current in (a).

South Atlantic. The detailed similarity of St. Helena case). However, a more deep and complete analysis will Current to the Azores Current suggests that the pres- be required to test this hypothesis. ence of the Strait of Gibraltar cannot be the cause of the Azores Current. The major forcing mechanism for Acknowledgments. The authors thank Professor the StHC and AzC could be thermodynamic. An in- Alain Colin de Verdière from the University of creased seasonal summer radiation, with the formation Bretagne Occidental in France for all of the fruitful of a strong seasonal thermocline, followed by incom- discussions and advice concerning the model that was plete winter erosion in the area, which causes the for- developed and then used in this paper. We also thank mation of a surface mixed layer, may be responsible for the two anonymous reviewers and Dr. Lynne Talley the formation and permanence of these subtropical sys- who provided the thorough and critical reviews of the tems (regardless of the existence of any other concur- manuscript and Arminda Monteiro for editing of the rent mechanism, like the MW point vortex for the AzC English grammar.

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Ϫ1 Ϫ3 FIG. 11. (a) Annual and zonal mean absolute velocity cross sections (m s ) with ␴␪ superimposed (kg m ), (left) between 30° and 5°W in the Southern Hemisphere and (right) between 40° and 20°W in the Northern Hemisphere. Blue numbers refer to the volume transport (Sv) marked over the current they describe. (b) Annual and zonal mean cross section through the whole Atlantic Ocean between 35° and 15°W, extending from 70°Sto70°N. Note that the equatorial zone has been excluded from discussion.

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APPENDIX Considering that the ocean circulation is subject to wind forcing at the surface and to the bottom con- Numerical Model Equations straints at the bottom boundary, the potential density a. Numerical solution of the ocean circulation model dataset was further completed using the Hellerman and The model equation in (13) may be written as Rosenstein (1983) 1° square monthly wind stress fields and the 5Ј gridded elevations/bathymetry for the world Ѩ2h 1 Ѩ␨ Ѩ2h 1 Ѩ␨ ␤ ͩ Ϫ ͪ ϩ ␷ ͩ Ϫ Ϫ ͪ ϭ (ETOPO5) bottom topography database. Both datasets u0 Ѩ Ѩ Ѩ 0 Ѩ Ѩ Ѩ z x f x z y f y f were interpolated to the same 0.5° ϫ 0.5° resolution Ѩ2h 1 Ѩ␨ Ѩ2h 1 Ѩ␨ ␤ base of the potential density. u ͩϪ ϩ ͪ ϩ ␷ ͩϪ ϩ ϩ ͪ. With this in mind, (A1) may be rewritten for the gr ѨzѨx f Ѩx gr ѨzѨy f Ѩy f surface and bottom boundary conditions, which be- ͑A1͒ come

1 0 Ѩ␨ ѨH 1 0 Ѩ␨ ␤H ѨH u ͫ ͵ ͩ ͪ dz Ϫ ͬ ϩ ␷ ͫ ͵ ͩ ͪ dz ϩ Ϫ ͬ ϭ 0 Ѩ Ѩ 0 Ѩ Ѩ f ϪH x x f ϪH y f y 1 0 Ѩ␨ 1 0 Ѩ␨ w Ϫ wЈ Ϫ ͭ ͵ ͩu ͪ dz ϩ ͵ ͫ␷ ͩ ϩ ␤ͪͬ dzͮ, ͑A2͒ E B gr Ѩ gr Ѩ f ϪH x f ϪH y

with

ѨH ѨH A Ј ϭϪ Ϫ ␷ ϩ ͱ V ␨ w u ϭϪ ͒ ϭϪ ͒ ϭϪ ͒ and B gr͑z H Ѩx gr͑z H Ѩy 2f ͑z H k ␶ ͪ ͩ ϫ ١ ϭ wE ␳ · . 0 f

ϫ ϫ ϫ The equation in (A1), applied to m isopycnic sur- where A, u0, and C are M N, N 1, and M 1 faces, together with (A2) forms an overdetermined sys- matrices, respectively, with M ϭ m ϩ 1 and N ϭ 2. ϩ tem of (m 1) linear equations with two unknowns u0 Using SVD, (A4) will become ␷ and 0 of the form T ϭ ͑ ͒ UWV u0 C, A5 u A ϩ ␷ A ϭ C 0 11 0 12 1 where U is a column-orthogonal (M ϫ N) matrix, W is · · a diagonal N ϫ N matrix of positive or zero elements w · ··· · ͑A3͒ i · · (the singular values), and VT is the transpose of an N ϫ ϩ ␷ ϭ u0A͑mϩ1͒1 0A͑mϩ1͒2 C͑mϩ1͒ N orthogonal matrix V. In the case of the Atlantic as a whole, it can be seen that both singular values are posi- ϫ Ϫ3 Ͻ Ͻ that are solved for each grid point in the Atlantic tive and are contained in the intervals 4 10 w1 ϫ Ϫ2 Ϫ6 Ͻ Ͻ ϫ Ϫ6 Ocean. 4.9 10 and 10 w2 7 10 , some orders of All of the terms of (A1) and (A2) can be estimated magnitude greater than the smallest double-precision ␷ directly from observations, except u0 and 0 and the machine error. Solving for the matrix of unknowns u0 ␨ ␷ relative vorticity term . To solve for the u0 and 0 gives in our case unknowns, a singular value decomposition method ϭ Ϫ1 T ͑ ͒ (SVD) is used. In the case of an overdetermined system u0 VW U C. A6 (more equations than variables), SVD produces a solu- The residuals associated with the u and ␷ estimation tion that is the best approximation in the least squares 0 0 can be calculated by minimization of the merit function sense and whose uncertainty can be found (Press et al. ␹ 2, with 1992). For the case here, system (A3) can be represented as ␹ 2 ϭ | Ϫ |2 ͑ ͒ Au0 C , A7 ϭ ͑ ͒ ␷ Au0 C, A4 and the u0 and 0 standard deviations will become

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2 2 1ր2 To close the system and to solve also for ␨, we have V1i ␴ ϭ ͚ͫ ͩ ͪ ͬ and u0 used an iterative method combined with the SVD so- ϭ w i 1 i lution of the system of m ϩ 1 equations. In the first ր k 1 2 V 2 1 2 iteration (k ϭ 1), we assume that ␨ ϭ ␨ ϭ 0(␤-spiral ␴ ϭ ͫ ͩ 2iͪ ͬ ͑ ͒ ␷ ͚ . A8 0 start) and the system to solve is iϭ1 wi

Ѩ2h Ѩ2h ␤ Ѩ2h Ѩ2h ␤ u1ͩ ͪ ϩ ␷ 1ͩ Ϫ ͪ ϭ u ͩϪ ͪ ϩ ␷ ͩϪ ϩ ͪ and 0 ѨzѨx 0 ѨzѨy f gr ѨzѨx gr ѨzѨy f

ѨH ␤H ѨH 1 0 u1ͩϪ ͪ ϩ ␷ 1ͩ Ϫ ͪ ϭ w Ϫ wЈ Ϫ ͫ ͵ ͑␷ ␤͒ dzͬ, ͑A9͒ 0 Ѩ 0 Ѩ E B gr x f y f ϪH

with used to recompute ␨1 and so on up to iteration k, according to the general transformation ѨH ѨH wЈ ϭϪu ϭϪ ͒ Ϫ ␷ ϭϪ ͒ and B gr͑z H Ѩx gr͑z H Ѩy Ѩ␷k Ѩuk k ϭ k ϩ ␷ k ϭ ␷ k ϩ ␷ ␨k ϭ Ϫ u u0 ugr; 0 gr; Ѩ Ѩ . k ␶ x y ͪ ͩ ϫ ١ ϭ wE ␳ · , ͑ ͒ 0 f A10 1 ␷ 1 ␨ k where the vector (u0, 0) is the first-iteration solution Once we have the value of , the system to solve with 1 ␷ 1 given by (A6) with residuals (A8). Now (u0, 0) will be SVD becomes

Ѩ2h 1 Ѩ␨k Ѩ2h 1 Ѩ␨k ␤ Ѩ2h 1 Ѩ␨k Ѩ2h 1 Ѩ␨k ␤ ukϩ1ͩ Ϫ ͪ ϩ ␷ kϩ1ͩ Ϫ Ϫ ͪ ϭ u ͩϪ ϩ ͪ ϩ ␷ ͩϪ ϩ ϩ ͪ and 0 ѨzѨx f Ѩx 0 ѨzѨy f Ѩy f gr ѨzѨx f Ѩx gr ѨzѨy f Ѩy f

1 0 Ѩ␨k ѨH 1 0 Ѩ␨k ␤H ѨH ukϩ1ͫ ͵ ͩ ͪ dz Ϫ ͬ ϩ ␷ kϩ1ͫ ͵ ͩ ͪ dz ϩ Ϫ ͬ ϭ 0 Ѩ Ѩ 0 Ѩ Ѩ f ϪH x x f ϪH y f y

1 0 Ѩ␨k 1 0 Ѩ␨k w Ϫ wЈ Ϫ ͭ ͵ ͩu ͪ dz ϩ ͵ ͫ␷ ͩ ϩ ␤ͪͬ dzͮ ͑ ͒ E B gr Ѩ gr Ѩ , A11 f ϪH x f ϪH y

with kϩ1 ϭ ͓͑ kϩ1͒2 ϩ ͑␷ kϩ1͒2͔1ր2 U u0 0 and

ѨH ѨH A U k ϭ ͓͑uk͒2 ϩ ͑␷ k͒2͔1ր2, ͑A12͒ Ј ϭϪ Ϫ ␷ ϩ ͱ V ␨ k 0 0 w u ϭϪ ͒ ϭϪ ͒ ϭϪ ͒, B gr͑z H Ѩx gr͑z H Ѩy 2f ͑z H we consider that the model iterative convergence is k ␶ achieved when ͪ ͩ ϫ ١ ϭ wE ␳ · , 0 f |Ukϩ1 Ϫ Uk| Յ␧. ͑A13͒ ϭ Ϫ2 2 Ϫ1 and AV 10 m s (Pedlosky 1987). kϩ1 ␷ kϩ1 A new SVD solution vector of the form (u0 , 0 ) If (A13) is true, then the velocity pattern at the refer- is obtained at each iteration. Defining ence level between two consecutive interactions is iden-

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␷ FIG. A1. Velocity vector (u0, 0) at the reference level.

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the deep western boundary return current. The associated error residuals are shown in Fig. A2 and appear to

be larger where the u0 current is stronger. Nevertheless it never exceeds 10Ϫ3 msϪ1. As an alternative to 2000 dbar, a reference level at 1500 dbar was also used for comparison. Figure A3 show the absolute current v at the 2000-dbar level when

the u0 referenced to 1500 dbar is added with the thermal wind vector vgr. Figure A3 looks similar to Fig. A1, revealing that differences arising from a different ref-

erence level are readily compensated by a u0 field at 1500 dbar that, once added with the thermal wind, re-

produces the u0 field when referenced to 2000 dbar. As was shown in Fig. A2, the hydrological fields in the South Atlantic tend to be less reliable than else-

where. That means that the u0 field will also be less reliable there. It should also be mentioned that the (ugr, ␷ gr) thermal wind is computed relative to the 2000-dbar level. When the bottom is shallower than 2000 dbar, the “bottom wedge” problem is dealt with by estimating FIG. A2. Error residuals of the solution at the 2000-dbar refer- the flow through below-bottom density calculation af- ence level. Note that residuals are greater where the current is ter objective mapping of the presently reconstructed stronger but remain much smaller than the current intensity itself. temperature and salinity fields (Roemmich 1983).

b. Nonlinearity impact tical. For the results presented in the main text, the value ␧ϭ10Ϫ3 msϪ1 was used. Comparison of the linear ␤-spiral case with the This way, we finally get the three-dimensional field present nonlinear model is of importance to understand ␤ of horizontal absolute velocity uh(x, y, z) in a large- what is improved. Figure A4 shows the linear -spiral ␷ ϭ scale context: u0 and 0 field at the z0 2000 dbar level of reference. This can be compared directly with the nonlinear case final͑ ͒ ϭ kϩ1͑ ͒ ϩ ͑ ͒ u x, y, z u0 x, y ugr x, y, z , presented in Fig. A1. It is clear that the ␤-spiral case is ␷final͑x, y, z͒ ϭ ␷ kϩ1͑x, y͒ ϩ ␷ ͑x, y, z͒, and much smoother than when the nonlinear relative vor- 0 gr ticity advection terms are present in the planetary-scale Ѩ␷final Ѩufinal balance of vorticity. It is expected that the new terms ␨ final͑x, y, z͒ ϭ Ϫ . ͑A14͒ Ѩx Ѩy can have a relative importance similar to the planetary vorticity advection term, at least in regions of more We note that, to obtain w(x, y, z), (8) can be vertically intense currents and, most important, in the equatorial integrated according to region, where the singularity introduced by the disap- ͑ ͒ ϭ w x, y, z wB pearance of the Coriolis term makes geostrophic equi- librium invalid. 1 z Ѩ Ѩ ϩ final ␨ final ϩ ␷final ␨ final ϩ ␤ In fact, we have confirmed that, on a planetary scale, ͵ ͫu Ѩ ͩѨ ͪͬ dz f ϪH x y the advection of relative vorticity predominates in regions of intense currents and in the equatorial region ͑A15͒ (although the equatorial zone is not analyzed here). To restricted by the boundary conditions (10) and (11). quantify such a difference, we have compared results

Figure A1 shows the u0 solution for the 2000-dbar obtained for the absolute horizontal velocity in both the Ϫ level of reference. Maximum values of about 0.1 m s 1 ␤-spiral and the new nonlinear cases. The comparison is

for |u0| are obtained in the tropical Caribbean area of given by the expression

͑ 2 ϩ ␷2 ͒1ր2 ϭ Ϫ ␷ ϭ ␷ Ϫ ␷ ͑ ͒ udif dif , with udif ulinear unonlinear and dif linear nonlinear, A16

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FIG. A3. Absolute velocity field at the 2000-dbar level. With the thermal wind calculated relative to the reference level of 1500 dbar, ␷ final ␷ final ␷ (u0, 0) is also calculated at this same level. The represented (u , ) is then calculated by adding to the (u0, 0) at 1500 dbar to the thermal wind at 2000 dbar but referenced to 1500 dbar. Note that the current patterns are identical to those of Fig. A1.

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␤ ␷ FIG. A4. The linear -spiral (u0, 0) field at reference level. This case appears to be much smoother than the nonlinear case of Fig. A1.

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