On the seasonal variability and eddies in the North Brazil Current: insights from model intercomparison experiments

Progress in Oceanography 48 (2001) 195–230 www.elsevier.com/locate/pocean

On the seasonal variability and eddies in the North Brazil Current: insights from model intercomparison experiments Bernard Barnier a,*, Thierry Reynaud a, Aike Beckmann b, Claus Bo¨ning d, Jean-Marc Molines a, Sally Barnard c, Yanli Jia c a

Laboratoire des Ecoulements, Ge´ophysiques et Industriels, Institut de Mecanique de Grenoble, BP 53, 38041 Grenoble Cedex 9, France b Alfred Wegener Institut, Bremerhaven, Germany c Southampton Oceanography Centre, Southampton, UK d Institut fu¨r Meereskunde, Kiel, Germany

Abstract The time dependent circulation of the North Brazil Current is studied with three numerical ocean circulation models, which differ by the vertical coordinate used to formulate the primitive equations. The models are driven with the same surface boundary conditions and their horizontal grid-resolution (isotropic, 1/3° at the equator) is in principle fine enough to permit the generation of mesoscale eddies. Our analysis of the mean seasonal currents concludes that the volume transport of the North Brazil Current (NBC) at the equator is principally determined by the strength of the meridional overturning, and suggests that the return path of the global thermohaline circulation is concentrated in the NBC. Models which simulate a realistic overturning at 24°N of the order of 16–18 Sv also simulate a realistic NBC transport of nearly 35 Sv comparable to estimates deduced from the most recent observations. In all models, the major part of this inflow of warm waters from the South Atlantic recirculates in the zonal equatorial current system, but the models also agree on the existence of a permanent coastal mean flow to the north-west, from the equator into the Carribean Sea, in the form of a continuous current or a succession of eddies. Important differences are found between models in their representation of the eddy field. The reasons invoked are the use of different subgrid-scale parameterisations, and differences in stability of the NBC retroflection loop because of differences in the representation of the effect of bottom friction according to the vertical coordinate that is used. Finally, even if differences noticed between models in the details of the seasonal mean circulation and water mass properties could be explained by differences in the eddy field, nonetheless the major characteristics (mean seasonal currents, volume and heat transports) appears to be at first order driven by the strength of the thermohaline circulation.  2001 Elsevier Science Ltd. All rights reserved.

* Tel.: +33 4 7682 5066; fax: +33 4 7682 5271. E-mail address: [email protected] (B. Barnier).

0079-6611/01/$ - see front matter  2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 7 9 - 6 6 1 1 ( 0 1 ) 0 0 0 0 5 - 2

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Contents 1.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

2. Mean flow and water masses 2.1. Water mass analysis . . . 2.2. Seasonal circulation in the 2.2.1. Circulation in summer 2.2.2. Circulation in winter . 2.3. Seasonal transports . . . . 2.3.1. Section at 40°W . . . . 2.3.2. Section at 10°N . . . .

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3. Instantaneous flow and eddies in the North Brazil Current 3.1. Eddy variability in the NBC/NECC region . . . . . . . . 3.2. Characteristics of NBC rings in SIGMA . . . . . . . . . 3.3. Ring generation in SIGMA . . . . . . . . . . . . . . . . . 3.4. Fate of NBC rings toward the Caribbean Sea . . . . . .

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4.

Summary and discussion

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Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

1. Introduction The current system of the western tropical Atlantic ocean is marked by an intense variability, apparently in response to seasonal changes in the wind stress. This region is of particular interest for the ocean general circulation since it is a place where strong western boundary currents make a major contribution to the inter-hemispheric transport of properties. A schematic of the circulation in this region, presented in a review paper by Stramma and Schott (1996), is summarised below. In the upper 900 meters, boundary currents transport surface, central and intermediate waters northward from the South Atlantic, and constitute the major component of the upper branch of the meridional overturning cell. In the deep western boundary current below, the lower branch of the cell carries the cold North Atlantic Deep Waters (NADW) into the southern hemisphere. Therefore, the current system in this region of the Atlantic can be understood as resulting from the interaction of two major factors: the thermohaline overturning cell driving inter-hemispheric exchanges confined to the western boundary; and the system of the wind driven zonal currents along the equator. The surface seasonal circulation, and in particular the northward advection of warm surface waters by the North Brazil Current (NBC) has received most attention, and the flow pattern and its variability is now qualitatively described (see Stramma & Schott, 1996, for a review). The most pronounced seasonal change observed in this area is in the onset of the eastward North Equatorial Counter Current (NECC) in summer, in relation to changes in the wind stress curl in the northwestern tropical Atlantic (Johns, Lee, Beardsley, Candela, Limeburner & Castro, 1998;

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Garzoli & Katz, 1993). The strength of the eastward flow is significantly increased by the retroflection of the NBC, which leaves the coast of Brazil at 5°N to turn eastward and feed the NECC near 40°W. This event is followed by a collapse of the NECC in winter into a weak and broad flow sometimes reversing westward (Richardson & Walsh, 1986). Using a large variety of observations collected during the World Ocean Circulation Experiment, Schott, Fischer and Stramma (1998) have recently quantified many aspects of currents and transports associated with the warm water inflow from the South Atlantic into the western North Tropical Atlantic. They confirmed the strong seasonal variability of the boundary current system north of the equator, but found no evidence of a significant seasonal variability in transport south of the equator. They estimate the NBC mean transport at 44°W to be 35 Sv with a small seasonal cycle of only 3 Sv. The other major source of variability in this current system comes from the mesoscale rings most of them detached from the NBC retroflection zone. NBC rings have been observed by Johns, Lee, Schott, Zantopp and Evans (1990) and Johns et al. (1998) using current meter moorings, by Didden and Schott (1993) using satellite altimetry, and by Richardson, Hufford, Limeburner and Brown (1994) using lagrangian drifters. After they have detached from the NBC, rings propagate northwestward along the coast of South America, and reach the Windward Islands where their fate is not well established. NBC rings are suspected to play a role not only in the northward transport of heat and salt, but also in the mixing of water properties, e.g. the dispersal of Amazon water (Muller-Karger, McClain & Richardson, 1988). Several aspects of the circulation in the western tropical Atlantic still need to be better understood. Quantification of the contribution of the various components of the circulation to the meridional transport of heat, salt and mass is needed. Four key issues are analysed is this work; 1. the relative importance of the wind-driven and thermohaline components of the flow; 2. the existence and origin of a continuous north-westward surface current along the coast of South America during the period when the NBC retroflects into the NECC; 3. the fate of the NBC rings when they reach the lesser Antilles, and their possible entrance into the Caribbean Sea; 4. the quantification of the variability of the flow and transports in this area to assess the significance of mean flow estimates from hydrography or current meter moorings. The present paper attempts to resolve these issues, based upon the solutions of model simulations carried out during the DYNAMO (Dynamics of North Atlantic Models) project which performed systematic intercomparison of three models of the North Atlantic circulation (DYNAMO Group, 1997). Willebrand et al. (2001, referred to as Wi01 hereafter) have discussed in great detail the general circulation simulated by the various numerical models used in DYNAMO. Thus, the output data from the various model simulations have provided the basis not only for model comparisons, but also for the sensitivity studies needed to assess the importance of the thermohaline circulation as a driving mechanism for the North Brazil Current. Additionally, the interest of using three different models, with very similar configurations and driven with exactly the same surface boundary condition, is to identify the robust features in the model solutions, which can then be compared with observations and further used as a basis for quantitative calculations.

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The numerics, configurations, and surface and lateral forcings applied to ocean circulation models used in the DYNAMO project are fully described in the final scientific report of the project (DYNAMO Group, 1997), and in Wi01. The model domain is the North Atlantic Between 20°S and 70°S, so the region of interest to this study, the western tropical Atlantic, is only a small part of the total modelled area. All three models use the same isotropic horizontal grid, 1/3° at the equator (37 km), which is fine enough at this latitude to permit the generation of mesoscale eddies. The major difference between the three models is the vertical coordinate. The first model, referred to as LEVEL, uses a geopotential (or z) coordinate system and is based on the GFDL-MOM numerical code (Cox, 1984; Do¨ scher, Bo¨ ning & Herrmann, 1994). A total of 30 levels are used in the vertical. The upper ocean (from the surface to 1000 m) is discretized with 12 levels, the vertical grid spacing increasing with depth from 35 m to 250 m. The second model, referred to as ISOPYCNIC, uses a potential density (or r) coordinate system and is based on the MICOM numerical code (Bleck & Smith, 1990; Bleck, 1998). The vertical discretization is made of 19 isopycnal layers of constant potential density s0. The density of the 10 top layers varies between 24.70 and 27.38, effectively covering the range of density observed in the upper 1000 m in the western tropical Atlantic (Wilson, Johns & Molinari, 1994). The third model, referred to as SIGMA, uses a topography following (or s) coordinate system based on the SPEM5 numerical code (Haidvogel, Wilkin & Young, 1991; Barnier, Marchesiello, de Miranda, Coulibaly & Molines, 1998). With 20 s-levels stretched to increase resolution near the surface, this model has 12 vertical levels in the upper ocean in the region of the North Brazil Current where the total depth is 3500 m. For the main DYNAMO experiment, the three models have been initialised with a state of rest using the climatology of Levitus (1982) for the month of September, and integrated over a period of 20 years. The atmospheric forcing driving these experiments is the monthly mean flux field derived from 6-hourly ECMWF analyses for the years 1986 to 1988 (Barnier, Siefridt & Marchesiello, 1995; Siefridt, 1994). The salinity forcing is a simple relaxation of the model surface salinity to the seasonal sea surface salinity of Levitus (1982). In the western tropical Atlantic, such a forcing parameterizes the effect of the Amazon river discharge on salinity. The last 5 years of these runs have served as the analysis period for the model intercomparisons and are also used for the present study. This period has been chosen after the convergence of the overturning was sufficiently established in all models (see Wi01 for discussion). Characteristics of the general circulation in the three models are discussed in Wi01. These model simulations produce overturning cells which are significantly different in strength and pattern. In all three models, the mean overturning is driven by the basin scale meridional density gradients, and therefore depends on the lateral conditions applied at the northern and southern limits. Differences in the large scale thermohaline circulation between models are explained in terms of different representation of localised processes. Most important is the amount and mixing of water properties of the overflow in the region of the Greenland–Iceland–Scotland ridges and sills. Details in the representation of the bathymetry also have their importance. For this study, several properties of interest concerning the various model experiments have been compiled in Table 1. It shows that the overturning in LEVEL is significantly smaller than those of the two other models. According to Wi01, this related to the weaker overflows and different flow–topography interactions (compared to SIGMA) and to excessive mixing south of the overflows (compared to ISOPYCNIC).

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Table 1 Characteristics of the various experiments discussed in the paper Model experiment

Vertical coordinate

Vertical discretization

Upper ocean resolution

Lesser Antilles

Overturning at 24°N

Heat transport at 24°N

SIGMA ISOPYCNIC LEVEL SIGMA-2

s r z s

20 20 30 20

12 10 12 12

750 m deep 75 m deep 75 m deep 3 Islands

18 16 12 12

1.12 1.20 0.85 0.85

levels layers levels levels

levels layers levels levels

Sv Sv Sv Sv

PW PW PW PW

The present study also makes use of the SIGMA-2 experiment, carried out with the s-coordinate model with similar configuration and forcing conditions, but with less smoothed topography and 3 additional islands in the region of the Lesser Antilles (see Wi01 for details). In the main DYNAMO experiment, only two Islands were considered in the Caribbean; the island of Cuba and one island for Hispaniola and Puerto Rico together. In the SIGMA-2 experiment a further three islands of 4–6 grid points each, are spread across the passage to act as a barier. Although still not very realistic because of numerical constraints in the representation of islands, this is an improvement of the representation of the topography considering the model resolution. As shown below, it is enough to provide some insight on the role of this arc of islands in influencing the passage of the NBC rings into the Caribbean Sea. But this experiment, which has an overturning cell significantly different from SIGMA, (in relation to different overflows at the northern sills, see Wi01) is also used as an additional sensitivity experiment in our attempt to achieve a better understanding of the relation between the NBC and the thermohaline circulation. 2. Mean flow and water masses In this section we provide an analysis of the water masses, and investigate the mean circulation in the western tropical Atlantic. This region is characterised by a large seasonal signal, and both summer and winter climatological seasons are studied. The climatological summer mean of the ocean field is obtained by averaging the field for the months of July, August and September over the five year duration of the intercomparison experiment. It therefore includes 15 monthly means. The same averaging is made for the months of January, February and March to provide the climatological winter mean. The region of study and the bottom topography for the ISOPYCNIC and SIGMA models are shown in Fig. 1. 2.1. Water mass analysis Surface waters in the tropical western Atlantic have distinctive T/S properties because of the very variable inputs of salt. The T/S relation relative to the depth range 0–1000 m has been studied for the region of retroflection of the North Brazil Current (Zone I in Fig. 1). Waters entering this area from the South Atlantic with the South Equatorial Current (SEC) mix with the fresh Amazon waters and with the waters flowing from the central North Atlantic. The water mass census for the summer period (Fig. 2) allows us to identify the three major

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Fig. 1. The region of the tropical Atlantic which is the focus of our study is shown, with the bottom topography (in meters, contour interval 500 m) for ISOPYCNIC and SIGMA. Sections at 40°W and 10°N shown by the heavy lines define the region (Zone I) where T/S census diagrams are calculated. The topography in LEVEL resembles rather closely the one of ISOPYCNIC.

water masses described by Wilson et al. (1994) from an oceanographic cruise in 1989 to the NBC retroflection region. The general shape of the T/S diagram for SIGMA and ISOPYCNIC is consistent with that obtained from the climatology of Reynaud, Legrand, Mercier and Barnier (1998), and also the one drawn by Wilson et al. (1994) based on hydrographic sections observed in August (their Fig. 3a). There are significant differences between LEVEL and the climatology. Relatively fresh surface waters (s0 above 24.5) are found in the depth range of 0–50 m with temperatures from 26°C to 29°C. The presence of these low salinity waters (34⬍35.6) is related to the discharge of the Amazon river and also to advection of low salinity waters from the north tropical ocean where large rainfall occurs in summer by the NEC. Note that in LEVEL no salinity ⬍35.2 is found, because the model uses a slightly different salinity forcing. All three models force the salinity equation with a relaxation to the same climatological data base (Levitus, 1982). However, LEVEL uses the climatological value of the salinity at the first model level (17.5 m), whereas because of their different formulations of the vertical co-ordinate, the two other models use the salinity at the surface (0 m). This yields significant differences in the Amazon region where low salinity waters are confined to the top 10 m. Above the s0=24 density surface, waters

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Fig. 2. Volumetric T/S diagrams in the summer season for the three DYNAMO models and the climatology of Reynaud et al. (1998) in the region of the tropical Atlantic defined in Fig. 1 as Zone I by the coast and the sections at 40°W and 10°N. The colour scale corresponds to the volume of water represented by a dot, in 1015 m3.

in LEVEL do not show the wide spread in salinity seen in both observations and the two other models. Instead, a large volume of water (dark blue in Fig. 2) has a salinity within a very narrow range (between 35.8 and 36.2). In winter (figure not shown), surface waters become saltier (S⬎34.5) and cooler, and no temperature above 28°C is found. The largest volume of water is found in all models in the temperature range of 26–27°C and the salinity range of 35.6–36.0. These waters are compared with the tropical Surface Waters (SW) that Wilson et al. (1994) identified with s0⬍24.5. Subsurface waters (24.5⬍s0⬍26 in the depth range of 50–200 m) are characterised in SIGMA and ISOPYCNIC by a broad salinity maximum (36⬍36.8) for temperatures between 18°C and 26°C. These correspond to waters of South-Atlantic origin brought into the region by the North

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Fig. 3. Mean surface currents in the summer season in LEVEL.

Brazil Under Current (NBUC) and the southern SEC. Their characteristics are similar to the Central Waters discussed by Wilson et al. (1994) and Stramma and Schott (1996). In winter (figure not shown) the salinity maximum extends up to 37 in SIGMA, but does not change in the other models. LEVEL shows a different behaviour with respect to this salinity maximum of Central Waters: between isopycnal surfaces s0=24.5 and s0=26, the salinity remains confined between 35.8 and 36.2. Between isopycnal surfaces s0=26 and s0=27, the T/S relationship shows a monotonic decrease of salinity and temperature with depth, very consistent with the observations. The scatter is low in SIGMA, and ISOPYCNIC, but is much larger in LEVEL mainly for waters between 10 to 14°C. This part of the T/S diagram describes the transition from the Central Waters to the Antarctic Intermediate Waters (AAIW), and is characterised by a monotonic stratification. The upper limit of the AAIW is given as the s0=27.1 at 500 m by Stramma and Schott (1996). It appears from the above analysis that the models have rich T/S properties. In the region of the NBC retroflection, four major water masses (Table 2) are identified, similar to those discussed by Wilson et al. (1994). This classification is retained for quantitative transport calculation in the region. Table 2 Density range of the major water masses in the NBC retroflection region

Layer Layer Layer Layer

1 2 3 4

Density range

Water type

Depth range at 30°W

s0⬍24.500 24.500⬍s0⬍27.125 27.125⬍s0⬍27.450 27.450⬍s0

Surface Waters (SW) Central Waters (CW) Intermediate Waters (IW) Deep Water (DW)

0–75 m 75–450 m 450–1000 m Below 1000 m

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2.2. Seasonal circulation in the thermocline The mean seasonal circulation of the surface layers in the western tropical Atlantic, as described by Stramma and Schott (1996), is qualitatively well reproduced by all models. The discussion, which will remain rather qualitative in this sub-section, will focus on circulation features which are incompletely elucidated. Transports associated with the circulation patterns pointed out below will be discussed in a quantitative manner in a following sub-section. 2.2.1. Circulation in summer Surface Waters: The salient features of the surface current system in summer are reproduced in all model solutions (the solution for LEVEL is shown in Fig. 3). The southern branch of the South Equatorial Current (sSEC), concentrated between 2°S and 4°S, feeds the cross-equatorial North Brazil Current (NBC) at the western boundary. This current flows along the coast until a large portion retroflects between 6°N and 8°N and flows to the south-east to feed the NECC at 5°N. The pattern of the summer mean flow suggests that part of the retroflected waters recirculates back into the NBC. A remarkable feature of all models is that, in contrast to earlier models studies based on the GFDL model (e.g. Philander & Pacanowski, 1986; Schott & Bo¨ ning, 1991) which showed negligible flow along the boundary north of the NECC, the retroflection here is only partial and does not interrupt the continuation of the boundary current towards the Caribbean Sea during this season (likely because of a greater overturning in the DYNAMO simulations, see Wi01). The models also suggest that the northern branch of the South Equatorial Current (nSEC) mainly feeds the NECC, but its contribution to the EUC (suggested by Stramma & Schott, 1996; Schott et al., 1998) seems to be small in all models. Central Waters: The circulation of the central waters (layer 2 in Table 2) is illustrated in Fig. 4 showing the mean velocity vectors for each model at a depth of 110 m (within the thermocline). The most prominent feature shown is the Equatorial Undercurrent (EUC) along the equator. In all the models this current is fed principally by the North Brazil Undercurrent (NBUC), a northward boundary current with a subsurface maximum, that originates between 12 and 14°S. Although earlier model studies predicted its existence, this undercurrent was only recently confirmed observationally by Stramma, Fischer and Reppin (1995), who detected it using direct velocity measurements and geostrophic velocities from hydrographic sections; they reported an alongshore velocity of 80 cm/s in November at 10°S and at 5.5°S. Schott et al. (1998) give observed velocities of ⬎70 cm/s at 5°S in October and March and estimated the transport associated with this current as 23 Sv. The NBUC is a strong feature in all models (Fig. 4). A vertical section at 8°S (not shown) shows a 150 km wide current flowing north, with a core at 100 or 150 m depth. It has an average speed in summer of 45–60 cm/s, according to the models. The current is strongly stratified (i.e. important temperature and salinity vertical gradients are found within the vein of the current), and it carries waters with a wide range of temperature and salinity. The core of the current carries high salinity waters (S⬎36.5), and just below the core of the current, at 200 m, a large salinity gradient occurs. In the present model simulations, the NBUC is a continuous boundary current, and can be considered as the lower part of the NBC north of the equator. As it flows north,

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Fig. 4.

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Mean subsurface currents at 110 m depth in the summer season in a) SIGMA, b) LEVEL, and c) ISOPYCNIC.

several branches of the current feed the zonal equatorial current system. A small branch feeds into the EUC directly at the equator, consistent with the scheme proposed by Schott et al. (1998). A second and larger branch retroflects at 5°N, like the surface NBC current. The circulation pattern is quite complicated, since a portion of the retroflected current flows eastwards with the NECC, while another portion flows back to the equator where it merges with the EUC; a signifi-

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Fig. 4 (continued)

cant portion of this flow recirculates back into the NBC around an anticyclonic eddy centered at 2.5°N, which could be compared with the Amazon eddy of Bruce, Kerling and Beatty (1985). The branch of the flow which continues along the coast also turns to the east at 8°N and merges with an equatorward flow which feeds the deeper part of the NECC and can be considered as the Guyana Undercurrent (GUC). Earlier CME simulations implied the existence of a similar, equatorward boundary current with a subsurface maximum (Schott & Bo¨ ning, 1991); some evidence for the GUC was produced by the measurements of Wilson et al. (1994). All three models sustain a similar scenario; in summer the GUC is mainly formed by the retroflection of the deeper part of the NBC, but it also includes waters from subtropical origin. Note that SIGMA and LEVEL show that the retroflection loop at 8°N is associated to an anticyclonic eddy which could be compared to the Demerara eddy discussed by Bruce et al. (1985). The last characteristic that is worth pointing out is that the retroflection of the deeper NBC at 8°N is not total and the current connects with the broad westward flow of the North Equatorial Current (NEC) beyond 10°N, and as for the surface waters, the deeper NBC continues into the Caribbean Sea. 2.2.2. Circulation in winter Surface Waters: There is a remarkable similarity in the winter circulation pattern (shown in Fig. 5 for SIGMA) between all the models. In this season, the eastward flow of the NECC has collapsed and is replaced by a north-westward flow. A remnant of the summer/fall retroflection pattern persists in the boundary current, but is shifted somewhat to the north. The deflected water, however, only penetrates to about 45°W, before turning north again and merging with the NEC. Nevertheless, north of 5°S, all models show a flow to the north-west over the whole area (excepted

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Fig. 5. Mean surface currents in the winter season in SIGMA.

just at the equator where the EUC may outcrop between 45°W and 25°W), and there is a continuation of the NBC towards the Antilles passages in winter as speculated some time ago by Philander and Pacanowski (1986). Central Waters: The similarity in the winter circulation pattern (shown for SIGMA in Fig. 6) between models extends below the surface, where the deep part of the NBC still shows a retroflec-

Fig. 6. Mean subsurface currents at 110 m depth in the winter season in SIGMA.

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tion, between 3°N and 5°N, but the water now feeds into the EUC. As for the surface flow, the retroflection of the NBC is only partial and the current finds its way along-shore into the Caribbean Sea. Note that the boundary current does not seem to be significantly stronger in this season than in summer. During the winter season there is a clear indication of an equatorward undercurrent from the north (the GUC), joining the retroflected NBC water. In contrast to the CME situation where this current appeared as a strong boundary flow emanating from the Caribbean, in the Dynamo solutions it is weaker and originates in the NEC at about 12°N. 2.3. Seasonal transports To quantify the seasonal circulation discussed above, based on the horizontal circulation patterns, a budget of the various water masses identified in Table 2 is performed at the limits the retroflection region (Zone I in Fig. 1). Summer and winter mean volume transports across the 40°W and 10°N sections, accumulated from the coast of South America to their crossing point at 40°W–10°N, have been calculated for each of the 3 density layers representing the various waters masses in the first 1000 m depth (as in Table 2). Temperature transports have also been calculated (as the time average of the instantaneous correlation between cross-section velocity and temperature, and thus include the eddy component). Heat transports are very similar to volume transports in their distribution (with a linear relationship), and will not be shown. Nevertheless, they are used is the discussion below. In this section, similarities and differences between model solutions are used better to understand and quantify the flow patterns in the region of interest. 2.3.1. Section at 40°W Summer and winter mean volume transports across 40°W, cumulated from the land (at 5°S) up to 10°N, are shown in Fig. 7 for the Surface, Central and Intermediate Waters altogether (i.e. waters with density s0=⬍27.45). The vertical patterns of the current across 40°W in summer are shown in Fig. 8 for each model. Summer season: The volume transport across 40°W in summer has a similar pattern in all models, and reflects the alternation of eastward and westward flows characteristic of the equatorial current system. Within the NBC, which is still south of the equator at this longitude (roughly between 3°S and 1°S), the surface waters enter the retroflection region at a rate of 38.3 Sv in SIGMA (the associated heat transport is 2.68 PW), 34.7 Sv in ISOPYCNIC (2.32 PW), both in excellent agreement with the estimate of 37 Sv obtained by Schott et al. (1998) from moorings and shipboard sections. This inflow is lower (20.5 Sv) in LEVEL (1.45 PW). The meridional overturning at 24°N in these models (Wi01) is respectively 18 Sv in SIGMA, 16 Sv in ISOPYCNIC and 12 Sv in LEVEL, suggesting the NBC is being strongly driven by the thermohaline circulation. Comparing of the results of SIGMA and SIGMA-2 (Fig. 7) confirms this suggestion. The NBC is smaller by 5 Sv in SIGMA-2, in relation to an overturning cell of 12 Sv at 24°N (see Wi01) which is 4 Sv smaller than in SIGMA. However, the volume transport in the NBC and its retroflection into the EUC is significantly larger in SIGMA-2 than in LEVEL, although both models have a similar overturning, as shown by Wi01. This difference can be partly attributed to a local difference in the circulation pattern. SIGMA-2 produces an elongated anticyclonic recirculation around the Parnaiba Ridge, a topographic feature located at 2°S, 38°W, which

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Fig. 7. Mean volume transports across 40°W for several of the DYNAMO models, in (a) summer and (b) winter, integrated from the coast of South America for waters of potential density s0⬍27.45. This includes the first 3 density layers defined in Table 2. Negative values indicate net westward transports. Currents to the west correspond to a decrease in transport (i.e. negative values get larger), and current to the east by an increase in transport (i.e. negative values get smaller). Units are in Sv (1 Sv=106 m3/s).

contributes to the enhancement of the transport in the NBC by 4 Sv. This feature is absent from LEVEL, but appears in SIGMA to a lesser extent because of the larger topographic smoothing, so its contribution to the transport at 40°W is negligible. There are differences between models in the vertical partition of the transport within the NBC. In LEVEL the current is concentrated within the first 500 m (Fig. 8b) and essentially transports SW and CW, whereas in the two other models it extends to greater depth (Fig. 8a,c) and so transports a significant amount of IW to the north (between 5 Sv and 8 Sv). The vertical structure of the NBC in the first 500 m depth before it crosses the equator is very similar in all the models and reflects the convergence of the shallow SEC, and the deeper NBUC. Maximum summer mean velocities are ⬎80 cm/s at the surface, and a subsurface core corresponding to the NBUC occurs

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Fig. 8. Vertical structure of the mean zonal currents (cm/s, interval of 5 cm/s) in summer, across 40°W in the upper 1000 m for (a) SIGMA, (b) LEVEL, and (c) ISOPYCNIC. Grey-shaded areas indicate eastward currents, and westward currents are in white. There are slightly more than 3 model grid points per degree (the resolution is 1/3° cos j, j being latitude).

between 100 m and 150 m, with maximum velocities ranging from 65 cm/s in SIGMA, to 40 cm/s in ISOPYCNIC and LEVEL. Between 1°S and 1°N, the EUC is responsible for an outflow to the east which in SIGMA is almost double (32.5 Sv) that in LEVEL and ISOPYCNIC (14 Sv). Correspondingly, velocities in the EUC (Fig. 8) are larger in SIGMA (55 cm/s) than in the two other models (30 cm/s to 35 cm/s). Since the wind forcing is the same in all models simulations, this indicates that a large part of the NBC feeds the EUC, as seen on the instantaneous flow (Figs. 12 and 13). This implies a strong retroflection of the NBC/NBUC turning back to the equator. Just north of the equator (1°N–4°N) the transport of the northern branch of the SEC (Fig. 7a) is unrealistically weak in ISOPYCNIC (2 Sv), and reaches more realistic values in LEVEL (7 Sv) and SIGMA (12 Sv). A vertical section of the velocity field (Fig. 8) shows that this current is confined to the upper 500 m, so the nSEC carries only SW and CW toward the coast of Brazil,

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which is consistent with its wind-driven nature. This current is continuously sheared from the surface (30 cm/s) to 500 m (5 cm/s) in SIGMA, whereas in LEVEL and ISOPYCNIC it appears split with a surface and a subsurface core, such a structure is seen in observations along a 44°W section in October when the EUC is weaker, but not in March when the EUC nearly outcrops and the flow pattern is more like in SIGMA (Schott et al., 1998). In ISOPYCNIC, these cores do not connect in the mean (it is likely that in this model the laplacian friction, which is less selective in wavenumber than the biharmonic friction used in the other models, induces a larger horizontal mixing of momentum between the EUC and the NECC, resulting in a particularly weak NECC below the mixed layer). The last feature of interest is the NECC. Its volume transport between 4°N and 9°N (Fig. 7a) is almost identical between the models (about 15 Sv), and the vertical structure of the current (Fig. 8) is also similar, although there are differences in the location of the core of the mean current. This indicates that this current is essentially wind driven. Indeed a strong thermohaline driving would induce a large difference between LEVEL and the other models. Interestingly, despite noticeable local differences between SIGMA and ISOPYCNIC, both model show very similar net (cumulative) transports of water and heat across the 40°W section (7 Sv and 0.7 PW), consistent with a similarity in the strength of the thermohaline circulation. The same comment holds for LEVEL and SIGMA-2, with a similar (but weaker) overturning, both models show the same cumulative transport across the section. Winter season: The transport in the NBC between 0 m and 1000 m (Fig. 7b) is the same as in Summer in LEVEL (20 Sv, 1.4 PW), but is reduced in SIGMA (29 Sv, 2.3 PW), ISOPYCNIC (24 Sv, 2.0 PW) and also in SIGMA-2 where it is very similar to LEVEL. The transports calculated for every type of water (not shown) indicate that the variability in these models is essentially caused by a reduction in the transport in SW and IW; the transport of CW (in the depth range 75 m to 450 m) is basically unchanged (see Table 3). Therefore, all models agree (including SIGMA-2) that the NBUC, which mainly occupies the central waters at this longitude, shows little seasonal variability (in very good agreement with the conclusions of Schott et al., 1998). This vein of current could be seen as a major component of the thermohaline circulation at this latitude. Table 3 Budget of volume transport (in Sv) for the surface (s0⬍24.500) and central (24.500⬍s0⬍27.125) waters across 40°W Model experiment

SIGMA

Water type

Surface Central LEVEL Surface Central ISOPYCNIC Surface Central SIGMA-2 Surface Central

NBC+SEC (westward)

EUC+NECC (eastward)

Budget (westward)

Summer

Winter

Summer

Winter

Summer

Winter

13.4+5.0 21.0+10.0 8.0+4.5 12.0+4.0 16.7 17.0+1.5 11.4+7.0 16.5+5.1

9.0+5.5 20.0+3.5 7.0+3.0 14.5+1.0 9.0 17.0+0.0 9.6+6.7 14.6+0.5

4.0+8.0 23.0+8.0 0.0+8.0 12.0+8.0 0.0+8.6 13.5+8.0 2.2+9.2 19.5+7.6

8.0+0.0 14.0+0.0 2.5+0.5 12.0+0.0 0.0 12.0+0.0 7.0+1.9 9.6+0.5

6.4 0.0 4.5 ⫺4.0 8.1 ⫺3.0 7.0 ⫺5.5

6.5 9.5 7.0 3.5 9.0 5.0 7.4 5.0

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The EUC transport is also reduced in winter, in the same proportion as the NBC. The crosssection velocities (figure not shown) indicate that this current is weaker and shallower in winter at this longitude. At this period of the year, the NECC has totally collapsed, and the nSEC is confined to the very near surface, so the transport north of 3°N remains fairly small. As in summer, the net (cumulative) transports of water and heat across the section are similar for SIGMA and ISOPYCNIC (about 16.5 Sv and 1.3 PW), but are lower (by almost 7 Sv and 0.7 PW) in LEVEL and SIGMA-2, reflecting the discrepancies observed in the strength of the thermohaline circulation. 2.3.2. Section at 10°N Volume transports at 10°N, accumulated eastward from land (70°W) to 40°W, are shown in Fig. 9 for the Surface, Central and Intermediate Water altogether (density layers 1–3 in Table 2).

Fig. 9. Mean volume transports across 10°N for the 3 DYNAMO models, in (a) summer and (b) winter, integrated from the coast of South America for waters of potential density s0⬍27.45. This includes the first 3 density layers defined in Table 2. Positive values indicate northward transports. Currents to the south correspond to a decrease in transport, and current to the north to an increase in transport. Units are in Sv (1 Sv=106 m3/s).

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Therefore, these transports involve the waters with densities s0⬍27.45 in the depth range 0–1000 m. The vertical current patterns across this section are shown in Fig. 10 to illustrate the baroclinic aspect of the flow. The heat transport across 10°N has also been calculated for every type of water identified in Table 2 and, although not shown, will be used in the discussion. Summer season: the northward transport (Fig. 9a) is concentrated in the NBC along the coast of North America; between 60°W and 62°W the transport is 17.5 Sv (1.3 PW) in SIGMA, 12 Sv (0.76 PW) in ISOPYCNIC, but only 3 Sv (0.3 PW) in LEVEL. SIGMA shows a very tight (1° wide) southward recirculation (5.5 Sv) just to the side of the NBC associated to a heat transport of 0.3 PW. This is the result of the Eulerian averaging of the anticyclonic NBC rings when blocked by the Antilles Arc. As will be shown in the next section (see Fig. 11), the rings follow basically the same path to the north-west throughout the year, but decelerate for a time while they interact with the topographic rise of the Antilles. The averaging of the Eulerian currents results in a northwestward flow along the coastal side of the path, and a reverse flow to the south-

Fig. 10. Vertical structure of the mean meridional currents (cm/s, interval of 5 cm/s) in summer, across 10°N in the upper 1000 meters for (a) SIGMA, (b) LEVEL, and (c) ISOPYCNIC. Grey-shaded areas indicate southward currents, and northward currents are in white. There are 3 model grid points per degree (the model resolution is 1/3° in longitude).

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Fig. 11. A snapshot of the near surface current speed in (a) SIGMA, (b) LEVEL, and (c) ISOPYCNIC at the end of summer during the 17th year of model integration (September 30). Units are in cm/s and contour interval is 20 cm/s. Grey areas outlines speeds above 20 cm/s. NBC eddies are identified as Ei, i=3–7 (see text). The numbering of the eddies is chronologically consistent between Figs. 11 and 12, eddy E1 being generated in early November.

east along the off-shore side. Therefore, an estimate of the net transport of the NBC including both contributions is 12 Sv to the north at 59°W, the same value as for ISOPYCNIC at this longitude. No similar pattern is seen in ISOPYCNIC which is the model with the smallest eddy activity (NBC rings are almost non-existent in this model). However, it is interesting to note that both models have a thermohaline circulation of equivalent strength, and also have similar net transport in the NBC. In contrast, LEVEL (and SIGMA-2) shows a much weaker NBC transport

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at this latitude, consistent with its weaker overturning. Nevertheless, NBC rings are noticeable features in this model, and an eddy-driven recirculation pattern (2.5 Sv) is also seen, which reduces the net transport across the 10°N section almost to zero. The two other models imply that the net transport across this section is 9.2 Sv leaving the region of interest to the north, compared with 6.3 Sv (SIGMA) and 7.2 Sv (ISOPYCNIC) that enters the domain from the east (at 40°W). So to close the budget in summer between the 10°N and 40°W the sections require there to be an upwelling of about 2 to 3 Sv from below 1000m. The models show differences in the vertical structure of the currents (Fig. 10). In LEVEL, the NBC is confined to the upper 75 m, and has a maximum summer mean velocity of 35 cm/s. Consequently, the transport (shown in Fig. 9) in LEVEL is essentially surface waters (s0⬍24.5). The NBC is also intensified near the surface in both ISOPYCNIC and SIGMA, both models showing a maximum mean current in summer of nearly 65 cm/s. However, these models still show a northward flow of the order of 5 cm/s (ISOPYCNIC) to 10 cm/s (SIGMA) at depths ⬎400 m along the shelf break, so according to them the NBC is transporting northward all three of the major water masses present in the main thermocline (SW, CW and IW defined in Table 2). SIGMA-2 contributes some quite interesting information here. As seen in Fig. 10, the SIGMA2 suggests a transport across 10°N that is similar to that of LEVEL (with however a larger transport in the boundary current). The vertical pattern of the current (not shown) is very much alike the one presented in Fig. 11 for LEVEL, with a current confined to the upper 200 m. In this model too, the northward transport is mostly comprised of SW with some CW, but no IW flows north with the western boundary current. The southward recirculation seen in the plot of the transport between 59°W and 55°W (Fig. 9) is related to the southward flow seen to the east of the NBC in the velocity section (Fig. 10). This flow is present in all models. In SIGMA and LEVEL, it has a subsurface maximum at 50 m depth, and could be considered as the signature of the GUC. ISOPYCNIC is slightly different, probably either because this model homogenises momentum within the mixed-layer, or because it contains no NBC rings at this latitude. Even so, the basic pattern of the flow in ISOPYCNIC is similar to that of the other models. The deeper extent of the NBC and its recirculation in SIGMA results from the greater eddy activity in this model (see section 3), with eddies propagating momentum deeper by form drag. Winter season: Once the NECC collapses, in every model the winter volume transport in the NBC (Fig. 9b) increases by a similar amount (苲3 Sv). It reaches 22 Sv (1.65 PW) in SIGMA, 14.5 Sv (1.02 PW) in ISOPYCNIC, and 6 Sv (0.76 PW) in LEVEL (SIGMA-2 shows a similar increase from 9 Sv to 12 Sv). The eddy driven recirculation is still very strong in SIGMA, and carries a significant amount of heat southwards (0.72 PW), so east of the recirculating flow (near 57°W) SIGMA again has a similar volume and heat transport to that of ISOPYCNIC (13 Sv and 0.9 PW), whereas LEVEL again shows lower transport, of about 7 Sv (0.4 PW). The most striking summer versus winter difference in all the models is the reversal of the transport in the open ocean east of 52°W to the north in winter. This is a result of the strong northward Ekman drift in winter, as can be seen in comparing the surface flow in SIGMA (Fig. 4a and Fig. 5). In Table 4, the summer to winter change in northward transport in the NEC in the surface layer is of the order of 4 Sv in all three models. This value of 4 Sv is a fair estimate of the summer to winter change in Ekman transport across this section, since the surface flow in the NEC at 10°N is dominated by the Ekman drift in winter. Considering the budget in the last

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Table 4 Budget of volume transport (in Sv) for the surface (s0⬍24.500) and central (24.500⬍s0⬍27.125) waters across 10°N Model experiment

SIGMA

Water type

Surface Central LEVEL Surface Central ISOPYCNIC Surface Central

NBC+NEC (northward)

NBC recirculation (southward)

Budget (northward)

Summer

Winter

Summer

Winter

Summer

Winter

6+1 10+1 3+0.2 0.5+0.2 4.2+0.1 3.5+1

7+4.8 12.2+0.5 4.7+4.3 2.1+⫺0.1 7+4.8 4+0

3.2 6.7 0.5 1.9 0.5 2.5

2 7.5 1 1.9 2 1

3.8 4.3 2.7 ⫺1.2 3.8 2

9.8 5.2 8 0.1 9.8 3

column of Table 4 which indicates a summer to winter change in the northward transport of the order of 5–6 Sv, it is reasonable to conclude that the seasonal transport fluctuations in this region are dominated by changes in Ekman transport. Indeed, Central and Intermediate Waters do not contribute to these variations in transport, and the vertical structure of the flow below the Ekman layer in winter (not shown) is very similar to that in summer as shown in Fig. 10. Summer to winter changes in the NBC transport are nearly identical in all models. This suggests that the variability of the surface current system is essentially wind driven. Bo¨ ning, Dieterich, Barnier and Jia (2001) have also found that the DYNAMO models generate similar amplitudes and patterns of the seasonal signal at 25°N. The partition of transport between the western boundary current and the interior flow up to the eastern boundary is summarised in Table 5 for SIGMA. In this model, the wind forcing is applied as a body force over the upper 50 m, so away from strong geostrophic or inertial currents, the transport between 0 and 50 m is a good approximation of the Ekman transport. From Table 5, it appears that in the NBC (0–1000 m) the volume transport (9.76 Sv) is more than double the Ekman transport (0–50 m) across the whole section (4.50 Sv). With a heat transport of 0.75 PW between 0 and 1000 m, the NBC accounts for more than half of the total heat crossing the 10° section (which is 1.02 PW from top to bottom). These numbers are similar in ISOPYCNIC in which the boundary current is as strong as in SIGMA, but would change the balance between boundary transport and Ekman transport in LEVEL because the latter’s weaker boundary current (with the same wind forcing, the Ekman transport is the same in all models). Table 5 Annual mean budget of meridional volume and heat transports at 10°N in SIGMA Transport

NBC (including recirculation)

Interior (excluding NBC)

Total across 10°N

Volume (Sv)

Volume (Sv)

Volume (Sv)

Heat (PW)

9.12 16.08 17.10

0.99 1.27 1.02

Heat (PW)

Heat (PW)

Surface to 50 m 4.62 0.50 4.50 0.49 Surface to 1000 m 9.76 0.75 6.32 0.52 Surface to bottom northward volume and heat transports (including AABW)

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The analyses performed in this section have shown that the discrepancies in the mean properties of the NBC between the models are consistent with the differences in their respective overturning. In addition, SIGMA and ISOPYCNIC have very similar net transports in the NBC despite indicating very different eddy activity. All this indicates that the strength of the thermohaline circulation is of primary importance in the determination of the heat and volume transport of the NBC. 3. Instantaneous flow and eddies in the North Brazil Current The three models have significantly different levels of eddy kinetic energy (eke), as shown by Wi01, so it is to be expected that they will not represent eddy variability in the same way. In this section we study the mesoscale eddies in the various models in the western tropical Atlantic, and attempt to clarify their impact on the mean flow as has been described in the above sections. 3.1. Eddy variability in the NBC/NECC region Fig. 11 shows a snapshot of the current speed near the surface in the three models in early fall, a time of the year when the NBC retroflection into the NECC is well developed. The mean flow pattern, with the double retroflection pattern of the NBC, first into the EUC, then into the NECC, is similar in all models as already described in previous sections, but differences appear in the eddy fields. There are signs of an eddy variability of very small amplitude in ISOPYCNIC in which coherent eddy patterns can hardly be discerned. The probable reason is the use of harmonic lateral friction, as already discussed in Wi01. Therefore in this model the instantaneous flow resembles the mean seasonal circulation, and clearly in the fall the retroflection does not interrupt the coastal flow to the north-west. In contrast, coherent mesoscale eddies are strong features in LEVEL and SIGMA (both use biharmonic friction). However, the strength of the eddies is significantly higher in SIGMA (SIGMA-2 also has eddies of very similar strength and number to those seen in SIGMA), although both models use the same friction coefficient, a point which will be discussed later on. North of 5°N, the circulation is dominated by coherent eddies (or rings) that propagate along the coast towards the Caribbean Sea. Four anticyclonic rings are seen in Fig. 11 in both models, more or less in the same stage. One appears to have recently detached from the retroflection loop and is crossing 10°N (E7). Another (E6) has reached the topographic rise which represents the arc of the Antilles Islands (note these islands are not explicitly represented in the models) between 60°W and 65°W. The ring appears to be strongly constrained by its interaction with the topography and can not pass through. In both models, the two rings seen in the Caribbean Sea (E5, E3+4 or E4) indeed originated in the NBC. Over the 5 years of the inter-comparison period, 32 rings crossed 10°N in SIGMA, an annual generation rate of 6.4. Rings are generated at roughly 2 monthly intervals, indicating that the generating process is active all year round and is not a seasonal feature related to the retroflection of the NBC into the NECC. This number of rings is consistent with the number of mesoscale features observed in the region by Johns et al. (1990) (JO90 hereafter). The greater strength of the NBC in SIGMA (Fig. 7), in relation to a larger overturning, is certainly responsible for the higher eddy velocities seen in SIGMA. However, the strength of the

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overturning cannot account for the large eddies observed in SIGMA-2, and so friction which is not similar in z or s coordinate models in this coastal region must also be considered. If the dissipative effects of the quadratic drag law used to parameterise bottom friction (see Wi01 for details) are similar in both models, the effects of the lateral friction used for numerical stability will differ because of the different vertical coordinates. In relation to the no-slip boundary condition applied to the stair-case topography in LEVEL, the lateral dissipation by the bi-harmonic operator is enhanced at the grid point nearest to the bottom because of the existence of large gradients in the side-wall boundary layer. No such boundary layer exists in the topography following coordinate model and lateral friction near the bottom remains of the same order as in the interior ocean. Therefore, SIGMA, and also SIGMA-2, may have less dissipation near the bottom than LEVEL, and this may explain the greater velocities observed both in the mean currents and in the NBC rings in the s-coordinate models. This issue of different effective bottom friction between these type of models has been recently discussed in de Miranda, Barnier and Dewar (1999) who reached similar conclusions. The levels of turbulent kinetic energy reflect these discrepancies between the models in their representation of eddy variability. SIGMA has by far the largest eke values (Table 6), very similar to those observed for example by JO90 at mooring site C (52.1°W, 8.5°N). For this reason, the properties of the NBC rings have been studied mainly using the results from this model. 3.2. Characteristics of NBC rings in SIGMA Fig. 12 shows a sequence of snapshots in SIGMA in which the evolution of the NBC rings is described over a two month period from April 12 to June 12, i.e. several months before the onset of the NECC. Note that SIGMA-2 is very similar to SIGMA with respect to NBC rings, and many of the comments that follow remain valid for this experiment. During this sequence, one ring (ring E5) forms and fully pinches off from the retroflection loop in the NBC into the EUC. E5 appears as an almost coherent mesoscale pattern as it crosses 5°N. Didden and Schott (1993) using sea surface height (ssh) anomalies from Geosat identified several coherent NBC rings north of 5°N. Another ring (E6) is forming in the retroflection loop, and appears as a coherent ring two weeks later. The two rings, which are seen entering the Caribbean Sea, were generated during the previous fall (E1) and early winter (E2) when the NECC was fully established. Rings E3 and E4 were generated in January and March, but merged by mid May because E3 was slowed down as it encountered the Trinidad–Tobago topographic rise (such ring merging has been reported by Didden & Schott, 1993). Table 6 Range of eddy kinetic energy at (55°W, 10°N) for various depth ranges Depth

SIGMA

LEVEL

ISOPYCNIC

0–500 m 500–1000 m 1000–1500 m 1500–2000 m

1000–100 cm2/s2 100–50 cm2/s2 50–25 cm2/s2 25–5 cm2/s2

500–100 cm2/s2 10–5 cm2/s2 5–1 cm2/s2 5–1 cm2/s2

50–5 cm2/s2 5–1 cm2/s2 5–1 cm2/s2 5–1 cm2/s2

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Fig. 12. A series of snapshot of the near surface current speed in SIGMA during the 17th year of model integration, on (a) April 12, (b) May 12, and (c) June 6. Units are in cm/s and contour interval is 20 cm/s. Grey areas outlines speeds above 20 cm/s. NBC eddies are identified as Ei, i=1–6 (see text).

Kinematic properties of the model rings are comparable to those in observed in the real world. The translation velocity determined from an Hovmuller diagram at 10°N (DYNAMO Group, 1997) varies between 10 and 12 cm/s, but because of their interactions with the topography and other rings, their translation speeds are more variable along their path to the northwest. Observations gives similar translation speed (9 cm/s in the longshore direction in Johns et al., 1998). Considering ring E7 in Fig. 11 as a typical ring, instantaneous velocities in the ring range from 75 cm/s to ⬎100 cm/s at 70 m depth, corresponding to swirl velocities of the order of 60–80

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cm/s. The diameter of the ring is 390 km if measured according to the 30 cm/s contour line, a size which corresponds to the 400 km proposed by JO90. As seen from the snapshots of Fig. 12, the sizes of the rings can vary during their life time, but remain in the range of typical observed values. Comparison with observations is still very good for the instantaneous velocity field. As an example, the time series of the vector velocity at (52.1°W, 8.5N), the location of Mooring C of JO90, is plotted in Fig. 13. Our figure is directly comparable to their Fig. 3b. The amplitude and variability of the model velocities are fairly realistic, showing a regular variability (in the 40–60 day range) in the upper 900 m where velocities decrease from 1 to 10 cm/s, and a strong

Fig. 13. Times series of velocity vector in SIGMA for various depths at the mooring site C (52.1°W, 8.5°N) of Johns et al. (1990). The period corresponds to the 3rd year of the model intercomparison period. The usual convention of northward velocities being positive and vertical is used. Units are m/s. The gap in the data correspond to two snapshots files that were lost.

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and rather steady southwestward flow of nearly 10–15 cm/s at greater depth in the deep western boundary current. The vertical coherence of the eddy variability is remarkable down to 600 m and still noticeable at 900 m. With these characteristics, the volume of water transported by a typical ring, estimated as the volume of the ring (400 km in diameter, reaching a depth of 600 m) divided by the time it takes to the ring to go through a section (with a phase speed of 10 cm/s), is estimated to 18 Sv. In annual mean this transport is estimated to 15 Sv. Fig. 14 shows the time series of the vertical temperature profile in the model at site C, for two independent years (year 3 and year 5 of the model inter-comparison period). During year 3 (Fig. 14a) six NBC rings (R1–R6) pass through the mooring site (and another one is arriving at the end of the year). The perturbation W4 is not a ring and has been identified as a shallow eddy (or unstable wave) generated into the NECC which has reached the site (and will continue to the

Fig. 14. Times series of temperature profile between 0 and 1000 m at the mooring site C (52.1°W, 8.5°N) of Johns et al. (1990). The two plots correspond to the 3rd and 5th years of the model intercomparison period. Units are in °C and contour interval is 1°C. Rings are identified according to the text.

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coast where it rapidly vanishes). This feature is discussed in the next subsection. Rings generated during summer and fall (R1, R5 and R6) have greater vertical extents. In year 5 (Fig. 14b) the signature of the four NBC rings only can be seen to 500 m depth, although the snapshots (as those shown in Fig. 13) clearly indicate that six NBC rings were generated during this year. NBC rings R9 and R10, which have a shallow signature in Fig. 14b, were generated in spring at the retroflection loop of the NBC into the EUC. Being smaller in size than the summer/fall rings, their signatures at site C did not reach deeper than 300 m. This indicates that despite a climatological seasonal forcing, there is significant inter-annual variability in the signal associated with the rings, ant that long term continuous observations will be necessary to improve our understanding of the NBC rings. 3.3. Ring generation in SIGMA This model solution strongly supports the idea that NBC rings are regularly generated throughout the year. According to season, the rings form either by pinching-off from the retroflection loop of the NBC into the EUC (in winter–spring, Fig. 12), or the retroflection loop into the NECC (summer–fall, Fig. 11a). This scenario is consistent with the observed variability of the currents in the region. Over five years of model simulation, NBC rings in SIGMA originated from one or other of the retroflection loops. In winter and spring the full separation of the ring usually occurs at 5°N. But in late summer and fall, when the NECC is fully developed, the separation region moves up to 8°N coinciding with the retroflection loop into the NECC. Although a detailed stability analysis has not been performed, the generating process is very likely to be shear instability, as suggested by the ratio of the eddy length scale to the internal deformation radius being less than one. (A map of this ratio, estimated as the ratio of the eddy potential energy to the eddy kinetic energy was published in DYNAMO Group, 1997.) During the summer/fall period, large wavelike westward-propagating structures have been observed in the NECC, east of the retroflection for a long time. Baroclinic Rossby waves have often been invoked to explain for their generation (JO90). In SIGMA, during the onset of the NECC in summer, it was observed that the meridional density gradient and the vertical shear progressively increased in the 3°N–8°N longitude band, creating conditions favourable for the growth of baroclinic instability (the non dimensional eddy length scale is of the order of 1–5 between 30°W and 50°W in this latitude band, see DYNAMO Group, 1997). By early fall, wavelike patterns begin to appear at 30–35°W in the region of shear between the nSEC and the NECC (Fig. 16), and these grow as they propagate north-westward. These perturbations can reach a large amplitude by the end of fall or early winter, when the reservoir of potential energy is at its maximum, so it is unclear whether they should be considered as wavelike perturbations or as coherent eddies. Note that these favourable instability conditions persist for a few months after the collapse of the NECC, and mesoscale variability can continue to be generated until the end of winter. This is responsible for the remnant of the NECC retroflection pattern that persists in the winter mean-flow (see section 2.2.2). Looking at 5 year long time-series of 3-day snapshots, it seems that NBC ring generation is not being caused by the passage of the waves, but both strongly interact: ring pinch-off in summer/fall often results from the merging of the waves with the retroflection loop. This interaction generally results in greater enhancement of the strength and size of the NBC rings during this season, relative to winter/spring. However, a very few

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cases were noted in which the wave-eddy was destroyed by interaction with the retroflection, which may have delayed but not prevented the generation of a ring. After such negative interaction, NBC rings can still be very intense, which indicates that the major reason for stronger rings in the summer/fall period is not the result of interaction with the waves, but rather the acceleration and increase in transport of the NBC (Fig. 7). In one event (eddy W4 in Fig. 14) it was noticed that the wave pattern did not interact with the retroflection loop, but moved westward and reached the coast of Brazil at 10°N where it rapidly dissipated. This is another indication that the NECC waves are not the main generating mechanism for the NBC rings. Finally, it is interesting to note on the snapshots in Fig. 12 that the current speed near the coast is weak between the rings. However, the velocities (not shown) are generally to the north-west, which is consistent with the mean current seen in Fig. 4. This situation is most common and suggests that a continuous flow in the direction of the Caribbean Sea exists independently of the rings. However, this current is weak, and the strength of the continuation of the NBC beyond the retroflection loop results largely from the averaging of the eddies. To obtain an accurate estimate of the contribution of the eulerian averaging of the eddies to the mean current is not really possible because each ring needs to be isolated from the background flow. A rough estimate can be obtained by estimating the contribution to the mean current of the mean swirl velocity resulting from successive passages of the rings. Considering that it takes about 28 days on average for a ring to pass across the 10°N line, and that about 6.4 rings cross it every year, a ring will be encountered along this section 179 days per year. Considering an average swirl velocity of 60 cm/s at 100 m (which is consistent with the stick plot of Fig. 13), simple arithmetic indicates that eddy averaging should generate a mean current of nearly 30 cm/s. This is similar to the northward velocity in the mean boundary current at 100 m depth in Fig. 10a. This estimate is certainly an upper limit since the rings do not follow exactly the same path along the coast. A value of 20 cm/s seems more reasonable, which suggests that at least the 2/3 of the mean flow may result from averaging the rings. This situation is very different in ISOPYCNIC in which the current is permanent. Note that cyclonic eddies have been observed in several occasions, usually inserted between anticyclones. They are able to reverse the coastal current so that it flows to the south-east. However, these eddies do not persist for very long and their signatures remain confined to the upper 100 m. It is difficult to compare them to those observed by Didden and Schott (1993) with Geosat. The generation of NBC rings in LEVEL differs from that in SIGMA. The number of rings generated each year is similar (six), but they pinch off further north, usually near 10°N. However, as in SIGMA, rings are also generated in late winter and spring when the NECC has collapsed, nevertheless stronger rings are generated in summer/fall when the retroflection of the current is into NECC. SIGMA-2 behaves like SIGMA, so it seems likely that the difference in the effective bottom friction between the z and s coordinate models (larger in LEVEL, see section 3.1) is responsible for a different dynamical equilibrium in the NBC, and favours the pinch-off of rings in SIGMA. This establishes a relation between the coordinate system used and the eddy variability in the NBC. 3.4. Fate of NBC rings toward the Caribbean Sea In both SIGMA and LEVEL, most NBC rings make their way into the Caribbean Sea (Figs. 11 and 12), despite the topographic rise of the Antilles Islands. Since these islands are not

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explicitly represented in the models, interaction with bottom topography is the only process which could prevent the rings from passing through in the model. This interaction has a true impact on the rings, which slow down and are sometimes blocked at the rise, ring merging (as in Fig. 12) and sometime damping occurring there. In LEVEL, this rise is quite realistic since the minimum depth can reach 75 m in this model, but nevertheless rings do pass through, probably because of their shallow extent. In SIGMA, NBC rings extend much deeper, but the topography of the Antilles is considerably smoothed (minimum depth of the order of 800 m), but in spite of their interacting strongly with the topography, the rings succeed in invading the Caribbean Sea. It is likely that the aspect ratio of the eddy vertical scale and the depth of the passage is an important parameter for this process, and is similar in both models. SIGMA-2 provides some insight on the role of the islands of the Lesser Antilles on the passage of the NBC rings into the Caribbean Sea. The three islands that were added to this experiment do not represent the archipelago realistically but were added to act as a topographic barrier. The topography is also slightly steeper, but the minimum depth has not been changed so the model passage is still deeper than in reality (as can be seen in Fig. 15, in which the geography of the islands can be seen). The presence of the islands has a drastic effect on the NBC rings. Figs. 15 and 16 show two snapshots of the current speed in SIGMA-2, one during mid-April and the other at the end of August, with a vertical section of the salinity along the path of the rings. The current speeds are directly comparable with those shown for SIGMA in Figs. 11 and 12 (similar time of the year). In April (Fig. 15), rings are seen in the Caribbean Sea in SIGMA-2, but they are much weaker, and not as coherent as those seen either to the east of the Islands or in the Caribbean Sea in SIGMA (Fig. 11a). In August, however, two strong coherent rings (reaching depth over 500 m) have passed the islands (Fig. 16), and the situation is very similar to that in SIGMA without islands (Fig. 11a). These rings are carrying low salinity Amazon water. Several years of model data have been analysed to understand the impact of the islands. It appears that the coherence of the rings is greatly reduced and sometimes destroyed by their interaction with the islands. The main result of this interaction is to disorganize the flux of anticyclonic vorticity passing through the passages. When an incident ring is particularly strong, as is the case for the summer/fall rings, it usually regains a coherent structure once the vorticity flux has passed through the islands (as in Fig. 16). The fate of weaker rings is not as clear. The vorticity flux corresponding to their passage does propagate into the Caribbean Sea, but not in the form of a strong and coherent mesoscale pattern. The impact of the islands on the real NBC rings is probably greater than portrayed by the model, likely because the number of islands is much larger than the three islands put in the model, and also because the real bottom topography is very much rougher, which increases the efficiency of the dissipative mechanisms. However, the present simulation suggests that the anticyclonic rings seen in the Caribbean Sea by Romaneessen (1993) and Nystuen and Andrade (1993) from Geosat sea surface height could well be generated by the flux of anticyclonic vorticity forced through the Antilles Islands by the NBC rings. A similar scenario has recently been suggested by Murphy, Hurlbut and O’Brien (1999) from numerical simulations carried out with a layered model. In any case, this flux is certainly an important forcing of the circulation in this region. Statistically, only half of the incident rings were found to make it through the passage without significantly losing their coherence.

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Fig. 15. Experiment SIGMA-2, including the Antilles Islands. Mid-April snapshots of the near surface current speed (grey indicates speed above 30 cm/s) in the western tropical Atlantic (upper plot), and of the vertical distribution of salinity (grey scale) along the path of NBC rings in the direction of the Caribbean Sea (bottom plot). The broken line in the upper plot indicates the section which follows the path of the eddies. Vertical lines in the bottom plot indicate the changes in direction of the section.

4. Summary and discussion The time dependent circulation of the North Brazil Current has been studied using three different numerical circulation models with resolution (isotropic, 1/3° at the equator) in principle fine enough to permit the generation of mesoscale eddies. A water mass analysis showed that model solutions have rich T/S properties with seasonal variability which agree reasonably well with observations, although all models do not perform alike with regard to the properties of Central Waters, the salinity of which is confined in a much too narrow range in LEVEL. Nevertheless, in the region of the NBC, it was possible in all models to identify the same four major water masses, similar to those derived from many observation based studies (Wilson et al., 1994) to

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Fig. 16. Experiment SIGMA-2, including the Antilles Islands. Same as in Fig. 15, but the snapshot is taken in midAugust. The white spots at 62°W (also in Fig. 15) are the model Lesser Antilles Islands.

investigate the circulation of the region. The same seasonal winds force the models. The wind driven part of the circulation, characterised by the onset of the NECC in summer and its collapse in winter is well represented in all models, and models also agree on the amplitude of the seasonal cycle (15 Sv in summer in the NECC at 40°W). Despite their identical grid resolution, each model depicts the eddy activity differently in the Western Tropical Atlantic. The ISOPYCNIC model has very low eke levels, and so no coherent eddy pattern is observed in this region of the ocean. This deficiency is attributed to the use of a peculiar harmonic (Laplacian) operator to parameterise lateral friction (see Wi01 for the detail formulation). The two other models, SIGMA and LEVEL, generate a significant eddy variability in the NBC region, but in the latter the eddies are significantly weaker in strength and vertical extent. Two reasons were invoked to explain for these differences but are difficult to quantify. The one suspected of being the most important, is the enhancement of lateral friction at points

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nearest to the bottom near the stair case topography in LEVEL as a result of the no-slip boundary condition. The other is a dynamical reason, related to differences in the large scale mean flow. In both models, rings are generated by pinch-off at the retroflection loops of the North Brazil Current, a current which reaches greater depth and for which the mean core velocity is significantly larger in SIGMA (800 m, 65 cm/s) than in LEVEL (400 m, 40 cm/s). These quantitative differences in the mean characteristics of the NBC are partly attributed to the weaker overturning in LEVEL, but the main consequence is that the retroflection loops are likely more unstable in SIGMA, hence driving the more intense eddy variability seen in this model. Turbulent kinetic energy levels reflect these differences between models. The flow field and its variability in SIGMA are more consistent with observational estimates. Ring generation in Sigma is continuous all year long, with six rings generated each year. These pinch off the retroflection loops of the NBC into the equatorial current system either at 5°N during winter/spring when the retroflection feeds the EUC, or at 8°N during summer/fall when a large part of the retroflection feeds the NECC. This suggests that the semi-permanent Amazon and Demerara Eddies, whose existence has been deduced from non-synoptic observations (Bruce et al., 1985), are no more than an under-sampled view of the migration through the region of vortex shedding. This suggestion by the model that there is continuous ring generation, has been shown to be compatible with observations, stronger rings being generated during the period of activity of the NECC. Potential Vorticity (PV) dynamics indicate that a western boundary current progressing northward from the southern hemisphere cannot continue to flow quietly along the coast after it has crossed the equator, but has to turn offshore (Anderson & Moore, 1979). This is one of the mechanisms that drives the retroflection of the North Brazil Current into the zonal equatorial current system. Another is the need for continuity in feeding the EUC driven by the large scale zonal pressure gradient, and the NECC (driven by the wind stress curl) part of the year. This is qualitatively well simulated in all DYNAMO models. However, potential vorticity conservation is achieved differently according to inertial and frictional effects. In the case of an inviscid fluid, the dynamics of the current are greatly influenced by inertia, and conservation of potential vorticity of the current after it crosses the equator may require that important quantities of anticyclonic vorticity are expelled from the current, which can be done by ring pinch-off. It seems that SIGMA agrees well with the inviscid scenario. If frictional effects are important, as it is the case in ISOPYCNIC, PV conservation could be obtained by dissipation, and ring shedding might not be necessary. The case of LEVEL is more complex because friction becomes dominant near the bottom in the side wall boundary layer. Therefore, the dynamics of the current are probably governed by a balance between inertia and dissipative mechanisms. The NBC is significantly weaker (less inertial) in LEVEL than it is in SIGMA (20 Sv for the former versus 35 Sv for the latter at the equator), and it is likely that the current is able to maintain its vorticity balance through dissipation for longer. As a result, shedding of coherent rings is different, and although rings are continuously generated in this model, at a rate that is very similar to Sigma, their pinchoff always occurs further north (8°N or 10°N). The importance of friction is confirmed by the results of the sensitivity experiment SIGMA-2. The process of ring generation and their north-westward drift has been investigated by Nof and Pichevin (1996) in a theoretical approach based on the integrated momentum balance of an inviscid retroflecting current along a wall. According to their theory, the retroflecting current exerts a

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flow force parallel to the coastline which cannot be balanced unless eddies are generated and thus removing momentum from the mean current. They also show that in a geometry similar to the NBC, planetary and topographic b-effect tend to produce the force which tears the ring off the retroflection region and drives it to the north-west. Their calculation of the momentum balance allowed them to calculated the major characteristics of the rings, which in many aspects compare well with rings characteristics derived from observations. However, the phenomenological behaviour of the ring predicted by the theory of Nof and Pichevin (1996) is in an even greater agreement with the results of SIGMA. In particular both suggest a periodic ring generation, which is not be interrupted as long as the retroflection persists. Being established that the retroflection of the NBC into the EUC is a permanent circulation feature, NBC rings should be constantly generated as two of the DYNAMO models suggest. These similarities encourage the hope that a thorough analysis of the momentum balance of the retroflection in the SIGMA in a more realistic framework can be used to verify the theory of Nof and Pichevin (1996). The question of the fate of NBC rings when they reach the Antilles Islands has been investigated with SIGMA from model experiments with or without this island arc. In the absence of islands, the topographic rise fails to prevent the rings from invading the Caribbean Sea (this is also the case in LEVEL). When the model included islands, the coherence of the rings is generally destroyed by the interaction with the islands, which is consistent with the disappearance of the rings in the altimetric observations. However, the anticyclonic vorticity of the rings is not totally dissipated in the model, and a flux of vorticity enters the Caribbean Sea. When the incident rings are particularly large, the induced flux of vorticity generally resumes a coherent form, thus generating eddies similar to the Caribbean eddies seen by satellite altimetry. Thus the NBC appears to be an important source of anticyclonic vorticity for the circulation in the Caribbean Sea. Despite differences in the eddy field, mean seasonal currents are qualitatively similar in all models (and in good agreement with circulation schemes deduced from observations). This may appear to be a paradox, but it is consistent with the fact that the mean circulation in this region is to first order driven by the large scale circulation. Indeed, quantitative differences between model solutions strongly suggest that the characteristics of the NBC/NECC system are principally determined by the strength of the thermohaline circulation, which sets the inflow conditions from the southern hemisphere. One strong conclusion of our study is that the volume transport in the North Brazil Current before it crosses the equator (defined here as the ensemble of the NBUC and the sSEC) is mainly determined by the meridional overturning. SIGMA, and ISOPYCNIC, with a realistic overturning at 24°N of 18 Sv and 16 Sv respectively, generate a NBC transport that is comparable to the 35 Sv deduced from the most recent observations (Schott et al., 1998), whereas in LEVEL this current is 20 Sv, in relation with an overturning of only 12 Sv. Interestingly, all models show transport in the NBUC/sSEC at the equator that is significantly larger than the transport required to close the overturning cell, suggesting that the return path of the global thermohaline circulation is concentrated in the NBC, as suggested by Schott et al. (1998), and Johns et al. (1998). However, this inflow of warm waters of South Atlantic origin does not continue northwards but for the most part recirculates in the zonal equatorial current system, a scenario which agrees particularly well with the one proposed by Schott et al. (1998). All models show a continuous north-westward flow in all their seasonal means along the coast of Brazil and Guiana and into the Caribbean Sea. This current is known to exist from observations in winter/spring, but in summer/fall a highly variable eddy-driven flow should be dominant. This

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is observed in SIGMA, and to a lesser degree in LEVEL, whereas ISOPYCNIC shows a steady current at all times. Nevertheless, all models agree about the seasonal mean of this current, so this coastal current is to be seriously considered as a pathway to the north for waters of South Atlantic origin. This current is weakest in LEVEL, and is stronger in the two other models (the contribution of the eddies being significant in SIGMA), indicating that it should be associated with a strong overturning cell, the upper branch of which returns to the north concentrated in the NBC. Observations have not been carried out for long enough to determine if a time-averaging of the NBC rings in summer/fall does in reality result in a mean north-westward flow as shown by the models. These results represent important changes from previous high resolution numerical model studies (the CME model, Schott & Bo¨ ning, 1991) which showed a total retroflection of the NBC into the NECC in summer/fall, but no continuous mean flow along the boundary in winter/spring when the NECC has collapsed. In this regard, the improved representation of the thermohaline circulation in the DYNAMO models is certainly at the origin of these differences. To conclude, the realistic aspect and the good quantitative agreement of instantaneous currents and eddies in SIGMA with relevant observations give credence to the Western Equatorial Atlantic circulation scheme proposed by this model. Differences and similarities between models pointed out the dominant role played by the global thermohaline circulation in the determination of the mean and eddy circulation in this region of the ocean, and emphasized the dependence of model solutions on the parameterisation of dissipative mechanisms and subgrid-scale phenomena.

Acknowledgements The work reported in this paper is part of the project DYNAMO which has been supported by the European Union Marine Science and Technology programme under contract no. MAS2-CT930060. This support is gratefully acknowledged. We would like to thank our colleagues M. Coulibaly, C. Dieterich, P. Herrmann, P. D. Killworth, M. Lee, C. Le Provost, A. New, and J. Willebrand who contributed to various stages of the project. We also acknowledge the provision of supercomputing facilities by the Rechenzentrum der Universita¨ t Kiel, Deutsches Klimarechenzentrum Hamburg, the Atlas Centre at the Rutherford Appleton Laboratory, and the Institut pour le De´ veloppement des Ressources en Informatique Scientifique of the Centre National de la Recherche Scientifique.

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