1. Introduction

The Antarctic Circumpolar Current (ACC) plays a major role in the global ocean circulation, as it is the only large-scale link between the different ocean basins. The dominant forcing of the ACC is the strong westerly winds that impart eastward momentum to the ocean. Meanwhile, the wind stress drives an equatorward motion of water in the Ekman layer. Because of continuity, there must be a poleward flow of waters to close this circulation.

Toggweiler and Samuels (1995) suggested that the quantity of deep water flowing southward out of the Atlantic Ocean is similar to the quantity of deep water removed from the interior of the ocean by Ekman divergence around Antarctica. As a result, the formation and outflow of North Atlantic Deep Water (NADW) from the Atlantic Ocean would be closely related to the Southern Ocean wind stress. These authors focused on the influence of Drake Passage since a net meridional geostrophic flow in this latitude band (necessarily in balance with a zonal pressure gradient) can only occur below the sill depth of the passage, that is, 2500 m. Consequently, the northward Ekman transport in the Southern Ocean connects to the southward geostrophic deep outflow from the Atlantic, Indian, and Pacific Oceans and, in particular, to the NADW formation regions in the North Atlantic.

A series of papers have dealt with the export of warm and intermediate water from the Southern Ocean to the South Atlantic, the South Pacific, and the Indian Oceans (Nof 2000, 2002, 2003; De Boer and Nof 2004). These studies were based on integrations of the linearized zonal momentum equations along specific closed contours. Each time, these integrations were carried out in analytical, quasi-linear models, first with rectangular geometry and continents and only zonal winds, then with more realistic geography and winds. All of them found a simple relation between the northward export of warm and intermediate water and the wind stress. Although the net northward transport equaled the Ekman transport in strength, the water exported to the equator originated in the Sverdrup interior and flowed northward along the eastern boundary (Nof 2003). These studies provide a theory for the equatorward export of water from the Southern Ocean that can be interestingly tested in the context of more complex ocean models.

The theory of Nof depends on several assumptions and simplifications. First, it does not take eddies into account. Gnanadesikan (1999) proposed a scaling for the NADW overturning cell intensity as a function of vertical diffusivity, Southern Ocean wind stress, and eddy thickness diffusivity, and also emphasized that neglecting eddies in the Southern Ocean could lead to an overestimated upwelling of NADW in that area. Hallberg and Gnanadesikan (2001) found that the leading order balance in the ACC dynamics is between the transport achieved by the eddies and the wind-driven Ekman transport and that changes in the Ekman fluxes due to modifications of the Southern Ocean wind stress are likely to be compensated by eddy mass fluxes more than by adiabatic upwelling of deep water. Drijfhout et al. (2003) investigated the effect of eddies on the upper branch of the thermohaline circulation with Lagrangian diagnostics applied to a global eddy-permitting ocean model. The presence of eddies was shown to modify significantly water mass motions by reduction of diapycnal mixing and partial compensation of Ekman fluxes.

The theory of Nof also neglects the direct effect of buoyancy forcing. Speer et al. (2000) as well as Karsten et al. (2002) suggested that, although the leading-order balance is between eddies and wind, the buoyancy forcing plays a critical role in the transformation of water masses. At next order, buoyancy is transported poleward across the fronts by the eddies so as to compensate for the surface forcing and the resulting cooling at the pole and heating in the subtropics. Karsten and Marshall (2002) constructed the residual circulation of the ACC from observations and found a leading order balance between buoyancy forcing and wind-driven circulation on the poleward flank of the ACC.

Hence, the theory proposed by Nof for the equatorward export of warm and intermediate waters from the Southern Ocean needs to be tested in more complex models that can take into account the processes neglected.

In the present study, the role of the Ekman transport in the export from Drake Passage is elucidated by tracing the motion of water masses with Lagrangian trajectories calculated from the velocity fields of two global ocean general circulation models (GCMs); one of them includes an eddy-induced effect in the archive of its mean annual velocity field. The other one is not eddy permitting but parameterizes the effect of ocean eddies on the large-scale circulation. This Lagrangian analysis provides a quantitative picture of the large-scale three-dimensional water motions in the Southern Ocean. In this approach we assume that water masses are advected with the large-scale velocity field and that smaller scale motion associated with 3D turbulence and isopycnal dispersion due to the stochasticity of eddy motions is mainly responsible for mixing the water mass characteristics. Moreover, this study aims at testing the theory of Nof, which does not consider eddy motions at all but only makes statements about the large-scale ocean circulation.

Lagrangian analyses have already been carried out in GCMs to sketch a global picture of the ocean circulation (Blanke et al. 2001; Speich et al. 2001), or the circulation in the Southern Ocean (Döös 1995; Nycander et al. 2002). These studies focused mainly on mass transfer intensities and pathways. Here, we aim at testing an analytical solution of the equatorward export from the Southern Ocean (Nof 2003). We will confront this theory with various Lagrangian diagnostics applied to both ocean models in order to sketch a model-independent picture of the export of water from Drake Passage.

This paper is organized as follows. Section 2 presents the global ocean models as well as the Lagrangian methodology, and discusses several choices that were made for both simulations along with some Eulerian diagnostics as first validation of the models. Section 3 describes the flow originating from Drake Passage by means of horizontal transport streamfunctions (Blanke et al. 1999). Section 4 focuses on the specific role of the Ekman transport in the equatorward export, with the help of a comparison of the numerical and analytical results. We present our conclusions in section 5.

2. Methodology

c. Data handling

To describe accurately the water mass circulation, we took into account the effect of time variability in the Lagrangian integrations. One way to do it is by archiving the GCM velocity fields with a sampling period shorter than the typical time scales of the modeled variability. It is essential to note that the sampling rate has an impact, or subsequent Lagrangian diagnostics. In ORCA2, Valdivieso da Costa and Blanke (2004) showed the convergence of trajectory error measurements for sampling time intervals shorter than the dominant period of forced and internal variability. Longer averaging periods that do not sample appropriately the seasonal cycle fail to yield accurate Lagrangian calculations. Consequently we chose a sampling period of 30 days for ORCA 2.

Another way to deal with variability is to include the mean effect of subsampled fluctuations by adding a bolus velocity u* = (u*, υ*) to the time-mean flow u = (u, υ). This bolus velocity expresses the temporal correlation between variations of density, or layer thicknesses, and velocity. On isopycnals, it can be defined as

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where the prime denotes deviations from a time-average; h and σ denote layer thickness and density, respectively. For more details on this calculation we refer to Hazeleger et al. (2003). This bolus velocity takes into account the mean effect of the eddies that can develop in OCCAM (Drijfhout et al. 2003). For computational cost considerations we used a seasonal mean field with a bolus velocity that includes the mean effect of eddies. This approach amounts to using the temporal-residual-mean circulation to advect water masses (McIntosh and McDougall 1996).

3. Lagrangian streamfunctions

Eastward flowing particles at Drake Passage (70°W) were integrated forward in time until they either reached a specified latitude in the Atlantic, Indian, or Pacific Oceans or completed one circum-Antarctic revolution and reached the 70°W section on its western flank. We used two sets of final sections: 32°S and the equator. The former section allows us to estimate the amount of water entering any of the ocean basins, whereas the equatorial section is northward enough to ensure that the intercepted waters are unlikely to be reinjected into the ACC after some recirculation in the southern subtropical gyres. We define the Atlantic (respectively, Indian and Pacific) transfer as the waters that originate from Drake Passage and cross the sections northward for the first time in the Atlantic (respectively, Indian and Pacific) Ocean. Similarly, we define the circum-Antarctic transfer as the waters that originate from Drake Passage but do not cross the equator before reaching the Drake Passage section on its western flank. Table 2 gives the values of the different mass transfers between Drake Passage and the two sets of final sections. Depending on the section we consider, particles may show drastically contrasted paths. For instance, some particles may reach 32°S for the first time in a given ocean basin but cross the equator in a different one because of recirculation and interocean exchange. This mechanism explains the differences in Table 2 between the 32°S and the equator transfers. The total export to 32°S is larger than the export to the equator because some circum-Antarctic waters transit north of 32°S, and are therefore included in the 32°S transfer, without reaching the equator.

Our Pacific “equatorial” section does not follow exactly the equator: the Torres Strait between New Guinea and Australia is so shallow that any significant contribution to the Indonesian Throughflow must pass first to the north of New Guinea. As the northernmost tip of New Guinea shelf is located a few tenths of a degree north of the equator, the flow from the South Pacific must cross the equator. Because such waters are likely to keep their Southern Hemisphere water mass properties, we shifted the equatorial section to 4°N west of 170°E in order not to intercept them on their way to the Indian Ocean.

There are significant differences between the formulations of both models (numerical code, restoring and forcing constraints, physical schemes, archiving parameters and strategy, Lagrangian trajectory code). Consequently, the values of the transfers can be quite different. However, common features appear in mass transfer patterns and intensities, suggesting that some robust features are captured by the GCMs.

Figure 2 shows the horizontal streamfunctions describing the whole circum-Antarctic recirculation in ORCA2 and OCCAM with a 10-Sv contour interval. The southern and northern extents of the pathways look very alike. Just after Drake Passage the ACC widens in the northward-flowing Malvinas Current. The northern edge of the ACC reaches 42°S in the Atlantic basin and shifts southward in the Indian. It remains south of about 50°S in the Pacific. On its southern flank, the ACC is bordered with the Antarctic continent and the gyres of the Weddell and Ross Seas. Figure 2 shows that the internal structure of the ACC is very different in ORCA2 and OCCAM: in ORCA2 it consists in a single and rather smooth current widening over topographic features, whereas in OCCAM it is composed of various separated currents merging and splitting, characterized by twisty courses. A careful comparison of the ocean bathymetry with the streamlines obtained in OCCAM suggests a large effect of topography on the ACC pathways, although not all separations and junctions of the smaller currents can be explained by bathymetry. The streamlines evidence the effects of the Mid-Atlantic Ridge between 0° and 20°W, the widening of the current over the Kerguelen Plateau at 70°E, the effects of the Macquarie Ridge and Campbell Plateau south of New Zealand, and those of the Pacific Antarctic Ridge between 140° and 160°E. In ORCA2, the ACC is steered only by major topographic features such as the Kerguelen and Campbell Plateaus. On the other hand, the core of the ACC spreads on the whole meridional extent of Drake Passage in ORCA2, whereas it is only located in the northern part of the passage in OCCAM. Most of these differences result from the coarser horizontal resolution of ORCA2. Both simulations also differ in the strengths of the recirculations in the Weddell Sea and Ross Sea gyres.

As mentioned above, 6–11 Sv of the water that completes a full revolution around Antarctica are caught in the subtropical gyres in the Atlantic, Indian or Pacific Oceans and are therefore counted as part of the 32°S transfer. The horizontal streamfunctions obtained for these waters are presented in Fig. 3 (now with a 1-Sv contour interval). The Atlantic and Indian subtropical gyres are the domains most likely visited. This transfer is slightly more important in ORCA2 than in OCCAM. In ORCA2, 12 Sv recirculate within the Weddell gyre, whereas this gyre is hardly involved in OCCAM. In OCCAM the pathway of the transfer is narrower in the Atlantic sector of the Southern Ocean. This is partly due to the eddy mass fluxes counteracting the Ekman flux (Drijfhout et al. 2003).

Upstream of 60°E, the northern extent of the ACC is located quite close to the subtropical front, but downstream it is closer to the subantarctic front defined by Orsi et al. (1995). The southern extent of the current shows a good agreement with the southern boundary of the ACC as diagnosed by Orsi et al. (1995).

Figure 4 illustrates the mass transfer from Drake Passage to the equatorial Atlantic and Indian Oceans in ORCA2 and OCCAM. Further Lagrangian analyses on this specific part of the export show that only a small amount of water (2.5 Sv in ORCA2 and 1 Sv in OCCAM) is directly exported to the Atlantic Ocean and takes part in the “cold route” (Rintoul 1991). The remaining 5–6 Sv follow an indirect path: they enter the Atlantic Ocean from the Indian Ocean by Agulhas leakage and flow equatorward within the Benguela Current. This water takes part in the “warm route” (Gordon 1986). About 1–2 Sv entered the Indian Ocean through Tasman leakage (Speich et al. 2002) after flowing in the Southern Pacific subtropical gyre. Interocean exchange between the (South) Pacific and Indian Oceans occurs by Tasman leakage; interocean exchange between the Indian and Atlantic Oceans occurs by Agulhas leakage. There is hardly any exchange between the South Pacific and Indian Oceans by the Indonesian Throughflow (IT): only 0.3 Sv in ORCA2 and 0.5 Sv in OCCAM are transfered directly from Drake Passage to the IT without excursion into the north equatorial or tropical Pacific Ocean. From Blanke et al. (2001) and Drijfhout et al. (2003) we infer that the thermohaline circulation (THC) in both models is about 15 Sv; the THC here is defined as the northward flow lighter than σ₀ = 27.6 across the Atlantic equator. The export from Drake Passage to the equatorial Atlantic is about 7 Sv, ; that is, half of the return flow of the THC. Lagrangian analyses show that two origins can be distinguished for the remaining 8 Sv: about 1 Sv of the return flow consists of deep waters being converted into lighter waters on their way from the Atlantic Ocean to the IT or Tasman leakage without ever crossing Drake Passage and is therefore not included in our study; the remaining 7 Sv are part of our export from Drake Passage to the equatorial Pacific Ocean. Out of these, about 6 Sv will eventually flow to the Indian Ocean through the IT after some recirculations in the tropical and equatorial North Pacific Ocean; the remainder (about 1 Sv) will skirt Australia clockwise and flow to the Indian Ocean by Tasman leakage.

In both models, all the water exported to the Atlantic equator along the direct cold route flows northward within the Malvinas Current until it reaches the Brazil–Malvinas confluence. It eventually flows eastward over the Mid-Atlantic Ridge in the South Atlantic Current (SAC), after having turned northwestward in the Benguela Current, in agreement with known circulation patterns of the Southern Atlantic Ocean (e.g., Sloyan and Rintoul 2000). The water exported from Drake Passage finally crosses the Atlantic equator as part of the western boundary current (North Brazil Current).

In OCCAM, all the water exported to the Atlantic equator first flows in the Malvinas Current. Therefore, the whole export to the Atlantic is drawn from water initially located north of 60°S at Drake Passage. In ORCA2 on the contrary, the northward export is drawn from water over the whole meridional extent of Drake Passage and part of the water even recirculates in the Weddell Sea gyre before flowing into the Indian Ocean. In both models the inflow to the Indian Ocean takes place in the southeastern part of the basin, that is, between 80° and 150°E.

The transfer from Drake Passage to the equatorial Indian Ocean only concerns a very small amount of water. All of it enters the Indian Ocean between 80° and 150°E, along with the water eventually exported to the Atlantic Ocean through Agulhas leakage. The northern tip of Madagascar is a bifurcation point. Most of the water arriving there turns southward with the Madagascar Current and flows into the Atlantic Ocean; a smaller fraction turns northward within the Somali Current and crosses the Indian equator.

Figure 5 shows the transfer from Drake Passage to the Pacific equator in ORCA2 and OCCAM. All the water enters the Pacific Ocean east of New Zealand. Some deviations from the direct path occur in the Atlantic and Indian subtropical gyres as well as in the Weddell Sea and Ross Sea gyres. Most of the water crosses the Pacific equator within the western boundary current (New Guinea Coastal Current). In the South Pacific the path is similar in both models and follows the broad curve of the interior subtropical gyre.

In OCCAM the recirculations in the Southern Ocean are generally less prominent than in ORCA2. This is likely caused by the inclusion of the eddy mass fluxes (Drijfhout et al. 2003). The path in the Southern Ocean is also much more convoluted than in ORCA2.

Our horizontal streamfunctions for the water exported to the equator follow the broad curve of the interior subtropical gyre, consistent with the numerical experiments of Nof (2003) and De Boer and Nof (2004). The flow is intensified in the eastern boundary currents between roughly 40° and 20°S before it crosses the basin westward between 25° and 15°S and, thereafter, flows equatorward in the western boundary currents. A significant proportion of the export to the Atlantic Ocean takes part in a counterclockwise circulation in the Indian subtropical gyre. The westward component of the transport at Drake Passage is very small, from almost 0 in OPA to about 4 Sv in OCCAM. Moreover, our Lagrangian experiments suggest that the export to the Indian–Pacific system does not include a counterclockwise circulation in the South Atlantic subtropical gyre. Nevertheless, the general picture shown by the streamfunctions bears some common features with the results obtained by Nof in a simple numerical model (Nof 2003).

4. Role of the Ekman transport

a. Nof’s analytical model

We first recall how Nof (2000, 2002, 2003) derived the equation for the northward export of warm and intermediate water from the ACC. The same analytical model was used in the three studies. It is composed of four layers. The upper one is flowing northward and is 500–1000 m deep and includes the thermocline and some intermediate water. Underneath is a very thick layer (3000–4000 m) of intermediate waters. The velocities in this layer are assumed to be small and negligible (but not necessarily the transports). A level of no motion is assumed at the top of the intermediate water layer. Underneath are two active layers that require meridional walls to lean against: the upper one contains the southward-flowing deep water (mainly NADW) and is about 1000 m thick; the deeper one accounts for the northward-flowing bottom water (AABW) and is about 100 m thick.

Nof’s study only focuses on the uppermost layer, as it is isolated from the deepest layers everywhere except at high latitudes. Even though the assumption of a level of no motion at the base of the upper layer is not justified at high latitudes, Nof claims that most of the integration contour is located close enough to the equator so that this assumption remains valid (see Nof 2002). His model does not include zonal friction, eddy fluxes, or drag processes, which are all important in the ACC.

The linearized Boussinesq equations for the upper layer are

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where u, υ, and w are the velocities in the x, y, and z directions (x is pointing eastward and y northward); f is the Coriolis parameter; ρ₀ is the uniform density of the motionless deep water; ρ = ρ (x, y, z) is the density of the moving layer; ρ′ = ρ − ρ₀ is the deviation of the density of the moving layer from the density of the passive layer; P is the deviation of the hydrostatic pressure from the pressure associated with a state of rest; and u′w′ and υ′w′ are the horizontal components of the Reynolds stress.

We define the vertically integrated pressure P* as

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where −ζ is the level of no motion and η is the free surface. Nof assumes compensation of surface pressure gradients at the base of the upper layer −ζ, which implies that deep motion is uncoupled from sea surface height variations. However, this does not imply that P is zero everywhere between P(−ζ) and P(bottom). It should be noted that this model only applies to ocean basins equatorward of the Southern Ocean, and outside the western boundaries. Nof included friction in the y-momentum equation, assuming that it is only important in the western boundary currents. Integration of Eqs. (2)–(5) together with the use of Leibniz’s formula for differentiation under the integral, P(−ζ) = 0, and P(η) = 0, gives

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where (τ^x, τ^y) are the two components of the wind stress and R is an interfacial friction coefficient.

Equations (7)–(9) give

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In the inviscid interior, we obtain the Sverdrup relation

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The Sverdrup relation in Eq. (11) only applies to the upper moving layer, integrated from −ζ to η. For this reason, bottom sources of vorticity are absent. This follows from Nof’s assumption of a level of no-motion at 500–1000-m depth.

Along a closed belt connecting the southernmost tips of the continents the integrated pressure gradients are zero, and integration of Eqs. (7)–(8) leads to

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where T is the net “equatorward” transport through the belt and l indicates the field component along the closed path. One should note that the transport is not strictly equatorward, but rather transverse to the integration path. By assuming that the integration belt only goes through regions where friction can be neglected, one gets the export equation:

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Therefore, the regions where Eq. (13) is valid exclude the ACC and the western boundary currents. It is worth noting that the RV term is neglected in Nof’s model when the transport across l is calculated. In reality the path l cuts through the ACC, the Malvinas Current, and the Agulhas Current, which makes this approximation questionable. Using some rough values, Nof estimates the error due to the interior frictional and eddy fluxes effects to O(1 Sv). Some studies (e.g., Gille 1997) have pointed out that the wind stress over the ACC is primarily balanced by topographic-induced drag, which is also omitted in Nof’s model. Whether this drag is confined to major ridges or more evenly distributed over most of the ACC path is still unclear. However, using the results of Gille (1997), Nof estimates the error due to the integration contour crossing the ACC in the vicinity of Drake Passage to about 15%–20% of the total transport, that is, 4–5 Sv. Nof’s model also neglects the Agulhas rings’ self-propulsion. Although there is no general agreement on the actual volume transport achieved by Agulhas rings, Nof comes up with a transport of 3–4 Sv that is omitted by his calculation. All in all, the uncertainty on the result equals about 10 Sv.

Nof’s numerical experiments were carried out in a 1½-layer isopycnic model including friction and inertial terms. They showed that lateral friction, linear drag and advection are negligible, as was assumed in the analytics. The transport in the numerical experiments also varies with the wind stress as stated by Eq. (13). These gave a net meridional transport entering the South Atlantic Ocean of 9 Sv and about 20 Sv entering the Indian–Pacific system (Nof 2000, 2002, 2003; De Boer and Nof 2004). Though the net equatorward transport T equals the Ekman transport, the authors suggested that the waters that reach the Northern Hemisphere ocean basins are not flowing in the Ekman layer, but in the Sverdrup interior along the eastern boundary in the easternmost portion of the subtropical gyres (Fig. 7 of Nof 2003). The transport T equals the Ekman transport but consists of the Ekman flow, the geostrophic flow, and the western boundary current. The last two are assumed to compensate in intensity. The water transported to the equator is, according to Nof, the eastern fraction of the geostrophic flow that equals the Ekman transport across the integration belt.

b. Testing Nof’s model in the GCMs

The Lagrangian export is herein defined as the waters that originate from Drake Passage and cross the equator northward in any of the three basins. All figures and comments relative to the Lagrangian export refer exclusively to these waters. The Lagrangian transports are almost equivalent to the transports in density space, after they have been transformed back to depth coordinates. This way, gyre-scale recirculations on isopycnal levels, but with north- and southward flows at different depths giving rise to a Deacon cell (Döös and Webb 1994), are automatically excluded from the Lagrangian transports studied here. The Lagrangian export corresponds to the northward (Ekman) transport poleward of the Deacon cell that directly connects to the interbasin exchange equatorward of the Deacon cell.

The Lagrangian export to the equator is separated into two distinct components: a part within the upper 1000 m and another one below 3000 m (see Fig. 6). The shallower part ranges from 18 Sv in OCCAM to 22 Sv in ORCA2, whereas the deeper component varies from 2 Sv in ORCA2 to 3.5 Sv in OCCAM. The latter is the northward flow of Antarctic Bottom Water (AABW), which is not addressed by Nof’s theory. It is worth noting that none of the export is located between 1000 and 3000 m. The export above 1000 m accounts for about 80% of the total export to the equator in OCCAM and 90% in ORCA2. However, ORCA2 and OCCAM are both known to lack a significant fraction of AABW. Thus the indicated proportions are likely to be overestimated.

Following Nof (2003) we define sections connecting the southernmost tips of South America, Africa, Australia, and New Zealand and apply Eq. (13) to the resulting closed paths. The total integration of the along-belt wind stress gives a net “equatorward” transport of 22.4 Sv in ORCA2 and 24.4 Sv in OCCAM, whereas the total transport exported from Drake Passage to the equator was found equal to 23.3 Sv in OCCAM and 23.6 Sv in ORCA2 (see Table 2). However, the component of the export below 3000 m should be omitted, because it is not addressed by Nof’s theory. The export is therefore reduced to about 20.1 Sv in OCCAM and 21.6 Sv in ORCA2. These numbers still compare well with the transport predicted by the export Eq. (13).

To test the export equation to individual basins, Eqs. (7)–(8) need to be integrated along a segment AB. In that case the effect of pressure gradients must be taken into account. The export equation becomes

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Both terms in Eq. (14) are of the same order. Because of numerical truncation errors in the calculation of pressure gradients, the second term can change significantly for small changes in the chosen integration path. Therefore the uncertainties in the following values are estimated around 2 Sv. In ORCA2 this transport is distributed as follows: 4 Sv flowing into the Atlantic Ocean, 7 Sv into the Indian Ocean, and 16 Sv into the Pacific Ocean. The values for OCCAM are 6, 8, and 10 Sv for the Atlantic, Indian, and Pacific Oceans, respectively. They are in reasonable agreement with the 9 Sv entering the Atlantic Ocean and 20 Sv entering the Indo–Pacific basin found by Nof using National Centers for Environmental Prediction (NCEP) reanalysis winds (Nof 2003). The difference stems from the use of different wind products and integration paths, and does not invalidate our integration belt. Although somewhat different, these values are in reasonable agreement with the Lagrangian exports to the Atlantic and Pacific Oceans (see Table 2), but an order of magnitude different for the Indian Ocean.

Consequently, applying Eq. (13) along the global belt connecting the continental tips in the Southern Ocean presumably yields a reasonable estimate of the actual mass export to the equator. On the other hand, our results suggest that the export equation cannot be applied blindly to individual basins. This limitation likely results from the subtropical “supergyre” connection between basins, which allows interocean exchange (De Ruijter 1982; Speich et al. 2002). Moreover, some exchange also occurs through nonlinear processes such as the Agulhas rings, which were not addressed by Nof.

According to Nof’s theory, the equatorward transport T flows in the Sverdrup interior along the eastern boundary. Figure 7 depicts the circulation in any basin of the Southern Hemisphere as proposed by Nof: the part exported to the equator is located between the eastern boundary B and C. The remainder of the Sverdrup flow recirculates poleward within the western boundary current (WBC). Thus, the width of the equatorward flow BC is such that

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with T_AB previously defined in Eq. (14).

If Nof’s theory were exact, the Lagrangian export integrated from the eastern boundary along 32°S would be distributed in the very eastern end of the section (lower panel of Fig. 7). Furthermore, it would equal the integrated Sverdrup transport along the segment BC, and the total integrated value T would be given by Eq. (14). Figures 4 and 5 provide evidence that the Lagrangian export in OCCAM and ORCA2 is concentrated in the eastern boundaries of the basins in the subtropical regions, especially at 32°S. We now compare the zonal distribution of the westward-integrated Lagrangian export and of the Sverdrup transport [Eq. (11)] along this latitude for the Atlantic, Indian, and Pacific basins (Figs. 8 and 9).

Figures 8 and 9 suggest good agreement between the Lagrangian export and the Sverdrup transport along segment BC for the Atlantic and Pacific basins. The transport exported from Drake Passage to the Indian equator is too small to draw any reliable conclusion. The fact remains that the export is not located only within the eastern boundary region in the analyzed GCMs.

We investigate whether the exported waters are Ekman fluxes or Sverdrup interior waters by computing the vertical distribution of the transport carried by the particles when they last cross 32°S on their way to the equatorial region, at 48°S, and at the initial section at Drake Passage (Fig. 6); 48°S is where the zonally integrated Ekman transport is the largest. The export takes place in two well-separated depth ranges: one above 1000 m and the other in the AABW flow below 3000 m. Furthermore, the vertical distribution of the deepest component hardly varies along the equatorward progression, which suggests no connection between the upper and lower flows.

At 32°S, the fraction of the export to the equator above 1000 m that is located within the upper 100 m is only 20% in ORCA2 and 15% in OCCAM. At 48°S, this fraction is 65% in ORCA2 and 50% in OCCAM. Furthermore, the distribution in longitude is rather homogeneous and shows no specific structure. Consequently, most of the export in the upper layer at 48°S is an Ekman flux. The fractions within the upper 100 m are 30% in ORCA2 and 50% in OCCAM at Drake Passage. So, a significant part of the initial export is also in the Ekman layer, despite a somewhat different general distribution: the upper and deeper components of the flow are connected since the sill depth at this section is only 3500 m.

The horizontal streamfunctions also show that the flow is largely concentrated near the eastern boundaries (Figs. 4–5) and follows Sverdrup dynamics. Therefore our experiments confirm Nof’s assessment: the export from the Southern Ocean to the equator is not in the Ekman layer; within the semienclosed ocean basins it follows the Sverdrup interior. However, farther upstream in the Southern Ocean this water does flow mostly in the Ekman layer.

5. Discussion and conclusions

The Southern Ocean is a key element of the THC since it is the only large-scale connection of all three basins. Our knowledge of the mechanisms that connect the ACC to the return flow of the THC is still incomplete. The purpose of this paper was to sketch a picture of the processes leading to the northward export of ACC waters from Drake Passage. Although this was done with the help of two global ocean models that differ in their conception (and particularly in their horizontal resolution), we derived robust assumptions by focusing on common features.

The Indian and Pacific Oceans are found to be the main destinations for the waters exported from the ACC since 85% of the 35 Sv exported enter these basins at 32°S. However, and because of interbasin exchanges, most of the export to the Indian Ocean ends up in the Atlantic by Agulhas leakage and, thus, follows the indirect warm water path. In comparison, the direct cold path is found to be weak with an average strength of 1 Sv, though being present in both simulations. The South Atlantic and Indian Oceans are therefore strongly connected, contrary to the South Pacific and Indian Oceans, despite a weak connection by Tasman leakage and Indonesian Throughflow.

In the coarse-resolution ORCA2 model, the effect of suppressing the stochastic scattering of trajectories is different from the effect in OCCAM. In ORCA2, the eddy motions are not resolved at all, nor the cross-stream length scale of swift and narrow currents. As a result, the Lagrangian streamfunctions that depict water mass transports are very smooth. In OCCAM, the cross-stream length scale of the currents is better resolved, as well as part of the eddy motions. Much of the synoptic, mesoscale variability is associated with the rather coherent motion of meandering streamlines. Time averaging in fixed space broadens meandering currents and as a result transport pathways. The construction of a residual mean circulation, as has been done for OCCAM, is almost equivalent to defining local stream coordinates and projecting the trajectory positions back to a fixed coordinate system that is associated with the spatial average of the stream coordinate systems (McIntosh and McDougall 1996). In this way, the cross-stream length scale of currents is preserved. The associated pathways, however, feature sharper boundaries than would be obtained by an Eulerian average of synoptic fields, in the model as well as in the real world. There is also less coherent, stochastic motion associated with the (sub)mesoscale. This kind of motion acts as dispersion on isopycnal surfaces and smooths the transport pathways further. It should be noted, however, that passages between different basins and/or current systems (almost) always reside in narrow currents. Both in our models and the real world the Lagrangian pathways between Drake Passage and the equator feature several constricting points where these pathways are focused in narrow, swift currents, namely, the ACC at Drake Passage and other locations downstream (south of Australia and New Zealand), and the western boundary currents where the interhemispheric exchange takes place. Outside these constricting points, stochastic motion will enhance exchange between (boundary) currents and interior in both directions, which will smooth the gradients of the Lagrangian streamfunction in recirculation areas and also enhance the amount of recirculation. Where interbasin exchange is confined to narrow passages because in the interior the connection between basins is blocked, the difference between the real world and the model is likely reduced, as in each case the Lagrangian streamfunction features sharp gradients set by the width of the current carrying the water mass. We hypothesize that the Lagrangian streamfunction obtained from the residual mean circulation in OCCAM would not differ that much from a “real world” streamfunction, the latter being only smoother in the recirculation regimes. This would be true even if individual trajectories in the real world would look much more chaotic than those obtained from an integration in OCCAM. Much of this disorder would be eliminated when integrating the trajectories into a transport streamfunction.

At 48°S, the transport exported from Drake Passage almost equals in strength the integrated Ekman transport at this latitude. However, our results suggest that the amount actually crossing the equator is reduced by about 30%. The rest is reinjected into the ACC after recirculation in the southern subtropical gyres. We suggest that the transport equation derived in Nof (2003) gives a fairly good estimate of the total export to the equator in the upper 1000 m. However, this equation cannot be applied to individual basins because of their connection by interocean exchange.

Our results support the theory of Nof that the water exported from the Southern Ocean flows toward the Atlantic and Indo–Pacific equator within the Sverdrup interior in the eastern part of these semienclosed basins, following the broad curve of the interior subtropical gyre. Upstream, a significant fraction of the same water that is exported from the Southern Ocean is contained within the Ekman layer. This holds especially at the tip of South America where the zonally integrated Ekman flow nearly equals the total export from the Southern Ocean. This nearly reconciles the theory of Nof with the ideas developed by Toggweiler and Samuels (1995): indeed, the former argued that the waters crossing the equator originate in the southern Sverdrup interior, whereas the latter assumed that the NADW overturning cell is closed by Ekman flow in the Southern Ocean. We find that the Ekman flow at the northern boundary of Drake Passage has become a Sverdrup interior flow at the latitudes where the South Atlantic, South Pacific, and Indian Oceans feature both an eastern and western boundary. As a consequence, the initial Ekman transport subducts while flowing northward and experiencing intense diapycnal motions because of the added effect of air–sea fluxes and interior diapycnal mixing with overlying lighter waters.