# Comparison of near-surface mean and eddy flows from two numerical models of the South Atlantic Ocean

Thierry Pendu,<fnref n="1" /> Bernard Barnier, Karine Béranger, and Jacques Verron

Laboratoire des Ecoulements Géophysiques et Industriels, Grenoble, France

**Abstract.** The near-surface mean and eddy flows simulated by two eddy-permitting models of the South Atlantic (S-coordinate Primitive Equation Model (SPEM) and Ocean Parallel (OPA) model) are compared. These models are intrinsically different by virtue of their vertical discretizations ($\sigma$ versus geopotential coordinates, respectively), so that their solutions differ essentialy through the representation of current-topography interactions. The path of the Agulhas Current, the generation process, the characteristics, and the subsequent trajectory of the Agulhas rings are differently affected by topography in the two models. Along the American western boundary, SPEM traps a larger part of the Antarctic Circumpolar Current (ACC) around the Falkland Plateau and consequently produces a stronger Malvinas Current, which overshoots far to the north, inshore of a rather realistic Brazil Current and Confluence regime. In contrast, OPA allows a large part of the ACC to flow across the Scotia Sea, produces a weaker Malvinas Current, traps the Brazil and Malvinas Currents along the American coast, and tends to distort the complex dynamics of the Confluence region and the Zapiola anticyclone. Some of these differences can be attributed to the particularities of each vertical coordinate system and to the representation of topographic slopes (staircases in OPA and facettes in SPEM). More generally, the topographic constraint (trapping of boundary currents and interaction of mean and eddy flows with bathymetry) is stronger in SPEM than in OPA. The topographic smoothing usually performed in sigma coordinate models removes mesoscale topographic roughness and reduces topographic slopes. This treatment is probably responsible for several of the differences observed in the numerical solutions.

## 1. Introduction

The most important difference between commonly used ocean numerical models probably relates to the formulation of their vertical coordinate. In the Dynamics of North Atlantic Models (DYNAMO) experiment [Willebrand et al., 2001] the solutions of a sigma coordinate model, a geopotential coordinate model, and an isopycnal coordinate model of the North Atlantic at a resolution of 1/3° were compared together. Despite the fact that these models were initialized and forced in a similar manner they produced significantly different results. In particular, the representation of overflow processes above the Greenland-Scotland Ridge was shown to depend strongly on the model considered and to affect the thermohaline circulation at basin scale. Furthermore, the horizontal currents did not interact with the bottom topography the same way in the three

models, leading to important dynamical differences in the basin interior and along the continental boundaries. A striking example from the DYNAMO experiment is provided by the dynamics of the North Brazil Current and its retroflection, which differ significantly between models [Barnier et al., 2001]. However, it is still unclear whether these differences are only related to the formulation of the vertical coordinate (terrain following versus geopotential) or to the characteristics of the model topography in each model (significantly smoother in the sigma coordinate model).

The South Atlantic is also an interesting area in which to investigate the strengths and weaknesses of different numerical ocean models. This basin is characterized by unique dynamical features such as the interaction of the Brazil Current (BC) with the Malvinas Current (MC) in the very energetic Confluence region, the presence of a strong eddy-driven anticyclonic circulation around the Zapiola Drift, the retroflection of the Ahulhas Current in the eastern part of the basin, and the northwestward spreading of warm and salty Agulhas eddies. The objective of this paper is to compare the near-surface solutions of a sigma coordinate model and a geopotential coordinate model of the South Atlantic at a resolution of 1/3°. The numerical configurations are presented in section 2, and the mean solution and eddy activity are presented in sections 3 and 4 for both models.

<footnote n="1">¹Now at Center for Ocean-Atmospheric Prediction Studies, Florida State University, Tallahassee, Florida.</footnote>
## 2. Model Configurations and Experiments

The geopotential coordinate and the sigma coordinate regional models used in this study will be hereinafter referred to respectively as Level and Sigma. The South Atlantic configurations of both models were independently developed for different research projects but are similar enough to allow a fruitful comparison of their solutions. Level and Sigma use the same resolution (1/3° in longitude and 1/3°cos(φ) in latitude φ), are forced by the same climatological seasonal surface fluxes (derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis, years 1979-1993), and have computational domains limited by open boundaries along 68°W (Drake Passage), 30°E (South Africa to Antarctica), and 16°S (Brazil to Angola). The differences are summarized below.

Level is based on the primitive equation Ocean Parallel (OPA) model, version 8.1 [Madec et al., 1998]. The present configuration is derived from the 1/3° Atlantic model developed for the Clipper project [Tréguier et al., 1999]. The Weddel Sea is excluded from the domain: a solid boundary has been added along 65.8°S, and the water mass transformation processes at work at southernmost latitudes are parameterized by a relaxation of the model temperature and salinity to the seasonal climatology of Reynaud et al. [1998] (hereinafter referred to as RLMB) in a 2.4° wide buffer zone south of 63.4°S. Forty-two geopotential levels are used on the vertical, and the bathymetry is identical to that used in the Clipper project (no smoothing applied, see Figure 1). Vertical mixing is achieved by a Turbulent Kinetic Energy (TKE) model [Blanke and Delecluse, 1993], reinforced by a convective adjustment in the case of static instability. The initial state is taken from the RLMB austral summer climatology. A net eastward throughflow of 140 Sv is prescribed across the meridional boundaries (the net mass flux across 16°S is set to zero). Level has been integrated over 15 years, while the mean solution and the mean eddy kinetic energy (EKE) have been computed over the last 5 years. It is worth noting that this mean solution differs only slightly from that obtained over the entire Atlantic in the Clipper project: the replacement of the Weddel Sea by a buffer zone and of the rest of the Atlantic by the northern open boundary did not adversely affect the model response in the area of interest over the integration period.

Sigma is based on SPEM (S-coordinate Primitive Equation Model [Haidvogel et al., 1991]), version 5.1, and was implemented at 1/3° on the South Atlantic from 16° to 75°S by Béranger [2000]. The model uses 25 sigma levels on the vertical, a smoothed topography (as recommended when using sigma coordinates) as displayed in Figure 1, a simple sea ice model in the Weddel Sea, and a Krauss and Turner mixed layer model. The stratification is initialized by the austral summer climatology of Levitus [1982], and an eastward net transport of 130 Sv is prescribed across 68°W and 30°E (zero net mass flux across 16°S). Sigma has been integrated over 24 years, while the mean solution and the EKE field have been computed over the last 6 years. Similar numerical

experiments were performed with SPEM in this basin by de Miranda et al. [1999] and de Miranda and Barnier [2000], but the surface forcing was too different from that of Level to allow a relevant comparison.

In terms of vertical resolution the difference between our geopotential and sigma coordinate models (43 and 25 levels, respectively) is of the same order as it was in the DYNAMO experiment (30 and 20 levels, respectively). This feature is expected to differentiate the dynamics of Level and Sigma. However, the spatial distribution of vertical levels is completely different in Sigma and Level: the number of vertical degrees of freedom remains constant throughout the domain in Sigma but depends on local depth in Level (it thus varies between 1 and 43). Since the vertical discretization methods fondamentally differ in the two models, the difference in the vertical resolution should also be considered as an intrinsic difference.

The three open boundary (OB) conditions implemented in both models evacuate the outgoing perturbations through radiation conditions and exert a relaxation of the model variables to a climatology (see Barnier et al. [1998] for the OB conditions in Sigma and Tréguier et al. [2000] for those in Level). The baroclinic variables are relaxed in both models to World Ocean Circulation Experiment (WOCE) section I6 [Park and Charriaud, 1997] at 30°E and to the RLMB climatology at 16°S. At 68°W the baroclinic variables are relaxed to the section of Roether et al. [1993] in Level and to the RLMB climatology in Sigma. Along each OB, barotropic perturbations are radiated outward, and the barotropic stream function is relaxed to a climatological profile. This method enables the models to adjust the lateral conditions to their interior dynamics without drifting too far away from the climatology [Tréguier et al., 2001]. Consequently, the local fluxes of individual water masses and depth-integrated transports across the open boundaries are not expected to be identical in the two simulations. Indeed, Figure 1 shows that the mean barotropic stream function profiles obtained along the OBs after spinup are significantly different. For this reason, and since the model simulations were conducted for too short a period to reach a thermodynamical equilibrium, our comparison will not address the thermodynamical differences and will be focused instead on surface and intermediate circulation features.

## 3. Mean Near-Surface Circulation

Plate 1 shows the mean circulation at 350 m for both models north of about 65°S. Since the solution in Level may be affected by the southern buffer zone, our comparisons will be restricted to north of about 60°S. The transports cited in the text correspond to depth-integrated flows.

### 3.1. Scotia Sea

In Sigma the Antarctic Circumpolar Current (ACC) entering at Drake Passage is concentrated along the northern shelf of the Scotia Sea. The greater part of the ACC (105 Sv) enters the western South Atlantic
<figure><img src="image_1.png" /><figcaption>**Figure 1.** The numerical configurations used in this study: domains, bottom topographies, and scheme of the yearly mean barotropic stream function profiles obtained after spinup along the open boundaries in each model: (a) sigma coordinate model and (b) geopotential coordinate model. Black arrows and associated numbers indicate the locations and intensities of barotropic currents across the open boundaries.</figcaption></figure>

above the North Scotia Ridge flowing north between the Falklands and south Georgia. This branch splits to give birth to the MC (70 Sv), which continues northward along the Argentinian shelf break toward the Confluence region and to the Subantarctic Front (35 Sv), which flows eastward along the Falkland escarpment at 50°S. Only 20% of the transport entering at Drake Passage (25 Sv) remains in the Scotia Sea and flows eastward within the Scotia Front.

In Level the prescribed transport in the ACC at Drake Passage (140 Sv) is 10 Sv greater than in Sigma. Unlike in Sigma, more than half (75 Sv) of it flows east-

ward across the Scotia Sea and passes south of south Georgia. The remaining part (65 Sv) of the ACC crosses the North Scotia Ridge to the north and enters the western South Atlantic. One half of this northward flow (35 Sv) reaches the Confluence region in the MC, and the other half feeds the Subantarctic Front whose position and transport are similar to that simulated by Sigma.

Several arguments may be put forward to explain the larger transport across the North Scotia Ridge in Sigma. One is the difference in the climatological fields to which the baroclinic variables are relaxed along the western OB (a climatology in Sigma and a synoptic section in
<figure><img src="image_2.png" /><figcaption>(b)</figcaption></figure>

<figure><img src="image_3.png" /></figure>

**Plate 1.** Six- and five year mean velocity vectors at 350 m: (a) sigma coordinate model and (b) geopotential coordinate model. Colors indicate the current intensities from blue (weak) to red (strong).
Level). The potential vorticity field associated with the meridional section at 68°W may contribute to the confinement of the ACC along the northern shelf of the Scotia Sea in Sigma and its subsequent anticyclonic circulation around the Falkland Plateau. This is probably not the major reason, however, since in both models the ACC veers strongly to the north just downstream of the open boundary (between 68° and 65°W).

The representation of the West Scotia Ridge may also affect the model solutions in that area: the strong ACC branch that flows eastward south of south Georgia in Level seems to interact with this ridge where it separates from the along-shelf vein (around 60°W, 58°S in Plate 1). In Sigma, on the contrary, this topographic structure has been eroded by the topographic smoothing and does not induce any significant steering of the ACC.

Another argument is the enhanced dissipation of momentum and/or vorticity in Level along the northern shelf of the Scotia Sea due to the presence of small-scale topographic structures (the topography is not smoothed) and, more probably, to higher sidewall lateral form stress. This frictional effect, peculiar to geopotential coordinate models, is due to the representation of isobaths as horizontal staircases [Adcroft and Marshall, 1998]. In sigma coordinate models, topography is instead represented as an ensemble of facettes, and isobaths are represented as piecewise-constant lines that do not induce any spurious momentum dissipation within along-slope currents away from the shallow land mask. This may partly explain why the part of the ACC that follows the Falkland Escarpment is weaker in Level than in Sigma and why a larger part of the ACC continues directly to the east.

A fourth element that probably contributes to the differences between models is the presence of steeper slopes in Level's unsmoothed bathymetry. This topographic difference is particularly marked along the northern shelf of the Scotia Sea and around the Falkland Plateau, and certainly has an impact on the topographic control of the rather barotropic ACC and on its subsequent division to the east and north.

Finally, the tendency of sigma coordinate models to produce currents that are more highly correlated with bottom topography than in other models [Willebrand, 2001] could also explain the trapping of most of the ACC around the Falkland Plateau. It is likely that this tendency is not intrinsic to the use of the sigma coordinate but is mainly due to the use of smoothed bathymetries. Dedicated process studies are required to determine better which consequences of topographic smoothing (weaker slopes, slightly deeper sills, and reduced bottom and lateral roughness) have the most impact on the numerical solutions.

## 3.2. Western Boundary Currents and Confluence

In both models, the BC appears as a coherent southward western boundary current near 20°S (the northernmost extent of the gyre). Its mean transport increases southward from 20 Sv at 25°S to nearly 50 Sv

at 38°S, with local maxima associated with inertial re-circulation cells. The BC transport at these latitudes does not differ much between models, mainly because the wind forcing is the same in both simulations.

However, the dynamical behavior of the BC is very different in the two models. The results of Sigma do not differ much from those described by de Miranda et al. [1999] and de Miranda and Barnier [2000]: the BC separates from the coast around 30°S and runs southward along the 1000 m isobath. The MC does not directly confront the BC in the Confluence region; it remains close to the shelf until it retroflects offshore between 40° and 36°S to join the BC in a strong and turbulent southward flow. As it turns, the current expels cold eddies, which drift northward between the shelf and the BC, bringing cold waters as far as 31°S, in what seems to be an overshoot of the MC. These circulation patterns are quite realistic, even though the northward overshoot of the MC appears exaggerated in comparison with drifter trajectories [Peterson et al., 1996].

The circulation in the Confluence region is quite different in Level. The BC does not separate from the coast until it meets the MC at 46°S, several hundred kilometers south of the observed confluence. The progression to the north of the MC is then stopped at this latitude, and the collision of both currents forms an eastward meandering flow.

The ability of Sigma to separate the BC from the coast at 30°S and to follow the 1000 m isobath is a consequence of using sigma coordinates. As has already been observed in process studies, boundary currents are usually more realistically positioned in this type of model because of a better representation of the topographic constraint [Haidvogel and Beckmann, 1999]. However, the presence of a stronger MC along the South American shelf, which, as already mentioned, is promoted by the topographic smoothing of the North Scotia Ridge and the Falkland Plateau, may also contribute to the overshooting of the MC and the separation of the BC. Even though the spurious form stress intrinsically generated by Level along the western boundary certainly affects the realism of the simulated BC, it is likely that an increase of the northward flow across the North Scotia Ridge (significantly too weak in Level) would increase the northward overshoot of the MC along the shelf and improve the separation of the BC in this model.

In Sigma a strong anticyclonic barotropic standing eddy (150 Sv) is found in the Argentine Basin, centered at (45°W, 45°S) above the Zapiola Drift. This so-called Zapiola anticyclone, confirmed by observations [Saunders and King, 1995; Boebel et al., 1999], was shown to be maintained in this region of closed f/H contours by eddy-driven potential vorticity fluxes [de Miranda et al., 1999]. The BC, after its southward excursion to 45°S, steers sharply northward and, at 40°S, flows eastward on the northern side of the Zapiola anticyclone in a jet associated with the Subtropical Front. The Subantarctic Front flows eastward on the southern side of the Zapiola anticyclone, the presence of which seems a determining factor for the location and intensification of the zonal fronts of the region.
In Level the MC and BÛ are both confined to the coast and only separate from it at their point of convergence at 46°S. Part of the BC steers northward (as in Sigma) and forms the Subtropical Front, which spreads over a wider latitude range (38°-47°S). As suggested by de Miranda et al. [1999], this latitudinal spreading in Level may be due to the absence (even at depth) of a closed recirculation above the Zapiola Drift, a feature whose presence in Sigma probably concentrates the Subtropical Front.

A separation of the mean flow over the topographic drift, characteristic of a Taylor column, is observed at 44°W, 47°S in Level, indicating that the eastward flow is affected by the Zapiola topographic feature. However, no closed circulation is generated around the topography, indicating that the processes at work in Sigma are not present in Level. The staircase-like representation of topography (in particular, that of sinuous isobaths) in Level probably explains the absence of the Zapiola anticyclone, through spurious momentum dissipation that can artificially increase the bottom drag and affect the eddy-topography interaction diagnosed in SPEM by de Miranda et al. [1999]. Thus the differences observed between model solutions in the region of the Argentine basin are likely the direct consequence of the choice of vertical coordinate. The realism of the mean flow simulated by Level may be improved by increasing the northward transport above the North Scotia Ridge and, consequently, the intensity of the MC, even though this type of model intrinsically tends to overestimate bottom and lateral momentum dissipation along staircase-like topographic slopes and thus alter current-topography interactions.

### 3.3. Major Eastward Currents

Between 40° and 10°W in Sigma the eastward route of the South Atlantic Current (Subtropical Front) progressively shifts southward from 40° to 45°S. When it reaches the Mid-Atlantic Ridge (MAR), it is closer to the ACC (Subantarctic Front), which follows an eastward meandering path in the 50°-46°S latitude band. Between the Zapiola Drift and the MAR, several meridional branches connect these two zonal currents. Both currents converge above the MAR (at 15°W, 45°S) and diverge again on the eastern side of the ridge. A branch steers southeastward and leaves the domain through the OB at 50°S after several meridional deflections correlated with topography; a northeastward branch heads toward the Agulhas region. The part of the ACC remaining within the Scotia Sea in Sigma circulates cyclonically around the South Sandwich Trench, takes an essentially eastward path, and joins the branch of the ACC that leaves the domain at 50°S. Coming out of the Weddel Sea along the Antarctic Peninsula, the Weddel Front (the northern limit of the Weddell Gyre) takes an eastward course along 60°S, interacting at different longitudes with the eastward currents located farther north.

West of the MAR in Level, the eastward flow consists of a broad zonal South Atlantic Current spread over the 40°-46°S latitude band but intensified in its southern

part and an eastward jet located farther south (50°S) in the Subantarctic Front. This latter feature is similar to that simulated by Sigma. These currents cross the MAR (15°W) in two branches north and south of 45°S and then converge with one another afterward. This contrasts with Sigma for which only the northern branch is observed. Downstream of the MAR, however, as in Sigma, Level simulates a southward veering of the currents, which then split into several branches either to join the Agulhas return current or to leave the domain farther south. In Level a substantial part of the ACC flows from the Drake Passage across the Scotia Sea. About 20 Sv of it passes to the south of South Orkney Island, is strongly deflected by the South Sandwich Trench, passes between south Georgia and the South Sandwich Islands, and then continues zonally to the eastern boundary.

These results show that the marked differences observed between the two model solutions in the Confluence region (location of the South Atlantic Current) and the Scotia Sea (path of the ACC) influence the location of zonal currents farther downstream, at least as far as the MAR. In addition, the eastward currents are significantly more deflected by the main topographic features (Zapiola Ridge, MAR, and South Sandwich Trench) in Sigma than in Level, although the latter model does show sensitivity to strong topographic features. These multiple local differences between the two models also contribute to differences observable at basin scale.

However, the model solutions become more similar as the ACC approaches the eastern OB. This is probably because the forcing of both models does not differ much along this open boundary: Rossby waves propagate this boundary information mainly westward and probably contribute to keeping both solutions comparable in the eastern part of the basin.

### 3.4. Agulhas Current

At 30°E the Agulhas Current (AC) is forced into the domain by a relaxation of tracers and baroclinic velocities to the same climatology in both models, but the mean barotropic transport of the AC at the eastern OB is lower in Sigma by 10 Sv (Figure 1). Animations show that the AC partly retroflects upstream of Cape Good Hope (around 22°E) in both models and that the mean velocity vectors obtained in Level between 20°E and about 0° do not correspond to a permanent circulation but mark the straight path of anticyclonic Agulhas rings (whose production mechanism is described in section 4). Unlike in Level, an anticyclonic retroreflection cell is found between 22° and 12°E in Sigma. It is permanent and fluctuates in shape and intensity. In both models the Agulhas return current leaves the domain and enters the Indian Ocean along the northern flank of the Agulhas Plateau.

Given the similarity of the lateral boundary forcing at the eastern OB in both simulations, the differences observed in the mean flow near the Agulhas retroreflection region and farther downstream are probably due to the currents interacting differently with topography. The respective effects on the simulated flow of the differences
in the formulation of the vertical coordinate and the
differences in the model topographies are not clear here,
and need to be investigated further.

4. Surface Mean Eddy Kinetic Energy

Figure 2 presents the mean surface EKE diagnosed
from the two simulations north of about 65°S. The sur-
face EKE derived from the combination of TOPEX/Po-
seidon and ERS-1/2 (T/P-E) altimetric data [*Ducet and
Le Traon, 1999*] is shown as a reference. The EKE will
be compared south of 20°S since the northern OB in-
duced spurious fluctuations in Sigma.

4.1. Western Boundary and Argentine Basin

As already noticed in SPEM by de Miranda et al.
[1999], unrealistically high EKE levels (compared to
T/P-E) are found in Sigma within the BC once this
current has separated from the shelf. In Level the EKE
level remains lower than in the real ocean along the BC,
which is trapped along the coast. Several reasons may
explain why Sigma produces much stronger variability
in this region. Related to the northward overshoot of
the cold MC, the inshore density front between the BC
and the shelf is very strong in this model and probably
enhances the baroclinic instability of the current. In
addition, the strong vorticity gradient (∂²v/∂x²) asso-
ciated with these opposing currents may also favor the
occurence of barotropic (shear) instability. The steeper
and rougher American shelf used in Level is likely to
have an opposite effect and to stabilize the BC barotrop-
ically through a strong topographic beta effect and/or
by the dissipation of its mean kinetic energy through
lateral friction. Additional sensitivity studies are re-
quired to identify clearly the origin of these differences.

The horizontal distribution of EKE in the Argentine
Basin is very realistic in Sigma: an EKE minimum
is found above the Zapiola Drift, and two EKE max-
ima extend eastward along the Subtropical and Sub-
antarctic Fronts with realistic levels. De Miranda et
al. [1999] verified that the Zapiola anticyclone is main-
tained by a turbulent potential vorticity flux into this
region of closed f/H contours. The strong interaction
between the mean flow, mesoscale turbulence, and slop-
ing bottom topography is reproduced well in this type
of model.

As seen in section 3, the path of the BC, its inter-
action with the MC, and the circulation above the Za-
piola Drift are not well simulated by Level. Since the
turbulent field is strongly coupled with the mean flow
in this area, a distortion of the EKE field is expected.
Indeed, only reasonable (although too weak) levels of
turbulence are produced in the Subantarctic Front. No
significant EKE is found within the model Subtropical
Front (along 46°S), strongly suggesting that its latitudi-
nal spreading had stabilized the current baroclinically
and barotropically by a flattening of the mean isopy-
cnals and a decrease of the horizontal shear of zonal
velocities.

4.2. Agulhas Eddies

In Sigma the EKE level reaches a maximum just west
of 20°E, within the core of the strong pulsating retroflec-

tion cell observed in the mean circulation. Probably
through baroclinic instability, as suggested by the de-
formation of the cell, six to eight eddies (generally pair
eddies made up of an anticyclone and its cyclonic coun-
terpart) are produced each year. These eddies often
remain close to the retroflection area and rapidly disap-
pear during their interaction with the AC. Few eddies
(three to four) are able to drift westward into the South
Atlantic. These anticyclonic (and cyclonic) mesoscale
structures have various sizes and shapes and scatter in
the Cape Basin over a wide range of latitude, as shown
by the homogeneous distribution of EKE in this region.
However, they tend to lose their dynamical coherence
before they reach the Walvis Ridge over a timescale of
about 2 years.

In Level the retroflection loop of the AC regularly ex-
tends westward along the shelf, up to about 20°E. Four
times a year, at very regular intervals, the AC pinches
off at the tip of the Agulhas Bank (22°E) and expels
a circular, coherent, surface-intensified anticyclone. All
these rings then take a west-northwestward path and
drift across the South Atlantic, as shown by the EKE
distribution in the Cape Basin (Figure 2). Animations
show that they remain equidistant and follow an almost
identical quasi-straight path up to the Walvis Ridge
without any significant meridional dispersion. The Ag-
ulhas Rings persist far beyond the ridge and begin to
show only slight differences in their trajectories after
they pass this topography. The regular shedding of Ag-
ulhas Rings in Level and subsequent invariant path fol-
lowed by the rings in the Subtropical Gyre strongly re-
minds the solution from the Fine Resolution Antarctic
Model [Lutjeharms and Webb, 1995], another geopoten-
tial coordinate model that was integrated at a compara-
ble resolution. On time average the repeated passage of
anticyclonic rings induces a strong northwestward cur-
rent between 20° and 10°E from the tip of Africa to
the Walvis Ridge and a strong countercurrent (to the
southeast) just south of it (Plate 1).

Both models thus produce very different types of Ag-
ulhas eddies through different mechanisms, but both
EKE fields at the surface retain certain observed fea-
tures. In the real ocean, about six to seven Agulhas
rings are produced each year at different locations in
the retroflection region, and those that drift westward
into the Atlantic scatter meridionally. These latter fea-
tures are qualitatively better simulated by Sigma than
by Level. However, only the Agulhas rings simulated by
Level are sufficiently coherent to persist and drift across
most of the Subtropical Gyre, as suggested by obser-
vations [Gordon and Haxby, 1990; Byrne et al., 1995].
This capability of Level may be due to the presence of a
rough bottom topography. This factor tends to confine
the EKE near the surface [Böning, 1989], i.e., probably
rebenders the Agulhas rings more surface-intensified and
less sensitive to the Walvis Ridge.

The numerical formulations of the two models and the
representation of the South African shelf and bottom
topography in the Cape Basin are sufficiently different
to influence considerably the instability processes that
generate the Agulhas eddies, the dynamical behavior of
<figure><img src="image_4.png" /><figcaption>Figure 2. Mean surface EKE (cm² s⁻²) fields: (a) sigma coordinate model, (b) geopotential coordinate model, and (c) EKE map deduced from the combination of TOPEX/Poseidon and ERS-1/2 altimetric data [Ducet and Le Traon, 1999].</figcaption></figure>
the eddies during their northwestward drift, and thus the mean circulation in the eastern South Atlantic. In this area, again, the choice of a particular vertical coordinate system and the smoothing of the model topography play a major role in shaping the simulation results, but estimating the respective contribution of these two elements requires further investigation.

**5. Discussion and Conclusion**

The near-surface mean and eddy flows produced by a geopotential coordinate model and a sigma coordinate model of the South Atlantic were compared. As required in these types of basin-scale simulations, both computational domains were limited by OBs, which behaved remarkably well, numerically and physically. This numerical approach ensures dynamical consistency between the lateral forcing and the interior solutions but does not lead to exactly the same lateral conditions in both simulations. However, the dynamical impact of these different OB conditions is expected to be limited, given the relaxation exerted on model variables along the OBs and the short integration period (15-20 years). Accordingly, most dynamical differences between the two model solutions are found along shelves (Scotia Sea and Confluence and Agulhas regions) and above the main topographic structures (South Sandwich Trench, MAR, and Zapiola Drift). This demonstrates that these differences are mostly due to different representations of current-topography interactions, a conclusion also drawn from the DYNAMO experiment [Willebrand et al., 2001]. Indeed, the present study may be seen as a complement to the DYNAMO experiment (similar models and strategy, same resolution).

As already noticed in this earlier comparative study, the staircase-like representation of topography in Level induces spurious form stress within along-slope currents along both the ocean bottom (around seamounts and along ridges) and the continental shelves. Adcroft and Marshall [1998] demonstrated that this problem affects the horizontal circulation along isobaths that are not aligned with a coordinate axis since such isobaths are discretized as horizontal staircases. This spurious effect is intrinsic to geopotential coordinate models and is expected to weaken most along-slope currents in Level. It would certainly be fruitful to reformulate the viscous stress tensor in geopotential coordinate models to avoid this spurious effect, as was done by Adcroft and Marshall in a shallow-water model. In Sigma, on the contrary, topographic slopes are not introduced as vertical staircases but as sloping segments, and away from the land mask (which induces spurious friction as in Level but only in the upper 200 m) the discretized isobaths are not represented as horizontal staircases but as piecewise constant segments that are not aligned with the model grid. For these reasons, in Sigma, no spurious lateral friction affects along-slope horizontal currents away from the coastline, either along continental shelves or around deep topographic structures: the topographic momentum dissipation is only achieved by bottom friction in Sigma. The representation of current-topography interaction is thus intrinsically dif-

ferent between the two models. This "intrinsic" argument probably explains why only Sigma realistically reproduces the observed strong anticyclone and associated EKE minimum above the Zapiola Drift, which, in turn, deviates the South Atlantic Current northward to its correct latitude and generates the observed EKE maximum along its path. Indeed, the two processes that were shown by de Miranda et al. [1999] to control the dynamics of the Zapiola anticyclone (eddy-topography interactions and bottom friction) are distorted and overestimated by the staircase-like representation of this large-scale topographic structure in Level. On the other hand, the location of along-shelf currents with regard to the cross-shore topographic gradient significantly differs between the two models. Level tends to trap the BC and AC along the American and African coasts respectively, whereas Sigma tends to align them with the shelf break. The same tendency was noted in the DYNAMO experiment within the western boundary currents, which were located inshore of the shelf break in the geopotential coordinate model and above it in the sigma coordinate model. This behavior is probably another consequence of the numerical formulations of each model.

However, it is likely that the representation of current-topography interactions in both models differs not only for these intrinsic reasons (formulations of the vertical coordinate and representation of topographic slopes) but also because mesoscale roughness has been removed from the Sigma topography. It is widely acknowledged that a certain amount of topographic smoothing is necessary for any application of a sigma coordinate model in order to reduce the numerical truncation errors intrinsic to the discretization of the primitive equations in this coordinate system [Barnier et al., 1998]. According to Böning [1989] and Barnier and Le Provost [1993], the absence of topographic roughness renders the mean flow more barotropic. This, in turn, is likely to increase current-topography correlations. Indeed, in the present application, Sigma exhibits a tendency to produce more vertically coherent flows than Level, especially in the Scotia Sea within the branch of the ACC that feeds the MC. This boundary current is more barotropic, more tightly trapped along the Falkland Plateau, and significantly stronger in Sigma than in Level. The substantial part of the ACC drained around the Falkland Plateau in Sigma may contribute to the excessive overshoot of the MC along the American shelf (up to 35°S) in this model. These findings suggest that other considerations related to ocean physics must also be considered in defining the topographic smoothing in sigma coordinate models. In the present case it is questionable whether or not the smoothing performed on the North Scotia Ridge significantly reduced discontinuities in the *f/H* contours and thus enabled a continuous propagation of information along the South American shelf from Drake Passage to Brazil. The remarkable, and probably unrealistic, continuity of the Malvinas Current in Sigma may simply be the result of excessively smooth *f/H* contours. More selective smoothing could thus significantly improve the solution of the sigma coordinate model. According to Böning [1989] and Barnier and Le Provost [1993], the
presence of mesoscale topographic roughness in Level should also make the eddy flow less sensitive to bottom topography. Keeping in mind that the processes that generate the Agulhas rings are different in the two models, the presence of bottom roughness in Level may intensify the velocity field near the surface within the Agulhas rings and allow them to drift above and far beyond the Walvis Ridge, unlike in Sigma.

It should also be noted that in the absence of topographic smoothing (except for a median filter used to interpolate the original topography from *Smith and Sandwell* [1997] onto the 1/3° model grid), slopes are significantly steeper in Level. This is likely to increase the local topographic beta effect and impede the separation of boundary currents like the BC. Despite steeper slopes, however, horizontal currents in Level are less correlated with topography in the basin interior (along the South Sandwich Trench, above the MAR, and near various seamounts). It is not clear whether this is another effect of lateral friction on the side wall at the bottom level. Thus Level has, a priori, the most realistic bathymetry, but its aforementioned intrinsic limitations may prevent it from taking full advantage of steeper slopes and a rougher ocean floor. Until now the question of topographic smoothing had been examined only in the context of sigma coordinate modeling, but it should also be addressed for geopotential coordinate models.

In conclusion, our analysis confirms that the numerical representation of current-topography interactions is substantially different in sigma and geopotential coordinate models and provides new insights into its effects on near-surface mean and eddy flows. The two models examined here differ mainly with respect to three factors: the vertical coordinate system (terrain following for Sigma and geopotential levels for Level), the representation of topographic slopes and isobaths (quasi-continuous in Sigma and staircases in Level), and the roughness of their topographies. The respective effects of these numerical differences on the simulated flows could not be quantified fully by the present investigation. Our present understanding is that before we can clearly evaluate the advantages or disadvantages of one coordinate system in relation to the other we need to quantify accurately the impact of topographic smoothing on model dynamics and clarify the way in which vertical and horizontal staircases affect along-slope currents in geopotential coordinate models. This will require further process-oriented sensitivity model studies.

**Acknowledgments.** This research was supported by a 2 year CNES postdoctoral fellowship. Most of this work was achieved when TP was visiting the Laboratoire des Ecoulements Géophysiques et Industriels. Supports for computations were provided by the Institut du Développement et des Ressources en Informatique Scientifique. We would like to thank James J. O'Brien for useful comments and two anonymous reviewers for helping us improving the paper.

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T. Penduff, Center for Ocean-Atmospheric Prediction
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