a. Parameterizations

Model parameterizations of subgrid-scale physics are more or less as for a preceding Atlantic-only model (New et al. 1995). However, as eddy-induced transports and diapycnal mixing are believed to play important roles in the Southern Ocean, we outline further details of these parameterized model processes.

Tracers and density are advected by the resolved or slowly time-varying mean flow and also by the eddy-induced horizontal “bolus velocity” [Gent and McWilliams 1990 (GM); McDougall and McIntosh 1996],

View Expanded

where h is isopycnal layer thickness and dashes and overbars represent “eddy” and “mean” quantities, respectively. This velocity is parameterized in the model by lateral diffusion of layer interface depth z(ρ). Hence Ψ*, the total horizontal bolus transport below a given isopycnal ρ, satisfies

Ψκ∇_Hzρ(2)

with Ψ* = 0 on the ocean floor. In the model, diffusivity κ does not vary in the vertical, so the bolus transport within each isopycnal layer (apart from the abyssal layer) is given by

huκ∇_Hh.(3)

This bolus transport also acts within the surface mixed layer where it varies in thickness.¹ Within the densest layer, since Ψ* = 0 on the ocean floor, we have instead

huκ∇_Hη,(4)

where η is the height of the top of the densest layer. The value of κ is parameterized as κ = u_dL, where u_d = 1 cm s⁻¹ and L is a horizontal length scale equivalent to the 1° grid resolution (hence κ ≈ 1000 m² s⁻¹). Further details of MICOM layer interface diffusion can be found in Langlois et al. (1997).

Diapycnal mixing in the model arises in three different ways (Nurser et al. 1999):

1. entrainment at the base of the model mixed layer (see Bleck et al. 1989) due to either surface forcing (surface buoyancy loss and turbulent kinetic energy input from the wind) or the convection that results from baroclinic shear (when dense water is driven over lighter water)

2. lateral mixing of T and S in the mixed layer, which, along with entrainment, we collectively term “surface mixing”;

3. turbulent diapycnal mixing at layer interfaces in the model interior, referred to here as “interior mixing” and represented (Hu 1996) by e_k+1/2, a (positive downward) vertical velocity across the interface between the layers, k and k + 1:

   

   

   View Expanded

   

   where κ_d is the coefficient of diapycnal mixing, parameterized here as κ_d = c/N, with c = 0.575 × 10⁻⁷ m² s⁻² and the buoyancy frequency N = −(g/ρ)(∂ρ/∂z). This parameterization yields values for κ_d ranging from O(0.1 cm² s⁻¹) in the upper thermocline to O(1.0 cm² s⁻¹) in the deep ocean. Applying (5) to the model thickness fields and area integrating, we can obtain a globally averaged diapycnal velocity at each layer interface. This average velocity increases with depth (reflecting the stratification-dependent parameterization for κ_d), ranging from 0.25–0.5 × 10⁻⁷ m s⁻¹ in the main thermocline to ∼10⁻⁷ m s⁻¹ in the deep ocean—the canonical value of Munk (1966).

b. Surface forcing

In a 30-yr integration, the model is forced with monthly mean climatological surface fluxes [Hellerman and Rosenstein (1983) wind stress, Esbensen and Kushnir (1981) heat fluxes and evaporation rate, and Jaeger (1976) precipitation rate]. To maintain realism in surface distributions of heat and salt it is, however, also necessary to relax the sea surface temperature (SST) and salinity to monthly mean climatological values (Levitus 1982). The method used here is similar to that of Haney (1971), although we use a fixed relaxation coefficient (λ) of 35 W m⁻² K⁻¹. The net downward heat flux is thus Q_net = Q_clim − λ(T − T_clim), the climatological flux (Q_clim) plus a relaxation flux, which is proportional to the difference between model mixed layer temperature (T) and climatological SST (T_clim). The freshwater flux is formulated likewise.

As in a similar Atlantic-only model (New et al. 1995), modified surface boundary conditions are used to represent the first-order effects of sea ice: the surface fluxes of heat and freshwater and the wind mixing power (but not the wind stress) are set to zero at “ice-covered” model gridpoints, defined as such if either climatological SST or model mixed layer temperature falls below −1.8°C (the approximate freezing point for seawater). The effects of sea ice, largely insulating and shielding the mixed layer from air–sea interaction, are thus simulated for a negligible increase in model integration time.

c. Spinup

To assess the relative steadiness of model water masses during spinup, we compute time series of area-integrated layer thickness anomalies (referenced to the start of the integration at time t = 0), Δh_k(t):

View Expanded

where h_i,j,k and ΔA_i,j are layer thickness and gridbox area at each gridpoint.

Figures 1a and 1b show Δh_k(t) for layers 1–20, over the 30-yr spinup, in the Southern Ocean, for zones south of 42.5°S and 25°–42.5°S, respectively (the choice of these zones, based on two distinct water mass transformation regimes, is made clear in Section 4b). Seasonal cycles of mixed layer–thermocline interaction are clear in Fig. 1. South of 42.5°S layers 7–10 display strong seasonal signals, while in the zone 25°–42.5°S layers 3–7 appear to interact with the mixed layer—indicating the ventilation of lighter layers in the equatorward zone.

The outstanding features of Figs. 1a,b, however, are the large interannual trends in the thickness of the denser unventilated layers. These trends of mean layer thickness, away from initial Levitus (1982) climatological values, are due to imbalances between formation rates, transports, and mixing rates for the water mass represented by each layer. These imbalances are further investigated in the detailed diagnosis of year 30, which follows. In the region south of 42.5°S over years 0–30, the mean thickness of layer 13 increases at an almost steady rate of 2.5 m yr⁻¹ (area-integrated, this corresponds to a gain in volume at the rate of 6 Sv—see Fig. 16b below), while layer 15 (σ = 27.88) thins at a similar rate (Fig. 1a). The zone 25°–42.5°S is dominated over years 0–20 of the spinup by an ∼3 m yr⁻¹ increase in the mean thickness of layer 15, while lighter layers decrease in thickness to varying degrees (Fig. 1b). However, the area-integrated thicknesses of layers that represent SAMW and AAIW (layers 8 and 9 south of 42.5°S; layers 6 and 7 in the zone 25°–42.5°S) show little change over years 20–30. This suggests that, for these model water masses, annually averaged import/export across zonal boundaries and formation/consumption rates within zones are reaching an equilibrium by year 30.

To assess the drift of layer temperature (and hence salinity), we compute monthly layer-mean temperature anomalies, ΔT_k(t), in the same two zones (thickness-weighting layer temperature at each gridpoint). Figure 2 shows the 30-yr time series, over the two Southern Ocean zones, of ΔT_k(t) for layers 6–16 (lighter layers are relatively thin and exhibit large seasonal temperature variability; denser layers have zero thickness). Temperature drifts are typically ±0.5°C over the 30-yr spinup. In general, intermediate waters (layers 6–10) cool while deep waters (layers 11–16) warm. As the model is isopycnic, these warming/cooling trends are exactly “balanced” by increases/decreases in salinity (temperature changes of ±0.5°C are accompanied by salinity changes of roughly ±0.1 psu). T–S curves, area-integrated in the same two zones, in years 1 and 30 (not shown) confirm that the T–S relationship for intermediate waters (σ < 27.52) shifts toward lower temperature and lower salinity over the 30-yr spinup. Although water mass characteristics do change during model spinup, these changes are reasonably small, that is, model water mass properties remain close to Levitus (1982) climatological values. Certainly, after 30 years, the properties of the intermediate waters have almost reached a steady state.

a. Surface density fluxes

We consider annual-mean surface density fluxes over the Southern Hemisphere oceans. Figure 3a shows the annual-mean climatological density flux, 〈D_clim〉 (we denote annual means by angle brackets), calculated from the flux fields of Esbensen and Kushnir (1981) and Jaeger (1976), as detailed in appendix A. The flux is defined as positive downward, so that positive values imply surface density gain, or an ocean-to-atmosphere flux of buoyancy. Figure 3b shows 〈D〉, the annual-mean total density flux forcing of the model ocean in year 30, which includes the relaxation heat and freshwater fluxes. Figures 3c and 3d show, respectively, the thermal and haline components of 〈D〉.

Broadly speaking, over the Southern Hemisphere of the model, surface waters gain density (lose buoyancy) over the subtropical gyres and lose density (gain buoyancy) at mid and high latitudes. The density gain in southwest sectors of the three subtropical gyres (South Atlantic, Pacific, and Indian) is associated with the separation (in the case of the Brazil and East Australia Currents) or retroflection (in the case of the Agulhas Current) of WBCs. Relatively warm, salty waters (see Figs. 4a,b) thus move south (Fig. 4c), are cooled (again largely via relaxation fluxes), and increase in density.

In contrast, there is strong density loss (again predominantly due to relaxation) at midlatitudes in the southwest Atlantic due to the heating of cold water flowing north in the Falkland Current (Figs. 4a,c) and also east of New Zealand. South of about 45°S freshening (Fig. 3d) dominates cooling (Fig. 3c), leading to weak density loss except south of New Zealand and in the southeast Pacific. With model relaxation fluxes taken into account, thermal and haline surface forcing are found to be in opposition (i.e., freshening tends to coincide with cooling) over broad regions of the Southern Ocean (see Figs. 3c,d). This may partly result from the fact that water is cold and fresh to the south and warm and salty to the north (Figs. 4a,b). Hence water pushed south of a mean position in the Levitus climatology is freshened and cooled whereas that pushed north is warmed and salinified.

Figure 5 shows the zonally-averaged annual-mean surface density flux over the Southern Ocean due to climatological (Fig. 5a) and total year 30 (Fig. 5b) heat and freshwater fluxes. Note that the total surface density gain north of 40°–45°S is two to three times stronger than that driven solely by the climatological fluxes. Note also that, in the zone south of 40°–45°S, the haline and thermal components of 〈D_clim〉 and 〈D〉 act in opposition. The general enhancement (relative to climatology) of model density loss due to haline forcing at high latitudes may reflect the effects of spring/summer sea ice melting around Antarctica (absent from the climatological E − P freshwater forcing, but implied by relaxation of surface salinity toward low values).

It is unclear to what extent the net model fluxes are more “correct” than the climatological fluxes. The climatological fluxes used here overestimate the globally averaged heat input. Moreover the surface flux observations are very sparse in the Southern Ocean (Josey et al. 1999), so the climatologies are unreliable here. Certainly the climatological flux field in Fig. 3a seems unrealistically smooth. The relaxation correction gives plausible structure in the fields, qualitatively similar to that produced in (for example) the coupled National Center for Atmospheric Research model (Gent et al. 1998), but may nevertheless show bias due to model weaknesses.

b. Ventilation sites, recirculation pathways, and mode water properties

We now consider the sources of thermocline water masses in the model, in particular the formation regions for AAIW and SAMW. McCartney (1977, 1982) identifies AAIW and SAMW formation sites in the subantarctic zone, a circumpolar band of width ∼5°, bounded to the north by the Subtropical Front (STF) and to the south by the Subantarctic Front (SAF). According to McCartney, AAIW forms during winter convection in the subantarctic zone of the southeast Pacific and Scotia Sea (McCartney 1977), while SAMW forms likewise at sites in the southeast Indian and mid/southeast Pacific Oceans (McCartney 1982).

The SAF is the northernmost of three major Southern Ocean fronts, the other two being the Polar Front (PF) and the continental water boundary (Whitworth 1988). Park et al. (1993) summarize surface temperatures and salinities that conventionally define these fronts. In the model, local gradients in surface temperature and/or salinity (Figs. 4a,b) provide some indication of the STF in the South Atlantic (where salinity varies from 34.2 to 35.8 psu in the Brazil–Falkland confluence zone), the SAF in the south Indian Ocean and east of New Zealand (defined by the 8°C isotherm), and the PF in Drake Passage (the 2°C isotherm). The model ACC (Fig. 4c) is coincident with these fronts.

Figure 6 shows Southern Ocean fields of late winter/early spring (September–November; see Fig. 7) maxima in mixed layer depth (Fig. 6a) and density (Fig. 6b). The notable feature in Fig. 6a is a band of deep mixing in the midlatitudes, where mixed layers deeper than 500 m are evident in the southeast Indian Ocean, the south Tasman Sea, and the southeast Pacific, a feature also seen in the Levitus (1982) climatology. Strong wintertime density input in the Aghulas and East Australian WBCs (Fig. 3c) weakens upper-ocean stratification. Weakly stratified waters are then strongly advected along the path of the ACC through the Indian and Pacific sectors (Fig. 4c), and further density gain leads to deep convective mixing. A similar model mixed layer evolution is reported by England et al. (1994). The density of these winter mixed layers thus increases systematically from west to east in both oceans, except to the east of New Zealand where the ACC swings northward and surface buoyancy is gained.

The field of year-round maximum mixed layer density identifies the end-of-winter water, which is subducted into the permanent thermocline of the Southern Ocean. In Fig. 6b the contours correspond to model layer densities, and thus delimit the zones in which each layer outcrops in late winter. The highest maximum surface density is between 27.74 and 27.82, in the southern Weddell Sea, indicating that the densest layer that can interact with the mixed layer (by entrainment at the mixed layer base) has σ = 27.82. In our model, this is the density of CDW and lighter NADW. Layers with σ > 27.82 (denser NADW/CDW or residual AABW) can therefore only be consumed (in the Southern Ocean) by interior diapycnal mixing. Moreover, the mixed layer is too light at high southern latitudes to permit the model to form AABW at the surface. On the other hand, layers with densities in the range 26.52 < σ < 27.22 (representing SAMW and light AAIW) do outcrop over large areas of the midlatitude Southern Ocean (see gray-shaded band in Fig. 6b), which exhibit deep winter mixing (compare Figs. 6a,b), suggesting that these layers are modified by both entrainment mixing and surface fluxes.

Figure 7 shows seasonal cycles of mixed layer depth at three selected latitudes (indicated by dotted lines in Fig. 6a), which intersect areas of year-round deepest mixing in Indian and Pacific sectors of the midlatitude Southern Ocean. In general, model mixed layer depth undergoes a strongly seasonal cycle, with deepest mixing (mixed layer depth >300 m, gray-shaded in Fig. 7) in the spring (August–December) and shallower mixing (<100 m) in late summer–autumn (January–June). A similar cycle was found in the model of England et al. (1994). At 55°S, 160°E–180°, south of New Zealand, deep mixed layers persist almost all year (with the exception of brief restratification in February–March), in agreement with observations (Heath 1981) that the water column remains nearly isothermal in the upper few hundred meters. Here SAMW may be formed over most of the year, rather than only during late winter.

Figures 8a–d show the austral spring (September) thickness of layers 6–9 (σ = 26.52, 26.80, 27.03, and 27.22), which represent light and dense varieties of SAMW and AAIW. Note the trend for thickness maxima to progressively move eastward with increasing density, again in both Indian and Pacific Oceans. These thickness maxima represent the “core” ventilation sites, and lie immediately northward of corresponding layer outcrops into the deepest winter mixed layers.

To give a qualitative picture of the recirculation of SAMW and AAIW, trajectories representing the ventilation of selected water masses are started from the positions at which appropriate model layers outcrop into the wintertime mixed layer, terminating when the layer is reentrained back into the mixed layer. We integrate year 30 monthly total (advective plus bolus) velocity fields to determine trajectories of fluid columns in individual layers. Using linear interpolation to determine velocity at arbitrary points in space and time, we time integrate these velocities with a simple Runge–Kutta scheme, updating the position of a fluid column 25 times per day. Typical trajectories of SAMW and AAIW are shown in Fig. 8. Dots indicate the position along a trajectory every five years.

Layers 6 and 7 (Figs. 8a,b) (σ = 26.52, 26.80, representative of light and dense varieties of SAMW), are ventilated in the mid/east South Pacific and south Indian Oceans. Trajectories started at the cores of several ventilation sites reveal a variety of fates: convergence on the Agulhas Current in the southwest Indian Ocean after 15 years; westward recirculation, ending with reentrainment into the mixed layer at midlatitudes of the Southern Ocean after 15–20 years; slow O(50 yr) northward spreading in the Tasman Sea; “escape” from the Southern Ocean to reach the western equatorial Pacific after 35 years (thereafter swept rapidly eastward to upwell into the mixed layer just south of the equator in the mid-Pacific). Layers 8 and 9 (Figs. 8c,d) (σ = 27.03, 27.22, representing light and dense AAIW) are ventilated in the southeast Pacific and the southwest Atlantic, respectively. Trajectories reveal that σ = 27.03 parcels take O(50 yr) to reach the western equatorial Pacific while σ = 27.22 parcels are typically swept rapidly eastward along circumpolar trajectories and reentrained into the mixed layer southwest of Australia after O(15 yr). The thickness fields of layers 8 and 9 suggest only weak northward spreading of AAIW in the South Atlantic.

How do the properties of model SAMW and AAIW compare with observations? Layers 6 and 7 (σ = 26.52 and 26.80) represent the light varieties of SAMW, which form in the Indian and Pacific Oceans. Figure 9 shows their (model) temperature and salinities in the Indian sector. Different temperature and salinity intervals are grayshaded in Fig. 9 to identify correspondence with observed modal properties. Sections of temperature and salinity at ∼32°S in the Indian Ocean (Toole and Warren 1993) indicate a light SAMW layer, between 60° and 70°E at 200–400 m with temperature and salinity in the ranges 13.0°–15.0°C and 35.30–35.50 psu. In the model, these temperature and salinity ranges are found on the σ = 26.52 isopycnal where it is most strongly ventilated in the mid–Indian Ocean (Figs. 9a,b). Likewise, SAMW with σ = 26.80, forming in the southeast Indian Ocean, can be traced by temperature and salinity in the ranges 10.5°–11.5°C and 34.85–35.15 psu. This is warmer and saltier than the observations of SAMW in the southeast Indian Ocean by Schodlok et al. (1997), who found temperature and salinity in the ranges 8.50°–9.50°C and 34.60–34.70 psu at depths of up to 600–700 m, although the T–S properties on σ = 26.80 do fall in this range where the layer outcrops south of Australia at around 45°S (Figs. 9c,d).

Model AAIW is best represented by the σ = 27.03 layer, for which the circumpolar temperature and salinity fields are shown in Figs. 10a,b. Georgi (1979) found that, in the southeast Pacific and South Atlantic, the modal properties of AAIW fall in the ranges 2.0°–7.0°C and 34.10–34.40 psu. The temperature and salinity on σ = 27.03 (Figs. 10a,b) and σ = 27.22 (not shown) do indeed fall in these ranges, over much of the Southern Ocean. In a global model based on the Geophysical Fluid Dynamics Laboratory code, England et al. (1993) show how the renewal of AAIW is concentrated in the southeast Pacific Ocean off southern Chile, from where a low salinity (34.10–34.40 psu) tongue extends north and west across the Pacific at around 1000 m. Figures 8c and 10b show that the corresponding AAIW in our model can be identified by a similar salinity minimum (34.25–34.40 psu).

Figure 10c is a meridional cross section of salinity through the upper 2000 m of the model, in the central Pacific at 160°W. This may be compared with the observations along that line presented by Reid (1965, his Fig. 3); also reproduced as Fig. II-13 of Schmitz (1996a). The AAIW salinity minimum lies at 800–1100 m, extending northward to 20°S with salinities of <34.4 psu, as in Reid’s section. However, salinities of <34.2 psu in the ACC region (around 50°S) only penetrate to ∼600 m rather than reaching 1000 m as in the observations; this may result from insufficiently deep winter mixing.

c. Interbasin transports and basin-by-basin water mass formation

Consider now the circulation across selected transects in and around the Southern Ocean. Figure 11 shows total (advective plus bolus) transports for each density-partitioned “layer.” The mixed-layer transport is apportioned (in the range 24.70 < σ < 28.13) between layers according to mixed layer density (the remaining “ML” transport is at σ < 24.70). The selected zonal transects (Figs. 11a,c,e) lie along 25°S across the South Atlantic, south Indian, and South Pacific, with meridional transects southward from the Cape of Good Hope to Antarctica along 20°E, from Tasmania to Antarctica along 146.25°E, and across Drake Passage at 65°W. The zonal South Atlantic section (a) illustrates the southward-flowing supply of NADW to the Southern Ocean and the northward return flow of water at lighter densities (the lower and upper branches of the thermohaline circulation), while the sections across the South Indian (c) and South Pacific (e) reveal the northward spreading of remnant NADW and CDW. The three meridional sections (Figs. 11b,d,f) show large eastward exchanges between the various sectors of the Southern Ocean as expected, reflecting transport by the ACC.

Across 25°S in the South Atlantic (Fig. 11a), 15.7 Sv of NADW (layers 14–16; σ = 27.82, 27.88, 27.93) flows south, balanced by a northward transport of various light and intermediate waters (layers 4–13). This is in broad agreement with the Saunders and King (1995) estimate of ∼15 Sv southward flow of deep waters through the South Atlantic into the Southern Ocean, made up of 21.7 Sv of southward-flowing NADW less 6.6 Sv of northward flowing AABW, balanced by northward fluxes of surface water (11.0 Sv) and intermediate water (4.1 Sv).

The NADW that reaches the Southern Ocean flows eastward and becomes indistinguishable from CDW. Across the section south of Africa (Fig. 11b), the combined transport of NADW and CDW (layers 13–15; σ = 27.74, 27.82, 27.88) amounts to 41.4 Sv, and the total ACC transport is 96.2 Sv, which, bearing in mind the model resolution, agrees reasonably well with the observed Drake Passage transport of ∼130 Sv (e.g., Schmitz 1996a).

The northward flow of 5.5 Sv of NADW/CDW across 25°S into the Indian Ocean, section (c), is less than recent observations suggest [e.g., Robbins and Toole (1997) estimate a deep northward flow of 11.9 Sv across ∼32°S]. Flow through the Indonesian archipelago results in a net southward transport of 25.4 Sv across (c), from the Indian to the Southern Ocean in the model, considerably larger than the hydrographic annual-mean estimate of ∼10 Sv (Fieux et al. 1996; Schmitz 1996a). The flow across 25°S in the Indian Ocean includes 11.6 Sv of very light (“ML,” σ < 24.70) “remnant” Indonesian throughflow, which has gained density across the Indian Ocean and in the Aghulas Current (Figs. 3b, 4c). After further density gain south of 25°S, these light flows pass into the Pacific sector across section (d), south of Tasmania, predominantly as part of a 28.5 Sv flow of SAMW (σ = 26.52, 26.80). The 121.7 Sv total transport across this section into the Pacific is augmented by the 25.4 Sv throughflow, which then, of course, returns northward across 25°S in the South Pacific (e). The remaining 96.3 Sv flows through the Drake Passage (f) and back into the Atlantic sector.

A 14.0 Sv northward flow of NADW/CDW in the Pacific sector is partly compensated by a 3.7 Sv southward flow of upper CDW (UCDW) (layers 12 and 13;σ = 27.64, 27.74). Applying inverse methods to transpacific sections at 28°S and 43°S, Wunsch et al. (1983) obtain a meridional circulation in the midlatitude South Pacific, dominated by a deep cell amounting to 12 Sv:NADW/CDW flows northward at depths of 3000–4000 m and mixes to a slightly lower density north of 43°S, returning southward at depths of 2000–3000 m as UCDW and North Pacific Deep Water (NPDW). Of the NADW/CDW flowing northward across 25°S in our model, 10.3 Sv does not return south. An underestimated return flow of UCDW/NPDW suggests that this deep cell is not correctly balanced by mixing in the Indo-Pacific.

We also show in Fig. 12 the water mass formation rates for each layer within the various basins, obtained as the balance of imports/exports and volumetric imbalances (further discussed in the next section). NADW/CDW (σ = 27.82, 27.88, 27.93) is consumed at rates of 4.0 Sv and 2.9 Sv in the Atlantic (Fig. 12a) and Indian (Fig. 12b) sectors, respectively, while forming at 1.2 Sv (through mixing of denser bottom water and overlying NADW/CDW layers) in the Pacific sector (Fig. 12c). South of 25°S, the net 5.7 Sv loss of NADW/CDW again compares well to an independently obtained consumption rate of 5.1 Sv due to interior diapycnal mixing (see section 4b). However, these consumption rates are much smaller than the combined 19.5 Sv northward export across 25°S in the Indian and Pacific Oceans. Note, however, that the 15.7 Sv of NADW imported into the Southern Ocean (across 25°S in the Atlantic sector) is significantly less than the combined 25.2 Sv consumed in, and exported from, the Southern Ocean, again emphasizing the importance of unsteadiness in this model at high densities. Taking this unsteadiness into account, the fate of model NADW is not unrealistic—the global circulation scheme of Schmitz (1996a) requires, for NADW, a northward export of ∼9 Sv into the Indian Ocean and a consumption of ∼5 Sv in the Southern Ocean.

At lower densities the model is, however, in balance. Figure 12b shows the formation of 19.8 Sv of SAMW (σ = 26.52, 26.80) in the Indian sector. If SAMW is instead defined to include waters of density up to 27.3, as in Speer et al. (1997), the formation rate is 24.6 Sv, in good agreement with the Speer et al. value of 25 Sv, estimated from the Da Silva (1994) flux climatology. SAMW is consumed at a rate of 15.9 Sv (Fig. 12c) in the Pacific sector, where AAIW (σ = 27.03, 27.22) forms at a rate of 8.5 Sv. The balance of AAIW in the South Atlantic is less straightforward: while 29.7 Sv is transported through Drake Passage (Fig. 11f) and 18.3 Sv continues eastward south of Africa (Fig. 11b), only 3.2 Sv is transported northward across 25°S in the Atlantic (Fig. 11a) with the remaining 7.2 Sv consumed in the Atlantic sector (Fig. 12a). The northward flow across 25°S spans a wide range of light and intermediate density classes (Fig. 11a). Note that Agulhas ring shedding is precluded by coarse model resolution, and this largely eliminates the possibility of a warm water path (Gordon 1986).

a. Theory

1) Problems in defining a meridional streamfunction zonally integrated along density surfaces

In the Boussinesq approximation the flow of water is nondivergent,

∇_zuwz(7)

writing ∇_z as the horizontal gradient operator at constant z and u as the horizontal velocity. Hence it is always possible to define a meridional overturning streamfunction integrated zonally on level surfaces

View Expanded

where z_b(x) is a zonally dependent bottom depth, and (8a) satisfies

View Expanded

where C(z, θ) is a closed loop with latitude θ and depth z constant.

However, problems arise in the definition of an overturning streamfunction zonally integrated on surfaces of constant density, resulting from the form of the continuity equation in density space:

View Expanded

writing ∇_ρ as the horizontal gradient operator at constant ρ and defining h = −∂z/∂ρ (so hδρ is the thickness of the layer sandwiched between the ρ + δρ and ρ isopycnals) and g as a diapycnal flux (from light to dense) per unit area. The crucial point is that there is a possibility of layer inflation, ∂h/∂t ≠ 0. Hence, in density space, the flow is not nondivergent. After integration of (9) around a closed zonal loop C(ρ, θ), holding latitude θ and density ρ constant, we have

View Expanded

Here term (A) represents isopycnal flow, term (B) represents diapycnal flow, and term (C) water mass unsteadiness. The unsteady term (C) on the right-hand side need not vanish. Hence we cannot in general define a streamfunction ψ to which we can relate the meridional transport on the isopycnal, and the diapycnal transport across the isopycnal, according to

View Expanded

for differentiating (11a) by y and (11b) by ρ, and summing, gives zero on the right-hand side, but the left-hand side is the unsteady term (C) in (10), which is in general not zero. As we see below, we can introduce a ψ to satisfy either (11a) or (11b), but not both simultaneously.

Note that the sign convention here is such that ψ increases with decreasing density (i.e., up through the water column) for northward flow, in agreement with the convention chosen for ψ_lev above. There are various approaches we could take to separate the time-dependent inflation term (C); here (below) we take a simple, physically meaningful decomposition.

2) Partitioning the meridional streamfunction into “transformation” and “unsteady” components

We now relate the meridional streamfunction zonally integrated on density surfaces to the diapycnal flux across density surfaces, making plain the intimate link between the two. Define the meridional streamfunction

View Expanded

to be the total northward transport of waters denser than ρ across the line of latitude θ = ϒ (by both resolved ν and bolus ν* velocities), where ρ_max is the maximum (bottom) density at that latitude. We further write

View Expanded

to be the total volume of fluid with density greater than ρ lying south of θ = ϒ. Note that ψ(ϒ, ρ), V(ϒ, ρ), and the other fields defined below depend on time, despite not being written with explicit time dependence.

If we then assume incompressibility (as in MICOM), it follows that the total diapycnal flow “down across” the ρ isopycnal (from light to dense) south of θ = ϒ,

View Expanded

must appear partly as volume inflation and partly as export (see Fig. 13a) according to

GρψρVρt.(14)

In the steady state, all of the flow across ρ must be exported, with G(ϒ, ρ) = ψ(ϒ, ρ), as noted by Speer (1997). However, the point is that, when the inflation rate ∂V(ϒ, ρ)/∂t ≠ 0, part of the diapycnal flow may be used to inflate the volume beneath ρ, and the streamfunction does not correspond exactly to the diapycnal flow, G(ϒ, ρ) ≠ ψ(ϒ, ρ). In particular,

View Expanded

Hence (see Fig. 13b), a divergence of fluid denser than ρ (∂ψ/∂ϒ > 0) need not imply a light-to-dense transformation at ϒ (∂G/∂ϒ > 0). Instead, it could imply a decrease in the volume of water with density greater than ρ at ϒ (∂²V/∂ϒ∂t < 0). On the other hand, the streamfunction ψ(ϒ, ρ) as defined above does have the useful property that it satisfies (11a); namely,

ψρU,(16)

where

View Expanded

is the northward transport of waters with density between ρ and ρ + δρ. Moreover, ψ = 0 at boundaries (seafloor, coasts) and is only nonzero at the ocean surface if there is depth-integrated flow—i.e., it looks like a streamfunction!

The “transformation streamfunction,” G(ϒ, ρ), of course gives the correct diapycnal flux, ∂G/∂ϒ, of waters at latitude ϒ. However, we now have (Fig. 13c)

View Expanded

[writing V = −∂V/∂ρ, so that V(ϒ, ρ)δρ is the volume of water with density between ρ and ρ + δρ south of ϒ]. Thus −∂G/∂ρ now includes the rate of inflation of the layer with density between ρ and ρ + δρ south of ϒ, together with the northward export across the latitude ϒ. Walin (1982) termed this sum the water mass formation rate M. Furthermore, of course, G(ϒ, ρ) will not in general be zero at the northern boundary of a closed basin, if the volume below the ρ isopycnal is inflating or deflating—that is, G(ϒ, ρ) does not look like a streamfunction.

So there are two candidate streamfunctions, ψ(ϒ, ρ) and G(ϒ, ρ), in terms of which we might wish to consider zonally integrated flow along surfaces of constant density. Both have deficiencies when the density structure is evolving: ψ(ϒ, ρ) gives the incorrect diapycnal flow (but correct isopycnal flow) and G(ϒ, ρ) the wrong isopycnal flow (but correct diapycnal flow). However, the important thing is that G(ϒ, ρ) has a clear physical interpretation, being the total flux of waters down across ρ, south of ϒ, and the deviation of G(ϒ, ρ) from ψ(ϒ, ρ) gives a simple and direct measure of the importance of water mass unsteadiness.

3) Diapycnal fluxes and density forcing

There must be some source of density to allow diapycnal flow across ρ, that is, G(ϒ, ρ) ≠ 0. This source is associated with either the surface outcrop of ρ or a convergence of the interior diapycnal density flux. Hence (Walin 1982; Speer and Tziperman 1992; Nurser et al. 1999):

View Expanded

Here

View Expanded

is the surface density gain through surface outcrops of ρ [ρ < ρ_m(x), where ρ_m(x) is the mixed layer density at x] south of latitude ϒ, where D_in is the surface density gain per unit area (see appendix A), and

View Expanded

is the total nonadvective density flux (positive from light to heavy) across ρ, south of ϒ, where D is the field of density flux across ρ and n = ∇ρ/|∇ρ| a unit vector normal to the ρ isopycnal surface. The contribution C(ϒ, ρ) results from cabbeling: density gain through mixing on ρ (see McDougall 1987).

A striking consequence of the above is that, for the particular case in which (i) the surface fluxes dominate mixing and (ii) the ocean is in steady state, it follows that

ψρFρ(22)

and we can infer the meridional overturning streamfunction in density coordinates from surface density forcing alone.

b. Diagnosis

1) The meridional streamfunction: Resolved and bolus transports

We calculate ψ(ϒ, σ), the meridional overturning streamfunction, as a function of σ. We choose to define ψ < 0 for an “anticlockwise” sense of overturning, as this is consistent with our direct relation between the meridional streamfunction and water mass transformation. Details of our evaluation of ψ(ϒ, σ) can be found in appendix B. An annual mean, 〈ψ(ϒ, σ)〉, is obtained by averaging 12 monthly instantaneous solutions for ψ(ϒ, σ). We also separately determine 〈ψ(ϒ, σ)〉 and 〈ψ*(ϒ, σ)〉, annual-mean overturning streamfunctions implied by mean (resolved) and bolus (parameterized, eddy-driven) transports, respectively, and discuss how these combine as a total streamfunction.

Figures 14a, 14c, and 14e show 〈ψ(ϒ, σ)〉, 〈ψ(ϒ, σ)〉, and 〈ψ*(ϒ, σ)〉 in the Southern Ocean south of 25°S. The dashed lines indicate σ^max_ml(ϒ), the zonal year-round maximum density of the mixed layer—a zonal maximum of the “end-of-winter” density field plotted in Fig. 6b. At latitude ϒ, water with σ < σ^max_ml(ϒ) outcrops into the mixed layer during part (or all) of the year, while water with σ > σ^max_ml(ϒ) can only change density by diapycnal mixing [hence the near-horizontal streamlines for σ > σ^max_ml(ϒ)]. The black mask indicates densities that are never reached at any time in the year, anywhere at a given latitude. We also present in Figs. 14b, 14d, and 14f, for the various model layers, corresponding annual-average volume fluxes northward across 42.5°S (the mean latitude of the core of the ACC), indicated by the dotted lines in Figs. 14a,c,e.

Three circulation cells are apparent in Fig. 14a. The low density cell implies density gain by lighter waters, representing circulation of the subtropical gyres. About 24 Sv of light (σ < 25.3) waters are imported from the north, gaining density in WBCs and along the midlatitude zonal extensions of those current systems (30°S to ∼42.5°S: see Figs. 3b, 4c). These waters then return northward with σ ≈ 25.8–26.8, including ∼8 Sv of SAMW (σ ≈ 26.5–26.8). This cell, since it is largely north of 42.5°S, is not evident in the layer-by-layer fluxes across 42.5°S (Fig. 14b).

A second, weaker, cell represents the lightening of NADW/CDW to AAIW, the Southern Ocean component of the thermohaline circulation: 6 Sv of water with 27.6 < σ < 27.8 flows south across 25°S, lightens to 27.3 < σ < 27.4 south of 55°S, and then returns northward. This water continues to gain buoyancy in the zone 42.5°–55°S, with density decreasing to 26.9 < σ < 27.2 (values typical of dense SAMW and light AAIW). In this range of density the flow ultimately exits the Southern Ocean across 25°S. This cell is also evident in the layer-by-layer flow across 42.5°S (Fig. 14b) that shows southward flowing layers with 27.38 ⩽ σ ⩽ 27.74 balanced by northward return flows at σ ⩽ 27.22.

Although there is no AABW formation in the model, Fig. 14a suggests a third circulation cell, extending almost to 60°S, involving a ∼2 Sv northward export of very dense waters (σ > 27.8) balanced by input of slightly lighter waters. The export of these very dense waters across 42.5°S reaches 3 Sv (Fig. 14b) and includes (unrealistic) northward transport in the density range of NADW (layers 14, 15; σ = 27.82, 27.88). We find that this spurious cell is due to the effect of unsteadiness and disappears when this is taken into account (see below).

In Figs. 14c and 14e, we decompose 〈ψ(ϒ, σ)〉 into 〈ψ(ϒ, σ)〉 and 〈ψ*(ϒ, σ)〉, annual-mean overturning streamfunctions implied by mean and bolus transports, respectively. Note that the diapycnal flows implied by 〈ψ(ϒ, σ)〉 and 〈ψ*(ϒ, σ)〉 are entirely spurious: the purpose of this decomposition is simply to show the strength of isopycnal bolus transport relative to other key quantities such as the zonally integrated Ekman drift. A structure very similar to the Deacon cell appears in Fig. 14c as an overturning of ∼24 Sv centered on σ = 27.5 at 45°S. Note, however, that this is not the Deacon cell as defined by Döös and Webb (1994), as averaging has been performed on isopycnals, not levels. The strength of this cell (18 Sv at 42.5°S), however, is in fact comparable to the zonally integrated Ekman drift (∼30 Sv at 42.5°S), suggesting a physical explanation similar to that for the Deacon cell.

To emphasize this further, we include in Fig. 14d the layer-by-layer advective fluxes (gray bars) prior to the apportionment of mixed layer fluxes into density classes, as well as the apportioned fluxes (black bars) used to generate the streamfunction in Fig. 14c. We see that indeed there is a very strong northward flux in the mixed layer—the ∼30 Sv Ekman flux. It is this flux, after apportionment into the lighter layers (layers 2–7; 24.70 < σ < 26.80), that gives the northward component of the cell (Fig. 14c; the black bars in Fig. 14d). Since these light layers carry southward transport where they are in the thermocline (gray bars for layers 5–7 in Fig. 14d), the total northward transport of our “quasi-Deacon cell” only reaches 18 Sv (rather then 30 Sv). The return southward transport is mostly carried in layer 15 (σ = 27.88), which is generally the bottom layer. So, apportioning the mixed layer flow into density classes has not eliminated this cell in the resolved flow, as it did in FRAM (Döös and Webb 1994), but merely weakened it. Since this cell does not appear in the “total” flow (Fig. 14a), it must be counterbalanced by the bolus transport.

Figure 15 shows an annual-mean, zonally averaged meridional section of layer interfaces across the Southern Ocean, illustrating how model layers tend to shoal toward Antarctica. Hence the bolus transport streamfunction

View Expanded

(where j is the unit vector in the direction of increasing latitude) is positive throughout the Southern Ocean (Fig. 14e): deep layers move northward and shallow layers southward. The eddy-driven overturning cell thus opposes the Deacon cell–like structure in the resolved flow. Peak bolus transports coincide with the steepest sloping isopycnals. The rapid equatorward decrease in the thickness of layer 15 (labeled in Fig. 15), σ = 27.88, gives a particularly strong northward bolus transport of that layer in the latitude range 40°–60°S, reaching 16 Sv at 42.5°S (Fig. 14f). The compensating bolus transports in the upper layers 5–13 are southward (Figs. 14e,f). The bolus transport in the mixed layer is negligible at 42.5°S, so we do not show the gray bars in Fig. 14f. At 42.5°S, layer 6 (σ = 26.52) is the layer that (on zonal average) lies immediately below the mixed layer, and hence is thinning toward the south most rapidly. It therefore has the strongest southward bolus transport. Farther north, the corresponding layer immediately below the mixed layer is lighter (see Fig. 15), so the strongest bolus transport occurs at lower densities (Fig. 14e).

Compared to Figs. 14c,d and 14e,f, there is relatively weak circulation at σ > 27.8 in Figs. 14a,b; that is, the resolved and bolus transports tend to cancel at high density. Strong southward deep flows (Figs. 14c,d) are supported by topography feeling a westward pressure drag (from the topography) that balances the surface eastward wind stress. These southward flows are balanced by northward bolus transport (Figs. 14e,f) in the bottom layers. Since the depth-integrated bolus transport disappears, lighter waters experience southward bolus transports (Figs. 14e,f), which weaken but do not entirely cancel (Figs. 14a,b) the northward Ekman drift (Figs. 14c,d).

a. The formation of SAMW and AAIW

The model provides a plausible picture of SAMW and AAIW formation and recirculation. In agreement with the observations reviewed by McCartney (1982), progressively denser varieties of model SAMW and AAIW form eastward of the Greenwich meridian, with modal potential density in the thermocline ranging from 26.52 in the mid–south Indian Ocean to 27.22 in the southwest Atlantic. Modal temperatures and salinities of SAMW and AAIW are close to observed values in the mid–Indian Ocean (Toole and Warren 1993) and in the southeast Pacific (Georgi 1979). However, mode waters south of Australia are warmer and saltier than recently observed SAMW (Schodlok et al. 1997). An eastward increase in winter surface density in both Indian and Pacific sectors of the Southern Ocean is associated with systematic buoyancy loss along the track of the ACC as it drifts southward across these sectors. This is also consistent with the eastward deepening of winter mixed layers in both south Indian and South Pacific Oceans, as shown in the Levitus (1982) climatology.

Our model supports the ideas of wintertime formation of AAIW and SAMW, with the strongest sources toward the east of south Indian and South Pacific sectors where mixed layers are deepest (McCartney 1977, 1982). Superposed onto the large-scale recirculating flow of SAMW/AAIW, there is a smaller component of AAIW originating from upwelling of NADW and upper CDW (Sverdrup et al. 1942). Exactly how these two components of AAIW combine together is unclear, but it seems that mixing occurs extensively along the ACC in winter mixed layers.

Previous GCM studies have highlighted problems that lead to incorrect representation of SAMW and AAIW. In an early version of the GFDL model without seasonal cycling, Toggweiler et al. (1989) found SAMW formation to be concentrated in two zones of intense convection adjacent to Australia, while AAIW failed to form. The Southern Ocean in that model was therefore dominated by light SAMW of southeast Indian Ocean origin, and T–S relationships in the southeast Pacific and South Atlantic showed thermocline water masses to be too light, warm, and salty.

In more recent GFDL model studies, progress has been made toward a better representation of the Southern Ocean (England 1993; England et al. 1993; England et al. 1994). However, problems inherent to such level-coordinate models remain. The prevalence of deep convection (due to density instabilities) at high latitudes (south of 60°S) is a major error in Bryan–Cox type models (e.g., England et al. 1994). The introduction of the GM scheme does, however, alleviate this problem (Danabasoglu and McWilliams 1995).

Without GM, the representation of AAIW in such models has proved problematic. England (1993) finds that AAIW is also sensitive to the level of horizontal diffusion (strong diffusion weakens the front at which AAIW subducts), the chosen geometry of Drake Passage (a wide Drake Passage strengthens the Deacon cell at the expense of equatorward-spreading AAIW), and the vertical buoyancy flux due to NADW upwelling in the Southern Ocean (enhanced NADW export to the Southern Ocean strengthens the halocline, allowing a more realistic low-salinity tongue of AAIW to form). Furthermore, England et al. (1993) find the formation of AAIW in the same model to be strongly dependent on the choice of a lateral diffusion scheme. Enhanced Cartesian mixing in an along-isopycnal sense brings more freshwater from the surface to intermediate model depth levels, increasing AAIW formation rates. By contrast, isopycnal advection and mixing are naturally represented in MICOM, which includes no spurious horizontal mixing terms. Layer properties are therefore largely conserved over long trajectories and timescales. This amounts to an important advantage over the GFDL model, for which mixing must be carefully tuned in order to achieve correct representation of AAIW.

Selected trajectories reveal that model SAMW and AAIW forms in the subtropics and midlatitudes of the Southern Ocean and then either follows a circumpolar path before reentrainment into the winter mixed layer north of the ACC or recirculates around one of the anticyclonic subtropical gyres in the Southern Hemisphere, on 10–50-yr timescales. This agrees with the schematic SAMW and AAIW ventilation patterns of McCartney (1982). Our trajectories do not, however, account for the diapycnal mixing of adjacent layers in the main thermocline. Associated with this mixing are upward velocities of around 0.3 × 10⁻⁷ m s⁻¹, implying 50-yr vertical displacements of typically 50 m. So, while the isopycnal trajectories calculated here do accurately represent the O(10–50 yr) ventilated pathways followed by subducted water, it should be appreciated that diapycnal mixing substantially determines the fate of a water parcel on longer timescales.

Ribbe and Tomczak (1997) recently used an “off-line” diffusion and advection model to advect an ideal tracer with the mean velocity field of FRAM, with the purpose of demonstrating the formation mechanisms and sites, and likely pathways, for SAMW. In that study, the use of mean fields (for logistical reasons) of convection depth and velocity implicitly omits the seasonal cycle and bolus transports (by transient eddies), effects which we have shown to be integral to the formation and recirculation of SAMW.

In using a seasonally forced isopycnic model that parameterizes bolus transports, we feel that we are able to more successfully represent the formation and recirculation of SAMW and AAIW. Table 3 summarizes the water-mass formation rates for SAMW and AAIW, in circumpolar zones and by ocean sectors. SAMW forms mainly in the zone 25°–42.5°S, at a rate of 11.3 Sv, while AAIW forms more strongly south of 42.5°S, at the somewhat weaker rate of 2.7 Sv. Regionally, SAMW (σ = 26.52, 26.80) forms predominantly in the south Indian Ocean, at a rate of 19.8 Sv, while AAIW (σ = 27.03, 27.22) forms mainly in the Pacific, at a rate of 8.5 Sv. Our Indian sector SAMW formation rate is in close agreement with an estimate of 25 Sv obtained by Speer et al. (1997) from the air–sea fluxes of Da Silva et al. (1994), but considerably more than Schmitz’s (1996a) asserted 4 Sv of USAMW (upper SAMW defined by the σ-range 26.5–26.8) forming and recirculating in the Indian Ocean. Our South Pacific AAIW formation rate also compares favorably with Speer et al. (1997), who obtain a formation rate of 7 Sv in the σ-range 26.95–27.15, while Schmitz (1996a) similarly suggests the formation of 11 Sv of UPIW and LOIW (upper and lower intermediate waters with σ in the range 26.8–27.5) in the southeast Pacific.

b. The Deacon cell and bolus transports

Our density-averaged streamfunction shows, in agreement with the circulation inferred by hydrography and consistent with plausible buoyancy forcing,

1. the import of dense NADW, lightening south of 42.5°S, and the northward export of AAIW

2. the import of light waters in the WBCs, cooled north of the ACC (25°–42.5°S) to form SAMW, which is exported northward.

Our results are, in these respects, broadly similar to those obtained with the idealized conceptual models of Johnson and Bryden (1989) and Marshall (1997). However, because the present model includes substantial diapycnal forcing, fluid can change density, and the cancellation between the Deacon cell and bolus transports is not complete. Note also that, with the parameterization of bolus velocity employed here, bolus transport within the mixed layer is actually northward because zonal-mean mixed layer depth increases to the south (Fig. 15), and therefore cannot balance the northward Ekman drift, as in the conceptual model of Johnson and Bryden (1989). Instead, the compensatory flow is in the layers immediately below the mixed layer.

This result differs from that found in the eddy-permitting FRAM model in which zonal correlations between isopycnal thickness and velocity balanced the zonal-mean circulation (Stevens and Ivchenko 1997), so that the Deacon cell was not evident in the overturning streamfunction plotted on density surfaces (Döös and Webb 1994). Why these results should differ so much is unclear. Compared to satellite altimeter observations (e.g., Chelton et al. 1990), the transient eddy activity is underestimated in FRAM (Stevens and Killworth 1992) for which the horizontal resolution is sufficient only to “permit,” rather than fully resolve, the eddies. On the other hand, parameterized bolus transports in the present model may be too strong in quiet regions of the ocean away from the ACC. The value of the interface diffusion coefficient used here (1000 m² s⁻¹) may be correct for eddy-rich regions (e.g., Lee et al. 1997), but may be unrealistically high away from the regions of strong eddy activity.

c. Shortcomings of the model

In the model, surface heat and freshwater fluxes comprise a seasonally varying climatological component, together with relaxation to (seasonally varying) surface temperature and salinity. Unfortunately observations are sparse in the Southern Ocean (e.g., Josey et al. 1999), so climatologies are unreliable. Also, the modeled Southern Ocean circulation may be unrealistic—for example, the ACC may be too broad (given the coarse horizontal resolution)—resulting in further sea surface temperature and salinity errors.

In the model Southern Ocean, the zonally averaged total heat flux is dominated by the relaxation term (see Fig. 5), with cooling in the zone 25°–42.5°S at rates of 10–20 W m⁻². Spanning such a broad range of latitude, this suggests that cooling may be underestimated here in the climatology. In contrast, the climatological freshwater flux seems surprisingly accurate. South of 42.5°S, freshening (due to precipitation and/or ice melting) slightly dominates cooling, giving weak buoyancy gain, while cooling dominates in the zone 25°–42.5°S (see again Fig. 5), driving strong buoyancy loss. There are no systematic shifts in the model buoyancy forcing (see Figs. 3a,b), which might be expected if the WBCs or ACC were mispositioned. It seems, moreover, that the field of climatological density forcing (Fig. 3a) is too smooth and that realistic details in the model forcing field (Fig. 3b) are, in a sense, “restored” by the relaxation scheme (e.g., due to climatological low salinity water off southern Chile, eastward extension of model WBCs at midlatitudes, etc.).

The intermediate and deep circulation of the model should be treated skeptically. In common with many other models, we use only a simple ice model and (poorly known) monthly mean climatological surface forcing. Furthermore, cabbeling is prohibited in this version of MICOM, thereby excluding another possible buoyancy sink. Hence the surface waters nowhere get dense enough for AABW to form. Furthermore, the choice of σ₀ as a vertical coordinate would lead to an ambiguity in the representation and dynamics of model AABW, even if it was correctly formed. AABW lies beneath NADW in the real world, despite that AABW has a lower value of σ₀ than NADW. The inclusion in the model of an arbitrary reference depth for σ, and thermobaric effects, is presently under development. Recent results suggest that σ₂ (σ referenced to 2000 m) might be a more suitable isopycnal coordinate (Sun 1997; Sun et al. 1999), with implications for dynamical balances in the Southern Ocean. Sun (1997) shows that, in global models based on σ₀ and σ₂ versions of MICOM, layer interfaces in the circumpolar zone 45°–60°S slope much more steeply to the surface in the σ₂ model. The σ₂ model thus features stronger circumpolar transports (e.g., a more realistic Drake Passage transport of 130 Sv) and, by inference, stronger bolus transports.

Finally, the parameterization of interior diapycnal mixing by the Hu (1996) scheme may be inadequate. That scheme has been recently superseded by the physically consistent scheme of McDougall and Dewar (1998), but the latter was not available when the present model was implemented. Poorly parameterized mixing may be a particular problem in the Pacific, owing to the large area and weak thermohaline forcing (i.e., slower meridional circulation) of that ocean. The consequent failure to form upper Circumpolar Deep Water (UCDW) (the end product of NADW/CDW mixing in the Pacific Ocean) and/or export this water mass to the Southern Ocean is a serious model flaw. Most of the ∼12 Sv of deep water thought to flow across 25°S into the South Pacific does not return as surface water but as UCDW (Callahan 1972; Wunsch et al. 1983). It may be that UCDW outcrops at high southern latitudes and is driven equatorward in the Ekman layer, which is freshened and lightened by surface fluxes to form SAMW and AAIW in the southeast Pacific (Schmitz 1996a); that is, lightening of deep waters to form AAIW may, in the real ocean, be a two-stage process: the first stage in the deep Pacific and the second near the surface in the Southern Ocean. Poor representation of UCDW in the present model may thus have implications for the realism of the thermohaline circulation. The model shows strong dense-to-light transformation of intermediate and dense waters within the Southern Ocean (up to 9.3 Sv south of 42.5°S; Fig. 17a). In the model most of the lightening of these intermediate waters is accomplished by mixing rather than surface forcing. Surface forcing does, however, have a great impact in freshening and cooling the intermediate waters in the model (Fig. 17b).

Taking these flaws into consideration, it is no surprise that the fate of NADW (closing the thermohaline circulation) is poorly represented in the present model. While 15.7 Sv of NADW flows into the Southern Ocean from the South Atlantic, 5.7 Sv of CDW/NADW is lightened by mixing processes in the Southern Ocean (south of 25°S), and 19.5 Sv is apparently exported across 25°S into the Indian and Pacific Oceans. Clearly then, the dense water masses are significantly unsteady, and we cannot therefore use the present model integration to determine whether, in the real world, NADW upwells globally (Drijfhout et al. 1996) or principally in the Southern Ocean (Döös and Coward 1997). All we can say is that, in the model, both processes appear to operate. Note however that the lightening of 5.7 Sv of CDW/NADW in the Southern Ocean agrees well (though perhaps coincidentally!) with Schmitz’s (1996a) estimate of 5 Sv.