1. Introduction
Observed ocean kinetic energy is dominated by mesoscale features (length scales of 10–100 km) (Ducet et al. 2000), with eddy kinetic energy often found to be 100 times larger than the mean (Wunsch 2007). In contrast, the vast majority of global general circulation model (GCM) simulations, particularly those used in paleoclimatic studies and in long-term climate projections, are often limited to coarse horizontal resolutions (i.e., >1°). These GCMs are obliged to parameterize the effects of unresolved flows, placing the burden of proof on modelers to demonstrate that their simulations accurately represent the flow characteristics under consideration. The Intergovernmental Panel on Climate Change (IPCC) Third Assessment Report (TAR) noted considerable debate regarding the adequacy of coarse-resolution ocean models and warned that results reliant on meridional heat transports from ocean models with >1° resolution should be treated cautiously (McAvaney et al. 2001). The Fourth Assessment Report (AR4) further identified the lack of a comprehensive suite of high-resolution global climate simulations as restricting the ability to draw firm conclusions from GCMs (Randall et al. 2007). Mesoscale-resolving ocean models are currently limited by computational constraints requiring nonglobal spatial domains with idealized boundary conditions and/or short integration periods that make it difficult to evaluate deep ocean flows (e.g., Smith et al. 2000; Oschlies 2002; Treguier et al. 2005). They also are commonly run as uncoupled ocean models with specified surface heat and freshwater fluxes, despite the knowledge that small changes in the buoyancy exchange between climate components (e.g., ocean and atmosphere) can have strong impacts on the ocean circulation (Weaver and Hughes 1992).
This study employs a suite of global coupled GCM simulations to explore the gap between coarse and mesoscale-resolving ocean models. The focus is on the Atlantic meridional overturning circulation (AMOC), which is responsible for the majority of poleward ocean heat transport in the Northern Hemisphere (Hall and Byrden 1982). The AMOC is generally considered to consist of an upper and lower limb (Lozier 2010; Wunsch 2002). The upper limb transports warm, saline surface water northward to deep-water formation sites predominately found in the Labrador and Greenland–Iceland–Norwegian (GIN) Seas. The lower limb transports the recently ventilated cold, dense North Atlantic Deep Water (NADW) southward. Among early attempts to model the lower limb of this circulation, the work by Stommel and Arons (1960) is perhaps the most influential. In their theoretical model, a strong deep western boundary current (DWBC) is required to compensate for the sources of dense water formation in high-latitude regions and to close the poleward transport in the interior. Although some of the assumptions made by Stommel and Arons (e.g., flat-bottomed ocean, uniform deep-water upwelling) can be difficult to justify, it was until recently widely thought that the flow of NADW occurs mainly within such a DWBC. Some hydrographic observations, albeit at only a limited number of locations along the western boundary (Talley and McCartney 1982; Molinari et al. 1992; Pickart 1992; Smethie et al. 2000), can be used to support such a view.
More recent observations of subsurface floats injected near the western boundary of the Labrador Sea most often do not continuously follow the DWBC. Instead, the floats are commonly advected into the North Atlantic deep interior before recirculating northward or continuing southward, toward the subtropics and tropics (Lavender et al. 2000; Fischer and Schott 2002; Bower et al. 2009; Lozier 2010). The important role of deep interior flows, suggested in these studies, questions the long-standing concept of the DWBC being the dominant pathway for NADW to enter the low-latitude Atlantic. A dominance of the DWBC pathway over the interior pathway is typically supported by coarse-resolution model simulations, as we shall illustrate. In such models the potential vorticity budget is necessarily distorted by the need to impose large lateral viscosity. In contrast, interior NADW pathways into the subtropics have been attributed to the effects of complex, finescale bathymetry and to eddy-driven recirculations, which are both unresolved in coarse-resolution GCMs.
The aim of this study is to evaluate the roles of horizontal grid resolution, bathymetry, and ocean viscosity on the AMOC, with an emphasis on the equatorward flow of NADW. A 1.8° (latitude) × 3.8° (longitude) resolution simulation is compared to three 0.2° × 0.4° simulations that have varying bathymetry and horizontal viscosity. Increasing grid resolution reduces the dependence on subgrid-scale parameterizations and has been shown to improve many features of the North Atlantic including the representation of boundary currents, heat transports, and kinetic energy (e.g., Bryan 1991; Oschlies 2002; Spence et al. 2008). In addition, there are reasons to think that variations in bottom topography, and the associated bottom pressure torques, play an important role in maintaining the large-scale meridional flows (Wunsch and Roemmich 1985; Hughes 2000; Hughes and Cuevas 2001). In coarse-resolution models, however, a large horizontal viscosity has to be imposed, thereby dampening the kinetic energy of the flow (Bryan et al. 1975; Jochum et al. 2008) and, as we shall demonstrate, suppressing the effect of bottom pressure torques on the structure of deep interior currents. In particular, we find that, while the zonally integrated AMOC of these simulations are striking similar, the zonal structures of the lower branch are markedly different. Specifically, NADW predominately follows a DWBC in the simulations that impose a high value for lateral viscosity. In contrast, interior pathways away from the DWBC become a robust feature of high-resolution simulations once ocean viscosity is reduced and bathymetry is better resolved.
2. Methods
This study uses the University of Victoria Earth System Climate Model (UVic ESCM), which couples a vertically integrated energy–moisture balance atmospheric model, a thermodynamic/dynamic sea ice model, and a land surface model with the Geophysical Fluid Dynamics Laboratory Modular Ocean Model (version 2.2) and is described in detail in Weaver et al. (2001). Control-state winds are prescribed from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) 50-Year Reanalysis (NCEP50) monthly-mean climatology (Kistler et al. 2001). In all experiments, the ocean model has 19 vertical levels and the same vertical diffusivity profile. The vertical resolution is coarse relative to most eddy-resolving models but is comparable to other global eddy-permitting coupled climate models (e.g., Jayne and Marotzke 2002). The barotropic momentum equations are solved by the implicit free-surface formulation of Dukowicz and Smith (1994). Surface freshwater fluxes are converted to fluxes of salt with a constant salt-to-freshwater mass ratio of 3.49 × 10−2. All models are integrated under orbital, atmospheric (CO2 = 295 ppm), and land surface conditions corresponding to the year 1900.
Three ocean eddy-permitting, global domain models with a horizontal resolution 0.2° × 0.4° are initiated from the interpolated 3000-yr equilibrium state of a 1.8° × 3.6° model (see Table 1). The high-resolution models have grid spacings finer than typical ocean eddy wavelengths (100–200 km) (Stammer 1997) but coarser than the Rossby radius of deformation at high latitudes (Smith et al. 2000; Oschlies 2002). Increasing model resolution permits a reduction in both tracer and momentum dissipation coefficients to more realistic values. The Reynolds grid number stability criterion of Bryan et al. (1975) suggests a reduction of the Laplacian horizontal mixing coefficient for momentum (AM) by roughly the factor increase in resolution to avoid erroneous computational modes. The high AM 0.2° × 0.4° simulation follows this criterion, using a fairly large AM value of 1.5 × 108 cm2 s−1 to ensure computational stability. However, the applicability of the Bryan et al. linear criterion to coupled model solutions based on primitive equations is not straightforward (e.g., Jochum et al. 2008). To make the dissipation more scale selective, one possibility is to employ the biharmonic form for lateral viscosity. However, this would require introducing different parameterizations for the different model resolutions, something we try to avoid in this intercomparison study. On the other hand, we would like to make a link with existing high-resolution models, such as the Fine Resolution Antarctic Model (FRAM). The FRAM is a primitive equation numerical model of the Southern Ocean (between 24° and 79°S), which has horizontal resolution of 0.25° × 0.5°. It was initiated with a Laplacian viscosity of 0.02 × 108 cm2 s−1 and subsequently switched to biharmonic viscosity to improve computational stability (FRAM Group 1991). Therefore, we also discuss a low AM 0.2° × 0.4° simulation, wherein the Laplacian viscosity coefficient was decreased to 0.1 × 108 cm2 s−1, which is computationally stable and increases the resolved eddy kinetic energy relative to the high AM run by roughly a factor of 4 (Spence et al. 2009). [Note that a simulation with Laplacian viscosity as low as in the FRAM (0.02 × 108 cm2 s−1) was initialized, but it was found to be computationally unstable on long time scales.] In particular, averaged around 55°N, the North Atlantic near-surface eddy kinetic energy of the low AM 0.2° × 0.4° simulation is 82 cm2 s−2, which is roughly one-third of satellite altimetry estimates (see plate 6 of Wunsch 2007). Note also that the along-isopycnal (AISO) and the Gent and McWilliams (1990) isopycnal thickness diffusion (AITH) tracer mixing coefficients are reduced to the same value in all three high-resolution models, roughly following the criterion of Bryan et al. (1975) (see Table 1).
Horizontal-resolution parameters and equilibration periods of the simulations. The terms AM, AISO, and AITH are the horizontal, isopycnal, and isopycnal thickness diffusion coefficients, respectively. The no-bath high AM and high AM 0.2° × 0.4° simulations were initiated from the equilibrium state of the 1.8° × 3.6° model, whereas the low AM 0.2° × 0.4° model was initiated from the final control state of the high AM 0.2° × 0.4° simulation.
Although the horizontal resolution of each model component (ocean, land, atmosphere, and sea ice) is increased in all the 0.2° × 0.4° simulations, only the high AM and low AM 0.2° × 0.4° simulations employ resolution-dependent ocean bathymetry (NGDC 2007) (Fig. 1). We also include a no-bath high AM 0.2° × 0.4° simulation that employs the same horizontal viscosity as the high AM 0.2° × 0.4° simulation and the same ocean bathymetry as the 1.8° × 3.6° simulation. This allows us to explicitly separate the influences of increasing grid resolution and finescale bathymetry. The number of landmasses and the shape of coastlines are held fixed to the 1.8° × 3.6° model grid in all high-resolution simulations by placing a minimum 125-m (ocean level 2) depth constraint on new bathymetry features.
Low and high resolution North Atlantic bathymetry used by the simulations.
Citation: Journal of Physical Oceanography 42, 1; 10.1175/2011JPO4584.1
The simulations presented here are among the longest integrated ocean eddy-permitting global climate simulations currently available. The no-bath high AM and high AM 0.2° × 0.4° simulations were initiated from the equilibrium state of the 1.8° × 3.6° model and equilibrated for an additional 50 years, while the low AM 0.2° × 0.4° model was initiated from the final control state of the high AM 0.2° × 0.4° simulation and equilibrated for an additional 50 years. Although these high-resolution models underrepresent oceanic eddy kinetic energy relative to observations, they nonetheless permit an evaluation of the role of model resolution, lateral viscosity, and bathymetry in the deep ocean circulation at a near-equilibrium state. Unless otherwise stated, all results presented in the following sections are determined from 5-yr means taken at the end of the model integration periods.
3. Results
a. Model simulations assessment
We begin with a brief evaluation of the UVic ESCM ability to simulate some key ocean climate components. Figure 2 shows the global ocean meridional heat transport produced by the model simulations along with the observational estimate of Ganachaud and Wunsch (2003). Each simulation exhibits poleward transport at all latitudes and an asymmetry across the equator. The simulated transports cover a wide range, sometimes exceeding the uncertainty range provided by Ganachaud and Wunsch (2003), but all values are within the range of other observational estimates (see Fig. 5 of Ganachaud and Wunsch 2003). Roughly ~70% of the total Northern Hemisphere heat transport produced by the model simulations occurs in the North Atlantic, which is also consistent with observed estimates. As shown by previous studies (e.g., Fanning and Weaver 1997; Bryan and Smith 1998; Spence et al. 2008), we find that Northern Hemisphere heat transport is highly sensitive to increasing resolution, with all high-resolution simulations producing substantially more heat transport than the 1.8° × 3.6° case. However, the large-scale Northern Hemisphere heat transport is dominated by the mean circulation, not eddies (Wunsch 1999; Talley 2003).
Total global ocean meridional heat transport (PW) produced by the simulations and observational estimates with uncertainties from Ganachaud and Wunsch (2003).
Citation: Journal of Physical Oceanography 42, 1; 10.1175/2011JPO4584.1
When AM is relatively large, the high-resolution bathymetry is found to have little effect on the total Northern Hemisphere heat transport (i.e., compare high AM 0.2° × 0.4° to no-bath high AM 0.2° × 0.4°). In contrast, the increased current speeds (discussed below), resulting from lower viscosity, are found to substantially increase the Northern Hemisphere heat transport (i.e., compare high AM 0.2° × 0.4° to low AM 0.2° × 0.4°). Although the diffusive heat flux is reduced at high resolution and the eddy heat flux is increased, they consistently remain less than 0.1 PW north of 20°N (not shown). However, locally the heat transport by small-scale and time-varying circulations can be of first-order importance by directly influencing the heat transport via advection and indirectly by modifying the mean flow and surface heat flux budgets, as described by Stammer (1997). Insufficient Northern Hemisphere ocean heat transport is a problem common to coarse-resolution models (e.g., Bryan 1991; Fanning and Weaver 1997; Bryan and Smith 1998; McAvaney et al. 2001). Overall, these results demonstrate that increasing horizontal resolution and lowering ocean viscosity can significantly increase Northern Hemisphere heat transport.
In agreement with previous modeling studies (Smith et al. 2000; Treguier et al. 2005), increased North Atlantic heat transport can be attributed to the improved resolution of the large-scale ocean currents. The simulated maximum near-surface (126-m depth) current speed of the Gulf Stream along 68°W increases from 13 cm s−1 at 1.8° × 3.6° to 67 cm s−1 in the low AM 0.2° × 0.4° simulation, with observed estimates in this region of 70 cm s−1 (Johns et al. 1995). The maximum near-surface speed of the Labrador Current near 55°W also increases from 4 to 16 cm s−1 between the 1.8° × 3.6° and the low AM 0.2° × 0.4° simulation, with observed values of roughly 30 cm s−1 (Flatau et al. 2003). The near-surface velocity field (Fig. 3) confirms that the representation of the Gulf Stream, North Atlantic Current, and Labrador Current are improved with increased grid and bathymetry resolution and decreased viscosity. We also note the presence of recirculations near the Grand Banks in the velocity field of the low AM 0.2° × 0.4° simulation.
Annual-mean North Atlantic velocity field at 126-m depth in each simulation. Only vectors at every fourth grid point are plotted for the 0.2° × 0.4° simulations to aid clarity. The velocity fields of all simulations are normalized to the scaling vector in panel (a).
Citation: Journal of Physical Oceanography 42, 1; 10.1175/2011JPO4584.1
Conservation of potential vorticity q imposes strong constraints on the ocean circulation. Specifically, if frictional and diabatic processes are considered weak, then ocean flow is expected to follow contours of constant q. For large-scale dynamics where the Rossby number is small, the contribution of relative vorticity to q is also small so that q is largely determined by the stretching term; namely, 
We evaluate q with potential density referenced to the 3000-m depth (σ3) as the vertical coordinate to clearly show intermediate depth waters. Figure 4 shows the simulated q field along the σ3 = 41.5 kg m−3 isopycnal, which corresponds to roughly 2000-m depth south of 50°N in the North Atlantic. Of particular interest is the large pool of nearly homogeneous low q (e.g., the darker blue color) to the west and northwest of the Mid-Atlantic Ridge (MAR) in the low AM 0.2° × 0.4° simulation; in the model solutions with high AM, this signature is much less pronounced. Observational (Talley and McCartney 1982; Lozier 1997; Bower and Hunt 2000a,b; Lozier 2010) and eddy-resolving modeling (Getzlaff et al. 2006; Nakamura and Kagimoto 2006) studies discuss a similar homogenized deep q pool. Its presence appears to support the conjecture that instabilities can drive an interior pathway of the low q LSW to the subtropics. We also find eddy kinetic energy in the low AM 0.2° × 0.4° simulation at 2140-m depth that exceed 30 cm2 s−2 on the northwest of the MAR (Fig. 5). Regardless of the mechanism, the fact that the q simulated by the low AM simulation hardly varies in this region suggests that little forcing is required to drive deep flow in any direction in this part of the North Atlantic. It may also be indicative of a nonlinear q regime (O’Dwyer and Williams 1997; see the appendix), which tends to be suppressed in the coarse-resolution model configuration.
Annual-mean North Atlantic potential vorticity (m−1 s−1), 
Citation: Journal of Physical Oceanography 42, 1; 10.1175/2011JPO4584.1
Eddy kinetic energy (cm2 s−2) for the low AM 0.2° × 0.4° simulation at 2140-m depth in the North Atlantic determined from snapshots taken every 5 days for one year.
Citation: Journal of Physical Oceanography 42, 1; 10.1175/2011JPO4584.1
Given the significant differences in the model design and output fields discussed above, the overall similarity in the structure and magnitude of the simulated zonally integrated AMOCs is somewhat surprising (Fig. 6). In particular, all of the simulations have NADW transports ranging from 19 Sv to 23 Sv (Sv ≡ 106 m3 s−1) that penetrate to roughly 3500-m depth, with a common cell structure. Observational estimates of the present-day NADW volume transport range from 13 Sv to 23 Sv (Ganachaud and Wunsch 2000; Smethie and Fine 2001; Lumpkin and Speer 2003; Talley et al. 2003). We do note that a modest poleward shift in the position of maximum NADW transport from south to north of 40°N can be attributed to the inclusion of high-resolution bathymetry. In general the AMOC in all of the simulations does not penetrate far enough into the GIN Seas, a deficiency that has been attributed to an inability of the model to transport surface waters effectively across the Iceland–Faroes Ridge (Weaver et al. 2001). The cold limb of the AMOC in most models, including this one, is also too shallow compared to observations, due to excess entrainment in the overflows from the Nordic Seas. while the simulated overturning in the North Atlantic is strikingly similar in the four experiments, it should be noted that the dominant pathway for upwelling of NADW has been found to be strongly dependent on grid resolution and horizontal viscosity (see Spence et al. 2009).
Simulated annual-mean Atlantic meridional overturning circulation (AMOC) transports (2-Sv contour intervals). Solid (dotted) lines represent clockwise (counterclockwise) flows.
Citation: Journal of Physical Oceanography 42, 1; 10.1175/2011JPO4584.1
b. Interior versus boundary pathway of NADW
The equatorward flow of NADW is widely regarded as an important indicator of climate on a wide range of time scales. It has gained much attention, particularly in paleoclimatic studies, where variations in NADW transport are commonly evoked to explain large-scale climate events (Bond et al. 1993; Rahmstorf 2002). As noted in section 1, some hydrographic observations could be interpreted as supporting the widely held view that most NADW enters the subtropics by closely following the deep western boundary pathway. However, recent observations of float trajectories provide evidence that recently ventilated LSW is often advected into the North Atlantic interior when entering the subtropics (Fischer and Schott 2002; Bower et al. 2009; Lozier 2010). Figure 7 shows the magnitude of the North Atlantic velocity field at a depth within the equatorward flowing limb of the AMOC. Observational estimates of the speed of the DWBC between roughly 30° and 55°N range from 5 to 20 cm s−1 (Pickart et al. 2005; Bower and Hunt 2000b; Fischer and Schott 2002). At coarse resolution the dominant velocity structure is shown to be a weak and broad DWBC that erroneously veers away from the western boundary between roughly 30° and 45°N. An intensified DWBC with speeds within the observed range is found in the no-bath high AM 0.2° × 0.4° simulation. The DWBC of the high AM 0.2° × 0.4° simulation also exhibits speeds within the observed range and the flow closely follows the western boundary, but there is also evidence of interior flows, which are predominantly southward (see Fig. 7c), near roughly 50°N. In the low AM 0.2° × 0.4° simulation, there is a dramatic increase in prevalence of interior flows, which extend into the subtropics by flowing along both western and eastern sides of the MAR, along with a reduced presence of the DWBC between roughly 30° and 50°N, and between 30° and 50°W (see Figs. 7d, 8). Comparable interior flows have been observed in the region between the Grand Banks and the MAR (Rhein et al. 2002; Bower et al. 2009) and on the eastern side of the MAR (Dickson et al. 1985). Overall, we find that, as the simulations become more realistic by lowering viscosity and increasing the grid and bathymetry resolution, the speed and position of the DWBC is improved and interior pathways of NADW outflow into the subtropics become prevalent.
Simulated annual-mean absolute current speed (mm s−1), 
Citation: Journal of Physical Oceanography 42, 1; 10.1175/2011JPO4584.1
Annual-mean meridional velocity υ (negative values are southward flows) for the low AM 0.2° × 0.4° simulation at 2140-m depth in the North Atlantic. Black contour lines are isobaths at 1000-m intervals. Dark blue and red corresponds to values of υ < 30 mm s−1 and υ > 20 mm s−1, respectively.
Citation: Journal of Physical Oceanography 42, 1; 10.1175/2011JPO4584.1
The dependence of NADW pathway partitioning between the interior and western boundary flows on viscosity is further illustrated in Fig. 9, which shows the simulated meridional velocity below 1400 m at 35° and 30°N in the Atlantic. Essentially, a lower horizontal viscosity leads to relatively strong southward interior currents, with deep water entering the low-latitude Atlantic between roughly 30° and 50°W, in addition to the DWBC. The southward interior flows are accompanied by northward velocities in several locations, particularly within 55°–60°W. As can be seen in Fig. 9, none of these interior features is present in the model simulation employing higher viscosity (i.e., with the value of ocean viscosity comparable to those typically imposed in coarse-resolution climate simulations).
Simulated annual-mean meridional velocity (mm s−1) below 1400 m at 35° and 30°N in the Atlantic. Velocity is shown on a linear scale. Dark blue corresponds to values of υ < 30 mm s−1.
Citation: Journal of Physical Oceanography 42, 1; 10.1175/2011JPO4584.1
The corresponding meridional transport, integrated from the eastern boundary and below 1500-m depth, that is, 
Simulated annual-mean AMOC transports (Sv) below 1500 m [i.e., 
Citation: Journal of Physical Oceanography 42, 1; 10.1175/2011JPO4584.1
c. Dynamical mechanism
In the observed North Atlantic Ocean, with ample topography and a large-scale convective-driven cell, there is little observational evidence that the subtropical gyre is in Sverdrup balance, even in the relatively quiescent region of the MAR (Wunsch and Roemmich 1985). Hughes and Cuevas (2001) present a convincing theoretical argument, confirmed by an eddy-permitting GCM simulation, showing that, for zonal strips of a few degrees latitude, the dominant balance in the area-integrated barotropic vorticity equation is the wind stress curl and bottom pressure torque, implying that real western boundary currents are largely inviscid—including in the deep ocean. If we remove the level of no motion assumption and, instead, integrate the linear vorticity balance [Eq. (1)] to the seafloor where z0 = −D, then the second term on the right-hand side of Eq. (2) becomes fwB = −fuB · ∇D, where wB = w(−D) and uB is the horizontal velocity at the seafloor, and there is no longer a simple relationship between the meridional transport and the wind stress curl. In this formulation the interior return flow required to balance the western boundary current will be a topographically steered current in which βV is balanced in part by the wB induced by bottom pressure torques (Hughes and Cuevas 2001).
Indeed, assuming that a representative value for the large-scale horizontal velocity near the bottom |uB| is 10−2 m s−1 and using |∇D| = 10−3 as a representative value for the magnitude of large-scale bottom topographic slopes, the associated near-bottom vertical velocity |wB| = |uB‖∇D| can be as large as 10−5 m s−1. This is an order of magnitude larger than typical values of surface Ekman pumping. It is also much larger than typical values of mixing-driven upwelling (assuming for the latter a vertical diffusivity of 10−4 m2 s−1 acting over a corresponding vertical scale of 103 m). Although the above estimate for |wB| is biased toward its upper limit (since the cross-slope component of uB is likely to be generally smaller than |uB|), it does suggest that the effect of bottom pressure torques can be very important.
Figure 11 shows the bottom pressure torque ρ0fwB for the coarse-resolution simulation along with the high AM and low AM 0.2° × 0.4° simulations. Note that wB is taken as the vertical velocity through the top of those grid cells that are located directly above the seafloor. Figure 11 is dominated by large positive and negative values on small length scales. As noted by Hughes and Cuevas (2001), this can be attributed to the large spatial gradients in bottom stress. This effect can be exacerbated by artificially large nonlinear and viscous forces generated by coarse vertical resolution of bottom topography, especially near large seafloor terraces. It is for this reason that we exclude the no-bath high AM 0.2° × 0.4° simulation from the figure. A comparison between Fig. 11 and Fig. 4d of Hughes and Cuevas (2001), noting that their GCM has 36 vertical levels, confirms that ρ0fwB provides a reasonable proxy of bottom pressure torque in the model.
Annual-mean North Atlantic bottom pressure torque (N m−3) estimated as ρ0fwB in which wB is the vertical velocity through the top of grid cells located directly above the seafloor, ρ0 is a reference density, and f is the Coriolis parameter. (d) A smoothed version of (c) via an area-mean filter.
Citation: Journal of Physical Oceanography 42, 1; 10.1175/2011JPO4584.1
For the coarse-resolution model, Fig. 11a shows bottom pressure torque signatures in the subpolar region, but they become much weaker in the subtropics. In the high AM 0.2° × 0.4° simulation, intense bottom pressure torques become evident throughout the subpolar region and along the western boundary of North America (Fig. 11b). In the low AM 0.2° × 0.4° case, the signature of bottom pressure torque is further amplified along the western boundary and becomes increasingly evident in the interior of the subtropical gyre near the Mid-Atlantic ridge [with absolute values O(10−6 N m−3) and with |wB| ≈ 10−5 m s−1, which is not uncommon] (Fig. 11c). The rugged bathymetry of the high-resolution simulations leads to noisy bottom pressure torque patterns. Figure 11d presents a smoothed version of the low AM 0.2° × 0.4° bottom pressure torque field, wherein each grid point is plotted as the mean of the surrounding 3 × 3 gridpoint area of Fig. 11c. The amplified bottom pressure torque signature in the low AM 0.2° × 0.4° simulation is not surprising because a reduction in horizontal viscosity should result, at least in the zonally and depth-integrated vorticity balance, in the input of vorticity by wind stress curl being largely balanced by bottom pressure torques. Locally, however, one may also expect changes in the advection of planetary vorticity βυ, including in the deep ocean. Indeed, even before analyzing this in more detail, we note that the spatial pattern of Figs. 7b,c resembles that of Figs. 11b,c for the high AM and low AM simulations. This suggests that bottom pressure torque may play an important role in maintaining the pathways of NADW outflows. The smoothed low AM 0.2° × 0.4° bottom pressure torque field (Fig. 11d) clarifies a tendency for large, positive torque values between 30° and 50°W to be positively correlated with the southward interior flows of Fig. 8.
We now compare the simulated meridional transport of the AMOC below 1500 m as function of longitude, 
Comparison of simulated annual-mean AMOC transports below 1500 m at 30°N, as given in Fig. 10, with that predicted by the linear vorticity balance, V = V1 + V2 with 
Citation: Journal of Physical Oceanography 42, 1; 10.1175/2011JPO4584.1
The discrepancy between simulated meridional transport VAMOC<1500m and that predicted by the linear vorticity V is largest for the high AM run. This can be attributed to strong frictional effects in the presence of topography, which tend to suppress the deep interior meridional flows implied by the bottom pressure torque. However, once the friction is reduced in the low AM case, the discrepancy becomes smaller and V tends to follow VAMOC<1500m, including reproducing the accumulation of about 7 Sv in the interior, between roughly 40° and 50°W. Essentially all of this transport is due to V2, demonstrating that bottom pressure torque is playing a central role in maintaining the deep meridional interior flows of the AMOC. The degree to which linear vorticity dynamics holds in the low AM model depends on latitude, but generally it does provide a first-order description of the large-scale flows in the deep interior.
We propose that, with increasing resolution and decreasing viscosity, bottom pressure torque becomes a key term in the vorticity balance of the deep interior and can account for much of the meridional vorticity advection. Although the spatial distribution of bottom pressure torque is quite noisy given the rugged bathymetry, the connection between the interior NADW flows (Fig. 8) and the bottom pressure torque (Fig. 11c) is illustrated, in an integral sense, in Fig. 12c. It remains unclear if bottom pressure torques cause or result from the deep interior flows (or both); however, one may consider bottom pressure torques as a necessary component for maintaining the interior flows in the deep North Atlantic.
4. Discussion
Assuming sources of deep, dense water in polar regions of the Atlantic and uniform upwelling elsewhere, Stommel and Arons (1960) proposed a highly influential model for circulation in the abyss. Their model, based on Eq. (1), implied weak poleward flow in the deep interior and strong DWBCs. Since then, the assumptions of uniform upwelling and continuous DWBCs have been questioned. In particular, microstructure measurements (e.g., Polzin et al. 1997) and tracer release experiments (e.g., Ledwell et al. 2000) have demonstrated that the diapycnal mixing driving the deep-water upwelling is far from being uniform. Furthermore, several recent studies find that subsurface floats injected near the western boundary of the Labrador Sea most often do not continuously follow the DWBC; instead, the floats are usually advected into the North Atlantic deep interior, with a portion of them following interior pathways toward the subtropics and tropics (Lavender et al. 2000; Fischer and Schott 2002; Bower et al. 2009; Lozier 2010). In addition, arguments have been presented suggesting that bottom topography, through the bottom pressure torque, can strongly modify large-scale meridional flows (Wunsch and Roemmich 1985; Hughes 2000; Hughes and Cuevas 2001).
Here we tried to demonstrate that models imposing high viscosity in the ocean, which is typical of those limited to coarse horizontal resolutions (i.e., >1°), are likely to have difficulty in simulating the observed interior pathways of deep-water flow toward the low-latitude Atlantic. Instead, most NADW in such models tends to follow the DWBC. In contrast, high-resolution simulations, wherein the ocean’s viscosity can be greatly reduced, are capable of producing interior pathways of NADW toward the subtropics that are, in many ways, not unlike those observed. These results may have important implications for climate simulations, including those dealing with climate changes in the past, as well as those used to project future climate. Some of these implications within a fully coupled model, albeit with a relatively coarse horizontal resolution in the ocean, have been discussed recently by Zhang (2010).
Acknowledgments
We are grateful for the support of Andrew Weaver and the University of Victoria Climate Lab. Special thanks to Marc d’Orgeville and Laura Ciasto of the University of New South Wales for their helpful comments. Infrastructure support from the University of Victoria and the University of New South Wales is also acknowledged. This study was supported by the Australian Research Council. We graciously thank the anonymous referees for their insightful comments.
APPENDIX
Uniformity of Deep-Water Potential Vorticity
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