a. Domain and horizontal grid

The model domain extends from 20°S in the South Atlantic to 72.6°N in the North Atlantic, and from 98°W to 17.2°E. It includes the Gulf of Mexico and the western part of the Mediterranean Sea, but excludes Hudson Bay. The southern extent of the domain was chosen to exclude the subtropical gyre in the South Atlantic and hence avoid strong western boundary currents impinging on the boundary. The northern boundary was placed at 72.6°N so that the 3°-wide restoring buffer zone is well beyond the Denmark Strait overflow region. The northern and southern boundaries are essentially the same as those used in the Dynamo Group (1997) experiments. The horizontal computational mesh is a Mercator grid with resolution of Δλ = 0.1°, Δϕ = 0.1° cosϕ, where λ, ϕ are longitude and latitude, respectively. The horizontal resolution varies from 11.1 km at the equator to 3.2 km at the northern boundary.

A key feature of the grid is that the horizontal grid spacing is less than or equal to the zonal-mean Rossby deformation radius at all latitudes. Figure 1 shows the grid spacing from the 0.28° global model and the 0.1° North Atlantic model, along with the zonally averaged first baroclinic mode Rossby radius R₁, where R₁ is related to the gravity wave speed C₁ for the first baroclinic mode by R₁ = C₁/f. The gravity wave speed was determined by solving a local eigenvalue problem in the column of water at each horizontal gridpoint using the buoyancy frequency computed from the time-mean density of the 0.1° model solution. Typical length scales for mesoscale eddies are linearly related to the Rossby radius [see Eq. (13) of Stammer (1997)] but are somewhat larger than it (compare estimates of the model eddy length scale from Fig. 18 below), so the eddies should be reasonably well resolved at all latitudes. The global 0.28° model fails to adequately resolve the Rossby radius at latitudes higher than about 35°N.

b. Vertical grid and bathymetry

The grid has 40 nonuniform vertical levels, which vary in thickness from about 10 m at the surface to 250 m at depth. The variation of level thickness with depth was chosen to follow a smooth Gaussian function of depth in order to minimize vertical discretization errors associated with the nonuniform spacing.

The topography was derived from the ¹/₁₂° ETOPO5 database from the National Geophysical Data Center. This dataset for ocean depth was first interpolated to the 0.1° Mercator grid, then the depth at each horizontal grid point was set equal to that of the nearest vertical level in the model. Sill depths were then compared with those given in Thompson (1995), and minor modifications to the topography were made at the Straits of Florida (where three grid points were excavated) and at the Faeroe Bank Channel (where about a dozen points along the narrowest portion of the channel were deepened by one or two levels). A more significant modification was required only at the Strait of Gibraltar, where the topography was modified in order to maintain a realistic minimum sill depth and a channel width of at least three horizontal grid points.

c. Subgrid-scale parameterizations

Biharmonic operators were used for horizontal mixing of momentum and tracers, as described in MSSM for the 0.28° global run. The viscosity and diffusivity vary spatially with the cube of the horizontal grid spacing and have equatorial values of 2.7 × 10¹⁰ m⁴ s⁻¹ and 0.9 × 10¹⁰ m⁴ s⁻¹, respectively. The viscosity was initially chosen as small as possible to minimize damping of the eddy field. The width of the Munk layer in the western boundary current associated with the biharmonic viscosity is order (ν/β)^1/5 = 15.5 km at 30°N, which compares with the grid spacing of 9.1 km at 30°N. Thus the Munk layer is only minimally resolved, and this may have adversely affected the simulation of the Gulf Stream south of the separation point at Cape Hatteras, which occasionally meandered too far from the coastline. Early in the spinup the viscosity and diffusivity were both increased by a factor of 3 (to the final values given above) in an attempt to reduce this problem.

Vertical viscosities and diffusivities were computed using the Richardson number formulation of Pacanowski and Philander (1981) with background values of 10⁻⁴ and 10⁻⁵ m² s⁻¹, respectively. The vertical mixing term was integrated explicitly, and two passes through a standard convective adjustment scheme were made each time step. A quadratic bottom stress of the form c|u|u was used at the ocean floor with drag coefficient c = 1.225 × 10⁻³.

d. Surface and boundary forcing

The wind stress was derived from the 6-hourly ECMWF TOGA Global Surface Analysis covering the model integration period June 1985–June 1996. Wind stresses were computed from the 10-m winds using the neutral drag coefficient of Large and Pond (1981). A bicubic interpolation routine was used to interpolate the wind stress components from the 1.125° Gaussian ECMWF grid to the model grid. Four 6-hourly fields were averaged to obtain the daily wind stresses, which were then linearly interpolated to each model time step to avoid excitation of spurious inertial oscillations (Jayne and Tokmakian 1997).

At the buffer zones near the northern, southern, and eastern boundaries of the model grid, the temperature and salinity were restored to the seasonal Levitus (1982) values at all depths (again interpolated every model day) with a restoring constant 1/τ that varies linearly from 1/15 to 0 days⁻¹ over the 3°-wide buffer zones. It should be noted that the climatological data does not represent the sharp horizontal gradients observed in actual section data. For example, in the northern buffer zone at 70°N the gross vertical stratification is well represented, but the temperature anomaly in the East Greenland Current is about 1° too warm and the isopycnals in the interior basin are too flat.

e. Initialization and integration procedure

The model was initialized with the ocean at rest and the temperature T and salinity S set equal to the June Levitus (1982) climatology. The model was then spun up from 1 June 1985 through 1 October 1990, driven by the ECMWF winds and the buoyancy forcing described above. This completed a 5.3-yr spinup. We then switched back to the 1 October 1985 wind stress and continued the integration through 1 July 1996. All the results shown in this paper are taken from data archived during this final 10.75-yr simulation.

The model was integrated with a nominal time step of 9 minutes. The limiting factor restricting the time step was the stability limit associated with vertical mixing in the top level, due to strong wind stresses accompanying storm fronts. During winter it was necessary to occasionally reduce the time step to 5 or 6 minutes in order to prevent such storms (usually in the North Sea) from causing the integration to diverge.

f. Sampling and time-averaged statistics

Because of the large amount of data involved, we chose to archive snapshots of the three-dimensional prognostic variables every 10 model days, which is adequate sampling for computing mean variables and second-moment statistics for mesoscale variability. In addition, a set of two-dimensional fields such as the sea surface height (SSH) were archived every 3 model days for time series analysis. The snapshot sampling introduces the possibility of aliasing of higher frequency variability into the statistics; however, we have not seen the expected signitures of this [e.g., the bands of enhanced eddy energy along constant latitude lines identified by Jaynes and Tokmakian (1997)]. Velocity components at the positions of several hundred current meter deployments were archived every model day. Finally, time series of several scalar quantities, including the global mean kinetic energy, temperature and salinity, and fluxes of mass, temperature, and salinity across various sections, were also archived. A description of the data archived is given in the appendix.

In this article we show various comparisons of mean variables and second-moment statistics between the 0.1° model and the North Atlantic sector of the third 0.28° global simulation (POP11) described in MSSM. Unless otherwise noted, the figures will show time-averaged results over the 3-yr period, 1 March 1991–1 March 1994, from both simulations. This period was chosen because in both simulations the solution had reached a quasi-equilibrium state as characterized by long-term changes in certain key variables. Shown in Figs. 2a and 2b are the domain-averaged kinetic energy and temperature, respectively, for the full 16-yr 0.1° simulation. The average temperature shows a clear annual cycle, as expected, since the heat flux is based on a repeating annual climatology. The mean temperature asymptotes to a stationary annual cycle after about 10 years of integration (calendar year 1990). The kinetic energy reaches a stationary value after only two or three years, which is a typical timescale for baroclinic adjustment of the velocity field to the initial density field. The 3-year interval for the time-averaged statistics corresponds roughly to years 7–9 in the plot.

a. Basin-scale near-surface and depth-integrated flow

The mean SSH, which reflects the near-surface geostrophic velocity field, is shown in Fig. 3a for the 0.1° and in Fig. 3b for the North Atlantic sector of the 0.28° simulation. Figures 4a,b show the corresponding BSFs.

The large-scale tropical (20°S–20°N) surface and vertically integrated flows are similar in the two simulations except within the southern buffer zone of the 0.1° model where two anticyclonic recirculations greater than 20 Sv (Sv ≡ 10⁶ m³ s⁻¹) appear in the BSF in the eastern and western sides of the basin. The similarity in the vertically integrated flow extends into midlatitudes in the eastern basin. This is consistent with the results of Bryan et al. (1995), who show (their Fig. 7b) that in these regions the vertically integrated transport is well approximated by the Sverdrup transport streamfunction, which is essentially the same for the two simulations. The Sverdrup transport streamfunction computed from the time-mean wind stress curl is shown in Fig. 4c. At more northerly latitudes, and at midlatitudes west of the Mid-Atlantic Ridge, the large-scale vertically integrated circulation differs markedly between the two models. More extensive differences are apparent in the near-surface flow field. This is especially true of the shape and geographical extent of the subtropical and subpolar gyres. The Azores Front is difficult to discern in the 0.28° SSH but is clearly visible in the 0.1° case as an eastward flowing current in the eastern half of the basin at 35°N. This current is discussed further in Section 3e. These differences in the large-scale flow patterns are reflected in essentially all of the time-mean fields (prognostic variables and turbulent statisctics), as discussed in more detail below.

The flow in the Caribbean Sea is similar in the two simulations, but in the 0.1° case a large, unrealistically stationary, anticyclonic ring appears in the Gulf of Mexico Loop Current that is not present in the 0.28° case. This large eddy formed during the ninth year (1989 of the production segment of the run) and persisted through the end of a 16-yr simulation. A similar stationary ring developed in some of the Community Modeling Effort (CME) experiments (Bryan et al. 1995). It has a significant effect on the current systems in the area as discussed in section 3b.

The Gulf Stream does not separate at Cape Hatteras in the 0.28° simulation, and a strong persistent anticyclonic circulation forms northeast of Cape Hatteras. This feature has also appeared in other marginally eddy-resolving simulations (Beckmann et al. 1994; Dengg 1996; Dynamo Group 1997). In the 0.1° simulation the Gulf Stream does separate as a jet at Cape Hatteras bounded by a cyclonic recirculation to the north and an anticyclonic recirculation to the south, apparent in both the surface and depth-integrated flow. As a result, the change in SSH across the front is stronger and more realistic, as is the corresponding geostrophic current. However, the path of the Gulf Stream extension is somewhat south of the observed path, as discussed in section 3c. Nevertheless, the path of the North Atlantic Current (NAC) south and east of Grand Banks, as well as its eastward turn at the “Northwest Corner” and its broader extension across the basin, are in good agreement with observations, as discussed in section 3d. In the 0.28° simulation the NAC continues eastward south of Grand Banks and extends too far zonally into the eastern basin. The geographical extent of the subpolar gyre in the 0.1° simulation is also very different from the 0.28° case, and this is clearly associated with the improved path of the NAC.

b. Circulation in the Caribbean and Gulf of Mexico

The main features of the seasonal and interannnual variability of the flow in the Caribbean Sea and Gulf of Mexico can been be seen in the transport across key passages. Figure 5 shows time series for the transports through the Straits of Florida (between Cuba and the Florida peninsula), Windward Passage (between Cuba and Haiti), and between Florida and the Bahamas at 26.5°N (between 80°W and 78.9°W) for the production segment of the 0.1° simulation. A 100-day running average was applied to each curve in order to filter out high frequencies. The flow in this region exhibited two distinct flow regimes in the 0.1° simulation. During the first 9 years of the integration (including the spinup), eddies were sporadically shed from westward meanders of the Loop Current at a rate of roughly one per year, which then propagated west into the Gulf of Mexico, in rough agreement with observations (Oey 1996). The Straits of Florida transport averaged 24.9 Sv from October 1985 through March 1989, which is less than the observed transport of about 30 Sv (Larsen 1992) but larger than most previous eddy-permitting calculations (Bryan et al. 1995). The flow through the Windward Passage was southward and averaged −5.3 Sv during this period, which compares quite well with the observed estimates of −4 to −7 Sv (Schmitz and McCartney 1993). During this period there was also a realistic magnitude and geographical distribution of eddy variability in the Gulf of Mexico (see section 5b and Fig. 17a). However, during year 1989 of the Production run a strong stable eddy formed in the region of the Loop Current, which persisted until the end of the run and affected the current systems in the entire region. The Straits of Florida transport decreased to 16.7 Sv, and the transport through Windward Passage reversed direction and averaged +5.2 Sv northward. The inflow into the Gulf of Mexico through Yucatan Strait must balance the outflow through the Straits of Florida, and hence it also decreased. The northward flow through Yucatan Strait became shallower and weaker and the southward recirculation on the eastern side of the strait was enhanced. Associated with these changes, the vertical shear in the central channel was greatly reduced. The drop in the Straits of Florida transport is largely compensated by the increased northward transport through Windward Passage so that the total transport through the Bahamas section is about the same in both flow regimes. However, not all of the water flowing northward through Windward Passage proceeds westward to join the Florida Current west of the Bahamas;some fraction flows north to the east of Abaco, and this evidently causes a slight drop in the transport through the Bahamas section. Before 1989 the Bahamas transport was 26.7 ± 2.2 Sv and after 1989 it dropped to 24.1 ± 2.5 Sv (where the ± indicates the rms variability for that period). This compares to observed transports from cable data (Larsen 1992) during the same period of 32.4 ± 2.9 Sv before 1989 and 31.3 ± 3.1 Sv after 1989. The total transport in the western boundary current including the Antilles Current is less effected by the Loop Current eddy: the mean northward transport at 26.5°N between 80°W and 75°W and above 1-km depth was 46.34 Sv from October 1985 through September 1989 and 46.54 Sv from March 1991 through February 1994.

The reason for the persistence and stability of this Loop Current eddy is not yet clear and will require much deeper analyses. Previous studies (Hurlburt and Thompson 1980; Oey 1996) have shown that the eddy shedding is surpressed when the vertical shear in Yucatan Strait is reduced, and as discussed above we do see a reduction in vertical shear when the stable Loop Current eddy is present. Another possibility is inadequate representation of the topography in the Caribbean. The large Loop Current eddy was fueled by a train of eddies from the Caribbean, many of which were originally spawned in the North Brazil Current retroflection. The model SSH variability is too strong in the Caribbean compared to satellite data as discussed below. Better resolution of sharp features of the topography could provide for greater dissipation of eddy energy in this region.

c. The Gulf Stream

The northwestern region of the subtropical gyre between Cape Hatteras and the Grand Banks of Newfoundland has been relatively intensively observed, contains one of the most energetic current systems in the World Ocean, and has proven to be particularly difficult to simulate realistically in basin to global scale models. Our focus in this section is an evaluation of the quality of the simulation of the time-averaged flow in this region, in particular the path, structure, and mass transport of the Gulf Stream. Aspects of the mesoscale variability in this region are described in section 5.

For the purposes of this evaluation we will compare the simulation against observations in the “stream coordinate” reference frame. Several observational studies (e.g., Halkin and Rossby 1985; Johns et al. 1995; Bower and Hogg 1996; hereafter HR85, JSBW95, and BH96, respectively) have shown that the variability of the Gulf Stream in this region is well characterized as the meandering of a coherent jet of relatively stable cross-stream structure rather than variability in the structure of the jet itself. Averaging in a Lagrangian reference frame fixed to and aligned with the stream axis thus avoids blurring the structure of the synoptic Gulf Stream and allows us to assess whether the model solution is able to achieve the observed peak velocities, transports, spatial scales, and structures.

Several methods have been developed for establishing the stream-coordinate system and computing statistics of the flow in this system. In the analysis of the model solution we have used the “mapping method” described by JSBW95 and BH96. In this procedure the stream axis is defined as the 12°C isotherm at 400-m depth (denoted as Z₁₂ below). For each snapshot of the solution, the shortest perpendicular from each model grid point to the Gulf Stream axis establishes the local cross-stream direction and distance at that grid point and time. We use the convention that the positive cross-stream direction points onshore. The downstream direction is established by the appropriate 90° rotation from the cross-stream direction. The local Eulerian velocities are rotated into the stream-coordinate system, then binned with a cross-stream coordinate resolution of 10 km at each longitude of the original model grid. Note that HR85 used an entirely different method and that JSBW95 use a hybrid method, combining the mapping method away from the central core of the jet with the “shear method” of Hall and Bryden (1985) within the jet. In averaging the flow quantities, rings are filtered from the statistics in a two-step procedure. In the first averaging pass, offshore points that have temperatures below 12°C and onshore points that have temperatures above 12°C are excluded. This eliminates data from the core of large rings. In a second averaging pass, offshore points that are more than 1.5°C below the mean obtained in the first pass, or onshore points with temperatures that exceed the mean by more than 1.5°C, are excluded. This is nearly identical to the procedure used in BH96. In fact, there is very little difference in the resulting mean downstream velocities between the unfiltered and either of the filtered datasets. The details of the filtering procedure could become more important in an analysis of cross-stream velocity or higher moment statistics.

The instantaneous Gulf Stream paths defined by Z₁₂ at 10-day intervals for the period from simulated day 2471 (Oct 1991) to 3921 (Oct 1995) are shown in Fig. 6. The mean path, an envelope of one standard deviation, and the extremal positions are superimposed. The corresponding Z₁₂ statistics of the Gulf Stream path from moored observations during the Gulf Stream Dynamics and Synoptic Ocean Prediction Experiments during the 1980s are reproduced from Table 1 of Watts et al. (1995). In contrast to many previous basin to global scale simulations of the North Atlantic, the Gulf Stream in this simulation separates from the boundary at Cape Hatteras rather than a few hunderd kilometers to the north. Further, the current separates as a jet without the spurious strong, tight anticyclonic eddy at the boundary that characterizes many previous simulations (Dengg et al. 1996) including the 0.28° global model as seen in Fig. 4b. However, the simulated Gulf Stream flows in a more zonal direction than observed after separation, resulting in a southward offset of the mean path of 1°–1.5° in latitude. The sharp northward excursion of the mean axis between 60°W and 55°W results in the simulated stream passing the tail of the Grand Banks closer to the mean position determined from Advanced Very High Resolution Radiometer observations (e.g., Auer 1987). The meander envelope is small, though somewhat broader than observed, west of 70°W and expands to a maximum in the vicinity of the New England Seamount Chain. The meridional gradient of the Eulerian mean SSH (Fig. 3a) has a minimum near 60°W where the meander envelope is largest. In the stream-coordinate frame no such minimum exists (not shown), indicating that there is no sudden decrease in the jet intensity there, but rather a smaller probability of it being found near the mean position. East of 57°W the meander envelope narrows again with some evidence for a quasi-stationary wave in the individual paths. BH96 note the presence of a mean cyclonic feature in the vicinity of 55°W, slightly farther west than the time-mean trough position in the simulation. While we do not have observed Z₁₂-derived path statistics in the region east of the New England Seamount Chain to compare against the model results, there does not seem to be an indication of such a dramatic dimunition of meandering in available SST-derived path statistics (Auer 1987).

The downstream velocity averaged in stream coordinates along the 73°W, 68°W, and 55°W meridians is shown in Fig. 7. These can be compared to Fig. 10b of HR85, Fig. 9a of JSBW95, and Fig. 16 of BH96, respectively. At 73°W (Fig. 7a) the model provides a very realistic simulation of the structure and magnitude of the downstream flow of the Gulf Stream. The velocity at the surface exceeds 190 cm s⁻¹, the width of the stream (as defined by the 0 cm s⁻¹ isotachs) at the surface is approximately 200 km, there is a subsurface velocity maximum on the offshore side of the stream, the cyclonic shear exceeds the anticyclonic shear, and the 10 cm s⁻¹ isotach reaches to 2300–2400 m with positive downstream flow down to the bottom under the core of the jet. All of these features are in quantitative agreement with the observational analysis of HR85, though they used a somewhat different method to define the stream average. These features also represent further improvement over the already quite successful simulation of Chao et al. (1996). In addition to an increase in the peak speed at the jet core, the present simulation has a distinct thermostad that was absent in their [bu1002]¹/₆° simulation, though at somewhat too warm temperature.

At 68°W (Fig. 7b), while the agreement with the observed structure described by JSBW95 is still qualitatively good, some quantitative discrepancies are apparent. In particular, the maximum surface speed is weaker than observed: 155 cm s⁻¹ versus >200 cm s⁻¹ (note however that the observational estimate required some extrapolation above 400 m). The transport per unit depth at the surface, however, is 140 Sv km⁻¹, in excellent agreement with the observed value. The model does reproduce the width of the jet at the surface (which is little different than at 73°W), indicating a somewhat broader central core in the current to bring the horizontally integrated transport up to the observed value. There is too little vertical shear in the model simulation, especially on the inshore side of the jet. The 0 cm s⁻¹ isotach on the inshore side of the current is displaced offshore approximately 25 km between the surface and the bottom in the model versus 75 km in the observations. As a consequence the transport per unit depth in the model asymptotes to a value of 10 Sv km⁻¹ below 200 m, whereas the observed transport vanishes at the bottom. The deepening of the subsurface velocity maximum on the offshore side is similar to the corresponding structure upstream and in good agreement with observations. A nearly barotropic westward flow in excess of 5 cm s⁻¹ in the northern recirculation region also agrees well with the observational estimate.

At 55°W (Fig. 7c) the model simulated downstream peak velocity at 550 m (the uppermost level of observations) is weaker than the observed maximum of 75 cm s⁻¹. In the model solution the surface jet is somewhat too broad, extending too far in the offshore direction. There is little difference in the shear on the cyclonic and anticyclonic sides of the jet, in agreement with observations (BH96). While the structure is more symmetrical about the jet core than for sections farther to the west (as observed), there is an apparent systematic offshore bias in the position of peak velocity compared to the analysis BH96. This may be partly due to their use of temperature at 550 m to define the Gulf Stream position rather than 400 m as used in JSBW95 and in the model analysis here. There is an offshore shift between the surface and deep velocity maximum of approximately 30 km, though little shift below 500 m as in the observations. The northern edge of the stream does tilt offshore with depth as observed, and the deep velocities in the central Gulf Stream of 10–20 cm s⁻¹ are in good quantitative agreement with observations. The northern recirculation is nearly barotropic as observed, but is too weak by about a factor of 3 at this longitude.

The net downstream transport of the Gulf Stream in stream coordinates, obtained by integrating the stream-averaged velocity over the area between the 0 cm s⁻¹ isotachs, is shown in Fig. 8. The observational estimates of Hogg (1992) and JSBW95 are shown for comparison. The increase in transport from 90 Sv at Cape Hatteras to 150 Sv at 55°W is in good agreement with the observed values. The local minima and maxima in the transport between 65°W and 55°W cannot be resolved by the available moored observations, but can be identified with the multiple closed recirculations on both the north and south sides of the Gulf Stream seen in the barotropic transport streamfunction in Fig. 4a. The total transport is decomposed into baroclinic and barotropic components following the definitions of Hogg (1992). The partition of transport between baroclinic and barotropic also agree well with the observed estimates. The flow at 73°W is approximately equipartioned between baroclinic and barotropic. The barotropic component of flow and, as a consequence, the deep velocities increase moving downstream from Cape Hatteras (apparent by comparing the area enclosed in the 10 cm s⁻¹ isotachs at the three longitudes in Fig. 7), accounting for all of the increase in total transport moving downstream. The model baroclinic transport decreases somewhat too rapidly downstream, resulting in a deficit of approximately 10%–20% with respect to the observations at 60°W and 55°W.

In summary, the major deficiency of the simulation of the Gulf Stream appears to be a southward displacement of the stream axis, and a small deficit of the vertical shear moving downstream from Cape Hatteras, resulting in thermocline and surface velocities that are slightly too weak. The deep velocities, breadth, and general structure of the Gulf Stream are all reasonably well simulated, however.

d. The North Atlantic Current

One of the more striking improvements seen in the mean circulation of the 0.1° simulation as compared to lower resolution experiments is in the region of the North Atlantic Current. The salient features of the mean current can be seen in the SSH field in Fig. 3a (and more clearly in the mean velocity field in the NAC region shown in Fig. 9b below). Southeast of the Grand Banks near (40°N, 45°W) the Gulf Stream splits into the NAC flowing northeastward, and into a broader flow to the south, some of which retroflects to the west as part of the recirculation south of the Gulf Stream, and the remainder turns eastward to become part of the Azores Current. As the NAC flows northeastward along the continental rise it exhibits three major meanders in its mean path with troughs located at 40°N, 44°N, and 47°N. As it passes Flemish Cap the NAC turns to the northwest where between 47°N and 53°N a train of four anticylonic rings appear on its east side at roughly (47°N, 39°W), (49°N, 41°W), (51°N, 44°W), and (53°N, 47°W). In this region, known as the “Northwest Corner,” these quasi-stationary eddies sharply deflect the current back toward the southeast. It then proceeds eastward and is concentrated mostly between 48°N and 51°N as it crosses 39°W. From there it fans out into a broader region as it flows eastward across the basin.

These features of the mean flow are in remarkably good agreement with the basic picture of the NAC described by Rossby (1996), based on the RAFOS float data taken in the Newfoundland Basin between 1993 and 1994, and confirmed by historical hydrographic data (Kearns and Rossby 1998). Figure 9a shows an observational estimate of the mean currents derived by Dutkiewicz (1997) from float data on the σ = 27.5 surface, and Fig. 9b shows the near-surface geostrophic currents determined from the mean SSH in the model. The troughs at 41°N, 44°N, and 47°N appear in both model and observations. They lie above the southeast Newfoundland Rise, the Newfoundland Seamounts, and to the east of Flemish Cap. The positions of these quasi-stationary meanders are believed to be strongly controlled by the topography. This contrasts with the situation in the Gulf Stream, which is a free jet with propagating meanders and eddies. The trough at 44°N in the observations is farther to the east than in the model, but there is good evidence that the NAC exhibited a rare eastward meander at this location during the period when the RAFOS float data were taken (Kearns and Rossby 1998). In the northwest branch of the NAC the two anticyclonic rings at 49°N and 51°N also appear in both model and observations. The prominent anticyclonic ring at 53°N in the model does not stand out in the data, although some of the float trajectories show the presence of such a feature (Rossby 1996, Fig. 10). However, even if this standing eddy exists, it is too strong and extends too far to the northwest in the simulation. This is reflected in the model eddy kinetic energy (EKE), shown in Fig. 15b and in the SSH variability (Figs. 17a,b). These show that the high energy regions in the NAC extend too far northwest compared to both the EKE measured by drifter data [Fig. 4 of Rossby (1996)] and to the SSH variability from satellite observations (Fig. 16c below). In spite of this dispcrepancy, the overall agreement between model and data is unprecedented in a basin-scale numerical model.

The mean currents in the 0.28° model shown in Fig. 9c bear little agreement with the observations. In the 0.28° case the Gulf Stream has a branch that flows along the continental rise from the southwest to the southeast side of Grand Banks where it encounters a large anticyclonic recirculation. This acts to divert some of the northeastward flow in this region back to the south. East of 44°W the NAC has two main eastward-flowing branches near 43°N and 46°N. Part of this northern branch does split off around 42.5°W and flows north to about 51°N where it turns eastward, in better agreement with the observed flow in the region of the Northwest Corner, but this constitutes only a fraction of the NAC flow east of 40°W.

The time-mean path of the NAC is quite stable and changes little from year to year; however, the flow is far from being a quasi-stationary front. The instantanous fields show a rich turbulent eddy field. Cyclonic and anticyclonic rings appear in roughly the locations one might expect from the meanders in the mean flow, but the transient lateral shifts of these eddies is large, and many are stretched and pinched by the surrounding flow. No single coherent eddy persists for more than about a year. The float data suggest the presence of a single quasi-permanent eddy at 42°N, 44°W called the “Mann Eddy.” In the simulation, this would be more aptly described as a region of weak anticyclonic flow that tends to be surrounded by cyclonic eddies but contains a single coherent eddy only part of the time. In the region of the Northwest Corner, cyclonic eddies spawned in the southward flowing Labrador Current often get squeezed between anticyclonic rings in the NAC and then propagate eastward, producing significant transfer of cold freshwater across the NAC front. This also occurs in the southern part of the NAC (40°N–46°N) but not as frequently. Westward propagating anticyclonic eddies also occasionally cross the NAC front in the simulation.

e. The Azores Current

Like the NAC, the basic features of the Azores Current (AC) are in reasonably good agreement with what is known from observations, and this is again in sharp contrast to the lower resolution models such as the 0.28° global simulation and the CME and Dynamo Group (1997) North Atlantic experiments. In the 0.1° simulation the AC is surface intensified and can be clearly seen in the mean SSH field. It constitutes the northeast portion of the recirculation in the subtropical gyre. Figure 10a shows the time-mean SSH in the 0.1° model in the central and eastern basin. The front appears as a strong zonal flow across the basin east of the Mid-Atlantic Ridge between 34°N and 36°N. Figure 10b is a snapshot of the instantaneous SSH from the 0.1° simulation. It shows that, as in the NAC, the flow in the AC is dominated by eddies and meanders, and is not a quasi-stationary front following the path of the time-mean flow. As discussed below, the eddy variability in the AC appears in the model SSH and EKE fields and is in reasonably good quantitative agreement with observations. Figure 10c shows the mean SSH in the 0.28° simulation. A weak front is visible to the east of 40°W at around 34°N, but overall the near-surface flow in the central and eastern subtropical gyre is very different than the 0.1° case.

In the 0.1° simulation the AC in the central and eastern basin (Fig. 10a) appears to be partially fed from the north by broad southward near-surface flow. The source region of the AC is in the transition zone between the Gulf Stream and the NAC, and in this respect the model is in agreement with the observational evidence (Klein and Siedler 1989; Käse and Krauss 1996). West of 35°W the AC is fed partly by waters from the southward branch of the Gulf Stream, which splits off south of Grand Banks near 38°N, 46°W, and partly by NAC water that is recirculated back toward the south around 43°N, 41°W. Klein and Siedler argue for two distinct paths of AC source water during summer months associated with these two sources. We have not yet analyzed the seasonal variability in the model, but it is hard to argue for any quasi-permanent currents that feed the AC because the flow is so turbulent in this region (Fig. 10b). The strong eddy field south and east of the NAC clearly plays an important role in forming the AC.

Vertical–meridional sections of the time-mean, zonally averaged, zonal currents between 35°W and 25°W in the upper two kilometers are shown in Fig. 11 from the 0.1° simulation (a) and the 0.28° simulation (b). In the 0.1° case the AC extends to a depth of approximately 2 km, and the total transport calculated from the time-mean zonal velocity at 32°W is 9.6 Sv, which is on the low end of observational estimates ranging between 10 and 15 Sv (Käse and Krauss 1996). The westward flows just to the north and south of the AC seen in the 0.1° case (Fig. 11a) are associated with recirculations in the eddy fields on either side of the front (cf. Figs. 10a,b). Instantaneous velocities in the current east of the Mid-Atlantic Ridge are in the range 20–45 cm s⁻¹ and are somewhat larger (35–60 cm s⁻¹) west of the ridge.

The 0.28° case (Fig. 11b) shows a weak front near the position of the AC around 34°N that extends to only 1-km depth. Two other fronts also appear in the 0.28° case, one in the western and central basin around 31°N and another across the entire basin along 26°–28°N (see Fig. 10c). In the 0.1° simulation a front is also seen that crosses the eastern basin at 28°N to 29°N, passing just north of the Canary Islands (Figs. 10a, 11a). In both simulations this is a wind-driven feature associated with strong wind stress curls off the west coast of Africa near 30°N. As discussed by Milliff et al. (1996), these are an effect of the land–sea temperature contrast: warmer temperatures over northwest Africa set up a persistent continental low pressure region, which diverts the local anticyclonic atmospheric winds and sets up strong quasi-permanent wind stress curl patterns off the African coast. This produces a front in the Sverdrup streamfunction at this latitude that extends all the way across the basin giving rise to a “C shaped” pattern in the subtropical gyre, as can be seen in Fig. 4c. There is observational evidence for such a C-shaped pattern in the western subtropical gyre (see Schmitz 1996, Figs. 67 and 68). There is apparently no evidence for a front in the eastern basin near 28°N (Stramma 1984; Schmitz 1996, Fig. 37), but such a front would be difficult to detect given its strong transient component (see Fig. 10b). In the 0.28° case the fronts at 27°N and 31°N produce a rough C-shaped pattern in the western subtropical gyre (Fig. 3b), but in the 0.1° case there is only a hint of such a feature in the SSH west of 60°W around 27°N (Fig. 3a). It is conceivable that in this case the absence of a C shape in the western subtropical tyre is associated with the Gulf Stream extension being too far south, as discussed in the last section.

Unlike the front at 28°N, the AC is not associated with strong offshore wind stress curl patterns. The Sverdrup streamfunction (Fig. 4c) does show a small front west of Gibraltar at the latitude of the AC, but it is much weaker than the front at 28°N. This agrees with the description given by Käse and Krauss (1996), who argue that wind stress curl is the dominant forcing within the subtropical gyre south of the AC, while north of the Azores Front the near-surface circulation is primarily driven by thermohaline processes.

a. Meridional heat transport

The meridional heat transport due to advection in the 0.1° run is shown in Fig. 12a for the two periods October 1985–September 1989 and March 1991–February 1994 along with the inverse model estimates of Macdonald (1998) and a recent estimate based on an atmospheric residual calculation (Trenberth 1998). The contribution from the diffusive heat flux associated with the biharmonic diffusion of temperature (not shown) is very small (order 10⁻⁴ PW). The total heat transport in both periods is in reasonably good agreement with the observational estimates south of 40°N. Farther north the model transport exceeds the Trenberth (1998) estimate, but falls within the uncertainty of the northernmost estimate of Macdonald (1998). These results should be interpreted with some caution since the model is not in thermodynamic equilibrium; however, the net heating of the basin was very small during the March 1991–February 1994 period: the global mean temperature changed by only −0.0052°C, corresponding to an area-averaged net cooling of 0.082 W m⁻². Thus the surface cooling is mostly balanced by the net input of heat through the buffer zones (i.e., the net heat gain from the southern boundary minus the heat loss through the northern boundary).

Noneddy-resolving level models with the Gent–McWilliams eddy parameterization (Gent and McWilliams 1990) have done well in reproducing the observed heat transport (Böning et al. 1995), but previous simulations with eddy-permitting level models have generally produced too weak heat transports. For example, the standard CME experiments at ¹/₃° and ¹/₆° produced transports of only about 0.5 PW at 25°N (Beckmann et al. 1994). Studies of the CME series of experiments demonstrated the sensitivity of the heat transport to a variety of modeling factors including forcing in the buffer zones at the open boundaries, as well as subgrid-scale mixing [for a review see Böning and Bryan (1996)]. MSSM found considerable sensitivity to the parameterization of surface heat flux in the 0.28° global simulations: the heat flux at 25°N in the North Atlantic increased from 0.7 to 1.0 PW upon switching from the Levitus (1982) restoring to the ECMWF climatological heat flux (Barnier et al. 1995).

Figure 12b shows the zonally averaged surface heat flux in the model along with the zonally averaged annual-mean ECMWF heat flux. At the equator the heat flux into the ocean is much larger than the climatological heat flux, and between 15°N and 30°N the net flux is close to zero, whereas the climatology expects a net heating of the ocean in this region. However, the heat flux over the entire domain south of 50°N is in agreement with the more recent estimates of Hasse et al. (1996, Fig. 2.19). Similar results were found in the Dynamo Group experiments (compare their Fig. 4.20). Between 48°N and 68°N the heat flux into the ocean is greater than the climatological flux with differences reaching 40 W m⁻² near 52.5°N. This is primarily associated with larger heat losses in the region of the NAC and in the western Labrador Sea. Averaged over the entire basin, the net surface heat flux out of the ocean is 6.2 W m⁻² for this 3-yr period, whereas the ECMWF climatological flux has an average heat loss of 13.1 W m⁻². Thus the restoring term in the surface heat flux [see Eq. (9) of MSSM] is supplying an average 6.9 W m⁻² into the ocean, implying that the surface temperature is cooler on average than the SST associated with the climatology by about 0.18°C.

The lower two curves in Fig. 12a show the contribution from the eddy heat fluxes for the two periods. These are relatively small compared to the total, so the majority of the heat transport is due to the time-mean flow. South of the equator the eddy fluxes contribute only a very small northward component. Between 0° and 35°N the eddy heat transport ranges between 0.1 and 0.25 PW southward, and at 35°N it changes sign to become a northward flux, as would be expected from the production of warm- and cold-core eddies in the Gulf Stream. These aspects of the eddy heat transport are in rough agreement with previous model studies at lower resolution (Böning and Bryan 1996).

b. Meridional overturning circulation

The meridional overturning streamfunction is shown in Fig. 13. The maximum overturning is 23.9 Sv at 33.2°N, 1140-m depth. This is farther south than in the 0.28° run, which has a maximum of 21.27 Sv at 44.2°N, 1160 m (MSSM, Fig. 15b). The increase near 1-km depth between 25°N and 35°N is associated with upwelling in the Gulf Stream south of the separation point, and the sudden decrease at 35°N is likely associated with the deepening of the Gulf Stream extension after separation (see section 3c). The strength of the heat transport is strongly tied to the magnitude of the overturning streamfunction. The overturning at middle and low latitudes is stronger during March 1991 through February 1994 than in the earlier period October 1985 to September 1989, and this is reflected in a stronger heat transport in this region, as seen in Fig. 12a. Böning et al. (1996) show that in a variety of different simulations the heat transport and maximum overturning at 25°N are linearly related, with an increase of about 0.1 PW for every 2 Sv increase in meridional overturning [see Fig. 15 and Fig. 4.12 of Dynamo Group (1997)]. Our results are consistent with this: the heat transport and maximum overturning at 25°N in the 0.1° run are 1.084 PW and 16.59 Sv for the earlier period, 1.198 PW and 19.03 Sv for the later period, and 1.019 PW and 16.44 Sv for the 0.28° run.

About 4 Sv of water crosses the northern ridges near 65°N. The southward flowing deep water reaches a depth of 1.6 km by 64°N, and about 2.2 km by 59°N just south of the latitude of Cape Farewell. The southward return flow is deeper than in the 0.28° simulation at all latitudes: note the 8 Sv contours lie at around 2–2.5 km compared to 1.7 km in the 0.28 case. The associated deep western boundary current (DWBC) is also much stronger in the 0.1° simulation. Figure 14 shows a cross section of the mean meridional velocity at 26.5°N west of Abaco Island in the Bahamas (cf. the 0.28° case in MSSM, Fig. 9b). The DWBC is stronger, narrower, and deeper than in the 0.28° simulation: the maximum southward velocity is at 2400 m versus 1700 m in the 0.28° run, and the total southward transport is 41.5 Sv compared to 26.8 Sv in the 0.28° run. Lee et al. (1996) estimate a southward transport of 40 Sv from moored current meter observations east of Abaco, which agrees well with our model results. However, they argued that their data imply substantial offshore meandering of the DWBC, whereas in the model the DWBC did not exhibit large meanders east of Abaco. Chave et al. (1997) found pulsations in the DWBC transport off Abaco, which they attributed mostly to time-dependent horizontal recirculations. Their observations, which extended farther offshore than those of Lee et al. (1996), indicated no substantial meandering of the current, and their estimated DWBC transport, after removing a correcting for recirculation, is 18.5 Sv. The time-mean horizontal circulation below 1-km depth does exhibit a tight recirculation in the model centered at around 26.2°N, 75.6°W that acts to strengthen the DWBC core in this region, but given the uncertainties in the observations, it is unclear at this point whether the model DWBC transport is realistic or too large.

a. Eddy kinetic energy

Figure 15 shows the near-surface (75–100 m) MKE (a) and EKE (b) from the 0.1° simulation, and the EKE for the 0.28° run is shown in (c). Comparing the MKE and EKE in Figs. 15a and 15b, it is clear that the maximum levels of eddy energy are concentrated in the vicinity of the major current systems, except near stable topographically controlled currents such as the Gulf Stream south of about 32°N, the Labrador Current, and the Greenland Current east of 50°W where it separates from the coast. This is what would be expected from eddies generated through baroclinic and barotropic instability. Similar correlations of the MKE and EKE distributions are found in lower resolution simulations (Dynamo Group 1997). In quieter regions, such as the interior of the subtropical gyre and in the eastern basin, the EKE lies mostly between 10 and 50 cm² s⁻², an order of magnitude higher than the MKE in these regions. This contrasts with the 0.28° case, where the EKE in the central and eastern basin is mostly less than 5 cm² s⁻². In general the energy levels tend to be higher in areas of deep ocean and fall off significantly over ridges and continental shelves.

It is noteworthy that in the regions of highest EKE, such as the Gulf Stream extension and the NAC, the level of EKE is comparable to or greater than the MKE, which indicates the highly turbulent nature of the flow. The volume-averaged MKE and EKE in the 0.1° model are 13.2 and 29.4 cm² s⁻², respectively, so the EKE is nearly 70% of the total energy. The MKE and EKE are 7.4 and 9.6 cm² s⁻², respectively, in the North Atlantic sector of the 0.28° model.

Both the 0.1° and 0.28° simulations show similar levels of EKE in the region surrounding the tropical current systems. The highest EKE levels in the Tropics are in the region of the North Brazil Current (NBC) retroflection off the coast of French Guiana near 8°N. The EKE is in excess of 1000 cm² s⁻² there and is in good agreement with the observations of Johns et al. (1990), who find a seasonal variation of the EKE ranging from 800 to 1500 cm² s⁻², with an annual average of 1000 cm² s⁻². Northwest of the NBC retroflection, a band of high EKE ranging from 500 to 1000 cm² s⁻² in the 0.1° case marks the path of the anticylonic eddies spawned in the retroflection that propagate into the Caribbean. Approximately five eddies per year are shed in the NBC retroflection, which compares with the observations in the range of three to eight per year: Johns et al. (1990) observed velocity fluctuations from current meters in the NBC retroflection with a 40–60 day periodicity, but not all of these were associated with eddies identifiable in the Geosat altimetry maps (Didden and Schott 1993);Richardson et al. (1994) estimated a lower bound of three eddies per year from the Geosat data, but more recent analysis of T/P data show a periodicity in the range of 40–80 days (Carton and Chao 1999) in agreement with the current meter data. In the region between the NBC retroflection and the Caribbean the EKE levels are higher than in the 0.28° case. In both models the internal Rossby radius is well resolved at these low latitudes. This suggests that the increased vertical resolution may also be important in the Tropics for properly simulating the eddy field (the 0.28° model has only 25 vertical levels).

The geographical distribution of EKE in the Gulf Stream and NAC is largely determined by the paths of the mean currents, and hence is very different in the 0.1° and 0.28° simulations. Since the mean path of the Gulf Stream and NAC is much closer to observations in the 0.1° case, the EKE distribution is also much better and is in reasonably good quantitative agreement with observations from both satellites and drifters. Stammer (1997) computes the surface geostrophic EKE from the surface slope variability measured by T/P, and finds energies as high as 3000 cm² s⁻² in the Gulf Stream extention near 65°W (cf. his Fig. 2: the 1000 cm² s⁻² contour is in rough agreement with the same contour in Fig. 15b). The high EKE region near 60°–65°W, 35°N in the model has too broad an extent in latitude, which is associated with the meander envelope being too broad in this region (cf. Fig. 6).

The EKE in the NAC region exceeds 1000 cm² s⁻², and this is again in agreement with both the satellite measurements [see Stammer (1997) for T/P, and Heywood et al. (1994) Fig. 3b for ERS-1 measurements] and with drifter data (see Rossby (1996) Fig. 4, and Brügge (1995) Fig. 11). The model also shows a patch of EKE above 2000 cm² s⁻² east of Flemish Cap, which may be too high. In the region of the Northwest Corner the model EKE extends too far to the northwest compared to all the observations, again reflecting the fact that the mean path of the NAC reaches too far northwest as discussed in section 3d.

In the subpolar gyre there is a patch of EKE between 200 and 500 cm² s⁻² west of Greenland at about 61°N where the East Greenland Current detaches from the coast and sheds a train of small anticyclonic eddies. The EKE is also large (500–1000 cm² s⁻²) in the region of the Denmark Strait overflow. Substantial EKE (above 200 cm² s⁻²) is also found in the Iceland–Faeroe and Faeroe–Scotland overflow regions. This energy is likely generated by processes associated with the vertical convection in the model (convective adjustment and explicit vertical mixing of tracers and momentum).

In the broader eastern extension of the NAC the eddy energy is also fairly high, exceeding 200 cm² s⁻² over the deeper parts of the northeast basin. South of about 48°N energy levels fall off to the east of the Mid-Atlantic Ridge (MAR), and are mostly in the range of 10–50 cm² s⁻². An exception is the Azores Front, where the energy ranges from 200 cm² s⁻² at 30°W to 100 cm² s⁻² at 20°W. There the EKE is somewhat higher than the MKE, again reflecting the turbulent nature of the Azores Front.

In the Western Mediterranean significant eddy activity produces energy levels from 200 to 500 cm² s⁻². This is completely absent in the 0.28° simulation where the EKE is less than 5 cm² s⁻² throughout the Mediterranean.

Another deficiency seen in previous simulations (e.g., Dynamo Group 1997) is in the intensity of EKE in the deep ocean, where there is typically no significant vertical penetration of EKE except beneath the strong currents. A vertical section of EKE along 48°N is shown in Fig. 16 for the 0.1° (a) and 0.28° (b) simulations. These can be compared to the data shown in Fig. 16c from moored current meters between 35°W and 10°W (Colin de Verdiere et al. 1989). Overall, the 0.1° simulation is in quantitatively good agreement with the observations as a function of both longitude and depth, while the 0.28° simulation is in general too weak and has a very different horizontal structure.

The 0.1° case shows the highest EKE in the region of the NAC between 43°W and 35°W. In the 0.28° case the NAC is displaced too far east and shows two areas of high variability: one in the deep basin between 40°W and 35°W and one above the western slopes of the MAR between 35°W and 30°W where the mean path of the NAC is mostly zonal (see Fig. 9c). Here the EKE at depth in the 0.28° case actually exceeds that in the 0.1° case because of the location of the NAC. On the eastern flank of the NAC the observations at 35°W show EKE levels up to 350 cm² s⁻² near the surface and a fairly constant level between 25 and 45 cm² s⁻² below 1.5 km. The 0.1° EKE is independent of depth below 1.5 km in this region with values ranging from 20 to 50 cm² s⁻² between 34°W and 35°W.

Over the MAR the eddy energy falls off significantly, especially at depth where the 0.1° EKE drops below 5 cm² s⁻² above the ridge, again in agreement with the observations. At depths greater than about 1 km the EKE is fairly constant across the eastern basin, with values in the range 2–3 cm² s⁻² below 3-km depth in both the observations and the 0.1° model. In the 0.28° case the EKE is mostly less than 0.5 cm² s⁻² below 3-km depth.

In the upper ocean the 0.1° EKE decreases across the basin east of the ridge. Note that the 10 cm² s⁻² contour lies between 1 and 1.5 km depth east of the ridge in both the 0.1° model and the observations. However, the maximum in EKE near 20°W and 1.5-km depth in the observations does not stand out in the 0.1° model, where between 32°W and 15°W the contours are essentially flat except for small-scale variations. In contrast, the EKE in the 0.28° case is less than 2 cm² s⁻² below 1–2 km in the entire eastern basin, and the 10 cm² s⁻² contour lies entirely above 500-m depth.

b. Surface height variability

The rms variability of the SSH field is shown in Fig. 17 for the two periods October 1985–September 1989 (a) and March 1991–February 1994 (b), and the satellite data from a blended T/P–ERS-1/2 product (Le Traon and Ogor 1998; Le Traon et al. 1998). is shown in (c). The satellite SSH variability was computed from ¼° × ¼° maps covering a 2-yr period from April 1995 to April 1997 every 10 days (this was the longest continuous multiyear period available from this product). There are some regions of very high variability in the data that do not appear in the model and are likely due to residual errors in the tidal model (P.-Y. Le Traon 1998, personal communication); these include the high-energy regions off the North American coast southwest of Nova Scotia, off the South American coast between 0° and 5°N, and possibly also the “bullets” of high variability that appear just south of the Florida Peninsula, in the North Sea southeast of Great Britain, and off the east coast of South America near 18°S.

The overall pattern of variability in the model is similar to the EKE map (Fig. 15b) with the largest variability in regions of strong currents and low variability over the continental shelves and in the topographically trapped currents. The model variability is similar in the two periods shown in Figs. 17a,b and the differences between these give an indication of the interannual variability of this field. The agreement between model and observations is quite good, both in terms of the geographical distribution and amplitude of variability, especially compared to previous simulations [for a comparison of the global SSH variability in the 0.28° model with two years of T/P data, see Fu and Smith (1996)]. The strongest variability is in the Gulf Stream extention and exceeds 50 cm in both model and observations. In the 0.28° case the maximum is less than 30 cm.

As in the EKE map, much of the improvement in the geographical distribution of the variability is associated with the improved representation of the mean currents:the Gulf Stream separation, the path of the NAC, and the Azores Current. Similarly, the major discrepancies between the model and data are associated with problems with the mean circulation in the model: the maximum variability in the Gulf Stream extension is too far south and too broad near 65°W, and the extent of the high variability in the region of the NWC is too far to the northwest. The presence of the Gulf of Mexico Loop Current eddy that developed in 1989 also adversely effects the model variability in the Gulf of Mexico (Fig. 17b); it reduces the variability in the central and western Gulf by preventing eddies from shedding and propagating westward and, since it is quite stable, it also reduces the variability in its own vicinity. In the earlier period (Fig. 17a) this persistent eddy was not present, and the variability in the gulf is in much better agreement with the satellite data. However, in the Caribbean the variability is high compared to the data even in the earlier period, reaching a maximum near 20°N, 85°W of more than 20 cm in the model compared to only 10 cm in the observations.

The variability in the Mediterranean is also in good agreement with the satellite data due to the presence of a strong mesoscale eddy field there. This is particularly true in the Western Mediterranean off the north African coast, where the Alboran gyre and other less stationary features show variability in excess of 10 cm in both model and observations. In the 0.28° case the variability is only about 2–3 cm in this region.

Another region of high variability is in the shallow North Sea. This signal appears in both the 0.1° and 0.28° simulations with about the same magnitude. Fu and Smith (1996) calculated the rms variability with a bandpass filter to retain only frequencies with 20–100 day periods and length scales larger than 1000 km (see their Fig. 7b). The variability in the North Sea in the 0.28° simulation is very strong in this band, suggesting the fluctuations are associated with the prevalent wind-driven intraseasonal barotropic oscillations identified in both the model and T/P data (Chao and Fu 1995; Fu and Davidson 1995). This variability also appears in the satellite data (Fig. 17c) with about the same magnitude.

In regions where the SSH variability is low, such as in the eastern basins and the Tropics, the satellite variability is higher than in the model. This may be due to noise in the observations: the background error in the blended T/P–ERS-1/2 product is order 2–3 cm (N. Ducet 1998, personal communication), which is the same order as the signal in the model, so the data and model are not necessarily inconsistent. The background noise in the blended T/P–ERS-1/2 data shown in Fig. 17c is significantly lower than in the T/P data alone, which is 3–5 cm in the North Atlantic (Tsaoussi and Koblinski 1994, Fig. 4d). The T/P and ERS-1/2 data were merged through an optimal interpolation method (Le Traon et al. 1998) that corrects for residual long wavelength errors still contained in the along-track data (mainly orbital error, but also inverted barometer and tidal errors). It is remarkable that in Fig. 17c the background error is low enough that the low-variability region delineating the path of the Labrador Current can be clearly seen. This current can be traced from the northwest Labrador Sea south to the Grand Banks, and its detailed path is similar in the model.

c. Eddy length scales and wavenumber–frequency spectra

In the last section it was shown that the amplitude and geographical distrubution of the SSH variability in the 0.1° simulation is in good agreement with the satellite observations and that discrepancies can mostly be attributed to problems with the simulation of the mean currents. In this section we show that the eddy length scale as a function of latitude and the wavenumber–frequency spectra in the Gulf Stream extension also agree well with the satellite data. Thus the model is reproducing the observed spectrum of eddy energy over a broad range of time and space scales.

Figure 18 shows eddy length scales for the 0.1° and 0.28° simulations compared to the length scale calculated from the T/P data. We use the SSH microscale length (Tennekes and Lumley 1972) as an estimate of the eddy length scale:

View Expanded

which is the ratio of the SSH variability to the slope variability along direction l. The brackets denote an average in time or space. In the limit of homogeneous turbulence it can be shown that for spatial averaging this ratio is equal to the mean-square wavenumber of the spectral energy density (the Fourier transform of the spatial correlation function of the surface height anomalies). To obtain an average length scale as a function of latitude, these averages were evaluated as both time averages and zonal averages across the basin; a similar procedure was used by MSSM to compute the global zonally averaged length scales in the 0.28° model. The curves in Fig. 18 show the meridional length scales from the models compared to the along-track length scale from T/P data. The latter was evaluated using the 2° × 2° gridded slope and height variability fields computed by Stammer (1997), and the zonal averages were taken only over the North Atlantic. A running average was applied to the model curves to filter out fluctuations on scales smaller than 2° in latitude. In the models the zonal and meridional scales are roughly equal everywhere except in the Tropics (15°S–15°N) where the zonal scale is significantly larger due to the zonal structure of the equatorial current systems. The satellite tracks are more closely aligned with the meridional direction in the Tropics, so the meridional scales from the model are more appropriate for comparison.

Both the 0.1° and 0.28° length scales show a decrease with increasing latitude, as would be expected for turbulence generated through baroclinic instability, where the eddy length scale should vary linearly with the Rossby deformation radius (Fig. 1). However, the 0.28° length scale is systematically larger than in the 0.1° case by 30 to 50 km at all latitudes. In both models the Rossby radius is well resolved at low latitudes, so we speculate that the higher vertical resolution in the 0.1° model (and hence better representation of the vertical structure of vortices) could be responsible for the smaller eddy length scales there.

The 0.1° and T/P length scales agree very well at all latitudes between 15°N and 55°N. The curves are relatively smooth in this region in spite of the fact that the numerators and denominators (not shown) vary significantly. For example, both slope and height variability increase substantially at the latitudes of the Gulf Stream extension and the NAC. This is an indication that the length scale is a fairly robust quantity. North of 55°N the discrepancy between the 0.1° and T/P scales is associated with a smaller slope variability in the data compared to the model; however, the 2° × 2° gridded data fields do not extend across the entire basin at these latitudes, so this difference may not be significant. In the Tropics the T/P length scale is low compared to the model because the observed slope variability is larger in the observations, while the height variabilities are comparable. The error in the T/P data is relatively large (4–5 cm) in the tropical Atlantic (Tsaoussi and Koblinsky 1994), which may account for some of this discrepancy.

Wavenumber–frequency spectra of the SSH in the Gulf Stream extention are shown in Fig. 19 for the 0.1° simulation (a), the T/P data (b), and (c) the 0.28° simulation. Spectra from both model and observations were computed using data sampled along the ascending and descending satellite ground tracks in a region bounded by 32°–42°N, 75°–50°W, and covering the period October 1992–October 1995. For 14 tracks crossing this region the wavenumber–frequency power spectrum was computed from the Fourier transform of the two-dimensional array (along-track distance vs time) of SSH, and the resulting power spectra were averaged over tracks to produce the plots. To reduce noise in the spectra, the log₁₀ plots were smoothed over three points in frequency. Similar spectra were computed by Fu and Smith (1996) for the T/P data and the 0.28° simulation for the 2-yr period starting in October 1992. They found that the 0.28° spectrum was too weak compared to the observed spectrum, reflecting its low overall energy level, and that it fell off too quickly at high frequecies and high wavenumbers, suggesting the need for higher resolution. These basic features of the 0.28° spectrum can also be seen by comparing Figs. 19b,c. The spectrum of the 0.1° SSH variability (Fig. 19a) is in much better agreement with the T/P spectra. The overall magnitude is much closer to the observed spectrum, and both spectra are nearly “white” in frequency at wavelengths between 100 and 300 km, and “red” at larger wavelengths. At wavelengths shorter than 100 km there is significantly more power in the T/P spectrum, but this may be in part due to noise in the data, which becomes comparable to the signal at wavelengths between 50 and 100 km (Stammer 1997). The spectral slope in frequency at periods of 20–100 days and wavelengths greater than 300 km is −2.5 in the 0.1° model and −1.8 in the T/P data, while the slope in wavenumber at wavelengths 100–300 km and periods greater than 100 days is −5.5 in the model and −4.4 in the T/P data. Thus the power spectrum in the model is evidently falling off too quickly, but it is still a vast improvement over the 0.28° case.

d. Summary and conclusions

In summary we have found that a numerical simulation of the North Atlantic Ocean at 0.1° shows remarkable improvements over previous lower-resolution simulations in reproducing features of both the time-mean circulation and the eddy variability over a broad range of time and space scales. The agreement between the 0.1° simulation and the observed circulation have allowed us to begin forming direct quantitative comparisons with in situ and remotely sensed observations at both local and basin scales.

The time-mean circulation exhibits several significant improvements relative to previous simulations: 1) the Gulf Stream separates at Cape Hatteras, and the peak velocities, transports, spatial scales, and structures in the Gulf Stream extension agree well with current meter data; 2) south of Grand Banks the Gulf Stream splits into the North Atlantic Current and a southward flow that feeds the Azores Current; 3) the time-mean path of the NAC is in good agreement with observations from float data, including the detailed positions of troughs and meanders that are apparently controlled by topographic features; and 4) this is probably the first realistic basin-scale simulation that captures the Azores Current, which constitutes the northeast recirculation in the subtropical gyre; its source, location, and total transport are consistent with observational estimates.

Notable discrepancies in the mean circulation compared to observations are: 1) the path of the Gulf Stream extention west of 55°W is displaced too far south by 1°–1.5°, the meander envelope has too broad a meridional extent between 65° and 57°W, and the vertical shear in the jet decreases too rapidly downstream of the separation at Cape Hatteras; 2) in the region of the Northwest Corner the North Atlantic Current separates from the coast farther north than observed by about 1.5°–2° lat; 3) 9 years into the simulation an unrealistically large and stable eddy appeared in the Gulf of Mexico Loop Current, which persisted until the end of the run and degraded the character of the mean circulation in the Gulf of Mexico and the Caribbean.

Overall, the eddy variability in the model is in excellent agreement with both satellite and in situ observations, including the magnitude and geographical distribution of eddy energy, the wavenumber–frequency spectrum of SSH in the Gulf Stream extension, the eddy length scale as a function of latitude, and the eddy energy at depth in the eastern basin. The eddy variability is highest in regions of strong currents, and discrepancies with observations are mostly associated with the problems in the mean circulation mentioned above.

While these results suggest that we are closely approaching a realistic solution at 0.1°, we cannot demonstrate the extent to which the solution has converged without still higher resolution experiments. A complete understanding of the reasons for the improvements seen in this simulation will require further analysis, but it is likely that one of the main factors contributing to its success is sufficient resolution of the first baroclinic Rossby radius. Finer resolution of topographic features and lower values of mixing coefficients may also have contributed.

Because the simulation was of relatively short duration (about 16 yr) it has not reached its equilibrium state, especially in the deep ocean, and we cannot yet determine if the model is capable of properly simulating the long-term evolution of water masses. Nevertheless, since the model density did not drift very far from its initial state (based on the Levitus climatology) during this short integration, we can say that it is able to obtain realistic simulations given the observed density distribution and realistic wind forcing.

The results from this and other simulations of comparable resolution will provide an important resource that can be used in combination with diverse observations in exploring the dynamics of the general circulation, in designing future observational systems, and developing subgrid-scale parameterizations for use in lower-resolution climate models.

Because of the enormous amount of data archived from this model, a complete analysis of the results presents a monumental task. For this reason we are attempting to make the model output available to the community. As a first step in this direction, a subset of the data is now publicly available, which includes three-dimensional time-mean fields of the prognostic variables and eddy kinetic energy, and a multiyear time series of the two-dimensional 10-day snapshots of sea surface height. Information on how to access this data is available on the internet at http://www.acl.lanl.gov/climate, or contact the authors.

Note added in proof: We discovered that in the runs presented in this paper the biharmonic viscosity and diffusivity were inadvertently set to scale like the sixth power of the horizontal grid spacing rather than the third power, as described in section 2c. We have since conducted a new 4-yr simulation starting from the beginning of 1987 of the production run presented here, but with two changes in the model configuration: 1) the mixing coefficients were reset to vary like the cube of the grid spacing as originally intended and 2) modifications to the topography were made in the region of the Lesser Antilles to better represent the rough topography there. The results of this new simulation are broadly in agreement with the results shown in this paper, but the simulation improved in two respects: 1) the persistent Loop Current eddy in the Gulf of Mexico was much improved and 2) the separation of the NAC in the Northwest Corner occurs at roughly the right location and is not displaced too far to the north as described in section 3d.