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  • View in gallery

    Meridional streamfunction in the coupled model (in Sv): (top) global streamfunction integrated across the basins, (middle) streamfunction in the Atlantic basin, and (bottom) streamfunction in the Pacific. The boxed in area and section represent the diagnostics used in this study.

  • View in gallery

    Sensitivity of the maximum value of the streamfunction ψMAX to the (a) heat flux: (∂ψMAX/∂Q) in Sv W−1 m2 and to the (b) freshwater flux: (∂ψMAX/∂Fw) in Sv m−1 s in the ocean model.

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    Sensitivity of the maximum value of the streamfunction ψMAX to the heat flux: (∂ψMAX/∂Q) in Sv W−1 m2 in the coupled ocean–energy–moisture balance model.

  • View in gallery

    Sensitivity of the maximum value of the streamfunction ψMAX to the freshwater flux: (∂ψMAX/∂Fw) in Sv m−1 s in the coupled ocean–energy–moisture balance model.

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    Sensitivity of the heat transport at 24°N to the heat flux: (∂HT/∂Q) in PW W−1 m2 in the ocean model.

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    Sensitivity of the maximum value of the streamfunction ψMAX to a column-by-column perturbation in the diapycnal mixing in the ocean model: (a) (∂ψMAX/∂κd) in Sv m−2 s and (b) (∂HT24°N/∂κd) in PW m−2 s.

  • View in gallery

    Sensitivity of the maximum value of the streamfunction ψMAX to a column-by-column perturbation in the diapycnal mixing: (∂ψMAX/∂κd) in Sv m−2 s in the coupled model.

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    Sensitivity of the maximum value of the streamfunction ψMAX to the wind stress: (top) zonal wind stress (∂ψMAX/∂τx). (bottom) Meridional wind stress (∂ψMAX/∂τy) in Sv N−1 m2 in the coupled ocean–energy balance model.

  • View in gallery

    Sensitivity of the maximum value of the streamfunction ψMAX to the wind stress: (top) zonal wind stress (∂ψMAX/∂τx). (bottom) Meridional wind stress (∂ψMAX/∂τy) in Sv N−1 m2 in the ocean model.

  • View in gallery

    Sensitivity of the streamfunction maximum to the zonal wind stress (∂ψMAX/∂τx) in Sv N−1 m2: (a) restoring boundary conditions, (b) mixed boundary conditions, and (c) flux boundary conditions. The three plots are on the same scale.

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    Surface currents around the African continent. The ocean model.

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    (a), (b) Difference in salinity (in 10−3 psu) between simulations with a wind stress perturbation (Δτx = 0.005 N m−2) imposed at (left) 30°S and (right) 42°S (both at 22°E), with an unperturbed simulation. (c), (d) Same as in (a), (b), but for the difference in near-surface currents (in m s−1), with the ocean model.

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An Adjoint Analysis of the Meridional Overturning Circulation in a Hybrid Coupled Model

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  • 1 Massachusetts Institute of Technology, Cambridge, Massachusetts
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Abstract

Multicentury sensitivities in a realistic geometry global ocean general circulation model are analyzed using an adjoint technique. This paper takes advantage of the adjoint model’s ability to generate maps of the sensitivity of a diagnostic (i.e., the meridional overturning’s strength) to all model parameters. This property of adjoints is used to review several theories, which have been elaborated to explain the strength of the North Atlantic’s meridional overturning. This paper demonstrates the profound impact of boundary conditions in permitting or suppressing mechanisms within a realistic model of the contemporary ocean circulation. For example, the so-called Drake Passage Effect in which wind stress in the Southern Ocean acts as the main driver of the overturning’s strength, is shown to be an artifact of boundary conditions that restore the ocean’s surface temperature and salinity toward prescribed climatologies. Advective transports from the Indian and Pacific basins play an important role in setting the strength of the overturning circulation under “mixed” boundary conditions, in which a flux of freshwater is specified at the ocean’s surface.

The most “realistic” regime couples an atmospheric energy and moisture balance model to the ocean. In this configuration, inspection of the global maps of sensitivity to wind stress and diapycnal mixing suggests a significant role for near-surface Ekman processes in the Tropics. Buoyancy also plays an important role in setting the overturning’s strength, through direct thermal forcing near the sites of convection, or through the advection of salinity anomalies in the Atlantic basin.

Corresponding author address: V. Bugnion, Center for Global Change Science, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139. Email: veronique@bugnion.org

Abstract

Multicentury sensitivities in a realistic geometry global ocean general circulation model are analyzed using an adjoint technique. This paper takes advantage of the adjoint model’s ability to generate maps of the sensitivity of a diagnostic (i.e., the meridional overturning’s strength) to all model parameters. This property of adjoints is used to review several theories, which have been elaborated to explain the strength of the North Atlantic’s meridional overturning. This paper demonstrates the profound impact of boundary conditions in permitting or suppressing mechanisms within a realistic model of the contemporary ocean circulation. For example, the so-called Drake Passage Effect in which wind stress in the Southern Ocean acts as the main driver of the overturning’s strength, is shown to be an artifact of boundary conditions that restore the ocean’s surface temperature and salinity toward prescribed climatologies. Advective transports from the Indian and Pacific basins play an important role in setting the strength of the overturning circulation under “mixed” boundary conditions, in which a flux of freshwater is specified at the ocean’s surface.

The most “realistic” regime couples an atmospheric energy and moisture balance model to the ocean. In this configuration, inspection of the global maps of sensitivity to wind stress and diapycnal mixing suggests a significant role for near-surface Ekman processes in the Tropics. Buoyancy also plays an important role in setting the overturning’s strength, through direct thermal forcing near the sites of convection, or through the advection of salinity anomalies in the Atlantic basin.

Corresponding author address: V. Bugnion, Center for Global Change Science, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139. Email: veronique@bugnion.org

1. Introduction

This article examines the sensitivity of the meridional overturning circulation (MOC; Wunsch 2002; Rahmstorf 2003) in realistic geography models to mixing parameters in the ocean and to surface forcings such as wind stress, heat, and freshwater fluxes. The objective is to use the results obtained with the adjoint model to review several theories, which have been elaborated to explain the intensity of the MOC and its associated heat transport.

  • Heat and freshwater fluxes exert a direct control over the buoyancy of the surface water in the North Atlantic, hence on convection and downwelling in the Labrador, Norwegian, and Greenland Seas (Broecker et al. 1985).
  • By transporting heat through the thermocline, diapycnal mixing can balance the upwelling of abyssal waters (Munk and Wunsch 1998).
  • Wind stress could determine the steady-state intensity of the overturning circulation through its dynamical control of upwelling in the Southern Oceans (Toggweiler and Samuels 1995; Gnanadesikan 1999).

Each section of this article will address one of these three hypotheses. The end of the paper will seek to quantitatively compare each of these mechanisms and their role in determining our knowledge of the MOC. This article will also demonstrate the efficiency of adjoint methods for such sensitivity analysis.

2. The numerical experiments

The analysis was performed on two sets of numerical experiments. The first uses an ocean general circulation model forced with so-called mixed boundary conditions. In the second experiment, the ocean model is coupled to an ocean–energy and moisture balance atmosphere. The adjoint of both configurations was derived and used for this sensitivity analysis.

a. The ocean model

The ocean model used in this work is the Massachusetts Institute of Technology (MIT) OGCM; it is described in detail in Marshall et al. (1997a, b). The configuration of the model used for this study has a realistic geography and bathymetry on a constant 4° × 4° resolution grid; it has 15 layers in the vertical with thicknesses ranging from 50 m near the surface to 690 m at the bottom. Time stepping is asynchronous (Bryan 1984). This model reproduces reasonably well the known large-scale features of the ocean circulation. The Redi tensor allows for the diffusion of tracers along three-dimensional isopycnal surfaces instead of horizontally (Redi 1982). The Gent–McWilliams (GM) scheme parameterizes the advective effect of the geostrophic eddies by considering a “bolus velocity,” which is added to the Eulerian-mean velocity (Gent and McWilliams 1990; Danabasoglu and McWilliams 1995). For numerical reasons the skew flux scheme of Griffies (Griffies 1998) is used, ensuring a well-behaved GM formulation. Table 1 summarizes the values used for key model parameters.

b. Energy and moisture balance atmosphere

To investigate the impact of atmospheric feedbacks, an energy and moisture balance model is coupled to the ocean model. The model is drawn from the work of Wang et al. (1999a, b) and Nakamura et al. (1994) with some minor modifications. This energy and moisture balance atmosphere is a highly parameterized zonally averaged transport model. The latitudinal profiles of atmospheric heat and freshwater transport are specified from observations and held fixed throughout the integration. However, the amplitude of each profile is determined as a function of the meridional temperature gradient at the ocean’s surface. The wind stress is not interactive and is derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis data from 1980 to 1987 (Trenberth et al. 1989). Including an interactive dynamic atmosphere was beyond the scope of this project and would have likely compromised the ability to derive a meaningful adjoint solution.

The flux of heat per unit area at the ocean–atmosphere boundary is determined from the sum of the net radiative forcing and the divergence of the atmospheric heat transport. The shortwave flux is held constant and the net longwave flux is parameterized as a function of the temperature of the atmosphere at the surface.

The parameterization of the intensity of the eddy sensible and latent heat transport is based on baroclinic stability theory (Held 1978; Stone and Miller 1980) and takes the form of a power law of the temperature gradient at 35°N–S. The latent heat calculation is also scaled with temperature in accord with the Clausius–Clapeyron relation.

The flux of freshwater per unit area into or out of the ocean is given by the divergence of the atmospheric transport of water vapor (Fw). The observed runoff (R) of freshwater from land is added to complete the atmospheric water budget.

The intensity of the atmospheric freshwater transport is determined from the same empirical and theoretical concepts as the one for the heat transport (Stone and Yao 1990); its latitudinal distribution is specified from observations (Schmitt et al. 1989; Reeh 1994; Perry et al. 1996; Jiang et al. 1999). To maintain a stable meridional overturning, separate latitudinal profiles are used for the Atlantic and Pacific basins. A common profile is used over the Southern Ocean.

c. Model spinup and coupling

The ocean model is spun up from rest by imposing a Haney-type boundary condition on the temperature tendency equation and a virtual salt flux on the equation determining the evolution of the salinity field (Haney 1971). The model requires approximately 3000 years for the deep ocean to equilibrate with the forcing:
i1520-0442-19-15-3751-e1
i1520-0442-19-15-3751-e2
Here Qobs and (EPR)obs are the annual mean fields derived by Jiang et al. (1999) from Trenberth and Solomon (1994), Schmitt et al. (1989), Reeh (1994), and Perry et al. (1996). The Tobs is the Levitus temperature (Levitus and Boyer 1994) and λs = (1/60) days.

The freshwater forcing field derived from observations has large uncertainties. This flux was not corrected by a term relaxing salinities toward observations. The unphysical nature of that type of boundary condition would have severely compromised the oceanic feedback mechanisms.

The energy and moisture balance model is coupled by changing the surface boundary conditions to the following form:
i1520-0442-19-15-3751-e3
i1520-0442-19-15-3751-e4
The subscript “mod” indicates the use of model fluxes. The relaxation of the sea surface temperature toward its zonal mean, Tzon, on a λ−1m = 60 day time scale is added to reproduce the effect of the atmospheric circulation, which is predominantly zonal. The observed runoff is from Reeh (1994) and Perry et al. (1996), it is scaled by a factor δ to ensure conservation of mass in the system. The coupled configuration of the model is integrated for a further 3000 years to allow for a complete equilibration.

Including seasonality in the forcing fields was beyond the scope of this initial analysis and the impact of a seasonal cycle on the sensitivity patterns remains to be investigated. It is, however, likely that by creating episodic convection, seasonally varying forcing could have a large impact on the high-latitude sensitivity fields and may make the model altogether undifferentiable.

d. Equilibrated state

The sea surface temperature at the end of the spinup period is similar to the Levitus climatology. The temperature after coupling and equilibration (not shown) has a more zonal structure, a consequence of the zonal nature of the energy balance model and of the relaxation of the sea surface temperatures to the zonal mean. The effect of the Gulf Stream and North Atlantic currents on the temperature distribution is, however, still clearly visible. The global average sea surface temperature differs by less than 0.3°C between the ocean-only and the coupled cases; both are very close to the observations.

The sea surface salinities diagnosed at the end of the ocean’s spinup run are in good agreement with observations in the Atlantic basin. The Pacific basin and the Southern Oceans are, however, fresher than observed. The global average sea surface salinity is 1.7 psu lower than observed, which is compensated by greater salinities at depth. Deviations in salinity are a common problem in ocean GCMs forced with freshwater or virtual salt fluxes (Jiang et al. 1999) because those fluxes are poorly known (Schmitt et al. 1989).

The salinity gradient in the Northern Atlantic in the coupled model is still weaker than observed, and the Southern Oceans are still too fresh; the overall sea surface salinity is, however, closer to observations by 1 psu.

The intensity of the MOC in the Atlantic is best compared to the estimates of 17 Sv (1 Sv ≡ 106 m3 s−1) derived at 24°N by Roemmich and Wunsch (1985) and of 15 Sv at 55°N estimated with inverse modeling methods by MacDonald and Wunsch (1996) and Ganachaud and Wunsch (2000). The MOC peaks at 29 Sv close to 55°N at the end of the spinup run; it is 17 Sv at 24°N (Fig. 1). The peak intensity decreases by 3 Sv after coupling in the energy and moisture balance model while the transport at 24°N increases by 2 Sv. These changes are relatively minor and indicate that the coupled model establishes a steady state, which is similar to the stable state obtained at the end of the ocean’s spinup.

At 24°N, the meridional overturning advects 1.1 PW northward in the Atlantic and the gyre contributes 0.1 PW of southward heat transport. The total heat transport in the Atlantic is within the uncertainty of the estimates derived by Ganachaud and Wunsch (2000) with inverse modeling methods, Trenberth and Caron (2001) from reanalysis data, or Hall and Bryden (1982) and Bryden et al. (1991) from hydrographic section data.

Both models underestimate the heat transported by the Pacific and Indian Oceans; this explains why the overall oceanic heat transport at 24°N is smaller by 0.5–0.9 PW than most observations. The atmospheric component of the coupled model transports 3.5 PW of heat in the Northern Hemisphere and 4 PW in the Southern Hemisphere, slightly less than observations (Trenberth and Caron 2001).

e. The adjoint model

The adjoint model provides the sensitivity of a diagnostic, here the strength of the MOC and the heat transport in the Atlantic, to all model parameters and boundary conditions in a single integration.

While this is an efficient way of providing complete sensitivity maps, the adjoint method is a linearization that requires the perturbation growth to remain linear to be valid. Previous work has shown that the adjoints of coarse-resolution ocean models remain accurate for 1–2 yr (Marotzke et al. 1999; van Oldenborgh et al. 1999; Galanti and Tziperman 2003). In the present configuration, the adjoint remains accurate over the 400-yr time scale of the experiments. The accuracy of the adjoint solutions was validated through a series of perturbation runs with the forward model, by adding a 1% perturbation to a single parameter at a single grid point. After 400 yr, the difference between the adjoint solution and the finite difference is 2.6% and never worse than 8%.

The adjoint model was integrated for 400 yr, which is sufficient for the sensitivities to all but the ocean’s slowest processes to have reached a quasi equilibrium. The model remains differentiable, in part, because the GM isopycnal mixing replaces convective mixing in regions of steeply sloping isopycnals during the model spinup.

f. Cost functions

Two different diagnostics of the circulation are used to verify the robustness of the solutions. The first is the average value of the meridional streamfunction ψ in the neighborhood of its maximum, between latitudes ϕ = 52° and 60°N at depths between 1055 and 1395 m in the Atlantic basin:
i1520-0442-19-15-3751-e5
The second diagnostic is the amount of heat transported by the zonally averaged circulation at 24°N in the Atlantic:
i1520-0442-19-15-3751-e6
Both diagnostics are highlighted in Fig. 1.

These two diagnostics allow us to separate features of the sensitivity patterns that are independent of the precise choice of the cost function from features that are strongly related to the local definition of the diagnostic. The robust patterns can be expected, a priori, to have the same sign since both the heat transport at 24°N and the maximum value of the streamfunction are positive. All results show sensitivities per model grid point; the sensitivities to diapycnal mixing are integrated through the water column.

g. Sensitivity to time-dependent forcing

In its uncoupled configuration, the ocean model is forced by a flux of freshwater that is fixed in time. In the coupled model, the freshwater flux is recalculated by the energy and moisture balance model at every time step. The adjoint sensitivity is therefore an initial value sensitivity. To reconstruct the sensitivity at time T to a perturbation applied and maintained from t = 0 to t = T, sensitivities need to be integrated over time:
i1520-0442-19-15-3751-e7
To obtain an accurate pattern, initial value sensitivities were calculated on a monthly basis for the first year, yearly for the next 10 years, and every 25 years for the remaining time period.
The same procedure is used to calculate the sensitivity to the heat flux forcing in the coupled model. The heat flux sensitivity in the stand-alone ocean model requires a similar procedure because of the time-dependent sensitivity to the surface temperature in the restoring term:
i1520-0442-19-15-3751-e8
In practice, the sensitivity to the surface temperature (∂ψMAX/∂T0) drops off quite rapidly and the climatological sensitivity is therefore determined by the boundary value sensitivities to the observed heat flux and restoring sea surface temperature.

3. The role of buoyancy forcing in convection and downwelling

Deep oceanic convection in the North Atlantic is driven by localized intense cooling events in the Norwegian, Labrador, and Greenland Seas. The near-surface buoyancy loss destabilizes the water column, which overturns and becomes vertically homogeneous on fairly rapid time scales (Jones and Marshall 1993). The hypothesis originally suggested by Stommel (1961) and later Broecker et al. (1985), and adopted by many authors (Broecker et al. 1990; Zaucker et al. 1994; Manabe and Stouffer 1995; Weaver 1995; Rahmstorf 1995) is that convection drives the MOC by forcing a southward flow at depth through mass convergence in the downwelling branch. Highly idealized simulations have, however, showed that convective mixing and downwelling are not necessarily collocated; it is the zonal density and pressure differential set up by the convection and downwelling patterns that drives the southward flow of the abyssal waters (Marotzke and Scott 1999).

a. Heat flux

The sensitivity pattern to the heat flux forcing is similar in both uncoupled (Fig. 2, top) and coupled cases (Fig. 3): both peak in the northern part of the Atlantic basin where convection is taking place. The maximum is in the Greenland Sea in the uncoupled version of the model and in the Labrador Sea in the coupled version. This is due to slightly different convection patterns in the two configurations. The sign of the sensitivity is such that an increase in the loss of heat by the ocean to the atmosphere (ΔQ > 0) leads to an increase in the magnitude of the streamfunction (ΔψMAX > 0). The flow patterns at depth (not shown) shows currents connecting the convection site with the deep western boundary current. The density of the deep western boundary current is therefore primarily determined by convection in the Labrador and Greenland Seas, hence, the large sensitivities at those sites.

Advective ocean temperature feedbacks do not play a role in the uncoupled model. Even the most rapid currents in the model will not transport information over more than a few hundred kilometers without seeing most of it dissipated by the relaxation time scale imposed on the SST. This confines large sensitivities to the neighborhood of the convection site.

The atmosphere communicates information across and between basins much more rapidly, which is evident from the zonally banded structure of the sensitivity pattern in Fig. 3. Sensitivities in the Northern Hemisphere are slightly positive in the 0°–35°N latitude band; they are slightly negative between 35° and 55°N and in the extreme northern part of the Atlantic basin. Adding heat into the ocean in the Tropics (ΔQ < 0) increases the equator–Pole temperature contrast, and by extension the south–north heat and moisture transport in the atmosphere. This increases high-latitude temperatures and decreases the salinity in that region. Both increase the water’s buoyancy near the sites of convection, which inhibits the overturning. The reverse logic applies north of 35°N, where increasing the flux of heat into the ocean will reduce the north–south temperature gradient, thereby increasing the overturning.

Because of the zonal nature of the atmospheric model, a perturbation imposed in the subtropical Pacific has the same impact on atmospheric transport and buoyancy in the northern Atlantic as a perturbation in the subtropical Atlantic. The instantaneous and absolute nature of this transport is one of the less realistic features of the model.

The patterns of sensitivity to the heat flux are quite robust to the definition of the diagnostic. High sensitivities are still observed in the Labrador and Greenland Seas when the definition of the cost function is the heat transport at 24°N (see Figs. 2 and 5). The negative sensitivities at 24°N in the eastern Atlantic are a local feature associated with that cost function.

b. Freshwater flux

The sensitivity of the overturning to the net freshwater forcing in the uncoupled (Fig. 2) and coupled models (Fig. 4) has a clear maximum in the polar region in the same location as the maximum sensitivity to the heat flux forcing.

The flux boundary condition on the surface salinity does not impose any constraint on the oceanic salt advection feedback, allowing the sensitivities to freshwater forcing to spread to the rest of the oceans. The sign of the sensitivity is such that a positive salinity perturbation (ΔFW > 0, i.e., more evaporation or less precipitation) increases the overturning. The salt advection feedback is positive: the overturning contributes to the transport of freshwater anomalies toward the Pole, where it can weaken the overturning, thereby reducing the advective mechanism (Marotzke and Stone 1995).

The role played by advection is evident from the development of the sensitivity (not shown): after approximately 50 years, moderate sensitivity values are seen extending westward from the Drake Passage into the Antarctic Circumpolar Channel (ACC) and eastward from the Cape of Good Hope into the Indian Ocean; they extend beyond the Indonesian throughflow to the tropical Pacific after 100 years. Since surface salinity perturbations have no direct impact on the atmospheric heat and moisture transport, the pattern calculated with the coupled model (Fig. 4) shows very similar advective pathways. These pathways, along with a new route dubbed the Tasman Leakage, are clearly identified in Lagrangian trajectory studies (Speich et al. 2001, 2002).

4. Mixing and tropical upwelling

The ocean is heated at the surface. According to Sandström’s theorem, which states that thermal forcing can only sustain a circulation if heating takes place at greater depth than cooling, this should confine the meridional overturning to a thin surface layer, leaving the abyss motionless (Sandström 1908). A deep circulation can only exist if the geopotential of the heating is lowered (Jeffreys 1925; Wunsch 2005). This can be achieved by mixing heat downward, through turbulent breaking of internal gravity waves (Gregg 1987; Polzin et al. 1997), a process parameterized by diapycnal diffusion in coarse-resolution models. Tides and wind stress are thought to provide the source of energy required to generate the ocean’s internal gravity wave spectrum (Munk and Wunsch 1998). While the deep ocean may be close to a vertical advective–diffusive balance, the upper-ocean certainly is not (see, e.g., Samelson and Vallis 1997). Ekman upwelling in the regions of wind stress divergence can, for example, influence the vertical velocity field and the structure of the thermocline (Vallis 2000), while the horizontal advection terms often dominate the heat budget.

The sensitivity to a column-by-column perturbation in diapycnal mixing (Fig. 6) is fairly robust, both to a change in cost function and to coupling to the atmosphere (Fig. 7). The equatorial and tropical regions dominate in all cases. The importance of the equatorial region can be traced to large sensitivities in the near-surface layers between 100 and 200 m. The connection to the wind stress divergence and Ekman up- and downwelling patterns is logical: Ekman upwelling compresses isopycnals in the equatorial region, thereby increasing the efficiency of the downward diffusion of heat. This process is particularly effective in the eastern part of the basin, where the easterly wind stress lifts the thermocline. Sensitivities are weaker outside of the band of Ekman upwelling because of the decrease in stratification associated with the downward motion.

There are two key differences between the coupled and uncoupled models. The streamfunction maximum is more sensitive to changes in the equatorial diffusivity when atmospheric feedbacks are included, and the sensitivities extend into the Pacific and Indian Oceans. The role played by the atmosphere is straightforward. Increasing diffusivities in a positively stratified environment will draw heat downward from the surface, thereby cooling it. This reduces the meridional temperature contrast and its associated atmospheric heat and moisture transport. The net result is to reduce the buoyancy of the water in the North Atlantic. The sensitivity analysis of the overturning to buoyancy forcing indicates that this will increase the intensity of the overturning circulation. This process is reversed north of 35°N, which explains the negative sensitivity bands in midlatitudes. The sensitivity pattern to wind stress (Fig. 8) is in many respects similar to the sensitivity to mixing, and can be explained by the effect of wind stress perturbations in inducing local upwelling and cooling of the surface.

5. Wind stress in the Southern Oceans

In a latitude band with no continental barriers, notably in the ACC, zonal mean pressure gradients must vanish. Toggweiler and Samuels (1995) outlined the following hypothesis: the divergence of the Ekman transport in the latitude band of the Drake Passage can only be balanced geostrophically below the depth of the topographic ridges. The vertical flows associated with this circulation could draw up much of the deep water formed in the northern part of the basin. Note that eddy transports cancel much of this Ekman-induced Deacon cell, but do not suppress it entirely (Danabasoglu and McWilliams 1995). Tsujino and Suginohara (1999) and Klinger et al. (2003, 2004) have questioned whether zonal periodicity is required for this mechanism to work. These authors have also analyzed the relative importance of wind stress in the polar versus subpolar regions in determining the strength of the MOC.

Three areas show unexpectedly high sensitivities to wind stress (Fig. 9): the region that includes the Agulhas Current and the Agulhas retroflection south of the Cape of Good Hope, the Indonesian throughflow, and the Chilean coastline. Between them, these three regions largely control the properties of the surface water exchanged between basins. The Agulhas Current and the Drake Passage allow water to flow into the Atlantic from the Indian and Pacific basins, and the Indonesian archipelago allows the exchange of water between the Pacific and the Indian Oceans.

Increasing the strength of the westerlies in the Agulhas basin (40°S) reduces the convergence of the Ekman transport, thereby weakening the Deacon cell. Increasing the winds where they peak (near 50°S) tends to intensify the Deacon cell. One could, therefore, anticipate positive sensitivities around 50°S and negative sensitivities farther north and south. This is approximately what is observed south of Africa in Fig. 9, but not throughout the rest of the ACC. A closer look at the vertical velocity pattern also highlights some unresolved issues. The wind-driven Ekman up- and downwelling extends at most to depths of 200 to 300 m. Below that level, vertical motion is confined to the vicinity of coastlines and sills. The highest sill and highest upwelling velocities are in the Drake Passage between Cape Horn and the Antarctic Peninsula. There is, however, very little sensitivity to the wind stress in that region. An idealized rectangular basin model is helpful in elucidating the channel dynamics. Figure 10 shows the sensitivity of the streamfunction maximum to the zonal wind stress in the region of the ACC for restoring mixed and flux surface boundary conditions. The sensitivities in the channel are 3 times larger under restoring boundary conditions than under flux boundary conditions. Rahmstorf and England (1997) performed similar experiments, with similar conclusions. These authors attributed the difference in sensitivity to the stabilizing thermal feedback effect: reduced heat transport leads to surface cooling in the convective region, which in turn enhances the overturning. This feedback is absent under restoring boundary conditions. While Rahmstorf and England (1997)’s focus was a feedback effect acting through advection in the North Atlantic, a similar feedback plays a role locally in the ACC. Wind stress perturbations induce similar responses in the Eulerian circulation in the three cases, but the eddy transport cancels much of the perturbation Eulerian circulation under mixed or flux boundary conditions. This bolus transport is associated primarily with salinity anomalies, which are suppressed under restoring boundary conditions.

The mechanism outlined by Toggweiler and Samuels (1995) plays a crucial role in determining the strength of the meridional overturning when the surface boundary conditions are formulated as restoring terms [this was the case in their analysis as in Tsujino and Suginohara (1999); Klinger et al. (2004)]. This mechanism does, however, lose much of its effectiveness when the surface fields are allowed to evolve constrained only by surface fluxes of heat and freshwater or in coupled models.

A second hypothesis is therefore proposed to explain the observed sensitivity pattern. It relies on a direct control of the properties, and in particular of the salinity, of the water allowed to enter or leave the Atlantic basin. It rests on the premise that the Atlantic is the saltiest of the world’s oceans.

Relying on the hypothesis that much of the North Atlantic Deep Water upwells in the Pacific and Indian Oceans, Gordon (1986) proposed two routes for the return flow of thermocline water: a cold water route through the Drake Passage and a warm water route by a branch of the Agulhas Current. Based on water temperature and heat flux characteristics, Gordon (1986) suggested that the warm water route was of primary importance. Rintoul (1991) used an inverse modeling approach and concluded that most of the water entered the South Atlantic via the cold water route of the Drake Passage.

Complex interactions exist over the Agulhas Plateau between the surface wind stress and the ocean currents. The model surface currents are shown for reference in Fig. 11. A branch of the Agulhas Current imports Indo-Pacific water (34.6 psu in the model) into the Atlantic. A westerly wind perturbation in that region would eventually weaken the meridional overturning. The region of positive sensitivity just south of the Agulhas retroflection exports Atlantic water to the rest of the world’s oceans. The same westerly wind perturbation imposed in that region would increase the overturning. Similarly, hindering the mass flow through the Indonesian throughflow increases the overturning. A southerly wind perturbation along the Chilean coastline (Fig. 9, bottom panel) would increase the overturning by diverting water out of the ACC, instead of allowing it into the Atlantic.

We know from the sensitivity to the freshwater flux (Fig. 2, bottom panel) that an increase in salinity in the Atlantic basin increases the overturning. The sign of the sensitivity at the gateways is related to the control, which wind stress exerts on the import and export of fresher water into the Atlantic basin. The Philippine and South China Seas, and the Chilean waters have some of the ocean’s lowest salinities (∼31 psu). Those are in fact some of the regions of largest discrepancy with the Levitus salinity climatology (Levitus et al. 1994).

Solid evidence for this hypothesis can be gathered through a simple perturbation analysis. A westerly wind stress perturbation of magnitude Δτx = 0.005 N m−2 was added at 42° and 30°S (both at 22°E). The resulting equilibrated response in the sea surface salinity and near surface currents is shown in Fig. 12. The perturbation imposed at 30°S (left panels), south of the Cape of Good Hope, weakens the model Agulhas Current. The model Benguela Current, which is fresher than the Agulhas, increases its strength to maintain a constant import of thermocline water into the Atlantic, thereby increasing the import of very fresh Southern Ocean water into the Atlantic at the expense of the saltier Indian Ocean water. The perturbation applied at 42°S (right panels), weakens the Benguela Current at the expense of the Agulhas branch, thereby allowing an increase in salinity of the Atlantic basin, and an increase in the meridional overturning’s strength.

This “gateway effect” is, however, weaker when the interactive energy and moisture balance atmosphere is coupled to the ocean model (see Fig. 8). The atmosphere’s response to the wind-induced temperature anomalies overwhelms the advective effects. The role of wind in the coupled model is predominantly a direct control of up- and downwelling in the Tropics.

6. Discussion

This paper has demonstrated that it is possible to calculate adjoint sensitivities on climatological time scales in coarse-resolution ocean and coupled models. Although this modeling framework reproduced reasonably well the large-scale features of the ocean’s circulation, a number of physical processes were represented in simplified terms, notably the resolution of the ocean’s mixed layer and of the western boundary current. The role of eddies in transporting tracers was parameterized in this model. Deriving the adjoint of an eddy-resolving model may present issues related to the rapid loss of information in shedding and reabsorbing eddies (Lea et al. 2000; Köhl and Willebrand 2001).

One advantage of the adjoint method is that it provides complete two- or three-dimensional maps of the sensitivity to parameters such as wind stress, buoyancy, or mixing. The adjoint method allows us to identify the sites or regions that have a key influence on the diagnostic. The present analysis has shown that, within this simplified framework, the MOC is most sensitive to direct heat flux forcing in the region where convection takes place, in the Labrador and Greenland Seas. The sensitivity to evaporation and precipitation is, however, concentrated in the Tropics of both hemispheres. How are temperature and salinity perturbations linked to the overturning? The first hypothesis relates changes in buoyancy to the “efficiency” of convection, and by extension downwelling and the overturning (Rahmstorf 1994). More precisely, the role of convection is to set the density of the deep western boundary current and of much of the western boundary. The “efficiency” of convection is really the control that it exerts on the zonal density contrast below the thermocline (Marotzke 1997; Scott and Marotzke 2002). The advection of salinity perturbations toward the sites of convection and downwelling by the Gulf Stream in the subtropical gyre and by the eddies in high latitudes is a key determinant of the sensitivity patterns. Atmospheric feedbacks play a role in the coupled model in setting a global sensitivity pattern to heat flux perturbations. These results support the notion that the MOC is thermally driven (Rahmstorf 1996) and inhibited by a net input of freshwater.

The second hypothesis focuses on the influence of temperature and salinity perturbations on the density of the abyssal water, and by extension on the amount of “mixing,” here diffusion, which must take place to upwell these waters. One would expect that, for constant diapycnal diffusivity, an increase in density would decrease the overturning. This is not observed. The third hypothesis links surface freshening or increases in temperature, notably in the Tropics, to a decrease in the buoyancy differential between surface and subthermocline waters. For a constant diffusivity, this should allow more upwelling (Huang 1999). The positive sensitivities to heat loss and evaporation contradict this hypothesis.

The adjoint model confirms the results of Scott and Marotzke (2002), that the overturning was most sensitive to changes in mixing in the Tropics. By increasing the stratification, wind-induced Ekman upwelling further increases the efficiency of the vertical mixing of heat. The atmosphere compounds this mechanism by allowing a direct feedback between a cooling of the surface waters in the Tropics and a decrease in the buoyancy of the water in the northern part of the Atlantic where convection and downwelling take place.

The hypothesis of a control of the overturning by upwelling in the Drake Passage was confirmed by the adjoint analysis only within the framework of pure restoring surface boundary conditions. Little support exists when the sea surface temperature and salinities are less constrained, notably under mixed boundary conditions and in the coupled model because the bolus transport associated with buoyancy perturbations cancel much of the upwelling associated with wind stress perturbations.

More evidence can be found to support a “gateway” hypothesis, with a three-way balance between the “cold water route” through the Drake Passage, the “warm and freshwater” route of the Benguela Current and the “warm and salty” water route of the Agulhas Current setting the salinity of the Atlantic Ocean and by extension the intensity of the MOC. This model does not address the question of the relative contributions of these regions to inflow of thermocline water into the Atlantic. It is unfortunate that large discrepancies exist in those regions between the Levitus climatology and the model’s surface salinity. More accurate forcing fields could remedy this problem.

In the coupled model, wind stress in the Tropics sustains the overturning through equatorial Ekman upwelling. Atmospheric feedback effects link directly the Tropics and the polar region where convection takes place. Wind in the Southern Oceans plays little role.

An important conclusion of this paper is the critical influence of the formulation of boundary conditions on the model’s sensitivity to perturbations; this is also explored in Bugion et al. (2006). The sensitivity to wind stress in the Southern Oceans proves this point quite dramatically. Circulation patterns, which may appear equally consistent with observations when forced with restoring terms or flux boundary conditions, can respond in very different ways to perturbations and changes in forcing. This limits the ability to draw robust conclusions from models forced with unphysical boundary conditions, such as salinity restoring terms. It also highlights the importance of providing physically meaningful boundary conditions to ocean models. The differences between the sensitivity patterns obtained with the ocean and coupled models also points to limitations in the former category of models, and suggests that this analysis be repeated with an atmospheric model with more complete physics and dynamics.

Acknowledgments

The research presented here was partially supported with funds from the U.S. Department of Energy.

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Fig. 1.
Fig. 1.

Meridional streamfunction in the coupled model (in Sv): (top) global streamfunction integrated across the basins, (middle) streamfunction in the Atlantic basin, and (bottom) streamfunction in the Pacific. The boxed in area and section represent the diagnostics used in this study.

Citation: Journal of Climate 19, 15; 10.1175/JCLI3821.1

Fig. 2.
Fig. 2.

Sensitivity of the maximum value of the streamfunction ψMAX to the (a) heat flux: (∂ψMAX/∂Q) in Sv W−1 m2 and to the (b) freshwater flux: (∂ψMAX/∂Fw) in Sv m−1 s in the ocean model.

Citation: Journal of Climate 19, 15; 10.1175/JCLI3821.1

Fig. 3.
Fig. 3.

Sensitivity of the maximum value of the streamfunction ψMAX to the heat flux: (∂ψMAX/∂Q) in Sv W−1 m2 in the coupled ocean–energy–moisture balance model.

Citation: Journal of Climate 19, 15; 10.1175/JCLI3821.1

Fig. 4.
Fig. 4.

Sensitivity of the maximum value of the streamfunction ψMAX to the freshwater flux: (∂ψMAX/∂Fw) in Sv m−1 s in the coupled ocean–energy–moisture balance model.

Citation: Journal of Climate 19, 15; 10.1175/JCLI3821.1

Fig. 5.
Fig. 5.

Sensitivity of the heat transport at 24°N to the heat flux: (∂HT/∂Q) in PW W−1 m2 in the ocean model.

Citation: Journal of Climate 19, 15; 10.1175/JCLI3821.1

Fig. 6.
Fig. 6.

Sensitivity of the maximum value of the streamfunction ψMAX to a column-by-column perturbation in the diapycnal mixing in the ocean model: (a) (∂ψMAX/∂κd) in Sv m−2 s and (b) (∂HT24°N/∂κd) in PW m−2 s.

Citation: Journal of Climate 19, 15; 10.1175/JCLI3821.1

Fig. 7.
Fig. 7.

Sensitivity of the maximum value of the streamfunction ψMAX to a column-by-column perturbation in the diapycnal mixing: (∂ψMAX/∂κd) in Sv m−2 s in the coupled model.

Citation: Journal of Climate 19, 15; 10.1175/JCLI3821.1

Fig. 8.
Fig. 8.

Sensitivity of the maximum value of the streamfunction ψMAX to the wind stress: (top) zonal wind stress (∂ψMAX/∂τx). (bottom) Meridional wind stress (∂ψMAX/∂τy) in Sv N−1 m2 in the coupled ocean–energy balance model.

Citation: Journal of Climate 19, 15; 10.1175/JCLI3821.1

Fig. 9.
Fig. 9.

Sensitivity of the maximum value of the streamfunction ψMAX to the wind stress: (top) zonal wind stress (∂ψMAX/∂τx). (bottom) Meridional wind stress (∂ψMAX/∂τy) in Sv N−1 m2 in the ocean model.

Citation: Journal of Climate 19, 15; 10.1175/JCLI3821.1

Fig. 10.
Fig. 10.

Sensitivity of the streamfunction maximum to the zonal wind stress (∂ψMAX/∂τx) in Sv N−1 m2: (a) restoring boundary conditions, (b) mixed boundary conditions, and (c) flux boundary conditions. The three plots are on the same scale.

Citation: Journal of Climate 19, 15; 10.1175/JCLI3821.1

Fig. 11.
Fig. 11.

Surface currents around the African continent. The ocean model.

Citation: Journal of Climate 19, 15; 10.1175/JCLI3821.1

Fig. 12.
Fig. 12.

(a), (b) Difference in salinity (in 10−3 psu) between simulations with a wind stress perturbation (Δτx = 0.005 N m−2) imposed at (left) 30°S and (right) 42°S (both at 22°E), with an unperturbed simulation. (c), (d) Same as in (a), (b), but for the difference in near-surface currents (in m s−1), with the ocean model.

Citation: Journal of Climate 19, 15; 10.1175/JCLI3821.1

Table 1.

Model parameters.

Table 1.
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