1. Introduction
The ability to represent the oceanic response to changes in mechanical and buoyancy forcings is of fundamental importance for understanding the climatic impact of increasing concentrations of atmospheric greenhouse gases (GHGs). The Southern Ocean is a key player in the earth’s climate for its importance in the global ocean circulation and water mass formation, interbasin connections, and air–sea exchanges of heat, freshwater, and tracer gases. The Antarctic Circumpolar Current (ACC), with a volume transport of 130–150 Sv (Sv ≡ 106 m3 s−1), is the strongest and longest current system in the World Ocean, linking all major ocean basins, and is related to a global meridional overturning circulation (MOC) that is responsible for a large meridional transport of heat and vertical transfer of carbon dioxide between the surface layers and the deep ocean (Rintoul et al. 2001). The interplay between the physical and biogeochemical systems could be shifting to a different equilibrium, as Southern Ocean temperatures, winds, and carbon uptake seem to be changing as a result of anthropogenic global warming (Gille 2002; Fyfe and Saenko 2006; Le Quéré et al. 2007).
Mesoscale oceanic eddies are believed to play a crucial role in the dynamical and thermodynamical balance of the Southern Ocean, contributing to the transport and mixing of tracers across the Southern Ocean and redistribution of momentum, potential vorticity, and energy (Ivchenko et al. 2008). Eddy fluxes must be parameterized in coarse-resolution climate models, with few examples of eddying climate models available. Because of the ubiquitous nature of energetic mesoscale eddies, as revealed by remote sensing of sea surface topography (e.g., Chelton et al. 2007), their parameterization is crucial for a correct representation of the meridional transport of tracers and eddy–mean flow interactions. Unlike most of the World Ocean, the ACC is a region where mesoscale eddies have first-order effects on the meridional transport of heat and other tracers (Ivchenko et al. 2008).
To recognize the importance of the Southern Ocean energetic eddy field, it is informative to compute the baroclinic time scale, Tbc = f −1
A complete dynamical understanding of the mechanisms setting the strength of the ACC and its associated MOC is still lacking, although theoretical (Karsten et al. 2002; Marshall and Radko 2003; Olbers et al. 2004; Olbers and Visbeck 2005) and modeling (Hallberg and Gnanadesikan 2001, 2006; Treguier et al. 2007) efforts have advanced our understanding. Marshall and Radko (2003) put forward a residual-mean framework for the Southern Ocean in which an Eulerian mean and an eddy-induced (or “bolus”) circulation set the total (or residual) MOC streamfunction. The Eulerian circulation is largely controlled by the northward wind-driven Ekman transport, whereas the eddy-induced circulation is believed to be generated by a vertical transfer of momentum by interfacial form stress. Northward Ekman fluxes act to increase the tilt of the isopycnals generating a store of APE in the ACC density front. The potential energy is then removed by baroclinic instability processes, spawning mesoscale eddies and resulting in a flattening of the isopycnals. Thus, since the mean and eddy-induced circulations oppose each other in the Southern Ocean, the balance between the two circulations will set the stratification across the ACC, its baroclinic transport, and overall residual MOC. For extensive reviews on the subject see Rintoul et al. (2001) and Saenko (2007).
Perhaps of equal importance to the above ideas of dynamical balances in the ACC system is the ongoing debate on the sensitivity of the Southern Ocean system to climate variability and change. Most state-of-the-art global coupled climate models predict an increase in the transport of the ACC owing to the projected strengthening in wind stress over the Southern Ocean (Fyfe and Saenko 2006). However, recent observational evidence (Böning et al. 2008) and fine-resolution ocean modeling studies (Hallberg and Gnanadesikan 2006; Meredith and Hogg 2006; Screen et al. 2009) suggest that eddy activity is also enhanced by anomalous surface forcing, leading to a compensation between equatorward Ekman transport and poleward eddy fluxes. Eddies are thus believed to act as a buffer against wind changes and, when this effect is properly represented in models, the isopycnal slope, ACC strength, and Southern Ocean MOC become fairly insensitive to projected climate change scenarios.
In this paper we attempt to reconcile observations and coupled model results with idealized perturbation experiments performed with two coupled climate models whose main difference is in the resolution of the oceanic component. We test the ability of an eddy-permitting coupled model to reproduce the observed apparent insensitivity of the ACC system to altered surface forcings. We show for the first time that eddy compensation, although still not perfect, is indeed active in a global coupled model with explicit eddies. Contrary to coarse-resolution coupled models, the eddy-permitting version leads to a dynamical response in agreement with recent observations (Böning et al. 2008) and theoretical predictions (Marshall and Radko 2003). We do not expect the eddy-permitting model to resolve all mesoscale activity and at all latitudes; however, it provides us with eddy fluxes naturally arising from the flow that can be compared to parameterized solutions. The most widely used eddy parameterization scheme is the one developed by Gent and McWilliams (1990, hereafter GM90) and Gent et al. (1995) and is incorporated in our coarse-resolution coupled model. We analyze the behavior of parameterized eddies under altered climates and question the ability of present numerical implementations of eddy fluxes for coarse-resolution models to respond to significant alterations in surface fluxes.
The paper is organized as follows. In section 2 we describe the models and experimental design. The ACC dynamical responses to different anomalous forcings are given in section 3. The role of oceanic eddy heat fluxes is addressed in section 4, together with repercussions for the atmospheric energy transport. In section 5 we propose an explanation for the inability of the eddy parameterization scheme to react to intense modifications in local isopycnal slopes and conclude.
2. The models and numerical experiments
In this study we use two different versions of the GFDL coupled climate model. The first one is CM2.1, which was used for the recent Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4), ranking among the best models in terms of reproducing the Southern Hemisphere (SH) westerly winds and ocean circulation (Russell et al. 2006; Saenko 2007; Sloyan and Kamenkovich 2007). The ocean model resolution is 1°, with a progressively finer meridional resolution equatorward of 30° reaching ⅓° at the equator and 50 unevenly spaced vertical levels. Because of its coarse resolution, the model employs the GM90 eddy parameterization, as implemented by Griffies (1998), and an along-isopycnal diffusion of tracers (Griffies et al. 1998). The isopycnal diffusion coefficient κI is set to a constant value of 600 m2 s−1. The GM90 eddy transfer diffusion coefficient κgm is proportional to the horizontal density gradient vertically averaged over the depth range of 100–2000 m. Minimum and maximum values of κgm are set to 100 and 600 m2 s−1, respectively (see the appendix for more details). The atmospheric model uses the finite volume dynamical core of Lin (2004), with 24 levels and a horizontal resolution of 2.5° × 2°. The formulation of the CM2.1 ocean model component as well as the preindustrial and climate change simulations have been extensively documented (Griffies et al. 2005; Gnanadesikan et al. 2006; Delworth et al. 2006), hence our focus here will be mainly on the description of the differences with its successor.
The second model, CM2.4, is the result of an ongoing effort at GFDL to develop and use fully coupled climate models with progressively finer spatial resolution to study how the explicit inclusion of smaller-scale processes influences the simulation of climate variability and change. The ocean model is the Modular Ocean Model, version 4, (MOM4) (Griffies et al. 2005) and now uses a squared isotropic grid, where dx ≅ dy at all latitudes, similar to the Mercator grid in the ocean-only study of Treguier et al. (2007). The oceanic resolution is ¼° (or 27.75 km) at the equator and progressively increases toward the poles reaching 13.8 km at 60°N/S and 9 km at 70°N/S. In addition to finer resolution, the ocean climate model does not use a parameterization of mesoscale eddy mixing and has more accurate numerics and substantially smaller viscosity. Specifically, tracers are advected by the second-order moment scheme of Prather (1986) with a weak limiter that prevents overly sharp gradients. Therefore, no explicit lateral diffusivity is required for numerical closure. Also, lateral friction is treated by hyperviscosity using a biharmonic Smagorinsky closure that is based on the properties of the flow (Griffies 2004). Consistent with the move toward finer oceanic resolution, the atmospheric horizontal resolution was increased to 1° × 1°, with nearly identical atmospheric physics and numerics in CM2.1 and CM2.4. The coupled models have been run for multiple century experiments using the computing facilities available at GFDL.
For both models we have performed three different simulations as follows:
a control integration (CTL, 2000 yr long for CM2.1 and 240 yr long for CM2.4) in which GHG concentrations are held fixed;
a climate change scenario simulating an increase in concentration of GHGs (1Pct2X, 200 yr long for CM2.1 and 100 yr long for CM2.4, starting from year 101 of CTL), in which CO2 concentrations are increased by 1% yr−1 until doubled and held fixed after that point;
a SH momentum-flux perturbation experiment (SHW3X; 200 yr long for CM2.1 and 40 yr long for CM2.4, starting from year 141 of CTL) in which an anomalous wind stress pattern is added to the wind stress felt by the ocean between 20° and 75°S. Three time periods are chosen to provide initial conditions for a three-member ensemble. The wind stress anomaly is derived as the difference in the late twenty-first century between a CM2.1 simulation with A1B radiative forcing and the control simulation. The anomaly is constant in time and multiplied by a factor of 3 [see Delworth and Zeng (2008) for a full description on the methodology, where the anomaly pattern used in this study is referred to as POS_3X].
To capture the eddy dynamics, resolved or parameterized, we have saved extra high-frequency diagnostics during a 10-yr interval for all integrations. The eddy-diagnostics segment corresponds to model years 171–180 (see Fig. 3), immediately after the flattening of CO2 concentration in experiment 1Pct2X and includes the last available years for experiment SHW3X in CM2.4. We will see that this is long enough into the integration to distinguish a significant local response for both experiments. We tested the effect of temporal averaging on the model data and concluded that globally integrated energetic fields started to be degraded with means longer than 5 days. We thus use data averaged over 5-day intervals in our analyses and present mean quantities for the period 176–180 yr (our calculations have been found to be insensitive to the integration time interval).
a. Southern Ocean circulation in the models
Figure 2 shows the 5-yr time-averaged EKE on the surface geostrophic flow in CM2.4 and from a merged Ocean Topography Experiment (TOPEX)/Poseidon, European Remote Sensing Satellite-1 (ERS-1), and ERS-2 satellite altimeter product averaged over the 2003–07 period. The model is in remarkably good agreement with observations in both basin-scale features and magnitude of eddy structures. Highly energetic western boundary currents such as the Gulf Stream, Kuroshio Extension, and Agulhas Current are well supported by the model, while the variability of the subtropical regions is still underestimated. Furthermore, the Southern Ocean stands out as one of the most energetic regions of the World Ocean throughout the meandering ACC belt. Here, large-scale and topographically controlled features are successfully reproduced by the coupled model with similar peaks in magnitude. The concomitance of enhanced EKE and strong baroclinically unstable flows, such as the ACC, indeed suggest that the release of APE by baroclinic instability is a viable mechanism for the generation of geostrophic eddies, as also previously discussed with the help of Fig. 1. Results from CM2.1 are not shown, because the coarse-resolution model fails to represent any variability other than in the equatorial oceans.
b. Surface forcings
Momentum and buoyancy flux put energy into the general circulation in the form of potential energy (PE) and kinetic energy (KE). The main source of mechanical energy to the ocean circulation is provided by the input of energy through wind stress. Wind-energy input is mainly due to work done by the zonal wind in the Southern Ocean (∼80%) and, to a lesser extent, the Kuroshio and Gulf Stream regions (Wunsch 1998). In the Southern Ocean, the mechanical energy is stored in the form of PE in the steep isopycnal tilt and then eddies spawned by instability processes help transfer momentum downward, where it is ultimately dissipated by bottom form drag. Equally important, eddies carry heat and mass poleward, playing a fundamental role in setting the residual circulation.
More importantly, superimposed on interannual variations, the rate of work done on the geostrophic circulation has increased significantly in the last decades owing to the strengthening and poleward shifting of the zonal wind stress in the SH (Huang et al. 2006; Gillet and Thompson 2003), raising the fundamental question of what the dynamical response of the oceanic circulation is to the extra mechanical energy input, both locally and remotely. This question prompted us to perform two sets of idealized perturbation experiments, as described above. Experiment SHW3X will address the impact of enhanced and poleward displaced SH winds on the oceanic circulation both when eddies are parameterized (CM2.1) or partially resolved (CM2.4), extending the study of Delworth and Zeng (2008). Of course, under climate change scenarios, stronger midlatitude winds are accompanied by an overall warming and increased hydrological cycle, and the more traditional experiment 1Pct2X will include the effect of changes in buoyancy forcing.
Figure 3 shows the time series of annual-mean SH-integrated wind work for the CM2.4 CTL run and the two perturbation experiments. Both the time evolution of W in 1Pct2X and the instantaneous increase in the case of the “switch on” SHW3X integration are evident in Fig. 3, where the 10-yr time band during which eddy diagnostics were saved is highlighted in gray.
The resulting zonally averaged wind stress, its curl, and associated zonally integrated Ekman transport (−∫τx/( fρ0)dx) are shown in Fig. 4 for the SH. Note that the wind stress felt by the ocean in CM2.1 is almost indistinguishable from that of CM2.4 (thin black and blue lines in Fig. 4a), as is its curl and northward Ekman transport. Also, since we apply the same perturbations to both models, the relative changes will be the same. In SHW3X the wind stress anomaly is much stronger than in 1Pct2X, as it will test the ocean sensitivity to mechanical forcing only. As a consequence, the zero wind-stress curl moves farther south in this simulation, with enhanced Ekman pumping anomalies, and the northward Ekman flux is almost doubled. The perturbed wind stress—time dependent for 1Pct2X and constant for SHW3X—acting on the ocean surface implies an anomaly on the mechanical energy input on the geostrophic flow, most notably in the SH.
3. Southern Ocean response to forcings
a. Zonal transport
Recent modeling studies (e.g., Fyfe and Saenko 2006) have suggested that, because of the intensifying and poleward shifting SH westerly winds, the dynamical response of the wind-driven circulation in the Southern Ocean would result in the ACC to shift southward, as well as to increase its mean transport. However, it is also true that not all of the IPCC-class climate models agree on the sign of the change in strength of the ACC, suggesting that there is no consensus on the future trend of the ACC.
Figure 5 shows the time series of the volume transport across Drake Passage in the two GFDL models. Superimposed on the internal interdecadal variability, the model with parameterized eddies exhibits a reduction in ACC transport in response to increasing concentrations of GHGs (1Pct2X, Fig. 5a). Further, the abrupt inclusion of a large positive momentum flux anomaly into the Southern Ocean is followed by an intense dynamical adjustment, after which the ACC approaches a transport about 60 Sv more vigorous than in the control (SHW3X, Fig. 5b).
A different picture emerges in an eddy-permitting regime where eddies are explicitly represented, as is the case for CM2.4 shown in Figs. 5c,d. After 250 years of the model control run, the Drake Passage transport in the CM2.4 has not yet reached an equilibrated state, and it looks like this could approach a transport of around 190 Sv, which is significantly higher than observations (∼140 Sv, Cunningham et al. 2003). However, no significant divergence from the control emerges throughout the 100-yr-long integration of experiment 1Pct2X. The insensitivity of the ACC transport to changes in mechanical forcing is even more evident when tested with the SHW3X anomalous wind stress field, resulting in only a small offset toward higher values, with no apparent spinup adjustment (Fig. 5d).
b. Sea surface height
The sea surface height (SSH) is a consequence of interior flow dynamics and structure. In the Southern Ocean, where the meridional momentum balance is geostrophic, the eastward zonal flow is related through the thermal wind to meridional surface pressure gradients. Thus, one might expect to diagnose changes in meridional SSH gradients in relation to changes in the strength of the ACC transport. In our control integrations, the zonally averaged SSH differences across the ACC belt are 1.2 m for CM2.1 and 2 m for CM2.4, consistent with a stronger volume flux through Drake Passage for the eddy-permitting model. In the SHW3X simulations, meridional SSH gradients increase to 1.9 m (+58%) and 2.2 m (+10%) for CM2.1 and CM2.4, respectively. As also shown by Landerer et al. (2007), these anomalies in SSH difference across the ACC highlight changes in zonal transport through Drake Passage, as depicted in Figs. 5b,d, where the volume transport strengthens by 46% in CM2.1 and 6% in CM2.4.
Figure 6 shows the zonally averaged SSH anomalies for the perturbation experiments in both models. Under the SHW3X forcing, weaker changes in gradient are readily evident for the eddy-permitting CM2.4 compared to CM2.1 (red lines). The overall SSH changes are significantly smaller in the 1Pct2X scenario; thus, anomalies had to be computed further into the integration (years 196–200) to better show the differences between the two models (blue lines). Nevertheless, due to modifications of thermohaline properties of the water column, detectable increases in the gradient exist, most notably in the coarse-resolution CM2.1 integration. In light of the consistent relationship between SSH gradients and ACC transport, it seems possible that SSH anomalies from climate models and, when sufficiently long records become available, altimetric observations might be used as a proxy for ACC transport variability and change.
c. Meridional density structure
The wind-stress curl anomaly shown in Fig. 4b, with its associated Ekman pumping, can significantly modify the background meridional density gradient, thereby altering through geostrophy the ACC baroclinic transport. For example, an increase in Ekman transport would steepen the isopycnals and hence, in the absence of any compensatory mechanisms, result in a more vigorous baroclinic transport of the ACC (Saenko 2007). Whether isopycnals across the ACC do modify their tilt under projected climate change scenarios—and more importantly in the observational record—is a matter of debate in the community since the increase in slope resulting from coarse-resolution ocean models is not consistent with recent observations (Böning et al. 2008).
Thus, we compare next the response of the meridional density structure in the upper Southern Ocean in the two models and show the results in Fig. 7.
As a consequence of the anomalous surface buoyancy and momentum flux in experiment 1Pct2X, CM2.1 shows the expected deepening and steepening of isopycnals (Fig. 7a); the altered SH winds of SHW3X generate an even greater response in slope throughout the latitudes of the ACC (Fig. 7b), consistent with the speed up of the ACC found in Fig. 5. A radically different picture is readily seen in the CM2.4 simulation shown in Figs. 7c,d. Here, consistent with the insensitivity of the ACC transport, the same anomalous surface forcings are not followed by a significant increase in the meridional density gradient, even when the system is heavily forced as in SHW3X. These results seem consistent with recent ocean modeling (Hallberg and Gnanadesikan 2006) and observational (Böning et al. 2008) studies, suggesting a potentially large compensatory effect mediated by eddy fluxes. We proceed with an exploration of the role of the eddy-induced transport in setting the Southern Ocean residual circulation in the models.
d. Meridional overturning circulation
A question remains on how to specify the eddy transfer diffusivity. Assuming κ to be a constant would be rather unrealistic as large spatial variations have been observed, for example, in the ACC region (e.g., Karsten and Marshall 2002). Visbeck et al. (1997) proposed that κ should be proportional to the isopycnal slope, and we use a similar approach here (see the appendix for more details on the implementation of isopycnal diffusion and eddy-induced advective processes in our coarse-resolution model). We note that, in the Southern Ocean, the mean transport is directed equatorward, while the eddy-induced transport is poleward, acting to relax the polar sloping front. Thus, the two opposing components will set the residual circulation, and we can envisage a strong dependence on the choice for the eddy closure and eddy transfer coefficient in this balance.
The broad features of the global residual MOC are maintained when comparing the two models with parameterized and permitted eddies (Fig. 8). However, some potentially important differences arise, especially in the Southern Ocean. Three main cells characterize the overturning streamfunction in the SH: the subtropical, the subpolar, and the deep cell (Fig. 8). Of these three, the subtropical cell remains unchanged across the two models, because it is mostly wind driven. The subpolar and in particular the deep cell strengthens in CM2.4. The deep cell is about four times stronger in the eddy-permitting case, likely because of a better topographical representation giving rise to a greater formation of Antarctic Bottom Water (AABW), as also suggested in Roberts et al. (2004). Enhanced diapycnal mixing over rough topography and a better represented, and more vigorous eddy-induced circulation might also drive the strength of the deep AABW cell (Ito and Marshall 2008). Within the subpolar cell, a so-called Deacon cell stands out in both models. It is well known that its existence is a consequence of representing the Southern Ocean circulation on depth space. Hence, for the remainder of the paper, we turn to potential density as our vertical coordinate for a correct representation of the transport of water masses (e.g., Hallberg and Gnanadesikan 2006; Treguier et al. 2007).
We start by describing results from the coarse-resolution case in which the transient meridional transport and its response to climate change relies on the GM90 parameterization. The residual, Eulerian, and eddy-induced contributions to the meridional circulations are shown in Fig. 9 for the CTL and 1Pct2X experiments. The strengthening of the SH westerly winds under the global warming scenario induces a stronger Eulerian circulation cell that, consistent with previous studies, intensifies by ∼6 Sv at the time of CO2 doubling (Saenko et al. 2005). The change in the mean transport, however, is not followed by an intensification of the eddy-induced transport (Ψ*GM, Fig. 9 bottom), which only increases ∼0.5 Sv, resulting in a change in residual transport entirely set by Eulerian changes.
A similar picture emerges from the SHW3X experiment in which the Eulerian transport increases by up to 15 Sv, again with differences <1 Sv in Ψ*GM (not shown). The inability of the GM90 parameterization, as implemented in GFDL models, to react to strong variations in local isopycnal slopes seems a robust feature (remember that SHW3X consists of a three-member ensemble), raising concerns over its implications for climate change simulations. We will expand on this topic in section 5 where a hypothesis for the GM90 behavior, supported by a sensitivity experiment, will be presented. Let us now investigate whether the fine-resolution coupled model exhibits a different balance between mean flow and transient eddies.
Results from CM2.4 are summarized in Fig. 10, where the residual streamfunction and its two contributions
(i) The magnitude of the residual circulation in CTL is significantly reduced in CM2.4, with 15 Sv of residual equatorward flow against 20 Sv in CM2.1, suggesting a possible stronger cancellation of the mean flow by eddy fluxes. Averaging zonally—and not along streamlines (see, e.g., Karsten and Marshall 2002; Treguier et al. 2007)—seems sufficient for highlighting the role of the transient eddies in cancelling the time-mean cross-isopycnal flow; as a result, vertical and closed contours are virtually missing in Ψres (Fig. 10, top). We note that the same changes in surface forcings are applied to both models and that they occur in a similar fashion at all longitudes. Thus, zonal or along-streamline averaging in the context of perturbation experiments is expected to result in the same different behavior for the two models.
(ii) The residual circulation is altered only weakly in the perturbed experiments, with a strengthening of ∼ 3 Sv in both 1Pct2X and SHW3X. Although SHW3X experiences a stronger increase in mean circulation, this is compensated by larger eddy fluxes—suggesting an “eddy-saturated regime.” The possibility of reaching a state in which the ACC transport is independent of wind stress was first discussed by Straub (1993), highlighting the role of eddies in facilitating the sink of momentum. This saturation is reached in the eddy-permitting model because, although a comparable intensification of the Eulerian cell is found for both CM2.1 and CM2.4, the southward eddy-induced circulation increases and compensates for the northward Ekman transport in the eddy-permitting integrations (Fig. 10, bottom), as opposed to the stiffness of the eddy closure scheme in CM2.1.
(iii) Not only is the deep cell more vigorous in the eddy-permitting model, but it also strengthens with increasing wind stress. This effect points to the role of mesoscale eddy transfer in controlling the strength of the “lower limb” of the MOC in the Southern Ocean (Ito and Marshall 2008), with implications for both paleoclimate and future climate scenarios.
The analysis of the eddy-permitting CM2.4 has revealed a Southern Ocean circulation in a quasi “eddy saturation regime” (Hallberg and Gnanadesikan 2001; Meredith and Hogg 2006) in which the larger wind-energy input results in an intensification of the mesoscale eddy activity that opposes and partly compensates for increases in Ekman transport, resulting in weaker changes of the residual circulation and ACC transport. Other than in the tropics (Jayne and Marotzke 2002), poleward eddy heat fluxes in the Southern Ocean are believed to be the strongest. The response of the heat transport mediated by mesoscale eddies to altered SH wind stress, and its influence on the atmosphere, is the subject of the next section.
4. Poleward heat transport
The role of the eddies in maintaining a quasi-constant meridional heat flux under different SH surface energy supply is manifested by their contribution to the total heat transport. In the CTL simulations, the eddy component is negative and stronger than the transport accomplished by the mean flow; thus, the total flux is directed poleward (Figs. 11a,d). As idealized anomalous surface forcings are applied to the models, the transport of heat by the mean flow (
As expected from the analysis of the MOC, differences with CM2.1 are significant. Parameterized eddies are not responsible for a substantial increase in eddy fluxes in the perturbation experiments (Figs. 11e,f), and the total advective transport of heat is thus modified. The different behavior in the two GFDL models is clearly illustrated in Fig. 12, where changes in the total advective heat transport (ΔΦo) are shown and deviations from the CTL are readily seen to be much reduced in CM2.4. Mesoscale eddies are very effective in balancing anomalous wind-energy input, as depicted by the solid red line in Fig. 12 for SHW3X, and it seems reasonable to suppose that with a finer resolution model we could achieve an even better compensation between eddy and mean flow transports.
Buoyancy gain in the Southern Ocean is also expected to change under increased concentrations of GHGs due to heat and precipitation anomalies. We note that, when both mechanical and buoyancy surface forcings are considered as simulated in the 1Pct2X integration (blue lines in Fig. 12), eddy fluxes seem less efficient in buffering the residual transport of heat. We can only speculate at this time that changes in the net air–sea buoyancy fluxes (both heat and freshwater) under climate change experiments, together with modifications in the wind stress, give rise to nontrivial modifications in transformation and formation rates of water masses, stratification, and diapycnal eddy fluxes in the mixed layer, leading to a reduction in the efficiency of the “eddy buffering” mechanism. We note that there is no buoyancy forcing in the eddy-saturation theory of Straub (1993) and that local and remote buoyancy forcings play a role in setting the stratification and transport of the ACC (Gnanadesikan and Hallberg 2000). Hence, diabatic forcings may well move the model away from an “eddy-saturated” state into a regime in which momentum flux does increase overturning, with little eddy generation (a “buoyancy dominated” state, Hallberg and Gnanadesikan 2001). This result could have implications for future and past simulations of the dynamics of the ACC. Experiments in which only the net buoyancy flux is altered are now being carried out in an attempt to disentangle the eddy response to each forcing.
a. Atmospheric response
Although a comprehensive comparison of differences in global climate change among the GFDL models is beyond the scope of this paper, it is possible to look for examples of atmospheric responses resulting from the finer resolution and explicit representation of eddy dynamics in the ocean component of CM2.4. It is somehow difficult to interpret how the oceanic resolution affects the atmospheric state and variability with the SHW3X simulations, as the model is in a way “decoupled” (i.e., the ocean feels the atmospheric wind stress plus an imposed anomaly, which is not felt by the atmosphere, although the oceanic response to this perturbation might feed back to the atmosphere). A clean comparison of the atmospheric response to the small scales in the ocean—parameterized versus permitted—can be achieved with the 1Pct2X integration.
Figure 12 illustrated that the oceanic response is very different depending on whether eddies are parameterized or permitted, in which case ΔΦo is greatly reduced. Depending on the time scales and latitudes, changes in energy transport in either the atmosphere or the ocean are, to a great extent, compensated by the other fluid so as to maintain a quasi-constant poleward transport of energy in the system (Bjerknes 1964). Thus, one would expect that a weaker change in oceanic energy transport would result in a weaker response in atmospheric energy transport, with general consequences for the climatic state.
The predicted change in the atmospheric energy transport (ΔΦa) for the 1Pct2X simulation is given in Fig. 13. At the latitudes of maximum ΔΦo (around 50°S, see Fig. 12), we also find the greatest changes in ΔΦa. They are of opposite sign and, it is supposed, compensate for the oceanic anomalies. Further, ΔΦa is considerably reduced, by about 50%, in CM2.4. To the extent that this result implies causality, it suggests that the eddies are not only a fundamental player in buffering the oceanic horizontal transport but also favor an atmospheric response (in this case indirect) that could potentially lead to significant changes in the overall climate under anomalous surface forcings. In fact, the results are consistent at all latitudes but are more pronounced in the Southern Ocean area where eddies play a greater role throughout latitude circles. A more in-depth analysis of the climate response to idealized changes in atmospheric CO2 concentration in the coarse and eddy-permitting model is underway.
5. Discussion and conclusions
Böning et al. (2008) recently provided compelling observational evidence for the insensitivity of the ACC and Southern Ocean MOC to decadal changes in wind stress. The observed trend is in contrast with coupled modeling studies carried to date, which generally foresee an increase in ACC transport and residual circulation (e.g., Saenko et al. 2005; Fyfe and Saenko 2006). However, studies using ocean-only and highly idealized coupled eddy-resolving models (Hallberg and Gnanadesikan 2006; Meredith and Hogg 2006) have demonstrated the possibility of reaching an “eddy-saturated regime” where poleward eddy-induced circulations largely compensate for the enhanced northward mean transport driven by increasing wind stress. The underlying mechanism can be summarized as follows. In the ACC region the anomalous mechanical stirring increases the tilt of the isopycnals through its associated Ekman fluxes. As a result, mesoscale eddies are spawned by baroclinic instability mechanisms, releasing the available potential energy previously stored in the density front, leading to a flattening of the isopycnals and an increase in EKE (Marshall and Radko 2003). The two opposing circulations, Eulerian mean (
In an effort to bring into agreement observations and climate model results, we have analyzed the Southern Ocean response to anomalous surface forcings with two global coupled models of different resolutions. Compared to the case in which eddies are parameterized and consistent with recent observational and idealized modeling studies, the eddy-permitting integrations of the GFDL CM2.4 coupled model show that eddies act as a buffer to atmospheric changes, and the magnitude of the oceanic circulation response is greatly reduced. Although compensation is far from perfect, changes in the eddy-induced circulation and associated poleward eddy fluxes partially compensate for the enhanced equatorward Ekman transport, leading to weak modifications in isopycnal slopes and ACC transport. One could speculate that with even finer oceanic resolution these changes would be further reduced. Also, the presence of active ocean eddy dynamics serves to reduce the change in ocean heat transport, leading to a significant reduction in the response of atmospheric heat transport anomalies. Further, the role of mesoscale eddies is certainly not restricted to the Southern Ocean region. For example, the Atlantic MOC (AMOC) weakening under the 1Pct2X scenario is reduced, at the time of CO2 doubling, from 29% in CM2.1 (Stouffer et al. 2006) to 12% in CM2.4. A comprehensive analysis on the repercussions for the Southern Hemisphere and global climate to permitted eddies will be pursued in a future study, and the role, both local and remote, of mesoscale eddies in the stability of the AMOC under climate change scenarios will be investigated.
The role of mesoscale eddies in the rectification of the Southern Ocean response to changes in momentum and buoyancy input, as envisaged by global warming scenarios, is thus of fundamental importance both for the local and remote impact on the circulation as well as for air–sea exchange, uptake, and sink of anthropogenic GHGs. However, coupled climate models are usually too coarse to resolve the Rossby radius and must rely on parameterizations to account for the effects of mesoscale eddies. A fundamental question emerging from eddy-permitting modeling efforts, and recent observations, is the effectiveness of the GM90 isopycnal tracer mixing parameterization. A crucial goal of the parameterization is to realistically represent meridional eddy transports as well as the feedbacks of the mesoscale eddies on the mean flow. Hence, for example, the value of the different parameters in GM90 might be chosen so as to accurately reproduce the total transport through Drake Passage and the time-mean energy transport in present-day conditions. This approach, however, does not guarantee a satisfactory behavior in altered climatic conditions. Indeed, results with the GFDL coarse-resolution model presented in this paper have highlighted the inability of GM90, as implemented in CM2.1, to react to intense modifications in local isopycnal slopes, with no apparent response in the parameterized eddy-induced advection to the perturbed wind and buoyancy-flux work. To better understand the limitations of the numerical implementation in CM2.1, we perform a sensitivity study on a parameter related to the isopycnal slope in GM90.
a. The maximum slope hypothesis for GM90
As introduced by Eq. (6), GM90 relates the eddy streamfunction Ψ*GM to an eddy transfer coefficient κgm and local isopycnal slope S. This gives rise to an eddy-induced advective transport.
For numerical stability purposes, ocean models, such as the one used in this study, often use a slope tapering technique for the GM90 parameterization to linearly taper off Ψ*GM and produce a constant eddy velocity across the surface diabatic layer, preventing the eddy streamfunction from going to infinity. Effectively, where isopycnals become “too” steep, S is capped by a maximum slope Smax, thereby defining a maximum eddy-induced volume flux κgm Smax. The choice of Smax is usually dictated by numerical necessities. Gnanadesikan et al. (2007) document the sensitivity of CM2.1 to the value of tapering parameter Smax in a control simulation with fixed radiative forcings.
In the CM2.1 simulations analyzed in the present paper and in Gnanadesikan et al. (2007), Smax is set to 1/500. This value strongly narrows the range of slopes under which GM90 can freely operate, and the GM90-induced overturning is unable to keep increasing significantly when the isopycnals steepen greater than 1/500, as is the case of the two perturbation experiments presented herein. The value chosen for Smax varies greatly among the different ocean components used in IPCC-class coupled models, and the choice may impact whether different models allow for a greater GM90 response to different surface forcings.
Thus, we tested the sensitivity of our results to Smax; consistent with simulations in Gnanadesikan et al. (2007), we chose 1/100 for the maximum slope value and repeated the experiment with altered westerly winds SHW3X. Now the GM90-induced streamfunction will have a much higher upper bound, and it is hypothesized that it will be able to respond more vigorously to surface mechanical forcings. Figure 14 shows the circulation response broken down into Ψres,
However, in our sensitivity experiment the parameterized eddy fluxes from the GM90 scheme are still responsible for a weaker compensation than seen in the CM2.4 simulation with explicitly permitted eddies. Setting the maximum slope Smax to a value five times larger has produced little improvement toward an insensitive overturning circulation, ACC transport (see dotted line in Fig. 6), and meridional density gradient (not shown). The differences could be the result of needing a still larger value of Smax in CM2.1, inadequacies of the chosen diffusivity parameterization (Griffies et al. 2005, appendix), or something else. We note that Gnanadesikan et al. (2007) showed that modifying the Smax parameter has some impact on the simulated climate of CM2.1 in various regions of the coupled model, most notably the Southern Ocean and North Atlantic. As is generally true in the development of coupled models, it is unclear whether the tuning exercises that led to Smax = 1/500 were based on the need to counteract errors in the ocean model itself or problems resulting from coupling to another component of the climate system. The importance of the present study, especially in light of the compelling observational study from Böning et al. (2008), is to bring the phenomenon of eddy saturation to the forefront of those key metrics used in climate model development. In fact, the GM90 parameterization in CM2.1 not only falls short in reproducing the eddy response to global warming scenarios but might also not properly represent mesoscale eddy dynamics under natural interannual variability of the wind stress in the Southern Ocean and elsewhere.
b. Final considerations
Results from a fine-resolution IPCC-class climate coupled model under present-day and altered forcings have been presented and compared to the same integrations with a coarse-resolution version of the same model. A principal focus was given to mesoscale dynamics in the Southern Ocean.
To summarize, we posit the following.
(i) Eddy compensation mechanisms are taking place in the GFDL CM2.4, confirming previous idealized studies and recent observations. Intensification of the mesoscale eddy field rectifies the Southern Ocean dynamical response to projected changes in mechanical and buoyancy forcing. However, the interplay between mean flow and mesoscale eddies in setting the residual circulation in the Southern Ocean, as well as the extent to which the balance between the two contributions would hold under altered climates, is still far from being resolved. Eddy compensation in the model is not perfect, especially in the case where both momentum- and buoyancy-flux anomalies are imposed, and it is not clear whether it should be.
(ii) Finer grid resolution in ocean modeling is the evolutionary path, but it should go along with (and provide ground for) advances in eddy parameterizations, as we clearly need better and improved representations of eddy transfer. Having recognized the limitations of present numerical implementations, much effort has been put recently into new numerical schemes for eddy fluxes that build on GM90 (Ferrari et al. 2008, 2010). Hopefully, this study, as well as fine-resolution modeling in general, will help refining much needed parameterizations.
The forthcoming World Climate Research Programme (WCRP) Coupled Model Intercomparison Project, phase 5 (CMIP5), set of experiments, on which the IPCC Fifth Assessment will be based, incites the need for more confidence in, and understanding of, the modeled climate system response to GHGs, where the Southern Ocean is key. Both finer-resolution eddy-resolving coupled models and better eddy parameterizations are needed. By moving toward finer resolutions, we could achieve an even better compensation between eddy and mean flow fluxes. Eddy control on the global ocean circulation and energy budget will thus likely become even stronger.
Acknowledgments
The authors thank Anand Gnanadesikan, Stephanie Downes, and Ron Pacanowski for useful comments. Two anonymous reviewers made very helpful suggestions that helped to improve the presentation of our results.
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APPENDIX
Neutral Physics in CM2.1
Although extensive discussions on the formulation and numerical implementation of the parameterization of mesoscale eddies in the GFDL CM2.1 can be found elsewhere (e.g., Griffies et al. 2005; Gnanadesikan et al. 2006, 2007), we summarize here the main characteristics of the implementation of the parameterization of isopycnal diffusion and eddy-induced advective (or, equivalently, skew diffusive) processes originally proposed by GM90 and Gent et al. (1995).
The particular choice of neutral diffusivity parameters is a mere result of an effort to reduce biases in the coupled model. Both the value of the diffusivity and details of how the coefficient is tapered for large neutral slopes have been shown to significantly alter the simulations within a coupled model [e.g., this paper and Gnanadesikan et al. (2007)].
Baroclinic time scale Tbc = f −1
Citation: Journal of Physical Oceanography 40, 7; 10.1175/2010JPO4353.1
Eddy kinetic energy (cm2 s−2) of the surface geostrophic flow for the fine-resolution GFDL climate model CM2.4 and the altimetric observational dataset: (a) CM2.4 CTL simulation averaged over years 176–180 with 5-day mean values and (b) merged TOPEX/Poseidon, ERS-1, and ERS-2 satellite altimeter product averaged over the 2003–07 period with 7-day mean data. Both EKE estimates are derived from SSH through geostrophy; an equatorial band of ±5° is masked because the geostrophic approximation does not hold there. A similar plot for the coarse-resolution model CM2.1 with the same high-frequency temporal averaging showed virtually no energetic signals other than in the equatorial region, and it is thus omitted. Note the logarithmic scale in all plots.
Citation: Journal of Physical Oceanography 40, 7; 10.1175/2010JPO4353.1
Annual mean of the wind work W = 〈τx〉 〈ug〉 (TW) on the surface geostrophic flow integrated over the SH region from 20° to 70°S in CM2.4. The gray area represents the time interval for the eddy diagnostics.
Citation: Journal of Physical Oceanography 40, 7; 10.1175/2010JPO4353.1
(a) Wind stress (Pa) in CM2.1 and CM2.4, (b) wind stress curl (Pa m−1) and its changes, and (c) northward Ekman transport (Sv) in the SH in CM2.4 for the three different experiments. All data are 5-yr averages between years 176 and 180. Standard deviations σ for the wind stress are given for both models.
Citation: Journal of Physical Oceanography 40, 7; 10.1175/2010JPO4353.1
Annual-mean Drake Passage volume transport (Sv) for (a),(b) CM2.1 and (c),(d) CM2.4 in CTL (black), the climate change scenario 1Pct2X (blue) and the altered SH westerly wind idealized experiment SHW3X (red). The gray areas represent the time interval chosen for the eddy diagnostics.
Citation: Journal of Physical Oceanography 40, 7; 10.1175/2010JPO4353.1
Zonally averaged SSH anomaly (m) in the Southern Ocean for the SHW3X (red lines) and 1Pct2X (blue lines) experiments. CM2.4 results are depicted by the solid lines, and CM2.1 results by the dashed lines. Anomalies were obtained by removing the CTL mean to the pentads 176–180 and 196–200 for SHW3X and 1Pct2X, respectively. The experiment CM2.1 SHW3XSmax (red dotted line) is discussed in section 5a.
Citation: Journal of Physical Oceanography 40, 7; 10.1175/2010JPO4353.1
Zonally averaged isopycnal surfaces of potential density referenced to the surface [σ0 = ρ (kg m−3–1000)] in the upper Southern Ocean: σ0 was chosen to better represent the upper ocean structure, although only minor differences were found when compared with σ2. Gray lines are for the CTL integrations and black lines are for the perturbation experiments shown at the top of each panel. Data were temporally averaged between model years 176 and 180.
Citation: Journal of Physical Oceanography 40, 7; 10.1175/2010JPO4353.1
Meridional overturning circulation (Sv) in depth space for the CTL integrations of (a) CM2.1 and (b) CM2.4. Also shown are the broad locations of the subtropical cell (STC), subpolar (SPC), and deep cell (DC) in the SH. The streamfunction in CM2.1 includes the contribution from parameterized eddy velocities. Contour interval is 3 Sv.
Citation: Journal of Physical Oceanography 40, 7; 10.1175/2010JPO4353.1
MOC (Sv) in σ2 density space for CM2.1 (left) CTL and (right) 1Pct2X experiments: (top) the residual meridional circulations, (middle) the contributions from the Eulerian transport 
Citation: Journal of Physical Oceanography 40, 7; 10.1175/2010JPO4353.1
MOC (Sv) in σ2 density space for CM2.4: (top) the residual Ψres, (middle) the Eulerian mean
Citation: Journal of Physical Oceanography 40, 7; 10.1175/2010JPO4353.1
Zonally and vertically integrated contributions to the poleward heat transport (PW) in CM2.4 and CM2.1: the total (
Citation: Journal of Physical Oceanography 40, 7; 10.1175/2010JPO4353.1
Changes in total oceanic heat transport ΔΦo (PW) in CM2.1 (dashed lines) and CM2.4 (solid lines) for the two perturbation experiments. Differences are computed for time-mean averages between model years 176 and 180.
Citation: Journal of Physical Oceanography 40, 7; 10.1175/2010JPO4353.1
Changes in total atmospheric heat transport ΔΦa (PW) in CM2.1 (dashed line) and CM2.4 (solid line) for the 1Pct2X experiment, averaged between years 176 and 180.
Citation: Journal of Physical Oceanography 40, 7; 10.1175/2010JPO4353.1
MOC (Sv) in σ2 density space for the three-member ensemble average of the Smax experiment: (top) residual circulation Ψres, (middle) Eulerian mean circulation
Citation: Journal of Physical Oceanography 40, 7; 10.1175/2010JPO4353.1