An idealized climate change simulation is used to investigate the energetics of the Atlantic meridional overturning circulation (AMOC) at the stages of its weakening and recovery. There is a good correlation between the strength of the AMOC and the available potential energy (APE) in the upper 3 km of the ocean, integrated north of 50°N or globally, both during the weakening and recovery. Buoyancy forcing is important at both stages. In the Southern Ocean, the APE gradually builds up and correlates with the depth of pycnocline in the Atlantic Ocean. This suggests that mechanical forcing plays an important role in the recovery of the AMOC.
 The response of the Atlantic meridional overturning circulation (AMOC) to changes in carbon dioxide (CO2) level in the atmosphere is a subject of intensive research. One reason for this is that the heat transported by the AMOC is thought to have a substantial influence on Northern Hemisphere climate. Simulations based on climate models show that the AMOC may weaken with increasing CO2. This weakening is generally thought to be the result of an increased resistance to deep water formation in the subpolar Atlantic, owing to surface waters being made lighter, with warming dominating over freshening [e.g., Gregory et al., 2005].
 However, the energetics and driving forces of the AMOC are not well understood. For example, Munk and Wunsch  presented arguments suggesting that the global ocean overturning, a major component of which is the AMOC, may need a substantial mixing against gravity to be maintained, perhaps localized in the regions of rough topography and along ocean boundaries. Toggweiler and Samuels , on the other hand, show that a strong AMOC can be simulated in the limit of no vertical mixing, but in the presence of winds south of 30°S. Both these studies, however, seem to agree on one key issue; i.e., to be maintained, the AMOC requires a continuous input of mechanical energy to the ocean and generation of available potential energy (APE).
 Recently, Gregory and Tailleux  used a set of climate models to demonstrate a very good temporal correlation between the AMOC weakening and the rate of kinetic energy (KE) generation by the pressure-gradient force, − uh ⋅ ∇ hp, integrated between 50°N and 70°N in the Atlantic Ocean (with u and p being, respectively, velocity vector and pressure, and with the “h” subscript indicating the horizontal components). This seems to support, as they point out, the buoyancy-driven interpretation of CO2-forced AMOC changes. Here we use a coupled climate model where, in response to a doubling of CO2, the AMOC first weakens but then recovers. The recovery happens despite a significant increase in the subpolar Atlantic buoyancy. It is demonstrated that the correlation found by Gregory and Tailleux  holds in our simulation too, including at the stage of AMOC recovery. We further illustrate that both at the stage of weakening and recovery, the AMOC strength correlates with the ocean APE north of 50°N, while the APE south of 50°S builds up gradually.
2 The model and experimental design
 We employ the second generation Canadian Earth System Model (CanESM2). It is composed of general circulation ocean and atmosphere models, as well as sea-ice, land and carbon cycle models. Since our focus here is on the ocean, we briefly describe only this component of CanESM2. For more details about the model, see Yang and Saenko  and references therein.
 The oceanic component of the model is a version of the Geophysical Fluid Dynamics Laboratory Modular Ocean Model with the Boussinesq and hydrostatic approximations. The horizontal resolution is 1.41° × 0.94° (longitude × latitude) and there are 40 vertical levels. The ocean model employs anisotropic viscosity [Large et al., 2001] and eddy transport [Gent and McWilliams, 1990] parameterizations. It also accounts for the effect of the dissipation of internal tides on deep ocean vertical mixing, implemented in a fashion similar to that described in Simmons et al. . Vertical mixing driven by buoyancy and shear is parameterized by the K-profile parameterization scheme [Large et al., 1994]. The ocean heat transport simulated by CanESM2 is extensively validated against observations in Yang and Saenko .
 We analyze the model's AMOC in two climate simulations. One of them is a long-term control simulation where atmospheric CO2 was held constant at 285 ppm level (hereafter CONTROL). The second simulation was branched from CONTROL after it was spun up for more than a thousand years. In this simulation (hereafter 2xCO2), the atmospheric CO2 concentration was abruptly doubled; i.e., set to 570 ppm.
 In response to the doubling of CO2 in the atmosphere, the AMOC first declines, until roughly the 5th decade (Figure 1a), and so does the near-surface density averaged between 50°N and 70°N in the Atlantic (Figure 1b). After the 5th decade, however, the AMOC gradually recovers, although the North Atlantic surface density in 2xCO2 remains considerably lower than in CONTROL (Figure 1). Furthermore, there is still a net heat gain by the ocean, including north of 50°N, several hundred years after the doubling of CO2 in the atmosphere.
 In an attempt to understand what sets the changes of the AMOC in our model, we first analyze, following Gregory and Tailleux , the conversion between the large-scale APE and KE; i.e., B = ∫ − uh ⋅ ∇ hp dV. The global map of time-mean B(x,y) = ∫ − uh ⋅ ∇ hp dz in CONTROL is shown in the upper panel of Figure 2 (cf. Figure 5 in Gregory and Tailleux ). The negative values between 40°S–60°S, also noted by Toggweiler and Samuels , are mainly the result of the work done against the local pressure gradient by the predominantly northward Ekman flux. Much of the large-scale APE generated by the negative B in this region is removed, as we discuss below, by mesoscale eddies. Very large positive values, indicating a generation of KE from APE, are found mostly within the strong boundary currents and in the regions of deep water formation in both hemispheres. Integrated globally, B = −0.54 TW, which is similar to its value in e.g. HadCM3 [Gregory and Tailleux, 2011]. The global negative B indicates that APE is generated from the (resolved) KE.
 However, integrated between 50°N and 70°N in the Atlantic, B > 0, which is consistent with Toggweiler and Samuels  and Gregory and Tailleux . In 2xCO2, the decadal-mean rate of KE generation by the pressure-gradient force in the subpolar Atlantic correlates well with the decadal-mean AMOC. Furthermore, this appears to be happening not only at the stage of AMOC weakening, such as found by Gregory and Tailleux , but also at the stage of AMOC recovery (Figure 2, lower). Gregory and Tailleux  argue that the correlation between the AMOC weakening and the subpolar Atlantic B supports a buoyancy-driven interpretation of AMOC changes. From Figure 2 (lower), one may argue that a similar interpretation applies at the stage of AMOC recovery, although the surface buoyancy in the subpolar Atlantic remains lower than in CONTROL (Figure 1b).
 We next consider changes in APE. Following Toggweiler and Samuels , the APE is defined here using the Lorenz approximation [Lorenz, 1955; Oort et al., 1989], , with ρ being the in situ density and overbar indicating horizontal averaging; the stability factor, , is a function of time and is evaluated at the midpoint of each model layer using the local depth as the reference for determining the potential density gradient [Toggweiler and Samuels, 1998]. To roughly include the upper and lower branches of the AMOC, Figure 3a shows time series of the APE integrated over the upper 3 km of the ocean. In 2xCO2, the upper ocean APE first declines, until about the fifth decade, but then recovers (although the stability factor increases). Both at the stage of decline and recovery, the decadal-mean APE in the upper ocean correlates well with the decadal-mean AMOC (Figure 4, lower). However, while the upper ocean APE almost completely recovers by the 15th decade in 2xCO2 on the global-mean, the spatial structure of the APE anomaly is highly non-uniform (Figure 4, upper). It is set by a combination of processes, including by changes in ocean circulation, surface buoyancy flux and dissipation [Toggweiler and Samuels, 1998]; if there is a change in the mean stratification, such as here, then it also contributes.
 In the North Atlantic, the APE decreases, except just west of Greenland and in the Barents Sea (Figure 4, upper). In the latter region, the near-surface density is only weakly affected by the CO2-induced changes in the ocean and climate. Integrated north of 50°N, the relative changes in the APE essentially follow the corresponding changes in the AMOC, both at the stage of weakening and recovery (Figure 3b). In the Southern Ocean, the APE gradually buildsup (Figure 3b, Figure 4, upper). South of the Antarctic Circumpolar Current (ACC), the relatively dense waters are brought from the abyss to the upper ocean by a strengthened wind-driven upwelling. This mechanism generates APE and, as proposed by Toggweiler and Samuels , could make it available for the AMOC. This possibility is discussed next.
4 Discussion: North Atlantic or Southern Ocean?
 AMOC is a global-scale phenomenon, and it seems reasonable to assume [e.g., Visbeck, 2007; Delworth and Zeng, 2008] that the generation of APE as far away as in the Southern Ocean contributes to the AMOC recovery and to the gradual rebuild of APE in the north.
Gregory and Tailleux  argue that the changes in the APE-KE conversion (B) that they found under increasing CO2 support a buoyancy-driven interpretation of AMOC changes, and not the mechanical mechanism of Toggweiler and Samuels . In particular, they observe that, integrated over the Southern Ocean, B becomes more negative (i.e., generating more APE), while the AMOC weakens in the simulations they analyze. However, in our 2xCO2 simulation the Southern Ocean B also becomes more negative, including at the stage of the AMOC recovery. Integrated south of 45°S, B decreases in 2xCO2 from −0.51 TW (1st decade) to −0.55 TW (5th decade) and to −0.61 TW (15th decade). Thus, while the strength of the AMOC does correlate with the subpolar Atlantic B, the mechanism of Toggweiler and Samuels  cannot be ruled out at the stage of AMOC recovery.
 However, the applicability of this argument to the Southern Ocean is not clear, given a strong eddy activity in the region. Part of the APE generated locally can be removed by mesoscale eddies, leading to a strengthened (in our 2xCO2 experiment – by about 2 Sv) eddy-induced meridional overturning. To include the effect of eddies, one can consider the residual APE-KE conversion [Gent et al., 1995]; i.e., Br = ∫ − Uh ⋅ ∇ hp dV, where , with being the Gent and McWilliams  eddy-induced transport velocity. The structure of Br(x,y) = ∫ − Uh ⋅ ∇ hpdz in CONTROL (not shown) is similar to B(x,y) in the upper panel of Figure 2, except the negative values between 40°S–60°S are pronounced less, whereas the large positive values in the regions of boundary currents are pronounced more. Integrated south of 45°S, Br decreases in 2xCO2 from −0.11 TW (1st decade) to −0.14 TW (5th decade) and then to −0.17 TW (15th decade). Again, at the stage of AMOC recovery the Toggweiler and Samuels  mechanism cannot be ruled out.
 However, the eddy-induced transport depends on the thickness diffusivity [e.g., Gent et al., 1995], which is a very uncertain parameter. It may depend on ocean baroclinicity and stratification, and hence on climate, in a way which is not well understood [Cessi, 2008]. It therefore remains to be seen if, in general, Br and/or B in the Southern Ocean can be useful quantities for making conclusions about the behavior of the AMOC in climate change simulations. Nevertheless, the accumulation of APE in the Southern Ocean, as illustrated here, further underlines a potentially very important role of this region for controlling long-term changes in the AMOC. It is also clear that mesoscale eddies, through their impact on the APE, are very important. Qualitatively, the Toggweiler and Samuels  results are supported by eddy-resolving models. Such models simulate a stronger meridional overturning in response to energy input from the Southern Ocean winds, with a weak impact on the transport of ACC [e.g., Morrison and Hogg, 2013]. In our coarse-resolution model, the transport of ACC in 2xCO2 increases by 6-7% (Figure 3c).
 In addition to the mechanism proposed by Toggweiler and Samuels , mechanical forcing can also be important through its impact on the mixing, and on the associated deepening of pycnocline and generation of APE by high-latitude cooling [e.g., Tsujino and Suginohara, 1999; Gnanadesikan, 1999; Klinger and Cruz, 2009; Tailleux and Rouleau, 2010]. Indeed, we find that the depth of pycnocline in the Atlantic Ocean, evaluated as in Gnanadesikan , closely follows the Southern Ocean APE (Figure 3b). This suggests that the recovery of AMOC is driven, at least in part, mechanically.
Gregory and Tailleux  presented ocean KE analysis of CO2-forced climate models, demonstrating a very good correlation between the rate of KE generation by the pressure-gradient force in the subpolar Atlantic and the simulated weakening of AMOC. Here, it is demonstrated that the correlation found by Gregory and Tailleux  also holds at the stage of the AMOC recovery. It is shown that both the weakening and recovery of the AMOC in our model correlates well with the APE integrated globally over the upper 3 km of the ocean, as well as with the APE integrated north of 50°N. The build up of APE in the Southern Ocean may have contributed to the AMOC recovery.
 I am grateful to Jonathan Gregory, Robert Toggweiler, and Andreas Schmittner for discussions. I also thank Warren Lee for his help with the model data.