Paleo proxy data suggest that the Atlantic meridional overturning circulation (AMOC) was shallower and weaker at the Last Glacial Maximum (LGM) than at present. In this study, we have identified the existence of a thermal threshold of the AMOC which may explain why many coupled climate models fail to simulate the weaker AMOC during the LGM. By using results obtained from a coupled climate model and conducting sensitivity simulations with an ocean general circulation model, we found that the sudden transition from the present-day AMOC to the weaker glacial AMOC occurs when we gradually change the degree of surface cooling from present-day to glacial conditions. This result is related to response of deep convection in the northern North Atlantic Ocean; moderate cooling enhances deep convection whereas sufficient cooling results in total covering of sea ice there and suppression of deep convection. The findings indicate the existence of a thermal threshold controlling the AMOC, where the present-day-type AMOC suddenly shifts to the weaker glacial AMOC once the surface cooling exceeds this threshold. We also demonstrate that wind stress forcing plays a critical role in controlling the value of the thermal threshold. Our study suggests that slight differences in the degree of surface cooling or wind stress forcing for LGM simulations could lead to the very different response of the AMOC during the LGM as reported in previous LGM simulations.
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 During the Last Glacial Maximum (LGM), ocean proxy data suggest that the Atlantic meridional overturning circulation (AMOC) was weaker and shallower than it is today [e.g., Lynch-Stieglitz et al., 2007]. For example, carbon isotope data from benthic foraminifera suggests that the depth of the boundary between North Atlantic Deep Water (NADW) and Antarctic Bottom Water (AABW) became shallower during the LGM [Labeyrie et al., 1992]. The value of 231Pa/230Th from sediment core collected in the subtropical Atlantic Ocean is significantly higher during the LGM (0.068) than during the Holocene (0.055), which indicates that the strength of the AMOC was reduced by up to 30% during the LGM [McManus et al., 2004].
 A coupled climate model is a powerful tool for reproducing and investigating the LGM climate. Because the steady-state simulation of the LGM has been a target of Paleoclimate Model Intercomparision Project (PMIP), various coupled climate models have challenged the LGM simulation by following the protocol proposed by PMIP [e.g.,Kageyama et al., 2001; Braconnot et al., 2007]. Substantial differences between the model responses of the glacial AMOC have been observed in these LGM simulations [Weber et al., 2007], with half of models simulating a weakening of the AMOC while the other half simulate a strengthening. For example, the National Center for Atmospheric Research Community Climate System Model (NCAR CCSM) succeeded in simulating the weaker AMOC during the LGM, which is consistent with paleo proxy data. On the other hand, the Model for Interdisciplinary Research On Climate (MIROC) employed in this study simulated a significantly stronger AMOC [Otto-Bliesner et al., 2007] as shown in Figure 1. Like MIROC, many coupled models have difficulty in reproducing the weaker AMOC during the LGM [e.g., Hewitt et al., 2001; Kitoh et al., 2001]. Although the result from NCAR CCSM suggested the importance of changes in salinity in the Southern Ocean [Shin et al., 2003], there is still debate about what factors control the response of the AMOC during the LGM.
 In this paper, based on present-day and LGM simulations by MIROC, we conducted a series of sensitivity simulations with an ocean general circulation model (OGCM), where surface heat, freshwater, and momentum flux conditions are separately exchanged between present-day and LGM conditions. From these results, we propose the existence of a thermal threshold of the AMOC which may explain why the response of the AMOC during the LGM is very different among state-of-the-art coupled climate model simulations. We also point out that wind stress forcing has a critical role in determining the value of this thermal threshold.
2. Model and Experimental Design
 The ocean model used in this study is COCO [Hasumi, 2006] which includes a dynamical sea ice model. This model constitutes the oceanic component of MIROC [Hasumi and Emori, 2004]. Simulations by the medium-resolution version of MIROC (with an atmospheric resolution of T42L20 and an oceanic resolution of ∼1°) listed in PMIP2 [Weber et al., 2007] are referenced in this study. The same resolution and model parameters as those of MIROC are applied in our OGCM simulations.
2.2. Surface Forcing
 The ocean model is forced by surface heat, freshwater, and momentum fluxes. The surface heat flux (FT) is calculated as
where α is surface albedo, Qsd is downward shortwave flux, ϵ is emissivity, Qld is downward longwave flux, σis Stephan-Boltzman constant, TSis sea surface temperature (over open ocean) or sea ice surface temperature (over ice-covered area),ρA is density of the atmosphere, CA is atmospheric heat capacity, CS is bulk coefficient for sensible heat flux, TA is surface air temperature, L is latent heat of water, CL is bulk coefficient for latent heat flux, qsat is saturated specific humidity, and qA is surface air specific humidity. The scalar parameters ϵ, σ, ρA, CA , and L are given as constant values. The parameters α and qsat are dependent on oceanic state: αis determined from sea ice concentration where higher albedo is specified for ice-covered grids, and qsat is a function of TS. The atmospheric variables Qsd, Qld, TA, and qA are given as the boundary conditions for the ocean. The bulk coefficients CS and CL are determined from bulk formulae [Kara et al., 2000] and dependent on surface wind speed which is also given as the boundary condition. In the ice-covered area, the sea ice model predicts sea ice concentration, thickness, velocity, and overlaying snow thickness based on two-category thickness representation, zero-layer thermodynamics [Semtner, 1976], and dynamics with elastic-viscous-plastic rheology [Hunke and Dukowicz, 1997].
 The surface freshwater flux (Fw) consists of evaporation (E), precipitation (P), and river runoff (R);
which is used for the ocean salinity boundary condition. The surface zonal and meridional wind stresses are also specified for the momentum boundary conditions of the ocean and sea ice.
2.3. Experimental Design
 We began with simulations CTL and LGM, which are respectively the reproduction of present-day and LGM climate by using an OGCM based on the sea surface boundary conditions obtained from MIROC. In CTL simulation, Qsd, Qlw, TA, qA, and surface wind speed are taken from MIROC present-day simulation (referred as Control in this paper) for the calculation of surface heat flux described above. Surface freshwater flux and surface wind stress taken from MIROC Control simulation are also given as salinity and momentum boundary conditions, respectively. In LGM simulation, they are all replaced by those taken from MIROC LGM simulation. The differences in specified surface boundary conditions between CTL and LGM are displayed inFigure 2.
 In order to separately evaluate the role of the heat, freshwater, and momentum fluxes, we also performed sensitivity simulations (LGM-heat, LGM-water, and LGM-wind) where surface flux boundary conditions taken from the MIROC simulations are switched back and forth between present-day and LGM conditions. In LGM-heat, boundary conditions are the same as CTL except that only Qsd, Qlw, TA, and qAare replaced by those from MIROC LGM simulations. In LGM-water (LGM-wind), surface freshwater flux (wind stress forcing) is taken from MIROC LGM simulation and the other boundary conditions are from MIROC Control simulation.
 The results from above-mentioned simulations motivated us to carry out additional experiments (HT-CTL, HT-water, and HT-wind series) where degree of sea surface cooling is gradually changed from present-day to LGM conditions. In HT-CTL series simulation, variables from MIROC Control simulation are mixed with those from LGM weighted by a cooling factor fc. For example, Qsd is given by
where Qsd(CTL) and Qsd(LGM) are Qsd taken from MIROC Control and LGM simulations, respectively. The other variables Qlw, TA, and qaare also given in the same manner. Note that the surface freshwater flux and wind stress forcing are taken from MIROC Control simulation in HT-CTL. HT-water (HT-wind) series simulations are the same as HT-CTL except that the surface freshwater flux (wind stress forcing) is from MIROC LGM simulation.
 The OGCM sensitivity simulations conducted in this study are summarized in Table 1. Note that present-day configuration of the land-sea mask and ocean floor topography is applied in all OGCM simulations. The model is integrated for more than 1000 years from the present temperature and salinity climatology [Steele et al., 2001] in each simulation. In all simulations, the model reaches a quasi-equilibrium state and the average of the last 100 years is analyzed.
The name of simulations is listed in the first column. In the second, third, and fourth columns, Control/LGM indicates that present-day/LGM MIROC simulation is used for calculating the sea surface heat, freshwater, and wind-stress fluxes, respectively. The symbol (-) in the second column indicates that surface heat flux condition is between Control and LGM (see text). The simulated maximum value of the AMOC is displayed in the last column (the parenthetic value is the difference from CTL).
3.1. Evaluation on Role of Heat, Freshwater, and Momentum Fluxes
 The CTL and LGM simulations well reproduced the results of MIROC, where the AMOC was observed to become significantly stronger in the LGM than CTL as we have seen in Figure 1. The difference in the AMOC between the CTL and LGM simulations should be a consequence of changes in surface heat, freshwater, or momentum fluxes, or a combination of these factors. In order to separately evaluate which flux changes are important, we carried out the LGM-heat, LGM-water, and LGM-wind simulations where only the heat, freshwater, or momentum flux condition is replaced from CTL to LGM, respectively. The last column ofTable 1displays the maximum values of the AMOC in each simulation. The AMOC becomes significantly weaker in the LGM-heat simulations, whereas it is slightly stronger in the LGM-water and LGM-wind simulations. Therefore, the significant strengthening of the AMOC in LGM is explained not by the effect of a single surface flux but by a combination of them. This finding differs from the results ofSchmittner et al. who found that the freshwater flux plays the dominant role in the weakening of the AMOC during the LGM. We expect that difficulties in reproducing a realistic hydrological cycle with their simple energy-moisture balance model may have caused the difference from our result. Our analysis is based on a fully coupled climate model, and slight increase of the AMOC in LGM-water is caused by decrease in amount of freshwater input into the northern North Atlantic (mainly due to reduction of river runoff input;Figure 2b), which appears a plausible response considering that the hydrological cycle becomes weaker in colder climates.
 Here, we focus on two questions regarding our findings. The first question relates to why changes in the heat flux leads to a weakening of the AMOC (see change from CTL to LGM-heat inTable 1) in spite of the polar amplification mechanism [e.g., Masson-Delmotte et al., 2006] where cooling is amplified in higher latitudes and the meridional temperature gradient becomes stronger during the LGM (see Figure 2a). The second question is why the AMOC responds to changes in surface fluxes in a nonlinear way; i.e., the combination of three fluxes strengthens the AMOC (see LGM in Table 1) although a single change in surface flux leads to either a slight increase (see LGM-water and LGM-wind inTable 1) or a significant decrease in the AMOC (see LGM-heat inTable 1).
3.2. The Thermal Threshold of the AMOC
 In order to address the first question regarding the influence of heat flux on the AMOC, the changes in the AMOC from CTL to LGM-heat were traced step-by-step here. To do this, we performed HT-CTL series simulations in which the difference in sea surface atmospheric condition between CTL and LGM was multiplied by a factor fc, and this anomalous heat flux condition was then applied to CTL (note that fc = 0 and fc = 1 for the HT-CTL series are equivalent to CTL and LGM-heat, respectively).
 The maximum values of AMOC simulated in HT-CTL series are plotted by red circles inFigure 3. These results confirm that the AMOC becomes stronger than CTL while the heat flux anomaly is not large (fc = 0.2 and 0.4) since meridional temperature gradient becomes larger as expected above. On the other hand, the AMOC suddenly becomes very weak once the degree of surface cooling exceeds a threshold value (fc = 0.6). This behavior of the AMOC is closely related to changes in the location of deep water formation and sea ice distribution (Figure 4). In CTL, although deep water formation in the Labrador Sea is missing, the model reasonably captures the observed deep water formation in the Greenland and Irminger Seas [Killworth, 1983; Pickart et al., 2003]. The site of deep water formation remains ice-free and atmospheric cooling there maintains the deep water formation and the AMOC. The situation remains basically unchanged while surface cooling is not large (fc = 0.2 and 0.4), although gradual shift in the maximum sea ice extent and the location of deep water formation toward lower latitudes are observed (not shown). However, the response of deep water formation suddenly changes when the degree of surface cooling becomes large enough for sea ice to cover the entire Greenland Sea (fc = 0.6;Figure 4b). Once this occurs during winter season, the air-sea heat flux almost vanishes due to the sea-ice insulation effect, and deep water formation completely ceases in the Greenland Sea. Although the deep convection in the Irminger Sea moves south of Greenland and contributes to the formation of the AMOC, the complete disappearance of the convection in the Greenland Sea leads to a significant weakening of the AMOC. Previous studies already suggested that the southward shift of deep water formations causes the weaker AMOC [e.g.,Rahmstorf, 1994; Ganopolski and Rahmstorf, 2001], however the important finding obtained in this study is that the reduction of the AMOC can be triggered purely by surface cooling without the addition of freshwater flux.
3.3. Role of Wind Stress on Determination of the Thermal Threshold
 As for the second question, the nonlinear response of the AMOC to changes in surface fluxes can be clearly explained by the results of the HT-water and HT-wind series of simulations (blue and green circles, respectively inFigure 2). In HT-water series (which are the same as HT-CTL series except that the freshwater flux condition is taken from LGM), the weakening of the AMOC takes place at fc = 0.8 in roughly the same way as in HT-CTL series. On the other hand, in the HT-wind series (the same as HT-CTL except under LGM wind-stress conditions), the weakening of the AMOC does not take place even at fc = 1.0 and the sudden weakening comes about at fc = 1.4; the threshold value of fc is significantly larger than those in HT-CTL (fc = 0.6) and HT-water (fc = 0.8) series. This demonstrates that the thermal threshold of the AMOC is not affected by changes in the background freshwater flux so much but significantly influenced by those in the wind stress forcing. The most significant difference in the wind stress between CTL and LGM is observed near the huge glacial ice sheets (Figure 2c). The wind stress over the northern Atlantic Ocean is also strongly affected by the appearance of the Laurentide ice sheet [e.g., Manabe and Broccoli, 1985]. Because the wind stress dynamically affects the sea ice, glacial changes in wind stress over the Atlantic Ocean may modify the response of sea ice distribution there to surface cooling. The increased wind-driven gyre circulation also helps to stabilize the AMOC by enhancing poleward salt transport [Oka et al., 2001; Timmermann and Goosse, 2004] as previous studies suggest that the Atlantic sub-polar gyre and its salt transport play an important role in the glacial AMOC [Montoya and Levermann, 2008; Montoya et al., 2011]. In either case, the wind stress changes have an important influence on the timing of the thermal transition of the AMOC. The nonlinear response of the AMOC is also explained by the existence of the thermal threshold of the AMOC and its dependence on the wind stress forcing.
4. Discussion and Concluding Remarks
 The results obtained in this study clearly explain why the response of the AMOC during the LGM becomes very different among state-of-the-art coupled climate model simulations.Figure 3 indicates that the thermal threshold of the AMOC under LGM wind stress forcing (fc= 1.4 in HT-wind series) is larger than the original LGM thermal condition of MIROC (i.e., fc = 1.0). This means that stronger surface cooling (i.e., 1.4 times greater cooling) than the original LGM simulation could result in the weaker AMOC in MIROC. It is also possible that different LGM wind stress may lead to the smaller AMOC in LGM by modifying the value of the thermal threshold. We expect the failure of many coupled models to simulate the weaker AMOC stems from the fact that the actual LGM climatic condition is located close to the thermal threshold of the AMOC. Therefore, it could be very sensitive to slight differences among models in sea surface cooling or wind stress forcing during the LGM whether or not the thermal transition of the AMOC takes place in the LGM simulations.
 The results obtained here also provide an important indication as to why the AMOC triggers abrupt climate changes during a glacial climate [Dansgaard et al., 1993] but not during an interglacial climate. We propose that the actual glacial climate is closely located around the thermal threshold, where the stadial periods of glacial climate stand just beyond the thermal threshold and the AMOC remains weak, whereas the interstadial periods is located below the threshold and the AMOC becomes relatively strong. Therefore, transitions from stadial to interstadial periods could cross the threshold and trigger a sudden strengthening of the AMOC. The thermal transition of the AMOC could then cause abrupt climate changes in a glacial climate. On the other hand, an interglacial climate is warm enough to avoid crossing the thermal threshold of the AMOC, and consequently large abrupt climate change is not realized under such conditions.
 This study implies that slight difference among models in surface cooling or wind stress forcing can lead to very different response of the AMOC during the LGM, depending on whether the simulated LGM is located beyond or below the above-mentioned thermal threshold. We demonstrated that the thermal threshold comes from nonlinear response of sea ice and deep convection over the North Atlantic to surface cooling. Here, we should note that response of sea ice over the North Atlantic Ocean is affected not only by local surface cooling over the North Atlantic Ocean but also by remote cooling over the other basins. Therefore, we do not deny the importance of the Southern Ocean pointed out by previous studies [e.g.,Shin et al., 2003]. In fact, our related recent work suggests that the SST differences among models in the Southern Ocean affect the cooling in the deep Atlantic Ocean, which in turn influences sea ice distribution in the North Atlantic Ocean and the AMOC during the LGM. In this study, we also pointed out a role of the wind stress in controlling the glacial AMOC. The glacial surface wind is significantly modified from today especially over the North Atlantic Ocean (Figure 2c) due to the existence of huge ice sheets in the northern hemisphere as previous studies suggested [e.g., Manabe and Broccoli, 1985]. We think that the careful investigation of the differences in wind stress among models may also give us additional insight into the glacial response of the AMOC and its discrepancy among models.
 We thank Anders Levermann and an anonymous reviewer for their helpful comments. This research was partially supported by the Japan Science and Technology Agency's Core Research for Evolution Science and Technology (JST/CREST). Akira Oka is also supported by KAKENHI 23684040. The OGCM simulations in this study were performed by HITACHI SR11000 at the Information Technology Center, University of Tokyo. Figures were prepared with the Dennou Library (developed by the GFD-Dennou Club).
 The Editor thanks Anders Levermann and an anonymous reviewer for their assistance in evaluating this paper.