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 Abrupt decadal climate changes during the last glacial-interglacial cycle are less pronounced during maximum glacial conditions and absent during the Holocene. To further understand the underlying dynamics, we conduct hosing experiments for three climate states: preindustrial (PI), 32 kiloannum before present (ka B.P.), and Last Glacial Maximum (LGM). Our simulations show that a stronger temperature inversion between the surface and intermediate layer in the South Labrador Sea induces a faster restart of convective processes (32 ka B.P. > LGM > PI) during the initial resumption of the Atlantic meridional overturning circulation (AMOC). A few decades later, an AMOC overshoot is mainly linked to the advection of warmer and saltier intermediate-layer water from the tropical Atlantic into the South Labrador Sea, which causes a stronger deep-water formation than that before the freshwater perturbation. This mechanism is most pronounced during the 32 ka B.P., weaker during the LGM and absent during the PI.
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 The last glacial-interglacial cycle, from ~120 kiloannum before present (ka B.P.) to the Holocene epoch (since ~10 ka B.P.), is punctuated by more than 20 abrupt climate changes, which can occur within a few decades [Dansgaard et al., 1993]. The magnitudes of these climate changes are stronger between 25 and 70 ka B.P., and less pronounced at maximum glacial conditions during the Last Glacial Maximum (LGM, ~21 ka B.P.). Furthermore, proxy evidence from North Atlantic deep-sea sediments demonstrates an absence of abrupt climate changes during the Holocene [e.g., Zhao et al., 1995]. Overall, these proxy records suggest that the potential and the signature of abrupt climate changes are nonuniform during different climate states throughout the last glacial-interglacial cycle. Furthermore, records of sedimentary nutrient proxy evidence and kinematic proxies indicate a notable correlation of abrupt climate changes and variations in the Atlantic meridional overturning circulation (AMOC) [e.g., McManus et al., 2004; Thornalley et al., 2011]. In the so-called “water hosing” experiments by numerical models, freshwater fluxes to the North Atlantic surface ocean have shown to be a potential key factor to modulate the strength and stability of the AMOC in regional and global climate change scenarios. Therefore, AMOC changes induced by freshwater perturbation have been used to induce abrupt climate changes [e.g., Manabe and Stouffer, 1995; Rahmstorf, 1996; Ganopolski and Rahmstorf, 2001; Prange et al., 2004; Liu et al., 2009].
 Models of different complexities commonly show that the mechanism for the AMOC reduction is strongly related to a surface freshening at deep-water formation sites in the North Atlantic. However, the underlying dynamics for an AMOC recovery after the end of the perturbation are potentially more diverse. For instance, Hu et al.  and Renold et al.  reveal a two-phase recovery of the AMOC during the present and the LGM, and they emphasize the roles of the Bering Strait and the Greenland-Iceland-Norwegian Sea (GIN Sea) on these AMOC variations, respectively. Using a model of intermediate complexity, Prange et al.  perform freshwater hosing experiments for different glacial background states and find a two-step relaxation for background conditions with convection sites in the South Labrador Sea and the GIN Sea, as well as a slower response for an AMOC background state without convection in the GIN Sea. By changing locations and magnitudes of freshwater perturbations, Otto-Bliesner and Brady  identify different recovery characteristics of the AMOC within hundreds of years after removing the freshwater perturbation. Their results also present the importance of southward expansion of polar sea ice, which can lead to an increase of colder and fresher water export into the high-latitude North Atlantic Ocean, accompanied by a meridional shift of the Intertropical Convergence Zone. Furthermore, it has been suggested that variations in the location of the freshwater perturbation in the high-latitude North Atlantic Ocean can induce changes in the northward transport of warm and saline subsurface water into the South Labrador Sea and the GIN Sea, which subsequently lead to a different reduction of deep-water formation despite a similar overall AMOC slowdown [Kleinen et al., 2009]. Moreover, the AMOC stability behavior and sensitivity to freshwater perturbations has been shown to be dependent on the background climate conditions [e.g., Ganopolski and Rahmstorf, 2001; Prange et al., 2003; Prange et al., 2004; Knorr and Lohmann, 2007].
 Here, we aim to investigate the underlying dynamics for the resumption process and overshoot phenomenon (a temporally more intensified state than that before freshwater perturbation) of the AMOC recovery, which may have operated differently during various stages of the last glacial-interglacial cycle. Therefore, we conduct hosing experiments for the three different climate states and examine the subsequent changes of the convective process in the North Atlantic, as well as the interplay with the changes in the tropical Atlantic on the AMOC. Special emphasis is given to spatiotemporal changes in the North Atlantic during the overall AMOC recovery in the three different climate states.
2 Model and Experimental Design
 We employ the Community Earth System Model (COSMOS), which is a fully coupled ocean-atmosphere-sea ice-land surface model [Jungclaus et al., 2006]. Our version of COSMOS has been applied and tested for the Cenozoic climate [Knorr et al., 2011; Stepanek and Lohmann, 2012] and glacial [Zhang et al., 2012] and interglacial climate states [Wei et al., 2012; Wei and Lohmann, 2012]. The ocean component is the ocean general circulation model MPIOM [Marsland et al., 2003], utilizing a curvilinear Arakawa-C grid with a formal horizontal resolution of ~3° × 1.8° and uneven 40 vertical layers, including the dynamics of sea ice formulated by viscous-plastic rheology [Hibler, 1979]. The atmospheric component ECHAM5 [Röckner et al., 2003] runs at a horizontal resolution of ~3.75° × 3.75° with 19 vertical levels and is complemented by the land surface scheme JSBACH [Raddatz et al., 2007] including a dynamical vegetation module [Brovkin et al., 2009]. Before conducting freshwater hosing experiments, the simulations for preindustrial (PI), LGM, and 32 ka B.P. (Table S1) have been run for over 2000 years to reach their respective quasi-equilibrium states. Orbital forcing is inferred from Berger , and the greenhouse gas concentrations use the reconstructions from ice cores, including CO2 [Indermühle et al., 1999], CH4 [Brook et al., 2000], and N2O [Sowers et al., 2003]. The major differences between their land-sea masks are due to sea level changes, corresponding to the changes of ice sheet coverage and thickness. Regarding the LGM simulation, the paleotopography data are provided by the Paleoclimate Modelling Intercomparison Project Phase III (PMIP3, http://pmip3.lsce.ipsl.fr/), with a sea level reduction of 116 m during the LGM compared to the PI, with associated ice sheet changes. In the 32 ka B.P. simulation, sea level is decreased by 80 m relative to the PI, accompanying with the changes of high-latitude ice sheets, e.g., Laurentide Ice Sheet, Fennoscandian Ice Sheet and Antarctic Ice Sheet [Köhler et al., 2011; Thompson and Goldstein, 2006; Peltier, 2004]. As a consequence of different land-sea masks, river runoff routes also change with respect to new adapted topographies [Hagemann and Dumenil, 1998]. To initialize different simulations, the ocean components are integrated from the Levitus  hydrographic data. The present atmosphere and vegetation are used as the initial conditions for the atmosphere and land surface components.
 When performing the freshwater perturbation experiments, a freshwater flux of 0.2 Sv (1 Sv = 106 m3/s) is added to the ice-rafted debris belt in the North Atlantic Ocean, around 40°N–55°N, 45°W–20°W of the central Atlantic Ocean [Zhao et al., 1995; Hemming, 2004]. The forcing lasts for 150 years, after which an additional 300 years are simulated for the AMOC recovery, i.e., without freshwater perturbation. The intensity of AMOC is presented by the maximum value of the meridional overturning stream function of the upper 200–3000 m and 30°N northward.
 At the end of the 150-year freshwater perturbation, the overall AMOC is suppressed to a comparable strength of ~5 Sv in all the three climate states, starting from different initial levels before the freshwater perturbations (18 Sv for PI, 19 Sv for LGM, and 25 Sv for 32 ka B.P.) (Figures 1a–1c). More details of temporal AMOC changes can be found in the supporting information (Figure S1). In experiment PI, the deep-water formation decreases in the South Labrador Sea and the GIN Sea at the end of freshwater perturbation (Figure S2). In experiments LGM and 32 ka B.P., an additional reduction of deep-water formation in the oceanic region south to Iceland (South-Icelandic Sea) is detected. According to the method introduced by Cheng et al. , the strength of deep-water formation in the GIN Sea is defined as the vertical maximum value of stream function in the oceanic region north to the Greenland-Scotland Ridge (north of 62°N). Hence, the difference between the AMOC strength and the deep-water formation in the GIN Sea can be used as an indicator of the intensity of the deep-water formation in the South Labrador Sea under PI conditions (Figure 1a) or the sum of deep-water formation in the South Labrador Sea and South-Icelandic Sea under 32 ka B.P. (Figure 1b) and LGM (Figure 1c) conditions.
 Interestingly, the following recovery stages exhibit a clear dependence on the climate background states despite the similar overall AMOC strength at the end of the 150 year freshwater perturbation (Figure 1). The most prominent differences are the overshoot characteristics during the recovery. In the following, we will subdivide the underlying dynamics of the overall AMOC recovery into two stages: one directly following the end of the freshwater perturbation that describes the initial resumption, and a superposed phase that coincides with the AMOC overshoot dynamics.
3.1 Initial Resumption of the AMOC
 In experiment PI, the deep-water formation in the South Labrador Sea reaches a minimum of ~5 Sv between 140 and 150 model years, whereas it is ~2 Sv in the GIN Sea. After the end of the freshwater perturbation, the increase of the AMOC occurs with an instant resumption of deep-water formation in the GIN Sea and the South-Icelandic Sea (Figures 1a and S2b). After the 360 model year (i.e., 110 years after stopping the freshwater perturbation), the deep-water formation and the AMOC have recovered to their starting levels prior to the freshwater perturbation (Figure 1a). This result is comparable to the work of Mignot et al. , who designed a similar experiment, using a negative anomalous salt flux corresponding to 0.35 Sv for 100 years between 50°N and 80°N. During the glacial time, the deep-water formation in the GIN Sea is quasi-terminated at the end of freshwater perturbation in the 32 ka B.P. experiment and shows a complete shutdown in our LGM run (Figures 1b and 1c). Meanwhile, the deep-water formation out of the GIN Sea, i.e., the sum of that in the South Labrador Sea and the South-Icelandic Sea, is diagnosed to be ~6 Sv in the 32 ka B.P. experiment and ~4 Sv in the LGM experiment (for the calculation algorithm, cf. Cheng et al. ). Subsequently, under LGM conditions, an instant restart of deep-water formation is found in the South Labrador Sea and the South-Icelandic Sea, whereas the restart in the GIN Sea occurs 30 years later (Figures 1c and S2f). As shown in Figure 1h, the initial resumption of the deep-water formation in the LGM experiment is accompanied by an instant deepening of annual mean mixed layer depth (AMMLD) in the South-Icelandic Sea. Equivalent variations are detected for winter mean mixed layer depth changes (Figure S3). In addition, a collapse of vertical density stratification is found in the South Labrador Sea, which is related to a modified salinity stratification and temperature inversion between the surface and intermediate layers that are generated during the freshwater perturbation (Figure 2c). The most significant temperature and salinity anomalies are found in the intermediate layer under 32 ka B.P. conditions. After deactivating the freshwater forcing, an instant collapse of water mass stratification is detected with respect to both the salinity stratification and the temperature inversion. Ultimately, a breakdown of density stratification is caused by the vertical temperature inversion. Along with the resumption of the convective process, the temperature inversion between the surface and intermediate layer becomes weaker (Figure 2). The most rapid recovery of convective processes occurs in the 32 ka B.P. experiment, which also highlights the role of temperature and salinity anomalies on AMOC recovery once the freshwater forcing is removed. The salinity changes associated with the surface freshening are detected down to 3000 m depth in the South Labrador Sea and 1000 m depth in the GIN Sea, respectively. Similarly, the salinity anomaly in the GIN Sea is particularly strong in the 32 ka B.P. experiment, which also shows the quickest breakdown of the salinity stratification and the temperature inversion after 250 model years (Figure 2).
 Sea ice cover shows an instant decrease after the end of freshwater perturbation and reaches a minimum accompanying with the occurrence of the AMOC overshoot (Figures 1f and 1g). During the process of AMOC recovery, freshwater from sea ice melting increases salinity stratification and counteracts the convective process. In the 32 ka B.P. experiment, the South Labrador Sea and the GIN Sea become ice free during the AMOC overshoot. However, after the AMOC overshoot, a rapid rebuildup of sea ice results from cold surface air temperature during the LGM (Figure 1f).
3.2 The AMOC Overshoot
 So far, we have shown that the initial resumption of the AMOC is strongly dependent on the background climate conditions. In the following, we will investigate the role of these conditions for the superposed overshoot characteristics during the overall AMOC recovery. Between 320 and 340 model years, the AMOC strength shows an overshoot of ~12 Sv in the 32 ka B.P. experiment, which is characterized by a water mass with high temperature and high salinity (HTHS) in the intermediate layer of the South Labrador Sea (Figures 1b and 2b). Approximately five decades later, similar water property anomalies and the corresponding AMOC overshoot (~5 Sv) are detected in the LGM experiment, but they are completely absent in the PI experiment.
 As shown in Figures 1d and 1e, the increase of salinity and temperature during the freshwater perturbation occurs with different rates as indicated by the field mean values for intermediate-layer water of the tropical Atlantic Ocean. These changes are negligible in the PI experiment and stronger in the LGM experiment, with the largest changes in the 32 ka B.P. experiment by showing an increase of 0.6 practical salinity unit (psu) and 2.1°C. These variations of intermediate-layer water properties in the tropical Atlantic Ocean are in agreement with proxy data and consistent with a reduced ventilation of cold intermediate water in conjunction with downward mixing of heat from the thermocline [Rühlemann et al., 2004]. The most pronounced tropical warming in the 32 ka B.P. experiment is in accordance with the largest reduction of the AMOC (Figures 1b and 1e). After the end of freshwater perturbation, initial levels of salinity and temperature are reached within a few decades. This indicates that the increase of salinity and temperature in the intermediate layer of the tropical Atlantic Ocean are linked to the freshwater perturbation in the North Atlantic. Overall, a stronger increase of salinity and temperature in the tropical Atlantic Ocean also favors a larger AMOC overshoot. More details of all-depth Atlantic water property changes are shown in the supporting information (Figures S5 and S6).
 In the comparison between the states during the suppressed AMOC and AMOC overshoot, the water mass change of the ocean north of 45°N exhibits reversed changes to the tropical Atlantic. The HTHS water is transported from the tropical Atlantic Ocean into the South-Icelandic Sea and the South Labrador Sea (Figure 3). Similar to the differences in the AMOC overshoot strength, the anomalous sea surface temperature is also most pronounced in the 32 ka B.P. experiment. More details are shown in the supporting information (see also Figure S4). After entering the South Labrador Sea, the intermediate-layer water is warmer and saltier due to the import of the HTHS water. Under a dominating impact of the temperature change, the intermediate-layer water becomes less dense than the surface water. Thus, the intermediate-layer water is ventilated into the surface, where it loses heat while keeping the salinity characteristics. This densification process generates an abrupt intensification of the convective process [cf. Knorr and Lohmann, 2003]. Accordingly, the lack of HTHS water in the South Labrador Sea leads to the absence of the AMOC overshoot in PI (Figures 1a and 2a).
 On the way northward, the HTHS tropical Atlantic water flows throughout the South-Icelandic Sea before entering the South Labrador Sea. A similar mechanism, as working on the vertical stratification in the South Labrador Sea, can result in a vigorous deep-water formation in the South-Icelandic Sea. Indeed, a pronounced deepening of AMMLD is found in the 32 ka B.P. and LGM experiments, as shown in Figure 1h. With focus on the temporal development, it is interesting to note that the occurrence of the most pronounced deepening of the AMMLD in the South-Icelandic Sea is prior to the AMOC overshoot under 32 ka B.P. and LGM conditions. During the AMOC overshoot, the AMMLD in the South-Icelandic Sea relaxes to the initial levels prior to the freshwater perturbation, while a maximum AMMLD in the South Labrador Sea is reached (Figures 1h and S8).
 The HTHS tropical Atlantic water is also found in the GIN Sea during the LGM, coinciding with the duration of the AMOC overshoot between 370 and 410 model years (Figure 2f). Nevertheless, it is not accompanied by an intensification of the deep-water formation (Figure 1c), but a substantial reduction of sea ice cover (Figure 1f). This suggests that the freshwater from sea ice melting constrains the convective processes during the AMOC overshoot. The anomaly of salinity and temperature in the GIN Sea is primarily a passive effect of the AMOC recovery, which is driven by the recovery of the deep-water formation in the South-Icelandic Sea and the South Labrador Sea.
4 Discussion and Conclusions
 Based on our freshwater hosing experiments, we detect two different stages during the overall AMOC recovery. Compared to the PI experiment, the resumption of the AMOC is abrupt and relatively fast under 32 ka B.P. and LGM conditions. The magnitude of the AMOC overshoot is particularly pronounced in the 32 ka B.P. experiment and weaker in the LGM experiment, while no overshoot occurs in the PI experiment. During the glacial time, the abruptness of AMOC recovery results from an instant growth of deep-water formation in the South-Icelandic Sea and the South Labrador Sea. The magnitude of the overshoot is mainly governed by the accumulation of heat and salinity in the intermediate layer of the tropical Atlantic Ocean during the freshwater perturbation, which enters the South Labrador Sea and induces hydrostatic instabilities. The associated changes can be interpreted as a combination of convective (hydrostatic instability) and advective feedbacks (heat, salinity advection from the tropical Atlantic), with different contributions of these feedbacks to the AMOC recovery depending on the climate background.
 Proxy records [e.g., Thornalley et al., 2011] and numerical simulations [e.g., Barker et al., 2010] indicate that the occurrence of an AMOC overshoot is closely related to the intensification of North Atlantic deep-water formation. After entering the eastern part of the northern North Atlantic Ocean, the warmer and saltier tropical intermediate-layer water separates and advects into the South Labrador Sea throughout the South-Icelandic Sea, and the GIN Sea, respectively. All locations might have the potential to dominate the AMOC recovery. Liu et al.  found that the overshoot is associated with a strong subsurface warming in the Nordic Sea, and they suggest a dominant role of the GIN Sea on the AMOC overshoot. According to our investigation, the intermediate-layer warming is accompanied by a strong reduction of sea ice cover, but not correlated with an intensification of deep-water formation in the GIN Sea. This behavior is mainly related to a stronger northward heat transport due to the recovered AMOC, which is mainly driven by the South Labrador Sea and the South-Icelandic Sea, and the restriction of deep-water formation in the GIN Sea by sea ice melting. Cheng et al.  identified the exchange between the North Atlantic and the GIN Sea as a key element in explaining the full magnitude of the AMOC overshoot during the Bølling-Allerød warming. Our experiments identify that the joint effect of the hydrographic changes in the South Labrador Sea and the intermediate-layer water properties of the tropical Atlantic Ocean acts as an alternative key player that governs the overshoot dynamics of the AMOC. Overall, a comparison between earlier investigations [e.g., Mignot et al., 2007; Knorr and Lohmann, 2007; Liu et al., 2009; Cheng et al., 2011] and this work suggests that similar mechanisms and feedbacks (convective and advective feedbacks) are important for the AMOC recovery. However, the individual contributions of different North Atlantic deep water formation sites during the AMOC resumption are dependent on the climate background state, as shown by our analysis. In this context our work provides a basis to integrate different studies on AMOC recovery into a common framework, beyond explanations invoking different model complexities and differences in the experimental setup. Furthermore, the underlying dependence of the overshoot dynamics on the background climate provides an explanation for the different climatic responses to the freshwater perturbations which are an intrinsic part of climate variability during glacial-interglacial cycles (e.g., the 8.2 ka B.P. event and the Heinrich events) [LeGrande and Schmidt, 2009; Hemming, 2004].
 We thank the colleagues of the Paleodynamics Group of Alfred-Wegener-Institut for Polar and Marine Research (AWI) for the continuing support and helpful discussions. This work was supported by the Helmholtz Graduate School for Polar and Marine Research (POLMAR) and the Helmholtz Climate Initiative Regional Climate Change (REKLIM).
 The Editor thanks an anonymous reviewer for assistance in evaluating this paper.