The fresh water advection into the Atlantic ocean by the overturning circulation (Fov) has been suggested as an indicator of the stability of the Atlantic Meridional Overturning Circulation (AMOC) through an advective feedback. This feedback is explored in transient simulations with a global climate model with and without flux adjustments. Flux adjustments are shown to alter the model near surface salinity, changing Fov from a net importer, to a net exporter of fresh water, mainly through correcting an Atlantic saline bias. The AMOC recovers in strength from a collapsed state, however, that in the experiment with flux adjustments recovers much later and more slowly than that without flux adjustments. This difference is traced back to the sign of Fov, confirming the indicator's importance for the AMOC and suggesting that model biases affecting Fov need to be addressed in order to assess the likelihood of irreversible changes in the AMOC.
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 Paleoclimate data has suggested that abrupt changes to climate may have been caused by the Atlantic Meridional Overturning Circulation (AMOC) switching from an “on” state, where it transports heat northwards in the Atlantic, to an “off” state [Rahmstorf, 2002]. It is thought that these abrupt changes may be related to the existence of bistability (where both “on” and “off” states of the AMOC can exist for a given forcing) as predicted by theoretical “box” models of the Atlantic [Stommel, 1961; Rahmstorf, 1996]. The existence of bistability is supported by experiments using Earth System Models of Intermediate Complexity [Rahmstorf et al., 2005], and, more recently, a coarse resolution global circulation model (GCM) with a dynamic atmosphere [Hawkins et al.2011], although there is disagreement amongst those models as to whether the present climate is bistable or monostable.
 The possible importance of the fresh water (FW) balance of the Atlantic to AMOC stability was first suggested by Rahmstorf , leading de Vries and Weber  to suggest that the FW flux by the AMOC into the South Atlantic (Fov) might be an important indicator of whether the AMOC is in a monostable or bistable regime. Various studies support the importance of Fov as an indicator for the stability of the AMOC in simple or intermediate complexity models [de Vries and Weber, 2005; Huisman et al.2010], though Sijp et al.  found that Fov is not always a good predictor.
Stouffer et al.  found that the AMOC in all complex GCMs tested recovered after a 1 Sverdrup (Sv = m3/s) hosing. Drijfhout et al.  suggest one reason for this may be a bias in the sign of Fov: in many GCMs the AMOC transports FW into the Atlantic in present day simulations, whereas observations and reanalyses suggest that the AMOC exports FW from the Atlantic [Hawkins et al.2011; Bryden et al.2011]. Recent results from the Coupled Model Intercomparison Project 5 (CMIP5) show that some state-of-the-art GCMs now have negative values of Fov [Weaver et al., 2012]. de Vries and Weber  found that perturbing surface salinity near 33°S in the Atlantic resulted in Fov becoming negative and a shift to a bistable AMOC regime.
 In this study, results are presented from fluxadjusted and non-fluxadjusted version of HadCM3, one with a positive and one with a negative Fov. The main aim of this study is to examine the relevance of the sign of Fov in transient simulations in a complex GCM. First, the hypothesis behind Fov as an indicator is summarized in section 2, and the climate models are described in section 3. The differences in Fov are investigated in section 4, and the implications for the transient response are explored in section 5 by applying FW perturbations to both experiments. Conclusions are presented in section 6.
2 The Advective Feedback
Fov is the net meridional fresh water transport by the overturning circulation and is calculated as
where is the zonally integrated meridional velocity, ⟨S(z)⟩is the zonally averaged salinity, and S0 is a reference salinity. Integrals and averages are taken over a latitude line at 34°S in the Atlantic.
 The total advection of fresh water (FW) through the southern boundary can be written where Faz is the transport associated with zonal gradients in velocity and salinity, and Fmix is the transport by mixing (including parameterized eddy processes). The total fresh water budget can then be written
where AFW is the Atlantic fresh water content, Fsf is the net surface flux (including contributions from precipitation, evaporation, river runoff and sea ice processes) and FN is the total advection of fresh water through the northern boundary. In this study, the northern boundary is chosen to be at 78°N between 21°W and 29°E (Fram Straits) and at 29°E between 71°N and 78°N. This boundary includes the GIN seas (where HadCM3 experiences significant convection associated with the AMOC) in the Atlantic, but distinguishes between the Atlantic and Arctic basins, since FW changes in the latter may not directly impact the AMOC.
 The motivation behind considering Fov as an indicator of AMOC stability originates with simple “box” model representations of the circulation [Stommel, 1961; Rahmstorf, 1996]. In these models, Fov = − QΔS ∕ S0 where Q is the volume transport of the AMOC and ΔS is the difference in salinity between the water imported to and exported from the Atlantic. They also represent the AMOC strength as being proportional to the meridional density gradient. Hence, a decrease in Q reduces the magnitude of Fov and affects the salinity of the Atlantic box (through equation (2)) which, through changing the density gradient, has a feedback onto the AMOC. If Fov < 0 initially then this is a positive feedback, and if Fov > 0 initially, a negative feedback. Although Rahmstorf  associates the presence of a positive (negative) advective feedback with a bistable (monostable) AMOC, it is unclear whether this is also true for a complex, fully coupled GCM where other oceanic and atmospheric feedbacks can occur, and the AMOC may not be controlled by the Atlantic salinity.
 These experiments are conducted using both flux adjusted (FA) and unfluxadjusted (UFA) versions of the global, coupled, climate model HadCM3. In FA, extra surface heat and FW fluxes are applied to “nudge” surface temperatures and salinities towards observational values. Further details of the model and flux adjustments are described in the Supporting Information.
4 Fov in HadCM3
 Like many other free running GCMs [Drijfhout et al.2011], unfluxadjusted HadCM3 (UFA) has a positive Fov (0.23 Sv at 34°S, Figure 1a) as previously noted by Pardaens et al. , however, when HadCM3 is fluxadjusted (FA), Fov is negative ( − 0.17 Sv). The value of Fov depends on velocity and salinity profiles across the section (Figures 1b and 1c): differences in velocity profiles are small, but those in salinity profiles are much larger. The near surface salinity in UFA is much fresher at 34°S than that in FA and in observations (blue line, taken from the EN3 data set [Ingleby and Huddleston, 2007]), whereas FA does a much better job at capturing the surface salinity. Although there are salinity biases at all depths, analysis (not shown) shows that the biggest differences in Fov arise from the near surface salinity biases. The large fresh bias in the top 500 m at 34°S in UFA is typical of the bias across the southern hemisphere rather than a local phenomenon (Figure 1d), and is not apparent in FA (Figure 1e).
4.2 Causes of the Biases
 Since it is suggested that the sign of Fov might be important for the stability of the AMOC, it is of interest to understand what aspect of the flux adjustment changes the sign of Fov. This will aid the development of future GCMs, improving the underlying physics and increasing confidence in future projections of the AMOC.
 To confirm the supposition that it is the FW fluxes that are important rather than heat flux adjustments, an experiment is conducted where the FW flux adjustments alone are applied, starting from initial conditions taken from UFA. Fov drifts from an initial positive value to a value of − 0.09 Sv after 300 years. At this point, several experiments are initialized using different simplifications of the FW flux adjustment field (see Supporting Information). The results of these experiments show that it is the adjustment of the net Atlantic FW fluxes that results in Fov < 0. By acting to salinify the Indo-Pacific and Southern Ocean and freshen the Atlantic, the water imported into the Atlantic in the upper ocean becomes saltier and Fov decreases. It has been shown previously that HadCM3 has too much evaporation in the subtropical Atlantic [Pardaens et al.2003] resulting in a net surface FW flux of − 0.76 Sv over the Atlantic in UFA, compared to estimated observational values of − 0.39 and − 0.44 Sv for a similar region [Rodríguez et al.2011]. The flux adjustments in FA overcompensate for this bias, resulting in a total surface FW flux of − 0.14 Sv in FA. Therefore, the flux adjustment field must also be compensating for salinity biases caused by inaccurate dynamics as well as the evaporative bias.
5 Hosing Experiments
 Although it is prohibitively expensive to test the stability of the AMOC in FA and UFA with hysteresis experiments, much can be learned about whether the advective feedback (section 2) behaves as predicted, and how the AMOC responds in transient “hosing” experiments. In these experiments, an additional 1 Sv of FW is added for 150 years to the North Atlantic (over 50–70°N, with a compensating flux applied over the rest of the ocean). After 150 years, the hosing flux is stopped and the model is allowed to recover.
 Figures 2a and 2b show the AMOC time series for the UFA and FA hosing runs, and the equivalent time series in control experiments where no hosing flux is applied. Both experiments experience a large weakening of the AMOC over the first 50 years of hosing. After 150 years of hosing, there is a substantial reduction in winter mixed layer depth (Figure S3) and the basin-wide circulation associated with sinking in the North Atlantic disappears (Figures 2e and 2f). With the disappearance of the AMOC cell, a shallow cell between 50 m and 700 or 1000 m associated with the Antarctic Intermediate Water (AAIW) becomes apparent. This cell is slightly stronger in FA than UFA. The Antarctic Bottom Water cell does not change significantly. Similar circulation patterns are also seen in the off states of FAMOUS (L. Allison, personal communication) calculated from the experiments of Hawkins et al. .
 The AMOC strength in UFA starts recovering relatively quickly, about 50 years after the hosing finishes, and increases quickly, reaching and overshooting its control values 100 years later. In FA, the AMOC takes 100 years longer to start recovering and recovers much more slowly, not approaching its control strength until more than 400 years later.
5.2 Exploring the Advective Feedback
 The presence of the advective feedback depends on several assumptions explored in this section: first, that the sign of Fov in the control indicates how the FW transport by the overturning circulation will evolve. Huisman et al.  found that the evolution of the anomalous advection of the background salinity by the AMOC is indeed predicted by Fov, however, there were also changes in advection caused by evolving salinity. In these experiments, it would therefore be expected that Fov decreases (increases) to zero from an initial positive (negative) value as the overturning circulation weakens. This indeed occurs during the first 50 years of the experiment (Figures S4b and S4d), although there are subsequent changes to Fov over years 50–200 as the AAIW FW transport replaces that of the AMOC, and later as the salinity field changes and the AMOC recovers. The initial change in Fov results in an anomalous import of FW in FA over years 0–600, acting to increase the FW of the Atlantic. In UFA, the opposite occurs, with the initial change in Fov resulting in an anomalous export of FW from the Atlantic over years 0–400, acting to salinify the Atlantic. Figure 3f (blue line) shows the difference between the experiments and the greater net freshening of FA than UFA by Fov.
 The second assumption is that a change in the advection of FW by the overturning circulation significantly alters the FW balance of the Atlantic. This assumption relies on other contributions (see equation (2)) changing little, however the FW content of the Atlantic is significantly altered by changes in both Faz and FN (Figures S4b and S4d). Although FA experiences a greater FW export through these terms than UFA, this is outweighed by the greater import of FW by Fov (Figure 3f). Hence, while it is not true that Fov dominates the FW balance of the Atlantic in either experiment, it does result in a greater freshening through net advection in FA than UFA, and hence a faster freshening and slower recovery of Atlantic FW content in FA (Figures 3c–3e).
 Changes in surface fluxes cause a ∼ 0.05 Sv freshening in both experiments when the AMOC is in the off state, acting as a stabilizing feedback (Figures S4a and S4c). This is a result of cooler North Atlantic surface temperatures (from reduced northwards heat transport) reducing evaporation and increasing the volume of sea ice melt in the Atlantic (as a result of greater ice formation in the Arctic). When the AMOC in UFA recovers, this freshening is removed, resulting in differences in FW input by surface fluxes (Figure 3e).
 The third assumption is that a change in the FW content of the Atlantic causes a corresponding change in the AMOC. This relationship is examined in Figures 3a and 3b. Although the relationship is not exact (there is a different relationship as the AMOC decreases and increases), there is a correspondence between the AMOC strength and the anomalous Atlantic salinity.
 It is not obvious that the AMOC strength should depend on the salinity of the Atlantic as a whole, rather than the salinity (or density) of the North Atlantic subpolar regions where deep water formation occurs. In these experiments, however, the salinity anomalies are large and dominate density anomalies, and it can be seen that the relative freshening of the Atlantic in FA compared to UFA results in the freshening of the upper (top 500 m) subpolar North Atlantic (Figure 4c).
 Both FA and UFA experience a freshening from the hosing in the subpolar north Atlantic, with a cessation of deep convection (Figure S3). The FW input by hosing is then trapped in the surface layers and transported meridionally by the wind-driven circulation, eddies and mixing. At the same time, the reduction in the AMOC reduces the meridional transport of FW into the South Atlantic. Before hosing, the upper ocean water imported into the Atlantic is much fresher in UFA than FA and this is compensated by greater surface FW loss, mainly in the tropics. Both models also experience a freshening from gyre transports into the South Atlantic. When there is a reduction in the meridional transport of relatively saline/fresh upper ocean water in FA/UFA, it results in a relative freshening/salinification throughout the South Atlantic (Figures 4a and 4b). A signal of greater freshening in FA than UFA spreads northwards into the subpolar North Atlantic, starting to arrive around year 180 (Figure 4c) when the AMOC in UFA starts to recover and the AMOC behavior of the two experiments diverges. If a negative Fov was achieved with increased Faz, rather than less surface FW loss in the tropics, the FW anomaly would be likely to originate closer to 30°S, however, it would be expected to move northwards in the same way, although the effects might be felt later.
 Although these results do not prove a causal link between Atlantic FW content and AMOC strength, they do add weight to the hypothesis that changes in the Atlantic FW content can play an important role in the recovery of the AMOC strength through its impact on subpolar densities. It is likely though that other process modifying local conditions also affect the AMOC and its transient behavior.
 Although the flux adjustments allow the temperature and salinity to evolve and allow coupling between the ocean surface and atmosphere, the heat flux adjustment could affect coupled feedbacks, impacting the sensitivity of the AMOC. To test whether the results in this study are affected, an additional experiment is performed using only FW flux adjustments but not heat flux adjustments (FWFA, Figure S5). Through correcting the salinity, but not temperature, there is an impact on the density (and hence the background circulation), however, the response of Fov and the Atlantic freshwater budget are similar to FA. There are differences in the timing of the AMOC and Atlantic salinity recovery, demonstrating that Atlantic salinity, whilst giving an indication of the AMOC recovery, does not determine the transient behavior. FW flux adjustments may affect the AMOC response, however, [Dijkstra and Neelin, 1999] find that there is little impact of FW flux adjustments on the hysteresis behavior when the unfluxadjusted model already has an AMOC such as in Figures 2c and 2d.
 Flux adjustments could affect processes such as convection that affect the AMOC, and, therefore, any results with a flux adjusted model should be examined carefully; however, the current study explores large scale feedbacks operating in both flux and unfluxadjusted models.
5.3 Implications for Stability
 Although the sign of Fov suggests that FA should have a stable AMOC off state, these experiments show a recovery of the AMOC, albeit a delayed and slow one. In an additional experiment with FA but applying 300 years of hosing (300 Sv years, slightly more total FW input than de Vries and Weber  and Hawkins et al.  used to achieve a steady AMOC off state), the AMOC starts to recover, although after even longer (not shown).
 The Atlantic salinity in FA recovers after the hosing period because of the large FW export by Faz (Figure S4b). This is a result of the southwards transport of surface fresh water input by the hosing freshening the Brazil current. Whilst it is not unexpected that the meridional fluxes adjust to export the excess 1 Sv of FW input by the hosing, the timescales on which this occurs will have a large impact on the total FW change and the effectiveness of the hosing. Swingedouw et al.  show that HadCM3 exports surface FW anomalies southwards from the subpolar gyre faster than other models in that study, resulting in a smaller AMOC sensitivity to hosing.
 These results could indicate that FA is not in a bistable regime, despite having Fov < 0, and that other advective components should be considered when analyzing the stability of the AMOC. Alternatively, it may be that, since Faz reduces the effective FW input by the hosing, FA requires greater or longer hosing to reach a stable off state. Since our simulations are limited in length and hence do not reach an equilibrium, it is impossible to categorically say that FA is not in a bistable regime.
 This study has analyzed idealized hosing experiments with the aim of understanding how the sign of Fov (the import or export of FW to the Atlantic by the overturning circulation) affects the transient recovery of the AMOC in a complex GCM. The main results are as follows:
 Following an FW perturbation to switch off the AMOC, the model with Fov < 0 stays 100 years more with the AMOC in the “off” state, and has a much slower recovery than the model with Fov > 0.
 The sign of Fov in the control does indicate the advective feedback experienced.
 Other components of advection, in particular the zonal component of the export from the South Atlantic, also play a large role in altering the FW content of the Atlantic. However, it is the different behavior of Fov that is responsible for the different AMOC behavior.
 Applying flux adjustments to nudge the temperature and salinity fields closer to observed values results in Fov switching from a positive, to a negative value. This is achieved mainly by correcting the saline bias of the Atlantic (which is partly due to an evaporative bias in the low latitude Atlantic).
 These results show that model biases can have a large impact on the AMOC sensitivity to FW forcing. To make credible assessments of the likelihood of an irreversible change in the AMOC, we must reduce model biases such as that in Fov through improving model representations of relevant processes.
 Support from P. Halloran and M. Menary in setting up the experiments is gratefully acknowledged. Thanks go to L. Allison, E. Hawkins and M. Palmer for their helpful comments and to two anonymous reviewers. This work was supported by the Joint DECC/Defra Met Office Hadley Centre Climate Programme (GA01101).