Separating Direct Heat Flux Forcing and Freshwater Feedback on AMOC Change Under Global Warming

The Atlantic meridional overturning circulation (AMOC) is predicted to weaken under global warming. Whether it is caused by heat flux or freshwater flux is under debate. Here we separate these two processes in changing the AMOC under global warming. The simulated AMOC is weakened during the first 600 years and then gradually recovered to its initial state, with heat flux and freshwater feedback dominating at different timescales. Global warming immediately puts freshwater into the Southern Ocean, which triggers the initial AMOC weakening via altering surface temperature. Concurrently, the extensive heat into the ocean surface increases the temperature over the subpolar North Atlantic, reducing the deep convection and thus the AMOC in the subsequent 50–150 years. Meanwhile, the Arctic sea ice melt leads to the AMOC shutdown. Subsequently, the salinity accumulation in the subtropical North Atlantic propagating northward to restart the North Atlantic deep convection is responsible for the AMOC recovery.

• The first study to separate the direct heat effect from freshwater feedback on the thermohaline circulation under global warming • The initial Atlantic meridional overturning circulation (AMOC) weakening is driven by freshwater feedback, while its continuous weakening is attributed to heat flux forcing • The AMOC collapse and recovery after 200 years is driven by the freshwater feedback

Supporting Information:
Supporting Information may be found in the online version of this article.
importance of these two fluxes in driving changes to AMOC is essential for reducing uncertainty surrounding AMOC weakening and its future trajectory (Reintges et al., 2017).The surface wind is supposed to alter the AMOC locally from the North Atlantic and remotely from the Southern Ocean (Lohmann et al., 2021;Marshall & Speer, 2012;Roach et al., 2022).Climate models predict a likely increase and poleward shift of the wind stress over the Southern Ocean (Meehl et al., 2007), which may influence the AMOC strength by introducing more deep outflow through the South Atlantic (Toggweiler & Samuels, 1995).
The contributions of heat flux and freshwater flux in driving the AMOC weakening under global warming, however, remain intensely debated.For instance, partially coupled integrations imposing the heat and freshwater flux separately on the ocean surface suggest that changes in surface heat flux play a more substantial role in AMOC weakening (Gregory et al., 2005(Gregory et al., , 2016;;Sandeep et al., 2020), consistent with diagnostic analyses based on fully coupled global warming simulations (Levang & Schmitt, 2020;Zhu et al., 2015).In contrast, some studies argue that AMOC weakening is primarily driven by changes in freshwater flux (Levang & Schmitt, 2020;Liu et al., 2019;Manabe & Stouffer, 1994;Sévellec et al., 2017;Skliris et al., 2020).They propose that the "wet-getting-wetter" pattern of hydrological change (Held & Soden, 2006), coupled with increased sea ice melt in subpolar regions, leads to decreased surface salinity and subsequent weakening of North Atlantic deep-water (NADW) formation.Moreover, several studies based on Arctic sea ice melt infer that declining AMOC under global warming is driven by freshwater flux input (Thornalley et al., 2018;Yang et al., 2016).The freshwater input in reducing the AMOC is evidenced in paleoclimate research in which they suggest that freshwater from ice sheet melt could enter the ocean and spread across the North Atlantic to reduce the AMOC (He & Clark, 2022;McManus et al., 2004).Moreover, the AMOC recovery at longer timescales is supposed to be associated with salinity anomalies that reduce high-latitude stratification and reinvigorate convection (Bonan et al., 2022;Krebs & Timmermann, 2007;Sigmond et al., 2020;Vellinga et al., 2002;Wu et al., 2011;Yin & Stouffer, 2007).
Due to the intricate interplay between heat and freshwater flux, accurately quantifying the individual contributions to AMOC changes remains challenging (Wen et al., 2018).Partially coupled simulations with climate models enable us to quantify the individual roles.However, previous studies often rely on forcing a climate model with equilibrium heat flux derived from global warming simulations, which we believe is already a response to AMOC weakening instead of a pure forcing (Gregory et al., 2005(Gregory et al., , 2016;;Sandeep et al., 2020).In this study, we focus on simulating climate change under increased greenhouse gas (GHG) concentrations with and without considering the surface freshwater feedback to better understand the response of AMOC to pure heat flux changes and freshwater feedback.

Model and Simulations
In this study, we utilize the Community Earth System Model (CESM1.0), a coupled climate system model developed by the U.S. National Center for Atmospheric Research.CESM has been extensively employed and validated for investigating Earth's past, present, and future climate dynamics (Hurrell, 2013;Wen & Yang, 2020).
The ocean model (POP2) and sea ice model (CICE4) adopt a uniform 3.6° spacing in the zonal direction and a non-uniform spacing in the meridional direction (ranging from 0.6° near the equator to a maximum of 3.4° at 35°N/S, then decreasing poleward).CAM5 consists of 26 vertical levels, while POP2 has 60 levels.
To quantify the heat and freshwater flux effect, two sets of experiments with and without freshwater feedback are conducted.The first group includes a 3,000-year control run (CTRL) and a 1,500-year 2 × CO2 run (2CO2).
The CTRL run uses a preindustrial CO2 concentration of 285 ppm to simulate a climate without global warming.It reaches an equilibrium state by the year 1500, and the subsequent 1,500 years of simulation are used for analysis.The 2 × CO2 run is an experiment of global warming, which begins in the year 1501 of the CTRL run, with CO2 concentration increasing by 1% per year for 70 years from 285 ppm and remaining at double the initial level from year 71 to year 1500.The difference between 2 × CO2 and CTRL represents the total effect, including both the direct heat flux effect and freshwater feedback.The second group also consists of a control run and a double-CO2 run; however, in these experiments, the surface freshwater flux into the ocean model is fixed at the monthly climatological value of the CTRL run to exclude its feedback to influence the ocean circulation under global warming.These experiments are named FixFW-CTRL and FixFW-2CO2, respectively.FixFW-CTRL is integrated for 1,500 years to achieve an equilibrium state and is then extended by another 1,500 years for analysis.The CO2 concentration is 285 ppm.FixFW-2CO2 begins in the year 1501 of FixFW-CTRL, with CO2 concentration increasing by 1% per year for 70 years from 285 ppm and remaining at double the initial level from year 71 to year 1500.The experiment design is summarized in Table S1 in Supporting Information S1.The difference between FixFW-2CO2 and FixFW-CTRL can be regarded as the direct heat flux effect without considering the freshwater feedback.Recall that the total effect has already been deduced from the difference between 2 × CO2 and CTRL.The effect of freshwater feedback can be obtained by subtracting the heat flux effect from the total effect.It should be noted that continent ice sheet melt is not included here.We only focus on the freshwater feedback from evaporation, precipitation, sea ice melt, and river runoff.Our previous work has used this set of experiments to analyze the freshwater feedback on global surface temperature and energy balance in global warming (Wen et al., 2018).Here we focus on the relative role of heat flux and freshwater feedback on AMOC evolution in the future 1,500 years.

AMOC Change
The AMOC index is defined as the maximum streamfunction in the range of 500-4,000 m over 20°N-70°N.The streamfunction across the Atlantic basin is calculated as: , where v is the ocean meridional velocity, (x1, x2) is the western and eastern boundary of Atlantic basin.The mean state of AMOC is 18 Sv (Sverdrups), consistent with that from ECCO-v4 ocean reanalysis (Ferreira et al., 2018) (Figure S2 in Supporting Information S1; Figure 1b).
The response of AMOC strength to global warming is characterized by a linear reduction during the first 200 years, followed by a steady off-state until year-600 with its strength reduced by 60%, and a gradual recovery for another 400 years, with the full recovery occurring at year-1,000 (black curve in Figure 1a).The simulated AMOC during the first 100 years falls within the range of AMOC weakening projected by CMIP5 models, which predict a 5%-45% decline by the end of the 21st century (Figure S1 in Supporting Information S1) (Cheng et al., 2013;Weijer et al., 2020).The eventual collapse of the AMOC after 200 years aligns with previous studies that have accounted for model biases by adjusting surface fluxes to observations (Liu et al., 2017).The subsequent recovery phase is consistent with other studies that focus on AMOC at longer timescales (Bonan et al., 2022;Haskins et al., 2019;Jackson, 2013;Jansen et al., 2018).
The AMOC weakening during the first 50 years under global warming is primarily triggered by the freshwater feedback (green curve in Figure 1a), the continued weakening during 50-150 years is dominated by the heat flux effect (red curve in Figure 1a), while the subsequent weakening and recovery are again driven by the freshwater feedback (green curve in Figure 1a).According to the AMOC evolution and the different importance of heat and freshwater flux, we define four stages for analysis.Stage I covers years 0-50, suggesting the very initial AMOC weakening due to freshwater feedback.Stage II encompasses years 50-150, representing the decline phase that heat flux dominates.Stage III spans years 500-600, corresponding to the collapsed phase of AMOC that freshwater dominates.Stage IV covers years 1,350-1,450, representing the final full recovery of AMOC.
The relative importance of heat and freshwater effects on AMOC can be clearly seen from the anomalous AMOC distribution.During Stage I, global warming immediately causes a reduction in the streamfunction by 2 Sv in the North Atlantic, particularly in regions where downward mass transport occurs (depicted in Figure 1b1).The most significant reduction is observed in the cell of the overturning circulation, situated at a depth of 1500 m and within the 30-50°N latitude range.This AMOC pattern resembles closely to AMOC change solely by freshwater forcing (Figure 1b9), indicating the dominant role of freshwater in triggering the initial AMOC weakening under global warming.Moving on the Stage II, the AMOC experiences further weakening with the maximum intensity reduced by 6 Sv (Figure 1b2) and is overwhelmingly caused by the heat effect (Figure 1b6).During Stage III, the AMOC is weakened much further with the maximum intensity reduced by 12 Sv, which is driven by the freshwater feedback (Figure 1b11).At this stage, the heat-driven AMOC is little changed, indicating the recovery of the heat-driven AMOC during this stage (Figure 1b7).During stage IV, the freshwater-driven AMOC recovers to its initial strength, which is responsible for the full recovery of AMOC under global warming.

Mechanism
The AMOC change under global warming is closely related to surface buoyancy flux since the momentum flux over the South Ocean is only slightly changed over 1,500 years (Figure S3 in Supporting Information S1).
Building on previous studies (Butler et al., 2016;de Boer et al., 2010;Ragen et al., 2022), we use the dynamic link between AMOC and meridional density gradients (MDG) across the Atlantic basin to comprehend the underlying mechanism associated with heat flux and freshwater feedback on AMOC change.The MDG is defined as the density difference between the Northern box (50-65°N, 60°W-10°E) and the Southern box (45-60°S, 60°W-20°E) averaged over the ocean upper 1400 m (Weber et al., 2007).The former is assumed to characterize the density of the North Atlantic deep water (NADW) formation region, where the sinking branch of AMOC occurs.An advantage of this approach is that changes in AMOC can be attributed to specific processes that modify the basin-scale density gradient, which is critical in setting the overturning strength.The evolution of MDG aligns with the AMOC evolution under global warming, with a linear decrease during the initial 200 years, followed by a steady off-state until year 600 and a gradual recovery for another 400 years (gray and black curve in Figure 2a).(a) Temporal evolution of percentage changes in Atlantic meridional overturning circulation (AMOC) induced by total effect (black curve), heat flux effect (red curve) and freshwater effect (green curve).The AMOC index is defined as the maximum streamfunction in the range of 500-4,000 m over 20°N-70°N.4 stages are outlined here as blue shadings.(b) Is for the AMOC pattern in the CTRL run (contours with an interval of 2 Sv) and its changes (shading; Sv) during 4 stages.The first panel is for AMOC change induced by the total effect, the second panel is for the heat flux effect and the third panel is for the freshwater flux effect. 1 Sv = 10 6 m 3 s −1 .

Freshwater Flux Effect
The AMOC evolution under global warming during 1,500 years resembles closely to freshwater-driven AMOC change (black and green curves in Figure 1a), suggesting the dominant role of freshwater in controlling the AMOC change in the future.Detailly, the freshwater feedback triggers the initial AMOC weakening and dominates the AMOC collapse and recovery (green curve in Figure 1a).The initial freshwater-driven AMOC weakening is caused by the sea surface density (SSD) change over the Southern Ocean (orange curve in Figure 2f), while its collapse and recovery are attributed to the SSD change over the NADW formation region (green curve in Figure 2f).We further decompose the freshwater-driven SSD change into temperature and salinity component and find that the initial MDG decrease and the resulting AMOC weakening is caused by the temperature change over the Southern Ocean (red curve in Figure 3f), while the further AMOC collapse and recovery is caused by the salinity change in the NADW formation region (blue curve in Figure 3e).
The freshwater feedback is responsible for the initial AMOC weakening by triggering Southern Ocean cooling.The doubled CO2 introduces increased freshwater flux into the Southern Ocean (Figure S4a in Supporting Information S1) due to increased precipitation and sea ice melt (Figure not shown).The freshening of the Southern Ocean may cool the sea surface temperature (Figure S4b in Supporting Information S1) by prohibiting the convective that usually ventilates the warm subsurface water into the ocean surface consistent with the hosing case over the Southern Ocean (Swingedouw et al., 2009).This cooling favors increasing the surface density locally (Figure S4d in Supporting Information S1) and decreases the MDG at the Atlantic section, which is responsible for the AMOC decrease during the first 50 years (Figure 1a).The Southern Ocean cooling in triggering the AMOC weakening is consistent with previous findings (Figure S2 in Zhang et al., 2021).The freshwater-driven AMOC recovers during years 50-150 because its induced sea surface temperature (SST) cooling over the NADW region plays a negative feedback to AMOC weakening (Figure S5b in Supporting Information S1) (Wen et al., 2018).
The freshwater effect again controls the AMOC collapse and subsequent recovery after 150 years, which is suggested to be related to sea surface salinity (SSS) and thus the SSD change over the NADW formation region.Global warming triggers Arctic sea ice melt (red curves in Figure S6 in Supporting Information S1), resulting in freshwater input into the ocean.This freshwater directly spreads southward and sweeps over the deep convection region, leading to a profound SSD decrease (Figure S6f in Supporting Information S1) and thus the AMOC shutdown after 150 years.The southward spread of freshwater from Arctic sea ice melt in reducing the AMOC is evidenced in previous works (Liu et al., 2017(Liu et al., , 2019;;Sévellec et al., 2017).
The freshwater-driven AMOC recovery after 600 years in our experiments is associated with a sufficient salinity buildup at low latitudes (Figure S5g in Supporting Information S1).The AMOC shutdown triggers a weakened northward current and a southward shift of the Intertropical Convergence Zone (ITCZ) (Vellinga et al., 2002;Yin & Stouffer, 2007).This leads to a strong salinity accumulation at the subtropical North Atlantic (Figure S5g in Supporting Information S1).Previous works have shown that the increased salinity over the subtropical North Atlantic stimulates large-scale baroclinic eddies, which propagate northward (Figure S6h in Supporting Information S1) to restart the deep convection in the northern North Atlantic (Bonan et al., 2022;Vellinga et al., 2002;Yin & Stouffer, 2007).

Heat Flux Effect
It has been shown above that the heat flux effect is responsible for the AMOC weakening during 50-150 years of global warming.Subsequently, the heat-driven AMOC recovers gradually to its initial state at year 200 and remains and its contribution from temperature (SSDn_t, red curve) and salinity (SSDn_s, blue curve).(b) Is for the surface density change over the Southern box (-SSDs, orange curve) and its contribution from temperature (-SSDs_t, red curve) and salinity (-SSDs_s, blue curve).The first row is for the total effect, the second row is heat flux effect, and the third row is for freshwater feedback.Units: kg/m 3 .at this equilibrium state thereafter.The heat flux in weakening the AMOC is consistent with the findings from other works (Gregory et al., 2005;Jansen et al., 2018).It is evident that the evolution of the heat-driven AMOC closely aligns with the MDG under pure heat forcing, particularly during the period of AMOC recovery (depicted in Figure 2c).By decomposing the MDG into north and south components, it shows that the heat-driven AMOC weakening is caused by the density decrease over the NADW formation region (green curve in Figures 2d and 4f), while its later recovery is driven by the density decrease over the South Ocean (orange curve in Figures 2d and 4g; the decreased density over the South Ocean favors the increase of MDG).
The heat-driven AMOC weakening and recovery are associated with the density change in the North Atlantic and the Southern Ocean.The increased GHGs directly warm the NADW formation region by providing extensive radiation flux into the ocean.The SST warming may decrease the density (red curve in Figures 3c and 4f), which prohibits deep convection and generates AMOC weakening.Concurrently, the increased GHGs can still warm the Southern Ocean, which may decrease the SSD locally at a lower rate and favor an increase of MDG (red curve in Figures 3d and 4g).As such, the decreased density in the NADW region is gradually compensated by the decreased density in the Southern Ocean, leading to a recovery of MDG and AMOC after Stage II.We note that the change of SSS in the northern North Atlantic resembles that of the AMOC, decreasing during 50-150 years and increasing gradually thereafter (blue curve in Figure 3c; Figures S7e-S7h in Supporting Information S1).Since the surface freshwater flux is fixed in the heat flux experiments, any changes in the salinity field can only be attributed to ocean circulation variations.Lead-lag correlation analysis between AMOC and SSS changes over the NADW region shows that the AMOC leads the SSS change by 12 years (Figure not shown), suggesting that the SSS change is a response to the AMOC.This demonstrates a positive feedback loop between SSS and AMOC changes.The SSS response over the NADW region promotes the increase of MDG and sustains the full recovery of heat-driven AMOC.

Conclusion and Discussion
We conduct sensitive experiments to quantify the individual role of heat flux forcing and freshwater feedback on AMOC change under global warming.Based on this state-of-the-art method, we find that the relative importance of these two roles changes at different timescales.The freshwater feedback is responsible for the initial AMOC weakening during the first 50 years, while the heat flux comes into play later and is responsible for the further reduction in the following 50-100 years.Afterward, the AMOC collapse and recovery are again caused by freshwater feedback.
Based on this state-of-the-art method, we show that the freshwater feedback dominates over the heat flux effect in driving the AMOC evolution for 1500 years.The heat flux only takes effect during 50-150 years.This is different from previous works that highlight the role of heat flux in driving the AMOC change in the future (Gregory et al., 2005(Gregory et al., , 2016;;Sandeep et al., 2020;Zhu et al., 2015).This inconsistency originates from the experiment design.The previous works usually use heat flux derived from fully coupled simulations that we believe already involve freshwater feedback.The freshwater feedback sometimes may exaggerate the role of the heat flux.For example, once the AMOC weakens by sea ice melt, the induced North Atlantic cooling may prohibit latent heat and longwave radiation flux emitted from the ocean to the atmosphere, resulting in more heat flux incoming into the ocean surface.Here, we have prescribed the surface freshwater flux and excluded its feedback when analyzing the role of heat flux in driving AMOC change.
Here we show that the heat flux and freshwater flux trigger AMOC recovery at different timescales.With respect to projections, our findings underscore the importance of improving the simulation of freshwater flux in 10.1029/2023GL105478 of 10 climate models to reduce AMOC uncertainty in the near future.We also show that the full recovery of AMOC is predominately driven by high-latitude salinity change.This supports the idea of Wu et al. (2011) andSigmond et al. (2020), who suggests that salinity is the primary driver of AMOC recovery.
It should be noted that this work does not consider the freshwater from ice sheet melt, which may underestimate the importance of freshwater feedback in changing the AMOC (Golledge et al., 2019;Li et al., 2023;Sadai et al., 2020).We suggest that the freshwater may play a much more important role in driving the AMOC weakening in the future when accounting for meltwater input from the ice sheet.Previous works have already shown that there is no AMOC recovery when accounting for the Antarctic ice sheet melt (Sadai et al., 2020).Moreover, it has been suggested that the Antarctic and Greenland ice sheet melt can accelerate the AMOC decline in the near future (Golledge et al., 2019;Li et al., 2023).The importance of freshwater in driving the AMOC weakening under global warming case shows some resemblance to paleoclimate evidence that meltwater can trigger AMOC shutdown and results in disastrous impacts (He & Clark, 2022).This work provides clues that reducing the uncertainty in freshwater flux projections helps to better predict the AMOC in the future.

Figure 1 .
Figure1.(a) Temporal evolution of percentage changes in Atlantic meridional overturning circulation (AMOC) induced by total effect (black curve), heat flux effect (red curve) and freshwater effect (green curve).The AMOC index is defined as the maximum streamfunction in the range of 500-4,000 m over 20°N-70°N.4 stages are outlined here as blue shadings.(b) Is for the AMOC pattern in the CTRL run (contours with an interval of 2 Sv) and its changes (shading; Sv) during 4 stages.The first panel is for AMOC change induced by the total effect, the second panel is for the heat flux effect and the third panel is for the freshwater flux effect. 1 Sv = 10 6 m 3 s −1 .

Figure 2 .
Figure 2. (a) Temporal evolution of changes in AMOC (black curve in left scale; unit is %) and meridional density gradient (gray curve in right scale; kg/m 3 ) in 2CO2 compared with CTRL.The meridional density gradient (MDG) is defined as the sea surface density (SSD) difference between the Northern box (50-65°N, 60°W-10°E; SSDn) and Southern box (45-60°S, 60°W-20°E; SSDs) averaged over the ocean surface 1,400 m, denoted as the SSDn-s.(b) Temporal evolution of changes in MDG (gray curve; the same as (a); kg/m 3 ) and its contribution from the Northern box (SSDn; green curve) and Southern box (SSDs; orange curve) in 2CO2 compared with CTRL.The positive value means an increase in MDG.For example, the -SSDs increase means the SSD change over the Southern box is responsible for the increase of MDG (actually the SSD over the Southern box is decreased because there is a minus sign before this term).(c, d) Are the same as (a, b), but for heat flux effect, while (e-f) are for freshwater feedback.

Figure 3 .
Figure 3. Decomposing SSDn and -SSDs change into temperature and salinity contributions.(a) Temporal changes in SSD over the Northern box (SSDn, green curve)and its contribution from temperature (SSDn_t, red curve) and salinity (SSDn_s, blue curve).(b) Is for the surface density change over the Southern box (-SSDs, orange curve) and its contribution from temperature (-SSDs_t, red curve) and salinity (-SSDs_s, blue curve).The first row is for the total effect, the second row is heat flux effect, and the third row is for freshwater feedback.Units: kg/m 3 .