Atlantic overturning collapses in global warming projections after 2100

doi:10.21203/rs.3.rs-5077014/v1

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Atlantic overturning collapses in global warming projections after 2100

https://doi.org/10.21203/rs.3.rs-5077014/v1

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The Atlantic Meridional Overturning Circulation (AMOC) strongly influences climate, particularly (but not exclusively) around the northern Atlantic, and its instabilities explain some of the largest abrupt regional climate shifts in Earth history1. For several decades, the risk of a collapse of this crucial circulation system in response to anthropogenic global warming has been discussed as a ‘low probability – high impact’ risk of our greenhouse gas emissions. Multiple lines of evidence have shown that this circulation is slowing down and may be at its weakest since at least a millennium2, and several studies have identified early warning signals in observations of an approaching tipping point3-6. Here we show, by analysing standard global warming simulations extended beyond the year 2100, that the circulation collapses in all IPCC-class climate models in the high emission scenarios and even in some moderate and low scenarios, despite the neglect of increasing Greenland meltwater influx. In most cases the collapse is initiated by a breakdown of deep convection already early in this century. We conclude that a collapse of the AMOC cannot be considered a low-probability event anymore.

Earth and environmental sciences/Climate sciences/Climate change/Climate and Earth system modelling

Earth and environmental sciences/Ocean sciences/Physical oceanography

The Atlantic Meridional Overturning Circulation (AMOC) transports warm upper-ocean water to the north, where it sinks and returns as cold, deep water to the South Atlantic. Changes in AMOC strongly impact northward ocean heat transport and the climate of the Atlantic mid and high latitudes, as well as anthropogenic carbon uptake by the ocean, sea level in the northern Atlantic and not least the location of tropical rainfall belts.

In 1961, it was demonstrated that a simple theoretical model of the AMOC possesses two modes of operation with possible abrupt transitions between the two when a bifurcation point (also called tipping point) is surpassed⁷. Paleoclimatic evidence points to major abrupt climate changes during the last glacial period with a focus on the northern Atlantic and with global repercussions, related to instabilities of the AMOC^1,8. In 1987, W. Broecker sternly warned in Nature of a possible AMOC collapse caused by anthropogenic warming⁹.

Earlier IPCC reports^10,11, however, argued that an abrupt collapse of the AMOC before 2100 was very unlikely (i.e. less than 10% probability in IPCC language), based on the absence of such events in future global warming projections. The latest, 6^th IPCC report¹² concluded: “There is medium confidencethat there will not be an abrupt collapse before 2100.” This lack of confidence was based on the assessment that model bias may considerably affect the sensitivity of the modelled AMOC to freshwater forcing: “tuning towards stability” and model biases¹² give climate models a tendency toward unrealistic stability^13-15. Furthermore, these models neglect increasing meltwater release from the Greenland ice sheet in their future projections.

Recent studies have looked for so-called early warning signals of an approaching AMOC tipping point^3-6. These studies used various observational data sets, including paleoclimatic proxy data, and invariably found such early warning signals, suggesting the tipping point could be passed even before 2050. However, data and methodological limitations mean that uncertainty about the proximity to the tipping point is large, and in our view will likely remain large with this approach.

Here, we analyse recent extensions of climate model simulations of the 6^th Coupled Model Intercomparison Project (CMIP6) beyond the year 2100, the time horizon of simulations discussed in the 6^th IPCC report. In many of the CMIP6 models discussed in the 6^th IPCC report, the AMOC collapses after the year 2100. In most cases the AMOC collapse is preceded by a cessation of deep oceanic convection in the high northern latitudes triggered in the early 21^st century.

Climate models from 53 modelling centres around the world contribute to CMIP6¹⁶ with climate change simulations, driven by standardized future emission scenarios¹⁷. We analyse the data of all those available CMIP6 model simulations which run beyond the year 2100. This set comprises 20 scenario-runs computed with 10 different models.

Under a high emission scenario (SSP585) the AMOC collapses in all 9 models that were run beyond 2100 (Figure 1, red). By 2100 the weakest AMOC volume transport at 26°N in a model where it eventually does not collapse is 9.9 Sv (1 Sv = 10⁶ m³/s; Supplementary Figure 1). In three scenario-runs the AMOC in 2100 is still stronger while eventually reaching a collapsed state (below 5 Sv) between years 2200 and 2300, but in all other runs, where it already collapses between years 2100 and 2200, its value in 2100 is already below 9 Sv. In all cases the collapse starts in the early 21^st Century (Fig. 1).

The latitude 26°N is most relevant for climate as it is where ocean heat transport peaks¹⁸, and the AMOC is monitored there since 2004 by an observing system in the RAPID project¹⁹. The downward trend measured by the RAPID array closely corresponds to that in the models (Fig. 1). If we take the value of 9.9 Sv as indicative of the AMOC being en route to collapse in models that stopped their runs in 2100 (Supplementary Figure 1), then the AMOC is en route to collapse in 69% of the models under the SSP585 scenario (Supplementary Figure 2).

Only two models (GISS-E2-1-G and GISS-E2-2-G) have been forced beyond 2100 with an intermediate emissions scenario (SSP245, Fig. 1, green). In the former, in 2 out of 14 ensemble members the AMOC declines below 10 Sv in the mid-22^nd Century and eventually collapses, while in other members it recovers, the difference merely being slightly different initial conditions²⁰. This is interpreted as a noise-induced transition when this model comes close to the AMOC tipping point. In the latter, none of the members collapsed. In 11 other models (not run past 2100) the AMOC drops in 2100 below the 9.9 Sv threshold. Under this medium emissions scenario the chance of an AMOC collapse is 39%.

Even in a low emission scenario in accord with the Paris agreement, the AMOC collapses in 2 out of 9 extended runs (Fig. 1). In one model, MRI-ESM2-0, the AMOC evolution in the high and low emission scenario is so similar (Supplementary Fig. 3) that a tipping point may already have been passed before year 2050, when the forcing in the low emission scenario starts to decrease, or even already at the beginning of this century, given the over 50-year time scale for an AMOC collapse to unfold. In addition, with this emission scenario 4 models that end their simulations in 2100 end with an AMOC below 9.9 Sv (Supplementary Fig. 1). Under this emission scenario the chance of an AMOC collapse is about 25% (Supplementary Figure 2).

In all three emission scenarios the spatial pattern of change in the AMOC is remarkably similar, with a relatively fast reduction in the North Atlantic subtropics and subpolar latitudes, and a slower southward expansion of this pattern until finally the weakening signal covers the whole Atlantic (Supplementary Fig. 4).

Figure 1 also shows that the associated drop in northward heat transport amounts to 70-80% of its present-day value, in accord with the assessment that presently the AMOC is responsible for 90% of the ocean heat transport at 26°N, and it experiences a drop of 75-90%. When the AMOC collapses a shallow wind-driven overturning cell remains (Supplementary Figure 4), which increases its heat transport as the temperature difference between surface and depth increases due to global warming.

In theoretical models an AMOC tipping point is associated with the so-called salt advection feedback or Stommel feedback⁷, which becomes unstable at this point. The existence of this AMOC bifurcation point has been confirmed in the full climate model hierarchy²¹ up to a state‐of‐the‐art global climate model²².

The rate of AMOC decline in the time series shown in Fig. 1 does not show where the tipping point is, because the increase in forcing (i.e. greenhouse gases) occurs at a similar time scale as the AMOC winding down after passing the tipping point. That is why model experiments to locate the tipping point are conducted with a very slow increase in forcing^22,23. Passing the tipping point means that the AMOC will grind to a halt by internal feedback from that point onward, even without further increase in forcing.

A critical part of the causal chain with a faster response time scale is the deep convection in the northern Atlantic, typically occurring in late winter to early spring at times when surface layer density reaches a maximum. Since this is thermally driven convection, with colder surface waters being mixed with somewhat warmer deep waters, this mixing warms the surface, increases surface heat loss and evaporation, and thus cools and densifies the water column – a crucial process for the density-driven AMOC.

Figure 2 shows the depth of the surface mixed layer in March at its maximum. Convection depths show significant variability up to around the year 2000 but start a continuous terminal decline after that. In both models, in the high-emissions scenario by the mid-21^st century deep convection has all but ceased, leaving only a typical wind-mixed surface layer depth of the order of 100 m.

Thermally driven ocean convection is known to have a tipping point itself: the northern convection regions are net-precipitation regions, so in the absence of deep mixing freshwater tends to accumulate in the surface layer, increasingly inhibiting mixing²⁴. This is another self-amplifying feedback which can shut down convection in the northern Atlantic^25,26.

In the low emission scenario, deep convection in the Nordic Seas declines more slowly. In the MRI model, halfway through the 22^nd century all convection ceased. In the UKESM model it remains active especially in the Nordic Seas, albeit with a much shallower mixed layer depth than before 2000, consistent with the fact that the AMOC does not collapse in this model contrary to the MRI model. While a shut-down of part of the deep convection areas will weaken the AMOC, a shutdown of all deep convection areas must be considered a precursor of a full AMOC shutdown.

Deep convection in the Nordic Seas appears to be the most resilient to global warming. Previous studies have shown than many CMIP5 and CMIP6 models show a deep-convection collapse by 2050 in the subpolar gyre region (i.e. Labrador and Irminger Seas)^27,28. This leads to rapid cooling over the northern Atlantic “with a substantial effect on surface temperature over Europe, precipitation pattern in the tropics … and a possible impact on the mean atmospheric circulation”²⁷. Thus, even if this does not lead to a full AMOC shutdown the societal impacts are likely serious.

In Fig. 3 we analyse the surface layer salinity and temperature, surface heat flux and sea ice cover in two models: the MRI ESM, where the AMOC collapses both in the low and high emissions scenarios following a very similar trajectory (Figs. 1 and 2), and in the UKESM where the AMOC collapses only in the high emission scenario. In the MRI ESM the salinity declines strongly, as precipitation minus evaporation (P-E) increases over the subpolar North Atlantic, amplified by a weakening AMOC bringing less salty subtropical water to the region (Stommel feedback; Supplementary Figure 6). The freshwater input from melting sea ice declines in the 21^st century (due to little sea ice left) and thus counteracts the freshening somewhat. The salinity reduction is substantially less in the low emission scenario due to a smaller increase in P-E and absent in the UKESM where the initial forcing by P-E is not strong enough to invoke the Stommel feedback. Observational data show that already today, salinity in the Irminger Sea is the lowest in 120 years of measurements²⁹.

Temperatures follow different trajectories. In the high emission case temperatures increase strongly after a temporary plateau or dip, as global warming overwhelms the regional loss of AMOC heat transport. In the low emission case in the MRI-ESM temperatures drop below pre-industrial in all three regions as the AMOC dies, in the Irminger Sea even down to 5°C below pre-industrial values. The cooling leads to a massive increase in sea ice cover. Heat loss through the ocean surface declines in all cases, reflecting the greatly reduced amount of heat brought to the region by the AMOC. In the UKESM the temperature modestly increases in the low emission scenario.

The changes in the ocean water density result from both salinity and temperature, as shown on the right scale on the corresponding panels in Fig. 4. Salinity changes dominate: the salinity decline causes ~2 kg/m³ density reduction in the low emissions scenario, only partly compensated by a ~0.5–1 kg/m³ density increase due to cooling. In the high emissions scenario, both the salinity-decline and warming add up to reduce density, with the salinity effect still dominating.

Figure 4 shows an observations-based subsurface ocean analysis product³¹. In the Irminger and Nordic Seas, mixed layer depths are at an all-time low, while in the Labrador Sea it has declined nearly to the low point observed during the 1970s Great Salinity Anomaly³². While decadal variability is large so final conclusions cannot yet be drawn, the observed evolution over the last decades is consistent with the model simulations eventually leading to a convection collapse. This supports our argument that the risk of an AMOC collapse is greater than previously thought.

The CMIP6 models we investigated point to a significantly higher AMOC collapse risk than previously thought: a high probability of collapse for high emissions, an intermediate probability for intermediate emissions, and even for low emissions, which limit global warming to below 2 °C, some collapse.

Our analysis shows that it is the freshening linked mainly to increasing precipitation in a warming climate which pushes the AMOC past tipping point. As the models neglect increasing meltwater from Greenland and many may have an inherently too stable AMOC, these models are likely to underestimate the danger of an AMOC collapse.

The climate response to an AMOC collapse and drop in northward ocean heat transport depends on the strength and pattern of fast feedbacks related to increasing sea-ice extent and atmospheric drying³³. In a pre-industrial control-climate the temperature drop in Western Europe can become 7°C (London)⁶, while in a global warming scenario this drop would be reduced to 3°C³³ – still a much larger and faster change than the projected temperature rise for low or intermediate emissions.

Further research efforts should urgently focus on (i) extending more intermediate emission scenarios beyond 2100, (ii) improving climate models after careful analysis of their AMOC stability properties, (iii) performing more future warming scenario simulations with full coupling of the Greenland Ice Sheet, (iv) analysing impacts of an AMOC collapse in global warming scenarios, and (v) systematic monitoring of deep convection in the relevant regions.

For policy and society, the increased likelihood of an AMOC collapse found in this and other studies urgently calls for stronger efforts to phase out fossil fuels fast enough to halt global warming as close to 1.5°C as possible, in line with the Paris Climate Accord.

Acknowledgements

We acknowledge the World Climate Research Programme's Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modelling groups (listed in Table S1 of this paper) for producing and making available their model output. For CMIP the U.S. Department of Energy's Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. We acknowledge the World Climate Research Programme, which, through its Working Group on Coupled Modelling, coordinated and promoted CMIP6. We thank the climate modelling groups for producing and making available their model output, the Earth System Grid Federation (ESGF) for archiving the data and providing access, and the multiple funding agencies who support CMIP6 and ESGF. The CMIP6 data was accessed and analyzed using the UK super-data-cluster JASMIN and Netherlands super-computer-cluster SURFsara. Figures in the manuscript were generated using python and figures with maps used the cartopy python package.

Author contributions

S.D. designed the study, J.M. and J.A. produced the figures, all authors analyzed the data, wrote and edited the paper.

Competing interests

The authors declare no competing interests.

Data Availability

The CMIP6 data used in this study is freely available online at https://esgf-node.llnl.gov/search/cmip6/. The observation-based data is available on the EN4 webpage in the references list.

Code Availability

Code used for this study will be uploaded on a github page under https://github.com/jmecki/AMOCcollapse

Rahmstorf, S. Ocean circulation and climate during the past 120,000 years. Nature419, 207-214 (2002). https://doi.org:10.1038/nature01090
Caesar, L., McCarthy, G. D., Thornalley, D. J. R., Cahill, N. & Rahmstorf, S. Current Atlantic Meridional Overturning Circulation weakest in last millennium. Nature Geoscience14, 118–120 (2021). https://doi.org:10.1038/s41561-021-00699-z
Boers, N. Observation-based early-warning signals for a collapse of the Atlantic Meridional Overturning Circulation. Nature Clim. Change11, 680-688 (2021). https://doi.org:10.1038/s41558-021-01097-4
Ditlevsen, P. & Ditlevsen, S. Warning of a forthcoming collapse of the Atlantic meridional overturning circulation Nature (2023). https://doi.org:10.1038/s41467-023-39810-w
Michel, S. L. L. et al. Early warning signal for a tipping point suggested by a millennial Atlantic Multidecadal Variability reconstruction. Nat Commun13, 5176 (2022). https://doi.org:10.1038/s41467-022-32704-3
van Westen, R. M., Kliphuis, M. A. & Dijkstra, H. A. Physics-based early warning signal shows that AMOC is on tipping course. Science Advances (2024). https://doi.org:10.1126/sciadv.adk1189
Stommel, H. Thermohaline Convection with Two Stable Regimes of Flow. Tellus13, 224-230 (1961). https://doi.org:10.1111/j.2153-3490.1961.tb00079.x
Broecker, W. S., Bond, G., Klas, M., Bonani, G. & Wolfi, W. A salt oscillator in the glacial Atlantic? 1. The concept. Paleoceanography and Paleoclimatology5, 469-477 (1990).
Broecker, W. Unpleasant surprises in the greenhouse? Nature328, 123 (1987).
Collins, M. et al., 2013: Long-term Climate Change: Projections, Commitments and Irreversibility. In: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex, and P.M. Midgley (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, USA, pp. 1029–1136, doi:10.1017/ cbo9781107415324.024.
Collins, M. et al., 2019: Extremes, Abrupt Changes and Managing Risks. In: IPCC Special Report on the Ocean and Cryosphere in a Changing Climate [Pörtner, H.-O., D.C. Roberts, V. Masson-Delmotte, P. Zhai, M. Tignor, E. Poloczanska, K. Mintenbeck, M. Nicolai, A. Okem, J. Petzold, B. Rama, and N. Weyer (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, USA, pp. 589-655, https://doi.org/10.1017/9781009157964.008.
Fox-Kemper, B., et al., 2021: Ocean, Cryosphere and Sea Level Change. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change [Masson-Delmotte, V., P. Zhai, A. Pirani, S.L. Connors, C. Péan, S. Berger, N. Caud, Y. Chen, L. Goldfarb, M.I. Gomis, M. Huang, K. Leitzell, E. Lonnoy, J.B.R. Matthews, T.K. Maycock, T. Waterfield, O. Yelekçi, R. Yu, and B. Zhou (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, USA, pp. 1211–1362, doi:10.1017/9781009157896.011.
Liu, W., Xie, S.-P., Liu, Z. & Zhu, J. Overlooked possibility of a collapsed Atlantic Meridional Overturning Circulation in warming climate. Science Advances, 7 (2017). https://doi.org:10.1126/sciadv.1601666
Mecking, J. V., Drijfhout, S. S., Jackson, L. C. & Andrews, M. B. The effect of model bias on Atlantic freshwater transport and implications for AMOC bi-stability. Tellus A: Dynamic Meteorology and Oceanography69 (2017). https://doi.org:10.1080/16000870.2017.1299910
Weijer, W. et al. Stability of the Atlantic Meridional Overturning Circulation: A Review and Synthesis. Journal of Geophysical Research: Oceans124, 5336-5375 (2019). https://doi.org:10.1029/2019jc015083
O’Neill, B. C. et al. The Scenario Model Intercomparison Project (ScenarioMIP) for CMIP6. Geosci. Model Dev.9, 3461–3482 (2016).
Eyring, V. et al. Overview of the Coupled Model Intercomparison Project Phase 6 (CMIP6) experimental design and organization. Geoscientific Model Development9, 1937-1958 (2016). https://doi.org:10.5194/gmd-9-1937-2016
Johns, W. E. et al. Towards two decades of Atlantic Ocean mass and heat transports at 26.5 degrees N. Philos Trans A Math Phys Eng Sci381, 20220188 (2023). https://doi.org:10.1098/rsta.2022.0188
McCarthy, G. D. et al. Measuring the Atlantic Meridional Overturning Circulation at 26°N. Progr. Oceanogr.130, 91-111 (2015). https://doi.org:10.1016/j.pocean.2014.10.006
Romanou, A. et al. Stochastic Bifurcation of the North Atlantic Circulation under a Midrange Future Climate Scenario with the NASA-GISS ModelE. J. Clim.36, 6141-6161 (2023). https://doi.org:10.1175/jcli-d-22-0536.1
Rahmstorf, S. et al. Thermohaline circulation hysteresis: a model intercomparison. Geophys. Res. Let.32, L23605 (2005). https://doi.org:10.1029/2005GL023655
van Westen, R. M. & Dijkstra, H. A. Asymmetry of AMOC Hysteresis in a State‐Of‐The‐Art Global Climate Model. Geophys. Res. Let.50 (2023). https://doi.org:10.1029/2023gl106088
Rahmstorf, S. Bifurcations of the Atlantic thermohaline circulation in response to changes in the hydrological cycle. Nature378, 145-149 (1995). https://doi.org:10.1038/378145a0
Welander, P. A simple heat-salt oscillator. Dyn. Atmos. Oceans6, 233-242 (1982).
Rahmstorf, S. A simple analytical model of seasonal open-ocean convection. Part I: Theory. Ocean Dyn.52, 26-35 (2001).
Kuhlbrodt, T., Titz, S., Feudel, U. & Rahmstorf, S. A simple model of seasonal open ocean convection. Part II: Labrador Sea stability and stochastic forcing. Ocean Dyn.52, 36-49 (2001).
Swingedouw, D. et al. On the risk of abrupt changes in the North Atlantic subpolar gyre in CMIP6 models. Ann N Y Acad Sci1504, 187-201 (2021). https://doi.org:10.1111/nyas.14659
Sgubin, G., Swingedouw, D., Drijfhout, S., Mary, Y. & Bennabi, A. Abrupt cooling over the North Atlantic in modern climate models. Nat Commun8 (2017). https://doi.org:10.1038/ncomms14375
Holliday, N. P. et al. Ocean circulation causes the largest freshening event for 120 years in eastern subpolar North Atlantic. Nat Commun11, 585 (2020). https://doi.org:10.1038/s41467-020-14474-y
Drijfhout, S., van Oldenborgh, G. J. & Cimatoribus, A. Is a Decline of AMOC Causing the Warming Hole above the North Atlantic in Observed and Modeled Warming Patterns? J. Clim.25, 8373-8379 (2012). https://doi.org:10.1175/jcli-d-12-00490.1
Killick, R. The Climate Data Guide: EN4 subsurface temperature and salinity for the global oceans., <https://climatedataguide.ucar.edu/climate-data/en4-subsurface-temperature-and-salinity-global-oceans> (2023).
Dickson, R. R., Meincke, J., Malmberg, S. A. & Lee, A. J. The "Great Salinity Anomaly" in the northern North Atlantic, 1968-82. Progr. Oceanogr.20, 103-151 (1988).
Drijfhout, S. Competition between global warming and an abrupt collapse of the AMOC in Earth's energy imbalance. Sci Rep5, 14877 (2015). https://doi.org:10.1038/srep14877
Mecking, J.V., Drijfhout, S.S. The decrease in ocean heat transport in response to global warming. Nat. Clim. Chang. 13, 1229–1236 (2023). https://doi.org:10.1038/s41558-023-01829-8

This study investigates changes in AMOC using 733 future climate projections from 36 CMIP6 models, respectively (Table S1). Data from the emission scenarios SSP126; SSP245, and SSP585 have been used for this study.

For the AMOC and all other variables annual averages were used, apart from the mixed-layer depth for which we took the annual maximum value which on the Northern Hemisphere occurs in March.

The AMOC was analyzed at fixed depth at 26°N, the depth being the depth of maximum overturning between 1950 and 2000. The reason for this is when choosing the maximum overturning at variable depth one starts picking up the shallow wind-driven Ekman cell when the deeper thermohaline part of the AMOC becomes weak and/or collapses. Since it is only this part of the AMOC that possesses a tipping point and can collapse we deemed it pertinent using a metric that is relevant for the thermohaline part of the AMOC. In Supplementary Figure 7 we show that this choice is not essential for detecting an AMOC collapse in the models, but it does somewhat enhance the amount of decline. Also, In Supplementary Figures 2 and 7 the structure of the wind-driven Ekman cell is clearly visible and that for the SSP585 scenarios Supplementary Figure 7 nicely illustrates how the thermohaline part of the AMOC with its deeper maximum declines over time, leaving in year 2300 only a wind-driven Ekman cell at 26°N.

The calculations of the heat transport at 26°N were largely performed in a previous study³⁴, extended with values from beyond 2100 with the same scripts as used in Ref[34].

To emphasize longer timeseries and eliminate intra-decadal natural variability all timeseries were smoothed by convoluting the data with a Gaussian that has a standard deviation of 7.5 years.

There is NO Competing Interest.

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Atlantic overturning collapses in global warming projections after 2100

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Abstract

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Introduction

Climate Model Simulations and Results

Mechanism of the AMOC collapse

Discussion

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Acknowledgements

Author contributions

Competing interests

References

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Supplementary Files

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