[1]René M. van Westen

1]Department of Physics, Institute for Marine and Atmospheric research
Utrecht, Utrecht University, Princetonplein 5, Utrecht, 3584 CC, the
Netherlands

# Substantial Risk of 21st Century AMOC Tipping even under Moderate Climate
Change

<EMAIL_ADDRESS>Elian Y.P. Vanderborght<EMAIL_ADDRESS>Michael
Kliphuis<EMAIL_ADDRESS>Henk A. Dijkstra<EMAIL_ADDRESS>[

###### Abstract

The Atlantic Meridional Overturning Circulation (AMOC) is a key component of
the climate system and considered to be a tipping element. There is still a
large uncertainty on the critical global warming level at which the AMOC will
start to collapse. Here we analyse targeted climate model simulations,
together with observations, reanalysis products and a suite of state-of-the-
art climate model results to reassess this critical global warming level. We
find a critical threshold of +3∘C global mean surface temperature increase
compared to pre-industrial with a lower bound of +2.2∘C (10%-Cl). Such global
mean surface temperature anomalies are expected to be reached after 2050. This
means that the AMOC is more likely than not ($\geq 50\%$) to tip within the
21st century under a middle-of-the-road climate change scenario and very
likely ($\geq 90\%$) to tip under a high emissions scenario. The AMOC collapse
induced cooling is shown to be offset by the regional warming over
Northwestern Europe during the 21st century, but will still induce severe
impacts on society.

###### keywords:

AMOC collapse, Climate change, Climate impacts

## Main

The Atlantic Meridional Overturning Circulation (AMOC) has been identified as
a tipping element in the climate system [1, 2]. The AMOC transports heat and
salt through the global ocean [3], and strong reductions in its strength
severely impact climate over large parts of the world [4, 5, 6]. Given these
potentially severe global consequences, it is not surprising that the present-
day AMOC is closely monitored along several arrays [7, 8, 9] in the Atlantic
Ocean.

The 20-year long observational AMOC strength time series from the RAPID-MOCHA
array at 26∘N [8] has been complemented by sea surface temperature (SST)-based
reconstructions [10, 11, 12, 13, 14]. These AMOC reconstructions indicate a
gradual weakening of the AMOC by a few Sverdrups (1 Sv = $10^{6}$ m3s-1) since
1900 and also suggest that the AMOC is approaching its tipping point [15, 16].
However, they may not adequately capture the AMOC behaviour and are prone to
false positive signals [6, 17].

AMOC strength projections from the Coupled Model Intercomparison Project
(CMIP) phase 6 (CMIP6) do not show evidence of a 21st century AMOC collapse,
and their projections appear quite insensitive with respect to the greenhouse
gas emission scenario used [18]. The sixth Intergovernmental Panel on Climate
Change (IPCC) report states with _medium confidence_ that an AMOC collapse
will not occur during the 21st century [19]. Moreover, an analysis of critical
global warming levels of tipping elements [2] finds that the AMOC is _likely_
to tip only above +4∘C global mean surface temperature increase with respect
to the pre-industrial level. This suggests a relatively stable AMOC, even
under high greenhouse gas emission scenarios such as the Shared Socioeconomic
Pathway (SSP) 3-7.0.

Recently, a quasi-equilibrium hosing simulation [6] with the Community Earth
System Model (CESM) showed that the pre-industrial AMOC collapses under the
imposed freshwater flux forcing. While this simulation was still idealised as
no climate change forcing was included, it provides the basis for developing
efficient diagnostics for an AMOC collapse under transient 21st century
forcing. Here, we conduct additional targeted CESM simulations of the 21st
century AMOC under climate change and compare the results with those of 24
CMIP6 models, with the aim to reassess the critical global warming level at
which the AMOC starts to collapse.

## AMOC Collapse in the Pre-industrial CESM

The quasi-equilibrium hosing simulation (see Methods, [6]) was conducted under
constant pre-industrial radiative forcing conditions. The AMOC strength is
plotted in Figure 1a versus the freshwater flux forcing ($F_{H}$) which
linearly increases from 0 to 0.66 Sv over 2,200 model years; the AMOC
collapses at about 0.525 Sv (model year 1,758 [6]). From this simulation the
dominant physical mechanisms of AMOC tipping can be quantified and used to
analyse model simulations under climate change.

Figure 1: Buoyancy and AMOC responses under the hosing. (a): The AMOC strength
at 1,000 m and 26∘N (yearly averages) under the quasi-equilibrium hosing and
for the two statistical steady states at constant forcing $F_{H}=0.18$ Sv and
$F_{H}=0.45$ Sv. The upper 1,000 m buoyancy ($B_{\mathrm{ocean}}$, yearly
averages) and surface buoyancy ($B_{\mathrm{surf}}$, yearly sums), spatially
averaged over the North Atlantic Ocean (40∘N – 60∘N). (b): Mean seasonal cycle
over the first 50 model years for the quantities plotted in panel a. (c): The
upper 1,000 m buoyancy $B_{\mathrm{ocean}}$ (yearly averages), decomposition
for the temperature ($B_{\mathrm{ocean}}^{T}$) and salinity
($B_{\mathrm{ocean}}^{S}$). (d): The surface buoyancy $B_{\mathrm{surf}}$
(yearly sums) decomposition for the heat fluxes ($B_{\mathrm{surf}}^{T}$) and
freshwater fluxes ($B_{\mathrm{surf}}^{S}$).

Before the collapse (Figure S1), the AMOC decline is linked to potential
density changes over the northern isopycnal outcropping region (located at
40∘N – 60∘N, Figure S1c). The AMOC over the isopycnal outcropping region is in
thermal wind balance with the meridional density gradient over this region
[20, 21]. The upper 1,000 m potential density changes over the isopycnal
outcropping region primarily drive the AMOC decline and we quantify these
changes by determining the upper ocean buoyancy ($B_{\mathrm{ocean}}$, see
Methods) over the region. The quantity $B_{\mathrm{ocean}}$ has indeed the
opposite response to that of the AMOC strength under the quasi-equilibrium
hosing (Figure 1a).

The outcropping of isopycnals at 40∘N – 60∘N is governed by surface winds,
interior mixing and loss of surface buoyancy ($B_{\mathrm{surf}}$) [20].
Interior ocean isopycnals only surface when $B_{\mathrm{surf}}$ remains net
negative over time scales longer than one year. There is a strong seasonal
cycle in both $B_{\mathrm{ocean}}$ and $B_{\mathrm{surf}}$, where the surface
buoyancy leads by about 2 months (Figure 1b). The surface buoyancy is
primarily driven by atmosphere-ocean heat fluxes and the relatively large
negative winter values cause strong vertical mixing (i.e., deep convection)
over the isopycnal outcropping region. Once $B_{\mathrm{surf}}$ switches sign,
there is no outcropping of isopycnals and only a weak and diffusive AMOC can
exist [22]. The quantity $B_{\mathrm{surf}}$ is linked to water mass
transformation and hence AMOC strength [23, 24] and indeed $B_{\mathrm{surf}}$
and AMOC strength have the opposite response under the hosing (Figure 1a).

From the temperature and salinity buoyancy decompositions of
$B_{\mathrm{ocean}}$ ($B_{\mathrm{ocean}}^{T}$ and $B_{\mathrm{ocean}}^{S}$,
respectively, see Methods) it is found that salinity perturbations weaken the
AMOC under the hosing (Figure 1c). The non-linear increase in
$B_{\mathrm{ocean}}^{S}$ after 1350 years ($F_{H}>0.4$ Sv) indicates a
positive salt-advection feedback. This feedback is destabilising the AMOC as
salinity anomalies are amplified through their effect on the AMOC strength and
pattern [25, 26]. The AMOC weakening and associated reduced meridional heat
transport result in lower SSTs (i.e., the characteristic AMOC fingerprint
[10]) and induce ocean buoyancy loss which stabilises the AMOC. The
$B_{\mathrm{ocean}}^{T}$ responses have a passive and opposite role to the
$B_{\mathrm{ocean}}^{S}$ responses.

The quantity $B_{\mathrm{surf}}$ is decomposed in a similar way (Figure 1d)
and the $B_{\mathrm{surf}}^{S}$ increase is primarily driven by the freshwater
flux forcing. Changes in AMOC strength, driven by freshening of the isopycnal
outcropping region, reduce the surface ocean and atmosphere temperatures.
These ocean-atmosphere temperature differences modify the heat fluxes (Figure
S2) and show that lower SSTs effectively lose less heat to the atmosphere and
reduce the magnitude of $B_{\mathrm{surf}}^{T}$. It should be noted that the
lower temperatures enhance sea-ice formation conditions around Greenland
($>60^{\circ}$N) and, via advection of sea ice, increase the sea-ice area over
the isopycnal outcropping region. The expanding sea-ice pack enhances the
albedo and strongly reduces the ocean-atmosphere fluxes [27]. The bottom line
is that the freshwater flux forcing increases $B_{\mathrm{surf}}^{S}$ and,
through complex AMOC feedbacks, leads to an equally important contribution in
$B_{\mathrm{surf}}^{T}$. For example, $B_{\mathrm{surf}}$ increased by 0.28 J
kg-1 for $F_{H}=0.45$ Sv (model years 1476 – 1525) compared to beginning of
the simulation, where $B_{\mathrm{surf}}^{S}$ contributed 47% and
$B_{\mathrm{surf}}^{T}$ contributed 53%.

The isopycnal outcropping region changes from loosing surface buoyancy to
gaining surface buoyancy around the AMOC tipping event ($F_{H}=0.525$ Sv,
model year 1750). Thereafter the region is gaining net buoyancy through its
surface. The collapse is caused by the destabilising salt-advection feedback
and a positive $B_{\mathrm{surf}}$ ensures that a collapsed state will be
reached. What is, however, most important from these results is that the
buoyancy diagnostics considered can be used to analyse AMOC behaviour in model
simulations under climate change forcing.

## The AMOC Collapse under Climate Change

From the quasi-equilibrium hosing we branched off 500-year long simulations
under constant freshwater flux forcing to find statistical equilibria for
$F_{H}=0.18$ Sv and $F_{H}=0.45$ Sv (Figure 1a, with more details in [28]).
The simulation with the higher freshwater flux forcing is closer to the AMOC
tipping point under constant pre-industrial radiative forcing conditions. From
the end of the statistical equilibria, we branched off the historical forcing
(1850 – 2005) followed by the Representative Concentration Pathway (RCP) 4.5
and 8.5 scenarios (2006 – 2100) while keeping the value of $F_{H}$ fixed for
each simulation. Finally, after the year 2100, we kept the forcing conditions
fixed at their 2100 forcing levels and ran the simulations for an additional
400 years (up to 2500) to find the statistical equilibria under these future
forcing conditions. Ice sheet dynamics are important on such long timescales,
but ice sheets are prescribed in the CESM simulations. Hence the long-term
results only represent equilibria under a substantially changed radiative
forcing, but with present-day ice sheets.

Figure 2: The AMOC responses under climate change. The AMOC strength at 1,000
m and 26∘N under the two climate change scenarios (Hist/RCP4.5 and
Hist/RCP8.5) and for (a): $F_{H}=0.18$ Sv and (b): $F_{H}=0.45$ Sv. For
reference, the AMOC collapse under the hosing is also shown and is centred
around the AMOC tipping event (black curve, top x-axis). The yellow shading
indicates the observed AMOC strength [29, 13]. The insets show the 2-meter
global mean surface temperature anomaly compared to the pre-industrial period
(1850 – 1899). The yearly-averaged surface temperature differences are
determined between the red (2075 – 2100) and blue (2000 – 2025) shaded periods
and are presented in panels c – f. The markers in panels c – f indicate non-
significant ($p\geq 0.05$, two-sided Welch’s t-test) differences.

The AMOC strengths at 1,000 m and 26∘N under the two climate change scenarios
are shown for the $F_{H}=0.18$ and $F_{H}=0.45$ cases in Figures 2a,b,
including the global mean surface temperature anomaly (see insets). For
$F_{H}=0.18$ Sv, the AMOC has a reasonable strength over the historical period
compared to present-day observations (Figures 2a) but its freshwater transport
at 34∘S (indicated by $F_{\mathrm{ovS}}$) is biased positive (Figure S3). On
the other hand, for $F_{H}=0.45$ Sv, the freshwater transport at 34∘S is in
the range of observations (Figure S3) but the historical AMOC strength is
weaker than in observations (Figures 2b). The quantity $F_{\mathrm{ovS}}$ is
an important indicator in AMOC tipping dynamics [30, 31, 32, 33, 5] and a
negative $F_{\mathrm{ovS}}$ sign indicates that the AMOC is closer to its
tipping point under the quasi-equilibrium hosing [6].

Up to 2020, the AMOC strength remains remarkably constant for the simulations
under climate change. Thereafter, the AMOC strength substantially weakens by 5
– 6 Sv under Hist/RCP4.5 and 8 – 9 Sv under Hist/RCP8.5 over the 21st century.
The AMOC weakening rates under Hist/RCP8.5 are comparable to that of the
hosing with a decline of 8 Sv over about 100 years (Figures 1a). The RCP4.5
and RCP8.5 scenarios show little differences in their AMOC responses up to
2050 and this is consistent with the results for the CMIP6 models [18].

The climate change scenarios for $F_{H}=0.45$ Sv both show AMOC collapses and
their AMOC strengths reduce to 1 Sv at the end of the simulations. The AMOC
strength in RCP4.5 ($F_{H}=0.45$ Sv) reduces by 3.9 Sv (-31%) in 2090 – 2100
(with respect to 1850 – 1899) and eventually collapses after 2150. This
suggests that, under this scenario, an AMOC tipping event occurs somewhere in
the 21st century. For $F_{H}=0.18$ Sv, only the AMOC under RCP8.5 collapses
and appears to stabilise around 3.5 Sv at the end of the simulation. In the
RCP4.5 (and $F_{H}=0.18$ Sv) scenario the AMOC weakens by 6.1 Sv (-36%) in
2090 – 2100 (with respect to 1850 – 1899) and eventually recovers to 15.7 Sv
(-6.7%) at the end of the simulation. This shows that quantifying an AMOC
collapse based on absolute AMOC anomalies or fractional changes [34] may
misinterpret an imminent collapse.

The extended simulations provide insight into the equilibria resulting under
fixed future climate forcing. Under RCP8.5 and for $F_{H}=0.18$ Sv, the AMOC
reduces to a weak and shallow ($<$ 1000 m) overturning cell and the quantity
$F_{\mathrm{ovS}}$ becomes negative (Figure S3). This is a typical
characteristic of an ‘AMOC weak’ state which is an additional statistical
equilibrium in the full hysteresis hosing simulation under pre-industrial
conditions [5, 28]. The AMOC states resulting at $F_{H}=0.45$ Sv have no clear
overturning cell and their $F_{\mathrm{ovS}}$ values become positive. These
AMOC characteristics link to an ‘AMOC off’ state as found under pre-industrial
conditions as a statistical equilibrium [28].

When comparing the two RCP4.5 simulations, the temperature responses over the
21st century (Figures 2c,d) are, however, very similar. The same holds for the
two RCP8.5 simulations over the 21st century (Figures 2e,f). The AMOC
weakening can (partly) offset the regional warming over Northwestern Europe
resulting in below-averaged surface temperature rise for a few European cities
in the 21st century (Figures S4a–d). The surface temperature anomalies at the
end of the simulation (i.e., the equilibrium temperatures, model years 2450 –
2499, Figure S4e–h) clearly show the strong AMOC-induced cooling when the AMOC
has collapsed and are most pronounced for $F_{H}=0.45$ Sv and the RCP4.5
scenario.

## The Buoyancy Responses under Climate Change

Also under climate change, the $B_{\mathrm{ocean}}$ over the isopycnal
outcropping region is related to the AMOC strength (Figures S5a–d). The
$B_{\mathrm{surf}}$ is significantly ($p<0.05$, [35]) increasing during the
21st century and the changes are smaller in the Hist/RCP4.5 (0.29 J kg-1 and
0.26 J kg-1) than in the Hist/RCP8.5 (0.49 J kg-1 and 0.44 J kg-1, for
$F_{H}=0.18$ Sv and $F_{H}=0.45$ Sv, respectively). As expected, the larger
increase in $B_{\mathrm{surf}}$ under Hist/RCP8.5 (compared to Hist/RCP4.5)
can be attributed to a larger radiative forcing (Figures S5a–d). The ocean
buoyancy decomposition into its temperature and salinity contributions
(Figures S5e–l) clearly shows that temperature responses are forcing the AMOC.
Prior to the AMOC decline of model year 2020, the temperature is weakening the
AMOC by buoyancy gain ($B_{\mathrm{ocean}}^{T}$) and thereafter salinity
responses ($B_{\mathrm{ocean}}^{S}$) start to dominate. This strong increase
in $B_{\mathrm{ocean}}^{S}$ indicates a destabilising salt-advection feedback.

The buoyancy responses under climate change are clearly different from those
of the quasi-equilibrium hosing simulation, because in the latter case the
ocean salinity responses ($B_{\mathrm{ocean}}^{S}$) are entirely responsible
for destabilising the AMOC. Another difference is that under climate change
the surface buoyancy increase is induced by heat flux
($B_{\mathrm{surf}}^{T}$) changes and the freshwater flux
($B_{\mathrm{surf}}^{S}$) changes have a negligible contribution. However,
once the AMOC starts to decline, we find comparable (with respect to the
quasi-equilibrium case) responses in the latent, sensible, longwave,
evaporation and precipitation contributions (Figure S6). The AMOC sea-ice
feedbacks are only relevant for the Hist/RCP4.5 and the $F_{H}=0.45$ Sv case
as the sea ice vastly extends under its AMOC collapse. For the other
simulations, the higher background temperatures melt almost all sea ice and
hence are limiting the destabilising sea-ice buoyancy contribution.

The AMOC collapses under the two RCP8.5 scenarios and the dynamics driving the
collapse shares similarities to that of the hosing simulation (Figure S5). The
$B_{\mathrm{surf}}$ increase levels off when the climate forcing becomes
constant in both RCP4.5 simulations. Depending on the freshwater flux forcing,
this results in either a negative $B_{\mathrm{surf}}$ or positive
$B_{\mathrm{surf}}$ in 2100 for $F_{H}=0.18$ Sv and $F_{H}=0.45$ Sv,
respectively. The AMOC eventually recovers for $F_{H}=0.18$ Sv (Figure 2a),
but for $F_{H}=0.45$ Sv the isopycnal outcropping region slowly gains buoyancy
between model years 2080 to 2150. This results in an AMOC decline of only 1 Sv
between 2100 and 2150 and thereafter it fully collapses. During the AMOC
collapse, $B_{\mathrm{surf}}$ further increases which is similar to the hosing
and RCP8.5 simulations. A net negative surface buoyancy is crucial for AMOC
stability [23, 24, 20, 21, 22] and an AMOC collapse is inevitable when
$B_{\mathrm{surf}}$ becomes positive.

## Surface Buoyancy Responses in CMIP6 models

As the $B_{\mathrm{surf}}$ over the isopycnal outcropping region is a
diagnostic of an imminent AMOC collapse, we have determined it for 24
different CMIP6 models under the historical forcing (1850 – 2014) followed by
the SSP2-4.5 and SSP5-8.5 (2015 – 2100) scenarios. In CMIP6 there are no
indications for an AMOC collapse by the year 2100 [18, 36]. This is not very
surprising as the typical AMOC collapse timescale is longer than 100 years and
only (substantial) AMOC weakening can be expected by 2100 (Figures 2a,b).

The behaviour of $B_{\mathrm{surf}}$ in CMIP6 models is similar to that in the
CESM simulations discussed above and the heat fluxes primarily drive the
increase over the 21st century (Figures 3a,b). The CMIP6 multi-model mean
$B_{\mathrm{surf}}$ trends (2000 – 2100) are 0.25 (0.15 – 0.37, 10% – 90%-Cl)
J kg-1 per century and 0.37 (0.22 – 0.54, 10% – 90%-Cl) J kg-1 per century for
Hist/SSP2-4.5 and Hist/SSP5-8.5, respectively (Figure 3c and Table S1). The
multi-model mean $B_{\mathrm{surf}}$ switches sign by 2043 and by 2036 with an
associated global warming of +1.96∘C (+1.52∘C to +2.37∘C, 10% – 90%-Cl, years
2038 – 2048) and +1.88∘C (+1.41∘C to +2.31∘C, 10% – 90%-Cl, years 2031 – 2041)
for Hist/SSP2-4.5 and Hist/SSP5-8.5, respectively (Figures 3e,f).

Figure 3: Surface buoyancy responses in the CMIP6. (a & b): The surface
buoyancy ($B_{\mathrm{surf}}$) decomposition for CMIP6 under the Hist/SSP2-4.5
and Hist/SSP5-8.5 scenarios. The multi-model mean and percentiles are smoothed
through a 11-year running mean. (c): The 24 CMIP6 models with the historical
(1850 – 1899) $B_{\mathrm{surf}}$ against the $B_{\mathrm{surf}}$ trends (2000
– 2100) for Hist/SSP2-4.5 (blue) and Hist/SSP5-8.5 (red). The error bars
indicate the 10% to 90%-Cl. The thin lines connect the two forcing scenarios
to the same climate model. The four CESM simulations (Figure 2) are also
displayed. The circled markers indicate at least one 11-year window with
positive $B_{\mathrm{surf}}$, the squared markers indicate that
$B_{\mathrm{surf}}$ remains negative. (d): Similar to panel c, but now for the
historical $B_{\mathrm{surf}}$ against the $F_{\mathrm{ovS}}$ (circled
markers) and AMOC strength (diamond markers). (e & f): The tipping time is
determined where the $B_{\mathrm{surf}}$ multi-model mean switches sign, using
the smoothed time series from panels a and b. The same procedure is repeated
by excluding the NESM3 (highest historical $B_{\mathrm{surf}}$) from the
multi-model mean, then the IPSL-CM6A-LR and NESM3 are excluded, and so on. The
associated temperature anomaly (over the same 11-year window) is also shown.

The magnitude of the $B_{\mathrm{surf}}$ trends is not dependent on the
historical $B_{\mathrm{surf}}$ value and larger $B_{\mathrm{surf}}$ trends can
be expected for higher emission scenarios (Figure 3c). It should be noted that
five CMIP6 models have a positive historical $B_{\mathrm{surf}}$ (1850 – 1899,
see Table S1). For example, the NESM3 (highest historical $B_{\mathrm{surf}}$)
has a very weak historical AMOC strength of 6.8 Sv (Figure 3d) and, in
combination with its negative historical $F_{\mathrm{ovS}}$, suggest that the
NESM3 reached an ‘AMOC weak’ state upon the historical initialisation. On the
other hand, the FGOALS-g3 (lowest historical $B_{\mathrm{surf}}$) has a strong
historical AMOC strength of 24.3 Sv and a positive $F_{\mathrm{ovS}}$ of 0.36
Sv and its $B_{\mathrm{surf}}$ does not change sign.

There is a tendency among the suite of CMIP6 models where models with
relatively large $B_{\mathrm{surf}}$ have relatively low $F_{\mathrm{ovS}}$
values ($R^{2}=0.66$) and weak AMOC strengths ($R^{2}=0.69$) for the
historical period. Similar relations in CMIP6 are found for the present-day
(1994 – 2020) period and CMIP6 biases in $F_{\mathrm{ovS}}$ and AMOC strength
influence their responses under climate change [36]. Previous work [37] and
the CESM results here (Figures 2 and S3) show that the case with historical
positive $F_{\mathrm{ovS}}$ and strong AMOC is more resilient under climate
change than the case with historical negative $F_{\mathrm{ovS}}$ and weak AMOC
strength. This indicates that the various model biases [36] upon
initialisation set the AMOC sensitivity under the applied forcing.

Excluding the five CMIP6 models with positive historical $B_{\mathrm{surf}}$
from the multi-model mean shifts the $B_{\mathrm{surf}}$ sign change to 2059
(warming of +2.27∘C) and 2050 (warming of +2.39∘C) for Hist/SSP2-4.5 and
Hist/SSP5-8.5, respectively (Figures 3e,f). For the 19 CMIP6 models with a
negative historical $B_{\mathrm{surf}}$, we report that 8 (10) models have
switched $B_{\mathrm{surf}}$ sign by mid 21st century and 14 (16) models by
the end of the 21st century under Hist/SSP2-4.5 (Hist/SSP5-8.5). Based on the
$B_{\mathrm{surf}}$ responses, we expect that most CMIP6 models will show an
AMOC tipping event when integrating the two SSP scenarios beyond 2100.

## The Present-day Forcing on the AMOC

Observational data is very limited to determine $B_{\mathrm{surf}}$ responses
and compare against CMIP6 under climate change. Instead, we use the reanalysis
product SODA3.15.2 (1980 – 2022) to analyse $B_{\mathrm{surf}}$ responses
under present-day climate change. The SODA3.15.2 has a mean AMOC strength of
16.8 Sv (not shown) and its $B_{\mathrm{surf}}$ is negative ($-0.23$ J kg-1)
and is increasing (Figure 4a) under climate change by 0.36 J kg-1 per century
($p<0.05$). The CMIP6 multi-model mean has, as explained above, a similar
trend under the Hist/SSP5-8.5 scenario (Figure 3b). When we linearly
extrapolate the SODA3.15.2 trend to zero (Figure 4b), we find that
$B_{\mathrm{surf}}$ changes sign by 2067 and when using the CMIP6 models this
is by 2086 (2065 – 2127, 10% – 90%-Cl) under Hist/SSP2-4.5 and by 2065 (2052 –
2095, 10% – 90%-Cl) under Hist/SSP5-8.5. The associated global warming in the
CMIP6 multi-model mean is +2.99∘C (+2.16∘C to +3.71∘C, 10% – 90%-Cl, years
2081 – 2091) for SSP2-4.5 and +3.37∘C (+2.52∘C to +3.93∘C, 10% – 90%-Cl, years
2060 – 2070) for SSP5-8.5.

Figure 4: The tipping point estimate based on surface buoyancy changes under
climate change. (a): The surface buoyancy ($B_{\mathrm{surf}}$) decomposition
for SODA3.15.2 (1980 – 2022) and the observed yearly-averaged global mean
surface temperature anomaly compared to the historical period (1850 – 1899).
(b): The linearly extrapolated $B_{\mathrm{surf}}$ for SODA3.15.2 (dashed gray
curve) and the CMIP6 multi-model mean $B_{\mathrm{surf}}$ trend (over the 21st
century) for the Hist/SSP2-4.5 and Hist/SSP5-8.5 scenarios. (c – e): The
vertical structure of temperature, salinity and potential density over 40∘N –
60∘N (Atlantic Ocean) and for the period 1980 – 2022. The black (red) curves
are the time means (trends) for 1980 – 2022, and are shown for EN4.2.2 and
SODA3.15.2. The significance [35] of the trends with depth are displayed on
the sides of each panel.

Because a positive $B_{\mathrm{surf}}$ is not consistent with the negative
present-day $B_{\mathrm{surf}}$ found in SODA3.15.2, we exclude the 13 CMIP6
models with a $B_{\mathrm{surf}}$ sign change before 2022 in any of the two
Hist/SSPs scenarios (Table S1). This results in a $B_{\mathrm{surf}}$ sign
change by 2084 (2063 – 2107, 10% – 90%-Cl, Hist/SSP2-4.5) and by 2060 (2047 –
2079, 10% – 90%-Cl, Hist/SSP5-8.5). The associated warming levels in the CMIP6
mean (of 11 models) are now +2.78∘C (+2.12∘C to +3.45∘C, 10% – 90%-Cl,
Hist/SSP2-4.5) and +2.89∘C (+2.28∘C to +3.40∘C, 10% – 90%-Cl, Hist/SSP5-8.5).
The critical temperature anomaly for AMOC tipping is about 3∘C and is robust
for the two different forcing scenarios. The projected tipping time is found
after 2050, but the timing strongly depends on the forcing scenario. Based on
the +3∘C warming threshold derived from the SODA3.15.2 extrapolation, none
(SSP2-4.5) and only 3 (SSP5-8.5) of the 24 CMIP6 models surpass this threshold
by mid century (2045 – 2055) and 15 of the CMIP6 (SSP2-4.5) and all of CMIP6
(SSP5-8.5) surpass it by the end of the century (2090 – 2100).

The positive $B_{\mathrm{surf}}$ trend in SODA3.15.2 suggests that the AMOC is
weakening under present-day climate change. Another line of evidence of AMOC
weakening is the vertical stratification increase over the isopycnal
outcropping region (Figures 4c–e), which enhances the upper ocean buoyancy.
The time means (1980 – 2022) of SODA3.15.2 are very close to the observational
product EN4.2.2. When comparing the temperature and salinity trends between
the two products, there are some deviations and these are mainly found in the
upper 200 m. These differences cancel out for the potential density trends,
which are comparable between the two products and, more importantly, are
primarily induced by positive temperature trends. Previous studies [38, 39]
and our buoyancy decomposition of the CESM under climate change (Figure S5)
demonstrate that global warming enhances the vertical temperature
stratification and induces the initial AMOC weakening.

Satellite observations between 1993 and 2020 show the characteristic warming
hole south of Greenland (Figure S7) and this has been linked to AMOC weakening
[10], but this interpretation has received substantial criticism [40, 13, 41].
The products EN4.2.2 and SODA3.15.2, together with reanalysis products
GLORS12V1 and ORAS5, realistically reproduce the observed SST trends over the
same period (Figure S7). There are, however, differences in the sea surface
salinity trends when comparing the different products. The time mean
temperature, salinity and potential density with depth are consistent among
the products, whereas the trends are less coherent. The ORAS5 has the largest
trend differences compared to EN4.2.2, in particular for salinity, and its
surface buoyancy does not show a significant trend over its total available
period (1985 – 2023, Figure S8a). The GLORYS12V1 does not provide the required
data to determine the surface buoyancy. Both observational and reanalysis
products are too short (28 years) to reliably test their significance on the
trends. Nevertheless, the results over the 1993 – 2020 period also indicate
that positive temperature anomalies dominate the vertical stratification
responses under climate change, leading to an increase of the upper ocean
buoyancy.

## Discussion

In three out of the four climate change CESM simulations shown here we find
that the AMOC collapses to a much ($<-80\%$) weaker state. This weaker state
is reached after the 21st century but a substantial AMOC weakening occurs
already during the 21st century. The initial AMOC weakening under climate
change is induced by transient temperature responses [38, 39] and thereafter
the dominant salt-advection feedback takes over [42]. The AMOC-induced cooling
over Northwestern Europe is strong enough to offset the regional warming under
climate change.

We have linked the AMOC collapse to the surface buoyancy over the isopycnal
outcropping region in the Atlantic Ocean (40∘N – 60∘N) for which there is a
strong theoretical support [20, 21, 22]. By first analysing the quasi-
equilibrium hosing simulation (without any climate change), we find that a
diagnostic for the AMOC tipping event is the sign change in the characteristic
net surface buoyancy loss. The destabilising salt-advection feedback, in
combination with surface buoyancy gain, results in an AMOC tipping event in
the CESM. Under the high emission scenario (Hist/RCP8.5), the surface buoyancy
always changes sign in the 21st century and the AMOC collapses beyond 2100. In
the middle-of-the-road scenario (Hist/RCP4.5), the AMOC weakening and surface
buoyancy increase are smaller compared to the high emission scenario. In this
scenario, depending on the background climate conditions and thus the initial
surface buoyancy value, this either results in (partial) AMOC recovery or in a
full AMOC collapse.

The reanalysis product SODA3.15.2 shows an increase in the surface buoyancy
and vertical stratification and both indicate that the AMOC is weakening under
present-day climate change. By linearly extrapolating the CMIP6 projections,
the AMOC tipping event occurs by 2065 (Hist/SSP5-8.5) and by 2086
(Hist/SSP2-4.5) and corresponds to a global warming of about +3∘C (+2.2∘C to
+3.9∘C, 10% – 90%-Cl). More than half of the CMIP6 models under SSP2-4.5
surpasses the +3∘C warming threshold by the end of the century and all of them
under SSP5-8.5, indicating that there is a substantial risk of AMOC tipping
under moderate climate change. The full AMOC collapse develops after 2100 and
it is therefore important to simulate to at least 2200 in the next generation
climate models of CMIP phase 7.

The quantity $F_{\mathrm{ovS}}$ is an important diagnostic and a negative
$F_{\mathrm{ovS}}$ sign appears to be connected to the salt-advection feedback
strength [30, 31, 32, 33, 6]. Note that this quantity can only be used under
quasi-equilibrium conditions and these conditions include the equilibration of
the lower level interior basin [39] in response to an imposed anomaly.
However, if the deep ocean has no time to equilibrate as a result of a large
freshwater flux change [4, 34] or rapid climate change, the $F_{\mathrm{ovS}}$
sign is a less clear indicator of the salt-advection feedback. Until now, the
observed AMOC decline is only gradual [10, 11, 12, 13, 14] and the negative
$F_{\mathrm{ovS}}$ trend [6] is still a useful early warning indicator.
Alternatively, the surface buoyancy is linked to the $F_{\mathrm{ovS}}$ and
AMOC strength and can be used under strong transient conditions as collapse
indicator. These relations are found for the historical period, the present-
day (1994 – 2020) period [36] and in a strongly eddying version of the CESM
(Figure S8b). The bottom line is that climate model biases [43, 44, 45, 37,
32, 36, 46, 47] need to be reduced to have a realistic AMOC sensitivity under
climate change.

Recent AMOC studies have (indirectly) questioned the sixth IPCC report’s
statement [19] on the possibility of an AMOC collapse before 2100 [15, 6, 36,
48]. Our study demonstrates again that the present-day AMOC is on route to
tipping. The previous critical temperature threshold of +4∘C (+1.4∘C to
+8.0∘C) warming [2] was based on enhanced ice and river run-off [1, 49] and
the results from a few CMIP phase 5 models [50, 51]. We link AMOC dynamics to
the surface buoyancy and, by using reanalysis and 24 different CMIP6 models,
we arrive at a critical temperature threshold of +3∘C (+2.2∘C to +3.9∘C)
warming for causing an AMOC tipping event. Under high emission scenarios this
temperature threshold will be reached after 2050 and is in agreement with
previous estimates [16, 17]. Note that these temperature thresholds are upper
bounds as enhanced Greenland Ice Sheet melt under future warming is not
considered in the CESM nor CMIP6. A positive note is that a lower emission
scenario can delay or prevent an AMOC collapse, as was demonstrated for the
CESM here. To limit the risk of a potential AMOC collapse in the foreseeable
future, global society needs to be on track of a low emission scenario (i.e.,
SSP1-1.9 and SSP1-2.6) and urgent climate action is needed to guarantee this.

## Methods

Climate Model Simulations

The CESM is a fully-coupled climate model and has horizontal resolutions of 1∘
for the ocean/sea-ice components and 2∘ for the atmosphere/land model
components. Mesoscale features such as ocean eddies are parameterised. We
imposed a slowly-varying freshwater flux forcing (i.e., quasi-equilibrium
approach) over the North Atlantic Ocean (20∘N – 50∘N) and compensated
elsewhere to conserve the total ocean salinity [6]. From the quasi-equilibrium
simulation, we branched off two simulations under their constant freshwater
flux forcing of $F=0.18$ Sv and $F=0.45$ Sv to find statistical equilibria
[28]. From the end of these statistical equilibria simulations, we imposed the
historical forcing (1850 – 2005) followed by either the RCP4.5 or RCP8.5
scenario (2006 – 2100) and with a constant freshwater flux forcing ($F=0.18$
Sv or $F=0.45$ Sv).

The high-resolution version of the CESM was retained from the iHESP project
[52] under the Hist/RCP8.5 scenario (and no freshwater flux forcing). The
high-resolution CESM version has a 0.1∘ for the ocean/sea-ice components and
0.25∘ for the atmosphere/land model components, and explicitly resolves ocean
eddies and tropical cyclones. A companion low-resolution version of the CESM
is available with the iHESP project, however, not all relevant variables were
stored to determine the surface buoyancy and hence we did not include this
simulation in our analysis.

For the CMIP6 models, we retained the historical forcing (1850 – 2014)
followed by the SSP2-4.5 and SSP5-8.5 (2015 – 2100) scenarios. Note that the
forcing scenarios are slightly different between the CESM simulations (the
RCPs) and CMIP6 (the SSPs). We retained the sea surface temperature (‘tos’),
sea surface salinity (‘sos’), total heat flux (‘hfds’), total freshwater flux
(‘wfo’), meridional velocity (‘vo’), salinity (‘so’) and surface air
temperature (‘tas’). Only 24 models (Table S1) provided all seven variables
for the different forcing scenarios and we selected one realisation
(‘r1i1p1f1’ or ‘r1i1p1f2’) for each CMIP6 model, the analysis is conducted on
their native grid.

The observational product EN4.2.2 (horizontal resolution of 1∘ $\times$ 1∘,
1900 – 2023) assimilates observations from various sources [53]. The
reanalysis products are steered towards observations and the products are the
SODA3.15.2 (horizontal resolution of 1/4∘ $\times$ 1/4∘, 1980 – 2022), the
GLORYS12V1 (horizontal resolution of 1/12∘ $\times$ 1/12∘, 1993 – 2020) and
the ORAS5 (horizontal resolution of 1/4∘ $\times$ 1/4∘, 1958 – 2023).

The AMOC strength The AMOC strength is defined as the total meridional volume
transport at 26∘N over the upper 1,000 m:

$\mathrm{AMOC}(y=26^{\circ}\mathrm{N})=\int_{-1000}^{0}\int_{x_{W}}^{x_{E}}v~{}\mathrm{d}x\mathrm{d}z$
(1)

When thermal wind balance is applicable for the AMOC (AMOCTWB), its strength
can be approximated by [20, 54]:

$\partial_{zz}\Psi=\frac{g}{\rho_{0}f}\left(\sigma_{\mathrm{b}}(z)-\sigma_{\mathrm{n}}(z)\right)$
(2)

with $g=9.8$ m s-2, $\rho_{0}=1027$ kg m-3, $f=1.2\times 10^{-4}$ s-1. The
terms $\sigma_{\mathrm{b}}$ and $\sigma_{\mathrm{n}}$ represent the
(spatially-averaged) potential density over the Atlantic basin (34∘S – 40∘N)
and the isopycnal outcropping region (40∘N – 60∘N) with depth. The AMOCTWB
represents the AMOC strength over the isopycnal outcropping region ($\approx
50^{\circ}$N) and captures variability on decadal to centennial time scales.
We determined the AMOCTWB at 1,000 m depth (Figures S1e,f). The potential
densities are determined using the Thermodynamic Equation of SeaWater 2010
(TEOS-10) toolkit [55], which uses ocean temperature and salinity as input.
Note that the CESM provides the potential density as standard output, but for
consistency with the buoyancy calculation (see below) and other reanalysis
products which do not provide the potential density as standard output, we
used the TEOS-10 toolkit.

Oceanic Buoyancy The ocean buoyancy and surface buoyancy [56] are defined as:

$\displaystyle B_{\mathrm{ocean}}(T,S)$
$\displaystyle=\frac{g}{\rho_{0}}\int_{z_{1}}^{z_{2}}\left(\sigma(z)-\sigma(z=0)\right)\mathrm{d}z$
(3a) $\displaystyle B_{\mathrm{surf}}$
$\displaystyle=\frac{g\alpha}{\rho_{0}C_{p}}Q_{\mathrm{heat}}+\beta
gS_{\mathrm{surf}}Q_{\mathrm{fresh}}=B_{\mathrm{surf}}^{T}+B_{\mathrm{surf}}^{S}$
(3b)

where $\sigma$ is the potential density (in kg m-3), $\alpha$ the thermal
expansion coefficient (in K-1), $C_{p}$ the oceanic heat capacity (in J kg-1
K-1), $Q_{\mathrm{heat}}$ the net heat input into the ocean (in J), $\beta$
the haline contraction coefficient (in kg g-1), $S_{\mathrm{surf}}$ the sea
surface salinity (in g kg-1) and $Q_{\mathrm{fresh}}$ the net freshwater input
into the ocean (in m). The term $Q_{\mathrm{heat}}$ ($Q_{\mathrm{fresh}}$) can
be further decomposed in, for example, the contribution by longwave radiation
and sensible heat fluxes (evaporation and freshwater flux forcing).

The temperature (salinity) contribution to ocean buoyancy changes can be
determined by using a reference salinity (temperature) and is indicated by
$B_{\mathrm{ocean}}(T,\overline{S})=B_{\mathrm{ocean}}^{T}$
($B_{\mathrm{ocean}}(\overline{T},S)=B_{\mathrm{ocean}}^{S}$). The monthly-
averaged references are determined over the first 50 years of the hosing
simulation and the historical period (1850 – 1899). The sea water properties
(e.g., $\alpha$, $C_{p}$, etc.) are determined using TEOS-10. The ocean
buoyancy and surface buoyancy are determined with monthly-averaged model
output and are then converted to yearly averages and yearly sums,
respectively.

The Freshwater Transport

The freshwater transport carried by the overturning component at 34∘S
($F_{\mathrm{ovS}}$) is determined as:

$F_{\mathrm{ovS}}=F_{\mathrm{ov}}(y=34^{\circ}\mathrm{S})=-\frac{1}{S_{0}}\int_{-H}^{0}\left[\int_{x_{W}}^{x_{E}}v^{*}\mathrm{d}x\right]\left[\langle
S\rangle-S_{0}\right]\mathrm{d}z$ (4)

where $S_{0}=35$ g kg-1 is a reference salinity. The $v^{*}$ is defined as
$v^{*}=v-\hat{v}$, where $v$ is the meridional velocity and $\hat{v}$ the
full-depth section spatially-averaged meridional velocity. The quantity
$\langle S\rangle$ indicate the zonally-averaged salinity and primed
quantities ($v^{\prime}$ and $S^{\prime}$) are deviations from their
respective zonal means.

Acknowledgments

The model simulation and the analysis of all the model output was conducted on
the Dutch National Supercomputer Snellius within NWO-SURF project 17239.

## Declarations

  * •

Funding – R.M.v.W., E.Y.P.V. and H.A.D. are funded by the European Research
Council through the ERC-AdG project TAOC (project 101055096).

  * •

Conflict of interest – The authors declare no competing interest

  * •

Ethics approval – Not applicable

  * •

Availability of data and materials – The (processed) model output will be made
available on Zenodo upon publication. The reanalysis and assimilation products
can be accessed through: SODA3.15.2 (http://www.soda.umd.edu), EN4.2.2.g10
(https://www.metoffice.gov.uk/hadobs/en4/), GLORYS12V1
(https://doi.org/10.48670/moi-00021) and ORAS5
(https://doi.org/10.24381/cds.67e8eeb7). The observational products are found
through: sea surface temperature observations (version 2.1, Level 4,
https://doi.org/10.24381/cds.cf608234), sea surface salinity observations
(Level 4, https://doi.org/10.48670/moi-00051) and observed global mean surface
temperature anomalies (version 6, https://www.ncei.noaa.gov/data/noaa-global-
surface-temperature/v6/access/timeseries/) The CMIP6 model output is provided
by the World Climate Research Programme’s Working Group on Coupled Modelling.

  * •

Code availability – The analysis scripts will be made available on Zenodo upon
publication.

  * •

Authors’ contributions – R.M.v.W., E.Y.P.V. and H.A.D. conceived the idea for
this study. M.K. performed the model simulation with the CESM. R.M.v.W.
conducted the analysis and prepared all figures. All authors were actively
involved in the interpretation of the analysis results and the writing
process.

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Figure S1: Atlantic Ocean water properties for the CESM (hosing). (a – d): The
zonally-averaged (Atlantic basin) and yearly-averaged temperature, salinity,
potential density and ocean buoyancy for the first 50 years of the hosing. The
top panels show the yearly-summed surface buoyancy components and the yearly-
maximum mixed layer depth. Panel c shows the potential density difference with
respect to the surface and the curves represent various isopycnals. (e): The
thermal wind balance AMOC approximation
(AMOC${}_{\mathrm{TWB}}(\sigma_{b},\sigma_{n})$, see Methods) under the
hosing. The thermal wind balance is decomposed into a component for which the
reference (i.e., first 50 model years) basin box potential density
(AMOC${}_{\mathrm{TWB}}(\overline{\sigma_{b}},\sigma_{n})$) is used, and the
reference north box potential density
(AMOC${}_{\mathrm{TWB}}(\sigma_{b},\overline{\sigma_{n}})$) is used. We also
show the AMOC strength at 1,000 m and 26∘N for comparison. (f): Similar to
panel e, but now the potential densities over the lower 1,000 m are fixed
(i.e., first 50 model years) and the upper 1,000 m are fixed. Figure S2:
Surface buoyancy decomposition for the CESM (hosing). (a – b): Climatology
over the first 50 model years of the surface buoyancy (40∘N – 60∘N, Atlantic
Ocean) and is decomposed into its different contributions for the (a): heat
fluxes and (b): freshwater fluxes. (c – d): The surface buoyancy difference
(with respect to the climatology) under the varying freshwater flux forcing
for the (c): heat fluxes and (d): freshwater fluxes. The time series are
displayed as yearly sums and are smoothed through a 25-year running mean to
reduce the variability. The inset in panel c shows the upwelling longwave (LW
$\uparrow$) and the downwelling longwave (LW $\downarrow$) contributions. The
inset in panel d shows the yearly-averaged sea-ice area (grid cells with sea-
ice fractions of at least 15%) between 40∘N – 60∘N. Note the different
vertical ranges for the panels. Figure S3: Atlantic Meridional Overturning
Circulation (AMOC) properties. (a & b): The freshwater transport carried by
the AMOC at 34∘S, $F_{\mathrm{ovS}}$. For reference, the $F_{\mathrm{ovS}}$
under the hosing is also shown and is centred around the AMOC tipping event
(black curve, top x-axis). The yellow shading indicates observed
$F_{\mathrm{ovS}}$ values [7, 32, 57]. (b – f): The AMOC streamfunction over
the last 50 years (model years 2450 – 2499). The contours indicate the
isolines for different AMOC values for the historical period (model years 1850
– 1899). Figure S4: The surface temperature responses under climate change. (a
– d): The yearly-averaged surface temperatures for five different cities
(diamond markers in inset) and the global mean under the two climate change
scenarios (Hist/RCP4.5 and Hist/RCP8.5) and for $F_{H}=0.18$ Sv and
$F_{H}=0.45$ Sv. The time series are displayed as anomalies compared to the
historical period (1850 – 1899) and are then smoothed through a 11-year
running mean. The yellow shading indicates the 21st century over which the
trends are displayed in the insets, the circled markers indicate non-
significant ($p\geq 0.05$, [35]) trends. (e – h): The equilibrium temperature
anomalies (compared to 1850 – 1899) at the end of the simulations, the circled
markers indicate non-significant ($p\geq 0.05$, two-sided Welch’s t-test)
differences. Figure S5: Buoyancy and AMOC responses under climate change.
Similar to Figure 1, but now under the two climate change scenarios
(Hist/RCP4.5 and Hist/RCP8.5) and for $F_{H}=0.18$ Sv and $F_{H}=0.45$ Sv. The
climatologies are shown in Figure S6. Figure S6: Surface buoyancy
decomposition under climate change. Similar to Figure S2, but now for the
different climate change simulations. The climatology (panels a – d) is
determined over model years 1850 – 1899. The time series for the heat fluxes
are shown in panels e – h and for the freshwater fluxes in panels i – l. Note
that there are two historical simulations (for $F_{H}=0.18$ Sv and
$F_{H}=0.45$ Sv) and hence the climatology and the model output between model
years 1850 – 2005 are identical when comparing the two climate change
scenarios (RCP4.5 and RCP8.5).  Figure S7: Present-day oceanic climate change
(1993 – 2020). (a – j): The sea surface temperature and sea surface salinity
trends (1993 – 2020) for satellite observations, EN4.2.2, SODA3.15.2,
GLORYS12V1 and ORAS5. (k – m): The vertical structure of temperature, salinity
and potential density between 40∘N – 60∘N (Atlantic Ocean, dotted lines in
panels a – j) and for the period 1993 – 2020. The black (red) curves are the
time means (trends) for 1993 – 2020 and are shown for the different products.
The diamond markers indicate the satellite observations. Figure S8: Surface
buoyancy changes under climate change. The surface buoyancy
($B_{\mathrm{surf}}$) decomposition for (a): ORAS5 and (b): the high-
resolution version of the CESM (iHESP) under the Hist/RCP8.5 scenario. The
inset in panel b shows yearly-averaged global mean surface temperature anomaly
compared to the historical period (1850 – 1899).
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Table S1: Overview of the CMIP6 models, ranked on their historical (1850 –
1899) surface buoyancy ($B_{\mathrm{surf}}$, in J kg-1) value, including their
historical freshwater transport at 34∘S ($F_{\mathrm{ovS}}$, in Sv) and AMOC
strength at 1,000 m and 26∘N (in Sv). For each CMIP6 model, we determined the
first 11-year window (e.g., 2055 $\rightarrow$ 2050 – 2060) where
$B_{\mathrm{surf}}$ switches sign and the associated global mean surface
temperature anomaly ($\Delta T_{g}$, in ∘C) compared to the historical period.
Similarly, the first 11-year window where the global surface temperature
anomaly exceeds 3∘C warming and the associated $B_{\mathrm{surf}}$ value. The
last two columns display the average $B_{\mathrm{surf}}$ change (i.e., linear
trend) over the 21st century, where bold indicates significant ($p<0.05$,
[35]) changes. For the CMIP6 mean, we first determined the multi-model mean
and then determined the presented quantities.