Main

The North Atlantic (NA), where the Atlantic Meridional Overturning Circulation (AMOC) transports both heat and carbon from the tropics, regulates global mean surface temperature and its variability in the present climate1,2. A substantial decline of the AMOC is expected under future global warming, weakening ocean heat transport along with increased freshwater flux into the NA3,4,5. The associated oceanic and atmospheric circulation changes include a shift in the Intertropical Convergence Zone, due to enhanced interhemispheric asymmetries in energy fluxes on the top of the atmosphere as well as in ocean heat uptake6,7. The NA is a hotspot for affecting global weather and climate8,9.

The NA covers only 15% of the global ocean surface but accounts for approximately 25% of the anthropogenic carbon (hereafter referred to as carbon) inventory of the world’s oceans10,11,12. The amount of carbon uptake in the NA is closely related to AMOC intensity due to the ocean mixing that modulates the solubility and subduction of carbon from the surface to the deep ocean13,14,15. Greater absorption of carbon by the NA from the atmosphere could delay global warming16,17,18,19. However, there is a large intermodel spread of NA carbon uptake among Earth system models (ESMs), which is partly due to a large intermodel spread of AMOC intensity20,21. Consequently, projection of future global warming is uncertain. Therefore, reducing the uncertainties in carbon uptake in the NA would greatly reduce the uncertainty of future global climate projections, including sea level rise, sea-ice retreat and extreme climate events22,23,24,25,26,27.

To reduce the uncertainty in carbon uptake in the NA and its associated Northern Hemisphere (NH) surface warming, here we develop an emergent constraint using the present-day sea surface salinity (SSS), which is derived based on a long-term period of hydrographic data with low observational uncertainties22,28. SSS is often used to investigate or represent upper ocean circulations because of its relationship with ocean density and hence its ability to affect the stability and vertical stratification of the water column29,30,31. In particular, SSS in the NA subpolar region is a well-known proxy for the AMOC because it reflects the AMOC-induced transport of warm and salty water from the subtropical NA32,33,34,35. We find that the present-day SSS in the NA subpolar region is a reliable indicator of AMOC strength and thus constrains the amount of NA carbon uptake in future climate and NH surface warming in ESMs.

Relationship between carbon uptake and warming

Figure 1 displays changes in surface temperature and cumulative carbon uptake amount in the NH during 2071–2100 compared with pre-industrial climate (1850–1900) as projected by 18 ESMs participating in Phase 6 of the Coupled Model Intercomparison (CMIP6) under the Shared Socioeconomic Pathways 5–8.5 (SSP5–8.5) simulations (Extended Data Table 1).

Fig. 1: Projections of future NH climate under a high-emission scenario.
figure 1

a,b, Future (2071–2100) changes relative to the pre-industrial period (1850–1900) from 18 CMIP6 ESMs under SSP5–8.5 simulation of surface temperature (a) and cumulative carbon uptake (b). The NA subpolar region is denoted by a blue outline in a and the NA domain is denoted by a green outline in b. Contours indicate an intermodel one standard deviation (s.d.) of future changes among ESMs. c, Future cumulative carbon uptake in the NA versus future surface temperature changes in the NH. Shadings show the future changes of global mean surface temperature and its correlation coefficient with cumulative carbon uptake in the NA is −0.70, which is slightly smaller than that with the NH surface temperature (r = −0.73). The purple dashed ellipse is calculated based on the multivariate normal distribution with 5–95% ranges. Correlation coefficient (Corre. coeff.), slope and P value determined by a two-sided Student’s t-test are also provided with a regression line (black solid line).

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The spatial distribution of future multimodel mean surface temperature changes is characterized by the strongest warming in the high latitudes of the NH, with a distinct weak warming in the NA subpolar region (outlined in Fig. 1a), a phenomenon known as the ‘warming hole’36 (Fig. 1a). These regions, including the NA subpolar and Arctic regions, also have a large intermodel uncertainty (Methods) due to either model bias or internal variability (Fig. 1a). Cumulative carbon uptake in the future is mainly concentrated in the NA with a large intermodel uncertainty (Fig. 1b)15,37. The projected multimodel mean NH surface warming from 1850–1900 to 2071–2100 is 5.9 ± 1.4 °C. An intermodel uncertainty (that is, ±1.4 °C) is defined as one standard deviation of the projected NH surface warming across CMIP6 ESMs. The projected multimodel mean of cumulative NA carbon uptake amount is 50.1 ± 10.7 PgC (Extended Data Fig. 1a). In CMIP Phase 5 (CMIP5) ESMs, the projected NH surface warming and cumulative NA carbon uptake amount are somewhat lower than those in CMIP6 ESMs, at 5.2 ± 1.0 °C and 47.6 ± 11.1 g PgC, respectively (Extended Data Fig. 1b). While CMIP6 ESMs have improved in simulating observed decadal fluctuations of sea surface temperature (SST) in the NA subpolar region compared with CMIP5 ESMs38, the ranges of intermodel uncertainty in CMIP5 and CMIP6 ESMs are similar (Extended Data Fig. 1).

Changes in NH surface temperature are statistically significantly and negatively correlated with cumulative NA carbon uptake (correlation coefficient, r = −0.73) among CMIP6 ESMs (Fig. 1c). Thus, ESMs with a larger NA carbon uptake systematically project a weaker future surface warming in the globe, and more so in the NH, compared with ESMs with a smaller NA carbon uptake. This robust intermodel relationship can be explained by a reduction in the greenhouse effect in models with a larger uptake of carbon from the atmosphere in the NA (Fig. 2). More specifically, a greater cumulative NA carbon uptake decreases the concentration of GHG in the atmosphere, which in turn leads to lower downward longwave radiation (Extended Data Fig. 2). In other words, a larger NA carbon uptake leads to a smaller increase in the downward longwave radiation in the NH, resulting in less surface warming of the NH (Fig. 2). Although the carbon uptake is confined to the NA, its influence reaches the whole NH surface temperatures. Therefore, reducing the uncertainty of NA carbon uptake in ESMs will reduce uncertainty in future NH surface warming, and consequently in future global warming. Although the Southern Ocean accounts for 40% of the global ocean’s carbon uptake and hosts robust meridional overturning circulation12,39,40,41,42, there is a large model uncertainty of simulated future carbon uptake in CMIP6 ESMs19,29, which is not well correlated to the future projected NH surface temperatures (Supplementary Fig. 1).

Fig. 2: Intermodel difference in the greenhouse effect response due to cumulative carbon uptake in the NA among CMIP6 models.
figure 2

Downward longwave changes in the NH against cumulative carbon uptake in the NA among ESMs. Shadings illustrate corresponding NH surface temperature change. The purple dashed ellipse is calculated based on the multivariate normal distribution with 5–95% ranges. Correlation coefficient (Corre. coeff.), slope and P value determined by a two-sided Student’s t-test are also provided with a regression line (black solid line).

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Strong link between carbon uptake and present-day salinity

The strength of the AMOC determines the NA carbon uptake because it regulates the poleward transport of carbon-rich and warm subtropical water to the sinking region15,37. Since April 2004, a direct measurement of the AMOC has been collected at 26° N43, but the overlapping period between the CMIP6 historical period and the direct observations is only 10 years (2005–2014), which is not long enough to discern a global warming signal from natural interdecadal variability; thus, it may not be appropriate to use the AMOC as an emergent constraint for the projected warming.

AMOC intensity is closely related to SSS and SST in the NA subpolar region44,45, but the SSS has a stronger intermodel correlation with the AMOC than that of the SST44 (Extended Data Fig. 3). The SSS is related to the subduction of carbon-enriched surface waters to the deep ocean through oceanic deep convection46,47. In addition, the SSS is associated with carbon uptake because it modulates the solubility pump. More specifically, a high SSS is linked to an increase in dissolved inorganic carbon concentration, and thus to a reduction in carbon uptake48, which is also confirmed in CMIP6 ESMs during the present-day climate (Supplementary Fig. 2). Therefore, SSS in the NA subpolar region (outlined in Fig. 1a) is a good indicator of AMOC intensity as well as the carbon uptake; thus, it is a suitable constraint based on a long-term period of reliable observational record.

Nevertheless, it is still necessary to consider the complexity of SSS and SST related to AMOC intensity, to avoid a simplification using the SSS49. First of all, the cumulative NA carbon uptake increases with GHG concentration under the SSP5–8.5 scenario in all ESMs. This implies that the ocean is able to absorb carbon from the atmosphere by the end of the twenty-first century without saturation (Extended Data Fig. 4). The present-day cumulative NA carbon uptake is highly correlated with the present-day SSS in the NA subpolar region (Fig. 3a). This implies that ESMs with a stronger AMOC tend to take up more carbon in the NA during the present-day, consistent with the notion that the intensity of ocean circulation determines the amount of carbon uptake14. Furthermore, it is found that the global heat–carbon coupling parameter (α) (Methods) is significantly correlated with the SSS in the NA subpolar region during the present-day (Extended Data Fig. 5). This suggests that we cannot exclude the possibility that the global ocean circulation also plays a role in determining the carbon uptake in the NA.

Fig. 3: Intermodel difference in cumulative carbon uptake in the NA and SSS in the NA subpolar region.
figure 3

a, Simulated present-day cumulative carbon uptake in the NA versus present-day SSS in the NA subpolar region for 18 CMIP6 ESMs. b, Future climate of SSS in the NA subpolar region under the SSP5–8.5 scenario versus that in the present-day climate. The marker, which is on the lower side of the 1:1 line, indicates that the present-day SSS is higher than the future SSS in ESMs. c, Future cumulative carbon uptake in the NA versus future SSS in the NA subpolar region. Shadings indicate the corresponding changes of surface temperature in the NH. The purple dashed ellipse is calculated based on the multivariate normal distribution with 5–95% ranges. Correlation coefficient (Corre. coeff.), slope and P value determined by a two-sided Student’s t-test are also provided with a regression line (black solid line).

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ESMs tend to simulate a lower SSS in the NA subpolar region in the future climate than that in the present-day (Fig. 3b), consistent with a decline in AMOC intensity from the present-day to the future climate. The intermodel distribution of present-day SSS in the NA subpolar region is highly correlated with that of the future climate (r = 0.60). Given that the SSS is an indicator of AMOC intensity in ESMs, this result implies that ESMs with higher SSS in the present-day (that is, strong AMOC) tend to simulate higher SSS in the NA subpolar region (that is, strong AMOC) in the future climate. Furthermore, there is a statistically significant positive intermodel relationship between the future SSS in the NA subpolar region and the future cumulative carbon uptake in the NA (r = 0.69) (Fig. 3c). Therefore, ESMs with higher SSS in the NA subpolar region (that is, strong AMOC) in the present-day climate tend to simulate a larger future cumulative NA carbon uptake (Fig. 3b,c).

Figure 3a–c also indicates that AMOC intensity, represented by the SSS in the NA subpolar region, is closely associated with the intermodel spread of cumulative carbon uptake in ESMs, both in the present-day and the future climate. Since the build-up of carbon is concentrated in the surface water through the air–sea carbon exchange, a poleward transport of carbon-enriched surface water and its penetration into deep ocean through the AMOC contributes to the amount of carbon uptake in the present-day and the future climate14. Indeed, the cumulative amount of carbon uptake at the end of the twenty-first century is highly correlated with that in the present-day (Supplementary Fig. 3), indicating that ESMs with an initially large uptake of carbon continue to take up more carbon in the future. Thus, ESMs with a high SSS in the NA subpolar region during the present-day tend to take up more carbon in the present-day (Fig. 3a) and this tendency will continue, leading to a larger uptake of carbon in the future (Fig. 3c). Consequently, the present-day SSS in the NA subpolar region is a key indicator of the amount of NA carbon uptake in the future. The changes in the amount of NA carbon uptake are associated with the future NH surface warming rate because an NA carbon uptake suppresses the greenhouse effect, and vice versa (Fig. 2). A similar conclusion is arrived on the causal link between SSS, the AMOC and NH warming, based on a composited analysis of two groups, one with higher and the other with lower present-day SSS in the NA subpolar region (Extended Data Fig. 6).

Reducing uncertainties in future NH surface warming

Climate model bias of the present-day SSS in the NA subpolar region could increase uncertainty in the future NH surface warming since it influences the amount of cumulative carbon uptake in the NA. Here we apply an emergent constraint to reduce the uncertainty in future NH surface warming based on the robust relationship between the present-day SSS in the NA subpolar region and the amount of cumulative NA carbon uptake.

The present-day SSS in the NA subpolar region has a strong negative correlation (r = −0.72) with future changes in NH surface temperature, and a strong positive correlation (r = 0.88) with cumulative carbon uptake in the NA (Fig. 4a,b). The observed SSS in the NA subpolar region and its uncertainty during 1981–2010, as obtained from the World Ocean Atlas 2018 (WOA18)50, is estimated to be 34.75 ± 0.04 practical salinity unit (psu, Methods). This value is similar to that obtained from the CMIP6 ESMs mean of 34.41 ± 0.70 psu. The emergent relationship constrains the uncertainty in future projections of the NH surface warming and cumulative NA carbon uptake. We assume that all ESMs are independent by using only one ensemble member from each ESM, although some ESMs share the same key physical components and codes51.

Fig. 4: Emergent constraints on NH surface warming and NA cumulative carbon uptake.
figure 4

a,b, Projected changes in NH surface temperature (a) and cumulative carbon uptake in the NA (b) under the SSP5–8.5 scenario versus SSS in the NA subpolar region in the present-day climate (1981–2010). The solid black line follows the linear regression of 18 CMIP6 models, while the dashed black lines indicate prediction errors with one s.d. (and 68% confidence intervals). The solid vertical purple line (shading) indicates the climatology (one standard error) of the WOA18. The slope and P value in Fig. 4a,b are obtained by a two-sided Student’s t-test. Shadings in b indicate the corresponding surface temperature change in the NH. c,d, Probability density functions for the projected NH surface warming (c) and cumulative carbon uptake changes in the NA (d) before (‘CMIP6 prior’, transparent) and after (‘after constraint’, opaque) when the emergent constraint is applied.

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The constrained probability density functions are derived from the conditional probability density functions of the emergent relationship and the observed SSS in the NA subpolar region (Methods). After incorporating the emergent constraint based on the observed SSS (Methods), the NH surface temperature warming is reduced from 5.9 ± 1.4 °C to 5.5 ± 1.0 °C (Fig. 4c) and the cumulative NA carbon uptake is increased from 50.1 ± 10.7 PgC to 54.7 ± 5.1 PgC under SSP5–8.5 (Fig. 4d). The uncertainties in future NH warming and cumulative carbon uptake are reduced by 30% and 53%, respectively.

Since carbon uptake in the NA alters global atmospheric CO2 concentration, it will also directly impact the future changes in global mean surface temperature. Therefore, there exists a strong relationship between the present-day SSS in the NA subpolar region and future global mean surface temperature changes in ESMs, with a significant negative correlation (r = −0.64) between the two. After incorporating the emergent constraints, the future global mean surface temperature is reduced from 4.7 °C ± 1.1 °C (before constraint) to 4.4 °C ± 0.8 °C (after constraint) with a 23% reduction in the uncertainty (Extended Data Fig. 7). This suggests that the projected global warming in the current ESMs is probably overestimated. To provide further evidence of the proposed emerging constraint, we conducted out-of-sample testing in CMIP5 ESMs22,52. Results support the proposed emerging constraint, reducing the uncertainty in the NH surface warming by 39% and in the cumulative NA carbon uptake by 26% (Extended Data Fig. 8).

The present-day AMOC strength during 2005–2014 as an emergent constraint results in a negative correlation with future NH surface temperature warming (r = −0.63) (Supplementary Fig. 4), which is lower than that using the SSS (r = −0.72 in Fig. 4a). NH warming is increased from 5.9 °C to 6.1 °C after the constraint, which is largely because the multimodel ensemble mean of AMOC intensity (17.4 sverdrups (Sv)) is stronger than the observed AMOC intensity (16.8 Sv). As mentioned above, the large variability and short duration of the observed AMOC lead to limitations of the AMOC-based constraint.

Discussion

We found that higher present-day SSS in the NA subpolar region, indicating stronger AMOC intensity, is associated with a larger amount of cumulative carbon uptake under global warming. This finding can be used to reduce the intermodel uncertainty in future changes in NH surface warming and cumulative carbon uptake. This constraint reduces intermodel uncertainty of future NH warming and NA carbon uptake by about 30% and 50%, respectively, under the SSP5–8.5 scenario (Fig. 4).

Current ESMs tend to underestimate the present-day SSS in the NA (Fig. 4a). Thus, the projected warming in NH is likely to be overestimated in the current ESMs, while the cumulative carbon uptake in NA is underestimated (Fig. 4c,d). Furthermore, we reached a similar conclusion using a low emission scenario with SSP1–2.6 in which the emergent relationship between the present-day SSS in the NA subpolar region and future NH warming is statistically significant (Supplementary Fig. 5). Our results also suggest that SSS in the NA subpolar region is a constraint on projected global warming rates. Therefore, sustained observations of SSS in the NA subpolar region are beneficial for an accurate projection of the global warming rate in the future. In addition, the emergent relationship between the present-day SSS and future NH warming is much stronger in the 18 CMIP6 ESMs that include the ocean biogeochemical model component (r = −0.72 in Fig. 4a) compared with that in the other 22 CMIP6 ESMs without that component (r = −0.53 in Supplementary Fig. 6). Therefore, it is essential to use ESMs with a carbon cycle to reduce the uncertainty in future NH and global warming.

Methods

CMIP5 and CMIP6 models

We used 31 ESMs based on CMIP6 (18 models) and CMIP5 (13 models); see detail in Extended Data Table 1 (refs. 53,54). ESMs with coupled ocean biogeochemistry schemes were applied within the context of both climate and ocean biogeochemical projections55,56. All model simulations cover the period 1850 to 2100 (1861–2100 for GFDL-ESM2G and GFDL-ESM2M, 1860–2100 for HadGEM2-CC) following historical forcing changes, including GHG, aerosols and natural variation over the period 1850–2005 (CMIP5) or 1850–2014 (CMIP6). CMIP6 models follow SSP5–8.5 simulations of the future (2015–2100). For CMIP5 models, the simulations follow the Representative Concentration Pathway 8.5 for 2006–2100.

Statistical methods for emergent relationship

We used a total least squares (TLS) method to fit a linear regression and a multivariate probability distribution function (PDF) to obtain the uncertainty range. TLS regression minimizes the perpendicular distances between the CMIP6 data points and the regression line. Therefore, the errors between the independent and dependent variables are uncorrelated. The multivariate PDF is a joint probability distribution of the data points, taking into account the relationships between all variables in the dataset to find the most likely distribution. This difference between TLS regression and multivariate PDF results in an asymmetric relationship between the regression line and the uncertainty range.

Global heat–carbon coupling parameter

We calculated the oceanic anthropogenic carbon storage (Cant) by vertically integrating the dissolved inorganic carbon throughout the historical simulation19. Global ocean heat storage (H) is calculated from the potential temperature of each grid cell. Temperature is converted to ocean heat storage by vertical integration through each model level and multiplied by a fixed value for density and heat capacity of 4.15 × 106 kg m−3 J K−1. Heat and carbon storage anomalies are calculated with respect to a pre-industrial control simulation to avoid the influence of climate drift. There is a linear correlation between the two variables, similar to the relationship between atmospheric warming and cumulative carbon emissions57. The global heat–carbon coupling parameter (α) is derived from a regression of anthropogenic ocean carbon storage (Cant) onto the ocean heat storage (H):

$$\alpha =\frac{\int H(x,y,t){{\mathrm{d}}A}}{\int {C}_\mathrm{{ant}}(x,y,t){{\mathrm{d}}A}}=\frac{\hat{H}(t)}{{\hat{C}}_\mathrm{{ant}}\left(t\right)}$$
(1)

\(\hat{H}\) and \({\hat{C}}_\mathrm{{ant}}\) are globally integrated values and A is the surface grid area. x, y and t are longitude, latitude and time. The value of α is generally in the range of 4.2 × 107 to 8.6 × 107 J mol−1.

Emergent constraint

PDFs of projected NH warming and carbon uptake in the NA were calculated following a previously established methodology58. The emergent relationship in this study was a linear regression of CMIP6 models between the simulated present-day state, x (surface salinity), and projected changes, y (NH surface temperature and cumulative carbon uptake in the NA), in the future (2071–2100). We used an ordinary least squares regression for linear regression and only one ensemble from each model for equal model weighting. The prior PDF assumed models followed a Gaussian distribution. The PDFs of observational constraints were defined as:

$$P\left(x\right)=\frac{1}{\sqrt{2\pi {{\sigma }_{x}}^{2}}}{\rm{\exp }}\left\{-\frac{{(x-\bar{x})}^{2}}{2{\sigma }_{x}^{2}}\right\}$$
(2)

where \(\bar{x}\) is the average of the observed surface salinity in the North Atlantic subpolar region for 1981–2010 (present-day) and σx is the corresponding standard error. The ‘prediction error’ of the emergent multimodel linear regression (\({\sigma }_{f}(x)\)) defines contours of equal probability density around the multimodel linear regression, which represent the probability density of y given x:

$$P\left\{\,y{\rm{|}}x\right\}=\frac{1}{\sqrt{2\pi {\sigma }_{f}^{2}}}{{\exp }}\left\{-\frac{{(\,y-f(x))}^{2}}{2{\sigma }_{f}^{2}}\right\}$$
(3)

where f(x) is the fitted value of the linear regression and σf is the prediction error of the linear regression. The emergent relationship was combined with the observational PDF by calculating the product of their PDFs and then integrating across the x-axis variable to derive a constrained PDF:

$$P\left(\,y\right)={\int }_{-{\rm{\infty }}}^{{\rm{\infty }}}P\left\{\,y| x\right\}P\left(x\right){{\mathrm{d}}x}$$
(4)

AMOC stream function

The stream function of the AMOC was calculated from the Atlantic Ocean meridional velocity v(x, y, z, t) of climate model outputs based on longitude (x), latitude (y), depth (z) and time (t) as:

$${\Psi }_{A}\left(\,y,z,t\right)={\int }_{z}^{H}{\int }_{{X}_\mathrm{{west}}}^{{X}_\mathrm{{east}}}v\left(x,y,z,t\right){{\mathrm{d}}x}{{\mathrm{d}}z}$$
(5)

where H is the sea bottom and Xwest and Xeast are the boundary. The AMOC stream function, ΨA, is measured in sverdrups (1 Sv = 106 m3 s−1). If models provided the stream function variable (‘msftmz’ and ‘msftyz’), we calculated the AMOC based on these data. The AMOC index was defined as the maximum of the AMOC stream function at a latitude of 26° N below 50 m, based on the observational monitoring standard in the Rapid Climate Change Meridional Overturning Circulation Heat-flux Array59.

Cumulative ocean carbon uptake

Anthropogenic air–sea CO2 flux was the difference between the air–sea CO2 flux (‘fgco2’) in historical simulations merged with future simulations and concurrent pre-industrial control (piControl) experiments. This definition of anthropogenic air–sea CO2 flux includes both the flux driven by increasing atmospheric CO2 concentrations and any flux from changes in the natural air–sea CO2 flux due to internal climate variability and climate change, such as changes in ocean circulation, wind conditions and primary production driven by anthropogenic and natural forcings29,31.

SSS and the Atlantic subpolar region

For observations, version 2 of the WOA18 annual climatology (1981–2010) of salinity was used for the observation-based constraint. The confidence interval of the observations was calculated from standard errors during the present-day. All output fields were analysed on a horizontal 1° × 1° interpolated model grid. The North Atlantic subpolar region is defined as 55° W–15° W and 45° N–65° N and the Northern Hemisphere is defined as 0–360° E and 10° N–90° N. The observed SSS in the NA subpolar region obtained from Multi Observation Global Ocean Sea Surface Salinity and Sea Surface Density60 was also analysed and its uncertainty during 1993–2014 was estimated as 34.78 ± 0.05 psu (Supplementary Fig. 4).

Intermodel uncertainty

One s.d. of the changes among ESMs is defined as an intermodel uncertainty. For Fig. 1a,b, shadings illustrate the signal of future climate changes by multimodel mean and contours illustrate the uncertainty of future climate changes by one s.d. among CMIP6 ESMs.