The emissions of anthropogenic carbon (Cant) since the beginning of industrialization through fossil-fuel burning, cement production, and land-use change have altered the global carbon cycle and climate (Friedlingstein et al., 2022). Around 40 % of the additional carbon since 1850 has accumulated in the atmosphere, where it represents the main anthropogenic greenhouse gas (IPCC, 2021). More than half of the emitted Cant has been taken up by the land biosphere (∼ 30 %) and the ocean (∼ 25 %) (Friedlingstein et al., 2022). The remaining ∼ 5 % is the budget imbalance, a mismatch between carbon emissions and sink estimates which cannot be explained yet (Friedlingstein et al., 2022). By each taking up around a quarter of the Cant emissions, the land biosphere and ocean sinks slow down global warming and climate change.

The ocean Cant sink is defined here as a combination of the uptake of newly emitted carbon and the change in the natural carbon inventory in the ocean due to changes in temperatures, winds, and the freshwater cycle caused by climate change (Joos et al., 1999; Frölicher and Joos, 2010; McNeil and Matear, 2013). The uptake rate of Cant on sub-millennial timescales is mainly determined by the ocean circulation and carbonate chemistry and only partly by biology (Sarmiento et al., 1998; Joos et al., 1999; Caldeira and Duffy, 2000; Sabine et al., 2004) despite the overall importance of marine biology for natural carbon fluxes (Falkowski et al., 1998; Steinacher et al., 2010). The rate-limiting process of Cant uptake is the circulation that transports surface waters with high Cant concentrations into the deeper ocean and allows waters with low or no Cant concentrations to upwell back to the ocean surface. The largest part of this ocean upwelling occurs in the Southern Ocean where strong westerlies drive northward Ekman transport of surface waters, which are then replaced by older, deeper water masses (Marshall and Speer, 2012; Talley, 2013; Morrison et al., 2015). These predominantly northward flowing waters take up Cant from the atmosphere and are eventually transferred to mode and intermediate waters that sink back into the ocean interior (Marshall and Speer, 2012; Talley, 2013). This overturning makes the Southern Ocean the largest marine Cant sink (∼ 40 % of global ocean Cant uptake) (Caldeira and Duffy, 2000; Mikaloff Fletcher et al., 2006; Frölicher et al., 2015; Terhaar et al., 2021b). Another region of large uptake rates is the North Atlantic (Caldeira and Duffy, 2000; Mikaloff Fletcher et al., 2006), where the Atlantic Meridional Overturning Circulation (AMOC) transports surface waters with high Cant (Pérez et al., 2013) and subsurface waters with low Cant concentrations northward (Ridge and McKinley, 2020). The subsurface waters outcrop in the subpolar North Atlantic where they take up Cant from the atmosphere (Ridge and McKinley, 2020). These high Cant waters are then ventilated by the AMOC into the deep ocean where the Cant is efficiently stored (Joos et al., 1999; Winton et al., 2013).

While the circulation determines the volume that is transported into the deeper ocean, the Revelle factor (Revelle and Suess, 1957; Sabine et al., 2004) determines the concentration of Cant in these water masses. The Revelle factor describes the biogeochemical capacity of the ocean to take up Cant. This biogeochemical capacity is strongly dependent on the amount of carbonate ions in the ocean that react with CO2 and H2O to form bicarbonate ions (Egleston et al., 2010; Goodwin et al., 2009; Revelle and Suess, 1957). The more CO2 is transferred via this reaction to bicarbonate ions, the more CO2 can be taken up again from the atmosphere. The available amount of carbonate ions for this reaction depends sensitively on the difference between ocean alkalinity and dissolved inorganic carbon (CT) (Fig. A2 in Appendix A) (Egleston et al., 2010; Goodwin et al., 2009; Revelle and Suess, 1957), highlighting the importance of alkalinity for the global ocean carbon uptake (Middelburg et al., 2020). As the buffer factor influences the Cant uptake, it also exerts a strong control on the transient climate response, i.e., the warming per cumulative CO2 emissions (Katavouta et al., 2018; Rodgers et al., 2020).

In addition to slowing global warming, the Cant uptake by the ocean also causes ocean acidification (Orr et al., 2005; Gattuso and Hansson, 2011; Kwiatkowski et al., 2020), i.e., a decline in ocean pH and carbonate ion concentrations. The decline in carbonate ion concentrations has negative effects on the growth and survival of many marine species, especially on calcifying organisms whose shells and skeletons are made up of calcium carbonate minerals (Orr et al., 2005; Fabry et al., 2008; Kroeker et al., 2010, 2013; Doney et al., 2020). Calcium carbonate minerals in the ocean exist mainly in the metastable forms of aragonite and high-magnesium calcite and the more stable form calcite. The stability of calcium carbonate minerals is described by their saturation states (Ω), which describe the product of the concentrations of calcium ([Ca2+]) and carbonate ions ([CO32-]) divided by their product in equilibrium. Reductions of saturation states of aragonite (Ωarag) and calcite (Ωcalc) have been shown to negatively impact organisms and ecosystems (Langdon and Atkinson, 2005; Kroeker et al., 2010; Bednaršek et al., 2014; Albright et al., 2016). Once saturation states drop below one, the water is undersaturated and actively corrosive towards the respective mineral form.

Accurately quantifying the ocean anthropogenic carbon sink is thus of crucial importance for understanding and quantifying the carbon cycle, global warming, and climate change, as well as ocean acidification. A better knowledge of the size of the historical and future ocean carbon sink and reduced uncertainties will hence not only lead to an improved understanding of the overall carbon cycle and global climate change (IPCC, 2021) but also allow targeted climate and ocean policies (IPCC, 2022). One of the key tools to assess the past, present, and future ocean carbon sink is Earth system models (ESMs). However, the simulated ocean Cant sink varies across the different ESMs (Frölicher et al., 2015; Wang et al., 2016; Bronselaer et al., 2017; Terhaar et al., 2021b), and the model differences grow over time; i.e., ESMs that simulate a small ocean Cant uptake over the last decades also simulate a small uptake over the 21st century (Fig. 1b) (Wang et al., 2016). Therefore, a better knowledge of the ocean Cant sink in the last decades would be one possibility to reduce uncertainties in the simulated ocean carbon from 1850 to 2100.

The large background concentration of CT in the ocean and the vast ocean volume make it difficult to directly observe the relatively small anthropogenic perturbations in the ocean interior. Therefore, different methods have been developed to estimate the accumulation of Cant in the ocean (Khatiwala et al., 2013), such as the ΔC* method (Gruber et al., 1996; Sabine et al., 2004) or the transient time distribution method (Hall et al., 2002) based on observations of inert tracers, like CFCs. These estimates result in an estimated ocean Cant inventory in 2010 of 155 ± 31 Pg C (Khatiwala et al., 2013) (Fig. 1b, Table 1) but do not or only partly include climate-driven changes in CT.

Further development of the ΔC* method into the eMLR(C*) method (Clement and Gruber, 2018) and more observations through new techniques, such as Biogeochemical-Argo (BGC-Argo) floats (Claustre et al., 2020), and more research cruises (Lauvset et al., 2021) will allow the increase in marine Cant to be quantified on shorter timescales and with reduced uncertainty. The increase in Cant from 1994 to 2007 by the eMLR(C*) method is 34 ± 4 Pg C (12 % uncertainty, Table 1) (Gruber et al., 2019a), again not accounting for potential climate-driven changes in CT. In addition to interior Cant estimates, surface ocean observations of the partial pressure of CO2 (pCO2) and new statistical methods, such as neural networks (Landschützer et al., 2016), have led to a variety of observation-based estimates of the air–sea CO2 flux (Rödenbeck et al., 2014; Zeng et al., 2014; Landschützer et al., 2016; Gregor et al., 2019; Watson et al., 2020; Iida et al., 2021; Gregor and Gruber, 2021; Chau et al., 2022). When subtracting the pre-industrial outflux of CO2 due to riverine carbon fluxes (Sarmiento and Sundquist, 1992; Aumont et al., 2001; Jacobson et al., 2007; Resplandy et al., 2018; Lacroix et al., 2020; Regnier et al., 2022) from these air–sea CO2 flux estimates, the global ocean Cant uptake can be derived (Friedlingstein et al., 2022), resulting in an estimated ocean Cant uptake from 1994 to 2007 of 29 ± 4 Pg C (14 % uncertainty, Table 1).

The difference of 5 Pg C between the interior and surface ocean mean estimates was attributed to outgassing of ocean CO2 caused by a changing climate and climate variability (Gruber et al., 2019a). However, simulations from ESMs of the sixth phase of the Coupled Model Intercomparison Project (CMIP6) estimate the climate-driven and externally forced climate-variability-driven air–sea CO2 flux from 1994 to 2007 to be only -1.6 ± 0.5 Pg C (Table A3). When averaging over an ensemble of ESMs, forced variability (e.g., due to the volcanic eruptions or varying emissions of CO2 and other radiative agents) is still preserved. However, unforced interannual-to-decadal variability is largely removed when averaging over an ensemble of ESMs. Although comparisons suggest that the ocean Cant uptake was low compared to atmospheric CO2 in the 1990s and high in the 2000s (Rödenbeck et al., 2013, 2022), a comparison of different Cant uptake estimates for different decadal-scale periods does not reveal any clear variability-related deviation for the 1994–2007 period (IPCC, 2021, AR6 WGI, chap. 5, Fig. 5.8; Canadell et al., 2021). Overall, uncertainties remain at present too large for any quantitative conclusions, but it seems unlikely that unforced variability causes an air–sea CO2 flux of -3.4 Pg C (difference between -5 Pg C from Gruber et al. (2019a) and -1.6 Pg C from ESMs), twice as large as the simulated flux from forced variability and climate change. It hence remains a challenge to derive the total ocean Cant sink from interior estimates that do not account for climate-driven changes in CT.

An alternative way of estimating the strength of the ocean carbon sink is the use of global ocean biogeochemical models forced with atmospheric reanalysis data (Sarmiento et al., 1992; Friedlingstein et al., 2022). From 1994 to 2007, the ocean biogeochemical hindcast models that participated in the Global Carbon Budget 2021 (Friedlingstein et al., 2022) simulate a Cant uptake of 26 ± 3 Pg C (Table 1). This estimate is 3 Pg C below the surface observation-based estimate, and the difference increases further after 2010 (Fig. 1a). Compared to the interior ocean Cant estimate, the simulated uptake by these hindcast models is 3–6 Pg C (10 %–19 %) smaller depending on the correction term that is used for climate-change-induced outgassing of natural CO2. Such differences between observation-based and simulated ocean Cant uptake could be explained regionally by systematic biases in models (Goris et al., 2018; Terhaar et al., 2020a, 2021a, b), as well as data sparsity (Bushinsky et al., 2019; Gloege et al., 2021).

Overall, the difference between ocean hindcast models, observation-based CO2 flux estimates, and interior ocean Cant estimates, as well as the uncertainties in the climate-driven change in CT and pre-industrial outgassing, indicate that uncertainties of the ocean Cant sink over the last decades remain substantial. The uncertainty of the Cant sink appears larger than the uncertainty typically given for an individual estimate of the Cant sink from a specific data product.

Another way to constrain the past, present, and future global ocean anthropogenic carbon sink is the use of process-based emergent constraints (Orr, 2002) that identify a relationship across an ensemble of ESMs between a relatively uncertain variable, such as the Cant uptake in the Southern Ocean, and a variable that can be observed with a relatively small uncertainty, such as the sea surface salinity in the subtropical–polar frontal zone in the Southern Ocean. The identified relationship is then combined with observations, in this example the sea surface salinity, to better estimate the uncertain variable, here the Cant uptake in the Southern Ocean (Terhaar et al., 2021b). Such relationships must be explainable by an underlying mechanism (Hall et al., 2019); i.e., higher sea surface salinity in the frontal zone leads to denser sea surface waters and stronger mode and intermediate water formation, which enhances the transport of Cant from the ocean surface to the ocean interior and allows hence for more Cant uptake. In recent years, process-based emergent constraints have successfully reduced uncertainties in simulated processes across ensembles of ESMs (Orr, 2002; Matsumoto et al., 2004; Wenzel et al., 2014; Kwiatkowski et al., 2017; Goris et al., 2018; Eyring et al., 2019; Hall et al., 2019; Terhaar et al., 2020a, 2021a, b; Bourgeois et al., 2022). In the ocean, for example, a bias towards smaller Cant uptake was identified in the Southern Ocean (Terhaar et al., 2021b). Similarly, ESMs from CMIP5 were shown to underestimate the future uptake of Cant in the North Atlantic due to smaller than observed sequestration of Cant into the deeper ocean (Goris et al., 2018). However, the relatively uncertain observation-based estimates of Cant sequestration (see section above) did not allow Goris et al. (2018) to reduce uncertainties. Similarly, the Cant uptake in the tropical Pacific Ocean across ESMs could be reduced with observations of the local surface ocean carbonate ion concentrations (Vaittinada Ayar et al., 2022), which is anti-correlated to the Revelle factor. Despite a better understanding of the regional Cant uptake, uncertainties of the global ocean Cant sink have not been reduced yet.

Here, we identify a mechanistic constraint for the global ocean Cant sink across 17 ESMs from CMIP6 (Table A1 in Appendix A). We demonstrate that a linear combination of three observable quantities, (1) the sea surface salinity in the subtropical–polar frontal zone in the Southern Ocean, (2) the strength of the AMOC at 26.5∘ N, and (3) the globally averaged surface ocean Revelle factor, can successfully predict the strength of the global ocean Cant sink across the CMIP6 ESMs (r2 of 0.87 for the global ocean Cant uptake from 1994 to 2007). The sea surface salinity in the subtropical–polar frontal zone in the Southern Ocean and the AMOC determine the strength of the two most important regions of mode, intermediate, and deep-water formation (Goris et al., 2018, 2022; Terhaar et al., 2021b). In addition, the Revelle factor accounts for biases in the biogeochemical buffer capacity of the ocean, i.e., the relative increase in ocean CT for a given relative increase in ocean pCO2 (Revelle and Suess, 1957). As the Revelle factor quantifies relative increases in ocean CT, the increase in surface ocean Cant depends on the Revelle factor and the natural surface ocean CT. Therefore, the Revelle factor in the ESMs was adjusted for model biases in natural surface ocean CT (see Sect. A1). Compared to observations, CMIP6 models represent the observation-based average strength of the AMOC from 2004 to 2020 (16.91 ± 0.49 Sv) (McCarthy et al., 2020) right but have a large inter-model spread (16.91 ± 3.00 Sv), underestimate the observed inter-frontal sea surface salinity (34.07 ± 0.02) and have a large inter-model spread (33.89 ± 0.13), and overestimate the surface-averaged Revelle factor that was derived by GLODAPv2 (10.45 ± 0.01) by 0.24 (10.73 ± 0.24) with the largest Revelle factor biases in the main Cant uptake regions (Fig. 2). The underestimation of the CT-adjusted Revelle factor by the ESM ensemble is mainly due to a bias towards concentrations of surface ocean carbonate ion concentrations that are smaller than the observed concentrations (Sarmiento et al., 1995), caused by a simulated difference of surface ocean alkalinity and CT that is smaller than the observed difference (Fig. A2).

As the present and future Cant uptake are strongly correlated across ESMs, the relationship identified here can also be used to constrain future projections of the global ocean Cant uptake. The global ocean Cant uptake from 2020 to 2100 increases from 156 ± 11 to 173 ± 8 Pg C (r2=0.56) under the high-mitigation, low-emission Shared Socioeconomic Pathway 1-2.6 (SSP1-2.6) that likely allows us to keep global warming below 2 ∘C (O'Neill et al., 2016; Riahi et al., 2017), from 251 ± 17 to 277 ± 9 Pg C (r2=0.74) under the middle-of-the-road SSP2-4.5, and from 407 ± 30 Pg C to 445 ± 12 Pg C (r2=0.87) under the high-emission, no-mitigation SSP5-8.5 (Fig. 1b). Overall, the future ocean Cant uptake in CMIP6 models is thus 9 %–11 % larger than simulated by ESMs and 32 %–62 % less uncertain depending on the future scenario. The correlation coefficient and hence the uncertainty reduction reduces – but remains still large – when atmospheric CO2 stops increasing (SSP1-2.6, SSP2-4.5). Larger uncertainties for stabilization than for near-exponential growth scenarios are expected, as the reversal of the atmospheric CO2 growth rate will exert a stronger external impact on the magnitude of the ocean carbon sink (McKinley et al., 2020).

The increase in projected uptake of Cant also increases the estimate of future ocean acidification rate. For ocean ecosystems, the threshold for water masses to become undersaturated towards specific calcium carbonate minerals (Ω=1) is of critical importance (Orr et al., 2005; Fabry et al., 2008; Doney et al., 2020), although negative effects for some calcifying organisms can already be observed at saturation states above one (Ries et al., 2009), and some calcifying organisms can even live in undersaturated waters (Lebrato et al., 2016). Over the 21st century, the volume of water masses in the global ocean that remain supersaturated towards the meta-stable calcium carbonate mineral aragonite is projected to decrease in CMIP6 from 283×106 km3 in 2002 (based on GLODAPv2 observations; Lauvset et al., 2016) to 194×106 ± 6×106 km3 under SSP1-2.6, to 143×106 ± 4×106 km3 under SSP2-4.5, and to 97×106 ± 4×106 km3 under SSP5-8.5. The constraint reduces these estimates to 186×106 ± 5×106, 138×106 ± 2×106, and 93×106 ± 2×106 km3, respectively (r2 = 0.31–0.69), resulting in an additional decrease in the available habitat for calcifying organisms of 3.7×106–7.4×106 km3 depending on the scenario. This additionally projected habitat loss is mainly located in the mesopelagic layer between 200 and 1000 m and thus affects organisms that live there permanently or temporarily during diel vertical migration (Behrenfeld et al., 2019). The additionally undersaturated volume corresponds to an area of 1.6–3.1 times the area of the Mediterranean Sea whose mesopelagic layer would be additionally undersaturated towards aragonite. However, the global character of the constraint and the uncertainty of the interior distribution of Cant do not allow us to localize these areas.

Emergent constraints across large datasets such as an ensemble of ESMs with hundreds of variables can always be found and might not necessarily be reliable and robust (Caldwell et al., 2014; Brient, 2020; Sanderson et al., 2021; Williamson et al., 2021). To test the robustness of emergent constraints, three criteria were proposed (Hall et al., 2019). The constraint must be relying on a well-understood mechanism, that mechanism must be reliable, and the constraint must be validated in an independent model ensemble.

Here, the well-understood mechanisms are the fundamental ocean biogeochemical properties such as the Revelle factor (Revelle and Suess, 1957), as well as the Southern Ocean and North Atlantic large-scale ocean circulation features that are known to be the determining factors for the ocean ventilation (Marshall and Speer, 2012; Talley, 2013; Buckley and Marshall, 2016). For the Southern Ocean, the verification of the link between sea surface salinity and Cant uptake was previously done by linking the sea surface salinity to the density and to the volume of intermediate and mode waters in each model. Furthermore, the robustness of the constraint was tested against changes in the definition of the inter-frontal zone (Terhaar et al., 2021b). In addition, other potential predictors were tested, such as the magnitude and seasonal cycle of sea-ice extent, wind curl, and the mixed layer depth, as well as upwelling strength of circumpolar deep waters. All these variables are known to influence air–sea gas exchange, freshwater fluxes, and circulation and, in turn, salinity and Cant uptake. However, none of these factors alone explains biases in the surface salinity and Cant uptake in the Southern Ocean. Therefore, the sea surface salinity that emerges as a result of all these individual processes represents, so far, the best variable in terms of mechanistic explanation and observational uncertainty to bias-correct models for Southern Ocean Cant uptake. Further evidence for the underlying mechanism of the relationship between Southern Ocean sea surface salinity and Cant uptake was provided by a later study that analyzed explicitly the stratification in the water column (Bourgeois et al., 2022). Here, we further showed that the Southern Ocean Cant uptake constrained by the Revelle factor and the inter-frontal sea surface salinity compares much better to observation-based estimates than the unconstrained estimate, further corroborating the identified regional constraint and mechanism (Sect. 3.2.1).

Similarly, it was shown that the transport of Cant by the AMOC is crucial for the Cant uptake in the North Atlantic (Winton et al., 2013; Goris et al., 2018; Brown et al., 2021). As the AMOC is predominantly observed at 26.5∘ N, a change to the definition is not possible. Instead, we replaced the AMOC as a predictor by another indicator for deep-water formation, namely the area of waters in the North Atlantic below which the water column is weakly stratified (see Sect. A1 and Table A4) (Hess, 2022). The results remain almost unchanged, indicating the robustness of the constraint and that the AMOC is indeed a good indicator for the stability of the water column in the North Atlantic and the associated deep-water formation. As for the Southern Ocean, we also made a regional two-dimensional constraint using the AMOC and the regional Revelle factor and compared it to observation-based Cant flux estimates. The good relationship between the AMOC and the North Atlantic Cant uptake improves the confidence in the AMOC as a valid predictor.

Eventually, we also tested the robustness of the biogeochemical predictor by varying the definition of the Revelle factor. First, the Revelle factor was only calculated north of 45∘ N and south of 45∘ S, assuming that the high-latitude regions are responsible for the largest Cant uptake, and second, the global Revelle factor was calculated by weighting the Revelle factor in each cell by the multi-model mean cumulative Cant uptake from 1850 to 2100 in that cell so that the Revelle factor in cells with larger uptake is more strongly weighted. Under both definitions, the results remain almost unchanged (Table A4). Furthermore, the Revelle factor has been shown here to improve the Cant uptake in the Atlantic and Southern Ocean and has been earlier shown to determine the Cant uptake in the tropical Pacific Ocean (Vaittinada Ayar et al., 2022), suggesting that the Revelle factor is a robust predictor of global and regional ocean Cant uptake.

To provide further indication of the importance of the AMOC and the Southern Ocean surface salinity and the three-dimensional constraint in general, we have compared simulated CFC-11, provided by 10 ESMs from CMIP6, with observed CFC-11 from GLODAPv2.2021 (Lauvset et al., 2021) (Sect. A4) and also compared the interior ocean distribution of Cant with observation-based estimates (Sabine et al., 2004; Gruber et al., 2019a) (Sect. A5). The comparison of CFCs demonstrates the importance of the AMOC for the ventilation of the North Atlantic, as ESMs with a low AMOC underestimate the observed subsurface CFC-11 concentrations in the North Atlantic. Similarly, ESMs with a small inter-frontal Southern Ocean surface salinity underestimate observed subsurface (below 200 m) CFC-11 concentrations in the Southern Hemisphere. In addition to the evaluation with observations of CFC, the comparison of the interior ocean Cant distribution demonstrates first that the ESMs on average represent the observation-based distributions within the margins of error (Tables A5 and A6). Only in the Southern Hemisphere does the ESM average remain below, as expected due to the average ESM bias towards inter-frontal sea surface salinities that are too low compared to observed ones, less formation of mode and intermediate waters, and hence relatively little storage of Cant in the Southern Hemisphere. When using the model that represents best the three predictors, GFDL-ESM4 (Geophysical Fluid Dynamics Laboratory ESM4; Dunne et al., 2020; Stock et al., 2020), the comparison to observation-based interior ocean Cant distribution becomes almost identical (Tables A7 and A8), suggesting that a better representation of these parameters indeed improves the simulation of Cant uptake and its distribution in the ocean interior.

To validate the constraint identified here in another model ensemble, we used all six ESMs of the CMIP5 ensemble that provided all necessary output variables (Table A1). As these six ESMs are not sufficient to robustly fit a function with four unknown parameters, we applied the predicted relationship by the CMIP6 models to the CMIP5 models and evaluated how well this relationship allows the simulated historical Cant uptake to be predicted by these models. The CMIP6-derived relationship allows us to predict the simulated Cant uptake with an accuracy of 3 % (± 5 Pg C) for the period from 1850 to 2014 and with an accuracy of 4 % (± 1.3 Pg C) for the period from 1994 to 2007 (Fig. A5). The largest uncertainty stems from the NorESM2-ME (Norwegian Earth System Model version 2) model, which simulates a historical AMOC strength of ∼ 30 Sv, almost twice as large as the observed AMOC strength and ∼ 9 Sv larger than all other CMIP6 ESMs over which the relationship was fitted. For such strong deviations from the observations and other ESMs, the linear relationship might not be applicable anymore. However, despite one out of six ESMs from CMIP5 having a particularly high AMOC, the relationship identified here still allows us to predict the simulated Cant uptake with small uncertainties and hence confirms its applicability.

Despite this robustness, emergent constraints are, by definition, always relying on the existing ESMs and on the processes that are represented by these ESMs. If certain processes are not implemented or implemented in the same way across all ESMs, biases over the entire model ensemble can occur that cannot be corrected by an emergent constraint (Sanderson et al., 2021). Possible non-represented processes in our case are, among others, changing freshwater input from the Greenland and Antarctic ice sheet that may impact the freshwater cycle and circulation in the Southern Ocean or the AMOC, as well as changes in riverine input of carbon over time. However, the expected effect of ice melt on sea surface salinity in the Southern Ocean and on the AMOC is small compared to the model spread (Bakker et al., 2016; Terhaar et al., 2021b), at least on the timescales considered here. Changing riverine carbon fluxes could, however, have a larger effect. So far, only one CMIP6 ESM, the CNRM-ESM2-1 (Séférian et al., 2019), has dynamic carbon riverine delivery that changes with global warming. In this model, carbon riverine delivery increases over the 20th century so that the interior ocean change in Cant in 2000 is around 19 Pg C smaller than the air–sea Cant uptake (Fig. A4). The situation reverses at the beginning of the 21st century so that riverine carbon delivery increases, and the interior ocean change in Cant becomes up to 60 Pg C larger than the air–sea Cant uptake. As such, riverine carbon delivery has the potential to enhance or decrease the ocean Cant inventory in addition to air–sea Cant uptake. This would also question the comparability of Cant inventory and air–sea Cant uptake estimates. However, the present state of the ESMs does not allow a quantitative assessment of this process, and future research is needed.

In addition, parametrizations of non-represented processes such as mesoscale and sub-mesoscale circulation features like small-scale eddies may lead to biases in the model ensemble. For individual models, it has been shown that changes in horizontal resolution and hence a more explicitly simulated circulation change the model physics and biogeochemistry and hence also the ocean carbon and heat uptake (Lachkar et al., 2007, 2009; Dufour et al., 2015; Griffies et al., 2015). However, an increase in resolution does not necessarily lead to improved simulations, and the changes in oceanic Cant uptake may be lower or higher, depending on the model applied. When increasing the NEMO (Nucleus for European Modelling of the Ocean) ocean model from a non-eddying version (2∘ horizontal resolution) to an eddying version (0.5∘), Lachkar et al. (2009) find a decrease in the sea surface salinity of around 0.1 at the Southern Ocean surface that brings the model further away from the observed salinity, a decrease in the volume of Antarctic intermediate water, and a decrease in the Southern Ocean uptake of CFC and hence likely also of Cant. This example corroborates the underlying mechanism of the emergent constraint in the Southern Ocean that higher sea surface salinity directly affects the formation of Antarctic intermediate water and the uptake of Cant. Another example can be found within the ESM ensemble of CMIP6. The MPI-ESM-1-2-HR and MPI-ESM-1-2-LR have a horizontal resolution of 0.4 and 1.5∘, respectively, but the same underlying ocean model. The high-resolution version has an inter-frontal salinity of 33.98, a Southern Ocean surface Revelle factor of 12.82, and a Southern Ocean Cant uptake from 1850 to 2005 of 56.4 Pg C. The coarser-resolution version has an inter-frontal sea surface salinity of 33.92, a Southern Ocean surface Revelle factor of 12.89, and a Southern Ocean Cant uptake of 58.0 Pg C. These differences are much smaller than the inter-model differences (33.66–34.15 for salinity, 12.14–13.11 for the Revelle factor, and 48.8–71.1 Pg C for the Southern Ocean Cant uptake) that result from different ocean circulation and biogeochemical models, sea-ice models, and atmospheric and land biosphere models, as well as the coupling between these models. These examples show that higher resolution does not necessarily lead to better results, affecting potentially the predictor and the predicted variable in the same way, and that differences in the underlying model components and spin-up and initialization strategies lead so far to much larger differences between ESMs than resolution does (Séférian et al., 2020). As long as simulations with higher resolution, which are also spun-up over hundreds of years (Séférian et al., 2016), are not yet available, and potentially important processes such as changing riverine fluxes and freshwater from land ice are not included, it remains speculative if higher resolution would lead to a reduction in inter-model uncertainty or even a better representation of the observations. Moreover, the relationships identified here that are based on the current understanding of physical and biogeochemical oceanography and that were tested for robustness in several ways may likely also exist across ensembles of eddy-resolving models.

The three-dimensional emergent constraint identified here reveals a bias towards an insufficient Cant uptake by the CMIP6 ESM ensemble, reduces uncertainties of the global ocean Cant sink, and leads to an enhanced process understanding of the Cant uptake in ESMs. The constraint was tested for robustness in multiple ways and across different model ensembles. It was evaluated regionally and globally against CFC measurements, against estimates of the interior ocean Cant accumulation, and against observation-based estimates of the air–sea CO2 flux globally and regionally. The constraint demonstrates that the global ocean Cant uptake can be estimated from three observable variables, the salinity in the subtropical–polar frontal zone in the Southern Ocean, the Atlantic Meridional Overturning Circulation, and the global surface ocean Revelle factor. The uncertainties of the regional ocean Cant uptake estimates in the Atlantic and Southern Ocean can also be reduced with the respective regional predictors. Improved or continuing observations of these quantities (Lauvset et al., 2016; Zweng et al., 2018; Locarnini et al., 2018; Claustre et al., 2020; McCarthy et al., 2020) and their representation and evaluation in ESMs and ocean models should therefore be of priority in the next years and decades. Although biogeochemical variables were tuned or calibrated in more ESMs in CMIP6 than in CMIP5 (Séférian et al., 2020), this tuning does not seem to result in better results than in untuned ESMs yet (Fig. A3).

Moreover, biases in these quantities and corrections for the late starting date may well be the reason for offset between models and observations over the last 30 years (Hauck et al., 2020; Friedlingstein et al., 2022). Although the constraints identified here cannot correct for misrepresentation of the unforced decadal variability, such variability likely plays a minor role when averaging results over longer periods. Indeed, we find good agreement between our estimate and the observation-based estimate from the Global Carbon Budget 2021 for the period from 1990 to 2020. This agreement suggests that the hindcast models underestimate the ocean Cant uptake. This underestimation is thus likely the explanation for the difference between models and the observation-based product in the Global Carbon Budget (Friedlingstein et al., 2022). However, the output of the Global Carbon Budget hindcast models is not publicly available for evaluating possible data–model differences for the inter-frontal sea surface salinity, the AMOC, and the Revelle factor.

Despite this step forward in the understanding of ESMs, a comprehensive research strategy that combines the measurements of important physical, biogeochemical, and biological parameters in the ocean with other data streams and modeling is needed. A comprehensive approach is necessary to improve our still incomplete understanding of the global carbon cycle and its functioning in the climate and Earth system over the past and under ongoing global warming.

The larger than previously estimated future ocean Cant sink corresponds to around 2 to 4 years of present-day CO2 emissions (∼ 10.5 Pg C yr-1) depending on the emission pathway. The larger ocean Cant sink thus increases the estimated remaining emission budget but only by a small amount. However, it also results in enhanced projected ocean acidification that may be harmful for large, unique ocean ecosystems (Fabry et al., 2008; Gruber et al., 2012; Kawaguchi et al., 2013; Kroeker et al., 2013; Doney et al., 2020; Hauri et al., 2021; Terhaar et al., 2021a).

This study follows recent approaches by the IPCC and climate science that suggest using the best available information about models instead of a multi-model mean to provide consistent and accurate information for climate science and policy (IPCC, 2021; Hausfather et al., 2022). The improved estimate provided here of the size of the global ocean carbon sink may help to close the carbon budget imbalance from 1850 onwards (Friedlingstein et al., 2022) and to improve the understanding of the overall carbon cycle and the global climate (IPCC, 2021). Eventually, a better understanding of the ocean carbon sink and the reduction of its uncertainties in the past and in the future will allow better-targeted climate and ocean policies (IPCC, 2022).