Modern air-sea flux distributions reduce uncertainty in the future ocean carbon sink

The ocean has absorbed about 25% of the carbon emitted by humans to date. To better predict how much climate will change, it is critical to understand how this ocean carbon sink will respond to future emissions. Here, we examine the ocean carbon sink response to low emission (SSP1-1.9, SSP1-2.6), intermediate emission (SSP2-4.5, SSP5-3.4-OS), and high emission (SSP5-8.5) scenarios in CMIP6 Earth System Models and in MAGICC7, a reduced-complexity climate carbon system model. From 2020–2100, the trajectory of the global-mean sink approximately parallels the trajectory of anthropogenic emissions. With increasing cumulative emissions during this century (SSP5-8.5 and SSP2-4.5), the cumulative ocean carbon sink absorbs 20%–30% of cumulative emissions since 2015. In scenarios where emissions decline, the ocean absorbs an increasingly large proportion of emissions (up to 120% of cumulative emissions since 2015). Despite similar responses in all models, there remains substantial quantitative spread in estimates of the cumulative sink through 2100 within each scenario, up to 50 PgC in CMIP6 and 120 PgC in the MAGICC7 ensemble. We demonstrate that for all but SSP1-2.6, approximately half of this future spread can be eliminated if model results are adjusted to agree with modern observation-based estimates. Considering the spatial distribution of air-sea CO2 fluxes in CMIP6, we find significant zonal-mean divergence from the suite of newly-available observation-based constraints. We conclude that a significant portion of future ocean carbon sink uncertainty is attributable to modern-day errors in the mean state of air-sea CO2 fluxes, which in turn are associated with model representations of ocean physics and biogeochemistry. Bringing models into agreement with modern observation-based estimates at regional to global scales can substantially reduce uncertainty in future role of the ocean in absorbing anthropogenic CO2 from the atmosphere and mitigating climate change.


Introduction
Since the industrial revolution, emissions due to industrial and land use activities have dramatically increased atmospheric carbon dioxide concentrations. Due to sinks in the ocean and terrestrial biosphere, less than half of these emissions remain in the atmosphere. The ocean has absorbed approximately 25% of anthropogenic emissions both in recent decades and cumulatively since 1750 (Canadell et al 2021, Friedlingstein et al 2022. This means that as atmospheric CO 2 has increased approximately exponentially, there has also been a comparable increase in the magnitude of ocean carbon sink (Raupach et al 2014, Ridge andMcKinley 2021). On millenial timescales, the ocean will absorb more than 80% of the total anthropogenic perturbation (Archer et al 2009, Cao andCaldeira 2010).
Detailed assessment of the ocean carbon sink's future state have largely focused on CMIP5 earth system model (ESM) projections under the RCP8.5 scenario of steadily increasing emissions through 2100 (Hoffman et al 2014, Schwinger et al 2014, Randerson et al 2015, McKinley et al 2016, Wang et al 2016, Fassbender et al 2017, Goris et al 2018. Without significant mitigation, the ocean will remain a strong sink for anthropogenic carbon through 2100, despite modest negative feedbacks due to ocean carbon chemistry and circulation changes. The response is similar in CMIP6 ESMs (Arora et al 2020).
Nearly 200 countries have signed the UNFCCC Paris Agreement, indicating a serious intent to rapidly mitigate emissions. These reductions, as well as the changed economics of renewable energy systems, are starting to shift the plausible future emission range away from the highest scenarios (Hausfather and Peters 2020). Aside from climate targets for 2030, many countries also put forward longterm targets-often net-zero CO 2 or net-zero greenhouse gas targets. Given that the ocean will continue to strongly influence the global-mean warming trajectory in the long-term, it is important to assess the future ocean carbon sink under scenarios of mitigation.
Raupach et al (2014) discussed the ocean sink in the context of the atmospheric fraction (AF), which is the fraction of annual fossil and land use emissions that remain in the atmosphere. They demonstrated that the near-constant AF of 0.44 from 1959-2013 cannot be explained by underlying mechanisms of the ocean and terrestrial biosphere sinks, but instead is attributable to the approximately exponential atmospheric pCO 2 growth rate. When the atmospheric pCO 2 growth rate slows, AF will be reduced, meaning that less of the emitted carbon will remain in the atmosphere (see figure SPM.7 in IPCC (2021)). For mitigation scenarios, the ratio of cumulative atmospheric load to cumulative emissions, or the cumulative atmospheric fraction (CAF) is preferable (Jones et al 2016) because it remains numerically well behaved as emissions approach zero. The CAF is also most directly relevant to climate outcomes that depend on the reservoir of atmospheric CO 2 , not its annual fluxes (Matthews et al 2020).
The global-mean ocean carbon sink will weaken in absolute magnitude as atmospheric pCO 2 growth rates slow (Cao and Caldeira 2010, Jones et al 2016, Zickfeld et al 2016, Schwinger and Tjiputra 2018, McKinley et al 2020, Canadell et al 2021, Ridge and McKinley 2021. Despite a reduced absolute magnitude, as long as the ocean overturning circulation continues to expose waters with additional carbon uptake capacity to the surface, the sink will continue (Zickfeld et al 2016). Under mitigation scenarios, CAF estimates for the 21st century should be substantially lower with mitigation than without (Jones et al 2016, IPCC 2021. In other words, the ocean will be able to do proportionally more to reduce climate warming as humans increasingly mitigate emissions.
Studies to date have focused on the global-mean ocean carbon sink estimated by reduced complexity models or ESMs. Quantitative uncertainty in the magnitude of the future ocean carbon sink under mitigation scenarios has not received much attention. The global-mean ocean carbon sink is the integrated result of the anthropogenic perturbation superimposed on a background of vigorous natural fluxes (McKinley et al 2017, Crisp et al 2022. To understand why models differ, local to regional fluxes must be considered since these are the scales on which physical and biogeochemical mechanisms of natural and anthropogenic carbon fluxes occur (McKinley et al 2016, Fay andMcKinley 2021). For anthropogenic fluxes specifically, advection and water mass transformation at regional scales dominate fluxes into (reemergence) and out of (subduction) the surface mixed layer, which is critical to the movement of anthropogenic carbon to and from the deep ocean (Bopp et al 2015, Iudicone et al 2016, Toyama et al 2017, Ridge and McKinley 2020. Mechanisms of future sink will also occur locally, and thus understanding why ESMs quantitatively differ in their projections requires consideration of the spatial distribution. Ridge and McKinley (2021) studied the threedimensional response of the ocean carbon sink to mitigation scenarios in one ESM, the Community Earth System Model Large Ensemble (Kay et al 2015). They found that the large-scale spatial distribution of the sink is largely conserved through 2100. The primary change is an increased or decreased amplitude of the sink in high or low emission scenarios. With strong mitigation (1.5 • C scenario), some regions that were previous sinks become sources to the atmosphere as thermocline waters with high anthropogenic carbon content are recirculated to the surface. This study investigates whether these estimates of future flux distributions are consistent across a range of ESMs.
Ocean hindcast models have been critical to the annual global carbon budget (GCB) since its inception (Hauck et al 2020, Friedlingstein et al 2022. Hindcast models are forced with observed meteorology to estimate the actual evolution of ocean physics and biogeochemistry in recent years. Yet their underlying structures and parameterizations are very similar to the ocean component models in their cousin ESMs. Thus, skill assessments for hindcast models likely provide some information about ESM fidelity. A recent assessment of long-term mean and average seasonal fluxes in the nine hindcast models used in the GCB 2020 (Friedlingstein et al 2020) revealed significant regional discrepancies from observation-based estimates (Fay and McKinley 2021).
A robust suite of full global coverage, monthly timescale observation-based products for surface ocean carbon content, from which air-sea CO 2 fluxes can be derived, have only recently become available (Rödenbeck et al 2015, Fay et al 2021. Though these are based on sparse data, they have high fidelity for the long-term mean and the average seasonal cycle of airsea CO 2 fluxes (Gloege et al 2021). Compared to independent data, modern observation-based products represent surface ocean carbon concentrations much better than hindcast models (Hauck et al 2020, Bennington et al 2022b). Given this new observational constraint, it is important to assess how the state-of-the-art ESMs from the sixth phase of the Coupled Model Intercomparison Project (CMIP6) suite represent modern-day mean fluxes. Do the CMIP6 ESMs demonstrate similar biases as identified for hindcast models by Fay and McKinley (2021)? What are the implications for uncertainty in projections of the future sink?
To address these issues, we analyze the ocean carbon sink response to emission scenarios with varying degrees of mitigation (SSP1-1.9, SSP1-2.6, SSP2-4.5, SSP5-3.4-OS, SSP5-8.5) from CMIP6. We also examine ocean carbon sink estimates from the reducedcomplexity climate carbon cycle model, MAGICC7, that was used in the creation of the SSP scenarios (Meinshausen et al 2020).

CMIP6 Simulations
This study utilizes concentration-driven simulations of ESMs performed as part of the sixth phase of the CMIP6. Monthly average simulated air-sea carbon dioxide fluxes (variable name: fgco2) for the five emission scenarios were obtained from the CMIP6 archive https://esgf-node.llnl.gov/search/cmip6/, (World Climate Research Programme, 2021) (table 1). For analyses, all modeled fluxes were conservatively regridded to a regular 1 • latitude by 1 • longitude grid using the xesmf module in Python. Simulated fluxes are integrated in space to obtain annual air-sea carbon fluxes for each ensemble member; ensemble means are used in analysis. Ensemble-means are used to damp internal variability. For CNRM, a carbon efflux of 0.78 PgC yr −1 that is due to natural inputs from rivers is removed (Séférian et al 2019); other ESMs do not include natural river carbon fluxes.

MAGICC7
MAGICC7 is a reduced-complexity climate carbon system model (section S1.1) calibrated to emulate CMIP5 ESMs (Meinshausen et al 2011(Meinshausen et al , 2020 and for the results shown here, the range of CMIP6 ESMs used for IPCC AR6 WG1 assessments (see Cross-Chapter Box 7.1 in IPCC AR6 WG1 (Forster et al 2021)). MAGICC7 simulates the land and globalmean ocean carbon sinks that occur in response to emissions. It was used to develop atmospheric carbon dioxide concentrations for the SSP scenarios (Meinshausen et al 2020), which were then input to the concentration-driven CMIP6 runs that we analyze here. For the comparison between the CMIP6 ensemble and MAGICC7, the probabilistic version of MAGICC7 has been calibrated to comprehensively reflect climate system response uncertainties (Forster et al 2021). Our comparisons are a consistency check between the ocean sink estimates from MAGICC7 and the ocean sink estimates resulting from the stateof-the-art CMIP6 suite driven with the atmospheric concentrations derived from MAGICC7.

Observation-based products
For the years 2010-2019, we compare the CMIP6 models to the currently-available ensemble of observation based products (table 2). These products are produced using machine learning and other statistical methods to extrapolate sparse pCO 2 observations to global coverage. All products estimate monthly fluxes for the 1980s to the 2020s, while two of the newest products start in 1959 (Rödenbeck et al 2022, Bennington et al 2022b). A suite of wind speed products is then used to estimate CO 2 flux (Fay et al 2021). These products have been shown to offer robust estimates of long-term mean CO 2 fluxes from global to regional scales (Fay and McKinley 2021, Gloege et al 2022, Bennington et al 2022b).
Observation-based products provide an estimate of the total air-sea CO 2 flux, the sum of the anthropogenic fluxes and outgassing due to the import of natural carbon from rivers (Crisp et al 2022). Since CMIP6 and MAGICC7 models estimate only anthropogenic fluxes, we remove the natural efflux due to rivers in each latitude band, based on the spatial distribution from Lacroix et al (2020) and the global total flux of +0.65 PgC yr −1 (Regnier et al 2022) (positive to the atmosphere).

Ratio of cumulative sink to cumulative emissions (CSF ocean )
The AF is the fraction of annual fossil and land use emissions that remain in the atmosphere

Results
As emissions accumulate through 2100 (figure 1(a), S1), the cumulative ocean sink ( figure 1(b)) follows a similar trajectory. With higher emissions, the ocean accumulates more carbon, and with lesser emissions, less carbon is absorbed by the ocean. However, the ratio of cumulative sink to cumulative emissions (CSF ocean ) has the opposite response (IPCC (2021)).
With accelerating emissions (SSP5-8.5 and SSP2-4.5), the ocean accumulates between 17% and 33% of the cumulative emissions after 2015. If emission rates decline, the ocean takes up a greater portion of emitted carbon, between 39% and 112% under SSP5-3.4-OS, SSP1-2.6 and SSP1-1.9 ( figure 1(c), table 3). For each scenario, there are significant differences between the maximum and minimum predictions ( figure 1(b)), with a spread of 30-50 PgC in the cumulative uptake by 2100 ocean sink in CMIP6 models (  (2022)) (figures 1(d), S1, S2; tables 3 and 4). This adjustment is accomplished by adding to all years the difference from 3 PgC yr −1 in 2020 for that CMIP6 or MAGICC7 model. Consistent with ESMs tending to underestimate the modern day sink (Hoffman et al 2014), uptake estimates here are increased in most cases. The reduced spread occurs because maximum uptake estimates are increased less than minimum estimates (tables 4 and 5). For SSP1-2.6 in CMIP6, the maximum and minimum are increased by about the same amount.
With this adjustment, the spread in ratios of sink to emissions (CSF ocean ) for CMIP6 is also reduced by 57% or more in all scenarios except SSP1-2.6 (figure 1(e); table 3). For SSP1-2.6 in CMIP6, there is a bimodal distribution of the projected cumulative sink and CSF ocean after the adjustment of the 2020 sink (figures 1(d) and (e)). This substantial reduction in spread, from homogenizing the present-day sink estimates, indicates that under most scenarios, half or more of future uncertainty is attributable to modern mean-state errors.
Newly available observation-based products offer the best-available constraint for mean air-sea CO 2 fluxes at basin to global scales (Gloege et al 2022, Bennington et al 2022b). To better understand the performance of the CMIP6 models suite, we compare them to the currently-available suite of products (table 2) for the 2010s (2010-2019). For this period, the large scale pattern of air-sea flux in the CMIP6 models is broadly comparable to the products (figure 2, left; S3). Outgassing occurs across much of the equatorial band, while uptake is greatest in the high northern latitudes and around 40 • S.
Looking to the future, we choose one model as an example of the CMIP6 suite, IPSL-CM6A-LR, to visualize expected air-sea flux changes. Changes in other models are similar (maps not shown, zonal means are compared in figure 3). If emissions continue on a very high emission trajectory (SSP5-8.5), the ocean will take up more carbon in the 2050s than in the 2010s (figure 2, right). By the 2090s, across  Under the lowest emission scenario (SSP1-1.9) by the 2050s, carbon uptake declines compared to the 2010s except in the high latitude Southern Ocean. By the 2090s, uptake further declines everywhere. In summary, change in the ocean carbon sink under future scenarios is rather spatially homogeneous, except in the Southern Ocean where the carbon uptake generally persists, and in the North Atlantic and  North Pacific where slowing uptake occurs under all scenarios.
Considering air-sea fluxes in zonal average allows for comparison of the CMIP6 suite to the modern spatial distribution ( figure 3, left), as well as the future change predicted by each ESMs (figure 3, right). At latitudes north of 55 • S, the CMIP6 ESMs capture the basic features of the observed flux distribution. However, the magnitude of modeled fluxes frequently lies outside the 2σ spread of the eight observation-based products. In the high latitude Southern Ocean, the observation-based products indicate a slight sink for 2010-2019, but the ESMs simulate from a large sink to a modest source.
In the future under both high, intermediate and low scenarios, the CMIP6 models all suggest a very similar response relative to their modern flux distribution. Under SSP5-8.5, the sink grows at all latitudes, with the strongest increase in the Southern Ocean. Under SSP2-4.5, most latitudes have a modest increase by 2050 and then a decline through 2090, while the Southern Ocean sink grows. Under SSP1-1.9, the sink reduces at all latitudes, with enhanced magnitude of reduction between 40 • S and 60 • S. The key point here is that despite the significant spread across the CMIP6 models for the 2010s ( figure 3, left), there is strong agreement with respect to the magnitude of future sink change ( figure 3, right). This finding applies to all five scenarios considered here. In other words, as for the global mean (figure 1), the modern state of the CMIP6 ESMs holds a significant portion of the uncertainty with respect to the magnitude of the future ocean sink across emission scenarios.

Discussion
The future ocean carbon sink will grow if emissions grown and decline if emissions decline. Yet, there remains substantial disagreement as to the magnitude of the projected ocean carbon sink within each scenario for both the CMIP6 ESM suite and the MAGICC7 ensemble (figure 1). Significant reduction in the spread of the future global-mean cumulative ocean sink can be achieved by adjusting the models to capture modern best-estimates (figure 1). Under most scenarios, 50% or more of uncertainty in the magnitude of the ocean carbon sink at 2100 can be eliminated (table 4 and 5). This indicates a strong connection between present-day and future mean-state biases. Under SSP1-2.6 in CMIP6, this adjustment leads to a tightening of projections into a bimodal distribution, but no reduction in total spread.
Global mean results from CMIP6 to MAGICC7 are in substantial agreement (figure 1), aside from the larger spread across the MAGICC7 ensemble. Homogenizing the global-mean sink to the same 2020 value also substantially reduces the future spread of MAGICC7 projections and increases the agreement with CMIP6 (figures 1(b) and (c); S1(b) and (c)). This provides another line of evidence that presentday bias is a major contributor to our future uncertainty. One notable difference between CMIP6 and MAGICC7 is that in the very high emission scenario (SSP5-8.5), the CMIP6 models suggest a slightly earlier weakening of the ocean carbon sinks around the 2080s, whereas MAGICC7 ensemble members tend to plateau at this time (figure S1). This difference may be due to reduction in the ocean overturning circulation that occurs in CMIP6 at this time (Liu et al 2022). While MAGICC7 does parametrize changes in the ocean's overturning circulation, these changes do not directly affect the ocean's carbon cycle response.
As noted in previous analyses (Jones et al 2016, IPCC 2021, the percentage of future emissions that will be stored in the ocean is strongly dependent on the emissions trajectory ( figure 1(d)). We show the uncertainty in estimates of CSF ocean can also be substantially reduced by addressing discrepancies in estimates of present-day fluxes ( figure 1(e)). Under SSP1-1.9 by 2100, cumulative emissions since 2015 and until the point of the net-zero emissions are around 209 PgC until 2055 and are then reduced again to 124 PgC by the end of the century due to net CO 2 removals (i.e. negative emissions) after 2055. With our proposed adjustment to the modern best-estimate, we would predict that all net cumulative emissions by 2100 would go into the ocean (128-147 PgC). Without adjustment, the predicted uptake has a much broader range (93 to 139 PgC) that would leave up to 12% of cumulative emissions in the atmosphere (figures 1(b) and (c); table 4). The difference in these predictions illustrates the value of reducing prediction uncertainty.
For CMIP6, there are substantial regional biases against modern observation-based data products. Zonal-mean fluxes from CMIP6 frequently lie outside the 2σ spread of the observation-based products (figure 3), a finding is consistent with recent regional assessment of related ocean hindcast models (Fay and McKinley 2021). While this finding is clear, the drivers of modeled mean-state biases are difficult to pinpoint. Air-sea CO 2 fluxes are the local emergent property of modeled representations of ocean circulation and biogeochemistry (Crisp et al 2022). Many studies have compared the mean, seasonal and interannual variability in air-sea CO 2 fluxes across models and to data-based estimates (Schuster et al 2013, McKinley et al 2017, Mongwe et al 2018, Gruber et al 2019, Hauck et al 2020, Fay and McKinley 2021, Fu et al 2022. These studies have identified biases and concluded that there is a need to improve model representations of ocean circulation, ecosystems, and terrestrial carbon fluxes into the ocean. However, a single dominant driver of model biases has not been identified. In-depth analysis of individual models will be required to identify the required development steps.
Spatial patterns of air-sea CO 2 exchange do not change substantially through the 21st century (figure 2), which is consistent with previous analysis of the CESM Large Ensemble (Ridge and McKinley 2021). While emissions increase, model regions of influx increase and regions of efflux decrease in magnitude (figure 2). There is some disagreement across models as to change in the northern middle to high latitudes under SSP5-8.5 (figure 3). Prior studies suggest modeled physical processes that could cause some of this spread. In the previous version of CESM under high emissions (RCP8.5), the future North Atlantic experiences large freshwater fluxes that increasingly limit carbon uptake (Ridge 2020, Ridge and McKinley 2020). Differential responses of the Atlantic Meridional Overturning Circulation and deep southward transport of anthropogenic carbon may also contribute to these differences (Yool et al 2021, Liu et al 2022. We demonstrate clear links between the future and the modern mean state of the ocean carbon sink in CMIP6 models and MAGICC7, and the future and the modern zonal distribution of the sink in CMIP6. This finding is consistent with Terhaar et al (2022) who propose to constrain CMIP6 ocean sink estimates using three observational constraints related to the modern mean ocean circulation and carbon chemistry. Previous analyses of CMIP5 models under high emission scenarios also pointed to the forward propagation of modern mean state errors (Hoffman et al 2014, Wang et al 2016). Future model development work can use newly-available observationbased products (table 2) as a target for regional mean fluxes in the modern era. This approach should lead to substantial reductions in uncertainty of future projections of the ocean carbon sink.
We propose that, in order to substantially reduce uncertainty in the future ocean carbon sink under a range of plausible emission scenarios, regional mean air-sea CO 2 fluxes from the newly-available suite of observation-based products should be used as a target for ocean biogeochemical model development. At the same time, it is important to emphasize the substantial uncertainty that remains in observation-based estimates. This is true if the global mean ocean carbon sink is quantified for a single year or for a decade: 3.0 ± 0.4 PgC yr −1 (1σ) for 2020 (Friedlingstein et al 2022); 2.5 ± 0.6 PgC yr −1 (1σ) for 2010-2019 (Friedlingstein et al 2020; figure 5.12 of Canadell et al 2021). Uncertainties at regional scales are even larger proportions of the mean ( figure 3, left). The sparsity of ocean carbon observations drives much of the uncertainty in observation-based estimates (Bushinsky et al 2019, Gloege et al 2021. At the same time as models are improved toward the observational constraints that are now available, tighter observational constraints should be developed. Observations can also provide the basis for a post-simulation correction (Gloege et al 2022, Bennington et al 2022b). Improving both observation-based estimates and models will better constrain the global carbon cycle, which in turn will better support the climate policymaking process (Peters et al 2017).

Conclusion
The future ocean carbon sink will grow in absolute magnitude as future carbon emissions grow, and decline in magnitude as emissions decline. However, the proportion of future cumulative emissions that get absorbed by the ocean will be much greater if mitigation occurs. As emissions decline, the proportion of cumulative emissions absorbed by the ocean could be as high as 120%. But as long as emissions continue to rise, the ocean will accumulate only 20%-30%.
While there is consensus across models as to these qualitative behaviors of the future ocean sink, significant quantitative uncertainties remain across all emission scenarios. These uncertainties can be substantially reduced by refining ocean models and the ocean components of ESMs to better represent the modern flux distribution that observation-based products can now constrain. Going forward, improving modeled representations of the modern ocean carbon sink offers a tractable path forward to improving ocean and global carbon cycle projections, and thus the trajectory of future climate change.

Data availability statement
The data used here are from the CMIP6 simulations performed by various modeling groups and publicly available from the CMIP6 archive: https://esgf-node. llnl.gov/search/cmip6/, WCRP (2021), last access: 20 July 2021. The carbon emissions scenarios within this article were obtained from the SSP database hosted by the IIASA Energy Program at https://tntcat.iiasa. ac.at/SspDb. MAGICC7 is available for download at https://magicc.org/download/magicc7 with the data used in this study being available at the following URL/DOI: 10.5281/zenodo.7679402.