# Revision of global carbon fluxes based on a reassessment of oceanic and riverine carbon transport

L. Resplandy, R. F. Keeling, C. Rödenbeck, B. B. Stephens, S. Khatiwala, K.

B. Rodgers, M. C. Long, L. Bopp, P. P. Tans

► To cite this version:

L. Resplandy, R. F. Keeling, C. Rödenbeck, B. B. Stephens, S. Khatiwala, et al. Revision of global carbon fluxes based on a reassessment of oceanic and riverine carbon transport. Nature Geoscience, 2018, 11, pp.504-509. 10.1038/s41561-018-0151-3. hal-03658679

HAL Id: hal-03658679

https://hal.science/hal-03658679v1

Submitted on 2 Oct 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Revision of global carbon fluxes based on a reassessment of oceanic and riverine carbon transport

L. Resplandy<sup>1*</sup>, R. F. Keeling<sup>2</sup>, C. Rödenbeck<sup>3</sup>, B. B. Stephens<sup>4</sup>, S. Khatiwala<sup>5</sup>, K. B. Rodgers<sup>6</sup>, M. C. Long<sup>6,4</sup>, L. Bopp<sup>7</sup> and P. P. Tans<sup>8</sup>

Measurements of atmospheric CO₂ concentration provide a tight constraint on the sum of the land and ocean sinks. This constraint has been combined with estimates of ocean carbon flux and riverine transport of carbon from land to oceans to isolate the land sink. Uncertainties in the ocean and river fluxes therefore translate into uncertainties in the land sink. Here, we introduce a heat-based constraint on the latitudinal distribution of ocean and river carbon fluxes, and reassess the partition between ocean, river and land in the tropics, and in the southern and northern extra-tropics. We show that the ocean overturning circulation and biological pump tightly link the ocean transports of heat and carbon between hemispheres. Using this coupling between heat and carbon, we derive ocean and river carbon fluxes compatible with observational constraints on heat transport. This heat-based constraint requires a 20-100% stronger ocean and river carbon transport from the Northern Hemisphere to the Southern Hemisphere than existing estimates, and supports an upward revision of the global riverine carbon flux from 0.45 to 0.78 PgC yr⁻<fnref n="1" />. These systematic biases in existing ocean/river carbon fluxes redistribute up to 40% of the carbon sink between northern, tropical and southern land ecosystems. As a consequence, the magnitude of both the southern land source and the northern land sink may have to be substantially reduced.

Studies over the past 25 years support the existence of a large net land biospheric CO₂ sink (for example, 0.5–2 PgC yr⁻<fnref n="1" />)<fnref n="1" />⁻³, dominated by a growing uptake in the Northern Hemisphere⁴⁻⁹. A primary basis for quantifying the land sink comprises atmospheric CO₂ measurements using atmospheric inverse calculations². These atmospheric inversions give fairly consistent short-term variations (seasonal to interannual) of the land sink over the past two decades²,¹⁰. However, significant uncertainties remain regarding the long-term partitioning between northern, tropical and southern land sinks⁶,¹¹. The potential for systematic error in inverse calculations weakens our ability to predict the response to anthropogenic changes and evaluate allowable carbon emissions compatible with mitigation strategies.

Uncertainties regarding the land sink magnitude and latitudinal distribution are in part connected to the uncertain impact of natural carbon fluxes on atmospheric CO₂. In inverse calculations, the sink emerges from the difference between observed CO₂ concentrations and the pattern expected from other processes including fossil fuel emissions¹², seasonal exchanges with the terrestrial biosphere¹³, ocean anthropogenic carbon uptake¹⁴ and natural flows of carbon linked to ocean circulation and rivers¹⁵,¹⁶. These natural flows include a north-south loop that takes up atmospheric carbon on land and over the ocean in the Northern Hemisphere, transports carbon from land to ocean, and releases carbon in the Southern Ocean¹⁷,¹⁸. This ocean/river loop, which carries carbon southward and is balanced by a return flow through the atmosphere, existed preindustrially and is still influencing atmospheric CO₂ gradients

today. Recent work has improved the quantification of fossil fuel emissions¹²,¹⁹,²⁰ and seasonal effects¹¹. As a result, the sum of the ocean, river and land fluxes is better constrained. Yet the land sink itself remains very sensitive to uncertainties in the ocean/river flux latitudinal distribution used as a priori constraints by atmospheric inversions²¹. There are two major issues with state-of-the-art atmospheric inversions: excessive CO₂ emissions from the land in the southern extra-tropics (7 of 11 models in ref. ²) and a considerable northern extra-tropical land sink considerably larger than suggested by ecosystem models and data-based inventories⁶,²²,²³ (9 of 11 models with the 2000–2004 sink > 1.3 PC yr⁻<fnref n="1" />; ref. ²). Here we show that previous estimates of the ocean/river loop were biased low, and that correcting this bias leads to a reduction in both the southern land source and northern land sink in atmospheric inversions.

To expose this bias, we introduce a heat-based constraint on the latitudinal distribution of natural ocean/river carbon fluxes. The heat constraint is relevant because the north-south carbon loop is largely driven by the overturning circulation, which also transports heat, leading to a coupling between carbon and heat transports.

## Tight coupling between heat and carbon transports

We first demonstrate that there is a strong heat-carbon coupling at the scale of individual ocean basins by examining the meridional ocean transports of heat and natural carbon in hydrographic data and in 11 models (nine Earth system and two ocean models, Fig. 1a). In the Atlantic Ocean, observations and models fall along a consistent linear relationship corresponding to a southward transport

<footnote n="1">¹Princeton University, Department of Geosciences and Princeton Environmental Institute, Princeton, NJ, USA. ²Scripps Institution of Oceanography, UCSD, La Jolla, CA, USA. ³Max Planck Institute for Biogeochemistry, Jena, Germany. ⁴National Center for Atmospheric Research, Boulder, CO, USA. ⁵Department of Earth Sciences, University of Oxford, Oxford, UK. ⁶Program in Atmospheric and Oceanic Sciences, Princeton University, Princeton, NJ, USA. ⁷Laboratoire de Météorologie Dynamique/Institut Pierre Simon Laplace, CNRS / ENS / Ecole Polytechnique/Sorbonne Université, Département de Géosciences, Ecole Normale Supérieure, Paris, France. ⁸Earth System Research Laboratory, NOAA, Boulder, CO, USA. *e-mail: laurer@princeton.edu</footnote>
<figure><img src="image_2.png" /><figcaption>**Fig. 1 |** Overturning circulation and biological pump link carbon and heat transport in ocean basins. **a,** Meridional transports (positive northward) of preindustrial carbon and heat from hydrographic data in the Atlantic Ocean<sup>28,72–76</sup> and from 11 models in the Atlantic and Indo-Pacific basins (no data were available for the Indo-Pacific). Solid line is a fit to Atlantic Ocean data (y = −0.30x − 0.15). Models with weak (solid oval) and strong (dashed oval) biological pump north–south asymmetry are indicated. **b,c,** Overturning circulation pathways (solid lines) and biologically driven bidirectional exchanges of carbon at high latitudes (dashed lines) (**b**) and their qualitative impact on transport across 20°N and 20°S (**c**). AMOC, Atlantic meridional overturning circulation. For details see Methods and Supplementary Tables 1 and 2.</figcaption></figure>

of 0.3 PgC yr⁻¹ per PW of northward heat transport. For the Indo-Pacific, where only model results are available, simulated transports align along this same relationship, but with larger residuals in the south. This link between carbon and heat partly arises from the control of temperature-driven solubility changes regulating annual CO₂ annual exchanges with the atmosphere (CO₂ is more soluble in colder waters)²⁴,²⁵. The carbon-to-heat ratio of −0.3 PgC yr⁻¹ per PW is, however, a third of the value expected from solubility alone (−0.9 PgC yr⁻¹ per PW). This lower ratio is related to the biological carbon pump, that is, the export and decomposition of organic matter, which maintains high dissolved inorganic carbon concentrations at depth. Thermal carbon uptake at high latitude is dampened because of the excess carbon brought to the surface in these regions by bidirectional vertical exchange with the deep ocean (Fig. 1b). Nevertheless, this biological dampening effect largely correlates with temperature, which explains the overall robust carbon-to-heat ratio of −0.3 PgC yr⁻¹ per PW. The Atlantic meridional overturning circulation transports warm surface waters northward and cold carbon-rich deep waters southward, and the gyre circulation in the Indo-Pacific Ocean transports warm surface waters poleward and carbon-rich deep waters equatorward (Fig. 1).

Despite the correlation between biological and thermal effects, the biological effect is also influenced by the degree to which upwelled carbon is re-exported to depth as sinking organic particles. This process introduces some decoupling between heat and carbon, mostly in the deep overturning cell involving Antarctic bottom water, which exchanges with the atmosphere principally in the Southern Hemisphere (Fig. 1b). This deep cell contributes little to heat transport, as heat is nearly conserved along the loop, but contributes to southward carbon transport, as carbon from the decomposition of sinking detritus accumulates along the loop before being outgassed in the south (Fig. 1c). This decoupling is stronger in the older waters of the South Indo-Pacific, yielding larger model residuals in this region due to inter-model differences in biological pump and deep cell transport (Fig. 1a).

A strong coupling between heat and carbon is also found at the global inter-hemispheric scale. Across the 11 models, the following relationship explain 85% of the variance in interhemispheric carbon transport:

$$A_C = -0.31(\pm 0.15) \times A_Q + 0.19(\pm 0.10) \\ \times A_{\text{BioPump}} - 0.65(r^2 = 0.85) \qquad (1)$$

Here A<sub>C</sub> (Pg yr<sup>-1</sup>) and A<sub>Q</sub> (PW) are the inter-hemispheric ‘transport asymmetries’ of carbon and heat, defined as the average of the global transports across 20°N and 20°S, and A<sub>BioPump</sub> (Pg yr<sup>-1</sup>) is the ‘biological pump asymmetry’, defined as the imbalance between the particulate carbon flux exported below 100 m depth south of 20°S and north of 20°N (Fig. 2). The relationship between equation (1) and individual model results is shown in Fig. 3 and Supplementary Fig. 1. A<sub>C</sub> and A<sub>Q</sub> would be zero if the transports across 20°N and 20°S were opposed and of the same magnitude. A<sub>BioPump</sub> would be zero if the particulate fluxes poleward of 20° were equal. In reality, the ocean takes up more natural carbon, loses more heat, and exports less particles in the north. A<sub>C</sub> is therefore oriented southward (negative), and A<sub>Q</sub> and A<sub>BioPump</sub> northward (positive). Note that estimates of A<sub>C</sub> in equation (1) involve small corrections for the river loop, because river influences were neglected in some models (see Methods). We find that carbon and heat transports are linked at the hemispheric scale with 0.31 ± 0.15 PgC yr<sup>-1</sup> transported southward per PW of heat transported northward, which is fully consistent with the relationship found in individual ocean basins in observations and models (Fig. 1a). In equation (1), A<sub>BioPump</sub> is diagnostic of the residual biological influences (deep cell decoupling) not already incorporated into the A<sub>Q</sub> term. A link between this residual effect and the high-latitude particulate flux is expected, because of the role the downward particle flux plays in countering the upwelling of carbon-rich water from depth. This linkage makes A<sub>BioPump</sub> a useful measure of the model differences in heat/carbon decoupling, which we can exploit to constrain A<sub>C</sub>.

## Heat constraint on ocean/river carbon fluxes

An accurate determination of A<sub>C</sub> is critical to establishing the north–south distribution of land carbon sinks using atmospheric inversions. To refine A<sub>C</sub>, we use equation (1) and estimates of A<sub>BioPump</sub> and A<sub>Q</sub>. Globally, two independent lines of evidence, based on atmospheric and satellite observations<sup>26</sup> and on atmospheric O₂ and CO₂ distributions<sup>27</sup>, give a reasonably strong constraint on the heat asymmetry A<sub>Q</sub> = 0.9 ± 0.2 PW, which is also in the range of looser constraints from hydrographic sections<sup>28</sup>. In contrast, the biological carbon pump and hence A<sub>BioPump</sub> are very poorly constrained by observations<sup>29–32</sup>. We therefore use A<sub>BioPump</sub> = 2.2 ± 1 PgC yr<sup>-1</sup>, based on the model ensemble mean value and its large uncertainty range (±2σ, Supplementary Fig. 1).

Applying A<sub>Q</sub> = 0.9 ± 0.2 PW and A<sub>BioPump</sub> = 2.2 ± 1 PgC yr<sup>-1</sup> in equation (1) yields A<sub>C</sub> = −0.52 ± 0.23 PgC yr<sup>-1</sup>, not far outside the
<figure><img src="image_3.png" /><figcaption>**Fig. 4 |** Observation-based estimates of carbon transport asymmetry</figcaption></figure>

$A_C$. Cases A-E: $A_C$ from ocean inversions (A) and $p_{CO_2}$-based estimates (B-E) are compared to the heat-based observational constraint on $A_C = -0.52 \pm 0.15$ PgC yr$^{-1}$ (grey shading). Ocean inversion-based $A_C$ derived from preindustrial fluxes implicitly incorporates the impact of rivers$^{37,41}$ (Supplementary Table 4). $p_{CO_2}$-based estimates for cases B$^{45}$, C$^{46}$ and D$^{44}$ are corrected for anthropogenic uptake$^{14,48}$ and river carbon discharge$^{38}$ (Supplementary Table 3 and Methods). $p_{CO_2}$-based case E is case D with a scaled-up river flux$^{38}$ of 0.78 PgC yr$^{-1}$ (Supplementary Table 5). Cases A and E are used to compute land sinks for Fig. 5. Error bars are the spread across inverse models reported in the original study$^{37}$ for case A, and the standard error of the uncertainties in anthropogenic, riverine and $p_{CO_2}$-based air-sea fluxes reported in Supplementary Table 3, 4 and 5 for cases B-E.

weaker land source in the Southern Hemisphere (0.10 PgC yr⁻¹ versus 0.34 PgC yr⁻¹), a weaker land sink in the Northern Hemisphere (2.26 PgC yr⁻¹ versus 2.56 PgC yr⁻¹) and a slightly weaker tropical land source (0.89 versus 0.95 PgC yr⁻¹). Overall, this shows a redistribution of ~40% of the land carbon sink (~0.5 PgC yr⁻¹ for 1990–2010).

## Multiple lines of evidence support revised carbon budget

The revised ocean/river flux proposed here is more concordant with oceanic and atmospheric constraints than previous estimated central values, as shown by five independent lines of evidence. First, the revision is consistent with the heat-based empirical constraint and with $p_{CO_2}$ data. Second, it is in optimal accord with best estimates of the global ocean carbon sink (air-sea + river = global ocean sink). Without the river upscaling, the central estimate of the $p_{CO_2}$-based air-sea flux (1.4 PgC yr⁻¹ in 2000$^{44}$) and of the river flux (0.45 PgC yr⁻¹; ref. 38) falls short in matching estimates of the net global ocean sink (2.18 PgC yr⁻¹; refs 14,48 and Supplementary Table 5). Third, the revision establishes a more credible distribution of land sinks by reducing the strong southern land source, which is a questionable feature of many recent atmospheric inversions². This source, needed to compensate an excessively strong ocean carbon sink in the southern extra-tropics, is implausible because of the absence of major land ecosystems south of 20°S. Our result suggests that the Southern Ocean carbon sink is weaker than previously thought (Fig. 5). Our revision also reduces the northern land sink, in line with studies suggesting that atmospheric inversions overestimate this sink

compared to bottom-up ecosystem models and inventories$^{11,22,23}$. It also yields a small reduction of the tropical land source, which reinforces the idea that atmospheric inversions overestimate the tropical land source and that a larger carbon sink is needed in tropical intact ecosystems to offset land-use emissions$^{3,6,11,50}$. Remaining uncertainties in the model used here (TM3) and other atmospheric transport models leave room to further increase the intact tropical ecosystems uptake and reduce the gap with bottom-up estimates. Fourth, the revised fluxes provide a relatively simple explanation for the evolution of the inter-hemispheric atmospheric $CO_2$ gradient, which increased quasi-linearly with fossil-fuel burning, but with a non-zero intercept of $-0.55 \pm 0.15$ ppm (Fig. 6). A simple dependence of this gradient on fossil-fuel burning can be explained by burning mostly occurring in the Northern Hemisphere, and assuming land sinks have evolved gradually with a history similar to that of fossil-fuel burning³. As shown in the Supplementary Information (section 5), the steady-state ocean/river transport required by the heat constraint ($A_C = -0.52 \pm 0.23$ PgC yr$^{-1}$) is able to maintain a stationary atmospheric $CO_2$ gradient between -0.7 and -0.4 ppm, consistent with the intercept ($-0.55 \pm 0.15$ ppm; Fig. 6 and Supplementary Fig. 5). This perspective, also consistent with atmospheric $^{13}$C gradient analyses⁵, suggests that the natural ocean/river loop could sustain a preindustrial inter-hemispheric atmospheric $CO_2$ gradient without necessarily invoking large shifts in land sinks prior to 1958$^{51,52}$.

Finally, the revised fluxes are in reasonable accord with the current understanding of river contributions (within their wide uncertainties). Despite early interpretations$^{16,17,38}$, river fluxes have been

<figure><img src="image_4.png" /><figcaption>**Fig. 5 |** Impact of ocean/river carbon asymmetry on land sinks. a,b, Land sinks obtained from the Jena CarboScope $CO_2$ atmospheric inversion (1990–2010 average): with ocean inversion-based carbon fluxes (case A, Fig. 4) (a) and with $p_{CO_2}$-based air-sea flux corrected for anthropogenic carbon uptake and a scaled-up river flux of 0.78 PgC yr$^{-1}$ (case E, Fig. 4) (b). Preindustrial fluxes are in black, anthropogenic perturbations centred on year 2000 (1990–2010 average) are in red. Steady-state meridional transports of preindustrial carbon across 20°S and 20°N are indicated in italics.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Fig. 6** | Revised ocean/river flux is consistent with atmospheric CO₂ data.</figcaption></figure>

Observed Mauna Loa (19.5° N, 155.6° W) to South Pole (90° S) gradient in atmospheric CO₂ between 1959 and 2014² as a function of fossil-fuel emissions⁹. Keeling and co-authors¹⁸ used the extrapolation back to zero emissions (y intercept) to estimate the north-south preindustrial gradient in atmospheric CO₂ assuming a steady state in land and ocean preindustrial components. Following this method, the y intercept gives a northern deficit of -0.55 ± 0.15 ppm, which is compatible with the Mauna Loa to South Pole gradient (grey shading) obtained by transporting our revised ocean/ river flux with the TM3 atmospheric transport model (see Supplementary Information section (5) and Supplementary Fig. 5).

largely overlooked in global carbon budgets. In support of our suggested upward revision, we note that the river carbon discharge has reported 2σ uncertainties of 100%⁵³,⁵⁴. Only 60% of ocean-draining continental areas are monitored, and extreme events not captured by traditional monthly sampling (storms and floods) may contribute 50% to the annual carbon discharge⁵⁵,⁵⁶. Furthermore, relatively low carbon discharge estimates³⁸ are tied to water budgets, which might underestimate drainage by ~50% compared to gauge measurements⁵⁵. Additional uncertainties arise from the poorly quantified carbon exchanges in inland and coastal waters²⁴ and with carbon-rich groundwaters⁵⁷,⁵⁸. Although the river flux uncertainty was always acknowledged to be large, we point out that there might be a systematic underestimation of its contribution in the context of global carbon budgets.

## Uncertainties and caveats

We acknowledge that our revision of the river component is subject to considerable uncertainty. Errors in the $p_{CO_2}$-based flux associated with wind, skin temperature effects⁴⁷,⁵⁹ and undersampling⁵⁰ could compensate for errors in the river flux. Considering an extreme scenario in which the contemporary air-sea flux is underestimated by 20% in the northern extra-tropics would add 0.1 PgCyr⁻¹ of southward transport, such that an upward revision of the river flux would no longer be needed to match the heat constraint. If the contemporary air-sea flux is also underestimated by 20% in the south, the upward revision would, however, still be required. Other sources of uncertainty are the Arctic air-sea flux and the human-induced increase in riverine carbon flux, both believed to be small enough that their uncertainties are not a major factor in this comparison (0.1 ± 0.05 PgCyr⁻¹ each yields uncertainty in $A_C$ of <0.03 PgCyr⁻¹)⁵³,⁶¹. However, these possible trade-offs between ocean and river fluxes have very little impact on the land flux estimate, which depends on the sum of the ocean and river components.

Our study is based on a single atmospheric transport model, but our conclusions regarding the sensitivity of land fluxes to ocean

priors cannot be strongly dependent on the model choice. Because inverse calculations effectively constrain the sum of land and ocean sinks within latitude bands²,²¹, the sensitivity of the inferred land sinks to a shift in the ocean fluxes must be shared across atmospheric models.

In this study, we have identified a systematic bias across a suite of ocean models that has a bearing on their use for assessing land sinks distribution. Dominant biases result from deficiencies in the physical transport and underscore the need for improvements in the representation of the meridional overturning circulation and its impact on heat and carbon transport. Large uncertainties in the biological pump limit the understanding of the global carbon cycle but are of second order. Within our model suite, those with the most realistic carbon asymmetries are models that combine a strong heat asymmetry and a strong iron limitation of primary productivity in the Southern Ocean (see Supplementary Information section (3)). We also show that it is possible to establish carbon fluxes matching observational heat transport constraints by combining contemporary $p_{CO_2}$ observations and a natural river discharge of carbon larger than recent estimates. This calls for improvements in river carbon transport estimates and the more systematic treatment of rivers in carbon budgets. The river loop that carries carbon from land to ocean is usually implicitly allocated to either the ocean (ocean inversions) or land (atmospheric inversions). Yet, this loop is mostly a natural steady-state feature that should be separated from the transient sinks when discussing anthropogenic changes. This distinction becomes more important if the river fluxes are subject to upwards revision.

## Methods

Methods, including statements of data availability and any associated accession codes and references, are available at https://doi.org/10.1038/s41561-018-0151-3.

Received: 21 July 2017; Accepted: 8 May 2018;
Published online: 11 June 2018

## References

1. Tans, P. P., Fung, I. Y. & Takahashi, T. Observational constraints on the global atmospheric CO₂ budget. *Science* **247**, 1431–1438 (1990).

2. Peylin, P. et al. Global atmospheric carbon budget: results from an ensemble of atmospheric CO₂ inversions. *Biogeosciences* **10**, 6699–6720 (2013).

3. Pan, Y. et al. A large and persistent carbon sink in the world's forests. *Science* **333**, 988–993 (2011).

4. Sarmiento, J. L. et al. Trends and regional distributions of land and ocean carbon sinks. *Biogeosciences* **7**, 2351–2367 (2010).

5. Keeling, C. D., Piper, S. C., Whorf, T. P. & Keeling, R. F. Evolution of natural and anthropogenic fluxes of atmospheric CO₂ from 1957 to 2003. *Tellus B* **63**, 1–22 (2011).

6. Schimel, D., Stephens, B. B. & Fisher, J. B. Effect of increasing CO₂ on the terrestrial carbon cycle. *Proc. Natl Acad. Sci. USA* **112**, 436–441 (2015).

7. Graven, H. D. et al. Enhanced seasonal exchange of CO₂ by northern ecosystems since 1960. *Science* **341**, 1085–1089 (2013).

8. Forkel, M. et al. Enhanced seasonal CO₂ exchange caused by amplified plant productivity in northern ecosystems. *Science* **351**, 696–699 (2016).

9. Quéré, C. L. et al. Global carbon budget 2016. *Earth Syst. Sci. Data* **8**, 605–649 (2016).

10. Bousquet, P. et al. Regional changes in carbon dioxide fluxes of land and oceans since 1980. *Science* **290**, 1342–1346 (2000).

11. Stephens, B. B. et al. Weak northern and strong tropical land carbon uptake from vertical profiles of atmospheric CO₂. *Science* **316**, 1732–1735 (2007).

12. Andres, R. J. et al. A synthesis of carbon dioxide emissions from fossil-fuel combustion. *Biogeosciences* **9**, 1845–1871 (2012).

13. Denning, A. S., Fung, I. Y. & Randall, D. Latitudinal gradient of atmospheric CO₂ due to seasonal exchange with land biota. *Nature* **376**, 240–243 (1995).

14. Khatiwala, S., Primeau, F. & Hall, T. Reconstruction of the history of anthropogenic CO₂ concentrations in the ocean. *Nature* **462**, 346–349 (2009).

15. Broecker, W. S. & Peng, T.-H. Interhemispheric transport of carbon dioxide by ocean circulation. *Nature* **356**, 587–589 (1992).

16. Sarmiento, J. L. & Sundquist, E. T. Revised budget for the oceanic uptake of anthropogenic carbon dioxide. *Nature* **356**, 589–593 (1992).
17. Aumont, O. et al. Riverine-driven interhemispheric transport of carbon. *Glob. Biogeochem. Cycles* **15**, 393–405 (2001).

18. Keeling, C. D., Piper, S. C. & Heimann, M. in *Aspects of Climate Variability in the Pacific and the Western Americas* (ed. Peterson, D. H.) 305–363 (American Geophysical Union, Washington, DC, 1989).

19. Gurney, K. R. et al. High resolution fossil fuel combustion CO₂ emission fluxes for the United States. *Environ. Sci. Technol.* **43**, 5535–5541 (2009).

20. Olivier, J. G. J., Janssens-Maenhout, G., Muntean, M. & Peters, J. A. H. W. *Trends in Global CO₂ Emissions: 2016 Report* (PBL Netherlands Environmental Assessment Agency, 2016); http://www.pbl.nl/en/publications/trends-in-global-co2-emissions-2016-report

21. Steinkamp, K. & Gruber, N. A joint atmosphere-ocean inversion for the estimation of seasonal carbon sources and sinks. *Glob. Biogeochem. Cycles* **27**, 732–745 (2013).

22. Houghton, R. A. Why are estimates of the terrestrial carbon balance so different? *Glob. Change Biol.* **9**, 500–509 (2003).

23. Houghton, R. A. et al. Carbon emissions from land use and land-cover change. *Biogeosciences* **9**, 5125–5142 (2012).

24. Brewer, P. G., Goyet, C. & Dyrssen, D. Carbon dioxide transport by ocean currents at 25°N latitude in the Atlantic Ocean. *Science* **246**, 477–479 (1989).

25. Keeling, R. F. & Peng, T.-H. Transport of heat, CO₂ and O₂ by the Atlantic's thermohaline circulation. *Philos Trans. R. Soc. Lond. B* **348**, 133–142 (1995).

26. Large, W. G. & Yeager, S. G. The global climatology of an interannually varying air-sea flux data set. *Clim. Dyn.* **33**, 341–364 (2009).

27. Resplandy, L. et al. Constraints on oceanic meridional heat transport from combined measurements of oxygen and carbon. *Clim. Dyn.* **47**, 3335 (2016).

28. Ganachaud, A. & Wunsch, C. Large-scale ocean heat and freshwater transports during the World Ocean Circulation Experiment. *J. Clim.* **16**, 696–705 (2003).

29. Schlitzer, R. in *Inverse Methods in Global Biogeochemical Cycles* (eds. Kasibhatla, P. et al.) 107–124 (American Geophysical Union, Washington, DC, 2000); https://doi.org/10.1029/GM114p0107

30. Henson, S. A. et al. Rapid emergence of climate change in environmental drivers of marine ecosystems. *Nat. Commun.* **8**, 14682 (2017).

31. Siegel, D. A. et al. Global assessment of ocean carbon export by combining satellite observations and food-web models. *Glob. Biogeochem. Cycles* **28**, 181–196 (2014).

32. DeVries, T. & Weber, T. The export and fate of organic matter in the ocean: new constraints from combining satellite and oceanographic tracer observations. *Glob. Biogeochem. Cycles* **31**, 2016GB005551 (2017).

33. Yeager, S. & Danabasoglu, G. Sensitivity of Atlantic meridional overturning circulation variability to parameterized Nordic Sea overflows in CCSM4. *J. Clim.* **25**, 2077–2103 (2011).

34. Wang, C., Zhang, L., Lee, S.-K., Wu, L. & Mechoso, C. R. A global perspective on CMIP5 climate model biases. *Nat. Clim. Change* **4**, 201–205 (2014).

35. Ma, X. et al. Western boundary currents regulated by interaction between ocean eddies and the atmosphere. *Nature* **535**, 533–537 (2016).

36. Doney, S. C. et al. Evaluating global ocean carbon models: the importance of realistic physics. *Glob. Biogeochem. Cycles* **18**, GB3017 (2004).

37. Mikaloff Fletcher, S. E. et al. Inverse estimates of the oceanic sources and sinks of natural CO₂ and the implied oceanic carbon transport. *Glob. Biogeochem. Cycles* **21**, GB1010 (2007).

38. Jacobson, A. R., Mikaloff Fletcher, S. E., Gruber, N., Sarmiento, J. L. & Gloor, M. A joint atmosphere-ocean inversion for surface fluxes of carbon dioxide: 1. Methods and global-scale fluxes. *Glob. Biogeochem. Cycles* **21**, GB1019 (2007).

39. Gerber, M. & Joos, F. Carbon sources and sinks from an ensemble Kalman filter ocean data assimilation. *Glob. Biogeochem. Cycles* **24**, GB3004 (2010).

40. DeVries, T. The oceanic anthropogenic CO₂ sink: storage, air-sea fluxes, and transports over the industrial era. *Glob. Biogeochem. Cycles* **28**, 631–647 (2014).

41. Gruber, N. et al. Oceanic sources, sinks, and transport of atmospheric CO₂. *Glob. Biogeochem. Cycles* **23**, GB1005 (2009).

42. Sarmiento, J. L. et al. Sea-air CO₂ fluxes and carbon transport: a comparison of three ocean general circulation models. *Glob. Biogeochem. Cycles* **14**, 1267–1281 (2000).

43. Murnane, R. J., Sarmiento, J. L. & Le Quéré, C. Spatial distribution of air-sea CO₂ fluxes and the interhemispheric transport of carbon by the oceans. *Glob. Biogeochem. Cycles* **13**, 287–305 (1999).

44. Rödenbeck, C. et al. Global surface-ocean pCO₂ and sea-air CO₂ flux variability from an observation-driven ocean mixed-layer scheme. *Ocean Sci.* **9**, 193–216 (2013).

45. Takahashi, T. et al. Climatological mean and decadal change in surface ocean pCO₂, and net sea-air CO₂ flux over the global oceans. *Deep Sea Res. Part II Top. Stud. Oceanogr.* **56**, 554–577 (2009).

46. Landschützer, P., Gruber, N., Bakker, D. C. E. & Schuster, U. Recent variability of the global ocean carbon sink. *Glob. Biogeochem. Cycles* **28**, 927–949 (2014).

47. Wanninkhof, R. et al. Global ocean carbon uptake: magnitude, variability and trends. *Biogeosciences* **10**, 1983–2000 (2013).

48. Khatiwala, S. et al. Global ocean storage of anthropogenic carbon. *Biogeosciences* **10**, 2169–2191 (2013).

49. Rödenbeck, C., Houweling, S., Gloor, M. & Heimann, M. CO₂ flux history 1982–2001 inferred from atmospheric data using a global inversion of atmospheric transport. *Atmos. Chem. Phys.* **3**, 1919–1964 (2003).

50. Grace, J., Mitchard, E. & Gloor, E. Perturbations in the carbon budget of the tropics. *Glob. Change Biol.* **20**, 3238–3255 (2014).

51. Conway, T. J. & Tans, P. P. Development of the CO₂ latitude gradient in recent decades. *Glob. Biogeochem. Cycles* **13**, 821–826 (1999).

52. Fan, S. et al. A large terrestrial carbon sink in North America implied by atmospheric and oceanic carbon dioxide data and models. *Science* **282**, 442–446 (1998).

53. Regnier, P. et al. Anthropogenic perturbation of the carbon fluxes from land to ocean. *Nat. Geosci.* **6**, 597–607 (2013).

54. Bauer, J. E. et al. The changing carbon cycle of the coastal ocean. *Nature* **504**, 61–70 (2013).

55. Clark, E. A., Sheffield, J., van Vliet, M. T. H., Nijssen, B. & Lettenmaier, D. P. Continental runoff into the oceans (1950–2008). *J. Hydrometeorol.* **16**, 1502–1520 (2015).

56. Bianchi, T. S. et al. Enhanced transfer of terrestrially derived carbon to the atmosphere in a flooding event. *Geophys. Res. Lett.* **40**, 116–122 (2013).

57. Kwon, E. Y. et al. Global estimate of submarine groundwater discharge based on an observationally constrained radium isotope model. *Geophys. Res. Lett.* **41**, 8438–8444 (2014).

58. Le Gland, G., Mémery, L., Aumont, O. & Resplandy, L. Improving the inverse modeling of a trace isotope: how precisely can radium-228 fluxes toward the ocean and submarine groundwater discharge be estimated? *Biogeosciences* **14**, 3171–3189 (2017).

59. Woolf, D. K., Land, P. E., Shutler, J. D., Goddijn-Murphy, L. M. & Donlon, C. J. On the calculation of air-sea fluxes of CO₂ in the presence of temperature and salinity gradients: air-sea CO₂ fluxes. *J. Geophys. Res. Oceans* **121**, 1229–1248 (2016).

60. Rödenbeck, C. et al. Data-based estimates of the ocean carbon sink variability – first results of the Surface Ocean pCO₂ Mapping intercomparison (SOCOM). *Biogeosciences* **12**, 7251–7278 (2015).

61. Schuster, U. et al. An assessment of the Atlantic and Arctic sea-air CO₂ fluxes, 1990–2009. *Biogeosciences* **10**, 607–627 (2013).

62. Lundberg, L. & Haugan, P. M. A Nordic seas–Arctic Ocean carbon budget from volume flows and inorganic carbon data. *Glob. Biogeochem. Cycles* **10**, 493–510 (1996).

63. Macdonald, A. M., Baringer, M. O., Wanninkhof, R., Lee, K. & Wallace, D. W. R. A 1998–1992 comparison of inorganic carbon and its transport across 24.5°N in the Atlantic. *Deep Sea Res. Part II Top. Stud. Oceanogr.* **50**, 3041–3064 (2003).

64. Holfort, J., Johnson, K. M., Schneider, B., Siedler, G. & Wallace, D. W. R. Meridional transport of dissolved inorganic carbon in the South Atlantic Ocean. *Glob. Biogeochem. Cycles* **12**, 479–499 (1998).

65. Álvarez, M., Ríos, A. F., Pérez, F. F., Bryden, H. L. & Rosón, G. Transports and budgets of total inorganic carbon in the subpolar and temperate North Atlantic. *Glob. Biogeochem. Cycles* **17**, 1002 (2003).

66. Johns, W. E. et al. Continuous, array-based estimates of Atlantic Ocean heat transport at 26.5°N. *J. Clim.* **24**, 2429–2449 (2011).

## Acknowledgements

L.R. was granted support by the Climate Program Office of the National Oceanic and Atmospheric Administration grant NA13OAR4310219. S.K. was supported by US National Science Foundation (NSF) grant OCE 10-60804. K.B.R. was supported by NASA award NNX14AL85G. N.C.A.R. is sponsored by the NSF. The authors also thank the groups developing MOM, MITgcm, NEMO and CMIP5 models for providing their model results.

## Author contributions

L.R. directed the analysis of the several data sets used here and shared responsibility for writing the manuscript. R.F.K. and B.B.S. shared responsibility for writing the manuscript. C.R. computed the land sinks. L.B., M.C.L. and K.B.R. provided model results. All authors contributed to the final version of the manuscript.

## Competing interests

The authors declare no competing interests.

## Additional information

*Supplementary information* is available for this paper at https://doi.org/10.1038/s41561-018-0151-3.

*Reprints and permissions information* is available at www.nature.com/reprints.

*Correspondence and requests for materials* should be addressed to L.R.

*Publisher's note:* Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Methods

**Observations of meridional transports of heat and preindustrial carbon in the Atlantic Ocean.** Estimates based on hydrographic data of ocean preindustrial carbon meridional transport are only available for the Atlantic Ocean. Supplementary Table 1 details the observations of heat and preindustrial carbon used for Fig. 1. Hydrographic data used for Fig. 1a were corrected for the influence of excess anthropogenic CO₂ (refs 14,48).

**Definition of carbon transport asymmetry $A_C$, heat asymmetry $A_Q$ and biological pump asymmetry $A_{BioPump}$.** Ocean transport asymmetry (A) is computed for carbon ($A_C$) and heat ($A_Q$) as the average of the steady-state northward transports across 20°N ($T_N$) and 20°S ($T_S$) (Fig. 2):

$$A = (T_N + T_S)/2 \text{ with } T \text{ and } A \text{ positive northward}$$

In the steady state, A must equal half of the difference between the net air-sea flux (plus the river discharge for $A_C$) north of 20°N ($F_N$) minus the flux south of 20°S ($F_S$):

$$A = (F_N - F_S)/2 \text{ with } F \text{ positive into the atmosphere}$$

This definition, which is not sensitive to air-sea fluxes in the tropics (20°S to 20°N), limits the impact of uncertainties on the tropical ocean and atmosphere dynamics, and provides a better metric of large-scale inter-hemispheric exchanges.

Carbon fluxes include air-sea fluxes and river discharge ($F_N = F_{N\text{air-sea}} + F_{N\text{river}}$), while heat fluxes include air-sea fluxes only ($F_N = F_{N\text{air-sea}}$), $F_S = F_{S\text{air-sea}} + F_{S\text{river}}$), while heat fluxes include air-sea fluxes only ($F_S = F_{S\text{air-sea}}$). As a result, $A_C$ can be written as the sum of air-sea exchanges ($A_{\text{air-sea}}$) and river discharge ($A_{\text{riv}}$) contributions:

$$A_C = A_{\text{air-sea}} + A_{\text{riv}} \\ \text{where } A_{\text{air-sea}} = (F_{\text{Nair-sea}} - F_{\text{Sair-sea}})/2 \\ \text{and } A_{\text{river}} = (F_{\text{Nriver}} - F_{\text{Sriver}})/2$$

We define the biological pump asymmetry in a similar manner to $A_C$, as the difference between the biogenic particulate carbon flux exported below 100 m depth south of 20°S ($E_{S\text{positive downward}}$) minus the flux north of 20°N ($E_{N\text{positive downward}}$) (Fig. 2):

$$A_{\text{BioPump}} = (E_S - E_N)/2$$

$A_{\text{BioPump}}$ represents the imbalance between the carbon particulate export south of 20°S and north of 20°N, and hence the maximum amount of carbon of biological origin available for inter-hemispheric transport (not all of the available carbon is transported).

**Earth-system and ocean models: transport, asymmetries and uncertainty.** We used the steady-state preindustrial air-sea fluxes of CO₂ and heat from nine Earth-system models (ESMs) and two ocean models (Supplementary Table 2). Seven of the nine ESMs participated in the Coupled Model Intercomparison Project Phase 5 (CMIP5): the Community Earth System Model CESM version CESM1-BGC; two versions of the Geophysical Fluid Dynamics Laboratory (GFDL) Earth System Models (ESM2M with a nominally level vertical coordinate, and the ESM2G with a density-based layered vertical oceans)⁴,⁶,⁷; the Institut Pierre Simon Laplace Coupled Model 5, version IPSL-CM5A-LR⁶; two versions of the Max Planck Institut für Meteorologie Earth System Model (low- and medium-resolution ocean: MPI-ESM-LR MPI-ESM-MR)⁶;³⁵; the Norwegian Earth System Model (NorESM1-ME)⁶⁰. We also added the preindustrial control simulation of two recent large-ensemble experiments from the CESM model (CESM-LE)⁶⁷,⁶⁸ and the GFDL model (GFDL-LE). Finally, we used two versions of the NEMO-PISCES ocean model (NEMO 3.6 – PISCESv2): a standard version⁶⁹ and a sensitivity perturbation experiment for which the constraint of iron limitation is removed.

We only used quasi-equilibrated preindustrial control simulations. For these simulations the drift in surface fluxes was small and corrected using linear regressions (drifts of <5 × 10⁻⁴ PgCyr⁻¹ and <1 × 10⁻⁵ PW in all models), and imbalances between ocean heat content and heat fluxes (<0.03 PW) and between carbon inventory and carbon fluxes (<0.02 PgCyr⁻¹) were also small⁷,⁰,¹. We accounted for these imbalances in the uncertainties in $A_C$ and $A_Q$. Model transports were computed from the multi-century mean preindustrial air-sea fluxes to isolate the natural steady-state transport. Model sections in Fig. 1 are at 30°S, 28°S, 23°S, 20°S, 15°S, 10°S, 5°S, 5°N, 10°N, 20°N, 30°N, 40°N, 50°N and 60°N.

The uncertainty in the asymmetry derived from the ESMs includes the interannual variability in ocean transport (±1 standard deviation over the simulation period) and the uncertainty associated with the imbalance in carbon and heat budgets (0.02 PgCyr⁻¹ and 0.03 PW) for $A_C$ and $A_Q$, as well as the uncertainty in the riverine discharge for $A_C$ (see section 'River carbon discharge correction' for details on river). We assume a 50% uncertainty for the northern and southern riverine carbon discharge, which leads to a 0.1 PgCyr⁻¹ uncertainty for $A_C$. The total uncertainty for $A_C$ ranges from 0.17 to 0.23 PgCyr⁻¹ across the ESMs.

**Asymmetries from existing ocean and river carbon flux estimates.** The carbon transport asymmetry $A_C$ was computed directly from inversion-based preindustrial ocean carbon fluxes¹⁷,⁴⁰ (case A, Fig. 4). Unlike previous studies that removed an estimate of the river contribution from inversion results to focus more specifically on air-sea CO₂ fluxes¹⁸,⁴¹, we retained the raw inversion results so that the river discharge was included in the computation of $A_C$. Uncertainties in Fig. 4 are as reported in the original study⁷ and represent the spread across inverse models.

$A_C$ was computed for four different $p_{\text{CO}_2}$-based estimates (cases B–E, Fig. 4). In these four cases, $A_C$ was computed by correcting $p_{\text{CO}_2}$ contemporary air-sea fluxes⁴⁴⁻⁴⁶ with the anthropogenic carbon uptake estimate of Khatiwala and co-authors⁴,⁴⁸ and by adding estimates of the river carbon discharge (for details on river correction see the next section). Our best estimate of the ocean/river fluxes combines the $p_{\text{CO}_2}$-based air-sea flux of ref. ⁴¹, corrected for anthropogenic carbon uptake⁴,⁴⁸ and by correcting for a river flux of 0.78 PgCyr⁻¹ so that mass conservation is ensured and better agreement with the heat-based constraint is reached. Note that any of the $p_{\text{CO}_2}$-based products would give similar results (Fig. 4). Uncertainties for the preindustrial air-sea fluxes reported in Supplementary Table 5 are computed as the standard error of the uncertainties in anthropogenic, riverine and $p_{\text{CO}_2}$-based air-sea fluxes. Error bars in Fig. 4 are computed from the uncertainties reported in Supplementary Tables 3, 4, and 5.

**River carbon discharge correction.** In equation (1), $A_C = A_{\text{air-sea}} + A_{\text{river}}$ where $A_{\text{air-sea}}$ is the air-sea flux contribution (excluding outgassing linked to river effects) and $A_{\text{river}}$ is the river loop contribution to inter-hemispheric exchange (Supplementary Fig. 6). We applied different levels of corrections for this river contribution to $A_C$.

All models include river freshwater inputs but not necessarily the associated carbon discharge. Three models (IPSL-CM5A-LR, NEMO-PISCES with and without iron limitation) include a riverine carbon discharge of 0.45 PgCyr⁻¹, in line with the estimate of ref. ¹⁸, directly yielding $A_C$. GFDL-ESM2M and GFDL-ESM2G include part of the riverine carbon discharge (0.1 PgCyr⁻¹) to compensate the steady-state calcite precipitation in sediments. All other ESMs do not include any river carbon discharge. As shown in Supplementary Fig. 6, we add to all simulated values of $A_C$ (except IPSL-CM5A-LR and the two NEMO-PISCES models) a southward contribution of -0.15 ± 0.05 PgCyr⁻¹, which is consistent with the riverine discharge of ref. ³⁸ that contributes a riverine contribution of $A_{\text{riv}} = -0.10 \text{ PgCyr}^{-1}$, and the associated pattern of CO₂ efflux of ref. ¹⁷ that adds a southward transport of -0.05 PgCyr⁻¹ to $A_{\text{air-sea}}$ (outgassing compensating the river input in the steady state; see standard scenario in their Fig. 2b). Note that we ignore the small amount of carbon already accounted for in the two GFDL models. Although we suggest in this study that the river estimate of 0.45 PgCyr⁻¹ needs upward revision (0.78 PgCyr⁻¹), equation (1) would not be very sensitive to this revision, changing $A_C$ by only -0.06 PgCyr⁻¹ and having no impact on the -0.31 and 0.19 regression factors.

$p_{\text{CO}_2}$-based carbon fluxes include the CO₂ outgassing via air-sea flux associated with the river carbon discharge ($F_{\text{efflux}}$ in Supplementary Fig. 6), but not the discharge itself² (F_{\text{river}} in Supplementary Fig. 6). We used the pattern and magnitude of the river carbon discharge $F_{\text{river}}$ of ref. ¹⁸ in cases B, C and D of Fig. 4 (0.45 PgCyr⁻¹), and a scaled-up version of that same pattern that matches a total inflow of 0.78 PgCyr⁻¹ in case E (Fig. 4). Finally, ocean inverse calculations of carbon fluxes implicitly include rivers and do not require any correction².

**Land sink estimates based on two sets of ocean/river fluxes.** We computed the land sinks using the Jena CarboScope CO₂ inversion over the period 1990–2010, representing an update of ref. ⁴⁹. We performed two atmospheric inverse calculations, one using ocean inversion-based ocean/river fluxes (Fig. 5a) and one using $p_{\text{CO}_2}$-based ocean/river fluxes (Fig. 5b). In both atmospheric inversions, the ocean flux is prescribed as a fixed prior without adjustments (that is, the ocean posterior flux equals the ocean prior flux). Case 1 uses the ocean inversion-based ocean/river fluxes reported in ref. ⁴¹ combined with the anthropogenic trend from 1990 to 2010 from refs ¹⁴,⁴⁸ (case A, Fig. 4). Case 2 uses the monthly 1990–2010 climatological air-sea CO₂ flux based on ocean $p_{\text{CO}_2}$ data¹⁴ (updated version oc_v1.2) (case E, Fig. 4). In case 2, we also use the 1990–2010 anthropogenic trend from refs ¹⁴,⁴⁸ to isolate the anthropogenic component from the natural component (Fig. 5b).

A fundamental difference between the two inversions is the way the riverine input is taken into account. The prescribed ocean flux of case 1 includes both the air-sea and river fluxes, whereas the prescribed ocean flux of case 2 only includes the air-sea CO₂ flux and excludes the river discharge. Rivers are therefore accounted for in the prescribed ocean sink in case 1 and in the land sink posterior in case 2. To compare both inversions, we separated the river discharge from the land sink in inversion case 2. Figure 5 and Supplementary Tables 4 and 5 present the results for cases 1 and 2.

**Data availability.** Model data for CESM1-BGC, GFDL-ESM2M, GFDL-ESM2G, IPSL-CM5A-LR, MPI-ESM-LR, MPI-ESM-MR and NorESM1-ME are available through the CMIP5 database (http://cmip.lnl.gov/cmip5/data_portal.html). Data from CESM-LE, GFDL-LE and the two NEMO-PISCES ocean models used in this study can be provided upon request to the authors M.C.L., K.B.R. and L.B., respectively.
**Code availability.** The code for the Jena Inversion model is available online at www.bgc-jena.mpg.de/~christian.roedenbeck/INVERSION/HOWTO/ or, upon request, from the correspondence author.

## References

62. Dunne, J. P. et al. GFDL's ESM2 Global Coupled Climate-Carbon Earth System Models. Part I: physical formulation and baseline simulation characteristics. *J. Clim.* **25**, 6646–6665 (2012).

63. Dunne, J. P. et al. GFDL's ESM2 Global Coupled Climate-Carbon Earth System Models. Part II: carbon system formulation and baseline simulation characteristics. *J. Clim.* **26**, 2247–2267 (2013).

64. Séférian, R., Iudicone, D., Bopp, L., Roy, T. & Madec, G. Water mass analysis of effect of climate change on air–sea CO₂ fluxes: the southern ocean. *J. Clim.* **25**, 3894–3908 (2012).

65. Ilyina, T. et al. Global ocean biogeochemistry model HAMOCC: model architecture and performance as component of the MPI-Earth system model in different CMIP5 experimental realizations. *J. Adv. Model. Earth Syst.* **5**, 287–315 (2013).

66. Tjiputra, J. F. et al. Evaluation of the carbon cycle components in the Norwegian Earth System Model (NorESM). *Geosci. Model Dev.* **6**, 301–325 (2013).

67. Long, M. C., Deutsch, C. & Ito, T. Finding forced trends in oceanic oxygen. *Glob. Biogeochem. Cycles* **30**, 2015GB005310 (2016).

68. Kay, J. E. et al. The Community Earth System Model (CESM) Large Ensemble Project: a community resource for studying climate change in the presence of internal climate variability. *Bull. Am. Meteorol. Soc.* **96**, 1333–1349 (2014).

69. Aumont, O., Ethé, C., Tagliabue, A., Bopp, L. & Gehlen, M. PISCES-v2: an ocean biogeochemical model for carbon and ecosystem studies. *Geosci. Model Dev.* **8**, 2465–2513 (2015).

70. Hobbs, W., Palmer, M. D. & Monselesan, D. An energy conservation analysis of ocean drift in the CMIP5 global coupled models. *J. Clim.* **29**, 1639–1653 (2015).

71. Séférian, R. et al. Inconsistent strategies to spin up models in CMIP5: implications for ocean biogeochemical model performance assessment. *Geosci. Model Dev.* **9**, 1827–1851 (2016).