Review of “Observation-constrained estimates of the global ocean carbon sink from Earth system model”

The study applies observational constraints to adjust Earth system model estimates of the global ocean carbon sink. The observational constraints are the sea surface salinity in the subtropical-polar front in the Southern Ocean (as applied previously by the authors in Terhaar et al, 2021), the Atlantic Meridional Overturning Circulation (AMOC) and the Revelle buffer factor. These observational choices are plausible and the benefits of applying them are clearly set out in an iterative manner in Figure 3. The outcome is a slight elevation of the global ocean carbon sink and almost a halving of the model uncertainty, which are important improvements.

The study is comprehensive and written up in a detailed manner. In places the level of detail seemed to detract from the central message, such as discussing the details of the biological contributions when that appears to be a rather minor contribution in the global carbon uptake for anthropogenic timescales.

The only concern I raise is the particular choice of the observational constraints and while this set of choices is plausible, there are other choices that might have led to similar improvements.

So including a discussion of other choices would be helpful to the reader. For example, would a measure of the strength of the winds at key locations provide a similar benefit to the measure of the AMOC or a measure of the winter mixed layer thickness derived from Argo be beneficial? The AMOC might be used here as a proxy for ocean ventilation, but that need not be the case with gyre-scale subduction not being causally related to the AMOC. The use of the Revelle buffer factor is a plausible constraint, but the justification for that could be expanded, see possible theoretical links that can be explored or are there other references that can be utilised?

In summary, this is a comprehensive study that provides a plausible adjustment of Earth system model output to improve their projections of the global ocean carbon sink. I think that this work is important and I recommend acceptance subject to the minor points raised being addressed.

Detailed points;

L47 The text is assuming that the AMOC is leading to the basin-scale subduction. I think that this statement is combining together two different processes. Subduction in ocean basins is primarily linked to the gyre circulation and the vertical and lateral transfer from the winter mixed layer to the thermocline. The AMOC is a longitudinally-averaged overturning circulation that contributes to the ventilation process by redistributing heat and tracers, but is not the same as subduction.

L50 The Revelle factor certainly does affect the capacity of the ocean  to take up carbon. This aspect could be expanded more. The  air-sea partitioning of carbon is affected by the buffer factor (Goodwin et al., 20008 & 2009; Katavouta et al., 2018). In addition, the air-sea equilibration timescale, tau, for carbon dioxide is affected by the buffer factor, tau =(h/K_g)(DIC/(B CO2) where h is mixed layer thickness, K_g is exchange velocity, DIC is dissolved inorganic carbon, B is the buffer factor and CO2 is dissolved CO2.

L106 Improve syntax,”so-estimated”

L109 Improve wording

L163 Adjust wording

L173 An important point is being made as the role of the salinity and AMOC in determining water-mass formation. A list of 4 references are provided, but are they being cited as to their work on water-mass formation or did they propose the connections tbetween salinity and the AMOC to water-mass formation?

Figure 3 is very clear and key to the study.

L230-231. Perhaps reword to make clearer.

L251 Cut hence.

L297 Buckley and Marshall provided a review of heat transport, but did they make the point about anthropogenic carbon uptake?

Appendix A3 Equation (2) and perhaps (3) are central to the study. I would recommend that this subsection moved into the heart of the paper.

References

Goodwin, P., R.G. Williams, A. Ridgwell and M.J. Follows, 2009. Climate sensitivity to the carbon cycle modulated by past and future changes in ocean chemistry. Nature Geosciences, doi:10.1038/ngeo416

Goodwin, P., M.J. Follows and R.G. Williams, 2008. Analytical relationships between atmospheric carbon dioxide, carbon emissions and ocean processes. Global Biogeochemical Cycles, 22, GB3030, doi:10.1029/2008GB003184

Katavouta, A., R.G. Williams, P. Goodwin and V. Roussenov, 2018. Reconciling   atmospheric and oceanic views of the Transient Climate Response to Emissions. Geophysical Research Letters, 45, 6205-6214, doi.org/10.1029/2018GL077849

In this manuscript, Terhars et al. investigate how Earth system models estimates of the global ocean carbon sink can be constrained by a combination of physical parameters (the sea-surface salinity and the strength of the Atlantic Meridional Overturning Circulation) and a biogeochemical parameter (the Revelle factor).

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The manuscript is timely, clearly written and proposes a sound methodology. The results are well explained and discussed through the manuscript. This work presents an important basis for the research community studying the ocean carbon cycle as this work proposes a first approach to bring together estimates of ocean carbon sink based on observational data with those based on Earth system models’ simulations. I liked very much the fact that the authors explain step by step the use of a suite of emergent constraints and then perform several validations to test the robustness of their approach.

I only have one major comment and a set of minor comments/suggestions that aims to clarify some point of the paper.

Major comments:

Although the authors did a great job in defining and applying observational constraints to improve Earth system models’ simulations/projections, they miss to thoroughly discuss how each physical or biological parameters are correlated between each other. For instance, pattern of sea-surface salinity is linked to water mass properties, which is in turn, tightly linked to large-scale circulation (deacon cells and the strength of the AMOC). Same caveat could hold for the buffer factor (globally average) which result from biological but also from chemical properties of the models.

If constraining fields are correlated between each other in the observations and/or in the ESMs, this might bring light on a more mechanistic explanation of the “cascade of errors” = hydrodynamics => large-scale circulation => buffer factor rather than a “sum of errors” = hydrodynamics + large-scale circulation + buffer factor. This might be needed as a justification of applying this set of observational constraints (avoid cherry picking).

In addition, for this ‘biological’ parameter, I think further discuss should be needed in the light of Figure A.1.2 which shows the correlation between surface buffer factor and the difference between alkalinity (AT) and total dissolved inorganic carbon (CT) at surface. It highly biases in either CT or AT that might result from the calibration of model alkalinity (as highlighted in several model reference papers or in Table 3 of Seferian et al. 2020 (https://link.springer.com/article/10.1007/s40641-020-00160-0/tables/3).

Finally, in the light of deficiency/weakness of observational-based estimates of the ocean carbon sink, it might be interesting to decompose your approach on regional/basin scale uptake. Driving mechanisms, long-term trends and variability of the North Atlantic carbon sink is better understood than those of the Southern Ocean (which suffer from incomplete observational mapping across seasons). As such, does the model (and your observational constraints) help to improve the agreement between model and observation-based estimates. Besides, does the ratio in carbon uptake in the North Atlantic and the Southern Ocean is well captured between models. In the context of this paper, I wonder how far this ratio might be an additional constraint to test or a verification measure to assess the robustness of your approach.

Regarding the conclusions of the paper, I think the authors could make a stronger point resulting from this work.

First, I might be relevant to discuss the consequence of this work on the carbon budget (Friedlingstein et al. 2022), especially in the context of the budget imbalance term. Revised (contrained) estimates appears to be about 10% higher than the unconstrained estimates. The magnitude of the revision is thus greater than the budget imbalance. What would be the consequence then? a weaker land-surface carbon sink?

On the other hand, in a context of improving estimates of the carbon feedbacks, what would be the revision of the Beta and Gamma as inferred from your approach. In might be interesting to include in your work ssp585-bgc (which has been conducted by most of the modelling center) and see how your approach works on ocean Beta and Gamma.

Minor comments:

L12: explain the buffer factor in the abstract

Figure 1: please use the same temporal baseline for panel a) and b). from 1950 onwards ?

L106 Improve syntax,”so-estimated”

L157: Many other papers have used emergent/observational constraints (Boé et al., Bourgeois et al., Cox et al., Douville et al., Plazzotta et al., Schlund et al., etc....) — They can also be listed here.

Figure 2: please add ‘the strength of’ before “the Atlantic meridional…”

Figure 3: Please add R-square for each panels c, e and g as an indication of the quality of the fit  

On this figure, it is unclear if model estimate are based on multiple realisation or just one single member

L237: one can also consider the CO2 mole fraction that is *really seen* by the ocean carbon module because of various treatment of the air-sea CO2 exchange (Hauck et al. 2020, already mentioned in this work)

L341: Conclusion — see above comments

Appendix: Biogeosciences allows more materials than short/letter paper, I would recommend to move some of the material of the appendix into the heart of the paper. Some of them are central to your work.

Table A.1.1 please consider adding data citation doi (where relevant) for improving the reproducibility of the work.

References:

Boé, J., Hall, A. & Qu, X. September sea-ice cover in the Arctic Ocean projected to vanish by  2100. Nat. Geosci. 2, 341–343 (2009).

Bourgeois, T., Goris, N., Schwinger, J. et al. Stratification constrains future heat and carbon uptake in the Southern Ocean between 30°S and 55°S. Nat Commun 13, 340 (2022). https://doi.org/10.1038/s41467-022-27979-5

Cox, P., Pearson, D., Booth, B. et al. Sensitivity of tropical carbon to climate change constrained by carbon dioxide variability. Nature 494, 341–344 (2013). https://doi.org/10.1038/nature11882

Douville H., M. Plazzotta (2017) Midlatitude summer drying : An underestimated threat in CMIP5 models ? Geophys. Res. Lett., 44, 9967-9975, doi:10.1002/2017GL075353

Hauck, J., Zeising, M., Le Quéré, C., Gruber, N., Bakker, D. C. E., Bopp, L., Chau, T. T. T., Gürses, Ö., Ilyina, T., Landschützer, P., Lenton, A., Resplandy, L., Rödenbeck, C., Schwinger, J., Séférian R.:Consistency and challenges in the ocean carbon sink estimate for the Global Carbon Budget. Front. Mar. Sci., 7, 852. https://www.frontiersin.org/article/10.3389/fmars.2020.571720, 2020.

Plazzotta, M. et al. : Land surface cooling induced by sulfate geoengineering constrained by major volcanic eruptions. Geophysical Research Letters, 45, 5663–5671. https://doi.org/10.1029/2018GL077583, 2018.

Schlund, M., Lauer, A., Gentine, P., Sherwood, S. C., and Eyring, V.: Emergent constraints on equilibrium climate sensitivity in CMIP5: do they hold for CMIP6?, Earth Syst. Dynam., 11, 1233–1258, https://doi.org/10.5194/esd-11-1233-2020, 2020.