Comments on Hybrid model estimate of the ocean carbon sink from1959 to 2022:

I read this with great interest, as the author brings together a number of essential points regarding the ways models are used with estimating marine carbon cycle fluxes and budgets. The critical point here is that GOBMs play a central role in providing “estimate” of ocean carbon uptake, but they suffer from some known limitations and caveats which may result in biases.  In my opinion this “letter manuscript” warrants concerted attention and further review, in my opinion it is very close to meeting the journal standard for publication.

Overall the scientific concept of using coupled models in conjunction with GOBMs is a very constructive recommendation, and in fact at the very least this approach deserves inclusion in the GCP-type analyses of marine carbon uptake.  I think it would be greatly beneficial if the author could consider whether ensemble simulations with ESMs could provide a means to get a more useful ESM-derived component of this story, as the ensemble-mean approach offers the real forced-trend (assuming enough members). 

On a related point, there is the issue of volcanoes, and the question of whether one risks double-counting something like Pinatubo by combining ESMs and GOBMs in the way described in the manuscript. Connecting this to my previous point, if I understand correctly Faye et al. (2023; GBC) ran a new ensemble with CESM1 without volcanoes, so I’m wondering if using an ensemble mean from such a set of runs and then combining this ensemble mean output with GOBM output as described in the manuscript would provide a way to avoid double-counting? 

Another point that should be addressed is seasonality and missing mechanisms. Both GOBMs and ESMs suffer from deficiencies in representing the seasonal cycle in pCO2, and as has been pointed out by Fassbender et al. (2022; GBC) there is a rectified effect of seasonal pCO2 variations onto the mean state. To the extent that biases in the seasonal cycle of pCO2 should thereby have an impact on the rate of uptake of CO2, this cannot be remedied by a hybrid model.

With this last point (seasonality) it would be good if the author could state in a sentence or two that there are fundamental “missing processes” in current models that won’t be fixed by building a hybrid product, that require further community attention.

A more minor point with Line 19: Didn’t Ernst Maier-Reimer investigate anthropogenic carbon uptake before Sarmiento (1992)?

But overall I think that this is a very valuable discussion, it’s very well-reasoned and represents a dose of constructive reflection, and should also motivate some careful thinking about how to improve the way in which models are applied to estimate carbon uptake by the ocean.

This manuscript provides an alternative procedure to estimate the historical ocean carbon sink by combining ocean-only models forced by atmospheric reanalysis and ESMs. This hybrid approach gives a total ocean sink that is close to the estimate of the Global Carbon Budget but with a significantly reduced uncertainty. The manuscript is clear and it would represent a valuable contribution to the effort of improving our estimates of ocean carbon sink. I think the manuscript is close to a form that could be published. I only have two observations regarding the significance of the results and the way they are presented.

The main “selling point” of this analysis is the reduced uncertainty in the hybrid estimate of total ocean carbon sink. However, part of this small uncertainty comes from a good agreement of the interannual variability across GOBMs, as it is highlighted by Fig. 1d. It is briefly mentioned that most models use either JRA55-do or ERA5 atmospehric forcing and that two models that use a different atmospheric forcing show some deviations. I think adding some considerations about this point would improve the manuscript. Maybe provide a count of how many models used each atmospheric forcing to give an idea of the diversity in the choices. Most interannual variability in these simulations will come from the atmospheric forcing and therefore, if there is little variability in the atmospheric forcing, you can’t expect a large interannual variability in the ocean CO2 uptake.

I understand that the procedure to extract the strengths of both classes of models is performed only considering global integrals of the ocean carbon uptake. Since, again, the main added value of this approach is the reduced uncertainty, and considering that regional differences across models in ocean C uptake might cancel each other’s out – i.e. a low Southern Ocean C sink might be compensated by a high N Atlantic C sink and show a similar global uptake of another model with opposite regional characteristics – I think it would be beneficial for the papers to briefly discuss this potential caveat. It is suggested that this approach could also be applied to regional budgets. That would be the place to briefly discuss the possibility of a larger uncertainty across GOBMs in a given region.

Minor corrections:

- Line 83: a verb seems to be missing.

- Line 130: a year is missing after “until”

Review of “Hybrid model estimate of the ocean carbon sink from 1959 to 2022” by Jens Terhaar

General comments

The present study of J. Terhaar proposes an innovative approach to evaluate the ocean carbon sink, by combining modelled results of forced global ocean-biogeochemical models (GOBMs) and fully coupled Earth System Models (ESMs). This approach uses the respective strength of the two modelling frameworks, as atmospheric forcings constrain GOBMs to reproduce the historical observed climate variability while the ESMs full coupling produces long-term trends more consistent with the exchanges existing between compartment (land, ocean, atmosphere).

The author shows that his new “hybrid” estimate stays in accordance with that of the Global Carbon Budget (GCB) initiative over the period 1959-2022, and allows to reduce the uncertainty of the ocean carbon sink by 70%.

However some major points need clarifications from my perspective:

• Mathematical formulation that would support this approach is lacking. How can we add up anomalies from GOBMs with ESMs when we know that there is a strong state dependency of the ocean carbon uptake on the ocean surface alkalinity (at least) ? How biases in coupled models can be combined with GOBMs (much less biased) ? For this question, I would be tempted to focus on models contributions that provide a consistent framework in terms of resolution and model version as a tested bed before extrapolating to the multi-model mean.
• The present text and figures do not allow to evaluate individual ESMs trends and spline fits, in order to compare them with the mean spline fit shown in Fig. 2a.
• The effect of the correction you applied on ESMs circulation and carbonate chemistry following Terhaar et al. (2022) is not properly discussed. I would at least expect a comparison of the results you obtained with your hybrid model in case with and in case without applying this ESM correction. As is, this post-processing appears to me as a “hidden tuning” of your hybrid model. You did not explain what is done on each ESM, and how it affects their trends, so it is rather opaque to the reader and do not allow to isolate (and evaluate) the good results of your hybrid model from that of your correction. Finally you conclude the study by a spectacular reduction of 70% of the uncertainty, but I wonder what part of this reduction may be due to your ESM correction ?
• The capacity of the model to fit with recent GCB estimates of the recent years is not discussed.

Finally, the denomination “hybrid” seems not adequate, as nowodays it is a terminology that people apply to models integrating both AI and process-based model. I would suggest to replace it by “composite” model as it takes benefit of the fully coupled ESMs for the trends and GOBMs for the simulated variability.

Specific comments by section

1. Introduction

L.56-59 In Takano et al. (2023) no specific corrections or adjustments have been done on the ESMs analyzed on their Fig. 4d, showing that the simulated ocean warming aligns with the observed ones. So, I wonder how the bias adjustments you made for the ESMs carbon sink will not indirectly affect these good OHC transient warming trend. Correcting the circulation will change the OHC too: did you try to apply the same correction that you applied on carbon to the OHC in order to evaluate how your correction supposes a different physical mean state ? It sounds contradictory to me to emphasize good properties resulting from circulation (as the OHC trend), but to correct the circulation to get a better carbon sink.

1. Results

L.83 “As there small inter-model differences [...]”: A verb is missing: As there is small... ?

L.90 Please, give more details on this bias adjustment. I understand that you already explained it in a paper (Terhaar et al., 2022), but as your hybrid method depends on this ESM pre-processing, the reader needs to really understand the implications of using it or not. The paragraph in Appendix (L. 199-205) in itself is not sufficient to understand the correction method you used.

L.131-132 “The difference before 2014 is likely due to a bias in the GOBMs [...] that also exists in ESMs but was corrected for”. As nothing shows your correction, the reader must believe you: please illustrate this correction by adding individual trends of ESMs members you used with and without your corrections on Figure 2a, as well as the GOBMs mean trend (extracted from Figure 1c). Moreover you may compute your hybrid estimate without correcting the ESMs and superimpose this result on Figure A1a. These analyses may help to demonstrate that, before 2014, the difference (hybrid – GOBMs) is of the same order that (ESM – corrected ESM), and so attributable to the bias of circulation and carbonate chemistry.

L.135-137 You state that the trend in the ocean carbon sink in the ESMs is too large after 2014 and that half of the difference is explained by the atmospheric CO2 trajectory: please show and explain how did you reach this conclusion. Why a half ? I see only one possibility to assess and quantify it, that would be to force GOBMs with atmospheric forcings extracted from the ESMs atmosphere with the prescribed atmospheric CO2 of SSP1-2.6 (as that would force GOBMs to follow the ESMs CO2 trajectory, and will allow a direct comparison between the two trajectories).

L.137-140 “The other half might be due ...” As is, it seems speculative, please clarify why the spin-up strategy of Huguenin et al. (2022) would help reduce the biased transient warming.

L.193 “Estimates... was used”: were used ?

L.210 “is the defined as”: is defined as ?

L.213 “so garantee”: to garantee ?

L.217 “at the start of the end of the timeseries”: at the starts and the end ?