The manuscript presents an application of an ensemble-based physical data assimilation technique to a global biogeochemical ocean model, with a focus on the effect of physical data assimilation on climate-relevant carbon estimates. The manuscript is mostly well written and offers some valuable insights on the effects of physical DA, but the text could be improved in places and several aspects of the DA experiments should be examined further.

general comments

One aspect that is becoming more important in modeling studies but is seemingly ignored in the current version of the manuscript is the reporting of model uncertainty -- even though ensembles are used to generate the results. The authors mention ranges of estimates when reporting results from other studies. However, in their own analysis, the focus is solely on the ensemble mean, without examining the full model ensemble or reporting any uncertainty estimates. It would be beneficial to explore ensemble-based ranges of estimates and compare them to the improvements brought about by data assimilation. This could lead to interesting questions, such as the extent to which data assimilation constrains estimates and whether the estimates improve in areas where they are more constrained. Additionally, figures like Fig. 4 and the seasonal difference plots could be enhanced by including uncertainty estimates, such as the ensemble standard deviation or the interquartile range.

The manuscript emphasizes carbon storage through physical transport, i.e. "upwelling and subduction of DIC, as well as the physical transport of other biogeochemical tracers" (l 60). However, the role of biological carbon fixation and sinking of particulate organic matter seems underexplored. Given that the model includes both slow and fast sinking detritus variables, a more comprehensive examination of these processes would be valuable. Here, it would help to clarify whether the biological carbon export at 200m (l 379 and following) is primarily due to sinking or physical transport. A closer examination or clearer description of the effects of the DA on the biological drivers of carbon export would help to improve the manuscript.

The assimilation of physical observations that only directly updates the physical variables can lead to "shocks" in the biogeochemical variables. It would be valuable to know if the authors observed any negative effects of daily physical updates on the biogeochemical state, such as unexpected phytoplankton blooms (for example, caused by a deepening of the mixed layer transporting nutrients, formerly below the mixed layer, to the surface).

Several aspects of the model setup and data assimilation process could benefit from further explanation or discussion. For instance, the restoration of surface salinity towards climatology may interfere with the assimilation of salinity data. It would be informative to know if the authors have experimented with switching off the nudging when or where salinity data is being assimilated, and how well the salinity climatology aligns with the assimilated data. Similarly, the exclusion of temperature observations from the DA when the model-observation difference exceeds 2.4°C could use a better explanation, as this seems to hinder assimilation where it might be most needed.

To improve readability, particularly for readers less familiar with data assimilation techniques and carbon modeling, brief explanations of key concepts and modeling choices would be beneficial. These would include descriptions of the term used to perturb atmospheric forcing, the role of ensemble inflation, and the rationale behind the choice of γ_DIC and γ_Alk in Equations 4 and 5 (see also my specific comments below). Currently, the manuscript often uses references to other studies to motivate implementation details, and an additional sentence here and there could help the reader to better understand these details without having to go through other papers.

In places, the structure of the manuscript can be improved to enhance clarity and flow. Sections 4.2 and 4.3 are quite lengthy and could be subdivided based on location (Southern Ocean, Atlantic) and the different data products used in the comparisons. Section 3, which contains results from the two ensemble simulations, could be merged with Section 4 to create a more cohesive results section.

Overall the figures look very good and are helpful, I only have a minor suggestion here: it might be more informative to report ASML-OBS instead of ASML-FREE in Figures 1-3. This would provide a clearer picture of the model error following data assimilation. Also, some of the figures, such as Figure 7, have lots of whitespace that could be reduced.

specific comments

L 8: "the mean CO2 uptake increases by 0.18 Pg C yr−1": Add "regionally" here to make it explicit that this increase is not a resulting global estimate.

L 40: "the model mean": It would be helpful to the reader to add a few words about the kind of models that were considered here.

L 65: "DIC" was used before the abbreviation is introduced here (l 59). The earlier sentence actually makes a quite similar point about subduction of DIC and also mentions upwelling, perhaps this could be made more concise.

L 65: "It was shown that assimilating ocean physics at the initial state of a model simulation has a stronger and more positive impact on the modeled carbon cycle than assimilating the BGC initial state": Is this due to the lack of BGC observations mentioned earlier, the importance of physical processes for carbon export, or a large physical model error that cannot be decreased through BGC DA? The next sentence brings up the question of which processes are most important. Maybe a few candidates could be named and briefly discussed here before going into the details of the DA algorithm.

L 70: "continuously assimilating ocean-physics for eleven years": A bit more detail could be useful here as well: What does assimilating ocean physics entail, what observations are being used for the DA here?

L 89: "The model allows for a variable mesh resolution": What is a typical coarse and fine resolution used in the model grid?

L 93: A salinity flux of 0.1m/day? Please describe this better.

L 96: "DIC" is introduced again, a quick search shows 7 introductions of "DIC", also counting captions.

L 117: "observations are weighted by distance": This is not a precise statement that could confuse some readers, express more clearly that the ensemble estimated correlation between a model grid point and an observation is down-weighted using a distance-based metric. Is vertical localization applied as well?

L 124: It would be useful to add equation numbers to all equations, even those that are not referenced in the text, so that they can be more easily referenced in other texts, such as this one.

Eq L 124: Why does a larger ensemble amplify rand? It does not seem that intuitive to have larger perturbations in a larger ensemble.

L 153: "model values are computed as the average of the grid points of the triangle enclosing the observation because the number of observations is fewer than model grid points": Averaging is required to interpolate the model solution at the observation locations, why is this dependent on the number of observations?

L 157: This information about the model grid is missing from Section 2.1 where the model grid is described for the first time. It would also be useful to describe the atmospheric forcing before describing the perturbation to it (Section 2.2.1).

L 171 "the river flux adjustment (...) is applied to the pCO2 products. ...": It is not entirely clear what this means, the focus here is just the CO2 flux associated with the oceans, I presume? The next sentence provides some more information but it seems to imply that the RECCAP2 CO2 flux is not being used for comparison, when previous sentences stated that it was. Some clearer language would be useful here.

L 183: Should the US East Coast be considered subpolar, are all regions characterized by seasonal stratification, or does SPSS stand for something different here? A alternative choice of region names may be suitable and would avoid confusion with the region names in the Southern Ocean.

L 185: Please explain "NAC".

Eq 1 and 2: Is there an easy to communicate motivation for the choice of γ_DIC and γ_Alk ?

Eq 1, 2 and 3: Previously Delta denoted the difference between ASML and FREE, is this still the case here? If so, are the regular terms (e.g. DIC in Eq 1 or the terms in γ_DIC) from the FREE experiment? This should be mentioned in the description.

L 220: Why not mention EN4-OA earlier when the other data products are introduced?

L 250: "at greater depth than 500 m, where the model’s subsurface temperature": The "subsurface" can be deleted here.

L 266: Please explain what a 15%-line is.

L 301: "In the more northern part of the STSS, which we call the STSS+, the CO2 uptake is reduced ...": The text here could be considered misleading because STSS+ is not defined as the northern part of the STSS, but as the part of the STSS with a positive CO2 flux difference. I would prefer a change in formulation that avoids this ambiguity, for example: "The part of the STSS characterized by a positive CO2 flux difference between ASML and FREE, which we call the STSS+ and in which the CO2 uptake is reduced, forms an outer (northern) ring around the STSS region." The same comment applies to STSS+ a few lines below.

L 373: "the effect of the DA is towards increased uptake of CO2 during boreal summer and autumn in ASML (Fig. 6g). This prevents summer outgassing": The increased summer uptake prevents summer outgassing, isn't this just describing the same effect? I would suggest rewording this sentence.

L 411: "(difference of FREE and SOCAT in (Fig. 9a); difference of ASML and SOCAT not shown)": The figure label claims that ASML - SOCAT is shown.

The manuscript describes a study assimilating temperature and salinity observations into a global physics-biogeochemistry ocean model, with the aim of improving the modelled air-sea CO₂ flux. The assimilation brought the model temperature and salinity closer to the assimilated observations, and had a mixed impact on the carbon variables and wider biogeochemistry. The global mean change was small, but could be regionally significant, with the mechanisms explored.

The experiments are well conceived, and the manuscript generally well written and well presented. I just have some comments where aspects could use clarifying or expanding on.

L51: “Data assimilation (DA) has been employed …” This paragraph doesn’t need to be comprehensive, but could be modified and expanded a little to more fully represent the available literature. Valsala and Maksyutov (2010, https://doi.org/10.1111/j.1600-0889.2010.00495.x) ran a global assimilation for 1996-2004; not multidecadal but almost as long as the present study. The paragraph states “In each of these studies, an Adjoint or Green’s Function DA approach is used”, but the Gerber et al. (2009) study referenced used an EnKF – another non-adjoint/Green’s function example is While et al. (2012, https://doi.org/10.1029/2010JC006815) who used a sequential analysis correction scheme to assimilate pCO2. The paragraph opens by talking about “DA studies of the air-sea CO2 flux” in general terms, only semi-clarifying later that it’s focussing on studies which directly assimilated pCO2 data. There have also been other studies which, like the present one, looked at the impact of assimilating other variables on the air-sea CO2 flux, e.g. Ciavatta et al. (2016; https://doi.org/10.1002/2015JC011496) and other papers from that group, and Ford and Barciela (2017, https://doi.org/10.1016/j.rse.2017.03.040).

L65: “It was shown that assimilating ocean physics at the initial state of a model simulation has a stronger and more positive impact on the modeled carbon cycle than assimilating the BGC initial state (Fransner et al., 2020).” In no way diminishing the motivation for this current study – which is undoubtedly important for the reasons stated in Fransner et al. (2020) and others – it could be clarified that this was a single model study and may or may not hold in general. The relative importance of physics vs biogeochemistry initialisation on different variables and time scales remains an open question – see e.g. the discussion in Section 4.4 of Lebehot et al. (2019, https://doi.org/10.1029/2019GB006186) and indeed the ultimate conclusions of this current manuscript.

L67: “Therefore the question arises which processes are most important when altered physics change CO2 fluxes in DA approaches.” I think I understand the meaning of this sentence, but it could be reworded for clarity.

L68: “to improve” – a better wording could be “to aim to improve”?

L75-79: The issues discussed by Park et al. (2018) and others, mentioned later in the manuscript, could be introduced at this point.

L103: “Alkalinity is restored by a fictional surface flux of 10m/yr.” Is there a reference for this, or was it introduced in this study?

L121: “After each assimilation step, corrections are applied to the analysis state to ensure the consistency of model physics.” Can you give an indication of whether these corrections need to be applied regularly or just occasionally?

L148: How is the weekly-resolution SSS used in the daily assimilation?

L153: “model values are computed as the average of the grid points of the triangle enclosing” – what’s done in the vertical?

L171: “For the comparison …” – this paragraph would benefit from a clearer explanation of what adjustments have been made to what products and why, including the model estimates from this study (which presumably have no river carbon inputs?).

L206: “we define the improvement as” – I’m in two minds whether calling the statistic “improvement” is good as it’s clear and intuitive, or if it should be more objective and phrased as “reduction in mean absolute difference” or something equally dry. On balance I’m happy how it is, given it’s clearly defined, but will keep this comment here for completeness. It can be a little odd when positive and negative improvement gets discussed (e.g. L254, L258).

L220: “EN4-OA” – this is a reasonable product to use for comparison, but my understanding is that it includes no observations beyond the assimilated data, just interpolation between data points. So calling it “partly-independent” or “non-assimilated” (L244) may be misleading. Furthermore, it could have been introduced in the previous section.

L228: “in particularly” – in particular

L240: “particularly much” – “particularly”

L241: “Albeit negative side effects of temperature assimilation” – how is it judged that the temperature assimilation is responsible?

Fig. 1 and others: My instinct would be to plot ASML – OBS rather than ASML – FREE. However, I’ve argued about this with coauthors on papers before, and appreciate others strongly feel ASML – OBS is the better choice. So I’m merely flagging it as something to consider, I can see the argument both ways.

L275: “see Appendix Text A1 for further discussion”. Appendix Text A1 is a single short paragraph, I don’t understand why it’s in an appendix. It would be better in the main manuscript, either here or in the Discussion section.

L276: “Thus, it can be assumed that the velocities in the upper part of the ocean are also well represented.” I don’t think you can make this assumption, certainly not for vertical velocities. See e.g. Raghukumar et al. (2015, https://doi.org/10.1016/j.pocean.2015.01.004) and Gasparin et al. (2021, https://doi.org/10.1016/j.ocemod.2021.101768). The data assimilation will continually update the observed variables to better match the observations, without necessarily leading to improvements in non-observed variables such as velocities – although of course that’s the aim. The current study certainly doesn’t seem to have the issues with vertical velocities the above studies do, but without providing assessment of the wider circulation there’s no guarantee it’s improved.

L280: “4 Results” – Section 3, “Effect of DA on ocean physics” is also results. Perhaps Section 4 should be “Effect of DA on ocean biogeochemistry”.

L282: “The ocean absorbs 2.78 Pg C dec⁻¹” – is this the correct unit? From Fig. 4a, it looks to be absorbing 2.78 Pg C yr⁻¹ on average over the decade.

L290: “air-sea CO2 flux (negative: into the ocean)” – if negative’s into the ocean shouldn’t it be “sea-air CO2 flux”?

L301: While STSS+ is broadly the northern bit and STSS- southern, it’s a bit more nuanced than that and that should be reflected in the text.

Fig. 5: Add to the caption that the lines in a and b denote the regions, and the hashing (striping?) denotes STSS+.

L462: “a pCO2-independent proxy for primary production” – I’m not sure “pCO2-independent” is needed here, I don’t quite understand what’s meant.

L480: “as the modelled phytoplankton growth is temperature-dependent” – how sure are you the change is due to the direct temperature dependence rather than the indirect influence of stratification and mixing changes?

L515: “There are two other data assimilating BGC model approaches” – there are many other data assimilating BGC model approaches! Perhaps a more accurate phrasing might be: “We compare here to two other data assimilating BGC model approaches …”

L524: “suggesting that a flawed representation of ocean physics as an argument for the models underestimating the CO2 flux trend is unlikely” – I broadly agree, though it may depend on how well the wider circulation is represented.

L559: “suggests that the physical processes are already well represented in FREE” – again I broadly agree, but there may still be pertinent limitations, especially depending on the time and space scale.

L565: “the adjustment of the ocean’s carbon cycle to changes in the circulation” – true, though it’s also possible that this might itself introduce biases in the carbon chemistry. See e.g. Lebehot et al. (2019, https://doi.org/10.1029/2019GB006186).