The ms. By Planchat et al. provides a new theoretical framework to analyze the magnitude and spatial distribution of the pre-industrial ocean outgassing. As explained by the authors, the topic is important because it allows to compare and eventually reconcile the magnitude of the anthropogenic ocean sink from models and observations and, in particular, the role of the inter-hemispheric carbon transport in shaping the spatial pattern of the outgassing. The topic fits well within the scope of Biogeosciences, the research is a novel contribution and important contribution to the field and, overall, the approach appears sound and robust. Yet, I have two main comments that I believe need to be addressed (I would say, moderate revisions):

- If I am overall convinced about the new framework, I am less convinced about the quantification that results from its application. This is important as there is a risk that the community will mostly remember the one sentence in the abstract that provides the new quantitative assessment of the pre-industrial ocean outgassing (0.49 PgC yr-1). I would thus suggest toning down this statement to better reflect the uncertainties associated with the quantification. Indeed, as explained by the authors in the main text, the assessment is  broadly consistent (by construction) with the one by Regnier et al. (0.65 – 0.1 for coastal) = 0.55 PgC yr-1, the remaining difference (0.06 PgC yr-1) being the contribution of the Alk imbalance. However, taken the fact that external sources/sinks of Alk (and their fate) are poorly constrained together with a C -Alk budget currently partly inconsistent, the impact of the disequilibrium on the air-sea flux remains highly uncertain in quantitative terms. Probably one of the best example is the uncertain contribution of the river PIC contribution to ocean Alk (as acknowledged by Middelburg, 2020), a flux that has for instance been significantly reduced in the recent work by Liu et al., 2024 (Nature Geoscience, mean value of 2.5 Tmol/yr). I am not suggesting here that the overall budget should be revised with new C-Alk external numbers (as I do acknowledge that this does not question the value of the framework), but I would be less assertive regarding the quantification and the fact that it helps reconciling observations and models, including in the abstract. I further elaborate on this point later in the review.

- I do very much appreciate complex science, but on this occasion, I found that it was sometimes hard to follow the argumentation developed in the paper. I hope that I have properly understood (most of) the proposed framework, but remain concerned about the overall ‘accessibility’ of the research to the broad readership of Biogeosciences. Part of the issue likely stems from choices made at the beginning of the research project, which were then adjusted later on (e.g., choice of external fluxes for the std simulation which are then ‘corrected’ through a series of steps that are not fully transparent). This makes the overall ms. highly complex and I recommend that the authors make an extra effort to improve the clarity of their ms. This is important in the context of my first major comment (readers might focus on key information in the abstract, without getting into the details of the complex ms.). Several of my comments that follow are suggestions in this direction.

Specific comments

- Line 47: “without apparent reasons”. This statement is not true. Reassessments have essentially followed new evidences from the literature.

- Fig.1: define GOBM in figure caption

- Lines 58-60: a few words of explanation regarding the possible underlying reasons for the major discrepancies in global air-sea flux and its spatial distribution across CMIP models would be useful.

- Lines 68-75 The Alk disequilibrium is central to this research but the introduction does not provide much explanation as to why the budget would have been outside equilibrium under pre-industrial times. I suggest elaborating on this aspect briefly.

- Line 79: what is a “practical framework” ?

- Line 88: should it not be (by convention) “positive fluxes are directed into the ocean”

- Line 92-93: This is not true, I believe. The values (at least for C) selected later on in the ms. are for pre-industrial times, including burial.

- Line 98: “When assuming a global Alk inventory equilibrium”. I am not sure that this is the best way to introduce the concept. In reality, the key assumption here is rather that the approach assumed no accumulation of C in the ocean (i.e., C inputs and outputs are balanced), without any assumption regarding Alk. Rather, I understand the Alk constrain as one used to account for the possibility of a time variant ocean C inventory during pre-industrial times.

- Line 105: this is an example where it would be useful to have the comment on line 88 implemented

- Figure 3 caption: theoretical (typo). Why primes for the variables here ?

- Figure 3 caption (line 2): “associated local imbalance”. Imbalance of what ? Check this here and everywhere else in the text

- Figure 3 caption (line 3): disequilibrium in Alk and DIC inventories. I suggest adding “inventories”

- lines 113-118 and Figure 3 caption (line 6): “CO2 concentration, and requires an air-sea carbon flux to restore equilibrium” “… to achieve equilibrium”. I am here confused with the use of “equilibrium”. By virtue of the pre-industrial outgassing, the ocean is not in a state of equilibrium with the atmosphere.  The whole concept is thus hard to grasp (do you mean steady-state ?). And is it straightforward that the ocean as a whole would have reached a state of “equilibrium” with the atmosphere ? Is it an assumption ? See also the following comment.

- lines 118-122: I glanced through both Humphreys and Planchat et al. (2023) and could not derive the proposed “model”. I recommend adding (in SI) more details elaborating on the conceptual model (including any underlying assumption needed to derive the key equations), taken its central role for the ms. In particular, is the Humphrey's approach (chemistry only) applicable to a framework where the ocean physics is explicitly incorporated ?

- line 125: This I suspect implies a framework where the land-atmosphere and ocean-atmosphere were both in steady state (along with a time invariant atmospheric C inventory) during pre-industrial times, yet with a disequilibrium state in the land and ocean C inventories through the land-ocean route (as materialized by the Alk imbalance ?). If correct, I believe that this aspect should then be better presented and discussed (e.g., are there any observational evidences for a time variant C inventory on land compensating the one in the ocean) ?

- line 142: again here a sentence where the notion of an “equilibrium” constrain remains unclear.

- line 150: typo “carbon flux as well as carbon and Alk disequilibria “. Please clarify what you mean by “potential” fluxes.

- line 168: “and assuming an ocean at equilibrium” (fig. B1). Fig B1 rather shows that the air-sea fluxes are in steady-state (in contrast to the C / ALK inventories). I think that this central idea (if correct) is not well introduced in general in the ms. Also why “assuming” ? Is this something that you have imposed in your simulations or is it arising from the model behavior ?

- Line 178: I could not derive eq. 19 in a straightforward way (I understand it, though).

- Line 207: your std simulations clearly rely on not up to date (and very low) river C inputs. What about POC ? I understand that you attempt a correction for this later on, but the whole procedure remains unclear and not sufficiently transparent to me (see comment section 2.3 below).

- Line 239: here you use ‘steady-state’ for the atmosphere, which I believe is clearer (see also comments on lines 113-122).

- section 2.3 and associated figure: I do not follow well the composite simulation strategy and its potential implications.

- Figure 4 caption: CaCO should be CaCO3. Please correct here and elsewhere.

- Figure 4 caption:  I do not understand to what exactly the contribution from local (or regional as in the figure) imbalance is referring to and how these values were constrained (it is not discussed in the text. Or is it lines 298-300 ? But I don’t get the math here). Does the “imbalance” always refer to the Alk:DIC imbalance ? If yes, this has to be specified here and elsewhere.

Lines 323-324: the statement appears obvious to me (is it not textbook knowledge that CaCO3 burial impacts the C budget and air-sea CO2 exchange ?). I am not sure what is precisely meant here.

Line 337: the description of the two disequilibria sensitivity runs induce an extra outgassing (due to a higher CaCO3 burial; I suspect that you should have a negative Alk disequilibrium here ?). These sensitivity runs thus operate in the opposite direction to the one in section 3.2.3 that follows (where the Alk imbalance induces a reduction of the outgassing). I found this really confusing. I suggest elaborating also on a sensitivity run that goes in the same direction as in 3.2.3 or at least - if I understood correctly-, I would stress this aspect more clearly (i.e. the Alk disequilibrium can generate increasing or decreasing air-sea CO2 exchange) – see also comment on lines 377-80 below.

Line 338-39: why counterintuitive ? – Is this not the effect of the carbonate counter pump (more carbonate precipitation and preservation inducing a CO2 source to the atmosphere) ?

Line 353-55: This central idea should appear much earlier in the ms.

Lines 372-275: These are important statements which are not properly reflected in the abstract (see main comment 1 above).

Lines 377-380: These statements are true but potentially misleading as they give the impression that the Alk imbalance will always lead to a reduction in the ocean outgassing. In fact, the opposite effect could also be obtained, if the burial terms are kept as they are, but if the Alk riverine input (see major comment 1 above) is decreased. Then the Alk imbalance (negative) should generate an additional outgassing compared to a budget based on an equilibrated Alk budget. I would reflect on this more transparently.

Line 400: Typo Table YY. Should it not be Fig 6a ?

Line 422: “tend to manifest locally, primarily in the northern hemisphere” Why, especially for the rivinorg run?

Line 430-431: would “local” or “within hemisphere” help clarify the statement ? That is, ….”with a carbon:Alk imbalance stemming from within-hemisphere (or local) riverine and burial fluxes”

Please find my review attached. I apologise to both editor and authors for the delay on the review.