I thank the Reviewer for what I consider a highly positive review, and appreciate his/her recognition of the value of what he/she refers to as a “data -first” approach. I greatly appreciate also his/her favorable comment regarding the demonstration in this manuscript that “simple box models are fully capable of resolving many aspects of planetary carbon chemistry.” That indeed was a major intent of this study.

I correct a statement in para 1 of the Review. The Reviewer refers to the use of heat transfer as a proxy for the transfer velocity from the atmosphere to the ocean. Actually the heat transfer proxy is for transfer from the mixed-layer (ML) ocean to the deep ocean. Transfer from the atmosphere to the ML makes use of a deposition velocity (that term is commonly used in the atmospheric chemistry community; the quantity is frequently referred to as piston velocity in the chemical oceanography community) that is more-or-less universal for low- to medium-solubility gases, after accounting for Henry's law solubility and water-side diffusion coefficient. As it turns out, the uptake rate is very insensitive to this deposition velocity, as examined in the manuscript.

In para 2 the Reviewer states that “model is described carefully and in exhaustive detail.” As emphasized in the manuscript, that was the intent, at least the careful part, not the exhaustive part. I would say better “described carefully and in complete detail” The Reviewer goes on to suggest that the manuscript be split into two papers, a pure model description and results. I would respectfully decline the suggestion. I find too often when I read a paper with modeling results, that it refers me to an earlier paper, which in turn refers me to yet an earlier paper. Here it is all together, soup to nuts; assumptions to model to results. I think that this complete presentation is a strength of the paper, not a shortcoming. I want the reader of the results paper to be aware of everything that has gone into the calculations, not to take the author’s word for what he or she did in the companion paper, nor to have to have both papers open at the same time, going back and forth between them.

In para 3 the Reviewer suggests that it is “unclear on how uncertainties in the underlying data (e.g., heat transfer, carbon stocks, and emission data) affect the results.” Actually much of the manuscript is directed to examination of the effects of these uncertainties or, where possible, to their elimination. First, I emphasize that the model is “concentration-driven”. That completely removes the effects of uncertainties of emissions (and for that matter uncertainties in uptake by the terrestrial biosphere) that would be inevitable and dominant in “emissions-driven” models, which are much more favored by the community. Use of the concentration driven approach readily allows examination of the dependence of rate (or better net transfer coefficient) on excess CO₂ (above preindustrial). That examination in turn shows a possible slight dependence of the net uptake rate (expressed as net transfer coefficient) in Fig 7c, that would be wholly indiscernible in examination of anthro stock (Fig. 7a) or net uptake rate itself (Fig 7b). The dependences of net uptake rate and net transfer coefficient on uncertainty in the transfer coefficient between the ML and the deep ocean are thoroughly examined in the manuscript (light blue band in multiple figures). I consider the ability to readily examine the effect of this uncertainty to be a great strength of the approach. The effect of propagated uncertainty in rate of heat uptake from the ML to the deep ocean is explicitly addressed in the discussion at lines 954-955 and is given for year 2022 as ± 20 %, 1-σ.

I note the Reviewer's comment about the carbonate saturation depth; however this would seem of little relevance to the present study. The referenced paper (Beaudreau et al., 2010) focuses on the time scale of the next 2000 years, whereas the present study examines changes over the Anthropocene 1750-2022.

Responses to specific comments

Regarding the linear regressions in Figure 2, as stated in the caption “Confidence intervals (CI) and fitting coefficients, 68 % CI, are shown with the fits.” I would think that these are sufficient measures of the uncertainties associated with the fits.

Regarding terminology in air-sea transfer of CO₂, the language of the manuscript is: “the global- annual-mean gas exchange velocity for water-side mass transport of CO₂, expressed in terms of the concentration of CO₂ (not DIC) on the water side of the interface is about 17 cm hr^-1.” In the development of the transfer coefficient expressed in terms of the atmospheric stock, Eq 3.13, it is necessary to convert from the water-side mass transfer coefficient to the gas-side mass transfer coefficient. This done in terms of concentrations (not gas-side partial pressure) via the concentration-concentration Henry's law solubility coefficient (Eq. 3.11), where the concentration on the gas-side is evaluated from the molar mixing ratio of CO₂ in the atmosphere x_CO2 and the molar concentration of dry air. This approach obviates the need to use the partial-pressure quantity and terminology commonly used in reporting local fluxes. The square bracket notation advocated by the Reviewer for water-side concentration is used in Eqs 3.18 - 3.20.

In conclusion I thank the Reviewer for the positive review. I hope that the responses suffice to allay the Reviewer's concerns over aspects of the presentation.

I thank Dr. Köhler for his Comment, and appreciate his interest in simple models such as that in the submitted manuscript. I respond to his comments seriatim; for convenience I paste in his comments.

1. Schwartz calculates in section 5.1 changes in 14C in the terrestrial biosphere as the residual of the 14C anthropogenic emissions (bomb 14C) and the changes in the three reservoirs atmosphere, mixed layer ocean and deep ocean. I believe this is not correct, since to my understanding the calculations do not consider how the 14C-free anthropogenic (fossil fuel-based) CO2 is entering the ocean. This can in my view only be considered properly, if the model is driven by CO2 emissions (and the related 14C content of the emissions which are different for fossil fuel fluxes or land use changes), and not if the model is driven by CO2 concentrations. I therefore believe the part in the draft on 14C is buggy and should be deleted. You find an example of an emission driven setup including 14C in an older paper of mine (Köhler, 2016, doi:10.1088/1748-9326/11/12/124016).

Response. The Commenter states that to his understanding “the calculations do not consider how the ¹⁴C-free anthropogenic (fossil fuel-based) CO₂ is entering the ocean.” Calculation of uptake of ordinary CO₂ by the global ocean by a concentration-driven model is the principal objective of the study; if treatment of this uptake is flawed, that would be fatal to the manuscript. If, on the other hand, the Commenter accepts the treatment of ordinary CO₂, then it would seem he must accept treatment of ¹⁴CO₂, which is also concentration-driven and which is the same as for ordinary CO₂, but for a very different time profile of atmospheric CO₂, and with the slight exception that the dissolution of ¹⁴CO₂ does not affect the CO₂-bicarbonate-carbonate equilibria, making the treatment even simpler than for ordinary CO₂. Driving the models by observed atmospheric CO₂ or ¹⁴CO₂ stocks eliminates reliance on emissions as well as the fact that these emissions are different for ordinary CO₂ and ¹⁴CO₂.

Evaluation of changes of ¹⁴C in the terrestrial biosphere (TB), to which the Commenter takes particular exception, is based on the conservation requirement that changes in ¹⁴C summed over the atmosphere, ocean, and TB compartments must equal anthropogenic emissions. Hence the change in ¹⁴C in the TB can be confidently evaluated as the difference between emissions and the sum of changes of ¹⁴C in the atmosphere (measured) and the global ocean (modeled here) shown in Fig. 9 of the manuscript.

Regarding the Commenter's statement that “how ¹⁴C-free anthropogenic (fossil fuel-based) CO₂ is entering the ocean can only be considered properly, if the model is driven by CO₂ emissions . . . and not if the model is driven by CO₂ concentrations,” I would respond that the requirement of models is that they represent the processes that are taking place in the real world, here the processes governing net uptake of CO₂ by the ocean. Hence representation of these processes should (must) be the same in an emissions-driven model as in a concentration-driven model. The motivation and great advantage of a concentration-driven model is that such a model allows examination of the treatment of uptake of CO₂ from the atmosphere to the ocean in isolation from other processes. The stock of atmospheric CO₂, which is needed to calculate uptake by the ocean, is confidently obtained from observations, as opposed to being calculated, so that there is no need for modeling net uptake of CO₂ by the terrestrial biosphere and no need for knowledge of anthropogenic emissions. I would hope that the Commenter would recognize and concur in the value of this approach.

1. Ocean heat content of the upper 300 m of the ocean is in von Schuckmann et al. (2023, Figure 8 in doi: 10.5194/essd-15-1675-2023) less than 100 ZJ in the years 1971-2020 from a total of 381 ZJ (about 1/4 in top 300m). The top 100 m should gain about a third of that number (< 33 ZJ or < 10% of the total heat content change), while here Schwartz calculates (Figure 2) from 1960-2023 a rise by ~150 ZJ in the top 100 m (from >450 ZJ in the total ocean, ->about 1/3 in top 100 m). So this heat content exercise seems to be at odd with the data.

Response. The Commenter suggests that the heat content of the upper 100 m should be 1/3 of that of the upper 300 m presented by von Schuckmann et al. (2023), i.e., 1/3 of 75 ZJ or 25 ZJ (The Commenter says 1/3 of 100 ZJ, or 33 ZJ), rather than the 169 ZJ shown in Fig. 2b of the manuscript and used in the calculations. This statement can be rebutted on several grounds.

First, the present analysis rests on the more recent study of heat uptake by the global ocean of Cheng et al. (2024a), of which von Schuckmann is a coauthor, rather than on the paper (von Schuckmann et al., 2023) cited by the Commenter. Von Schuckmann et al. (2023) analyzed data only through year 2020, whereas Cheng et al. (2024a) extended the analysis through year 2023 obtaining total global ocean heat content (OHC) 464 ZJ, well in excess of the 339 ZJ through year 2020, and for the upper 300 m, about 183 ZJ. The increases in total OHC in 2021, 2022, and 2023 were 18, 19, and 18 ZJ, respectively (their Fig. 1a); these subsequent increases account for much of the difference between OHC reported by Cheng et al. (2024a) versus von Schuckmann et al. (2023).

The question also arises what fraction of the secular heat increase of global OHC over the Anthropocene has been taken up in the top 100 m. Both Cheng et al. (2024a) and von Schuckmann et al. (2023) present global OHC by depth intervals, with the top interval, i.e., the interval nearest the surface being 0 to 300 m, for which Cheng et al. (2024a) give the incremental heat content as about 183 ZJ. The Commenter suggests that the heat uptake of the top 100 m should be apportioned equally between the depth intervals 0-100 m, 100-200 m, and 200-300 m, i.e., about a third of the increase of the top 300 m going into the top 100 m, which would only be about 61 ZJ. However, as developed below, such uniform apportioning would seem very unlikely.

Cheng et al. (2024b, of which von Schuckmann is also a coauthor) give the increase in global ocean surface temperature over the period 1960-2023 as 0.8 K. Under the assumption that the incremental temperature of the top 100 m is the same as that at the surface the heat of the top 100 m as the product of Earth surface area 5.10 E14 m², ocean area fraction 0.29, and volumetric heat capacity of seawater 4.11 E06 J m^-3 K^-1, yielding the increase in heat content of the top 100 m over this period is 119 ZJ, or about 65 % of the increment in the top 300 m given by Cheng et al. (2024a) and much more comparable to the value given in Fig. 2b of the present manuscript.

A further source of information is systematic time series of ocean temperature at sub-annual intervals, as a function of depth gridded to 0.1 yr intervals and 10 m vertical resolution, based on systematic measurements along commercial shipping lanes through the HRXBT (high-resolution expendable bathythermograph) project https://www-hrx.ucsd.edu/index.html. An example is shown in Fig. 1 which is based on Sutton and Roemmich (2001), extended, constituting the mean over a section extending north from Auckland NZ, 37˚S, to 30˚S (600 km). Data such as these are highly pertinent to the depth at which the mixed layer, which is tightly coupled thermally to the atmosphere, is decoupled from the deeper ocean. The time-depth profile of temperature T from that data set, Fig 1a, shows the penetration of heat due to the annual cycle of insolation from the surface to a depth of about 100 m; this penetration of the surface temperature is reflected also in the deseasonalized temperature, T_d, Fig 1b. Perhaps most illustrative of the decoupling between the ML and the deep ocean is Fig. 1c, which shows sharp maximum in the gradient of temperature with depth at about 75 to 100 m, the latter taken as the depth of the ML in the present study (75 m has been used by some earlier investigators as noted in the manuscript). Similar conclusions about the penetration of the annual signal can be drawn from other studies in this project (e.g., Wijffels and Meyers, 2004).

Fig. 1, Time-depth profiles of ocean temperature, deseasonalized temperature T_d, and the derivative of T_d with depth, dT_d/dz. Mean over a section extending north from Auckland NZ, 37˚S, to 30˚S (600 km) evaluated from data of Sutton and Roemmich (2001), as extended. Data were provided by Philip Sutton and are available through the Scripps High Resolution XBT program (www-hrx.ucsd.edu)

With respect specifically to the suggestion of the Commenter that the heat uptake in the first 300 m should be apportioned equally between 0-100 m, 100-200 m, and 200-300 m, Fig. 2 shows the temperature and the rate of temperature increase over these three intervals, again evaluated from the data of Sutton and Roemmich (2001, as extended). The slopes of the mean temperatures over the period 1986-2019, show that the apportionment of heat uptake in these three depth bands is 46 %, 31 %, and 23 %, respectively, that is, much greater heat uptake in the top 100 m, consistent with the treatment in the present manuscript that separates the ML from the deep ocean at 100 m.

Fig. 2. Deseasonalized ocean temperatures obtained from measurements between Auckland NZ, 37˚S, to 30˚S (600 km) averaged over the depth bands 0-100 m, 100-200 m, and 200-300 m for the period 1986-2019, together with least-squares fits, with indicated slopes (1-σ uncertainties in each of the slopes about 0.002 K yr^-1).  

In sum, all these considerations lend strong support to the treatment of the uptake of excess heat by the global ocean in the top 100 m over the years 1960-2023 as a model for the uptake of excess CO₂ over the Anthropocene.

1. To my knowledge the term „piston velocity“ is mainly (only?) used in the context of air-sea gas exchange, while it is here used for the exchange between mixed layer ocean and deep ocean.

Response. I accept the Commenter's concern of possible confusion between the term “piston velocity”, as commonly used to denote the rate of transfer of gases between the atmosphere and the mixed layer ocean, and as used in the present manuscript to denote the rate of exchange, per area, of water between the mixed layer and the deep ocean. To avoid such confusion I would use the term “exchange velocity” in lieu of “piston velocity” to denote this exchange rate, but with the same meaning as in the manuscript.

I thank the Commenter for raising the several questions and stimulating my thinking along these lines. I hope that my responses will resolve the Commenter's concerns.

References

Cheng, L., von Schuckmann, K., Miniére, A., Hakuba, M. Z., Purkey, S., Schmidt, G. A., and Pan, Y.: Ocean heat content in 2023, Nat. Rev. Earth Environ., 5, 232–234, https://doi.org/10.1038/s43017-024-00539-9, 2024a.

Cheng, L., Abraham, J., Trenberth, K. E., Boyer, T., Mann, M. E., Zhu, J., Wang, F., Yu, F., Locarnini, R., Fasullo, J., Zheng, F., Li, Y., Zhang, B., Wan, L., Chen, X., Wang, D., Feng, L., Song, X., Liu, Y., Reseghetti, F., Simoncelli, S., Gouretski, V., Chen, G., Mishonov, A., Reagan, J., Von Schuckmann, K., Pan, Y., Tan, Z., Zhu, Y., Wei, W., Li, G., Ren, Q., Cao, L., and Lu, Y.: New record ocean temperatures and related climate indicators in 2023, Adv. Atmos. Sci., 41, 1068–1082, https://doi.org/10.1007/s00376-024-3378-5, 2024b.

Sutton, P. J. H. and Roemmich, D.: Ocean temperature climate off North‐East New Zealand, New Zealand Journal of Marine and Freshwater Research, 35, 553-565, DOI: 10.1080/00288330.2001.9517022, 2001.

von Schuckmann, K., Minière, A., Gues, F., Cuesta-Valero, F. J., Kirchengast, G., Adusumilli, S., Straneo, F., Ablain, M., Allan, R. P., Barker, P. M., Beltrami, H., Blazquez, A., Boyer, T., Cheng, L., Church, J., Desbruyeres, D., Dolman, H., Domingues, C. M., García-García, A., Giglio, D., Gilson, J. E., Gorfer, M., Haimberger, L., Hakuba, M. Z., Hendricks, S., Hosoda, S., Johnson, G. C., Killick, R., King, B., Kolodziejczyk, N., Korosov, A., Krinner, G., Kuusela, M., Landerer, F. W., Langer, M., Lavergne, T., Lawrence, I., Li, Y., Lyman, J., Marti, F., Marzeion, B., Mayer, M., MacDougall, A. H., McDougall, T., Monselesan, D. P., Nitzbon, J., Otosaka, I., Peng, J., Purkey, S., Roemmich, D., Sato, K., Sato, K.,

Wijffels, S. and Meyers, G.: An intersection of oceanic waveguides: Variability in the Indonesian throughflow region, J. Phys. Oceanogr., 34, 1232–1253, 2004. 

I appreciate the Reviewer's characterization of the model developed in the present study as “indeed elegant,” and his/her observation that the model exhibits “surprising fidelity to some of the newer reconstructions as tuned.” (It is not clear whether in using the phrase “as tuned” the Reviewer is referring what he/she characterizes as “newer reconstructions” or to the present model. Here I would simply state that there is no tuning in the present model.)

The Reviewer expresses concern that the present manuscript presents “an update and slight modification to a >50 year old model,” that is, a model with a few global compartments, here the atmosphere, the mixed-layer (ML) ocean and the deep ocean (DO). The strong justification for revisiting such a modeling framework at the present time is the availability of time-dependent measurements of global ocean heat content and its rate of increase, permitting determination of the net heat transfer coefficient from the ML ocean to the deep ocean, and its uncertainty. This heat transfer coefficient serves as a proxy for the transfer coefficient of excess (anthropogenic) dissolved inorganic carbon (DIC) from the ML to the DO, the rate limiting step of uptake of excess atmospheric CO₂ by the DO, one of two long term sinks for this excess CO₂ (the other being the terrestrial biosphere), permitting confident calculation of this net uptake rate and its uncertainty. The present model also takes advantage of improved understanding of mass transfer rates between the atmosphere and of CO₂-DIC chemistry, although this improved understanding is of only secondary importance to the net drawdown of excess atmospheric CO₂ because of near-equilibrium between the atmosphere and the ML, which makes transfer between the ML and the DO the rate controlling step in this uptake.

The reviewer goes on to suggest that the present model “nevertheless seems inferior to alternatives in its treatment of several processes due to its simplicity.” The Reviewer continues “While simplicity is arguably a virtue and this model does have fewer terms than most, my sense is that it would be comparably easy to implement the OCIM [Ocean Circulation Inverse Model].” The Reviewer then advocates use of the OCIM in lieu of the present three-compartment model, stating “I would trust the results from the OCIM considerably more because it allows for plausible 3D circulation.” Here I would observe first that the use of the ocean uptake rate of excess heat from the atmosphere to the ocean automatically accounts for ocean circulations. The open-source version of OCIM, the AWESOME OCIM (John et al., 2020), uses a model grid with 2° latitude by 2° longitude boxes, and 24 vertical levels, i.e., order ~ 10⁵ grid cells. Application of such a model requires a matrix of transfer coefficients, which albeit sparse, involving coupling of a given grid cell only with its neighbors, also consists nonetheless of order ~ 10⁵ elements. Such a model for the present application, examination of uptake of excess CO₂ by the global ocean would be massive overkill. Moreover use of such a model would run totally counter to the philosophy underlying the present study, namely that of all parameters (and their uncertainties) being observationally based. Here the transfer coefficient from the ML to the DO is obtained from the measured rate of uptake of heat by the global ocean; the inverse transfer coefficient is obtained by the requirement of zero net transfer at steady state. In any event, as shown in Fig. 14 of the present manuscript, the central value of the time-dependent anthropogenic stock of DIC in the global ocean obtained with the present model, with its two independent parameters, is virtually identical to the stock calculated by the Ocean Circulation Inverse Model (DeVries, 2022) and to the assessed stock of anthropogenic DIC in the global ocean based on measurement campaigns. Just because a more complex model can be used, that does not mean that a more complex model should be used.

Finally the Reviewer suggests that the present model “should be marketed as a teaching/communications tool rather than a scientific tool.” To this I take great exception. The model developed in this study, a three-compartment, two-parameter, concentration-driven model for the extent, net rate, and net transfer coefficient characterizing uptake of excess atmospheric CO₂ by the global ocean over the Anthropocene, should be viewed as an important, novel contribution to the research literature, in great part because of its simplicity, and in great part also because the parameters are derived entirely from observations without tuning. As well, the model presents ranges of uncertainty in the several quantities that derive from uncertainty in observations, mainly net rate of heat uptake by the global ocean. Yes, the model is simple, and yes it provides insight, but those features of the model should be viewed as a strengths of the model and of a research paper that presents the development the model and the results of its application, not as grounds for “marketing” the model merely as “a teaching/communications tool rather than a scientific tool.”

With regard to the Reviewer's supposition that a simple model such as this may have been used in other applications, such application would not be surprising, given the historical importance of such simple models. The novelty here rests on the transfer coefficients being derived entirely from observations, mainly the rate of uptake of excess heat by the global ocean.

In conclusion, I hope that the recapitulation here of the motivation and approach of this study, and the responses presented here to the concerns raised by the Reviewer will serve to convince the Reviewer of the value of the model developed and applied in this study. I would hope as well that the Reviewer will come to appreciate the importance of the findings obtained in this study, and also the confidence that can be placed in them, toward quantifying the ocean sink of excess atmospheric CO₂ and toward improved understanding of the controlling processes.

References

DeVries, T.: The Ocean Carbon Cycle, Annu. Rev. Env. Resour., 47, 317–341, https://www.annualreviews.org/content/journals/10.1146/annurev-environ-120920 111307, 2022.

John, S.G., Liang, H., Weber, T., DeVries, T., Primeau, F., Moore, K., Holzer, M., Mahowald, N., Gardner, W., Mishonov, A. and Richardson, M.J. AWESOME OCIM: A simple, flexible, and powerful tool for modeling elemental cycling in the oceans. Chem. Geol., 533, 119403. https://www.sciencedirect.com/science/article/pii/S0009254119305327, 2020.

I appreciate the review and the overall assessment. I expect to be able to accommodate most of the Reviewer’s suggestions in the revision.

In his review Dr. Crisp accurately summarizes the advantages of this study. I am gratified by his statement, “The primary advantages of the model described here are its relative simplicity and associated mechanistic transparency.” That statement indeed captures the intent of the study. The review rather accurately states the approach of the study: “The exchange of carbon between these global reservoirs is determined by diffusion coefficients, directly traceable to available, time-dependent observations of the atmospheric CO₂ concentration and ocean heat transport.” I think Dr. Crisp meant to use the term “transfer coefficients,” which are the quantities I adduced and used in the paper, rather than “diffusion coefficients.” Dr. Crisp continues, “Because measurements of stocks and fluxes of carbon between the ML and DO are not adequate, the piston velocity is derived from the rate of heat uptake by the global ocean over the past 50 years.” Here I would demur slightly; the approach of the study was to use measured geophysical quantities that are independent of the carbon system, of which the rate of heat uptake by the global ocean is key, rather than to calculate stocks and fluxes based on measurements in the carbon system, adequate or not.

From a philosophical perspective I would take some exception to the Reviewer's statement “Changes in carbon stocks predicted by this model are then validated against global totals derived from global ocean biogeochemistry models (GOBMs) by the Global Carbon Project. First, the present model is not “predictive; it is diagnostic;” thus better “changes in carbon stocks calculated with this model . . .” Second, in general, I would say, models are not “validated, except, perhaps, for their use in regulatory contexts; they are evaluated , by comparison with observations. Third, the results of the present model are not evaluated (or “validated”) in this study by comparison with the calculated time series obtained with other, more complex, models; they are simply compared. The key comparison with GOBMs in the paper is Figure 13b. Given the inter-model spread in the time-dependent net atmosphere-ocean transfer coefficients obtained from the several GOBMs, I would certainly not use the results of those models as a standard for validating, or evaluating, the results of the present model (or any model). Rather I would stay with the neutral language of the paper (line 800) “. . . the atmosphere-ocean flux calculated with the 3C-CDM agrees closely with the results of most of the models, with the uncertainty range of the 3C-CDM, about ± 20 % 1 SD, essentially overlapping the data reported by the several models contributing to the GOBM protocol.” To this I would add, as shown in Fig. 14, that the model results compare well with limited available measurements.

The Reviewer calls attention (positively) to the indication from the present model results (he cites Fig. 4 for the net transfer coefficient from the MD to the DO, but perhaps more saliently in Fig. 7b for the net transfer coefficient from the atmosphere to the ocean) of decrease of about 17% in transfer coefficient over the Anthropocene. This is an important finding coming out of this study, noted in the Abstract and the Discussion. The ability to tease out such a small change relies on examination of the intensive quantity, the net transfer coefficient; such a small change would not be evident in examination of the extensive quantity net transfer rate and even more so in examination of time-dependent extent of uptake. Certainly it would seem essential to plot results of future studies as net transfer coefficient in order to discern such slight changes. As the Reviewer accurately notes, I was loath to ascribe a single reason for such decrease; the model indicates decrease in equilibrium solubility of CO₂ (as DIC) and also increased return flux from the DO to the ML as contributing factors.

Finally, the Reviewer notes that “. . . any CHANGE in ocean dynamics associated with climate change that alters the net ML to DO transport of carbon could have significant consequences for the efficiency of the ocean sink,” and goes on to state, “The author is strongly encouraged to reinforce this point.” While I concur with the statement of the Reviewer, and accept his suggestion that I call attention to this, I would have to add to that, that such a change would rest upon a change in the heat transport coefficient that drives the net uptake of CO₂. Much more important than the implications of such a change on CO₂ uptake would be the implications of such change in heat transport in Earth's climate system itself, to which the effect on net transport of CO₂ from the ML to the DO would be a mere codicil.

RESPONSES TO MINOR POINTS

Line 12. Noted.

Line 140, 145. All rolled into net deforestation/afforestation; will be clarified. The minor roles of weathering and sedimentation on the centennial time scale will likewise be noted.

Line 153. Will be clarified.

Line 180. Does not seem to require justification. The treatment does not rest on the near equality between loss of carbon from the TB by LUC and uptake by the TB due to enhanced atmospheric CO₂ is a happenstance that does not affect the reasoning. No change.

Line 689-670.The subject of the para is the increase, during pre-bomb Anthropocene, of ¹⁴C stocks in atmosphere, ML, and DO and the complementary decrease in stock in the TB, required for the closed system examined here. Prior to emissions of ¹⁴C-free CO₂ during the pre-bomb Anthropocene, the atmosphere and the TB were in near isotopic equilibrium, i.e., having the same Δ¹⁴C. Introduction of ¹⁴C-free CO₂ into the atmosphere associated with fossil fuel combustion led to a decrease of Δ¹⁴C of atmospheric CO₂, perturbing the dynamic isotopic equilibrium between the two compartments. The tendency toward restoration of the dynamic isotopic equilibrium between the two compartments in response to a perturbation would require adjustment of the stocks of ¹⁴C (and ¹²C) in the two compartments in the direction of achieving the same Δ¹⁴C in each compartment; this would occur mainly by net transfer of ¹⁴C from the TB to the atmosphere, with the resultant decrease in ¹⁴C stock in the TB prior to 1950 shown in Fig. 9. Also, net transfer of ¹⁴C from the TB to the atmosphere as a component of LUC emissions (total C emissions 0 - 1.2 Pg yr^-1 during this period) would be dwarfed by net transfer of ¹⁴C associated with total C exchange between the TB and atmosphere (GPP), increasing from roughly 120 Pg yr^-1 to perhaps 180 Pg yr^-1 over this period.

Lines 904-905. I suggest that the Reviewer may be a bit optimistic in the accuracy of satellite-based measurements of net carbon uptake by the TB. As an example I cite a recent survey of above-ground carbon biomass (El Masri and Xiao, 2025) as calculated from five satellite-based global data sets, which yielded a 25% standard error in the global quantity, with much greater variation when examined as a function of latitude. I would welcome the opportunity to chat offline with the Reviewer regarding his statement on recent space-based estimates of net atmosphere to TB carbon flux. Pending that I leave the statement unchanged.

Line 902. The purpose of the paragraph starting here is to set the scene for the contrast between the conventional approach using emissions-driven process models with large numbers of compartments and processes and parameters and the approach taken in this study of a simple model with three compartments and two independent, observationally constrained parameters. The reviewer suggests reorganizing the paragraph. I think the contrast is better as it is. No change.

Line 954-959. I appreciate the Reviewer's characterization of the two sentences as “perhaps the most profound scientific conclusion presented in this paper,” and his desire to improve the impact of the paragraph. On re-reading the paragraph I think the impact comes through loud and clear. No change.

Final remark about readability. I will take the opportunity in revising the paper to look for where commas might improve the readability.

Again, I thank the Reviewer for his attention to the manuscript, its objectives, its findings, its conclusions.

Reference

El Masri, B., & Xiao, J. (2025). Comparison of global aboveground biomass estimates from satellite observations and dynamic global vegetation models. J. Geophys. Res.: Biogeosci, 130, e2024JG008305. https://doi.org/10.1029/2024JG008305