Three-Compartment, Two Parameter, Concentration-Driven Model for Uptake of Excess Atmospheric CO<sub>2</sub> by the Global Ocean

Schwartz, Stephen E.

doi:https://doi.org/10.5194/egusphere-2024-2893

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https://doi.org/10.5194/egusphere-2024-2893

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23 Sep 2024

| 23 Sep 2024

Status: this preprint is open for discussion.

Three-Compartment, Two Parameter, Concentration-Driven Model for Uptake of Excess Atmospheric CO₂ by the Global Ocean

Stephen E. Schwartz

Abstract. This paper develops, applies, and examines a transparent three-compartment model for the amounts of CO₂ (dissolved inorganic carbon, DIC) in the mixed-layer and deep ocean, over the Anthropocene driven by the observed amount of atmospheric CO₂. The model has two independent parameters, the piston velocity v_p characterizing the rate of water exchange between the mixed-layer ocean (ML) and the deep ocean (DO), and the atmosphere-ocean deposition velocity for low- to intermediate-solubility gases k_am. The net uptake of CO₂ into the ocean is only weakly dependent on k_am, so the net uptake rate depends almost solely on v_p. This piston velocity is determined from the measured the rate of uptake of heat by the global ocean from the 1960's to the present as 7.5 ± 2.2 m yr^‑1, 1-σ. The resultant modeled net uptake flux of anthropogenic atmospheric CO₂ by the global ocean at year 2022 is 2.84 ± 0.6 Pg yr^-1; the corresponding net transfer coefficient, the net anthropogenic uptake flux divided by the stock of excess atmospheric CO₂ is 0.010 ± 0.002 yr^-1. This net transfer coefficient appears to decrease slightly (~ 17 %) over the Anthropocene, attributed to the decrease of the equilibrium solubility of CO₂ (as dissolved inorganic carbon) in seawater due to the uptake of additional CO₂ over this period and to increasing slight return flux from the DO to the ML. Modeled DIC in the global ocean and net atmosphere-ocean fluxes compare well with observations and with current carbon cycle models (both concentration-driven and emissions-driven). Uptake of anthropogenic carbon by the terrestrial biosphere is calculated as the difference between emissions and the sum of increases in atmospheric and ocean stocks. The model is examined for radiocarbon over the industrial era, over the period during which radiocarbon was influenced by emissions of ¹⁴C-free CO₂ mainly from fossil fuel combustion, and the period dominated by ¹⁴C emissions from atmospheric weapons testing. A variant of the model with only two compartments and one parameter, v_p, treating the atmosphere and the mixed-layer ocean as a single compartment in equilibrium, performs essentially as well as the three-compartment, two-parameter model. Although the concentration-driven model developed here cannot be used prognostically (to assess model skill in replicating atmospheric CO₂ over the industrial period or to examine response to changes in emissions), it is useful diagnostically to examine the disposition of excess carbon into the pertinent global compartments as a function of time over the Anthropocene and for confidently representing ocean uptake of excess CO₂ in emissions-driven models.

Received: 16 Sep 2024 – Discussion started: 23 Sep 2024

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RC1:
'Comment on egusphere-2024-2893', Anonymous Referee #1, 04 Nov 2024 reply
I read the manuscript (MS) by Stephen E. Schwartz with great interest. The manuscript details a carbon cycle model that aims to quantify the partitioning of anthropogenic CO₂ emissions between the terrestrial biosphere and the ocean. Unlike other models, the one proposed here does not rely on existing parameterizations but rather strives for a data-first approach. For example, the transfer velocity of CO₂ from the atmosphere to the ocean uses heat transfer data as a proxy, rather than approximations of difficult-to-obtain CO₂ concentration measurements. Being more of a paleo person, I find this approach elegant and intuitive. I also applaud the author for demonstrating that simple box models are fully capable of resolving many aspects of planetary carbon chemistry.
The model is described carefully and in exhaustive detail, which brings me to the main points I struggled with in the manuscript. With the exception of the Discussion and Conclusions sections, the language used throughout the manuscript is extremely technical, full of acronyms, and rather difficult to read. While a detailed model description is both welcome and necessary, the manuscript in its current form is unlikely to appeal to a broader audience. I suggest splitting the manuscript into two parts: a pure model description submitted to Geoscientific Model Development and a shortened, less technical submission focusing on model results, perhaps in Biogeosciences. This strategy would likely increase the appeal and reach of the manuscript.
Further, I understand that the manuscript provides an updated estimate for CO₂ uptake by the oceans, but I remain unclear on how uncertainties in the underlying data (e.g., heat transfer, carbon stocks, and emission data) affect the results. This may already be addressed in the manuscript, but a straightforward discussion of these uncertainties, presented in plain language in the discussion section, would be very welcome.
Lastly, I wonder whether changes in carbonate saturation depth can truly be ignored (see, e.g., Boudreau et al. 2010). While these changes may be small on the timescale considered here, they are likely to affect ocean pH in the coming decades.
Specific Comments

Figure 2: Are the confidence intervals in this figure the CI for the regression, or for the prediction? What confidence level is depicted (1, 2, or 3σ?) Also, since these are linear regressions, maybe add the regression stats (r², p-value)?

339: differentiate between the dissolved concentration and atmospheric by using pCO₂ and [CO₂]_aq ?

Boudreau, Bernard P., Jack J. Middelburg, Andreas F. Hofmann, and Filip J. R. Meysman. 2010. “Ongoing Transients in Carbonate Compensation.” Global Biogeochemical Cycles 24. doi:10.1029/2009gb003654.

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Citation: https://doi.org/10.5194/egusphere-2024-2893-RC1
- AC1: 'Reply on RC1', Stephen E. Schwartz, 18 Nov 2024 reply
  
  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.
  
  Reply
  
  Citation: https://doi.org/10.5194/egusphere-2024-2893-AC1
CC1:
'Comment on egusphere-2024-2893', Peter Köhler, 11 Nov 2024 reply

Since I am interested in simple models myself I found this approach with a few equations at least interesting and I had a closer look at this draft, which led me to make the following 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).

2. Ocean heat content of the upper 300m 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 100m 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 100m (from >450 ZJ in the total ocean, ->about 1/3 in top 100m). So this heat content exercise seems to be at odd with the data.

3. 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.

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Citation: https://doi.org/10.5194/egusphere-2024-2893-CC1
- AC2:
  'Reply on CC1', Stephen E. Schwartz, 03 Dec 2024 reply
  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.
  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.
  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.
  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.
  
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  Citation: https://doi.org/10.5194/egusphere-2024-2893-AC2

Stephen E. Schwartz

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Short summary

The net uptake coefficient of anthropogenic CO₂ by the global ocean (net uptake flux divided by excess atmospheric CO₂ stock above preindustrial) calculated with a simple, transparent, three-compartment concentration-driven model with two independent parameters is determined to be 0.010 ± 0.002 yr^-1 (net uptake flux at year 2022 2.84 ± 0.6 Pg yr^-1). This result compares well with observations and with much more complex carbon cycle models.


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Three-Compartment, Two Parameter, Concentration-Driven Model for Uptake of Excess Atmospheric CO2 by the Global Ocean

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Three-Compartment, Two Parameter, Concentration-Driven Model for Uptake of Excess Atmospheric CO₂ by the Global Ocean