Stephen E. Schwartz

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 oceans over the Anthropocene, driven by the observed amount of atmospheric CO₂. The model has two independent parameters, a piston velocity v_p characterizing the rate of water exchange between the mixed-layer ocean (ML) and the deep ocean (DO), and an 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 rate of uptake of heat by the global ocean from the 1960s to the present as 7.5 ± 2.2 m yr⁻¹, 1σ. The resultant modeled net uptake flux of anthropogenic atmospheric CO₂ by the global ocean in the year 2022 is 2.84 ± 0.6 Pg yr⁻¹, and 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; this decrease is attributed to the decrease in the equilibrium solubility of CO₂ (as dissolved inorganic carbon) in seawater due to the uptake of additional CO₂ over this period and slightly increasing 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, used to calculate 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, compares well with available measurements of ocean radiocarbon and with other models. A variant of the model with only two compartments and a single 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), the model is useful diagnostically to examine the disposition of excess carbon into pertinent global compartments as a function of time over the Anthropocene. More importantly, the model and the parameters developed here can be used with confidence to represent ocean uptake of excess CO₂ in emissions-driven models.

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.

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.

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.

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.

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.

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.

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.

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.

The rate at which atmospheric carbon dioxide (CO₂) would decrease in response to a decrease in anthropogenic emissions or cessation (net zero emissions) is of great scientific and societal interest. Such a decrease in atmospheric CO₂ on the centennial scale would be due essentially entirely to transfer of carbon into the world ocean (WO) and the terrestrial biosphere (TB), which are sink compartments on this timescale. The rate of decrease in excess atmospheric CO₂ and the apportionment of this decrease into the two sink compartments have been examined in two prior model intercomparison studies, subsequent either to a pulse emission of CO₂ or to abrupt cessation of anthropogenic CO₂ emissions. The present study examines and quantifies inter-model anticorrelation in those studies in the net rate and extent of uptake of CO₂ into the two sink compartments. Specifically, in each study the time-dependent coefficients characterizing the net transfer rate into the two sink compartments (evaluated as the net transfer rate normalized to excess atmospheric CO₂ above the pre-pulse amount for the pulse experiment or as the net transfer rate divided by excess atmospheric CO₂ above the preindustrial amount for the abrupt cessation experiment) were found to exhibit strong anticorrelation across the participating models. That is, models for which the normalized rate of uptake into the WO was high exhibited low uptake rate into the TB and vice versa. This anticorrelation in net transfer rate results in anticorrelation in net uptake extent into the two compartments that is substantially greater than would be expected simply from competition for excess CO₂ between the two sink compartments. This anticorrelation, which is manifested in diminished inter-model diversity, can lead to artificially enhanced confidence in current understanding of the consequences of potential future reductions of CO₂ emissions and in the global warming potentials of non-CO₂ greenhouse gases relative to that of CO₂.