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

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.