• analytical theory;
  • ice age carbon cycle;
  • numerical model;
  • ocean biogeochemistry;
  • ocean ventilation

[1] A simple analytical framework is developed relating the atmospheric partial pressure of CO2 to the globally-averaged concentrations of respired carbon (equation image) and dissolved carbonate (equation image) in the ocean. Assuming that the inventory of carbon is conserved in the ocean-atmosphere system (i.e. no seawater-sediment interactions), the resulting formula of equation image = −0.0053Δ equation image + 0.0034Δ equation image suggests that atmospheric pCO2 would decrease by 5.3% and increase by 3.4% when equation image and equation image increase by 10 μmol kg−1, respectively. Using this analytical framework along with a 3-D global ocean biogeochemistry model, we show that the response of atmospheric pCO2 to changes in ocean circulation is rather modest because ∼30% of the change in atmospheric pCO2 caused by the accumulation of respired carbon is countered by a concomitant accumulation of dissolved carbonate in deep waters. Among the suite of circulation models examined here, the largest reduction in atmospheric pCO2 of 44–88 ppm occurs in a model where reduced overturning rates of both southern and northern sourced deep waters result in a four-fold increase in the Southern Ocean deep water ventilation age. On the other hand, when the ventilation rate of the southern-sourced water decreases, but the overturning rate of North Atlantic Deep Water increases, the resulting decrease in atmospheric pCO2 is only 14–34 ppm. The large uncertainty ranges in atmospheric pCO2 arise from uncertainty in how surface productivity responds to circulation change. Although the uncertainty is large, this study suggests that a synchronously reduced rate for the deep water formation in both hemispheres could lead to the large glacial reduction in atmospheric pCO2 of 80–100 ppm.