Properties of the ocean as a function of time. (a) After 4.5 Gyr, 1 TO has entered the mantle, ultimately leaving 1 TO on the surface. (b) The concentration of CO₂ in the oceans tracks closely with the atmospheric CO₂ inventory, following Henry’s law. (c) Prior to equilibration, the pH initially spikes because the initial concentrations of carbonate and bicarbonate in the calcite-saturated oceans are also very high. Following equilibration, the pH gradually becomes more alkaline as the abundance of CO₂ in the atmosphere and ocean gradually decreases. (d) The total DIC at the ocean surface, which includes aqueous CO₂, carbonate, and bicarbonate, tracks closely with the atmospheric CO₂ budget. On all plots, dots represent measurements of PIE (4.5 Gyr) properties with uncertainties.