Extended Data Fig. 1: Preindustrial Atlantic \(\left[ {{{{\mathrm{CO}}}}_3^{2 - }} \right]_{{{{\mathrm{as}}}}}\) vs DIC_as as shown in Fig. 1.

Data are from ref. ¹⁵, based on the calculation method from ref. ¹⁶. Black curve represents the best fit of the data. Simply put, when a water mass sequesters more atmospheric CO₂, it has lower \(\left[ {{{{\mathrm{CO}}}}_3^{2 - }} \right]_{{{{\mathrm{as}}}}}\) and higher DIC_as, and vice versa. For example, adding CO₂ into a package of water would increase its DIC_as. At the same time, because the added CO₂ would convert some \(\left[ {{{{\mathrm{CO}}}}_3^{2 - }} \right]_{{{{\mathrm{as}}}}}\) into bicarbonate, its \(\left[ {{{{\mathrm{CO}}}}_3^{2 - }} \right]_{{{{\mathrm{as}}}}}\) should decrease. Thus, the negative \(\left[ {{{{\mathrm{CO}}}}_3^{2 - }} \right]_{{{{\mathrm{as}}}}}\)–DIC_as correlation is exactly expected from the CO₂ system theory³⁰. See ref. ¹⁶ and Methods for detailed discussions.