Temperature effect on seawater fCO.sub.2 revisited: theoretical basis, uncertainty analysis and implications for parameterising carbonic acid equilibrium constants

The sensitivity of the fugacity of carbon dioxide in seawater (fCO.sub.2) to temperature (denoted Ï, reported in % °C.sup.-1) is critical for the accurate fCO.sub.2 measurements needed to build global carbon budgets and for understanding the drivers of air-sea CO.sub.2 flux variability across the ocean. However, understanding and computing Ï have been restricted to either using empirical functions fitted to experimental data or determining it as an emergent property of a fully resolved marine carbonate system, and these two approaches are not consistent with each other. The lack of a theoretical basis and an uncertainty estimate for Ï has hindered resolving this discrepancy. Here, we develop a new approach for calculating the temperature sensitivity of fCO.sub.2 based on the equations governing the marine carbonate system and the van 't Hoff equation. This shows that, to first order, ln (fCO.sub.2) should be proportional to 1/tK (where t.sub.K is temperature in kelvin), rather than to temperature, as has previously been assumed. This new approach is, to first order, consistent with calculations from a fully resolved marine carbonate system, which we have incorporated into the PyCO2SYS software. Agreement with experimental data is less convincing but remains inconclusive due to the scarcity of direct measurements of Ï, particularly above 25 °C. However, the new approach is consistent with field data, performing better than any other approach for adjusting fCO.sub.2 by up to 10 °C if spatiotemporal variability in its single fitted coefficient is accounted for. The uncertainty in Ï arising from only measurement uncertainty in the main experimental dataset where Ï has been directly measured is in the order of 0.04 % °C.sup.-1, which corresponds to a 0.04 % uncertainty in fCO.sub.2 adjusted by +1 °C. However, spatiotemporal variability in Ï is several times greater than this, so the true uncertainty due to the temperature adjustment in fCO.sub.2 adjusted by +1 °C using the most widely used constant Ï value is around 0.24 %. This can be reduced to around 0.06 % using the new approach proposed here, and this could be further reduced by more measurements. The spatiotemporal variability in Ï arises mostly from the equilibrium constants for CO.sub.2 solubility and carbonic acid dissociation (K1â and K2â), and its magnitude varies significantly depending on which parameterisation is used for K1â and K2â. Seawater fCO.sub.2 can be measured accurately enough that addit