Temperature effect on seawater <i>f</i> CO ₂ revisited: theoretical basis, uncertainty analysis and implications for parameterising carbonic acid equilibrium constants

Abstract. The sensitivity of the fugacity of carbon dioxide in seawater (fCO2) to temperature (denoted υ, reported in % °C−1) is critical for the accurate fCO2 measurements needed to build global carbon budgets and for understanding the drivers of air–sea CO2 flux variability across the ocean. However, understanding and computing υ 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 υ has hindered resolving this discrepancy. Here, we develop a new approach for calculating the temperature sensitivity of fCO2 based on the equations governing the marine carbonate system and the van 't Hoff equation. This shows that, to first order, ln (fCO2) should be proportional to 1/tK (where tK 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 υ, particularly above 25 °C. However, the new approach is consistent with field data, performing better than any other approach for adjusting fCO2 by up to 10 °C if spatiotemporal variability in its single fitted coefficient is accounted for. The uncertainty in υ arising from only measurement uncertainty in the main experimental dataset where υ has been directly measured is in the order of 0.04 % °C−1, which corresponds to a 0.04 % uncertainty in fCO2 adjusted by +1 °C. However, spatiotemporal variability in υ is several times greater than this, so the true uncertainty due to the temperature adjustment in fCO2 adjusted by +1 °C using the most widely used constant υ 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 υ arises mostly from the equilibrium constants for CO2 solubility and carbonic acid dissociation (K1∗ and K2∗), and its magnitude varies significantly depending on which parameterisation is used for K1∗ and K2∗. Seawater fCO2 can be measured accurately enough that additional experiments should be able to detect spatiotemporal variability in υ and distinguish between different parameterisations for K1∗ and K2∗. Because the most widely used constant υ was coincidentally measured from seawater with roughly global average υ, our results are unlikely to significantly affect global air–sea CO2 flux budgets, but they may have more important implications for regional budgets and studies that adjust by larger temperature differences.