Temperature effect on seawater ƒCO₂ revisited: theoretical basis, uncertainty analysis, and implications for parameterising carbonic acid equilibrium constants

Abstract. The sensitivity of the fugacity of carbon dioxide in seawater (ƒCO₂) to temperature (denoted υ, reported in % °C^–1) is critical for the accurate ƒCO₂ measurements needed to build global carbon budgets and for understanding the drivers of air-sea CO₂ flux variability across the global ocean. Yet understanding and computing this property have until now been restricted to either using purely 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 to calculating the temperature sensitivity of ƒCO₂ based on the equations governing the marine carbonate system and the van ‘t Hoff equation. This shows that ln(ƒCO₂) should be proportional to 1/t_K (where t_K is temperature in K) to first order, rather than to temperature as has previously been assumed. Our new approach is consistent with experimental data, although more measurements are needed to confirm this, particularly at temperatures above 25 °C. It is consistent with field data, performing better than any other approach for adjusting ƒCO₂ data by up to 10 °C. It is also consistent with calculations from a fully resolved marine carbonate system, which we have incorporated into the PyCO2SYS software. The uncertainty in υ arising from only measurement uncertainty in the scarce experimental data with which υ has been directly measured is on the order of 0.04 % °C^–1, which corresponds to a 0.04 % uncertainty in ƒCO₂ 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 ƒCO₂ adjusted by +1 °C using the most widely used constant υ value is around 0.24 %. This can be reduced to around 0.06 % by using the new approach proposed here, and this could be further reduced with more measurements. The spatiotemporal variability in υ arises 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 ƒCO₂ can be measured accurately enough that additional experiments should be able to detect spatiotemporal variability in υ and distinguish between the 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 may have more important implications for regional budgets and studies that adjust by larger temperature differences.