Ocean pCO2 calculated from dissolved inorganic carbon, alkalinity, and equations for K1 and K2: validation based on laboratory measurements of CO2 in gas and seawater at equilibrium

The partial pressure of carbon dioxide in the oceanʹs surface waters, precisely expressed as the fugacity (fCO2) is determined from dissolved inorganic carbon (DIC) and total alkalinity (TA), and the first and second dissociation constants of carbonic acid, K1 and K2. The original measurements of K1 and K2 reported by Mehrbach et al. [Mehrbach, C., Culberson, C.H., Hawley, J.E., Pytkowicz, R.M., 1973. Measurement of the apparent dissociation constants of carbonic acid in seawater at atmospheric pressure. Limnol. Oceanogr. 18, 897–907] are reformulated to give equations for pK1 and pK2 (pK=−log10K) as a function of seawater temperature and salinity, consistent with the “total hydrogen ion” concentration scale: pK1=3633.86/T−61.2172+9.67770lnT−0.011555 S+0.0001152 S2 pK2=471.78/T+25.9290−3.16967lnT−0.01781 S+0.0001122 S2By equilibrating solutions of seawater with gas mixtures of known composition, we demonstrate that the above formulations of K1 and K2 give calculated fCO2 values that agree with equilibrated values to 0.07±0.50% (95% confidence interval, fCO2 up to 500 μatm). Formulations of K1 and K2 based on other studies resulted in calculated fCO2 values approximately 10% lower than the measurements. Equilibrations at fCO2 above 500 μatm yielded measured fCO2 values higher than calculated values by on average 3.35±1.22% (95% confidence interval). The cause for the fCO2 dependence of the results is not known. The uncertainties in pK1 and pK2 were combined with the analytical uncertainties typical of contemporary measurements of DIC and TA to reveal the expected reliability of seawater fCO2 calculated from these parameters. For example, an uncertainty of 1.0 μmol kg−1 in DIC and 2 μmol kg−1 in TA (1 standard deviation (s.d.)) will result in uncertainty of the calculated fCO2 of 1% or ±3.5 μatm at 350 μatm (1 s.d.).