Timothy J. Lueker, Andrew G. Dickson, Charles D. Keeling

15 December 1999

**Abstract**

The partial pressure of carbon dioxide in the ocean’s surface waters, precisely expressed as the fugacity (ƒCO_{2}) is determined from dissolved inorganic carbon (DIC) and total alkalinity (TA) , and the first and second dissociation constants of carbonic acid (*K*_{1} and *K*_{2}) The original measurements of *K*_{1} and *K*_{2} 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 p*K*_{1} and p*K*_{2} ( p*K* = -log 10 K) as a function of seawater temperature and salinity, consistent with the ‘‘total hydrogen ion’’ concentration scale:

p*K*_{1} = 3633.86/*T* – 61.2172 + 9.67770ln*T* – 0.011555 S + 0.0001152* S*^{2}

p*K*_{2} = 471.78/*T* + 25.9290 – 3.16967ln*T* – 0.01781 S + 0.0001122* S*^{2}

By equilibrating solutions of seawater with gas mixtures of known composition, we demonstrate that the above formulationsof *K*_{1} and *K*_{2} give calculated ƒCO_{2} values that agree with equilibrated values to 0.07 ± 0.50% (95% confidence interval, ƒCO_{2} up to 500 μatm) . Formulations of *K*_{1} and *K*_{2} based on other studies resulted in calculated ƒCO_{2} values approximatel- 10% lower than the measurements. E+uilibrations at ƒCO_{2} above 500 μatm yielded measured ƒCO_{2} values higher than calculated values by on average 3.35 ± 1.22% (95% confidence interval)) The cause for the ƒCO_{2} dependence of the results is not known.

The uncertainties in p*K*_{1} and p*K*_{2} were combined with the analytical uncertainties typical of contemporary measurements of DIC and TA to reveal the expected reliability of seawater ƒCO_{2} 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 ƒCO_{2} of 1% or ±3.5 μatm at 350 μatm (1 s.d.).