Ž.Marine Chemistry 70 2000 105–119www.elsevier.nlrlocatermarchemOcean pCO calculated from dissolved inorganic carbon,2alkalinity, and equations for K and K : validation based on12laboratory measurements of CO in gas and seawater at2equilibriumTimothy J. Lueker), Andrew G. Dickson, Charles D. KeelingScripps Institution of Oceanography, UniÕersity of California, San Diego, 341 Endurance Hall, 9500 Gilman DriÕe, La Jolla,CA 92093-0236, USAReceived 15 May 1999; received in revised form 14 December 1999; accepted 15 December 1999AbstractŽ.The partial pressure of carbon dioxide in the ocean’s surface waters, precisely expressed as the fugacity fCO is2Ž. Ž.determined from dissolved inorganic carbon DIC and total alkalinity TA , and the first and second dissociation constantswof carbonic acid, K and K . The original measurements of K and K reported by Mehrbach et al. Mehrbach, C.,12 12Culberson, C.H., Hawley, J.E., Pytkowicz, R.M., 1973. Measurement of the apparent dissociation constants of carbonic acidxin seawater at atmospheric pressure. Limnol. Oceanogr. 18, 897–907 are reformulated to give equations for pK and pK12Ž.pKsylog K as a function of seawater temperature and salinity, consistent with the ‘‘total hydrogen ion’’ concentration10scale:pK s3633.86rTy 61.2172q9.67770lnTy 0.011555 Sq 0.0001152 S21pK s 471.78rTq25.9290y 3.16967lnTy 0.01781 Sq0.0001122 S22By equilibrating solutions of seawater with gas mixtures of known composition, we demonstrate that the above formulationsŽof K and K give calculated fCO values that agree with equilibrated values to 0.07" 0.50% 95% confidence interval,12 2.fCO up to 500 matm . Formulations of K and K based on other studies resulted in calculated fCO values212 2approximately 10% lower than the measurements. Equilibrations at fCO above 500 matm yielded measured fCO values22Ž.higher than calculated values by on average 3.35" 1.22% 95% confidence interval . The cause for the fCO dependence of2the results is not known.The uncertainties in pK and pK were combined with the analytical uncertainties typical of contemporary measure-12ments of DIC and TA to reveal the expected reliability of seawater fCO calculated from these parameters. For example, an2)Corresponding author. Tel.: q1-619-534-4230x19.Ž.E-mail address: [email protected] T.J. Lueker .0304-4203r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž.PII: S0304-4203 00 00022-0()T.J. Lueker et al.r Marine Chemistry 70 2000 105–119106y1 y1ŽŽ..uncertainty of 1.0 mmol kg in DIC and 2 mmol kg in TA 1 standard deviation s.d. will result in uncertainty of theŽ.calculated fCO of 1% or "3.5 matm at 350 matm 1 s.d. . q 2000 Elsevier Science B.V. All rights reserved.2Keywords: equilibrium constants; carbonic acid; fugacity of carbon dioxide; dissolved inorganic carbon; titration alkalinity1. IntroductionThe continuing increase of atmospheric CO re-2sults in a net flux of carbon into the surface oceans.Quantifying this oceanic sink for CO is vital to our2understanding of the carbon cycle, especially forreducing uncertainties in predictions of the impact ofŽfuture CO emissions on climate see, e.g. IPCC,2.1996; Joos, 1996 . The uptake of carbon by theoceans is currently being evaluated from severalŽ.ocean carbon models Orr, 1996 . To calculate thenet air–sea flux of CO , the models must determine2D pCO , the difference between the CO partial22pressure in the atmosphere, and that of the surfaceocean, more precisely expressed as the CO fugacity2Ž.Ž .fCO Weiss, 1974; DOE, 1994 . The fCO is22often computed from a knowledge of seawater tem-perature, salinity, and the variables dissolved inor-Ž. Ž.ganic carbon DIC and total alkalinity TA , in partŽbecause the concentrations of DIC and TA ex-.pressed in moles per kilogram of seawater remainconstant while seawater undergoes changes in tem-Žperature andror pressure see Dyrssen and Sillen,´.1967 . The DIC and TA are related to fCO with the2first and second dissociation constants of carbonicacid in seawater K and K . Accurate knowledge of12K and K in seawater is a prerequisite for compar-12ing the ocean carbon model results to direct mea-surements of CO parameters in the oceans. Accu-2rate values of the constants are also needed forcalculating ocean inventories of anthropogenic car-bon, and other aspects of ocean carbon cycle re-Ž.search see, e.g. Brewer et al., 1997 .Recognizing the importance of obtaining accuratedeterminations of K and K , several researchers12have published measurements of these and relatedŽquantities Hansson, 1972, 1973a,b; Mehrbach, 1973;Mehrbach et al., 1973; Millero, 1979, 1995; Plath etal., 1980; Johansson and Wedborg, 1982; Dicksonand Millero, 1987, 1989; Goyet and Poisson, 1989;.Roy et al., 1993 . In addition, a number of investiga-tors have examined the thermodynamic consistencyof various formulations of the constants with analyti-cal measurements made on seawater samplesŽTakahashi et al., 1976; Dickson, 1977; Millero etal., 1993; Stoll et al., 1993; Clayton et al., 1995; Lee,1996; Lee and Millero, 1995; Lee et al., 1996, 1997;Murphy, 1996; Lueker, 1998; McElligot et al., 1998;.Wanninkhof et al., 1999 . Unfortunately, these manystudies have not resulted in a consensus regardingthe ‘‘best’’ choice of expressions for K and K as12a function of salinity and temperature.Here we demonstrate how well seawater fCO2can be predicted from DIC and TA, and equationsfor K and K based on the measurements of12Ž.Mehrbach et al. 1973 . While more narrow in scopethan some previous studies, our methods apply di-rectly to the calculation of fCO from DIC and TA.2In our laboratory the pCO of seawater was brought2to a known and verified value with compressed gasmixtures calibrated in the standards laboratory ofC.D. Keeling. The CO concentrations in both the2seawater solutions and the gases were determinedwith rigorously established measurement uncertain-ties. The results of the seawater equilibrations sup-port the accuracy of formulations based on the mea-Ž.surements of Mehrbach Mehrbach et al., 1973 .Ž.Previously, Dickson and Millero 1987, 1989 ad-Ž.justed the data of Mehrbach et al. 1973 to providewxinterpolation equations based on the H concen-swstration scale. Here, we have readjusted Mehrbach’soriginal data to the ‘‘total hydrogen ion’’ concentra-tion scale to provide equations compatible with otherdissociation constant formulations for importantŽ.1acid–base species in