Dissociation Constants for Carbonic Acid Determined from Field

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Deep-Sea Research I 49 (2002) 1705–1723

Dissociation constants for carbonic acid determined from ﬁeld measurements

Frank J. Milleroa,*, Denis Pierrota, Kitack Leea,b, Rik Wanninkhofb, Richard Feelyc, Christopher L. Sabinec, Robert M. Keyd, Taro Takahashie a Rosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149-1098, USA b NOAA Atlantic Oceanographic and Meteorological Laboratory, 4301 Rickenbacker Cswy, Miami, FL 33149, USA c NOAA Paciﬁc Marine and Environmental Laboratory, 7600 San Point Way NE, Seattle, WA 98115, USA d Atmospheric and Ocean Science Program, Princeton University, Princeton, NJ 08544, USA e Lamont-Doherty Earth Observatory, Columbia University, Palisades, NY 10964-8000, USA

Received 20 April 2001; received in revised form 1 April 2002; accepted 24 June 2002

Abstract

A number of workers have recently shown that the thermodynamic constants for the dissociation of carbonic acid in seawater of Mehrbach et al. are more reliable than measurements made on artificial seawater. These studies have largely been confined to looking at the internal consistency of measurements of total alkalinity (TA), total inorganic carbon dioxide (TCO2) and the fugacity of carbon dioxide (fCO2). In this paper, we have examined the field measurements of pH, fCO2, TCO2 and TA on surface and deep waters from the Atlantic, Indian, Southern and Pacific oceans to determine the pK1; pK2 and pK2 pK1: These calculations are possible due to the high precision and accuracy of the field measurements. The values of pK2 and pK2 pK1 over a wide range of temperatures (1.6–381C) are in good agreement (within 70.005) with the results of Mehrbach et al. The measured values of pK1 at 41C and 201C are in reasonable agreement (within 70.01) with all the constants determined in laboratory studies. These results indicate, as suggested by internal consistency tests, that the directly measured values of pK1þpK2 of Mehrbach et al. on real seawater are more reliable than the values determined for artificial seawater. It also indicates that the large differences of pK2 pK1 (0.05 at 201C) in real and artificial seawater determined by different investigators are mainly due to differences in pK2: These differences may be related to the interactions of boric acid with the carbonate ion. The values of pK2 pK1 determined from the laboratory measurements of Lee et al. and Lueker et al. at low fCO2 agree with the field-derived data to 70.016 from 51Cto251C. The values of pK2 pK1 decrease as the fCO2 or TCO2 increases. This effect is largely related to changes in the pK2 as a function of fCO2 or TCO2. The values of fCO2 calculated from an input of TA and TCO2, which require reliable values of pK2 pK1; also vary with fCO2. The field data at 201C has been used to determine the effect of changes of TCO2 on pK2 giving an empirical relationship:

TCO2 4 pK2 ¼ pK2 1:6 Â 10 ðTCO2 2050Þ 1 which is valid at TCO2>2050 mmol kg . This assumes that the other dissociation constants such as KB for boric acid are not affected by changes in TCO2. The slope is in reasonable agreement with the laboratory studies of Lee et al. and 4 4 Lueker et al. (1.2 Â 10 to 1.9 Â 10 ). This equation eliminates the dependence of the calculated fCO2 on the level

*Corresponding author. Tel.: +1-305-361-4706; fax: +1-305-361-4144. E-mail addresses: [email protected] (F.J. Millero).

of fCO2 or TCO2 in ocean waters (s ¼ 29:7 matm in fCO2). An input of pH and TCO2 yields values of fCO2 and TA that 1 are in good agreement with the measured values (722.3 matm in fCO2 and 74.3 mmol kg in TA). The cause of the decrease in pK2 at high fCO2 is presently unknown. The observed inconsistencies between the measured and computed 1 fCO2 values may be accounted for by adding the effect of organic acid (B8 mmol kg ) to the interpretation of the TA. Further studies are needed to elucidate the chemical reactions responsible for this effect. r 2002 Elsevier Science Ltd. All rights reserved.

þ þ 2 1. Introduction ½H SWS ¼½H Ff1þ½SO4 T=KHSO4 þ½F T=KHFg

(KHSO4 and KHF are the dissociation constants for The carbon dioxide system in the oceans can be HSO4 and HF, respectively, and the subscripts F characterized using any two of the four measur- and T represent the concentration of the free and able parameters, pH, total alkalinity (TA), fuga- total proton). city of carbon dioxide (fCO2) and the total The stoichiometric dissociation constants pK1 inorganic carbon dioxide (TCO2) providing that and pK2 have been determined by a number of constants are available for the other acid/base workers (Mehrbach et al., 1973; Hansson, 1973; species in seawater. Dissociation constants of Goyet and Poisson, 1989; Roy et al., 1993). A carbonic acid are needed to calculate the compo- summary of these results is given in Table 1. The nents of the CO2 system from these measurements. standard errors (1s) of the fits of the experimental The stoichiometric dissociation of carbonic acid in measurements to functions of temperature and seawater are given by salinity are 0.002–0.007 for pK1 and 0.006–0.013 CO þ H O3Hþ þ HCO; ð1Þ for pK2. The measurements made by Mehrbach 2 2 3 et al. (1973) were made on real seawater; while the 3 þ 2 other studies were made in artificial seawater. HCO3 H þ CO3 : ð2Þ Mehrbach et al. (1973) determined pK1 from The dissociation constants K1 and K2 are defined potentiometric titrations and pK1+pK2 by addi- by tions of NaHCO3 to seawater devoid of CO2 until þ the pH was constant (pH=[pK1+pK2]/2, when K1 ¼½H ½HCO3 =½CO2; ð3Þ TCO2=CA, the carbonate alkalinity). They calcu- þ 2 lated pK2 by subtracting the pK1 from the K2 ¼½H ½CO3 =½HCO3 ; ð4Þ measured values of pK1+pK2. Hansson (1973) where the brackets are used to denote the determined the values of pK1 and pK2 from 1 concentration in mol kg of seawater and the potentiometric titrations of Na2CO3 in artificial proton concentration is on the seawater scale, seawater (without F and B(OH)3). Goyet and

Table 1 Summary of measurements made on the dissociation constants of carbonic acid in seawater by various workersa

Author Temp. range (1C) Salinity range Std. Errorb Values at S ¼ 35 and 251C

pK1 pK2 pK1 pK2 Hansson (1973) 5–30 20–40 0.007 0.009 5.850 8.942 Mehrbach et al. (1973) 2–35 26–43 0.006 0.010 5.837 8.955 Goyet and Poisson (1989) 1–40 10–50 0.007 0.011 5.848 8.919 Dickson and Millero (1987) 0–35 20–43 0.008 0.013 5.845 8.945 Roy et al. (1993) 0–45 5–45 0.002 0.006 5.847 8.916

a All the constants have been converted to the seawater scale. b The standard errors are 1s from ﬁts of pK1 and pK2 as a function of temperature and salinity. F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723 1707

Poisson (1989) determined the values of pK1 and Carbonic Acid Constants pK from potentiometric titrations of Na CO in 6.2 2 2 3 Goyet & Poisson artiﬁcial seawater (without B(OH)3). Roy et al. 6.1 Hansson (1993) determined the values of pK1 in artiﬁcial Mehrbach et al. seawater (devoid of F and B(OH)3) measuring 6.0 Roy et al.

the cell potential with a hydrogen silver–silver 1 5.9 chloride electrode system. These measurements pK S = 35 were made on solutions with various amounts of 5.8 NaHCO3 that were equilibrated with gas mixtures σ = 0.0061 of CO2 and H2. Roy et al. (1993) determined the 5.7 values of pK2 from potentiometric measurements in artificial seawater with mixtures of NaHCO 5.6 3 -10 0 10 20 30 40 50 and Na2CO3. Temperature (oC) Millero (1979) examined the pK1 and pK2 determined by Hansson (1973) and Mehrbach 5.97 et al. (1973) using thermodynamic equations that Hansson could be extrapolated to pure water. Dickson and 5.94 Mehrbach et al. Millero (1987) combined the measurements of Roy et al. 5.91 Mehrbach et al. (1973) and Hansson (1973) to 1 produce constants that were suggested for general 5.88 t = 25oC use in oceanography. The more recent measure- pK ments of Goyet and Poisson (1989) and Roy et al. 5.85 σ = 0.0065 (1993) were in reasonable agreement and were 5.82 combined by Millero (1995). More recently the examination of the internal consistency of labora- 5.79 tory (Lee et al., 1996; Lueker et al., 2000) and field 10 15 20 25 30 35 40 45 (Wanninkhof et al., 1999; Lee et al., 2000) Salinity measurements of fCO , TCO and TA have 2 2 Fig. 1. Values of pK1 of various workers for carbonic acid indicated that the constants of Mehrbach et al. (Mehrbach et al., 1973; Hansson, 1973; Goyet and Poisson, (1973) are more reliable than those of other 1989; Roy et al., 1993) as a function of temperature (S ¼ 35) and salinity (251C). Goyet and Poisson (1989) did not make any workers. The calculation of fCO2 from an input 1 of TA and TCO and calculations of other measurements at 25 C so these results are not shown as a 2 function of salinity. The smooth curve is calculated from parameters from an input of fCO2 and TA or Eq. (5). TCO2 require reliable values of pK2 pK1 (or K2=K1). Thus, the field measurements suggest that temperature in Kelvin) the values pK2 pK1 from Mehrbach et al. (1973) 3 5 2 are more reliable than other laboratory studies. pK1 ¼8:712 9:460 Â 10 S þ 8:56 Â 10 S Comparisons of dissociation constants mea- þ 1355:1=T þ 1:7976 ln ðTÞð5Þ sured in the laboratory as a function of temperature (t ¼ 0–401CatS ¼ 35) and salinity (S ¼ 15– with a standard error s ¼ 0:0064: This fit indicates 42 at 251C) are shown in Figs. 1 and 2. The values that all the measurements of pK1 are internally of pK1 as a function of temperature and salinity consistent to 0.01, which is close to the standard error are in reasonably good agreement. All the values of the individual fits (see Table 1). A closer look of of pK1 determined in the laboratory studies as a the individually fitted data indicates that the values of function of temperature (T1K) and salinity (Hans- pK1 of Mehrbach et al. (1973) are in good agreement son, 1973; Mehrbach et al., 1973; Goyet and with the measurements of Goyet and Poisson (1989) Poisson, 1989; Roy et al., 1993) can be represented and Roy et al. (1993) at low temperatures, but differ by (ln is log to the base e and T is the absolute by as much as 0.01 near 201C. 1708 F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723

Carbonic Acid Constants 0.020 9.6 0.015 ) 2σ Goyet & Poisson 0.010 9.4 Hansson 0.005 Mehrbach et al. 0.000 9.2 Roy et al.

(Meas - Calc (Meas -0.005 1 2 -0.010 9.0 pK -2σ pK

S = 35 ∆ -0.015 8.8 -0.020 0 1020304050 σ = 0.018 o 8.6 Temperature ( C)

Goyet & Poisson 8.4 -10 0 10 20 30 40 50 Hansson Mehrbach et al. o Temperature ( C) Roy et al.

9.4 0.08 0.06 Hannson ) 9.3 0.04 2σ Mehrbach et al. 9.2 Roy et al. 0.02 0.00

9.1 - Calc (Meas 2 -0.02 t = 25oC 2 σ pK -0.04 -2 9.0 pK

∆ -0.06 8.9 -0.08 0 1020304050 o 8.8 σ = 0.012 Temperature ( C) 8.7 Fig. 3. Differences between the measured (Mehrbach et al., 01020304050 1973; Hansson, 1973; Goyet and Poisson, 1989; Roy et al., Salinity 1993) and the calculated values of the combined equation (Eqs. (5) and (6)) of pK1 and pK2 as a function of temperature Fig. 2. Values of pK2 of various workers for carbonic acid (S ¼ 20–42). (Mehrbach et al., 1973; Hansson, 1973; Goyet and Poisson, 1989; Roy et al., 1993) as a function of temperature (S ¼ 35) and salinity (251C). Goyet and Poisson (1989) did not make any measurements at 251C so these results are not shown as a with a s ¼ 0:019: The overall standard error of the function of salinity. The smooth curve is calculated from fit to Eq. (6) is close to two times the standard Eq. (6). error of the individual fits (Table 1). The deviations of the individual measurements of pK1 and pK2 from the values calculated from A comparison of the laboratory measurements Eqs. (5) and (6) are shown in Fig. 3 (on the 1 of pK2 as a function of temperature (t ¼ 0–401Cat seawater pH scale, mol kg ). Most of the devia- S ¼ 35) and salinity (S ¼ 15–42 at 251C) is shown tions in pK1 are within 2s of the individual fits. in Fig. 2. All the values of pK2 determined in the The deviations in pK2 are much larger, but within laboratory studies (Hansson, 1973; Mehrbach 2s of the individual fits. The values of pK2 pK1 et al., 1973; Goyet and Poisson, 1989; Roy et al., determined in artificial seawater are also compared 1993) can be represented by (T=K) to the results of Mehrbach et al. (1973) in Fig. 4 (on the seawater pH scale, mol kg1). Except at 5 2 pK2 ¼ 17:0001 0:01259S 7:9334 Â 10 S low temperatures, the seawater results of Mehr- þ 936:291=T 1:87354 lnðTÞ bach et al. (1973) are all higher by about 0.04–0.05 than those determined in artificial seawater. Since 2 2:61471 S=T þ 0:07479 S =T ð6Þ the field and laboratory internal consistency F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723 1709

0.04 or pH and TCO2. Uncertainties of 70.04 in pK2 7 K 7 0.02 ( 9.7% in 2) can lead to errors of 26 matm in

Calc) fCO2 from an input of TA and TCO2 (Mojica 0.00 Prieto and Millero, 2002).

-0.02 In this paper, we derive values of pK1,pK2 and (Meas - 1 pK2 pK1 from 6000 sets of field measurements of -0.04 - pK f 2 pH, TA, TCO2 and CO2 on the NSF/JGOFS, NOAA/OACES and DOE/WOCE cruises in the pK -0.06 ∆ ∆ Atlantic, Pacific, Southern and Indian oceans. The -0.08 -10 0 10 20 30 40 50 results will be used to examine the reliability of the o Temperature ( C) measured values of pK1,pK2 and pK2 pK1 from various laboratory studies. Goyet and Poisson Hansson Roy et al. 0.04 2. Quality of the field data used

0.02

Calc) The ﬁeld measurements used in this study were 0.00 taken from the cruises listed in Table 2. The data are available from Carbon Data Information (Meas -

1 -0.02 Analysis Center (CDIAC-http://cdiac.ornl.gov/

- pK -0.04

2 oceans/woce. All the Principal Investigators that

pK -0.06 made the measurements are listed in a Table on the

∆ web site. Surface data from the Southern Ocean -0.08 10 20 30 40 50 JGOFS cruises from Hawaii to New Zealand and Salinity New Zealand to the Ross Sea were also used (Millero et al., 1999). We examined only the Fig. 4. Differences between the measured (Hansson, 1973; samples where all four parameters were measured. Goyet and Poisson, 1989; Roy et al., 1993) values of pK 2 The pH measurements were made by spectroscopic pK1 for carbonic acid with the results of Mehrbach et al. (1973) as fitted by Dickson and Millero (1987) as a function of methods (Clayton and Byrne, 1993) for all the temperature and salinity. The dotted line shows the approx- stations except for the potentiometric measure- imate offset in the values determined in artificial seawater and ments made on the S4I cruise in the Southern real seawater. Ocean. The spectroscopic pH measurements were made at 251C except for the N. Atlantic measurements made at 201C. All the pH measurements calculations support the pK2 pK1 measurements have been converted to the seawater scale (Dick- of Mehrbach et al. (1973), the measurements by son, 1984; Millero, 1995). The pK of the pH others (Hansson, 1973; Goyet and Poisson, 1989; indicator was calibrated by Clayton and Byrne Roy et al., 1993) appear to be in error. Since the (1993) with TRIS buffers (Khoo et al., 1977). pK1 measurements of all the laboratory studies are Recently, DeValls and Dickson (1998) have shown in reasonable agreement, the values of pK2 that the values of pH assigned to the TRIS buffer determined from potentiometric titrations in arti- by Khoo et al. (1977) are too low by 0.0047. ficial seawater also appear to be in error. Because it is uncertain that this correction should Uncertainties of 70.01 in pK1 and 70.04 in pK2 be made to the pK of the indicator and the pH can lead to significant errors in the calculated measurements, it has not been made to the field parameters of the CO2 system (Mojica Prieto and data. This could result in a bias of 0.005 in the pH Millero, 2002). For example, an uncertainty of measurements and resultant values of pK1 and 70.01 in pK1 (72.5% in K1) can lead to errors of pK2. Recent potentiometric and spectroscopic 710 matm in fCO2 from an input of TA and TCO2 measurements on seawater (Mojica Prieto and 1710 F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723

Table 2 Cruise data used to determine the dissociation constants of carbonic acid

Location Number Temp. (1C) Salinity Parameters

Deep waters N. Atlantic Ocean a (A16R) 1368 20 34.3–35.5 pH , TA, TCO2, fCO2 (A20) 420 20 34.3–35.5 (A22) 340 20 34.3–35.5 (24N) 773 20 34.3–37.3

Indian Ocean (I8N R) 1368 20 34.5–35.1

S. Paciﬁc Oceanb (P14/P15) 2146 20 34.2–35.0

Total 6415 20 34.3–37.3

c d d Southern Ocean (S4I) 1065 4 34.2–34.8. pH , TA, TCO2 , fCO2

Surface waterse a Atlantic Ocean 193 8.6–29 33–37 pH , TA, TCO2, fCO2 Indian Ocean 128 10–29 33–36 Southern Ocean 30 1.7–4.2 33–35

Total 321 8.6–29 35.570.6

a Spectroscopic pH measurements made at 251C except for A16R where the measurements were made at 201C. They have been converted to the seawater scale. b Data from the Paciﬁc WOCE P16, P17, P18 and P19 have not been used in this study. For the ﬁrst two expeditions, very few alkalinity samples were analyzed without using the CRM solutions for the alkalinity. During P18, fCO2 was measured using a shaker bottle method of Neill et al. (1997), whereas it was measured using a gas recirculation method of Chipman et al. (1993) for all other expeditions. The P18 fCO2 data appear to be inconsistent with the data from all other expeditions. During P19, no alkalinity was measured. c Potentiometric pH measurements at 251C on the seawater scale. d The TCO2 and fCO2 were measured at 41C by the Lamont group (Takahashi et al., 2002). e The surface values of pH, TA and TCO2 were determined on samples collected from CTD casts at depths between 0 and 30 m. The values of fCO2 were made on line (B5–6 m) near the in situ temperature.

Millero, 2002) indicate that the differences be- Tans of NOAA/CMDL). The conversions of the tween the potentiometric and spectroscopic meth- measured partial pressure of CO2,(pCO2) to the ods are within 70.002. The fCO2 measurements fugacity (fCO2) were made using the equations were made in a batch mode at 41Cor201C listed in Wanninkhof and Thoning (1993), which (Chipman et al., 1993) for deep waters or in a are based on the earlier equations developed by continuous mode (Wanninkhof and Thoning, Weiss (1974). Differences in these quantities are 1993) near the in situ temperature for surface small (B1 matm) compared to the precision of waters. The concentration of CO2 in the air measurements. The TA measurements were made equilibrated with seawater at a known temperature by potentiometric titrations (Millero et al., 1993) was measured using an IR analyzer or gas and the TCO2 was measured by coulometry chromatograph, which were repeatedly calibrated (Johnson et al., 1993). Certified reference materials using several standard gas mixtures of known CO2 (CRMs) were used to adjust all the TA and TCO2 concentrations up to 1400 ppm (determined by P. measurements (Dickson, 1997), except the TCO2 F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723 1711 measurements on S4I. CRMs measured on this 3 þ þ 2 ½PO ¼½P =f1 þ½H =KP3 þ½H =ðKP2KP3Þ cruise were within 2 mmol/kg from the certified 4 T þ 3 value. The precisions of the field measurements are þ½H =ðKP1KP2KP3Þg; ð11Þ 7 7 7 1 0.001 for pH, 1% for fCO2, 4 mmol kg for þ 1 ½SiðOHÞ O ¼½Si =f1 þ½H =KSig; ð12Þ TA and 72 mmol kg for TCO2. The accuracy of 3 T the TA and TCO measurements are close to the 2 where the concentration of boron, [B]T= precision because all the field measurements used 0.000416(S/35) mol kg1 (Uppstrom,. 1974) and standards that were reproduced to near the the concentrations of total phosphate [P]T and precision of the measurements. The uncertainties silica [Si]T are taken from the at-sea measurements of the pH measurements are larger than the (mol kg1). As mentioned earlier, the seawater pH precision due to the uncertainties in the pH scale was used throughout this paper and all the assigned to the TRIS buffers used in the calibra- constants used have been converted to this scale tion and the errors involved in the corrections to in (Dickson and Millero, 1987; Millero, 1995). The situ temperatures. We estimate that the errors in required dissociation constants for HSO4 and field pH measurements could be as large as 70.01 HF are taken, respectively, from Dickson (1990) due to these calibration problems. The accuracy of and Dickson and Riley (1979). The values of fCO measurements for the water samples is 2 1 2 [SO4 ]T=0.0293(S/35) mol kg and [F ]T= assumed to be close to the precision. 0.00007(S/35) mol kg1 (Millero, 1996). The con- 2 centrations of OH , HPO4 , Si(OH)3O in deep waters contribute less than 0.3% to TA; while 3. Calculations B(OH)4 can contribute 4% to TA in surface waters and 2% in deep waters (Millero, 1996). The methods used to determine the values of The components of the carbonate system are pK1,pK2 and pK2 pK1 have been given by Lee determined from et al. (1996). The calculations require the determi- ½CO ¼f CO K ; ð13Þ nation of the carbonate alkalinity (CA), which is 2 2 0 defined by (Dickson, 1984) ½HCO3 ¼2TCO2 CA 2½CO2; ð14Þ 2 CA ¼½HCO3 þ2½CO3 2 þ ½CO ¼CA TCO2 þ½CO2; ð15Þ ¼ TA ½BðOHÞ4 þ½H ½OH 3 2 3 ½HPO4 2½PO4 ½SiðOHÞ3O : ð7Þ where K0 is the solubility constant for CO2 (Weiss, 1974). The constants are determined from Contributions from minor weak acids including þ organic acids are assumed to be negligible. The K1 ¼½H ½HCO3 =½CO2 þ concentrations of the individual components ¼½H f2TCO2 CA 2½CO2g=½CO2; ð16Þ (mol kg1) are determined from the appropriate þ 2 dissociation constants for boric acid (KB; Dickson, K2 ¼½H ½CO3 =½HCO3 1990), water (KW; Millero, 1995), phosphoric (KPi; f½HþðCA TCO þ½CO Þg Millero, 1995), and silicic acid (Millero, 1995) on ¼ 2 2 ; ð17Þ f2TCO CA 2½CO g the seawater pH scale: 2 2 þ 2 2 ½BðOHÞ4 ¼½BT=f1 þ½H =KBg; ð8Þ K2=K1 ¼½CO2½CO3 =½HCO3

þ f½CO2ðCA TCO2 þ½CO2Þg ½OH ¼KW=½H ; ð9Þ ¼ 2 : ð18Þ fð2TCO2 CA 2½CO2g 2 þ þ ½HPO4 ¼f½PT½H =KP3g=f1 þ½H =KP3 As is clear from Eq. (18), the ratio of K2=K1 is þ 2 nearly independent of the pH and can be þ½H =ðKP2KP3Þ determined from measurements of TA, TCO þ 3 2 þ½H =ðKP1KP2KP3Þg; ð10Þ and fCO2. This is important since errors in the 1712 F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723

Table 3 1 1 Effect of temperature (25–01C) on the pH of seawater (S ¼ 30–40, TA=2300 mmol kg and TCO2=2100 mmol kg ) DpH/DT (1C1)

Salinity Mehrbacha Hanssonb D&Mc G&Pd Roye

30 0.0158 0.0149 0.0156 0.0165 0.0166 35 0.0157 0.0148 0.0155 0.0164 0.0166 40 0.0156 0.0148 0.0154 0.0163 0.0164

Effect of change in temperature (25–41C) on the calculated pK1 — 0.0168 0.0042 +0.0147 +0.0165

a Mehrbach et al. (1973). b Hansson (1973). c Dickson and Millero (1987). d Goyet and Poisson (1989). e Roy et al. (1993). measurement of pH do not strongly affect the by the fact that the Mehrbach et al. (1973) values estimates of pK2 pK1: of pK2 pK1 are more reliable than the measure- Since most of the measurements of pH were ments made on artificial seawater (Mojica Prieto made at 251C, it is necessary to estimate their and Millero, 2002). values at lower or higher temperatures. This Uncertainties in the measured parameters result requires knowledge of the constants K0; K1 and in values of pK1,pK2 and pK2pK1 with devia- K2 for the CO2 system. The values of DpH/DT tions of 70.006 in pK1, 70.010 in pK2 and determined from the presently available constants 70.010 in pK2 pK1: Larger errors in pH will are given in Table 3 (Mehrbach et al., 1973; affect the uncertainty of the values determined for Hansson, 1973; Goyet and Poisson, 1989; Roy pK1 and pK2 by 70.01, but not seriously affect the et al., 1993). The values of DpH/DT are nearly values of pK2 pK1 (see Eq. (18)). It should be independent of salinity and temperature from pointed out that all the calculations were made at 251Cto01C (Millero, 1995) and range from 1 atm and not at the in situ pressure. 0.0148 to 0.0166 at S ¼ 35: These can be compared to directly measured values of DpH/DT of 0.0150– 0.0165 for seawater with the same ratio of TA/ 4. Measurements made on deep waters TCO2 (Millero, 1995). The differences in the values at a constant temperature of DpH/DT calculated using different constants are not important for small changes in temperature 4.1. Measurements of fCO2 at 201C (51C), but are quite important for large changes in temperature (251C) (see Table 3 for calculations of We have first examined the results where the pK1). Since the values of DpH/DT can differ, we fCO2 was measured at 201C and the pH at 201Cor have determined their values using the CO2 Sys 251C for surface and deep waters (see Table 2). program (Lewis and Wallace, 1998) for each The adjustments of the pH measurements from 25 sample. Since the Mehrbach et al. (1973) constants to 201C have been made using the CO2 Sys appear to be more internally consistent with field program (Lewis and Wallace, 1998) as discussed measurements (Clayton et al., 1995; McElligott above. The resulting values of pK1,pK2 and et al., 1998; Wanninkhof et al., 1999; Lee et al., pK2 pK1 are shown as a function of depth 1997, 2000), we have used these constants to (expressed in terms of hydrostatic pressure) where determine the values of DpH/DT from the mea- water samples were collected, in Fig. 5 and sured values of TA and TCO2. This is supported tabulated in Table 4. The values with deviations F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723 1713

20oC Data greater than 2s (0.04 for pK1 and 0.08 for pK2) have been eliminated (B3.8%) from the plots. 5.96 pK = 5.888 + 0.010 This cuts down the scatter in the data, but does not 5.94 1 change the average values of pK1=5.88870.010, 5.92 pK2=9.03570.019 and pK2 pK1 ¼ 3:1487 1 5.90 0:019: The average salinity for all the samples pK 5.88 was S ¼ 34:970:5 which is the same as the deep 5.86 waters. As shown in Eqs. (5) and (6) and Figs. 1 and 2, the values of pK1 and pK2 are not a strong 5.84 0 2000 4000 6000 function of salinity (DpK1=DSE0:0048 and DpK2=DSE0:012). The pK1 changes by 0.003 pK = 9.035 + 0.019 9.15 2 and pK2 changes by 0.006 for a change in salinity 9.10 of 0.5, which is within the experimental error. A 2 9.05 comparison of the calculated values of pK1 and pK 9.00 pK2 with those obtained in earlier studies (Mehr- bach et al., 1973; Hansson, 1973; Goyet and 8.95 Poisson, 1989; Roy et al., 1993) is shown in Fig. 6. 8.90 1 0 2000 4000 6000 The measured values of pK1 at 20 C agree with the 3.30 constants of Mehrbach et al. (1973), Dickson and pK - pK = 3.148 + 0.019 3.25 2 1 Millero (1987), Goyet and Poisson (1989) and Roy et al. (1993) to within 0.007. The pK1 values of 1 3.20 Hansson (1973) show much larger deviations

- pK - 3.15 2 (0.01). The values of pK2 and pK2 pK1 at 201C pK 3.10 are in excellent agreement (0.005) with the results 3.05 of Mehrbach et al. (1973) (pK2 ¼ 9:035 and 3.00 pK2 pK1 ¼ 3:153). The values of pK2 and pK2 0 2000 4000 6000 pK1 agree to within 0.02 with the measure- Pressure (db) ments of Hansson (1973) and the equations of Fig. 5. Calculated values of pK1; pK2 and pK2pK1 at 201Cas Dickson and Millero (1987). The studies of Goyet a function of depth for deep waters from the Atlantic, Indian, and Poisson (1989) and Roy et al. (1993) show Paciﬁc and Southern oceans. The value listed is the average of all the data and is depicted by the horizontal line. much larger deviations (0.03).

Table 4 Calculated values of pK1; pK2 and pK2 pK1 (S ¼ 35) at various temperatures (on the seawater pH scale)

Data Waters pK1 pK2 pK2 pK1 41C Deepa 6.06270.009 9.32170.020 3.25770.020 Surfaceb 6.05770.005 9.32470.008 3.25870.008 Lee et al.c 6.05870.006 9.30370.011 3.24570.011 Lueker et al.c — — 3.24170.013 201C Deepd 5.88870.010 9.03570.019 3.14870.019 Surfaceb 5.87970.005 9.03270.008 3.15270.008 Lee et al.c 5.88870.006 9.01170.011 3.13970.014 Lueker et al.c — — 3.14170.013

a Adjustments of 0.002 in pK1 and 0.006 in pK2 were made to correct the values from an average salinity of 34.570.3 to 35.00 using Eqs. (5) and (6). b At S ¼ 35 and estimated from Eqs. (19)–(21). c Values at low fCO2 less than 600 matm. d Adjustments of 0.0005 in pK1 and 0.001 in pK2 to correct for an average salinity of 34.970.6 to 35.0 using Eqs. (5) and (6). 1714 F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723

20oC Data 4oC Data 0.012 6.12 pK = 6.064 + 0.010 0.009 pK1 1 0.006 6.10 lc 0.003 1 6.08 0.000 pK -0.003 6.06 Meas - Ca -0.006 6.04 -0.009 -0.012 6.02 Han Mehr D&M Goyet Roy Surface 0 2000 4000 6000 9.40 0.04 9.38 pK2 = 9.321 + 0.021 0.03 pK2 9.36 lc

0.02 2 9.34 pK 0.01 9.32

Meas - Ca 9.30 0.00 9.28 -0.01 9.26 Han Mehr D&M Goyet Roy Surface 0 2000 4000 6000 3.34

0.05 3.32 pK2 - pK1 = 3.256 + 0.020 0.04 3.30 1 pK2 - pK1

lc 0.03 3.28 - pK 2 3.26 0.02 pK 3.24 0.01 Meas - Ca 3.22 0.00 3.20 -0.01 0 2000 4000 6000 Han Mehr D&M Goyet Roy Surface Pressure (db)

Fig. 6. Comparisons of the ﬁeld calculated values of pK1; pK2 Fig. 7. Calculated values of pK1; pK2 and pK2 pK1 at 41Cas and pK2 pK1 at 201C with the smoothed literature values and a function of depth for deep waters from the Atlantic, Indian, the average value for surface measurements. The surface values Paciﬁc and Southern oceans. The value listed is the average of were calculated from Eqs. (19)–(21). all the data and is depicted by the horizontal line.

4.2. Measurements of fCO2 at 41C Mehrbach et al. (1973) gave values of pK1 at 41C that were in good agreement with the literature We next examined the measurements made in values; while the others did not, we used them in the Southern Ocean where the TCO2 and fCO2 all the conversions. These large corrections in pH were determined at 41C by the Lamont Group lead to uncertainties in the calculated values of (Takahashi et al., 2002). The measurements of pH pK1 and pK2 at 41C, but do not affect the and TA on this cruise were made by potentio- calculated values of pK2 pK1: The calculated metric methods (Millero et al., 1993) corrected values of pK1,pK2 and pK2 pK1 are shown using measurements on CRM. The pH measure- in Fig. 7. The average values found are ments were made at 251C; thus, the corrections to pK1=6.06470.010, pK2=9.32170.021 and pK2 41C are quite large and a function of the constants pK1 ¼ 3:25670:020: The values of pK2 and pK2 used. Since the conversion with the constants of pK1 at 41C adjusted to S ¼ 35 are shown in Fig. 8. F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723 1715

4oC Data Surface Data 0.008 6.2

0.006 pK1 6.1 Indian Atlantic

c 0.004 6.0 Southern 1 0.002 pK 5.9 0.000 σ = 0.005 Meas - Cal -0.002 5.8

-0.004 5.7 -0.006 -5 0 5 10 15 20 25 30 35 Han Mehr D&M Goyet Roy Surface 9.5 0.05 9.4 Indian 0.04 9.3 Atlantic pK2 Southern 2 c 9.2 0.03 pK 9.1 0.02 9.0 σ = 0.009 0.01

Meas - Cal 8.9 0.00 8.8 -5 0 5 10 15 20 25 30 35 -0.01 3.35 Han Mehr D&M Goyet Roy Surface 0.05 3.30 Indian Atlantic 0.04 1 3.25 Southern pK2 - pK1 c - pK 3.20 0.03 2

pK 3.15 0.02 σ = 0.009 3.10 0.01 Meas - Cal 3.05 0.00 -5 0 5 10 15 20 25 30 35 -0.01 Temperature (oC) Han Mehr D&M Goyet Roy Surface Fig. 9. Calculated values of pK1; pK2 and pK2 pK1 for Fig. 8. Comparisons of the ﬁeld calculated values of pK1; pK2 surface waters from the Indian, Atlantic, and Southern oceans and pK2 pK1 at 41C with the smoothed literature values. The as a function of temperature. The lines were calculated from surface values were calculated from Eqs. (19)–(21). Eqs. (19)–(21).

The results are in reasonable agreement with the Atlantic and Southern oceans are shown in Fig. 9 results of Mehrbach et al. (1973) (pK2=9.315 and as a function of temperature and salinity pK2 pK1 ¼ 3:258) and Goyet and Poisson (1989) (t ¼1:6–351C and S ¼ 34–37) and have been (pK2=9.307 and pK2 pK1 ¼ 3:249). The mea- fitted to the equations (T=K) sured values of pK1 at 41C are all in reasonable agreement (0.007) with the laboratory studies. pK1 ¼ 6:359 0:00664S 0:01322ðT 273:15Þ þ 4:989 Â 105ðT 273:15Þ2; ð19Þ 5. Measurements made on surface waters pK2 ¼ 9:867 0:01314S 0:01904ðT 273:15Þ þ 2:4480 Â 105ðT 273:15Þ2; ð20Þ The field measurements of TA, TCO2,pH (251C), and pCO2 for surface waters have been pK2 pK1 ¼ 3:510 0:0064S used to calculate the values of pK1,pK2 and pK2 0:006711ðT 273:15Þð21Þ pK1: The results for waters from the Indian, 1716 F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723 with standard deviations of s ¼ 0:005 in pK1, s ¼ 1:967035S ln T 0:008 in pK and s ¼ 0:008 in pK pK : The 2 2 1 ðs ¼ 0:010Þ: ð23Þ effect of salinity on pK1 and pK2 from the surface data is slightly higher than literature data These equations give pK values somewhat different (DpK =DSE0:0048 and DpK =DSE0:012). This 1 2 from those given by Eqs. (19) and (20) (within is not surprising due to the limited salinity range of 75% for K and 78% for K ). However, since the field data. The values calculated from 1 2 Eqs. (19) and (20) are based on field data with Eqs. (19)–(21) at 41C and 201C are compared to relatively narrow salinity range, we feel that these the values calculated for the deep waters in Table 4 equations are the best representation of the and Figs. 6 and 8. The agreement is reasonable carbonic acid dissociation constants in seawater. and within the combined experimental error. The surface values of pK2 pK1 are in excellent agreement with the deep-water values and results of Mehrbach et al. (1973) indicating that the 7. Comparisons of pK2 pK1 with laboratory uncertainties in pK1 and pK2 at 41Cand201C are measurements related to errors in pH. The reliability of our values of pK2 pK1 for deep and surface waters can be examined using the recent laboratory measurements of Lee et al. 6. Estimations of pK1 and pK2 as a function of salinity and temperature (1996) and Lueker et al. (2000) for seawater. The values of pK2 pK1 from the measurements of All the field measurements clearly demonstrate Lee et al. (1996) as a function of temperature are shown in Fig. 10. The values of pK2 pK1 appear that the values of pK2 pK1 from the measurements of Mehrbach et al. (1973) are more reliable to be a linear function of temperature as found for than those determined in the other laboratory the field measurements (see Fig. 9). The spread of studies. This is largely due to differences in the the results at a given temperature is related to values of pK determined in real and artificial changes in the values as a function of fCO2 2 1 seawater. The values of pK determined from the (Fig. 10b). The values of pK2 pK1 at 4 C and 1 1 field data do not favor a given set of laboratory 20 C at low fCO2 are compared to our values in measurements. This is partly due to uncertainties Table 4. The agreement is within 0.01 at each of in the spectroscopic pH measurements and errors these temperatures and is satisfactory. The values in the calculation of in situ values of pH from of pK2 pK1 from the measurements of Lueker et al. (2000) as a function of temperature are measurements made at 251C. The recent pK1 and shown in Fig. 11. The values of pK2 pK1 also pK1+pK2 measurements of Mojica Prieto and Millero (2002) have shown to be in good agreement appear to be a linear function of temperature. The with the work of Mehrbach et al. (1973). These spread of some of the results at a given tempera- studies have been combined (Mojica Prieto and ture are related to changes in the values as a Millero, 2002) to give (ln=the base -e logarithm) function of fCO2 (Fig. 11). The scatter is much greater in the Lueker et al. (2000) data than the 4 2 pK1 ¼43:6977 0:0129037S þ 1:364 Â 10 S results of Lee et al. (1996). The results at low fCO2, þ 2885:378=T þ 7:045159 ln T however, are in reasonable agreement within 0.01 with other workers (Table 4). The effect of fCO ðs ¼ 0:0056Þ; ð22Þ 2 on the values of pK2 pK1 is hard to explain. The data of Lee et al. (1996) indicate that the 4 2 pK2 ¼452:0940 þ 13:142162S 8:101 Â 10 S dependence on fCO2 is largely due to the variation þ 21263:61=T þ 68:483143 ln T of pK2. This tends to point to changes in the interactions as a function of fCO2 being related to þð581:4428S þ 0:259601S2Þ=T 2 changes in the ratio of CO3 /HCO3 . F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723 1717

Lee et al. Lueker et al. 3.30

3.25 3.24

o 3.20 5.6 C o o 3.20 5 C 1 13.3 C 1 o 3.15 o 15 C 20 C o

- pK o 18 C

- pK 3.16 2 25 C

2 o 3.10 o 25 C

pK 35 C pK 3.05 3.12

3.00 3.08 2.95 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 o Temperature ( C) Temperature (oC)

3.30

3.25 3.24 5.6oC 3.20 o 13.3 C 5oC

1 3.20 o o 3.15 20 C 1 15 C 25oC o

- pK 18 C

2 o 3.10 - pK 3.16 o 35 C 2 25 C pK

3.05 pK 3.12 3.00 3.08 2.95 200 400 600 800 1000 1200 1400 1600 1800 µ 0 300 600 900 1200 1500 1800 fCO2 ( atm) µ fCO2( atm) Fig. 10. Values of pK2 pK1 determined from the measurements of Lee et al. (1996) as a function of temperature (top) and Fig. 11. Values of pK2 pK1 determined from the measure- fCO2 (bottom). ments of Lueker et al. (2000) as a function of temperature (top)

and fCO2 (bottom).

The recent studies of Mojica Prieto and Millero HCO3 can be due to (2002) indicate that the differences in the values of HCO3 þ BðOHÞ3 ¼ BðOHÞ2CO3 þ H2O: ð24Þ pK1 and pK2 in real and artificial seawater are related to interactions of the borate and carbonate Although this reaction would lower g(HCO3 ), the system. At 251C the values of pK1 in artificial magnitude of this interaction that they found is B seawater with boric acid are 0.01 lower than in not large enough to lower the pK1 by 0.01. Similar 2 artificial seawater without boric acid; while, the interactions between B(OH)3 and CO3 would not 2 values of pK2 in artificial seawater with boric acid be expected to increase g(CO3 ). Further studies of are higher B0.04 than seawater without boric mixtures of boric and carbonic acid mixtures are acid. The interactions responsible for these differ- needed to elucidate these interactions. ences are not clear. The increase in K1 in real If the borate–carbonate ion interactions are seawater can be attributed to a decrease in the assumed to be significant, then the following activity coefficient of HCO3 , g(HCO3 ) and the considerations may be advanced in order to decrease in K2 can be attributed to an increase in account for the observed decrease in pK2 (or 2 2 the activity coefficient of CO3 , g(CO3 ). If one increase in K2) with increasing fCO2. The value assumes that the repulsive interactions between of K2 is related to the value in water at 2 0 B(OH)4 and HCO3 and CO3 are small, one can 0 ionic strength, K ; and the activity coefficients, 2 2 attribute the changes in g(HCO3 ) and g(CO3 )to gðiÞ; by interactions with B(OH) . McElligott and Byrne 3 0 þ 2 K2 ¼ K fgðHCO Þ=gðH ÞgðCO Þg: ð25Þ (1998) have shown the interactions of B(OH)3 and 2 3 3 1718 F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723

The increase in K2 can be attributed to an in- 150 crease in g(HCO) or a decrease in g(CO2). Since Ave =26.6 µatm 3 3 σ = 29.7 µatm

) 100 the value of pK1 is not strongly dependent on f CO2, the changes in g(HCO3 ) cannot be very 50 great. This is in agreement with the studies of McElligott and Byrne (1998). Model calculations 0 (meas - calc of CO2 system in seawater (Millero and Pierrot, 2 -50 1998) as a function of TCO2 do not yield large fCO 2

changes in g(HCO )org(CO ). It should be ∆ 3 3 -100 noted that the activity coefﬁcients for B(OH)3 and (A) B(OH)4 would also depend on the concentrations -150 2 0 500 1000 1500 of HCO3 and CO3 via ionic interactions. Hence, µ the value of KB would vary with fCO2, and the fCO2 ( atm) direction of its changes depends upon the nature of 150 the interactions and ion pairs. This means that our Ave = 0 µatm present understanding of the ionic interactions σ = 22.7 µatm ) 100 affecting the carbonate system in seawater is deﬁcient. 50

0 (meas - calc 2 8. Proposed dependence of K2 on TCO2 -50 fCO

∆ Our determinations of pK2 from the ﬁeld -100 (B) data do not show any effect of fCO2 on the Corrected -150 calculated values within the experimental error 0 500 1000 1500 of the calculations as shown in Fig. 5. This is fCO (µatm) not surprising since at 201C, the effect is quite 2 small (see Figs. 10 and 11). Internal consistency Fig. 12. Differences between the measured and calculated tests, however, do show this effect (Lueker et al., values of fCO2 from an input of TA and TCO2 as a function 2000; Lee et al., 2000). The differences in the of fCO2 using the combined constants of Mehrbach et al. (1973) and Mojica Prieto and Millero (2002) (Eqs. (22) and (23)). The measured and calculated values of fCO2 using an values in panels (A) and (B) were determined without and with input of TA and TCO2 (which require reliable the correction for changes in pK2 as a function of TCO2 values of pK2 pK1) are shown in Fig. 12A for all (Eq. (26)). The dotted line in (A) is an estimate of the offset at the stations listed in Table 2. The average high fCO2. differences in fCO2 are 26.6 matm while the standard errors are 29.7 matm. The deviations at fCO2 above B600 matm are greater than at low relationship fCO , apparently due to changes in the pK pK 2 2 1 pKTCO2 ¼ pK 1:6 Â 104ðTCO 2050Þð26Þ (Lueker et al., 2000; Lee et al., 2000). The 2 2 2 differences of the measured and calculated which is valid at 201C and at TCO2>2050 1 values of fCO2 as a function of TCO2 (Fig. 13A) mmol kg . Similar calculations at 41C were not show larger deviation at high TCO2. At values possible since the values of fCO2 of all the waters 1 of TCO2 less than 2050 mmol kg , the deviations are below 680 matm. As shown in Fig. 14, the are independent of the TCO2. By adjusting the values of the slope of pK2 as a function of fCO2 1 values of pK2 above 2050 mmol kg , it was at 201C or TCO2 found from the ﬁeld data are in possible to lower the average deviations to reasonable agreement with the values determined 0 matm and the standard error to 22.7 matm (see from the laboratory measurements of Lee et al. Figs. 12B and 13B). This resulted in the empirical (1996) and Lueker et al. (2000) (1.2 Â 104 to F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723 1719

150 0.00000 Ave = 26.6 µatm -0.00001 100 σ = 29.7 µatm 2 c) -0.00002 fCO 50 -0.00003 ∆ ∆ )/ 1 0 -0.00004 -pK (meas - cal 2

2 -0.00005 -50 (pK -0.00006 ∆ fCO ∆ ∆ ∆ -100 -0.00007 (A) (A) -150 -0.00008 0 5 10 15 20 25 30 35 40 1800 1900 2000 2100 2200 2300 2400 TCO (µmol kg-1) Lee et al. 2 Lueker et al. 150 20oC Field Data µ Ave = 0 atm 0.0000 100 σ = 22.7 µatm c)

50 2 -0.0001 TCO

∆ 0 ∆ )/ 1 (meas - cal 2 -0.0002 -50 -pK 2 fCO ∆ (pK ∆ -100 ∆ (B) ∆ Corrected -0.0003 (B) -150 1800 1900 2000 2100 2200 2300 2400 0 5 10 15 20 25 30 35 40 TCO (µmol kg-1) 2 Temperature (oC) Fig. 13. Differences between the measured and calculated Fig. 14. Comparison of the slopes of pK as a function of fCO values of fCO from an input of TA and TCO as a function 2 2 2 2 and TCO obtained from the field data at 201C with the of TCO using the combined constants of Mehrbach et al. 2 2 measurements of Lee et al. (1996) and Lueker et al. (2000) as a (1973) (top) and Mojica Prieto and Millero (2002) (bottom) function of temperature. (Eqs. (22) and (23)). The values in (A) and (B) were determined without and with the correction for changes in pK2 as a function of TCO2 (Eq. (26)). The dotted line in (A) is an When pH values are used with TCO2 or TA for estimate of the offset at high TCO2. the computation of fCO2, the results are not sensitively affected by the uncertainties in K1 and K2: For example, for an input of pH and TCO2 an 4 1.9 Â 10 ). The values at other temperatures uncertainty of 0.01 in pK1 yields an error of (t1C) can be estimated from the linear fit (Fig. 14) 10 matm in fCO2; while an uncertainty of 0.04 in of the results of Lee et al. (1996) and Lueker et al. pK2 leads to an error of 7 matm. The errors in the 4 (2000), DðpK2 pK1Þ=DTCO2¼2:65 Â 10 þ calculated values of fCO2 from an input of pH and 6 1 5:74 Â 10 t with a unit of kg mmol . As dis- TCO2 are examined in Fig. 15A. The average error cussed earlier, the borate–carbonate ion interac- is 9.5 matm and the standard error is 21.8 matm. tions would affect not only the K2 for carbonic When the value of pK2 using Eq. (26) is used (see acid, but also the KB for boric acid. Hence, the Fig. 15B), the average error remains unaffected, proposed relationships include the combined and is 11.8 matm with the standard error is effects on K2 and KB; and should be considered 22.3 matm. Thus, when using an input of pH and as an empirical expression which is intended to TCO2, the correction of pK2 at high TCO2 correct for imperfections of the chemical model does not strongly influence the calculated values used. of fCO2. The effect of an addition of 0.0047 to 1720 F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723

Input pH and TCO2 Input of pH and TCO2 100 30 80 Ave = 9.5 µatm σ µ 60 = 21.8 atm ) 20 -1 m)

at 40 10 µ

( 20 2

mol kg mol 0

0 µ fCO

∆ -10 ∆ -20 TA ( TA -1 ∆ µ -40 (A) -20 Average = 3.2 molkg -1 -60 σ = 4.1 µmol kg (A) 1800 1900 2000 2100 2200 2300 2400 -30 1800 1900 2000 2100 2200 2300 2400 µ -1) TCO2 ( mol kg µ -1 TCO2 ( mol kg ) 100 30 80 Ave = 11.8 µatm 20 60 σ = 22.3 µatm ) -1 m)

at 40 10 µ

( 20 2

mol kg mol 0

0 µ fCO

∆ -10 ∆ -20 TA ( TA

-40 (B) ∆ -20 Average = -1.7 µmol kg-1 -60 σ = 4.3 µmol kg-1 (B) 1800 1900 2000 2100 2200 2300 2400 -30 TCO (µmol kg-1) 1800 1900 2000 2100 2200 2300 2400 2 µ -1 TCO2 ( mol kg ) 100 30 pH + 0.0047 80 20 µatm ) 60 Ave = 21.1 -1 m) σ = 23.8 µatm 10

at 40 µ

( 20 2

mol kg mol 0

0 µ fCO -10 ∆ TA ( TA

-20 ∆ pH ∆ -20 µ -1 -40 + 0.0047 (C) Average = -3.9 mol kg (C) σ= 4.1 µmol kg-1 -60 -30 1800 1900 2000 2100 2200 2300 2400 1800 1900 2000 2100 2200 2300 2400 µ -1 µ -1 TCO2 ( mol kg ) TCO2 ( mol kg ) Fig. 15. Comparison of the measured and calculated values of Fig. 16. Comparison of the measured and calculated values of TA from an input of pH and TCO2 using the combined fCO2 from an input of pH and TCO2 using the combined constants of Mehrbach et al. (1973) and Mojica Prieto and constants of Mehrbach et al. (1973) and Mojica Prieto and Millero (2002) (Eqs. (22) and (23)). The values in (A) and (B) Millero (2002) (Eqs. (22) and (23)). The values in (A) and (B) were determined without and with the correction for changes in were determined without and with the correction for changes in pK2 as a function of TCO2 (Eq. (26)). The values in (C) have pK2 as a function of TCO2 (Eq. (26)). The values in (C) have been determined by increasing the pH by 0.0047. been determined by increasing the pH by 0.0047. the pH (DeValls and Dickson, 1998) is shown 1.7 mmol kg1 and the standard error is increased in Fig. 15C. The addition increases not only the to 4.3 mmol kg1. Thus, when using an input of pH fCO2 deviations, but also the average error to and TCO2, the correction of pK2 at high TCO2 21.1 matm. These results indicate that an increase improves slightly the calculated values of TA. The of the pH by 0.0047 is not needed when calculating effect of an addition of 0.0047 to the pH (DeValls fCO2. and Dickson, 1998) is shown in Fig. 16C. The The errors in the calculated values of TA from addition causes the average deviation in TA to be 1 an input of pH and TCO2 are examined in 3.9 mmol kg and does not strongly affect the Fig. 16A. The average error is 3.2 mmol kg1 and standard error. These results indicate that the the standard error is 4.1 mmol kg1. The correction correction of the pH by 0.0047 is not needed to of the value of pK2 using Eq. (26) is shown in make reliable calculations of fCO2 and TA from Fig. 16B. The average error is decreased to an input of pH and TCO2. It should be pointed F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723 1721 out that an input of pH and TA to calculate fCO2 are totally dissociated at pH of normal seawater and TCO2 yields similar results. (8.2–7.9). Using the shipboard data obtained during Paciﬁc WOCE P14/15, the effect of this hypothetical organic acid on computed fCO2 9. Possible effects of organic acids values is demonstrated below. Fig. 17A shows that the difference between the The ﬁeld data shown in Figs. 12 and 13 as well observed and computed fCO2 values at 201C as the laboratory data presented by Lee et al. increases systematically with increasing fCO2 for (1996) and Lueker et al. (2000) demonstrate that seawater. The computed fCO2 values were ob- the difference between the observed and computed tained using the observed values for TCO2, fCO2 values increase systematically for waters with alkalinity, salinity and the concentrations of greater fCO2 and TCO2 concentrations. As discussed earlier, this may be accounted for by an increase in K2 (or a combined effect of K2 for carbonic acid and KB for boric acid) with WOCE P14 & P15 150 increasing TCO2 for fCO2. The increase in K2 may be accounted for in terms of assumed borate– m) 100 2 at carbonate ion pairs. However, since the CO3 µ concentration in ocean waters decreases with 50 increasing fCO and TCO , the g(CO2) value 2 2 3 0 tends to increase and hence K2 is expected to decrease with waters with high fCO2 values. Thus, -50 (meas - calc) ( - calc) (meas this hypothesis is somewhat inconsistent with the 2 -100 No Organics known distribution of carbon chemistry in the fCO

∆ (A) ∆ oceans. Accordingly, an alternative hypothesis is -150 considered. Of various organic matter dissolved in 0 200 400 600 800 1000 1200 1400 1600 1800 1 ocean waters (B80 mmol kg in surface waters fCO (µatm) B 1 2 and 40 mmol kg in deep waters as total 150 dissolved organic carbon, DOC), a portion of m) 100 DOC might be composed of weak organic acids. at Since these acids are included in the titrimetric µ determination of the TA, extra terms for organic 50 acids must be added to the definition of the 0 alkalinity (Eq. (7)). However, since neither the -50 detailed nature of DOC nor the dissociation ( - calc) (meas constants for organic acids are well known, the 2 -100 Organics fCO effect of organic acids on the alkalinity cannot be ∆ (B) ∆ determined rigorously in each water sample. -150 Nevertheless, we attempt to estimate possible 0 200 400 600 800 1000 1200 1400 1600 1800 µ effects of organic acids by making the following fCO2 ( atm) assumptions. First, the concentration of weak Fig. 17. (A) Differences between the measured and calculated organic acids in seawater is assumed to be values of fCO2 at 201C from an input of the WOCE P14/P15 1 uniformly 8 mmol kg throughout water columns. TA and TCO2 data using the constants of Mehrbach et al. In view of the fact that DOC decreases from the (1973). (B) The differences for the same data computed by the surface to deep waters by a factor of two to three, addition of an organic acid term to the definition of the alkalinity. A constant organic acid concentration of this assumption may be an oversimplification for 8 mmol kg1 and a pK of 4 have been assumed. The systematic the real ocean. Second, since the pK values for deviation of fCO2 in waters with greater fCO2 has been organic acids in lake waters are generally 3–4, they eliminated. 1722 F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723 silicate and phosphate. Fig. 17B shows the differ- a comparison between the 14C incubation method and ence computed using a constant amount of organic the mixed layer carbon budget. Deep-Sea Research I 40, acids (8.0 mmol kg1) by adding to the alkalinity 151–169. Clayton, T., Byrne, R.H., 1993. Spectrophotometric seawater equation (Eq. (7)) a single term for organic acid pH measurements: total hydrogen ion concentration scale with a pK of 4. The resulting fCO2 difference calibration of m-cresol purple and at-sea results. Deep-Sea values scatter above and below the zero line evenly Research 40, 2115–2129. yielding a mean difference of 2.6 matm. The Clayton, T., Byrne, R.H., Breland, J.B., Feely, R.A., Millero, magnitude of scatter is consistent with the F.J., Campbell, D.M., Murphy, P.P., Roberts, M., 1995. uncertainty in computed fCO values resulting The role of pH measurements in modern oceanic CO2- 2 system characterizations: precision and thermodynamic from the stated uncertainties in the measurements consistency. Deep-Sea Research 42, 411–429. of TCO2 and alkalinity. Thus, the observed DeValls, T.A., Dickson, A.G., 1998. The pH buffers based on systematic trend for deviations of the computed 2-amino-2-hydroxymethyl-1,3-propanediol (‘‘tris’’) in synthetic seawater. Deep-Sea Research 45, 1541–1554. fCO2 values can be eliminated by this hypothesis as satisfactorily as the K hypothesis. Testing of Dickson, A.G., 1984. pH scales and proton transfer reactions in 2 saline media such as seawater. Geochimica et Cosmochimi- this hypothesis will require chemical characteriza- ca Acta 48, 299–2308. tion of organic acids dissolved in seawater, Dickson, A.G., 1990. Thermodynamics of the dissociation of especially their changes in concentrations and boric acid in synthetic seawater from 273.15 to 318.15 K. properties geographically and with water depth. Deep-Sea Research 37, 755–766. Furthermore, the alkalinity values hitherto re- Dickson, A.G., 1997. Reference material batch information (http://www-mpl.ucsd.edu/people/adickson/CO2 QC/Level1/ ported for shipboard operations as well as for Batches.html). laboratory experiments using natural seawaters Dickson, A.G., Riley, J.P., 1979. The estimation of acid include unspecified contributions from dissolved dissociation constants in seawater from potentiometric organic acids. As the precision of measurements titrations with strong base. I. The ion product of water— improves for the alkalinity, TCO , fCO and pH, Kw. Marine Chemistry 7, 89–99. 2 2 Dickson, A.G., Millero, F.J., 1987. A comparison of the the effects of organic acids could manifest equilibrium constants for the dissociation of carbonic acid themselves as imperfections in the chemical models in seawater media. Deep-Sea Research 34, 1733–1743. for seawater, which are commonly used for Goyet, C., Poisson, A., 1989. New determination of carbonic geochemical and global carbon cycle model acid dissociation constants in seawater as a function of studies. temperature and salinity. Deep-Sea Research 36, 1635–1654. Hansson, I., 1973. A new set of acidity constants for carbonic acid and boric acid in seawater. Deep-Sea Research 20, 461–478. Acknowledgements Johnson, K.M., Wills, K.D., Butler, D.B., Johnson, W.K., Wong, C.W., 1993. Coulometric total carbon dioxide The authors wish to acknowledge the support of analysis for marine studies: maximizing the performance of an automated gas extraction system and coulometric the National Oceanic and Atmospheric Adminis- detector. Marine Chemistry 44, 167–187. tration and the Oceanographic section of the Khoo, K.H., Ramette, R.W., Culberson, C.H., Bates, R.G., National Science Foundation for supporting this 1977. Determination of hydrogen ion concentrations in research. They also acknowledge the partial seawater from 5 to 401C: standard potentials at salinities support by the Joint Institute for the Study of from 20 to 45%. Analytical Chemistry 49, 29–34. Lee, K., Millero, F.J., Campbell, D.M., 1996. The reliability the Atmosphere and Ocean (JISAO) under NOAA of the thermodynamic constants for the dissociation Cooperative Agreement #NA67RJO155, JISAO of carbonic acid in seawater. Marine Chemistry 55, contribution #821, NOAA. 233–246. Lee, K., Millero, F.J., Wanninkhof, R., 1997. The carbon dioxide system in the Atlantic Ocean. Journal of Geophy- sical Research 102, 15696–15707. References Lee, K., Millero, F.J., Byrne, R.H., Feely, R.A., Wanninkhof, R., 2000. The recommended dissociation constants for Chipman, D.W., Marra, J., Takahashi, T., 1993. Primary carbonic acid in seawater. Geophysical Research Letters 27, production at 471N and 201W in the North Atlantic Ocean: 229–232. F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723 1723

Lewis, E., Wallace, D.W.R., 1998. Basic program for CO2 the JGOFS APFZ Transit, Survey and Process 1 Cruises. system in seawater. ORNL/CDIAC-105, Oak Ridge Na- University of Miami Technical Report, No. RSMAS tional Laboratory. 99-004.

Lueker, T.J., Dickson, A.G., Keeling, C.D., 2000. Ocean pCO2 Mojica Prieto, F., Millero, F.J., 2002. The determination of calculated from dissolved inorganic carbon, alkalinity, and pK1+pK2 in seawater as a function of temperature and equations for K1 and K2; validation based on laboratory salinity. Geochimica et Cosmochimica Acta 66, 2529–2540. measurements of CO2 in gas and seawater at equilibrium. Neill, C., Johnson, K.M., Lewis, E., Wallace, D.W.R., 1997. Marine Chemistry 70, 105–119. Accurate headspace analysis of fCO2 in discrete water 0 McElligott, S., Byrne, R.H., 1998. Interaction of B(OH)3 and samples using batch equilibration. Limnology and Oceano- HCO3 in seawater: formation of B(OH)2CO3 . Aquatic graphy 49, 867–870. Geochemistry 3, 345–356. Roy, R.N., Vogel, K.M., Moore, C.P., Pearson, T., Roy, L.N., McElligott, S., Byrne, R.H., Lee, K., Wanninkhof, R., Millero, Johnson, D.A., Millero, F.J., Campbell, D.M., 1993. The F.J., Feely, R.A., 1998. Discrete water column measure- dissociation constants of carbonic acid in seawater at

ments of CO2 fugacity and pHT in seawater: a comparison salinities 5 to 45 and temperatures 0 to 451C. Marine of direct measurements and thermodynamic calculations. Chemistry 44, 249–267. Marine Chemistry 60, 63–73. Takahashi, T., Chipman, D.W., Rubin, S.A., Sweeney, C.,

Mehrbach, C., Culberson, C.H., Hawley, J.E., Pytkowicz, Sutherland, S.C., 2002. The measurement of pCO2 and R.N., 1973. Measurement of the apparent dissociation TCO2 in seawater during the WOCE Line S4I: RVIB constants of carbonic acid in seawater at atmospheric Nathaniel B. Palmer Cruise 96/3. Technical Report to the pressure. Limnology and Oceanography 18, 897–907. Carbon Dioxide Information and Analysis Center Millero, F.J., 1979. The thermodynamics of the carbonate (CDIAC), Oak Ridge, TN. Lamont-Doherty Earth Ob- system in seawater at atmospheric pressure. Geochimica et servatory of Columbia University, Palisades, NY, p. 25. Cosmochimica Acta 43, 1651–1661. Uppstrom,. L.R., 1974. Boron/chlorinity ratio of deep-sea Millero, F.J., 1995. The thermodynamics of the carbonic acid water from the Paciﬁc Ocean. Deep-Sea Research 21, system in the oceans. Geochimica et Cosmochimica Acta 59, 161–162. 661–667. Wanninkhof, R., Thoning, K., 1993. Measurements of fugacity

Millero, F.J., 1996. Chemical Oceanography. CRC Press, Boca of CO2 in surface water using continuous and discrete Raton, FL, 469pp. sampling methods. Marine Chemistry 44, 189–205. Millero, F.J., Pierrot, D., 1998. A chemical equilibrium model Wanninkhof, R., Lewis, E., Feely, R.A., Millero, F.J., 1999. for natural waters. Aquatic Geochemistry 4, 153–199. The optimal carbonate dissociation constants for determin-

Millero, F.J., Zhang, J.Z., Lee, K., Campbell, D.M., 1993. ing surface water pCO2 from alkalinity and total inorganic Titration alkalinity of seawater. Marine Chemistry 44, carbon. Marine Chemistry 65, 291–301. 153–165. Weiss, R.F., 1974. Carbon dioxide in water and seawater: Millero, F.J., Zhu, X., Pierrot, D., Jolliff, J., Degler, E., 1999. the solubility of a non-ideal gas. Marine Chemistry 2, The Carbon Dioxide System in the Southern Ocean during 203–215.