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 pK1 þpK2 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 51C to 251C. 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: pK2TCO2 ¼ pK2 1:6 104 ðTCO2 2050Þ which is valid at TCO2>2050 mmol kg1. 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 Lueker et al. (1.2 104 to 1.9 104). 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). 0967-0637/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 7 - 0 6 3 7 ( 0 2 ) 0 0 0 9 3 - 6
F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723
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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 are in good agreement with the measured values (722.3 matm in fCO2 and 74.3 mmol kg1 in TA). The cause of the decrease in pK2 at high fCO2 is presently unknown. The observed inconsistencies between the measured and computed fCO2 values may be accounted for by adding the effect of organic acid (B8 mmol kg1) 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.
1. Introduction The carbon dioxide system in the oceans can be characterized using any two of the four measurable parameters, pH, total alkalinity (TA), fugacity of carbon dioxide (fCO2) and the total inorganic carbon dioxide (TCO2) providing that constants are available for the other acid/base species in seawater. Dissociation constants of carbonic acid are needed to calculate the components of the CO2 system from these measurements. The stoichiometric dissociation of carbonic acid in seawater are given by CO2 þ H2 O3Hþ þ HCO 3;
ð1Þ
2 þ HCO 3 3H þ CO3 :
ð2Þ
The dissociation constants K1 and K2 are defined by K1 ¼ ½Hþ ½HCO 3 =½CO2 ;
ð3Þ
K2 ¼ ½Hþ ½CO2 3 =½HCO3 ;
ð4Þ
where the brackets are used to denote the concentration in mol kg1 of seawater and the proton concentration is on the seawater scale,
½Hþ SWS ¼ ½Hþ F f1 þ ½SO2 4 T =KHSO4 þ ½F T =KHF g (KHSO4 and KHF are the dissociation constants for HSO 4 and HF, respectively, and the subscripts F and T represent the concentration of the free and total proton). The stoichiometric dissociation constants pK1 and pK2 have been determined by a number of workers (Mehrbach et al., 1973; Hansson, 1973; Goyet and Poisson, 1989; Roy et al., 1993). A summary of these results is given in Table 1. The standard errors (1s) of the fits of the experimental measurements to functions of temperature and salinity are 0.002–0.007 for pK1 and 0.006–0.013 for pK2. The measurements made by Mehrbach et al. (1973) were made on real seawater; while the other studies were made in artificial seawater. Mehrbach et al. (1973) determined pK1 from potentiometric titrations and pK1+pK2 by additions of NaHCO3 to seawater devoid of CO2 until the pH was constant (pH=[pK1+pK2]/2, when TCO2=CA, the carbonate alkalinity). They calculated pK2 by subtracting the pK1 from the measured values of pK1+pK2. Hansson (1973) determined the values of pK1 and pK2 from potentiometric titrations of Na2CO3 in artificial 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
Hansson (1973) Mehrbach et al. (1973) Goyet and Poisson (1989) Dickson and Millero (1987) Roy et al. (1993) a b
Temp. range (1C)
5–30 2–35 1–40 0–35 0–45
Salinity range
20–40 26–43 10–50 20–43 5–45
Std. Errorb
Values at S ¼ 35 and 251C
pK1
pK2
pK1
pK2
0.007 0.006 0.007 0.008 0.002
0.009 0.010 0.011 0.013 0.006
5.850 5.837 5.848 5.845 5.847
8.942 8.955 8.919 8.945 8.916
All the constants have been converted to the seawater scale. 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
Carbonic Acid Constants 6.2 Goyet & Poisson Hansson Mehrbach et al. Roy et al.
6.1
pK1
6.0 5.9
S = 35
5.8 σ = 0.0061
5.7 5.6 -10
0
10
20
30
40
50
o
Temperature ( C) 5.97
Hansson Mehrbach et al. Roy et al.
5.94 5.91
pK1
Poisson (1989) determined the values of pK1 and pK2 from potentiometric titrations of Na2CO3 in artificial seawater (without B(OH)3). Roy et al. (1993) determined the values of pK1 in artificial seawater (devoid of F and B(OH)3) measuring the cell potential with a hydrogen silver–silver chloride electrode system. These measurements were made on solutions with various amounts of NaHCO3 that were equilibrated with gas mixtures of CO2 and H2. Roy et al. (1993) determined the values of pK2 from potentiometric measurements in artificial seawater with mixtures of NaHCO3 and Na2CO3. Millero (1979) examined the pK1 and pK2 determined by Hansson (1973) and Mehrbach et al. (1973) using thermodynamic equations that could be extrapolated to pure water. Dickson and Millero (1987) combined the measurements of Mehrbach et al. (1973) and Hansson (1973) to produce constants that were suggested for general use in oceanography. The more recent measurements of Goyet and Poisson (1989) and Roy et al. (1993) were in reasonable agreement and were combined by Millero (1995). More recently the examination of the internal consistency of laboratory (Lee et al., 1996; Lueker et al., 2000) and field (Wanninkhof et al., 1999; Lee et al., 2000) measurements of fCO2, TCO2 and TA have indicated that the constants of Mehrbach et al. (1973) are more reliable than those of other workers. The calculation of fCO2 from an input of TA and TCO2 and calculations of other parameters from an input of fCO2 and TA or TCO2 require reliable values of pK2 pK1 (or K2 =K1 ). Thus, the field measurements suggest that the values pK2 pK1 from Mehrbach et al. (1973) are more reliable than other laboratory studies. Comparisons of dissociation constants measured in the laboratory as a function of temperature (t ¼ 0–401C at S ¼ 35) and salinity (S ¼ 15– 42 at 251C) are shown in Figs. 1 and 2. The values of pK1 as a function of temperature and salinity are in reasonably good agreement. All the values of pK1 determined in the laboratory studies as a function of temperature (T1K) and salinity (Hansson, 1973; Mehrbach et al., 1973; Goyet and Poisson, 1989; Roy et al., 1993) can be represented by (ln is log to the base e and T is the absolute
1707
o
t = 25 C
5.88 5.85 5.82
σ = 0.0065
5.79 10
15
20
25
30
35
40
45
Salinity Fig. 1. Values of pK1 of various workers for carbonic acid (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 function of salinity. The smooth curve is calculated from Eq. (5).
temperature in Kelvin) pK1 ¼ 8:712 9:460 103 S þ 8:56 105 S 2 þ 1355:1=T þ 1:7976 ln ðTÞ
ð5Þ
with a standard error s ¼ 0:0064: This fit indicates that all the measurements of pK1 are internally consistent to 0.01, which is close to the standard error of the individual fits (see Table 1). A closer look of the individually fitted data indicates that the values of pK1 of Mehrbach et al. (1973) are in good agreement with the measurements of Goyet and Poisson (1989) and Roy et al. (1993) at low temperatures, but differ by as much as 0.01 near 201C.
F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723
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0.020
Carbonic Acid Constants Goyet & Poisson Hansson Mehrbach et al. Roy et al.
9.4 9.2
pK2
∆ pK1 (Meas - Calc)
9.6
9.0
S = 35
8.8
0.015
2σ
0.010 0.005 0.000 -0.005 -0.010
-2σ
-0.015 -0.020 0
σ = 0.018
8.6 8.4 -10
0
10
10
20
30
40
30 o
40
50
Goyet & Poisson Hansson Mehrbach et al. Roy et al.
50
o
Temperature ( C) 0.08
∆ pK 2 (Meas - Calc)
9.4 Hannson Mehrbach et al. Roy et al.
9.3 9.2
pK2
20
Temperature ( C)
9.1 t = 25oC
9.0 8.9
0.06
2σ
0.04 0.02 0.00 -0.02
-2σ
-0.04 -0.06 -0.08 0
8.8
10
20
30
40
50
Temperature ( C)
8.7 0
10
o
σ = 0.012 20
30
40
50
Salinity Fig. 2. Values of pK2 of various workers for carbonic acid (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 function of salinity. The smooth curve is calculated from Eq. (6).
A comparison of the laboratory measurements of pK2 as a function of temperature (t ¼ 0–401C at S ¼ 35) and salinity (S ¼ 15–42 at 251C) is shown in Fig. 2. All the values of pK2 determined in the laboratory studies (Hansson, 1973; Mehrbach et al., 1973; Goyet and Poisson, 1989; Roy et al., 1993) can be represented by (T=K) pK2 ¼ 17:0001 0:01259S 7:9334 105 S2 þ 936:291=T 1:87354 lnðTÞ 2:61471 S=T þ 0:07479 S 2 =T
ð6Þ
Fig. 3. Differences between the measured (Mehrbach et al., 1973; Hansson, 1973; Goyet and Poisson, 1989; Roy et al., 1993) and the calculated values of the combined equation (Eqs. (5) and (6)) of pK1 and pK2 as a function of temperature (S ¼ 20–42).
with a s ¼ 0:019: The overall standard error of the fit to Eq. (6) is close to two times the standard error of the individual fits (Table 1). The deviations of the individual measurements of pK1 and pK2 from the values calculated from Eqs. (5) and (6) are shown in Fig. 3 (on the seawater pH scale, mol kg1). Most of the deviations in pK1 are within 2s of the individual fits. The deviations in pK2 are much larger, but within 2s of the individual fits. The values of pK2 pK1 determined in artificial seawater are also compared to the results of Mehrbach et al. (1973) in Fig. 4 (on the seawater pH scale, mol kg1). Except at low temperatures, the seawater results of Mehrbach et al. (1973) are all higher by about 0.04–0.05 than those determined in artificial seawater. Since the field and laboratory internal consistency
F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723
∆ pK 2 - pK1(Meas - Calc)
0.04 0.02 0.00 -0.02 -0.04 -0.06 -0.08 -10
0
10
20
30
40
50
Temperature (oC)
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or pH and TCO2. Uncertainties of 70.04 in pK2 (79.7% in K2 ) can lead to errors of 726 matm in fCO2 from an input of TA and TCO2 (Mojica Prieto and Millero, 2002). In this paper, we derive values of pK1, pK2 and pK2 pK1 from 6000 sets of field measurements of pH, TA, TCO2 and fCO2 on the NSF/JGOFS, NOAA/OACES and DOE/WOCE cruises in the Atlantic, Pacific, Southern and Indian oceans. The results will be used to examine the reliability of the measured values of pK1, pK2 and pK2 pK1 from various laboratory studies.
Goyet and Poisson Hansson Roy et al.
2. Quality of the field data used
∆ pK 2 - pK1(Meas - Calc)
0.04 0.02 0.00 -0.02 -0.04 -0.06 -0.08 10
20
30
40
50
Salinity
Fig. 4. Differences between the measured (Hansson, 1973; Goyet and Poisson, 1989; Roy et al., 1993) values of pK2 pK1 for carbonic acid with the results of Mehrbach et al. (1973) as fitted by Dickson and Millero (1987) as a function of temperature and salinity. The dotted line shows the approximate offset in the values determined in artificial seawater and real seawater.
calculations support the pK2 pK1 measurements of Mehrbach et al. (1973), the measurements by others (Hansson, 1973; Goyet and Poisson, 1989; Roy et al., 1993) appear to be in error. Since the pK1 measurements of all the laboratory studies are in reasonable agreement, the values of pK2 determined from potentiometric titrations in artificial seawater also appear to be in error. Uncertainties of 70.01 in pK1 and 70.04 in pK2 can lead to significant errors in the calculated parameters of the CO2 system (Mojica Prieto and Millero, 2002). For example, an uncertainty of 70.01 in pK1 (72.5% in K1 ) can lead to errors of 710 matm in fCO2 from an input of TA and TCO2
The field measurements used in this study were taken from the cruises listed in Table 2. The data are available from Carbon Data Information Analysis Center (CDIAC-http://cdiac.ornl.gov/ oceans/woce. All the Principal Investigators that made the measurements are listed in a Table on the web site. Surface data from the Southern Ocean JGOFS cruises from Hawaii to New Zealand and New Zealand to the Ross Sea were also used (Millero et al., 1999). We examined only the samples where all four parameters were measured. The pH measurements were made by spectroscopic methods (Clayton and Byrne, 1993) for all the stations except for the potentiometric measurements made on the S4I cruise in the Southern Ocean. The spectroscopic pH measurements were made at 251C except for the N. Atlantic measurements made at 201C. All the pH measurements have been converted to the seawater scale (Dickson, 1984; Millero, 1995). The pK of the pH indicator was calibrated by Clayton and Byrne (1993) with TRIS buffers (Khoo et al., 1977). Recently, DeValls and Dickson (1998) have shown that the values of pH assigned to the TRIS buffer by Khoo et al. (1977) are too low by 0.0047. Because it is uncertain that this correction should be made to the pK of the indicator and the pH measurements, it has not been made to the field data. This could result in a bias of 0.005 in the pH measurements and resultant values of pK1 and pK2. Recent potentiometric and spectroscopic measurements on seawater (Mojica Prieto and
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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 (A16R) (A20) (A22) (24N)
1368 420 340 773
20 20 20 20
34.3–35.5 34.3–35.5 34.3–35.5 34.3–37.3
pHa, TA, TCO2, fCO2
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
Southern Ocean (S4I)
1065
4
34.2–34.8.
pHc, TA, TCO2d, fCO2d
pHa, TA, TCO2, fCO2
Surface waterse Atlantic Ocean Indian Ocean Southern Ocean
193 128 30
8.6–29 10–29 1.7–4.2
33–37 33–36 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 between the potentiometric and spectroscopic methods are within 70.002. The fCO2 measurements were made in a batch mode at 41C or 201C (Chipman et al., 1993) for deep waters or in a continuous mode (Wanninkhof and Thoning, 1993) near the in situ temperature for surface waters. The concentration of CO2 in the air equilibrated with seawater at a known temperature was measured using an IR analyzer or gas chromatograph, which were repeatedly calibrated using several standard gas mixtures of known CO2 concentrations up to 1400 ppm (determined by P.
Tans of NOAA/CMDL). The conversions of the measured partial pressure of CO2, (pCO2) to the fugacity (fCO2) were made using the equations listed in Wanninkhof and Thoning (1993), which are based on the earlier equations developed by Weiss (1974). Differences in these quantities are small (B1 matm) compared to the precision of measurements. The TA measurements were made by potentiometric titrations (Millero et al., 1993) and the TCO2 was measured by coulometry (Johnson et al., 1993). Certified reference materials (CRMs) were used to adjust all the TA and TCO2 measurements (Dickson, 1997), except the TCO2
F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723
measurements on S4I. CRMs measured on this cruise were within 2 mmol/kg from the certified value. The precisions of the field measurements are 70.001 for pH, 71% for fCO2, 74 mmol kg1 for TA and 72 mmol kg1 for TCO2. The accuracy of the TA and TCO2 measurements are close to the precision because all the field measurements used standards that were reproduced to near the precision of the measurements. The uncertainties of the pH measurements are larger than the precision due to the uncertainties in the pH assigned to the TRIS buffers used in the calibration and the errors involved in the corrections to in situ temperatures. We estimate that the errors in field pH measurements could be as large as 70.01 due to these calibration problems. The accuracy of fCO2 measurements for the water samples is assumed to be close to the precision.
3. Calculations The methods used to determine the values of pK1, pK2 and pK2 pK1 have been given by Lee et al. (1996). The calculations require the determination of the carbonate alkalinity (CA), which is defined by (Dickson, 1984) CA
½HCO 3
þ 2½CO2 ¼ 3 ¼ TA ½BðOHÞ4 þ ½Hþ ½OH 3 ½HPO2 4 2½PO4 ½SiðOHÞ3 O :
ð7Þ
Contributions from minor weak acids including organic acids are assumed to be negligible. The concentrations of the individual components (mol kg1) are determined from the appropriate dissociation constants for boric acid (KB ; Dickson, 1990), water (KW ; Millero, 1995), phosphoric (KPi ; Millero, 1995), and silicic acid (Millero, 1995) on the seawater pH scale: þ ½BðOHÞ 4 ¼ ½BT =f1 þ ½H =KB g;
ð8Þ
½OH ¼ KW =½Hþ ;
ð9Þ
þ þ ½HPO2 4 ¼ f½PT ½H =KP3 g=f1 þ ½H =KP3 þ 2
þ ½H =ðKP2 KP3 Þ þ ½Hþ 3 =ðKP1 KP2 KP3 Þg;
ð10Þ
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þ þ 2 ½PO3 4 ¼ ½PT =f1 þ ½H =KP3 þ ½H =ðKP2 KP3 Þ
þ ½Hþ 3 =ðKP1 KP2 KP3 Þg; ½SiðOHÞ3 O ¼ ½SiT =f1 þ ½Hþ =KSi g;
ð11Þ ð12Þ
where the concentration of boron, [B]T= . 0.000416(S/35) mol kg1 (Uppstrom, 1974) and the concentrations of total phosphate [P]T and silica [Si]T are taken from the at-sea measurements (mol kg1). As mentioned earlier, the seawater pH scale was used throughout this paper and all the constants used have been converted to this scale (Dickson and Millero, 1987; Millero, 1995). The required dissociation constants for HSO 4 and HF are taken, respectively, from Dickson (1990) and Dickson and Riley (1979). The values of 1 [SO2 and [F]T= 4 ]T=0.0293(S/35) mol kg 1 0.00007(S/35) mol kg (Millero, 1996). The con centrations of OH, HPO2 4 , Si(OH)3O in deep waters contribute less than 0.3% to TA; while B(OH) 4 can contribute 4% to TA in surface waters and 2% in deep waters (Millero, 1996). The components of the carbonate system are determined from ½CO2 ¼ f CO2 K0 ;
ð13Þ
½HCO 3 ¼ 2TCO2 CA 2½CO2 ;
ð14Þ
½CO2 3 ¼ CA TCO2 þ ½CO2 ;
ð15Þ
where K0 is the solubility constant for CO2 (Weiss, 1974). The constants are determined from K1 ¼ ½Hþ ½HCO 3 =½CO2 þ ¼ ½H f2TCO2 CA 2½CO2 g=½CO2 ;
ð16Þ
K2 ¼ ½Hþ ½CO2 3 =½HCO3
¼
f½Hþ ðCA TCO2 þ ½CO2 Þg ; f2TCO2 CA 2½CO2 g
2 K2 =K1 ¼ ½CO2 ½CO2 3 =½HCO3 f½CO2 ðCA TCO2 þ ½CO2 Þg ¼ : fð2TCO2 CA 2½CO2 g2
ð17Þ
ð18Þ
As is clear from Eq. (18), the ratio of K2 =K1 is nearly independent of the pH and can be determined from measurements of TA, TCO2 and fCO2. This is important since errors in the
F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723
1712
Table 3 Effect of temperature (25–01C) on the pH of seawater (S ¼ 30–40, TA=2300 mmol kg1 and TCO2=2100 mmol kg1) DpH/DT (1C1) Salinity
Mehrbacha
30 35 40
0.0158 0.0157 0.0156
Hanssonb 0.0149 0.0148 0.0148
Effect of change in temperature (25–41C) on the calculated pK1 — 0.0168
D & Mc
G & Pd
Roye
0.0156 0.0155 0.0154
0.0165 0.0164 0.0163
0.0166 0.0166 0.0164
0.0042
+0.0147
+0.0165
a
Mehrbach et al. (1973). Hansson (1973). c Dickson and Millero (1987). d Goyet and Poisson (1989). e Roy et al. (1993). b
measurement of pH do not strongly affect the estimates of pK2 pK1 : Since most of the measurements of pH were made at 251C, it is necessary to estimate their values at lower or higher temperatures. This requires knowledge of the constants K0 ; K1 and K2 for the CO2 system. The values of DpH/DT determined from the presently available constants are given in Table 3 (Mehrbach et al., 1973; Hansson, 1973; Goyet and Poisson, 1989; Roy et al., 1993). The values of DpH/DT are nearly independent of salinity and temperature from 251C to 01C (Millero, 1995) and range from 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/ TCO2 (Millero, 1995). The differences in the values of DpH/DT calculated using different constants are not important for small changes in temperature (51C), but are quite important for large changes in temperature (251C) (see Table 3 for calculations of pK1). Since the values of DpH/DT can differ, we have determined their values using the CO2 Sys program (Lewis and Wallace, 1998) for each sample. Since the Mehrbach et al. (1973) constants appear to be more internally consistent with field measurements (Clayton et al., 1995; McElligott et al., 1998; Wanninkhof et al., 1999; Lee et al., 1997, 2000), we have used these constants to determine the values of DpH/DT from the measured values of TA and TCO2. This is supported
by the fact that the Mehrbach et al. (1973) values of pK2 pK1 are more reliable than the measurements made on artificial seawater (Mojica Prieto and Millero, 2002). Uncertainties in the measured parameters result in values of pK1, pK2 and pK2pK1 with deviations of 70.006 in pK1, 70.010 in pK2 and 70.010 in pK2 pK1 : Larger errors in pH will affect the uncertainty of the values determined for pK1 and pK2 by 70.01, but not seriously affect the values of pK2 pK1 (see Eq. (18)). It should be pointed out that all the calculations were made at 1 atm and not at the in situ pressure.
4. Measurements made on deep waters at a constant temperature 4.1. Measurements of fCO2 at 201C We have first examined the results where the fCO2 was measured at 201C and the pH at 201C or 251C for surface and deep waters (see Table 2). The adjustments of the pH measurements from 25 to 201C have been made using the CO2 Sys program (Lewis and Wallace, 1998) as discussed above. The resulting values of pK1, pK2 and pK2 pK1 are shown as a function of depth (expressed in terms of hydrostatic pressure) where water samples were collected, in Fig. 5 and tabulated in Table 4. The values with deviations
F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723
20oC Data 5.96 pK1 = 5.888 + 0.010
5.94
pK1
5.92 5.90 5.88 5.86 5.84 0
2000
4000
6000
pK2 = 9.035 + 0.019
9.15
pK2
9.10 9.05 9.00 8.95 8.90 0
2000
4000
6000
3.30 pK2 - pK1 = 3.148 + 0.019
pK2 - pK1
3.25 3.20 3.15 3.10 3.05 3.00 0
2000
4000
6000
Pressure (db)
Fig. 5. Calculated values of pK1 ; pK2 and pK2 pK1 at 201C as a function of depth for deep waters from the Atlantic, Indian, Pacific and Southern oceans. The value listed is the average of all the data and is depicted by the horizontal line.
1713
greater than 2s (0.04 for pK1 and 0.08 for pK2) have been eliminated (B3.8%) from the plots. This cuts down the scatter in the data, but does not change the average values of pK1=5.88870.010, pK2=9.03570.019 and pK2 pK1 ¼ 3:1487 0:019: The average salinity for all the samples was S ¼ 34:970:5 which is the same as the deep waters. As shown in Eqs. (5) and (6) and Figs. 1 and 2, the values of pK1 and pK2 are not a strong function of salinity (DpK1 =DSE0:0048 and DpK2 =DSE0:012). The pK1 changes by 0.003 and pK2 changes by 0.006 for a change in salinity of 0.5, which is within the experimental error. A comparison of the calculated values of pK1 and pK2 with those obtained in earlier studies (Mehrbach et al., 1973; Hansson, 1973; Goyet and Poisson, 1989; Roy et al., 1993) is shown in Fig. 6. The measured values of pK1 at 201C agree with the constants of Mehrbach et al. (1973), Dickson and Millero (1987), Goyet and Poisson (1989) and Roy et al. (1993) to within 0.007. The pK1 values of Hansson (1973) show much larger deviations (0.01). The values of pK2 and pK2 pK1 at 201C are in excellent agreement (0.005) with the results of Mehrbach et al. (1973) (pK2 ¼ 9:035 and pK2 pK1 ¼ 3:153). The values of pK2 and pK2 pK1 agree to within 0.02 with the measurements of Hansson (1973) and the equations of Dickson and Millero (1987). The studies of Goyet and Poisson (1989) and Roy et al. (1993) show 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 a
pK1
pK2
pK2 pK1
41C
Deep Surfaceb Lee et al.c Lueker et al.c
6.06270.009 6.05770.005 6.05870.006 —
9.32170.020 9.32470.008 9.30370.011 —
3.25770.020 3.25870.008 3.24570.011 3.24170.013
201C
Deepd Surfaceb Lee et al.c Lueker et al.c
5.88870.010 5.87970.005 5.88870.006 —
9.03570.019 9.03270.008 9.01170.011 —
3.14870.019 3.15270.008 3.13970.014 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).
F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723
1714
4oC Data 6.12
pK1
pK1 = 6.064 + 0.010
6.10 pK1
Meas - Calc
20oC Data 0.012 0.009 0.006 0.003 0.000 -0.003 -0.006 -0.009 -0.012
6.08 6.06 6.04 6.02
Han
0
Mehr D&M Goyet Roy Surface
2000
0.04
6000
pK2 = 9.321 + 0.021
9.38 0.03
pK2
0.02
9.36 pK2
Meas - Calc
4000
9.40
0.01
9.34 9.32 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
pK2 - pK1
0.03 0.02
pK2 - pK1
Meas - Calc
0.04
pK2 - pK1 = 3.256 + 0.020
3.32 3.30 3.28 3.26 3.24
0.01
3.22
0.00
3.20 0
-0.01 Han
Mehr D&M Goyet Roy Surface
2000
4000
6000
Pressure (db)
Fig. 6. Comparisons of the field calculated values of pK1 ; pK2 and pK2 pK1 at 201C with the smoothed literature values and the average value for surface measurements. The surface values were calculated from Eqs. (19)–(21).
Fig. 7. Calculated values of pK1 ; pK2 and pK2 pK1 at 41C as a function of depth for deep waters from the Atlantic, Indian, Pacific and Southern oceans. The value listed is the average of 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 values; while the others did not, we used them in all the conversions. These large corrections in pH lead to uncertainties in the calculated values of pK1 and pK2 at 41C, but do not affect the calculated values of pK2 pK1 : The calculated values of pK1, pK2 and pK2 pK1 are shown in Fig. 7. The average values found are pK1=6.06470.010, pK2=9.32170.021 and pK2 pK1 ¼ 3:25670:020: The values of pK2 and pK2 pK1 at 41C adjusted to S ¼ 35 are shown in Fig. 8.
We next examined the measurements made in the Southern Ocean where the TCO2 and fCO2 were determined at 41C by the Lamont Group (Takahashi et al., 2002). The measurements of pH and TA on this cruise were made by potentiometric methods (Millero et al., 1993) corrected using measurements on CRM. The pH measurements were made at 251C; thus, the corrections to 41C are quite large and a function of the constants used. Since the conversion with the constants of
F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723 o 4 C Data
Surface Data 6.2
0.008 pK1
0.002 0.000
6.0 5.9
-0.002
5.8
-0.004
5.7
σ = 0.005
-5
-0.006 Han 0.05
9.4
0.04
9.3
pK2
0.03 0.02
5
10
15
20
25
30
35
Indian Atlantic Southern
9.2 9.1 σ = 0.009
9.0
0.01
8.9
0.00
8.8 -5
-0.01
0
5
10
15
20
25
30
35
3.35
Han
Mehr D&M Goyet Roy Surface
3.30
0.04
pK2 - pK1
0.03 0.02
pK2 - pK1
0.05
Meas - Calc
0
9.5
Mehr D&M Goyet Roy Surface
pK2
Meas - Calc
Indian Atlantic Southern
6.1
0.004 pK1
Meas - Calc
0.006
1715
Indian Atlantic Southern
3.25 3.20 3.15 σ = 0.009
3.10
0.01
3.05
0.00
-5
0
5
10
15
20
25
30
35
Temperature (oC)
-0.01 Han
Mehr D&M Goyet Roy Surface
Fig. 8. Comparisons of the field calculated values of pK1 ; pK2 and pK2 pK1 at 41C with the smoothed literature values. The surface values were calculated from Eqs. (19)–(21).
The results are in reasonable agreement with the results of Mehrbach et al. (1973) (pK2=9.315 and pK2 pK1 ¼ 3:258) and Goyet and Poisson (1989) (pK2=9.307 and pK2 pK1 ¼ 3:249). The measured values of pK1 at 41C are all in reasonable agreement (0.007) with the laboratory studies.
Fig. 9. Calculated values of pK1 ; pK2 and pK2 pK1 for surface waters from the Indian, Atlantic, and Southern oceans as a function of temperature. The lines were calculated from Eqs. (19)–(21).
Atlantic and Southern oceans are shown in Fig. 9 as a function of temperature and salinity (t ¼ 1:6–351C and S ¼ 34–37) and have been fitted to the equations (T=K) pK1 ¼ 6:359 0:00664S 0:01322ðT 273:15Þ þ 4:989 105 ðT 273:15Þ2 ;
5. Measurements made on surface waters The field measurements of TA, TCO2, pH (251C), and pCO2 for surface waters have been used to calculate the values of pK1, pK2 and pK2 pK1 : The results for waters from the Indian,
ð19Þ
pK2 ¼ 9:867 0:01314S 0:01904ðT 273:15Þ þ 2:4480 105 ðT 273:15Þ2 ;
ð20Þ
pK2 pK1 ¼ 3:510 0:0064S 0:006711ðT 273:15Þ
ð21Þ
F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723
1716
with standard deviations of s ¼ 0:005 in pK1, s ¼ 0:008 in pK2 and s ¼ 0:008 in pK2 pK1 : The effect of salinity on pK1 and pK2 from the surface data is slightly higher than literature data (DpK1 =DSE0:0048 and DpK2 =DSE0:012). This is not surprising due to the limited salinity range of the field data. The values calculated from Eqs. (19)–(21) at 41C and 201C are compared to the values calculated for the deep waters in Table 4 and Figs. 6 and 8. The agreement is reasonable 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 uncertainties in pK1 and pK2 at 41C and 201C are related to errors in pH.
6. Estimations of pK1 and pK2 as a function of salinity and temperature All the field measurements clearly demonstrate that the values of pK2 pK1 from the measurements of Mehrbach et al. (1973) are more reliable than those determined in the other laboratory studies. This is largely due to differences in the values of pK2 determined in real and artificial seawater. The values of pK1 determined from the field data do not favor a given set of laboratory measurements. This is partly due to uncertainties in the spectroscopic pH measurements and errors in the calculation of in situ values of pH from measurements made at 251C. The recent pK1 and pK1+pK2 measurements of Mojica Prieto and Millero (2002) have shown to be in good agreement with the work of Mehrbach et al. (1973). These studies have been combined (Mojica Prieto and Millero, 2002) to give (ln=the base -e logarithm) pK1 ¼ 43:6977 0:0129037S þ 1:364 104 S2 þ 2885:378=T þ 7:045159 ln T ðs ¼ 0:0056Þ;
ð22Þ
pK2 ¼ 452:0940 þ 13:142162S 8:101 104 S2 þ 21263:61=T þ 68:483143 ln T þ ð581:4428S þ 0:259601S 2 Þ=T
1:967035S ln T ðs ¼ 0:010Þ:
ð23Þ
These equations give pK values somewhat different from those given by Eqs. (19) and (20) (within 75% for K1 and 78% for K2 ). However, since Eqs. (19) and (20) are based on field data with relatively narrow salinity range, we feel that these equations are the best representation of the carbonic acid dissociation constants in seawater.
7. Comparisons of pK2 pK1 with laboratory measurements 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. (1996) and Lueker et al. (2000) for seawater. The values of pK2 pK1 from the measurements of Lee et al. (1996) as a function of temperature are shown in Fig. 10. The values of pK2 pK1 appear to be a linear function of temperature as found for the field measurements (see Fig. 9). The spread of the results at a given temperature is related to changes in the values as a function of fCO2 (Fig. 10b). The values of pK2 pK1 at 41C and 201C at low fCO2 are compared to our values in Table 4. The agreement is within 0.01 at each of these temperatures and is satisfactory. The values of pK2 pK1 from the measurements of Lueker et al. (2000) as a function of temperature are shown in Fig. 11. The values of pK2 pK1 also appear to be a linear function of temperature. The spread of some of the results at a given temperature are related to changes in the values as a function of fCO2 (Fig. 11). The scatter is much greater in the Lueker et al. (2000) data than the results of Lee et al. (1996). The results at low fCO2, however, are in reasonable agreement within 0.01 with other workers (Table 4). The effect of fCO2 on the values of pK2 pK1 is hard to explain. The data of Lee et al. (1996) indicate that the dependence on fCO2 is largely due to the variation of pK2. This tends to point to changes in the interactions as a function of fCO2 being related to changes in the ratio of CO2 3 /HCO3 .
F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723
Lee et al.
1717
Lueker et al.
3.30
3.24
3.25 o
pK2 - pK1
3.15 3.10
o
3.20
pK2 - pK1
5.6 C o 13.3 C o 20 C o 25 C o 35 C
3.20
3.05
5C o 15 C o 18 C o 25 C
3.16 3.12
3.00
3.08 2.95 0
5
10
15
20
25
30
35
40
0
5
o
Temperature ( C)
10
15
20
25
30
Temperature (oC)
3.30 3.25
3.24 o
pK2 - pK1
3.15 3.10 3.05
o
5C o 15 C o 18 C o 25 C
3.20
pK2 - pK1
5.6 C o 13.3 C o 20 C o 25 C o 35 C
3.20
3.16 3.12
3.00 2.95 200
3.08 400
600
800 1000 1200 1400 1600 1800
fCO2 (µatm)
Fig. 10. Values of pK2 pK1 determined from the measurements of Lee et al. (1996) as a function of temperature (top) and fCO2 (bottom).
The recent studies of Mojica Prieto and Millero (2002) indicate that the differences in the values of pK1 and pK2 in real and artificial seawater are related to interactions of the borate and carbonate system. At 251C the values of pK1 in artificial seawater with boric acid are B0.01 lower than in artificial seawater without boric acid; while, the values of pK2 in artificial seawater with boric acid are higher B0.04 than seawater without boric acid. The interactions responsible for these differences are not clear. The increase in K1 in real seawater can be attributed to a decrease in the activity coefficient of HCO 3 , g(HCO3 ) and the decrease in K2 can be attributed to an increase in 2 the activity coefficient of CO2 3 , g(CO3 ). If one assumes that the repulsive interactions between 2 B(OH) 4 and HCO3 and CO3 are small, one can 2 attribute the changes in g(HCO 3 ) and g(CO3 ) to interactions with B(OH)3. McElligott and Byrne (1998) have shown the interactions of B(OH)3 and
0
300
600
900
1200
1500
1800
fCO2(µatm)
Fig. 11. Values of pK2 pK1 determined from the measurements of Lueker et al. (2000) as a function of temperature (top) and fCO2 (bottom).
HCO 3 can be due to HCO 3 þ BðOHÞ3 ¼ BðOHÞ2 CO3 þ H2 O:
ð24Þ
Although this reaction would lower g(HCO 3 ), the magnitude of this interaction that they found is not large enough to lower the pK1 by 0.01. Similar interactions between B(OH)3 and CO2 3 would not be expected to increase g(CO2 3 ). Further studies of mixtures of boric and carbonic acid mixtures are needed to elucidate these interactions. If the borate–carbonate ion interactions are assumed to be significant, then the following considerations may be advanced in order to account for the observed decrease in pK2 (or increase in K2 ) with increasing fCO2. The value of K2 is related to the value in water at 0 ionic strength, K20 ; and the activity coefficients, gðiÞ; by 2 þ K2 ¼ K20 fgðHCO 3 Þ=gðH ÞgðCO3 Þg:
ð25Þ
F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723
8. Proposed dependence of K2 on TCO2 Our determinations of pK2 from the field data do not show any effect of fCO2 on the calculated values within the experimental error of the calculations as shown in Fig. 5. This is not surprising since at 201C, the effect is quite small (see Figs. 10 and 11). Internal consistency tests, however, do show this effect (Lueker et al., 2000; Lee et al., 2000). The differences in the measured and calculated values of fCO2 using an input of TA and TCO2 (which require reliable values of pK2 pK1 ) are shown in Fig. 12A for all the stations listed in Table 2. The average 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 fCO2, apparently due to changes in the pK2 pK1 (Lueker et al., 2000; Lee et al., 2000). The differences of the measured and calculated values of fCO2 as a function of TCO2 (Fig. 13A) show larger deviation at high TCO2. At values of TCO2 less than 2050 mmol kg1, the deviations are independent of the TCO2. By adjusting the values of pK2 above 2050 mmol kg1, it was possible to lower the average deviations to 0 matm and the standard error to 22.7 matm (see Figs. 12B and 13B). This resulted in the empirical
150
∆ fCO2(meas - calc)
The increase in K2 can be attributed to an in2 crease in g(HCO 3 ) or a decrease in g(CO3 ). Since the value of pK1 is not strongly dependent on fCO2, the changes in g(HCO 3 ) cannot be very great. This is in agreement with the studies of McElligott and Byrne (1998). Model calculations of CO2 system in seawater (Millero and Pierrot, 1998) as a function of TCO2 do not yield large 2 changes in g(HCO 3 ) or g(CO3 ). It should be noted that the activity coefficients for B(OH)3 and B(OH) 4 would also depend on the concentrations 2 of HCO 3 and CO3 via ionic interactions. Hence, the value of KB would vary with fCO2, and the direction of its changes depends upon the nature of the interactions and ion pairs. This means that our present understanding of the ionic interactions affecting the carbonate system in seawater is deficient.
Ave =26.6 µatm σ = 29.7 µatm
100 50 0 -50 -100
(A) -150 0
500
1000
1500
fCO2 (µatm) 150
∆ fCO2(meas - calc)
1718
Ave = 0 µatm σ = 22.7 µatm
100 50 0 -50 -100
(B)
Corrected -150 0
500
1000
1500
fCO2 (µatm) Fig. 12. Differences between the measured and calculated values of fCO2 from an input of TA and TCO2 as a function of fCO2 using the combined constants of Mehrbach et al. (1973) and Mojica Prieto and Millero (2002) (Eqs. (22) and (23)). The values in panels (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 estimate of the offset at high fCO2.
relationship pK2TCO2 ¼ pK2 1:6 104 ðTCO2 2050Þ
ð26Þ
which is valid at 201C and at TCO2>2050 mmol kg1. Similar calculations at 41C were not possible since the values of fCO2 of all the waters are below 680 matm. As shown in Fig. 14, the values of the slope of pK2 as a function of fCO2 at 201C or TCO2 found from the field data are in reasonable agreement with the values determined from the laboratory measurements of Lee et al. (1996) and Lueker et al. (2000) (1.2 104 to
F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723
100
0.00000
Ave = 26.6 µatm σ = 29.7 µatm
-0.00001
∆ (pK2-pK1)/∆ ∆fCO2
∆ fCO2 (meas - calc)
150
1719
50 0 -50 -100
-0.00002 -0.00003 -0.00004 -0.00005 -0.00006 -0.00007
(A) -150 1800
1900
2000
2100
2200
2300
(A)
-0.00008 0
2400
5
10
15
TCO2 (µmol kg ) Ave = 0 µatm σ = 22.7 µatm
50 0 -50 -100
Corrected -150 1800
1900
(B)
2000
25
30
35
40
0.0000
2100
2200
2300
∆ (pK2-pK1 )/∆ ∆TCO2
∆ fCO2 (meas - calc)
150 100
20
Lee et al. Lueker et al. o 20 C Field Data
-1
-0.0001
-0.0002
-0.0003
(B)
2400
-1
TCO2 (µmol kg ) Fig. 13. Differences between the measured and calculated values of fCO2 from an input of TA and TCO2 as a function of TCO2 using the combined constants of Mehrbach et al. (1973) (top) and Mojica Prieto and Millero (2002) (bottom) (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 estimate of the offset at high TCO2.
1.9 104). The values at other temperatures (t1C) can be estimated from the linear fit (Fig. 14) of the results of Lee et al. (1996) and Lueker et al. (2000), DðpK2 pK1 Þ=DTCO2 ¼ 2:65 104 þ 5:74 106 t with a unit of kg mmol1. As discussed earlier, the borate–carbonate ion interactions would affect not only the K2 for carbonic acid, but also the KB for boric acid. Hence, the proposed relationships include the combined effects on K2 and KB ; and should be considered as an empirical expression which is intended to correct for imperfections of the chemical model used.
0
5
10
15
20
25
30
35
40
o
Temperature ( C) Fig. 14. Comparison of the slopes of pK2 as a function of fCO2 and TCO2 obtained from the field data at 201C with the measurements of Lee et al. (1996) and Lueker et al. (2000) as a function of temperature.
When pH values are used with TCO2 or TA for 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 uncertainty of 0.01 in pK1 yields an error of 10 matm in fCO2; while an uncertainty of 0.04 in pK2 leads to an error of 7 matm. The errors in the calculated values of fCO2 from an input of pH and TCO2 are examined in Fig. 15A. The average error is 9.5 matm and the standard error is 21.8 matm. When the value of pK2 using Eq. (26) is used (see Fig. 15B), the average error remains unaffected, and is 11.8 matm with the standard error is 22.3 matm. Thus, when using an input of pH and TCO2, the correction of pK2 at high TCO2 does not strongly influence the calculated values of fCO2. The effect of an addition of 0.0047 to
F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723
1720
Input of pH and TCO2 30 -1
∆TA (µmol kg )
∆fCO2 (µatm) ∆
Input pH and TCO2 100 80 Ave = 9.5 µatm σ = 21.8 µatm 60 40 20 0 -20 -40 -60 1800 1900 2000
(A) 2100
2200
2300
0 -10
2300
pH + 0.0047 2000
2200
2300
2400
10 0 -10 -20
2300
2400
TCO2 (µmol kg-1)
Average = -1.7 µmol kg-1 σ = 4.3 µmol kg-1
-30 1800
2400
(C) 2100
2000 2100 2200 TCO2 (µmol kg-1)
-1
∆TA (µmol kg )
(B)
Ave = 21.1 µatm σ = 23.8 µatm
1900
1900
(A)
20
30
-20 -40 -60 1800
Average = 3.2 µmolkg-1 σ = 4.1 µmol kg-1
-20
30
-1 ∆TA (µmol kg ) ∆
∆fCO2 (µatm) ∆ ∆ fCO2 (µatm)
100 80 60 40 20 0
10
-30 1800
2400
-1 TCO2 (µmol kg )
100 80 Ave = 11.8 µatm 60 σ = 22.3 µatm 40 20 0 -20 -40 -60 1800 1900 2000 2100 2200 TCO2 (µmol kg-1)
20
1900
2000 2100 2200 TCO2 (µmol kg-1)
20
(B) 2300
2400
pH + 0.0047
10 0 -10 Average = -3.9 µmol kg-1 -1 -30 σ= 4.1 µmol kg 1800 1900 2000 2100 2200 TCO2 (µmol kg-1) -20
(C) 2300
2400
Fig. 15. Comparison of the measured and calculated values of fCO2 from an input of pH and TCO2 using the combined constants of Mehrbach et al. (1973) and Mojica Prieto and Millero (2002) (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 values in (C) have been determined by increasing the pH by 0.0047.
Fig. 16. Comparison of the measured and calculated values of TA from an input of pH and TCO2 using the combined constants of Mehrbach et al. (1973) and Mojica Prieto and Millero (2002) (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 values in (C) have been determined by increasing the pH by 0.0047.
the pH (DeValls and Dickson, 1998) is shown in Fig. 15C. The addition increases not only the fCO2 deviations, but also the average error to 21.1 matm. These results indicate that an increase of the pH by 0.0047 is not needed when calculating fCO2. The errors in the calculated values of TA from an input of pH and TCO2 are examined in Fig. 16A. The average error is 3.2 mmol kg1 and the standard error is 4.1 mmol kg1. The correction of the value of pK2 using Eq. (26) is shown in Fig. 16B. The average error is decreased to
1.7 mmol kg1 and the standard error is increased to 4.3 mmol kg1. Thus, when using an input of pH and TCO2, the correction of pK2 at high TCO2 improves slightly the calculated values of TA. The effect of an addition of 0.0047 to the pH (DeValls and Dickson, 1998) is shown in Fig. 16C. The addition causes the average deviation in TA to be 3.9 mmol kg1 and does not strongly affect the standard error. These results indicate that the correction of the pH by 0.0047 is not needed to make reliable calculations of fCO2 and TA from an input of pH and TCO2. It should be pointed
F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723
The field data shown in Figs. 12 and 13 as well as the laboratory data presented by Lee et al. (1996) and Lueker et al. (2000) demonstrate that the difference between the observed and computed fCO2 values increase systematically for waters with 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 increasing TCO2 for fCO2. The increase in K2 may be accounted for in terms of assumed borate– carbonate ion pairs. However, since the CO2 3 concentration in ocean waters decreases with increasing fCO2 and TCO2, the g(CO2 3 ) value tends to increase and hence K2 is expected to decrease with waters with high fCO2 values. Thus, this hypothesis is somewhat inconsistent with the known distribution of carbon chemistry in the oceans. Accordingly, an alternative hypothesis is considered. Of various organic matter dissolved in ocean waters (B80 mmol kg1 in surface waters and B40 mmol kg1 in deep waters as total dissolved organic carbon, DOC), a portion of DOC might be composed of weak organic acids. Since these acids are included in the titrimetric determination of the TA, extra terms for organic acids must be added to the definition of the alkalinity (Eq. (7)). However, since neither the detailed nature of DOC nor the dissociation constants for organic acids are well known, the effect of organic acids on the alkalinity cannot be determined rigorously in each water sample. Nevertheless, we attempt to estimate possible effects of organic acids by making the following assumptions. First, the concentration of weak organic acids in seawater is assumed to be uniformly 8 mmol kg1 throughout water columns. In view of the fact that DOC decreases from the surface to deep waters by a factor of two to three, this assumption may be an oversimplification for the real ocean. Second, since the pK values for organic acids in lake waters are generally 3–4, they
WOCE P14 & P15 150
∆ fCO2(meas - calc) (µatm)
9. Possible effects of organic acids
are totally dissociated at pH of normal seawater (8.2–7.9). Using the shipboard data obtained during Pacific WOCE P14/15, the effect of this hypothetical organic acid on computed fCO2 values is demonstrated below. Fig. 17A shows that the difference between the observed and computed fCO2 values at 201C increases systematically with increasing fCO2 for seawater. The computed fCO2 values were obtained using the observed values for TCO2, alkalinity, salinity and the concentrations of
100 50 0 -50 -100
No Organics
(A)
-150 0
200 400 600 800 1000 1200 1400 1600 1800
fCO2 (µatm) 150
∆ fCO2(meas - calc) (µatm)
out that an input of pH and TA to calculate fCO2 and TCO2 yields similar results.
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100 50 0 -50
Organics
-100
(B)
-150 0
200 400 600 800 1000 1200 1400 1600 1800
fCO2 (µatm) Fig. 17. (A) Differences between the measured and calculated values of fCO2 at 201C from an input of the WOCE P14/P15 TA and TCO2 data using the constants of Mehrbach et al. (1973). (B) The differences for the same data computed by the addition of an organic acid term to the definition of the alkalinity. A constant organic acid concentration of 8 mmol kg1 and a pK of 4 have been assumed. The systematic deviation of fCO2 in waters with greater fCO2 has been eliminated.
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silicate and phosphate. Fig. 17B shows the difference computed using a constant amount of organic acids (8.0 mmol kg1) by adding to the alkalinity equation (Eq. (7)) a single term for organic acid with a pK of 4. The resulting fCO2 difference values scatter above and below the zero line evenly yielding a mean difference of 2.6 matm. The magnitude of scatter is consistent with the uncertainty in computed fCO2 values resulting from the stated uncertainties in the measurements of TCO2 and alkalinity. Thus, the observed systematic trend for deviations of the computed fCO2 values can be eliminated by this hypothesis as satisfactorily as the K2 hypothesis. Testing of this hypothesis will require chemical characterization of organic acids dissolved in seawater, especially their changes in concentrations and properties geographically and with water depth. Furthermore, the alkalinity values hitherto reported for shipboard operations as well as for laboratory experiments using natural seawaters include unspecified contributions from dissolved organic acids. As the precision of measurements improves for the alkalinity, TCO2, fCO2 and pH, the effects of organic acids could manifest themselves as imperfections in the chemical models for seawater, which are commonly used for geochemical and global carbon cycle model studies.
Acknowledgements The authors wish to acknowledge the support of the National Oceanic and Atmospheric Administration and the Oceanographic section of the National Science Foundation for supporting this research. They also acknowledge the partial support by the Joint Institute for the Study of the Atmosphere and Ocean (JISAO) under NOAA Cooperative Agreement #NA67RJO155, JISAO contribution #821, NOAA.
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