ORNL/COIAC-105 

Program Dav~lopad ~or 

C£J2 5y5tam caluUlatiOtl6 

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Department of Applied 5eienee 

Srookhaven National lAboratory 

I 

cat1lon Dioxide Information Analysis C4!nter 

Oak Ridge National Laboratory 
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document. 
nN~~ 

K~ '~L APR 7 1998 

Master Coo\r I .J 

PROGRAM DEVELOPED 

FOR 

C02 SYSTEM CALCULATIONS 

Ernie Lewis and Doug Wallace 

Department of Applied Science 

Brookhaven National Laboratory 

Upton, New York 

Prepared by Linda J. Allison 

Carbon Dioxide Information Analysis Center 

Oak Ridge National Laboratory 

Oak Ridge, Tennessee 

Environmental Sciences Division 

Publication No. 4735 

Date Published: February 1998 

Preparation funded by 

Budget Activity Number KP 12 02 03 0 

Published by the 

Carbon Dioxide Information Analysis Center 

OAK RIDGE NATIONAL LABORATORY 

Oak Ridge, Tennessee 37831-6335 

managed by 

ORNIJCDIAC-105 

LOCKHEED MARTIN ENERGY RESEARCH CORP. 

for the 

U.S. DEPARTMENT OF ENERGY 

Environmental Sciences Division 

Office of Biological and Environmental Research 

under contract DE-AC05-960R22464 
CONTENTS 

PREFACE • • . • • • • • • . . . • • • • • . • • • • • • . • • • . . • • • . • • . • . . . . . . • • . . . . • • . . • . . v 

1. INTRODUCTION . .............................................. . 1 

2. C02 SYSTE~ IN' SEAWATER • • • • • • • • • • • • • • • • • • • • • • • • • • • . • • • • • • • • • • • 1 

3. PROGRAM C02SYS INFORMATION •••••••••••••••••••••••••.••.••.• 2 

4. VERSION IDSTORY • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • . • • • • • • . . 3 

S. SIN'GLE-INPUT MODE • • • • • . . • . . . • • • • • • • . • • . • • . • . . . • • • • . • • . . • . . • . . 4 

6. BATCH-INPUT MODE 5 

6.1 Inputs . • • • • • • • . • • . • • • • • • • . • • . • . • • • . • . • . • • • . . . • . . . . • . • . . . . . . . 5 

6.2 Missing Values • • • • • • • • • • • • • • • • • • • • • • • • • • • • • . • • • . • • . . • • • • • • • . . 6 

6.3 Output 7 

7. CHOICES FOR CONSTANTS IN THIS PROGRAM •••....•.•••....•.•..• 7 

7.1 Constant Choices 1 to 5 . . • • • . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . • . . . 9 

7.2 GEOSECS Choice • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • . • • • • • . 9 

7.3 Peng Choice 10 

7.4 Freshwater Choice • . . . • • • • . • . . • • • . . . . . . . . . . . • • . . • . . . • . . . . . . . . . 11 

8. ALKALIN'ITY 11 

9. Kso CHOICES 

4 

12 

10. fC02 AND pC02 •••• 12 

11. REVELLE FACTOR 13 

12. CALCIUM SOLUBILITY • • • • • • • • • • • • • • • . . • • . • • • • • • • • • • • • • • • . • • • • • . 13 

13. PRESSURE EFFECTS • • • • • • • • • • • • • • • . • .• • • • • • • • . • • • • • • • • • • • • • • • • • • 14 

14. pH SCALES •• 15 

15. ON-SCREEN INFORMATION 16 

ll1 
16. ADDITIONAL INFORMATION • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 16 

17. ACKNOWLEDGMENTS 17 

18. REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 

APPENDIX A: TYPOGRAPIDCAL ERRORS • • • • • • • • • • • • • • • • • . • . • • • • • • . . A-1 

iv 
PREFACE 

Investigators interested in studying the ocean carbonate system are not in complete agreement 

on how to calculate inorganic carbon speciation in seawater. Over the years there have been 

many determinations and reviews of the constants used to describe the dissociation of carbon 

dioxide (CO:z) in the ocean, but no universally accepted set of constants exists. Several subtly 

different pH scales remain in common use, as do variations in the defmition of total alkalinity 

and arguments over the relative merits of reporting the partial pressure vs the fugacity of C02• 

As ocean C02 measurements become steadily more accurate and investigators seek to evaluate 

very small changes in concentrations, these issues grow in importance. 

We recently released a computer program that we hope will be of general use and perhaps 

help to clear up some of the confusion. Given any two of the four measurable carbonate 

system parameters, this program calculates the other two, together with the inorganic carbon 

speciation and the saturation of calcite and aragonite. The program also allows the user to 

select from four different pH scales and several sets of dissociation constants widely cited in 

the literature. 

Run in "single input" mode, the program reports calculated results together with the sensitivity 

of the calculated parameters to uncertainties in input parameters, constants, and the like. Run 

in "batch input" mode, the program can be used to process large data sets, such as cruise data 

derived from spreadsheets. In writing the code we spent considerable time cross-checking the 

relevant literature and checking units and scales. We are reasonably confident that the 

program itself does not introduce any errors and is consistent with the primary literature. 

The program is written in compiled MICROSOFT QuickBASIC and runs under DOS on 

almost any personal computer processor. As a result, the user interface is functional but not 

flashy. The program includes on-line documentation, as well as a listing of typographical 

errors and inconsistencies culled from the literature. We may develop a MICROSOFT Visual 

Basic for Applications version if the demand for it is sufficient 

More information on this program is available from Ernie Lewis at Brookhaven National 

Laboratory (see Sect. 16 for contact information). This work was supported by the U.S. 

Department of Energy, Office of Biological and Environmental Research, under Contract No. 

DE-AC02-76CH00016. 

v 
1. INTRODUCTION 

The program C02SYS performs calculations relating parameters of the carbon dioxide (CO:J 

system in seawater and freshwater. The program uses two of the four measurable parameters 

of the C02 system [total alkalinity (TA), total inorganic C02 (TCO:J, pH, and either fugacity 

(fC02) or partial pressure of C02 (pCO:J] to calculate the other two parameters at a set of 

input conditions (temperature and pressure) and a set of output conditions chosen by the user. 

It replaces and extends the programs C02SYSTM.EXE, FC02TC02.EXE, PHTC02.EXE, and 

C02BTCH.EXE, which were released in May 1995. It may be run in single-input mode or 

batch-input mode and has a variety of options for the various constants and parameters used. 

An on-screen information section is available that includes documentation on various topics 

relevant to the program. This program may be run on any 80 x 86 computer equipped with 

the DOS operating system by simply typing C02SYS at the prompt after loading the 

executable file C02SYS.EXE. 

2. C02 SYSTEM IN SEAWATER 

The C02 system in seawater is characterized by four measurable parameters: TA, TC02 (i.e., 

the sum of the dissolved C02 , the carbonate, and the bicarbonate), pH, and either fC02 or 

pC02 • pC02 is the partial pressure of C02 in wet (100% water-saturated) air which is in 

equilibrium with the sample. Both fC02 and pC02 are proportional to the dissolved C02 • 

The fugacity is about 0.3% to 0.4% lower than the partial pressure over the range of interest, 

due to the nonideality of C02 • TA and TC02 are independent of temperature and pressure; 

fC02 , pC02 , and pH are not. The knowledge of any two of these parameters, along with the 

temperature, salinity, pressure, abundances of other constituents of seawater, and the relevant 

equilibrium constants, allows the determination of the other two parameters. 

Unfortunately, this is not as easy as it sounds. The two definitions of alkalinity in current 

usage differ in how minor species are treated. Four different pH scales [total, seawater, free, 

and NBS (National Bureau of Standards, now the National Institute of Standards and 

Technology)] are in current usage (it is even more complicated in the literature, where the 

distinction between the total scale and the seawater scale has not always been made). The 

situation with the equilibrium constants is potentially more confusing: There are several 

different formulations of K1 and K2 (the first and second dissociation constants of carbonic 

acid in seawater) and also several formulations for the other dissociation constants of interest, 

on various pH and concentration scales. 

Many of these differences are slight, but their importance is in direct proportion to the desired 

precision of the calculated values. The correction for the nonideality of C02 , for instance, is 

only around 0.3% under most conditions, but this correction is near the precision of some 

measurements systems. The difference in the definitions of alkalinity consists mainly in· the 

treatment of phosphate. This difference may seem minor, but a modest phosphate 

concentration, such as 3 micro-moles per kilogram of seawater (.umollkg-SW), can result in a 

difference in fC02 (or pCO:J of 20 micro-atmospheres (.uatm) or more, when calculated from 

TA and TC02 , depending on the definition of alkalinity. This difference, therefore, is quite 

significant. 

1 
We evaluated several other programs that performed calculations relating the seawater COl 

system parameters. These programs differed in the values of the constants used and in what 

contributions to the alkalinity were considered. To get an idea of the differences, we ran three 

programs with the following inputs: TA = 2300 .umollkg-SW; TC02 = 2000 ,umollkg-SW; no 

phosphate or silicate (two of the programs did not have an option to include these); and 

temperature (0C), salinity [on the Practical Salinity Scale (PSS)], and pressure (in dbar) equal 

to 20, 35, and 0, respectively. The results were as follows: 

pC02 HCo3- CO/-

Program (Jlatm) pH pH scale (Jlmollkg) (.umollkg) 

1 336 8.229 Free 1767 223 

2 351 8.088 Seawater 1772 216 

3 330 8.247 NBS 1782 208 

As can be seen, the pH values are on different pH scales and thus are difficult to compare. 

The values for pC02, though, should be the same regardless of pH scale, as should the values 

for the concentrations of HC03- and Col-. 

Closer inspection (this means looking at the codes) reveals some of the reasons for the 

differences. Program 1 did not include the contribution of OH to the alkalinity (which would 

be about 5 ,umollkg-SW), nor did it include the contributions of phosphate and silicate. It used 

the K1 and ~ values from Goyet and Poisson (1989) and the value of K80 from the data of 

Khoo et al. (1977), but refit by other investigators. It did not include a cori-ection for the 

nonideality of C02 , but did include pressure corrections. Program 2 did not include the 

contributions of phosphate and silicate, but did include pressure corrections and a correction 

for the nonideality of COl. The values of K1 and Kl were those of Roy et al. (1993), and the 

value of K80 was that of Dickson (1990a). Program 3 did include the contributions of 

phosphate an'a silicate, but had no corrections for the nonideality of C02 or for pressure. The 

values of K1 and~ used were from Mehrbach et al. (1973). Each of the programs used a 

different value for KB, the dissociation constant for boric acid. 

It can thus be seen how different programs, with no coding errors, can yield very different 

results. Because of this, we decided to provide a single program that encompassed a wide 

variety of choices for C02 system constants, pH scales, etc., in order to facilitate the 

assessment of the C02 system calculations to such choices. 

3. PROGRAM C02SYS INFORMATION 

The program C02SYS is designed for either single-input mode or batch-input mode, and 

allows for a variety of options, including the choice of various formulations for K1 and K2, 

two distinct formulations for K80 (Dickson 1990a; Khoo et al. 1977), the choice of four pH 

scales (free, total, NBS, or seawater), and the use of either fC02 or pC02 • 

2 
Any two C02 system parameters (T A, TC02 , fC02 or pC02 , and pH) may be chosen as the 

inputs from which the other two parameters will be calculated. Contributions to the alkalinity 

from phosphate, silicate, and OH are included, as are the effects of pressure and the 

nonideality of C02 • An on-screen information section is available that includes discussions of 

the various options and provides references for the values used and for other topics that are 

relevant to the program. Every effort has been made to make this program as correct, 

complete, and user-friendly as possible. However, the program is not fail-safe, and some 

familiarity with the C02 system in seawater is assumed. Most of the fits to the constants are 

valid only over a restricted range of salinities (mostly 20 to 40). Values outside of this range 

should not be expected to yield correct results. 

The units used for the variables in this program are micro-moles per kilogram of seawater 

(umollkg-SW) for concentrations of TA, TC02 , etc.; micro-atmospheres (.uatm) for pC02 and 

fC02 ; and parts per million (ppm) for the mole ratio of C02 in dry air. All temperatures are 

in °C, all salinities are on the PSS, and all pressures are in dbar. Depth in meters may be used 

instead of pressure; these parameters differ by only 3% at 10,000 dbar and less at lower 

pressures, well within the uncertainties of the pressure effects on the equilibrium constants. In 

this documentation, units for the concentration of [H•], necessary to clearly define the pH 

scale, are mollkg-SW for the total, seawater, and free pH scales (note that the original 

defmition in the literature for the free pH scale was in molal units), and mollkg-H20 (molal) 

for the NBS scale (by definition). 

Because the equilibrium constants given in the literature are on various pH scales and in 

various concentration units (molar, molal, or mollkg-SW), it is imperative that they be 

converted correctly to the desired scale. In developing this program, much work was done to 

ensure that these conversions were made correctly. Data are sparse for many of the constants. 

Those values used in this program were those we chose to be the best from the available data. 

Many errors and inconsistencies were found in the literature. In writing this program, a list of 

these typographical errors was compiled. This list is included as an Appendix to this report 

because it may be of interest to those involved in calculations for the carbonate system. 

Although most of the errors are very minor, it is hoped that the use of this list will save time 

and effort for anyone wishing to delve further into the topic. 

Occasionally, for certain inputs of TC02 and fC02 or pC02 , the system has no solution for the 

given input conditions. If this situation arises in single-input mode, the user is notified and the 

parameters may be re-entered. If this occurs in batch-input mode, -999 is printed for TA, pH, 

and the other calculated parameters for that sample. 

4. VERSION IDSTORY 

The programs C02SYSTM.EXE, FC02TC02.EXE, PHTC02.EXE, and C02BTCH.EXE were 

released in May 1995. To the best of our knowledge, no serious errors have been found in 

these programs. One possible problem is that the fits for the constants are not valid for 

extrapolation to salinity 0. 

Program C02SYS replaces and extends the four programs listed above. 

3 
Version 0.00, from February 1997, was only preliminary and should not be used for 

calculations. The pressure corrections to the carbonate solubilities were incorrect. 

Version 1.02 was released in March 1997. The pressure corrections to the pH scale 

conversions were done incorrectly. These errors had a very minor effect in most cases. 

Version 1.03 was released in May 1997. It is believed to be accurate. 

Version 1.04 was released later in May 1997. It differs from version 1.03 only cosmetically 

(typographical errors were corrected, etc.). No differences should exist between calculations 

performed using this version and version 1.03. 

Version 1.05 was released in October 1997. It differs from version 1.04 cosmetically (e.g., 

typographical errors were corrected) and in that some different code was used for better 

efficiency (no code errors were found). No differences should exist between calculations 

performed using this version and versions 1.03 and 1.04. 

5. SINGLE-INPUT MODE 

In single-input mode, after selection of the various options for the values of the constants, etc., 

the user is prompted for the following: 

• salinity, 

• concentrations of phosphate and silicate, 

• input temperature and pressure (or depth}, 

• output temperature and pressure (or depth), and 

• two known C02 system parameters at the input conditions. 

The input temperature and pressure, at which the values of the two known C02 system 

parameters are given, may be those at which measurements were performed in the laboratory, 

for example, while the output conditions may refer to in situ conditions. The program will use 

"default" values for a variable (i.e., the last value occurring for that particular variable, given 

in parentheses) when the user hits the "enter" key. These default values may be useful for 

comparing the effects that various formulations of the constants have on the calculated 

parameters. 

The program will then calculate the other two C02 system parameters at the input conditions. 

TA and TC02 , which do not vary with temperature and pressure, are used to calculate the pH 

and fC02 or pC02 at the output conditions. Also calculated for both the input and the output 

conditions are 

• the sensitivity of the output results to small variations of the inputs; 

• the contributions to the alkalinity and carbon speciation; 

• fC02 and pC02 in wet (1 00% saturated) air; 

• xC02 (the mole fraction of C02 in dry air assuming 1 atm total pressure); 

• Omega (the degree of saturation) for calcite and for aragonite; 

• the Revelle factor (homogeneous buffer factor); 

4 
• pH values on all four pH scales (total, seawater, free, and NBS); and 

• the values ofpK1, pK2 , pKw, and pK8 on the chosen pH scale. 

The user may scroll forward or backward through the various screens. Information is available 

on-screen for the various options and can be accessed while running the program. 

The program lists the estimated accuracy of Ko and the 2S (two standard deviation) precision 

of the constants K1 and K2 to allow an estimate to be made of the uncertainty of the fmal 

answer caused by the uncertainty in the equilibrium constants. 

6. BATCH-INPUT MODE 

6.1 Inputs 

Batch-input mode is designed to be used with large data sets, such as files created by 

MICROSOFT EXCEL or other spreadsheet programs. In this mode, data are read from an 

input flle and results are calculated and printed to an output flle. Mter the various options are 

chosen, the user is prompted for: 

• the name of the input file, 

• the name of the output flle, 

• the number of header lines in the input me, 

• the number of ID fields preceding the data for each sample, 

• a numeric value to denote missing data, and 

• an option to flag samples containing missing data. 

Each line in the input file must contain the following fields for one sample: 

• the ID fields (the number of which is selected by the user), 

• salinity (on the PSS), 

• total phosphate (in .umollkg-SW), 

• total silicate (in .umollkg-SW), 

• temperature (°C) of the input C02 system parameters, 

• pressure (dbar) of the input C02 system parameters, 

• temperature (°C) for output conditions, 

• pressure (dbar) for output conditions, 

• the first known C02 system parameter, and 

• the other known C02 system parameter. 

It is VERY IMPORTANT that the input data be in the correct format and that the correct 

order of the C02 system parameters be followed: 

• TA will always come first if used; 

• TC02 (if used) will precede any parameter except TA; 

• pH (if used) is next; 

• fC02 (or pCOz) will always be last if used. 

5 
( 

Units used are J.Lmollkg-SW and J.Latm. Six example data files, CASEl.INP-CASE6.INP, are 

included with the program; there is one data file for each of the choices of C02 system input 

parameters. Following is the sample data file CASEl.INP: · 

This is CASEl.INP, a test program for C02SYS. It works for case 1. 

linel, 35., 3., 55., 20., 0, S, 1000, 2400., 2200. 

line2, 35., 0, 0, 20, 0, 5, 1000, 2400., 2300. 

line3, 33., 2., 122., 15, 0, S, 0, 2300., 2200. 

line4, 35., 0, 0, 20, 0, 15, 0, 2300., 2100. 

lineS, 33., 3., 2., 25, 0, 10, 100, 2200., 2100. 

In this example, the input data are comma-separated (this is recommended), but they may also 

be space-separated. For space-separated data, the ID fields MUST be within double quotes; 

for comma-separated data, this is not required. (Note that MICROSOFT EXCEL puts double 

quotes around each double quote when importing a CSV file.) It can occur that for certain 

inputs of TC02 and fC02 (or pCOz), 1he system has no solution for the given input conditions. 

If this occurs, -999 is printed for the TA, pH, and the other calculated parameters. 

6.2 Missing Values 

Because a data set may contain values that are missing or unknown, the user may defme a 

numeric value to be the missing-value designator (MVD). If an MVD is not defined by the 

user, the default value -9 will be used. IT IS IMPERATIVE THAT A VALUE BE 

PROVIDED IN EACH OF TIIE INPUT DATA FIELDS; therefore, unknown values should 

always be set equal to the MVD. 

If the MVD is input for one of the C02 system parameters, no calculations will be made and 

each output variable will be given the value of the MVD. If the MVD is input for one of the 

non-C02 system parameters, a default value will be used in calculations and that sample will 

be flagged (if that option has been chosen). HOWEVER, the MVD will be printed in the 

output file for that variable. OBVIOUSLY, CAUTION SHOULD BE USED IN 

INTERPRETING TIIE RESULTS WHEN THERE ARE MISSING VALUES IN THE INPUT 

FILE. 

The defaults used are 

• salinity: 35; 

• total phosphate: 0 J.Lmollkg-SW; 

• total silicate: 0 J.Lmollkg-SW; 

• input temperature: 20°C; 

• input pressure: 0 dbar; 

• output temperature: the value of the input temperature; and 

• output pressure: the value of the input pressure. 

6 
6.3 Output 

The output file will contain header lines with the following: 

• the input file name and the date; 

• the choice of constants, K50 , and pH scale; 

• any other header lines input 4

by the user; and 

• labels for the output fields. 

The output data are comma-separated with one line per sample. Each line will contain the 

same fields as the input data plus the following calculated values: 

• the other two C02 system parameters at the input conditions, 

• pH and fC02 (or pCOz) at the output conditions, 

• Omegas for calcite and aragonite at the input conditions, 

• [HC03-] and [CO/-] at the input conditions, 

• Omegas for calcite and aragonite at the output conditions, and 

• [HC03-] and [C03

2

-] at the output conditions. 

If the user chooses to flag missing data, an extra field will be appended. This field will 

contain the MVD value if there are missing data or a zero if there are no missing data. The 

pH values are reported on the scale chosen by the user. To load the output file into 

MICROSOFT EXCEL, simply open it as comma-separated with the extension "CSV'. 

7. CHOICES FOR CONSTANTS IN THIS PROGRAM 

A large number of values are needed in the calculations. These include the following: 

• the various dissociation constants: 

o K1 and K2 for carbonic acid, 

o KB for boric acid, 

o Kw for water, 

o K50 for the bisulfate ion, 

o Kp for hydrogen fluoride, 

o Kp1 , KP2, and KP3 for phosphoric acid, and 

o Ksi for silicic acid; 

• Ksp(calcite) and Ksp(aragonite), the saturation solubility products for calcite and aragonite; 

• the pressure dependence of the dissociation constants and the solubility products; 

• the concentrations of the various species assumed to be proportional to the salinity (the 

concentrations of phosphate and silicate may vary and are input by the user): 

o TB for total boron, 

o TS for total sulfate, 

o TF for total fluoride, and 

o TCa for total calcium; 

• Ko, the solubility of C02 in seawater; 

• the vapor pressure of water above seawater; 

• the virial coefficients of C02 and C02-air; and 

7 
• f 8 , the activity coefficient of the hydrogen ion. 

These values have been determined by many different investigators in many ways. Most 

assume values of temperature and salinity within ranges typically found in the oceans, so the 

use of values outside these ranges may result in fits being extrapolated beyond the region 

where data were collected. 

There are eight choices for the constants used in this program. They differ mostly in the 

formulation of K1 and K2 , but there are other slight differences as well, which are described 

below. These eight choices are 

1. Roy et al. (1993); 

2. Goyet and Poisson (1989); 

3. Hansson (1973a,b), refit by Dickson and Millero (1987); 

4. Mehrbach et al. (1973), refit by Dickson and Millero (1987); 

5. Dickson and Millero's fit of the combined Hansson/Mehrbach data; 

6. GEOSECS Choice (Takahashi et al. 1982); 

7. Peng Choice (Peng et al. 1987); and 

8. Freshwater Choice. 

Constants are converted to the appropriate pH and concentration scales, if necessary. before 

calculations are made. 

In all cases, Ko, the solubility of C02 in seawater, is from Weiss (1974), who combined the 

measurements of Murray and Riley ( 1971) with some of his own and fit the resulting data. 

Estimates of the accuracy of Ko vary from 0.2% (Weiss 1974) to 0.5% (Dickson and Riley 

1978). The virial coefficients of C02 and C02-air are from Weiss (1974). The vapor pressure 

of H20 above seawater is from Weiss and Price (1980). The concentrations of sulfate and 

fluoride are from Morris and Riley (1966) and Riley (1965), respectively. The value of Kso is 

from either Khoo et al. (1977) or Dickson (1990a) (this is a choice the user makes). Both of 

these are given in units of mol/kg-H20 and both are (inherently) on the free pH scale. Kp is 

from Dickson and Riley (1979). It is also (inherently) on the free pH scale and is given in 

units of mol/kg-H20. Sulfate and fluoride contribute almost nothing to the alkalinity under 

most circumstances, but their concentrations and dissociation constants are important in 

converting between the various pH scales. The value used for f 8 , the activity coefficient of 

the hydrogen ion (also necessary in converting between pH scales) is from the fit given in 

Takahashi et al. (1982), except for the Peng Choice, in which case the fit given in Peng et al. 

(1987) is used. 

The relevant equilibrium constants that defme the speciation of C02 in seawater, K1 and K2 , 

have been determined for various temperatures and salinities by several different investigators. 

Four sets of measurements remain worthy of consideration. These measurements were made 

by Roy et al. (1993) on the total pH scale in units of mollkg-Hp, Goyet and Poisson (1989) 

on the seawater pH scale in units of mol/kg-SW, Hansson (1973a,b) on the total pH scale in 

units of mollkg-SW, and Mehrbach et al. (1973) on the NBS pH scale in units of mollkg-SW. 

The data of Hansson (1973a,b) and Mehrbach et al. (1973), both separately and together, have 

been refit by Dickson and Millero (1987) on the seawater scale in units of mollkg-SW. Both 

8 
GEOSECS (Takahashi et al. 1982) and Peng et al. (1987) used the fit given in 

Mehrbach et al. (1973). 

The following are approximate 2S precisions of the fits of the data: (Remember that precision 

and accuracy are NOT the same!): 

Source 

Roy et al. (1993) 

Goyet and Poisson (1989) 

Hansson (1973a,b), refit by Dickson and Millero (1987) 

Mehrbach et al. (1973), refit by Dickson and Millero (1987) 

Dickson and Millero (1987), combined fit 

Mehrbach et al. (1973) 

Freshwater Choice 

7.1 Constant Choices 1 to 5 

Kt ~ 

2% 1.5% 

2.5% 4.5% 

3% 4% 

2.5% 4.5% 

4% 6% 

1.2% 2% 

0.5% 0.7% 

Constant Choices 1 to 5 differ only in the values of K1 and K2 and are therefore discussed 

together. The value of KB is from Dickson (1990b) and TB is from Uppstrom (1974). The 

calcium concentration used is from Riley and Tongudai (1967). The values of Ksp for calcite 

and aragonite are from Mucci (1983). The effects of pressure on K1 and K2 are from Millero 

(1995). The effects of pressure on KB are from Millero (1979) (but without the salinity 

dependence). Note that typographical errors in Millero (1995) include a factor of 1000 left out 

of the defmition of Kappa and an incorrect value and incorrect units for the gas constant R 

(see Appendix A). The pressure correction for Ksp for calcite is from Ingle (1975) and that for 

aragonite from Millero (1979). 

The defmition of alkalinity used is that of Dickson (1981): 

TA = [HCOJ + 2[C03] + [B(OH)4] + [OH] + [HP04] + 2[P04] + [Si0(0H)3] + [HS] 

+ 2[S] + [NHJ- [H]- [HS04]-[HF]- [HJlOJ, 

except that the contributions from HS, S, and NH3 are not included. 

Values for Kw, Kp1, KP2, KP3, and Ks; are from Millero (1995), where they are given on the 

seawater scale. 

7.2 GEOSECS Choice 

The GEOSECS option was designed to replicate the calculations performed in the GEOSECS 

atlases by Takahashi et al. (1982). These calculations were made on the NBS pH scale using 

the values of K1 and K2 from Mehrbach et al. (1973) and the value of K8 from Lyman (1957) 

as fit by Li et al. (1969). 

9 
The defmition of alkalinity used was 

which did not include effects of OH, phosphate, or silicate. No correction was applied for the 

nonideality of C02 (thus implying fC02 and pC02 are the same). The boron concentration was 

from Culkin (1965) and is about 1% lower than that used for Constant Choices 1 to 5. A fit 

for fH was given for salinities of 20 to 40. 

Some typographical errors in the GEOSECS report were noted and corrected: in the pressure 

dependence of K2 , the given value 26.4 should be 16.4, and in.the equation for In Kw, the 

expression Clln T should be C*ln T. One can verify these corrections by checking the original 

references for Takahashi et al. (1982). The ratio Ksp(aragonite) I Ksp(calcite) is given as 1.48 

in the original reference (Berner 1976), but the value of 1.45 given in the GEOSECS report 

was used both in that work and in this program for the GEOSECS Choice. The GEOSECS 

report also contains a discussion on the effects of OH, phosphate, and silicate (see pp. 79-82, 

especially Table 1 on p. 81, of Takahashi et al. 1982). From this discussion, it can be seen 

how important the effects of these species can be, especially for the calculated value of fC02 

(or pCO~. The GEOSECS table also has a typographical error: 17.8 for Aw in Pacific 

Surface Water should be 7 .8. 

7.3 Peng Choice 

This choice replicates the calculation scheme used by Peng et al. (1987), which is similar to 

that of GEOSECS (Takahashi et al. 1982). This scheme has been used extensively by 

modelers. Peng et al. (1987) worked on the NBS pH scale and included effects of phosphate, 

silicate, and OH, but did not distinguish between fC02 and pC02• The values of K1 and K2 

used were from Mehrbach et al. (1973) as given in that paper, and the value of K8 was from 

Lyman (1957) as fit by Li et al. (1969). The boron concentration was from Culkin (1965) and 

is about 1% lower than that used for Constant Choices 1 to 5. The value of fH given in their 

paper was NOT the same as that given in the GEOSECS report as claimed; rather, it had been 

rounded off and was therefore about 1% higher, corresponding to a change of 0.004 in pH. 

Note that the check value given in Peng et al. (1987) does not match either fit. 

Peng et al. (1987) did not treat calcite and aragonite solubility or pressure effects. However, 

these effects are included in the program C02SYS for the Peng Choice by using values for 

solubility and pressure dependence of K1, K2, and K8 from GEOSECS and values for the 

pressure dependence of OH and phosphate and silicate dissociation as are used in Constant 

Choices 1 to 5. 

Peng et al. (1987) used KP2 and KP3from Kester and Pytkowicz (1967), Ksi from Sillen et al. 

(1964, p. 751), and Kw from Millero (1979). 

The defmition of alkalinity used by Peng et al. (1987) is 

This equation differs from the equation for TA of Dickson (1981) which is used in Constant 

10 
Choices 1 to 5 mainly in that it is greater by an amount equal to the total phosphate: 

This difference seems insignificant, but under certain conditions it can affect the calculated 

fC02 appreciably. 

7.4 Freshwater Choice 

The defmition of alkalinity used in this case is 

Kp ~.and Kw are from Millero (1979): Kw is a refit of data from Harned and Owen (1958); 

K1 is a refit of the data of Harned and Davis (1943); and K2 is a refit of the data of Harned 

and Scholes (1941). Pressure effects on these constants are from Millero (1983). 

The activity coefficient of H+, fu, does NOT equal 1 at salinity 0 due to liquid junction effects 

(included in its defmition). It has also been found to be electrode dependent. Thus, even 

though the values of pH on the free, total, and seawater scales will coincide at salinity 0, the 

value on the NBS scale will differ. For these reasons, for this choice only, a pH value is 

given without reference to a pH scale. 

Only one set of measurements of K1 and K2 have been made in seawater at salinity <10. 

Although the values can be extrapolated to salinity 0, they change by a considerable amount 

over this interval: between salinities 0 and 5, K1 varies by a factor of 2 and K2 varies by a 

factor of 6.5 to 9.2, depending on temperature; for comparison, between salinities 5 and 35, K1 

varies by a factor of less than 1.5 and K2 varies by a factor of less than 3. Thus, a fit of K1 

and ~ for values of salinity in this range would be prone to large uncertainty. For this 

reason, only values of K1 and K2 valid at salinity 0 (freshwater) are used. 

8. ALKALINITY 

The defmition of alkalinity (TA) used in this program for Constant Choices 1 to 5 is the same 

as that of Dickson (1981): 

TA = [HC03] + 2[C03] + [B(OH)4] + [OH] + [HPOJ + 2[POJ + [Si0(0H)3] + [HS] 

+ 2[S] + [NH3]-[H]- [HS04]-[HF)- [Hj»04). 

except that the contributions of HS, S, and NH3 are not included. 

For the Peng Choice, the defmition of Peng et al. (1987) is used. The main difference is that 

it is greater by an amount equal to the total phosphate: 

Though this seems small, it can have a large effect on the calculated fC02• For instance, when 

11 
fC02 (or pCOz) is calculated from TA and TC02 , a modest phosphate concentration such as 3 

J,Lmollk.g-SW, can result in a difference of 20 J.Latm or more, depending on which definition of 

alkalinity is used. 

The definition used for the GEOSECS Choice is from Takahashi et al. (1982): 

and for the Freshwater Choice is 

TA = [HCO:J + 2[CO:J + [OH] - [H] . 

In this program values of alkalinities are given in micromoles per kilogram of seawater 

(J.Lmollkg-SW). 

9. Kso CHOICES 

4 

Kso is def'med to be the dissociation constant for the reaction 

4 

thus, 

Kso = [H] * [SOJ I [HSOJ . 4 

There are two equations for KSO 4 that are still in current usage: Khoo et al. (1977) and 

Dickson (1990a). Although many older papers used values of Khoo et al. (1977), the values 

of Dickson (1990a) are now recommended. The values of Khoo et al. (1977) are between 15 

to 45% lower than those of Dickson, depending primarily on temperature. The main effect of 

this difference will occur when converting from one pH scale to another, or when working on 

a scale for which equilibrium constants must be converted (e.g., most constants were 

detennined on either the total scale or the seawater scale). The use of the Dickson values 

when converting from the total pH scale to the free pH scale will result in pH values that are 

0.015 to 0.03 units lower than those obtained using values of Khoo et al. (1977). 

10. fC02 AND pC02 

The fugacity of C02 (fCOz) in water is defined to be the fugacity of C02 in air which is in 

equilibrium with the water. The partial pressure of C02 in wet (100% water-saturated) air 

(pC02) is defined to be the product of the mole fraction of C02 in wet air and the total 

pressure. This is the same as the product of the mole fraction of C02 in dry air [xCOz(dry)] 

and (p101 - p~ ), where P~!zo is the vapor pressure of water above seawater. At pressures of the 

order of 1 atm, fC02 in arr is about 0.3% lower than the pC02 due to the nonideality of C0 2 

(Weiss 1974). This program assumes a pressure near 1 atm (where most equilibrators function) 

for the conversion between partial pressure and fugacity. 

12 
fC02 is related to TC02 and pH by the following equation: 

where [C02*] is the concentration of dissolved C02 , Ko is the solubility coefficient of C02 in 

seawater, and K1 and Kz are the first and second dissociation constants for carbonic acid in 

seawater. 

Units for fC02 and pC02 in this program are ,uatm. The value of xC02(dry) given in this 

program assumes Ptot = 1 atm. GEOSECS (Takahashi et al. 1982) and Peng et al. (1987) did 

not distinguish between fC02 and pC02 , nor did some other programs that we have evaluated. 

11. REVELLE FACTOR 

The Revelle, or homogeneous buffer, factor is the percentage change in fC0 2 (or pCOz) caused 

by a 1% change in TC02 at constant alkalinity. It depends on temperature, salinity, and the 

total alkalinity and TC02 (or any combination of two of the C02 system parameters) of the 

sample. It is calculated at both the input and output conditions using the following: 

Revelle factor= (dfCO/dTCOz) I (fCOJTC02) 

at constant T A. 

Normal seawater values are between 8 and 20. 

12. CALCIUM SOLUBll..ITY 

The solubility product (Ksp) is calculated for both calcite and aragonite, and the saturation 

states are given in terms of the solubility ratio, Omega, which is defined as 

· Thus, values of Omega <1 represent conditions of undersaturation, and values of Omega > 1 

represent conditions of oversaturation. 

The concentration of calcium, [Ca2+], is assumed to be proportional to the salinity, and the 

carbonate concentration, [CO/-], is calculated from TC02 , pH, and the values of K1 and K2 

for carbonic acid. For Constant Choices 1 to 5, the calcium concentration used is from Riley 

and Tongudai (1967). The values of Ksp for calcite and aragonite are from Mucci (1983). The 

pressure correction for ~P for calcite is from Ingle (1975) and that for aragonite is from 

Millero (1979). 

13 
For the GEOSECS Choice and the Peng Choice, the concentration of calcium is from Culkin 

(1965). The value of Ksp for calcite is from Ingle (1975). [GEOSECS had referenced Ingle et 

al. (1973), but this is incorrect.] The value of Ksp for aragonite is from Berner (1976). 

(Berner stated that KsP for aragonite is 1.48 times Ksp for calcite; GEOSECS gave and used the 

value 1.45 instead of 1.48. The program C02SYS also uses 1.45.) The pressure corrections to 

these constants are from Takahashi et al. (1982). [The original reference given for the 

pressure corrections is not valid, and the fit used appears to be new to Takahashi et al. 

(1982).] 

13. PRESSURE EFFECTS 

The equilibrium constants depend on pressure as well as on temperature and salinity. Data are 

scarce on the effects of pressure on these constants in seawater, and most values are estimated 

from molal volume data. Few measurements have been made for K1 and K2 (of carbonic acid) 

and KB (of boric acid) at only a few combinations of temperature, salinity, and pressure in 

seawater (mostly in artificial seawater). All work assumed that fH, the activity coefficient of 

H+ (including liquid junction effects), is independent of pressure. Some of the pH scale 

conversions do depend on pressure, however. Values of the constants should be (1) converted 

initially to the seawater or NBS pH scale WITHOUT pressure-corrected pH scale conversions, 

(2) then corrected for pressure, and (3) then converted to the desired pH scale WITH 

pressure-corrected pH scale conversions. Measurements have also been made for the effects of 

pressure on the solubility of calcite and aragonite in seawater. 

Depth in meters and pressure in decibars are used interchangeably in this program. They 

differ by only 3% at 10,000 dbar and less at lower pressures-well within the uncertainties of 

the pressure effects on the constants. No salinity dependence of the pressure corrections is 

used in this program. 

For the Freshwater Choice, the effects of pressure on Kt> K2 , and Kw are from Millero (1983). 

Peng et al. (1987) did not consider the effects of pressure, but they are included in the 

program C02SYS for the Peng Choice. For Constant Choices 1 through 5 and the Peng 

Choice, the effects of pressure on the values of Kp1 , KP2, and KP3 are from Millero (1995). 

The only mention of Ksi was in Millero (1995), where it is stated that the values have been 

estimated from the values of boric acid, but they are not listed in the table. In the program 

C02SYS, the values used are the same as those for the pressure effects on KB given in Millero 

(1995). For the effects of pressure on Kw, the fit given in Millero (1983) is used. GEOSECS 

did not include the effects of OH, phosphate, or silicate, so these are irrelevant for that choice. 

For the GEOSECS Choice and the Peng Choice, the effects of pressure on K1, K2 , and KB are 

those given in the GEOSECS report (Takahashi et al. 1982). The reference given there is 

Culberson and Pytkowicz (1968), but the fits are actually those from Edmond and Gieskes 

(1970) who, in tum, quote Li (personal communication). In the fit for the correction for K2 

due to pressure, the GEOSECS report had the value 26.4, but the value 16.4 was used, which 

was consistent with their calculations, as well as with the fit given in Edmond and Gieskes 

(1970). The effects of pressure on the solubility of calcite and aragonite are also those from 

Takahashi et al. (1982). [The original reference given in that work for the pressure corrections 

14 
( 

is not valid, and the fit used appears to be new to Takahashi et al. (1982).] 

For the Constant Choices 1 to 5, the effects of pressure on K1 and K2 are from Millero (1995), 

and those for K8 are from Millero (1979), but without the salinity dependence. These fits are 

from the data of Culberson and Pytkowicz (1968). The effects of pressure on K50 and KF are 

from Millero (1995). Note that typographical errors in Millero (1995) include a fa1:tor of 1000 

left out of the definition of Kappa and an incorrect value and incorrect units for the gas 

constant R. The pressure correction for Ksp for calcite is from Ingle (1975) and that for 

aragonite is from Millero (1979). 

14. pH SCALES 

The various pH scales are interrelated by the following equations: 

(-pH~ 

· a = 10 = 1 * B B B sws 

and 

B = B /(1 + TS/K. ) = B 1(1 + TS{K80 + TF/K \, tree tot so4 ..n 4 F' 

where 

a8 is the activity and / 8 is the activity coefficient of the H+ ion (this includes liquid junction 

effects), 

TS and 1F are the concentrations of S04

2

- and fluoride, and 

Kso and KF are the dissociation constants of HSO 4 - and HF in seawater. 

4 

The conversions depend on temperature, salinity, and pressure. At 20°C, salinity 35, and 1 

atm, pH values on the total scale are approximately 

• 0.09 units lower than those on the free scale, 

• 0.01 units higher than those on the seawater scale, and 

• 0.13 units lower than those on the NBS scale. 

The concentration units for a8 on the NBS scale are mollkg-Hp. The concentration units used 

in the program C02SYS for [H+] on the other scales are mo1/kg-SW (note that the free scale 

was originally defmed in units of mollkg-Hp). The difference between mollkg-SW and 

mollkg-H20 is about 0.015 pH units at salinity 35 (the difference is nearly proportional to 

salinity). The seawater scale was formerly referred to as the total scale, and each scale is still 

sometimes referred to as the other in the literature. 

The fit of / 8 used in this program is valid from salinities 20 through 40. f 8 has been found to 

be electrode-dependent, and does NOT equal 1 at salinity 0 due to the liquid junction 

potential. 

15 
Values on the NBS pH scale are only accurate to 0.005 (at best). 

All work on pressure effects on pH has assumed that f" is independent of pressure. 

For discussions of the various pH scales see Dickson (1984, 1993), Millero et al. (1993), 

Butler (1992), or Culberson (1981). Attention is required because in some of these references 

the distinction between the total and the seawater pH scales was not made. 

15. ON-SCREEN INFORMATION 

An information section that may be accessed from several places in the program provides 

on-screen help for the following topics: 

1. General information (Introduction) 

2. pH Scales 

3. fC02 and pC02 

4. Kso Choices 

4 5. Batch-Input Mode 

6. GEOSECS Choice 

7. Peng Choice 

8. Freshwater Choice 

9. Pressure Effects 

10. Calcium Carbonate Solubility (Omega values) 

11. Alkalinity 

12. Revelle Factor 

13. Constants Used 

16. ADDITIONAL INFORMATION 

For questions, comments, or to report any problems, please contact: 

Ernie Lewis or Doug Wallace 

Department of Applied Science 

P. 0. Box 5000 

Brookhaven National Laboratory 

Upton, NY 11973-5000 

elewis@bnl.gov 

(516)344-7406 

wallace@bnl.gov 

(516)344-2945 

A very useful reference for all aspects of the C02 system in seawater is the Handbook of 

Methods for the Analysis of the Various Parameters of the Carbon Dioxide System in Sea 

Water (DOE 1994). The web site for information on this reference is 

16 
http://www-mpl.ucsd.edu/people/adickson!C02_QC/. 

A listing of the errata in this handbook is also available at this site. 

A copy of the printed report may be obtained from the Carbon Dioxide Information Analysis 

Center at no charge while supplies last. Requests should be addressed to: 

Address: 

Telephone: 

Electronic Mail: 

Carbon Dioxide Information Analysis Center 

Oak Ridge National Laboratory 

Post Office Box 2008 

Oak Ridge, Tennessee 37831-6335, U.S.A. 

423-574-0390 or 423-574-3645 (Voice) 

423-574-2232 (Fax) 

Internet: cdiac@ornl.gov 

Other particularly useful references are Park (1969), Skirrow (1975), Butler (1991), Millero 

and Sohn (1992), and Millero (1995) (see Appendix A for a listing of some of the errata in 

this paper). 

Appendix A lists some typographical errors found in the references for this report as well as in 

other papers on this topic. 

17. ACKNOWLEDGMENTS 

Significant help, advice, and clarification on all aspects of the C02 system in seawater were 

supplied by Dr. Andrew Dickson, Scripps Institution of Oceanography. Many helpful 

comments were supplied by Dr. Rik Wanninkof, NOAA/AOML/OCD and Dr. Dave Chipman, 

Lamont-Doherty Earth Observatory. We would also like to acknowledge Dr. Frank Millero of 

the Rosenstiel School of Marine and Atmospheric Sciences at the University of Miami for his 

numerous contributions to this field. 

This work was supported by the U.S. Department of Energy Office of Biological and 

Enviromental Research under contract DE-AC02-76CH00016, through a project entitled 

"Inorganic Carbon for the World Ocean Circulation Experiment- World Hydrographic 

Program" (D. W. R. Wallace and K. M. Johnson, Principal Investigators). 

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Butler, J. N. 1991. Carbon Dioxide Equilibria and Their Applications. Lewis Publishers, Inc., 

Chelsea, Mich. 

17 
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Culberson, C. H. 1981. Direct potentiometry. pp. 187-261. In M. Whitfield and D. Jagner 

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19 
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Geology 2:263-69. 

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and D. M. Campbell. 1993. The dissociation constants of carbonic acid in seawater at 

salinities 5 to 45 and temperatures 0 to 45°C. Marine Chemistry 44:249-67. 

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Sillen, L. G., A. E. Martell, and J. Bjerrum. 1964. Stability constants of metal-ion complexes, 

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20 
( 

Skirrow, G. 1975. The dissolved gases- Carbon dioxide. pp. 1-192. In J.P. Riley and G. 

Skirrow (eds.), Chemical Oceanography, Vol. 2. Academic,Press, New York. 

Takahashi, T., R. T. Williams, and D. L. Bos. 1982. Carbonate chemistry. pp. 77-83. In W. S. 

Broecker, D. W. Spencer, and H. Craig, GEOSECS Pacific Expedition, Volume 3: 

Hydrographic Data 197J-1974. National Science Foundation, Washington, D.C. 

Uppstrom, L. R. 1974. The boron/chloronity ratio of deep-sea water from the Pacific Ocean. 

Deep-Sea Research 21:161-2. 

Weiss, R. F. 1974. Carbon dioxide in water and seawater: The solubility of a non-ideal gas. 

Marine Chemistry 2:203-15. 

Weiss, R. F., and B. A. Price. 1980. Nitrous oxide solubility in water and seaVJater. Marine 

Chemistry 8:347-59. 

21 
APPENDIX A: 

TYPOGRAPHICAL ERRORS 

APPENDIX A: TYPOGRAPIDCAL ERRORS 

This Appendix lists errors that have been found in references for the program documentation 

as well as in other papers related to this topic; however, the listing is not meant to be 

comprehensive. Although many corrections are extremely minor, it is hoped that this 

compilation will save both time and effort for those who use it. Last revision version 1.08, 

10-13-97. 

Campbell, D. M., F. J. Millero, R. Roy, L. Roy, M. Lawson, K. M. Vogel, and C: 

Porter-Moore. 1993. The standard potential for the hydrogen-silver, silver chloride 

electrode in synthetic seawater. Marine Chemistry 44:221-33. 

• On p. 230 in Eq. 37: The expression "In KHso "should be "log10 (KHSo )." 4 4 

Chen, H., R. Wanninkhof, R. A. Feely, and D. Greeley. 1995. Measurement of fugacity of 

carbon dioxide in seawater: an evaluation of a method based on infrared analysis. NOAA 

Technical Memorandum ERL AOML-85. Atlantic Oceanographic and Meteorological 

Laboratory, Miami. 

• On p. 15: Table 2 states, "1. In our work (expressed in terms of the seawater hydrogen 

scale): ... "; however, the formula for K8 given is on the total scale, and the formulae for 

KPZ, ~, and K5; are on the NBS scale. It is unclear whether these formulae were 

converted. 

• On pp. 15 and 16: The formulae for Total Borate (TB) are incorrect. They should read: 

"Total Borate (TB) = 0.00001188 * S" for cases 1 and 3, and "Total Borate (TB) = 

0.00001173 * S" for case 2. 

• On p. 24, two lines under Table 3: The expression "dXCO/dT' should be 

"d(lnXCO:z)/dT." 

Clayton, T. D., and R. H. Byrne. 1993. Spectrophotometric seawater pH measurements: total 

hydrogen ion concentration scale calibration of m-cresol purple and at-sea results. 

Deep-Sea Research 40: 2115-29. 

• On p. 2119 in Eq. 12b: The second "-47.986" should be "+114.723." 

Clayton, T. D., R. H. Byrne, J. A. Breland, R. A. Feely, F. J. Millero, D. M. Campbell, P. P. 

Murphy, and M. F. Lamb. 1995. The role of pH measurements in modern oceanic 

C02-system characterization: Precision and thermodynamic consistency. Deep-Sea 

Research II 42:411-29. 

• In Table 2 on p. 419: In the equation for pK1w the value "9.794" should be "9.7944." 

• In Table 2 on p. 419: KF as given is expressed in units mo1/kg-Hp. 

• On p. 427: The reference for Johnson et al. (1992) should be "Analytical 

Chemistry 64: .... " 

Dickson, A. G. 1990a. Standard potential of the reaction: AgCl(s) + lf.zH2(g) = Ag(s) + 

HCl(aq), and the standard acidity constant of the ion HS04-in synthetic seawater from 

273.15 to 318.15 K. Journal of Chemical Thermodynamics 22:113-27. 

A-3 
• The title has two consecutive "ands." 

• On p. 121 in Table 4: The term "e9" should be "e8." 

Dickson, A. G. 1990b. Thermodynamics of the dissociation of boric acid in synthetic seawater 

from 273.15 to 318.15 K. Deep-Sea Research 37:755-66. 

• On p. 756 after Table 1: The expression "ms = m35*I3/I5" should be "ms = m3s*l/I3s·" 

• On p. 762 in Eq. 18: The term "a.z" should be "a. 3 ." 

Dickson, A. G., and F. I. Millero. 1987. A comparison of the equilibrium constants for the 

dissociation of carbonic acid in seawater media. Deep-Sea Research 34:1733-43. 

• On p. 1738: The expression "2(A-1)" in the second equation should be "(2A-1)." 

• Corrigenda 1989. Deep-Sea Research 36:983. 

o This corrects a typographic error in p. 1739 in Table 4: In the equation for pK2* for 

Hansson, the value "0.000116 *S2 " should be "0.000132 *S2

." 

o Also, on p. 1740 in Table 5: The second equation should read "pK2*," not "pK1*." 

o Also, in the third equation in Table 5 (p. 1740): The term "0.00668 S" should be 

"0.0068 S." 

Dickson, A. G., and J.P. Riley. 1979a. The estimation of acid dissociation constants in 

seawater media from potentiometric titrations with strong base. I. The ionic product of 

water-Kw. Marine Chemistry 7:89-99. 

• On p. 97 in Equation 7: The value "0.9415" should be "0.09415." 

Dickson, A. G., and J. P. Riley. 1979b. The estimation of acid dissociation constants in 

seawater media from potentiometric titrations with strong base. IT. The dissociation of 

phosphoric acid. Marine Chemistry 7:101-109. 

• (From A. Dickson, personal communication) In the equation for pKZP in the abstract and 

in Table IT on p. 109: The number "4.176" should be "4.196." 

• On p. l09 in Table IT: Units should be "mo1/kg-soln," not "mo1/kg-Hz0." 

Goyet, C., and E. Peltzer. 1994. Comparison of the August-September 1991 and 1979 surface 

partial pressure of C02 distribution in the Equatorial Pacific Ocean near 150° W. Marine 

Chemistry 45:257-66. 

• On p. 261: The term "0.098T' should be "0.0098T." 

• Also, the reference given (UNESCO. 1987. Thermodynamics of the carbon dioxide 

system in seawater. UNESCO Technical Papers in Marine Science 51.) does not discuss 

this equation or the one above it. 

Goyet, C., and A. Poisson. 1989. New determination of carbonic acid dissociation constants in 

seawater as a function of temperature and salinity. Deep-Sea Research 36:1635-54. 

• In the Abstract and Tables 4 and 5: The symbol "T' represents both oc and K. 

A-4 
• On p. 1645 in Table 4: The fits which allow "extrapolation to S = 0" contain a constant 

term and thus do not match the "S = 0" values. 

Hansson, I. 197~a. A new set of acidity constants for carbonic acid and boric acid in seawater. 

Deep-Sea Research 20:461-78. 

• On p. 467, line 17: The phrase "four temperatures" should read "four salinities." 

• On p. 470 in Table 3: The term "moles" should be "millimoles." 

Lee, K., and F. J. Millero. 1995. Thermodynamic studies of the carbonate system in seawater. 

Deep-Sea Research 42:2035-61. 

• On p. 2037 after Eq. 3: The value for the concentrations of SO 4 should be proportional 

to "S/35," not "35/S." 

• On p. 2038 after Eq. 5: The concentrations of S04 and F should be proportional to 

"S/35," not "35/S." 

• On p. 2056, two lines up: The statement ''The calculated values of pK2 (S = 35) ... " 

should NOT have the expression "(S = 35)," as the fit has a salinity dependence. 

• On p. 2058: The actual title for the reference of Clayton and Byrne is 

"Spectrophotometric seawater pH measurements: Total hydrogen ion concentration scale 

calibration of m-cresol purple and at-sea results." 

• On p. 2061 in the equation for In K8: The expression "log {[H+lswJ[H.hf' 

should be "In { [H•Jswsf[H+h}." 

• On p. 2061 in the equation for In KHso : The value "114.273" should be "114.723" and 

the expression "2968fl"' should be "2698/T." 

• On p. 2061: The values for the concentrations of S04 , F, and B should be proportional 

to "S/35," not "35/S." 

Mehrbach, C., C. H. Culberson, J. E. Hawley, and R. M. Pytkowicz. 1973. Measurement of 

the apparent dissociation constants of carbonic acid in seawater at atmospheric pressure. 

Limnology and Oceanography 18:897-907. 

• On p. 898 in Table 1: The "Ft" term in Eq. 5 is negative the "Ft in Eq. 6. 

Millero, F. 1979. The thermodynamics of the carbonate system in seawater. Geochemica et 

Cosmochemica Acta 43:1651-1661. 

• On p. 1651, in Eq. 4: The expression "Cfl"' should be "C*T." 

Millero, F. J. 1983. Influence of pressure on chemical processes in the sea. Chapter 43. In J. P. 

Riley and R. Chester (eds.), Chemical Oceanography. Academic Press, New York. 

• On p. 51, for Table 43.29 to be correct: 

o in Eq. 94: The value "-26.69" should be "-25.59." 

o in Eq. 95: The term "0.1700t" should be "0.0800t." 

Millero, F. J. 1995. Thermodynamics of the carbon dioxide system in the oceans. Geochemica 

et Cosmochemica Acta 59:661-77. 

A-5 
• On p. 664: Equation 32 uses Khoo's value of K850 (Khoo et al. 1977), but on p. 667 it 

is stated that Khoo's value is unreliable and should 4

not be used. This is unclear. 

• On p. 667: In the first full paragraph it is stated that the values of K850 were 

determined from Eq. 30 after Roy's constants were converted to the SWS pH scale. The 

value of KHSo is needed to convert pH scales and cannot be found from Eq. 30. 

• On p. 668: It 1s stated thahthe total pH scale should be used; however, in the next 

paragraph, Roy's constants are converted to the seawater scale, and this scale is used 

for most of the rest of the paper. 

• On p. 669, in the title for Fig. 10: The equations are misnumbered. Equations 46 and 47 

should be Eqs. 48 and 49, and Eqs. 48 and 49 should be Eqs. 50 and 51. 

• On p. 669, Eq. 52: The constant KB is on the total pH scale (this was not stated but can 

be determined from the reference). 

• On p. 670, Eq. 63: The constant Kw is on the seawater pH scale (this wasn't stated but 

is consistent with programs of Millero). 

• On p. 670: The given check value after Eq. 64 of "1.6 j..l.mol/kg" should be "6.2 JJ.mol/kg." 

There is no easy way to see bow 1.6 was obtained. 

• On p. 670, Eqs. 65, 66, and 67: These are on the seawater pH scale (this was not 

stated, but can be determined from the DOE Handbook). 

• On p. 671, after Eq. 71: The check values "0.792" and "0.204" should be "0.852" and 

c "0.140." If pH= 8.2 is used, or if KP3 is increased by a factor of 1.55, the given check 

values are close. 

• On p. 671, Eq. 72: The constant Ksi is on the seawater pH scale (this was not stated but 

can be determined from the DOE Handbook) . 

. • On p. 671, after Eq. 73: For the given values "I= 0.7" and "t = 25°C," the value of 

PKsi is given as "9.47." (molality). However, when these two values are used, the actual 

resultant value of pK5i is "9.365" (molality) which corresponds to "9.380" in 

molJkg-soln. Two scenarios would explain the discrepancy: (1) either "t" is incorrect 

(plugging in the value t = 20°C would give the value of pK5i as 9.47), or (2) the pH 

scale is incorrect (the value for pK5i of 9.38 on the total pH scale= 9.47 on the 

seawater scale in the same concentration units). 

• On p. 671, after Eq. 73: Using the values given for pK5i of "9.47" and for pH of "7.5" 

yields "0.0106 [Sih," rather than "0.0127 [Sih." 

• On p. 671, Eq. 74: The pH scale on which K15 is given is not stated. From the original 

reference, it was determined in artificial seawater without F, so it must be on the total 

pH scale. 

• On p. 671, after Eq. 75: The value for pK15 at t = 25°C and S = 35, is incorrectly given 

as "6.98" and should be "6.51." The value "6.98" can be obtained, however, by 

plugging in t = 25°C and S = 0. 

• On p. 671, after Eq. 75: The value of "0.768" is consistent with the value for pK15 of 

"6.98" (which is incorrect). The correct value should be "0.9071." 

• On p. 671, Eq. 76: The pH scale on which KNH is given isn't stated. From the original 

reference it is on the seawater scale. 4 

• On p. 671, after Eq. 77: The value for pKNH of "9.19" is incorrect and should be 

"9.26." It is not clear how the incorrect valu~ was obtained. 

• On p. 671, after Eq. 77: The value "0.020" is consistent with "9.19" (which is 

incorrect). It should be "0.017." 

• On p. 672, column 2: A parameter is defmed as "X= TA!I'C02 ." Note that Goyet et al. 

(1993) in a paper on a similar topic (Goyet, C., F. J. Millero, A. Poisson, and 

A-6 
D. Shafer. 1993. Temperature dependence of C02 fugacity in seawater. Marine 

Chemistry 44:205-219) defme a parameter as "X= TCO/fA." This difference in 

definitions could cause confusion. 

• On p. 673, Eq. 86: If fC02 at 20°C AND X are known, then fC02 at ANY temperature 

can be calculated exactly! The only way to know X is to know TA AND TC02 , and 

either one of these and fC02 at 20°C is also sufficient to fmd fC02 at any temperature. 

• On p. 675, after Eq. 90: The value and the units for R are incorrect. The true value is 

"R = 83.145 bar-cm3/(mol-K)." 

• On p. 675, column 1: The reference to Millero (1989) should probably be Millero 

(1983b). 

• On p. 675, Eq. 92: There are no values of b2 in Table 9. Probably they are equal to 0; 

this would be consistent with previous work. 

• On p. 675: The left-hand side ofEq. 92 should be (lOOO)*AK, or the last two columns 

in Table 9 should be 1000*b1 and 1000*b2 in order to be correct. 

• On p. 675 in Table 9: The values of ao. at, and a 2 for HP and HzS are the 

FRESHWATER values given in Millero (1983). 

• On p. 675 in Table 9: There are no a and b values for Si(OH)3• Before the heading 

"Conclusions" on the same page it is stated that they are "estimated" from those of 

boric acid. It is unclear whether or not it is meant that they are assumed to be equal to 

those for boric acid. 

• On p. 675 in Table 9: The value of at for B(OH)3 should be "+0.1622" to agree with 

Millero (1979). 

• On p. 675 in Table 9: The values of at for calcite and aragonite should be "+0.5304" to 

agree with Millero '(1979). 

• On p. 675 in Table 9: The value of -ao for aragonite should be "-46.0" (or "-45.96") 

to agree with Millero (1979). 

• On p. 675 in Table 9: The value of b 1 for calcite should be "+0.3692" to agree with 

Millero (1979). 

• On p. 677, in column 2: There is a problem with the reference "Millero, F. J. (1982). 

The thermodynamics of seawater at one atmosphere. Ocean Sci. Eng. 7: 403-60." It 

should probably read: 

o Millero, F. J. (1976). The thermodynamics of seawater at one atmosphere. American 

Journal of Science 276:1035-77. 

o Millero, F. J. (1982). Thermodynamics of seawater: the PVT properties. Ocean Sci. 

Eng. 7: 403-60. 

Millero, F. J., T. Plese, and M. Fernandez. 1988. The dissociation of hydrogen sulfide in 

seawater. Limnology and Oceanography 33:269-74. 

• On p. 271 just before Eq. 7: It is stated that the NBS and the total pH scales are related 

by "aH' = fH * [H+h," but this does not include fluoride. The relation usually used is 

"aH' = fH * [H+1sws ," which does include fluoride. This means that the fa used in this 

equation is the activity coefficient for seawater containing no fluoride. 

• On p. 273: The fit for fH combines data which were taken in seawater (artificial and 

actual) containing fluoride with values that were taken in artificial seawater without 

fluoride. 

A-7 
Millero, F. J., and M. L. Sohn. 1992. The carbonate system. pp. 267-319. In F. J. Millero and 

M. L. Sohn, Chemical Oceanography. CRC Press, Boca Raton, Fla 

• On p. 275: There is ambiguity and inconsistency in the defmitions and distinctions 

between the total and the seawater pH scales. 

• On p. 276: Equation 31 should read "A= -1226.966 .... " 

• On p. 276: Equation 36 is incorrect in several places: the denominator in the first 

expression should be squared, and the terms CH and COH should not be in the 

numerator but rather by themselves. This expression also makes the approximation that 

Kl* >> :Kz*. 

• On p. 279: The right-hand side of Eq. 52 should read: 

"pK1 + (-840.39!1' + 19.894 -3.0189 In T) * s~ + 0.0068 S." 

• On p. 280: The last term in Eq. 56 should be "0.0217 S," not "1.0217 S." 

• On p. 281: The last term in Eq. 65 should be "0.01767 S," not "1.01767 S." 

• On p. 281: The second equals sign in Eq. 72 should be a minus sign. 

• On p. 282 in Eq. 79: The term "63.9806" should be "63.806." 

• On p. 286: Equation 96 has brackets and parentheses missing in several places. 

• Fits for the constants are from the following sources: 

o p. 273: The fit for Kw is from Millero (1979) from data of Hansson (1973 a,b). 

o p. 273: The equations for 11 V and 11K for Kw are from Millero (1983). 

o p. 276: The fit for PHso is from Millero (1986). 

o pp. 279 and 280: The ~uations for K1 and K2 are from Dickson and Millero ( 1987) 

from the combined data of Hansson (1973 a,b) and Mehrbach et al. (1973). 

o p. 280: The equations for 11 V and 11 K for the constants K1 and K2 are from 

Millero (1979). 

o p. 281: The fit for K8 is from Millero (1979) from data of Hansson (1973a,b). 

o p. 281: The equations for 11 V and 11K for K8 are from Millero (1979). 

o p. 281: The fits for Ksp for calcite and aragonite are from Millero (1979). 

o pp. 281 and 282: The equations for 11 V and 11K for calcite are from Ingle (1975). 

o p. 282: The equations for 11 V and 11K for aragonite are from Millero (1979). 

o p. 282: The pH variation with T and Pis from Millero (1979). 

• These are the source references: 

o Millero, F. J. 1979. Geochemica et Cosmochemica Acta 43:1651-61. 

o Dickson, A. G., and F. J. Millero. 1987. Deep-Sea Research 34:1733-43; see also 

Dickson, A. G., and F. J. Millero. 1989. Deep-Sea Research 36:983. 

o Millero, F. J. 1983. Influence of pressure on chemical processes in the sea. Chapter 

43. In J.P. Riley and R. Chester (eds.), Chemical Oceanography. Academic Press, 

New York. 

o Millero, F. J. 1986. Limnology and Oceanography 31:839-47. 

o Ingle, S. E. 1975. Marine Chemistry 3:301-19. 

Millero, F. J., J. Z. Zhang, S. Fiol, S. Sotolongo, R.N. Roy, K. Lee, and S. Mane. 1993. The 

use of buffers to measure the pH of seawater. Marine Chemistry 44:143-52. 

• On p. 149, Eq. 23, and on p. 150, Eqs. 25 and 27: The multiplication sign (x) should 

be a division sign (/). 

A-8 
Millero, F. J., J. Z. Zhang, K. Lee, and D. M. Campbell. 1993. Titration alkalinity of seawater. 

Marine Chemistry 44:153-66. 

• On p. 156, column 2, about 10 lines down: The expression "14±1 mM" should be 

"14 ± 1 JJM." 

Peng, T. H., T. Takahashi, W. S. Broecker, and J. Olafsson. 1987. Seasonal variability of 

carbon dioxide, nutrients and oxygen in the North Atlantic surface water: Observations and 

a model. Tellus 39B:439-58. 

• On p. 455: The fit of fH is NOT the same as the one in GEOSECS, as claimed, but 

rather is rounded off. It is about 1% higher (this results in a change of 0.004 in pH). 

• On p. 456: The given check value for /J:i does not match the fit given in that paper or 

the GEOSECS fit. 

• NOTE: On p. 455, Eq. A3: This definition of TA is different from that of Dickson; it is 

higher by an amount equal to the total phosphate. 

Roy, R.N., L. N. Roy, K. M. Vogel, C. Porter-Moore, T. Pearson, C. E. Good, F. J. Millero, 

and D. M. Campbell. 1993. The dissociation constants of carbonic acid in seawater at 

salinities 5 to 45 and temperatures 0 to 45°C. Marine Chemistry 44:249-67. 

• On p. 254 in the label for Fig. 2: The expression "3m(C03

2

T' should be "2m(C0/1." 

• On pp. 254 and 258: The authors claim 2S precisions of "0.004" in pK1 and "0.006" in 

p~. From Andrew Dickson (personal communication, 1997), these should be "0.008" 

in pK1 and "0.006" in pK2 • 

• On p. 257: The authors use Khoo's value for K50 , not Dickson's, but reference 

Dickson earlier (p. 252). · 

4 

• Erratum. 1994. Marine Chemistry 45:337. This replaces Tables 3 and 4. 

• Erratum. 1996. Marine Chemistry 52:183. This fixes a typographic error in the Abstract 

on p. 249: In the equation for In K1*: The last term should have S raised to the power 

1.5. It also fixes a typographic error in Eq. 34 on p. 256: The value "310.48919" should 

be "2310.48919." 

Takahashi, T., R. T. Williams, and D. L. Bos. 1982. Carbonate chemistry. pp. 77-83. In W. S. 

Broecker, D. W. Spencer, and H. Craig, GEOSECS Pacific Expedition, Volume 3, 

Hydrographic Data 1973-1974. National Science Foundation, Washington, D.C. 

• On p. 79 in No. 5 in list of constants: In the equation for K{(P), the value "26.4" 

should be "16.4." 

• On p. 79: The reference in No. 6. in the list of constants should actually be Ingle, S. E. 

1975. Marine Chemistry 3:301-19. Reference [21] is not correct. 

• On p. 79 in the equation for Ksp'(aragonite): The value "1.45" should be "1.48" [this is 

what Berner uses on p. 722 of Berner (1976)]. 

• On p. 79 in No. 8 in the list of constants: Reference [20] is not correct; that Culberson 

reference is only indirectly related to the topic under discussion. 

• On p. 79 in the equation for K5;(calcite,P): The plus sign should be an equals sign. 

A-9 
• On p. 80 in the equation for In Kw': The expression "ClinT" should be "C*lnT." 

• On p. 81 in Table 1: The value "17.8" for Pacific Surface Water should be "7.8." 

UNESCO. 1987. Thermodynamics of the carbon dioxide system in seawater. UNESCO 

Technical Papers in Marine Science 51. 

• On p. 50: The term ".00116" in the equation for pK2* should be "0.000132." 

Weiss, R. F., and B. A. Price. 1980. Nitrous oxide solubility in water and seawater. Marine 

Chemistry 8:347-59. 

-.Errata. 1980. Marine Chemistry 9:221. 

• On p. 355, Table m, row 5, column 2: The value "4.245" should be "5.245." 

• On p. 355: Line 3 below Table m should read: " ... 1.1% and 1.5%, respectively, below 

our results." 

A-10