### 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 

## OakRidge 

## NationalLaboratoryThis report has been reproduced directly from the best available copy. Available to DOE and DOE contractors from the Office of Scientific and Technical Information, P.O. Box 62. Oak Ridge, TN 37831; prices avdable from (423) 576-8401, FTS 626-8401. Available to the public from the National Technical Information Service, U.S. Department of Commerce, 5285Port Royal Rd., Splnlgfield, VA 22181.

This report was preparec:l as an account of work aponsorec:l by an agency of the Unitec:l States Government. Neither the Unitec:l States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or aaaumea any legal liability or responsibility for the accuracy, completeness. or ueefulness of any Information, apparatus, product, or process dilcloeec:l, or reprewrts that ita uee would not infringe privately ownad rights. Reference herein to any specific commercial product, proceaa, or aarvice by trade name, trademark, manufacturer, or otherwile, doesnot necualrily conatituta or Imply ita endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authora expreaaed herein do not neceaaarlly state or reflect thoee of the Unitec:l States Government or any agency thereof.

# DISCLAIMER 

# Portions of this document may be illegible electronic image products. Images are produced from the best available original document.

## nN~~

# K~**'~L** APR 7 1998 

# Master Coo\r I 

### .J 

# PROGRAM DEVELOPED FOR C02 

# SYSTEM CALCULATIONS

Ernie 

### Lewis and Doug Wallace Department ofApplied 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 ofBiological 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. PRESSUREEFFECTS • •• ••••• ••• •••• . •.• • •••••• . •• ••••• • • • ••• ••• • • 14 14. pH SCALES •• 

### 15 15. ON-SCREEN INFORMATION 

### 16

ll116. ADDITIONALINFORMATION • • • • • • • • •• • • • • • • • • • •• • • • • • • • • • • • • • • • • 16 17. ACKNOWLEDGMENTS 17 18. REFERENCES

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 APPENDIX A: TYPOGRAPIDCALERRORS • • • • • • • • • • • • • • • •• . • . • • • • • • . . 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 ofthe constants used to describe the dissociation ofcarbon dioxide (CO:z) in the ocean, but no universally accepted set ofconstants exists. Several subtly differentpH scales remain in common use, as do variations in the defmition oftotal alkalinity and arguments overthe relative merits ofreporting the partial pressure vs the fugacity ofC02• 

### 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 computerprogram that we hope will be ofgeneral use and perhaps help to clearup some ofthe confusion. Given any two ofthe four measurable carbonate system parameters, this program calculates the other two, together with the inorganic carbon speciation and the saturation ofcalcite and aragonite. The program also allows the user to select from four different pH scales and several sets ofdissociation constants widely cited in the literature. Run in "single input" mode, the program reports calculated results together with the sensitivity ofthe 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 itselfdoes 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 ifthe 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 ofEnergy, Office ofBiological and Environmental Research, under Contract No. DE-AC02-76CH00016.



### v

### 1. INTRODUCTION The program C02SYS performs calculations relating parameters ofthe carbon dioxide (CO:J system in seawater and freshwater. The program uses two ofthe four measurable parameters ofthe C02 

### system [total alkalinity (TA), total inorganic C02 

### (TCO:J, pH, and either fugacity (fC02) 

### orpartial pressure ofC02 

### (pCO:J] to calculate the other two parameters at a set of input conditions (temperature and pressure) and a set ofoutput 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 ofoptions 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 ofthe dissolved C02, 

### the carbonate, and the bicarbonate), pH, and either fC02

### or pC02 • 

### pC02 

### is the partial pressure ofC02 

### 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% lowerthan the partial pressure over the range ofinterest, due to the nonideality ofC02• 

### TA and TC02 

### are independent oftemperature and pressure; fC02, 

### pC02 , 

### and pH are not. The knowledge ofany two ofthese parameters, along with the temperature, salinity, pressure, abundances ofother constituents of seawater, and the relevant equilibrium constants, allows the determination ofthe othertwo parameters. Unfortunately, this is not as easy as it sounds. The two definitions ofalkalinity in current usage differ in how minor species are treated. Four different pH scales [total, seawater, free, and NBS (National Bureau ofStandards, now the National Institute ofStandards 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 ofK1 

### and K2 

### (the first and second dissociation constants ofcarbonic acid in seawater) and also several formulations for the other dissociation constants ofinterest, on various pH and concentration scales. Many ofthese differences are slight, but their importance is in direct proportion to the desired precision ofthe calculated values. The correction for the nonideality ofC02, 

### 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 ofalkalinity consists mainly in·the treatment ofphosphate. This difference may seem minor, but a modest phosphate concentration, such as 3 micro-moles per kilogram ofseawater (.umollkg-SW), can result in a difference in fC02 

### (orpCO:J of20 micro-atmospheres (.uatm) ormore, when calculated from TA and TC02, 

### depending on the definition ofalkalinity. This difference, therefore, is quite significant.

1

### We evaluated several other programs that performed calculations relating the seawaterCOl system parameters. These programs differed in the values ofthe constants used and in what contributions to the alkalinity were considered. To get an idea ofthe differences, we ran three programs with the following inputs: TA

# =2300 .umollkg-SW; TC02

# =2000 ,umollkg-SW; no phosphate or silicate (two ofthe 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 ofpH scale, as should the values for the concentrations ofHC03- 

### and

# Col-. Closer inspection (this means looking at the codes) reveals some ofthe reasons for the differences. Program 1 did not include the contribution ofOH 

### to the alkalinity (which would be 

### about 

### 5 ,umollkg-SW), nor did it include the contributions ofphosphate and silicate. It used the K1

### and**~** 

### values from Goyet and Poisson (1989) and the value ofK80 

### from the data of Khoo et al. 

### (1977), butrefitby other investigators. It did not include a cori-ection for the nonideality ofC02 , 

### but did include pressure corrections. Program 2 did not include the contributions ofphosphate and silicate, but did include pressure corrections and a correction for the nonideality ofCOl. The values ofK1 

### and Klwere those ofRoy et al. (1993), and the value ofK80 

### was that ofDickson (1990a). Program 3 did include the contributions of phosphate an'a silicate, but had no corrections for the nonideality ofC02 

### or for pressure. The values ofK1**and~** 

### used were from Mehrbach et al. (1973). Each ofthe 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 ofthis, we decided to provide a single program that encompassed a wide variety ofchoices for C02 

### system constants, pH scales, etc., in order to facilitate the assessment ofthe C02 

### system calculations to such choices.

3. PROGRAM C02SYS INFORMATION The program C02SYS is designed for either single-input mode orbatch-input mode, and allows for a variety ofoptions, including the choice ofvarious formulations for K1

### and K2, 

### two distinct formulations for K80 

### (Dickson 1990a; Khoo et al. 1977), the choice offour pH scales (free, total, NBS, or seawater), and the use ofeither fC02 

### orpC02 •

2

### Any two C02 

### system parameters (T 

### A, TC02, 

### fC02 

### orpC02, 

### 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 ofpressure and the nonideality ofC02• An 

### on-screen information section is available that includes discussions of the various options and provides references for the values used and for othertopics that are relevant to the program. Every efforthas 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 seawateris assumed. Most ofthe fits to the constants are valid only over

# arestricted range ofsalinities (mostly 20 to 40). Values outside ofthis range should not be expected to yield correct results. The units used for the variables in this program are micro-moles per kilogram ofseawater (umollkg-SW) for concentrations ofTA, TC02, 

### etc.; micro-atmospheres (.uatm) for pC02 

### and fC02 ; 

### and parts per million (ppm) for the mole ratio ofC02 

### 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 ofpressure; these parameters differ by only 3% at 10,000 dbar and less at lower pressures, well within the uncertainties ofthe 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-H2

### 0 (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 ofthe 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 ofinterest to those involved in calculations for the carbonate system. Although most ofthe errors are very minor, it is hoped that the use ofthis list will save time and effort for anyone wishing to 

### delve further into the topic. Occasionally, for certain inputs ofTC02 

### and fC02 

### orpC02, 

### the system has no solution for the given input conditions. Ifthis 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 ofour 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.

3Version 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 ofthe various options for the values ofthe constants, etc., the user is prompted for the following:

• salinity, • concentrations ofphosphate and silicate, • input temperature and pressure (or depth}, • output temperature and pressure (or depth), and • two known C02 system parameters atthe input conditions. The input temperature and pressure, at which the values ofthe 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 thatparticular variable, given in parentheses) when the user hits the "enter" key. These default values may be useful for comparing the effects that various formulations ofthe constants have on the calculated parameters. The program 

### will then calculate the othertwo 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 orpC02 at the output conditions. Also calculated for both the input and the output conditions are

• the sensitivity ofthe output results to small variations ofthe inputs; • the contributions to the alkalinity and carbon speciation; • fC02 and pC02 in wet (100% saturated) 

### air; • xC02 (the mole fraction ofC02 in dry air assuming 1 atmtotal pressure); • Omega (the degree ofsaturation) 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 , 

### pK 2 , 

### pKw, and pK8 

### on the chosen pH scale. The usermay scroll forward orbackward 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 ofthe constants K1 

### and K2 

### to allow an estimate to be made ofthe uncertainty ofthe 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 spreadsheetprograms. In this mode, data are read from an input flle and results are calculated and printed to an output flle. Mterthe various options are chosen, the user is prompted for:

• the name ofthe input file, • the name ofthe output flle, • the number ofheader lines in the input me, • the number ofID 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 ofwhich is selected by the user), • salinity (on the PSS), • total phosphate (in 

### .umollkg-SW), • total silicate (in 

### .umollkg-SW), • temperature (°C) ofthe input C02 

### system parameters, • pressure (dbar) ofthe input C02 

### systemparameters, • 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 ofthe C02 

### system parameters be 

### followed:

• TA will always come first ifused; • TC02 

### (ifused) will precede any parameter except TA; • pH (ifused) is next; • fC02 

### (orpCOz) will always be last 

### ifused.



### 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 ofthe choices ofC02 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 MICROSOFTEXCEL puts double quotes around each double quote when importing a CSV file.) It can occur that for certain inputs ofTC02 and fC02 (orpCOz),1he systemhas no solution for the given input conditions. Ifthis occurs, -999 isprinted for the TA, pH, andthe other calculated parameters. 6.2 Missing Values Because a data set may contain values that are missing orunknown, the user may defme a numeric value to be the missing-value designator (MVD). Ifan MVD is not defined by the user, the default value -9 will be used. IT IS IMPERATIVE THATA VALUE BE PROVIDED IN EACH OF TIIE INPUT DATA FIELDS; therefore, unknown values should always be set equal to the MVD. Ifthe MVD is input for one ofthe C02 system parameters, no calculations will be made and each output variable will be given the value ofthe MVD. Ifthe MVD is input for one ofthe non-C02 system parameters, a default value will be used in calculations and that sample will be flagged (ifthat option has been chosen). HOWEVER, the MVD will be printed in the output file for that variable. OBVIOUSLY, CAUTION SHOULD BE USED IN INTERPRETING TIIERESULTS 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 ofthe input temperature; and • output pressure: the value ofthe 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 ofconstants, 

### K 50 , 

### and pH scale; • any otherheader 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 othertwo 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 [C032-] 

### at the output conditions. 

### Ifthe user chooses to flag missing data, an extra field will be appended. This field will contain the MVD value ifthere are missing data ora zero ifthere 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 INTHIS PROGRAM A large number ofvalues are needed in the calculations. These include the following:

• the various dissociation constants: o 

### K1 

### and K 2 

### for carbonic acid, o 

### KB for boric acid, o 

### Kw for water, o K 50 

### 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 ofthe dissociation constants and the solubility products; • the concentrations ofthe various species assumed to be proportional to the salinity (the concentrations ofphosphate and silicate may vary and are input by the user): o 

### TB for total boron, o 

### TS for total sulfate, o TFfor total fluoride, and o 

### TCa for total calcium; 

## • Ko, the solubility ofC02 

### in seawater; • the vapor pressure ofwater above seawater; • the virial coefficients ofC02 

### and C02

### -air; and 7

### • f 8, 

### the activity coefficient ofthe hydrogen ion. These values have been determined by many different investigators in many ways. Most assume values oftemperature and salinity within ranges typically found in the oceans, so the use ofvalues 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 ofthe combined Hansson/Mehrbach data; 6. GEOSECS Choice (Takahashi et al. 1982); 7. Peng Choice (Peng etal. 1987); and 8. Freshwater Choice. Constants are converted to the appropriate pH and concentration scales, ifnecessary. before calculations are made. 

### In all cases, 

## Ko, the solubility ofC02 

### in seawater, is from Weiss (1974), who combined the measurements ofMurray and Riley (1971) with some ofhis own and fit the resulting data. Estimates ofthe accuracy of

## Ko vary from 0.2% (Weiss 1974) to 0.5% (Dickson and Riley 1978). The virial coefficients ofC02 

### and C02

### -air are from Weiss (1974). The vapor pressure ofH2

### 0 above seawater is from Weiss and Price (1980). The concentrations ofsulfate and fluoride are from Morris and Riley (1966) and Riley (1965), respectively. The value ofKso is from either Khoo et al. (1977) orDickson (1990a) (this is 

### a choice the user makes). Both of these are given in units ofmol/kg-H2

### 0 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 ofmol/kg-H2

### 0. 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

### f8 , 

### 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 ofC02 

### in seawater, K1 

### and K2, 

### have been determined for various temperatures and salinities by several different investigators. Four sets ofmeasurements remain worthy ofconsideration. These measurements were made by Roy et al. (1993) on the total pH scale 

### in units ofmollkg-Hp, Goyet and Poisson (1989) on the seawater pH scale in units ofmol/kg-SW, Hansson (1973a,b) on the total pH scale in units ofmollkg-SW, and Mehrbach et al. (1973) on the NBS pH scale in units ofmollkg-SW. The data ofHansson (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 ofmollkg-SW. Both



### 8GEOSECS (Takahashi et al. 1982) and Peng et al. (1987) used the fit given in Mehrbach et al. (1973). The following are approximate 2S precisions ofthe fits ofthe data: (Remember that precision and accuracy are NOTthe 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 K1and 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 Kspfor calcite and aragonite are from Mucci (1983). The effects ofpressure on K1 and K2 are from Millero (1995). The effects ofpressure 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 ofthe 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 ofalkalinity used is that ofDickson (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 ofK1 and K2 from Mehrbach et al. (1973) and the value ofK8 from Lyman (1957) as fit by Li et al. (1969).

9The defmition ofalkalinity used was

which did not include effects ofOH, phosphate, orsilicate. No correction was applied for the nonideality ofC02 (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 of20 to 40. Some typographical errors in the GEOSECS report were noted and corrected: in the pressure dependence ofK2 , 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 ofOH, phosphate, and silicate (see pp. 79-82, especially Table 1 on p. 81, ofTakahashi et al. 1982). Fromthis discussion, it can be seen how important the effects ofthese species can be, especially for the calculated value offC02 (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 ofGEOSECS (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 ofphosphate, 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 K 8 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 NOTthe same as that given in the GEOSECS report as claimed; rather, it had been rounded offand was therefore about 1% higher, corresponding to a change of0.004 in pH. Note that the check value given in Peng et al. (1987) does not match eitherfit. 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 ofK1 , K2, and K8 from GEOSECS and values for the pressure dependence ofOH 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 ofalkalinity used by Peng et al. (1987) is

This equation differs from the equation for TA ofDickson (1981) which is used in Constant 10Choices 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 itcan affect the calculated fC02 appreciably. 

### 7.4 Freshwater Choice The defmition ofalkalinity used in this case is



### Kp**~.and** 

### Kw are from Millero (1979): 

### Kw is a refit ofdata from Harned and Owen (1958); K1 is a refit ofthe data ofHarned and Davis (1943); and K2 is a refit ofthe data ofHarned and Scholes (1941). Pressure effects on these constants are from Millero (1983). The activity coefficient ofH+,

### fu, does NOT equal 1 at salinity 

### 0 due to liquidjunction effects (included in its defmition). It has also been found to be electrode dependent. Thus, even though the values ofpH on the free, total, and seawater scales will coincide at salinity 0, the value on the NBS scale will differ. Forthese reasons, for this choice only, a pH value is given without reference to a pH scale. Only one set ofmeasurements ofK1 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 overthis interval: between salinities 

### 0 and 5, K1 varies by a factor of2 and K2 varies by a factor of6.5 to 9.2, depending on temperature; for comparison, between salinities 5 and 35, K 1 varies by a factor ofless than 1.5 and K2 varies by a factor ofless than 3. Thus, a fit ofK1 and**~** for values ofsalinity in this range would be prone to large uncertainty. Forthis reason, only values of K1 and K2 valid at salinity 

### 0 (freshwater) are used.



### 8. ALKALINITY The defmition ofalkalinity (TA) used in this program for Constant Choices 1 to 5 is the same as that ofDickson (1981): 

### TA

# =[HC03] 

### +2[C03] 

### + [B(OH)4] 

### + [OH] 

### + [HPOJ 

### + 2[POJ

### + [Si0(0H)3] 

### + [HS] + 2[S] 

### + [NH3]- [H]- [HS04]- [HF)- [Hj»0 4). except that the contributions ofHS, S, and NH3 are not included. Forthe Peng Choice, the defmition ofPeng 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• Forinstance, when 11fC02 (orpCOz) is calculated from TA and TC02, a modest phosphate concentration such as 3 J,Lmollk.g-SW, can result in a difference of20 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 ofalkalinities are given 

### in micromoles perkilogram ofseawater (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 KSO4 that are still in current usage: Khoo et al. (1977) and Dickson (1990a). Although many olderpapers used values ofKhoo et al. (1977), the values ofDickson (1990a) are now recommended. The values ofKhoo et al. (1977) are between 15 to 45% lowerthan those ofDickson, 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 ofthe Dickson values when converting from the total pH scale to the free pH scale will result in pHvalues that are 0.015 to 0.03 units lowerthan those obtained using values ofKhoo et al. (1977).



### 10. fC02 

### AND pC02 The fugacity ofC02 (fCOz) in water is defined to be the fugacity ofC02 in air which is in equilibrium with the water. The partial pressure ofC02 in wet (100% water-saturated) air (pC02) is defined to be the product ofthe mole fraction ofC02in wet air and the total pressure. This is the same as the product ofthe mole fraction ofC02 in dry air [xCOz(dry)] and (p101 -**p~ ),**  where**P~!zo** is the vapor pressure ofwater above seawater. At pressures ofthe order of 1 atm, fC02 

### in 

### arr is about 0.3% lower than the pC02due to the nonideality ofC02 (Weiss 1974). This program assumes a pressure near 1 atm (where most equilibrators function) for the conversion between partial pressure and fugacity.

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

where [C02*] is the concentration ofdissolved C02 , 

## Ko is the solubility coefficient ofC02 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 ofxC02(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, orhomogeneous buffer, factor is the percentage change in fC02 (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 oftwo ofthe C02 system parameters) ofthe sample. It is calculated at both the input and output conditions using the following: Revelle 

### factor= (dfCO/dTCOz) I 

### (fCOJTC02) at constant TA. 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 ofthe solubility ratio, Omega, which is defined as

·Thus, values ofOmega <1 represent conditions ofundersaturation, and values ofOmega >1

represent conditions ofoversaturation. The concentration ofcalcium, [Ca 2+], is assumed to be proportional to the salinity, and the carbonate concentration, [CO/-], is calculated from TC02, pH, and the values ofK1 and K2 for carbonic acid. For Constant Choices 1 to 5, the calcium concentration used is from Riley and Tongudai (1967). The values ofKsp 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).

13Forthe GEOSECS Choice and the Peng Choice, the concentration ofcalcium is from Culkin (1965). The value ofKsp 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 ofpressure on these constants in seawater, and most values are estimated from molal volume data. Few measurements have been made for K1 and K2 (ofcarbonic acid) and 

### KB (ofboric acid) at only a few combinations oftemperature, salinity, and pressure in seawater (mostly in artificial seawater). All work assumed that

## fH, the activity coefficient of H+ (including liquidjunction effects), is independent ofpressure. Some ofthe pH scale conversions do depend on pressure, however. Values ofthe constants should be (1) converted initially to the seawater orNBS 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 ofcalcite and aragonite in seawater. Depth in meters and pressure in decibars are used interchangeably in this program. They differby 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 ofthe pressure corrections is used in this program. Forthe Freshwater Choice, the effects ofpressure on 

### Kt> K 2 , and 

### Kw are from Millero (1983). Peng et al. (1987) did not consider the effects ofpressure, but they are included in the program C02SYS for the Peng Choice. ForConstant Choices 1 through 5 and the Peng Choice, the effects ofpressure on the values of

### Kp1 , 

### KP2, and 

### KP3 are from Millero (1995). The only mention ofKsi was in Millero (1995), where it is stated that the values have been estimated from the values ofboric acid, butthey 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). Forthe effects ofpressure on 

### Kw, the fit given in Millero (1983) is used. GEOSECS did not include the effects ofOH, phosphate, or silicate, so these are irrelevant for that choice. Forthe GEOSECS Choice and the Peng Choice, the effects ofpressure on 

### K1, 

### K 2, 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 ofpressure on the solubility ofcalcite 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 toTakahashi et al. (1982).] Forthe Constant Choices 1 to 5, the effects ofpressure on K1and K2 are from Millero (1995), and those for 

### K8 are from Millero (1979), but without the salinity dependence. These fits are fromthe data ofCulberson and Pytkowicz (1968). The effects ofpressure on 

### K50 and KF are from Millero (1995). Note that typographical errors in Millero (1995) include a fa1:tor of 1000 left out ofthe definition ofKappa 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 ofthe H+ion (this includes liquidjunction effects), TS and 

### 1Fare the concentrations ofS042

- and fluoride, and Kso and KF are the dissociation constants ofHSO4- 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 lowerthan 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 ofmollkg-Hp). The difference between mollkg-SW and mollkg-H2

### 0 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. 

### f8 has been found to be electrode-dependent, and does NOTequal 1 at salinity 0 due to the liquidjunction potential. 15Values 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 ofpressure. For discussions ofthe various pH scales see Dickson (1984, 1993), Millero et al. (1993), Butler (1992), or Culberson (1981). Attention is required because in some ofthese references the distinction between the total and the seawaterpH 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-InputMode 

### 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, ortoreport any problems, please contact: Ernie Lewis or Doug Wallace Department ofApplied 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 ofthe C02 system in seawater is the 

### Handbook of Methodsfor theAnalysis ofthe Various Parameters ofthe Carbon Dioxide System in 

### Sea Water (DOE 1994). The web site for information on this reference is 16http://www-mpl.ucsd.edu/people/adickson!C02_QC/. A listing ofthe errata 

### in this handbook is also available atthis site. A copy ofthe 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 OakRidge, Tennessee 37831-6335, U.S.A. 423-574-0390 or423-574-3645 (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 ofsome ofthe 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 ofthe C02 system 

### in seawater were supplied by Dr. Andrew Dickson, Scripps Institution ofOceanography. 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. FrankMillero of the Rosenstiel School ofMarine and Atmospheric Sciences at the University ofMiami for his numerous contributions to this field. This work was supported by the 

### U.S. Department ofEnergy Office ofBiological 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).



### 18. REFERENCES Berner, R. A. 1976. The solubility ofcalcite and aragonite in seawater in atmospheric pressure and 34.5%o salinity.American Journal of Science 276:713-30. Butler, J. N. 1991. Carbon Dioxide Equilibria and Their Applications. Lewis Publishers, Inc., Chelsea, Mich.

17

### Butler, J. N. 1992. Alkalinity titration in seawater: How accurately can the data be fitted by an equilibrium model? Marine Chemistry 

### 38:251-82. Culberson, C. H. 1981. Direct potentiometry. pp. 187-261. In M. Whitfield and D. Jagner (eds.), Marine Electrochemistry: A Practical Introduction. John Wiley and Sons, New York. Culberson, C. H., and R. M. Pytkowicz. 1968. Effect ofpressure on carbonic acid, boric acid, and the pH ofseawater. Limnology and 

### Oceanography 

### 13:403-17. Culkin, 

### F. 1965. The major constituents ofsea water. pp. 121-61. In

### J. 

### P. Riley and G. Skirrow (eds.), Chemical Oceanography. 

### Academic Press, New York. Dickson, A. 

### G. 1981. 

### An exact defmition oftotal alkalinity and a procedure for the estimation ofalkalinity and total inorganic carbon from titration data. Deep-Sea Research 

### 28A:609-23. Dickson, A. 

### G. 1984. pH scales and proton-transferreactions in saline media such as sea water. Geochemica et CosmochemicaActa 

### 48:2299-2308. Dickson, A. 

### G. 1990a Standard potential ofthe reaction: AgCl(s) 

### +**~ig)** 

# =Ag(s) 

### + HCl(aq), and the standard acidity constant ofthe ion HS04- 

### in synthetic seawater from 273.15 to 318.15 

### K. Journal ofChemical Thermodynamics 

### 22:113-27. Dickson, A. 

### G. 1990b. Thermodynamics ofthe dissociation ofboric acid in synthetic seawater from 273.15 to 318.15 K. 

### Deep-Sea Research 

### 37:755-66. Dickson, A. 

### G. 1993. pH buffers for sea water media based on the total hydrogen concentration scale. Deep-Sea Research 

### 40:107-18. Dickson, A. 

### G., and 

### F. J. Millero. 1987. A comparison ofthe equilibrium constants for the dissociation ofcarbonic acid in seawater media Deep-Sea Research 

### 34:1733-43.

-. 1989. Corrigenda. Deep-Sea Research 

### 36:983. Dickson, A. 

### G., and 

### J.P. Riley. 1978. The effect ofanalytical error on the evaluation ofthe components ofthe aquatic carbon-dioxide system. Marine Chemistry 

### 6:77-85. Dickson, A. 

### G., and 

### J.P. Riley. 1979. The estimation ofacid dissociation constants in seawater media from potentiometric titrations with strong base. I. 

### The ionic product of water-Kw. Marine Chemistry 

### 7:89-99. DOE (U.S. Department ofEnergy). 1994. Handbook of methodsfor the analysis ofthe various parameters ofthe carbon dioxide system in sea water. Version 2. 

### ORNUCDIAC-74. A. 

### G. Dickson and C. Goyet (eds.), Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department ofEnergy, Oak Ridge, Tenn.

18Edmond, 

### J. M., and 

### J. M. T. M. Gieskes. 1970. On the calculation ofthe degree ofsaturation of seawater with respect to calcium carbonate under in situ conditions. Geochemica et CosmochemicaActa 34:1261-91. Goyet, C., and 

### A. Poisson. 1989. New determination ofcarbonic acid dissociation constants in seawater as a function oftemperature and salinity. Deep-Sea Research 36:1635-54. Hansson, I. 1973a. A new set ofacidity constants for carbonic acid and boric acid in sea water. Deep-Sea Research 20:461-78. Hansson, 

### I. 1973b. The determination ofdissociation constants ofcarbonic acid in synthetic sea water in the salinity range of20-40%o and temperatUre range of5-30°C.Acta Chemica Scandanavia 27:931-44. Harned, H. S., and R. Davis, Jr. 1943. The ionization constant ofcarbonic acid in water and the solubility ofcarbon dioxide in water and aqueous salt solutions from 0 to 50°. Journal oftheAmerican Chemical Society 65:2030-37. Harned, H. S., and B. B. Owen. 1958. The Physical Chemistry ofElectrolyte Solutions. American Chemical Society Monograph Series. Reinhold Pub. Corp., New York. Harned, H. S., and S. R. Scholes, Jr. 1941. The ionization constant ofHC03- from 0 to 50°. Journal oftheAmerican Chemical Society 43:1706-09. Ingle, S. E. 1975. Solubility ofcalcite in the ocean. Marine Chemistry 3:301-19. Ingle, S. E., C. H. Culberson, J. E. Hawley, and R. 

### M. Pytkowic2:. 1973. The solubility of calcite in seawater at atmospheric pressure and 35%o salinity. Marine Chemistry 1:295-307. Kester, D. R., and R. 

### M. Pytkowicz. 1967. Determination ofthe apparent dissociation constants ofphosphoric acid in seawater. Limnology and Oceanography 12:243-52. Khoo, K. H., R. W. Ramette, C. H. Culberson, and R. G. Bates. 1977. Determination of hydrogen ion concentrations in seawater from 5 to 40°C: Standard potentials at salinities from 20 to 45%o. Analytical Chemistry 49(1):29-34. Li, Y. H., 

### T. Takahashi, and 

### W. S. Broecker. 1969. Degree ofsaturation ofCaC03 in the oceans. Journal ofGeophysicalResearch 74:5507-25. Lyman, J. 1957. Buffer mechanism of sea water. Ph.D. thesis. University ofCalifornia, Los Angeles. Mehrbach, C., C. H. Culberson, 

### J. E. Hawley, and R. M. Pytkowicz. 1973. Measurement of the apparent dissociation constants ofcarbonic acid in seawater at atmospheric pressure. Limnology and Oceanography 18:897-907.

19Millero, F. J. 1979. The thermodynamics ofthe carbonate system in seawater. Geochemica et CosmochemicaActa 43:1651-61. Millero, F. J. 1983. Influence ofpressure on chemical processes in the sea. pp. 1-88. In J. P. Riley and 

### R. Chester (eds.), Chemical Oceanography. Academic Press, New York. Millero, F. J. 1995. Thermodynamics ofthe carbon dioxide system in the oceans. Geochemica et CosmochemicaActa 59:661-77. Millero, F. J., and M. L. Sohn. 1992. Chemical Oceanography. CRC Press, BocaRaton, Fla Millero, 

### F. J., J. 

### Z. Zhang, S. Fiol, S. Sotolongo,

### R.N. Roy, 

### K. Lee, and 

### S. Mane. 1993. The use ofbuffers to measure the pH ofseawater. Marine Chemistry 44:143-52. Morris, A. 

### W., and J.P. Riley. 1966. The bromide/chlorinity and sulphate/chlorinity ratio in ·sea water. Deep-Sea Research 13:699-705. Mucci, A. 1983. The solubility ofcalcite and aragonite in seawater at various salinities, temperatures, and one atmosphere total pressure. AmericanJournal of Science 283:781-99. Murray, C. N., and J.P. Riley. 1971. The solubility ofgases in distilled water and seawater. IV. Carbon dioxide. Deep-Sea Research 18:533-41. Park, P. 

### K. 1969. Oceanic C02 system: An evaluation often methods ofinvestigation. Limnology and Oceanography 14:179-86. Peng, T. H., T. Takahashi, W. S. Broecker, and J. Olafsson. 1987. Seasonal variability of carbon dioxide, nutrients and oxygen in the northern North Atlantic surface water: Observations and model. Tellus 39B:439-58. Riley, J.P. 1965. The occurrence ofanomalously high fluoride concentrations in the North Atlantic. Deep-Sea Research 12:219-20. Riley, J.P., and M. Tongudai. 1967. The major cation/chlorinity ratios in sea water. Chemical Geology 2:263-69. 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 ofcarbonic acid in seawater at salinities 5 to 45 and temperatures 0 to 45°C. Marine Chemistry 44:249-67.

-. 1994. Erratum. Marine Chemistry 45:337.

-. 1996. Erratum. Marine Chemistry 52:183. Sillen, L. G., A. E. Martell, and J. Bjerrum. 1964. Stability constants ofmetal-ion complexes, 2nd ed. Special Publication No. 17. Chemical Society (Great Britain), London. [Referenced in Takahashi et al. 1982 as Sillen and Martel (1964).]

20( Skirrow, G. 1975. The dissolved gases- Carbon dioxide. pp. 1-192. 

### InJ.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 ofdeep-sea water from the Pacific Ocean. Deep-Sea Research 21:161-2. Weiss, R. F. 1974. Carbon dioxide in water and seawater: The solubility ofa 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 otherpapers 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 

### "shouldbe "log 10 (KHSo )." 4 4 

### Chen, H., R. Wanninkhof, R. A. 

### Feely, and D. Greeley. 1995. Measurement offugacity of carbon dioxide in seawater: an evaluation ofa 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 ofthe seawaterhydrogen scale):

..."; however, the formula for 

### K 8 

### given is on the total scale, and the formulae for KPZ,**~,** 

### and K 5; 

### 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 ofm-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 ofpH 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." • InTable 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 ofthe reaction: AgCl(s) + lf.zH2

### (g) = 

### Ag(s) + HCl(aq), and the standard acidity constant ofthe ion HS04

### -in synthetic seawater from 273.15 to 318.15 K. Journal ofChemical 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 ofthe dissociation ofboric 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

## /I 5" 

### should be "ms = 

### m3s*l/I3

### s·" • On p. 762 in Eq. 18: The term 

## "a.z" should be "a. 3 ." 

### Dickson, A. G., and F. 

### I. Millero. 1987. A comparison ofthe equilibrium constants for the dissociation ofcarbonic 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 *S 2." o 

### Also, onp. 1740 in Table 5: The second equation should read "pK2

### *," not "pK 1 

### *." 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 ofacid dissociation constants in seawatermedia 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 ofacid 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 ofthe August-September 1991 and 1979 surface partial pressure ofC02 

### 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 ofthe 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 ofcarbonic acid dissociation constants in seawater as a function oftemperature 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 ofacidity constants for carbonic acid and boric acid in seawater. Deep-Sea Research 20:461-78.

• On p. 467, line 17: The phrase "fourtemperatures" 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 ofthe carbonate system in seawater. Deep-Sea Research 42:2035-61.

• On p. 2037 afterEq. 3: The value for the concentrations ofSO4 should be proportional to "S/35," not "35/S." • On p. 2038 afterEq. 5: The concentrations ofS04 and 

### F should be proportionalto "S/35," not "35/S." • On p. 2056, two lines up: The statement ''The calculated values ofpK2 (S 

# =35)

..." should NOThave the expression "(S 

### = 35)," as the fit has a salinity dependence. • On p. 2058: The actual title for the reference ofClayton and Byrne is "Spectrophotometric seawaterpH measurements: Total hydrogen ion concentration scale calibration ofm-cresol purple and at-searesults." • 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 ofS04, 

### 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 ofcarbonic 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 ofthe carbonate system in seawater. Geochemica et CosmochemicaActa 43:1651-1661.

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

### F. 

### J. 1983. Influence ofpressure on chemical processes in the sea. Chapter43. 

### 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 ofthe carbon dioxide system in the oceans. Geochemica et CosmochemicaActa 59:661-77. A-5• On p. 664: Equation 32uses Khoo's value ofK850 (Khoo et al. 1977), but on p. 667 it is stated that Khoo's value is unreliable and should4 not be used. This is unclear. • On p. 667: In the first full paragraph it is stated that the values ofK850 were determined from Eq. 30 afterRoy's constants were converted to the SWS pH scale. The value ofKHSo is needed to convert pH scales and cannot be found from Eq. 30. • On p. 668: It1s 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 ofthe rest ofthe 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 seawaterpH scale (this wasn't stated but is consistent with programs ofMillero). • On p. 670: The given check value afterEq. 64 of"1.6j..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 seawaterpH scale (this was not stated, but can be determined from the DOE Handbook). • On p. 671, afterEq. 71: The check values "0.792" and "0.204" should be "0.852" and 

### c "0.140." IfpH= 8.2 is used, or ifKP3 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, afterEq. 73: Forthe 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 ofpK5iis "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 ofpK5ias 9.47), or (2) the pH scale is incorrect (the value for pK 5iof9.38 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 pK5iof"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 att = 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 pK 15 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 similartopic (Goyet, C., F. J. Millero, 

### A. Poisson, and 

### A-6D. Shafer. 1993. Temperature dependence ofC02 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: IffC02 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 ofthese and fC02 at 20°C is also sufficient to fmd fC02 at any temperature. • On p. 675, afterEq. 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 ofb2 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, orthe last two columns in Table 9 should be 1000*b1and 1000*b2 in order to be correct. • On p. 675 in Table 9: The values of

# ao. at, and a2 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 ornot it is meant that they are assumed to be equal to those for boric acid. • On p. 675 

### in Table 9: The value ofat for B(OH)3 should be "+0.1622" to agree with Millero (1979). • On p. 675 

### in Table 9: The values ofat 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 ofb 1for 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 ofseawater at one atmosphere. Ocean Sci. Eng. 7: 403-60." It should probably read: o Millero, F. 

### J. (1976). The thermodynamics ofseawater at one atmosphere.American Journal of Science 276:1035-77. o Millero, F. 

### J. (1982). Thermodynamics ofseawater: the PVT properties. Ocean Sci. Eng. 7: 403-60. Millero, F. J., T. Plese, and M. Fernandez. 1988. The dissociation ofhydrogen sulfide 

### in seawater. Limnology and Oceanography 33:269-74.

• On p. 271 justbefore 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 seawatercontaining no fluoride. • On p. 273: The fit forfH combines data which were taken in seawater (artificial and actual) containing fluoride with values that were taken in artificial seawater without fluoride.

A-7Millero, 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 seawaterpH 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 notbe in the numerator but ratherby themselves. This expression also makes the approximation that 

### Kl* 

### >> :Kz*. • On p. 279: The right-hand side ofEq. 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 ofHansson (1973 a,b). o p. 273: The equations for 

### 11V and 

### 11Kfor 

### Kw are from Millero (1983). o p. 276: The fit for PHso is from Millero (1986). o pp. 279 and 280: The

### ~uations for K 1 and K2 are from Dickson and Millero (1987) from the combined data ofHansson (1973 a,b) and Mehrbach et al. (1973). 

### o p. 280: The equations for 

### 11V and 

### 11K for the constants 

### K 1and 

### K2 

### are from Millero (1979). o p. 281: The fit for K8 is from Millero (1979) from data ofHansson (1973a,b). o p. 281: The equations for 

### 11V and 

### 11Kfor 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 

### 11V and 

### 11Kfor calcite are from Ingle (1975). o p. 282: The equations for 

### 11V and 

### 11Kfor 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 CosmochemicaActa43:1651-61. 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 ofpressure 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 ofbuffers to measure the pH ofseawater. 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

I

# -------------------------------~-- IMillero, 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 NOTthe same as the one in GEOSECS, as claimed, but rather is rounded off. It is about 1% higher (this results in a change of0.004 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: Onp. 455, Eq. A3: This definition ofTA is different from that ofDickson; 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 ofcarbonic 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 forFig. 2: The expression "3m(C032

### T' should be "2m(C0/1." • On pp. 254 and 258: The authors claim 2S precisions of "0.004" in pK1and "0.006" in**p~.** FromAndrew 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 K 1*: 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 ofconstants: 

### 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 ofconstants 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 Berneruses on p. 722 ofBerner (1976)]. • On p. 79 in No. 8 in the list ofconstants: 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 ofthe 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

# mshould read: "

...1.1% and 1.5%, respectively, below our results."

A-10