Package 'seacarb' reference manual

Title:	Seawater Carbonate Chemistry
Description:	Calculates parameters of the seawater carbonate system and assists the design of ocean acidification perturbation experiments.
Authors:	Jean-Pierre Gattuso [aut, cre, cph], Jean-Marie Epitalon [aut], Heloise Lavigne [aut], James Orr [aut], Bernard Gentili [ctb], Mathilde Hagens [ctb], Andreas Hofmann [ctb], Jens-Daniel Mueller [ctb], Aurélien Proye [ctb], James Rae [ctb], Karline Soetaert [ctb]
Maintainer:	Jean-Pierre Gattuso <[email protected]>
License:	GPL (>= 2)
Version:	3.3.3
Built:	2024-11-23 05:03:18 UTC
Source:	https://github.com/jpgattuso/seacarb-git

Example data file for function at

Description

The variables are:

volume: Volume of acid added to the sample in ml
E: Potential measured during the titration in mV
temperature: Temperature in degrees Celsius
weight: Weight of the sample in g
S: Salinity
normality : Normality of the acid
ETris: Potential used for the calibration of the electrode in mV
pHTris: pH used for the calibration of the electrode with the TRIS buffer

Usage

alkalinityalkalinity

Format

A data frame with 29 rows and 8 variables

Source

Data come from a potentiometric titration performed by Steeve Comeau.

pH value of the AMP buffer

Description

pH value of the AMP buffer (on the total scale in mol/kg)

Usage

amp(S=35,T=25)
amp(S=35,T=25)

Arguments

`S`	Salinity, default is 35
`T`	Temperature in degrees Celsius, default is 25oC

Details

Note that the arguments can be given as a unique number or as vectors. If the lengths of the vectors are different, the longer vector is retained and only the first value of the other vectors is used. It can therefore be critical to use vectors of the same length.

Value

AMP

pH value of the AMP buffer (on the total scale in mol/kg)

Author(s)

Jean-Pierre Gattuso [email protected]

References

Dickson A. G., Sabine C. L. and Christian J. R., 2007 Guide to best practices for ocean CO2 measurements. PICES Special Publication 3, 1-191.

Examples

	##Example from Dickson et al. (2007)
	amp(S=35,T=25)
##Example from Dickson et al. (2007)
	amp(S=35,T=25)

Bjerrum plot

Description

Plot the concentration of the various ionic forms of a molecule as a function of pH

Usage

bjerrum(K1=K1(), K2=NULL, K3=NULL, phmin=2, phmax=12, by=0.1, conc=1, 
     type="l", col="black",  ylab="Relative concentration (%)", add=FALSE, ...)
     bjerrum(K1=K1(), K2=NULL, K3=NULL, phmin=2, phmax=12, by=0.1, conc=1, 
     type="l", col="black",  ylab="Relative concentration (%)", add=FALSE, ...)

Arguments

`K1`	First dissociation constant
`K2`	Second dissociation constant, default is NULL
`K3`	Third dissociation constant, default is NULL
`phmin`	Minimum pH value, default is 2
`phmax`	Maximum pH value, default is 12
`by`	Increment on the pH axis, default is 0.1
`conc`	concentration of molecule, default is 1
`type`	Type of plot, default is line
`col`	Color of plot, default is black
`ylab`	Label of Y axis, default is (mol/kg)
`add`	false:start new, true: add to current, default is false
`...`	Graphical parameters (see `par`) and any further arguments of plot, typically `plot.default`, may also be supplied as arguments to this function. Hence, the high-level graphics control arguments described under `par` and the arguments to `title` may be supplied to this function.

Details

Note that the concentration is plotted in mol/kg only if conc is given is mol/kg

Author(s)

Karline Soetaert [email protected]

References

Zeebe, R. E. and Wolf-Gladrow D. A., 2001 CO2 in seawater: equilibrium, kinetics, isotopes. Amsterdam: Elsevier, 346 pp.

Examples

## Plot the bjerrum plot for the carbonate system using the default values
bjerrum(K1(),K2(),main="DIC speciation",lwd=2) 
abline(v=-log10(K1()),col="grey")
mtext(side=3,at=-log10(K1()),"pK1")
abline(v=-log10(K2()),col="grey")
mtext(side=3,at=-log10(K2()),"pK2")
legend("left",lty=1:3,lwd=2,legend=c(expression(CO[2]),expression(HCO[3]^"-"),
	expression(CO[3]^"2-")))

## Plot the bjerrum plot for phosphate using the default values
bjerrum(K1p(),K2p(),K3p(),main="phosphate speciation",lwd=2)
legend("left",lty=1:4,lwd=2,legend=c(expression(H[3]~PO[4]),
	expression(H[2]~PO[4]^"-"),
expression(HPO[4]^"2-"),expression(PO[4]^"3-")))

## Plot the bjerrum plot for the carbonate system using the values other 
##	than the default ones, showing the effect of temperature
bjerrum(K1(T=25,S=35),K2(T=25,S=35),conc=1.3,main="effect of temperature" )
bjerrum(K1(T=0,S=35),K2(T=0,S=35),conc=1.3,add=TRUE,col="red")
legend("left",lty=1,col=c("black","red"),legend=c("T=25 oC","T=0 oC"))
legend("right",lty=1:3,legend=c(expression(CO[2]),expression(HCO[3]^"-"),
	expression(CO[3]^"2-")))

## Plot the bjerrum plot for the carbonate system using the values other 
##	than the default ones, showing the effect of salinity
bjerrum(K1(T=25,S=35),K2(T=25,S=35),conc=1.3,main="effect of salinity" )
bjerrum(K1(T=25,S=5),K2(T=25,S=5),conc=1.3,add=TRUE,col="blue")
legend("left",lty=1,col=c("black","blue"),legend=c("S=35","S=5"))
legend("right",lty=1:3,legend=c(expression(CO[2]),expression(HCO[3]^"-"),
	expression(CO[3]^"2-")))

## Plot the bjerrum plot for the carbonate system using the values other 
##	than the default ones, showing the effect of pressure
bjerrum(K1(P=0),K2(P=0),conc=1.3,main="effect of pressure" )
bjerrum(K1(P=300),K2(P=300),conc=1.3,add=TRUE,col="green")
legend("left",lty=1,col=c("black","green"),legend=c("P=0","P=300"),title="atm")
legend("right",lty=1:3,legend=c(expression(CO[2]),expression(HCO[3]^"-"),
	expression(CO[3]^"2-")))
## Plot the bjerrum plot for the carbonate system using the default values
bjerrum(K1(),K2(),main="DIC speciation",lwd=2) 
abline(v=-log10(K1()),col="grey")
mtext(side=3,at=-log10(K1()),"pK1")
abline(v=-log10(K2()),col="grey")
mtext(side=3,at=-log10(K2()),"pK2")
legend("left",lty=1:3,lwd=2,legend=c(expression(CO[2]),expression(HCO[3]^"-"),
	expression(CO[3]^"2-")))

## Plot the bjerrum plot for phosphate using the default values
bjerrum(K1p(),K2p(),K3p(),main="phosphate speciation",lwd=2)
legend("left",lty=1:4,lwd=2,legend=c(expression(H[3]~PO[4]),
	expression(H[2]~PO[4]^"-"),
expression(HPO[4]^"2-"),expression(PO[4]^"3-")))

## Plot the bjerrum plot for the carbonate system using the values other 
##	than the default ones, showing the effect of temperature
bjerrum(K1(T=25,S=35),K2(T=25,S=35),conc=1.3,main="effect of temperature" )
bjerrum(K1(T=0,S=35),K2(T=0,S=35),conc=1.3,add=TRUE,col="red")
legend("left",lty=1,col=c("black","red"),legend=c("T=25 oC","T=0 oC"))
legend("right",lty=1:3,legend=c(expression(CO[2]),expression(HCO[3]^"-"),
	expression(CO[3]^"2-")))

## Plot the bjerrum plot for the carbonate system using the values other 
##	than the default ones, showing the effect of salinity
bjerrum(K1(T=25,S=35),K2(T=25,S=35),conc=1.3,main="effect of salinity" )
bjerrum(K1(T=25,S=5),K2(T=25,S=5),conc=1.3,add=TRUE,col="blue")
legend("left",lty=1,col=c("black","blue"),legend=c("S=35","S=5"))
legend("right",lty=1:3,legend=c(expression(CO[2]),expression(HCO[3]^"-"),
	expression(CO[3]^"2-")))

## Plot the bjerrum plot for the carbonate system using the values other 
##	than the default ones, showing the effect of pressure
bjerrum(K1(P=0),K2(P=0),conc=1.3,main="effect of pressure" )
bjerrum(K1(P=300),K2(P=300),conc=1.3,add=TRUE,col="green")
legend("left",lty=1,col=c("black","green"),legend=c("P=0","P=300"),title="atm")
legend("right",lty=1:3,legend=c(expression(CO[2]),expression(HCO[3]^"-"),
	expression(CO[3]^"2-")))

Total boron concentration (mol/kg)

Description

total boron concentration ( $mol\ kg^{-1}$ )

Usage

bor(S, b)
bor(S, b)

Arguments

`S`	Salinity, default is 35
`b`	"l10" for using the formulation of Lee et al. (2010), "u74" for using the Uppstrom (1974), or "k18" for using the Kulinski et al. (2018), default is "u74"

Details

Note that the formulation of Kulinski et al. (2018) is specifically designed for the Baltic Sea. Three formulations are described in their paper:

based on their measurements: TB = [umol/kg] = 10.838 * S + 13.821
based on Kremling (1970 and 1972): TB [umol/kg] = 11.44 * S + 12.6; R2 = 0.95
consensus regression (Kremling + their data): TB [umol/kg] = 11.405 * S + 11.869; R2 = 0.97s

The latter formulation is used here.

Value

bor

total boron concentration ( $mol\ kg^{-1}$ ))

Author(s)

Heloise Lavigne, Aurelien Proye and Jean-Pierre Gattuso [email protected]

References

DOE 1994 Handbook of methods for the analysis of the various parameters of the carbon dioxide system in sea water. ORNL/CDIAC-74. Oak Ridge,Tenn.: Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory.

Kulinski K., Szymczycha B., Koziorowska K., Hammer K. & Schneider B., 2018. Anomaly of total boron concentration in the brackish waters of the Baltic Sea and its consequence for the CO2 system calculations. Marine Chemistry. doi:s10.1016/j.marchem.2018.05.007.

Lee K., Tae-Wook K., Byrne R.H., Millero F.J., Feely R.A. and Liu Y-M, 2010 The universal ratio of the boron to chlorinity for the North Pacific and North Atlantic oceans. Geochimica et Cosmochimica Acta 74 1801-1811.

Uppstrom L.R., 1974 The boron/chlorinity ratio of the deep-sea water from the Pacific Ocean. Deep-Sea Research I 21 161-162.

Examples

bor(35, "l10")
bor(35, "l10")

Buffer parameters of the seawater carbonate system

Description

Returns buffer parameters of the seawater carbonate system.

Usage

buffer(flag, var1, var2, S = 35, T = 25, Patm = 1, P = 0, Pt = 0, Sit = 0, 
  k1k2 = "x", kf = "x", ks = "d", pHscale = "T", b = "u74", warn = "y", 
  eos = "eos80", long = 1e+20, lat = 1e+20)
buffer(flag, var1, var2, S = 35, T = 25, Patm = 1, P = 0, Pt = 0, Sit = 0, 
  k1k2 = "x", kf = "x", ks = "d", pHscale = "T", b = "u74", warn = "y", 
  eos = "eos80", long = 1e+20, lat = 1e+20)

Arguments

`flag`	select the couple of variables available. The flags which can be used are: flag = 1 pH and CO2 given flag = 2 CO2 and HCO3 given flag = 3 CO2 and CO3 given flag = 4 CO2 and ALK given flag = 5 CO2 and DIC given flag = 6 pH and HCO3 given flag = 7 pH and CO3 given flag = 8 pH and ALK given flag = 9 pH and DIC given flag = 10 HCO3 and CO3 given flag = 11 HCO3 and ALK given flag = 12 HCO3 and DIC given flag = 13 CO3 and ALK given flag = 14 CO3 and DIC given flag = 15 ALK and DIC given flag = 21 pCO2 and pH given flag = 22 pCO2 and HCO3 given flag = 23 pCO2 and CO3 given flag = 24 pCO2 and ALK given flag = 25 pCO2 and DIC given
`var1`	enter value of the first variable in mol/kg, except for pH and for pCO2 in $\mu$ atm
`var2`	enter value of the second variable in mol/kg, except for pH
`S`	Salinity
`T`	Temperature in degrees Celsius
`Patm`	Surface atmospheric pressure in atm
`P`	Hydrostatic pressure in bar (surface = 0)
`Pt`	Concentration of total phosphate in mol/kg; set to 0 if NA
`Sit`	Concentration of total silicate in mol/kg; set to 0 if NA
`k1k2`	"cw" for using K1 and K2 from Cai & Wang (1998), "l" from Lueker et al. (2000), "m02" from Millero et al. (2002), "m06" from Millero et al. (2006), "m10" from Millero (2010), "mp2" from Mojica Prieto et al. (2002), "p18" from Papadimitriou et al. (2018), "r" from Roy et al. (1993), "sb21" from Shockman & Byrne (2021), "s20" from Sulpis et al. (2020), and "w14" from Waters et al. (2014). "x" is the default flag; the default value is then "l", except if T is outside the range 2 to 35oC and/or S is outside the range 19 to 43. In these cases, the default value is "w14".
`kf`	"pf" for using Kf from Perez and Fraga (1987) and "dg" for using Kf from Dickson and Riley (1979 in Dickson and Goyet, 1994). "x" is the default flag; the default value is then "pf", except if T is outside the range 9 to 33oC and/or S is outside the range 10 to 40. In these cases, the default is "dg".
`ks`	"d" for using Ks from Dickon (1990), "k" for using Ks from Khoo et al. (1977), default is "d"
`pHscale`	choice of pH scale: "T" for the total scale, "F" for the free scale and "SWS" for using the seawater scale, default is "T" (total scale)
`b`	Concentration of total boron. "l10" for the Lee et al. (2010) formulation or "u74" for the Uppstrom (1974) formulation, default is "u74"
`warn`	"y" to show warnings when T or S go beyond the valid range for constants; "n" to supress warnings. The default is "y".
`eos`	"teos10" to specify T and S according to Thermodynamic Equation Of Seawater - 2010 (TEOS-10); "eos80" to specify T and S according to EOS-80.
`long`	longitude of data point, used when eos parameter is "teos10" as a conversion parameter from absolute to practical salinity.
`lat`	latitude of data point, used when eos parameter is "teos10".

Details

The Lueker et al. (2000) constants for K1 and K2, the Perez and Fraga (1987) constant for Kf and the Dickson (1990) constant for Ks are recommended by Dickson et al. (2007). It is, however, critical to consider that each formulation is only valid for specific ranges of temperature and salinity:

For K1 and K2:

Cai and Wang (1998): S ranging between 0 and 40 and T ranging between 0.2 and 30oC.
Lueker et al. (2000): S ranging between 19 and 43 and T ranging between 2 and 35oC.
Millero et al. (2002): S ranging from 34 to 37 and T ranging between -1.6 and 35oC.
Millero et al. (2006): S ranging between 0.1 and 50 and T ranging between 1 and 50oC.
Millero (2010): S ranging between 1 and 50 and T ranging between 0 and 50oC. Millero (2010) provides a K1 and K2 formulation for the seawater, total and free pH scales. Therefore, when this method is used and if P=0, K1 and K2 are computed with the formulation corresponding to the pH scale given in the flag "pHscale".
Mojica Prieto et al. (2002): S ranging from 5 to 42 and T ranging between 0 and 45oC.
Papadimitriou et al. (2018): S ranging from 33 to 100 and T ranging between -6 to 25oC.
Roy et al. (1993): S ranging between 5 and 45 and T ranging between 0 and 45oC.
Shockman & Byrne (2021): for K2, S ranging from 19.6 to 41 and T ranging between 15 to 35oC. For K1, formulation is that of Waters et al.
Sulpis et al. (2020): S ranging from 30.7 to 37.6 and T ranging between -1.7 to 31.8oC.
Waters et al.(2014): S ranging between 1 and 50 and T ranging between 0 and 50oC. Waters (2014) provides a K1 and K2 formulation for the seawater, total and free pH scales. Therefore, when this method is used and if P=0, K1 and K2 are computed with the formulation corresponding to the pH scale given in the flag "pHscale".

For Kf:

Perez and Fraga (1987): S ranging between 10 and 40 and T ranging between 9 and 33oC.
Dickson and Riley (1979 in Dickson and Goyet, 1994): S ranging between 0 and 45 and T ranging between 0 and 45oC.

For Ks:

Dickson (1990): S ranging between 5 and 45 and T ranging between 0 and 45oC.
Khoo et al. (1977): S ranging between 20 and 45 and T ranging between 5 and 40oC.

The arguments can be given as a unique number or as vectors. If the lengths of the vectors are different, the longer vector is retained and only the first value of the other vectors is used. It is recommended to use either vectors with the same dimension or one vector for one argument and numbers for the other arguments.

Pressure corrections and pH scale:

For K0, the pressure correction term of Weiss (1974) is used.
For K1, K2, pK1, pK2, pK3, Kw, Kb, Khs and Ksi, the pressure correction was applied on the seawater scale. Hence, if needed, values were first transformed from the total scale to the seawater scale, the pressure correction applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).
For Kf, the pressure correction was applied on the free scale. The formulation of Dickson and Riley (1979 in Dickson and Goyet, 1994) provides Kf on the free scale but that of Perez and Fraga (1987) provides it on the total scale. Hence, in that case, Kf was first transformed from the total scale to the free scale. With both formulations, the pressure correction was applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).
For Ks, the pressure correction was applied on the free scale. The pressure correction was applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).
For Kn, The pressure correction was applied on the seawater scale. The pressure correction was applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).

long and lat are used as conversion parameters from absolute to practical salinity: when seawater is not of standard composition, practical salinity alone is not sufficient to compute absolute salinity and vice-versa. One needs to know the density. When long and lat are given, density is inferred from WOA silicate concentration at given location. When they are not, an arbitrary geographic point is chosen: mid equatorial Atlantic. Note that this implies an error on computed salinity up to 0.02 g/kg.

Value

The function returns a data frame containing the following columns:

`PhiD`	PhiD, chemical buffer factor (dpH/d[DIC]); input/output of dissolved CO2 (unit pH per mol/kg)
`BetaD`	BetaD, homogeneous or Revelle buffer factor (dln(pCO2)/dln[DIC]); input/output of dissolved CO2
`PiD`	PiD, chemical buffer factor (dpCO2/d[DIC]); input/output of dissolved CO2 ( $\mu atm$ per mol/kg)
`PhiB`	PhiB, chemical buffer factor (dpH/d[DIC]); from input/output of bicarbonate (unit pH per mol/kg)
`BetaB`	BetaB, homogeneous buffer factor (dln(pCO2)/dln[DIC]); input/output of bicarbonate
`PiB`	PiB, chemical buffer factor (dpCO2/d[DIC]); input/output of dissolved CO2 ( $\mu atm$ per mol/kg)
`PhiC`	PhiC, chemical buffer factor (dpH/d[DIC]); input/output of carbonate (unit pH per mol/kg)
`BetaC`	BetaC, homogeneous buffer factor (dln(pCO2)/dln[DIC]); input/output of carbonate
`PiC`	PiC, chemical buffer factor (dpCO2/d[DIC]); input/output of carbonate ( $\mu atm$ per mol/kg)
`PhiH`	PhiH, chemical buffer factor (dpH/d[ALK]); input/output of strong acid (unit pH per mol/kg)
`PiH`	PiH, chemical buffer factor (dpCO2/d[ALK]); input/output of strong acid ( $\mu atm$ per mol/kg)

Author(s)

Heloise Lavigne, Aurelien Proye and Jean-Pierre Gattuso [email protected]

References

Cai W. J., and Wang Y., 1998. The chemistry, fluxes, and sources of carbon dioxide in the estuarine waters of the Satilla and Altamaha Rivers, Georgia. Limnology and Oceanography 43, 657-668.

Dickson A. G., 1990 Standard potential of the reaction: AgCI(s) + 1/2H2(g) = Ag(s) + HCI(aq), and the standard acidity constant of the ion HSO4 in synthetic sea water from 273.15 to 318.15 K. Journal of Chemical Thermodynamics 22, 113-127.

Dickson A. G., Sabine C. L. and Christian J. R., 2007 Guide to best practices for ocean CO2 measurements. PICES Special Publication 3, 1-191.

Khoo H. K., Ramette R. W., Culberson C. H. and Bates R. G., 1977 Determination of Hydrogen Ion Concentration in Seawater from 5 to 40oC: Standard Potentials at Salinities from 20 to 45. Analytical Chemistry 49, 29-34.

Frankignoulle M., 1994 A complete set of buffer factors for acid/base CO2 system in seawater. Journal of Marine Systems 5, 111-118.

Lee K., Tae-Wook K., Byrne R.H., Millero F.J., Feely R.A. and Liu Y-M, 2010 The universal ratio of the boron to chlorinity for the North Pacific and North Atlantoc oceans. Geochimica et Cosmochimica Acta 74 1801-1811.

Lueker T. J., Dickson A. G. and Keeling C. D., 2000 Ocean pCO2 calculated from dissolved inorganic carbon, alkalinity, and equations for K1 and K2: validation based on laboratory measurements of CO2 in gas and seawater at equilibrium. Marine Chemistry 70 105-119.

Millero F. J., 2010 Carbonate constant for estuarine waters. Marine and Freshwater Research 61: 139-142.

Millero F. J., Graham T. B., Huang F., Bustos-Serrano H. and Pierrot D., 2006 Dissociation constants of carbonic acid in seawateras a function of salinity and temperature. Marine Chemistry 100, 80-84.

Perez F. F. and Fraga F., 1987 Association constant of fluoride and hydrogen ions in seawater. Marine Chemistry 21, 161-168.

Roy R. N., Roy L. N., Vogel K. M., Porter-Moore C., Pearson T., Good C. E., Millero F. J. and Campbell D. M., 1993. The dissociation constants of carbonic acid in seawater at salinities 5 to 45 and temperatures 0 to 45oC. Marine Chemistry 44, 249-267.

Schockman, K.M., Byrne, R.H., 2021. Spectrophotometric determination of the bicarbonate dissociation constant in seawater, Geochimica et Cosmochimica Acta.

Uppstrom L.R., 1974 The boron/chlorinity ratio of the deep-sea water from the Pacific Ocean. Deep-Sea Research I 21 161-162.

Examples


## Computation with a couple of variables
buffer(flag=8, var1=8.2, var2=0.00234, S=35, T=25, Patm=1, P=0, Pt=0, 
	Sit=0, pHscale="T", kf="pf", k1k2="l", b="u74")

## Using vectors as arguments
flag <- c(8, 2, 8)
var1 <- c(8.2, 7.477544e-06, 8.2)
var2 <- c(0.002343955, 0.001649802, 2400e-6)
S <- c(35, 35, 30)
T <- c(25, 25, 30)
P <- c(0, 0, 0)
Pt <- c(0, 0, 0)
Sit <- c(0, 0, 0)
kf <- c("pf", "pf", "pf")
k1k2 <- c("l", "l", "l")
pHscale <- c("T", "T", "T")
b <- c("l10", "l10", "l10")
buffer(flag=flag, var1=var1, var2=var2, S=S, T=T, P=P, Pt=Pt, 
	Sit=Sit, kf=kf, k1k2=k1k2, pHscale=pHscale, b=b)


## Test for all flags 

flag <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 21, 22, 23, 24, 25)

var1 <- c(8.200000, 7.477544e-06, 7.477544e-06, 7.477544e-06, 7.477544e-06, 8.2, 
	8.2, 8.2, 8.2, 0.001685024, 0.001685024, 0.001685024,  0.0002888382, 
	0.0002888382, 0.002391252, 264.2008, 264.2008, 264.2008, 264.2008, 264.2008)

var2 <- c(7.477544e-06, 0.001685024, 0.0002888382, 0.002391252, 0.001981340, 
	0.001685024, 0.0002888382, 0.002391252, 0.001981340, 0.0002888382, 0.002391252,
	0.001981340,  0.002391252, 0.001981340, 0.001981340, 8.2, 0.001685024, 
	0.0002888382, 0.002391252, 0.001981340)

buffer(flag=flag, var1=var1, var2=var2)

## Computation with a couple of variables
buffer(flag=8, var1=8.2, var2=0.00234, S=35, T=25, Patm=1, P=0, Pt=0, 
	Sit=0, pHscale="T", kf="pf", k1k2="l", b="u74")

## Using vectors as arguments
flag <- c(8, 2, 8)
var1 <- c(8.2, 7.477544e-06, 8.2)
var2 <- c(0.002343955, 0.001649802, 2400e-6)
S <- c(35, 35, 30)
T <- c(25, 25, 30)
P <- c(0, 0, 0)
Pt <- c(0, 0, 0)
Sit <- c(0, 0, 0)
kf <- c("pf", "pf", "pf")
k1k2 <- c("l", "l", "l")
pHscale <- c("T", "T", "T")
b <- c("l10", "l10", "l10")
buffer(flag=flag, var1=var1, var2=var2, S=S, T=T, P=P, Pt=Pt, 
	Sit=Sit, kf=kf, k1k2=k1k2, pHscale=pHscale, b=b)


## Test for all flags 

flag <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 21, 22, 23, 24, 25)

var1 <- c(8.200000, 7.477544e-06, 7.477544e-06, 7.477544e-06, 7.477544e-06, 8.2, 
	8.2, 8.2, 8.2, 0.001685024, 0.001685024, 0.001685024,  0.0002888382, 
	0.0002888382, 0.002391252, 264.2008, 264.2008, 264.2008, 264.2008, 264.2008)

var2 <- c(7.477544e-06, 0.001685024, 0.0002888382, 0.002391252, 0.001981340, 
	0.001685024, 0.0002888382, 0.002391252, 0.001981340, 0.0002888382, 0.002391252,
	0.001981340,  0.002391252, 0.001981340, 0.001981340, 8.2, 0.001685024, 
	0.0002888382, 0.002391252, 0.001981340)

buffer(flag=flag, var1=var1, var2=var2)

Buffer factors of the seawater carbonate system as defined by Hagens and Middelburg (2016)

Description

Returns the suite of buffer factors presented in Table 3 of Hagens and Middelburg (2016), as well as the proton concentration buffer factor (beta.H of Hofmann et al, 2010) and the classic Revelle factor. For practical purposes, this function excludes the nitrate and nitrite acid-base systems presented in this paper, as well as the fully protonoted form of sulfate (H2SO4) and fully deprotonated form of sulfide (S2-), as their contributions to total alkalinity under natural seawater conditions are negligible. Its input arguments are identical to those in the carbfull function of seacarb.

Usage

buffergen(flag, var1, var2, S=35, T=25, Patm=1, P=0, Pt=0, Sit=0, k1k2="x", kf="x",
                 ks="d", pHscale="T", b="u74", gas="potential", NH4t=0, HSt=0)buffergen(flag, var1, var2, S=35, T=25, Patm=1, P=0, Pt=0, Sit=0, k1k2="x", kf="x",
                 ks="d", pHscale="T", b="u74", gas="potential", NH4t=0, HSt=0)

Arguments

`flag`	select the couple of variables available. The flags which can be used are: flag = 1 pH and CO2 given flag = 2 CO2 and HCO3 given flag = 3 CO2 and CO3 given flag = 4 CO2 and ALK given flag = 5 CO2 and DIC given flag = 6 pH and HCO3 given flag = 7 pH and CO3 given flag = 8 pH and ALK given flag = 9 pH and DIC given flag = 10 HCO3 and CO3 given flag = 11 HCO3 and ALK given flag = 12 HCO3 and DIC given flag = 13 CO3 and ALK given flag = 14 CO3 and DIC given flag = 15 ALK and DIC given flag = 21 pCO2 and pH given flag = 22 pCO2 and HCO3 given flag = 23 pCO2 and CO3 given flag = 24 pCO2 and ALK given flag = 25 pCO2 and DIC given
`var1`	Value of the first variable in mol/kg, except for pH and for pCO2 in $\mu$ atm
`var2`	Value of the second variable in mol/kg, except for pH
`S`	Salinity
`T`	Temperature in degrees Celsius
`Patm`	Surface atmospheric pressure in atm, default is 1 atm
`P`	Hydrostatic pressure in bar (surface = 0)
`Pt`	Concentration of total phosphate in mol/kg; set to 0 if NA
`Sit`	Concentration of total silicate in mol/kg; set to 0 if NA
`k1k2`	"cw" for using K1 and K2 from Cai & Wang (1998), "l" from Lueker et al. (2000), "m02" from Millero et al. (2002), "m06" from Millero et al. (2006), "m10" from Millero (2010), "mp2" from Mojica Prieto et al. (2002), "p18" from Papadimitriou et al. (2018), "r" from Roy et al. (1993), "sb21" from Shockman & Byrne (2021), "s20" from Sulpis et al. (2020), and "w14" from Waters et al. (2014). "x" is the default flag; the default value is then "l", except if T is outside the range 2 to 35oC and/or S is outside the range 19 to 43. In these cases, the default value is "w14".
`kf`	"pf" for using Kf from Perez and Fraga (1987) and "dg" for using Kf from Dickson and Riley (1979 in Dickson and Goyet, 1994). "x" is the default flag; the default value is then "pf", except if T is outside the range 9 to 33oC and/or S is outside the range 10 to 40. In these cases, the default is "dg".
`ks`	"d" for using Ks from Dickson (1990) and "k" for using Ks from Khoo et al. (1977), default is "d"
`pHscale`	"T" for the total scale, "F" for the free scale and "SWS" for using the seawater scale, default is "T" (total scale)
`b`	Concentration of total boron. "l10" for the Lee et al. (2010) formulation or "u74" for the Uppstrom (1974) formulation, default is "u74"
`gas`	used to indicate the convention for INPUT pCO2, i.e., when it is an input variable (flags 21 to 25): "insitu" indicates it is referenced to in situ pressure and in situ temperature; "potential" indicates it is referenced to 1 atm pressure and potential temperature; and "standard" indicates it is referenced to 1 atm pressure and in situ temperature. All three options should give identical results at surface pressure. This option is not used when pCO2 is not an input variable (flags 1 to 15). The default is "potential" and should be a unique value..
`NH4t`	Concentration of total ammonium in mol/kg; set to 0 if NA
`HSt`	Concentration of total hydrogen sulfide in mol/kg; set to 0 if NA

Details

For K1 and K2:

Cai and Wang (1998): S ranging between 0 and 40 and T ranging between 0.2 and 30oC.
Lueker et al. (2000): S ranging between 19 and 43 and T ranging between 2 and 35oC.
Millero et al. (2002): S ranging from 34 to 37 and T ranging between -1.6 and 35oC.
Millero et al. (2006): S ranging between 0.1 and 50 and T ranging between 1 and 50oC.
Millero (2010): S ranging between 1 and 50 and T ranging between 0 and 50oC. Millero (2010) provides a K1 and K2 formulation for the seawater, total and free pH scales. Therefore, when this method is used and if P=0, K1 and K2 are computed with the formulation corresponding to the pH scale given in the flag "pHscale".
Mojica Prieto et al. (2002): S ranging from 5 to 42 and T ranging between 0 and 45oC.
Papadimitriou et al. (2018): S ranging from 33 to 100 and T ranging between -6 to 25oC.
Roy et al. (1993): S ranging between 5 and 45 and T ranging between 0 and 45oC.
Shockman & Byrne (2021): for K2, S ranging from 19.6 to 41 and T ranging between 15 to 35oC. For K1, formulation is that of Waters et al.
Sulpis et al. (2020): S ranging from 30.7 to 37.6 and T ranging between -1.7 to 31.8oC.
Waters et al.(2014): S ranging between 1 and 50 and T ranging between 0 and 50oC. Waters (2014) provides a K1 and K2 formulation for the seawater, total and free pH scales. Therefore, when this method is used and if P=0, K1 and K2 are computed with the formulation corresponding to the pH scale given in the flag "pHscale".

For Kf:

Perez and Fraga (1987): S ranging between 10 and 40 and T ranging between 9 and 33oC.
Dickson and Riley (1979 in Dickson and Goyet, 1994): S ranging between 0 and 45 and T ranging between 0 and 45oC.

For Ks:

Dickson (1990): S ranging between 5 and 45 and T ranging between 0 and 45oC.
Khoo et al. (1977): S ranging between 20 and 45 and T ranging between 5 and 40oC.

Pressure corrections and pH scale:

For K0, the pressure correction term of Weiss (1974) is used.
For K1, K2, pK1, pK2, pK3, Kw, Kb, Khs, Ksi and K2si, the pressure correction was applied on the seawater scale. Hence, if needed, values were first transformed from the total scale to the seawater scale, the pressure correction applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).
For Kf, the pressure correction was applied on the free scale. The formulation of Dickson and Riley (1979 in Dickson and Goyet, 1994) provides Kf on the free scale but that of Perez and Fraga (1987) provides it on the total scale. Hence, in that case, Kf was first transformed from the total scale to the free scale. With both formulations, the pressure correction was applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).
For Ks, the pressure correction was applied on the free scale. The pressure correction was applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).
For Kn, the pressure correction was applied on the seawater scale. The pressure correction was applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).

Value

The function returns a list containing the following matrices:

`Carbfull`	Output of the carbfull function that is used within buffergen
`dALK.dH`	Sensitivity of ALK to a change in proton concentration (dimensionless). Species-specific.
`dtotX.dH`	Sensitivity of an acid-base species to a change in proton concentration (dimensionless). Species-specific.
`dALK.dX`	Sensitivity of ALK to a change in an acid-base species (dimensionless). Species-specific.
`dtotX.dX`	Sensitivity of an acid-base species to a change in its total concentration (dimensionless). Species-specific.
`dALK.dpH`	Sensitivity of ALK to a change in pH (mol/kg-soln). Species-specific.
`dtotX.dpH`	Sensitivity of an acid-species to a change in pH (mol/kg-soln). Species-specific.
`dH.dALK`	Sensitivity of proton concentration to a change in ALK (dimensionless). Values are the same for all species and all acid-base systems, except for the fluoride and sulfate acid-base systems, which slightly deviate due to pH scale conversion effects.
`dH.dtotX`	Sensitivity of an acid-species to a change in its total concentration (dimensionless). Values are the same for all species of a specific acid-base system.
`dX.dALK`	Sensitivity of an acid-species to a change in its total concentration (dimensionless). Species-specific.
`dX.dtotX`	Sensitivity of an acid-species to a change in its total concentration (dimensionless). Species-specific.
`dpH.dALK`	Sensitivity of pH due to a change in ALK ((mol/kg-soln)-1). Values are the same for all species and all acid-base systems, except for the fluoride and sulfate acid-base systems, which slightly deviate due to pH scale conversion effects.
`dpH.dtotX`	Sensitivity of pH due to a change in the total concentration of an acid-base system ((mol/kg-soln)-1). Values are the same for all species of a specific acid-base system.
`beta.H`	proton concentration buffer factor (Eq.4 of Hagens and Middelburg (2016), dimensionless)
`RF`	Revelle factor (dimensionless)

If the total concentration of an acid-base system is 0, the values of the buffer factors corresponding to all species of that acid-base system return NA.

Author(s)

Mathilde Hagens [email protected]

References

Hagens M. and Middelburg J. J., 2016 Generalised expressions for the response of pH to changes in ocean chemistry. Geochimica et Cosmochimica Acta 187 334-349.

Examples


## With a couple of variables
buffergen(flag=8, var1=8.2, var2=0.00234, S=35, T=25, P=0, Patm=1.0, Pt=0, Sit=0,
	pHscale="T", kf="pf", k1k2="l", ks="d", b="u74", gas="potential", NH4t=0, HSt=0)

## With a couple of variables and non-zero nutrient concentrations
buffergen(flag=8, var1=8.2, var2=0.00234, S=35, T=25, P=0, Patm=1.0, Pt=5e-6, Sit=2e-6,
	pHscale="T", kf="pf", k1k2="l", ks="d", b="u74", gas="potential", NH4t=10e-6, HSt=0.1e-6)

## Using vectors as arguments
flag <- c(8, 2, 8)
var1 <- c(8.2, 7.477544e-06, 8.2)
var2 <- c(0.002343955, 0.001649802, 2400e-6)
S <- c(35, 35, 30)
T <- c(25, 25, 30)
P <- c(0, 0, 0)
Pt <- c(0, 0, 0)
Sit <- c(0, 0, 0)
kf <- c("pf", "pf", "pf")
k1k2 <- c("l", "l", "l")
pHscale <- c("T", "T", "T")
b <- c("l10", "l10", "l10")
gas <- c("potential")
NH4t <- c(0, 0, 0)
HSt <- c(0, 0, 0)
buffergen(flag=flag, var1=var1, var2=var2, S=S, T=T, P=P, Pt=Pt, Sit=Sit, 
  kf=kf, k1k2=k1k2, pHscale=pHscale, b=b, gas=gas, NH4t=NH4t, HSt=HSt)

## Test with all flags 
flag <- c((1:15), (21:25))
var1 <- c(8.200000, 7.308171e-06, 7.308171e-06, 7.308171e-06, 7.308171e-06, 
	8.2, 8.2, 8.2, 8.2, 0.001646857, 0.001646857, 0.001646857, 0.0002822957, 
	0.0002822957, 0.00234, 258.2164, 258.2164, 258.2164, 258.2164, 258.2164 )
var2 <- c(7.308171e-06, 0.001646857, 0.0002822957, 0.00234, 0.001936461, 
	0.001646857, 0.0002822957, 0.00234, 0.001936461, 0.0002822957, 
	0.00234, 0.001936461,  0.00234, 0.001936461, 0.001936461, 8.2, 
	0.001646857, 0.0002822957, 0.00234, 0.001936461)
buffergen(flag=flag, var1=var1, var2=var2)
## With a couple of variables
buffergen(flag=8, var1=8.2, var2=0.00234, S=35, T=25, P=0, Patm=1.0, Pt=0, Sit=0,
	pHscale="T", kf="pf", k1k2="l", ks="d", b="u74", gas="potential", NH4t=0, HSt=0)

## With a couple of variables and non-zero nutrient concentrations
buffergen(flag=8, var1=8.2, var2=0.00234, S=35, T=25, P=0, Patm=1.0, Pt=5e-6, Sit=2e-6,
	pHscale="T", kf="pf", k1k2="l", ks="d", b="u74", gas="potential", NH4t=10e-6, HSt=0.1e-6)

## Using vectors as arguments
flag <- c(8, 2, 8)
var1 <- c(8.2, 7.477544e-06, 8.2)
var2 <- c(0.002343955, 0.001649802, 2400e-6)
S <- c(35, 35, 30)
T <- c(25, 25, 30)
P <- c(0, 0, 0)
Pt <- c(0, 0, 0)
Sit <- c(0, 0, 0)
kf <- c("pf", "pf", "pf")
k1k2 <- c("l", "l", "l")
pHscale <- c("T", "T", "T")
b <- c("l10", "l10", "l10")
gas <- c("potential")
NH4t <- c(0, 0, 0)
HSt <- c(0, 0, 0)
buffergen(flag=flag, var1=var1, var2=var2, S=S, T=T, P=P, Pt=Pt, Sit=Sit, 
  kf=kf, k1k2=k1k2, pHscale=pHscale, b=b, gas=gas, NH4t=NH4t, HSt=HSt)

## Test with all flags 
flag <- c((1:15), (21:25))
var1 <- c(8.200000, 7.308171e-06, 7.308171e-06, 7.308171e-06, 7.308171e-06, 
	8.2, 8.2, 8.2, 8.2, 0.001646857, 0.001646857, 0.001646857, 0.0002822957, 
	0.0002822957, 0.00234, 258.2164, 258.2164, 258.2164, 258.2164, 258.2164 )
var2 <- c(7.308171e-06, 0.001646857, 0.0002822957, 0.00234, 0.001936461, 
	0.001646857, 0.0002822957, 0.00234, 0.001936461, 0.0002822957, 
	0.00234, 0.001936461,  0.00234, 0.001936461, 0.001936461, 8.2, 
	0.001646857, 0.0002822957, 0.00234, 0.001936461)
buffergen(flag=flag, var1=var1, var2=var2)

Buffer capacities of the seawater carbonate system from Egleston et al. (2010), corrected and enhanced

Description

Returns the six buffer factors of the seawater carbonate system as defined by Egleston, Sabine and Morel (2010), denoted here as ESM. Also returns the classic Revelle factor (relative change in pCO2 over that for DIC). In ESM, there are errors in the equations in Table 1 for $S$ , $\Omega_{DIC}$ , and $\Omega_{Alk}$ . These errors have been corrected here. The results of this routine have been validated: when input concentrations of Pt and Sit are set to zero, they produce results that are identical to those shown in ESM's Fig. 2. But when Pt and Sit are nonzero, contributions from phosphoric and silicic acid systems are taken into account, an improvement to the Egleston et al. (2010) approach. This routine was inspired and adapted from seacarb's “buffer” function. Its input arguments are indentical to those in the “buffer” and “carb” functions of seacarb.

Usage

buffesm(flag, var1, var2, S = 35, T = 25, Patm = 1, P = 0, Pt = 0, Sit = 0, 
  k1k2 = "x", kf = "x", ks = "d", pHscale = "T", b = "u74", warn = "y", 
  eos = "eos80", long = 1e+20, lat = 1e+20)
buffesm(flag, var1, var2, S = 35, T = 25, Patm = 1, P = 0, Pt = 0, Sit = 0, 
  k1k2 = "x", kf = "x", ks = "d", pHscale = "T", b = "u74", warn = "y", 
  eos = "eos80", long = 1e+20, lat = 1e+20)

Arguments

`flag`	select the couple of variables available. The flags which can be used are: flag = 1 pH and CO2 given flag = 2 CO2 and HCO3 given flag = 3 CO2 and CO3 given flag = 4 CO2 and ALK given flag = 5 CO2 and DIC given flag = 6 pH and HCO3 given flag = 7 pH and CO3 given flag = 8 pH and ALK given flag = 9 pH and DIC given flag = 10 HCO3 and CO3 given flag = 11 HCO3 and ALK given flag = 12 HCO3 and DIC given flag = 13 CO3 and ALK given flag = 14 CO3 and DIC given flag = 15 ALK and DIC given flag = 21 pCO2 and pH given flag = 22 pCO2 and HCO3 given flag = 23 pCO2 and CO3 given flag = 24 pCO2 and ALK given flag = 25 pCO2 and DIC given
`var1`	enter value of the first variable in mol/kg, except for pH and for pCO2 in $\mu$ atm
`var2`	enter value of the second variable in mol/kg, except for pH
`S`	Salinity
`T`	Temperature in degrees Celsius
`Patm`	Surface atmospheric pressure in atm, default 1 atm
`P`	Hydrostatic pressure in bar (surface = 0)
`Pt`	Concentration of total phosphate in mol/kg; set to 0 if NA; when nonzero, account for phosphoric acid system, unlike in Egleston et al. (2010).
`Sit`	Concentration of total silicate in mol/kg; set to 0 if NA; when nonzero, account for silicic acid system, unlike in Egleston et al. (2010).
`k1k2`	"cw" for using K1 and K2 from Cai & Wang (1998), "l" from Lueker et al. (2000), "m02" from Millero et al. (2002), "m06" from Millero et al. (2006), "m10" from Millero (2010), "mp2" from Mojica Prieto et al. (2002), "p18" from Papadimitriou et al. (2018), "r" from Roy et al. (1993), "sb21" from Shockman & Byrne (2021), "s20" from Sulpis et al. (2020), and "w14" from Waters et al. (2014). "x" is the default flag; the default value is then "l", except if T is outside the range 2 to 35oC and/or S is outside the range 19 to 43. In these cases, the default value is "w14".
`kf`	"pf" for using Kf from Perez and Fraga (1987) and "dg" for using Kf from Dickson and Riley (1979 in Dickson and Goyet, 1994). "x" is the default flag; the default value is then "pf", except if T is outside the range 9 to 33oC and/or S is outside the range 10 to 40. In these cases, the default is "dg".
`ks`	"d" for using Ks from Dickon (1990), "k" for using Ks from Khoo et al. (1977), default is "d"
`pHscale`	choice of pH scale: "T" for the total scale, "F" for the free scale and "SWS" for using the seawater scale, default is "T" (total scale)
`b`	Concentration of total boron. "l10" for the Lee et al. (2010) formulation or "u74" for the Uppstrom (1974) formulation, default is "u74"
`warn`	"y" to show warnings when T or S go beyond the valid range for constants; "n" to supress warnings. The default is "y".
`eos`	"teos10" to specify T and S according to Thermodynamic Equation Of Seawater - 2010 (TEOS-10); "eos80" to specify T and S according to EOS-80.
`long`	longitude of data point, used when eos parameter is "teos10" as a conversion parameter from absolute to practical salinity.
`lat`	latitude of data point, used when eos parameter is "teos10".

Details

For K1 and K2:

Cai and Wang (1998): S ranging between 0 and 40 and T ranging between 0.2 and 30oC.
Lueker et al. (2000): S ranging between 19 and 43 and T ranging between 2 and 35oC.
Millero et al. (2002): S ranging from 34 to 37 and T ranging between -1.6 and 35oC.
Millero et al. (2006): S ranging between 0.1 and 50 and T ranging between 1 and 50oC.
Millero (2010): S ranging between 1 and 50 and T ranging between 0 and 50oC. Millero (2010) provides a K1 and K2 formulation for the seawater, total and free pH scales. Therefore, when this method is used and if P=0, K1 and K2 are computed with the formulation corresponding to the pH scale given in the flag "pHscale".
Mojica Prieto et al. (2002): S ranging from 5 to 42 and T ranging between 0 and 45oC.
Papadimitriou et al. (2018): S ranging from 33 to 100 and T ranging between -6 to 25oC.
Roy et al. (1993): S ranging between 5 and 45 and T ranging between 0 and 45oC.
Shockman & Byrne (2021): for K2, S ranging from 19.6 to 41 and T ranging between 15 to 35oC. For K1, formulation is that of Waters et al.
Sulpis et al. (2020): S ranging from 30.7 to 37.6 and T ranging between -1.7 to 31.8oC.
Waters et al.(2014): S ranging between 1 and 50 and T ranging between 0 and 50oC. Waters (2014) provides a K1 and K2 formulation for the seawater, total and free pH scales. Therefore, when this method is used and if P=0, K1 and K2 are computed with the formulation corresponding to the pH scale given in the flag "pHscale".

For K0:

Perez and Fraga (1987): S ranging between 10 and 40 and T ranging between 9 and 33oC.
Dickson and Riley (1979 in Dickson and Goyet, 1994): S ranging between 0 and 45 and T ranging between 0 and 45oC.

For Ks:

Dickson (1990): S ranging between 5 and 45 and T ranging between 0 and 45oC.
Khoo et al. (1977): S ranging between 20 and 45 and T ranging between 5 and 40oC.

Pressure corrections and pH scale:

For K0, the pressure correction term of Weiss (1974) is used.
For K1, K2, pK1, pK2, pK3, Kw, Kb, Khs and Ksi, the pressure correction was applied on the seawater scale. Hence, if needed, values were first transformed from the total scale to the seawater scale, the pressure correction applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).
For Kf, the pressure correction was applied on the free scale. The formulation of Dickson and Riley (1979 in Dickson and Goyet, 1994) provides Kf on the free scale but that of Perez and Fraga (1987) provides it on the total scale. Hence, in that case, Kf was first transformed from the total scale to the free scale. With both formulations, the pressure correction was applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).
For Ks, the pressure correction was applied on the free scale. The pressure correction was applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).
For Kn, The pressure correction was applied on the seawater scale. The pressure correction was applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).

Value

The function returns a data frame containing the following columns:

`gammaDIC`	$\gamma_{DIC}$ , ocean's capacity to buffer changes in [CO2] due to accumulation of CO2 from the atmosphere $(\partial ln[CO_2]/\partial DIC)^{-1}$ (units = mol/kg; multiply by 1000 to get mmol/kg, i.e., the units presented in Egleston et al., 2010)
`betaDIC`	$\beta_{DIC}$ , ocean's capacity to buffer changes in [H+] due to accumulation of CO2 from the atmosphere $(\partial ln[H^+]/\partial DIC)^{-1}$ (units = mol/kg)
`omegaDIC`	$\Omega_{DIC}$ , ocean's capacity to buffer changes in $[CO_3^{2-}]$ due to accumulation of CO2 from the atmosphere $(\partial ln[CO_3^{2-}]/\partial DIC)^{-1}$ ; same as $(\partial ln \Omega_A / \partial DIC)^{-1}$ and $(\partial ln \Omega_C / \partial DIC)^{-1}$ (units= mol/kg)
`gammaALK`	$\gamma_{Alk}$ , ocean's capacity to buffer changes in [CO2] due to changes in alkalinity $(\partial ln[CO_2]/\partial ALK)^-1$ (units = mol/kg)
`betaALK`	$\beta_{Alk}$ , ocean's capacity to buffer changes in [H+] due to changes in alkalinity $(\partial ln[H^+]/\partial ALK)^{-1}$ (units = mol/kg)
`omegaALK`	$\Omega_{Alk}$ , ocean's capacity to buffer changes in $[CO_3^{2-}]$ due to changes in alkalinity $(\partial ln[CO_3^{2-}]/\partial ALK)^{-1}$ ; same as $(\partial ln \Omega_A / \partial ALK)^{-1}$ and $(\partial ln \Omega_C / \partial ALK)^{-1}$ (units = mol/kg)
`R`	Revelle factor, relative change in $[CO_2]$ or $pCO_2$ over the relative change in DIC $(\partial ln[CO_2]/\partial ln DIC)^{-1}$ (unitless)

Author(s)

James Orr [email protected]

References

Cai W. J., and Wang Y., 1998. The chemistry, fluxes, and sources of carbon dioxide in the estuarine waters of the Satilla and Altamaha Rivers, Georgia. Limnology and Oceanography 43, 657-668.

Dickson A. G., Sabine C. L. and Christian J. R., 2007 Guide to best practices for ocean CO2 measurements. PICES Special Publication 3, 1-191.

Egleston, E. S., Sabine, C. L. and Morel, F. M. M., 2010 Revelle revisited: Buffer factors that quantify the response of ocean chemistry to changes in DIC and alkalinity, Global Biogeochem. Cycles 24, GB1002, doi:10.1029/2008GB003407.

Khoo H. K., Ramette R. W., Culberson C. H. and Bates R. G., 1977 Determination of hydrogen ion concentration in seawater from 5 to 40oC: standard potentials at salinities from 20 to 45. Analytical Chemistry 49, 29-34.

Frankignoulle M., 1994 A complete set of buffer factors for acid/base CO2 system in seawater. Journal of Marine Systems 5, 111-118.

Millero F. J., 2010 Carbonate constant for estuarine waters. Marine and Freshwater Research 61: 139-142.

Perez F. F. and Fraga F., 1987 Association constant of fluoride and hydrogen ions in seawater. Marine Chemistry 21, 161-168.

Schockman, K.M., Byrne, R.H., 2021. Spectrophotometric determination of the bicarbonate dissociation constant in seawater, Geochimica et Cosmochimica Acta.

Uppstrom L.R., 1974 The boron/chlorinity ratio of the deep-sea water from the Pacific Ocean. Deep-Sea Research I 21 161-162.

Examples


## Computation with a couple of variables
buffesm(flag=8, var1=8.2, var2=0.00234, S=35, T=25, P=0, Pt=0, 
	Sit=0, pHscale="T", kf="pf", k1k2="l", b="u74")

## Using vectors as arguments
flag <- c(8, 2, 8)
var1 <- c(8.2, 7.477544e-06, 8.2)
var2 <- c(0.002343955, 0.001649802, 2400e-6)
S <- c(35, 35, 30)
T <- c(25, 25, 30)
P <- c(0, 0, 0)
Pt <- c(0, 0, 0)
Sit <- c(0, 0, 0)
kf <- c("pf", "pf", "pf")
k1k2 <- c("l", "l", "l")
pHscale <- c("T", "T", "T")
b <- c("l10", "l10", "l10")
buffesm(flag=flag, var1=var1, var2=var2, S=S, T=T, P=P, Pt=Pt, 
	Sit=Sit, kf=kf, k1k2=k1k2, pHscale=pHscale, b=b)

## Test for all flags 
flag <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 21, 22, 23, 24, 25)

var1 <- c(8.200000, 7.477544e-06, 7.477544e-06, 7.477544e-06, 7.477544e-06, 8.2, 
	8.2, 8.2, 8.2, 0.001685024, 0.001685024, 0.001685024,  0.0002888382, 
	0.0002888382, 0.002391252, 264.2008, 264.2008, 264.2008, 264.2008, 264.2008)
var2 <- c(7.477544e-06, 0.001685024, 0.0002888382, 0.002391252, 0.001981340, 
	0.001685024, 0.0002888382, 0.002391252, 0.001981340, 0.0002888382, 0.002391252,
	0.001981340,  0.002391252, 0.001981340, 0.001981340, 8.2, 0.001685024, 
	0.0002888382, 0.002391252, 0.001981340)
buffesm(flag=flag, var1=var1, var2=var2)

## Compute 2 additional factors of interest (ratios of relative changes)
be <- buffesm(flag=flag, var1=var1, var2=var2, S=S, T=T, P=P, Pt=Pt, 
	Sit=Sit, kf=kf, k1k2=k1k2, pHscale=pHscale, b=b)
#     Ratio of gammaDIC/betaDIC = d ln [H+] / d ln pCO2
      Hfac <- (be$gammaDIC/be$betaDIC)                         #H+ factor
#     Ratio of gammaDIC/omegaDIC = d ln [CO32-] / d ln pCO2
      Satfac <- (be$gammaDIC/be$omegaDIC)                      #Saturation factor

## Computation with a couple of variables
buffesm(flag=8, var1=8.2, var2=0.00234, S=35, T=25, P=0, Pt=0, 
	Sit=0, pHscale="T", kf="pf", k1k2="l", b="u74")

## Using vectors as arguments
flag <- c(8, 2, 8)
var1 <- c(8.2, 7.477544e-06, 8.2)
var2 <- c(0.002343955, 0.001649802, 2400e-6)
S <- c(35, 35, 30)
T <- c(25, 25, 30)
P <- c(0, 0, 0)
Pt <- c(0, 0, 0)
Sit <- c(0, 0, 0)
kf <- c("pf", "pf", "pf")
k1k2 <- c("l", "l", "l")
pHscale <- c("T", "T", "T")
b <- c("l10", "l10", "l10")
buffesm(flag=flag, var1=var1, var2=var2, S=S, T=T, P=P, Pt=Pt, 
	Sit=Sit, kf=kf, k1k2=k1k2, pHscale=pHscale, b=b)

## Test for all flags 
flag <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 21, 22, 23, 24, 25)

var1 <- c(8.200000, 7.477544e-06, 7.477544e-06, 7.477544e-06, 7.477544e-06, 8.2, 
	8.2, 8.2, 8.2, 0.001685024, 0.001685024, 0.001685024,  0.0002888382, 
	0.0002888382, 0.002391252, 264.2008, 264.2008, 264.2008, 264.2008, 264.2008)
var2 <- c(7.477544e-06, 0.001685024, 0.0002888382, 0.002391252, 0.001981340, 
	0.001685024, 0.0002888382, 0.002391252, 0.001981340, 0.0002888382, 0.002391252,
	0.001981340,  0.002391252, 0.001981340, 0.001981340, 8.2, 0.001685024, 
	0.0002888382, 0.002391252, 0.001981340)
buffesm(flag=flag, var1=var1, var2=var2)

## Compute 2 additional factors of interest (ratios of relative changes)
be <- buffesm(flag=flag, var1=var1, var2=var2, S=S, T=T, P=P, Pt=Pt, 
	Sit=Sit, kf=kf, k1k2=k1k2, pHscale=pHscale, b=b)
#     Ratio of gammaDIC/betaDIC = d ln [H+] / d ln pCO2
      Hfac <- (be$gammaDIC/be$betaDIC)                         #H+ factor
#     Ratio of gammaDIC/omegaDIC = d ln [CO32-] / d ln pCO2
      Satfac <- (be$gammaDIC/be$omegaDIC)                      #Saturation factor

Parameters of the seawater carbonate system

Description

Returns parameters of the seawater carbonate system.

Usage

carb(flag, var1, var2, S=35, T=25, Patm=1, P=0, Pt=0, Sit=0,
        k1k2="x", kf="x", ks="d", pHscale="T", b="u74", gas="potential", 
        warn="y", eos="eos80", long=1.e20, lat=1.e20)carb(flag, var1, var2, S=35, T=25, Patm=1, P=0, Pt=0, Sit=0,
        k1k2="x", kf="x", ks="d", pHscale="T", b="u74", gas="potential", 
        warn="y", eos="eos80", long=1.e20, lat=1.e20)

Arguments

`flag`	select the couple of variables available. The flags which can be used are: flag = 1 pH and CO2 given flag = 2 CO2 and HCO3 given flag = 3 CO2 and CO3 given flag = 4 CO2 and ALK given flag = 5 CO2 and DIC given flag = 6 pH and HCO3 given flag = 7 pH and CO3 given flag = 8 pH and ALK given flag = 9 pH and DIC given flag = 10 HCO3 and CO3 given flag = 11 HCO3 and ALK given flag = 12 HCO3 and DIC given flag = 13 CO3 and ALK given flag = 14 CO3 and DIC given flag = 15 ALK and DIC given flag = 21 pCO2 and pH given flag = 22 pCO2 and HCO3 given flag = 23 pCO2 and CO3 given flag = 24 pCO2 and ALK given flag = 25 pCO2 and DIC given
`var1`	Value of the first variable in mol/kg, except for pH and for pCO2 in $\mu$ atm
`var2`	Value of the second variable in mol/kg, except for pH
`S`	Salinity
`T`	Temperature in degrees Celsius
`Patm`	Surface atmospheric pressure in atm, default is 1 atm
`P`	Hydrostatic pressure in bar (surface = 0)
`Pt`	Concentration of total phosphate in mol/kg; set to 0 if NA
`Sit`	Concentration of total silicate in mol/kg; set to 0 if NA
`k1k2`	"cw" for using K1 and K2 from Cai & Wang (1998), "l" from Lueker et al. (2000), "m02" from Millero et al. (2002), "m06" from Millero et al. (2006), "m10" from Millero (2010), "mp2" from Mojica Prieto et al. (2002), "p18" from Papadimitriou et al. (2018), "r" from Roy et al. (1993), "sb21" from Shockman & Byrne (2021), "s20" from Sulpis et al. (2020), and "w14" from Waters et al. (2014). "x" is the default flag; the default value is then "l", except if T is outside the range 2 to 35oC and/or S is outside the range 19 to 43. In these cases, the default value is "w14".
`kf`	"pf" for using Kf from Perez and Fraga (1987) and "dg" for using Kf from Dickson and Riley (1979 in Dickson and Goyet, 1994). "x" is the default flag; the default value is then "pf", except if T is outside the range 9 to 33oC and/or S is outside the range 10 to 40. In these cases, the default is "dg".
`ks`	"d" for using Ks from Dickson (1990) and "k" for using Ks from Khoo et al. (1977), default is "d"
`pHscale`	"T" for the total scale, "F" for the free scale and "SWS" for using the seawater scale, default is "T" (total scale)
`b`	Concentration of total boron. "l10" for the Lee et al. (2010) formulation or "u74" for the Uppstrom (1974) formulation, default is "u74"
`gas`	used to indicate the convention for INPUT pCO2, i.e., when it is an input variable (flags 21 to 25): "insitu" indicates it is referenced to in situ pressure and in situ temperature; "potential" indicates it is referenced to 1 atm pressure and potential temperature; and "standard" indicates it is referenced to 1 atm pressure and in situ temperature. All three options should give identical results at surface pressure. This option is not used when pCO2 is not an input variable (flags 1 to 15). The default is "potential".
`warn`	"y" to show warnings when T or S go beyond the valid range for constants; "n" to supress warnings. The default is "y".
`eos`	"teos10" to specify T and S according to Thermodynamic Equation Of Seawater - 2010 (TEOS-10); "eos80" to specify T and S according to EOS-80.
`long`	longitude of data point, used when eos parameter is "teos10" as a conversion parameter from absolute to practical salinity.
`lat`	latitude of data point, used when eos parameter is "teos10".

Details

For K1 and K2:

Cai and Wang (1998): S ranging between 0 and 40 and T ranging between 0.2 and 30oC.
Lueker et al. (2000): S ranging between 19 and 43 and T ranging between 2 and 35oC.
Millero et al. (2002): S ranging from 34 to 37 and T ranging between -1.6 and 35oC.
Millero et al. (2006): S ranging between 0.1 and 50 and T ranging between 1 and 50oC.
Millero (2010): S ranging between 1 and 50 and T ranging between 0 and 50oC. Millero (2010) provides a K1 and K2 formulation for the seawater, total and free pH scales. Therefore, when this method is used and if P=0, K1 and K2 are computed with the formulation corresponding to the pH scale given in the flag "pHscale".
Mojica Prieto et al. (2002): S ranging from 5 to 42 and T ranging between 0 and 45oC.
Papadimitriou et al. (2018): S ranging from 33 to 100 and T ranging between -6 to 25oC.
Roy et al. (1993): S ranging between 5 and 45 and T ranging between 0 and 45oC.
Shockman & Byrne (2021): for K2, S ranging from 19.6 to 41 and T ranging between 15 to 35oC. For K1, formulation is that of Waters et al.
Sulpis et al. (2020): S ranging from 30.7 to 37.6 and T ranging between -1.7 to 31.8oC.
Waters et al.(2014): S ranging between 1 and 50 and T ranging between 0 and 50oC. Waters (2014) provides a K1 and K2 formulation for the seawater, total and free pH scales. Therefore, when this method is used and if P=0, K1 and K2 are computed with the formulation corresponding to the pH scale given in the flag "pHscale".

For Kf:

Perez and Fraga (1987): S ranging between 10 and 40 and T ranging between 9 and 33oC.
Dickson and Riley (1979 in Dickson and Goyet, 1994): S ranging between 0 and 45 and T ranging between 0 and 45oC.

For Ks:

Dickson (1990): S ranging between 5 and 45 and T ranging between 0 and 45oC.
Khoo et al. (1977): S ranging between 20 and 45 and T ranging between 5 and 40oC.

Pressure corrections and pH scale:

For K0, the pressure correction term of Weiss (1974) is used.
For K1, K2, pK1, pK2, pK3, Kw, Kb, Khs and Ksi, the pressure correction was applied on the seawater scale. Hence, if needed, values were first transformed from the total scale to the seawater scale, the pressure correction applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).
For Kf, the pressure correction was applied on the free scale. The formulation of Dickson and Riley (1979 in Dickson and Goyet, 1994) provides Kf on the free scale but that of Perez and Fraga (1987) provides it on the total scale. Hence, in that case, Kf was first transformed from the total scale to the free scale. With both formulations, the pressure correction was applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).
For Ks, the pressure correction was applied on the free scale. The pressure correction was applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).
For Kn, The pressure correction was applied on the seawater scale. The pressure correction was applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).

Value

The function returns a data frame containing the following columns:

`S`	Salinity
`T`	Temperature in degrees Celsius
`Patm`	Surface atmospheric pressure in atm
`P`	Hydrostatic pressure in bar
`pH`	pH
`CO2`	CO2 concentration (mol/kg)
`pCO2`	"standard" pCO2, CO2 partial pressure computed at in situ temperature and atmospheric pressure ( $\mu$ atm)
`fCO2`	"standard" fCO2, CO2 fugacity computed at in situ temperature and atmospheric pressure ( $\mu$ atm)
`pCO2pot`	"potential" pCO2, CO2 partial pressure computed at potential temperature and atmospheric pressure ( $\mu$ atm)
`fCO2pot`	"potential" fCO2, CO2 fugacity computed at potential temperature and atmospheric pressure ( $\mu$ atm)
`pCO2insitu`	"in situ" pCO2, CO2 partial pressure computed at in situ temperature and total pressure (atm + hydrostatic) ( $\mu$ atm)
`fCO2insitu`	"in situ" fCO2, CO2 fugacity computed at in situ temperature and total pressure (atm + hydrostatic) ( $\mu$ atm)
`HCO3`	HCO3 concentration (mol/kg)
`CO3`	CO3 concentration (mol/kg)
`DIC`	DIC concentration (mol/kg)
`ALK`	ALK, total alkalinity (mol/kg)
`OmegaAragonite`	Omega aragonite, aragonite saturation state
`OmegaCalcite`	Omega calcite, calcite saturation state

Note

Warning: pCO2 estimates below 100 m are subject to considerable uncertainty. See Weiss (1974) and Orr et al. (2015)

Author(s)

Heloise Lavigne, James Orr and Jean-Pierre Gattuso [email protected]

References

Cai W. J., and Wang Y., 1998. The chemistry, fluxes, and sources of carbon dioxide in the estuarine waters of the Satilla and Altamaha Rivers, Georgia. Limnology and Oceanography 43, 657-668.

Dickson A. G. and Riley J. P., 1979 The estimation of acid dissociation constants in seawater media from potentiometric titrations with strong base. I. The ionic product of water. Marine Chemistry 7, 89-99.

Dickson A. G., Sabine C. L. and Christian J. R., 2007 Guide to best practices for ocean CO2 measurements. PICES Special Publication 3, 1-191.

Millero F. J., 1995. Thermodynamics of the carbon dioxide system in the oceans. Geochimica Cosmochimica Acta 59: 661-677.

Millero F. J., 2010. Carbonate constant for estuarine waters. Marine and Freshwater Research 61: 139-142.

Millero F. J., Graham T. B., Huang F., Bustos-Serrano H. and Pierrot D., 2006. Dissociation constants of carbonic acid in seawater as a function of salinity and temperature. Marine Chemistry 100, 80-84.

Orr J. C., Epitalon J.-M. and Gattuso J.-P., 2015. Comparison of seven packages that compute ocean carbonate chemistry. Biogeosciences 12, 1483-1510.

Perez F. F. and Fraga F., 1987 Association constant of fluoride and hydrogen ions in seawater. Marine Chemistry 21, 161-168.

Schockman, K.M., Byrne, R.H., 2021. Spectrophotometric determination of the bicarbonate dissociation constant in seawater, Geochimica et Cosmochimica Acta.

Uppstrom L.R., 1974 The boron/chlorinity ratio of the deep-sea water from the Pacific Ocean. Deep-Sea Research I 21, 161-162.

Waters, J., Millero, F. J., and Woosley, R. J., 2014. Corrigendum to “The free proton concentration scale for seawater pH”, [MARCHE: 149 (2013) 8-22], Marine Chemistry 165, 66-67.

Weiss, R. F., 1974. Carbon dioxide in water and seawater: the solubility of a non-ideal gas, Mar. Chem., 2, 203-215.

Weiss, R. F. and Price, B. A., 1980. Nitrous oxide solubility in water and seawater, Marine Chemistry, 8, 347-359.

Zeebe R. E. and Wolf-Gladrow D. A., 2001 CO2 in seawater: equilibrium, kinetics, isotopes. Amsterdam: Elsevier, 346 pp.

Examples


## 1. With a couple of variables
carb(flag=8, var1=8.2, var2=0.00234, S=35, T=25, P=0, Patm=1.0, Pt=0, Sit=0,
	pHscale="T", kf="pf", k1k2="l", ks="d", b="u74")

## 2. Using vectors as arguments
flag <- c(8, 2, 8)
var1 <- c(8.2, 7.477544e-06, 8.2)
var2 <- c(0.002343955, 0.001649802, 2400e-6)
S <- c(35, 35, 30)
T <- c(25, 25, 30)
P <- c(0, 0, 0)
Pt <- c(0, 0, 0)
Sit <- c(0, 0, 0)
kf <- c("pf", "pf", "pf")
k1k2 <- c("l", "l", "l")
pHscale <- c("T", "T", "T")
b <- c("l10", "l10", "l10")
carb(flag=flag, var1=var1, var2=var2, S=S, T=T, P=P,
	Pt=Pt, Sit=Sit, kf=kf, k1k2=k1k2, pHscale=pHscale, b=b)

## 3. Special case: when input pH is on NBS scale (not a standard option in seacarb) 
##    -> example for pH-Alk input pair (flag 8) and Cai & Wang (1998) K1,K2 
pHNBS <- c(8.2, 8.1, 8.0)
talk <- c(2300, 2350, 2400) * 1e-6
S <- c(35, 32.5, 30)
T <- c(25, 15, 10)

## 3a. convert pHNBS to pHSWS (using total activity coeff. fH), then use carb with pHscale="SWS"
pHSWS <- pHnbs2sws(pHNBS, S=S, T=T)
carb(flag=8, var1=pHSWS, var2=talk, S=S, T=T, P=0, Patm=1.0, Pt=0, Sit=0,
	pHscale="SWS", kf="pf", k1k2="cw", ks="d", b="u74")

## 3b. conversely for input pairs without pH,  convert computed pH on SWS scale to NBS scale, 
##     with function pHsws2nbs
##    -> example for Alk-DIC input pair (flag 15) and Cai & Wang (1998) K1,K2 
dic <- c(2000., 2030., 2060) * 1e-6
output = carb(flag=15, var1=talk, var2=dic, S=S, T=T, P=0, Patm=1.0, Pt=0, Sit=0,
	pHscale="SWS", kf="pf", k1k2="cw", ks="d", b="u74")
pHNBS  = pHsws2nbs(output$pH, S=S, T=T)

## 4. Test with all flags 
flag <- c((1:15), (21:25))
var1 <- c(8.200000, 7.308171e-06, 7.308171e-06, 7.308171e-06, 7.308171e-06, 
	8.2, 8.2, 8.2, 8.2, 0.001646857, 0.001646857, 0.001646857, 0.0002822957, 
	0.0002822957, 0.00234, 258.2164, 258.2164, 258.2164, 258.2164, 258.2164 )
var2 <- c(7.308171e-06, 0.001646857, 0.0002822957, 0.00234, 0.001936461, 
	0.001646857, 0.0002822957, 0.00234, 0.001936461, 0.0002822957, 
	0.00234, 0.001936461,  0.00234, 0.001936461, 0.001936461, 8.2, 
	0.001646857, 0.0002822957, 0.00234, 0.001936461)
carb(flag=flag, var1=var1, var2=var2)

## 5. Test using a data frame 
data(seacarb_test_P0)	#test data set for P=0 (surface)
tab <- seacarb_test_P0[14:19,]

## 5a. method 1 using the column numbers
carb(flag=tab[[1]], var1=tab[[2]], var2=tab[[3]], S=tab[[4]], T=tab[[5]], 
P=tab[[6]], Sit=tab[[8]], Pt=tab[[7]])

## 5b. method 2 using the column names
carb(flag=tab$flag, var1=tab$var1, var2=tab$var2, S=tab$S, T=tab$T, 
P=tab$P, Sit=tab$Sit, Pt=tab$Pt)

## 1. With a couple of variables
carb(flag=8, var1=8.2, var2=0.00234, S=35, T=25, P=0, Patm=1.0, Pt=0, Sit=0,
	pHscale="T", kf="pf", k1k2="l", ks="d", b="u74")

## 2. Using vectors as arguments
flag <- c(8, 2, 8)
var1 <- c(8.2, 7.477544e-06, 8.2)
var2 <- c(0.002343955, 0.001649802, 2400e-6)
S <- c(35, 35, 30)
T <- c(25, 25, 30)
P <- c(0, 0, 0)
Pt <- c(0, 0, 0)
Sit <- c(0, 0, 0)
kf <- c("pf", "pf", "pf")
k1k2 <- c("l", "l", "l")
pHscale <- c("T", "T", "T")
b <- c("l10", "l10", "l10")
carb(flag=flag, var1=var1, var2=var2, S=S, T=T, P=P,
	Pt=Pt, Sit=Sit, kf=kf, k1k2=k1k2, pHscale=pHscale, b=b)

## 3. Special case: when input pH is on NBS scale (not a standard option in seacarb) 
##    -> example for pH-Alk input pair (flag 8) and Cai & Wang (1998) K1,K2 
pHNBS <- c(8.2, 8.1, 8.0)
talk <- c(2300, 2350, 2400) * 1e-6
S <- c(35, 32.5, 30)
T <- c(25, 15, 10)

## 3a. convert pHNBS to pHSWS (using total activity coeff. fH), then use carb with pHscale="SWS"
pHSWS <- pHnbs2sws(pHNBS, S=S, T=T)
carb(flag=8, var1=pHSWS, var2=talk, S=S, T=T, P=0, Patm=1.0, Pt=0, Sit=0,
	pHscale="SWS", kf="pf", k1k2="cw", ks="d", b="u74")

## 3b. conversely for input pairs without pH,  convert computed pH on SWS scale to NBS scale, 
##     with function pHsws2nbs
##    -> example for Alk-DIC input pair (flag 15) and Cai & Wang (1998) K1,K2 
dic <- c(2000., 2030., 2060) * 1e-6
output = carb(flag=15, var1=talk, var2=dic, S=S, T=T, P=0, Patm=1.0, Pt=0, Sit=0,
	pHscale="SWS", kf="pf", k1k2="cw", ks="d", b="u74")
pHNBS  = pHsws2nbs(output$pH, S=S, T=T)

## 4. Test with all flags 
flag <- c((1:15), (21:25))
var1 <- c(8.200000, 7.308171e-06, 7.308171e-06, 7.308171e-06, 7.308171e-06, 
	8.2, 8.2, 8.2, 8.2, 0.001646857, 0.001646857, 0.001646857, 0.0002822957, 
	0.0002822957, 0.00234, 258.2164, 258.2164, 258.2164, 258.2164, 258.2164 )
var2 <- c(7.308171e-06, 0.001646857, 0.0002822957, 0.00234, 0.001936461, 
	0.001646857, 0.0002822957, 0.00234, 0.001936461, 0.0002822957, 
	0.00234, 0.001936461,  0.00234, 0.001936461, 0.001936461, 8.2, 
	0.001646857, 0.0002822957, 0.00234, 0.001936461)
carb(flag=flag, var1=var1, var2=var2)

## 5. Test using a data frame 
data(seacarb_test_P0)	#test data set for P=0 (surface)
tab <- seacarb_test_P0[14:19,]

## 5a. method 1 using the column numbers
carb(flag=tab[[1]], var1=tab[[2]], var2=tab[[3]], S=tab[[4]], T=tab[[5]], 
P=tab[[6]], Sit=tab[[8]], Pt=tab[[7]])

## 5b. method 2 using the column names
carb(flag=tab$flag, var1=tab$var1, var2=tab$var2, S=tab$S, T=tab$T, 
P=tab$P, Sit=tab$Sit, Pt=tab$Pt)

Parameters of the seawater carbonate system with boron addition

Description

Returns parameters of the seawater carbonate system when boron is added.

Usage

carbb(flag, var1, var2, S=35, T=25, Patm=1, P=0, Pt=0, Sit=0, 
  k1k2="x", kf="x", ks="d", pHscale="T", b="u74", gas="potential", badd=0, 
  warn="y", eos = "eos80", long = 1e+20, lat = 1e+20)carbb(flag, var1, var2, S=35, T=25, Patm=1, P=0, Pt=0, Sit=0, 
  k1k2="x", kf="x", ks="d", pHscale="T", b="u74", gas="potential", badd=0, 
  warn="y", eos = "eos80", long = 1e+20, lat = 1e+20)

Arguments

`flag`	select the couple of variables available. The flags which can be used are: flag = 1 pH and CO2 given flag = 2 CO2 and HCO3 given flag = 3 CO2 and CO3 given flag = 4 CO2 and ALK given flag = 5 CO2 and DIC given flag = 6 pH and HCO3 given flag = 7 pH and CO3 given flag = 8 pH and ALK given flag = 9 pH and DIC given flag = 10 HCO3 and CO3 given flag = 11 HCO3 and ALK given flag = 12 HCO3 and DIC given flag = 13 CO3 and ALK given flag = 14 CO3 and DIC given flag = 15 ALK and DIC given flag = 21 pCO2 and pH given flag = 22 pCO2 and HCO3 given flag = 23 pCO2 and CO3 given flag = 24 pCO2 and ALK given flag = 25 pCO2 and DIC given
`var1`	Value of the first variable in mol/kg, except for pH and for pCO2 in $\mu$ atm
`var2`	Value of the second variable in mol/kg, except for pH
`S`	Salinity
`T`	Temperature in degrees Celsius
`Patm`	Surface atmospheric pressure in atm, default is 1 atm
`P`	Hydrostatic pressure in bar (surface = 0)
`Pt`	Concentration of total phosphate in mol/kg; set to 0 if NA
`Sit`	Concentration of total silicate in mol/kg; set to 0 if NA
`k1k2`	"cw" for using K1 and K2 from Cai & Wang (1998), "l" from Lueker et al. (2000), "m02" from Millero et al. (2002), "m06" from Millero et al. (2006), "m10" from Millero (2010), "mp2" from Mojica Prieto et al. (2002), "p18" from Papadimitriou et al. (2018), "r" from Roy et al. (1993), "sb21" from Shockman & Byrne (2021), "s20" from Sulpis et al. (2020), and "w14" from Waters et al. (2014). "x" is the default flag; the default value is then "l", except if T is outside the range 2 to 35oC and/or S is outside the range 19 to 43. In these cases, the default value is "w14".
`kf`	"pf" for using Kf from Perez and Fraga (1987) and "dg" for using Kf from Dickson and Riley (1979 in Dickson and Goyet, 1994). "x" is the default flag; the default value is then "pf", except if T is outside the range 9 to 33oC and/or S is outside the range 10 to 40. In these cases, the default is "dg".
`ks`	"d" for using Ks from Dickson (1990) and "k" for using Ks from Khoo et al. (1977), default is "d"
`pHscale`	"T" for the total scale, "F" for the free scale and "SWS" for using the seawater scale, default is "T" (total scale)
`b`	Concentration of total boron. "l10" for the Lee et al. (2010) formulation or "u74" for the Uppstrom (1974) formulation, default is "u74"
`gas`	used to indicate the convention for INPUT pCO2, i.e., when it is an input variable (flags 21 to 25): "insitu" indicates it is referenced to in situ pressure and in situ temperature; "potential" indicates it is referenced to 1 atm pressure and potential temperature; and "standard" indicates it is referenced to 1 atm pressure and in situ temperature. All three options should give identical results at surface pressure. This option is not used when pCO2 is not an input variable (flags 1 to 15). The default is "potential".
`badd`	Amount of boron added in mol/kg.
`warn`	"y" to show warnings when T or S go beyond the valid range for constants; "n" to supress warnings. The default is "y".
`eos`	"teos10" to specify T and S according to Thermodynamic Equation Of Seawater - 2010 (TEOS-10); "eos80" to specify T and S according to EOS-80.
`long`	longitude of data point, used when eos parameter is "teos10" as a conversion parameter from absolute to practical salinity.
`lat`	latitude of data point, used when eos parameter is "teos10".

Details

For K1 and K2:

Cai and Wang (1998): S ranging between 0 and 40 and T ranging between 0.2 and 30oC.
Lueker et al. (2000): S ranging between 19 and 43 and T ranging between 2 and 35oC.
Millero et al. (2002): S ranging from 34 to 37 and T ranging between -1.6 and 35oC.
Millero et al. (2006): S ranging between 0.1 and 50 and T ranging between 1 and 50oC.
Millero (2010): S ranging between 1 and 50 and T ranging between 0 and 50oC. Millero (2010) provides a K1 and K2 formulation for the seawater, total and free pH scales. Therefore, when this method is used and if P=0, K1 and K2 are computed with the formulation corresponding to the pH scale given in the flag "pHscale".
Mojica Prieto et al. (2002): S ranging from 5 to 42 and T ranging between 0 and 45oC.
Papadimitriou et al. (2018): S ranging from 33 to 100 and T ranging between -6 to 25oC.
Roy et al. (1993): S ranging between 5 and 45 and T ranging between 0 and 45oC.
Shockman & Byrne (2021): for K2, S ranging from 19.6 to 41 and T ranging between 15 to 35oC. For K1, formulation is that of Waters et al.
Sulpis et al. (2020): S ranging from 30.7 to 37.6 and T ranging between -1.7 to 31.8oC.
Waters et al.(2014): S ranging between 1 and 50 and T ranging between 0 and 50oC. Waters (2014) provides a K1 and K2 formulation for the seawater, total and free pH scales. Therefore, when this method is used and if P=0, K1 and K2 are computed with the formulation corresponding to the pH scale given in the flag "pHscale".

For Kf:

Perez and Fraga (1987): S ranging between 10 and 40 and T ranging between 9 and 33oC.
Dickson and Riley (1979 in Dickson and Goyet, 1994): S ranging between 0 and 45 and T ranging between 0 and 45oC.

For Ks:

Dickson (1990): S ranging between 5 and 45 and T ranging between 0 and 45oC.
Khoo et al. (1977): S ranging between 20 and 45 and T ranging between 5 and 40oC.

Pressure corrections and pH scale:

For K0, the pressure correction term of Weiss (1974) is used.
For K1, K2, pK1, pK2, pK3, Kw, Kb, Khs and Ksi, the pressure correction was applied on the seawater scale. Hence, if needed, values were first transformed from the total scale to the seawater scale, the pressure correction applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).
For Kf, the pressure correction was applied on the free scale. The formulation of Dickson and Riley (1979 in Dickson and Goyet, 1994) provides Kf on the free scale but that of Perez and Fraga (1987) provides it on the total scale. Hence, in that case, Kf was first transformed from the total scale to the free scale. With both formulations, the pressure correction was applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).
For Ks, the pressure correction was applied on the free scale. The pressure correction was applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).
For Kn, The pressure correction was applied on the seawater scale. The pressure correction was applied as described by Millero (1995), and the value was transformed back to the required scale (T, F or SWS).

Value

The function returns a data frame containing the following columns:

`S`	Salinity
`T`	Temperature in degrees Celsius
`Patm`	Surface atmospheric pressure in atm
`P`	Hydrostatic pressure in bar
`pH`	pH
`CO2`	CO2 concentration (mol/kg)
`pCO2`	"standard" pCO2, CO2 partial pressure computed at in situ temperature and atmospheric pressure ( $\mu$ atm)
`fCO2`	"standard" fCO2, CO2 fugacity computed at in situ temperature and atmospheric pressure ( $\mu$ atm)
`pCO2pot`	"potential" pCO2, CO2 partial pressure computed at potential temperature and atmospheric pressure ( $\mu$ atm)
`fCO2pot`	"potential" fCO2, CO2 fugacity computed at potential temperature and atmospheric pressure ( $\mu$ atm)
`pCO2insitu`	"in situ" pCO2, CO2 partial pressure computed at in situ temperature and total pressure (atm + hydrostatic) ( $\mu$ atm)
`fCO2insitu`	"in situ" fCO2, CO2 fugacity computed at in situ temperature and total pressure (atm + hydrostatic) ( $\mu$ atm)
`HCO3`	HCO3 concentration (mol/kg)
`CO3`	CO3 concentration (mol/kg)
`DIC`	DIC concentration (mol/kg)
`ALK`	ALK, total alkalinity (mol/kg)
`OmegaAragonite`	Omega aragonite, aragonite saturation state
`OmegaCalcite`	Omega calcite, calcite saturation state

Note

Warning: pCO2 estimates below 100 m are subject to considerable uncertainty. See Weiss (1974) and Orr et al. (2015)

Author(s)

Heloise Lavigne, James Orr and Jean-Pierre Gattuso [email protected]

References

Cai W. J., and Wang Y., 1998. The chemistry, fluxes, and sources of carbon dioxide in the estuarine waters of the Satilla and Altamaha Rivers, Georgia. Limnology and Oceanography 43, 657-668.

Dickson A. G., Sabine C. L. and Christian J. R., 2007 Guide to best practices for ocean CO2 measurements. PICES Special Publication 3, 1-191.

Khoo H. K., Ramette R. W., Culberson C. H. and Bates R. G., 1977 Determination of Hydrogen ion concentration in seawater from 5 to 40oC: standard potentials at salinities from 20 to 45. Analytical Chemistry 49, 29-34. Lee K., Tae-Wook K., Byrne R.H., Millero F.J., Feely R.A. and Liu Y-M, 2010 The universal ratio of the boron to chlorinity for the North Pacific and North Atlantoc oceans. Geochimica et Cosmochimica Acta 74 1801-1811.