Henry's constant mol/(kg/atm)

Description

Henry's constant mol/(kg/atm)

Usage

K0(S=35, T=25, P=0, Patm=1, warn="y")

Arguments

Details

This formulation is only valid for specific ranges of temperature and salinity:

• S ranging between 0 and 45 and T ranging between -1 and 45oC.

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.

For pressure corrections: the pressure correction term of Weiss (1974) is used.

Value

Author(s)

Jean-Marie Epitalon, Aurelien Proye, and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

References

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

Examples

  K0(S=35,T=25,P=0)

First dissociation constant of carbonic acid (mol/kg)

Description

First dissociation constant of carbonic acid (mol/kg)

Usage

K1(S=35, T=25, P=0, k1k2="x", pHscale="T", kSWS2scale="x", ktotal2SWS_P0="x", warn="y")

Arguments

Details

The Lueker et al. (2000) constant is recommended by Guide to Best Practices for Ocean CO2 Measurements (2007). It is, however, critical to consider that each formulation is only valid for specific ranges of temperature and salinity:

• 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): formulation is that of Waters et al (2014). See below.

• 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".

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.

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).

Value

Author(s)

Jean-Marie Epitalon and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

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.

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.

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

Millero F. J., Pierrot D., Lee K., Wanninkhof R., Feely R., Sabine C. L., Key R. M. and Takahashi T., 2002. Dissociation constants for carbonic acid determined from field measurements. Deep Sea Research Part I: Oceanographic Research Papers 49:1705-1723.

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.

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

Mojica Prieto F. J. and Millero F. J., 2002. The values of pK1 + pK2 for the dissociation of carbonic acid in seawater. Geochimica et Cosmochimica Acta 66, 2529-2540.

Papadimitriou S., Loucaides S., Rérolle V. M. C., Kennedy P., Achterberg E. P., Dickson A. G., Mowlem M. and Kennedy H., 2018. The stoichiometric dissociation constants of carbonic acid in seawater brines from 298 to 267 K. Geochimica et Cosmochimica Acta 220, 55-70.

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..

Sulpis O., Lauvset S. K. and Hagens M., 2020. Current estimates of K1* and K2* appear inconsistent with measured CO2 system parameters in cold oceanic regions. Ocean Science 16, 847-862.

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.

See Also

K2.

Examples

  K1(S=35,T=25,P=0,k1k2="l",pHscale="T")

First dissociation constant of phosphoric acid (mol/kg)

Description

First dissociation constant of phosphoric acid (mol/kg)

Usage

K1p(S=35, T=25, P=0, pHscale="T", kSWS2scale="x", warn="y")

Arguments

Details

This formulation is only valid for specific ranges of temperature and salinity:

• S ranging between 0 and 45 and T ranging between 0 and 45oC.

The pressure correction was applied on the seawater scale. Hence, 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).

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

Author(s)

Jean-Marie Epitalon, Heloise Lavigne, Aurelien Proye and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

References

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

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.

See Also

K2p, K3p.

Examples

  K1p(35,25,0)

Second dissociation constant of carbonic acid (mol/kg)

Description

Second dissociation constant of carbonic acid (mol/kg)

Usage

K2(S=35, T=25, P=0, k1k2="x", pHscale="T", kSWS2scale="x", ktotal2SWS_P0="x", warn="y")

Arguments

Details

The Lueker et al. (2000) constant is recommended by Guide to Best Practices for Ocean CO2 Measurements (2007). It is, however, critical to consider that each formulation is only valid for specific ranges of temperature and salinity:

• 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): S ranging from 19.6 to 41 and T ranging between 15 to 35oC.

• 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".

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.

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).

Value

Author(s)

Jean-Marie Epitalon, Heloise Lavigne, Aurelien Proye and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

References

The Lueker et al. (2000) constant is recommended by Guide to Best Practices for Ocean CO2 Measurements (2007). The Roy et al. (1993) constant is recommended by DOE (1994).

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.

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.

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

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.

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

Mojica Prieto F. J. and Millero F. J., 2002. The values of pK1 + pK2 for the dissociation of carbonic acid in seawater. Geochimica et Cosmochimica Acta 66, 2529-2540.

Papadimitriou S., Loucaides S., Rérolle V. M. C., Kennedy P., Achterberg E. P., Dickson A. G., Mowlem M. and Kennedy H., 2018. The stoichiometric dissociation constants of carbonic acid in seawater brines from 298 to 267 K. Geochimica et Cosmochimica Acta 220, 55-70.

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..

Sulpis O., Lauvset S. K. and Hagens M., 2020. Current estimates of K1* and K2* appear inconsistent with measured CO2 system parameters in cold oceanic regions. Ocean Science 16, 847-862.

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.

See Also

K1.

Examples

  K2(35,25,0)

Second dissociation constant of phosphoric acid (mol/kg)

Description

Second dissociation constant of phosphoric acid (mol/kg)

Usage

K2p(S=35, T=25, P=0, pHscale="T", kSWS2scale="x", warn="y")

Arguments

Details

This formulation is only valid for specific ranges of temperature and salinity:

• S ranging between 0 and 45 and T ranging between 0 and 45oC.

The pressure correction was applied on the seawater scale. Hence, 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).

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

Author(s)

Jean-Marie Epitalon, Heloise Lavigne, Aurelien Proye and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

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.

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

See Also

K1p, K3p.

Examples

  K2p(35,25,0)

Second dissociation constant of Si(OH)4

Description

Second dissociation constant of Si(OH)4 (mol/kg)

Usage

K2si(S=35, T=25, P=0, pHscale="T", kSWS2scale="x", ktotal2SWS_P0="x")

Arguments

Details

This equation is modified from Wischmeyer et al. (2003), who fitted the temperature-dependent K2si from Nordstrom et al. (1990) for freshwater to a value of 12.56 for T=25 and an ionic strength of 0.5 mol/kg. The temperature and salinity ranges in which it is valid are not well constrained.

The pressure correction is applied on the seawater scale. Hence, values are first transformed from the total scale to the seawater scale, the pressure correction applied as described by Millero (1995), and the value is transformed back to the required scale (T, F or SWS).

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

Author(s)

Mathilde Hagens (M.Hagens@uu.nl)

References

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

Nordstrom D. K., L. N. Plummer, D. Langmuir, E. Busenberg, H. M. May, B. F. Jones, D. L. Parkhurst, 1990 Revised chemical equilibrium data from major mineral reactions and their limitations. In: Melchior, D.C., R. L. Bassett (Eds.) Chemical Modeling of Aqueous Systems. IIACS Series 416. American Chemical Society, Washington, DC.

Wischmeyer A. G., Y. Del Amo, M. Brzezinski, D. A. Wolf-Gladrow, 1995 Theoretical constraints on the uptake of silicic acid species by marine diatoms. Marine Chemistry 82: 13-29.

Examples

  K2si(S=35, T=25, P=0, pHscale="T")

Third dissociation constant of phosphoric acid (mol/kg)

Description

Third dissociation constant of phosphoric acid (mol/kg)

Usage

K3p(S=35, T=25, P=0, pHscale="T", kSWS2scale="x", warn="y")

Arguments

Details

This formulation is only valid for specific ranges of temperature and salinity:

• S ranging between 0 and 45 and T ranging between 0 and 45oC.

The pressure correction was applied on the seawater scale. Hence, 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).

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

Author(s)

Jean-Marie Epitalon, Heloise Lavigne, Aurelien Proye and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

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.

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

See Also

K1p, K2p.

Examples

  K3p(35,25,0)

Dissociation constant of boric acid (mol/kg)

Description

Dissociation constant of boric acid (mol/kg)

Usage

Kb(S=35, T=25, P=0, pHscale="T", kSWS2scale="x", ktotal2SWS_P0="x", warn="y")

Arguments

Details

This formulation is only valid for specific ranges of temperature and salinity:

• S ranging between 5 and 45 and T ranging between 0 and 45oC.

The pressure correction is applied on the seawater scale. Hence, values are first transformed from the total scale to the seawater scale, the pressure correction applied as described by Millero (1995), and the value transformed back to the required scale (T, F or SWS).

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

Author(s)

Jean-Marie Epitalon, Heloise Lavigne, Aurelien Proye and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

References

Dickson A. G., 1990 Thermodynamics of the dissociation of boric acid in synthetic seawater from 273.15 to 318.15 K. Deep-Sea Research 375, 755-766.

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.

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.

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

Examples

  Kb(S=35,T=25,P=0,pHscale="T")

Equilibrium constant of hydrogen fluoride (mol/kg)

Description

Stability constant of hydrogen fluoride (mol/kg)

Usage

Kf(S=35, T=25, P=0, kf="x", pHscale="T", Ks_p0="x", Ks_p="x", warn="y")

Arguments

Details

The Perez and Fraga (1987) constant is recommended by Guide to Best Practices for Ocean CO2 Measurements (2007). The Dickson and Riley (1979 in Dickson and Goyet, 1994) constant is recommended by DOE (1994).

It is, however, critical to consider that each formulation is only valid for specific ranges of temperature and salinity:

• 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.

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.

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).

Value

Author(s)

Jean-Marie Epitalon, Heloise Lavigne, Aurelien Proye and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

References

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.

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.

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

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

Examples

  Kf(S=35,T=25,P=0,kf="pf",pHscale="T")

Dissociation constant of hydrogen sulfide (mol/kg)

Description

Dissociation constant of hydrogen sulfide (mol/kg)

Usage

Khs(S=35, T=25, P=0, pHscale="T", warn="y")

Arguments

Details

This formulation is only valid for specific ranges of temperature and salinity:

• S ranging between 0 and 45 and T ranging between 0 and 45oC.

The pressure correction is applied on the seawater scale. Hence, the values are first transformed from the total scale to the seawater scale, the pressure correction applied as described by Millero (1995), and the value is transformed back to the required scale (T, F or SWS).

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

Author(s)

Karline Soetaert K.Soetaert@nioo.knaw.nl and Heloise Lavigne

References

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

Examples

  Khs(S=35,T=25,P=0, pHscale="T")

Dissociation constant of ammonium (mol/kg)

Description

Dissociation constant of ammonium on the total scale (mol/kg)

Usage

Kn(S=35, T=25, P=0, pHscale="T", warn="y")

Arguments

Details

This formulation is only valid for specific ranges of temperature and salinity:

• S ranging between 0 and 45 and T ranging between 0 and 45oC.

The pressure correction is applied on the seawater scale. Hence, values are first transformed from the total scale to the seawater scale, the pressure correction applied as described by Millero (1995), and the value is transformed back to the required scale (T, F or SWS).

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

Author(s)

Karline Soetaert K.Soetaert@nioo.knaw.nl and Heloise Lavigne

References

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

Examples

  Kn(S=35,T=25,P=0, pHscale="T")

Stability constant of hydrogen sulfate (mol/kg)

Description

Stability constant of hydrogen sulfate (mol/kg)

Usage

Ks(S=35, T=25, P=0, ks="d", warn="y")

Arguments

Details

The Dickson (1990) constant is recommended by Guide to Best Practices for Ocean CO2 Measurements (2007). It is, however, critical to consider that each formulation is only valid for specific ranges of temperature and salinity:

• 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.

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.

The pressure correction is applied on the free scale as described by Millero (1995), and the value transformed back to the required scale (T, F or SWS).

Value

Author(s)

Heloise Lavigne, Aurelien Proye and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

References

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.

Examples

  Ks(S=35,T=25,P=0, ks="d")

Dissociation constant of Si(OH)4

Description

Dissociation constant of Si(OH)4 on total scale (mol/kg)

Usage

Ksi(S=35, T=25, P=0, pHscale="T", kSWS2scale="x", warn="y")

Arguments

Details

This formulation is only valid for specific ranges of temperature and salinity:

• S ranging between 0 and 45 and T ranging between 0 and 45oC.

The pressure correction is applied on the seawater scale. Hence, values are first transformed from the total scale to the seawater scale, the pressure correction applied as described by Millero (1995), and the value is transformed back to the required scale (T, F or SWS).

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

Author(s)

Karline Soetaert K.Soetaert@nioo.knaw.nl and Heloise Lavigne

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.

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

Examples

  Ksi(S=35, T=25, P=0, pHscale="T")

Solubility product of aragonite (mol/kg)

Description

Solubility product of aragonite (mol/kg)

Usage

Kspa(S=35, T=25, P=0, warn="y")

Arguments

Details

This formulation is only valid for specific ranges of temperature and salinity:

• S ranging between 5 and 44 and T ranging between 5 and 40oC.

Pressure coorection was performed as described by Millero (1995).

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

Author(s)

Aurelien Proye and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

References

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

Mucci A., 1983 The solubility of calcite and aragonite in seawater at various salinities, temperature, and one atmosphere total pressure. American Journal of Science 283: 780-799.

See Also

Kspc.

Examples

Kspa(S=35,T=25,P=0)

Solubility product of calcite (mol/kg)

Description

Solubility product of calcite (mol/kg)

Usage

Kspc(S=35, T=25, P=0, warn="y")

Arguments

Details

This formulation is only valid for specific ranges of temperature and salinity:

• S ranging between 5 and 44 and T ranging between 5 and 40oC.

The pressure coorection was performed as described by Millero (1995).

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

Author(s)

Aurelien Proye and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

References

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

Mucci A., 1983 The solubility of calcite and aragonite in seawater at various salinities, temperature, and one atmosphere total pressure. American Journal of Science 283: 780-799.

See Also

Kspa.

Examples

	Kspc(S=35,T=25,P=0)

Ion product of water (mol2/kg2)

Description

Ion product of water (mol2/kg2)

Usage

Kw(S=35, T=25, P=0, pHscale="T", kSWS2scale="x", warn="y")

Arguments

Details

This formulation is only valid for specific ranges of temperature and salinity:

• S ranging between 0 and 45 and T ranging between 0 and 45oC.

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).

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

Author(s)

Heloise Lavigne, Aurelien Proye and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

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.

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

Examples

  Kw(S=35,T=25,P=0,pHscale="T")

Carbonate saturation state for magnesian calcites

Description

Calculates the calcium carbonate saturation state for magnesian calcite

Usage

Om(x, flag, var1, var2, k1k2='x', kf='x', ks="d", pHscale="T", b="u74")

Arguments

Details

It is important to note that this function is only valid for:

• Salinity = 35

• Temperature = 25 degrees Celsius

• Hydrostatic pressure = 0 bar (surface)

• Concentration of total phosphate = 0 mol/kg

• Concentration of total silicate = 0 mol/kg

Note that the stoichiometric solubility products with respect to Mg-calcite minerals have not been determined experimentally. The saturation state with respect to Mg-calcite minerals is therefore calculated based on ion activities, i.e.,

\Omega_{x} = \frac{ \{Ca^{2+}\}^{1-x} \{Mg^{2+}\}^{x} \{CO_{3}\}^{2-} } { K_{x} }

The ion activity {a} is calculated based on the observed ion concentrations [C] multiplied by the total ion activity coefficient, \gamma_T, which has been determined experimentally or from theory (e.g. Millero & Pierrot 1998): {a}=\gamma_T[C]. Because a true equilibrium cannot be achieved with respect to Mg-calcite minerals, K_x represents a metastable equilibrium state obtained from what has been referred to as stoichiometric saturation (Thorstenson & Plummer 1977; a term not equivalent to the definition of the stoichiometric solubility product, see for example Morse et al. (2006) and references therein). In the present calculation calcium and magnesium concentrations were calculated based on salinity. Total ion activity coefficients with respect to Ca^{2+}, Mg^{2+}, and CO_{3}^{2-} were adopted from Millero & Pierrot (1998).

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).

Value

The function returns a list with

Author(s)

Heloise Lavigne, Andreas J. Andersson and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

References

Only the references related to the saturation state of magnesian calcite are listed below; the other references are listed under the carb function.

Andersson A. J., Mackenzie F. T., Nicholas R. B., 2008, Life on the margin: implications of ocean acidification on Mg-calcite, high latitude and cold-water marine calcifiers. Marine Ecology Progress Series 373, 265-273.

Bischoff W. D., Mackenzie F. T. and Bishop F. C., 1987. Stabilities of synthetic magnesian calcites in aqueous solution: comparison with biogenic materials. Geochimica et Cosmochimica Acta 51:1413-1423.

Millero F. J. and Pierrot D., 1998. A chemical equilibrium model for natural waters. Aquatic Geochemistry 4, 153-199.

Morse J. W., Andersson A. J. and Mackenzie F. T., 2006. Initial responses of carbonate-rich shelf sediments to rising atmospheric pCO2 and ocean acidification: Role of high Mg-calcites. Geochimica et Cosmochimica Acta 70, 5814-5830.

Plummer L. N. and Mackenzie F. T., 1974. Predicting mineral solubility from rate data: application to the dissolution of magnesian calcites. American Journal of Science 274:61-83.

Thorstenson D.C. and Plummer L.N., 1977. Equilibrium criteria for two component solids reacting with fixed composition in an aqueous phase-example: the magnesian calcites. American Journal of Science 277, 1203-1233.

Examples

Om(x=seq(0.01, 0.252, 0.01), flag=8, var1=8.2, var2=0.00234, 
  k1k2='x', kf='x', ks="d", pHscale="T", b="u74")

Coefficients used for pressure-correcting the equilibrium constants

Description

Pressure corrections are based on the following equations:

\ln{\frac{K_{i}^{P}}{K_{i}^{0}}} = -\frac{\Delta V_{i}}{RT}.P + 0.5\frac{\Delta K_{i}}{RT}.P^{2}

with

\Delta V_{i} = a_{0} + a_{1}T + a_{2}T^{2}

and

\Delta K_{i} = b_{0} + b_{1}T + b_{2}T^{2}

The variables are:

• K indicating the type of equilibrium constant

• coefficient a_0

• coefficient a_1

• coefficient a_2

• coefficient b_0

• coefficient b_1

• coefficient b_2

Usage

Pcoeffs

Format

A data frame with 15 rows and 7 variables

Details

For Kb, to be consistent with Millero (1979) a2 was changed to -2.608e-3 instead of 2.608e-3 (value given in Millero, 1995) For Kw, coefficients are from Millero (1983).

Source

Millero F. J., 1979 The thermodynamics of the carbonate system in seawater. Geochemica et Cosmochemica Acta 43: 1651-1661.

Millero F. J., 1983 Influence of pressure 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 of the carbon dioxide system in the oceans. Geochimica Cosmochimica Acta 59: 661-677.

See Also

Pcorrect

Pressure correction of equilibrium constants

Description

Computes the pressure correction of the equilibrium constants

Usage

Pcorrect(Kvalue, Ktype, T=25, S=35, P=0, pHscale="T", 
  kconv2ScaleP0="x", kconv2Scale="x", warn="y")

Arguments

Details

• The pressure correction is applied on the seawater scale for K1, K2, K1p, K2p, K3p, Kb, Khs, Kn, Ksi, K2si and Kw. Hence the K value is first converted on the seawater scale if needed. After pressure correction, the constant is converted back to the initial pH scale.

• The pressure correction is applied on the free scale for Kf.

• There is no issue of pH scale for Ks, Kspa and Kspc.

Value

The equilibrium constant given in argument but after pressure correction

Author(s)

Heloise Lavigne and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

References

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

See Also

Pcoeffs

Examples

k10 <- K1(T=25, P=0, S=35)
Pcorrect(Kvalue=k10, Ktype="K1", P=300, T=25, S=35, pHscale="T")

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

alkalinity

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)

Arguments

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

Author(s)

Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

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.

See Also

tris, pHslope, pH.

Examples

	##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, ...)
     

Arguments

Details

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

Author(s)

Karline Soetaert K.Soetaert@nioo.knaw.nl

References

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

See Also

matplot, par, speciation.

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-")))

Total boron concentration (mol/kg)

Description

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

Usage

bor(S, b)

Arguments

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

Author(s)

Heloise Lavigne, Aurelien Proye and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

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")

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)

Arguments

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:

Author(s)

Heloise Lavigne, Aurelien Proye and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

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)

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)

Arguments

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, 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:

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 m.hagens@uu.nl

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)

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)

Arguments

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 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.

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:

Author(s)

James Orr James.Orr@lsce.ipsl.fr

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.

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.

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
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)

Arguments

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:

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 jean-pierre.gattuso@imev-mer.fr

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., 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.

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., 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.

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.

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)

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)

Arguments

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:

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 jean-pierre.gattuso@imev-mer.fr

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., 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. 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., 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.

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.

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

## With a couple of variables
carbb(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", badd=0)

Parameters of the seawater carbonate system - extension of carb

Description

Returns parameters of the seawater carbonate system, including the ammonium and sulfide acid-base systems, as well as full acid-base speciation

Usage

carbfull(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

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, 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 data frame containing the following columns:

Note

Warning: pCO2 estimates below 100 m are subject to considerable uncertainty. See Weiss (1974) and Orr et al. (2014)

Author(s)

Heloise Lavigne, James Orr, Mathilde Hagens and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

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., 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 22, vol49 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.

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., 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., 2014. Comparison of seven packages that compute ocean carbonate chemistry. Biogeosciences Discussions 11, 5327-5397.

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.

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], Mar. Chem. 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, Mar. Chem., 8, 347-359.

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

Examples

## With a couple of variables
carbfull(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
carbfull(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", "potential", "potential")
NH4t <- c(0, 0, 0)
HSt <- c(0, 0, 0)
carbfull(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)
carbfull(flag=flag, var1=var1, var2=var2)

Converts depth in meters to pressure in dbar

Description

Converts depth in meters to pressure in dbar

Usage

d2p(depth, lat=40)

Arguments

Value

Author(s)

Heloise Lavigne and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

References

Saunders P. M., 1981. Practical conversion of pressure to depth. J. Phys. Oceanogr. 11: 573-574.

See Also

p2d

Examples

d2p(depth=7500, lat=30)  

Numerical derivatives of seawater carbonate system variables

Description

Returns numerical derivatives of the seawater carbonate system output variables with respect to input variables.

Usage

derivnum(varid, 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 = 1e+20, lat = 1e+20)

Arguments

Details

This subroutine has same input parameters as subroutine carb(). For details on these parameters, refer to documentation of 'carb'.

This subroutine computes partial derivatives of each output variable with respect to each of the input variable (including each of the two chosen carbonate system variables, each of the nutrients (total silicon and total phosphorus), temperature, and salinity.

It computes these derivatives (dy/dx) using the method of central differences, i.e.,

• for dx, it adds a positive and negative perturbation, same and equal in magnitude, to each input variable, one at a time, and

• for dy, it then computes the corresponding induced change in output variables

All arguments but the first (varid), can be given as scalers or vectors. If the lengths of the vectors differs, only the longest vector is retained and the other arguments are set equal to the first value of the other vectors are used. Hence users should use either vectors with the same dimension or one vector for one argument and scalars for others; otherwise, results may not be as intended.

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:

If all input data have the same 'flag' value, returned data frame does not show derivatives of input pair of carbonate system variables. For example, if all input flags are 15, the input pair is DIC and ALK; hence, derivatives of DIC and ALK are not returned.

Units of derivative dy/dx is unit(y)/unit(x) where unit(x) are as follows:

Author(s)

Jean-Marie Epitalon, James Orr, and Jean-Pierre Gattusojean-pierre.gattuso@imev-mer.fr

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., 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 22, vol49 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.

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., 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.

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.

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, Marine Chemistry, 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) For the input pair ALK and DIC (var1 and var2 when flag=15)
##    compute derivatives of all output varialbes 
##    with respect to DIC (i.e., var2)
derivnum(varid='var2', flag=15, var1=2300e-6, var2=2000e-6, 
         S=35, T=25, P=0, Patm=1.0, Pt=0, Sit=0,
         pHscale="T", kf="pf", k1k2="l", ks="d", b="u74")

## 2) For the input pair pH and ALK (var1 and var2 when flag=8)
##    compute derivatives of all output variables 
##    with respect to [H+] concentration
derivnum(varid='var1', 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")

## 3) Using vectors as arguments and compute derivatives of all output 
##    variables with respect to temperature
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("u74", "u74", "u74")
derivnum(varid='T', flag=flag, var1=var1, var2=var2, S=S, T=T, P=P,
         Pt=Pt, Sit=Sit, kf=kf, k1k2=k1k2, pHscale=pHscale, b=b)

# For more examples of use of derivnum.R,
# consult the code of seacarb's errors routine.

Convert temperature and salinity from EOS-80 to TEOS-10

Description

Converts in situ temperature to conservative temperature and practical to absolute salinity (SA). Salinity conversion depends on total alkalinity as well as the concentrations of dissolved inorganic carbon, nitrate and silicate.

Usage

eos2teos_chem(SP, T, P=0, TA=2300e-6, DIC=2000e-6, NO3=0, SIOH4=0)

Arguments

Details

Conversion from practical to absolute salinity depends on carbonate system parameters and ion concentration which mostly affect water density anomalies.

Value

The function returns a data frame containing the following columns:

Author(s)

Jean-Marie Epitalon

References

McDougall T. J., Jackett D. R., Millero F. J., Pawlowicz R. and Barker P. M., 2012. A global algorithm for estimating Absolute Salinity. Ocean Science 8, 1123-1134.

Pawlowicz R., Wright D. G. and Millero F. J., 2011. The effects of biogeochemical processes on oceanic conductivity/salinity/density relationships and the characterization of real seawater. Ocean Science 7, 363-387.

Pawlowicz R., 2013. What every oceanographer needs to know about TEOS-10 (The TEOS-10 Primer). http://www.teos-10.org/

See Also

teos2eos_chem does the reverse, eos2teos_geo, sp2sa_chem

package gsw

Examples

   # Calculate Conservative Temperature and Absolute Salinity of a sample with 
   # Practical salinity of 35 psu, in-situ temperature of 18 deg C,
   # at 0 dbar and total alkalinity of 0.00234 mol/kg and DIC of 0.00202 mol/kg
   f <- eos2teos_chem(SP=35, T=18, P=0, TA=0.00234, DIC=0.00202)
   CT <- f$CT     # Conservative Temperature
   SA <- f$SA     # Absolute Salinity

Convert temperature and salinity from EOS-80 to TEOS-10

Description

Converts in situ to conservative temperature and practical to absolute salinity (SA). Salinity conversion depends on depth and geographic location.

Usage

eos2teos_geo(SP, T, P=0, long=1.e20, lat=1.e20)

Arguments

Details

Conversion from practical to absolute salinity depends on water density anomaly which is correlated with silicate concentration. This function relies on silicate concentration taken from WOA (World Ocean Atlas) to evaluate density anomaly.

Value

The function returns a data frame containing the following columns:

Author(s)

Jean-Marie Epitalon

References

McDougall T. J., Jackett D. R., Millero F. J., Pawlowicz R. and Barker P. M., 2012. A global algorithm for estimating Absolute Salinity. Ocean Science 8, 1123-1134.

Pawlowicz R., 2013. What every oceanographer needs to know about TEOS-10 (The TEOS-10 Primer). http://www.teos-10.org/

See Also

teos2eos_geo does the reverse, eos2teos_chem, sp2sa_geo, package gsw

Examples

   # Calculate conservative temperature and absolute salinity of a sample with 
   # Practical salinity of 35 psu, in situ temperature of 18 deg C,
   # depth is 10 dbar and location is 188 degrees East and 4 degrees North.
   f <- eos2teos_geo(SP=35, T=18, P=10, long=188, lat=4)
   CT <- f$CT     # Conservative temperature
   SA <- f$SA     # Absolute salinity

Uncertainty propagation for computed marine carbonate system variables

Description

Estimates combined standard uncertainties in computed carbonate system variables by propagating inout uncertainties (standard uncertainties) in six input variables, including (Orr et al., Mar. Chem., in press):

• the input pair of carbonate system variables,

• the 2 input nutrients (silicate and phosphate concentrations),

• temperature and salinity. It also accounts for

• the errors in the key dissociation constants pK0, pK1, pK2, pKb, pKw, pKspa and pKspc

• the error in total boron

Usage

errors(flag, var1, var2, S=35, T=25, Patm=1, P=0, Pt=0, Sit=0, 
              evar1=0, evar2=0, eS=0.01, eT=0.01, ePt=0, eSit=0, 
              epK=c(0.002, 0.0075, 0.015, 0.01, 0.01, 0.02, 0.02),
              eBt=0.02, method = "ga", r=0.0, runs=10000,
              k1k2='x', kf='x', ks="d", pHscale="T", b="u74", gas="potential", 
              warn="y", eos = "eos80", long = 1e+20, lat = 1e+20)

Arguments

Details

Complete information on routine uncertainty propagation for the marine carbon dioxide system can be found in Orr et al. (in press). This function requires users to specify each input standard uncertainty as either the standard deviation or the standard error of the mean. The latter implies much smaller propagated uncertainties, but is appropriate only when interested in the error in the mean, not the error of a given measurement. Beware that it is easy to fool oneself when using the standard error of the mean rather than the standard deviation.

This function requires different types of standard uncertainties:

• Standard uncertainties for evar1, evar2, eS, eT, ePt, eSit (same units as the input data, e.g., mol/kg);

• Standard uncertainties in pK units for epK; and

• Standard uncertainties in relative fractional units (between 0.0 and 1.0) for eBt.

This function propagates standard uncertainty from input to output variables using one of three methods:

• Gaussian: The Gaussian method is the standard technique for estimating a computed variable's (z) second moment (its variance or standard deviation) based on a first-order approximation to z. More precisely, we use here the basic 1st order, 2nd moment uncertainty analysis (a type of Taylor expansion), assuming no covariance between input variables. This is the approach used by Dickson and Riley (1978). It is the default method.

• Method of moments: The method of moments is a more general form of the Gaussian method. But in addition, it also accounts for covariance between input variables. In this case, the 'errors' routine allows the user to specify a value of the correlation coefficient 'r', having a value between -1.0 and 1.0, to indicate the correlation between standard uncertainties of the input pair of carbonate system variables. That correlation is used to compute the covariance. But by default, it is assumed that there is no covariance (r=0.0).

• Monte Carlo: The Monte Carlo method is a brute-force approach relying on repeated random sampling of input errors, adding those to each input variables, calculating the corresponding output variables for each sample, and finally assessing the standard deviation in each output variables.

This function has many input parameters that are identical to those in the carb function. For their details, refer to the 'carb' documentation.

All parameters may be scalars or vectors except epK, eBt, method, runs, and gas.

• runs and eBt must be scalars

• method and gas must each consist of a character string

• epK may be a vector of 7 values. In that case, it must list errors for pK0, pK1, pK2, pKb, pKw, pKspa and pKspc, respectively. That set of errors is identical for all input data. Alternatively, users may specify 'epK=NULL' or 'epK=0' to set all 7 values to zero and thus neglect errors in the equilibrium constants.

In constrast, for evar1, evar2, r, eS, eT, ePt and eSit:

• if they are vectors, they represent standard uncertainties associated with each data point

• if they are scalars (single real numbers), they represent one standard uncertainty value each associated to all data points

The same remark applies to parameter r (correlation coefficient).

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 2-dimensional dataframe, with the following columns:

If all input data have the same 'flag' value, the returned data frame does not show combined standard uncertainties on input pair of carbonate system variables. For example, if all input flags are 15, the input pair is DIC and ALK; hence, errors on DIC and ALK are not returned.

Correlation coefficient

By default, 'r' is zero. However, for some pairs the user may want to specify a different value. For example, measurements of pCO2 and pH are often anti-correlated. The same goes for two other pairs: 'CO2 and CO3' and 'pCO2 and CO3'. But even for these cases, care is needed before using non-zero values of 'r'.

When the user wishes to propagate standard uncertainties for an individual measurement, 'r' should ALWAYS be zero if each member of the input pair is measured independently. In this case, we are interested in the correlation between the uncertainties in those measurements, not in the correlation between the measurements themselves. Uncertainties from those measurements are probably not correlated if they come from different instruments. Conversely, if users are interested in the error in the mean of a distribution of measurements (i.e., if they are propagating standard errors instead of standard deviations), one should then also account for the correlation between the measurements of the two variables of the input pair.

For input pairs where one member is pH (flags 1, 6, 7, 8, 9, and 21), this 'errors' function automatically inverses the sign of 'r'. The reason for that is that the associated derivatives are computed in terms of the hydrogen ion concentration (H+), not pH. Therefore for each of these 6 flags, if the user wants to compute their own 'r' that should be done by (1) using the H+ concentration instead of pH, and (2) inversing the sign of that computed 'r' before passing it as an argument to this routine. Usually though (when not calculating r for pH), the user may just use the 'r' in the expected way. For example, to include the covariance term when there is a perfect anticorrelation of pH with pCO2, one would use 'r=-1.0'.

Computation time

Computation time depends on the method chosen; the Monte Carlo method takes much longer to execute. The computational time required for the Monte Carlo method is proportional to the number of runs. More runs, implies improved accuracy: runs = 10000 appears a minimum to obtain an accuracy of less than 1%. Accuracy is inversely proportional to the number of runs.

Computation time also depends on the chosen pair of input variables. For example, with the input pair DIC and Total alkalinity (flag=15), it is much longer than for input pair pH and Total alkalinity (flag=8)

Author(s)

Jean-Marie Epitalon, James Orr, and Jean-Pierre Gattusojean-pierre.gattuso@imev-mer.fr

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., 1978 The effect of analytical error on the evaluation of the components of the aquatic carbon-dioxide system, Marine Chemistry, 6, 77-85.

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., 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 22, vol49 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.

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., 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., Dickson A. and Gattuso J.-P., in press. Routine uncertainty propagation for the marine carbon dioxide system. Marine Chemistry.

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.

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.

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, Marine Chemistry, 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) For the input pair ALK and DIC (var1 and var2 when flag=15),
## compute resulting uncertainty from given uncertainty on ALK and DIC (5 umol/kg)
## and default uncertainties in dissociation constants and total boron
## using the default method (Gaussian)
errors(flag=15, var1=2300e-6, var2=2000e-6, S=35, T=25, P=0, Patm=1.0, Pt=0, Sit=0, 
       evar1=5e-6, evar2=5e-6, eS=0, eT=0, ePt=0, eSit=0, 
       pHscale="T", kf="pf", k1k2="l", ks="d", b="u74")
## Typical output:
## H             pH          CO2           fCO2      pCO2      HCO3          ...
## 3.721614e-10  0.01796767  5.441869e-07  19.25338  19.31504  9.170116e-06  ...

## 2) Do the same as in one, but assign a 4% uncertainty to total boron
##    This uncertainty is the amount by which estimates from Lee et al (2010) and 
##    Uppstrom (1974) differ. The default for the latter is eBt=0.02.
errors(flag=15, var1=2300e-6, var2=2000e-6, S=35, T=25, P=0, Patm=1.0, Pt=0, Sit=0, 
       evar1=5e-6, evar2=5e-6, eS=0, eT=0, ePt=0, eSit=0, eBt=0.04,
       pHscale="T", kf="pf", k1k2="l", ks="d", b="u74")

## 3) For the input pair pH and ALK (var1 and var2 when flag=8)
## compute standard errors in output variables from errors in input variables, i.e., 
## for pH (0.005 pH units) and in ALK (5 umol/kg), along with
## errors in total dissolved inorganic phosphorus (0.1 umol/kg) and
## total dissolved inorganic silicon (2 umol/kg) concentrations, while
## assuming no uncertainty in dissociation constants & boron, using the Gaussian method:
errors(flag=8, var1=8.25, var2=2300e-6,  S=35, T=25, P=0, Patm=1.0, Pt=0, Sit=0, 
       evar1=0.005, evar2=5e-6, eS=0, eT=0, ePt=0.1, eSit=2, epK=0, eBt=0,
       method="ga", pHscale="T", kf="pf", k1k2="l", ks="d", b="u74")

## 4) For the input pair pCO2 and pH (var1 and var2 when flag=21)
## compute standard errors in output variables from errors in input variables, i.e., 
## for pCO2 (2 uatm) and pH (0.005 pH units), with no uncertainties in Pt and Sit
## nor in the dissociation constants BUT a perfect anticorrelation between pCO2 and pH,
## (the input pair) using the Method of moments:
errors(flag=21, var1=400, var2=8.1,  S=35, T=25, P=0, Patm=1.0, Pt=0, Sit=0, 
       evar1=2, evar2=0.005, eS=0, eT=0, ePt=0.0, eSit=0, epK=0, eBt=0, 
       method="mo", r=-1.0, pHscale="T", kf="pf", k1k2="l", ks="d", b="u74")

## 5) Use vectors as arguments and compute errors on all output variables
## using Monte Carlo method taking into account input errors on pH, ALK, DIC
## and dissociation constants (pKx)
flag <- c(8, 15)
var1 <- c(8.2, 0.002394, 8.25)
var2 <- c(0.002343955, 0.002017)
S <- c(35, 35)
T <- c(25, 25)
P <- 0
Pt <- 0
Sit <- 0
evar1 <- c(0.005, 2e-6)
evar2 <- c(2e-6, 2e-6)
epKx <- c(0.002, 0.01, 0.02, 0.01, 0.01, 0.01, 0.01)
eBtx = 0.01
method <- "mc"
kf <- "pf"
k1k2 <- "l"
pHscale <- "T"
b <- "u74"
## NOTE that the following is executable but enclosed in "donttest" 
## because it takes too long to run when submiting to CRAN
## and is therefore rejected
errors(flag=flag, var1=var1, var2=var2, S=S, T=T, P=P, Pt=Pt, Sit=Sit, 
       evar1=evar1, evar2=evar2, eS=0, eT=0, ePt=0, eSit=0, epK=epKx, eBt=eBtx,
       method=method, runs=10000, kf=kf, k1k2=k1k2, pHscale=pHscale, b=b)

Converts the CO2 fugacity to CO2 partial pressure

Description

Converts fCO2 (fugacity of CO2) into pCO2 (partial pressure in CO2)

Usage

f2pCO2(T = 25, Patm=1, P=0, fCO2)

Arguments

Value

Note

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

Author(s)

Heloise Lavigne, Jean-Pierre Gattuso, and James Orr jean-pierre.gattuso@imev-mer.fr

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.

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

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

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.

See Also

p2fCO2.

Examples

f2pCO2(T=25, Patm=1.0, P=0, fCO2=380)  

fCO2 at in situ temperature

Description

Correction to compensate for the difference in temperature between the temperature of measurement and in situ temperature.

Usage

fCO2insi(fCO2lab = 400, Tlab = 20, SST = 19)

Arguments

Value

Note

The empirical correction applied is from Takahashi (1993) as recommended by Pierrot et al. (2009)

Author(s)

Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

References

Pierrot D., Neill C., Sullivan K., Castle R., Wanninkhof R., Lüger H., Johannessen T., Olsen A., Feely R. A. and Cosca C. E., 2009. Recommendations for autonomous underway pCO2 measuring systems and data-reduction routines. Deep-Sea Res. II 56, 512-522.

Takahashi T., Olafsson J., Goddard J. G., Chipman D. W. and Sutherland S. C., 1993. Seasonal variation of CO2 and nutrients in the high-latitude surface oceans: a comparative study. Glob. Biogeochem. Cycles 7, 843-878.

See Also

f2pCO2, pCO2insi.

Examples

fCO2insi(fCO2lab = 400, SST = 15, Tlab = 16)

Total activity coefficient for H+

Description

Compute total hydrogen ion activity coefficient. The activity coefficient (fH) is used to convert from H+ concentration on SWS scale to H+ activity (ah), as used for NBS scale; likewise fH is used to make the conversion in the opposite direction, from the NBS scale to the SWS scale. Here, fH is taken from Takahashi et al (1982, GEOSECS Pacific Expedition, Chap 3, p. 80) who say: fH is the total activity coeff., which includes contributions from HSO4- and HF [as well as H+].

Takahashi et al. (1982) computed a relationship for fH based on the experimental data from Culberson & Pytkowicz (1973), who determined it experimentally as a function of temperature and salinity. The approach is old and full of uncertainty. Newer approaches are more complicated (Pitzer equations) and big uncertainties remain (Marion et al., 2011; Pilson, 2013).

Usage

fH(S=35, T=25)

Arguments

Details

This total activity coefficient appears in the following basic chemistry equation: ah = fH * hsws, where ah is the activity of hydrogen ion, fH is the total activity coefficient, and hsws = [H+] + [HSO4-] + [HF]. In other words, hsws is the total hydrogen ion conccentration on the seawater scale.

The two pH scales of concern are defined as pHNBS = -log10(ah) and pHSWS = -log10(hsws).

Value

Author(s)

James Orr james.orr@lsce.ipsl.fr

References

Culberson, C.H., & Pytkowicz, R.M. (1973). Ionization of water in seawater. Marine Chemistry, 1(4), 309-316.

Marion G.M., Millero F.J., Camoes M.F., Spitzer P., Feistel R., Chen C.T.A. 2011. pH of seawater. Marine Chemistry 126 89-96.

Pilson M.E.Q. (2013) An introduction to the chemistry of the sea, 2 edn. Cambridge, UK: Cambridge University Press.

Takahashi T., Williams R.T., and Ros D.L. (1982) Carbonate chemistry. GEOSECS Pacific Expedition, Volume 3, Hydrographic Data 1973-1974, 77-83.

See Also

pHnbs2sws and pHsws2nbs

Examples

## Compute fH
   f = fH(T=25, S=35)
   print(f)
## Check value: The result is 0.7134043

Conversion factors to change the pH scale of dissociation constants

Description

Conversion factors from the total scale to the free and seawater scales

Usage

kconv(S=35, T=25, P=0, kf, Ks, Kff, warn="y")

Arguments

Details

It is critical to consider that each formulation is valid in specific ranges of temperature and salinity:

• 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.

Note that kconv may be called in many functions (i.e. K1, K2, K1p, K2p, K3p, Kw, Ksi, K2si, etc...) without user controls it. To force a particular formulation for Kf, it is recommended to call kconv() first then pass the resulting conversion factors to these functions.

Value

The function returns a list with 6 conversion factors :

Author(s)

Karline Soetaert K.Soetaert@nioo.knaw.nl

References

Dickson A.G. and F.J. Millero, 1987 A comparison of the equilibrium constants for the dissociation of carbonic acid in seawater media. Deep-Sea Research 34:1733-1743.

See Also

pHconv.

Examples

##To convert dissociation constants from the total scale to the free scale
## (at salinity=35, temperature=25oC and atmospheric pressure):
kconv(35,25,0)
conv <- kconv()
 c(K1_total=K1(),K1_SWS=K1()*conv$ktotal2SWS,K1_free=K1()*conv$ktotal2free)  

variable for internal use

Description

nothing

Perturbation of the seawater carbonate system

Description

Describes the various approaches that can be used to alter the seawater carbonate system. Its main purpose is to assist the design of ocean acidification perturbation experiments.

Usage

oa(flag, var1, var2, pCO2f, pCO2s=1e6, S=35, T=25, P=0, 
	Pt=0, Sit=0, k1k2='x', kf='x', ks="d", pHscale="T", plot=FALSE, 
	b="u74", eos = "eos80", long = 1e+20, lat = 1e+20)

Arguments

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).

Value

The function returns a list built as follows:

Warnings

• It is recommended to use concentrated solutions of acid or base in order to add small volumes.

• The addition of strong acid does not simulate well natural ocean acidification (higher concentration of dissolved inorganic carbon at constant total alkalinity) since it generates a decrease in total alkalinity while dissolved inorganic carbon is kept constant.

• Other important advice is provided in Gattuso and Lavigne (2009), Schulz et al. (2009) and in the “Guide for Best Practices on Ocean Acidification Research and Data Reporting” (https://www.iaea.org/sites/default/files/18/06/oa-guide-to-best-practices.pdf)

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.

Author(s)

Heloise Lavigne and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

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.

Gattuso J.-P. and Lavigne H., 2009 Technical note: approaches and software tools to investigate the impact of ocean acidification. Biogeosciences 21, 6:2121-2133.

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.

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.

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.

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.

Schulz K. G., Barcelos e Ramos J., Zeebe R. E. and Riebesell U., 2009 CO2 perturbation experiments: similarities and differences between dissolved inorganic carbon and total alkalinity manipulations. Biogeosciences 6, 2145-2153.

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.

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

See Also

carb, pgas, pmix, ppH, pTA.

Examples

oa(flag=24, var1=384, var2=2325e-6, pCO2s=1e6, pCO2f=793, S=34.3, T=16, 
	P=0, pHscale="T", kf="pf", k1k2="l", ks="d", plot=TRUE, b="u74")

Converts pressure in dbar to depth in meters

Description

Converts pressure in dbar to depth in meters

Usage

p2d(pressure, lat=40)

Arguments

Value

Author(s)

Heloise Lavigne and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

References

Saunders P. M., 1981. Practical conversion of pressure to depth. J. Phys. Oceanogr. 11: 573-574.

See Also

d2p

Examples

p2d(pressure=7686, lat=30)  

Converts pCO2 (partial pressure in CO2) into fCO2 (fugacity of CO2)

Description

Converts pCO2 (partial pressure in CO2) into fCO2 (fugacity of CO2)

Usage

p2fCO2(T = 25, Patm=1, P=0, pCO2)

Arguments

Value

Note

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

Author(s)

Heloise Lavigne, Jean-Pierre Gattuso, and James Orr jean-pierre.gattuso@imev-mer.fr

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.

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

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.

See Also

f2pCO2.

Examples

p2fCO2(T=25, Patm=0.97, P=0, pCO2=380)  

Converts partial pressure of CO2 to mole fraction of CO2

Description

Converts pCO2 (partial pressure of CO2) into xCO2 (mole fraction of CO2)

Usage

p2xCO2(S=35, T=25, Patm=1, pCO2)

Arguments

Details

The xCO2 (ppm) is computed from pCO2 (\muatm) using the following equation: xCO2 = pCO2 / (Patm - pH2O), where pH20 is the vapor pressure of seawater computed following best practices (Dickson et al., 2007). That computed pH20 is identical, when rounded to the 4th decimal place, with that computed by the equation from Weiss and Price (1980).

Value

Note

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

Author(s)

James Orr james.orr@lsce.ipsl.fr

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.

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

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

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

See Also

x2pCO2 and vapress

Examples

## Convert atmospheric pressure from mbar to atm
   Patm_mbar = 1052                 # in millibar
   Patm      = Patm_mbar / 1013.25  # in atm
## Compute xCO2 from pCO2
   pCO2 = 380
   xCO2 = p2xCO2(T=25, S=35, Patm=Patm, pCO2=pCO2)
   print(xCO2)
## The result is 377.1546 ppm 

pCO2 at in situ temperature

Description

Correction to compensate for the difference in temperature between the temperature of measurement and in situ temperature.

Usage

pCO2insi(pCO2lab = 400, Tlab = 20, SST = 19)

Arguments

Value

Note

The empirical correction applied is from Takahashi (1993) as recommended by Pierrot et al. (2009)

Author(s)

Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

References

Pierrot D., Neill C., Sullivan K., Castle R., Wanninkhof R., Lüger H., Johannessen T., Olsen A., Feely R. A. and Cosca C. E., 2009. Recommendations for autonomous underway pCO2 measuring systems and data-reduction routines. Deep-Sea Res. II 56, 512-522.

Takahashi T., Olafsson J., Goddard J. G., Chipman D. W. and Sutherland S. C., 1993. Seasonal variation of CO2 and nutrients in the high-latitude surface oceans: a comparative study. Glob. Biogeochem. Cycles 7, 843-878.

See Also

f2pCO2, fCO2insi.

Examples

pCO2insi(pCO2lab = 400, SST = 15, Tlab = 16)

pCa

Description

Calculates the changes in the saturation states of aragonite and calcite resulting from the manipulation of the calcium concentration

Usage

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

Arguments

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:

Note

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

Author(s)

Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

References

Ben-Yaakov S. and Goldhaber M. B., 1973 The influence of sea water composition on the apparent constants of the carbonate system. Deep-Sea Research 20, 87-99.

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.

Gattuso J.-P. and Lavigne H, 2009 Perturbation experiments to investigate the impact of ocean acidification: approaches and software tools. Biogeosciences 6, 4413-4439.

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.

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.

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.

Examples

pCa(flag=15, var1=2302e-6, var2=2050e-6, Ca=0.01028, S=35, T=20, P=0, 
	Pt=0, Sit=0, pHscale="T", kf="pf", k1k2="l", ks="d", b="u74") # with normal Ca concentration
pCa(flag=15, var1=2302e-6, var2=2050e-6, Ca=0.01028/2, S=35, T=20, P=0, 
	Pt=0, Sit=0, pHscale="T", kf="pf", k1k2="l", ks="d", b="u74") # with 0.5 * Ca concentration

Potentiometric pH

Description

Calculation of potentiometric pH

Usage

	pH(Ex=-67,Etris=-72.4,S=35,T=25)
	

Arguments

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

Author(s)

Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

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.

See Also

tris, amp, pHslope.

Examples

	##Example from Dickson et al. (2007)
	pH(Ex=-67,Etris=-72.4,S=35,T=25)

Conversion of pH

Description

Converts pH from one scale to another one chosen between the total scale, the free scale and the seawater scale

Usage

pHconv(flag=1, pH=8.10, S=35, T=25, P=0, ks="d")

Arguments

Details

The Dickson (1990) constant is recommended by the Guide to Best Practices for Ocean CO2 Measurements (2007). It is critical to consider that each formulation is valid in specific ranges of temperature and salinity:

• 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.

Value

The function returns the values of pH converted

Author(s)

Heloise Lavigne and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

References

Dickson A.G. and F.J. Millero, 1987 A comparison of the equilibrium constants for the dissociation of carbonic acid in seawater media. Deep-Sea Research 34:1733-1743.

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.

See Also

kconv.

Examples

##To convert pH=8.10 from the seawater scale to the total scale
##at salinity=35, temperature=25oC and atmospheric pressure:

  pHc <- pHconv(flag=1, pH=8.10, S=35, T=25, P=0, ks="d")

##note that pHc is the value of the pH converted in total scale

## By using vectors
## to convert the pH values : 8, 8.05, 8.10, 8.15, 8.20 
## from the free to the total scale

pH <- c(8, 8.05, 8.10, 8.15, 8.20)
pHc <- pHconv(flag=2, pH=pH, S=35, T=25, P=0, ks="d")

## note that pHc is a vector containing the value of the pH converted 
## to the total scale

pH at in situ temperature and pressure

Description

pH at in situ temperature and pressure

Usage

pHinsi(pH=8.2, ALK=2.4e-3, Tinsi=20, Tlab=25, Pinsi=0, S=35, Pt=0, Sit=0, 
  k1k2 = "x", kf = "x", ks="d", pHscale = "T", b="u74", eos = "eos80", 
  long = 1e+20, lat = 1e+20)

Arguments

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

Author(s)

Jean-Pierre Gattuso, jean-pierre.gattuso@imev-mer.fr

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.

Hunter K. A., 1998. The temperature dependence of pH in surface seawater. Deep-Sea Research (Part I, Oceanographic Research Papers) 45(11):1919-1930.

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.

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.

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.

Examples

  pHinsi(pH=8.2,ALK=2.4e-3,Tinsi=25,Tlab=25,Pinsi=200,S=35,Pt=0,Sit=0)

Converts pH from NBS to SWS scale

Description

Converts pH on NBS scale to pH on SWS scale pCO2. The NBS-to-SWS conversion is done with the total activity coefficient fH (combined activity coeff for H+, HSO4-, and HF) from Takahashi et al. (1982) based on data from Culberson and Pytkowicz (1973). The approach is old and full of uncertainty. Newer approaches are more complicated (Pitzer equations) and big uncertainties remain (Marion et al., 2011; Pilson, 2013).

Usage

pHnbs2sws(pHNBS, S=35, T=25)

Arguments

Details

The pHSWS is computed from pHNBS using the total activity coefficient and relying on the following basic chemistry equation: ah = fH * hsws, where ah is the activity of hydrogen ion, fH is the total activity coefficient, and hsws = [H+] + [HSO4-] + [HF]. In other words, hsws is the hydrogen ion concentration on the seawater scale.

The two pH scales are defined as pHNBS = -log10(ah) and pHSWS = -log10(hsws).

Value

Author(s)

James Orr james.orr@lsce.ipsl.fr

References

Culberson, C.H., & Pytkowicz, R.M. (1973). Ionization of water in seawater. Marine Chemistry, 1(4), 309-316.

Marion G.M., Millero F.J., Camoes M.F., Spitzer P., Feistel R., Chen C.T.A. 2011. pH of seawater. Marine Chemistry 126 89-96.

Pilson M.E.Q. (2013) An introduction to the chemistry of the sea, 2 edn. Cambridge, UK: Cambridge University Press.

Takahashi T., Williams R.T., and Ros D.L. (1982) Carbonate chemistry. GEOSECS Pacific Expedition, Volume 3, Hydrographic Data 1973-1974, 77-83.

See Also

fH and pHsws2nbs

Examples

## Convert pHNBS to pHSWS
   pHNBS = 8.0                          # pH on the NBS scale
   pHSWS = pHnbs2sws(pHNBS, T=25, S=35) # pH on the SWS scale
   print(pHSWS)
## Check value: the result should be 7.853336

Slope of the calibration curve of a pH electrode

Description

Slope of the calibration curve of a pH electrode (percent of theoretical slope)

Usage

pHslope(Etris=-72.4,Eamp=4.9,S=35,T=25)

Arguments

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

Author(s)

Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

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.

See Also

tris, amp, pH.

Examples

	##Example from Dickson et al. (2007)
	pHslope(Etris=-72.4,Eamp=4.9,S=35,T=25)

Calculates pHT from results of spectrophotometric measurements

Description

Calculates pH of a water sample from absorbance ratios R, obtained from spectrophotometric measurements with pH indicator dyes (on the total scale in mol/kg-soln)

Usage

pHspec(S=35, T=25, R=1, d="mCP", k="m18", warn="y")

Arguments

Details

The model used to calculate the return value of this function is based on experimental data. It is critical to consider that the formulation refers to the conditions studied during the characterization experiment and is only valid for the studied ranges of temperature and salinity:

• Mueller and Rehder (2018): S ranging between 0 and 40, T ranging between 5 and 35oC, and the dye used being m-Cresol purple (mCP) with R referring to the ratio of absorbances at wavelengths 578 and 434 nm.

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

Author(s)

Jens Daniel Mueller jens.mueller@io-warnemuende.de Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

References

Mueller, J. D. and Rehder, G., 2018 Metrology for pH Measurements in Brackish Waters - Part 2: Experimental Characterization of Purified meta-Cresol Purple for Spectrophotometric pHT Measurements. Frontiers in Marine Science 5:177, 1-9. https://doi.org/10.3389/fmars.2018.00177

See Also

amp, pHslope, pH. tris,

Examples

	##Example should give test value pHT = 7.6713
	 pHspec(S=35, T=25, R=1, d="mCP", k="m18", warn="y")

Converts pH from SWS to NBS scale

Description

Converts pH on SWS scale to pH on NBS scale pCO2. The SWS-to-NBS conversion is done with the total activity coefficient fH (combined activity coeff for H+, HSO4-, and HF) from Takahashi et al. (1982) based on data from Culberson and Pytkowicz (1973). The approach is old and full of uncertainty. Newer approaches are more complicated (Pitzer equations) and big uncertainties remain (Marion et al., 2011; Pilson, 2013).

Usage

pHsws2nbs(pHSWS, S=35, T=25)

Arguments

Details

The pHNBS is computed from pHSWS using the total activity coefficient and relying on the following basic chemistry equation: ah = fH * hsws, where ah is the activity of hydrogen ion, fH is the total activity coefficient, and hsws = [H+] + [HSO4-] + [HF]. In other words, hsws is the hydrogen ion concentration on the seawater scale.

The two pH scales are defined as pHNBS = -log10(ah) and pHSWS = -log10(hsws).

Value

Author(s)

James Orr james.orr@lsce.ipsl.fr

References

Culberson, C.H., & Pytkowicz, R.M. (1973). Ionization of water in seawater. Marine Chemistry, 1(4), 309-316.

Marion G.M., Millero F.J., Camoes M.F., Spitzer P., Feistel R., Chen C.T.A. 2011. pH of seawater. Marine Chemistry 126 89-96.

Pilson M.E.Q. (2013) An introduction to the chemistry of the sea, 2 edn. Cambridge, UK: Cambridge University Press.

Takahashi T., Williams R.T., and Ros D.L. (1982) Carbonate chemistry. GEOSECS Pacific Expedition, Volume 3, Hydrographic Data 1973-1974, 77-83.

See Also

fH and pHnbs2sws

Examples

## Convert pHSWS to pHNBS
   pHSWS = 7.853336                     # pH on the SWS scale
   pHNBS = pHsws2nbs(pHSWS, T=25, S=35) # pH on the NBS scale
   print(pHNBS)
## Check value: the result should be 8.0

pTA

Description

Calculates the carbonate chemistry following addition of CO_3^{2-} or HCO_3^-

Usage

pTA(flag, sys=0, var1, var2, pCO2a, co3, hco3, S=35, T=20, P=0, 
	Pt=0, Sit=0, k1k2="x", kf="x", ks="d", pHscale="T", b="u74", 
	eos = "eos80", long = 1e+20, lat = 1e+20)

Arguments

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 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.

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:

Note

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

Author(s)

Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

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., 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.

Gattuso J.-P. and Lavigne H., 2009 Perturbation experiments to investigate the impact of ocean acidification: approaches and software tools. Biogeosciences 6, 4413-4439.

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.

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.

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.

Examples

pTA(flag=24, sys=0, var1=384, var2=2302e-6, pCO2a=384, co3=260e-6, 
	hco3=1000e-6, S=34.3, T=16, P=0, pHscale="T", kf="pf", k1k2="l", ks="d", b="u74")

pTA(flag=24, sys=1, var1=384, var2=2302e-6, pCO2a=384, co3=260e-6, 
	hco3=1000e-6, S=34.3, T=16, P=0, pHscale="T", kf="pf", k1k2="l", ks="d", b="u74")

pgas

Description

Calculates the carbonate chemistry after changes in pCO2 generated by gas bubbling

Usage

pgas(flag, var1, var2, pCO2g, S=35, T=20, P=0, Pt=0, Sit=0, k1k2="x", 
	kf="x", ks="d", pHscale="T", b="u74", eos = "eos80", long = 1e+20, lat = 1e+20)

Arguments

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:

Note

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

Author(s)

Jean-Pierre Gattuso and Heloise Lavigne jean-pierre.gattuso@imev-mer.fr

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., 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.

Gattuso J.-P. and Lavigne H, 2009 Perturbation experiments to investigate the impact of ocean acidification: approaches and software tools. Biogeosciences 6, 4413-4439.

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.

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.

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.

Examples

pgas(flag=15, var1=2302e-6, var2=2050e-6, pCO2g=750, S=35, T=20, P=0, 
	Pt=0, Sit=0, pHscale="T", kf="pf", k1k2="l", ks="d", b="u74") 

pmix

Description

Calculates the carbonate chemistry after mixing of two water samples with different pCO2

Usage

pmix(flag, var1, var2, pCO2s, wf, S=35, T=20, P=0, Pt=0, Sit=0, k1k2="x", 
	kf="x", ks="d", pHscale="T", b="u74", eos = "eos80", long = 1e+20, lat = 1e+20)

Arguments

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:

Note

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

Author(s)

Jean-Pierre Gattuso and Heloise Lavignejean-pierre.gattuso@imev-mer.fr

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., 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.

Gattuso J.-P. and Lavigne H., 2009. Perturbation experiments to investigate the impact of ocean acidification: approaches and software tools. Biogeosciences 6, 4413-4439.

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.

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.

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.

Examples

pmix(flag=24, var1=384, var2=2302e-6, pCO2s=1e6, wf=0.003, S=34.3, 
	T=16, P=0, pHscale="T", kf="pf", k1k2="l", ks="d", b="u74")

ppH

Description

Calculates the carbonate chemistry after pH manipulations through addition of acid or base

Usage

ppH(flag, sys, var1, var2, pCO2a, vol, N, S=35, T=20, P=0, Pt=0, 
	Sit=0, pHscale="T", k1k2="x", kf="x", ks="d", eos = "eos80", 
	long = 1e+20, lat = 1e+20)

Arguments

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:

Note

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

Author(s)

Jean-Pierre Gattuso and Heloise Lavignejean-pierre.gattuso@imev-mer.fr

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.

Gattuso J.-P. and Lavigne H., 2009 Perturbation experiments to investigate the impact of ocean acidification: approaches and software tools. Biogeosciences 6, 4413-4439.

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.

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.

See Also

buffer.

Examples

ppH(flag=24, sys=0, var1=384, var2=2302e-6, pCO2a=384, vol=-12e-3, 
	N=0.01, S=34.3, T=16, P=0, pHscale="T", kf="pf", k1k2="l", ks="d")

ppH(flag=24, sys=1, var1=384, var2=2302e-6, pCO2a=384, vol=-12e-3, 
	N=0.01, S=34.3, T=16, P=0, pHscale="T", kf="pf", k1k2="l", ks="d")

Molar ratio of CO2 released vs CaCO3 precipitated

Description

Returns the molar ratio of CO2 released vs CaCO3 precipitated described by Frankignoulle et al. (1994).

Usage

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

Arguments

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:

Author(s)

Jean-Pierre Gattuso and Heloise Lavigne jean-pierre.gattuso@imev-mer.fr

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.

Frankignoulle M., Canon C. and Gattuso J.P., 1994 Marine calcification as a source of carbon dioxide- Positive feedback of increasing atmospheric CO2. Limnology and Oceanography 2, 458-462.

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.

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.

See Also

speciation.

Examples

## Calculation using the numerical example given in Frankignoulle et al. (1994)
psi(flag=24, var1=350, var2=2400e-6, S=35, T=25, P=0, Pt=0, 
	Sit=0, pHscale="T", kf="pf", k1k2="l", ks="d")

Density of seawater (kg/m3)

Description

Calculates the density of seawater (kg\ m^{-3})

Usage

rho(S = 35, T = 25, P = 0)

Arguments

Value

Author(s)

Aurelien Proye and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr

References

Millero F. J. and Poisson A., 1981 International one-atmosphere equation of state of seawater. Deep-Sea Research 28A, 625-629.

Examples

	rho(35,25,0)

From absolute to practical salinity

Description

Converts from absolute to practical salinity (SP). Salinity conversion depends on total alkalinity as well as the concentrations of dissolved inorganic carbon, nitrate and silicate.

Usage

sa2sp_chem(SA, TA=2300e-6, DIC=2000e-6, NO3=0, SIOH4=0)

Arguments

Details

Convert from absolute to practical salinity from carbon system parameters and ion concentration which most affect water density anomalies.

Value

Author(s)

Jean-Marie Epitalon

References

McDougall T. J., Jackett D. R., Millero F. J., Pawlowicz R. and Barker P. M., 2012. A global algorithm for estimating Absolute Salinity. Ocean Science 8, 1123-1134.

Pawlowicz R., Wright D. G. and Millero F. J., 2011. The effects of biogeochemical processes on oceanic conductivity/salinity/density relationships and the characterization of real seawater. Ocean Science 7, 363-387.

Pawlowicz R., 2013. What every oceanographer needs to know about TEOS-10 (The TEOS-10 Primer). http://www.teos-10.org/

See Also

sp2sa_chem does the reverse, sa2sp_geo

Examples

   # Calculate the practical salinity of a sample with Absolute Salinity of 35 g/kg,
   # Total Alkalinity of 0.00234 mol/kg and DIC of 0.00202 mol/kg
   SP <- sa2sp_chem(SA=35, TA=0.00234, DIC=0.00202)

From absolute to practical salinity

Description

Converts from absolute to practical salinity based on depth and geographic location.

Usage

sa2sp_geo(SA, P=0, long=1.e20, lat=1.e20)

Arguments

Details

This function is almost an alias of subroutine gsw_SP_from_SA from gsw package on which it relies. The only difference is in that depth and location are optional. If location is not given, or incomplete (either longitude or latitude missing), an arbitrary location is chosen: the mid equatorial atlantic ocean. Note that this implies an error on computed SA ranging from 0 up to 0.02 g/kg.

Value