Calculates the calcium carbonate saturation state for magnesian calcite
Om(x, flag, var1, var2, k1k2='x', kf='x', ks="d", pHscale="T", b="u74")The function returns a list with
Mg-calcite saturation state for minimally prepared biogenic Mg-calcite.
Mg-calcite saturation state for cleaned and annealed biogenic Mg-calcite.
mole fraction of magnesium ions, note that the function is only valid for x ranging between 0 and 0.25
select the couple of variables available. The flags which can be used are:
flag = 1 pH and CO2 given
flag = 2 CO2 and HCO3 given
flag = 3 CO2 and CO3 given
flag = 4 CO2 and ALK given
flag = 5 CO2 and DIC given
flag = 6 pH and HCO3 given
flag = 7 pH and CO3 given
flag = 8 pH and ALK given
flag = 9 pH and DIC given
flag = 10 HCO3 and CO3 given
flag = 11 HCO3 and ALK given
flag = 12 HCO3 and DIC given
flag = 13 CO3 and ALK given
flag = 14 CO3 and DIC given
flag = 15 ALK and DIC given
flag = 21 pCO2 and pH given
flag = 22 pCO2 and HCO3 given
flag = 23 pCO2 and CO3 given
flag = 24 pCO2 and ALK given
flag = 25 pCO2 and DIC given
Value of the first variable in mol/kg, except for pH and for pCO2 in \(\mu\)atm
Value of the second variable in mol/kg, except for pH
"cw" for using K1 and K2 from Cai & Wang (1998), "l" from Lueker et al. (2000), "m02" from Millero et al. (2002), "m06" from Millero et al. (2006), "m10" from Millero (2010), "mp2" from Mojica Prieto et al. (2002), "p18" from Papadimitriou et al. (2018), "r" from Roy et al. (1993), "sb21" from Shockman & Byrne (2021), "s20" from Sulpis et al. (2020), and "w14" from Waters et al. (2014). "x" is the default flag; the default value is then "l", except if T is outside the range 2 to 35oC and/or S is outside the range 19 to 43. In these cases, the default value is "w14".
"pf" for using Kf from Perez and Fraga (1987) and "dg" for using Kf from Dickson and Riley (1979 in Dickson and Goyet, 1994). "x" is the default flag; the default value is then "pf", except if T is outside the range 9 to 33oC and/or S is outside the range 10 to 40. In these cases, the default is "dg".
"d" for using Ks from Dickson (1990) and "k" for using Ks from Khoo et al. (1977), default is "d"
"T" for the total scale, "F" for the free scale and "SWS" for using the seawater scale, default is "T" (total scale)
Concentration of total boron. "l10" for the Lee et al. (2010) formulation or "u74" for the Uppstrom (1974) formulation, default is "u74"
Heloise Lavigne, Andreas J. Andersson and Jean-Pierre Gattuso jean-pierre.gattuso@imev-mer.fr
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).
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.
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")
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