| Title: | Solver Suite for Alkalinity-PH Equations |
| Version: | 2.1.0 |
| Date: | 2021-04-09 |
| Depends: | R (≥ 2.10) |
| Imports: | stats |
| Description: | Universal and robust algorithm for solving the total alkalinity-pH equation presented in G. Munhoven (2013) <doi:10.5194/gmd-6-1367-2013> and G. Munhoven (2021) <doi:10.5194/gmd-2020-447>. The total alkalinity-pH equation relates total alkalinity and pH for a given set of acid-base concentrations in a given water sample, among which carbonic acid. This package is particularly useful in marine chemistry involving dissolved inorganic carbon. Original package in Fortran can be found at <doi:10.5281/zenodo.4328965>. |
| Encoding: | UTF-8 |
| URL: | https://CRAN.R-project.org/package=SolveSAPHE |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Repository: | CRAN |
| RoxygenNote: | 7.1.0 |
| NeedsCompilation: | no |
| Packaged: | 2021-05-01 17:35:04 UTC; jean-marie |
| Author: | Jean-Marie Epitalon [aut, cre, cph], Jean-Pierre Gattuso [cph], Guy Munhoven [aut] |
| Maintainer: | Jean-Marie Epitalon <jean-marie.epitalon@orange.fr> |
| Date/Publication: | 2021-05-01 17:50:03 UTC |
Conversion ratio H_SWS/H_free from free pH-scale to SWS scale
Description
Function returns the ratio H_SWS/H_free as a function of temperature, salinity and pressure
Usage
ACVT_HSWS_O_HFREE(t_k, s, p_bar)Arguments
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
Value
ratio |
Ratio H_SWS/H_free |
Author(s)
Guy Munhoven and Jean-Marie Epitalon
Examples
ACVT_HSWS_O_HFREE(t_k=298,s=35, p_bar=0)
Conversion ratio H_Tot/H_free from free pH-scale to Total scale
Description
Function returns the ratio H_Tot/H_free as a function of temperature, salinity and pressure
Usage
ACVT_HTOT_O_HFREE(t_k, s, p_bar)Arguments
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
Value
ratio |
Ratio H_Tot/H_free |
Author(s)
Guy Munhoven and Jean-Marie Epitalon
Examples
ACVT_HTOT_O_HFREE(t_k=298,s=35, p_bar=0)
Dissociation constant of ammonium in sea-water [mol/kg-SW]
Description
Function returns the dissociation constant of ammonium in sea-water [mol/kg-SW]
Usage
AK_AMMO_1_YAMI95(t_k, s, p_bar)Arguments
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
Details
pH scale: SWS
Value
KNH |
Dissociation constant of ammonium in mol/kg-SW |
Author(s)
Guy Munhoven and Jean-Marie Epitalon
References
Yao and Millero (1995), Millero (1995) for pressure correction
Examples
AK_AMMO_1_YAMI95(t_k=298,s=35, p_bar=0)
Boric acid dissociation constant KB in mol/kg-SW
Description
Calculates boric acid dissociation constant in mol/kg-SW on the total pH-scale
Usage
AK_BORA_DICK90(t_k, s, p_bar)Arguments
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
Details
pH scale: Total
Value
KB |
Dissociation constant of boric acid in mol/kg-SW |
Author(s)
Guy Munhoven and Jean-Marie Epitalon
References
Dickson (1990, eq. 23) – also Handbook (2007, eq. 37), Millero (1979) pressure correction
Examples
AK_BORA_DICK90(t_k=298,s=35, p_bar=0)
Henry's constant K0 in (mol/kg-SW)/atmosphere
Description
Calculates Henry's constant (K0) based on Weiss (1979) formulation
Usage
AK_CARB_0_WEIS74(t_k, s)Arguments
t_k |
temperature in Kelvin |
s |
Salinity in psu |
Details
currently no pressure correction
Value
K0 |
Henry's constant mol/(kg/atm) |
Author(s)
Guy Munhoven and Jean-Marie Epitalon
References
Weiss R. F., 1974 Carbon dioxide in water and seawater: the solubility of a non-ideal gas. Marine Chemistry 2, 203-215.
Examples
AK_CARB_0_WEIS74(t_k=298,s=35)
First dissociation constant of carbonic acid in mol/kg-SW from Luecker et al.
Description
Calculates first dissociation constant of carbonic acid in mol/kg-SW on the total pH-scale, following Luecker et al. (2000)
Usage
AK_CARB_1_LUEK00(t_k, s, p_bar)Arguments
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
Details
pH scale: Total
Value
K1 |
First dissociation constant of carbonic acid in mol/kg-SW |
Author(s)
Guy Munhoven and Jean-Marie Epitalon
References
Luecker et al. (2000) – also Handbook (2007), Millero (1979) pressure correction
Examples
AK_CARB_1_LUEK00(t_k=298,s=35, p_bar=0)
First dissociation constant of carbonic acid in mol/kg-SW from Millero et al. (1995)
Description
Calculates first dissociation constant of carbonic acid in mol/kg-SW on the SWS pH-scale.
Usage
AK_CARB_1_MILL95(t_k, s, p_bar)Arguments
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
Details
pH scale: SWS
Value
K1 |
First dissociation constant of carbonic acid in mol/kg-SW |
Author(s)
Guy Munhoven and Jean-Marie Epitalon
References
Millero (1995, eq 50 – ln K1(COM)), Millero (1982) pressure correction
Examples
AK_CARB_1_MILL95(t_k=298,s=35, p_bar=0)
First dissociation constant of carbonic acid in mol/kg-SW, from Roy et al.
Description
Calculates first dissociation constant of carbonic acid in mol/kg-SW on the total pH-scale, following Roy et al. (1993)
Usage
AK_CARB_1_ROYE93(t_k, s, p_bar)Arguments
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
Details
pH scale: Total
Value
K1 |
First dissociation constant of carbonic acid in mol/kg-SW |
Author(s)
Guy Munhoven and Jean-Marie Epitalon
References
Roy et al. (1993) – also Handbook (1994), Millero (1979) pressure correction
Examples
AK_CARB_1_ROYE93(t_k=298,s=35, p_bar=0)
Second dissociation constant of carbonic acid in mol/kg-SW from Luecker et al.
Description
Calculates second dissociation constant of carbonic acid in mol/kg-SW on the total pH-scale, following Luecker et al. (2000)
Usage
AK_CARB_2_LUEK00(t_k, s, p_bar)Arguments
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
Details
pH scale: Total
Value
K2 |
Second dissociation constant of carbonic acid in mol/kg-SW |
Author(s)
Guy Munhoven and Jean-Marie Epitalon
References
Luecker et al. (2000) – also Handbook (2007), Millero (1979) pressure correction
Examples
AK_CARB_2_LUEK00(t_k=298,s=35, p_bar=0)
Second dissociation constant of carbonic acid in mol/kg-SW from Millero et al. (1995)
Description
Calculates second dissociation constant of carbonic acid in mol/kg-SW on the SWS pH-scale.
Usage
AK_CARB_2_MILL95(t_k, s, p_bar)Arguments
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
Details
pH scale: SWS
Value
K2 |
Second dissociation constant of carbonic acid in mol/kg-SW |
Author(s)
Guy Munhoven and Jean-Marie Epitalon
References
Millero (1995, eq 51 – ln K2(COM)), Millero (1979) pressure correction
Examples
AK_CARB_2_MILL95(t_k=298,s=35, p_bar=0)
Second dissociation constant of carbonic acid in mol/kg-SW from Roy et al.
Description
Calculates second dissociation constant of carbonic acid in mol/kg-SW on the total pH-scale, following Roy et al. (1993)
Usage
AK_CARB_2_ROYE93(t_k, s, p_bar)Arguments
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
Details
pH scale: Total
Value
K2 |
Second dissociation constant of carbonic acid in mol/kg-SW |
Author(s)
Guy Munhoven and Jean-Marie Epitalon
References
Roy et al. (1993) – also Handbook (1994), Millero (1979) pressure correction
Examples
AK_CARB_2_ROYE93(t_k=298,s=35, p_bar=0)
Dissociation constant of hydrogen sulfide in sea-water
Description
Function returns the dissociation constant of hydrogen sulfide in sea-water
Usage
AK_H2S_1_MILL95(t_k, s, p_bar)Arguments
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
Details
pH scale: SWS (according to Yao and Millero, 1995, p. 82: "refitted if necessary")
Total (according to Lewis and Wallace, 1998)
We stick to SWS here for the time being
The fits from Millero (1995) and Yao and Millero (1995) derive from Millero et al. (1988), with all the coefficients multiplied by -ln(10)
Value
KHS |
Dissociation constant of hydrogen sulfide in mol/kg-SW |
Author(s)
Guy Munhoven and Jean-Marie Epitalon
References
Millero et al. (1988) (cited by Millero (1995), Millero (1995) for pressure correction
Examples
AK_H2S_1_MILL95(t_k=298,s=35, p_bar=0)
Dissociation constant of hydrogen fluoride in sea-water [mol/kg-SW]
Description
Function returns the dissociation constant of hydrogen fluoride [mol/kg-SW]
Usage
AK_HF_PEFR87(t_k, s, p_bar)Arguments
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
Details
pH scale: Total (according to Handbook, 2007)
Value
KHF |
Dissociation constant of hydrogen fluoride in mol/kg-SW |
Author(s)
Guy Munhoven and Jean-Marie Epitalon
References
Perez and Fraga (1987), Millero (1995) for pressure correction
Examples
AK_HF_PEFR87(t_k=298,s=35, p_bar=0)
Dissociation constant of hydrogen sulfate (bisulfate) in sea-water
Description
Function returns the dissociation constant of hydrogen sulfate [mol/kg-SW]
Usage
AK_HSO4_DICK90(t_k, s, p_bar)Arguments
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
Details
pH scale: Total (according to Handbook, 2007)
Value
KSO |
Dissociation constant of hydrogen sulfate in mol/kg-SW |
Author(s)
Guy Munhoven and Jean-Marie Epitalon
References
Dickson (1990) – also Handbook (2007), Millero (1995) for pressure correction
Examples
AK_HSO4_DICK90(t_k=298,s=35, p_bar=0)
First dissociation constant of phosphoric acid (H3PO4) in seawater
Description
Calculates first dissociation constant of phosphoric acid on the SWS pH-scale
Usage
AK_PHOS_1_MILL95(t_k, s, p_bar)Arguments
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
Details
pH scale: SWS
Value
KP1 |
First dissociation constant of phosphoric acid in mol/kg-SW |
Author(s)
Guy Munhoven and Jean-Marie Epitalon
References
Yao and Millero (1995), Millero (1995) for pressure correction
Examples
AK_PHOS_1_MILL95(t_k=298,s=35, p_bar=0)
Second dissociation constant of phosphoric acid (H3PO4) in seawater
Description
Calculates second dissociation constant of phosphoric acid on the SWS pH-scale
Usage
AK_PHOS_2_MILL95(t_k, s, p_bar)Arguments
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
Details
pH scale: SWS
Value
KP2 |
Second dissociation constant of phosphoric acid in mol/kg-SW |
Author(s)
Guy Munhoven and Jean-Marie Epitalon
References
Yao and Millero (1995), Millero (1995) for pressure correction
Examples
AK_PHOS_2_MILL95(t_k=298,s=35, p_bar=0)
Third dissociation constant of phosphoric acid (H3PO4) in seawater
Description
Calculates third dissociation constant of phosphoric acid on the SWS pH-scale
Usage
AK_PHOS_3_MILL95(t_k, s, p_bar)Arguments
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
Details
pH scale: SWS
Value
KP3 |
Third dissociation constant of phosphoric acid in mol/kg-SW |
Author(s)
Guy Munhoven and Jean-Marie Epitalon
References
Yao and Millero (1995), Millero (1995) for pressure correction
Examples
AK_PHOS_3_MILL95(t_k=298,s=35, p_bar=0)
First dissociation constant of sillicic acid (H4SiO4) in seawater
Description
Calculates first dissociation constant of sillicic acid on the SWS pH-scale
Usage
AK_SILI_1_MILL95(t_k, s)Arguments
t_k |
temperature in Kelvin |
s |
Salinity in psu |
Details
pH scale: SWS (according to Dickson et al, 2007)
No pressure correction available
Value
KSi |
First dissociation constant of sillicic acid in mol/kg-SW |
Author(s)
Guy Munhoven and Jean-Marie Epitalon
References
Yao and Millero (1995) cited by Millero (1995)
Examples
AK_SILI_1_MILL95(t_k=298,s=35)
Water dissociation constant Kw in (mol/kg-SW)^2
Description
Calculates water dissociation constant Kw in (mol/kg-SW)^2 on the SWS pH-scale
Usage
AK_W_MILL95(t_k, s, p_bar)Arguments
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
Details
pH scale: SWS
Value
Kw |
Dissociation constant of water in (mol/kg-SW^2 |
Author(s)
Guy Munhoven and Jean-Marie Epitalon
References
Millero (1995) for value at p_bar = 0, Millero (pers. comm. 1996) for pressure correction
Examples
AK_W_MILL95(t_k=298,s=35, p_bar=0)
Solver for the total alkalinity-pH equations
Description
Determines [H+] from Total alkalinity and dissolved total elements in sea water. Universal and robust algorithm from Munhoven (2013) with Newton- Raphson iterations
Usage
solve_pH_from_AT(p_alktot, p_dicvar, p_bortot, p_po4tot, p_siltot,
p_nh4tot, p_h2stot, p_so4tot, p_flutot, p_pHscale, p_dicsel,
p_askVal=FALSE, p_dissoc, p_temp=18, p_sal=35, p_pres=0, p_hini)Arguments
p_alktot |
Total alkalinity (mol/kg) |
p_dicvar |
Value of a carbonate system related variable : DIC, [CO2*], [HCO3-] or [CO3–] (mol/kg) See below parameter p_dicsel |
p_bortot |
Total boron concentration (mol/kg) |
p_po4tot |
Total phosphate concentration (mol/kg) |
p_siltot |
Total silicate concentration (mol/kg) |
p_nh4tot |
Total ammonia concentration (mol/kg) |
p_h2stot |
Total sulfide concentration (mol/kg) |
p_so4tot |
Total sulphate concentration (mol/kg) |
p_flutot |
Total fluor concentration (mol/kg) |
p_pHscale |
Chosen pH scale: "T" for the total scale, "F" for the free scale and "SWS" for using the seawater scale |
p_dicsel |
Carbonate variable selector (default = DIC). See parameter p_dicvar above. Values are: "DIC" : p_dicvar = DIC (Dissolved Inorganic Carbon) "CO2" : p_dicvar = [CO2*] "HCO3" : p_dicvar = [HCO3-] "CO3" : p_dicvar = [CO3–] |
p_askVal |
Optional boolean - set to TRUE if you want this function to return error on alkalinity, along with [H+] concentration value. Default is FALSE |
p_dissoc |
Named list of all dissociation constants. The list is optional but, if given, it should contain all members listed below excepted K2_Sil, which is itself optional. Member names are : K1_DIC : First dissociation constant of carbonic acid (mol/kg) on chosen scale K2_DIC : Second dissociation constant of carbonic acid (mol/kg) on chosen scale K_BT : Dissociation constant of boric acid (mol/kg) on chosen scale K1_PO4 : First dissociation constant of phosphoric acid (mol/kg) on chosen scale K2_PO4 : Second dissociation constant of phosphoric acid (mol/kg) on chosen scale K3_PO4 : third dissociation constant of phosphoric acid (mol/kg) on chosen scale K_Sil : First dissociation constant of sillicic acid (mol/kg) on chosen scale K2_Sil : Second dissociation constant of sillicic acid (mol/kg) on chosen scale. It is optional. If K2_Sil is absent from the list, then SiO2(OH)2 ion is not considered in the alkalinity equation. Only SiO(OH)3 ion is. K_NH4 : Dissociation constant of ammonium (mol/kg) on chosen scale K_H2S : Dissociation constant of hydrogen sulfide (mol/kg) on chosen scale K_HSO4 : Dissociation constant of hydrogen sulfate (mol/kg) on free scale K_HF : Dissociation constant of hydrogen fluoride (mol/kg) on free scale K_H2O : Dissociation constant of water (mol/kg) on chosen scale Note that all dissociation constants shall be expressed in chosen pH scale except K_HF and K_HSO4 which shall be in free scale. If the list is not given, these constants, excepted K2_Sil, will be calculated. |
p_temp |
Temperature in degree Celsius, to compute dissociation constants when p_dissoc is not given |
p_sal |
Salinity, in pratical salinty unit (psu), to compute dissociation constants when p_dissoc is not given |
p_pres |
Pressure, in bars, to compute dissociation constants when p_dissoc is not given |
p_hini |
Optional initial value of [H+] concentration If p_dicsel = "CO3", a vector of two initial values are expected since there may be two solutions for pH. Else, one initial value is expected |
Details
Formulations used when calculating dissociation constants:
Carbonate if Total pH scale: Luecker et al. (2000) – also Handbook (2007)
Carbonate if SWS or Free pH scale: Millero et al. (1995) – also Handbook (2007)
Boric acid: Dickson (1990, eq. 2 3) – also Handbook (2007, eq. 37)
Phosphoric acid: Yao and Millero (1995)
Silicic acid: Yao and Millero (1995) cited by Millero (1995)
Ammonium: Yao and Millero (1995)
Hydrogen sulfide: Millero et al. (1988) (cited by Millero (1995)
Hydrogen sulfate: Dickson (1990) – also Handbook (2007)
Fluoric acid if Total pH scale: Perez and Fraga (1987)
Fluoric acid if SWS or Free pH scale: Dickson and Riley (1979)
Water: Millero (1995)
This function does not support vectors as arguments, only scalar values.
Value
If p_dicsel is "CO3", there may be one or two solutions for [H+], else there is only one. In case there are two solutions, both are returned.
If you set p_askVal to TRUE, the function returns a data frame containing the following columns:
zh : [H+] concentration value(s) in the chosen pH scale
val : Error(s) on total alkalinity, that is the deviation between total alkalinity calculated from [H+] and given total alkalinity
If you set p_askVal to FALSE (default), the function returns only [H+] concentration value(s) in the chosen pH scale.
Author(s)
Guy Munhoven and Jean-Marie Epitalon
References
Munhoven G. Munhoven G. (2013) Mathematics of the total alkalinity-pH equation - pathway to robust and universal solution algorithms: the SolveSAPHE package v1.0.1. Geoscientif. Model Dev., 1367-1388
Examples
## Compute [H+] from Alkalinity total and DIC, on total pH scale
p_dissoc <- list()
p_dissoc$K1_DIC <- 1.421828e-06
p_dissoc$K2_DIC <- 1.081555e-09
p_dissoc$K_BT <- 2.526573e-09
p_dissoc$K1_PO4 <- 0.02408434
p_dissoc$K2_PO4 <- 1.076024e-06
p_dissoc$K3_PO4 <- 1.600484e-09
p_dissoc$K_Sil <- 4.071935e-10
p_dissoc$K_NH4 <- 5.380823e-10
p_dissoc$K_H2S <- 3.087264e-07
p_dissoc$K_HSO4 <- 0.1003021 # on free scale
p_dissoc$K_HF <- 0.00176441 # on free scale
p_dissoc$K_H2O <- 5.97496e-14
solve_pH_from_AT(p_alktot=2.5e-3, p_dicvar=2e-3, p_bortot=0.0004157, p_po4tot=0, p_siltot=0,
p_nh4tot=0, p_h2stot=0, p_so4tot=0.0282, p_flutot=6.832e-05, p_pHscale="T",
p_dicsel="DIC", p_dissoc=p_dissoc)
## Giving inital [H+] value and asking for final error on alkalinity, on seawater pH scale
result <- solve_pH_from_AT(p_alktot=0.00234, p_dicvar=0.001936461, p_bortot=0.0004157, p_po4tot=0,
p_siltot=0, p_nh4tot=0, p_h2stot=0, p_so4tot=0.0282, p_flutot=6.832e-05,
p_pHscale="SWS",p_dicsel="DIC", p_dissoc=p_dissoc, p_askVal=TRUE, p_hini=1.e-8)
H <- result$zh
error <- result$val
## Compute [H+] from Alkalinity total and CO3, on total free scale
H <- solve_pH_from_AT(p_alktot=0.00240, p_dicvar=2.775481e-04, p_bortot=0.0004157, p_po4tot=0,
p_siltot=0, p_nh4tot=0, p_h2stot=0, p_so4tot=0.0282, p_flutot=6.832e-05,
p_pHscale="F", p_dicsel="CO3", FALSE, p_dissoc=p_dissoc)
H1 <- H[1]
if (H[2] != 1) print ( c("Second solution : ", H[2]))