| Title: | Solver Suite for Alkalinity-PH Equations |
|---|---|
| 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>. |
| Authors: | Jean-Marie Epitalon [aut, cre, cph], Jean-Pierre Gattuso [cph], Guy Munhoven [aut] |
| Maintainer: | Jean-Marie Epitalon <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 2.1.0 |
| Built: | 2024-12-19 06:40:32 UTC |
| Source: | CRAN |
Function returns the ratio H_SWS/H_free as a function of temperature, salinity and pressure
ACVT_HSWS_O_HFREE(t_k, s, p_bar)ACVT_HSWS_O_HFREE(t_k, s, p_bar)
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
ratio |
Ratio H_SWS/H_free |
Guy Munhoven and Jean-Marie Epitalon
ACVT_HSWS_O_HFREE(t_k=298,s=35, p_bar=0)ACVT_HSWS_O_HFREE(t_k=298,s=35, p_bar=0)
Function returns the ratio H_Tot/H_free as a function of temperature, salinity and pressure
ACVT_HTOT_O_HFREE(t_k, s, p_bar)ACVT_HTOT_O_HFREE(t_k, s, p_bar)
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
ratio |
Ratio H_Tot/H_free |
Guy Munhoven and Jean-Marie Epitalon
ACVT_HTOT_O_HFREE(t_k=298,s=35, p_bar=0)ACVT_HTOT_O_HFREE(t_k=298,s=35, p_bar=0)
Function returns the dissociation constant of ammonium in sea-water [mol/kg-SW]
AK_AMMO_1_YAMI95(t_k, s, p_bar)AK_AMMO_1_YAMI95(t_k, s, p_bar)
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
pH scale: SWS
KNH |
Dissociation constant of ammonium in mol/kg-SW |
Guy Munhoven and Jean-Marie Epitalon
Yao and Millero (1995), Millero (1995) for pressure correction
AK_AMMO_1_YAMI95(t_k=298,s=35, p_bar=0)AK_AMMO_1_YAMI95(t_k=298,s=35, p_bar=0)
Calculates boric acid dissociation constant in mol/kg-SW on the total pH-scale
AK_BORA_DICK90(t_k, s, p_bar)AK_BORA_DICK90(t_k, s, p_bar)
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
pH scale: Total
KB |
Dissociation constant of boric acid in mol/kg-SW |
Guy Munhoven and Jean-Marie Epitalon
Dickson (1990, eq. 23) – also Handbook (2007, eq. 37), Millero (1979) pressure correction
AK_BORA_DICK90(t_k=298,s=35, p_bar=0)AK_BORA_DICK90(t_k=298,s=35, p_bar=0)
Calculates Henry's constant (K0) based on Weiss (1979) formulation
AK_CARB_0_WEIS74(t_k, s)AK_CARB_0_WEIS74(t_k, s)
t_k |
temperature in Kelvin |
s |
Salinity in psu |
currently no pressure correction
K0 |
Henry's constant mol/(kg/atm) |
Guy Munhoven and Jean-Marie Epitalon
Weiss R. F., 1974 Carbon dioxide in water and seawater: the solubility of a non-ideal gas. Marine Chemistry 2, 203-215.
AK_CARB_0_WEIS74(t_k=298,s=35)AK_CARB_0_WEIS74(t_k=298,s=35)
Calculates first dissociation constant of carbonic acid in mol/kg-SW on the total pH-scale, following Luecker et al. (2000)
AK_CARB_1_LUEK00(t_k, s, p_bar)AK_CARB_1_LUEK00(t_k, s, p_bar)
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
pH scale: Total
K1 |
First dissociation constant of carbonic acid in mol/kg-SW |
Guy Munhoven and Jean-Marie Epitalon
Luecker et al. (2000) – also Handbook (2007), Millero (1979) pressure correction
AK_CARB_1_LUEK00(t_k=298,s=35, p_bar=0)AK_CARB_1_LUEK00(t_k=298,s=35, p_bar=0)
Calculates first dissociation constant of carbonic acid in mol/kg-SW on the SWS pH-scale.
AK_CARB_1_MILL95(t_k, s, p_bar)AK_CARB_1_MILL95(t_k, s, p_bar)
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
pH scale: SWS
K1 |
First dissociation constant of carbonic acid in mol/kg-SW |
Guy Munhoven and Jean-Marie Epitalon
Millero (1995, eq 50 – ln K1(COM)), Millero (1982) pressure correction
AK_CARB_1_MILL95(t_k=298,s=35, p_bar=0)AK_CARB_1_MILL95(t_k=298,s=35, p_bar=0)
Calculates first dissociation constant of carbonic acid in mol/kg-SW on the total pH-scale, following Roy et al. (1993)
AK_CARB_1_ROYE93(t_k, s, p_bar)AK_CARB_1_ROYE93(t_k, s, p_bar)
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
pH scale: Total
K1 |
First dissociation constant of carbonic acid in mol/kg-SW |
Guy Munhoven and Jean-Marie Epitalon
Roy et al. (1993) – also Handbook (1994), Millero (1979) pressure correction
AK_CARB_1_ROYE93(t_k=298,s=35, p_bar=0)AK_CARB_1_ROYE93(t_k=298,s=35, p_bar=0)
Calculates second dissociation constant of carbonic acid in mol/kg-SW on the total pH-scale, following Luecker et al. (2000)
AK_CARB_2_LUEK00(t_k, s, p_bar)AK_CARB_2_LUEK00(t_k, s, p_bar)
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
pH scale: Total
K2 |
Second dissociation constant of carbonic acid in mol/kg-SW |
Guy Munhoven and Jean-Marie Epitalon
Luecker et al. (2000) – also Handbook (2007), Millero (1979) pressure correction
AK_CARB_2_LUEK00(t_k=298,s=35, p_bar=0)AK_CARB_2_LUEK00(t_k=298,s=35, p_bar=0)
Calculates second dissociation constant of carbonic acid in mol/kg-SW on the SWS pH-scale.
AK_CARB_2_MILL95(t_k, s, p_bar)AK_CARB_2_MILL95(t_k, s, p_bar)
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
pH scale: SWS
K2 |
Second dissociation constant of carbonic acid in mol/kg-SW |
Guy Munhoven and Jean-Marie Epitalon
Millero (1995, eq 51 – ln K2(COM)), Millero (1979) pressure correction
AK_CARB_2_MILL95(t_k=298,s=35, p_bar=0)AK_CARB_2_MILL95(t_k=298,s=35, p_bar=0)
Calculates second dissociation constant of carbonic acid in mol/kg-SW on the total pH-scale, following Roy et al. (1993)
AK_CARB_2_ROYE93(t_k, s, p_bar)AK_CARB_2_ROYE93(t_k, s, p_bar)
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
pH scale: Total
K2 |
Second dissociation constant of carbonic acid in mol/kg-SW |
Guy Munhoven and Jean-Marie Epitalon
Roy et al. (1993) – also Handbook (1994), Millero (1979) pressure correction
AK_CARB_2_ROYE93(t_k=298,s=35, p_bar=0)AK_CARB_2_ROYE93(t_k=298,s=35, p_bar=0)
Function returns the dissociation constant of hydrogen sulfide in sea-water
AK_H2S_1_MILL95(t_k, s, p_bar)AK_H2S_1_MILL95(t_k, s, p_bar)
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
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)
KHS |
Dissociation constant of hydrogen sulfide in mol/kg-SW |
Guy Munhoven and Jean-Marie Epitalon
Millero et al. (1988) (cited by Millero (1995), Millero (1995) for pressure correction
AK_H2S_1_MILL95(t_k=298,s=35, p_bar=0)AK_H2S_1_MILL95(t_k=298,s=35, p_bar=0)
Function returns the dissociation constant of hydrogen fluoride [mol/kg-SW]
AK_HF_PEFR87(t_k, s, p_bar)AK_HF_PEFR87(t_k, s, p_bar)
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
pH scale: Total (according to Handbook, 2007)
KHF |
Dissociation constant of hydrogen fluoride in mol/kg-SW |
Guy Munhoven and Jean-Marie Epitalon
Perez and Fraga (1987), Millero (1995) for pressure correction
AK_HF_PEFR87(t_k=298,s=35, p_bar=0)AK_HF_PEFR87(t_k=298,s=35, p_bar=0)
Function returns the dissociation constant of hydrogen sulfate [mol/kg-SW]
AK_HSO4_DICK90(t_k, s, p_bar)AK_HSO4_DICK90(t_k, s, p_bar)
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
pH scale: Total (according to Handbook, 2007)
KSO |
Dissociation constant of hydrogen sulfate in mol/kg-SW |
Guy Munhoven and Jean-Marie Epitalon
Dickson (1990) – also Handbook (2007), Millero (1995) for pressure correction
AK_HSO4_DICK90(t_k=298,s=35, p_bar=0)AK_HSO4_DICK90(t_k=298,s=35, p_bar=0)
Calculates first dissociation constant of phosphoric acid on the SWS pH-scale
AK_PHOS_1_MILL95(t_k, s, p_bar)AK_PHOS_1_MILL95(t_k, s, p_bar)
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
pH scale: SWS
KP1 |
First dissociation constant of phosphoric acid in mol/kg-SW |
Guy Munhoven and Jean-Marie Epitalon
Yao and Millero (1995), Millero (1995) for pressure correction
AK_PHOS_1_MILL95(t_k=298,s=35, p_bar=0)AK_PHOS_1_MILL95(t_k=298,s=35, p_bar=0)
Calculates second dissociation constant of phosphoric acid on the SWS pH-scale
AK_PHOS_2_MILL95(t_k, s, p_bar)AK_PHOS_2_MILL95(t_k, s, p_bar)
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
pH scale: SWS
KP2 |
Second dissociation constant of phosphoric acid in mol/kg-SW |
Guy Munhoven and Jean-Marie Epitalon
Yao and Millero (1995), Millero (1995) for pressure correction
AK_PHOS_2_MILL95(t_k=298,s=35, p_bar=0)AK_PHOS_2_MILL95(t_k=298,s=35, p_bar=0)
Calculates third dissociation constant of phosphoric acid on the SWS pH-scale
AK_PHOS_3_MILL95(t_k, s, p_bar)AK_PHOS_3_MILL95(t_k, s, p_bar)
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
pH scale: SWS
KP3 |
Third dissociation constant of phosphoric acid in mol/kg-SW |
Guy Munhoven and Jean-Marie Epitalon
Yao and Millero (1995), Millero (1995) for pressure correction
AK_PHOS_3_MILL95(t_k=298,s=35, p_bar=0)AK_PHOS_3_MILL95(t_k=298,s=35, p_bar=0)
Calculates first dissociation constant of sillicic acid on the SWS pH-scale
AK_SILI_1_MILL95(t_k, s)AK_SILI_1_MILL95(t_k, s)
t_k |
temperature in Kelvin |
s |
Salinity in psu |
pH scale: SWS (according to Dickson et al, 2007)
No pressure correction available
KSi |
First dissociation constant of sillicic acid in mol/kg-SW |
Guy Munhoven and Jean-Marie Epitalon
Yao and Millero (1995) cited by Millero (1995)
AK_SILI_1_MILL95(t_k=298,s=35)AK_SILI_1_MILL95(t_k=298,s=35)
Calculates water dissociation constant Kw in (mol/kg-SW)^2 on the SWS pH-scale
AK_W_MILL95(t_k, s, p_bar)AK_W_MILL95(t_k, s, p_bar)
t_k |
temperature in Kelvin |
s |
Salinity in psu |
p_bar |
pressure in bar |
pH scale: SWS
Kw |
Dissociation constant of water in (mol/kg-SW^2 |
Guy Munhoven and Jean-Marie Epitalon
Millero (1995) for value at p_bar = 0, Millero (pers. comm. 1996) for pressure correction
AK_W_MILL95(t_k=298,s=35, p_bar=0)AK_W_MILL95(t_k=298,s=35, p_bar=0)
Determines [H+] from Total alkalinity and dissolved total elements in sea water. Universal and robust algorithm from Munhoven (2013) with Newton- Raphson iterations
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)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)
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 |
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.
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.
Guy Munhoven and Jean-Marie Epitalon
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
## 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]))## 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]))