| TAfit {AquaEnv} | R Documentation |
TAfit
Description
PUBLIC function: calculates [TA] and [SumCO2] (and optionally K\_C02 and E0) from a titration curve using an optimization procedure (nls.lm from R package minpack.lm)
Usage
TAfit(ae, titcurve, conc_titrant, mass_sample, S_titrant=NULL,
TASumCO2guess=0.0025, E0guess=0.4, type="HCl", Evals=FALSE,
electrode_polarity="pos", K_CO2fit=FALSE,
equalspaced=TRUE, seawater_titrant=FALSE,
pHscale="free", debug=FALSE, k_w=NULL, k_co2=NULL, k_hco3=NULL,
k_boh3=NULL, k_hso4=NULL, k_hf=NULL,
nlscontrol=nls.lm.control(), verbose=FALSE,
k1k2="roy", khf="dickson", datxbegin=0, SumCO2Zero=FALSE)Arguments
ae |
an object of type aquaenv: minimal definition, contains all information about the system: T, S, d, total concentrations of nutrients etc (Note that it is possible to give values for SumBOH4, SumHSO4, and SumHF in the sample other than the ones calculated from salinity) |
titcurve |
a table containing the titration curve: basically a series of tuples of added titrant solution mass and pH values (pH on free proton scale) or E values in V |
conc_titrant |
concentration of the titrant solution in mol/kg-soln |
mass_sample |
the mass of the sample solution in kg |
S_titrant |
the salinity of the titrant solution, if not supplied it is assumed that the titrant solution has the same salinity as the sample solution |
TASumCO2guess |
a first guess for [TA] and [SumCO2] to be used as initial values for the optimization procedure |
E0guess |
first guess for E0 in V |
type |
the type of titrant: either "HCl" or "NaOH" |
Evals |
are the supplied datapoints pH or E (V) values? |
electrode_polarity |
either "pos" or "neg": how is the polarity of the Electrode: E = E0 -(RT/F)ln(H+) ("pos") or -E = E0 -(RT/F)ln(H+) ("neg")? |
K_CO2fit |
should K\_CO2 be fitted as well? |
equalspaced |
are the mass values of titcurve equally spaced? |
seawater_titrant |
is the titrant based on natural seawater? (does it contain SumBOH4, SumHSO4, and SumHF in the same proportions as seawater, i.e., correlated to S?); Note that you can only assume a seawater based titrant (i.e. SumBOH4, SumHSO4, and SumHF ~ S) or a water based titrant (i.e. SumBOH4, SumHSO4, and SumHF = 0). It is not possible to give values for SumBOH4, SumHSO4, and SumHF of the titrant. |
pHscale |
either "free", "total", "sws" or "nbs": if the titration curve contains pH data: on which scale is it measured? |
debug |
debug mode: the last simulated titration tit, the converted pH profile calc, and the nls.lm output out are made global variables for investigation and plotting |
k_w |
a fixed K\_W can be specified |
k_co2 |
a fixed K\_CO2 can be specified; used for TA fitting: give a K\_CO2 and NOT calculate it from T and S: i.e. K\_CO2 can be fitted in the routine as well |
k_hco3 |
a fixed K\_HCO3 can be specified |
k_boh3 |
a fixed K\_BOH3 can be specified |
k_hso4 |
a fixed K\_HSO4 can be specified |
k_hf |
a fixed K\_HF can be specified |
nlscontrol |
nls.lm.control() can be specified |
verbose |
verbose mode: show the traject of the fitting in a plot |
k1k2 |
either "roy" (default, Roy1993a) or "lueker" (Lueker2000) for K\_CO2 and K\_HCO3. |
khf |
either "dickson" (default, Dickson1979a) or "perez" (Perez1987a) for K\_HF |
datxbegin |
at what x value (amount of titrant added) does the supplied curve start? (i.e. is the complete curve supplied or just a part?) |
SumCO2Zero |
should SumCO2==0? |
Value
a list of up to five values ([TA] in mol/kg-solution, [SumCO2] in mol/kg-solution, E0 in V, K1 in mol/kg-solution and on free scale, sum of the squared residuals)
Author(s)
Andreas F. Hofmann. Maintained by Karline Soetaert (Karline.Soetaert@nioz.nl).
Examples
## Not run:
####################################
# Calculating TA from titration data
####################################
#### 1.) proof of concept ##########
####################################
####################################
# generate "data":
S <- 35
t <- 15
SumCO2 <- 0.002000
TA <- 0.002200
initial_ae <- aquaenv(S=S, t=t, SumCO2=SumCO2, TA=TA)
mass_sample <- 0.01 # the mass of the sample solution in kg
mass_titrant <- 0.003 # the total mass of the added titrant solution
# in kg
conc_titrant <- 0.01 # the concentration of the titrant solution in
# mol/kg-soln
S_titrant <- 0.5 # the salinity of the titrant solution (the
# salinity of a solution with a ionic strength
# of 0.01 according to:
# I = (19.924 S) / (1000 - 1.005 S)
steps <- 20 # the amount of steps the mass of titrant is
# added in
type <- "HCl"
ae <- titration(initial_ae, mass_sample, mass_titrant, conc_titrant,
S_titrant, steps, type)
plot(ae, ae$delta_mass_titrant, what="pH", newdevice=FALSE)
# the input data for the TA fitting routine: a table with the added
# mass of the titrant and the resulting free scale pH
titcurve <- cbind(ae$delta_mass_titrant, ae$pH)
# for the TA fitting procedure all total quantities except SumCO2
# (SumNH4, SumH2S, SumH3PO4, SumSiOH4, SumHNO3, SumHNO2, SumBOH3,
# SumH2SO4, SumHF) need to be known. However, the latter three
# can be calculated from salinity as it is done in this example.
fit1 <- TAfit(initial_ae, titcurve, conc_titrant, mass_sample,
S_titrant)
fit1
# E (V) values as input variables: generate E values using
# E0=0.4 V and the nernst equation
tottitcurve <- convert(titcurve[,2], "pHscale", "free2sws", S=S,
t=t)
# (Nernst equation relates E to TOTAL [H+] (DOE1994, p.7,
# ch.4, sop.3), BUT, if fluoride is present, its SWS, so
# we use SWS!
Etitcurve <- cbind(titcurve[,1], (0.4 - ((PhysChemConst$R/10)
*initial_ae$T/PhysChemConst$F)
*log(10^-tottitcurve))) # Nernst equation
fit2 <- TAfit(initial_ae, Etitcurve, conc_titrant, mass_sample,
S_titrant, Evals=TRUE, verbose=TRUE)
fit2
# k_co2 fitting: one K_CO2 (k_co2) for the whole titration curve
# is fitted, i.e. there is NO correction for K_CO2 changes due to
# changing S due to mixing with the titrant
fit3 <- TAfit(initial_ae, titcurve, conc_titrant, mass_sample,
S_titrant, K_CO2fit=TRUE)
fit3
# assume the titrant has the same salinity as the sample
# (and is made up of natural seawater, i.e. containing SumBOH4,
# SumH2SO4 and SumHF as functions of S), then the "right" K_CO2
# should be fitted i.e we do NOT give the argument S_titrant
# and set the flag seawater_titrant to TRUE
ae <- titration(initial_ae, mass_sample, mass_titrant,
conc_titrant, steps=steps, type=type,
seawater_titrant=TRUE)
titcurve <- cbind(ae$delta_mass_titrant, ae$pH)
fit4 <- TAfit(initial_ae, titcurve, conc_titrant, mass_sample,
K_CO2fit=TRUE, seawater_titrant=TRUE)
fit4
# fitting of TA, SumCO2, K_CO2 and E0
Etitcurve <- cbind(titcurve[,1], (0.4 - ((PhysChemConst$R/10)
*initial_ae$T/PhysChemConst$F)
*log(10^-titcurve[,2])))
fit5 <- TAfit(initial_ae, Etitcurve, conc_titrant, mass_sample,
K_CO2fit=TRUE, seawater_titrant=TRUE, Evals=TRUE)
fit5
# fitting of non equally spaced data:
neqsptitcurve <- rbind(titcurve[1:9,], titcurve[11:20,])
fit6 <- TAfit(initial_ae, neqsptitcurve, conc_titrant,
mass_sample, seawater_titrant=TRUE,
equalspaced=FALSE)
fit6
#add some "noise" on the generated data
noisetitcurve <- titcurve * rnorm(length(titcurve),
mean=1, sd=0.01) #one percent error possible
plot(ae, ae$delta_mass_titrant, what="pH", type="l", col="red",
xlim=c(0,0.003), ylim=c(3,8.1), newdevice=FALSE)
par(new=TRUE)
plot(noisetitcurve[,1],noisetitcurve[,2], type="l",
xlim=c(0,0.003), ylim=c(3,8.1))
fit7 <- TAfit(initial_ae, noisetitcurve, conc_titrant,
mass_sample, seawater_titrant=TRUE)
fit7
# 2.) test with generated data from Dickson1981 #
#################################################
#################################################
conc_titrant = 0.3 # mol/kg-soln
mass_sample = 0.2 # kg
S_titrant = 14.835 # is aequivalent to the ionic strength
# of 0.3 mol/kg-soln
SumBOH3 = 0.00042 # mol/kg-soln
SumH2SO4 = 0.02824 # mol/kg-soln
SumHF = 0.00007 # mol/kg-soln
# convert mass of titrant from g to kg
sam <- cbind(sample_dickson1981[,1]/1000, sample_dickson1981[,2])
dicksonfit <- TAfit(aquaenv(t=25, S=35, SumBOH3=SumBOH3,
SumH2SO4=SumH2SO4, SumHF=SumHF), sam,
conc_titrant, mass_sample,
S_titrant=S_titrant, debug=TRUE)
dicksonfit
#TA Dickson1981: 0.00245
#SumCO2 Dickson1981: 0.00220
# => not exactly the same! why?
# a.) does salinity correction (S_titrant) matter or not?
##########################################################
# without salinity correction
dicksontitration1 <- titration(aquaenv(t=25, S=35, SumCO2=0.00220,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4,
SumHF=SumHF, TA=0.00245),
mass_sample=mass_sample,
mass_titrant=0.0025,
conc_titrant=conc_titrant,
steps=50, type="HCl")
# with salinity correction
dicksontitration2 <- titration(aquaenv(t=25, S=35, SumCO2=0.00220,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4,
SumHF=SumHF, TA=0.00245),
mass_sample=mass_sample,
mass_titrant=0.0025,
conc_titrant=conc_titrant,
S_titrant=S_titrant,
steps=50, type="HCl")
plot(dicksontitration1, xval=dicksontitration1$delta_mass_titrant,
what="pH", xlim=c(0,0.0025), ylim=c(3,8.2), newdevice=FALSE,
col="red")
par(new=TRUE)
plot(dicksontitration2, xval=dicksontitration2$delta_mass_titrant,
what="pH", xlim=c(0,0.0025), ylim=c(3,8.2), newdevice=FALSE,
col="blue")
par(new=TRUE)
plot(sam[,1], sam[,2], type="l", xlim=c(0,0.0025), ylim=c(3,8.2))
# => salinity correction makes NO difference, because the relation
# between total sample and added titrant is very large:
# salinity only drops from 35 to 34.75105
#BUT: there is an offset between the "Dickson" curve and our curve:
plot(dicksontitration2$pH - sam[,2])
# b.) does it get better if we fit K_CO2 as well?
#################################################
dicksonfit2 <- TAfit(aquaenv(t=25, S=35, SumBOH3=SumBOH3,
SumH2SO4=SumH2SO4, SumHF=SumHF), sam,
conc_titrant, mass_sample,
S_titrant=S_titrant, debug=TRUE,
K_CO2fit=TRUE)
dicksonfit2
#TA Dickson1981: 0.00245
#SumCO2 Dickson1981: 0.00220
# => yes it does, but it is not perfect yet!
# c.) differing K values
#########################
# Dickson uses fixed K values that are slightly different than ours
dicksontitration3 <- titration(aquaenv(t=25, S=35, SumCO2=0.00220,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4,
SumHF=SumHF, TA=0.00245, k_w=4.32e-14,
k_co2=1e-6, k_hco3=8.20e-10,
k_boh3=1.78e-9, k_hso4=(1/1.23e1),
k_hf=(1/4.08e2)),
mass_sample=mass_sample,
mass_titrant=0.0025,
conc_titrant=conc_titrant,
steps=50, type="HCl",
S_titrant=S_titrant, k_w=4.32e-14,
k_co2=1e-6, k_hco3=8.20e-10,
k_boh3=1.78e-9, k_hso4=(1/1.23e1),
k_hf=(1/4.08e2))
plot(dicksontitration3, xval=dicksontitration3$delta_mass_titrant,
what="pH", xlim=c(0,0.0025), ylim=c(3,8.2), newdevice=FALSE,
col="blue")
par(new=TRUE)
plot(sam[,1], sam[,2], type="l", xlim=c(0,0.0025), ylim=c(3,8.2))
plot(dicksontitration3$pH - sam[,2])
# => no offset between the pH curves
# => exactly the same curves!
dicksonfit3 <- TAfit(aquaenv(t=25, S=35, SumBOH3=SumBOH3,
SumH2SO4=SumH2SO4, SumHF=SumHF, k_w=4.32e-14,
k_co2=1e-6, k_hco3=8.20e-10, k_boh3=1.78e-9,
k_hso4=(1/1.23e1), k_hf=(1/4.08e2)),
sam, conc_titrant, mass_sample,
S_titrant=S_titrant, debug=TRUE,
k_w=4.32e-14, k_co2=1e-6, k_hco3=8.20e-10,
k_boh3=1.78e-9, k_hso4=(1/1.23e1),
k_hf=(1/4.08e2))
dicksonfit3
# PERFECT fit!
plot(sam[,1], sam[,2], xlim=c(0,0.0025), ylim=c(3,8.2), type="l")
par(new=TRUE)
plot(tit$delta_mass_titrant, calc, xlim=c(0,0.0025), ylim=c(3,8.2),
type="l", col="red")
## End(Not run)