# TAfit 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) ```r 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? ## Returns 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) ## Examples ```r ## 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) ``` ## Author(s) Andreas F. Hofmann. Maintained by Karline Soetaert (Karline.Soetaert@nioz.nl).

TAfit function