# Copyright (C) 2024 James Orr
# This file is part of seacarb.
# Seacarb is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or any later version.
# Seacarb is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along with seacarb; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
#
# Convert pHSWS to pHNBS using the total hydrogen ion activity coefficient, which depends on T and S
pHsws2nbs <- function(pHSWS, S=35, T=25){
# --------------------------------------------------------------------------------------------------------------
# phSWS = -log10([H+]sws) #pH on the SWS scale (-log10 of the concentration)
# pHNBS = -log10(ah) #pH on the NBS scale (-log10 of the activity, not the concentration)
#
# Note:
# -----
# ah = fH * [H+]sws
# where ah is the activity of hydrogen ion,
# fH is the total activity coefficient, and
# [H+]sws = [H+] + [HSO4-] + [HF], or in other words "the hydrogen ion conccentration on the seawater scale"
# --------------------------------------------------------------------------------------------------------------
#
# The SWS-to-NBS conversion is done with the total activity coefficient fH (combined activity coeff for H+, HSO4-, and HF)
# from Takahashi (1982) based on data from Culberson and Pytkowicz (1973). The approach is old and full of uncertainty.
# Newer approaches are more complicated (Pitzer equations) and big uncertainties remain (Marion et al., 2011; Pilson, 2013).
#
# Culberson, CH, & Pytkowicz, RM (1973). Ionization of water in seawater. Marine Chemistry, 1(4), 309-316.
#
# Marion GM, Millero FJ, Camoes MF, Spitzer P, Feistel R, Chen CTA. 2011. pH of seawater. Marine Chemistry 126: 89-96
#
# Pilson MEQ. 2013. An introduction to the chemistry of the sea, 2 edn. Cambridge, UK: Cambridge University Press.
#
# Takahashi, T. et al (1982). Carbonate chemistry. GEOSECS Pacific Expedition, Volume 3, Hydrographic Data 1973-1974, 77-83.
hSWS <- 10^(-pHSWS)
ah <- fH(S=S, T=T) * hSWS
pHNBS <- -log10(ah)
return(pHNBS)
}
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