R/Ks.R

In seacarb: Calculates parameters of the seawater carbonate system

# Copyright (C) 2008 Jean-Pierre Gattuso and Héloïse Lavigne and Aurélien Proye
#
# 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
#
#
"Ks" <-
function(S=35,T=25,P=0){

nK <- max(length(S), length(T), length(P))

##-------- Creation de vecteur pour toutes les entrees (si vectorielles)

if(length(S)!=nK){S <- rep(S[1], nK)}
if(length(T)!=nK){T <- rep(T[1], nK)}
if(length(P)!=nK){P <- rep(P[1], nK)}


#-------Constantes----------------

#---- issues de equic----
tk = 273.15;           # [K] (for conversion [deg C] <-> [K])
TK = T + tk;           # T [C]; TK [K]
Cl = S / 1.80655;      # Cl = chlorinity; S = salinity (per mille)
cl3 = Cl^(1/3);   
ION = 0.00147 + 0.03592 * Cl + 0.000068 * Cl * Cl;   # ionic strength
iom0 = 19.924*S/(1000-1.005*S);
ST = 0.14/96.062/1.80655*S;   # (mol/kg soln) total sulfate


bor = (416.*(S/35.))* 1e-6;   # (mol/kg), DOE94  

	#--------------------------------------------------------------
	#------------------ Ks ----------------------------------------
	#       Dickson (1990)
	#     
	#       Equilibrium constant for HSO4- = H+ + SO4--
	#
	#       K_S  = [H+]free [SO4--] / [HSO4-]
	#       pH-scale: free scale !!!
	#
	#       the term log(1-0.001005*S) converts from
	#       mol/kg H2O to mol/kg soln
	
	
	tmp1 = -4276.1 / TK + 141.328 -23.093*log(TK);
	tmp2 = +(-13856 / TK + 324.57 - 47.986 * log(TK))*sqrt(iom0);
	tmp3 = +(35474 / TK - 771.54 + 114.723 * log(TK))*iom0;
	tmp4 = -2698 / TK *(sqrt(iom0)*iom0) + 1776 / TK *iom0 *iom0;
	                                       
	
	lnKs = tmp1 + tmp2 + tmp3 + tmp4 + log(1-0.001005*S);
		
	Ks = exp(lnKs);

# ------------------- Pression effect --------------------------------
for(i in (1:nK)){

if (P[i] > 0.0)
{
		
	RGAS = 8.314510;        # J mol-1 deg-1 (perfect Gas)  
	R = 83.14472;             # mol bar deg-1 
	                        # conversion cm3 -> m3          *1.e-6
        	                  #            bar -> Pa = N m-2  *1.e+5
	                        #                => *1.e-1 or *1/10
		
		
	# index: K1 1, K2 2, Kb 3, Kw 4, Ks 5, Kf 6, Kspc 7, Kspa 8,
	#        K1P 9, K2P 10, K3P 11
	
	#----- note: there is an error in Table 9 of Millero, 1995.
	#----- The coefficients -b0 and b1
	#----- have to be multiplied by 1.e-3!

	#----- there are some more errors! 
	#----- the signs (+,-) of coefficients in Millero 95 do not
	#----- agree with Millero 79
	
		
		
	a0 = c(-25.5, -15.82, -29.48, -25.60, -18.03, -9.78, -48.76, -46, -14.51, -23.12, -26.57);
	a1 = c(0.1271, -0.0219, 0.1622, 0.2324, 0.0466, -0.0090, 0.5304, 0.5304, 0.1211, 0.1758, 0.2020);
	a2 = c(0.0, 0.0, 2.608*1e-3, -3.6246*1e-3, 0.316*1e-3, -0.942*1e-3, 0.0, 0.0, -0.321*1e-3, -2.647*1e-3, -3.042*1e-3);
	b0 = c(-3.08*1e-3, 1.13*1e-3, -2.84*1e-3, -5.13*1e-3, -4.53*1e-3, -3.91*1e-3, -11.76*1e-3, -11.76*1e-3, -2.67*1e-3, -5.15*1e-3, -4.08*1e-3);
	b1 = c(0.0877*1e-3, -0.1475*1e-3, 0.0, 0.0794*1e-3, 0.09*1e-3, 0.054*1e-3, 0.3692*1e-3, 0.3692*1e-3, 0.0427*1e-3, 0.09*1e-3, 0.0714*1e-3);
	b2 = c(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0);
	
	deltav = c(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0);
	deltak = c(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0);
	lnkpok0 = c(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0);
	
	for (ipc in 1:length(a0))
	{
	  deltav[ipc]  =  a0[ipc] + a1[ipc] *T[i] + a2[ipc] *T[i]*T[i];
	  deltak[ipc]   = (b0[ipc]  + b1[ipc] *T[i] + b2[ipc] *T[i]*T[i]);  
	  lnkpok0[ipc]  = -(deltav[ipc] /(R*TK[i]))*P[i] + (0.5*deltak[ipc] /(R*TK[i]))*P[i]*P[i];
	}

	Ks[i] <- Ks[i]*exp(lnkpok0[5])
}
}
attr(Ks,"unit") = "mol/kg-soln"	
attr(Ks,"pH scale") = "free scale"
return(Ks)
}