R/K3p.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
#
#
"K3p" <-
function(S=35,T=25,P=0,pHscale="T"){

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

##-------- 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)}
if(length(pHscale)!=nK){pHscale <- rep(pHscale[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   

	# --------------------- Phosphoric acid ---------------------
	#
	#   Guide to Best Practices in Ocean CO2 Measurements 2007 Chap 5 p 15 
	#  
	#   Ch.5 p. 15
	#
		
	lnK3P = -3070.75 / TK - 18.141 + (17.27039 / TK + 2.81197) * sqrt(S) + (-44.99486 / TK - 0.09984) * S;
	
	K3P = exp(lnK3P);
	
	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];
		}
		

		K3P[i] = K3P[i]*exp(lnkpok0[11]);
		
	}
}

###----------------pH scale corrections
factor <- rep(NA,nK)
pHsc <- rep(NA,nK)
for(i in (1:nK)){   
 if(pHscale[i]=="T"){factor[i] <- 1 ; pHsc[i] <- "total scale"}
 if(pHscale[i]=="F"){factor[i] <- kconv(S=S[i], T=T[i], P=P[i])$ktotal2free ; pHsc[i] <- "free scale"}
 if(pHscale[i]=="SWS"){factor[i] <- kconv(S=S[i], T=T[i], P=P[i])$ktotal2SWS ; pHsc[i] <- "seawater scale"}
K3P[i] <- K3P[i]*factor[i]
}

	attr(K3p,"unit")     = "mol/kg-soln"
	attr(K3p,"pH scale") = pHsc
	return(K3P)
}