Nothing
R/aquaenv_private_DSApHfunctions.R
In AquaEnv: Integrated Development Toolbox for Aquatic Chemical Model Generation
Defines functions
dHAdH_uni
dAdH_uni
dH2AdH_bi
dHAdH_bi
dAdH_bi
dH3AdH_tri
dH2AdH_tri
dHAdH_tri
dAdH_tri
dTAdH
dTAdKdKdS
dTAdKdKdT
dTAdKdKdp
dTAdKdKdSumH2SO4
dTAdKdKdSumHF
revelle
# derivatives of species concentrations of a univalent acid with respect to [H+]
dHAdH_uni <- function(H, SumA, K)
{
dHAdH_uni <- (1/(H+K) - H/(H^2 + 2*H*K + K^2))*SumA
}
dAdH_uni <- function(H, SumA, K)
{
dAdH_uni <- - K/(H^2 + 2*H*K + K^2)*SumA
}
# derivatives of species concentrations of a bivalent acid with respect to [H+]
dH2AdH_bi <- function(H, SumA, K1, K2)
{
dH2AdH_bi <- ((2*H/(H*K1 + K1*K2 + H^2)) - ((H^2*(2*H+K1))/(H*K1 + K1*K2 + H^2)^2)) * SumA
}
dHAdH_bi <- function(H, SumA, K1, K2)
{
dHAdH_bi <- ((K1/(H*K1 + K1*K2 + H^2)) - ((H*K1*(2*H+K1))/(H*K1 + K1*K2 + H^2)^2)) * SumA
}
dAdH_bi <- function(H, SumA, K1, K2)
{
dAdH_bi <- (- ((K1*K2*(2*H+K1))/(H*K1 + K1*K2 + H^2)^2)) * SumA
}
# derivatives of species concentrations of a trivalent acid with respect to [H+]
dH3AdH_tri <- function(H, SumA, K1, K2, K3)
{
dH3AdH_tri <- ((3*H^2/(H*K1*K2 + K1*K2*K3 + H^2*K1 + H^3)) - ((H^3*(2*H*K1 + K1*K2 + 3*H^2))/(H*K1*K2 + K1*K2*K3 + +H^2*K1 + H^3)^2)) * SumA
}
dH2AdH_tri <- function(H, SumA, K1, K2, K3)
{
dH2AdH_tri <- ((2*H*K1/(H*K1*K2 + K1*K2*K3 + H^2*K1 + H^3)) - ((H^2*K1*(2*H*K1 + K1*K2 + 3*H^2))/(H*K1*K2 + K1*K2*K3 + +H^2*K1 + H^3)^2)) * SumA
}
dHAdH_tri <- function(H, SumA, K1, K2, K3)
{
dHAdH_tri <- ((K1*K2/(H*K1*K2 + K1*K2*K3 + H^2*K1 + H^3)) - ((H*K1*K2*(2*H*K1 + K1*K2 + 3*H^2))/(H*K1*K2 + K1*K2*K3 + +H^2*K1 + H^3)^2)) * SumA
}
dAdH_tri <- function(H, SumA, K1, K2, K3)
{
dAdH_tri <- (- ((K1*K2*K3*(2*H*K1 + K1*K2 + 3*H^2))/(H*K1*K2 + K1*K2*K3 + +H^2*K1 + H^3)^2)) * SumA
}
# PRIVATE function:
# calculates the derivative of [TA] with respect to [H+]: the buffer factor
dTAdH <- function(ae) # object of class aquaenv
{
with (ae,
{
H <- 10^(-pH)
res <- ( dHAdH_bi (H, SumCO2, K_CO2, K_HCO3)
+ 2 * dAdH_bi (H, SumCO2, K_CO2, K_HCO3)
+ (- K_W/H^2)
+ dAdH_uni (H, SumBOH3, K_BOH3)
+ dHAdH_tri (H, SumH3PO4, K_H3PO4, K_H2PO4, K_HPO4)
+ 2 * dAdH_tri (H, SumH3PO4, K_H3PO4, K_H2PO4, K_HPO4)
+ dH2AdH_bi (H, SumSiOH4, K_SiOH4, K_SiOOH3)
+ 2 * dHAdH_bi (H, SumSiOH4, K_SiOH4, K_SiOOH3)
+ dAdH_uni (H, SumNH4, K_NH4)
+ dHAdH_bi (H, SumH2S, K_H2S, K_HS)
+ 2 * dAdH_bi (H, SumH2S, K_H2S, K_HS)
- 1
- dH3AdH_tri(H, SumH3PO4, K_H3PO4, K_H2PO4, K_HPO4)
- dHAdH_bi (H, SumH2SO4, K_H2SO4, K_HSO4)
- dHAdH_uni (H, SumHF, K_HF)
- dHAdH_uni (H, SumHNO3, K_HNO3)
- dHAdH_uni (H, SumHNO2, K_HNO2)
- 2 * dH2AdH_bi (H, SumH2SO4, K_H2SO4, K_HSO4)
)
return (res) # derivative of [TA] with respect to [H+]: the buffer factor
})
}
# PRIVATE function:
# calculates the derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to salinity S
dTAdKdKdS <- function(ae) # object of class aquaenv
{
with (ae,
{
epsilon <- S * Technicals$epsilon_fraction
TAplus <- c()
TAminus <- c()
if (((length(SumCO2) > 1) || (length(pH) > 1)) && (length(S)==1) && (length(p)==1) && (length(t)==1))
{
for (i in 1:max(length(SumCO2), length(pH)))
{
if (length(SumCO2) > 1) {co2 <- i} else {co2 <- 1}
if (length(pH) > 1) {ph <- i} else {ph <- 1}
TAplus <- c(TAplus, aquaenv(S=(S+epsilon), t=t, p=p,
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
TAminus <- c(TAminus, aquaenv(S=(S-epsilon), t=t, p=p,
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
}
}
else
{
for (s in 1:length(S))
{
for (pe in 1:length(p))
{
if (length(pH) > 1) {i <- max(s,pe)} else {i <- 1}
if (length(SumCO2) > 1) {x <- max(s,pe)} else {x <- 1}
TAplus <- c(TAplus, aquaenv(S=(S[[s]]+epsilon[[s]]), t=t, p=p[[pe]],
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
TAminus <- c(TAminus, aquaenv(S=(S[[s]]-epsilon[[s]]), t=t, p=p[[pe]],
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
}
}
}
return ((TAplus - TAminus)/(2*epsilon)) # derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to salinity S
})
}
# PRIVATE function:
# calculates the derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to temperature T
dTAdKdKdT <- function(ae) # object of class aquaenv
{
with (ae,
{
epsilon <- t * Technicals$epsilon_fraction
TAplus <- c()
TAminus <- c()
if (((length(SumCO2) > 1) || (length(pH) > 1)) && (length(S)==1) && (length(p)==1) && (length(t)==1))
{
for (i in 1:max(length(SumCO2), length(pH)))
{
if (length(SumCO2) > 1) {co2 <- i} else {co2 <- 1}
if (length(pH) > 1) {ph <- i} else {ph <- 1}
TAplus <- c(TAplus, aquaenv(S=S, t=(t+epsilon), p=p,
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
TAminus <- c(TAminus, aquaenv(S=S, t=(t-epsilon), p=p,
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
}
}
else
{
for (s in 1:length(S))
{
for (pe in 1:length(p))
{
if (length(pH) > 1) {i <- max(s,pe)} else {i <- 1}
if (length(SumCO2) > 1) {x <- max(s,pe)} else {x <- 1}
TAplus <- c(TAplus, aquaenv(S=S[[s]], t=(t+epsilon), p=p[[pe]],
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
TAminus <- c(TAminus, aquaenv(S=S[[s]], t=(t-epsilon), p=p[[pe]],
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
}
}
}
return ((TAplus - TAminus)/(2*epsilon)) # derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to temperature T
})
}
# PRIVATE function:
# calculates the derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to gauge pressure p
dTAdKdKdp <- function(ae) # object of class aquaenv
{
with (ae,
{
if (min(p) == 0)
{
epsilon <- rep(Technicals$epsilon_fraction, length(p))
}
else
{
epsilon <- p * Technicals$epsilon_fraction
}
TAplus <- c()
TAminus <- c()
if (((length(SumCO2) > 1) || (length(pH) > 1)) && (length(S)==1) && (length(p)==1) && (length(t)==1))
{
for (i in 1:max(length(SumCO2), length(pH)))
{
if (length(SumCO2) > 1) {co2 <- i} else {co2 <- 1}
if (length(pH) > 1) {ph <- i} else {ph <- 1}
TAplus <- c(TAplus, aquaenv(S=S, t=t, p=(p+epsilon),
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
if(p == 0) { ptemp <- 0 } else { ptemp <- (p-epsilon) }
TAminus <- c(TAminus, aquaenv(S=S, t=t, p=ptemp,
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
}
}
else
{
for (s in 1:length(S))
{
for (pe in 1:length(p))
{
if (length(pH) > 1) {i <- max(s,pe)} else {i <- 1}
if (length(SumCO2) > 1) {x <- max(s,pe)} else {x <- 1}
TAplus <- c(TAplus, aquaenv(S=S[[s]], t=t, p=(p[[pe]]+epsilon[[pe]]),
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
if(p[[pe]] == 0) { ptemp <- 0 } else { ptemp <- (p[[pe]]-epsilon[[pe]]) }
TAminus <- c(TAminus, aquaenv(S=S[[s]], t=t, p=ptemp,
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
}
}
}
return ((TAplus - TAminus)/(2*epsilon)) # derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to depth d
})
}
# PRIVATE function:
# calculates the derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to the total sulfate concentration (influence via scale conversion)
dTAdKdKdSumH2SO4 <- function(ae) # object of class aquaenv
{
with (ae,
{
epsilon <- SumH2SO4 * Technicals$epsilon_fraction
TAplus <- c()
TAminus <- c()
if (((length(SumCO2) > 1) || (length(pH) > 1)) && (length(S)==1) && (length(p)==1) && (length(t)==1))
{
for (i in 1:max(length(SumCO2), length(pH)))
{
if (length(SumCO2) > 1) {co2 <- i} else {co2 <- 1}
if (length(pH) > 1) {ph <- i} else {ph <- 1}
TAplus <- c(TAplus, aquaenv(S=S, t=t, p=p,
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE,
SumH2SO4_Koffset=epsilon, revelle=FALSE)$TA)
TAminus <- c(TAminus, aquaenv(S=S, t=t, p=p,
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE,
SumH2SO4_Koffset=-epsilon, revelle=FALSE)$TA)
}
}
else
{
for (s in 1:length(S))
{
for (pe in 1:length(p))
{
if (length(pH) > 1) {i <- max(s,pe)} else {i <- 1}
if (length(SumCO2) > 1) {x <- max(s,pe)} else {x <- 1}
TAplus <- c(TAplus, aquaenv(S=S[[s]], t=t, p=p[[pe]],
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE,
SumH2SO4_Koffset=epsilon[[s]], revelle=FALSE)$TA)
TAminus <- c(TAminus, aquaenv(S=S[[s]], t=t, p=p[[pe]],
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE,
SumH2SO4_Koffset=-epsilon[[s]], revelle=FALSE)$TA)
}
}
}
return ((TAplus - TAminus)/(2*epsilon)) # derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to the total sulfate concentration (influence via scale conversion)
})
}
# PRIVATE function:
# calculates the derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to the total fluoride concentration (influence via scale conversion)
dTAdKdKdSumHF <- function(ae) # object of class aquaenv
{
with (ae,
{
epsilon <- SumHF * Technicals$epsilon_fraction
TAplus <- c()
TAminus <- c()
if (((length(SumCO2) > 1) || (length(pH) > 1)) && (length(S)==1) && (length(p)==1) && (length(t)==1))
{
for (i in 1:max(length(SumCO2), length(pH)))
{
if (length(SumCO2) > 1) {co2 <- i} else {co2 <- 1}
if (length(pH) > 1) {ph <- i} else {ph <- 1}
TAplus <- c(TAplus, aquaenv(S=S, t=t, p=p,
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE,
SumHF_Koffset=epsilon, revelle=FALSE)$TA)
TAminus <- c(TAminus, aquaenv(S=S, t=t, p=p,
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE,
SumHF_Koffset=-epsilon, revelle=FALSE)$TA)
}
}
else
{
for (s in 1:length(S))
{
for (pe in 1:length(p))
{
if (length(pH) > 1) {i <- max(s,pe)} else {i <- 1}
if (length(SumCO2) > 1) {x <- max(s,pe)} else {x <- 1}
TAplus <- c(TAplus, aquaenv(S=S[[s]], t=t, p=p[[pe]],
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE,
SumHF_Koffset=epsilon[[s]], revelle=FALSE)$TA)
TAminus <- c(TAminus, aquaenv(S=S[[s]], t=t, p=p[[pe]],
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE,
SumHF_Koffset=-epsilon[[s]], revelle=FALSE)$TA)
}
}
}
return ((TAplus - TAminus)/(2*epsilon)) # derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to the total fluoride concentration (influence via scale conversion)
})
}
# PRIVATE function:
# calculates the revelle factor
revelle <- function(ae) # object of class aquaenv
{
CO2_0 <- ae$CO2
SumCO2_0 <- ae$SumCO2
dSumCO2 <- SumCO2_0*Technicals$revelle_fraction
dCO2 <- c()
CO2new <- c()
with (ae,
{
if (((length(SumCO2) > 1) || (length(TA) > 1)) && (length(S)==1) && (length(p)==1) && (length(t)==1))
{
for (i in 1:max(length(SumCO2), length(TA)))
{
if (length(TA) > 1) {ta <- i} else {ta <- 1}
if (length(SumCO2) > 1) {co2 <- i} else {co2 <- 1}
CO2new <<- c(CO2new, aquaenv(t=t, S=S, p=p,
SumCO2=(SumCO2[[co2]]+dSumCO2[[co2]]), SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF, k_co2=K_CO2, k_hco3 = K_HCO3,
TA=TA[[ta]], pH=NULL, fCO2=NULL, CO2=NULL, speciation=TRUE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$CO2)
}
}
else
{
for (s in 1:length(S))
{
for (pe in 1:length(p))
{
for (te in 1:length(t))
{
if (length(TA) > 1) {i <- max(s,pe,te)} else {i <- 1}
if (length(SumCO2) > 1) {x <- max(s,pe,te)} else {x <- 1}
j <- max(s,pe,te)
CO2new <<- c(CO2new, aquaenv(t=t[[te]], S=S[[s]], p=p[[pe]],
SumCO2=(SumCO2[[x]]+dSumCO2[[x]]), SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]], k_co2=K_CO2[[j]], k_hco3 = K_HCO3[[j]],
TA=TA[[i]], pH=NULL, fCO2=NULL, CO2=NULL, speciation=TRUE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$CO2)
}
}
}
}
})
dCO2 <- CO2new - CO2_0
return((dCO2/dSumCO2) * (SumCO2_0/CO2_0)) # the revelle factor
}
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AquaEnv documentation built on May 1, 2019, 9:09 p.m.
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Defines functions dHAdH_uni dAdH_uni dH2AdH_bi dHAdH_bi dAdH_bi dH3AdH_tri dH2AdH_tri dHAdH_tri dAdH_tri dTAdH dTAdKdKdS dTAdKdKdT dTAdKdKdp dTAdKdKdSumH2SO4 dTAdKdKdSumHF revelle
# derivatives of species concentrations of a univalent acid with respect to [H+]
dHAdH_uni <- function(H, SumA, K)
{
dHAdH_uni <- (1/(H+K) - H/(H^2 + 2*H*K + K^2))*SumA
}
dAdH_uni <- function(H, SumA, K)
{
dAdH_uni <- - K/(H^2 + 2*H*K + K^2)*SumA
}
# derivatives of species concentrations of a bivalent acid with respect to [H+]
dH2AdH_bi <- function(H, SumA, K1, K2)
{
dH2AdH_bi <- ((2*H/(H*K1 + K1*K2 + H^2)) - ((H^2*(2*H+K1))/(H*K1 + K1*K2 + H^2)^2)) * SumA
}
dHAdH_bi <- function(H, SumA, K1, K2)
{
dHAdH_bi <- ((K1/(H*K1 + K1*K2 + H^2)) - ((H*K1*(2*H+K1))/(H*K1 + K1*K2 + H^2)^2)) * SumA
}
dAdH_bi <- function(H, SumA, K1, K2)
{
dAdH_bi <- (- ((K1*K2*(2*H+K1))/(H*K1 + K1*K2 + H^2)^2)) * SumA
}
# derivatives of species concentrations of a trivalent acid with respect to [H+]
dH3AdH_tri <- function(H, SumA, K1, K2, K3)
{
dH3AdH_tri <- ((3*H^2/(H*K1*K2 + K1*K2*K3 + H^2*K1 + H^3)) - ((H^3*(2*H*K1 + K1*K2 + 3*H^2))/(H*K1*K2 + K1*K2*K3 + +H^2*K1 + H^3)^2)) * SumA
}
dH2AdH_tri <- function(H, SumA, K1, K2, K3)
{
dH2AdH_tri <- ((2*H*K1/(H*K1*K2 + K1*K2*K3 + H^2*K1 + H^3)) - ((H^2*K1*(2*H*K1 + K1*K2 + 3*H^2))/(H*K1*K2 + K1*K2*K3 + +H^2*K1 + H^3)^2)) * SumA
}
dHAdH_tri <- function(H, SumA, K1, K2, K3)
{
dHAdH_tri <- ((K1*K2/(H*K1*K2 + K1*K2*K3 + H^2*K1 + H^3)) - ((H*K1*K2*(2*H*K1 + K1*K2 + 3*H^2))/(H*K1*K2 + K1*K2*K3 + +H^2*K1 + H^3)^2)) * SumA
}
dAdH_tri <- function(H, SumA, K1, K2, K3)
{
dAdH_tri <- (- ((K1*K2*K3*(2*H*K1 + K1*K2 + 3*H^2))/(H*K1*K2 + K1*K2*K3 + +H^2*K1 + H^3)^2)) * SumA
}
# PRIVATE function:
# calculates the derivative of [TA] with respect to [H+]: the buffer factor
dTAdH <- function(ae) # object of class aquaenv
{
with (ae,
{
H <- 10^(-pH)
res <- ( dHAdH_bi (H, SumCO2, K_CO2, K_HCO3)
+ 2 * dAdH_bi (H, SumCO2, K_CO2, K_HCO3)
+ (- K_W/H^2)
+ dAdH_uni (H, SumBOH3, K_BOH3)
+ dHAdH_tri (H, SumH3PO4, K_H3PO4, K_H2PO4, K_HPO4)
+ 2 * dAdH_tri (H, SumH3PO4, K_H3PO4, K_H2PO4, K_HPO4)
+ dH2AdH_bi (H, SumSiOH4, K_SiOH4, K_SiOOH3)
+ 2 * dHAdH_bi (H, SumSiOH4, K_SiOH4, K_SiOOH3)
+ dAdH_uni (H, SumNH4, K_NH4)
+ dHAdH_bi (H, SumH2S, K_H2S, K_HS)
+ 2 * dAdH_bi (H, SumH2S, K_H2S, K_HS)
- 1
- dH3AdH_tri(H, SumH3PO4, K_H3PO4, K_H2PO4, K_HPO4)
- dHAdH_bi (H, SumH2SO4, K_H2SO4, K_HSO4)
- dHAdH_uni (H, SumHF, K_HF)
- dHAdH_uni (H, SumHNO3, K_HNO3)
- dHAdH_uni (H, SumHNO2, K_HNO2)
- 2 * dH2AdH_bi (H, SumH2SO4, K_H2SO4, K_HSO4)
)
return (res) # derivative of [TA] with respect to [H+]: the buffer factor
})
}
# PRIVATE function:
# calculates the derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to salinity S
dTAdKdKdS <- function(ae) # object of class aquaenv
{
with (ae,
{
epsilon <- S * Technicals$epsilon_fraction
TAplus <- c()
TAminus <- c()
if (((length(SumCO2) > 1) || (length(pH) > 1)) && (length(S)==1) && (length(p)==1) && (length(t)==1))
{
for (i in 1:max(length(SumCO2), length(pH)))
{
if (length(SumCO2) > 1) {co2 <- i} else {co2 <- 1}
if (length(pH) > 1) {ph <- i} else {ph <- 1}
TAplus <- c(TAplus, aquaenv(S=(S+epsilon), t=t, p=p,
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
TAminus <- c(TAminus, aquaenv(S=(S-epsilon), t=t, p=p,
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
}
}
else
{
for (s in 1:length(S))
{
for (pe in 1:length(p))
{
if (length(pH) > 1) {i <- max(s,pe)} else {i <- 1}
if (length(SumCO2) > 1) {x <- max(s,pe)} else {x <- 1}
TAplus <- c(TAplus, aquaenv(S=(S[[s]]+epsilon[[s]]), t=t, p=p[[pe]],
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
TAminus <- c(TAminus, aquaenv(S=(S[[s]]-epsilon[[s]]), t=t, p=p[[pe]],
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
}
}
}
return ((TAplus - TAminus)/(2*epsilon)) # derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to salinity S
})
}
# PRIVATE function:
# calculates the derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to temperature T
dTAdKdKdT <- function(ae) # object of class aquaenv
{
with (ae,
{
epsilon <- t * Technicals$epsilon_fraction
TAplus <- c()
TAminus <- c()
if (((length(SumCO2) > 1) || (length(pH) > 1)) && (length(S)==1) && (length(p)==1) && (length(t)==1))
{
for (i in 1:max(length(SumCO2), length(pH)))
{
if (length(SumCO2) > 1) {co2 <- i} else {co2 <- 1}
if (length(pH) > 1) {ph <- i} else {ph <- 1}
TAplus <- c(TAplus, aquaenv(S=S, t=(t+epsilon), p=p,
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
TAminus <- c(TAminus, aquaenv(S=S, t=(t-epsilon), p=p,
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
}
}
else
{
for (s in 1:length(S))
{
for (pe in 1:length(p))
{
if (length(pH) > 1) {i <- max(s,pe)} else {i <- 1}
if (length(SumCO2) > 1) {x <- max(s,pe)} else {x <- 1}
TAplus <- c(TAplus, aquaenv(S=S[[s]], t=(t+epsilon), p=p[[pe]],
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
TAminus <- c(TAminus, aquaenv(S=S[[s]], t=(t-epsilon), p=p[[pe]],
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
}
}
}
return ((TAplus - TAminus)/(2*epsilon)) # derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to temperature T
})
}
# PRIVATE function:
# calculates the derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to gauge pressure p
dTAdKdKdp <- function(ae) # object of class aquaenv
{
with (ae,
{
if (min(p) == 0)
{
epsilon <- rep(Technicals$epsilon_fraction, length(p))
}
else
{
epsilon <- p * Technicals$epsilon_fraction
}
TAplus <- c()
TAminus <- c()
if (((length(SumCO2) > 1) || (length(pH) > 1)) && (length(S)==1) && (length(p)==1) && (length(t)==1))
{
for (i in 1:max(length(SumCO2), length(pH)))
{
if (length(SumCO2) > 1) {co2 <- i} else {co2 <- 1}
if (length(pH) > 1) {ph <- i} else {ph <- 1}
TAplus <- c(TAplus, aquaenv(S=S, t=t, p=(p+epsilon),
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
if(p == 0) { ptemp <- 0 } else { ptemp <- (p-epsilon) }
TAminus <- c(TAminus, aquaenv(S=S, t=t, p=ptemp,
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
}
}
else
{
for (s in 1:length(S))
{
for (pe in 1:length(p))
{
if (length(pH) > 1) {i <- max(s,pe)} else {i <- 1}
if (length(SumCO2) > 1) {x <- max(s,pe)} else {x <- 1}
TAplus <- c(TAplus, aquaenv(S=S[[s]], t=t, p=(p[[pe]]+epsilon[[pe]]),
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
if(p[[pe]] == 0) { ptemp <- 0 } else { ptemp <- (p[[pe]]-epsilon[[pe]]) }
TAminus <- c(TAminus, aquaenv(S=S[[s]], t=t, p=ptemp,
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$TA)
}
}
}
return ((TAplus - TAminus)/(2*epsilon)) # derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to depth d
})
}
# PRIVATE function:
# calculates the derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to the total sulfate concentration (influence via scale conversion)
dTAdKdKdSumH2SO4 <- function(ae) # object of class aquaenv
{
with (ae,
{
epsilon <- SumH2SO4 * Technicals$epsilon_fraction
TAplus <- c()
TAminus <- c()
if (((length(SumCO2) > 1) || (length(pH) > 1)) && (length(S)==1) && (length(p)==1) && (length(t)==1))
{
for (i in 1:max(length(SumCO2), length(pH)))
{
if (length(SumCO2) > 1) {co2 <- i} else {co2 <- 1}
if (length(pH) > 1) {ph <- i} else {ph <- 1}
TAplus <- c(TAplus, aquaenv(S=S, t=t, p=p,
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE,
SumH2SO4_Koffset=epsilon, revelle=FALSE)$TA)
TAminus <- c(TAminus, aquaenv(S=S, t=t, p=p,
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE,
SumH2SO4_Koffset=-epsilon, revelle=FALSE)$TA)
}
}
else
{
for (s in 1:length(S))
{
for (pe in 1:length(p))
{
if (length(pH) > 1) {i <- max(s,pe)} else {i <- 1}
if (length(SumCO2) > 1) {x <- max(s,pe)} else {x <- 1}
TAplus <- c(TAplus, aquaenv(S=S[[s]], t=t, p=p[[pe]],
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE,
SumH2SO4_Koffset=epsilon[[s]], revelle=FALSE)$TA)
TAminus <- c(TAminus, aquaenv(S=S[[s]], t=t, p=p[[pe]],
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE,
SumH2SO4_Koffset=-epsilon[[s]], revelle=FALSE)$TA)
}
}
}
return ((TAplus - TAminus)/(2*epsilon)) # derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to the total sulfate concentration (influence via scale conversion)
})
}
# PRIVATE function:
# calculates the derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to the total fluoride concentration (influence via scale conversion)
dTAdKdKdSumHF <- function(ae) # object of class aquaenv
{
with (ae,
{
epsilon <- SumHF * Technicals$epsilon_fraction
TAplus <- c()
TAminus <- c()
if (((length(SumCO2) > 1) || (length(pH) > 1)) && (length(S)==1) && (length(p)==1) && (length(t)==1))
{
for (i in 1:max(length(SumCO2), length(pH)))
{
if (length(SumCO2) > 1) {co2 <- i} else {co2 <- 1}
if (length(pH) > 1) {ph <- i} else {ph <- 1}
TAplus <- c(TAplus, aquaenv(S=S, t=t, p=p,
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE,
SumHF_Koffset=epsilon, revelle=FALSE)$TA)
TAminus <- c(TAminus, aquaenv(S=S, t=t, p=p,
SumCO2=SumCO2[[co2]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF,
TA=NULL, pH=pH[[ph]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE,
SumHF_Koffset=-epsilon, revelle=FALSE)$TA)
}
}
else
{
for (s in 1:length(S))
{
for (pe in 1:length(p))
{
if (length(pH) > 1) {i <- max(s,pe)} else {i <- 1}
if (length(SumCO2) > 1) {x <- max(s,pe)} else {x <- 1}
TAplus <- c(TAplus, aquaenv(S=S[[s]], t=t, p=p[[pe]],
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE,
SumHF_Koffset=epsilon[[s]], revelle=FALSE)$TA)
TAminus <- c(TAminus, aquaenv(S=S[[s]], t=t, p=p[[pe]],
SumCO2=SumCO2[[x]], SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]],
TA=NULL, pH=pH[[i]], fCO2=NULL, CO2=NULL, speciation=FALSE, dsa=FALSE, ae=NULL, from.data.frame=FALSE,
SumHF_Koffset=-epsilon[[s]], revelle=FALSE)$TA)
}
}
}
return ((TAplus - TAminus)/(2*epsilon)) # derivative of [TA] with respect to changes in the dissociation constants (Ks) times the derivative of the dissociation constants with respect to the total fluoride concentration (influence via scale conversion)
})
}
# PRIVATE function:
# calculates the revelle factor
revelle <- function(ae) # object of class aquaenv
{
CO2_0 <- ae$CO2
SumCO2_0 <- ae$SumCO2
dSumCO2 <- SumCO2_0*Technicals$revelle_fraction
dCO2 <- c()
CO2new <- c()
with (ae,
{
if (((length(SumCO2) > 1) || (length(TA) > 1)) && (length(S)==1) && (length(p)==1) && (length(t)==1))
{
for (i in 1:max(length(SumCO2), length(TA)))
{
if (length(TA) > 1) {ta <- i} else {ta <- 1}
if (length(SumCO2) > 1) {co2 <- i} else {co2 <- 1}
CO2new <<- c(CO2new, aquaenv(t=t, S=S, p=p,
SumCO2=(SumCO2[[co2]]+dSumCO2[[co2]]), SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3, SumH2SO4=SumH2SO4, SumHF=SumHF, k_co2=K_CO2, k_hco3 = K_HCO3,
TA=TA[[ta]], pH=NULL, fCO2=NULL, CO2=NULL, speciation=TRUE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$CO2)
}
}
else
{
for (s in 1:length(S))
{
for (pe in 1:length(p))
{
for (te in 1:length(t))
{
if (length(TA) > 1) {i <- max(s,pe,te)} else {i <- 1}
if (length(SumCO2) > 1) {x <- max(s,pe,te)} else {x <- 1}
j <- max(s,pe,te)
CO2new <<- c(CO2new, aquaenv(t=t[[te]], S=S[[s]], p=p[[pe]],
SumCO2=(SumCO2[[x]]+dSumCO2[[x]]), SumNH4=SumNH4, SumH2S=SumH2S, SumH3PO4=SumH3PO4, SumSiOH4=SumSiOH4, SumHNO3=SumHNO3, SumHNO2=SumHNO2,
SumBOH3=SumBOH3[[s]], SumH2SO4=SumH2SO4[[s]], SumHF=SumHF[[s]], k_co2=K_CO2[[j]], k_hco3 = K_HCO3[[j]],
TA=TA[[i]], pH=NULL, fCO2=NULL, CO2=NULL, speciation=TRUE, dsa=FALSE, ae=NULL, from.data.frame=FALSE, revelle=FALSE)$CO2)
}
}
}
}
})
dCO2 <- CO2new - CO2_0
return((dCO2/dSumCO2) * (SumCO2_0/CO2_0)) # the revelle factor
}
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