R/wvp.R
In denis-chabot/fishMO2: Calculate and Plot SMR, O2crit and SDA, and convert between oxygen units
Defines functions
wvp
Documented in
wvp
##' Water vapor pressure as a function of water temperature and salinity
##'
##' Calculates water vapor pressure, given water temperature and salinity,
##' using a variety of methods. This is required to convert partial pressure of
##' oxygen into saturation or concentration units and vice-versa.
##'
##' Output: water vapor pressure above fresh or sea water in kPa.
##'
##' Note: this function is not intended to calculate vapor pressure above ice.
##' Also, water vapor pressure is not affected by atmospheric pressure
##'
##' Methods for vapor pressure calculation above fresh water:
##'
##' \describe{ \item{IAPWS}{ This is the 'official' formulation from the
##' International Association for the Properties of Water and Steam (Wagner &
##' Pruss 1993), Eq. 2.5 p. 399. The valid range of this formulation is 273.16
##' <= K <= 647.096 and is based on the ITS90 temperature scale. }
##'
##' \item{BensonKrause}{ Eq. 23 of Benson and Krause, 1980 }
##'
##' \item{GreenCarritt}{ Green & Carritt 1967 (see also table 2 Benson & Krause
##' 1984) without salinity correction, in atm converted to kPa }
##'
##' \item{WMO2008}{ Annex 4B, Guide to Meteorological Instruments and Methods
##' of Observation, WMO Publication No 8, 7th edition, Geneva, 2008. }
##'
##' \item{Antoine}{ http://www.watervaporpressure.com }
##'
##' \item{Weiss}{ Weiss & Price 1980 eq 10 p. 350, in atm converted to kPa }
##'
##' \item{GoffGratch}{ Smithsonian Meteorological Tables, 5th edition, p. 350,
##' 1984, in hPa then converted to kPa } }
##'
##' Methods for salinity correction: \describe{ \item{Chabot}{ My own
##' polynomial fit passing through origin to Robinson 1954's data, Table II p.
##' 451 gives values of delta vp for different chlorinities. Chlorinity changed
##' into salinity according to Lyman (1969) }
##'
##' \item{Green}{ From table 2 in Benson & Krause (1984) }
##'
##' \item{none}{ Removes salinity correction, same as leaving \code{s} to its
##' default value of zero } }
##'
##' @param t Temperature in °C
##' @param s Salinity in parts per thousand
##' @param method One of "IAPWS", "BensonKrause", "GreenCarritt","WMO2008",
##' "Antoine", "Weiss", "GoffGratch". See Details.
##' @param sal_method One of "Chabot", "Green" or "none". See Details.
##' @return A vector of same length as parameter t
##' @note This assumes that air temperature above the water surface is that of
##' the water. The effect of salinity is negligible, but it is nevertheless
##' included in the calculation if the user provides salinity.
##' @section Warnings: \code{s} must be of length 1 or same length as t. This
##' is not checked by the function at present so errors could occur if this is
##' not respected.
##' @author Denis Chabot
##' @seealso %% ~~objects to See Also as \code{\link{help}}, ~~~
##' @references Benson B.B. and Krause D.Jr. (1980) The concentration and
##' isotopic fractionation of gases dissolved in freshwater in equilibrium with
##' the atmosphere. 1. Oxygen. \emph{Limnology and Oceanography}, 25, 662-671.
##'
##' Benson B.B. and Krause D.Jr. (1984) The concentration and isotopic
##' fractionation of oxygen dissolved in freshwater and seawater in equilibrium
##' with the atmosphere. \emph{Limnology and Oceanography}, 29, 620-632.
##'
##' Green, E. J. and Carritt, D. E. (1967) New tables for oxygen saturation of
##' seawater. \emph{Journal of Marine Research}, 25, 140-147.
##'
##' Lyman, J. (1969) Redefinition of salinity and chlorinity. \emph{Limnology
##' and Oceanography}, 27, 928-929.
##'
##' Robinson R. A. (1954) The vapour pressure and osmotic equivalence of sea
##' water. \emph{Journal of the Marine Biological Association of the United
##' Kingdom}, 33, 449-455.
##'
##' Wagner, W. and Pruss, A. (1993) International Equations for the Saturation
##' Properties of Ordinary Water Substance. Revised According to the
##' International Temperature Scale of 1990. Addendum to J. Phys. Chem. Ref.
##' Data 16, 893 (1987) \emph{Journal of Physical and Chemical Reference Data},
##' 22, 783. http://dx.doi.org/10.1063/1.555926.
##'
##' Wagner, W. & Pruss, A. (2002) The IAPWS formulation 1995 for the
##' thermodynamic properties of ordinary water substance for general and
##' scientific use. \emph{Journal of Physical and Chemical Reference Data},
##' 31(2), 387-535.
##' @examples
##'
##' wvp(t=c(0,5,10))
##' wvp(t=c(0,5,10), s=35)
##'
##' @export wvp
wvp <-
function(t, s=0,
method=c("IAPWS", "BensonKrause", "GreenCarritt","WMO2008", "Antoine", "Weiss", "GoffGratch"),
sal_method = c("Chabot", "Green", "none")
) {
Temp_K <- 273.15 + t # Most formulas use T in [K]
# Formulas using [C] use the variable t
method <- match.arg(method)
switch(method,
IAPWS = {
Tc = 647.096 # Temperature at the critical point in °K
Pc = 22064 # Vapor pressure at the critical point in kPa
a1 = -7.85951783
a2 = 1.84408259
a3 = -11.7866497
a4 = 22.6807411
a5 = -15.9618719
a6 = 1.80122502
tau = 1 - Temp_K/Tc
ln_p_pc = (a1*tau + a2*tau^1.5 + a3*tau^3 + a4*tau^3.5 + a5*tau^4 + a6*tau^7.5)*Tc/Temp_K
ln_p = ln_p_pc + log(Pc)
wvp0 = exp(ln_p)
},
BensonKrause = {
a1 = 11.8571
a2 = 3840.70
a3 = 216961
vp = exp(a1 - (a2/Temp_K) - (a3/Temp_K^2)) # in atm
wvp0 = 101.325 * vp # in kPa
},
GreenCarritt = {
a1 = 18.1973
a2 = 373.16
a3 = 3.1813e-7
a4 = 26.1205
a5 = 1.8726e-2
a6 = 8.03945
a7 = 5.02802
wvp0 <- 101.325 * exp(a1 * (1-a2/Temp_K) + a3 *(1-exp(a4*(1- Temp_K/a2)))
- a5 * (1 - exp(a6 * (1-a2/Temp_K))) + a7 *log(a2/Temp_K))
},
WMO2008 = {
a1 = 6.112
a2 = 17.62
a3 = 243.12
vp = a1 * exp(a2 * Temp_K/(a3 + Temp_K)) # hPa
wvp0 = vp/10 # kPa
},
Antoine = {
# Antoine equation, http://www.watervaporpressure.com = Temp in °C
a1 = 8.07131
a2 = 1730.63
a3 = 233.426
vp = 10^(a1 - (a2/(a3+t))) # mm Hg
wvp0 = vp * 0.1333224 # kPa
},
Weiss = {
a1 = 24.4543
a2 = 67.4509
a3 = 4.8489
vp = a1 - a2*(100/Temp_K) - a3*log(Temp_K/100) # in atm
wvp0 = 101.325 * vp # in kPa
},
GoffGratch = {
Ts = 373.16 # steam point temperature in K
ews = 1013.246 # saturation pressure at steam point temperature, normal atmosphere
a1 = -7.90298
a3 = 5.02808
a4 = 1.3816*10^-7
a5 = 11.344
a6 = 8.1328*10^-3
a7 = -3.49149
log10ew = a1 * (Ts/Temp_K -1) + a3*log10(Ts/Temp_K) - a4*(10^(a5*(1-Temp_K/Ts))) +
a6 * (10^(a7*(Ts/Temp_K -1)) -1) + log10(ews)
ew = 10^log10ew # hPa
wvp0 = ew/10 # kPa
}
)
# salinity correction
sal_method = match.arg(sal_method)
switch(sal_method, # quality of salinity correction can be checked by comparison with Robinson's data, Water_vapor_pressure_decrease_for_seawater.Rda
Chabot = {
a1 = 5.197e-04
a2 = 1.226e-08
wvpS = wvp0 * (1 - (a1*s + a2*s^3) )
},
Green = {
a1 = 5.37e-4
wvpS = wvp0 * (1 - a1 * s)
},
none = {
wvpS = wvp0
}
)
wvpS
}
denis-chabot/fishMO2 documentation built on July 16, 2020, 1:53 a.m.
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Defines functions wvp
Documented in wvp
##' Water vapor pressure as a function of water temperature and salinity
##'
##' Calculates water vapor pressure, given water temperature and salinity,
##' using a variety of methods. This is required to convert partial pressure of
##' oxygen into saturation or concentration units and vice-versa.
##'
##' Output: water vapor pressure above fresh or sea water in kPa.
##'
##' Note: this function is not intended to calculate vapor pressure above ice.
##' Also, water vapor pressure is not affected by atmospheric pressure
##'
##' Methods for vapor pressure calculation above fresh water:
##'
##' \describe{ \item{IAPWS}{ This is the 'official' formulation from the
##' International Association for the Properties of Water and Steam (Wagner &
##' Pruss 1993), Eq. 2.5 p. 399. The valid range of this formulation is 273.16
##' <= K <= 647.096 and is based on the ITS90 temperature scale. }
##'
##' \item{BensonKrause}{ Eq. 23 of Benson and Krause, 1980 }
##'
##' \item{GreenCarritt}{ Green & Carritt 1967 (see also table 2 Benson & Krause
##' 1984) without salinity correction, in atm converted to kPa }
##'
##' \item{WMO2008}{ Annex 4B, Guide to Meteorological Instruments and Methods
##' of Observation, WMO Publication No 8, 7th edition, Geneva, 2008. }
##'
##' \item{Antoine}{ http://www.watervaporpressure.com }
##'
##' \item{Weiss}{ Weiss & Price 1980 eq 10 p. 350, in atm converted to kPa }
##'
##' \item{GoffGratch}{ Smithsonian Meteorological Tables, 5th edition, p. 350,
##' 1984, in hPa then converted to kPa } }
##'
##' Methods for salinity correction: \describe{ \item{Chabot}{ My own
##' polynomial fit passing through origin to Robinson 1954's data, Table II p.
##' 451 gives values of delta vp for different chlorinities. Chlorinity changed
##' into salinity according to Lyman (1969) }
##'
##' \item{Green}{ From table 2 in Benson & Krause (1984) }
##'
##' \item{none}{ Removes salinity correction, same as leaving \code{s} to its
##' default value of zero } }
##'
##' @param t Temperature in °C
##' @param s Salinity in parts per thousand
##' @param method One of "IAPWS", "BensonKrause", "GreenCarritt","WMO2008",
##' "Antoine", "Weiss", "GoffGratch". See Details.
##' @param sal_method One of "Chabot", "Green" or "none". See Details.
##' @return A vector of same length as parameter t
##' @note This assumes that air temperature above the water surface is that of
##' the water. The effect of salinity is negligible, but it is nevertheless
##' included in the calculation if the user provides salinity.
##' @section Warnings: \code{s} must be of length 1 or same length as t. This
##' is not checked by the function at present so errors could occur if this is
##' not respected.
##' @author Denis Chabot
##' @seealso %% ~~objects to See Also as \code{\link{help}}, ~~~
##' @references Benson B.B. and Krause D.Jr. (1980) The concentration and
##' isotopic fractionation of gases dissolved in freshwater in equilibrium with
##' the atmosphere. 1. Oxygen. \emph{Limnology and Oceanography}, 25, 662-671.
##'
##' Benson B.B. and Krause D.Jr. (1984) The concentration and isotopic
##' fractionation of oxygen dissolved in freshwater and seawater in equilibrium
##' with the atmosphere. \emph{Limnology and Oceanography}, 29, 620-632.
##'
##' Green, E. J. and Carritt, D. E. (1967) New tables for oxygen saturation of
##' seawater. \emph{Journal of Marine Research}, 25, 140-147.
##'
##' Lyman, J. (1969) Redefinition of salinity and chlorinity. \emph{Limnology
##' and Oceanography}, 27, 928-929.
##'
##' Robinson R. A. (1954) The vapour pressure and osmotic equivalence of sea
##' water. \emph{Journal of the Marine Biological Association of the United
##' Kingdom}, 33, 449-455.
##'
##' Wagner, W. and Pruss, A. (1993) International Equations for the Saturation
##' Properties of Ordinary Water Substance. Revised According to the
##' International Temperature Scale of 1990. Addendum to J. Phys. Chem. Ref.
##' Data 16, 893 (1987) \emph{Journal of Physical and Chemical Reference Data},
##' 22, 783. http://dx.doi.org/10.1063/1.555926.
##'
##' Wagner, W. & Pruss, A. (2002) The IAPWS formulation 1995 for the
##' thermodynamic properties of ordinary water substance for general and
##' scientific use. \emph{Journal of Physical and Chemical Reference Data},
##' 31(2), 387-535.
##' @examples
##'
##' wvp(t=c(0,5,10))
##' wvp(t=c(0,5,10), s=35)
##'
##' @export wvp
wvp <-
function(t, s=0,
method=c("IAPWS", "BensonKrause", "GreenCarritt","WMO2008", "Antoine", "Weiss", "GoffGratch"),
sal_method = c("Chabot", "Green", "none")
) {
Temp_K <- 273.15 + t # Most formulas use T in [K]
# Formulas using [C] use the variable t
method <- match.arg(method)
switch(method,
IAPWS = {
Tc = 647.096 # Temperature at the critical point in °K
Pc = 22064 # Vapor pressure at the critical point in kPa
a1 = -7.85951783
a2 = 1.84408259
a3 = -11.7866497
a4 = 22.6807411
a5 = -15.9618719
a6 = 1.80122502
tau = 1 - Temp_K/Tc
ln_p_pc = (a1*tau + a2*tau^1.5 + a3*tau^3 + a4*tau^3.5 + a5*tau^4 + a6*tau^7.5)*Tc/Temp_K
ln_p = ln_p_pc + log(Pc)
wvp0 = exp(ln_p)
},
BensonKrause = {
a1 = 11.8571
a2 = 3840.70
a3 = 216961
vp = exp(a1 - (a2/Temp_K) - (a3/Temp_K^2)) # in atm
wvp0 = 101.325 * vp # in kPa
},
GreenCarritt = {
a1 = 18.1973
a2 = 373.16
a3 = 3.1813e-7
a4 = 26.1205
a5 = 1.8726e-2
a6 = 8.03945
a7 = 5.02802
wvp0 <- 101.325 * exp(a1 * (1-a2/Temp_K) + a3 *(1-exp(a4*(1- Temp_K/a2)))
- a5 * (1 - exp(a6 * (1-a2/Temp_K))) + a7 *log(a2/Temp_K))
},
WMO2008 = {
a1 = 6.112
a2 = 17.62
a3 = 243.12
vp = a1 * exp(a2 * Temp_K/(a3 + Temp_K)) # hPa
wvp0 = vp/10 # kPa
},
Antoine = {
# Antoine equation, http://www.watervaporpressure.com = Temp in °C
a1 = 8.07131
a2 = 1730.63
a3 = 233.426
vp = 10^(a1 - (a2/(a3+t))) # mm Hg
wvp0 = vp * 0.1333224 # kPa
},
Weiss = {
a1 = 24.4543
a2 = 67.4509
a3 = 4.8489
vp = a1 - a2*(100/Temp_K) - a3*log(Temp_K/100) # in atm
wvp0 = 101.325 * vp # in kPa
},
GoffGratch = {
Ts = 373.16 # steam point temperature in K
ews = 1013.246 # saturation pressure at steam point temperature, normal atmosphere
a1 = -7.90298
a3 = 5.02808
a4 = 1.3816*10^-7
a5 = 11.344
a6 = 8.1328*10^-3
a7 = -3.49149
log10ew = a1 * (Ts/Temp_K -1) + a3*log10(Ts/Temp_K) - a4*(10^(a5*(1-Temp_K/Ts))) +
a6 * (10^(a7*(Ts/Temp_K -1)) -1) + log10(ews)
ew = 10^log10ew # hPa
wvp0 = ew/10 # kPa
}
)
# salinity correction
sal_method = match.arg(sal_method)
switch(sal_method, # quality of salinity correction can be checked by comparison with Robinson's data, Water_vapor_pressure_decrease_for_seawater.Rda
Chabot = {
a1 = 5.197e-04
a2 = 1.226e-08
wvpS = wvp0 * (1 - (a1*s + a2*s^3) )
},
Green = {
a1 = 5.37e-4
wvpS = wvp0 * (1 - a1 * s)
},
none = {
wvpS = wvp0
}
)
wvpS
}
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