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carbon_chemistry_coefficients.jl
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struct CarbonChemistryCoefficients{FT}
Cᵈⁱᶜₖ₀ :: FT
Cᵈⁱᶜₖ₁ᵣ₉₃ :: FT
Cᵈⁱᶜₖ₂ᵣ₉₃ :: FT
Cᵈⁱᶜₖ₁ₘ₉₅ :: FT
Cᵈⁱᶜₖ₂ₘ₉₅ :: FT
Cᵈⁱᶜₖ₁ₗ₀₀ :: FT
Cᵈⁱᶜₖ₂ₗ₀₀ :: FT
Cᵇₖ₁ :: FT
Cᴴ²ᴼₖ₁ :: FT
Cᴾᴼ⁴ₖ₁ :: FT
Cᴾᴼ⁴ₖ₂ :: FT
Cᴾᴼ⁴ₖ₃ :: FT
Cˢⁱᵗₖ₁ :: FT
Cᴴ²ˢₖ₁ :: FT
Cᴺᴴ⁴ₖ₁ :: FT
Cᴴᶠᵦ₁ :: FT
Cᴴᶠₖ₁ :: FT
Cᴴˢᴼ⁴ₖ₁ :: FT
Cᶜᵃˡᶜⁱᵗᵉₛₚ :: FT
Cᵃʳᵃᵍᵒⁿⁱᵗᵉₛₚ :: FT
Cᴮᵀ :: FT
Cᶠᵀ :: FT
Cᶜᵃ :: FT
Cˢᴼ⁴ :: FT
H⁺ₛoverH⁺ₜ :: FT
H⁺ₜoverH⁺₃ :: FT
H⁺ₛoverH⁺₃ :: FT
end
"""
CarbonChemistryCoefficients(Θᶜ, Sᴬ, Δpᵦₐᵣ)
Return dissociation coefficients necessary to solve for the distribution of carbonate species.
"""
@inline function CarbonChemistryCoefficients(Θᶜ, Sᴬ, Δpᵦₐᵣ)
# Need a conversion from Absolute Salinity, Sᴬ, to Practical Salinity, Sᴾ
Sᵖ = Sᴬ
# Sᴾ = Sᴬ / (1.0 - 0.35 * Sᴬ / 35.0) ??
# What about converting temperature from Conservative Temperature to potential temperature?
Θᴷ = Θᶜ + Θᴷ_0ᵒC
# Also need to convert from Absolute Pressure, Pᴬ, to Applied Pressure in bars, the pressure relative to (1x) atm
return CarbonChemistryCoefficients(
Fᵈⁱᶜₖ₀(Θᴷ, Sᵖ, Pᵈⁱᶜₖ₀),
Fᵈⁱᶜₖ₁ᵣ₉₃(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᵈⁱᶜₖ₁ᵣ₉₃),
Fᵈⁱᶜₖ₂ᵣ₉₃(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᵈⁱᶜₖ₂ᵣ₉₃),
Fᵈⁱᶜₖ₁ₘ₉₅(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᵈⁱᶜₖ₁ₘ₉₅)/H⁺ₛoverH⁺ₜ(Θᴷ, Sᵖ, Δpᵦₐᵣ),
Fᵈⁱᶜₖ₂ₘ₉₅(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᵈⁱᶜₖ₂ₘ₉₅)/H⁺ₛoverH⁺ₜ(Θᴷ, Sᵖ, Δpᵦₐᵣ),
Fᵈⁱᶜₖ₁ₗ₀₀(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᵈⁱᶜₖ₁ₗ₀₀),
Fᵈⁱᶜₖ₂ₗ₀₀(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᵈⁱᶜₖ₂ₗ₀₀),
Fᵇₖ₁(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᴮₖ₁),
Fᴴ²ᴼₖ₁(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᴴ²ᴼₖ₁)/H⁺ₛoverH⁺ₜ(Θᴷ, Sᵖ, Δpᵦₐᵣ),
Fᴾᴼ⁴ₖ₁(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᴾᴼ⁴ₖ₁)/H⁺ₛoverH⁺ₜ(Θᴷ, Sᵖ, Δpᵦₐᵣ),
Fᴾᴼ⁴ₖ₂(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᴾᴼ⁴ₖ₂)/H⁺ₛoverH⁺ₜ(Θᴷ, Sᵖ, Δpᵦₐᵣ),
Fᴾᴼ⁴ₖ₃(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᴾᴼ⁴ₖ₃)/H⁺ₛoverH⁺ₜ(Θᴷ, Sᵖ, Δpᵦₐᵣ),
Fˢⁱᵗₖ₁(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pˢⁱᵗₖ₁)/H⁺ₛoverH⁺ₜ(Θᴷ, Sᵖ, Δpᵦₐᵣ),
Fᴴ²ˢₖ₁(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᴴ²ˢₖ₁)/H⁺ₛoverH⁺ₜ(Θᴷ, Sᵖ, Δpᵦₐᵣ),
Fᴺᴴ⁴ₖ₁(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᴺᴴ⁴ₖ₁)/H⁺ₛoverH⁺ₜ(Θᴷ, Sᵖ, Δpᵦₐᵣ),
Fᴴᶠᵦ₁(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᴴᶠᵦ₁),
Fᴴᶠₖ₁(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᴴᶠₖ₁),
Fᴴˢᴼ⁴ₖ₁(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᴴˢᴼ⁴ₖ₁), # Leave on the free scale
Fᶜᵃˡᶜⁱᵗᵉₛₚ(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᶜᵃˡᶜⁱᵗᵉₛₚ),
Fᵃʳᵃᵍᵒⁿⁱᵗᵉₛₚ(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᵃʳᵃᵍᵒⁿⁱᵗᵉₛₚ),
Bᵀᴼᵀ(Sᵖ, Pᴮᵀᴼᵀ),
Fᵀᴼᵀ(Sᵖ, Pᶠᵀᴼᵀ),
Caᵀᴼᵀ(Sᵖ, Pᶜᵃᵀᴼᵀ),
SO₄ᵀᴼᵀ(Sᵖ, Pˢᴼ⁴ᵀᴼᵀ),
H⁺ₛoverH⁺ₜ(Θᴷ, Sᵖ, Δpᵦₐᵣ),
H⁺ₜoverH⁺₃(Θᴷ, Sᵖ, Δpᵦₐᵣ),
H⁺ₛoverH⁺₃(Θᴷ, Sᵖ, Δpᵦₐᵣ),
)
end
# Gas constant
gasconst_bar_cm3_o_mol_k = 83.14472 # Handbook (2007)
# 0 degrees centigrade in Kelvin
Θᴷ_0ᵒC = 273.15 # Handbook (2007)
@inline Θᴷ₁₀₀(Θᴷ) = Θᴷ/100
@inline Sᴾ⁰⁵(Sᵖ) = sqrt(Sᵖ)
@inline ΘᵒC(Θᴷ) = Θᴷ - Θᴷ_0ᵒC
Base.@kwdef struct Pᵈˢᵖ{FT}
a₀ :: FT = - 34.8
end
@inline ΔSᵖ(Sᵖ, params = Pᵈˢᵖ) = Sᵖ + params().a₀
@inline Rₜ(Θᴷ) = gasconst_bar_cm3_o_mol_k * Θᴷ
Base.@kwdef struct Pᴴ²⁰ˢʷ{FT}
a₀ :: FT = 1.0
a₁ :: FT = - 0.001005
end
"""
H₂Oˢʷ(Sᵖ, Pᴴ²⁰ˢʷ)
Return the mass of pure water in one kg of seawater
of practical salinity, `Sᵖ`.
References: "libthdyct" -- derived by Munhoven (1997) from data by Millero (1982)
"Handbook (2007)" -- Handbook (2007)
pH scale: N/A
"""
@inline function H₂Oˢʷ(Sᵖ, params = Pᴴ²⁰ˢʷ)
(; a₀, a₁) = params()
return a₀ + a₁ * Sᵖ
end
#H₂Oˢʷ(Sᵖ, Pᴴ²⁰ˢʷ) = 1. - 0.0010049*Sᵖ # libthdyct
Base.@kwdef struct Pᵘˢ{FT}
a₀ :: FT = 0.019924
end
"""
μₛ(Sᵖ)
Return ionic strength in mol/kg-SW, for given practical salinity, `Sᵖ`.
References: "libthdyct" -- derived by Munhoven (1997) from data by Millero (1982)
"Handbook (2007)" -- Handbook (2007)
pH scale: N/A
"""
@inline μₛ(Sᵖ, params = Pᵘˢ) = (params().a₀ * Sᵖ) / H₂Oˢʷ(Sᵖ) # Handbook (2007)
# μₛ(Sᵖ) = (0.019920 * Sᵖ) / H₂Oˢʷ(Sᵖ, Pᴴ²⁰ˢʷ)# libthdyct
Base.@kwdef struct Pᴮᵀᴼᵀ{FT}
a₀ :: FT = 0.000416
a₁ :: FT = 35.0
a₂ :: FT = 1.0
end
"""
Bᵀᴼᵀ(Sᵖ, Pᴮᵀᴼᵀ)
Return total borate concentration in mol/kg-SW given practical salinity, `Sᵖ`.
References: Uppström (1974), cited by Dickson et al. (2007, chapter 5, p 10)
Millero (1982) cited in Millero (1995)
"""
@inline function Bᵀᴼᵀ(Sᵖ, params = Pᴮᵀᴼᵀ)
(; a₀, a₁, a₂) = params()
return a₀ * (Sᵖ / a₁) / a₂
end
#Bᵀᴼᵀ(Sᵖ, Pᴮᵀᴼᵀ) = 0.000232 * (Sᵖ/1.80655)/10.811
Base.@kwdef struct Pᶜᵃᵀᴼᵀ{FT}
a₀ :: FT = 0.02127
a₁ :: FT = 40.078
a₂ :: FT = 1.80655
end
"""
Caᵀᴼᵀ(Sᵖ, Pᶜᵃᵀᴼᵀ)
Return calcium concentration in mol/kg-SW given practical salinity, `Sᵖ`.
References: Culkin and Cox (1966),
Culkin (1967),
Riley and Tongudai (1967)
"""
@inline function Caᵀᴼᵀ(Sᵖ, params = Pᶜᵃᵀᴼᵀ)
(; a₀, a₁, a₂) = params()
return (a₀ / a₁) * (Sᵖ / a₂)
end
# Caᵀᴼᵀ(Sᵖ, Pᶜᵃᵀᴼᵀ) = 0.010282*(Sᵖ/35.)
Base.@kwdef struct Pᶠᵀᴼᵀ{FT}
a₀ :: FT = 6.8e-5
a₁ :: FT = 35.0
end
"""
Fᵀᴼᵀ(Sᵖ, Pᶠᵀᴼᵀ)
Return total fluoride concentration in mol/kg-SW given practical salinity, `Sᵖ`.
References: Culkin (1965) (???)
"""
@inline function Fᵀᴼᵀ(Sᵖ, params = Pᶠᵀᴼᵀ)
(; a₀, a₁) = params()
return a₀ * (Sᵖ / a₁)
end
Base.@kwdef struct Pˢᴼ⁴ᵀᴼᵀ{FT}
a₀ :: FT = 0.1400
a₁ :: FT = 96.062
a₂ :: FT = 1.80655
end
"""
SO₄ᵀᴼᵀ(Sᵖ, Pˢᴼ⁴ᵀᴼᵀ)
Return total sulfate concentration in mol/kg-SW given practical salinity, `Sᵖ`.
References: Morris, A.W. and Riley, J.P. (1966) quoted in Handbook (2007)
"""
@inline function SO₄ᵀᴼᵀ(Sᵖ, params = Pˢᴼ⁴ᵀᴼᵀ)
(; a₀, a₁, a₂) = params()
return (a₀ / a₁) * (Sᵖ / a₂)
end
#SO₄ᵀᴼᵀ(Sᵖ, Pˢᴼ⁴ᵀᴼᵀ) = 0.028234*(Sᵖ/35.)
Base.@kwdef struct Pᴺᴴ⁴ᵀᴼᵀ{FT}
a₀ :: FT = 0.0001
a₁ :: FT = 17.031
a₂ :: FT = 1.80655
end
# I cannot independently verify this equation. It is not in the Handbook (2007)
#"""
#NH₄ᵀᴼᵀ(Sᵖ, Pᴺᴴ⁴ᵀᴼᵀ)
#
#Return total ammonium concentration in mol/kg-SW given practical salinity, `Sᵖ`.
#References: Yamamoto (1995)
#"""
#@inline function NH₄ᵀᴼᵀ(Sᵖ, params = Pᴺᴴ⁴ᵀᴼᵀ)
# (; a₀, a₁, a₂) = params()
# return (a₀ / a₁) * (Sᵖ / a₂)
#end
#
#Base.@kwdef struct Pᴾᴼ⁴ᵀᴼᵀ{FT}
# a₀ :: FT = 0.0001
# a₁ :: FT = 94.971
# a₂ :: FT = 1.80655
#end
#
#"""
#PO₄ᵀᴼᵀ(Sᵖ, Pᴾᴼ⁴ᵀᴼᵀ)
#
#Return total phosphate concentration in mol/kg-SW given practical salinity, `Sᵖ`.
#References: Millero (1995)
#"""
#@inline function PO₄ᵀᴼᵀ(Sᵖ, params = Pᴾᴼ⁴ᵀᴼᵀ)
# (; a₀, a₁, a₂) = params()
# return (a₀ / a₁) * (Sᵖ / a₂)
#end
#
#Base.@kwdef struct Pˢⁱᴼ³ᵀᴼᵀ{FT}
# a₀ :: FT = 0.0001
# a₁ :: FT = 60.084
# a₂ :: FT = 1.80655
#end
#
#"""
#SiO₃ᵀᴼᵀ(Sᵖ, Pˢⁱᴼ³ᵀᴼᵀ)
#
#Return total silicate concentration in mol/kg-SW given practical salinity, `Sᵖ`.
#References: Millero (1995)
#"""
#@inline function SiO₃ᵀᴼᵀ(Sᵖ, params = Pˢⁱᴼ³ᵀᴼᵀ)
# (; a₀, a₁, a₂) = params()
# return (a₀ / a₁) * (Sᵖ / a₂)
#end
#
#Base.@kwdef struct Pᴴ²ˢᵀᴼᵀ{FT}
# a₀ :: FT = 0.0001
# a₁ :: FT = 34.082
# a₂ :: FT = 1.80655
#end
#
#"""
#H₂Sᵀᴼᵀ(Sᵖ, Pᴴ²ˢᵀᴼᵀ)
#
#Return total hydrogen sulfide concentration in mol/kg-SW given practical salinity, `Sᵖ`.
#References: Dickson (1990)
#"""
#@inline function H₂Sᵀᴼᵀ(Sᵖ, params = Pᴴ²ˢᵀᴼᵀ)
# (; a₀, a₁, a₂) = params()
# return (a₀ / a₁) * (Sᵖ / a₂)
#end
Base.@kwdef struct Pᵈⁱᶜₖ₀{FT}
a₀ :: FT = -60.2409
a₁ :: FT = 93.4517
a₂ :: FT = 23.3585
b₀ :: FT = 0.023517
b₁ :: FT = - 0.023656
b₂ :: FT = 0.0047036
end
"""
Fᵈⁱᶜₖ₀(Θᴷ, Sᵖ, Pᵈⁱᶜₖ₀)
Return hydration constant of CO₂ in (mol/kg-SW)/atm given temperature
in K, `Θᴷ`, practical salinity, `Sᵖ`, and coefficients, `Pᵈⁱᶜₖ₀`.
CO₂ + H₂O <-> H₂CO₃
References: Weiss (1979)
pH scale : N/A
Note : currently no pressure correction
"""
@inline function Fᵈⁱᶜₖ₀(Θᴷ, Sᵖ, params = Pᵈⁱᶜₖ₀)
(; a₀, a₁, a₂, b₀, b₁, b₂) = params()
return exp(
a₀ +
a₁/Θᴷ₁₀₀(Θᴷ) +
a₂*log(Θᴷ₁₀₀(Θᴷ)) +
(
b₀ +
b₁*(Θᴷ₁₀₀(Θᴷ)) +
b₂*Θᴷ₁₀₀(Θᴷ)*Θᴷ₁₀₀(Θᴷ)
)*Sᵖ
)
end
Base.@kwdef struct Pᵈⁱᶜₖ₁ᵣ₉₃{FT}
a₀ :: FT = 2.83655
a₁ :: FT = -2307.1266
a₂ :: FT = - 1.5529413
b₀ :: FT = - 0.20760841
b₁ :: FT = - 4.0484
b₂ :: FT = 0.08468345
b₃ :: FT = - 0.00654208
v₀ :: FT = - 25.5
v₁ :: FT = - 0.151
v₂ :: FT = 0.1271
k₀ :: FT = - 3.08e-3
k₁ :: FT = - 0.578e-3
k₂ :: FT = 0.0877e-3
end
"""
Fᵈⁱᶜₖ₁ᵣ₉₃(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᵈⁱᶜₖ₁ᵣ₉₃)
Return the first dissociation constant of carbonic acid in mol/kg-SW, given
temperature in K, `Θᴷ`, practical salinity, `Sᵖ`, applied pressure,
`Δpᵦₐᵣ`, and coefficients, `Pᵈⁱᶜₖ₁ᵣ₉₃`.
H₂CO₃ <-> HCO₃⁻ + H⁺
References: Roy et al. (1993) -- also Handbook (1994)
Millero (1979) pressure correction
pH scale : Total
Valid range: T: 0-45 S: 5-45.
Note : converted here from mol/kg-H2O to mol/kg-SW
"""
@inline function Fᵈⁱᶜₖ₁ᵣ₉₃(Θᴷ, Sᵖ, Δpᵦₐᵣ, params = Pᵈⁱᶜₖ₁ᵣ₉₃)
(; a₀, a₁, a₂, b₀, b₁, b₂, b₃, v₀, v₁, v₂, k₀, k₁, k₂) = params()
ln_kc1_p0 = (a₀ +
a₁/Θᴷ +
a₂*log(Θᴷ)
+ (
b₀ +
b₁/Θᴷ
)*Sᴾ⁰⁵(Sᵖ)
+ b₂*Sᵖ
+ b₃*Sᵖ*Sᴾ⁰⁵(Sᵖ)
)
"Pressure correction for applied pressure /= 0"
ln_kc1_pp = (-(v₀ +
v₁*ΔSᵖ(Sᵖ) +
v₂*ΘᵒC(Θᴷ))
+(
k₀ +
k₁*ΔSᵖ(Sᵖ) +
k₂*ΘᵒC(Θᴷ)
)*(Δpᵦₐᵣ/2.)
)*(Δpᵦₐᵣ/Rₜ(Θᴷ))
return exp(ln_kc1_p0 + ln_kc1_pp) * H₂Oˢʷ(Sᵖ)
end
Base.@kwdef struct Pᵈⁱᶜₖ₂ᵣ₉₃{FT}
a₀ :: FT = - 9.226508
a₁ :: FT = -3351.6106
a₂ :: FT = - 0.2005743
b₀ :: FT = - 0.106901773
b₁ :: FT = - 23.9722
b₂ :: FT = 0.1130822
b₃ :: FT = - 0.00846934
v₀ :: FT = - 15.82
v₁ :: FT = 0.321
v₂ :: FT = - 0.0219
k₀ :: FT = 1.13e-3
k₁ :: FT = - 0.314e-3
k₂ :: FT = - 0.1475e-3
end
"""
Fᵈⁱᶜₖ₂ᵣ₉₃(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᵈⁱᶜₖ₂ᵣ₉₃)
Return the second dissociation constant of carbonic acid in mol/kg-SW, given
temperature in K, `Θᴷ`, practical salinity, `Sᵖ`, applied pressure, `Δpᵦₐᵣ`, and
coefficients, `Pᵈⁱᶜₖ₂ᵣ₉₃`.
HCO₃⁻ <-> CO₃²⁻ + H⁺
References: Roy et al. (1993) -- also Handbook (1994)
Millero (1979) pressure correction
pH scale : Total
Valid range: T: 0-45 S: 5-45.
Note : converted here from mol/kg-H2O to mol/kg-SW
"""
@inline function Fᵈⁱᶜₖ₂ᵣ₉₃(Θᴷ, Sᵖ, Δpᵦₐᵣ, params = Pᵈⁱᶜₖ₂ᵣ₉₃)
(; a₀, a₁, a₂, b₀, b₁, b₂, b₃, v₀, v₁, v₂, k₀, k₁, k₂) = params()
ln_kc2_p0 = (a₀ +
a₁/Θᴷ +
a₂*log(Θᴷ)
+ (
b₀ +
b₁/Θᴷ
)*Sᴾ⁰⁵(Sᵖ)
+ b₂*Sᵖ
+ b₃*Sᵖ*Sᴾ⁰⁵(Sᵖ)
)
"Pressure correction for applied pressure /= 0"
ln_kc2_pp = (-(v₀ +
v₁*ΔSᵖ(Sᵖ) +
v₂*ΘᵒC(Θᴷ))
+(
k₀ +
k₁*ΔSᵖ(Sᵖ) +
k₂*ΘᵒC(Θᴷ)
)*(Δpᵦₐᵣ/2.)
)*(Δpᵦₐᵣ/Rₜ(Θᴷ))
return exp(ln_kc2_p0 + ln_kc2_pp) * H₂Oˢʷ(Sᵖ)
end
Base.@kwdef struct Pᵈⁱᶜₖ₁ₘ₉₅{FT}
a₀ :: FT = 2.18867
a₁ :: FT = -2275.0360
a₂ :: FT = - 1.468591
b₀ :: FT = - 0.138681
b₁ :: FT = - 9.33291
b₂ :: FT = 0.0726483
b₃ :: FT = - 0.00574938
v₀ :: FT = - 25.5
v₁ :: FT = - 0.151
v₂ :: FT = 0.1271
k₀ :: FT = - 3.08e-3
k₁ :: FT = - 0.578e-3
k₂ :: FT = 0.0877e-3
end
"""
Fᵈⁱᶜₖ₁ₘ₉₅(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᵈⁱᶜₖ₁ₘ₉₅)
Return the first dissociation constant of carbonic acid in mol/kg-SW, given
temperature in K, `Θᴷ`, practical salinity, `Sᵖ`, applied pressure,
`Δpᵦₐᵣ`, and coefficients, `Pᵈⁱᶜₖ₁ₘ₉₅`.
H₂CO₃ <-> HCO₃⁻ + H⁺
References: Millero (1995, eq 50 -- ln K1(COM))
Millero (1982) pressure correction
pH scale: SWS
"""
@inline function Fᵈⁱᶜₖ₁ₘ₉₅(Θᴷ, Sᵖ, Δpᵦₐᵣ, params = Pᵈⁱᶜₖ₁ₘ₉₅)
(; a₀, a₁, a₂, b₀, b₁, b₂, b₃, v₀, v₁, v₂, k₀, k₁, k₂) = params()
ln_kc1_p0 = (a₀ +
a₁/Θᴷ +
a₂*log(Θᴷ)
+ (
b₀ +
b₁/Θᴷ
)*Sᴾ⁰⁵(Sᵖ)
+ b₂*Sᵖ
+ b₃*Sᵖ*Sᴾ⁰⁵(Sᵖ)
)
"Pressure correction for applied pressure /= 0"
ln_kc1_pp = (-(v₀ +
v₁*ΔSᵖ(Sᵖ) +
v₂*ΘᵒC(Θᴷ))
+(
k₀ +
k₁*ΔSᵖ(Sᵖ) +
k₂*ΘᵒC(Θᴷ)
)*(Δpᵦₐᵣ/2.)
)*(Δpᵦₐᵣ/Rₜ(Θᴷ))
return exp(ln_kc1_p0 + ln_kc1_pp)
end
Base.@kwdef struct Pᵈⁱᶜₖ₂ₘ₉₅{FT}
a₀ :: FT = - 0.84226
a₁ :: FT = -3741.1288
a₂ :: FT = - 1.437139
b₀ :: FT = - 0.128417
b₁ :: FT = - 24.41239
b₂ :: FT = 0.1195308
b₃ :: FT = - 0.00912840
v₀ :: FT = - 15.82
v₁ :: FT = 0.321
v₂ :: FT = - 0.0219
k₀ :: FT = 1.13e-3
k₁ :: FT = - 0.314e-3
k₂ :: FT = - 0.1475e-3
end
"""
Fᵈⁱᶜₖ₂ₘ₉₅(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᵈⁱᶜₖ₂ₘ₉₅)
Return the second dissociation constant of carbonic acid in mol/kg-SW, given
temperature in K, `Θᴷ`, practical salinity, `Sᵖ`, applied pressure, `Δpᵦₐᵣ`, and
coefficients, `Pᵈⁱᶜₖ₂ₘ₉₅`.
HCO₃⁻ <-> CO₃²⁻ + H⁺
References: Millero (1995, eq 51 -- ln K2(COM))
Millero (1979) pressure correction
pH scale: SWS
"""
@inline function Fᵈⁱᶜₖ₂ₘ₉₅(Θᴷ, Sᵖ, Δpᵦₐᵣ, params = Pᵈⁱᶜₖ₂ₘ₉₅)
(; a₀, a₁, a₂, b₀, b₁, b₂, b₃, v₀, v₁, v₂, k₀, k₁, k₂) = params()
ln_kc2_p0 = (a₀ +
a₁/Θᴷ +
a₂*log(Θᴷ)
+ (
b₀ +
b₁/Θᴷ
)*Sᴾ⁰⁵(Sᵖ) +
b₂*Sᵖ +
b₃*Sᵖ*Sᴾ⁰⁵(Sᵖ)
)
"Pressure correction for applied pressure /= 0"
ln_kc2_pp = (-(v₀ +
v₁*ΔSᵖ(Sᵖ) +
v₂*ΘᵒC(Θᴷ))
+(
k₀ +
k₁*ΔSᵖ(Sᵖ) +
k₂*ΘᵒC(Θᴷ)
)*(Δpᵦₐᵣ/2.)
)*(Δpᵦₐᵣ/Rₜ(Θᴷ))
return exp(ln_kc2_p0 + ln_kc2_pp)
end
Base.@kwdef struct Pᵈⁱᶜₖ₁ₗ₀₀{FT}
a₀ :: FT = 61.2172
a₁ :: FT = -3633.86
a₂ :: FT = - 9.67770
b₀ :: FT = 0.011555
b₁ :: FT = - 0.0001152
v₀ :: FT = - 25.5
v₁ :: FT = - 0.151
v₂ :: FT = 0.1271
k₀ :: FT = - 3.08e-3
k₁ :: FT = - 0.578e-3
k₂ :: FT = 0.0877e-3
end
"""
Fᵈⁱᶜₖ₁ₗ₀₀(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᵈⁱᶜₖ₁ₗ₀₀)
Return the first dissociation constant of carbonic acid in mol/kg-SW, given
temperature in K, `Θᴷ`, practical salinity, `Sᵖ`, applied pressure,
`Δpᵦₐᵣ`, and coefficients, `Pᵈⁱᶜₖ₁ₗ₀₀`.
H₂CO₃ <-> HCO₃⁻ + H⁺
References: Luecker et al. (2000) -- also Handbook (2007)
Millero (1979) pressure correction
pH scale: Total
"""
@inline function Fᵈⁱᶜₖ₁ₗ₀₀(Θᴷ, Sᵖ, Δpᵦₐᵣ, params = Pᵈⁱᶜₖ₁ₗ₀₀)
(; a₀, a₁, a₂, b₀, b₁, v₀, v₁, v₂, k₀, k₁, k₂) = params()
log10_kc1_p0 = (a₀ +
a₁/Θᴷ +
a₂*log(Θᴷ)
+ (
b₀ +
b₁*Sᵖ
)*Sᵖ
)
"Pressure correction for applied pressure /= 0"
ln_kc1_pp = (-(v₀ +
v₁*ΔSᵖ(Sᵖ) +
v₂*ΘᵒC(Θᴷ))
+(
k₀ +
k₁*ΔSᵖ(Sᵖ) +
k₂*ΘᵒC(Θᴷ)
)*(Δpᵦₐᵣ/2.)
)*(Δpᵦₐᵣ/Rₜ(Θᴷ))
return 10^(log10_kc1_p0) * exp(ln_kc1_pp)
end
Base.@kwdef struct Pᵈⁱᶜₖ₂ₗ₀₀{FT}
a₀ :: FT = - 25.9290
a₁ :: FT = - 471.78
a₂ :: FT = 3.16967
b₀ :: FT = 0.01781
b₁ :: FT = - 0.0001122
v₀ :: FT = - 15.82
v₁ :: FT = 0.321
v₂ :: FT = - 0.0219
k₀ :: FT = 1.13e-3
k₁ :: FT = - 0.314e-3
k₂ :: FT = - 0.1475e-3
end
"""
Fᵈⁱᶜₖ₂ₗ₀₀(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᵈⁱᶜₖ₂ₗ₀₀)
Return the second dissociation constant of carbonic acid in mol/kg-SW, given
temperature in K, `Θᴷ`, practical salinity, `Sᵖ`, applied pressure, `Δpᵦₐᵣ`, and
coefficients, `Pᵈⁱᶜₖ₂ₗ₀₀`.
HCO₃⁻ <-> CO₃²⁻ + H⁺
References: Luecker et al. (2000) -- also Handbook (2007)
Millero (1979) pressure correction
pH scale: Total
"""
@inline function Fᵈⁱᶜₖ₂ₗ₀₀(Θᴷ, Sᵖ, Δpᵦₐᵣ, params = Pᵈⁱᶜₖ₂ₗ₀₀)
(; a₀, a₁, a₂, b₀, b₁, v₀, v₁, v₂, k₀, k₁, k₂) = params()
log10_kc2_p0 = (a₀ +
a₁/Θᴷ +
a₂*log(Θᴷ)
+ (
b₀ +
b₁*Sᵖ
)*Sᵖ
)
"Pressure correction for applied pressure /= 0"
ln_kc2_pp = (-(v₀ +
v₁*ΔSᵖ(Sᵖ) +
v₂*ΘᵒC(Θᴷ))
+(
k₀ +
k₁*ΔSᵖ(Sᵖ) +
k₂*ΘᵒC(Θᴷ)
)*(Δpᵦₐᵣ/2.)
)*(Δpᵦₐᵣ/Rₜ(Θᴷ))
return 10^(log10_kc2_p0) * exp(ln_kc2_pp)
end
Base.@kwdef struct Pᴮₖ₁{FT}
a₀ :: FT = - 8966.90
a₁ :: FT = - 2890.53
a₂ :: FT = - 77.942
a₃ :: FT = 1.728
a₄ :: FT = - 0.0996
b₀ :: FT = 148.0248
b₁ :: FT = 137.1942
b₂ :: FT = 1.62142
c₀ :: FT = - 24.4344
c₁ :: FT = - 25.085
c₂ :: FT = - 0.2474
d₀ :: FT = 0.053105
v₀ :: FT = - 29.48
v₁ :: FT = 0.295
v₂ :: FT = 0.1622
v₃ :: FT = - 0.002608
k₀ :: FT = - 2.84e-3
k₁ :: FT = 0.354e-3
end
"""
Fᵇₖ₁(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᴮₖ₁)
Return boric acid dissociation constant in mol/kg-SW, given temperature in K,
`Θᴷ`, practical salinity, `Sᵖ`, applied pressure, `Δpᵦₐᵣ`, and coefficients, `Pᴮₖ₁`.
References: Dickson (1990, eq. 23) -- also Handbook (2007, eq. 37)
Millero (1979) pressure correction
pH scale : total
"""
@inline function Fᵇₖ₁(Θᴷ, Sᵖ, Δpᵦₐᵣ, params = Pᴮₖ₁)
(; a₀, a₁, a₂, a₃, a₄, b₀, b₁, b₂, c₀, c₁, c₂, d₀, v₀, v₁, v₂, v₃, k₀, k₁) = params()
ln_kb_p0 = ((a₀ +
Sᴾ⁰⁵(Sᵖ)*(a₁ +
Sᴾ⁰⁵(Sᵖ)*(a₂ +
Sᴾ⁰⁵(Sᵖ)*(a₃ +
Sᴾ⁰⁵(Sᵖ)* a₄
)))) / Θᴷ
+ b₀ +
Sᴾ⁰⁵(Sᵖ)*(
b₁ +
b₂*Sᴾ⁰⁵(Sᵖ)
) +
(c₀ +
Sᴾ⁰⁵(Sᵖ)*(
c₁ +
c₂*Sᴾ⁰⁵(Sᵖ))
) * log(Θᴷ)
+ d₀*Sᴾ⁰⁵(Sᵖ)*Θᴷ
)
"Pressure correction for applied pressure /= 0"
ln_kb_pp = (-(v₀ +
v₁*ΔSᵖ(Sᵖ) +
v₂*ΘᵒC(Θᴷ) +
v₃*ΘᵒC(Θᴷ)*ΘᵒC(Θᴷ))
+(
k₀ +
k₁*ΔSᵖ(Sᵖ)
)*(Δpᵦₐᵣ/2.)
)*(Δpᵦₐᵣ/Rₜ(Θᴷ))
return exp(ln_kb_p0 + ln_kb_pp)
end
Base.@kwdef struct Pᴴ²ᴼₖ₁{FT}
a₀ :: FT = 148.9802
a₁ :: FT = -13847.26
a₂ :: FT = - 23.6521
b₀ :: FT = - 5.977
b₁ :: FT = 118.67
b₂ :: FT = 1.0495
c₀ :: FT = - 0.01615
v₀ :: FT = - 20.02
v₁ :: FT = 0.1119
v₂ :: FT = - 0.1409E-02
k₀ :: FT = - 5.13e-3
k₁ :: FT = 0.0794e-3
end
"""
Fᴴ²ᴼₖ₁(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᴴ²ᴼₖ₁)
Return dissociation constant of water in (mol/kg-SW)^2, given temperature in K,
`Θᴷ`, practical salinity, `Sᵖ`, applied pressure, `Δpᵦₐᵣ`, and coefficients, `Pᴴ²ᴼₖ₁`.
References: Millero (1995) for value at p_bar = 0
Millero (pers. comm. 1996) for pressure correction
pH scale : SWS
"""
@inline function Fᴴ²ᴼₖ₁(Θᴷ, Sᵖ, Δpᵦₐᵣ, params = Pᴴ²ᴼₖ₁)
(; a₀, a₁, a₂, b₀, b₁, b₂, c₀, v₀, v₁, v₂, k₀, k₁) = params()
ln_kw_p0 = (a₀ +
a₁/Θᴷ +
a₂*log(Θᴷ) +
(b₀ +
b₁/Θᴷ +
b₂*log(Θᴷ)
)*Sᴾ⁰⁵(Sᵖ) +
c₀*Sᵖ
)
"Pressure correction for applied pressure /= 0"
ln_kw_pp = (-(v₀ +
v₁*ΘᵒC(Θᴷ) +
v₂*ΘᵒC(Θᴷ)*ΘᵒC(Θᴷ))
+(
k₀ +
k₁*ΘᵒC(Θᴷ)
)*(Δpᵦₐᵣ/2.)
)*(Δpᵦₐᵣ/Rₜ(Θᴷ))
return exp(ln_kw_p0 + ln_kw_pp)
end
Base.@kwdef struct Pᴾᴼ⁴ₖ₁{FT}
a₀ :: FT = 115.54
a₁ :: FT = -4576.752
a₂ :: FT = - 18.453
b₀ :: FT = 0.69171
b₁ :: FT = - 106.736
b₂ :: FT = - 0.01844
b₃ :: FT = - 0.65643
v₀ :: FT = - 14.51
v₁ :: FT = 0.1211
v₂ :: FT = - 0.321E-03
k₀ :: FT = - 2.67e-3
k₁ :: FT = 0.0427e-3
end
"""
Fᴾᴼ⁴ₖ₁(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᴾᴼ⁴ₖ₁)
Return the first dissociation constant of phosphoric acid (H3PO4) in seawater, given
temperature in K, `Θᴷ`, practical salinity, `Sᵖ`, applied pressure, `Δpᵦₐᵣ`, and coefficients, `Pᴾᴼ⁴ₖ₁`.
References: Yao and Millero (1995)
Millero (1995) for pressure correction
pH scale : SWS
"""
@inline function Fᴾᴼ⁴ₖ₁(Θᴷ, Sᵖ, Δpᵦₐᵣ, params = Pᴾᴼ⁴ₖ₁)
(; a₀, a₁, a₂, b₀, b₁, b₂, b₃, v₀, v₁, v₂, k₀, k₁) = params()
ln_kp1_p0 = (a₀ +
a₁/Θᴷ +
a₂*log(Θᴷ) +
(
b₀ +
b₁/Θᴷ
)*Sᴾ⁰⁵(Sᵖ) +
(
b₂ +
b₃/Θᴷ
)*Sᵖ)
"Pressure correction for applied pressure /= 0"
ln_kp1_pp = (-(v₀ +
v₁*ΘᵒC(Θᴷ) +
v₂*ΘᵒC(Θᴷ)*ΘᵒC(Θᴷ))
+(
k₀ +
k₁*ΘᵒC(Θᴷ)
)*(Δpᵦₐᵣ/2.)
)*(Δpᵦₐᵣ/Rₜ(Θᴷ))
return exp(ln_kp1_p0 + ln_kp1_pp)
end
Base.@kwdef struct Pᴾᴼ⁴ₖ₂{FT}
a₀ :: FT = 172.1033
a₁ :: FT = - 8814.715
a₂ :: FT = - 27.927
b₀ :: FT = 1.3566
b₁ :: FT = - 160.340
b₂ :: FT = - 0.05778
b₃ :: FT = 0.37335
v₀ :: FT = - 23.12
v₁ :: FT = 0.1758
v₂ :: FT = - 0.002647
k₀ :: FT = - 5.15e-3
k₁ :: FT = 0.09e-3
end
"""
Fᴾᴼ⁴ₖ₂(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᴾᴼ⁴ₖ₂)
Return the second dissociation constant of phosphoric acid (H3PO4) in seawater, given
temperature in K, `Θᴷ`, practical salinity, `Sᵖ`, applied pressure, `Δpᵦₐᵣ`, and coefficients, `Pᴾᴼ⁴ₖ₂`.
References: Yao and Millero (1995)
Millero (1995) for pressure correction
pH scale : SWS
"""
@inline function Fᴾᴼ⁴ₖ₂(Θᴷ, Sᵖ, Δpᵦₐᵣ, params = Pᴾᴼ⁴ₖ₂)
(; a₀, a₁, a₂, b₀, b₁, b₂, b₃, v₀, v₁, v₂, k₀, k₁) = params()
ln_kp2_p0 = (a₀ +
a₁/Θᴷ +
a₂*log(Θᴷ) +
(
b₀ +
b₁/Θᴷ
)*Sᴾ⁰⁵(Sᵖ) +
(
b₂ +
b₃/Θᴷ
)*Sᵖ)
"Pressure correction for applied pressure /= 0"
ln_kp2_pp = (-(v₀ +
v₁*ΘᵒC(Θᴷ) +
v₂*ΘᵒC(Θᴷ)*ΘᵒC(Θᴷ))
+(
k₀ +
k₁*ΘᵒC(Θᴷ)
)*(Δpᵦₐᵣ/2.)
)*(Δpᵦₐᵣ/Rₜ(Θᴷ))
return exp(ln_kp2_p0 + ln_kp2_pp)
end
Base.@kwdef struct Pᴾᴼ⁴ₖ₃{FT}
a₀ :: FT = - 18.126
a₁ :: FT = - 3070.75
a₂ :: FT = 2.81197
a₃ :: FT = 17.27039
a₄ :: FT = - 0.09984
a₅ :: FT = - 44.99486
v₀ :: FT = - 26.57
v₁ :: FT = 0.2020
v₂ :: FT = - 3.042e-3
k₀ :: FT = - 4.08e-3
k₁ :: FT = 0.0714e-3
end
"""
Fᴾᴼ⁴ₖ₃(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᴾᴼ⁴ₖ₃)
Return the third dissociation constant of phosphoric acid (H3PO4) in seawater, given
temperature in K, `Θᴷ`, practical salinity, `Sᵖ`, applied pressure, `Δpᵦₐᵣ`, and coefficients, `Pᴾᴼ⁴ₖ₃`.
References: Yao and Millero (1995)
Millero (1995) for pressure correction
pH scale : SWS
"""
@inline function Fᴾᴼ⁴ₖ₃(Θᴷ, Sᵖ, Δpᵦₐᵣ, params = Pᴾᴼ⁴ₖ₃)
(; a₀, a₁, a₂, a₃, a₄, a₅, v₀, v₁, v₂, k₀, k₁) = params()
ln_kp3_p0 = (a₀ +
a₁/Θᴷ +
(
a₂ +
a₃/Θᴷ
)*Sᴾ⁰⁵(Sᵖ) +
(
a₄ +
a₅/Θᴷ
)*Sᵖ)
"Pressure correction for applied pressure /= 0"
ln_kp3_pp = (-(v₀ +
v₁*ΘᵒC(Θᴷ) +
v₂*ΘᵒC(Θᴷ)*ΘᵒC(Θᴷ))
+(
k₀ +
k₁*ΘᵒC(Θᴷ)
)*(Δpᵦₐᵣ/2.)
)*(Δpᵦₐᵣ/Rₜ(Θᴷ))
return exp(ln_kp3_p0 + ln_kp3_pp)
end
Base.@kwdef struct Pˢⁱᵗₖ₁{FT}
a₀ :: FT = 117.40
a₁ :: FT = - 8904.2
a₂ :: FT = - 19.334
b₀ :: FT = 3.5913
b₁ :: FT = - 458.79
b₂ :: FT = - 1.5998
b₃ :: FT = 188.74
c₀ :: FT = 0.07871
c₁ :: FT = - 12.1652
v₀ :: FT = - 29.48
v₁ :: FT = 0.0
v₂ :: FT = 0.1622
v₃ :: FT = - 0.002608
k₀ :: FT = - 2.84e-3
k₁ :: FT = 0.354e-3
end
"""
Fˢⁱᵗₖ₁(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pˢⁱᵗₖ₁)
Return the first dissociation constant of silicic acid (H4SiO4) in seawater, given
temperature in K, `Θᴷ`, practical salinity, `Sᵖ`, applied pressure, `Δpᵦₐᵣ`, and coefficients, `Pˢⁱᵗₖ₁`.
References: Yao and Millero (1995) cited by Millero (1995)
pH scale : SWS (according to Dickson et al, 2007)
Note : No pressure correction available
Note : converted here from mol/kg-H2O to mol/kg-sw
"""
@inline function Fˢⁱᵗₖ₁(Θᴷ, Sᵖ, Δpᵦₐᵣ, params = Pˢⁱᵗₖ₁)
(; a₀, a₁, a₂, b₀, b₁, b₂, b₃, c₀, c₁, v₀, v₁, v₂, v₃, k₀, k₁ ) = params()
ln_ksi1_p0 = (a₀ +
a₁/Θᴷ +
a₂*log(Θᴷ) +
(b₀ +
b₁/Θᴷ
)*sqrt(μₛ(Sᵖ)) +
(b₂ +
b₃/Θᴷ
)*μₛ(Sᵖ) +
(c₀ +
c₁/Θᴷ
)*μₛ(Sᵖ)*μₛ(Sᵖ))
"Pressure correction : currently none"
"ln_ksi1_pp = 0."
"Pressure correction for applied pressure /= 0
estimated from borate as suggested by Millero (1995)"
ln_kb_pp = (-(v₀ +
v₁*ΔSᵖ(Sᵖ) +
v₂*ΘᵒC(Θᴷ) +
v₃*ΘᵒC(Θᴷ)*ΘᵒC(Θᴷ))
+(
k₀ +
k₁*ΔSᵖ(Sᵖ)
)*(Δpᵦₐᵣ/2.)
)*(Δpᵦₐᵣ/Rₜ(Θᴷ))
return exp(ln_ksi1_p0 + ln_kb_pp) * H₂Oˢʷ(Sᵖ, Pᴴ²⁰ˢʷ)
end
Base.@kwdef struct Pᴴ²ˢₖ₁{FT}
a₀ :: FT = 225.838
a₁ :: FT = - 13275.3
a₂ :: FT = - 34.6435
a₃ :: FT = 0.3449
a₄ :: FT = - 0.0274
v₀ :: FT = - 14.80
v₁ :: FT = 0.0020
v₂ :: FT = - 0.400E-03
k₀ :: FT = 2.89e-3
k₁ :: FT = 0.054e-3
end
"""
Fᴴ²ˢₖ₁(Θᴷ, Sᵖ, Δpᵦₐᵣ, Pᴴ²ˢₖ₁)
Return the dissociation constant of hydrogen sulfide in sea-water, given temperature in K,
`Θᴷ`, practical salinity, `Sᵖ`, applied pressure, `Δpᵦₐᵣ`, and coefficients, `Pᴴ²ˢₖ₁`.
References: Millero et al. (1988) (cited by Millero (1995)
Millero (1995) for pressure correction
pH scale : - SWS (according to Yao and Millero, 1995, p. 82: "refitted if necessary")
- Total (according to Lewis and Wallace, 1998)
Note : we stick to SWS here for the time being
Note : the fits from Millero (1995) and Yao and Millero (1995)
derive from Millero et al. (1988), with all the coefficients
multiplied by -ln(10)
"""
@inline function Fᴴ²ˢₖ₁(Θᴷ, Sᵖ, Δpᵦₐᵣ, params = Pᴴ²ˢₖ₁)
(; a₀, a₁, a₂, a₃, a₄, v₀, v₁, v₂, k₀, k₁) = params()
ln_kh2s_p0 = (a₀ +
a₁/Θᴷ +
a₂*log(Θᴷ) +