Digital Supplement of the paper
Numerical implementation and oceanographic application of the
thermodynamic potentials of liquid water, water vapour, ice, seawater and
humid air – Part 1: Background and equations
R. Feistel1, D.G. Wright2, D.R. Jackett3, K. Miyagawa4, J.H. Reissmann5, W. Wagner6, U.
Overhoff6, C. Guder6, A. Feistel7 and G.M. Marion8
1
Leibniz-Institut für Ostseeforschung, Seestraße 15, D-18119 Warnemünde, Germany
Bedford Institute of Oceanography, Dartmouth, NS B2Y 4A2, Canada
3
CSIRO Marine and Atmospheric Research, GPO Box 1538, Hobart, TAS 7001, Australia
4
4-12-11-628, Nishiogu, Arakawa-ku, Tokyo 116-0011, Japan
5
Bundesamt für Seeschifffahrt und Hydrographie, Bernhard-Nocht-Straße 78, 20359 Hamburg,
Germany
6
Ruhr-Universität Bochum, Lehrstuhl für Thermodynamik, D-44780 Bochum, Germany
7
Technische Universität Berlin, Einsteinufer 25, D-10587 Berlin, Germany
8
Desert Research Institute, Reno, NV, USA
2
In this supplement, tables with groups of thermodynamic properties are summarized,
corresponding to the particular section number of the main text, as given in the table caption.
The names of available library routines for the property are set in a distinct font type.
The implemented potential functions are reported in Table 1 of the paper.
Table S1: Conversion functions between molar and mass fractions of humid air, section 2.4.
Here, MA = 0.02896546 kg mol–1 is the currently best value of the molar mass of dry air, and
MW = 0.018015268 kg mol–1 is the molar mass of pure water. In the original dry-air
formulation of Lemmon et al. (2000) and in the SIA version 1.0, the older value of MA =
28.958 6 g mol–1 was used.
Quantity
Library function
Molar mass of humid air
air_molar_mass_si
Mass fraction of dry air
air_massfraction_air_si
Mass fraction of vapour
air_massfraction_vap_si
Mole fraction of air
air_molfraction_air_si
Mole fraction of vapour
air_molfraction_vap_si
Formula
M AV =
1
(1 − A) / M W + A / M A
xA
1 − (1 − xA )(1 − M W / M A )
1 − xA
1− A =
1 − xA (1 − M A / M W )
A(M W / M A )
xA =
1 − A(1 − M W / M A )
1− A
1 − xA =
1 − A(1 − M W / M A )
A=
SI Unit
kg
mol
kg
kg
kg
kg
mol
mol
mol
mol
Eq.
(S1.1)
(S1.2)
(S1.3)
(S1.4)
(S1.5)
2
Table S2: Properties derived from the Helmholtz function f F (T , ρ ) of fluid water, section
3.1.
Quantity
Library function
Formula
Specific isobaric heat capacity
flu_cp_si
 f TFρ 2 ρ

F
cP = T  F
−
f
TT 
F
 2 f ρ + ρf ρρ

Specific isochoric heat capacity
flu_cv_si
cv = −T fTTF
Specific enthalpy
flu_enthalpy_si
h = f F − T fTF + ρf ρF
Specific entropy
flu_entropy_si
η = − f TF
( )
Thermal expansion coefficient
flu_expansion_si
f TFρ
α=
F
F
2 f ρ + ρf ρρ
Specific Gibbs energy
flu_gibbs_energy_si
g = f F + ρ f ρF
Specific internal energy
flu_internal_energy_si
u = f F − T f TF
Isentropic compressibility
flu_kappa_s_si
κs =
Isothermal compressibility
flu_kappa_t_si
Adiabatic lapse rate
flu_lapserate_si
f
κT =
Γ=
ρ
F
) ( )
+ ρf ρρ − ρ f
F 2
Tρ
1
ρ (2 f ρ + ρf ρρ )
2
F
F
fTFρ / ρ
ρ( f
Absolute pressure
flu_pressure_si
Sound speed
flu_soundspeed_si
(2 f
F
)
F 2
Tρ
−f
F
TT
(2 f
F
ρ
F
+ ρf ρρ
)
P = ρ 2 f ρF
c= ρ
2
( )
fTTF f ρρF − fTFρ
f
F
TT
Eq.
J
kg K
(S2.1)
J
kg K
J
kg
J
kg K
(S2.3)
1
K
(S2.5)
J
kg
J
kg
fTTF / ρ 2
F
TT
SI Unit
2
+ 2 ρf ρF
(S2.2)
(S2.4)
(S2.6)
(S2.7)
1
Pa
(S2.8)
1
Pa
(S2.9)
K
Pa
(S2.10)
Pa
(S2.11)
m
s
(S2.12)
3
Table S3. Properties derived from the Gibbs function g Ih (T , P ) of ice, section 3.2.
Quantity
Library function
Chemical potential
ice_chempot_si
Formula
µ = g Ih
Specific isobaric heat capacity
ice_cp_si
Ih
c p = −T gTT
Density
ice_density_si
1
g PIh
ρ=
Specific enthalpy
ice_enthalpy_si
h = g Ih − T g TIh
Specific entropy
ice_entropy_si
η = − gTIh
Thermal expansion coefficient
ice_expansion_si
α=
Ih
g TP
g PIh
Specific Helmholtz energy
ice_helmholtz_energy_si
f = g Ih − P g PIh
Specific internal energy
ice_internal_energy_si
u = g Ih − T g TIh − P g PIh
Isentropic compressibility
ice_kappa_s_si
κs =
Ih Ih
Ih
Ih
g TP
g TP − g TT
g PP
Ih
g PIh g TT
Ih
g PP
g PIh
SI Unit
J
kg
J
kg K
kg
m3
J
kg
J
kg K
Eq.
(S3.1)
(S3.2)
(S3.3)
(S3.4)
(S3.5)
1
K
J
kg
J
kg
(S3.7)
1
Pa
(S3.9)
1
Pa
(S3.10)
(S3.6)
(S3.8)
Isothermal compressibility
ice_kappa_t_si
κT = −
Adiabatic lapse rate
ice_lapserate_si
Γ=−
Ih
g TP
Ih
g TT
K
Pa
(S3.11)
Isochoric pressure coefficient
ice_p_coefficient_si
β =−
Ih
gTP
Ih
g PP
Pa
K
(S3.12)
m3
kg
(S3.13)
Specific volume
ice_specific_volume_si
v =g
Ih
P
4
Table S4. Properties derived from the saline part g S (S A , T , P ) of the Gibbs function of
seawater, section 3.3.
Quantity
Library function
ln
Activity coefficient
sal_act_coeff_si
Activity potential
sal_act_potential_si
Activity of water
sal_activity_w_si
Saline excess
chemical potential
sal_chempot_h2o_si
Relative chemical
potential
sal_chempot_rel_si
Chemical coefficient
sal_chem_coeff_si
SI Unit
Eq.
1
(S4.1)
1
(S4.2)
 g S − S A g SS 
a W = exp 

 RWT 
1
(S4.3)
µ WS = g S − S A g SS
J
kg
(S4.4)
µ = g SS
J
kg
(S4.5)
Formula
γ
= ln (1 − S A ) − S A +
γ id
1 7
i


g i (T , P ) S A + (1 − S A ) S Ai / 2−1
∑
g1 (T ) i =3
2


Mixing entropy
sal_mixentropy_si
Mixing volume
sal_mixvolume_si
Osmotic coefficient
sal_osm_coeff_si
Specific enthalpy
of sea salt
sal_saltenthalpy_si
Specific entropy
of sea salt
sal_saltentropy_si
Specific volume
of sea salt
sal_saltvolume_si
J
kg
J
kg
S
DS = S A2 g SS
Dilution coefficient
sal_dilution_si
Mixing enthalpy
sal_mixenthalpy_si
1 7
g i (T , P )S Ai / 2−1
∑
g1 (T ) i =3
ψ = ln(1 − S A ) +
S
D = S A g SS
∆h = hS (w1S1 + w2 S 2 , T , P )
− w1h (S1 , T , P ) − w2 h ( S 2 , T , P)
S
S
∆η = − gTS (w1S1 + w2 S 2 , T , P )
+ w g (S , T , P ) + w2 g ( S 2 , T , P)
S
1 T
1
S
P
1 1
S
T
∆v = g (w S + w2 S 2 , T , P )
− w1 g PS (S1 , T , P ) − w2 g PS ( S 2 , T , P)
(g
φ =−
S
)
− S A g SS (1 − S A )
S A RST
hS =
g S − Tg TS
SA
ηS = −
vS =
gTS
SA
g PS
SA
(S4.6)
(S4.7)
J
kg
(S4.8)
J
kg K
(S4.9)
m3
kg
(S4.10)
1
(S4.11)
J
kg
(S4.12)
J
kg K
(S4.13)
m3
kg
(S4.14)
5
Table S5. Properties of humid air derived from the Helmholtz function f AV ( A, T , ρ ) , Eq.
(2.7), section 3.4. Subscripts on f AV indicate partial derivatives with respect to the natural
independent variables A, T or ρ. Note that the adiabatic lapse rate is given with respect to
pressure rather than altitude and refers to subsaturated humid air, often referred to as “dryadiabatic” in the meteorological literature. The so-called “moist-adiabatic” lapse rate is given
in section 5.8.
Quantity
Library function
Formula
Specific isobaric heat capacity
air_f_cp_si
2


fTAV
ρ
ρ
AV
cP = T  AV
−
f
TT 
AV
 2 f ρ + ρf ρρ

Specific isochoric heat capacity
air_f_cv_si
cv = −T fTTAV
Specific enthalpy
air_f_enthalpy_si
h = f AV − T fTAV + ρf ρAV
Specific entropy
air_f_entropy_si
η = − fTAV
J
kg K
J
kg
J
kg K
Thermal expansion coefficient
air_f_expansion_si
fTAV
α = AV ρ AV
2 f ρ + ρf ρρ
1
K
Specific Gibbs energy
air_f_gibbs_energy_si
g = f AV + ρ f ρAV
Specific internal energy
air_f_internal_energy_si
u = f AV − T fTAV
Isentropic compressibility
air_f_kappa_s_si
(
κs =
Isothermal compressibility
air_f_kappa_t_si
Adiabatic lapse rate
air_f_lapserate_si
f
AV
TT
ρ
AV
) (
+ ρf ρρ − ρ f
1
ρ (2 f ρ + ρf ρρ
2
AV
AV
)
AV 2
Tρ
)
fTAV
ρ /ρ
ρ( f
Absolute pressure
air_f_pressure_si
Sound speed
air_f_soundspeed_si
(2 f
AV
)
AV 2
Tρ
−f
AV
TT
(2 f
2
AV
ρ
AV
+ ρf ρρ
)
AV
P = ρ fρ
(
f AV f AV − f AV
c = ρ TT ρρ AV Tρ
fTT
2
)
Eq.
J
kg K
(S5.1)
J
kg
J
kg
fTTAV / ρ 2
κT =
Γ=
)
SI Unit
2
+ 2 ρf ρAV
(S5.2)
(S5.3)
(S5.4)
(S5.5)
(S5.6)
(S5.7)
1
Pa
(S5.8)
1
Pa
(S5.9)
K
Pa
(S5.10)
Pa
(S5.11)
m
s
(S5.12)
6
Table S6: Partial derivatives of the Gibbs function of liquid water, g W (T , P ) , section 4.1,
expressed as partial derivatives of the Helmholtz function, f F (T , ρ ) . Subscripts indicate
partial derivatives with respect to the respective variables. Here, ρ is the density of liquid
pure water at given T and P. The library function vap_g_si for vapour is defined equivalently
with respect to f F taken at the vapour density ρ.
Expression in
g W (T , P )
Library function
P
Equivalent in
f F (T , ρ )
Unit
Eq.
ρ 2 f ρF
Pa
(S6.1)
f F + ρf ρF
J kg −1
(S6.2)
ρ −1
m 3 kg −1
(S6.3)
f TF
J kg −1 K −1
(S6.4)
m 3 kg −1 Pa −1
(S6.5)
m 3 kg −1 K −1
(S6.6)
J kg −1 K −2
(S6.7)
W
g
liq_g_si
g PW
liq_g_si
g TW
liq_g_si
W
g PP
liq_g_si
−
F
f TFρ
W
g TP
liq_g_si
W
g TT
liq_g_si
1
ρ (2 f ρ + ρf ρρF )
3
ρ (2 f ρF + ρf ρρF )
ρ ( f TFρ )
−
(2 f ρF + ρf ρρF )
2
f
F
TT
7
Table S7a: Thermodynamic properties derived from the Gibbs function (4.4) of seawater,
g SW (S A , T , P ) , section 4.2, and its temperature, pressure and salinity derivatives. The
superscript SW on g is suppressed for simplicity.
Quantity
Library function
Density
sea_density_si
Formula
SI Unit
ρ = g P−1
kg
m3
J
kgK
J
kg
J
kg
J
kg
J
kgK
J
kgK
1
Pa
1
Pa
m
s
K
Pa
Specific entropy
sea_entropy_si
η = − gT
Specific enthalpy
sea_enthalpy_si
h = g − T gT
Specific internal energy
sea_internal_energy_si
u = g − T gT − P g P
Specific Helmholtz energy
f = g − PgP
Specific isobaric heat capacity
sea_cp_si
cP = −T gTT
Specific isochoric heat capacity
2
cv = T (g TP
− g TT g PP ) / g PP
Isothermal compressibility
sea_kappa_t_si
Isentropic compressibility
sea_kappa_s_si
Sound speed
sea_soundspeed_si
Adiabatic lapse rate
sea_lapserate_si
Chemical potential of water
sea_chempot_h2o_si
κ T = − g PP / g P
2
κ s = (gTP
− gTT g PP ) / (g P g TT )
2
c = g P g TT / (g TP
− g TT g PP )
Γ = − g TP / gTT
Chemical potential of sea salt
µ S = g + (1 − S A )g S
J
kg
J
kg
Barodiffusion ratio
k P = P g SP g SS
1
µ W = g − SA g S
Eq.
(S7.1)
(S7.2)
(S7.3)
(S7.4)
(S7.5)
(S7.6)
(S7.7)
(S7.8)
(S7.9)
(S7.10)
(S7.11)
(S7.12)
(S7.13)
(S7.14)
8
Table S7b: Thermodynamic properties derived from the Gibbs function (4.4) of seawater,
g SW (S A , T , P ) , section 4.2, and its temperature, pressure and salinity derivatives. The
superscript SW on g is suppressed for simplicity. Thermal and haline contraction coefficients
with respect to potential temperature and potential enthalpy are given here in terms of the
Gibbs potential for completeness. A full discussion of these quantities is given in section 4.3.
The potential Gibbs energy gθ is defined as g θ ≡ g (S A ,θ , Pr ) where θ is absolute potential
temperature in kelvins and Pr is the associated absolute reference pressure in pascals.
Quantity
Library function
Thermal expansion coefficient
sea_g_expansion_t_si
Formula
α = g TP / g P
Thermal expansion coefficient
w.r.t. potential temperature
Haline contraction coefficient
w.r.t. potential enthalpy
βθ =
βΘ =
1
K
1
K
Eq.
(S7.15)
θ
g TP gθθ
g P g TT
g TP
αh = −
g P g TT θ
kg
J
(S7.17)
β = − g SP g P
1
(S7.18)
1
(S7.19)
1
(S7.20)
αθ =
Thermal expansion coefficient
w.r.t. potential enthalpy
Haline contraction coefficient
sea_g_contraction_t_si
Haline contraction coefficient
w.r.t. potential temperature
SI Unit
(
)
g TP g ST − g θSθ − g SP g TT
g P g TT
(
)
g TP g ST − g θS / θ − g SP g TT
g P g TT
(S7.16)
9
Table S8: Partial derivatives of the enthalpy potential function h SW (S A ,η , P ) of seawater, Eq.
(4.5), section 4.3, expressed as partial derivatives of the Gibbs function g SW (S A , T , P ) of
seawater, Eq. (4.4). Subscripts indicate partial derivatives with respect to the respective
variables. The superscripts SW on g and h are omitted for simplicity.
Expression in
h SW (S A ,η , P )
Library function
Equivalent in
g SW (S A , T , P )
η
– gT
h
sea_h_si
g – TgT
hS
sea_h_si
hη
gS
SI Unit
J
kg K
J
kg
J
kg
Eq.
(S8.1)
(S8.2)
(S8.3)
T
K
(S8.4)
gP
m3
kg
(S8.5)
2
g SS g TT − g ST
g TT
g
− ST
g TT
J
kg
(S8.6)
K
(S8.7)
g SP g TT − g ST g TP
g TT
m3
kg
(S8.8)
sea_h_si
hηP
sea_h_si
1
g TT
g
− TP
g TT
kg K 2
J
K
Pa
hPP
sea_h_si
2
g TT g PP − g TP
g TT
m3
kg Pa
sea_h_si
hP
sea_h_si
hSS
sea_h_si
hSη
sea_h_si
hSP
sea_h_si
hηη
−
(S8.9)
(S8.10)
(S8.11)
10
Table S9: Thermodynamic properties derived from the enthalpy h SW (S A ,η , P ) of seawater,
Eq. (4.5), section 4.3, and its entropy, pressure and salinity derivatives. The superscripts SW
on h is suppressed for simplicity. Entropy is available from in-situ temperature using Eq.
(S8.1).
Quantity
Library function
SI Unit
Eq.
1
hP
kg
m3
(S9.1)
Temperature
sea_temperature_si
T = hη
K
(S9.2)
Relative chemical potential
µ = hS
Specific Gibbs energy
g = h − η hη
Specific internal energy
u = h − PhP
Specific Helmholtz energy
f = h − η hη − PhP
Density
Formula
ρ=
T
hηη
J
kg
J
kg
J
kg
J
kg
J
kgK
Specific isobaric heat capacity
cP =
Isentropic compressibility
κs = −
1
Pa
c=
m
s
K
Pa
Sound speed
Adiabatic lapse rate
hPP
hP
hP
− hPP
Γ = hηP
(S9.3)
(S9.4)
(S9.5)
(S9.6)
(S9.7)
(S9.8)
(S9.9)
(S9.10)
11
Table S10: Thermodynamic properties derived from the enthalpy h SW (S A ,η , P ) of seawater,
Eq. (4.5), section 4.3, and its entropy, pressure and salinity derivatives. The superscripts SW
on h is suppressed for simplicity. Note that potential temperature is given here as absolute
potential temperature in the basic SI unit, K, rather than °C. Entropy is available from in-situ
temperature or potential temperature, η (S A , T , P ) = η (S A ,θ , Pr ) , using Eq. (S7.2) which
appears in the library as sea_entropy_si (SA, T, P) or sea_entropy_si (SA, θ, Pr). Entropy
can also be determined from in-situ enthalpy or potential enthalpy,
η SW (S A , h, P ) = η SW S A , hθ , Pr , using Eq. (4.35) which appears in the library as
sea_eta_entropy_si (SA, h, P) or sea_eta_entropy_si (SA, hθ, Pr). The parameter η refers
to entropy as the property (S7.2) derived from the Gibbs potential gSW of seawater.
(
)
Quantity
Library function
Potential enthalpy
sea_potenthalpy_si
Potential temperature
sea_pottemp_si
Potential density
sea_potdensity_si
Eq.
hθ
J
kg
(S10.1)
θ = hηθ
K
(S10.2)
1
hPθ
kg
m3
(S10.3)
hηP
1
K
(S10.4)
1
K
(S10.5)
kg
J
(S10.6)
1
(S10.7)
1
(S10.8)
1
(S10.9)
αT =
Thermal expansion coefficient
w.r.t. potential temperature
sea_h_expansion_theta_si
Thermal expansion coefficient
w.r.t. potential enthalpy
sea_h_expansion_h_si
Haline contraction coefficient
w.r.t. potential temperature
Sea_h_contraction_theta_si
Haline contraction coefficient
w.r.t. potential enthalpy
sea_h_contraction_h_si
SI Unit
ρθ =
Thermal expansion coefficient
sea_h_expansion_t_si
Isothermal haline contraction
sea_h_contraction_t_si
Formula
hP hηη
hηP
αθ =
θ
P ηη
h h
αh =
β=
θ
P η
h h
hSη hηP − hSP hηη
βθ =
Θ
hηP
β =
hP hηη
θ
hSθη hηP − hSP hηη
θ
hP hηη
hSθ hηP − hSP hηθ
hP hηθ
12
Table S11: Partial derivatives of the Gibbs function of humid air, g AV ( A, T , P ) , section 4.4,
expressed as partial derivatives of the Helmholtz function, f AV ( A, T , ρ ) . Subscripts indicate
partial derivatives with respect to the respective variables. Computed iteratively from Eq.
(4.38), ρ is the density of humid air at given values of A, T and P.
Expression in
g AV ( A, T , P )
Library function
P
Equivalent in
f AV ( A, T , ρ )
SI Unit
Eq.
ρ 2 f ρAV
Pa
(S11.1)
f AV + ρf ρAV
J kg −1
(S11.2)
f AAV
J kg −1
(S11.3)
ρ −1
m 3 kg −1
(S11.4)
fTAV
J kg −1 K −1
(S11.5)
AV
g
air_g_si
g AAV
air_g_si
g PAV
air_g_si
gTAV
air_g_si
AV
g AA
air_g_si
AV
g AT
air_g_si
f
AV
AA
ρ ( f AAV
ρ )
−
AV
(2 f ρ + ρf ρρAV )
J kg −1
(S11.6)
f
AV
AT
AV
ρf AAV
ρ f ρT
−
(2 f ρAV + ρf ρρAV )
J kg −1 K −1
(S11.7)
m 3 kg −1
(S11.8)
ρ (2 f ρ + ρf ρρAV )
m 3 kg −1 Pa −1
(S11.9)
fTAV
ρ
AV
ρ 2 f ρ + ρf ρρAV
m 3 kg −1 K −1
(S11.10)
J kg −1 K −2
(S11.11)
2
f AAV
ρ
AV
ρ 2 f ρ + ρf ρρAV
AV
g AP
air_g_si
AV
g PP
air_g_si
(
−
AV
gTP
air_g_si
AV
gTT
air_g_si
)
1
3
AV
(
)
ρ ( fTAV
ρ )
−
AV
(2 f ρ + ρf ρρAV )
2
f
AV
TT
13
Table S12: Thermodynamic properties derived from the Gibbs function g AV ( A, T , P ) of
humid air, Eq. (4.37), section 4.4, and its temperature, pressure and air-fraction derivatives.
The superscript AV on g is suppressed for simplicity. The molar mass of humid air MAV is
given by Eq. (2.8). R = 8.314472 J mol–1 K–1 is the molar gas constant.
Quantity
Library function
Density
air_g_density_si
ρ = 1/ g P
Specific entropy
air_g_entropy_si
η = − gT
Specific enthalpy
air_g_enthalpy_si
h = g − T gT
Partial enthalpy of vapour
h W = g − T gT − Ag A + AT g AT
Specific internal energy
air_g_internal_energy_si
u = g − T gT − P g P
Specific Helmholtz energy
f = g − PgP
Specific isobaric heat capacity
air_g_cp_si
cP = −T gTT
Specific isochoric heat capacity
air_g_cv_si
2
cv = T (g TP
− g TT g PP ) / g PP
Thermal expansion coefficient
air_g_expansion_si
Isothermal compressibility
air_g_kappa_t_si
Isentropic compressibility
air_g_kappa_s_si
Compressibility factor
air_g_compressibilityfactor_si
Sound speed
air_g_soundspeed_si
Adiabatic lapse rate
air_g_lapserate_si
Formula
α = g TP / g P
κT = − g PP / g P
2
κ s = (gTP
− gTT g PP ) / (g P g TT )
Z AV = M AV
Pg P
RT
2
c = g P g TT / (g TP
− g TT g PP )
Γ = − g TP / gTT
SI Unit
kg
m3
J
kgK
J
kg
J
kg
J
kg
J
kg
J
kgK
J
kgK
1
K
1
Pa
1
Pa
1
m
s
K
Pa
Chemical potential of vapour
µ W = g − Ag A
Chemical Coefficient
DA = A 2 g AA
J
kg
J
kg
Air contraction coefficient
air_g_contraction_si
β = − g AP g P
1
Eq.
(S12.1)
(S12.2)
(S12.3)
(S12.4)
(S12.5)
(S12.6)
(S12.7)
(S12.8)
(S12.9)
(S12.10)
(S12.11)
(S12.12)
(S12.13)
(S12.14)
(S12.15)
(S12.16)
(S12.17)
14
Table S13: Partial derivatives of the enthalpy potential function h AV ( A,η , P ) of humid air, Eq.
(4.40), section 4.5, expressed as partial derivatives of the Gibbs function g AV ( A, T , P ) of
humid air, Eq. (4.37). Subscripts indicate partial derivatives with respect to the respective
variables. The superscripts AV on g and h are omitted for simplicity.
Expression in
h AV ( A,η , P )
Library function
Equivalent in
g AV ( A, T , P )
η
– gT
h
air_h_si
g – TgT
hA
air_h_si
hη
gA
SI Unit
J
kg K
J
kg
J
kg
Eq.
(S13.1)
(S13.2)
(S13.3)
T
K
(S13.4)
gP
m3
kg
(S13.5)
2
g AA gTT − g AT
gTT
g
− AT
gTT
J
kg
(S13.6)
K
(S13.7)
g AP gTT − g AT gTP
gTT
m3
kg
(S13.8)
air_h_si
hηP
air_h_si
1
g TT
g
− TP
g TT
kg K 2
J
K
Pa
hPP
air_h_si
2
g TT g PP − g TP
g TT
m3
kg Pa
air_h_si
hP
air_h_si
hAA
air_h_si
hAη
air_h_si
hAP
air_h_si
hηη
−
(S13.9)
(S13.10)
(S13.11)
15
Table S14: Thermodynamic properties derived from the enthalpy h AV ( A,η , P ) of humid air,
Eq. (4.40), section 4.5, and its derivatives with respect to dry-air mass fraction, entropy and
pressure. The superscripts AV on h and g are suppressed for simplicity. If the temperature
(S14.2) is evaluated at a pressure different from that used for the computation of the entropy,
T is regarded as “potential temperature”, θ , referenced to this pressure. The adiabatic lapse
rate is given with respect to pressure rather than altitude and refers to subsaturated humid air,
often referred to as “dry-adiabatic” in the meteorological literature.
Quantity
Library function
SI Unit
Eq.
1
hP
kg
m3
(S14.1)
Temperature
air_temperature_si
T = hη
K
(S14.2)
Relative chemical potential
µ = hA
Specific Gibbs energy
g = h − η hη
Specific internal energy
u = h − PhP
Specific Helmholtz energy
f = h − η hη − PhP
Density
Formula
ρ=
T
hηη
J
kg
J
kg
J
kg
J
kg
J
kgK
Specific isobaric heat capacity
cP =
Isentropic compressibility
κs = −
1
Pa
c=
m
s
K
Pa
Sound speed
Adiabatic lapse rate
hPP
hP
hP
− hPP
Γ = hηP
(S14.3)
(S14.4)
(S14.5)
(S14.6)
(S14.7)
(S14.8)
(S14.9)
(S14.10)
16
Table S15: Properties of the saturation equilibrium, section 5.1, computed from the variables
T, P, ρ V and ρ W , the iteratively determined solution of Eqs. (5.2) - (5.4)
Quantity
Library function
Formula
SI Unit
Eq.
T
K
(S15.1)
Boiling temperature
liq_vap_boilingtemperature_si
liq_vap_temperature_si
Evaporation entropy
liq_vap_entropy_evap_si
f TF (T , ρ W ) − f TF (T , ρ V )
Liquid entropy
liq_vap_entropy_liq_si
− f TF (T , ρ W )
Vapour entropy
liq_vap_entropy_vap_si
− f TF (T , ρ V )
J
kg
kg
m3
kg
m3
J
kg
J
kg
J
kg
J
kg K
J
kg K
J
kg K
P
Pa
(S15.11)
m3
kg
(S15.12)
m3
kg
(S15.13)
m3
kg
(S15.14)
Chemical potential
liq_vap_chempot_si
f F (T , ρ W ) +
P
ρ
W
Liquid density
liq_vap_density_liq_si
Vapour density
liq_vap_density_vap_si
ρW
Evaporation enthalpy
liq_vap_enthalpy_evap_si
Tf TF (T , ρ W ) − Tf TF (T , ρ V )
ρV
Liquid enthalpy
liq_vap_enthalpy_liq_si
f F (T , ρ W ) +
Vapour enthalpy
liq_vap_enthalpy_vap_si
f F (T , ρ V ) +
P
ρ
− Tf TF (T , ρ W )
W
P
− Tf TF (T , ρ V )
ρV
(S15.2)
(S15.3)
(S15.4)
(S15.5)
(S15.6)
(S15.7)
(S15.8)
(S15.9)
(S15.10)
Vapour pressure
liq_vap_vapourpressure_si
liq_vap_pressure_liq_si
liq_vap_pressure_vap_si
Evaporation volume
liq_vap_volume_evap_si
Liquid volume
Vapour volume
1
ρV
−
1
ρW
1
ρW
1
ρV
17
Table S16: Properties of the melting equilibrium, section 5.2, computed from the variables T,
P and ρ W , the iteratively determined solution of Eqs. (5.6), (5.7).
Quantity
Library function
Formula
SI Unit
Eq.
T
K
(S16.1)
Chemical potential
ice_liq_chempot_si
g Ih (T , P )
Liquid density
ice_liq_density_liq_si
ρW
Ice density
ice_liq_density_ice_si
1
g (T , P )
Melting enthalpy
ice_liq_enthalpy_melt_si
TgTIh (T , P ) − Tf TF (T , ρ W )
Melting temperature
ice_liq_meltingtemperature_si
ice_liq_temperature_si
Ice enthalpy
ice_liq_enthalpy_ice_si
g Ih (T , P ) − TgTIh (T , P )
Melting entropy
ice_liq_entropy_melt_si
g TIh (T , P ) − f TF (T , ρ W )
Liquid entropy
ice_liq_entropy_liq_si
− f TF (T , ρ W )
Ice entropy
ice_liq_entropy_ice_si
− g TIh (T , P )
J
kg
kg
m3
kg
m3
J
kg
J
kg
J
kg
J
kg K
J
kg K
J
kg K
P
Pa
(S16.11)
m3
kg
(S16.12)
m3
kg
(S16.13)
m3
kg
(S16.14)
Liquid enthalpy
ice_liq_enthalpy_liq_si
Ih
P
f F (T , ρ W ) +
P
ρ
W
− Tf TF (T , ρ W )
(S16.2)
(S16.3)
(S16.4)
(S16.5)
(S16.6)
(S16.7)
(S16.8)
(S16.9)
(S16.10)
Melting pressure
ice_liq_meltingpressure_si
ice_liq_pressure_liq_si
Melting volume
ice_liq_volume_melt_si
1
ρW
− g PIh (T , P )
1
Liquid volume
ρW
Ice volume
g (T , P )
Ih
P
18
Table S17: Properties of the sublimation equilibrium, section 5.3, computed from the
variables T, P and ρ V , the iteratively determined solution of Eqs. (5.9), (5.10).
Quantity
Library function
Formula
SI Unit
Eq.
T
K
(S17.1)
Chemical potential
ice_vap_chempot_si
g Ih (T , P )
Vapour density
ice_vap_density_vap_si
ρV
Ice density
ice_vap_density_ice_si
1
g (T , P )
Sublimation enthalpy
ice_vap_enthalpy_subl_si
TgTIh (T , P ) − Tf TF (T , ρ V )
Sublimation temperature
ice_vap_sublimationtemp_si
ice_vap_temperature_si
Ice enthalpy
ice_vap_enthalpy_ice_si
g Ih (T , P ) − TgTIh (T , P )
Sublimation entropy
ice_vap_entropy_subl_si
g TIh (T , P ) − f TF (T , ρ V )
Vapour entropy
ice_vap_entropy_vap_si
− f TF (T , ρ V )
Ice entropy
ice_vap_entropy_ice_si
− g TIh (T , P )
J
kg
kg
m3
kg
m3
J
kg
J
kg
J
kg
J
kg K
J
kg K
J
kg K
P
Pa
(S17.11)
m3
kg
(S17.12)
m3
kg
(S17.13)
m3
kg
(S17.14)
Vapour enthalpy
ice_vap_enthalpy_vap_si
Ih
P
f F (T , ρ V ) +
P
ρ
V
− Tf TF (T , ρ V )
(S17.2)
(S17.3)
(S17.4)
(S17.5)
(S17.6)
(S17.7)
(S17.8)
(S17.9)
(S17.10)
Sublimation pressure
ice_vap_sublimationpressure_si
ice_vap_pressure_vap_si
Sublimation volume
ice_vap_volume_subl_si
1
ρV
− g PIh (T , P )
1
Vapour volume
ρV
Ice volume
g (T , P )
Ih
P
19
Table S18: Single-phase properties of the seawater-ice equilibrium, section 5.4, and sea-ice
properties, superscript SI, computed from the variables SA, T, P and ρ W , the iteratively
determined solution of Eqs. (5.12), (5.13).
Quantity
Library function
Formula
SI Unit
Eq.
T
K
(S18.1)
Brine salinity
sea_ice_brinesalinity_si
sea_ice_salinity_si
SA
kg
kg
(S18.2)
Chemical potential
g Ih (T , P )
J
kg
(S18.3)
Brine density
sea_ice_density_sea_si
Brine enthalpy
sea_ice_enthalpy_sea_si
1
g (S A , T , P ) + 1 / ρ W
1
Ih
g P (T , P )
P
f F (T , ρ W ) + W − Tf TF (T , ρ W )
Ice enthalpy
sea_ice_enthalpy_ice_si
g Ih (T , P ) − TgTIh (T , P )
Brine entropy
sea_ice_entropy_sea_si
− f TF (T , ρ W ) − gTS (S A , T , P )
Ice entropy
sea_ice_entropy_ice_si
− gTIh (T , P )
kg
m3
kg
m3
J
kg
J
kg
J
kg K
J
kg K
P
Pa
(S18.10)
m3
kg
(S18.11)
Freezing temperature
sea_ice_freezingtemperature_si
Ice density
sea_ice_density_ice_si
S
P
ρ
Melting pressure
sea_ice_meltingpressure_si
Brine volume
Ice volume
1
ρW
+ g PS (S A , T , P )
g
Ih
P
(T , P )
Expansion coefficient of sea ice
SI
α SI = g TP
(S SI , T , P ) / g PSI (S SI , T , P )
Adiabatic lapse rate of sea ice
SI
Γ SI = − g TP
(SSI , T , P ) / g TTSI (SSI ,T , P )
m3
kg
1
K
K
Pa
(S18.4)
(S18.5)
(S18.6)
(S18.7)
(S18.8)
(S18.9)
(S18.12)
(S18.13)
(S18.14)
20
Table S19: Properties of the seawater evaporation equilibrium, section 5.5, computed from the
variables SA, T, P, ρ V and ρ W , the iteratively determined solutions of Eqs. (5.27) - (5.29).
Quantity
Library function
Formula
SI Unit
Eq.
T
K
(S19.1)
Boiling temperature
sea_vap_boilingtemperature_si
sea_vap_temperature_si
Brine salinity
sea_vap_brinesalinity_si
(S19.2)
SA
sea_vap_salinity_si
Brine density
sea_vap_density_sea_si
1
g (T , P )
Vapour density
sea_vap_density_vap_si
ρV
Brine enthalpy
sea_vap_enthalpy_sea_si
g Ih (T , P ) − TgTIh (T , P )
Brine entropy
sea_vap_entropy_sea_si
− g TIh (T , P )
Vapour entropy
sea_vap_entropy_vap_si
− f TF (T , ρ V )
kg
m3
kg
m3
J
kg
J
kg
J
kg K
J
kg K
P
Pa
(S19.9)
1
m3
kg
(S19.10)
m3
kg
(S19.11)
Vapour enthalpy
sea_vap_enthalpy_vap_si
Ih
P
f F (T , ρ V ) +
P
ρ
V
− Tf TF (T , ρ V )
(S19.3)
(S19.4)
(S19.5)
(S19.6)
(S19.7)
(S19.8)
Vapour pressure
sea_vap_vapourpressure_si
sea_vap_pressure_si
Vapour volume
ρV
Brine volume
g PIh (T , P )
21
(
)
Table S20: Derivatives of the Gibbs function g AW w A , T , P , Eq. (5.58), section 5.8, of wet air
expressed in terms of the Gibbs functions g AV ( A, T , P ) , Eq. (4.37), of humid air,
and g W (T , P ) , Eq. (4.2), of liquid water. The latency operator ΛAW is specified in Eqs. (5.61) (5.62). The chemical coefficient DA is defined in Eq. (S12.16). The function A(T, P) is the
solution of Eq. (5.48).
(
Derivative of g AW w A , T , P
Library function
)
Expression in g AV ( A, T , P ) and g W (T , P )
w A AV  w A
g + 1 −
A
A

g AV − g W
g AW
liq_air_g_si
g wAW
A
liq_air_g_si
 W
 g

Equation
(S20.1)
(S20.2)
g TAW
liq_air_g_si
A
A
w AV  w A
g T + 1 −
A
A

 W
 g T

(S20.3)
g PAW
liq_air_g_si
w A AV  w A
g P + 1 −
A
A

 W
 g P

(S20.4)
g wAW
A A
w
liq_air_g_si
g wAW
A
T
liq_air_g_si
g wAW
A
P
liq_air_g_si
AW
g TT
liq_air_g_si
AW
g TP
liq_air_g_si
AW
g PP
liq_air_g_si
0
wA
A
wA
A
 AV
 g TT


g TAV − g TW
A
AV
g P − g PW
A
(Λ [η ])2   w A  W
− AW
 + 1 − A  g TT
DA

 
(S20.5)
(S20.6)
(S20.7)
(S20.8)
 AV Λ AW [η ]Λ AW [v ]   w A  W
 gTP +
 + 1 −
 gTP
DA
A 

 
(S20.9)
 AV (Λ AW [v ])2   w A  W
 g PP −
 + 1 −
 g PP


D
A
A




(S20.10)
wA
A
22
Table S21: Selected properties of wet air computed from the Gibbs function (5.58),
g AW w A , T , P , section 5.8, and its partial derivatives, Table S20. The superscript AW is
suppressed here for simplicity. The latency operator ΛAW is specified in Eqs. (5.61) - (5.62).
The function A = Asat(T, P) is the solution of Eq. (5.48). The lapse rate of wet air is often
regarded as the “moist-adiabatic” lapse rate in the meteorological literature.
(
)
Quantity
Library function
Specific isobaric heat capacity
liq_air_g_cp_si
cP = −T gTT
Density
liq_air_g_density_si
ρ = 1/ gP
Specific entropy
liq_air_g_entropy_si
η = − gT
Specific enthalpy
liq_air_g_enthalpy_si
h = g − T gT
Evaporation enthalpy
liq_air_enthalpy_evap_si
LAW
= TΛ AW [η ]
P
Thermal expansion coefficient
liq_air_g_expansion_si
Isothermal compressibility
liq_air_g_kappa_t_si
Adiabatic lapse rate
liq_air_g_lapserate_si
Air mass fraction
liq_air_massfraction_air_si
Liquid mass fraction
liq_air_liquidfraction_si
Vapour mass fraction
liq_air_vapourfraction_si
α = g TP / g P
Formula
κT = − g PP / g P
Γ = − g TP / gTT
SI Unit
J
kg K
kg
m3
J
kg K
J
kg
J
kg
1
K
1
Pa
K
Pa
Eq.
(S21.1)
(S21.2)
(S21.3)
(S21.4)
(S21.5)
(S21.6)
(S21.7)
(S21.8)
A = Asat(T, P)
1
(S21.9)
wW = 1 − wA / A
1
(S21.10)
w V = (1 / A − 1)w A
1
(S21.11)
23
(
)
(w
Table S22: Partial derivatives of the enthalpy potential function h AW w A ,η , P of wet air, Eq.
)
(5.63), section 5.8, expressed as partial derivatives of the Gibbs function g AW A , T , P of
wet air, Eq. (5.58). Subscripts indicate partial derivatives with respect to the respective
variables. The superscripts AW on g and h are omitted for simplicity. Because of minor
practical relevance, derivatives with respect to wA are omitted.
Expression in
h AW w A ,η , P
Library function
Equivalent in
g AW w A , T , P
η
– gT
(
)
h
liq_air_h_si
hη
(
)
g – TgT
SI Unit
J
kg K
J
kg
Eq.
(S22.1)
(S22.2)
T
K
(S22.3)
gP
m3
kg
(S22.4)
liq_air_h_si
1
g TT
g
− TP
g TT
kg K 2
J
K
Pa
hPP
liq_air_h_si
2
g TT g PP − g TP
g TT
m3
kg Pa
liq_air_h_si
hP
liq_air_h_si
hηη
liq_air_h_si
hηP
−
(S22.5)
(S22.6)
(S22.7)
(
)
Table S23: Selected properties of wet air computed from the enthalpy (5.63), h AW w A ,η , P ,
section 5.8, and its partial derivatives, Table S22. The superscript AW is suppressed here for
simplicity. The lapse rate of wet air is often regarded as the “moist-adiabatic” lapse rate in the
meteorological literature.
Quantity
Library function
Density
liq_air_h_density_si
Temperature
liq_air_h_temperature_si
Specific isobaric heat capacity
liq_air_h_cp_si
Isentropic compressibility
liq_air_h_kappa_s_si
Adiabatic lapse rate
liq_air_h_lapserate_si
SI Unit
Eq.
1
hP
kg
m3
(S23.1)
T = hη
K
(S23.2)
J
kg K
(S23.3)
Formula
ρ=
cP =
T
hηη
κs = −
hPP
hP
Γ = hηP
1
Pa
K
Pa
(S23.4)
(S23.5)
24
(
)
Table S24: Derivatives of the Gibbs function g AI w A , T , P , Eq. (5.73), section 5.9, of ice air
expressed in terms of the Gibbs functions g AV ( A, T , P ) , Eq. (4.37), of humid air, and
g Ih (T , P ) , of ice Ih, section 2.2. The latency operator ΛAI is specified in Eqs. (5.76) - (5.77).
The chemical coefficient DA is defined in Eq. (S12.16). The function A(T, P) is the solution of
Eq. (5.70).
(
Derivative of g AW w A , T , P
Library function
)
Expression in g AV ( A, T , P ) and g Ih (T , P )
w A AV  w A
g + 1 −
A
A

g AV − g Ih
g AI
ice_air_g_si
g wAIA
ice_air_g_si
g TAI
ice_air_g_si
w A AV
gT
A
g PAI
ice_air_g_si
w A AV
gP
A
g wAIA wA
ice_air_g_si
g wAIAT
ice_air_g_si
g wAIA P
ice_air_g_si
AI
g TT
ice_air_g_si
AI
g TP
ice_air_g_si
AI
g PP
ice_air_g_si
A

+ 1 −


+ 1 −

 Ih
 g

 Ih
 g T

w A  Ih
g P
A 
wA
A
0
wA
A
wA
A
 AV
 gTT


g TAV − g TIh
A
AV
g P − g PIh
A
(Λ [η ])2  + 1 − wA  g Ih
− AI
TT
DA  
A 
Equation
(S24.1)
(S24.2)
(S24.3)
(S24.4)
(S24.5)
(S24.6)
(S24.7)
(S24.8)
 AV Λ AI [η ]Λ AI [v ]   w A  Ih
 g TP +
 + 1 −
 g TP
DA
A 

 
(S24.9)
 AV (Λ AI [v ])2   w A  Ih
 g PP −
 + 1 −
 g PP


D
A
A




(S24.10)
wA
A
25
Table S25: Selected properties of ice air computed from the Gibbs function (5.73),
g AI w A , T , P , section 5.9, and its partial derivatives, Table S24. The superscript AI is
suppressed here for simplicity. The latency operator ΛAI is specified in Eqs. (5.76) - (5.77).
The function A = Asat(T, P) is the solution of Eq. (5.70). The lapse rate of ice air is often
regarded as the “moist-adiabatic” lapse rate in the meteorological literature.
(
)
Quantity
Library function
Specific isobaric heat capacity
ice_air_g_cp_si
c P = −T g TT
Density
ice_air_g_density_si
ρ = 1/ gP
Specific entropy
ice_air_g_entropy_si
η = − gT
Specific enthalpy
ice_air_g_enthalpy_si
h = g − T gT
Sublimation enthalpy
ice_air_enthalpy_subl_si
LAI
P = TΛ AI [η ]
Sublimation pressure
ice_air_sublimationpressure_si
P subl = 1− x AAV P
Thermal expansion coefficient
ice_air_g_expansion_si
Isothermal compressibility
ice_air_g_kappa_t_si
Adiabatic lapse rate
ice_air_g_lapserate_si
Air mass fraction
ice_air_massfraction_air_si
Solid mass fraction
ice_air_solidfraction_si
Vapour mass fraction
ice_air_vapourfraction_si
Formula
(
SI Unit
)
α = g TP / g P
κT = − g PP / g P
Γ = − g TP / gTT
J
kg K
kg
m3
J
kg K
J
kg
J
kg
J
kg
1
K
1
Pa
K
Pa
Eq.
(S25.1)
(S25.2)
(S25.3)
(S25.4)
(S25.5)
(S25.6)
(S25.7)
(S25.8)
(S25.9)
A = Asat(T, P)
1
(S25.10)
w Ih = 1 − w A / A
1
(S25.11)
w V = (1 / A − 1)w A
1
(S25.12)
26
(
)
(w
Table S26: Partial derivatives of the enthalpy potential function h AI w A ,η , P of ice air, Eq.
)
(5.78), section 5.9, expressed as partial derivatives of the Gibbs function g AI A , T , P of ice
air, Eq. (5.73). Subscripts indicate partial derivatives with respect to the respective variables.
The superscripts AI on g and h are omitted for simplicity. Because of minor practical
relevance, derivatives with respect to wA are omitted.
Expression in
h AI w A ,η , P
Library function
Equivalent in
g AI w A , T , P
η
– gT
(
)
h
ice_air_h_si
hη
(
)
g – TgT
SI Unit
J
kg K
J
kg
Eq.
(S26.1)
(S26.2)
T
K
(S26.3)
gP
m3
kg
(S26.4)
ice_air_h_si
1
g TT
g
− TP
g TT
kg K 2
J
K
Pa
hPP
ice_air_h_si
2
g TT g PP − g TP
g TT
m3
kg Pa
ice_air_h_si
hP
ice_air_h_si
hηη
ice_air_h_si
hηP
−
(S26.5)
(S26.6)
(S26.7)
(
)
Table S27: Selected properties of ice air computed from the enthalpy, h AI w A ,η , P , Eq.
(5.78), section 5.9, and its partial derivatives, Table S26. The superscript AI is suppressed
here for simplicity. The lapse rate of ice air is sometimes regarded as the “moist-adiabatic”
lapse rate in the meteorological literature.
Quantity
Library function
Density
ice_air_h_density_si
Temperature
ice_air_h_temperature_si
Specific isobaric heat capacity
ice_air_h_cp_si
Isentropic compressibility
ice_air_h_kappa_s_si
Adiabatic lapse rate
ice_air_h_lapserate_si
Formula
SI Unit
Eq.
1
hP
kg
m3
(S27.1)
T = hη
K
(S27.2)
J
kg K
(S27.3)
ρ=
cP =
T
hηη
κs = −
hPP
hP
Γ = hηP
1
Pa
K
Pa
(S27.4)
(S27.5)
27
Table S28: Properties of wet ice air, section 5.10, computed from A, T, P, wA and w as a
solution of Eqs. (A60) - (A65)
Quantity
Library function
Air fraction of humid air
liq_ice_air_airfraction_si
Formula
A
SI Unit Equation
kg
kg
kg
kg
(S28.1)
Air fraction of wet ice air
liq_ice_air_dryairfraction_si
wA
Liquid fraction of wet ice air
liq_ice_air_liquidfraction_si
kg
kg
(S28.3)
Solid fraction of wet ice air
liq_ice_air_solidfraction_si
 wA 

w W = w1 −
A 

 wA 
Ih

w = (1 − w)1 −
A


kg
kg
(S28.4)
Vapour fraction of wet ice air
liq_ice_air_vapourfraction_si
1

w V = w A  − 1
A 
Density
liq_ice_air_density_si
ρ = (w A / A)ρ AV + w W ρ W + w Ih ρ Ih
Specific enthalpy
liq_ice_air_enthalpy_si
h = w A / A h AV + w W h W + w Ih h Ih
Specific entropy
liq_ice_air_entropy_si
Pressure
liq_ice_air_pressure_si
Isentropic freezing level
liq_ice_air_ifl_si
Isentropic melting level
liq_ice_air_iml_si
Temperature
liq_ice_air_temperature_si
η = (w A / A)η AV + w Wη W + w Ihη Ih
kg
kg
kg
m3
J
kg
J
kg K
(
)
(S28.2)
(S28.5)
(S28.6)
(S28.7)
(S28.8)
P
Pa
(S28.9)
P at w = 1
Pa
(S28.10)
P at w = 0
Pa
(S28.11)
T
K
(S28.12)
28
Table S29: Properties of sea air, section 5.11, computed from SA, A, T, P, ρW and ρAV as a
solution of Eqs. (5.88) - (5.92)
Quantity
Library function
Air fraction of humid air
sea_air_massfraction_air_si
Condensation temperature
sea_air_condense_temp_si
Density of humid air
sea_air_density_air_si
Vapour density
sea_air_density_vap_si
Formula
SI Unit Equation
A = A cond (S A , T , P )
kg
kg
(S29.1)
T
K
(S29.2)
ρ AV
ρ V = (1 − A)ρ AV
Latent Heat
sea_air_enthalpy_evap_si
AV
LSA
− AhAAV − h SW + S A hSSW
P =h
Specific entropy of humid air
sea_air_entropy_air_si
η AV = − gTAV
kg
m3
kg
m3
J
kg
J
kg K
(S29.3)
(S29.4)
(S29.5)
(S29.6)