650 
R. Feistel et al.: Oceanographic application and numerical implementation of TEOS-10: Part 1 
Ocean Sci., 6, 633-677, 2010 
www.ocean-sci.net/6/633/2010/ 
Brine Salinity of Antarctic Sea Ice 
Fig. 6. Brine salinity computed from Eq. (S18.2) at given tem 
perature and normal pressure, compared with measured results for 
Antarctic sea ice. Symbol “F”: data of Fischer (2009), “G”: data of 
Gleitzetal. (1995). 
vapour and of water in seawater, 
/ 3e sw \ 
g v (r,P)=g sw (S A ,r,P)-S A ^^j ■ (5.26) 
In terms of the Primary Standard functions and their indepen 
dent variables (Sect. 2), Eq. (5.26) is expressed as the system 
f V .V ,V fW , W f W , „S n „S 
J + P J P = J + P J P + g ~ ¿Ag s (5.27) 
(p V ) 2 / p V = P (5-28) 
(p W ) 2 / p W = P, (5-29) 
which exploits the relations (Eqs. S2.6, S2.ll, 4.4 and 
S7.12) to avoid stacked numerical iterations. The function 
/ F (P, p v ) is abbreviated here by / v , and similarly for f w 
and their partial derivatives. Equations (5.27), (5.28), (5.29) 
provide three conditions for the five unknowns S A , T, P, p v 
and p w , so two of these parameters must be specified, usu 
ally from the set S A , T, P, to complete the system. Once 
this choice is made, the system can be solved as discussed in 
Appendix A7. 
Once the values of S A , T, P, p v and p w are computed 
from the iteration of Eqs. (5.27)-(5.29) at the given evapora 
tion conditions, various equilibrium properties can be deter 
mined from the formulae given in Table S19. 
We use the name “sea vapour” to refer to a composite 
system consisting of seawater and vapour in thermodynamic 
equilibrium. Its Gibbs function g sw (Ssv, T, P) depends on 
absolute temperature T, absolute pressure P and the mass 
fraction of salt, which is the “bulk” or “sea-vapour” salinity 
Ssv; the Gibbs function is expressed as 
g sw (S sw ,T,P) (5.30) 
= (1 -b)g y (T,P)+bg sw (S A ,T,P). 
Here, b—Ssv/S A <l is the mass fraction of brine. The brine 
salinity Sa(T, P) is a function of temperature and pressure 
controlled by the equilibrium Eq. (5.26). For a compact writ 
ing of the partial derivatives of Eq. (5.30) it is useful to define 
a formal latency operator of sea vapour, 
AsvW -A (5.31) 
Here, z is a certain thermodynamic function. For example, 
the equilibrium condition Eq. (5.26) can be written in the 
form 
Asvtg] = 0. 
(5.32) 
The total differential of Eq. (5.32) is commonly known as the 
Clausius-Clapeyron differential equation of this phase tran 
sition: 
( a -^m d, A+ f^i) d p 
V ds A Jr P A V 3T J. 
S,P 
^3A S y [g]^ 
dP =0 
S,T 
(5.33) 
The first term is the chemical coefficient (Eq. S4.6), 
T,P 
sigh- 
(5.34) 
From the second and third terms of Eq. (5.32) we infer the 
derivatives of the brine salinity, 
35a 
dT 
= -S A 
AsvM 
D S ’ 
(5.35) 
PdSA 
V 3p 
T 
= S A 
AsvM 
D S 
(5.36) 
With the help of these relations we can compute thermo 
dynamic properties of sea vapour from the partial deriva 
tives of the Gibbs function (Eq. 5.30) as given in Table S7 
for seawater if the salinity Sa considered there is substi 
tuted by the sea-vapour salinity Ssv a 'id the Gibbs func 
tion g sw (S A , T, P) by g sv (Ssv, T, P). The Gibbs function 
of sea vapour, Eq. (5.30), is implemented as the function 
sea_vap_g_si in the library.