R. Feistel et al.: Oceanographic application and numerical implementation of TEOS-IO: Part 1 
649 
www.ocean-sci.net/6/633/2010/ 
Ocean Sci., 6, 633-677, 2010 
IOC et al., 2010). From the second and third terms of 
Eq. (5.17) we infer the derivatives of the brine salinity to be 
fdS A \ 
V dT J l 
Sa 
AsiM 
D S 
(5.19) 
and is available from the function 
sea_ice_expansion_seaice_si in the library. The 
third term on the right hand side of Eq. (5.24) is the melting 
rate, Eq. (5.21), multiplied by the isobaric melting volume 
of sea ice, function sea_ice_volume_melt_si, 
(3Sa 
V dP 
T 
= Sa 
AsiM 
D S 
(5.20) 
Vf = AsiM = v sw -S A < 
dv 
sw' 
,.Ih 
dS A 
(5.25) 
T,P 
With the help of these relations we can compute thermody 
namic properties of sea ice from the partial derivatives of the 
Gibbs function (Eq. 5.14) as given in Table S7 for seawa 
ter if the salinity S A considered there is substituted by the 
sea-ice salinity Ssi and the Gibbs function g sw (S A , T, P) by 
g SI (5si, T, P). The Gibbs function of sea ice, Eq. (5.14), is 
implemented as the function sea_ice_g_si in the library. 
Related to the intrinsic phase transition, certain properties 
of interest are very specific for a composite system like sea 
ice and not listed in Table S7. Using Eq. (5.19), the isobaric 
melting rate, i.e. the increase of the brine fraction b=Ssi/S A 
upon warming is 
(_ fr A siM 
(5.21) 
The isobaric heat capacity of sea ice computed from 
Eqs. (5.14), (S7.6) and (5.19), 
cp — — T 
9 2 g SI 
dT 2 
Ssi,P 
= (1 
b)c^ + be 
sw 
p 
L 
si 
db\ 
WJs sl ,P 
(5.22) 
consists of the single-phase contributions of ice, c ] p , and 
brine, c® w , as well as a latent part, and is implemented as 
sea_ice_cp_seaice_si. In the latter term, the coefficient 
L S p in front of the melting rate, Eq. (5.21), is the isobaric la 
tent heat of sea ice, 
4 : = rAsifo] = AsiM = 
a/7 sw \ 
d — - 
dS A ) T 
(5.23) 
and is available from the function 
sea_ice_enthalpy_melt_si in the library. The enthalpy 
of the brine, /; sw , is computed from Eq. (S7.3), and the 
enthalpy of ice, h m , is computed from Eq. (S3.4). 
Similarly, the thermal expansion of sea ice is computed 
from Eqs. (5.14), (S7.15) and (5.19), 
dv 
si ' 
/ a 2„si 
dr 
Ssi'P 
'dv sw \ 
dT 
Sa,P 
chM 
9T )p 
(5.24) 
The specific volume of the brine, u sw , is computed from 
Eq. (S7.1), and that of ice, i; 1 * 1 , from Eq. (S3.13). 
Since the freezing-point lowering due to pressure always 
exceeds the adiabatic lapserate of seawater, cold seawater 
may freeze and decompose into ice and brine during adia 
batic uplift but this can never happen to a sinking parcel. This 
freezing process can destabilize the water column, e.g. off the 
Antarctic shelf (Foldvik and Kvinge, 1974), since the ther 
mal expansion of sea ice, a sl —gj l p /g^}, Eq. (5.24), func 
tion sea_ice_expansion_seaice_si in the library, and 
consequently also the adiabatic lapserate (McDougall and 
Feistel, 2003) of sea ice, r SI =—g^ P /g^ T , Eq. (S18.14), 
possess large negative values near the freezing point (Feis 
tel and Flagen, 1998). These and related properties can be 
evaluated directly from the partial derivatives of the Gibbs 
function of sea ice, Eq. (5.14), implemented as the function 
sea_ice_g_si in the library, in terms of the in situ tem 
perature. For a seawater parcel, the potential temperature 
that corresponds to the freezing point under pressure is some 
what ill-defined physically since it is practically impossible 
to lift a parcel at the freezing point to the surface isentropi- 
cally without decomposition into ice and brine. Freezing of 
a seawater parcel cannot occur at any depth as long as its 
potential temperature referenced to the surface is higher than 
its freezing point temperature T llz ( S A , Pso) computed from 
Eq. (5.11) at the surface pressure Pso, as discussed by Jack- 
ett et al. (2006). 
As an observational example, the brine salinity, 
Eq. (S18.2), of Antarctic sea ice at normal pressure is 
shown in Fig. 6 in comparison to measurements of con 
centrated brines by Gleitz et al. (1995) and Fischer (2009). 
Note that only freezing point measurements at salinities less 
than 40gkg _1 were used for the construction of IAPWS-08 
(Feistel, 2008). 
5.5 Equilibrium seawater-vapour 
The vapour pressure of seawater is usually computed as 
a function of temperature T and Absolute Salinity S A , 
givingP vap (S A ,T). Similarly, the boiling temperature of 
seawater is computed as a function of absolute pressure P 
and Absolute Salinity S A , giving 7' hnl1 (S,\. P), and the equi 
librium brine salinity is computed as a function of T and 
P, giving S brme (P, P). The defining condition for each of 
these quantities is equality of the chemical potentials of water