658 
R. Feistel et al.: Oceanographic application and numerical implementation of TEOS-IO: Part 1 
Ocean Sci., 6, 633-677, 2010 
www.ocean-sci.net/6/633/2010/ 
Entropy Bounds of Wet Ice Air 
10000 
9000 
8000 
7000 
6000 
5000 
4000 
3000 
2000 
-1000 
-0 
-1000 
-2000 
0 10 20 30 40 50 60 70 80 90 100 
Air Fraction in % 
Fig. 12. Valid entropy values of wet ice air, “WIA”, computed 
from Eq. (S28.8) are restricted to narrow wedge-shaped regions 
depending on the air fraction w A between 0 and 100% for 
selected pressures P as shown. Only points (w A , rj) selected 
from these regions permit valid solutions of case 5 discussed in 
Appendix A12. At the upper entropy bound of wet ice air, wet 
air starts freezing, indicated as “Freezing” on the 1000 Pa case in 
the diagram. At the lower entropy bound of wet ice air, ice air 
starts melting, indicated as “Melting”. The locus of the wedge 
tips at various pressures is the triple line, shown dashed, at which 
ice, liquid water and water vapour coexist in the presence of air, 
Eq. (S28.8). Freezing and melting curves were computed with 
the library functions ice_liqjneltingtemperature_si 
in conjunction with ice_air_g_entropy_si and 
liq_air_g_entropy_si. For running w A , the triple line is com 
puted by calling the sequence set_liq_ice_air_eq_at_a, 
liq_ice_air_temperature_si, 
liq_ice_air_pressure_si and air_g_entropy_si. 
The first case is considered in Sect. 5.12. Note that sea air 
does not contain ice at temperatures above the freezing point 
of seawater. Nonetheless, air saturation and relative humid 
ity of humid air is defined relative to ice if the temperature 
is below the freezing point of pure water, even though no 
stable ice phase is present in the interval between the freez 
ing temperatures of pure water and of the system’s seawater 
component. 
Similar to Eq. (5.26), the condition for this equilibrium is 
equal chemical potentials of water in seawater, Eq. (S7.12), 
and of water in humid air, Eq. (S12.15): 
g AV 
- A 
9g AV \ 
3 A ) j p 
Sa 
9g sw 
dS A 
T,P 
(5.88) 
In terms of the Primary Standard functions and their indepen 
dent variables (Sect. 2), Eq. (5.88) is expressed by the system 
g SW (S A , T, P)=/ f (t, p w ) +P/p w + g s (S A , T, P) (5.89) 
(5.90) 
g AV = / AV (A,7\p AV ) +P/p AV 
(5.91) 
The independent variables in this scheme are the total pres 
sure, P, the pure-water density, p w , the humid-air density, 
p AV , the temperature, T , the Absolute Salinity, Sa, and 
the air fraction, A. Note that p w is merely a formal prop 
erty here - the density that liquid pure water has at given T 
and P. Expressing the chemical potentials in Eq. (5.88) by 
means of Eqs. (5.89) and (5.91), provides three equations in 
the six unknowns so three of the independent variables must 
be specified to complete the system. Once this is done, the 
remaining unknowns may be determined by iterative numer 
ical methods. Two important cases are considered in detail 
in Appendix A13. 
Selected properties of sea air are given in Table S29. The 
latent heat ¿® A of sea air is defined here as the enthalpy re 
quired to evaporate a small amount of water from seawater to 
humid air by heating at constant pressure. A derivation of the 
latent-heat equation is given in (Feistel et al., 2010a), similar 
to the latent heat of melting sea ice, Eq. (5.23). 
5.12 Equilibrium humid air - seawater - ice 
In contrast to sea air, Sect. 5.11, humid air in equilibrium 
with sea ice, referred to as sea-ice air here, is saturated be 
cause it is in equilibrium with salt-free ice, Sect. 5.9. The 
phases of sea-ice air are simultaneously in pairwise mutual 
equilibria, seawater with ice (sea ice, Sect. 5.4), ice with hu 
mid air (ice air, Sect. 5.9), and seawater with humid air (sea 
air, Sect. 5.11). Most of the properties of sea-ice air are avail 
able from the related library functions described in those sec 
tions, therefore we have refrained from implementing a spe 
cial sea-ice-air module. For completeness, we mention that 
the equilibrium conditions for sea-ice air consist of two equa 
tions between the chemical potentials of water in the three 
present phases, Eqs. (5.11), (5.70) and (5.88): 
g D '=g SW -^A 
9g SW 
dS A 
=g AV -A 
T,P 
9g AV \ 
3 A J T p 
(5.93) 
The latent heat of sea-ice air includes the transfer of water 
between the phases by melting, evaporation and sublimation. 
The resulting isobaric latent heat of sea-ice air is, expressed 
per kg of molten ice (Feistel et al., 2010a), 
sia _ «; av (AaiM) 2 /£>a + w sw (A S i[h]f/D s 
p w Ay A M [h]/D A + w sw A sl [h]/D s ■ ( - }