R. Feistel et al.: Oceanographic application and numerical implementation of TEOS-IO: Part 1 
657 
www.ocean-sci.net/6/633/2010/ 
Ocean Sci., 6, 633-677, 2010 
Upper Entropy Bound of Ice Air 
Air Fraction in % 
Temperature of Wet Ice Air 
Air Fraction A in % 
Fig. 10. Valid entropy values of ice air computed from Eq. (5.79) 
as arguments of enthalpy h AI ^u; A , rj, are bounded above 
by roof-shaped curves, depending on the air fraction w A be 
tween 0 and 100% for selected pressures P as shown. At the 
entropy bound on the right, the ice phase is completely sub 
limated, given by the solution r=r subl (.P va P) G f case 2 in 
Appendix All, and labelled “Frost Point” in the figure. At 
the left boundary lines radiating from the lower left portion 
of the figure, the ice phase starts melting, Eq. (5.5), labelled 
here as “Melting” lines. The locus of the roof tops at various 
pressures is the triple line, shown dashed, at which ice, liquid 
water and vapour coexist in the presence of air, as described in 
Sect. 5.10, Eq. (S28.8). Freezing curves were computed with 
the library functions ice_liqjneltingtemperature_si 
and ice_air_g_entropy_si, and frost point curves 
were determined using ice_air_f rostpoint.si and 
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 independent variables in this scheme are the total pres 
sure, P, the liquid density, p w , the humid-air density, p AV , 
the temperature, T, and the air fraction, A. Expressing the 
chemical potentials in Eq. (5.83) by means of Eqs. (5.84) 
and (5.86), gives four equations in these five unknowns so 
that one of the independent variables must be specified to 
complete the system. Once this is done, the remaining 
variables may be solved for iteratively as discussed in Ap 
pendix A12. Three important cases of different initially 
known properties corresponding to this system are discussed 
there. If the relative mass fractions of the three phases are 
required, then an additional condition is required to fix these 
quantities, since at constant T and P the water-ice mass ratio 
Fig. 11. Temperature of wet ice air as a function of the air fraction, 
T(A), computed as described under case 1, Appendix A12. 
can still change. The two additional cases, 4 and 5, consid 
ered in Appendix A12 address this requirement. 
Figure 11 corresponds to case 1 in the Appendix A12 with 
fixed dry air fraction, A. It illustrates that the temperature 
of wet ice air differs only very little from the triple-point 
temperature of water, almost independent of pressure, caus 
ing the adiabatic lapse rate under these conditions to be very 
small. Note that the curve shown here neglects the solubility 
of air in water which could result in temperature effects of 
similar order. 
Figure 12 shows results corresponding to case 5 from Ap 
pendix A12 in which the dry-air fraction, w A , entropy, rj, and 
the liquid fraction of the condensed part, w—w w f(w w +w lh ) 
are specified. If an air parcel is lifted with the first two quanti 
ties fixed, then w varies between 0 at the melting level (com 
pletely frozen condensate), and 1 at the freezing level (com 
pletely molten condensate). Four valid wedge-shaped Wet- 
Ice-Air (WIA) regions are shown in this figure correspond 
ing to pressures of 1000, 10000, 101 325 and 1 000 000 Pa. 
Only points (w A , i)) selected from these wedge-shaped re 
gions permit valid solutions in this case. 
Selected properties of wet ice air included as library rou 
tines are listed in Table S28. 
5.11 Equilibrium humid air - seawater 
Humid air in equilibrium with seawater, referred to as sea 
air, is subsaturated because the vapour pressure of seawater 
is lower than that of pure water. 
In contrast to wet air, the liquid part of sea air can nei 
ther entirely evaporate nor freeze, i.e., as long as there is salt 
in the system there will always be a liquid fraction. Since 
there must be a gas fraction, too, whenever air is present, 
the composite system seawater - humid air can exist under 
ambient conditions only in two forms, with or without ice.