652 
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/ 
Temperature T / K 
800 
700 
600 
500 
400 
300 
200 
Fig. 7. Temperature-pressure phase diagram of seawater in the 
vicinity of the triple point. At different salinities, the triple point 
(TP), i.e. the equilibrium between liquid seawater, ice and vapour 
is displaced along the sublimation line (in bold) of the ice-vapour 
equilibrium. Note that the triple-point pressure can change by a fac 
tor of 2 while the vapour-pressure lowering at constant temperature 
is only of order 10% or less. 
P = (p W ) 2 / p W (5-47) 
Equations (5.44)-(5.47) provide four conditions for the five 
unknowns Sa, T, P, p v and p w . Any one of the five parame 
ters may be specified to complete the system which may then 
be solved as discussed in Appendix A9. 
If any one of the three variables Sa, T, P is specified, the 
other two are determined by the above conditions. Figure 7 
shows the displacement of the triple point along the sublima 
tion line as a function of salinity. 
In the library, the equilibrium properties P, T and Sa of 
sea-ice vapour are available from the functions 
sea.ice.vap.pressure.si, 
sea_ice_vap_temperature_si and 
sea_ice_vap_salinity_si. Note that the equilibrium 
conditions are actually determined by calling one of 
set_sea_ice_vap_eq_at-p, 
set_sea_ice_vap_eq_at_t or 
set_sea_ice_vap_eq_at_s, depending on which of 
pressure, temperature or salinity is specified. Thus, one of 
these ’’set-’’-routines must be called before accessing P, 
T or Sa using the above function calls, but all three equi 
librium properties corresponding to the specified parameter 
choice are available once the appropriate ’’set-’’-routine is 
executed. 
5.8 Equilibrium humid air - liquid water 
The state in which humid air is in equilibrium with liquid wa 
ter is commonly referred to as “saturated air”, the “dewpoint” 
or the “condensation point”. The condition for this equilib 
rium is equal chemical potentials of liquid water, Eq. (4.2), 
and of water in humid air, Eq. (S12.15), 
S AV -A 
dA ) T p 6 
(5.48) 
In terms of the Primary Standard functions and their inde 
pendent variables (Sect. 2), Eq. (5.48) is expressed using the 
relations 
g w (T,P) = / F (r,p w ) + P/p w (5.49) 
(5.50) 
g AV = / AV (A,r,p AV ) +P/p AV 
(5.51) 
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. Using Eqs. (5.49) 
and (5.51) to eliminate the Gibbs potential in favour of the 
Helmholtz potentials results in three equations for these five 
unknowns. 
For the numerical solution, two of the five unknowns as 
well as starting values for the remaining unknowns must be 
specified. Four important cases are considered in detail in 
Appendix A10. 
No matter which of the four cases considered in the ap 
pendix is applied to compute the equilibrium between liquid 
water and humid air, the numerical solution of Eqs. (5.48)- 
(5.52) provides a consistent set of equilibrium values for A, 
T,P, p w and p AV which is then available for the computa 
tion of any other property of either saturated humid air or 
liquid water in this state. 
For example, at given temperature T and total pressure P, 
the partial vapour pressure of saturated air is available in the 
form 
Psat, calc =x AV p (5.53) 
from the solution obtained for A (T, P), using 
library function liq_air_massf raction_air_si 
and then converting to the mole fraction of vapour, 
x AV =l — x^ v (A), Eq. (SI.5), using the library function 
air_molf raction_vap-si. The comparison with ex 
perimental data for the saturated vapour pressure (Feistel et 
al., 2010a), Fig. 8, permits an estimate of the effect of the 
cross-virial coefficients Baw(T), Caaw(T) and Caww(T’)