656 
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/ 
from Eqs. (5.70)-(5.72) and case 3 from Appendix All, see 
Table S25. For the computation of the partial T — P deriva 
tives of g AI , the first derivatives of A sat (T, P) are required. 
Taking the respective derivatives of Eq. (5.70) we get the iso- 
baric drying rate, 
_ ^Aai M 
V 3t ) P d a 
and the isothermal drying rate, 
(5.74) 
3^ Sat \ ^satAAlM 
3p ) T Da 
(5.75) 
of humid air, i.e. the decrease of its saturated air fraction A sat 
due to heating or compression. The chemical coefficient D A 
is defined in Eq. (S12.16). The latency operator Aai of ice 
air used here is defined for the specific entropy, p AI =—g A1 , 
of the form 
AaiM = t] AW - A 
dn AW 
dA 
- n 
Ih 
T,P 
(5.76) 
and for the specific volume u AI =g AI of the form 
AaiM = v AV - A 
dv AV 
dA 
— V 
Ih 
T,P 
(5.77) 
The partial derivatives of the Gibbs function g AI (w A , T, P), 
Eq. (5.73), of ice air are given in Table S24. Properties of 
ice air computed from this Gibbs function are given in Ta 
ble S25. 
For the description of isentropic processes such as the up 
lift of ice air in the atmosphere, enthalpy h Al (w A , rj, P) com 
puted from the Gibbs function (Eq. 5.73) is a useful thermo 
dynamic potential: 
h Al = g Al - T 
3g AI \ 
dT ) w a p 
(5.78) 
For this purpose, temperature T in Eq. (5.78) must be deter 
mined from entropy rj by numerically solving the equation 
3g AI \ 
3 T ) W A'P 
(5.79) 
computed at that reference level from the partial derivatives 
of h Al (w A ,)). P r ). Such properties derived from the poten 
tial function h Al at the reference pressure are commonly re 
ferred to as “potential” properties in meteorology (von Be- 
zold, 1888; von Helmholtz, 1888). Examples are the poten 
tial enthalpy, he, 
h 6 =h A1 (w A ,r],P r y (5.80) 
the potential temperature, 9, in °C, obtained from Eq. (S27.2), 
Tq+ Ô — 
' dh Al (ui A ,i],P r y 
3 n 
w A ,p T 
and the potential density, pe, from Eq. (S27.1), 
(5.81) 
Pe 
dh Al (w A , T], P r ) 
dP r 
W A ,Pr 
(5.82) 
The related library functions are 
ice_air_potenthalpy_si, Eq. (5.80), 
ice_air_pottemp_si, Eq. (5.81), and 
ice_air_potdensity_si, Eq. (5.82). Ice air can exist 
only below an upper bound of entropy as shown in Fig. 10, 
given by either melting or the complete sublimation of the 
ice phase. 
5.10 Equilibrium humid air - liquid water - ice 
With the additional presence of air in the gas phase, the com 
mon triple point of water is expanded to a triple line in the 
A —T—P phase space, similar to the triple line of seawater, 
Fig. 3, in which the amount of salt present adds a new in 
dependent degree of freedom. When humid air, liquid wa 
ter and ice coexist, the given conditions simultaneously sat 
isfy the equilibrium conditions (Eqs. 5.48 and 5.70) of equal 
chemical potentials of water in all three phases: 
8AV -<^L=a=a 
In terms of the Primary Standard functions and their indepen 
dent variables (Sect. 2), Eq. (5.83) is expressed by the system 
The partial derivatives of the enthalpy h Al (w A ,rj,P) are 
computed from those of the Gibbs function, Table S24, as 
given in Table S26. 
Selected properties of ice air computed from the enthalpy 
(Eq. 5.78) and its partial derivatives are given in Table S27. 
Many meteorological processes such as adiabatic uplift 
of an ice-air parcel conserve specific humidity and entropy 
to very good approximation. In particular, if a parcel is 
moved this way to some reference pressure P=P r , all of 
the thermodynamic properties given in Table S27 can be 
g w (T,P) = / F (V,p w ) + P/p w 
g AV = / AV (A,P,p AV ) +P/p AV 
(5.84) 
(5.85) 
(5.86)