R. Feistel et al.: Oceanographic application and numerical implementation of TEOS-IO: Part 1 
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Ocean Sci., 6, 633-677, 2010 
on the validity of this formulation at higher densities. 
From the data scatter at low densities we may estimate the 
experimental uncertainty to be better than 0.5%. Ambient 
air has a density of typically 1 kg m -3 or less. At about 
lOkgm -3 , an error of about 2% must be expected if the 
second virial coefficients Baw(T) is omitted. The same 
error occurs at 100 kg m -3 with Baw(T) included but is 
reduced to 1% if the coefficients Caaw(T) and Caww(T) 
are considered, too. 
A practically important quantity is the relative humid 
ity, RF1, which expresses the deviation of the air fraction 
A of a given sample of humid air from the saturation value 
A sat (T, P) belonging to the same temperature and pressure, 
computed as the solution of Eq. (5.48) in the scenario of 
case 3 from Appendix A10. Out of several options available 
from the literature, two different definitions are implemented 
and attributed here to the WMO 3 and to the CCT 4 , 
RH„Mo(;l.:r.f>) = i _ , <5- 5 *> 
and 
X AV /^\ 
RHcct (A,T,P)= ,.,. v -. (5.55) 
x AV (A sat (r, P)) 
with the mole fraction x AV =l—x^ v (A) fromEq. (2.12). Ac 
cording to Jacobson (2005), the WMO defines the relative 
humidity as given in Eq. (5.54). This definition is also given 
by other sources such as Gill (1982). Alternatively, internal 
discussion documents of BIPM CCT-WG6 (Jeremy Lovell- 
Smith, private communication, 2010) consider as a suitable 
option for the definition of relative humidity the commonly 
used formula (Eq. 5.55). This definition is also recom 
mended in a recent document of WMO (2008), in contrast to 
Eq. (5.54). The definition of relative humidity given by the 
International Union of Pure and Applied Chemistry (IUPAC, 
1997) is similar to Eq. (5.55) but uses the ratio of the partial 
pressure of water vapour in humid air to the pressure of sat 
urated, air-free vapour, and does not exactly match 100% at 
saturation. 
In the library, the conversion functions from air fraction 
to relative humidity are implemented as 
liq_air_rh_wmo_from_a_si and 
liq_air_rh_cct_f rom_a_si. Their inverse functions are 
1 
~~ 1 +RHwMO x (l/A sat (T, P) - 1) 
and, from Eqs. (2.9) and (2.11), 
^ 1—RH CCT xxy V (A sat (T, P)) 
_ 1-RHcct xx^ v (A sat (r,P)) x (1 -M W /M A ) 
(5.56) 
(5.57) 
3 WMO: World Meteorological Organisation, www.wmo.int 
4 CCT: Consultative Committee for Thermometry, 
www.bipm.org/en/committees/cc/cct/ 
a) Vapour Pressure Data of Saturated Humid Air 
b) Vapour Pressure Data of Saturated Humid Air, magnified 
Fig. 8. Experimental data for the saturated vapour pressure p sat - ex P 
of humid air at different pressures P and temperatures T as reported 
in (Feistel et al., 2010a), in comparison to p sat . ca l c computed from 
Eqs. (5.53), (S21.9) and (S1.5). Symbol “o”: formula Eq. (2.7) 
without cross-virial coefficients, “B”: formula with the second 
cross-virial coefficient Baw(T), “C”: formula with the second and 
third cross-virial coefficients Baw{T), Caaw(T), Caww(T)- The 
smaller scatter is magnified in panel (b). The improvement real 
ized by including the C coefficients is effective mainly at densities 
higher than 100 kg m -3 . 
They are implemented in the library as 
liq_air_a_from_rh_wmo_si and 
liq_air_a_f rom_rh_cct_si. 
With “wet air” we refer to a composite system of liquid 
water and humid air with the mass fractions w A of dry air, 
uj v of vapour and w w of liquid water, w A +w w +w w =l. 
The mutual equilibrium requires A sat (T, P)—w A /w AS/ , with 
u) AV =u) A +u) V =l—being the gaseous mass fraction. 
The Gibbs function of wet air reads (Feistel et al., 2010a)