R. Feistel et al.: Oceanographic application and numerical implementation of TEOS-IO: Part 1
653
www.ocean-sci.net/6/633/2010/
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 humidity,
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). According
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 recommended
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 saturated,
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 realized
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)
