R. Feistel et al.: Oceanographic application and numerical implementation of TEOS-IO: Part 1 
675 
www.ocean-sci.net/6/633/2010/ 
Ocean Sci., 6, 633-677, 2010 
must then be specified. Two important cases are considered 
in the following. 
Case 1: Equilibrium at given salinity, Sa, temperature, 
T, and pressure, P 
At given T and P, humid air can approximately be con 
sidered as an ideal mixture of air and vapour. The partial 
pressure P vap of vapour is computed from the vapour pres 
sure of liquid water at given T by solving Eq. (5.1), neglegt- 
ing the effect of salt in the water. The vapour density fol 
lows from Eq. (4.3) as p y —l/gJ,(T, P vap ) and the air den 
sity from p A =l/g AV (l, T, P — P vap ). The air fraction is 
then computed from A—p A /(p A +p v ). With A, T and P 
available, the required liquid water density estimate can be 
specified as, p w = 1 /p A ' (P, P), and the humid air density es 
timate as p AV =l/g AV (A, T, P), which are easily calculated 
from the related Gibbs functions, Eqs. (4.2) and (4.37). The 
saline part g s (SA, T, P) of the Gibbs function (Eq. 2.2) and 
its derivatives can be computed directly with the given pa 
rameters Sa, T and P. Using A.S' \=0, AP=0 and AP=0, the 
linear system (Eqs. A66-A68) can now be solved iteratively 
for A, p w and p AV . 
In particular, this solution provides the specific humidity 
q= 1 —A(Sa, T, P) of subsaturated humid air in equilibrium 
with seawater as a function of salinity, temperature and pres 
sure (see Feistel et al., 2010a for details). 
The equilibrium is computed in this way by the library 
call set_sea_air_eq_at_s_t_p or by the functions 
sea_air_massfraction_air_si or 
sea_air_entropy_air_si. 
Case 2: Equilibrium at given salinity, Sa, air fraction, 
A, and pressure, P 
At given A and P, humid air can be considered approx 
imately as an ideal mixture of air and vapour. The partial 
pressure P vap =x AV P of vapour is computed from the to 
tal pressure P and the mole fraction x av (A), Eq. (2.11). 
In turn, the boiling temperature 7'=7' holl (P vap ) of water is 
computed from Eq. (5.1), neglecting here the lowering due 
to dissolved salt. With A, T and P available, the density 
estimate of liquid water, p w —l/g^(T,P), and of humid 
air, p AV =l/g AV (A, T, P), is easily calculated from the re 
lated Gibbs functions, Eqs. (4.2) and (4.37), as well as the 
saline part # s (Sa, 7. P) of the Gibbs function (Eq. 2.2) and 
its derivatives. Using ASa=0, A4=0 and AP=0, the linear 
system (Eqs. A66-A68) can now be solved iteratively for T, 
p w and p AV . 
In particular, the solution of case 2 provides the conden 
sation temperature T—T cond (SA, A, P) of humid air in con 
tact with seawater, as a function of salinity, air fraction and 
pressure. The condensation temperature p cond is higher than 
the dewpoint temperature of humid air. Humid air with a 
temperature T>7’ cond causes water to evaporate from the sea 
surface. Humid air with a temperature T < P cond results in 
condensation of water at the sea surface (for details, see Feis 
tel et al., 2010a). 
This equilibrium is computed by the library 
call set_sea_air_eq_at_s_a_p or by the function 
sea_air_condense_temp_si. 
Supplementary material related to this 
article is available online at: 
http://www.ocean-sci.net/6/633/2010/ 
os-6-633-2010- supplement.pdf. 
Acknowledgements. The authors like to thank Trevor McDougall 
for important contributions to various details of this paper, as well 
as Sebastian Herrmann and Michael Fischer for providing vapour- 
pressure and sea-ice data, respectively. The authors are grateful to 
Allan H. Harvey, IAPWS, and Jeremy Lovell-Smith, BIPM CCT- 
WG6, for substantial hints and clarifying discussions regarding the 
different definitions of relative humidity. This paper contributes to 
the tasks of the SCOR/IAPSO Working Group 127 on Thermody 
namics and Equation of State of Seawater. DW acknowledges par 
tial support from the Department of Fisheries and Oceans’ Center 
for Ocean Model Development for Applications. 
The source code of the library is available from the Digital Sup 
plement of Part 2 of this paper (Wright et al., 2010a), information 
on subsequent updates will be posted on the TEOS-10 website, 
http://www.teos-10.org. 
We are very deeply moved and saddened by the sudden death of our 
good friend, kind colleague and excellent co-author, Dan Wright. 
Edited by: R. Tailleux 
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