R. Feistel et al.: Oceanographic application and numerical implementation of TEOS-IO: Part 1 
637 
www.ocean-sci.net/6/633/2010/ 
Ocean Sci., 6, 633-677, 2010 
Fig. 3. Range of validity of the IAPWS-08 Gibbs function of seawa 
ter and uncertainty of density estimates calculated from this func 
tion. Region A: oceanographic standard range, B: extension to 
higher salinities, C: hot concentrates, D: zero-salinity limit, E: ex 
trapolation into the metastable region below 0 °C. 
the vapour equation down to 50 K is implemented that per 
mits the computation of sublimation properties to this limit 
(IAPWS, 2008c; Feistel et al., 2010a). Vapour cannot rea 
sonably be expected to exist below 50 K (Feistel and Wag 
ner, 2007). No ice forms other than Ih occur naturally under 
oceanographic conditions. 
The Gibbs function g m (T,P) together with its first and 
second partial derivatives is implemented as the library func 
tion ice_g_si. 
2.3 Sea salt dissolved in water 
The Gibbs function g sw (S A . T. P) of seawater (IAPWS, 
2008a; Feistel, 2008) is expressed as the sum of a Gibbs 
function for pure water, g w (T,P). numerically avail 
able from the IAPWS-95 formulation, and a saline part, 
g S (S A ,T.P): 
g sw (S A ,T,P)=g w (T,P)+g s (S A ,T,P). (2.1) 
Flere, salinity is expressed as Absolute Salinity S A , the mass 
fraction of dissolved salt in seawater, which for standard sea 
water equals the Reference-Composition Salinity within ex 
perimental uncertainty (Millero et al., 2008; Wright et al., 
2010b). 
In representing the properties of Standard Seawater, the 
range of validity of the Gibbs function for seawater is shown 
in Fig. 3. For temperatures in the oceanographic standard 
range, salinities up to 40 g/kg are properly described up to 
100 MPa. For higher salinities up to 120 g/kg and tempera 
tures up to 80 °C, the application is restricted to atmospheric 
pressure (101 325 Pa). Up to saturation, the salinity of cold 
concentrated brines agrees well with Antarctic sea-ice data 
(Fig. 6). For hot concentrates (region F in Fig. 3) the partial 
derivatives of density are not reliable. New density measure 
ments (Millero and Fluang, 2009; Safarov et al., 2009) have 
led to some recent improvements and an option to use an ex 
tension introduced by Feistel (2010) is included in the library 
(Wright et al., 2010a). Nevertheless, reliability of results for 
this region remains limited by the sparseness of data and the 
possibility of precipitation of calcium minerals (Marion et 
al., 2009) which would degrade the accuracy of the Refer 
ence Composition approximation in this region. 
The saline part g s (S A , T. P) of the Gibbs function to 
gether with its first and second partial derivatives is imple 
mented as the library function sal_g_si. 
Note that the arguments of the Gibbs function are temper 
ature and pressure rather than temperature and density as in 
the Flelmholtz function. Since the Gibbs function of pure 
water is expressed in terms of the corresponding Flelmholtz 
function, sea_g_si is only available at library level 3 where 
implicitly determined quantities, such as density in terms of 
temperature and pressure, are considered. 
The function g s (S A , T. P) is constructed as a series expan 
sion with respect to salinity. Based on the theory of ideal and 
electrolytic solutions (Planck, 1888; Landau and Lifschitz, 
1964; Falkenhagen et al., 1971), this expansion consists of 
salinity-root and logarithmic terms and takes the form 
7 
g S = 81 (T)S A In (T, P)Sf. (2.2) 
7=2 
Flere, the expansion coefficients are defined as 
gi(T) = x (gioo + gnor) (2.3) 
g2(T, P) = x (S2jk - 0.5g 1Jk In s u ) r jyt k (2.4) 
% j.k 
g<(T, P) = x Y^g i]k x J Tt k , i = 3...7 (2.5) 
^ j.k 
with g u =l Jkg -1 , 5 u =35.16504gkg -1 x40/35, and the co 
efficients gjjk are given in the IAPWS Release 2008. 
The reduced temperature is t—(T—To)/T*. 7o=273.15 K, 
P*=40 K, the reduced pressure is tt=(P—Po)/P*, 
Po=101 325 Pa, P*=10 8 Pa. 
The explicit separation of the expansion coefficients of 
Eq. (2.2) is required for the accurate determination of cer 
tain properties which in the zero-salinity limit possess a nu 
merical singularity that can be analytically resolved. In some 
equations such as for the computation of potential temper 
ature, one or more terms of the expansion (Eq. 2.2) cancel 
analytically. Implementing the numerical solution of such an