636 
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/ 
a) Density - Temperature Diagram of Liquid Water and Vapour 
1300 
1200 
1100 
1000 
900 
800 
700 
600 
500 
400 
300 
200 
100 
Phase Diagram of Ice Ih 
100 MPa 
1 MPa 
Po 
lOkPa 
100 Pa 
1 Pa 
10 mPa 
100 gPa 
1 jaPa 
10 nPa 
Temperature T /K 
b) Density - Temperature Diagram of Liquid Water 
360 
350 
340 
330 
320 
310 
300 
290 
280 
270 
260 
250 
950 1000 1050 1100 1150 1200 1250 
Density p /(kg m ~ 3 ) 
Fig. 1. Panel (a) Validity region (bounded by bold lines) of the 
IAPWS-95 Helmholtz potential for fluid water with isobars as indi 
cated. Panel (b) Magnified view of the small region corresponding 
to the standard oceanographic (“Neptunian”) range. TP: triple point 
gas-liquid-solid, CP: critical point. The deviation of the vapour- 
pressure line from the 101 325 Pa isobar in the liquid region is be 
low the graphical resolution of panel (b). Freezing-point lowering 
occurs with the addition of sea salt. To deal with this effect in the 
case of seawater, the extension of the pure water properties into the 
metastable liquid region just above the line marked “Freezing Point 
Lowering” is required. 
al., 2000) in combination with air-water cross-virial coeffi 
cients (Hyland and Wexler, 1983; Harvey and Huang, 2007; 
Feistel et al., 2010a). These potential functions are used 
as the Primary Standard for pure water (liquid, vapour and 
solid), seawater and humid air from which all other proper 
ties are derived by mathematical operations, i.e. without the 
need for additional empirical functions. 
Fig. 2. Range of validity (bold curves) of the Gibbs function of ice 
Ih and uncertainty of density. 
2.1 Fluid water 
The validity range of the IAPWS-95 Helmholtz potential 
/ F (T, p) for fluid water (IAPWS, 2009a; Wagner and PruB, 
2002) as a function of temperature T and density p is shown 
in Fig. la in a density-temperature diagram. It is confined 
to the pressure interval between the isobars of lOnPa and 
1 GPa, below the upper temperature bound of 1000 °C and 
by the phase transition lines with ice and the liquid-vapour 
2-phase region. Below the critical temperature, this region 
separates the stable vapour phase at low density from the sta 
ble liquid phase at high density. Only a small fraction of this 
region (a subset of the sliver to the right of the high density 
side of the phase transition boundary) belongs to the “Nep 
tunian” oceanographic standard range (Fig. lb). In the pres 
ence of dissolved sea salt, the freezing point is lowered so 
that the liquid phase of water is extended into the ice and 
vapour regions indicated in Fig. lb. 
The Helmholtz function f F (T,p) together with its first 
and second partial derivatives is implemented as the library 
function f lu_f_si. 
2.2 Ice 
The IAPWS-06 Gibbs function g Ih (T. P) of hexagonal ice Ih 
(Feistel and Wagner, 2006; IAPWS, 2009b) covers the entire 
region of its stable existence (Fig. 2). In the region of low 
temperature and high pressure the function behaves reason 
ably although no experimental data were available when the 
function was constructed. Below 100K, there are still open 
scientific questions regarding the possible phase transition to 
a proton-ordered ice XI or the existence of a density mini 
mum. The Gibbs function is valid to even lower pressures 
(Feistel and Wagner, 2007) not shown here because the sub 
limation curve is restricted by the validity of the IAPWS-95 
equation for vapour, Fig. la. In the library, an extension of