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 indicated.
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 vapourpressure
line from the 101 325 Pa isobar in the liquid region is below
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 coefficients
(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 properties
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 stable
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 “Neptunian”
oceanographic standard range (Fig. lb). In the presence
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 reasonably
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 minimum.
The Gibbs function is valid to even lower pressures
(Feistel and Wagner, 2007) not shown here because the sublimation
curve is restricted by the validity of the IAPWS-95
equation for vapour, Fig. la. In the library, an extension of
