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Full text: Numerical implementation and oceanographic application of the thermodynamic potentials of liquid water, water vapour, ice, seawater and humid air : Part 1: background and equations

R. Feistei et al.: Oceanographic application and numerical implementation of TEOS-IO: Part 1 
635 
www.ocean-sci.net/6/633/2010/ 
Ocean Sei., 6, 633-677, 2010 
Table 1. Hierarchy of thermodynamic potentials and their elementary constituents implemented in the library. 
Potential 
Level 
Routine 
Parent 
System 
Reference 
f(T, p) 
1 
f lu.f.si 
Primary 
Fluid water 
Sect. 2.1 
8 lh (T, P) 
1 
ice_g_si 
Primary 
Ice Ih 
Sect. 2.2 
gi(T, P) 
1 
sal-g_term_si 
Primary 
Seawater 
Eq. (2.2) 
/V, p) 
1 
dry_f_si 
Primary 
Dry Air 
Eq. (2.6) 
Baw(T) 
1 
air_bawjn3mol 
Primary 
Humid Air 
Sect. 2.4 
Caww(T) 
1 
air_cawwjn6mol2 
Primary 
Humid Air 
Sect. 2.4 
Caaw(P) 
1 
air_caawjn6mol2 
Primary 
Humid Air 
Sect. 2.4 
g s (S A , T, P) 
2 
sal.g.si 
gi 
Seawater 
Eq. (2.2) 
/ mlx (A, T, p) 
2 
air_f jnix_si 
B AW> 
Caww, 
Caaw 
Humid Air 
Eq. (2.13) 
/ av (A, t, p) 
2 
air_f_si 
/F /A> /mix 
Humid Air 
Eq. (2.7) 
g w (T, P) 
3 
liq_g_si 
/ F 
Liquid water 
Eq. (4.2) 
g w (T, P) 
3 
vap_g_si 
f 
Water vapour 
Eq. (4.3) 
g sw (S A , T, P) 
3 
sea_g_si 
g W , g S 
Seawater 
Eq. (4.4) 
h sw (S A , /], P) 
3 
sea_h_si 
^sw 
Seawater 
Eq. (4.5) 
g ÄV (A, T, P) 
3 
air_g_si 
f AW 
Humid Air 
Eq. (4.37) 
h AW (A, r], P) 
3 
air_h_si 
g AW 
Humid Air 
Eq. (4.40) 
g sl (S sh T, P) 
4 
sea_ice_g_si 
g SW ,g m 
Seawater + 
ice 
Eq. (5.14) 
g sv (S SV , T, P) 
4 
sea_vap_g_si 
g SW , g W 
Seawater 
+ water 
vapour 
Eq. (5.30) 
g AW (w A , T, P) 
4 
liq_air_g_si 
g W ,g AW 
Liquid water 
+ humid air 
Eq. (5.58) 
Ä AW (uJa, r], P) 
4 
liq_air_h_si 
g AW 
Liquid water 
+ humid air 
Eq. (5.63) 
g M (wA, T, P) 
4 
ice_air_g_si 
g 1 * 1 , g AW 
Ice 
+ humid air 
Eq. (5.73) 
h M (w A , r], P) 
4 
ice_air_h_si 
g Al 
Ice 
+ humid air 
Eq. (5.78) 
gW_F03(j^ p 
5 
f it_liq_g_f 03_si 
Fit of / F 
Liquid water 
IAPWS (2009c) 
g WJF97 (r> p) 
5 
f it_liq_g_if 97_si 
Fit of / F 
Liquid water 
IAPWS (2007) 
gVJF97^ />) 
5 
fit vap g if97 si 
Fit of / F 
Water vapour 
IAPWS (2007) 
library decided that the published molar equation can be con 
verted to the mass-based form used here and in the planned 
IAPWS document (IAPWS, 2010), and that this should be 
implemented using the latest value for the molar mass of dry 
air (Picard et al., 2008) rather than the originally published 
one. For consistency with the IAPWS formulation, the molar 
mass of dry air of the SIA library is updated in the SIA ver 
sion 1.1, attached as a supplement to the companion paper 
(Wright et al., 2010a), in contrast to the obsolete value used 
in SIA version 1.0 which is consistent with the formulation 
of Feistel et al. (2010a). 
2 Level 1: Thermodynamic potentials - the primary 
standard 
As described in the related background articles, the vast 
amount of quantitative information available from extensive 
sets of experimental thermodynamic data for water, ice, sea 
water and air is represented in a compact way by the em 
pirical coefficients of only four independent functions, a 
Helmholtz function f F (T,p) of fluid water referred to as 
IAPWS-95 (IAPWS, 2009a; Wagner and PruG, 2002), a 
Gibbs function g m (T,P) of ice, referred to as IAPWS-06 
(IAPWS, 2009b; Feistel and Wagner, 2006), a Gibbs func 
tion g s (Sa, T, P) of sea salt dissolved in water which is re 
ferred to as IAPWS-08 (IAPWS, 2008a; Feistel, 2003, 2008), 
and a Helmholtz function f A (T,p) for dry air (Lemmon et
	        
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