www.ocean-sci.net/6/633/2010/
Ocean Sci., 6, 633-677, 2010
R. Feistel et al.: Oceanographic application and numerical implementation of TEOS-IO: Part 1
Table A2. Coefficients of Eq. (A25)
665
i
n
k
Üi
h
0
0.999842594E+3
0.1965221E+5
0.3239908E+1
0.850935E-4
1
0.6793952E-1
0.1484206E+3
0.143713E-2
—0.612293E-5
2
—0.909529E-2
—0.2327105E+1
0.116092E-3
0.52787E-7
3
0.1001685E-3
0.1360477E-1
—0.577905E-6
4
—0.1120083E-5
-0.5155288E^1
5
0.6536332E-8
Equation (A18) provides an estimate of the density p w
in kgm -3 of freezing pure water as a function of absolute
temperature T in K from a correlation fit between 252 and
273 K.
Equation (A26) provides an estimate of the brine salinity
Sa in kg kg -1 of sea ice at given absolute temperature T in
K and absolute pressure P in Pa from the empirical laws of
Clausius-Clapeyron and Raoult:
T-T t -x(P
aT
Pt)
(A26)
The IAPWS-95 triple point is P t =611.654771 007 894 Pa,
r t =273.16K, the Raoult coefficient is «=—0.217 (Feis
tel et ah, 2008) and the Clausius-Clapeyron coefficient is
X=—74.3x 10 -9 KPa -1 (Feistel and Wagner, 2006). When
solved for the freezing temperature T (Sa, P), Eq. (A26)
gives
Tt + x(P-Pt)
1 — «5a
(A27)
and when solved for the melting pressure P (Sa, T), it gives
1
p^p t + -(T -T t -aTS A )- (A28)
X
A7 Conditions for seawater in equilibrium with water
vapour (Sect. 5.5)
To determined conditions under which water vapour will
be in equilibrium with seawater, we first linearize the three
Eqs. (5.27)-(5.29) with respect to small changes of the five
unknowns Sa, T, P, p v and p w to obtain:
SasIs&Sa - (/7 - /7 + g S T ~ S A g S ST ) AT (A29)
“ Gw +*!--Sas!/’) aî>
_ f w _ f v , s _ n s 7 ,
/ f +g S A g s
- p W f? p AT + ^ - (2fj + P W fJ p ) AP V (A30)
- p W /*Ar + ^ - (2/ p w + p w /7) Ap w (A31)
_ w f w
P Jp pW
To iteratively solve the system (Eqs. 5.27, 5.28, 5.29) for
Sa, T, P, p v and p w using Eqs. (A29)-(A31), two further
equations must be added which specify an additionally im
posed pair of conditions, commonly AT—Q and A,S' \ =0 (if
the temperature and the salinity are specified) or AP=0 and
ASa =0 (if the pressure and the salinity are specified).
Auxiliary empirical equations are used to determine initial
estimates for Sa, T, P, p v and p w .
The function (Eq. A32) is the inverse of Eq. (A10) and
estimates the boiling temperature T in K of the seawater-
vapour equilibrium at given brine salinity Sa in kg kg -1 and
absolute pressure P in Pa from the Clausius-Clapeyron and
Raoult laws for T <640 K:
fi_
T la 2
1
+ —In
a 2
|-(1-«5a)
'1
(A32)
with an rms error equal to 0.01 in ln(P/P t ). The constants
are P t =611.654 771 007 894 Pa, P t =273.16K, «=-0.57,
ai=-19.873 100 570 9116, a 2 =-3.089 754 373 529 98.
The empirical formula P?»P WP80 (5p, P48) of Weiss and
Price (1980)
P wp80 1 00 K
...... ( A33 )
In
101 325 Pa
= 24.4543 - 67.4509-
Î48
- 4.8489 In
T4&
100 K
- 0.0005445 P
for the vapour pressure of seawater with Practical Salinity
0<5p<40 and IPTS-48 temperature 273 K<74s <313 K is
very accurate (Feistel, 2008). For the estimates required here,
the raw conversion 74s «7’ and 5p« 1000 5\ is sufficiently
precise.
Formula (Eq. A34), obtained from Eq. (A33) and Raoult’s
law, computes a brine salinity estimate Sa in kg kg -1 for
seawater-vapour equilibrium at given absolute temperature
T in K and absolute pressure P in Pa:
5a«
1
a
pWP80 T ) \
? 7'
(A34)
