Geology Reference
In-Depth Information
where
The density of sea ice
ρ
i
(kg/m
3
) can be calculated from
the following equation, given by
Pounder
[1965], where
the ice temperature
T
i
is in °C:
2
3
FT
4 732 22 45
.
.
T
064
.
T
0 01074
.
T
for
(3.29)
si
si
si
si
2
T
229
.
si
917 014
.
T
(3.36)
si
si
2
3
FT
8999 1309
T
55 27
.
T
071
.
T
for
si
si
si
si
22 9
.
T
30
(3.30)
si
3.4.4. Air Volume Fraction
Air volume fraction (or bulk ice density) is not a
property that can be accurately measured. So, it is usually
obtained by subtracting the summation of volume fraction
of the other components from the total volume fraction
(i.e., 1):
3.4.2. Solid Salt Volume Fraction
The mass of solid salts at a given depth is proportional
to the mass of brine:
m m
b
(3.31)
ss
V
V
V
V
V
V
V
V
pi
a
1
b
ss
(3.37)
where
A
is a function of temperature, determined from
the phase equilibrium diagram, as presented in Table 3.5.
This relation can be written as
si
si
si
si
Due to brine drainage, the air volume can be significant
as air replaces some brine pockets. For this reason some
studies use the total porosity (
V
T
), which is the summa-
tion of the brine and air volume fractions:
ss ss
VA
bb
(3.32)
from which an expression for the solid salt volume frac-
tion can be derived:
VVV
T
a
(3.38)
b
V
V
V
V
ss
bb
(3.33)
A
However, air volume fraction, which can be derived from
the bulk ice density, must be known accurately.
Cox and
Weeks
[1983] developed equations to calculate the total
porosity of sea ice.
The calculated effect of ice temperature on brine,
solid ice, and air volume fractions, calculated from equa-
tions (3.26), (3.33), (3.35), and (3.37) is presented in
Figure 3.17 for ice density of 900 kg/m
3
and salinity of
10‰. The most important feature in the figure is the
si
ss
si
and
ρ
b
can be obtained from equation (3.22). The solid salt
density
ρ
ss
can be assumed to be constant =1500 kg/m
3
.
3.4.3. Pure Ice Volume Fraction
The mass of pure ice is
mMmm
b
ss
(3.34)
pi
si
1. 0
0.9
0.8
0.7
0.6
0.5
Replacing the mass terms in the above equations by
multiplication of density and volume, the above equation
can be solved for the pure ice volume fraction
V
pi
/
V
si
using
Brine volume fraction
Ice volume fraction
Air volume fraction
V
V
V
V
pi
si
bb
1
A
(3.35)
si
pi
pi
si
0.4
Table 3.5
Values of the constant
A
versus average ice
temperature
T
i
(°C).
T
si
0.3
0.2
0.1
0.0
-30
A
T
si
A
−2
0
−16
44.952
−4
0.148
−18
50.808
-25
-20
-15
-10
-5
0
−6
0.387
−20
56.851
Ice temperature (°C)
−8
0.660
−22
63.015
−10
8.256
−24
217.168
Figure 3.17
Variation of brine, air, and pure ice volume frac-
tions versus temperature for first‐year ice of constant density
900 kg/m
3
and salinity 10‰ [
Shokr and Sinha,
1995].
−12
30.493
−26
537.697
−14
38.421
−28
842.341
