Geology Reference
In-Depth Information
and salinity 10‰ at temperatures below −8.2 °C, volume
fractions of brine and pure ice are weak functions of
temperature. Above that temperature, brine volume frac-
tions increase almost exponentially with temperature.
This observation implies that the dielectric constant of
FY ice becomes mainly a function of ice salinity below,
say, −12 °C.
To simulate the permittivity of MY ice, it was calcu-
lated using the assumption of spherical air bubble
inclusions. Results are presented in Figure 3.31.
Permittivity varies almost linearly with density but does
not vary with temperature. This is because temperature
has no effect on the air volume fraction. Results also
show that permittivity is almost independent of the
shape of air bubbles, which means that MY ice is an
isotropic dielectric.
Temperature dependence of the complex dielectric
constant and brine permittivity are shown in Figure 3.32
from calculations using the spherical brine pocket
assumption. Both permittivity and loss increase sharply
at temperatures above −5 and −11 °C for salinities of
10‰ and 20‰, respectively. These are the temperatures at
which the brine volume fraction reaches 0.1. Recall that,
at this value, the assumption in the dielectric mixing
model regarding the mutual interaction between inclu-
sions is adjusted. The sharp increase in permittivity near‐
freezing temperatures is accompanied with a sharp
increase in brine volume and a decrease in brine salinity
(Figure 3.18). At these temperatures, charged molecules
of water, not free ions in liquid brine, give rise to a high
permittivity. A peak in the loss factor is noticeable at
about −22.9 °C, similar to a peak in brine salinity
(Figure 3.18)
.
Below this temperature, a considerable
mass of salt freezes in brine pockets and brine salinity
decreases accordingly. This effect reverses the trend of
loss below −22.9 °C; i.e., it decreases as temperature con-
tinues to decrease (a result of brine pockets shrinkage).
Two observations can be concluded upon comparing
results from Figure 3.32 and 3.18. The first is the simi-
larity between the temperature dependence of sea ice
permittivity and brine volume. This implies that per-
mittivity is influenced by the overall composition of the
material, of which brine volume is the most important
parameter in the case of FY ice. The second is the simi-
larity between temperature dependence of the loss fac-
tor and brine salinity when the ice temperature is low
enough so that the brine volume fraction is less than
0.1. This implies that the dielectric loss is influenced by
detailed properties of individual inclusion elements,
i.e., brine salinity in this case. The loss depends also on
the shape and characteristic dimensions of brine pock-
ets, as will be shown later. The permittivity of brine
decreases linearly as temperature decreases and stabi-
lizes at a value around 15 below −22 °C (precipitating
temperature of sodium chloride) (Figure 3.32). The
dielectric loss of brine has a peak at −13 °C. Both brine
permittivity and loss depend only on brine salinity,
which is driven by ice temperature.
Applications of the above PVD‐based formulations are
limited to the cases when the dimensions of the inclusions
are at most an order of magnitude less than the wave-
length of the propagating wave. That is because the model
does not take into account scattering from inclusion ele-
ments. This assumption is appropriate for the purpose of
studying the C‐band wave interaction with brine pockets,
since their major axis is typically a few millimeters in
length [
Weeks and Ackley,
1982]. For air bubbles in MY
ice, it has been found that less than 5% of bubbles in MY
Figure 3.31
Calculated permittivity of multiyear ice in the C‐band versus ice temperature and density for a con-
stant salinity of 2‰, assuming a spherical air bubble shape [
Shokr and Sinha,
1995].
