498
M. Hallikainen
Any water in the snowpack collects at points of contact between the grains. The geometry and
porosity of snow at high and low liquid water contents have been examined by Colbeck (1981).
He concluded that snow, like any porous material, has two distinct regimes of liquid saturation.
In the lower range, called the pendular regime, air is continuous throughout the pore space, and
liquid occurs in the forms of isolated inclusions. In the higher range of liquid saturation, the
funicular regime, the liquid is continuous throughout the pore space and air occurs as distinct
bubbles trapped by narrow constrictions in the pores. There is a sharp transition between the
two regimes.
The metamosphism caused by melting and freezing changes the microstructure of snow; the
grains become rounded during the melting process, and some of the smaller grains disappear
completely. Snow that has undergone several melt-freeze cycles tends to form multiple clusters.
The density of dry newly fallen snow is of the order of 0.1 g/cm 3 . Metamorphism increases the
density so that it is of the order of 0.3 g/cm 3 • Under extreme conditions the density may be
as high as 0.5 g/cm 3 • The snow grain size increases, due to metamorphism, from 0.2 mm for
new snow to 1-2 mm for refrozen snow. The snowpack can include several layers with different
physical properties, often with thin icy layers between them. The liquid water content of snow
may be up to more than 10% by volume.
18.4 Dielectric Properties of Sea Ice and Snow
18.4.1 Sea ice
Sea ice consists of pure ice, brine inclusions and air bubbles. In order to understand the
dielectric behavior of sea ice, the permittivity of water, brine, and pure ice are reviewed first.
18.4.1.1 Pure water and sea water
Compared with other natural media, the complex permittivity of water is exceptionally high.
This is due to its polar molecular structure (Debye, 1929). Dissolved salts in sea water (salinity
up to 35 0/00 by weight) increase the ionic conductivity. Consequently, the dielectric loss factor
of sea water is higher than that of pure water at frequencies below 10 GHz. The salinity of liquid
brine in sea ice is governed by its temperature and can exceed 200 0/00 at low temperatures.
The dielectric behavior of pure water follows the Debye equation (Debye, 1929). Sea water
contains dissolved salts, including NaCl, MgCI2, Na2S04, CaCh, and KCl, and the average
salinity in the oceans is 32.54 0/00 (Anderson, 1960). Salts increase the dielectric loss of water
by adding free charge carriers. Hence, the loss factor of sea water includes an additional term
due to ionic conductivity and the complex permittivity of sea water follows the modified Debye
equation,
fswO - f swoo
. (J'sw
€sw = €.woo + 1 + '2 f - J -
J 7l" Tsw
€o
(18.13)
where €swoo is the high-frequency limit of €sw, €swO is the static dielectric constant of sea water,
f is the frequency, Tsw is the relaxation time of sea water, O"sw is the ionic conductivity of sea
water, and €o is the dielectric constant of vacuum.
Figure 18.4 shows the complex permittivity of pure and sea water (salinity 32.54 0/00 ) at O°C
and 20°C. The real part is practically independent of salinity. The imaginary part is governed
by the Debye relaxation process at frequencies above 10 GHz and by the ionic conductivity at
frequencies below 3 GHz.
M. Hallikainen
Any water in the snowpack collects at points of contact between the grains. The geometry and
porosity of snow at high and low liquid water contents have been examined by Colbeck (1981).
He concluded that snow, like any porous material, has two distinct regimes of liquid saturation.
In the lower range, called the pendular regime, air is continuous throughout the pore space, and
liquid occurs in the forms of isolated inclusions. In the higher range of liquid saturation, the
funicular regime, the liquid is continuous throughout the pore space and air occurs as distinct
bubbles trapped by narrow constrictions in the pores. There is a sharp transition between the
two regimes.
The metamosphism caused by melting and freezing changes the microstructure of snow; the
grains become rounded during the melting process, and some of the smaller grains disappear
completely. Snow that has undergone several melt-freeze cycles tends to form multiple clusters.
The density of dry newly fallen snow is of the order of 0.1 g/cm 3 . Metamorphism increases the
density so that it is of the order of 0.3 g/cm 3 • Under extreme conditions the density may be
as high as 0.5 g/cm 3 • The snow grain size increases, due to metamorphism, from 0.2 mm for
new snow to 1-2 mm for refrozen snow. The snowpack can include several layers with different
physical properties, often with thin icy layers between them. The liquid water content of snow
may be up to more than 10% by volume.
18.4 Dielectric Properties of Sea Ice and Snow
18.4.1 Sea ice
Sea ice consists of pure ice, brine inclusions and air bubbles. In order to understand the
dielectric behavior of sea ice, the permittivity of water, brine, and pure ice are reviewed first.
18.4.1.1 Pure water and sea water
Compared with other natural media, the complex permittivity of water is exceptionally high.
This is due to its polar molecular structure (Debye, 1929). Dissolved salts in sea water (salinity
up to 35 0/00 by weight) increase the ionic conductivity. Consequently, the dielectric loss factor
of sea water is higher than that of pure water at frequencies below 10 GHz. The salinity of liquid
brine in sea ice is governed by its temperature and can exceed 200 0/00 at low temperatures.
The dielectric behavior of pure water follows the Debye equation (Debye, 1929). Sea water
contains dissolved salts, including NaCl, MgCI2, Na2S04, CaCh, and KCl, and the average
salinity in the oceans is 32.54 0/00 (Anderson, 1960). Salts increase the dielectric loss of water
by adding free charge carriers. Hence, the loss factor of sea water includes an additional term
due to ionic conductivity and the complex permittivity of sea water follows the modified Debye
equation,
fswO - f swoo
. (J'sw
€sw = €.woo + 1 + '2 f - J -
J 7l" Tsw
€o
(18.13)
where €swoo is the high-frequency limit of €sw, €swO is the static dielectric constant of sea water,
f is the frequency, Tsw is the relaxation time of sea water, O"sw is the ionic conductivity of sea
water, and €o is the dielectric constant of vacuum.
Figure 18.4 shows the complex permittivity of pure and sea water (salinity 32.54 0/00 ) at O°C
and 20°C. The real part is practically independent of salinity. The imaginary part is governed
by the Debye relaxation process at frequencies above 10 GHz and by the ionic conductivity at
frequencies below 3 GHz.