Physical Basis for Microwave Remote Sensing ...
493
where ko is the wave number in free space. The power absorption coefficient ~a is defined as
~a = 2a
(18.8)
It is often expressed in dB/m through the relation
~a(dB/m) = 8.686a(Np/m)
(18.9)
18.2.4 Extinction and scattering coefficient
The total electromagnetic loss in a scattering medium consists of absorption loss (electromagnetic power transformed into other forms of energy, such as heat) and scattering loss (energy
is caused to travel in directions other than that of the incident radiation). Scattering loss is
caused by particles of different E embedded in a host medium. The extinction coefficient (total
loss) is thus
(18.10)
where ~s denotes the scattering loss.
Penetration depth. Part of a wave incident upon the surface of a medium from the air in
the direction z is transmitted across the boundary into the medium. The penetration depth is
defined as the depth 6p at which (Ulaby et al., 1986)
(18.11)
where z is the direction normal to the surface, P( 6p ) is the transmitted power at 6p , and P(O+)
is the transmitted power just beneath the surface. If scattering in the medium is ignored,
~e == ~a = 2a and if, additionally, a does not depend on z,
1
R
6 - - - -
p -
~a - kOE"
E"« E'
(18.12)
The penetration depth indicates the maximum depth of the medium that contributes to the
backscattering coefficient and brightness temperature.
18.3 Physical Properties of Sea Ice and Snow
18.3.1 Sea ice
Sea ice is composed of fresh-water ice, inclusions of liquid brine and air bubbles. Fresh water
ice forms from sea water at temperatures below the freezing point of sea water. Some of the
salt liquid is entrapped within the ice forming microscopic pockets of brine. The salinity of
brine is much higher than that of sea water and depends on the temperature of the surrounding
ice with which it is in thermal equilibrium. The composition of sea ice is shown in Figure 18.1.
At a temperature of -lODe brine forms only 0.7% of sea ice of 1 part per thousand salinity. At
-2°e it is 2.7%. The air content by weight is negligible but by volume it may be up to 10%
for first-year sea ice.
The brine pockets are usually elongated and their average length is of the order of millimeters.
Their dimensions are determined by the temperature. The average salinity of sea water in the
493
where ko is the wave number in free space. The power absorption coefficient ~a is defined as
~a = 2a
(18.8)
It is often expressed in dB/m through the relation
~a(dB/m) = 8.686a(Np/m)
(18.9)
18.2.4 Extinction and scattering coefficient
The total electromagnetic loss in a scattering medium consists of absorption loss (electromagnetic power transformed into other forms of energy, such as heat) and scattering loss (energy
is caused to travel in directions other than that of the incident radiation). Scattering loss is
caused by particles of different E embedded in a host medium. The extinction coefficient (total
loss) is thus
(18.10)
where ~s denotes the scattering loss.
Penetration depth. Part of a wave incident upon the surface of a medium from the air in
the direction z is transmitted across the boundary into the medium. The penetration depth is
defined as the depth 6p at which (Ulaby et al., 1986)
(18.11)
where z is the direction normal to the surface, P( 6p ) is the transmitted power at 6p , and P(O+)
is the transmitted power just beneath the surface. If scattering in the medium is ignored,
~e == ~a = 2a and if, additionally, a does not depend on z,
1
R
6 - - - -
p -
~a - kOE"
E"« E'
(18.12)
The penetration depth indicates the maximum depth of the medium that contributes to the
backscattering coefficient and brightness temperature.
18.3 Physical Properties of Sea Ice and Snow
18.3.1 Sea ice
Sea ice is composed of fresh-water ice, inclusions of liquid brine and air bubbles. Fresh water
ice forms from sea water at temperatures below the freezing point of sea water. Some of the
salt liquid is entrapped within the ice forming microscopic pockets of brine. The salinity of
brine is much higher than that of sea water and depends on the temperature of the surrounding
ice with which it is in thermal equilibrium. The composition of sea ice is shown in Figure 18.1.
At a temperature of -lODe brine forms only 0.7% of sea ice of 1 part per thousand salinity. At
-2°e it is 2.7%. The air content by weight is negligible but by volume it may be up to 10%
for first-year sea ice.
The brine pockets are usually elongated and their average length is of the order of millimeters.
Their dimensions are determined by the temperature. The average salinity of sea water in the