Geology Reference
In-Depth Information
(a)
(b)
1. 0
1. 0
ϵ
v
0.8
0.8
ϵ
v
ϵ
h
6.0
6.0
0.4
0.4
0.2
0.2
ϵ
h
0.0
0.0
0.0
0.0
20
40
60
80
20
40
60
80
Incidence angle
Incidence angle
Figure 7.18
Plots of the microwave emissivity using Kirchhoff's law calculated from Fresnel equations using
dielectric constant that represents (a) freshwater ice and (b) seawater.
strong absorbers are poor reflectors and vice versa. In the
infrared region, open water is a good absorber and there-
fore a good emitter with emissivity values around 0.98.
Similarly, in the longwave spectrum fresh snow is a good
absorber with its emissivity very close to one. In the
microwave range the Fresnel reflection and consequently
the emissivity depend on the dielectric constant of the
material since the reflection coefficient
R
in equations
(7.9) and (7.10) is a function of this parameter. Figure 7.18
includes plots of microwave emissivity calculated using
equations (7.18) and (7.19) using two values of dielectric
constant: (3.0-
j
0), which represents freshwater, and (18.5-
j
31.3), which represents seawater (this value is valid for
microwave frequency of 35 GHz and temperature of
20 °C [
Reese
, 2013]). Due to its high dielectric constant
the seawater has considerably less microwave emissivity
than sea ice, especially in the horizontal polarization. This
is the basis of sea ice and water discrimination in many ice
parameter retrieval algorithms from microwave data. The
peak emissivity in vertical polarization from water occurs
near 80°and from ice near 60° (i.e., ice has a smaller
Brewster angle than water). It should be mentioned that
the wind‐driven surface roughness of seawater will lower
the reflectance and therefore raise the emissivity.
hypothetical material that absorbs all incident radiation
at all frequencies or just a certain band of frequencies
and therefore reflects none. In other words, a blackbody
is a perfect absorbent and perfect emitter of energy. At
room temperature, a blackbody appears extremely black
to the eye—hence the origin of its name. The behavior of
a given material with regard to being a blackbody varies
depending on the frequency of the incident EM wave. In
the optical band, many surfaces approach the ideal
blackbody behavior in terms of their ability to absorb the
solar radiation. Examples include soot, carbide, silicon, and
platinum. In the TIR band water and ice absorb radiation
well and therefore can be considered nearly blackbodies.
In the microwave (and radio wave) bands the absorptive
properties of water and ice differ from each other and
none of them is considered a blackbody.
The total radiation flux
R
B
(in W/m
2
) emitted by a
blackbody at temperature
T
(in Kelvins) varies as the
fourth power of the physical temperature of the body.
The relationship is known as the Stefan‐Boltzmann law:
4
RT
B
(7.20)
b
where
σ
b
is the Stefan‐Boltzmann constant (5.671 × 10
‐8
W/m
2
· K
4
). Using a quantum mechanics model, Max
Planck developed an expression for the radiation flux
density
R
B
(
f
) from a blackbody at a given frequency
f
and
physical temperature
T
(in Kelvins), which is known as
Planck's equation:
7.3.3. Brightness Temperature
Emission in the Mid-IR, FIR, TIR, and microwave
regions is expressed in terms of brightness temperature
T
b
, which is defined as the temperature of a blackbody
that emits the same amount of radiation observed by the
sensor. The justification for this parameter is rooted in
the fact that the emitted radiation from a blackbody is
modeled by a deterministic equation. A blackbody is a
3
Rf
hf
ce
2
1
()
(7.21)
B
2
hf kT
/
1
where
h
is Planck's constant,
k
is Boltzmann's constant,
and
c
is the speed of light. The emitted energy reaches a
