Geology Reference
In-Depth Information
7.3.2.4. Absorption and Scattering Losses
Absorption and scattering are two mechanisms of
loss of an EM wave while propagating in a medium.
They have direct impact on remote sensing observa-
tions because the reflected or emitted radiation from
the surface is affected by either one or both forms of
losses in volume and the atmosphere. When the radia-
tion interacts with an atom, the latter may be excited to
a higher energy level. This energy may transform into
kinetic energy when the atom collides with other atoms,
raising the temperature of the medium. This loss of
energy is known as absorption. On the other hand, if
the excited atom emits the extra energy immediately
(i.e., within nanoseconds) as a photon (should be at the
same frequency as the frequency of the propagating
EM wave), then this process is known as atomic scatter-
ing (or just scattering). The scattering may also be
caused by reflection of the EM wave off tiny elements
such as dust particles in the atmosphere. Brief informa-
tion about absorption and scattering processes in the
atmosphere as well as the atmospheric agents that trig-
ger them is presented in section 7.7.1.
Absorption and scattering are defined by their relevant
coefficients. The absorption coefficient
α
(also called the
attenuation coefficient) is defined as the fractional
decrease in the intensity of the radiation
dI
over a dis-
tance
dx.
It has dimension of L
−1
.
The optical depth is the negative natural logarithm of the
fraction of radiation transmitted through the material.
Zero value means fully transparent material. This term is
used in a simplified version of radiative transfer equation
throughout this topic [e.g., equation (7.57)] and also to
retrieve ice surface temperature using microwave observa-
tions (section 10.5).
Conservation of energy implies that the amount of
incident energy is equal to the sum of the reflected, trans-
mitted, and absorbed energy. Therefore, in a simplified
view, reflectivity, transmissivity, and absorptivity should
add up to 1. Since most materials, including ice, are
opaque to thermal radiation, it is safe to assume that the
sum of reflectivity and absorptivity equals one in this
case. This means that good reflectors are poor absorbers
and vice versa. This principle of conservation of energy is
known as Kirchhoff 's law.
7.3.2.5. Emitted Radiation (Re‐radiation)
Part of the incident solar radiation in the VIS and NIR
bands is absorbed and later re‐radiated (emitted) at longer
wavelengths in the TIR, FIR, or microwave spectral
region. Most of the energy emitted by the Earth's surface,
with its temperature ranging roughly between −50 and
50 °C, is in the TIR regions. Unlike other radiometric pro-
cesses, incident radiation does not appear explicitly in the
emission process. Emission is determined by the emissivity
of the material (a function of physical composition), its
physical temperature, and surface roughness. The latter
determines the angular distribution of the emitted radia-
tion. In the TIR region, emission is a measure of how an
object radiates heat after its temperature rises as a result of
energy absorption. In the microwave region emission is more
of a function of the molecular properties of the medium.
The concept of emissivity is introduced in the next
section, but it is appropriate to introduce its connection
to the reflectivity to support further discussions of the
radiometric processes in this section. Under thermal equi-
librium the object must emit the same amount of energy
that has been absorbed. This entails that emissivity and
absorptivity are equal. This principle of conservation of
energy is a corollary of the well‐known Kirchhoff law of
thermal radiation. It takes the following form:
dI
I
()
xdx
(7.14)
If
α<1.0 part of the radiation is attenuated within the depth
of the material. If α>1.0 all radiation is attenuated within the
unit width
. In general, both
I
and
α
depend on frequency,
and if this equation is integrated over a finite distance
x
in
the atmosphere between
x
= 0 where
I
=
I
0
, and
x
=
X
, then
X
(7.15)
II
exp
(
xdx
)
0
0
Similar equations can be written for the scattering loss
coefficient
σ
(
x
) if
α
in equations (7.14) and (7.15) is
replaced with
σ
. If both absorption and scattering coex-
ist, then they can be combined into what is known as the
extinction coefficient
κ
:
()
1
()
(7.18)
v
v
()
1
()
(7.19)
(7.16)
h
h
The integral of the loss coefficient in equation (7.15),
whether it is absorption, scattering, or extinction, with
respect to the distance
x
is called the optical thickness
τ
, which is dimensionless. The intensity of the radiation
decreases over a given distance according to the equation
The reflectivity in the above equations can be obtained
by taking the square of the reflection coefficients from
equations (7.4) and (7.5) similar to the calculations from
equations (7.11) and (7.12). Qualitatively speaking, the
equations indicate that, for optical and thermal radiation,
strong absorbers at a given wavelength are also strong
emitters at or around the same wavelength. Note that
IIe
0
(7.17)
