Geology Reference
In-Depth Information
dimensions of IFOV of that channel (13 km × 15 km as
shown in Table 7.4). Therefore, only a slight overlap exists
between adjacent pixels. Gridded data are commonly
used in applications because they facilitate integration of
data between sensors. However, the integrity of the data
is reduced due to averaging the radiation from a few
overlapping IFOVs. It is better to use the original swath
data, especially when integrating data from different
sensors. This point is explained later through an applica-
tion of sea ice concentration retrieval (section 10.2.2).
As explained in section 7.3.3 the observed radiation by
passive microwave sensors is converted into brightness
temperature. The radiation has contributions from four
sources as shown in Figure 7.25: surface radiation,
upwelling atmospheric radiation, reflected downwelling
atmospheric radiation, and reflected space radiation. The
simple algebraic radiative transfer (RT) equation that
describes this summation is the basis for many algorithms
of sea ice geophysical parameter retrieval from passive
microwave remote sensing:
T
k Tze
()
()
z
d
()
z
(7.59)
downref
0
where
T
(
z
) is the temperature of the atmosphere at height
z
and
τ
′(
z
) is the atmospheric opacity from the surface
to a height
z
. The constant
k
in equation (7.59) is
introduced to account for the approximation of the
diffuse reflection from rough surfaces as being along the
line of sight. Its value depends on the distribution of
τ
and
the degree of isotropy of the diffuse reflection assumed at
the surface [
Gloersen et al.,
1978]. Strictly speaking, the
integrals in equations (7.58) and (7.59) should be carried
out over the entire hemisphere.
Assuming constant temperature and atmospheric
attenuation profiles in equations (7.58) and (7.59), and
substituting the results of the integrations back into
equation (7.57), a simplified form of the RT equation can
be written as
TT eT e T ee
T
*
(
1
)
*
(
1
)(
1
)
b LRL
air
air
RL
)
e
2
(
1
2
sp
RL
TTe TT
(
1
)
e
(
1
)
Te
b
RL RL
up
down-ref
sp
(7.60)
(7.57)
Here,
T
ai
*
is the effective physical temperature of the
radiating layer of the atmosphere (theoretically, it should
be the entire atmospheric column). This parameter is
usually defined as a weighted‐average atmospheric tem-
perature in the lower troposphere
T
air
[
Gloersen et al.,
1978].
Svendsen et al.
[1983] used the following approximation,
which is considered to be sufficiently good, given the
uncertainties in the value of the atmospheric opacity:
where
T
b
is the observed radiation,
ε
RL
and
T
RL
are the
emissivity and the average physical temperature of
the radiating layer,
τ
is the total (integrated) atmos-
pheric opacity, which is wavelength dependent,
T
up
is
the upwelling atmospheric radiation,
T
(Tdown−ref),
is the
reflected downwelling radiation, and
T
sp
is the average
temperature of free space;
T
up
and
T
(Tdown−ref),
are given by
the equations
*
09
(7.61)
()
z
(7.58)
T
T
T
T ze dz
()
()
up
air
air
0
2
1
3
4
Emission
Absorption
Reflection
Figure 7.25
Sketch showing the components of the observed radiation by a passive microwave sensor. The
component numbers 1, 2, 3, and 4 represent the emission from the surface, upwelling radiation from the
atmosphere (
T
up
), reflected downwelling radiation (
T
(Tdown−ref),
), and reflected space radiation (
T
sp
); respectively.
