Geography Reference
In-Depth Information
obtain an object's brightness temperature (i.e. without
correcting for emissivity), we can invert Equation (5.2) as
follows:
5.3.5 Atmosphericcorrection
While observations using TIR data focus on the atmo-
spheric windows as previously described, water in the
atmosphere between the water and the sensor is still one
of the largest sources of error. For images acquired from
a satellite in earth orbit, the sensors are recording at
the top of the atmosphere (TOA) and therefore observe
the radiation originally emitted from the earth's surface
(i.e.
L
g
) after it has passed through the atmosphere. This
emitted spectral radiance measured at the sensor (
L
s
)is
influenced by many factors related to its path through
the atmosphere and factors such as the viewing geometry
of the sensor and sun. These factors can be summarised
by two factors: an additive spectral radiance contribution
(i.e. path radiance,
L
p
) resulting from upwelling spectral
radiance contributed by the atmosphere, and a multi-
plicative factor (i.e. transmissivity,
c
2
T(
λ
,
W
)
=
ln
1
(5.3)
c
1
λ
5
W
+
λ
To determine T
r
rather than the brightness temperature
from the measured TIR spectral radiance at a particular
wavelength, we shouldfirst apply the emissivity correction
(Equation5.1) for
W
before calculating temperature using
Equation 5.3. When implementing these equations, care
needs to be taken with the units (e.g., wavelength is
in m, not
m) and with the precision and number of
significant digits for any computer software used in the
calculation or else small errors in the calculation may be
artificially magnified.
Note that while we describe here the general form of
the corrections, they should be applied for individual
bands and pixels, and adjusted according to the specific
spectral characteristics of the sensor as described by its
spectral response function. The band centre wavelength
is generally used for calculations. An effective band centre
for a sensor band can be determined by weighting all
wavelengths within the defined sensor spectral band using
for the band-specific spectral response function.
μ
) which is due to the
attenuation by atmospheric absorption and scattering of
spectral radiance emitted by the surface and not reach-
ing the sensor. The correction of
L
s
to determine
L
g
is
as follows:
τ
λ
−
λ
L
s
(
)
L
p
(
)
L
g
(
λ
)
=
(5.4)
τ
(
λ
)
where:
L
g
=
land-leaving spectral radiance at a particular
wavelength (Wm
−
2
5.3.4 ProcessingofTIRimagedata
m
−
1
sr
−
1
)
μ
sensor spectral radiance (Wm
−
2
m
−
1
sr
−
1
)
L
s
=
μ
While some remote sensing data processing methods,
such as geo-rectification, are common for all remote
sensing data, the emitted nature of TIR remote sensing
requires some different processing techniques compared
to remote-sensing of reflected radiation. These special
techniques will be described here, but for information on
standard pre-processing, readers are referred to remote
sensing textbooks (e.g., de Jong, et al., 2004; Mather 2004;
Lillesand et al., 2008).
Required radiometric corrections of the data compen-
sate for both the effect of the atmosphere on what is
measured at the satellite, as well as between-image dif-
ferences such as changes in the emissivity of the surface
due to short-term factors such as wind blowing across
the water surface. Radiometric corrections can be time-
consuming and can be applied with different levels of
processing depending on the application for which the
data are to be used. To derive quantitative temperature
values from raw TIR data requires either that a radiomet-
ric correction be applied to the data, or some form of
other calibration data be used for an empirical correction
(e.g., see Section 5.6.4 for an example with SSTs).
path spectral radiance (Wm
−
2
m
−
1
sr
−
1
)
L
p
=
μ
τ =
transmissivity (unitless)
λ =
is the wavelength of the sensor (e.g., the band
centre wavelength)
To determine
L
g
from
L
s
accurately it is essential to
correct for atmospheric conditions as even on clear days
there will be an effect from atmospheric gases and water
vapour. Smoke, dust or haze can result in large effects.
TIR radiation also cannot be sensed through clouds or
fog, so standard remote sensing practices should be used
to identify and mask these in the image. Once
L
g
has
been determined from
L
s
using Equation 5.4, T
r
can be
determined using Equation 5.3.
L
p
and
τ
can be determined for the specific image date
using a radiative transfermodel such asMODTRAN(Berk
et al., 1989), 6S (Kotchenova, et al., 2006), or FLAASH
(Adler-Golden et al., 1999) to calculate all aspects of
scattering and transmissionof radiance through the atmo-
sphere. However, such models are time-consuming and
require input data which may not be available real-time,
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