IEEE Geoscience and Remote Sensing Magazine - December 2021 - 229

characterized by four sources: 1) solar radiation directly
reflected off the ground, 2) light directly reflected off the
atmosphere into the sensor, 3) light scattered by the atmosphere
and reflected off the ground, and 4) light reflected
off surrounding regions on the ground and then scattered
before reaching the sensor (constituting the adjacency effect)
[17], [18]. These effects are illustrated in Figure 3. A
model for the reflectance at the sensor ysensor
is given by [15]
yy Tatmg
sensor=+
yT TT yy T TTr
1
sg .-+- .-ys
()
avgs
g
avg
,
(3)
where ys is the reflectance of the surface of interest, Tg
gaseous transmittance, yatm is the reflectance of the atmosphere,
T.
is the
and Tare
the upward and downward scattering
transmittances, r is the ratio between the diffuse and total
transmittance for the ground-to-sensor path, s is the spherical
albedo of the atmosphere, and yavg
is the average surface
reflectance in a region around a pixel, which is used to account
for scattering (adjacency) effects [15].
Physics-based atmospheric correction algorithms then
try to obtain the ground reflectance ys
reflectance ysensor
assume that individual aerosol and gas concentrations
are uniform across the scene (resulting in a single transmittance
spectrum being computed for each gas) [19],
[22]. While this is true for some gases (such as ammonium,
oxygen, methane, carbon dioxide, and so on) that
are fairly constant in the atmosphere [20], it is far from
true for aerosols, which may show significant variation in
space [23], [24]. The aerosol concentration can change depending
on the environment (e.g., in large cities and rural
areas), and thus it must be provided by users of existing
algorithms [20]. Moreover, standard aerosol types often
do not adequately represent the scene being processed,
leading to inaccuracies in the retrieved spectra [25]. In addition,
experimental studies have found that aerosol optical
thickness has significant spatial variability within a
single scene [23], [26] and is often correlated with cloud
concentrations [26].
Some works attempted to estimate the aerosol optical
from the at-sensor
by solving (3). In the overall working of
these algorithms, the first step for atmospheric compensation
consists of retrieving the atmospheric parameters necessary
to represent the quantities in (3), mainly consisting of
an aerosol description (visibility and type of aerosol) and the
amount of water vapor for each pixel [19]. They are typically
based on variations of the so-called three-band ratio technique,
which is an important step to quantify the amount of
water vapor for each pixel. The three-band ratio technique
basically compares ratios of radiances measured near the
edges of a number of spectral wavelengths that are known
to present heavy water vapor absorption (e.g., at around
0.91, 0.94, and 1.14 μm), using this information to derive
the column water vapor information for each pixel [5], [20].
After the necessary parameters have been estimated, (3) can
be solved for the ground reflectance, and an optional postprocessing
step can be employed (called spectral polishing) to
remove artifacts from the correction process [19].
Physics-based models can represent and account for
the interaction between solar radiation and the atmosphere
very accurately. However, for this accuracy to translate
into meaningful surface reflectance estimates, these
models require precise information about atmospheric
properties, which is very difficult to obtain in practice.
This is especially true for scattering and absorption by
aerosols, which are hard to characterize accurately due
to their spatial and temporal variability [21]. Inaccuracies
in the estimation of these parameters (which include the
atmospheric visibility, aerosol model type, and an atmospheric
model) introduce errors in the retrieved surface
reflectance spectra that can be significant and spectrally
nonuniform [22].
Furthermore, unlike water vapor compensation, which
is performed on a pixel-by-pixel basis, most methods
DECEMBER 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
thickness for smaller patches of the image individually
by using shadow detection results [27], an approach that
depends on the presence of a large number of shadowed
pixels. However, acquiring precise data for an accurate
and possibly spatially variable atmospheric correction is
generally difficult, which means that the results of common
atmospheric compensation methods can be subject
to significant errors [23]. For instance, a number of studies
have investigated the residual errors in surface reflectance
data after the application of atmospheric compensation
methods by comparing the processed results with
in situ data and by using simulations. These studies found
that, generally, there is still an appreciable error in the retrieved
reflectances. As an example, errors in the retrieved
reflectance by atmospheric corrections due to the spatial
variability of the aerosol optical thickness above southern
England were found to be as high as 1.7%, with errors of
(a)
(b)
Light Source
(c)
(d)
Viewer
Terrain
FIGURE 3. The effects of the atmosphere on the acquired hyperspectral
image. The sources of radiation are represented by (a)
light directly reflected by the atmosphere to the sensor, (b) light
scattered by the atmosphere and reflected by the ground, (c) light
directly reflected by the ground, and (d) light reflected by surrounding
regions on the ground and then scattered to the sensor.
229
IEEE Geoscience and Remote Sensing Magazine - December 2021

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