IEEE Geoscience and Remote Sensing Magazine - June 2019 - 13

use a sky radiance fraction function instead of scaling the
downwelling irradiance by the sky-view factor in (8) and
(11), in turn obtaining a wavelength- and angle-dependent term accounting for the non-Lambertian nature of
the sky reflectance [44].
As shown in these equations, many factors are involved
in the radiative transfer process. Each of these factors affects
the spectral intensity and shape of the sensor-measured radiance spectrum and can ultimately result in a significant
amount of spectral variability. The sources of variability
may be broadly categorized into four areas: atmosphere,
illumination, acquisition geometry, and adjacent environment. In the following section, we examine the effects of
this variability through a detailed analysis based on the radiative transfer model equations just described.
ANALYSIS OF ENVIRONMENTALLY INDUCED VARIABILITY
Most of the variability in an observed spectrum is due to
atmosphere and illumination, and these sources of variability have indeed been the most widely investigated [36],
[45]-[48]. Many have shown, either by simulation or by
field experiments, how much the spectral radiance for a
single material can vary under different atmospheric conditions [e.g., aerosol/gas types and concentrations or water
vapor (WV) profiles] [46] and illumination conditions (e.g.,
shadowing or sky-dome obstruction) [36], [45], [47], [48].
To investigate adjacency effects and secondary illumination, Goa et al. [48] looked at radiance measurements of
targets placed between tree lines and exposed to different
illumination conditions; these measurements were then
compared with synthetic radiance spectra simulated according to a model based on (5)-(7). The results revealed
the importance of accounting for the secondary illumination term Lobst (m), which is often neglected, and showed
that it can play an important role in cases where, for instance, the target is in shadow and surrounded by tall and
brightly lit objects [35]. Similar considerations can be made
for the effects of adjacent materials in terms of both Ladj (m)
and 61 - ra (m) S (m)@. They may not be negligible, especially
when ra (m) & r (m) [37], that is, when adjacent materials are
more reflective than target materials (such as targets surrounded by brighter backgrounds and, in particular, targets
in shadow) [35], [49]. Viewing conditions and acquisition
geometry also play important roles in the spectral variability of materials [46], [50], especially topographic effects
that may considerably increase or decrease the direct and
diffuse illumination of the target. For example, consider a
sun zenith angle of 25°, a slope angle of the target surface
of 15° away from the sun, and a null azimuthal difference
between the sun and the slope orientation. In this case, the
direct illumination would decrease by approximately 15%
compared with the flat-terrain case. For the same geometry
but with a sun zenith angle of 45°, the decrease would be
approximately 30%.
The atmospheric effects of transmittance and visibility in general tend to vary slowly with respect to spatial
JUNE 2019

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

position and are often assumed to be stationary over a
full scene. This assumption can fail for wide-area remote
sensing or with shallow slant-angled views (called oblique
sensing) [50], [51], where the target-to-sensor path distance
may vary considerably over a scene. Other sources of variability, such as columnar WV [52], clouds, shadows, and
obstacles (e.g., leafy canopies and buildings), can be quite
spatially nonstationary. Topographic effects also exhibit a
strong spatial nonstationarity within a scene. In part, this is
because of the increased range of the sensor viewing angle
within a scene [50], [51], but a further effect of oblique sensing is that surfaces that were previously hidden become visible (e.g., walls of a building as well as the roof or trunks
of trees as well as the canopy) [51]. Adjacency effects are
intrinsically nonstationary, of course, because they depend
on the spatial variations of surface materials in the examined scene.
A summary of these considerations is given in Table 2.
Graphical examples showing how these sources of variability manifest themselves on the sensor-reaching radiance are
provided in the following section.
EXAMPLES OF ENVIRONMENTALLY
INDUCED VARIABILITY EFFECTS
An example experiment is shown in Figure 4, where at-sensor radiance spectra in the VNIR were synthetically generated by exploiting spectral signatures from the ASTER spectral library [53]. The spectral reflectance r Cu (m) of copper
was used for the target material. This was chosen because it
has a smooth reflectance spectrum and exhibits both low
reflectivity (in the blue/green portions of the VIS) and medium/high reflectivity (in the red and NIR). To illustrate the
effects of adjacent and obstacle materials with respect to the
copper, we used a rangeland reflectance spectrum r Rl (m),
with very low reflectivity across the full VNIR; an olive
canopy reflectance spectrum r Ol (m), with high reflectivity
in the NIR only; and an aluminum reflectance spectrum
r Al (m), with higher reflectivity across the full VNIR. A plot
of these four spectra is shown in Figure 4(a).
In this example, we used the MODTRAN (i.e., MODerate
resolution atmospheric TRANsmission) 5 radiative transfer
code [54] to simulate radiation transfer in the atmosphere
in combination with the physical models expressed by
(10)-(12). A typical airborne remote sensing scenario was
reproduced by making reference to a real hyperspectral data
collection campaign performed in May 2013 with the SIM.
GA hyperspectral sensor (511 spectral channels in the VNIR
with a full width at half maximum of about 2 nm), flying
over the city of Viareggio, Italy [55]. The parameters are listed in Table 3, where the values of the varied parameters are
reported in curly brackets. One single parameter was varied
each time by keeping the others fixed at the basic configuration value highlighted in boldface. In Figure 4(b)-(h), the
spectra corresponding to the basic configurations are displayed in blue in each plot. Each plot legend shows how the
other colors are assigned to the variations.
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IEEE Geoscience and Remote Sensing Magazine - June 2019

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