VISIBILITY AND SHADOW OF STEEP SLOPES IN SIDELOOK SPOT IMAGERY
Figure 1 depicts a general situation of slope exposure, westward of the flight
path direction. The sun, normally, is east of the scene. The satellite in this
case is in westlook mode.
The slope angle is SI.
Let <|>2 be the angle between slope exposure and lookdirection, and <f>3 the angle
between slope exposure and (sun azimuth + 180°).
It follows from fig. 1 that
tan 82 = tan 61 * cos <\>2 and
tan 63 = tan 81 * cos <f>3
{based on: cos <J>2 = BF1 / BF2
BF1 = h / tan 81
BF2 = h / tan 82 }
The slope is not seen by the satellite, and therefore not imaged, if 82 > view-
angle.
The slope is in shadow if 83 sun elevation. This shadowed slope is seen by the
satellite if 82 =< view angle.
To analyze a particular slope, the slope angle 8 is given, as it can be chosen.
The viewangle X and the sun elevation y are also known, as they are provided in
the peripheral data of the image CCT.
Substitution of X for 82 and y for 83 will give the corresponding values for <j>2
and <f>3, respectively. The range of exposure directions with invisibility and
with shadowed slopes extends over a value of <J>2 and <f>3 degrees on either side
of, respectively, the lookdirection and the direction (sun azimuth + 180°).For a
more elaborate discussion, the reader is referred to Nossin (1990). A wide range
of slope expositions and slope angles can be analyzed this way.
THE IGLO
All slopes possible in any terrain could be represented by a dome (an iglo)
where each point on the (hemi)sphere corresponds to a specific combination of
slope exposure direction and slope angle (represented by the tangent to the iglo
surface at that point). This iglo, illuminated by the sun, at an azimuth and el
evation as given in the CCT peripheral data, would have a shadow zone which cor
responds to the graph of all possible shadowed slopes in the terrain, under that
particular illumination, represented again by points on the iglo surface as des
cribed above. It is by no means certain that all possible slopes do indeed occur
in the terrain, but if they occur then, for their specific combination of expo
sure direction and slope angle, their shadow (if any) would fall within the
shadow area on this iglo.
Similarly, the iglo, looked at from the satellite in side-look, under the speci
fied incidence angle and lookdirection, will have an invisible sector, made of
all points on its surface which correspond to the combination of slope angle and
exposure direction of slopes in the terrain invisible to the satellite from that
lookangle,- again, if such slopes do occur in the terrain.
Figure 2 attempts to elucidate this.
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