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olar zenith
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ant bands.
id two-way
L turbidity
ingles of 29
d by Koepke
A soil surface is an imperfect diffuse reflector.
Therefore the reflection behaviour will be a
function of relative magnitude of diffuse and
direct radiation and of solar zenith angle
(Makarova et al (1973), after Kondratyev et al
1981). Bartman (1980) and Larson and Barkstrom
(1977) established maps in which the surface
reflectance at a certain solar zenith angle is
converted to standard reflectance. This formula
implies a relatively large influence of solar
zenith angle due to the non diffuse behaviour of
natural surfaces. Applying this formula a standard
surface reflectance of for instance 20.0 percent
would give for a solzr zenith angle of 60 degrees a
sun dependent reflectance of 22.0 and for 29
degrees of 16.3 percent. These formulas are
probably dependent of the type of surface and
wavelength.
With increasing solar zenith angle the amount of
shadow will increase especially in rough areas and
areas with a high drainage density. Although an
higher amount of shadow at a certain sun elevation,
will lead to a decrease in reflectance this effect
will be counteracted by the difference between the
solar zenith angle dependent reflectance of May and
January. Sloping areas with various expositions
will react different from relatively flat areas.
Finally it must be noted that the reflectance of
parts of the playa with hygroscopic salts are a
function of the time of the day and hence of the
time of Landsat overpass.
4. CONVERSION OF JANUARY AND MAY DATA
The reflectance values calculated for the top of
the atmosphere cannot be compared directly. As is
shown, these values can be converted to reflectance
at the surface, if turbidity, as a function of
wavelength and solar zenith angle, are known. But
even in that case, reflectance values have to be
corrected for sun elevation to get comparable data
for both days.
Since there is much uncertainty in these
calculations other approaches are to be followed.
These may be the assumption that the upper and
lower limits or the PI and P99 of both data sets
are equal. It can also be assumed that the shape of
the feature space plots are comparable. Another way
is the selection of reference surfaces which are
constant for both days.
All approaches have disadvantages:
- Upper and lower limits for both dates are not
necessarily the same. One of the days may have
lower or higher reflectance values, for instance
due to the fact that very wet surfaces or sealed
surfaces are present in May or January. The
advantage of using PI and P99 is laid in the fact
that the influence of misregistrations is
minimized.
- The assumption of similar shapes of the feature
space may be wrong.
- Reflectance of reference objects may not be
constant.
In order to compare the results of calculations,
reflectance values of May are converted in values
comparable with the January data.
Ultimately that approach has been adopted in
which a reference object has been chosen, since
this will give the most reliable results. A part of
the footslope area with low relief intensity has
been selected. There may be some changes in
reflectance due to the influence of vegetation of
this object. The fact that parts of the complete
bare playa however have to be corrected in the same
way in all bands leads to the assumption that this
approach is still not too bad. Bands 1, 4 and 7 of
May have to be multiplied by respectively 0.919,
0.882 and 0.913 in order to get values comparable
with January reflectance at the top of the
5. RESULTS AND INTERPRETATION
The reflectance values of May and January are made
comparable with the aid of a reference surface.
Apart from this radiometric transformation also
geometrically the May image was converted with the
January data with the aid of ground control points.
A first order transformation has been applied,
which gave an estimated standard error of less than
a pixel in both directions according to the
statistical analysis. In this way both the location
and the reflectance values are comparable now.
In order to study the changes a large range of
images and plots can be made. The construction and
interpretation of 1, 4, 7 combinations of both
data, with a linear stretch between the same
limits, is a good first approach. A compariéon of
both images will give a good overview of spatial
dynamics.
It is also possible to make multitemporal
combinations or perform division or subtraction of
bands of the two days after the geometrical and
radiometrical corrections. Three types of
multitemporal images can be discriminated: a colour
combination, a ratio and a difference product.
Again the use of band 1, 4 and 7 is most promising.
- colour combinations
Useful products are combinations in which a primary
colour is assigned to one day and a secondary
colour to the other day. An example is a
combination of band 1 of May in red and band 1 of
January in cyan. If no changes occur, the grey
tones represent the relative reflectance.
- ratio
A division of one band in May (corrected) by the
same band in January will give a ratio of 1 for
pixels with unchanged reflectance, above 1 for
pixels with a relatively high reflectance in May
and below 1 for a high January value of
reflectance. Lines with a constant ratio in plots
connect points with the same relative decrease or
increase in reflectance.
- difference
An image made by subtraction of January from May
(corrected) would also give a value of 1 in the
case of no change, above 1 for a relatively high
reflectance in May, and below 1 for a low May
reflectance. Still there is an important difference
between the ratio and difference image. In this
latter image the same value will be found for all
points with the same absolute decrease or increase
in reflectance. The choice out of the two latter
products will depend on the type and cause of
change. For a simplified hypothetical example the
difference will be explained (table 2). Assume the
reflectance of surface 1 to be 0 % and the
reflectacne of two surfaces with a different
mineralogical composition respectively 20 % and 40
%. If due to a special event, surface 2 and 3
changes in such a way that both surfaces are
covered for 50 % with surface cover type A, the
reflectance will change to respectively 10 % and 20
%. A ratio image will give in this case the same
value for this identical change. A comparable
example will be given for the difference image.
Again the reflectance of the three surfaces are
respectively 0 %, 20 % and 40 %. However the
reflectance of surface 2 is now made up for 50 % of
surface cover A and 50 % of surface B. If the
amount of cover with A increases for both surface 2
and 3 with 50 % the reflectance will change
respectively to 0 % and 20 %. A difference image
will give now the same value for this identical
change. The second hypothetical example is also