are not overlapped, hence they can be considered as the
elements of a linear space. The TC transformation is an
orthonormal rotation in this space. The choice of the axes was
based on the analysis of several images (a posteriori or real
image based choice of axes). The Greenness (GN) is proved to
be a good indicator of the vegetation in land applications, but
it is sensitive to the soil moisture and also to the atmospheric
conditions. Our goal was to find another TC-like
transformation, that keeps the advantages of original GN, but
is free of its non-vegetation dependence. That is the new GN
should be sensitive for vegetation conditions and insensitive for
soil and atmospheric conditions. Keeping in mind this threefold
goal, let us take the axes of a new frame of reference in the
apparent reflectance space of TM bands as:
1. reflectance of a bright, dry soil,
2. reflectance of a vivid green vegetation,
3. apparent reflectance of the full haze
atmosphere.
From the six TM bands, only the first four proved to be useful
in the transformation. Thus, the ATC transformation is the
following:
ATC, = YO, P.., @)
ja
where
Pay = mL, | Ey cos, (3)
is the apparent reflectance in the j-th TM band, and
0.24113 . 0.36693 0.53991 — 0.71813
0; =| -0.25258 -0.24235 -0.63656 0.68722
0.86327 0.19657 -0.46296 -0.04223
In eq. (2.1) L,; = DC; + B; is the measured radiance in the
j-th band (o; and 6, are calibration constants and DC, is the
digital count number), Ey; is the global incident radiation in the
j-th band at the top of the atmosphere, 0, is the Sun zenith
angle.
The first two indices obtained from ATC show similar
behaviour as the Brightness (BR) and Greenness (GN) indices
of the original TC, thus we keep the original names. The third
index exhibits a strong correlation with the normal optical
depth, ó, so we call it Haziness (HN).
This new GN is still affected by the soil and the atmosphere,
yet they can be manipulated using the other two quantities BR
and HN in order to reduce the non-vegetation effects.
We performed detailed model calculations to analyze the ATC
transformation using five values of the soil moisture content,
several values of the percent vegetation cover between 0 and
100% and ten values of the horizontal visibility (5-50 km). In
Figs. 1. and 2 it can be seen that GN is not independent of BR
and HN, as we expected. Similarly, there is a good linear
dependence between HN and the aerosol optical depth at
550 nm (0,,,,), but there is a BR dependence too (Fig. 3.).
These nonlinear dependencies can be eliminated or at least
significantly reduced by applying another, nonlinear
transformations in the GN-HN and BR-GN planes. The
resulting BR, GN and HN indices are almost free from
interdependencies. In Figures 4-5 it can be seen that the
interdependence of the indices and their dependence on ó and
soil parameters are minimal. With additional investigations
based on more accurate soil and vegetation reflectance
measurements, further improvements can be achieved.
Now we can approximate the connection between HN and 6,5;
with a single line (Figure 6).
Up to this point we have two parameters obtained by using the
full ATC transformation:
1. the BR, GN vegetation index pair for every pixel,
and
a) this pair is independent from the
atmospheric conditions
b) GN is independent of the soil conditions;
2. d,..ss for every pixel, representing the atmospheric
conditions.
In Figure 7-8 the original GN and the ATC GN can be seen as
a function of horizontal visibility (that is of 5) and of soil
parameters. It is clearly seen that while GN depends strongly on
atmospheric and soil conditions, this dependence for ATC GN
is actually very weak.
Let us summarize the main advantages of the above described
procedure (which we call — together with the procedure
described later — Atmospheric Correction Algorithm Based on
ATC, ACABA):
1. The HN is proportional to 6 => the real
reflectances are retrievable from measured
radiances.
2. The GN is free from atmospheric and soil
moisture effects = >
a) unnecessity of solving RTE for
surface canopy investigation
(vegetation monitoring, yield
forecasting/estimation).
b) an opportunity of onboard
calculation of a green vegetation
sensitive quantity free from
atmospheric and soil moisture
effects is given.
3. The computation of ATC indices is simple
and very fast, thus it can be done even for
every pixel of a full TM image.
In multitemporal/sensor applications a vegetation index specific
of the given satellite sensor/date is not a suitable quantity; we
have to obtain a real physical parameter, usually the surface
reflectance factor (p). To do this, we completed the ACABA
with the solution of RTE by using an RTC. In the full ACABA,
we can retrieve p using ô,.,ss (for every pixel) from ATC and
the 5S and 6S code (Tanré et al. 1985) as RTC. This approach
represents a major difference between the "traditional" methods,
where the ó is characteristic either of an average atmosphere or
only of a part of the image (but is extrapolated over a large
area), and ACABA.
THE FULL ACABA
Let the RTE given in the following from:
LS -
mj
6.
p; E(5,8) e ' * L, (4)
d
T
788 International Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998
pd: (9 ES ^ PP Uh. ^ uj f? P "4 X[phpi uud 79. (f 3A M ss UD s
-
Un
