790
, , ozone.
(X,y) = exp (-T )
„ozone,,. . , ozone, „ ,
T (A,y 0 ) = exp (-T /cos0o)
(see equation 9).
5 COMPUTER IMPLEMENTATION NOTE
The values for the radiance received by TM have to be
calculated from the digital number (DN) retrieved from
CCT's. The absolute radiances can be calculated from
equation (23) and tables 3 and 4.
(RMAX -RMIN )
b b
255
= DN. + RMIN,
b b
(23)
where is the radiance received by TM in band b,
RMAXft the minimum radiance required to saturate
detector response (i.e, for DN = 255), RMIN^ the
spectral radiance corresponding to a DN^ = 0 and DN^
the digital number in TM spectral band b as obtained
from CCT.
Table 3. Dynamic ranges of Landsat TM data processed
prior to August 1983 (Scrounge System) (Barker,1984).
spectral bands
TM1
TM2
TM3
TM4
RMIN
(mW.cm 2
sr
-1 -1,
.ym )
-0.15
-0.28
-0.12
-0.15
RMAX
(mW.cm 2
sr
-1 -Is
• ym )
15.84
30.82
23.46
22.43
Table
after
4. Dynamic
January 15
ranges of Landsat TM
1984 (Tips) (Barker,
data processed
1984)
spectral bands
TM1
TM2
TM3
TM4
RMIN
(mW.cm 2
sr
1 .ym X )
-0.15
-0.28
-0.12
-0.15
RMAX
(mW.cm 2
sr
" 1 .ym~ 1 )
15.21
29.68
20.43
20.62
The computer implementation of the atmospheric cor
rection algorithm is fast, since after calculation
of the atmospheric variables, the correction consists
of solving only equations (3) and (4) which have to
be calculated pixel-per-pixel.
The atmospheric correction algorithm was implemented
on the IBM 3081 computer of the Ministry of National
Education of the French Community (Brussels) at the
cluster of the Royal Museum of Central Africa
(Tervuren, Belgium) in Fortran IV. The operating
system is OS/VS. On a 512*512 image, less than 25
seconds CPU time was used.
6 SENSITIVITY ANALYSIS
6.1 Description of the variable ranges selected
The influence of changes in the following variables
was examined :
1 visibility range;
2 solar zenith angle;
3 ozone optical thickness;
4 solar extraterrestrial irradiance.
While the influence of one variable was studied, the
values of the other variables wad kept constant at a
certain 'mean value'.
6.2 Analysis of the behaviour of the algorithm in
relation to variable changes
Using equations (3) and (4) one obtains equation (24)
, „2
-Ç— (L^ + L^ -
tot PR HG
A
X
\ 0 \ 0
a (A,A 0 ) (L - (Lp R + l^ g ))}
(24)
where C = n^ (1—p) = 1.7658.
Consider now Fig. 2. Equation (25) is a linear
function.
y = ax + b
(25)
Coefficient a gives the slope of the line, b is the
intersection with the y-axis, c is the intersection
with the x-axis. Comparison of equation (24) with
equation (25) gives
y = L
x = L
1.7658
tot
tot
(28)
b = -
tot
{L
PR
+ L
HG
Cx(A,A 0 )(L - (LpJ +
l a ))}
HG
(29)
Coefficient a will only change if the total trans
missivity T(A) changes, this means when the visibi
lity range (V), ozone optical thickness (T oz °ne (X)
or wavelength (A) change. In other words, if the
total transmissivity does not change, one will obtain
parallel lines if the results for different sets of
input values are plotted on one graph, since the
slope b doesn't change.
6.3 Results of the sensitivity analysis
The results of the sensitivity analysis are represen
ted in table 5. Table 6 gives the digital numbers and
their corresponding radiances for each spectral
band, which were used to obtain table 5.
The digital number DN=11 for band 4 corresponds to
the 'darkest pixel' or 'clear water' reflectance on
the Landsal
From table
the ozone c
results toe
logical vif
solar extre
carefully.
easily and
and meteorc
Table 5. Re
Variable
or
parameter
V
at 485 nm
at 560 nm
at 660 nm
at 485 nm
at 560 nm
at 660 nm
ozone
485
ozone
r 560
ozone
r 660
830
at 485 nm
at 560 nm
at 660 nm
E 0 (90,485)
Eo(90,560)
Eq(90,660)
E 0 (90,830)
at 485 nm
at 560 nm
at 660 nm
Table 6. Di
radiances t
spectral
band