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