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