789 
elected, where 
reference band. 
orse than for 
86) advises to 
able or even 
resolution 
dvantage over the 
CZCS and TM is 
his possibility 
he first sensor 
ions. With the 
ded. Care should 
on a TM image, 
dir-looking, 
n account oblique 
eric correction 
DIANCE AND SKY- 
eigh path 
ximation as 
ed by air 
sunlight, 
the satellite's 
uation (5) 
(5) 
olar spectral 
tance, T air the 
on 3.3) and p^ 
quation (6) 
(6) 
nd T the total 
irradiance, 
and the wave- 
(7) 
ar extraterres- 
he earth's orbit 
n day. The 
errestrial 
bs (1981:246-247) 
e TM sensor 
gaussian curve : 
elength A can be 
1956) 
(8) 
from their 
T X = exp ( -T X /cos 0 O ) (9) 
where T X is the transmittance, T X the optical 
thickness, 0o the solar zenith angle and x = air, aero 
ozone or total. 
For the ozaone optical thickness (and hence for the 
ozone transmittance) a fixed value may be choosen for 
each wavelength. For TM in Belgian applications 
following values were choosen : 
ozone 
T 
'4 8 5 
0.015 
ozone 
T 
56 0 
0.025 
To obtain K^ er °, one takes in account the ratios of 
the effective cross sections of Mie particles 
(a^er°) ag g-[ ven e q ua tion (16), and the particle 
density at height z (N aero (z)). 
550 ~(550) 
aero X 
3-a 
(16) 
One obtains now equation (17) 
3.912 
K^ er ° (z) - 
(- 
N 
'(0) 
V 
0.0116)(”) 
A 
a-3 
(17) 
ozone 
T 
6 6 0 
0.014 
The particle density N aer ° (z) can be approximated by 
the set of equations (18) 
x OZOne =0.001 
8 3 0 
The Rayleigh phase functions can be calculated for 
nadir-looking satellite from 
p M (^±)= (l+cos 2 0 o ) 
in which 0 O is the solar zenith angle. 
(10) 
3.2 Skyglitter 
The skyglitter is for a nadir-looking satellite given 
by equation (11) 
l hg = P E oT tot T air P M (40 (ID 
The three equations (5), (6) and (11) are now com 
bined in equation (12) 
t . t T. „ozone 2 air r M, . . 
l pr l hg = E ° T T {p ({,j) + 
+ p (ip) (T (yo ) + T )} (12) 
where the total transmittance is written as 
T tot = T ozone 
55 exp(-(z-5.5) /H^) z < 5.5 km 
5.5 <z< 18 km (18) 
55 exp(-(z-18 ) /H^) 
z > 18 km 
where H x = 0.886 + 0.0222 V and H 2 = 3.77 km. 
The set of equation (18) is developed by Me Clatchey 
et al. (1972) which is based on 79 series of measure 
ments by Elterman (1968, 1970). 
The Mie optical thickness (by scattering of aerosol 
particles) is defined as 
aero 
K A 
(z)dz 
(19) 
With equations (17), (18) and (19) equation (20) to 
calculate the aerosol optical thickness at a height 
(z >18 km) can be set up by integration 
H 2 exp (-5.5/H^ 
The ozone transmittance is squared since the light 
has to pass the ozone layer twice. 
3.3 Mie optical thickness 
The visibility range or meteorological range V was 
introduced by Koschmieder (1938) and is related to 
the scattering or attenuation coefficient K (0), 
defined by Middleton (1957). This relationship is 
given in equation (13) 
V 
_ 3.912 
(13) 
in which K^(0) is the total scattering coefficient at 
height 0 m, and wavelength X. 
Since 
K (0) = K air (0) + K aer0 (0) (14) 
550 550 550 
where K550 (0) is the air molecule scattering 
coefficient, at height Om and wavelength 550 nm and 
K||ro (0) the 
aerosol scattering coefficient, at 
height 0 m and wavelength 550 nm. 
One obtains equation (15) 
Kffo° (0) = ~~ ~ K550 (0) (15) 
For satellite observations, z is equal to °°, and 
one obtains 
T»"°a) - <i|U - o.omx^r 
V À 
{H(l-exp(-5.5/H)) + 12.5 exp (-5.5/H) + 
3.77 exp(-5.5/H)} (21) 
where V is the visibility range or meteorological 
range, X the wavelength and H = 0.886 + 0.0222iV 
a is normally equal to 4. 
Data on the meteorological range can be obtained in 
Belgium from the Royal Meteorological Institute 
(KMI/IRM) for 20 stations (measured every three hours) 
in the monthly synoptical observations. 
4 CALCULATION OF THE AEROSOL PATH RADIANCE RATIO 
The aerosol path radiance ratio a (A,Ao) is first used 
in equation (2). It is possible to set up an equation 
for aerosol path radiance analogous to equation (5). 
The aerosol path radiance ratio is then expressed by 
equation (22), assuming that the phase function is 
independent of the wavelenght 
ot(X, X 0 ) 
3.QYO / *\ \ n /_ ■* \ _OZOn6 / \ 
t (X) E 0 (D,X) T (A,y,Uo) 
T (X 0) Eo(DjÀo)T (X 0 > y>yo) 
Equation (15) is valid for standard conditions 
(temperature 15°C, atmospheric pressure 1013 mb), 
were Kfir ( 0 ) = Q.0116 km“ 1 
where 
„ozone,. . „ozone ,, . „ozone ,, . 
T (X,y,y 0 ) = T (A,y).T (A,y 0 )