p ' ( X., ) = apparent reflectance 
Z.(X,) = measured spectral radiance (l/m' 2 sr~V m ') 
E s (X,) = extraterrestrial solar irradiance 
X, = sensor spectral bandpass 
d = multiplicative factor to account for the variation in the ’solar constant’ with julian 
day 
0 s = solar zenith angle 
0 „ — view zenith angle 
cf> = relative azimuth angle 
p ( X, ) = surface reflectance 
P a ( X j. 0 s , 0 „, 4> ) = atmospheric reflectance 
S ( X, ) = atmospheric spherical albedo 
T ( X,, 0 ) = total along path atmospheric transmittance at zenith angle 9 
7(x,,e) = e' t<M/C0S(8, + f d (x,.e) 
e t( X )/C0S(9) = atmospheric transmittance for direct solar radiation 
f d (X,, 9) = atmospheric transmittance factor for diffuse solar radiation 
x ( X, ) = atmospheric optical thickness 
7 , ( X,, 0 s , 0 1 , ) = total gaseous transmittance 
The gaseous transmittance is dependent on the atmospheric components (O 3 , H 2 O, O 2 and CO 2 ) 
and on the illumination and viewing geometry and is computed as: 
e s ■ 6 J = n, 4 ,, 7 ? 1 o,. e s • e„, f/ ?1 ) 
U gi = gaseous content 
2.2 The Computational Procedure 
2.2.1 The 5S Procedure . The aerosol optical parameters (phase function P(0. X), single scattering 
albedo uo 0 ( X, ), asymmetry factor g(X,), and extinction coefficient), and the Rayleigh optical 
depth are required in the calculation of the atmospheric functions. These are obtained for 10 
discrete wavelengths ranging from 0.25\un to 4.00\im. 
The aerosol optical parameters are obtained for a specific aerosol model which is defined by 
the volume fraction of the four basic aerosol components specified in the World Meteorological 
Organization report (WMO 1986), these are: dust-like, oceanic, water-soluble and soot com 
ponents. The volume fraction of each aerosol component in the selected aerosol model is used 
as the weighting factor in determining the aerosol optical parameters for the specified aerosol 
model. The extinction coefficient is normalised at a reference wavelength of X = 550 nm. The 
aerosol content is fixed in the computation by entering either the aerosol optical depth x * (550 nm) 
at the reference wavelength or the horizontal visibility V (in km). In this case, the aerosol 
optical depth is derived by assuming the aerosol vertical profile described by McClatchey et 
al. (1971). The aerosol optical depth at each of the 10 discrete wavelengths is obtained by 
multiplying (550nm) by the appropriate extinction coefficient. 
The Rayleigh optical depth is obtained for any atmosphere which is defined by the pressure 
and temperature atmospheric profiles. 
The atmospheri 
mittances (dirt 
atmospheric s 
atmospheric p 
The remaining 
the discrete w 
of the sensor, 
approximate l 
includes an ite 
an increment 
detector specti 
bandpass: 
p‘(A,) = 
In the above 
bandpass, wh< 
<KX) = 
7 S (X) = 
AX = in 
2.2.2 The Ps 
pre-computatio: 
aerosol model: 
a separate set 
and gaseous 
bandpass. T1 
pre-computed 
atmospheric 
2.2.2.1 Pre-C 
depth have t 
interpolation 
across the sp 
response func 
bandpass deft 
of the detecto: 
as: 
t*(X,) 
t*(X,) 
A similar prc 
across a detf 
obtained froi 
106