107 
julian 
The atmospheric reflectance (for the Rayleigh and aerosol atmospheres), the scattering trans 
mittances (direct and diffuse) on the Sun-target (0 s ) and target-satellite (0„ ) paths and the 
atmospheric spherical albedo are then computed for the 10 discrete wavelengths using the 
atmospheric parameters. 
The remaining computations estimate intermediate values of the atmospheric functions from 
the discrete wavelength values to interpolate over discrete increments in the spectral bandpass 
of the sensor, compute the gaseous absorption in each increment of the spectral bandpass, and 
approximate the interaction between these two effects by multiplication. The computation 
includes an iteration loop from the lower limit to the upper limit of the spectral bandpass, with 
an increment of 5nm. The values for each increment are then convolved with the relative 
detector spectral response and the solar spectral irradiance in the summation across the spectral 
bandpass: 
^ : 4>(\).£ s (\).p , (\).A\ 
P’(M= ' ,, 
AX 
In the above equation subscripts 1 and 2 denote the lower and upper limits of the spectral 
bandpass, where, 
<i>(A) = detector spectral response 
E S (X) = solar spectral irradiance 
AX. = incremental step. 
[ C0 2 ) 
2.2.2 The Pseudo-Code Procedure : The modified procedure of the pseudo-code involves 
pre-computation of aerosol, Rayleigh, and gaseous absorption optical parameters; for particular 
aerosol models and atmospheric temperature and pressure profiles. Each aerosol model requires 
a separate set of aerosol parameters, each atmospheric profile requires a separate set of Rayleigh 
and gaseous absorbing parameters. Separate parameter sets are required for each spectral 
bandpass. This constraint limits the selection of the aerosol model and atmospheric profile to 
pre-computed parameter sets; but sets can be derived for any required aerosol model and 
atmospheric profile. 
tiering 
optical 
for 10 
2.2.2.1 Pre-Computed Parameters : The aerosol optical parameters and the Rayleigh optical 
depth have been computed using the 5S procedure for the 10 discrete wavelengths. The 5S 
interpolation procedure is used to estimate the parameter values at 5nm increments of wavelength 
across the spectral bandpass of the sensor. The parameters are convolved using the detector 
response function and the solar spectral irradiance; the summation across the sensor spectral 
bandpass defines a bandpass integrated parameter which accounts for the wavelength dependence 
ted by 
ogical 
t com- 
is used 
aerosol 
tl The 
i50 nm) 
aerosol 
hey et 
ted by 
of the detector response and solar irradiance. The Rayleigh optical depth in a band i is computed 
as: 
Xj>(\)E s (X)T*(A)A\ 
}_ K y(\)E s (T) AX 
t*(X.,) = Rayleigh optical depth in sensor channel i. 
A similar procedure can be used for gaseous absorption parameters where they remain constant 
across a detector band. Alternatively, for non-uniform absorption, the parameters can be 
obtained from 5S at 5nm intervals across the band. 
iressure