105 
icifically 
provide 
rocedure 
rie code 
ance for 
ospheric 
outlines 
lospheric 
er codes 
Richter 
lands 1-5 
spherical 
th, view 
t in that 
mination 
'ithin the 
irameters 
lure for 
ric data: 
models, 
the two 
ithin the 
lectances 
lospheric 
criteria. 
: and the 
stored as ’look-up’ arrays. The user is therefore restricted to the selection of pre-defined 
atmospheric models, a characteristic aerosol type and, pre-defined spectral bandpass. The actual 
operational code computes the surface reflectance using the inversion coefficients /4 (A,), B(h,\ 
which are computed as functions of gaseous transmittance, the direct and diffuse scattering 
transmittance and atmospheric reflectance, and the spherical albedo S(A,). These are obtained 
for a specified illumination and viewing geometry, aerosol optical depth and spectral bandpass. 
The operational code for these tasks requires approximately 100 lines of program. 
At present five standard atmospheric models may be selected in the pseudo-code: Tropical, 
Mid-latitude Summer, Mid-latitude Winter, Sub-Arctic Summer and Sub-Arctic Winter, as 
included within the 5S code. Initially, only the 5S continental aerosol model has been selected 
for use in conjunction with the four spectral bands of the ATSR-2 sensor. 
To further reduce the computational load bandpass integrated Rayleigh and aerosol atmospheric 
parameters are used in the code to compute the scattering tranmittance, atmospheric reflectance 
and, the spherical albedo in a single iteration; 5S uses 5nm incremental computations across the 
spectral band. The bandpass integration procedure can be extended to include the gaseous 
absorption parameters if absorbing levels remain uniform across the bandpass. 
The 5S code is designed to derive the sensor apparent reflectance from the Lambertian surface 
reflectance, for a given atmospheric state; similarly, the pseudo-code can be used to compute 
the apparent reflectance from the Lambertian surface reflectance for comparison of the 
pseudo-code output with 5S. The inversion to retrieve the surface reflectance from the apparent 
reflectance (Telliet, 1992) is demonstrated in section (2). 
2 DESCRIPTION OF THE COMPUTER CODES 
2.1 Operational Procedure Utilised in 5S and the Pseudo-code 
s that by 
lospheric 
reference 
orrection 
The apparent reflectance relates the measured radiance in a sensor channel to the solar irradiance 
incident at the top of the atmosphere and can be expressed as: 
n.¿(A,) 
P (A,)“ — 
E s (\ ).d. cos(0 s ) 
the solar 
a satellite 
lospheric 
mbertian 
estimates 
lectance, 
flectance 
using an 
To compute the apparent reflectance from uniform Lambertian surface reflectance in either 
5S or the 5S pseudo-code, the procedure is to estimate: the gaseous transmission and the total 
scattering transmittance on the illumination and viewing atmospheric paths, the atmospheric 
reflectance and, the spherical albedo. The sensor signal is first estimated without gaseous 
absorption, then multiplied by the gaseous transmission factor to estimate the apparent 
reflectance: 
p , (A 1 )-r 9 (A l .e I .e > ). 
Pq O,.' 
40- 
pO,) 
1 -p(A,).S(A,) 
.T(A,. 0 s ).T(A,, 9„) 
the time 
dons are 
therefore 
del. 
run time. 
:al depth 
ted are, 
g albedo 
>sol type, 
eters are 
The inversion procedure to compute surface reflectance from the apparent reflectance can be 
derived from the above equation as: 
•40,) 
1 
r B (A,,e s .0„).T(A,,e s ).T(A,,ej 
^0,) = 4(A,).p’(A,) + SO,) 
po.) 
Y(K) 
[ 1 + SO,).I" (A,)] 
B 0 ,) = - 
P a(A,,0 f .0„.«t>) 
T( A,, 0 S )T( A,, 0„)