109 
amount 
profile, 
(Tanre et 
profile 
iteration 
to derive 
nittances 
bandpass 
sorption, 
a. 
produced 
eometries 
ntrations 
the four 
E )M P !MAX 
p‘ s (\,) = apparent reflectance predicted by 5S 
p‘= apparent reflectance predicted by 5S pseudo-code 
n = number of data points within data set. 
The highest £4 and values obtained in each of the ATSR-2 spectral bands are listed in 
table (1). The largest discrepancies between the pseudo-code and 5S predictions occur in the 
ATSR-2 lb sensor channel, with a greatest single difference of approximately 1.9%. The 
discrepancies increase with increasing x ^ (550 nm) in all channels, but are most noticeable in 
channels V2 and lb. These are the channels which demonstrate the most pronounced spectral 
variation in gaseous absorption across the bands. 
The time taken to produce the total number of data sets, using a 5S code which had been 
modified to iterate through the illumination and viewing geometries, atmospheric settings and, 
surface reflectances was 13hrs 40min, the 5S pseudo-code completed the task in under 4 minutes, 
a reduction by a factor in excess of 200; the processing was conducted on a PC 486DX 
microprocessor operating at 50MHz . 
ATSR-2 SENSOR CHANNEL 
VI 
V2 
V3 
lb 
(%) 
(%) 
(%) 
(%) 
Average Error 
0.161 
0.182 
0.112 
0.660 
Maximum Error 
0.756 
1.031 
0.587 
1.905 
Table 1 : Maximum % difference between the predictions of the 5S 
model and those of the 5S pseudo-code. Data selected from all data 
sets and bands. 
4 DISCUSSION 
:flectance 
the test. 
1 by the 
ercentage 
nt within 
The pre-computation used in the 5S pseudo-code has been restricted to key atmospheric 
parameters which are independent of atmospheric path length. The exception is the aerosol 
phase function P ( 0 ): for this the phase angle 0 is dependent on the illumination and viewing 
geometry. The value of £(0) for any phase angle in the range 0° to 145° is derived in the 
pseudo-code using a functional fit to the 5S bandpass interpolated values: 
£(©) = A + Be ( ~ C9) + Dexp l ' e( '" 6>> 
A to E are the least squares fitting coefficients and ip (radians) represents a maximum modelled 
phase angle equivalent to 145°. The alternative procedure would be to interpolate for a given 
phase angle from a look-up array. 
An additional functional relationship has also been obtained to relate x A (550 nm) to the horizontal 
visibility V (km) over the range of visibilities 5 to 200 (km)\ 
x' 1 (550 nm) = A+ B/ln(V) + C/\n(V) z + £>/ln(l/) 3 +£/ln(K ) 4 
where A to £ are the least squares fitting coefficients. In the pseudo-code the aerosol con 
centration can therefore be specified in terms of T'VSSOnm) or as a horizontal visibility range. 
Dis-engaging pre-computation of the atmospheric parameters allows the remaining operational 
code to be concise. The actual pseudo-code is generated from the appropriate sections of the 
5S subroutines which compute the Rayleigh and aerosol atmospheric reflectance (ATMREF), 
the total scattering transmission on the two atmospheric paths and the spherical albedo (SCATRA 
& function TRANS) and, the total gaseous transmittance on the two atmospheric paths (ABSTRA). 
The complete operating code is approximately 100 lines and reduces run time by a factor in