129 
unction of 
50 - 
nospheric 
relength X 
ingths the 
+0 - 
| 
A much 
thickness 
l 30 ': 
ty of both 
¿0 
similarly 
^ 20 
hd known 
V 
ch defines 
1,0- 
efines this 
[ 1 ] 
I outgoing 
n ATSR-2 
Figure 1. Table of expected radiances measured by ATSR-2 channel 1 (555 nm) for a range of values of 
surface albedo and boundary layer visibility. 
b, we can 
. Here we 
ambertian, 
scribed in 
f visibility 
etrieval of 
efficient T 
[ 2 ] 
R E (U) — + ^/tr| [3] 
The array element R E {i,j) is equal to zero if and only if the contours defined by R N on the nadir surface and 
R at on the along-track surface intersect at albedo i and visibility j. In fact the value of R E (i,j ) gives the 
sensor error required to reconcile the expected nadir and along-track radiance values for albedo i and visibility j 
with the measured values. In general there will not be a zero element in the array due to the discreet sampling of 
the error surface, and so the minimum valued element is used, R E (i$ ,j 0 ). Estimates of albedo and visibility are 
improved by performing bi-parabolic interpolation on the error surface surrounding the located minimum - 
at 550nm. 
ited for all 
r defines a 
rated over 
iasured by 
le pairs of 
intours for 
s also pre- 
irresponds 
low, if the 
spond to a 
pies of the 
mospheric 
measured 
operation, 
rd array is 
j — 0.5 (/? £ (/q + l,y 0 ) R E (ip Wo)) 
■ 2* £ (wo)-* e ( i . + U)-'M i i -M,)’ 
and 
_ 0 -fo*(w<, l) ~ R B (hJo ~ Q) 
y “ " 2* r (wo)- A(Wo+1) - - 1) 
The method has the advantage of being operationally fast, due to pre-computation. Computationally expensive 
forward modelling code may be used to generate accurate radiance tables. In addition further information 
available such as atmospheric pressure, ground altitude and aerosol type may be used without cost. A 
disadvantage is storage of the large number of radiance tables needed for different solar/view geometries. 
However the radiance surface may be accurately approximated using a small number of values, as the radiance 
varies almost linearly with reflectance and smoothly with visibility. 
3 - RESULTS 
This section presents results and sensitivity analysis of the algorithm using simulated data. The simulation uses 
the LOWTRAN-7 atmospheric model coupled with models of surface bi-directional reflectance. The band-pass 
function and geometric and quantisation characteristics of the ATSR-2 sensor are modelled to give expected 
sensor output Since the same atmospheric modelling code is used in generation of both radiance tables and