2 ATMOSPHERIC CORRECTION SCHEME 
The satellite-sensor recorded radiance, L(A) in 
mW/(cm 2 sr pm) is calculated from (Hughes and 
Henderson-Sellers, 1982) 
L(*) = 0.01 COS e g K e (A) [G DN + I]/ir (2) 
where 6 is the solar zenith angle, K is the 
correction factor for Sun-Earth distance variation, 
DN is the digital count, G is the percentage spectral 
albedo per count, I is the percentage intercept alb 
edo (Lauritson et al., 1979) and e(A) is given by 
e(A) = / E(X l ) cf>( A 1 )d A 1 (3) 
0 
where ^ is a dummy integration variable, E(A) is 
the solar irradiance on the top of atmosphere for 
mean Sun-Earth distance per unit projected area 
(Thekaekara et al., 1969) and <t>(A) is the sensor 
response function which is normalized to unity, i.e. 
/ $(A)dA = 1 (4) 
so that 
estimated using an expression given by Singh et al. 
(1985). To calculate surface reflectances from the 
AVHRR data an iterative method was adopted which is 
summarized below. 
To start with p was set equal to zero. An average 
continental type aerosol was assumed (Janza, 1975) 
and path radiances were estimated from equation (7). 
Clearly path radiances estimated in this manner would 
be underestimated, the diffuse surface radiance, 
L S (A), calculated from equations (2), (6) and (7) 
would be overestimated. When this value of L S (A) is 
substituted in equation (8) then the resulting 
diffuse reflectance would be larger than the actual 
value. In the next step of iteration this value of 
reflectance is used in equation (7) and the above 
procedure is repeated. Using reasoning parallel to 
the above it is apparent that the reflectivity 
obtained from the second iteration step would be 
smaller than the actual value. This procedure is 
continued until a desired convergence is reached, 
i.e. until the absolute ’difference in reflectivities 
from nth and (n+l)th iteration steps is found to be 
smaller or equal to a prefixed threshold value. The 
threshold is determined from equation (8) with radi 
ance which is equivalent to half a digital number. 
This iterative procedure has been tested using ten 
AVHRR scenes and for most cases only three or four 
iterations were required and there was only one case 
for which about seven iterations were required for 
the desired convergence. The atmospherically 
corrected NDVI was then evaluated from 
Î (A) = <KA)/ / ^(A 1 )dA 1 
(5) 
where the values of <f>(A) can be estimated from 
Lauritson et al. (1979). On the other hand the 
satellite-sensor recorded radiance may be expressed 
as 
L(A) = L pR (A) + L pa (A) + L g (A)t(A,0) (6) 
where L r (A) is the Rayleigh path radiance, L & (A) is 
the aerosol path radiance, L (A) is the diffuse 
surface radiance, t(A,0) is the diffuse transmittance 
from surface being viewed to the sensor and 0 is the 
zenith angle of a ray from surface being viewed to 
the sensor. In writing equation (6), separability 
of the Rayleigh and aerosol atmospheres has been 
assumed (Gordon, 1978). Within the single scattering 
approximation an expression for path radiance may be 
written as 
L (A) = E(A)KT (A,0,0 ) t (A) x 
px v ' oz v s' x v 
[P x ( ¥-) + P(M S )P X ( *+)] (7) 
where T is the two way transmittance through the 
ozone layer, t is the optical thickness, P is the 
phase function, is the scattering angle, p is 
the surface reflectivity and x = R for Rayleigh 
scattering processes and x = a for aerosol scattering 
processes. Further details can be found in Singh 
and Cracknell (1986). For a Lambertian surface the 
diffuse reflectance is defined by 
P (A) = ttL (A)/E (A) (8) 
s 8 
where E (A) is the global solar irradiance on the 
surface? Note that the global solar irradiance is 
not known without experimentation and it changes 
with solar elevation, wavelength and optical 
thickness. In this work global solar irradiance was 
NDVI , PQ2) - cOi) 
p(A2) + p ( A ]_ ) 
(9) 
If the atmospheric correction algorithm were perfect 
then it would suffice to define vegetation index (VI) 
as VI = p(A2)/ p(A^). The reason for retaining the 
form of equation (9) similar to the form of 
equation (1) is to further compensate for residual 
atmospheric contributions and to compensate 
(partially) for changing solar zenith angle, varying 
global irradiance and topographic effects. 
Topographic effects on remotely sensed data are 
difficult to correct for. From the work of Duggin 
et al. (1982) and Singh and Cracknell (1985, 1986) 
it seems that there are at least three factors which 
contribute to the satellite data as view angle 
changes: (a) the larger the view angle the larger 
is the atmospheric path length and hence the larger 
will be atmospheric contribution; (b) natural sur 
faces are non-Lambertian whereas remotely sensed 
radiances are assumed to be from Lambertian surfaces 
and (c) solar irradiation on the surface as seen by 
a remote sensor along a scan line is not necessarily 
uniform and this is because of shadows cast by 
vertical relief (natural as well as man made). An 
approximate atmospheric correction scheme which has 
been outlined above and which has been applied to a 
number of images by Singh and Cracknell (1985, 1986) 
indicates that a significant amount of view angle 
dependence of atmospheric effects caused by (a) above 
can be removed. However, it is not yet possible to 
correct remotely sensed data due to causes (b) and 
(c) above. 
3 DATA USED 
The AVHRR/2 data from N0AA-7 satellite which have 
been used in this preliminary investigation were 
collected at 14:37 GMT on 20 August, 1984 at the 
Dundee University satellite-data receiving station. 
The selected area is the United Kingdom from about 
50 to 55 degrees latitude. The western part 
including Ireland were cloudy. Only those pixels 
were selected for which raw NDVI values were positive. 
This constraint eliminates water pixels, and to some