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