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 (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) =
(5)

where the values of (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