153
be explained by the variability of the stratospheric aerosol thickness during the period of one month or some
unfiltered tropospheric events or in homogeneity in the longitudinal distribution of the stratospheric aerosol.
Figure 5, shows the comparison between the wavelength exponent of the aerosol deduced from the two channels
of AVHRR (0.63(xm and 0.87(im) and from the three wavelengths of the Mauna Loa data set (0.38|im,0.50(J.m
and 0.78|J,m). Both data sets shows a change in the wavelength exponent suggesting an evolution of the size
distibution of the stratospheric aerosol to bigger particles. The King's model gives an exponent of -0.75 that can
be observed in July and August 1991.
The data of Mauna Loa are very useful for comparison purposes but cannot give the spatial distribution of the
stratospheric aerosol. As shown by figure 6 , the largest concentration were located in the 10° South to 10° North
zone and the maximum value is double of the largest value observed at Mauna Loa.
NDYI = -
( 1 )
3. CORRECTION EQUATION FOR NDVI 30 DAY COMPOSITE
The AVHRR data used in this study was Global Area Coverage (GAC) data from the NOAA-11 satellite. The
NDVI is computed from AVHRR visible (0.63|im) and near infrared (0.87|im) preflight calibrated digital
counts, DCj and DC 2 according to Equation 1.
DC 2 -DC 1
DC 2 +DC 1
If we want to correct only for the perturbation caused by the stratospheric aerosol, in order to be able to
compare these data with historical data sets that had no atmospheric correction, we can approximate the
stratospheric aerosol effect on each channel, by:
DC perturbed _ ^Stratosphere ^ + T( ^ s ) T((Iv ) D ccorrected (2)
Where p s , |i v and $ are the cosine of the solar zenith angle, the cosine of the view angle and the
azimuthal difference between the Sun and the sensor respectively
^^stratosphere j s stratospheric aerosol path radiance.
T(p.) is the transmission (upward for |i v , downward for |i s ) of the aerosol layer.
The stratospheric path radiance is computed using King stratospheric aerosol model (King et al,1984).
For 17 view angles, 22 sun zenith angles, 81 relative azimuth angles and 10 optical depths (ranging from 0.05
to 0.5) a table that gives the path radiance in both channels was computed a computer code using the successive
order of scattering method (Deuze et al, 1989).
The transmission has been fitted in both channels using the following approximate formula:
T(P)
= e-O^h)
(3)
The accuracy of the approximation is sufficient for the NDVI correction scheme as shown by figure 7a-b. For
angles ranging from nadir to 70° and optical depth ranging from 0.05 to 0.5 the approximation was compared to
the "exact" computation performed using the successive order of scattering code (Deuzd et al,1989).
4. ERROR BUDGET
The error in the NDVI correction is different for different cover type. We selected bare soil and deciduous forest
as the two extreme cases. The solar zenith angle is fixed to 45° as an average of the variation between summer
and winter and the viewing angle to nadir because the composite process trends to reject off nadir pixels. The
approximation of equation ( 2 ) to correct the stratospheric effect is unavoidable, to properly correct the data one
will have to take into account the non-lambertianity of both atmosphere and surface. For the surface, the
directional properties are not available so far. The error made on NDVI can be approximated by the study of Lee
and Kaufman (1986), from their paper they pointed out error up to 0.04 for turbid atmosphere, this refer to the
net error on NDVI due to non-lambertianity. In our case, the error to be considered should be lower, we estimate
this error as 0.02 NDVI unit in case of high optical depth (0.6) and to 0.01 for lower optical depth (0.3).
Two other sources have to be considered, the error due to incorrect optical depth and the error done by using an
improper aerosol model. Table 1 gives for the two surfaces considered, the NDVI at the top of the atmosphere
for a 0.05 tropospheric aerosol optical depth and a tropical atmospheric profile, it gives also the effect on NDVI
of a high and average (0.6, 0.3) stratospheric aerosol optical depth, as well as the error associated with an
uncertainty of ±0.05 optical depth. The error due to change in size distribution is also reported for an optical
depth of 0.3, by varying the wavelength exponent from the King et al model values to 0. From this table, the
rms error of the correction scheme can be computed, it is of the order of 0.01 for optical depth of 0.3 and double
for optical depth of 0.6. The overall accuracy of the correction is then to correct 80% of the effect.
