i Detection of Smoke and Dust Aerosols Using Multi-sensor Satellite ...

with Eq. (7.4) in which the symbol SZA ’assumes to be the correct SZA,
R R / cos( SZA)
(7.4)
Therefore, the relative error between two responses R’and R ’could be calculated with
Eq. (7.5).
R R R cos( SZA) cos( SZA)
1 1 1
R R cos( SZA) cos( SZA SZA)
where ΔSZA is the difference between two solar zenith angles SZA ’and SZA’.
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(7.5)
The theoretical impact of mis-registration on L1B measurement for both directions is
plotted in Fig. 7.6, with one, two, or three -pixel BBR shift. In scan direction, the impact
changes rapidly at both ends but slowly in the middle. Since the change of SZA is
quasi-linear in track direction, the impact of BBR shift along-track on L1B measurement
has almost the same quasi-linear trend.
The SZA in one granule is different with geo-location and seasons, the largest relative
error could be estimated with the curves in Fig. 7.7 by defining the largest SZA of one
granule and corresponding BBR shift. The curves computed with Eq. (7.5) by setting
ΔSZA as 0.01 o , 0.03 o , 0.05 o , or 0.1 o show that the relative error increases with the positive
ΔSZA and decreases with negative ΔSZA. The curve changes slowly at the small SZA
range while rapidly at the large SZA range. The relative error could reach to 0.5%, if
there is 0.1 o ΔSZA, when SZA is about 65 o .