11 
NDVM3.0 
0 
VDV7 and dashed lines, 
NDVI and the NDVI* 
1.20. The abscissa is the 
Results are presented for 
atm. The two oval areas 
ices (high NDVI). (after 
EFFECT 
images are based on 
and correction of the 
wing we shall discuss 
rfects from the image 
g measurements with 
radiance (solar light 
e reaching the surface) 
n order to use it in 
ttering phase function 
re the following three 
rosolloading 
Bctance. Therefore, it is 
rosol loading and effect 
th radiance should be 
ection stem from the 
nosphere p* (given in 
(1) 
where 0 is the view direction, 0 O is the solar zenith angle and <)> is the azimuth of the 
scattered radiation from the solar beam. PaiQ^o.^) is the path radiance. Note that the path 
radiance is attenuated by atmospheric absorption. Fd(0 o ) is the normalized downward total 
flux for zero surface reflectance, equivalent to the total downward transmission. Its value is 
less than 1.0 due to aerosol and molecular absorption and due backscattering of sunlight to 
space. T(0) is the upward total transmission into the direction of the satellite field of view. 
For low values of the surface reflectance (e.g. p<0.05) the effect of the path radiance 
on p* is large mainly in the short wavelengths, but many surface covers (vegetation water 
and some soils) are also dark in the red (0.60-0.68 pm) and blue (0.4-0.48 pm) wavelengths. 
But in order to use eq. 1 to estimate accurately the path radiance p a and from it the optical 
thickness, the surface reflectance of these dark pixels have to be estimated within a small 
uncertainty of ±0.005 to ±0.01. 
Kaufman and Sendra (1988) showed that for images with known presence of green 
forests the dark pixels can be determined as pixels with the highest NDVI from which pixels 
with lowest reflectance in the near IR are chosen. For these pixels the reflectance in the red 
channel can be assumed as p=0.02±0.01 and used to derive the aerosol optical thickness. 
Comparison between a histogram of optical thicknesses derived using this method and 
independent measurements by a sunphotometer (see Fig. 3) show a very good agreement. 
Application of the optical thickness to corrections for remote sensing of the vegetation 
index, shows how the difference between the NDVI measured from the Landsat MSS in a 
hazy and a clear day (18 days apart) decreases to almost zero by the correction (see Fig. 4). 
Note that in order to derive the optical thickness from the path radiance, some assumption 
on the aerosol size distribution and refractive index have to be made. The aerosol particles 
have to be assumed spherical and homogeneous in order to use the Mie theory in the 
calculations. Since same assumptions are used in the correction process, large part of the 
errors in the aerosol model cancel out (Kaufman and Sendra, 1988). 
CLEAR 
HAZY 
CLEAR HAZY 
t I 
T 1 T 
0.0 0.5 1.0 1.5 
OPTICAL THICKNESS - BAND 1 
k 
-r~i—r~l—I—I—I—r~i—p-l 
0.0 0.5 1.0 
OPTICAL THICKNESS - BAND 2 
Fig. 3: Histograms of the aerosol optical thickness derived from Landsat MSS using the dark dense 
vegetation detection technique (a): band 1 (0.55 pm) and band 2 (0.65 pm for a clear day (20 August 
1982) and a hazy day (2 August 1982). The arrows show the corresponding measurements from 
ground-based sunphotometer. Note the excellent agreement between the satellite derived optical 
thickness and the ground truth for band 2 which is more appropriate for this application since the 
surface reflectance for vegetation is darker and more predictable (After Kaufman and Sendra, 1988).