2 - METHOD 
The top-of-atmosphere directional randiances measured by the ATSR-2 instrument are a complex function of 
incoming solar irradiance, surface bi-directional reflectance and scattering and absorption by atmospheric 
aerosols and permanent gases. Scattering by fixed gases, or Rayleigh scattering, decreases with wavelength X 
approximately as X -4 . Although significantly influencing radiance measurements at shorter wavelengths the 
predictable atmospheric composition allows simple correction of radiances for Rayleigh scattering. A much 
greater cause of uncertainty is scattering and absorption by tropospheric aerosols. The aerosol optical thickness 
is less dependent on wavelength, varying roughly with X -1 . The high spatial and temporal variability of both 
aerosol composition and concentration makes it difficult to decouple aerosol scattering from the similarly 
variable surface reflectance. Furthermore, although the ATSR-2 bands have been positioned to avoid known 
molecular absorptions, some aerosols cause significant absorption across the solar reflected spectrum. 
The bi-directional reflectance distribution function (BRDF) is the function of a reflecting surface which defines 
how the outgoing radiant flux from a surface relates to the incoming radiant flux. Nicodemus (1977) defines this 
as 
where 6 and <f) are solid angles in spherical co-ordinates, subscripts i and r refer to incoming and outgoing 
radiation and L and E are radiance and irradiance respectively. Retrieval of the full surface BRDF from ATSR-2 
channels is limited since measurement is made at only two view angles. 
Considering the case of atmospheric correction from two measurements at a given wavelength, we can 
realistically retrieve only two parameters to describe the surface BRDF and atmospheric profile. Here we 
present a method to retrieve the surface hemispherical albedo, approximating the surface BRDF as Lambertian, 
and the atmospheric aerosol loading, assuming known aerosol composition. Aerosol loading is described in 
terms of the equivalent meteorological range, or visibility. Specifying aerosol loading in terms of visibility 
offers a physically based parameterisation independent of wavelength or aerosol type. Accuracy of retrieval of 
ground visibility using ATSR-2 is also of interest. The visibility V is related to the total extinction coefficient T 
by the relation 
where T is defined as the sum of molecular and aerosol extinctions along a horizontal path evaluated at 550nm. 
Using an atmospheric model, a two dimensional array of top-of-atmosphere radiances is pre-computed for all 
continuous surface. Figure 1 shows an example of such a surface radiances measured at nadir integrated over 
the bandwidth of the ATSR channel 1 using the LOWTRAN-7 model. Now, a new radiance value measured by 
the channel corresponds to a contour on this surface. This contour represents the locus of all possible pairs of 
similarly to a contour of possible (albedo,visibility) pairs which could have produced the radiance. Now, if the 
vertical projection of the contours on the two surfaces intersect, then the intersection point will correspond to a 
value of (albedo,visibility) consistent with both nadir and along-track radiance measurements. Examples of the 
contour intersection are shown in figures 2 and 3. 
The method of contour intersection is exploited to give a fast and simple implementation of atmospheric 
correction from two views. First tables R N (i,j) and Rat 0 ' ,j) are pre-computed of expected satellite measured 
radiances at nadir and the along-track direction respectively for values of albedo i and visibility j. In operation, 
given new sensor measurements R N and R AT of nadir and along-track radiances respectively, a third array is 
computed to give values of the error metric 
[ 1 ] 
V = 
3.912 
[ 2 ] 
T 
values of surface albedo and aerosol loading within the expected range. By interpolation, this array defines a 
(albedo,visibility) which could have given rise to the measured value of radiance. Several such contours for 
different top-of-atmosphere radiance values are drawn in figure 1. An array of radiance values is also pre 
computed for the along-track scan of the same surface. A new measured radiance in this channel corresponds