3.2.1 Atmospheric Correction & Reflectance
Normalisation
It would clearly be an advantage to model the atmospheric and BRDF effects
by physical models and estimate the corrected image in terms of a normalised
reflectance factor. The added value would be the link this gives to physical
models of the relationship between earth parameters of interest and the
measured reflectance. Obviously, a reflectance is closer to a material property
and therefore resolves the problem of monitoring.
If reference targets in the image have measured reflectances (ie the invariant
or pseudo-invariant targets) it is possible to get close to reflectances
from the empirical approach. However, it will never be clear how much residual
atmosphere and BDRF effect remains. Obviously, most natural targets chosen
as 'invariant' will have some BRDF which may not be known and that effect
will be folded into the final image data.
Assuming the data are accurately calibrated to radiances, there are different
ways to describe the process of correction. One is as follows:
An equation relating the recorded radiance sensed at altitude h above the
target to the target reflectance factor is:
where:
is the radiance observed by the instrument from altitude h, with look (or view) direction
and sun direction
at wavelength
;
is the effective irradiance at the target, or
where:
is the irradiance at the target for a 'black' earth;
s is the sky hemispherical albedo; and
* is the background earth albedo.
is the beam transmittance through the layer between the surface and altitude h in direction mv;
is the target directional reflectance factor;
is the environmental reflectance due to the background albedo or:
is the diffuse transmittance for a layer of thickness h and for initial beam direction mv.
is the path radiance of light which did not interact with the surface; and
is the glint term that is most significantly present over water covered targets and is sometimes present over land targets.
If the atmosphere is characterised then it is possible to retrieve the directional
reflectance factor () for each pixel. This term needs careful
definition as there are many different types of 'reflectance' used.
The directional reflectance factor () as used here is defined as:
in which the irradiance (
) is the sum of diffuse and direct
terms and the fraction of diffuse (fd) is included as a parameter. The assumption
that the irradiance can be characterised in this context by the sun position
and the fraction of diffuse radiation is one that needs evaluation. The
value of using this form of reflectance is that it corresponds to what is
measured in the field using an irradiance radiometer or a reference standard.
The physical approach depends on two steps. The first is to determine this
reflectance factor for a surface by atmospheric correction. In atmospheric
correction, the atmospheric terms are modelled and measured from image and
ancillary data. The reflectance factor in an image may be obtained iteratively
if the atmospheric turbidity makes the adjacency and other atmosphere/surface
interactions significant. The second step is to normalise the reflectance
factor in some way to account for its BRDF variation.
In order to go from the reflectance factor to such a corrected value, however,
we effectively need to assume that:
where 
is the angular variation function that is assumed
to characterise the land surface type and be normalised to 1.0 at a reference
pair of sun and view angles and standard atmosphere. Then 'corrected' data
are reachable as:
The value of getting to this point is that both 
and 
can be interfaced with radiative transfer models to obtain parameters
for the earth's surface by inversion. The inversion may be simple (such
as end member methods) or sophisticated (such as complete nonlinear modelling).
This physical approach is obviously highly sophisticated but demands a level
of data quality and time in value adding that sometimes cannot economically
be committed. However, if the end products are of high information value
and valued by the client it is clearly an approach that could be pursued.
