These corrections would bring TM-3 data closer to AVHRR-1 and equally increase TM-4 and AVHRR-2. 
The University of Bristol (Harrison et al., 1993b) suggests that the LANDS AT TM image calibration 
relies on a statistically based approach using ground spectroradiometric measurements ("empirical line 
method"). Spectra were taken for selected bare soil fields sufficiently large to be located in the imagery. 
After modifying the spectra to account for the satellite sensor bandwidths, they were regressed with the 
satellite ones to get the factors to convert the entire scene to radiance and reflectance units. 
The resampling of field based spectral data into multispectral space is defined by the particular 
remotely sensed data set. Thus, as the bandwidth of the LANDSAT TM is relatively broad, filter functions 
mimicking the TM response have been convolved with the spectroradiometer data. As for the AVIRIS case 
and due to its small bandwidth, gaussian filters centered upon each AVIRIS band have to be applied to the 
spectroradiometer data. Application of these techniques allows the field spectroscopic data to be expressed 
in a multispectral space very similar to that defined by LANDSAT TM and AVIRIS. 
Regarding LANDSAT - AVHRR intercomparison, fortunately AVHRR ch. 1 and 2 correspond fairly 
well to LANDSAT TM ch. 3 and 4, respectively. Over bare light soil, however, AVHRR ch. 1, due to its 
larger halfwidth, may yield lower values than TM ch. 3 and over dense vegetation, the opposite may occur. 
In the near infrared AVHRR ch. 2, reflectance is understimated over vegetation as compared to TM ch. 4. 
3.1.2. Correction for atmospheric effects. Standard procedures based on LOWTRAN or 5S codes need as 
input the instantaneous aerosol model, and this is generally difficult to obtain. Aerosol models may be 
adjusted internally by the selection of the model type and visibility range, by analysis of the image contrast 
or by analysing the signal over water surfaces. An approximate way to solve this problem is by means of 
spectral solar transmittance measurements These in fact provide optical depth as function of wavelength, 
information which can also be extracted from the radiative transfer code. By adjusting the aerosol model 
with iterative choices of the external parameters (visibility, relative fraction of the aerosol components, etc) 
it is possible to tune the radiative transfer model to the optical depth measured values. Then the correction 
can be achieved by regressing planetary albedo vs surface albedo assuming Lambertian reflection functions. 
To determine the optical depth of the atmosphere, the Free University of Berlin used an actinometer 
which allows almost simultaneous measurements of direct solar radiation in eight specific spectral bands. 
For a single measurement, the corresponding value that would be measured at the TOA has to be known. 
This "extraterrestrial" value is determined by "Langley plots" (Fig. 2), for which a day with constant 
atmospheric conditions (constant turbidity, constant humidity, no clouds) is required (Billing et al., 1993b). 
Optical depths derived from actinometer measurements (Fig. 3) can then be used to correct satellite 
images. To derive quantitative properties such as surface albedo or surface temperature, the influence on the 
satellite signal of atmospheric absorption and scattering has to be considered. This can be done with 
radiative transfer codes such as LOWTRAN-7 or 5S. The aerosol input parameters of these codes have to be 
adjusted in a way that the radiative transfer in the atmosphere at the time of the satellite overpass can be 
simulated with reasonable accuracy. The adjustment is done by a comparison of spectral optical depths 
measured at the satellite overpassing time with those computed by the radiative transfer code. 
For a number of surface albedos, planetary albedo is computed and integrated over the filter range of 
each channel. The resultant relationship between surface and planetary albedo can be fitted by a quadratic 
regression. The second order term represents the radiation reflected from the surface and scattered back 
downward again. It amounts to a few percent only, so the linear regression can be used for most purposes to 
express surface albedo as function of the apparent albedo measured by the satellite. 
RELATIVE AIRMASS 
Fig. 2. Actinometer calibration by "Langley-plots" for two selected wavelengths. Values (in Volts) that 
would be measured at the TOA are determined by extrapolating straight lines to a relative airmass of M = 0.