The ATCOR 2 Method

Processing of bands in the solar region (400 - 2500 nm)

The total signal at the sensor consists of three components: path radiance, reflected radiation from the viewed pixel and radiation from the neighborhood (see Figure 1). The atmospheric conditions (water vapor content, aerosol type, visibility) for a scene can be estimated using the SPECTRA module. Then, the surface reflectance spectrum of a target in the scene can be viewed as a function of the selected atmospheric parameters. It can be compared to typical library spectra.


Figure 1 : Schematic sketch of radiation components for a flat terrain.

Component 1 : path radiance; radiation scattered by the atmosphere
Component 2 : reflected radiation from the viewed pixel
Component 3 : radiation reflected by the neighborhood and scattered into the view direction (adjacency effect)
Only component 2 contains information from the viewed pixel.

DN is the digital number recorded in a certain spectral channel, c0, c1 are the offset and gain of the radiometric calibration relating the DN to the at-sensor radiance L=c0 + c1*DN. The reflectance calculation is performed iteratively:

If the adjacency range R is selected as R=0 then steps 2 to 4 are omitted. This may sometimes be of interest when determining the influence of the adjacency effect.

Processing of bands in the thermal region (8 - 13 um)

This section applies to Landsat-4/5 Thematic Mapper band 6, Landsat-7 ETM+ band 6, ASTER, and possible future thermal band sensors.
Figure 2 shows the radiation components in the thermal region. These are: path radiance emitted by the atmosphere between ground and sensor, emitted ground radiance (surface with temperature T and emissivity e), and reflected downwelling thermal atmospheric flux. The influence of the adjacency effect, i.e. scattered radiation from the neighborhood, can usually be neglected in the thermal spectral region, since the scattering efficiency of the atmosphere decreases strongly with wavelength.


Figure 2 : Schematic sketch of thermal radiation components for a flat terrain.

Component 1 : path radiance: radiation emitted by the atmosphere.
Component 2 : emitted surface radiation from the viewed pixel (emissivity e, temperature T).
Component 3 : reflected downwelling thermal atmospheric flux F, the reflected component is L3=r*F/pi, where r=1-e is the reflectance of the (opaque) surface.
Component 2 contains the essential information from the viewed pixel.

For a sensor with n thermal channels there are n equations with n+1 unknowns, namely the n surface emissivities plus a surface temperature. So, the system of equations is always underdetermined. Several possibilities exist to address this problem. In the ATCOR model, the user can select a constant surface emissivity, e.g. 0.98 (TM band 6: 10.5-12.5 um, ASTER band 13: 10.3-11.0 um) for a scene or a surface cover dependent value.

After emissivity selection the surface radiance can be calculated for the chosen atmospheric conditions (water vapor, aerosol content) and is converted to a surface temperature using a 2nd order polynomial approximation of the radiance-temperature relationship. For multi-band thermal data the normalized emissivity method (NEM), adjusted NEM, and in-scene atmospheric correction (ISAC) can also be selected.

Accuracy of the Method

The accuracy of the method depends on several factors :

In the thermal region, the surface temperature retrieval additionally depends on the appropriate surface emissivity map. If the deviation of the true surface emissivity to the assumed emissivity is less than 0.02, then the temperatures will be accurate to about 1-1.5 K. Larger deviations occur if the emissivity estimate is not close to reality. As a rule of thumb, a surface temperature error of about 0.5-0.7 K per 0.01 emissivity error for surface temperatures much higher than the boundary layer air temperature.

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last modified: DS, 18.10.14