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.
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:
- Step 1: the influence of the neighborhood is neglected, i.e. the path radiance (component 1) is subtracted and the remaining signal (components 2 & 3) converted into an equivalent surface reflectance.
- Step 2: a low pass filtered reflectance image of step 1 is calculated to obtain the large-scale average neighborhood reflectance. The filter size can be specified by the user (typically 1-2 km, corresponding to a range of R=0.5 - 1 km for the adjacency effect).
- Step 3: Adjacency effect: the atmospheric scattering of radiation between adjacent fields of different reflectances is taken into account by adding the weighted difference of step 1 and step 2 reflectance to the step 1 reflectance. The weighting function (ratio of diffuse to direct transmittance) is a measure of the scattering efficiency of the atmosphere.
- Step 4: Spherical albedo effect: the global flux on the ground depends on the large-scale (1 km) average reflectance. The global flux in the atmospheric LUT's is calculated for a fixed reflectance=0.15 . This iteration performs the update for the spatially varying average reflectance map of the current scene, if the adjacency range R > 0 .
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.
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.
- In case of a cover-dependent emissivity value,
a surface (brightness) temperature image is calculated based on an
emissivity estimate for each pixel derived from the reflective bands
of the sensor. Three emissivity classes are currently being used:
- soil/asphalt/sand/mixed pixels (emissivity = 0.96)
- vegetation (emissivity = 0.97)
- water and unclassified pixels (emissivity = 0.98)
The criterion for vegetation is a ratio vegetation index NIR/RED > 2, the criterion for soil is a reflectance > 10% in the RED band.
- The emissivity classification is available as a separate file with the extension "*_emi3.bsq". The values are coded as byte data with a scale factor of 100, so the data value 97 corresponds to an emissivity value of 0.97 .
- The temperature channel is appended as the last band. Results are in degree Celsius multiplied by the user-defined scale factor (default=4). In case of possible negative Celsius temperatures the user can specify an offset to stay within the byte data range (0-255) or use a scale factor of 10, in which case the results (reflectance and temperature) will be stored as signed integer (16 bit data range).
Accuracy of the Method
The accuracy of the method depends on several factors :
- radiometric calibration accuracy of the sensor (typically 3-10%)
- radiative transfer code : accuracy of Modtran® 4 is better than 5 % in the atmospheric window regions
- correct choice of atmospheric input parameters: user responsibility
- For near nadir view angles (off-nadir angle < 10 degree), a flat terrain
and avoiding the specular
and backscattering regions an accuracy of the retrieval of surface reflectance
of +/-0.02 (reflectance < 0.10) and +/-0.04 (reflectance > 0.40) is possible
For larger off-nadir view angles bidirectional effects can play a strong role.
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.