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Atmospheric Scatter Background

(See Landsat & Sentinel-2 Conversion to SR Tutorials drop-down menu for step-by-step conversion to surface reflectance based on image-based atmospheric correction)

The path of solar radiation to Earth's surface then to a satellite sensor involves many interactions. The first graphic below (Jenson, 2007) shows various paths of incoming solar radiation. Ls is the total radiance at the sensor, which is a function of erroneous additive path radiance of Path 2 and Path 4. Path 2, diffuse irradiance, includes Rayleigh scattering and Mie scattering. Path 4 is reflectance from neighboring areas.

Ultimately, the goal of satellite imagery atmospheric correction and conversion to surface reflectance is to retrieve surface reflectance values similar to values measured at the surface (where a device can accurately and more simply measure the ratio of incoming radiation to the amount reflected).

 

Overall, the result of the incoming solar radiation interactions is to erroneously add to Top of Atmosphere (TOA) satellite sensor reflectance (as is also shown in the simplified diagram below). (TOA reflectance is the ratio of the total radiance at the sensor [Ls above] to total incoming radiation at the top of the atmosphere [where satellites are located]). Image-based atmospheric correction removes/deducts Path 2 (above) scatter/path radiance. Path 2 radiance is the predominant additive scatter and erroneously increases visible and near infrared (NIR) reflectance (though it increases NIR much less than visible reflectance). Path 2 includes Rayleigh scatter which is the scattering of light by molecules (particles much smaller than wavelengths of light), where smaller wavelengths scatter much more than larger wavelengths and is the reason why the sky is blue on a clear day (blue light has smaller wavelengths than green or red). Path 2 also includes Mie scatter (includes haze) and is the scattering of light by particles with a similar size to the light wavelengths; Mie is more of a larger wavelength scatter than Rayleigh scatter. Clearer days have less overall scatter but a higher ratio of blue light to red light scatter (because clearer days have more Rayleigh scatter); while, conversely, hazier days have more overall scatter but a smaller ratio of blue light to red light scatter (because hazier days have more Mie scattter which results in more larger wavelengths being scattered). Atmospheric scatter reflectance is deducted from Top of Atmosphere (TOA) reflectance in order to calculate surface reflectance. Near infrared radiation (not shown below) scatters a very small amount, though is should still be deducted (it is the longest wavelengths that should be deducted; see Relative Scatter Calculator page for specific values).

Atmospheric scatter diagram for satellite imagery atmospheric correction and surface reflectance

 

An image-based method to convert to surface reflectance (to account for the erroneous increase in reflectance at the satellite sensor due to atmospheric scatter) is called dark object subtraction (DOS) and was developed by Chavez (1988). The theory behind DOS is that in a satellite image scene with tens of millions of pixel (which satellite imagery commonly has), there should be some pixels that have zero reflectance; the reason there is not (in visible and NIR bands) is due to atmospheric scattering erroneously increasing reflectance values. DOS does not consider secondary scattering into shadowed areas (Chavez, 1996). Chavez (1996) then deducted .01 from the established scatter reflectance value (so that the established dark object/value had a surface reflectance of .01) because of "the fact that very few targets on the Earth's surface are absolute black, so an assumed one-percent minimum reflectance is better than zero percent" (Chavez, 1996).

Blue scatters the most (includes Rayleigh scattering), followed by green, red, then NIR (scatter amounts for bandwidths larger than NIR are very negligible at best, and do not need to be deducted). A clearer atmosphere has less overall scatter and a higher ratio of scatter between smaller and longer wavelengths than a hazier atmosphere; conversely, a hazier atmosphere has more overall scatter and more equal scatter between bands (Chavez, 1988). There should be a power relationship between wavelength and scatter amount that changes for different atmospheric conditions, which is shown in the diagram below from Chavez (1988).

 

References

Chavez, P.S., Jr. 1996. Image-based atmospheric corrections–revisited and improved. Photogrammetric Engineering and Remote Sensing 62(9): pp.1025-1036.

Chavez, P.S., Jr. 1988. An improved dark-object subtraction technique for atmospheric scattering correction of multispectral data. Remote Sensing of Environment 24: pp.459-479.

Jensen, J. R. (2007). Remote sensing of the environment: An earth resource perspective (2nd ed.). Upper Saddle River, NJ: Pearson Education, Inc.