Removing atmospheric effects from satellite images is tricky, since the theoretical foundations are not completed understood, it is difficult to model the physical conditions, and also because we generally lack many information regarding the atmospheric condition at the time and location of satellite image acquisition.
One procedure that attempts to partially remove atmospheric effects is implemented in the SNAP software application, that is released by ESA and mainly devoted to the processing of Sentinel data, both optical and radar.
This method is named "Rayleigh Correction" and attempts to mitigate gaseous and Rayleigh effects. It does however do not consider aerosol effects.
In the screenshot below you see how to open the method window.
The GUI allows to select the bands to be corrected (B2-4 in the example below), besides other parameters (e.g., sea-level pressure). For this example the output resolution was changed to 10 meters, to match that of input bands (B2-4). The other parameters were left unchanged.
The two windows below display a an example of Sentinel 2 data (S2A MSI, 2017-05-27) pre- and post- Rayleigh correction. The displayed zone is comprised between Chivasso to the West and Verolengo to the East, and the Po River to the South and the Canale Cavour to the North (Piedmont, Italy).
In the upper window the original image is displayed as a 4-3-2 composite. In the lower window the same zone is represented using a 4-3-2 composite of Rayleigh-corrected bands.
The original bands are darker and with a low contrast, while the corrected bands present a larger chromatic variance. Note that the lightest pixels in the original band tend to saturate to white, somewhat loosing information.
Water, vegetation and urban constructions are more vivid and looks like more "natural", with more chromatic variations than in the original bands.
