Conversion of Landsat ToA reflectance to BoA reflectance with an equation

Question

I am using temporal datasets from Landsat 5, 7 and 8. 
Since I have many datasets I would like to include the conversion from ToA(top of atmosphere) to BoA(bottom of atmosphere) reflectance into a script using Arcpy.

Is there an equation to convert the ToA  reflectance to BoA  reflectance? 
I have checked the Landsat data users handbook but I could not find any formula:

toferkey · Answer

As they mentioned, you will need some kind of atmospheric or radiative tranfer model to convert to surface reflectance. Try looking into py6s. Python libraries are available already such as this one: https://py6s.readthedocs.io/en/latest/installation.html

Answered by toferkey on December 12, 2020

Mike Liu · Answer

The relationship between TOA reflectance to BoA reflectance is not linear but can be well approximated by second-order polynomials. You can check py6s, try some cases, and fit the second order polynomials then it is possible to find the simplified equation to fit into into Arcpy.

Answered by Mike Liu on December 12, 2020

Conversion of Landsat ToA reflectance to BoA reflectance with an equation

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