I am working on aerosol retrieval using a radiative transfer equation with Landsat 8 OLI, and I am having difficulty determining the raster-based path radiance. I am using the formula by Felix C. Seidel (2011); Hadjimitsis (2009); Themistocleous (2016). see attached file. Whenever I try to compute the AOD after inverting the equation, there is always a negative value under the square root. from the image attached file "the last two equations'.
When inverting the radiative transfer equation (Chandrasekhar radiative transfer equation, eq.(2.3) from Seidel(2011)) you do not need to perform the expansion of an exponent because you can obtain the analytical solution of the equation
(1-N)=exp(-\tau \eta)
Even in this case you will still need to satisfy the condition N
When inverting the radiative transfer equation (Chandrasekhar radiative transfer equation, eq.(2.3) from Seidel(2011)) you do not need to perform the expansion of an exponent because you can obtain the analytical solution of the equation
(1-N)=exp(-\tau \eta)
Even in this case you will still need to satisfy the condition N
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