doubt about diffuse transmittance equation-reg

[ivgbhavani]

Greetings to all,
I want to understand the diffuse transmittance equation properly mentioned in most of ocean color literature, attached screenshot. why we are dividing rayleigh optical thickness with 2 but not aerosol optical thickness and Ozone optical thickness.
I am not sure , i can ask these kind of questions or not in  this platform.
I will be happy if some one have explanation or any literature.

Thanks in advance

[amiribr]

The diffused transmittance equation is an approximation and slightly empirical. The diffused transmittance should be calculated using a fully coupled radiative transfer simulations. However, for operational retrieval purposes, approximations are made for example (https://doi.org/10.1364/AO.18.003587 and https://doi.org/10.1364/AO.20.004175). The 0.5 in Rayleigh is associated with the fact that the scattering function is symmetric, thus half of the energy could scatter forward and half backward. I would refer you to this excellent document for a detailed explanation:
http://www.oceanopticsbook.info/view/atmospheric_correction/atmospheric_transmittances#Eq:difftrans
and our Atmospheric Correction TM document: https://oceancolor.gsfc.nasa.gov/docs/technical/NASA-TM-2016-217551.pdf