The problem of the probability density function (PDF) of the irradiance fluctuations of an electromagnetic wave propagating through a turbulent atmosphere is being investigated for several decades. Tatarskii and deWolf succesfully investigated the cases of weak and very strong turbulence. The intermediate regime still imposes a number of physical questions in spite of considerable progress in the last few years. Many models have been proposed and studied [1-7], none is complete and some of them impose difficulties in understanding the physics of the process.
"A "Splitting Source" Model For The Statistics Of Irradiance Scintillations", Proc. SPIE 0813, Optics and the Information Age, (1 January 1987); doi: 10.1117/12.967190; https://doi.org/10.1117/12.967190