Polarized-radiation transfer in stochastic finite planar atmospheric media

Abstract

In this work, we investigate the polarized-radiation transfer problem in a planar stochastic atmospheric medium. A solution is presented for an arbitrary extinction function, which was assumed to be continuous in position and to exhibit fluctuations about the Gaussian distributed mean. The joint probability distribution function of the integral transform of these Gaussian random functions was used to calculate the ensemble-averaged quantities, such as the reflectivity and transmissivity, for an arbitrary correlation function. A modified Gaussian probability distribution function was used to average the solution to exclude probable negative values of the optical space variable. The deterministic solutions for the total intensity and the difference function, which were used to describe the polarized radiation, were obtained using the Pomraning–Eddington technique. The numerical results were presented for the Gaussian and modified Gaussian probability density functions for different degrees of polarization.