Stochastic transfer of polarized radiation in finite cluttered atmospheric media with dual statistical analysis

The stochastic transfer of polarized radiation in a finite cluttered atmospheric medium (e.g. clouds) is investigated, the solution being presented for arbitrary absorption and scattering cross sections. The extinction function of the medium is assumed to be a continuous random function of position, with fluctuations about the mean taken as Gaussian distributed. The deterministic analytical solution is obtained by using Pomraning–Eddington technique with weight function method. Two correlated random variables appear in the solution, namely the optical space variable and the medium optical thickness. The dual Gaussian probability density function of these two random variables is derived, from which the ensemble-averaged solution is calculated for an arbitrary correlation function. The first and the second statistical moments of some quantities of interest, such as radiant energy, net flux, reflectivity and transmissivity, are obtained. Numerical calculations are performed for specular-reflecting boundaries and an incident flux of radiation upon the medium from one side (x=0)(x=0) and with no flux from other side (x=L)(x=L).