Theoretical and numerical studies of electromagnetic wave scattering from random media with random rough surfaces and discrete particles

The multiple scattering effect of electromagnetic waves scattered from random media such as rain, atmospheric clouds, ocean surfaces, deserts and terrain is important in radar communications and remote sensing. These random media, in general, consist of randomly distributed particles and random rough surfaces. Three different models for random media with a slab geometry containing randomly distributed particles and planar or random rough surfaces are formulated and studied: (i) A slab of random medium with planar boundaries and randomly distributed spherical particles; (ii) A slab of random medium with Gaussian statistical type random rough surface boundaries (small surface roughness) and randomly distributed spherical particles; (iii) A slab of random medium with Gaussian statistical type random rough surface boundaries (moderate surface roughness) and randomly distributed spherical particles. Numerical illustrations are given for random media with optical thicknesses from 0.1 to 5, mean size parameters of the particles from 0.3 to 3.5, and various surface root-mean-square heights and correlation lengths.; For a random medium with rough surface boundaries, the Kirchhoff rough surface scattering theory is used to determine the transmittivity and reflectivity matrices which relate the scattered waves to the incident waves. These matrices are employed to set up a pair of boundary conditions for the vector radiative transfer equation. By solving the vector radiative transfer equation with such boundary conditions, we obtain the volume scattering solution which includes the rough surface boundary effect. The volume scattering solution and the rough surface scattering solution combine to give the complete solution for the scattered waves. The scattered waves are calculated for arbitrarily polarized incident waves and expressed in terms of the modified Stokes vectors. The modified Stokes vectors are then used to construct the Mueller matrices. Polarization signatures are obtained from the Mueller matrices at the backscattering direction. The Mueller matrices are found to have some symmetrical properties and there are eight nonvanishing elements.