The incoherent specific intensities for the waves scattered by a random distribution of particles with rough surfaces are derived. Since large roughness scales are considered, the diffuse scattering contributions to the like and cross polarized scattering cross sections are given by the full wave solutions. The scattering matrix in the expression for the equation of transfer is given by a weighted sum of the scattering matrix for the smooth particle and the diffuse contribution due to the rough surface of the particle. Illustrative examples are presented for the propagation of a circularly polarized wave normally incident upon a parallel layer of particles. Particles with different surface height spectral density functions, roughness scales, complex permittivities and sizes are considered. Both first order (single scatter) and multiple scatter solutions are provided and the results for particles with smooth and rough surfaces are compared.
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