A scattering model for forested area

A forested area is modeled as a volume of randomly oriented and distributed disc-shaped, or needle-shaped leaves shading a distribution of branches modeled as randomly oriented finite-length, dielectric cylinders above an irregular soil surface. Since the radii of branches have a wide range of sizes, the model only requires the length of a branch to be large compared with its radius which may be any size relative to the incident wavelength. In addition, the model also assumes the thickness of a disc-shaped leaf or the radius of a needle-shaped leaf is much smaller than the electromagnetic wavelength. The scattering phase matrices for disc, needle, and cylinder are developed in terms of the scattering amplitudes of the corresponding fields which are computed by the forward scattering theorem. These quantities along with the Kirchoff scattering model for a randomly rough surface are used in the standard radiative transfer formulation to compute the backscattering coefficient. Numerical illustrations for the backscattering coefficient are given as a function of the shading factor, incidence angle, leaf orientation distribution, branch orientation distribution, and the number density of leaves. Also illustrated are the properties of the extinction coefficient as a function of leaf and branch orientation distributions. Comparisons are made with measured backscattering coefficients from forested areas reported in the literature.