Bidirectional transmittance and reflectance models for soil signature analysis.

The propagation of radiation in an absorbing-scattering soil with constant or spatial variation of the refractive index is investigated. The soil consists of a plane parallel with Fresnel reflection at the boundaries and is exposed at one boundary to a diffuse or collimated incident radiation. The discrete spherical harmonics method using Marshak boundary conditions is introduced to approximate the directional hemispherical reflectance and transmittance as well as the bidirectional reflectance. The effect in spatial variation of the refractive index on the reflectance and transmittance predictions is examined. A comparison of the directional transmittance and reflectance with the literature results demonstrates that the present method gives accurate results for optically thin and thick soil with a maximum relative error in all cases less than 1%. The bidirectional radiance for variable refractive index soils also shows excellent agreement as compared to the literature results. The results demonstrated that the anisotropic soil interfaces cause a significant decrease of energy reflected and transmitted as well as the bidirectional reflectance.

Discrete spherical harmonics method for radiative transfer in scalar planar inhomogeneous atmosphere.

The radiative transfer problems in a participating inhomogeneous scalar planar atmosphere, subjected to diffuse or collimated incidence, are investigated using the discrete spherical harmonics method. In developing the method, the radiative intensity is expanded in a finite series of Legendre polynomials and the resulting first-order coupled differential equations of radiance moments are expressed in a set of discrete polar directions. The method is applied to homogeneous/inhomogeneous atmospheres of various anisotropic scattering degrees and thicknesses, and reflective boundary conditions. The discrete spherical harmonics method albedo, transmittance, and radiative intensity predictions agree well with benchmark literature results. Additionally, numerical predictions show that the discrete spherical harmonics method using Mark boundary conditions are more efficient than using Marshak boundary conditions.