The scattering of radiation from a surface comprised of randomly distributed plates of differing reflective properties

Using the equation of radiative transfer, we have studied the reflection and re-emergence of radiation from a statistically rough surface comprised of randomly distributed plates of differing reflectivities. The albedo and emergent angular distribution are obtained and compared with some approximate deterministic results; significant differences are noted. An estimate of the variance in the albedo is also given. The radiative transfer equation is solved using a two-dimensional stochastic ansatz of the same functional form as the random reflection coefficient. Applications to ice floes, tree canopies, the remote sensing of a forest of leaves and to the paint industry are noted.