Reflection from a field of randomly located vertical protrusions: errata

Abstract

Reflection from a field of randomly located, thin vertical cylinders is analyzed. The bidirectional reflectivity Rdf for the direct solar beam (first reflection) is Rdf(s,z,θ0,θ)=rc(-z cosz+sinz)1-exp[-s(tanθ0+tanθ)]4(cotθ0+cotθ),where z is the azimuth (in radians) measured in a horizontal plane from the antisolar direction, θ0 is the zenith angle of the solar beam, θ is the viewing zenith angle, s is the projection on a vertical plane of cylindrical sections over a unit area, and rc is the Lambert law spectral reflectivity of the cylinders. The bidirectional reflectivity thus tends to rcπ tanθ0/4 at the azimuth π and at very large viewing zenith angles, such that tanθ ≫ tanθ0 and tanθ0 ⩾ 1. A comparison with the bidirectional reflectivities measured over dense vegetation of a Florida swamp indicates that this model describes a highly significant component of this canopy reflection. The possibility of extracting information about the reflectivity of the plants material (rc) and about the canopy structure (s) from the reflectivities measured at various solar elevations is discussed and an approach for such extraction is formulated. The extraction of rc appears practical; that of s, difficult.