A hemispherical–directional reflectance model as a tool for understanding image distinctions between cultivated and uncultivated bare surfaces

This paper discusses a model to predict the normalized hemispherical–directional reflectance function for soil or rocky surfaces of a given roughness under conditions of outdoor illumination. These surfaces are simulated by geometrical shapes similar to beads merging into each other, characterized by three parameters. In addition, the shape of the surface is characterized by the directivity factor DR, expressing the differences between the maximum and the minimum deviations of its height, calculated along all possible directions. The surface is illuminated by a hemispherical light source created by a number of point sources of given light intensities. The light energy is scattered from the surface, in accordance the quasi-Lambertian function. The distribution of the surface reflectance, as viewed from all the possible directions, can be described for all the possible illumination conditions expressed by the solar zenith and the horizontal angles for a given hemisphere light distribution of a definite optical thickness. This represents the hemispherical–directional reflectance distribution function, HDRDF, of the surface. The HDRDF function is normalized to the nadir viewpoint and visualized for a given illumination condition. The model assumes that the HDRDF of a surface contains information about the directivity of the surface shape, as described by the directivity factor of the surface hemispherical–directional reflectance function DHDRDF. This factor, expressing the asymmetry of the HDRDF with respect to the solar principal plane (SPP), is strongly correlated with the DR. The use of both factors, the DR and DHDRDF, enables us to understand the distinctions between soil surface images with height irregularities of directional character that create a furrow microrelief, and irregularities spread non-directly, randomly, depending on whether the soil has been cultivated or not. The model was tested on directional reflectance data measured in the visible, the near and the middle infrared spectra for cultivated surface with furrows, as well as for three uncultivated desert loess and rocky surfaces situated in Israel.