In the case where a vegetation cover can be regarded as a collection of individual, discrete plant crowns (such as forest, woodland, savanna, or shrubland), the geometric-optical effects of the shadows that the crowns cast on the background and on one another strongly condition the brightness of the vegetation cover as seen from a given viewpoint in the hemisphere. At the "hotspot," when illumination and viewing positions coincide, shadows are hidden behind plant crowns and the scene appears bright. As the viewing position diverges from that of illumination, the shadows behind the crowns are progressively revealed and the scene darkens. Because, in general, the shadows will not be circular, the amount of shadow revealed will be a function of both the zenith and azimuth angles by which the viewing and illumination positions diverge, rather than a simple phase angle between them. This effect creates an assymetric hotspot, in which the shape of the hotspot is related to the shape of the plant crowns in the scene. At large zenith angles, mutual shadowing of crowns becomes an important factor. Illumination shadows will tend to fall on other crowns, rather than the background, and will preferentially shadow the lower portions of adjacent crowns. Further, these shadows will be preferentially obscured since adjacent crowns will also tend to obscure the lower portions of other crowns. This effect produces a "bowl-shaped" BRDF in which the scene brightness increases at the function's edges. Our paper derives formulas describing the hotspot and mutual-shadowing effects and presents examples that show how the shape of the BRDF is dependent on the shape of the crowns, their density, their brightness relative to the background, and the thickness of the layer throughout which the crown centers are distributed.
