Geometric-optical bidirectional reflectance modeling of the discrete crown vegetation canopy: effect of crown shape and mutual shadowing

In the case where a vegetation cover can be regarded as a collection of individual, discrete plant crowns, 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. An asymmetric hotspot, in which the shape of the hotspot is related to the shape of the plant crowns in the scene, is created. At large zenith angles illumination shadows 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´ bidirectional reflectance distribution function (BRDF) in which the scene brightness increases at the function´s edges. Formulas describing the hotspot and mutual-shadowing effects are derived, and 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 are presented