A unified model of bidirectional reflectance distribution function for the vegetation canopy

An accurate and operational bidirectional reflectance distribution function (BDRF) canopy model is the basis of quantitative vegetation remote sensing. The canopy reflectance should be approximated as the sum of the single scattering reflectance arising from the sun, ρ1, and the multiple scattering reflectance arising from the canopy, ρm, as their directional characteristics are dramatically different. Based on the existing BRDF model, we obtain a new analytical expression of ρ1 and ρm in this paper, which is suitable for different illumination conditions and different vegetation canopies. According to the geometrical optic model at the leaf scale, the anisotropy of ρ1 can be ascribed to the geometry of the object, sun and the sensor, multiple scale clumping, and the fraction of direct solar radiation and diffuse sky radiation. Then, we parameterize the area ratios of four components: the sunlit foliage, sunlit ground, shadow foliage and shadow ground based on a Poisson distribution, and develop a new approximate analytical single scattering reflectance model. Assuming G=0.5, a recollision probability theory based scattering model is developed which considers the effects of diffuse sky radiation, scattering inside the canopy and rebounds between the canopy and soil. Validation using ground measurements of maize and black spruce forest proves the reliability of the model.