An Analytic BRDF Model of Canopy Radiative Transfer and Its Inversion
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Radiative transfer modeling of the bidirectional reflectance distribution function (BRDF) of leaf canopies is a powerful tool to relate multiangle remotely sensed data to biophysical parameters of the leaf canopy and to retrieve such parameters from multiangle imagery. However, the approximate approaches for multiple scattering that are used in the inversion of existing models are quite limited, and the sky radiance frequently is simply treated as isotropic. This paper presents an analytical model based on a rigorous canopy radiative transfer equation in which the multiple-scattering component is approximated by asymptotic theory and the single-scattering calculation, which requires numerical integration to properly accommodate the hotspot effect, is also simplified. Because the model is sensitive to angular variation in sky radiance, we further provide an accompanying new formulation for directional radiance in which the unscattered solar radiance and single-scattering radiance are calculated exactly, and multiple-scattering is approximated by the well-known two-stream Dirac delta function approach. A series of validations against exact calculations indicates that both models are quite accurate, especially when the viewing angle is smaller than 55 degrees. The Powell algorithm is then used to retrieve biophysical parameters from multiangle observations based on both the canopy and the sky radiance distribution models. The results using the soybean data of Ranson et al. to recover four of nine soybean biophysical parameters indicate that inversion of the present canopy model retrieves leaf area index well. Leaf angle distribution was not retrieved as accurately for the same dataset, perhaps because these measurements do not describe the hotspot well. Further experiments are required to explore the applicability of this canopy model.