AN ANALYTIC BRDF MODEL OF CANOPY RADIATIVE-TRANSFER AND ITS INVERSION

Radiative transfer modeling of the bidirectional reflectance distribut ion function (BRDF) of leaf canopies is a powerful tool to relate mult iangle remotely sensed data to biophysical parameters of the leaf cano py and to retrieve such parameters from multiangle imagery. However, t he 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 anal ytical 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 numerica l integration to properly accommodate the hotspot effect, is also simp lified. Because the model is sensitive to angular variation in sky rad iance, we further provide an accompanying new formulation for directio nal radiance in which the unscattered solar radiance and single-scatte ring radiance are calculated exactly, and multiple-scattering is appro ximated by the well-known a two-stream approach. A series of validatio ns against exact calculations indicates that both models are quite acc urate, especially when the viewing angle is smaller than 55 degrees. T he Powell algorithm is then used to retrieve biophysical parameters fr om multiangle observations based on both the canopy and the sky radian ce distribution models. The results using the soybean data of Ranson c t al. to recover four of nine soybean biophysical parameters indicate that inversion of the present canopy model retrieves leaf area index w ell. Leaf angle distribution was not retrieved as accurately for the s ame dataset, perhaps because these measurements do not describe the ho tspot well. Further experiments are required to explore the applicabil ity of this canopy model.