Li Xiaowen_1995


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466 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 33, NO. 2, MARCH 1995 A Hybrid Geometric Optical-Radiative Transfer Approach for Modeling Albedo and Directional Reflectance of Discontinuous Canopies Xiaowen Li, Alan H. Strahler, Member, ZEEE, and Curtis E. Woodcock Abstruct- A new model for the bidirectional reflectance of a vegetation cover combines principles of geometric optics and radiative transfer. It relies on gap probabilities and path length distributions to model the penetration of irradiance from a parallel source and the single and multiple scattering of that irradiance in the direction of an observer. The model applies to vegetation covers of discrete plant crowns that are randomly centered both on the plane and within a layer of variable thickness above it. Crowns assume a spheroidal shape with arbitrary height to width ratio. Geometric optics easily mod- els the irradiance that penetrates the vegetation cover directly, is scattered by the soil, and exits without further scattering by the vegetation. Within a plant crown, the probability of scattering is a negative exponential function of path length. Within-crown scattering provides the source for singly-scattered radiation, which exits with probabilities proportional to further path-length distributions in the direction of exitance (including the hotspot effect). Single scattering provides the source for double scattering, and then higher order pairs of scattering are solved successively by a convolution function. Early validations using data from a conifer stand near Howland, Maine, show reasonable agreement between modeled and observed reflectance. I. INTRODUCTION HE purpose of this paper is to present a new model T for the directional reflectance of vegetation canopies and to show some initial results from attempts to validate the model using data currently available. The new model draws heavily from past work in geometric optics, and also includes multiple scattering effects in a manner similar to radiative transfer models-hence the new model’s description as a hy- brid geometric-optical radiative-transfer model. Additionally, the model is formulated explicitly to deal with discontinuous canopies, where the presence of gaps in the canopy has significant effects on both the amount of irradiance passing directly through the canopy and the directional reflectance of the canopy-and in particular, the hotspot. Thus, gap probabilities play a major role in this new model by influencing the calculation of the distribution of pathlengths through the canopy, the distribution of single-scattering source radiation, and the calculation of an openness factor which is used to Manuscript received September 14, 1993; revised September 6, 1994.
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