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Multiple-scattering scheme useful for geometric optical modeling

Geometrical optical (GO) models have been widely used in remote sensing applications because of their simplicity and ability to simulate angular variation of remote sensing signals from the Earth's surface. GO models are generally accurate in the visible part of the solar spectrum, but less accurate in near-infrared (NIR) part in which multiple scattering in plant canopies is the strongest. Although turbid-media radiative transfer (RT) methods have been introduced to GO models to cope with the second-order and higher order scattering, the problem of canopy geometrical effects on multiple scattering still remains and becomes the main obstacle in GO model applications. In this paper, we propose and test a multiple scattering scheme to simulate angular variation in multiply scattered radiation in plant canopies. This scheme is based on various view factors between sunlit and shaded components (both foliage and background) in the canopy and allows the geometrical effects to propagate to the second-order and higher order scattering simulations. As the view factors depend on the canopy geometry, the scheme is particularly useful in GO models. This new scheme is implemented in the 4-Scale Model, which previously used band-specific multiple scattering factors. After the use of the scheme, these factors are removed and the multiple scattering at a given wavelength and angle of observation can be automatically computed. Improvements made with this scheme are shown in comparison with the top-of-canopy (i.e., PARABOLA) and airborne (i.e., POLDER) measurements with modeled results with and without the scheme. Examples of canopy-level hyperspectral signatures simulated using the scheme are also shown.