Multiple-scattering scheme useful for geometric optical modeling

Abstract—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 vis-ible 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 ef-fects on multiple scattering still remains and becomes the main ob-stacle in GO model applications. In this paper, we propose and test a multiple scattering scheme to simulate angular variation in mul-tiply 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 geo-metrical 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 [4], which previ-ously used band-specific multiple scattering factors. After the use of the scheme, these factors are removed and the multiple scatt-tering at a given wavelength and angle of observation can be au-tomatically 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 hyperspec-tral signatures simulated using the scheme are also shown. Index Terms—Directional remote sensing, geometrical optics (GOs), hyperspectral, multiple scattering, view factors. I