Summary
The dependence of the albedo on illumination direction is analyzed by constructing a canopy model in which the individual leaves are planar, Lambertian reflectors. Leaf transmission is treated separately, and is assumed to be proportional to the cosine of the zenith angle of the leaf normal. Effects of shading and obscuration are formulated assuming random distribution of the leaves with respect to the viewing and illumination directions. Variants of the model with different azimuthal leaf distributions are created and discussed as explicit expressions of the viewing/illumination geometry and the canopy characteristics.
The canopy spectral single-scattering albedo factors, which are the conditional probabilities of a photon escaping from the canopy after a first reflection or a first transmission, are obtained by numerical integration over a hemisphere of the bidirectional reflectance and transmittance factors. Our analysis identifies the ratio of the projection of leaf area on the vertical plane perpendicular to the principal plane to that on a horizontal plane as the parameter that controls the dependence of the albedo on the solar zenith angle. The albedo factor due to the leaf transmittance generally increases with the zenith angle of illuminating beam more sharply than that due to the leaf reflectance.
Model variants with various azimuthal distributions are compared with measured albedo of soybeans. Second and higher order scatterings are accounted for in a simplified way. The degree to which a model variant fits the measured albedo and its change with the solar zenith angle depends both on the leaf inclination angleand the azimuthal distribution of the leaf area.
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Otterman, J., Brakke, T.W. Dense canopy albedo as a function of illumination direction: Dependence on structure and leaf transmittance. Theor Appl Climatol 43, 3–16 (1991). https://doi.org/10.1007/BF00865038
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DOI: https://doi.org/10.1007/BF00865038