Dense canopy albedo as a function of illumination direction: Dependence on structure and leaf transmittance

SummaryThe 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.

[1]  D. Kimes Modeling the directional reflectance from complete homogeneous vegetation canopies with various leaf-orientation distributions , 1984 .

[2]  J. Otterman Plane with protrusions as an atmospheric boundary , 1981 .

[3]  D. Deering,et al.  A sphere-scanning radiometer for rapid directional measurements of sky and ground radiance: The PARABOLA field instrument , 1984 .

[4]  Daniel S. Kimes,et al.  Diurnal variations of vegetation canopy structure , 1983 .

[5]  Elizabeth M. Middleton,et al.  Surface anisotropy and hemispheric reflectance for a semiarid ecosystem , 1987 .

[6]  M. Verstraete Radiation transfer in plant canopies - Transmission of direct solar radiation and the role of leaf orientation , 1987 .

[7]  T. Eck,et al.  The albedo of a tropical evergreen forest , 1980 .

[8]  J. B. Stewart The albedo of a pine forest , 1971 .

[9]  F. E. Nicodemus,et al.  Geometrical considerations and nomenclature for reflectance , 1977 .

[10]  H. T. Breece Iii,et al.  Bidirectional scattering characteristics of healthy green soybean and corn leaves in vivo. , 1971, Applied optics.

[11]  J. Otterman,et al.  Albedo of a Forest Modeled as a Plane with Dense Protrusions , 1984 .

[12]  K. Ranson,et al.  Inferring spectral reflectances of plant elements by simple inversion of bidirectional reflectance measurements , 1987 .

[13]  T. F. Eck,et al.  Bidirectional reflectances of selected desert surfaces and their three-parameter soil characterization , 1990 .

[14]  G. Suits The calculation of the directional reflectance of a vegetative canopy , 1971 .

[15]  J. Otterman Reflection from soil with sparse vegetation , 1981 .

[16]  W. Verhoef Light scattering by leaf layers with application to canopy reflectance modelling: The SAIL model , 1984 .

[17]  Richard L. Thompson,et al.  Inversion of vegetation canopy reflectance models for estimating agronomic variables. V. Estimation of leaf area index and average leaf angle using measured canopy reflectances , 1984 .

[18]  G H Weiss,et al.  Reflection from a field of randomly located vertical protrusions: errata. , 1984, Applied optics.

[19]  J. Smith,et al.  Bidirectional scattering of light from tree leaves , 1989 .

[20]  T. Brakke,et al.  Penetration of sunlight into a canopy: Explicit models based on vertical and horizontal leaf projections , 1986 .

[21]  N. Goel,et al.  Simple Beta Distribution Representation of Leaf Orientation in Vegetation Canopies1 , 1984 .

[22]  J. Otterman Bidirectional and hemispheric reflectivities of a bright soil plane and a sparse dark canopy , 1985 .