Abstract

The radiation from different directions can be specified by upward and downward radiation vectors, and the interactions of the radiation with a leaf or with a vegetative canopy can be specified by matrices. The Kubelka-Munk equations, which are applicable only to a canopy with horizontal and Lambertian leaves, can then be extended to describe the directional transfer of radiation in a canopy with nonhorizontal, non-Lam-bertian leaves. In the extended Kubelka-Munk equations, variables are upward and downward radiation vectors, and the coefficients are matrices. The solutions are found from which the bidirectional vegetative canopy reflectance, including azimuthal variations, can be obtained. Simplified and approximate methods are presented for a canopy with leaves without azimuthal preference in order to reduce the execution time.

© 1985 Optical Society of America

Simple equation to approximate the bidirectional reflectance from vegetative canopies and bare soil surfaces

C. L. Walthall, J. M. Norman, J. M. Welles, G. Campbell, and B. L. Blad
Appl. Opt. 24(3) 383-387 (1985)

Coupled atmosphere/canopy model for remote sensing of plant reflectance features

Siegfried A. W. Gerstl and Andrew Zardecki
Appl. Opt. 24(1) 94-103 (1985)

Modeling the directional reflectance from complete homogeneous vegetation canopies with various leaf-orientation distributions

D. S. Kimes
J. Opt. Soc. Am. A 1(7) 725-737 (1984)

Reflectance of a vegetation canopy using the Adding method

K. Cooper, J. A. Smith, and D. Pitts
Appl. Opt. 21(22) 4112-4118 (1982)

Specular, diffuse, and polarized light scattered by two wheat canopies

V. C. Vanderbilt, L. Grant, L. L. Biehl, and B. F. Robinson
Appl. Opt. 24(15) 2408-2418 (1985)