SCATTERING BY LAMBERTIAN-LEAVES CANOPY - DEPENDENCE ON LEAF-AREA PROJECTIONS

A single-scattering model is constructed for a canopy with Lambertian leaves. The azimuthal distribution of the leaves is represented by fra ctional abundances of the leaf-area in the cardinal directions with re spect to the Sun. The canopy bi-directional reflectances are found to be controlled by the projections of the leaf-areas onto horizontal and vertical planes. The sum of the leaf-area projections onto the horizo ntal plane determines the reflectance to the zenith when the Sun is at the zenith. For a complete canopy this reflectance is [GRAPHICS] wher e w(xh) is the fractional projection onto the horizontal plane of leaf -area of leaf-category x, g(x) is the leaf reflectance (assumed equal to the leaf transmittance), and Psi(x) is the zenith angle of the leaf normal for this category. As the view and solar zenith angles deviate from the nadir, the change in the reflectance in the principal plane of the Sun is controlled by the difference in the leaf-area projection s onto the vertical plane of the leaves with leaf-normals in opposite quadrants in the principal plane. When these two leaf-categories are i dentical (other than in their azimuths), a large region around the zen ith exhibits the Lambertian viewing property, that is, the reflectance does not change with the view or illumination directions. Forward sca ttering and backscattering, which become intense when both the illumin ation zenith angle theta 0, and the view zenith angle theta v, are lar ge (approach 90 degrees) while Psi is not small (or when Psi is large while theta 0, and theta v, are not small), are controlled by the slim of these two leaf-area projections. The reflectance has then the limi ting value g sin Psi'(cot theta 0 + cot theta v), where g and Psi char acterize the two leaf categories with normals in the principal plane. This expression represents a generalization of a result obtained for a field of thin vertical cylinders,