Inferring parameters for canopies nonuniform in azimuth by model inversion

Abstract Limitations on inferring canopy parameters through model inversion are assessed. By analyzing a simple model of bidirectional reflectances for a canopy with azimuthally nonuniform leaf distributions, we establish that for any leaf inclination a “Lambertian-viewing” cone exists around the nadir (for a range of solar zenith angles). In this region, leaf inclination and leaf azimuth do not materially affect the bidirectional reflectance (which is effectively constant) and therefore cannot be inferred from the measurements. Under this viewing / illumination geometry, only the product r cos Ψ can be inferred for a complete canopy and r cos 2 Ψ ΔL for a sparse canopy (or more complicated products that involve an additional term which is a function of the solar zenith angle, leaf azimuth, and leaf zenith angle), where r is leaf reflectance, Ψ is zenith angle of leaf normal and ΔL is leaf area per unit horizontal area. Thus, the leaf reflectance r itself cannot be inferred then. This suggests that r cos Ψ and ΔLcos Ψ are very basic canopy parameters, influencing the canopy bidirectional reflectances. The leaf reflectance r can be determined only if Ψ is inferred, which becomes possible outside the “Lambertian-viewing” cone, that is, when viewing at larger view zenith angles at several view azimuths. These limitations are predicated on the Lambertian leaf reflectance characteristics, and would not apply when leaf reflection has a pronounced specular component. To assess the limitations of measurements in a planar scan, we reformulate our model of bidirectional reflectances by a change in the coordinate system, expressing leaf orientation by two projection ratios of the leaf area. We establish that when viewing solely in the solar principal plane, the projection ratio q (projection of leaf area on the principal plane divided by that on the horizontal plane) cannot be inferred, since it does not appear in the expression for the bidirectional reflectance. Characterization of the “hot spot”, for which the view direction is close to the direction of illumination, is formulated in terms of the width of the cone of the view angles around the direction of illumination in which the reflectance is significantly enhanced. Determination of this cone width calls for narrow field-of-view measurements in the “hot spot” region, after other canopy model parameters have been determined from measurements outside the “hot spot”.