A canopy reflectance model based on an analytical solution to the multiple scattering equation

Abstract

An approximation to the radiative transfer equation for solar radiation in relatively full, homogeneous plant canopies is presented and solved analytically for solar zenith angles less than 60°. The model predicts reflectance at any depth in the canopy and in any direction and may be inverted with bidirectional reflectance measurements. It may be analytically integrated over the hemisphere at any depth, which makes it useful for energy balance studies, in particular for calculating albedo and intercepted photosynthetically active radiation. The fact that it may be calibrated with directional reflectance measurements and the exact nature of the solution may make it an improvement over the two-stream approximation as applied to canopy scattering problems. No biophysical or single leaf spectral measurements are needed for this inversion, only physically based bounds on the parameters. The model was fit to data at two sun angles and two wavebands (visible and NIR) to within the assumed errors on the reflectance data. The calculated albedos are insensitive to achievable measurement errors. Some of the parameter values themselves found by the inversion agree reasonably well with independent measurements, but the uncertainties introduced by the data noise are rather large. However, the agreement is good enough to demonstrate that the model is physically realistic.