A hybrid geometric optical-radiative transfer approach for modeling albedo and directional reflectance of discontinuous canopies

A new model for the bidirectional reflectance of a vegetation cover combines principles of geometric optics and radiative transfer. It relies on gap probabilities and path length distributions to model the penetration of irradiance from a parallel source and the single and multiple scattering of that irradiance in the direction of an observer. The model applies to vegetation covers of discrete plant crowns that are randomly centered both on the plane and within a layer of variable thickness above it. Crowns assume a spheroidal shape with arbitrary height to width ratio. Geometric optics easily models the irradiance that penetrates the vegetation cover directly, is scattered by the soil, and exits without further scattering by the vegetation. Within a plant crown, the probability of scattering is a negative exponential function of path length. Within-crown scattering provides the source for singly-scattered radiation, which exits with probabilities proportional to further path-length distributions in the direction of exitance (including the hotspot effect). Single scattering provides the source for double scattering, and then higher order pairs of scattering are solved successively by a convolution function. Early validations using data from a conifer stand near Howland, Maine, show reasonable agreement between modeled and observed reflectance.