A bidirectional reflectance model for nonrandom canopies

The general array model (GAR) is extended to calculate bidirectional reflectance (reflectance as a function of angle of view and angle of illumination) of a plant stand. The new model (BIGAR) defines the plant canopy as one or more foliage-containing ellipsoids arranged in any desired pattern. Foliage is assumed randomly distributed within each ellipsoid, with a specified distribution of inclination angles and random azimuthal orientation distribution. A method of specifying sub-ellipsoids that contain foliage of varying properties is discussed. Foliage is assumed to scatter radiation in a Lambertian fashion. The soil bidirectional reflectance is modelled separately as a boundary condition. The reflectance of any given grid point within the plant stand is calculated from the incident radiation (direct beam, diffuse sky, and diffuse scattered from the soil and foliage) and a view weighting factor that is based upon how much of the view is occupied by that particular grid point. Integrating this over a large number of grid locations provides a prediction of the bidirectional reflectance. Model predictions are compared with measurements in corn and soybean canopies at three stages of growth. The model does quite well in predicting the general shape and dynamics of the measured bidirectional reflectance factors, and rms errors are typically 10% to 15% (relative) of the integrated reflectance value. The effect of rows is evident in both the measurements and the model in the early part of the growing season. The presence of tassles in the corn may be the cause of unpredicted row effects later in the season. Predicted nadir reflectances are accurate for soybean, but are low for full cover corn. The presence of specular reflection causes the model to slightly underpredict reflectances looking toward the sun at large solar zenith angles