Extending a turbid medium BRDF model to allow sloping terrain with a vertical plant stand

This paper extends the turbid medium approach used for modeling bidirectional reflectance from horizontal plant canopies to sloping terrain with a vertically oriented plant stand. Previous treatments have accounted for terrain slope by simple adaptation to an inclined plane of models for horizontal surfaces. However, such treatments implicitly assume that plants grow perpendicularly to the surface, despite the fact that plant stems continue to grow vertically on slopes. We investigate the differences between our new "vertical growth" model and the more usual "perpendicular to the surface growth" model in terms of the effect on canopy albedo and bidirectional reflectance factors. Although the effect of leaf angle distribution on the albedo is different for both the vertical-growth and perpendicular-growth models, it appears to be a much smaller effect than that due to terrain slope. For the bidirectional reflectance factors (BRF's), the magnitude and sign of the differences between the two models varies with the direction of observation, the slope, and the leaf angle distribution, and, can exceed 10% for a planophile canopy. A comparison between modeled and measured data shows that model predictions under the vertical growth assumption are consistent with measurements, whereas the assumption of perpendicular growth can lead to large errors.