Evaluating the use of Beer's law for estimating light interception in canopy architectures with varying heterogeneity and anisotropy

Light interception in plant canopies is most commonly estimated using a simple one-dimensional turbid medium model (i.e., Beer's law). Inherent in this class of models are assumptions that vegetation is uniformly distributed in space (homogeneous) and in many cases that vegetation orientation is uniformly distributed (isotropic). It is known that these assumptions are violated in a wide range of canopies, as real canopies commonly have heterogeneity at multiple scales and almost always have highly anisotropic leaf angle distributions. However, it is not quantitatively known under what conditions these assumptions become problematic given the difficulty of robustly evaluating model results for a range of canopy architectures. In this study, assumptions of vegetation homogeneity and isotropy were evaluated under clear sky conditions for a range of virtually-generated crop canopies with the aid of a detailed three-dimensional, leaf-resolving radiation model. Results showed that Beer's law consistently over predicted light interception for all canopy configurations. For canopies where the plant spacing was comparable to the plant height, Beer's law performed poorly, and over predicted daily intercepted sunlight by up to similar to 115%. For vegetation with a highly anisotropic leaf inclination distribution but a relatively isotropic leaf azimuth distribution, the assumption of canopy isotropy (i.e., G = 0.5) resulted in relatively small errors. However, if leaf elevation and azimuth were both highly anisotropic, the assumption of canopy isotropy could introduce significant errors depending on the orientation of the azimuthal anisotropy with respect to the sun's path.