On the hotspot effect of leaf canopies: Modeling study and influence of leaf shape

Abstract

Hotspot is a prominent feature of the reflectance distribution of a vegetation canopy consisting of finite size foliage. It depends on the geometric dimension and spatial organization of vegetation elements, and therefore has a potential for diagnosing canopy geometric structure. In the context of this study, we first reconcile different notations used by previous workers. This leads to geometrically quantifying the cross-correlation function, which is essential for the hotspot modeling. A comprehensive formulation for the hotspot effect at both leaf and canopy levels is then developed, by generally parameterizing some basic parameters such as mean area of shadows and overlap between shadows cast by scatterers. A rectangle model is proposed to account for the influence of noncircular shape of scatterers on the hotspot effect, and explicit expressions for both the cross-correlation function and the hotspot width are obtained. It is shown that for a leaflike object, the angular hotspot width progressively broadens with an increase of m, the ratio of mean leaf width to the length. For the whole canopy, the relative distribution of the hotspot intensity mainly depends on this ratio. That is, the cross-correlation function decreases more rapidly for smaller m as the viewing direction diverges from the illumination direction. As a result, canopy reflectance increases with m, particularly in the region around the hotspot point where the reflectance distribution strongly relies on the ratio m. For m = π / 4 , the rectangle model produces nearly same result as the disk model. This indicates this rectangle model is more realistic and flexible than those based on circle-shaped scatterers (leaves) or their shadows, which is the common assumption underlying in most existing hotspot models.