A rotated ellipsoidal angle density function improves estimation of foliage inclination distributions in forest canopies

The ‘ellipsoidal distribution’, in which angles are assumed to be distributed parallel to the surface of an oblate or prolate ellipsoid, has been widely used to describe the leaf angle distribution (LAD) of plant canopies. This ellipsoidal function is constrained to show a probability density of zero at an inclination angle of zero; however, actual LADs commonly show a peak probability density at zero, a pattern consistent with functional models of plant leaf display. A ‘rotated ellipsoidal distribution’ is described here, which geometrically corresponds to an ellipsoid in which small surface elements are rotated normal to the surface. Empirical LADs from canopy and understory species in an old-growth coniferous forest were used to compare the two models. In every case the rotated ellipsoidal function provided a better description of empirical data than did the non-rotated function, while retaining only a single parameter. The ratio of G-statistics for goodness of fit for the two functions ranged from 1.03 to 3.88. The improved fit is due to the fact that the rotated function always shows a probability density greater than zero at inclination angles of zero, can show a mode at zero, and more accurately characterizes the overall shape of empirical distributions. ©2000 Published by Elsevier Science B.V. All rights reserved.