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 distribut ed parallel to the surface of an oblate or prolate ellipsoid, has been wide ly used to describe the leaf angle distribution (LAD) of plant canopies. Th is ellipsoidal function is constrained to show a probability density of zer o at an inclination angle of zero;however, actual LADs commonly show a peak probability density at zero, a pattern consistent with functional models o f plant leaf display. A 'rotated ellipsoidal distribution' is described her e, which geometrically corresponds to an ellipsoid in which small surface e lements are rotated normal to the surface. Empirical LADs from canopy and u nderstory species in an old-growth coniferous forest were used to compare t he two models. In every case the rotated ellipsoidal function provided a be tter 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 densit y greater than zero at inclination angles of zero, can show a mode at zero, and more accurately characterizes the overall shape of empirical distribut ions. (C)2000 Published by Elsevier Science B.V. All rights reserved.