The distribution of foliage density with foliage angle estimated from inclined point quadrat observations

Abstract

Estimation of the distribution of foliage density with foliage angle from contact frequency data for a number of quadrat inclinations involves solution of a Fredholm integral equation of the first kind. The kernel is known from the work of Warren Wilson and Reeves, and the observed contact frequencies constitute the given function f(β). The solution is g(α), the foliage angle density function. f (β) is known at only a finite number of points, and each value contains inevitable sampling errors. The structure of the solution is such that g(β) is consequently subject to serious errors. A technique involving smoothing of the data is developed with the aim of minimizing this difficulty. The technique is critically discussed and applied to observations of Warren Wilson on lucerne leaves. The analysis indicates that the distribution of leaf angle is roughly symmetrical about the mean angle, with a standard deviation of about 15°.