Linear Functionals of the Foliage Angle Distribution as Tools to Study the Structure of Plant Canopies

Abstract

In 1967, Miller showed how average foliage density could be computed from contact frequency data. It formalized mathematically the idea posed earlier by Warren Wilson of estimating the leaf area index as a linear combination of measured values of the contact frequency. Recently, it has been shown that Miller's result is a special case of a general transformation that allows linear functionals defined on the (generally unknown) foliage angle distribution (foliage angle functionals) to be evaluated as linear functionals defined on the (measured) contact frequency (contact frequency functionals). This result has important consequences for the use of foliage angle functionals in the study of the structure of plant canopies. For example, it allows Warren Wilson's idea to be extended to the evaluation of such functionals, and thereby simplifies greatly their actual evaluation.

In this paper, we first motivate and review the use of foliage angle functionals in the study of plant canopies; then we introduce new functionals (the segmented foliage density and the moments); and finally, we use numerical experimentation with synthetic data to illustrate the advantages of having formulas for the foliage angle functionals of interest that are defined explicitly in terms of the (measured) contact frequency.