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Linear functionals of foliage angle density

Published online by Cambridge University Press:  17 February 2009

R. S. Anderssen  and
D. R. Jackett
D. R. Jackett
Affiliation:
Division of Mathematics and Statistics, CSIRO, P.O. Box 1965, Canberra City, A.C.T. 2601.
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Abstract

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Knowledge about the foliage angle density g(α) of the leaves in the canopy of trees is crucial in foresty mangement, modelling canopy reflectance, and environmental monitoring. It is usually determined from observations of the contact frequency f(β) by solving a version of the first kind Fredholm integral equation derived by Reeve (Appendix in Warren Wilson [22]). However, for inference purposes, the practitioner uses functionals defined on g(α), such as the leaf area index F, rather than g(α) itself. Miller [12] has shown that F can be computed directly from f(β) without solving the integral equation. In this paper, we show that his result is a special case of a general transformation for linear functionals defined on g(α). The key is the existence of an alternative inversion formula for the integral equation to that derived by Miller [11].

Type
Research Article
Information
The ANZIAM Journal , Volume 25 , Issue 4 , April 1984 , pp. 431 - 442
Copyright
Copyright © Australian Mathematical Society 1984

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