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The foliage density equation revisited

Published online by Cambridge University Press:  17 February 2009

John Boris Miller
John Boris Miller
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria 3168
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Abstract

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The foliage density equation is the means by which the foliage density g in a leaf canopy, as a function of the angle of inclination of the leaves, is to be estimated from discrete data gathered using photometric methods or point quadrats. It is an integral equation relating f, a function of angle estimated from measurements, to the unknown function g. The explicit formula for g is known and depends upon f and its first three derivatives; the operator f →, g is unbounded, and the problem is ill posed.

In this paper we give the form of g when f is a trigonometric polynomial, extending earlier results due to J. R. Philip. This provides a means of estimating g without directly estimating the derivatives of f from numerical data. To assess the reliability of the method we discuss the convergence of Fourier series representations of f and g.

Type
Research Article
Information
The ANZIAM Journal , Volume 27 , Issue 4 , April 1986 , pp. 387 - 401
Copyright
Copyright © Australian Mathematical Society 1986

References

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