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AGROCLIMATOLOGY

Inclusion of the Fractal Dimension of Leafless Plant Structure in the Beer-Lambert Law

Department of Plant Science, McGill University, Macdonald Campus, 21,111 Lakeshore, Ste-Anne-de-Bellevue, Quebec, Canada H9X 3V9

Corresponding author (cydp{at}musica.mcgill.ca)

The Beer-Lambert law is commonly used to describe the relationship between the proportion of light penetrating a plant canopy and the leaf area index (LAI). Although the geometric distribution of leaf area has a potential effect on the ability of a plant to intercept light, the equation contains no term to account for it. In this study, the geometric distribution of leaf area was quantified by the fractal dimension of leafless plant structure (FD). The objective was to evaluate the contribution of plant structure complexity to the Beer-Lambert law, by including FD in the equation. The crop was soybean [Glycine max. (L.) Merr.]. Data were collected according to a block design with four blocks and five weekly repeated measures. The analyzed variables were LAI and light penetration (% per plant), and FD, estimated using leafless plants photographed from the side that allowed the maximum appearance of branches and petioles. Statistical analyses were performed week by week, on weekly means and on block means. When LAI and FD were significantly correlated (i.e., at the end of canopy development and on weekly means), inclusion of either variable as regressor in the equation provided similar goodness-of-fit. In other instances, inclusion of FD as a multiplicative factor of LAI increased the r² value up to 0.31. In all instances, the correlation between light penetration and FD was stronger than between light penetration and LAI. In summary, the application of the Beer-Lambert law for light penetration into the canopy is improved by inclusion of FD.

Abbreviations: FD, fractal dimension • LAI, leaf area index

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