Inclusion of the fractal dimension of leafless plant structure in the Beer-Lambert law

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 eff ect 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 a rea was quantified by the fractal dimension of leafless plant structure (PD ). The objective was to evaluate the contribution of plant structure comple xity to the Beer-Lambert law, by including FD in the equation. The crop was soybean [Glycine mar. (L.) Merr.]. Data were collected according to a bloc k design with four blocks and five weekly repeated measures. The analyzed v ariables mere LAI and light penetration (% per plant), and FD, estimated us ing leafless plants photographed from the side that allowed the maximum app earance of branches and petioles. Statistical analyses were performed week by week, on weekly means and on block means. When LAI and PD were significa ntly correlated (i.e., at the end of canopy development and on weekly means ), inclusion of either variable as regressor in the equation provided simil ar goodness-of fit. In other instances, inclusion of FD as a multiplicative factor of LAI increased the r(2) value up to 0.31. In all instances, the c orrelation between light penetration and FD was stronger than between light penetration and LAI. In summary, the application of the Beer-Lambert law f or light penetration into the canopy is improved by inclusion of FD.