Correcting for the clumping effect in leaf area index calculations using one-dimensional fractal dimension

The clumping effect is the main issue causing the heterogeneity in vegetation canopies and the underestimation of leaf area index (LAI) obtained using indirect measurement methods. Significant efforts have been exerted to correct for the clumping effect and derive the true LAI. Recent research has shown that the fractal dimension (FD) is directly related to the clumping effect of foliage, yet practical methods are needed to calculate field estimates. Considering that widely used LAI applications such as digital hemispherical photography (DHP), tracing radiation and architecture of canopies (TRAC), and digital cover photography (DCP) estimate LAI with one-dimensional (1D) gap probability and gap size data, we propose a method to correct for the clumping effect using 1D FD. Resulting formulae describing the relationship between LAI, CI, and 1D FD were based on the box-counting method (BCM) and a binomial distribution model. Sixty-four simulated scenes including four RAdiation transfer Model Intercomparison (RAMI) actual canopies and field measurements from nine plots (four orchard plots and five coniferous forest plots) were used to validate the novel method. Results showed good agreement with reference LAI values for simulated scenes (R2 = 0.96 and RMSE = 0.35). The 1DFD method generated higher LAI estimates compared with the LAI measured using TRAC at the four orchard plots especially at high canopy closure, while its results were more consistent with LAI obtained by litter collection than those of comparable methods at coniferous forest plots (bias from-13.5% to 9.9% for DCP images, from-3.0% to 19.7% for DHP images, and from-3.8% to 17.0% for TRAC transects). Our validation efforts indicate that the method proposed herein corrects for the clumping effect of vegetated canopies more effectively with DCP images, DHP images, and TRAC measurement when compared with traditional indirect optical methods. The 1DFD method is expected to improve indirect measurement accuracy of LAI.