Using fractal dimension to correct clumping effect in leaf area index measurement by digital cover photography

The leaf area index (LAI), defined as one-half of the total green leaf area per unit horizontal ground surface area, is a key parameter in agriculture, forestry, ecology, and other fields. The clumping index (CI) accounts for the nonrandom spatial distribution of the foliage elements in the canopy, thereby considerably influencing the accuracy of LAI estimation with optical field-based instruments. Most of the traditional clumping effect correction methods for LAI measurements are based on the theory developed for one-dimensional (1D) data of the vegetation canopy. The development of new methods remains necessary for LAI measurement with two-dimensional (2D) data, including images from digital cover photography (DCP). We found that the fractal dimension (FD) of a 2D ground-based DCP image is an effective tool for correcting the clumping effect and estimating the LAI. The universal formula was derived to describe the relationship between the LAI and FD for randomly distributed leaves using the box-counting method (BCM) and the Boolean model. For the clumped leaves, the universal formula is related to the FD, LAI, and CI. The LAI and CI can be calculated with the FD and gap probability derived from DCP images. Eighteen simulated scenes of different vegetation structure patterns, three realistic canopy scenes of the fourth phase of the radiative transfer model intercomparison (RAMI), and field-measured data acquired from 5 plots in 4 temporal phases were provided to validate the method. The results showed good agreement with the reference (R-2 = 0.93 and RMSE = 0.46 for simulated data; uncertainty from 0.31 to 1.05 for realistic canopy; R-2 = 0.85 and RMSE = 0.34 for field-measured data). This validation with downward DCP images shows that the proposed FD method assesses the clumping effect more thoroughly compared to the clumping effect correction methods originally designed for 1D data. The FD method is expected to improve the measurement accuracy of LAI with DCP images, especially for heterogeneous canopies.