Errors in the Estimation of Leaf Area Density From Aerial LiDAR Data: Influence of Statistical Sampling and Heterogeneity

Abstract

In this study, several approaches were evaluated for estimation of the 3-D distribution of leaf area from aerial light detection and ranging (LiDAR) data. Two general leaf area density (LAD) inversion methods were evaluated against “synthetic” LiDAR data for a range of grid resolutions and canopy architectures: 1) inversion based on cumulative transmission of LiDAR pulses through the volume of interest (i.e., the cumulative distribution function (CDF) of transmission, or Beer’s law), and 2) inversion based on the probability density function (PDF) of beam propagation distance within the volume of interest (i.e., probability distribution fitting). Results indicated that the Beer’s law-based method consistently outperformed the PDF-based methods. In a homogeneous canopy, the average error in LAD estimation using the Beer’s law approach decreased exponentially as the number of voxel statistical samples <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N_{v}}$ </tex-math></inline-formula> (i.e., laser pulses reaching the voxel) was increased. The normalized error also decreased exponentially as leaf area index of the voxel LAI <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>v</i></sub> increased. Heterogeneity increased the magnitude of errors in LAD inversion, with errors tending to increase as vegetation density increased, but plant spacing had a negligible impact. For sufficiently dense heterogeneous canopies, there was an optimal voxel size that balanced errors due to poor statistical sampling (small voxels) and errors due to crown-scale heterogeneity that violated the turbid medium assumption (large voxels). This optimum, if present, occurred at around <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N_{v}=40}$ </tex-math></inline-formula> or a voxel width of 2 m regardless of canopy geometry. Sub-crown-scale clumping had a minimal effect on average errors in estimated LAD for the tree geometries explored in this work.