Estimators and Confidence Intervals for Plant Area Density at Voxel Scale with T-LiDAR

Abstract

9Terrestrial LiDAR becomes more and more popular to estimate leaf and plant area density. 10Voxel-based approaches account for this vegetation heterogeneity and significant work has 11 been done in this recent research field, but no general theoretical analysis is available. 2• Our unbiased estimators are consistent in a wider range of validity than the usual ones, 26 especially for the unbiased MLE, which is consistent when the beam number is as low as 5. 27The unbiased MLE is efficient, meaning it reaches the lowest residual errors that can be 28 expected (for an unbiased estimator). Also the unbiased MLE does not require any bias 29 correction when path lengths are unequal. 30• When elements are small (or voxel is large), 10 3 beams entering the voxel leads to some 31 confidence intervals ≈ ±10%, but when elements are larger (or voxel smaller), it can remain 32 wider than ±50%, even for a large beam number. This is explained by the variability of 33 element positions between vegetation samples. Such a result shows that a significant part of 34 residual error can be explained by random effects. 35• Confidence intervals are much smaller (±5 to 10%) when LAD estimates are averaged over 36 several small voxels, typically within a horizontal layer or in the crown of individual plants. 37In this context, our unbiased estimators show a reduction of 50% of the radius of confidence 38 intervals, in comparison to usual estimators. 39Our study provides some new ready-to-use estimators and confidence intervals for attenuation 40 coefficients, which are consistent and efficient within a fairly large range of parameter values. 41The consistency is achieved for a low beam number, which is promising for application to 42 airborne LiDAR data. They entail to raise the level of understanding and confidence on LAD Highlights: 52• Voxel-based estimations of LAD/PAD may lack of consistency and efficiency 53• We propose new estimators based on theoretical derivation and numerical simulations 54• Estimators for confidence intervals are also provided 55• New estimators should help determine the most appropriate voxel resolution 56 57

Mapping forest leaf area density from multiview terrestrial lidar

“…These results indicate that leaf area density is increasingly overestimated when total path length is relatively short, as predicted by Pimont et al. (2018). From this figure, one can see a sharp increase in the mean bias and the standard deviation in leaf area density estimates (centre curve in Figure 2) which occurs on average across all sites around 30 m of total probe length.…”

“…Terrestrial laser scanning (TLS) has been shown to enable the mapping of leaf area density in forests (Béland et al., 2011, 2014; Grau et al., 2017; Hosoi & Omasa, 2006; Pimont et al., 2018). The use of observations from terrestrial laser scanners provides two fundamental advantages over traditional passive methods for deriving leaf area density in forests: (a) the elements intercepting laser light are positioned in 3D space, and (b) the intensity of the returned light is measured.…”

“…The former can be obtained using different methods like reflectance threshold (Béland, Baldocchi, et al., 2014), semantic segmentation (Wang et al., 2020) or machine learning (Krishna Moorthy et al., 2019). The latter relies on theoretical approaches using the contact frequency (Béland et al., 2011; Hosoi & Omasa, 2006; Warren Wilson, 1959), maximum likelihood estimation (Pimont et al., 2018), or the Beer‐Lambert law (Béland et al., 2014; Ross, 1981). All of these approaches rely on assumptions about leaf size within the reference volume, the random distribution of the leaves inside the volume, and require considering the leaf projection factor which is a function of the orientation of leaves.…”

Fragmentation disrupts the seasonality of Amazonian evergreen forests

“…The volume occupied by vegetation within each transect was divided into 1 m 3 voxels, and the PAD calculated for each of these voxels (Supplementary Figure 1d). This procedure was done in the LiDAR data voxelization software AMAPVox 48,49 . AMAPvox tracks every laser pulse through a 3D grid (voxelized space) to the last recorded hit.…”

“…Different estimation procedures are provid ed in the AMAPVox software. We used the Free Path Length estimator first developed for single return TLS in Pimont and colleagues 49 and later extended to the multiple return case 50 . The common assumption made for all estimation procedures in AMAPvox is to consider vegetation elements as randomly distributed within a voxel (thereby neglecting within voxel clumping) and to express the directional gap probability (or directional transmittance) as a function of the optical path length of laser pulse through a voxel and the local extinction coefficient 51 .…”