On seeing the wood from the leaves and the role of voxel size in determining leaf area distribution of forests with terrestrial LiDAR

Terrestrial LiDAR scanners have been shown to hold great potential for estimating and mapping three dimensional (3-D) leaf area distribution in forested environments. This is made possible by the capacity of LiDAR scanners to record the 3-D position of every laser pulse intercepted by plant material. The laser pulses emitted by a LiDAR scanner can be regarded as light probes whose transmission and interception may be used to derive leaf area density at different spatial scales using the Beer–Lambert law or Warren Wilson's contact frequency method among others. Segmenting the canopy into cubic volumes –or voxels- provides a convenient means to compute light transmission statistics and describe the spatial distribution of foliage area in tree crowns. In this paper, we investigate the optimal voxel dimensions for estimating the spatial distribution of within crown leaf area density. We analyzed LiDAR measurements from two field sites, located in Mali and in California, with trees having different leaf sizes during periods with and without leaves. We found that there is a range of voxel sizes, which satisfy three important conditions. The first condition is related to clumping and requires voxels small enough to exclude large gaps between crowns and branches. The second condition requires a voxel size large enough for the conditions postulated by the Poisson law to be valid, i.e., a turbid medium with randomly positioned leaves. And, the third condition relates to the appropriate voxel size to pinpoint the location of those volumes within the canopy which were insufficiently sampled by the LiDAR instrument to derive reliable statistics (occlusion effects). Here, we show that these requirements are a function of leaf size, branching structure, and the predominance of occlusion effects. The results presented provide guiding principles for using voxel volumes in the retrieval of leaf area distributions from terrestrial LiDAR measurements.