Simulation and quantification of the fine-scale spatial pattern and heterogeneity of forest canopy structure: A lacunarity-based method designed for analysis of continuous canopy heights

Forests canopies are dynamic, continuously varying, three-dimensional structures that display substantial heterogeneity in their spatial arrangement at many scales. At the stand-level, fine-scale spatial heterogeneity influences key canopy processes and contributes to the diversity of niche space and maintenance of forest biodiversity. We present a quantitative method that we developed based on a novel application of two well-established statistical techniques – lacunarity analysis and principal component analysis (PCA) – to determine the fine-scale (0.5–33 m) spatial heterogeneity found in the outer surface of a forest canopy. This method was specifically designed for the analysis of continuous canopy height data generated by airborne LiDAR systems or digital photogrammetry; however, in this study we demonstrate our method using a large, well-documented dataset composed of simulated canopy surfaces only. We found that the magnitude of the lacunarity statistic was strongly associated with canopy cover ( R 2 = 0.85) and gap volume ( R 2 = 0.84), while the pattern of decline in lacunarity across discrete measurement scales was related to many size- and density-related attributes of stand and canopy structure (0.27 ≤ R 2 ≤ 0.58) and their diverse vertical and horizontal spatial distributions. PCA uncovered two major gradients of spatial heterogeneity from the 10 dimensions of our original lacunarity dataset. The stronger of these two gradients reflected the continuous variation in canopy cover and gap volume, while a second, more subtle gradient was associated with the array of possible vertical and horizontal spatial configurations that might define any one measure of canopy cover. We expect that this quantitative method can be used to support a broad range of practical applications in sustainable forest management, long-term ecological monitoring, and forest science. Further research is required to understand how these statistical estimates and gradients of measured spatial heterogeneity relate to other ecologically relevant patterns of forest composition, structure, and function.