Nonscalability of Fractal Dimension to Quantify Canopy Structural Complexity from Individual Trees to Forest Stands

Canopy structural complexity is a critical emergent forest attribute, and light detection and ranging (lidar)-based fractal dimension has been recognized as its powerful measure at the individual tree level. However, the current lidar-based estimation method is highly sensitive to data characteristics, and its scalability from individual trees to forest stands remains unclear. This study proposed an improved method to estimate fractal dimension from lidar data by considering Shannon entropy, and evaluated its scalability from individual trees to forest stands through mathematical derivations. Moreover, a total of 280 forest stand scenes simulated from the terrestrial lidar data of 115 trees spanning large variability in canopy structural complexity were used to evaluate the robustness of the proposed method and the scalability of fractal dimension. The results show that the proposed method can significantly improve the robustness of lidar-derived fractal dimensions. Both mathematical derivations and experimental analyses demonstrate that the fractal dimension of a forest stand is equal to that of the tree with the largest fractal dimension in it, manifesting its nonscalability from individual trees to forest stands. The nonscalability of fractal dimension reveals its limited capability in canopy structural complexity quantification and indicates that the power-law scaling theory of a forest stand underlying fractal geometry is determined by its dominant tree instead of the entire community. Nevertheless, we believe that fractal dimension is still a useful indicator of canopy structural complexity at the individual tree level and might be used along with other stand-level indexes to reflect the “tree-to-stand” correlation of canopy structural complexity.