LiDAR-derived Lorenz-entropy metric for vertical structural complexity: A comparative study of tropical dry and moist forests

Abstract

This study introduces an Entropy-based index: the Lorenz-entropy (LE) index, which we have developed by integrating Light Detection And Ranging (LiDAR), econometrics, and forest ecology. The main goal of the LE is to bridge the gap between theoretical entropy concepts and their practical applications in monitoring vertical structural complexity of tropical forest ecosystems. The LE index quantifies entropy by analyzing Relative Height (RH) metrics (representing a one-dimensional (1D) canopy structure metric) distributions from full-waveform LiDAR across successional stages in a tropical dry forest (TDF) and a tropical rainforest. To validate the LE trends derived from LiDAR, we extended the analysis using inventory-based two-dimensional (2D) and three-dimensional (3D) metrics, specifically basal area and biomass. The consistency of trends between the 1D LiDAR-derived LE and the inventory-based 2D and 3D metrics reinforces the LE's ability to capture and monitor structural complexity reliably across different measurement dimensions.

Our findings demonstrated that LE captures the changes in entropy as a function of successional stages, reflecting how canopy structure evolves towards homogeneity and complexity. Our statistical analysis revealed significant differences between successional stages (ANOVA, α = 0.05, p < 2e-16), with LE increasing substantially from early to late stages and plateauing at climax, where vertical structure (entropy) stabilizes. The mean LE increased by 1.70$\times {10}^{-2}$ between late and climax stages, with a small effect size (Cohen's d = 0.25), indicating minor differences in complexity. The LE index, calculated from biomass and basal area, confirming that as forests mature, entropy and vertical structural complexity increase. Furthermore, the sensitivity analysis showed that LE is most responsive to RHs variability during intermediate stages, suggesting that structural development is most dynamic during this phase. These results demonstrate the potential of the LE index as a tool for ecological analysis and monitoring forest dynamics.