Patterns of covariance between airborne laser scanning metrics and Lorenz curve descriptors of tree size inequality

The Lorenz curve, as a descriptor of tree size inequality within a stand, has been suggested as a reliable means for characterizing forest structure and distinguishing even from uneven-sized areas. The aim of this study was to achieve a thorough understanding on the relations between airborne laser scanning (ALS) metrics and indicators based on Lorenz curve ordering: Gini coefficient (GC) and Lorenz asymmetry (S). Exploratory multivariate analysis was carried out using correlation tests, partial least squares (PLS), and an information-theoretic approach for multimodel inference (MMI). Best subset linear model was selected for GC and S prediction, as variable transformations yielded no improvement in the relation of ALS with the given response. Relative variable importance based on the MMI model showed that GC is best predicted by ALS metrics expressing canopy coverage, return dispersion, and low-high percentile combinations. Although ALS metrics showed no correlation with S, they did so against its constituting components: the proportions of basal area (M g) and stem density (x g) stocked above the mean quadratic diameter. The study of PLS loading vectors illustrated how ALS metrics explain variance in opposing directions for each of these components, so that their effects cancel each other out in the overall S. Cross-validation showed that only marginal differences are nevertheless found between predicting S directly or as the sum M g and x g estimations. The differing relation of diverse ALS metrics was therefore observed for M g and x g. The conclusions obtained by this research may assist in selecting relevant Lorenz curve descriptors for forest structure characterization, as well as in variable reduction strategies for their wall-to-wall prediction by means of ALS metrics.