Comparison of airborne laser scanning methods for estimating forest structure indicators based on Lorenz curves

The purpose of this study was to compare a number of state-of-the-art methods in airborne laser scanning (ALS) remote sensing with regards to their capacity to describe tree size inequality and other indicators related to forest structure. The indicators chosen were based on the analysis of the Lorenz curve: Gini coefficient (GC), Lorenz asymmetry (LA), the proportions of basal area (BALM) and stem density (NSLM) stocked above the mean quadratic diameter. Each method belonged to one of these estimation strategies: (A) estimating indicators directly; (B) estimating the whole Lorenz curve; or (C) estimating a complete tree list. Across these strategies, the most popular statistical methods for area-based approach (ABA) were used: regression, random forest (RF), and nearest neighbour imputation. The latter included distance metrics based on either RF (NN–RF) or most similar neighbour (MSN). In the case of tree list estimation, methods based on individual tree detection (ITD) and semi-ITD, both combined with MSN imputation, were also studied. The most accurate method was direct estimation by best subset regression, which obtained the lowest cross-validated coefficients of variation of their root mean squared error CV(RMSE) for most indicators: GC (16.80%), LA (8.76%), BALM (8.80%) and NSLM (14.60%). Similar figures [CV(RMSE) 16.09%, 10.49%, 10.93% and 14.07%, respectively] were obtained by MSN imputation of tree lists by ABA, a method that also showed a number of additional advantages, such as better distributing the residual variance along the predictive range. In light of our results, ITD approaches may be clearly inferior to ABA with regards to describing the structural properties related to tree size inequality in forested areas.