Valbuena, R., Packalen, P., Tokola, T. and Maltamo, M. 2014. Canonical Correlation Analysis for Interpreting Airborne Laser Scanning Metrics along the Lorenz Curve of Tree Size Inequality. Baltic Forestry 20(2): 326-332

The objective of this study was to explore the explanatory capacity of airborne laser scanning (ALS) metrics with regard to tree size inequality properties from the forest. With this purpose, we selected the analysis of the Lorenz curve as a method for determining complexity in forest structure. The Lorenz curve is a representation of the relations of relative dominance among trees in the forest. Therefore, it presents a detailed description of the balance between overstory and understory, providing with valuable information on the degree of inequality among tree sizes in the forest. The methodology chosen was a canonical correlation analysis (CCA) of ALS metrics against regular quantiles along the Lorenz curve. Results demonstrated that most explanatory power can be yielded from indices of concentration of return heights, such as the L-coefficient of variation (i.e., Gini coefficient). This is highly relevant as it demonstrates the Lorenz curves from tree sizes and return heights to be closely related. Moreover, the study of separate canonical components allowed us to observe the correlation of certain metrics with each segment of the curve, detailing the effects that can be observed in ALS surveys in relation with tree stocking balance relations in multilayered forests. The first CCA component was more related to the dominant canopy, and therefore it influences the ALS surveys in a greater extent. This dominant layer is mainly described by canopy cover metrics, and thus it depends mainly on the forest stand relative density. The second CCA component was more related to the development of the understory, which influences the total amount of returns observed and the skewness of their heights. Future research studying the Lorenz curve from ALS surveys could provide forest inventories with important relations on forest structural characteristics.

Key words: airborne laser scanning, forest inventory, tree size inequality, Lorenz curve, canonical correlation analysis