%0 Articles
%T Forest structure indicators based on tree size inequality and their relationships to airborne laser scanning
%A Valbuena, Rubén
%D 2015
%J Dissertationes Forestales
%V 2015
%N 205
%R doi:10.14214/df.205
%U http://dissertationesforestales.fi/article/1988
%X The subject of this doctoral thesis is the non-spatial indices of horizontal differentiation that can be used as indicators of forest structural complexity, specifically as descriptors of tree size inequality. The body of the thesis focuses primarily on the indicators themselves, while the appended articles tackle issues mainly related to their practical estimation using airborne laser scanning (ALS) remote sensing. The overall research is framed in the context of developing a system of indicators that can be applied at pan-European level, whose implementation in practice is foreseen in the advent of national ALS surveying programmes.

A list of indicators available in the scientific literature for describing forest structural heterogeneity by means of horizontal differentiation was tested. Indices based on the theory of information demonstrated critical inconsistencies, which rendered them inadequate for describing tree size inequality. This was revealed using the theory on intrinsic ordering, and illustrated with diversity and equitability profiles. The use of Shannon, and similar indices based on generalized entropy, to describe diversity between size classes, which has been common practice, is therefore discouraged. The link between majorization and Lorenz ordering was established for the specific case of tree size distributions, discussing the reliability of analysing the Lorenz curve to fully describe size inequality in tree populations.

In forest science, the Lorenz curve relates stem frequency distributions to their corresponding basal area-weighted distributions. Indicators based on the Lorenz curve, such as the Gini coefficient (GC), were therefore chosen for their ALS-based estimation. Adding an indicator describing Lorenz curve’s asymmetry was deemed necessary for describing relative understorey development. Research demonstrated the convenience of using the basal area larger than the mean (BALM), as it defined the position of the Lorenz curve inflexion point, which depicts the quadratic mean diameter (QMD). It was observed that, when using Lorenz curves to describe forest structure, the position of the QMD should be compared with the Lorenz curve of a theoretical uniform DBH distribution, which represents maximum entropy. Accordingly, this thesis includes a discussion of how Lorenz ordering can be used as a method, providing a scale for simultaneously comparing relative dispersion and entropy.

In conclusion, the final recommended indicators are GC and BALM, since this bivariate description of forest structure fully characterises the relationships of relative dominance among trees in a forest population. The most similar neighbour (MSN) imputation of tree lists is defended as a substantially convenient method for predicting these indicators by ALS.