Height-diameter models for King Boris fir (Abies borisii regis Mattf.) and Scots pine (Pinus sylvestris L.) in Olympus and Pieria Mountains, Greece

Abstract

In forest science and practice, the total tree height is one of the basic morphometric attributes at the tree level and it has been closely linked with important stand attributes. In the current research, sixteen nonlinear functions for height prediction were tested in terms of their fitting ability against samples of Abies borisii regis and Pinus sylvestris trees from mountainous forests in central Greece. The fitting procedure was based on generalized nonlinear weighted regression. At the final stage, a five-quantile nonlinear height-diameter model was developed for both species through a quantile regression approach, to estimate the entire conditional distribution of tree height, enabling the evaluation of the diameter impact at various quantiles and providing a comprehensive understanding of the proposed relationship across the distribution. The results clearly showed that employing the diameter as the sole independent variable, the 3-parameter Hossfeld function and the 2-parameter Näslund function managed to explain approximately 84.0% and 81.7% of the total height variance in the case of King Boris fir and Scots pine species, respectively. Furthermore, the models exhibited low levels of error in both cases (2.310m for the fir and 3.004m for the pine), yielding unbiased predictions for both fir (−0.002m) and pine (−0.004m). Notably, all the required assumptions for homogeneity and normality of the associated residuals were achieved through the weighting procedure, while the quantile regression approach provided additional insights into the height-diameter allometry of the specific species. The proposed models can turn into valuable tools for operational forest management planning, particularly for wood production and conservation of mountainous forest ecosystems.