Abstract
Diameter measurements along the stem, which are the basis for taper models, usually have a hierarchical structure. Mixed-effects models, where fixed and random effects are distinguished, are a possible solution for this type of data. However, in order to fully absorb the potential of this method, random effects prediction, which requires additional measurements (diameter along stem), is recommended. This article presents a comparison of various fitting methods (mixed- and fixed-effects model approaches) of the variable-exponent taper model created by Kozak for determining the outside bark diameter along the stem and predicting the tree volume of Scots pine trees in west Poland. During the analysis, it was assumed that no additional measured data were available for practical use; therefore, for the mixed-effects model approach, fixed effects prediction without random effects was applied. Both fitting strategies were compared based on modeling and an independent validation data set. The comparison of mixed- and fixed-effects fitting strategies for the diameter along the stem indicated that the taper model fitted using the mixed-effects model approach better fit the data. Moreover, the error rate for the total tree volume prediction for the independent data set was lower for the mixed-effects model solution than for the fixed-effects one.
Highlights
The tree stem shape, which, in many cases, is characterized by analyzing the variability of tree parameters relative to the height change along the tree [1], as well as the volume resulting from it, is one of the most important types of theoretical and practical information used in the forestry and timber industry
These models allow us to determine the diameter of a tree at any height, and as a consequence, the desired volume and biomass [2], as well as the amounts of various products that can be obtained from a tree after cutting [3]
The linear model, developed on the basis of 15 relative tree heights, determines the longitudinal shape of the tree on the basis of the share of 15 sections of the tree volume was the first Polish taper model elaborated for Scots pine [6]
Summary
The tree stem shape, which, in many cases, is characterized by analyzing the variability of tree parameters (mainly diameter) relative to the height change along the tree [1], as well as the volume resulting from it, is one of the most important types of theoretical and practical information used in the forestry and timber industry. One of the ways to define the longitudinal shapes of trees is to develop special models known as taper functions. These models allow us to determine the diameter of a tree at any height, and as a consequence, the desired volume and biomass [2], as well as the amounts of various products that can be obtained from a tree after cutting [3]. One group of taper models are linear models that describe the longitudinal shape of a tree using a certain number of diameters at different relative tree heights [4,5]. The linear model, developed on the basis of 15 relative tree heights, determines the longitudinal shape of the tree on the basis of the share of 15 sections of the tree volume was the first Polish taper model elaborated for Scots pine [6].
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