Modelling and localizing a stem taper function for Pinus radiata in Spain

Abstract

The parsimonious taper function proposed by Riemer et al. (1995. Allg. Forst.- Jagdztg. 166(7): 144–147) was fitted for radiata pine (Pinus radiata D. Don) stems in Spain by using a nonlinear mixed modelling approach. Eight candidate models (all possible expansion combinations of the three fixed parameters with random effects) were assessed, and the mixed model with three random effects performed the best according to the goodness-of-fit statistics. An evaluation data set was used to assess the performance of these models in predicting stem diameter along the bole, as well as total stem volume. Four prediction approaches were compared: one subject (tree) specific (SS) and three population specific (ordinary least squares (OLS), mean (M), and population averaged (PA)). The SS responses for a tree were estimated from a prior stem diameter measurement available for that tree, whereas OLS, M, and PA were obtained from the fixed-effects model, from the fixed parameters of mixed-effects models, and by computing mean predictions from the mixed-effects models over the distribution of random effects, respectively. Prediction errors were greater for the M and PA responses than for the OLS response, and therefore, from the prediction point of view, the use of the mixed-effects models is not recommended when an additional stem diameter measurement is not available. The mixed model with three random effects was also selected as the best model for SS estimations. Measurement of an additional stem diameter at a relative tree height of approximately 0.5 provided the best calibrations for stem diameters along the bole and total stem volume predictions. The SS approach increased the flexibility and efficiency of the selected mixed-effects model for localized predictions and thus improved the overall predictive capacity of the base model.

Compatible System for Predicting Total and Merchantable Stem Volume over and under Bark, Branch Volume and Whole-Tree Volume of Pine Species

“…Most of the research on tree volume has focused on the modelling of stem total volume and volume profiles, commonly through the use of taper equations (e.g., [18][19][20][21][22][23]). Such equations predict the upper stem diameter at any point on the tree bole, with the aim of determining possible end uses for a single log.…”

“…Such equations predict the upper stem diameter at any point on the tree bole, with the aim of determining possible end uses for a single log. Therefore, they are important tools for establishing the most appropriate type of silvicultural management for the desired tree dimensions and associated end uses (e.g., [18][19][20][21][22][23]). Different stem profile modelling approaches have been developed during the last decades for this goal.…”

Desarrollo de una función de perfil mediante modelos mixtos para Pinus sylvestris en Turquía: selección de parámetros fijos a expandir

“…en este y otros trabajos (e.g. Gómez-García et al 2013, Arias-Rodil et al 2015, se recomienda el empleo de modelos mixtos para el ajuste de funciones de perfil ya que permiten considerar la estructura jerárquica característica de los conjuntos de datos empleados para el desarrollo de las mismas. Se evaluaron los modelos mixtos tanto mediante el análisis de sus ajustes (comparando los estadísticos AIC y BIC) como de sus calibraciones (comparando el estadístico EMC).…”

“…Los resultados obtenidos por estos autores podrían deberse a que emplearon el método FOCE para ajustar el modelo y el método FO para la calibración (Yang y Huang 2013). En el presente estudio, al igual que en otro previamente realizado por Arias-Rodil et al (2015), se emplea el método FOCE para ambas fases, observándose que el mismo modelo se comporta mejor en los dos casos.…”

“…Numerosos estudios han utilizado modelos mixtos para desarrollar funciones de perfil (e.g. Tasissa y Burkhart 1998, Trincado y Burkhart 2006, Gómez-García et al 2013, Arias-Rodil et al 2015.…”