GENERAL HEIGHT-DIAMETER EQUATION WITH BIOLOGICAL ATTRIBUTES FOR Pinus taeda L. STANDS

Abstract

The aim of this study was to develop an equation with biological attributes and general applicability, to represent the height-diameter relationship for Pinus taeda L. stands, with and without thinning, in the Middle West region of Santa Catarina state, Brazil. The data came from 652 permanent plots, with 428 to 740 m2, located in forest stands with ages ranging from 4.6 to 35.2 years, in which the total heights of about 20% of the trees were measured, in addition to the dominant trees. The functions developed by Harrison, Michailoff, Prodan and Stoffels & Van Soest were fitted with their parameters linear function of stand variables, based on the Gauss-Newton algorithm. In general, the Harrison model, fitted with the parameter linear function of age (t), site index (S), coefficient of variation of the tree diameters in the plot (CV d ) and basal area of the plot (G), showed the best statistical performance to represent the height-diameter relationship, biological consistency and general applicability for stands of Pinus taeda.

General Height-Diameter Equation Depending on the Stand Variables, for Eucalyptus benthamii

“…Similar to the results found in this study, Téo et al (2017) reported the best statistical performance for Harrison et al (1986) model adjusted with its parameters expressed as a linear function of stand variables, to represent the heightdiameter relationship of Pinus taeda L. in the Midwest region of Santa Catarina State, Brazil. The different versions of the Harrison et al (1986) model, adjusted by Téo et al (2017), also presented negative bias (MD).…”

“…The Harrison et al (1986) model adjusted with its parameters expressed as a linear function of stand variables, by ordinary least squares, produced distribution of studentized residuals without heteroscedasticity and without evidences of non-normality, then weighted least squares regression with Parresol (1993) and Huber (1964) methods were not necessary (Figure 2). Téo et al (2017) reported studentized residuals without heteroscedasticity, but with evidences of non-normality of the residuals, especially with large residuals at both extremes of the distribution of errors for the Harrison et al (1986) 3). Among the different versions of the Harrison et al (1986) 3,1978 -3,33 7,19 Where: EM = modeling efficiency; MAD PRESS = average of the PRESS differences; MAD PRESS = average of the PRESS absolute differences; P5 = 5% percentile value of the PRESS residuals; P95 = 95% percentile value of the PRESS residuals.…”

“…The parameter estimation of the functions was made with PROC NLIN procedure in the software program SAS ® University Edition, based on the Gauss-Newton iterative method. The studies of Harrison et al (1986) and Téo et al (2017) provided the basis to obtain the initial values of the parameters of the heightdiameter functions. The final estimates of the parameters of the height-diameter equations should exclude zero in its 95% confidence band, indicating that there are only nonzero values for the parameters and then, they are always significant (Téo et al, 2017).…”

“…The height-diameter relationship is susceptible to several factors, such as site quality (Retslaff et al, 2015;Vendruscolo et al, 2015), age (Machado et al, 2011;Paulo et al, 2011;Soares & Tomé, 2002;Téo et al, 2017), stand density (Araújo et al, 2012;Silva et al, 2016;Téo et al, 2017), crown size (Machado et al, 2015), species (Azevedo et al, 2011;Donadoni et al, 2010;Hess et al, 2014;Sanquetta et al, 2013) and the sociological position of the trees (Costa et al, 2014;Leduc & Goelz, 2009;Martins et al, 2016). Retslaff et al (2015) reported that the use of the variables dominant height and site index produced height-diameter equations with more homogeneous and narrow residues distribution.…”

“…In Brazil, it is common to use empirical models to represent height-diameter relationship (Oliveira et al, 2011;Rufino et al, 2010). However, it is more appropriate to use theoretical models, which have an implicit hypothesis associated with the characteristics of the height-diameter relationship and considering the causes and effects of different variables on the height-diameter relationship (Téo et al, 2017).…”