Variable-Exponent Taper Equation Based on Multilevel Nonlinear Mixed Effect for Chinese Fir in China

Abstract

A variable-exponent taper equation was developed for Chinese fir (Cunninghamia lanceolate (Lamb.) Hook.) trees grown in southern China. Thirty taper equations from different groups of models (single, segmented, or variable-exponent taper equation) were compared to find the excellent basic model with S-plus software. The lowest Akaike information criteria (AIC), Bayesian information criteria (BIC), and -2loglikelihood (-2LL) was chosen to determine the best combination of random parameters. Single taper models were found having the lowest precision, and the variable-exponent taper equations had higher precision than the segmented taper equations. Four variable-exponent taper models that developed by Zeng and Liao, Bi, Kozak, Sharma, and Zhang respectively, were selected as basic model and had no difference in fit statistics between them. Compared with the model without seldom parameter, the nonlinear mixed-effects (NLME) model improves the fitting performance. The plot-level NLME model was found not to remove the residual autocorrelation. The tree-level and two-level NLME model had better simulation accuracy than the plot-level NLME model, and there were no significant differences between the tree-level and two-level NLME model. Variable-exponent taper model developed by Kozak showed the best performance while considering two-level or tree-level NLME model, and produced better predictions for medium stems compared to lower and upper stems.

Constructing Coupling Model of Generalized B-Spline Curve and Crown (CMGBCC) to Explore the 3D Modeling of Chinese Fir Polymorphism

“…SpeedTree is currently a more professional and complete tree 3D modeling software [31]. The trunk of the Chinese fir is straight; therefore, the Chinese fir shaving equation could be taken for the 3D model of the trunk as the outer contour constraint [32][33][34]. Then, the skeleton of the 3D trunk model was constructed in the speed tree, and the Chinese fir bark texture map was added.…”

Incorporating stand density effects and regression techniques for stem taper modeling of a Larix principis-rupprechtii plantation

“…The mixed model consists of fixed parameters and random parameters, and the random parameters are added to the fixed parameters of the nonlinear model, which vary with changes in different blocks. Zhang et al (2021) established the variableexponent taper equation for Chinese fir and found that the nonlinear mixed effect model based on the tree-level effect performed the best. Therefore, in this study, a nonlinear mixed effect model was developed according to tree-level effects.…”

“…Therefore, in this study, different random parameters were combined separately. The optimal combination of fixed and random parameters was determined by comparing the minimum values of the statistics: Akaike's information criterion (AIC), Bayesian information criterion (BIC) and twice the negative log-likelihood (−2LL; Scolforo et al, 2019;Liu et al, 2020;Zhang et al, 2021), their expressions are provided at later section (equations 12~15).…”

“…The variable-exponent taper equation, one of the most extensively used methods in forest properties modeling and analysis, which describe stem shape with a changing exponent or variable from ground to top to represent theneiloid, paraboloid, conic, and several intermediate forms (Kozak, 1988). Its act by changing the independent variableexponent in the continuous function, better estimates of the tree stem shape can be obtained, and the method can be applied to tree stems of any shape (Zhang et al, 2021). Many studies have indicated that the variable-exponent taper equation is usually subject to less bias and is more precise in estimating diameters at different heights (Kozak, 1988;Muhairwe, 1999).…”

“…Compared to traditional regression, nonlinear quantile regression tends to be more efficient and accurate, especially in evaluating values other than the conditional average (Smale et al, 2014). Moreover, this type of model can be used to obtain the regression of the conditional mean and the regression results for arbitrary quantile points, thus providing a wide range of applications, including self-thinning boundary lines (Zhang et al, 2021), diameter growth models (Bohora and Cao, 2014) and tree height diameter models (Rust, 2014).…”