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.
Highlights
Stem profile equations, commonly known as taper equations, which refer to the general decrease in the regular outline of a solid body from its base to its tip
The segmented taper equation [6,7,8,9] refers that several polynomials representing different parts of the tree stem are connected through the inflection point, and the tree stem is assumed as concave, paraboloid and conical respectively from bottom to top
A nonlinear mixed model method has been utilized for fitting Max and Burkhart segmented taper equation, and the results shows that mixed effect model can improve the fitting precision of the model [20].Chinese fir is a native coniferous timber tree species in China with a long cultivation history, which is widely distributed in 18 provinces and regions in southern China
Summary
Commonly known as taper equations, which refer to the general decrease in the regular outline of a solid body from its base to its tip. The segmented taper equation [6,7,8,9] refers that several polynomials representing different parts of the tree stem are connected through the inflection point, and the tree stem is assumed as concave, paraboloid and conical respectively from bottom to top. More complex iterative operation as well as more fitting data and experience are required for the estimation of segmented taper equation inflection point. The variableexponent taper equation [10,11,12,13] refers that the tree stem shape can be better estimated through the change of the independent variable exponent in the continuous function, which can be applied for theoretically describing the tree stem of any shape. Variable-exponent taper equation shows better imitative effect and application prospect [10,13,14,15] than other two taper equations
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