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

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.

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Development of a stem taper equation and modelling the effect of stand density on taper for Chinese fir plantations in Southern China

PeerJ ◽

10.7717/peerj.1929 ◽

2016 ◽

Vol 4 ◽

pp. e1929 ◽

Cited By ~ 3

Author(s):

Aiguo Duan ◽

Sensen Zhang ◽

Xiongqing Zhang ◽

Jianguo Zhang

Keyword(s):

Predictive Accuracy ◽

Southern China ◽

Model Development ◽

Stand Density ◽

Chinese Fir ◽

Planting Density ◽

Jiangxi Province ◽

Stem Taper ◽

Taper Equation ◽

Taper Equations

Chinese fir (Cunninghamia lanceolata) is the most important commercial tree species in southern China. The objective of this study was to develop a variable taper equation for Chinese fir, and to quantify the effects of stand planting density on stem taper in Chinese fir. Five equations were fitted or evaluated using the diameter-height data from 293 Chinese fir trees sampled from stands with four different densities in Fenyi County, Jiangxi Province, in southern China. A total of 183 trees were randomly selected for the model development, with the remaining 110 trees used for model evaluation. The results show that the Kozak’s, Sharma/Oderwald, Sharma/Zhang and modified Brink’s equations are superior to the Pain/Boyer equation in terms of the fitting and validation statistics, and the modified Brink’s and Sharma/Zhang equations should be recommended for use as taper equations for Chinese fir because of their high accuracy and variable exponent. The relationships between some parameters of the three selected equations and stand planting densities can be built by adopting some simple mathematical functions to examine the effects of stand planting density on tree taper. The modelling and prediction precision of the three taper equations were compared with or without incorporation of the stand density variable. The predictive accuracy of the model was improved by including the stand density variable and the mean absolute bias of the modified Brink’s and Sharma/Zhang equations with a stand density variable were all below 1.0 cm in the study area. The modelling results showed that the trees have larger butt diameters and more taper when stand density was lower than at higher stand density.

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Stem volume models with random coefficients for Pinus kesiya in Tanzania, Zambia, and Zimbabwe

Canadian Journal of Forest Research ◽

10.1139/x01-019 ◽

2001 ◽

Vol 31 (5) ◽

pp. 879-888 ◽

Cited By ~ 16

Author(s):

Kalle Eerikäinen

Keyword(s):

Variable Exponent ◽

Generalized Least Squares ◽

General Assumption ◽

Random Coefficients ◽

Stem Volume ◽

Random Parameters ◽

Pinus Kesiya ◽

Taper Equation ◽

Volume Models ◽

Taper Models

The aim of the study was to estimate stem volume and taper models for Pinus kesiya (Royle ex Gordon). The volume function provides a simple prediction model for the stem volume. Taper models were developed for over- and under-bark diameters. The under-bark taper curve was determined with the variable-exponent taper equation, whereas the over-bark taper curve was derived from the predicted under-bark taper model using the variable-exponent form of the bark-thickness model. Because of the spatial correlation structures of the data, the general assumption of uncorrelated residuals did not hold. In addition, the models were assumed to contain random parameters that vary from stand to stand and from tree to tree. Therefore, the fixed and random parameters of the models were estimated with the generalized least squares technique. The results of the study show that the mixed models for stem volume and taper are more reliable volume and diameter predictors for P. kesiya than earlier taper and volume functions.

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My last words on taper equations

The Forestry Chronicle ◽

10.5558/tfc80507-4 ◽

2004 ◽

Vol 80 (4) ◽

pp. 507-515 ◽

Cited By ~ 105

Author(s):

Antal Kozak

Keyword(s):

Variable Exponent ◽

Practical Applications ◽

Fit Statistics ◽

University Of British Columbia ◽

Models Comparison ◽

History Of ◽

Species Groups ◽

Taper Equations ◽

The University ◽

Taper Models

A brief review of the nearly half century of research related to taper equations in the Faculty of Forestry at the University of British Columbia is presented. Two new variable-exponent taper models, the 2001 and 2002 models, are introduced and compared to Kozak's 1988 and 1994 models. This comparison, based on 38 species groups consisting of 53 603 trees, demonstrated that the 2002 model is consistently the best overall model of the four, and the 2001 model is the simplest in form and the best for estimating merchantable height. The results of this study also indicate that several fit statistics and lack-of-fit statistics should be used to create indices for ranking taper models for practical applications, instead of only a few. Key words: taper, variable-exponent, history of taper models, comparison of taper models, evaluations of taper models

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Peer Review #1 of "Development of a stem taper equation and modelling the effect of stand density on taper for Chinese fir plantations in Southern China (v0.1)"

10.7287/peerj.1929v0.1/reviews/1 ◽

2016 ◽

Keyword(s):

Peer Review ◽

Southern China ◽

Stand Density ◽

Chinese Fir ◽

Stem Taper ◽

Taper Equation

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Effects of upper stem measurements on the predictive ability of a variable-exponent taper equation

Canadian Journal of Forest Research ◽

10.1139/x98-120 ◽

1998 ◽

Vol 28 (7) ◽

pp. 1078-1083 ◽

Cited By ~ 12

Author(s):

Antal Kozak

Keyword(s):

Measurement Errors ◽

Variable Exponent ◽

Predictive Ability ◽

Diameter Measurement ◽

Breast Height ◽

Taper Equation ◽

Taper Equations

Like several other taper equations, the predictive ability of Kozak's (1988. Can. J. For. Res. 18: 1363-1368) variable-exponent taper equations can also be improved by an additional upper stem outside bark diameter measurement. This study indicated that improvements were small and were mainly restricted to increasing the precision of the estimates. Also, it was demonstrated that if additional diameter measurements are justified, they should be taken between 40 and 50% of the height above breast height for greatest improvement. Measurement errors in upper stem diameters and in their heights above breast height affected both the precision and bias of predictions.

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A Comparative Evaluation of Three Stem Profile Equations for Three Precious Tree Species in Southern China

Forests ◽

10.3390/f11060669 ◽

2020 ◽

Vol 11 (6) ◽

pp. 669

Author(s):

Jun Jiang ◽

Jie Li ◽

Lifeng Pang ◽

Angang Ming

Keyword(s):

Tree Species ◽

Southern China ◽

Tectona Grandis ◽

Prediction Errors ◽

Relative Height ◽

Taper Equation ◽

Erythrophleum Fordii ◽

Individual Trees ◽

Taper Equations ◽

The Tropics

Accurately describing the stem curve of precious tree species and estimating the quantity of various types of wood and their volume in the tropics can provide technical support for reasonable bucking. This study utilized Erythrophleum fordii, Castanopsis hystrix and Tectona grandis as study objects. Forty replicates of each species were used for a total of 120 individual trees. Their tape equations were constructed using simple tape equations, segmented taper equations and variable form taper equations. Statistical indicators were utilized to determine the best taper equation for the three types of precious tree species. A number of methods were compared and analyzed, including the index of correlation, the residual sum of squares, the mean prediction error, the variance of prediction errors and the root mean square error. Finally, a preliminary quantitative analysis was conducted to determine the trends of these three types of tree species. The result shows that the precision of the three predictions developed for each species is high, and, in particular, the segmented taper equations with optimized algorithms is the best. The tendency of the three species to vary was shown to be the highest for T. grandis in the range of 0.0 to 0.8 for its relative height, followed by E. fordii, while the variation of C. hystrix was the smallest. However, in the range of 0.8 to 1.0 relative height, the variation of Castanopsis hystrix was the largest, and the variation of both E. fordii and T. grandis were almost the same. Therefore, the segmented taper equations with optimization algorithms was recommended to fit the three types of tree species in the tropics. These types of equations can be used to estimate the stumpage and timber quantity and as a guide reasonable bucking for these three species.

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A variable-exponent taper equation

Canadian Journal of Forest Research ◽

10.1139/x88-213 ◽

1988 ◽

Vol 18 (11) ◽

pp. 1363-1368 ◽

Cited By ~ 158

Author(s):

A. Kozak

Keyword(s):

Variable Exponent ◽

Computing Time ◽

Variable Form ◽

Diameter At Breast Height ◽

Breast Height ◽

Taper Function ◽

Taper Equation ◽

Taper Equations ◽

Different Parts

A different approach to fitting taper equations has been developed, which eliminates the necessity of using several functions to predict diameter inside bark at different parts of the stem. The variable form taper function is easy to develop and saves computing time. For the data used in this study, it predicted tree profile as a function of height, diameter at breast height, and height from the ground with less bias than many of the taper-estimating systems found in the literature.

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