A variable-exponent taper equation

1988 ◽  
Vol 18 (11) ◽  
pp. 1363-1368 ◽  
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.

Effects of adding tree, stand, and site variables to Kozak's variable-exponent taper equation

1994 ◽  
Vol 24 (2) ◽  
pp. 252-259 ◽  
Author(s):  
Charles K. Muhairwe ◽  
Valerie M. LeMay ◽  
Antal Kozak
Keyword(s):  
Variable Exponent ◽  
Lodgepole Pine ◽  
Site Class ◽  
Breast Height ◽  
Red Cedar ◽  
Taper Function ◽  
Quadratic Mean Diameter ◽  
Taper Equation ◽  
The Cost ◽  
Total Tree

Crown class, site class, and breast-height age were incorporated into Kozak's variable-exponent taper equation (A. Kozak. 1988. Can. J. For. Res. 18: 1363–1368) for three species: Douglas-fir (Pseudotsugamenziesii (Mirb.) Franco), western red cedar (Thujaplicata Donn), and aspen (Populustremuloides Michx.). For lodgepole pine (Pinuscontorta Dougl.), crown ratio, breast-height age, and quadratic mean diameter were incorporated into Kozak's taper equation. The effects of adding these variables to the exponent part of the taper equation on the prediction abilities of the taper model were assessed for prediction of diameter inside bark along the stem, total tree volume, and tree merchantable height. It was found that apart from the use of crown ratio for lodgepole pine, the additional variables resulted in only marginal improvements to the published version of Kozak's taper function. Therefore, the cost of measuring these additional variables is not justifiable.

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

1998 ◽  
Vol 28 (7) ◽  
pp. 1078-1083 ◽  
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.

Bark Thickness and Bark Volume in Southwestern Oregon Douglas-Fir

1990 ◽  
Vol 5 (1) ◽  
pp. 5-8 ◽  
Author(s):  
Douglas A. Maguire ◽  
David W. Hann
Keyword(s):  
Pseudotsuga Menziesii ◽  
Douglas Fir ◽  
Bark Thickness ◽  
Breast Height ◽  
Taper Equation ◽  
Taper Equations ◽  
Height Predictions

Abstract A segmented polynomial taper equation for southwestern Oregon Douglas-fir (Pseudotsuga menziesii) predicts double bark thickness (dbt) at any point above breast height. Below breast height predictions assume conformity to a neiloid frustrum. The equations facilitate estimation of inside bark diameter (dib) given outside bark (dob) measurements. Bark volume and bark biomass can also be estimated when supplemented with existing dib taper equations developed for southwestern Oregon. West J. Appl. For. 5(1):5-8.

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

Forests ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 126
Author(s):  
Sensen Zhang ◽  
Jianjun Sun ◽  
Aiguo Duan ◽  
Jianguo Zhang
Keyword(s):  
Variable Exponent ◽  
Southern China ◽  
Information Criteria ◽  
Chinese Fir ◽  
Tree Level ◽  
Mixed Effect ◽  
Basic Model ◽  
Taper Equation ◽  
Taper Equations ◽  
Taper Models

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.

scholarly journals Calibrating a Segmented Taper Equation with Two Diameter Measurements

2009 ◽  
Vol 33 (2) ◽  
pp. 58-61 ◽  
Author(s):  
Quang V. Cao
Keyword(s):  
Pinus Taeda ◽  
Loblolly Pine ◽  
Polynomial Regression ◽  
Stem Diameter ◽  
Laser Technology ◽  
Breast Height ◽  
Tree Data ◽  
Pinus Taeda L ◽  
Taper Equation ◽  
Taper Equations

Abstract Recent advances in laser technology help make possible accurate and affordable measurements of upper-stem diameters. These measurements can be used to calibrate results from a taper equation to improve the accuracy of diameter predictions along the tree bole. Felled-tree data from a loblolly pine (Pinus taeda L.) plantation were used to evaluate two methods for calibrating outputs from a segmented taper equation with parameters either obtained from the data in this study or originally published by <xref ref-type="bibr" rid="B5-2124">Max and Burkhart (1976</xref>, Segmented polynomial regression applied to taper equations, For. Sci. 22:283–289). For outside-bark diameters, although a simple calibration for dbh gave desirable results, a better calibration involving both dbh and an upper-stem diameter provided significant improvements in predicting tree taper. Results varied depending on where the diameter was measured, with optimum gains obtained when the upper-stem diameter was measured at the midpoint between breast height and the tree tip. For inside-bark diameters, the calibration for inside-bark dbh actually produced inferior predictions, whereas the calibration based on both dbh and an upper-stem diameter offered only modest improvements over the unadjusted predictions.

Variable-form taper functions for four Alberta tree species

1992 ◽  
Vol 22 (2) ◽  
pp. 210-223 ◽  
Author(s):  
R.M. Newnham
Keyword(s):  
Tree Species ◽  
Variable Exponent ◽  
Significant Loss ◽  
Stem Form ◽  
Data Set ◽  
Variable Form ◽  
Form Function ◽  
Taper Function ◽  
Form Model ◽  
Unbiased Estimates

The variable-form taper function was tested on a data set of 5074 trees, consisting of jack pine (Pinusbanksiana Lamb.), lodgepole pine {Pinuscontorta Dougl.), white spruce (Piceaglauca (Moench) Voss), and trembling aspen (Populustremuloides Michx.), from Alberta. When compared with the results of tests performed on the same data using the variable-exponent function and the segmented polynomial model, the variable-form model was found to be superior (based on residual mean squares) for estimating both upper stem diameter ratios and total stem volumes. The two pine species could be combined and a single taper function used without significant loss of accuracy. Stem form in two of the volume sampling regions was significantly different from that in other regions of the province, but this may have been because the samples were not representative of the two regions. The variable-form function gave accurate and unbiased estimates of both merchantable height and merchantable volume.

The Prediction of Heartwood Diameter in Radiata Pine Trees

1974 ◽  
Vol 4 (4) ◽  
pp. 524-529 ◽  
Author(s):  
W. E. Hillis ◽  
Nell Ditchburne
Keyword(s):  
Radiata Pine ◽  
Regression Equation ◽  
Tree Age ◽  
Cross Sectional ◽  
Diameter At Breast Height ◽  
Breast Height ◽  
Pine Trees ◽  
High Degree ◽  
Heartwood Diameter ◽  
Different Parts

Cross-sectional characteristics of Pinusradiata trees grown in different parts of Australia were examined. A regression equation which related heartwood diameter at a given age of the tree to the diameter at breast height outside bark and the product of the tree age and its diameter at 5 years gave a high degree of correspondence between observed and predicted heartwood diameter.

scholarly journals Estimation of Genetic Parameters and Wood Yield Selection Index in a Clonal Trial of Korean Pine (Pinus koraiensis) in Northeastern China

2021 ◽  
Vol 13 (8) ◽  
pp. 4167
Author(s):  
David Kombi Kaviriri ◽  
Huan-Zhen Liu ◽  
Xi-Yang Zhao
Keyword(s):  
Selection Index ◽  
Tree Height ◽  
Stem Volume ◽  
Korean Pine ◽  
Branch Number ◽  
Basal Diameter ◽  
Diameter At Breast Height ◽  
Breast Height ◽  
Stem Straightness ◽  
Clonal Trial

In order to determine suitable traits for selecting high-wood-yield Korean pine materials, eleven morphological characteristics (tree height, basal diameter, diameter at breast height, diameter at 3 meter height, stem straightness degree, crown breadth, crown height, branch angle, branch number per node, bark thickness, and stem volume) were investigated in a 38-year-old Korean pine clonal trial at Naozhi orchard. A statistical approach combining variance and regression analysis was used to extract appropriate traits for selecting elite clones. Results of variance analysis showed significant difference in variance sources in most of the traits, except for the stem straightness degree, which had a p-value of 0.94. Moderate to high coefficients of variation and clonal repeatability ranged from 10.73% to 35.45% and from 0.06% to 0.78%, respectively. Strong significant correlations on the phenotypic and genotypic levels were observed between the straightness traits and tree volume, but crown breadth was weakly correlated to the volume. Four principal components retaining up to 80% of the total variation were extracted, and stem volume, basal diameter, diameter at breast height, diameter at 3 meter height, tree height, and crown height displayed high correlation to these components (r ranged from 0.76 to 0.98). Based on the Type III sum of squares, tree height, diameter at breast height, and branch number showed significant information to explain the clonal variability based on stem volume. Using the extracted characteristics as the selection index, six clones (PK105, PK59, PK104, PK36, PK28, and K101) displayed the highest Qi values, with a selection rate of 5% corresponding to the genetic gain of 42.96% in stem volume. This study provides beneficial information for the selection of multiple traits for genetically improved genotypes of Korean pine.

scholarly journals Global Tree Taper Modelling: A Review of Applications, Methods, Functions, and Their Parameters

Forests ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 913
Author(s):  
Serajis Salekin ◽  
Cristian Higuera Catalán ◽  
Daniel Boczniewicz ◽  
Darius Phiri ◽  
Justin Morgenroth ◽  
...  
Keyword(s):  
Measurement Techniques ◽  
Principal Component ◽  
Climatic Conditions ◽  
Modern Times ◽  
Taper Function ◽  
Complex Functions ◽  
Artificial Neural Network Ann ◽  
Species Specific ◽  
Simple Equations ◽  
Taper Equations

Taper functions are important tools for forest description, modelling, assessment, and management. A large number of studies have been conducted to develop and improve taper functions; however, few review studies have been dedicated to addressing their development and parameters. This review summarises the development of taper functions by considering their parameterisation, geographic and species-specific limitations, and applications. This study showed that there has been an increase in the number of studies of taper function and contemporary methods have been developed for the establishment of these functions. The reviewed studies also show that taper functions have been developed from simple equations in the early 1900s to complex functions in modern times. Early taper functions included polynomial, sigmoid, principal component analysis (PCA), and linear mixed functions, while contemporary machine learning (ML) approaches include artificial neural network (ANN) and random forest (RF). Further analysis of the published literature also shows that most of the studies of taper functions have been carried out in Europe and the Americas, meaning most taper equations are not specifically applicable to tropical tree species. Developing well-conditioned taper functions requires reducing the variation due to species, measurement techniques, and climatic conditions, among other factors. The information presented in this study is important for understanding and developing taper functions. Future studies can focus on developing better taper functions by incorporating emerging remote sensing and geospatial datasets, and using contemporary statistical approaches such as ANN and RF.

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