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.

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.

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.

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.

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.

scholarly journals Selection of mixed-effects parameters in a variable–exponent taper equation for birch trees in northwestern Spain

2013 ◽  
Vol 70 (7) ◽  
pp. 707-715 ◽  
Author(s):  
Esteban Gómez-García ◽  
Felipe Crecente-Campo ◽  
Ulises Diéguez-Aranda
Keyword(s):  
Variable Exponent ◽  
Mixed Effects ◽  
Birch Trees ◽  
Northwestern Spain ◽  
Taper Equation ◽  
Selection Of

scholarly journals Taper Equations for Five Major Commercial Tree Species in Manitoba, Canada

2007 ◽  
Vol 22 (3) ◽  
pp. 163-170 ◽  
Author(s):  
Ryan J. Klos ◽  
G. Geoff Wang ◽  
Qing-Lai Dang ◽  
Ed W. East
Keyword(s):  
Populus Tremuloides ◽  
Picea Glauca ◽  
Pinus Banksiana ◽  
White Spruce ◽  
Jack Pine ◽  
Volume Estimation ◽  
Trembling Aspen ◽  
Stem Form ◽  
Taper Equation ◽  
Taper Equations

Abstract Kozak's variable exponent taper equation was fitted for balsam poplar (Populus balsamifera L.), trembling aspen (Populus tremuloides Michx.), white spruce (Picea glauca [Moench] Voss), black spruce (Picea mariana [Mill.] B.S.P.), and jack pine (Pinus banksiana Lamb.) in Manitoba. Stem taper variability between two ecozones (i.e., Boreal Shield and Boreal Plains) were tested using the F-test. Regional differences were observed for trembling aspen, white spruce, and jack pine, and for those species, separate ecozone-specific taper equations were developed. However, the gross total volume estimates using the ecozone-specific equations were different from those of the provincial equations by only 2 percent. Although the regional difference in stem form was marginal within a province, a difference of approximately 7 percent of gross total volume estimation was found when our provincial taper equations were compared with those developed in Alberta and Saskatchewan. These results suggest that stem form variation increases with spatial scale and that a single taper equation for each species may be sufficient for each province.

Integrated Systems for the Estimation of Tree Taper and Volume

1973 ◽  
Vol 3 (1) ◽  
pp. 90-94 ◽  
Author(s):  
J. P. Demaerschalk
Keyword(s):  
Integrated Systems ◽  
Total Height ◽  
Breast Height ◽  
Taper Equations ◽  
Diameter Outside Bark ◽  
Volume Equations

The desirability and the advantages of deriving taper equations from existing volume equations are discussed. It is demonstrated that the most common types of volume equations can be converted to compatible taper equations. These mathematical stem profile expressions yield tree volumes for any desired stump height and top diameter outside bark from inputs of diameter breast height outside bark and total height.

scholarly journals Pupil diameter measurement errors as a function of gaze direction in corneal reflection eyetrackers

2013 ◽  
Vol 45 (4) ◽  
pp. 1322-1331 ◽  
Author(s):  
Julie Brisson ◽  
Marc Mainville ◽  
Dominique Mailloux ◽  
Christelle Beaulieu ◽  
Josette Serres ◽  
...  
Keyword(s):  
Measurement Errors ◽  
Pupil Diameter ◽  
Gaze Direction ◽  
Diameter Measurement ◽  
Corneal Reflection

Application of a geometrical volume equation to species with different bole forms

1986 ◽  
Vol 16 (2) ◽  
pp. 311-314 ◽  
Author(s):  
G. B. MacDonald ◽  
R. R. Forslund
Keyword(s):  
Diameter Measurement ◽  
Stem Analysis ◽  
Individual Tree ◽  
Breast Height ◽  
Centre Of Gravity ◽  
Variable Equation ◽  
Input Variables ◽  
Volume Equation ◽  
Volume Estimates ◽  
Geometrical Equation

Stem analysis of 20 Abiesbalsamea (L.) Mill., 68 Piceamariana (Mill.) B.S.P., 19 Piceaglauca (Moench) Voss, 31 Populustremuloides Michx., and 37 Betulapapyrifera Marsh. revealed form variation between species. A volume equation based on the paracone (a geometrical solid midway between a paraboloid and a cone) estimated individual tree volume within 10% of the true volume (at the 95% confidence level) for all species. The input variables required were total height and diameter at a relative height of 0.2 for Betulapapyrifera and 0.3 for the other four species. If breast-height diameter was used, the effect of form variation on the accuracy of volume prediction was more pronounced. In this case, the geometrical equation modified for each species according to the average centre of gravity provided more consistently accurate volume estimates than either the paracone equation or Honer's transformed variable equation. For all species, the diameter measurement position was more critical than the version of the geometrical equation selected.

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