Converting Volume Equations to Compatible Taper Equations

1972 ◽  
Vol 18 (3) ◽  
pp. 241-245 ◽  
Author(s):  
J. P. Demaerschalk
Keyword(s):  
Taper Equations ◽  
Volume Equations

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 Volume and Taper Equations for Thinned and Unthinned Loblolly Pine Trees in Cutover, Site-Prepared Plantations

1997 ◽  
Vol 21 (3) ◽  
pp. 146-152 ◽  
Author(s):  
Gudaye Tasissa ◽  
Harold E. Burkhart ◽  
Ralph L. Amateis
Keyword(s):  
Pinus Taeda ◽  
Loblolly Pine ◽  
Analysis Data ◽  
The South ◽  
Stem Analysis ◽  
Pine Trees ◽  
Pinus Taeda L ◽  
Taper Equations ◽  
Volume Equations

Abstract Stem analysis data from loblolly pine (Pinus taeda L.) trees grown in cutover, site-prepared plantations across the South were used to develop total and merchantable cubic-foot volume equations and implicit taper relationships for thinned and unthinned conditions. The data were obtained from trees felled during plot establishment for a thinning study and from trees felled during the second thinning of a portion of the same plots 12 yr later. The volume equations presented can be used to predict volume to any specified height or diameter limit for loblolly pine trees in thinned and unthinned stands on cutover site-prepared areas. The taper relationships enable the prediction of upper stem diameters and heights. South. J. Appl. For. 21(3):146-152.

scholarly journals Nondestructive Sampling Applications of the Tele-Relaskop in Forest Inventory

1997 ◽  
Vol 21 (2) ◽  
pp. 75-83
Author(s):  
Robert C. Parker
Keyword(s):  
Analytical Techniques ◽  
Growth And Yield ◽  
Software Systems ◽  
Horizontal Distance ◽  
Tree Form ◽  
Practical Applications ◽  
Standing Trees ◽  
Volume Equation ◽  
Taper Equations ◽  
Volume Equations

Abstract The Tele-Relaskop dendrometer permits accurate upper stem measurements of diameter and height on standing trees for volume and form computations without destructive sampling. Its 8 x magnification and system of scales and relative measurement units facilitates measurements from any convenient distance. Horizontal and vertical percentages of the horizontal distance from the instrument to the tree axis are converted to defined units of measure during computations. Practical applications of the Tele-Relaskop are in growth and yield studies, CFI measurements, traditional volume equation construction, and inventory computations where numerical evaluation of tree form and/or volume is desired. Applications involving computations beyond stem diameters at calculated heights require a microcomputer and specialized software containing analytical techniques for the numerical description of tree form, one of which is a polynomial taper model. These software systems are available to link Tele-Relaskop procedures to traditional inventory processing. Single-tree taper equations are used to calculate tree volume to user-defined merchantability limits, and the volumes are fitted to a combined variable regression model to produce volume equations for use in inventory computations. Coefficients from the volume equations and multiple-tree, species-average taper equations can be used by inventory processors to compute gross tree volumes. Taper coefficients can also be used to compute scaling diameters of variable log length segments within inventory sample trees. South. J. Appl. For. 21(2):75-83.

scholarly journals Tree Taper Model Volume Equations: I. Bark Taper Equations for California Conifers

Hilgardia ◽  
1995 ◽  
Vol 62 (2) ◽  
pp. 1-14 ◽  
Author(s):  
Lee C. Wensel ◽  
Craig M. Olson
Keyword(s):  
Taper Equations ◽  
Volume Equations ◽  
Taper Model

Evolution, history, and use of stem taper equations: A review of their development, application, and implementation

2020 ◽  
Author(s):  
John Paul McTague ◽  
Aaron R. Weiskittel
Keyword(s):  
Laser Scanning ◽  
Sustainable Forest Management ◽  
Current Knowledge ◽  
Stem Form ◽  
Stem Taper ◽  
Primary Means ◽  
Time Requirements ◽  
Taper Equations ◽  
Volume Equations ◽  
Development Application

Stem taper equations, which predict the change in form from ground to tip, have become the primary means for estimating volume. They can provide predictions with similar levels of accuracy as volume equations, but with greater flexibility, a wider range of potential uses, and consistency between taper and volume. This review is a synthesis of current knowledge and an assessment of challenges for future refinement. It primarily focuses on the history and evolution of stem taper model forms. Additional focal areas covered are: (1) the use of additional covariates beyond diameter at breast height and total height; (2) alternative statistical parameterization methods like parametric, semi-parametric, and non-parametric; (3) key considerations for proper development, application, and use of these equations such as sample size requirements, local calibration, and evaluation; and (4) a synthesis of key findings, future opportunities, and ongoing challenges. Emerging technologies, such as terrestrial laser scanning (TLS) offer an unprecedented opportunity to measure stem form in much greater detail at significantly lower costs and time requirements than traditional methods. Overall, continued development, refinement, and application of stem taper equations will remain important given the critical nature of tree volume for science, accurate inventories, and ultimately, sustainable forest management.

Segmented Quadratic Taper Equations for Spruce and Fir in the Northeast

1989 ◽  
Vol 6 (3) ◽  
pp. 123-126 ◽  
Author(s):  
Dale S. Solomon ◽  
Terry D. Droessler ◽  
Ronald C. Lemin
Keyword(s):  
Analysis Data ◽  
Red Spruce ◽  
Stem Analysis ◽  
Validation Data ◽  
Data Set ◽  
Error Analyses ◽  
Taper Equation ◽  
Taper Equations ◽  
Total Tree ◽  
Volume Equations

Abstract Segmented quadratic taper equations were developed from red spruce and balsam fir stem analysis data in the Northeast. Estimated diameters and volumes from the taper equations were compared with actual diameters and volumes in a validation data set, and were found to be precise and have negligible bias in prediction. The derived volume from the taper equation was also compared to existing total tree volume equations for spruce and fir. The error analyses showed the segmented taper equations provided an accurate and precise alternative to total tree volume equations. North. J. Appl. For. 6:123-126, September 1989.

Estimating the accuracy of volume equations using taper equations of stem profile

1988 ◽  
Vol 18 (8) ◽  
pp. 1002-1007 ◽  
Author(s):  
Greg S. Biging
Keyword(s):  
Measurement Error ◽  
Simple Model ◽  
Numerical Technique ◽  
Total Error ◽  
Model Misspecification ◽  
Volume Estimation ◽  
White Fir ◽  
Taper Equations ◽  
Volume Equations ◽  
Selection Of

Comparisons of log volume estimation techniques are performed using the equations of Smalian, Huber, and Newton, and a numerical technique using cubic splines. The data utilized were obtained by predicting diameters at various points along the stem from two paper equations for white fir. Results indicate that Newton's and Huber's equations were the most accurate, followed by the cubic spline and Smalian's equation, respectively. This technique facilitated partitioning of the total error in volume estimation into measurement error and error due to model misspecification arising when the taper of logs could not be exactly described by a simple model such as a frustum of a paraboloid. For the taper relationships analyzed it was shown that the error due to the selection of an inappropriate mensurational model is less than 5% for a measurement distance of 16 ft (4.9 m) for all models tested and can be substantially reduced by applying the formulae only to logs positioned above basal swell. Systematic measurement error was assessed analytically and found to range between 1 and 4%. Thus, total error in volume estimation was less than 9% for all methods tested.

Use of Taper Curve Solved by an Algebraic Method in Silvicultural Research

1986 ◽  
Vol 62 (6) ◽  
pp. 529-532 ◽  
Author(s):  
Guillaime Thérien ◽  
Claude Camiré
Keyword(s):  
Spline Function ◽  
Algebraic Method ◽  
Solution Model ◽  
Algebraic Solution ◽  
Silvicultural Treatments ◽  
Volume Equation ◽  
Taper Equation ◽  
Taper Equations ◽  
Cubic Spline Function ◽  
Volume Equations

Taper equations are commonly used to predict the bole shape and to calculate its volume. In this study, a new algebraic solution model is proposed for research purposes. This model was found to be as accurate as cubic spline function and simple to use. It would be particularly appropriate for research on stand reactions after silvicultural treatments. The study also evaluated compatible volume equations. The required accuracy can be obtained only with a volume equation taking into account a form class coefficient. Key words: balsam fir, taper equation, volume equation, algebraic solution model

scholarly journals Equations for Estimating Bark Volume and Thickness of Commercial Trees in British Columbia

1981 ◽  
Vol 57 (3) ◽  
pp. 112-115 ◽  
Author(s):  
A. Kozak ◽  
R. C. Yang
Keyword(s):  
British Columbia ◽  
Data Base ◽  
Predictive Power ◽  
Bark Thickness ◽  
Breast Height ◽  
Species Groups ◽  
Taper Equations ◽  
Volume Equations

Volume and thickness of bark were studied for 32 species groups of British Columbia. Over 32,000 trees constituted the data base to derive bark volume equations. Because of its simplicity and good predictive power, the equation of Vb = a'HTbDBHcBTd is recommended for bark volume prediction. The possibility to develop bark taper equations and to estimate bark thickness at any given height above breast height were also investigated.

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