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.

A geometrical tree volume model based on the location of the centre of gravity of the bole

1982 ◽  
Vol 12 (2) ◽  
pp. 215-221 ◽  
Author(s):  
Robert R. Forslund
Keyword(s):  
Volume Estimation ◽  
Diameter Measurement ◽  
Stem Form ◽  
Total Height ◽  
Volume Model ◽  
Breast Height ◽  
Centre Of Gravity ◽  
Geometrical Form ◽  
Volume Equation ◽  
Diameter Outside Bark

A tree bole model describing a geometrical form in between a paraboloid and cone "paracone" has been developed. The model is based on empirical evidence that the average centre of gravity of aspen (Populustremuloides Michx.) boles without branches lies at 3/10 of the bole height from its base. Outside bark bole volume, V (cubic decimetres), can therefore be estimated nondestructively from the total height, H (metres), and the diameter outside bark, dK (centimetres), measured at a relative height, K, as follows:[Formula: see text]Based on a sample of 70 aspen stems, this equation estimates individual bole volume from total bole length or height and from a single diameter measurement, either at the 3/10 position or at the breast-height position, as accurately as Smalian's formula using seven diameter measurements. Based on the sample, the 3/10 position should be chosen over breast height wherever breast height lies below 20 or above 60% of the total height. It is important that care be taken in the measurement of the diameter due to the sensitivity of the volume equation to diameter variation. In addition to volume estimation, the paracone model provides a comparison profile around which stem form variation within and among species may be observed.

On critical-height sampling

1986 ◽  
Vol 16 (6) ◽  
pp. 1310-1313 ◽  
Author(s):  
Paul C. Van Deusen ◽  
Walter J. Meerschaert
Keyword(s):  
Spatial Patterns ◽  
Critical Height ◽  
Breast Height ◽  
Unbiased Estimates ◽  
Volume Equation ◽  
Volume Estimates ◽  
The Relationship ◽  
Tree Spatial Patterns

Critical-height sampling is shown to provide unbiased estimates of per-acre cubic volume if the sample trees are selected at stump height to determine if they are to be tallied. Selection at breast height implicitly assumes that the tree is a cylinder from breast height to stump height. It is also shown that unbiased estimates of merchantable volume can be obtained with critical-height sampling. The relationship between variances from critical-height sampling and the usual horizontal point procedure requiring volume estimates is shown to depend on tree spatial patterns. This is also true for growth estimates. A definite benefit of critical-height sampling is that no volume equation is needed.

scholarly journals Spruce Budworm Defoliation and Growth Loss in Young Balsam Fir: Estimation of Volume Growth Based on Stem Analysis and Increment Cores at Breast Height

1996 ◽  
Vol 13 (2) ◽  
pp. 73-78 ◽  
Author(s):  
Harald Piene ◽  
Janine D'Amours ◽  
Alan A. Bray
Keyword(s):  
Volume Growth ◽  
Basal Area ◽  
Spruce Budworm ◽  
Balsam Fir ◽  
Stem Analysis ◽  
Individual Tree ◽  
Breast Height ◽  
Individual Tree Growth ◽  
Growth Loss ◽  
Changes Over Time

Abstract Comparisons of estimates of volume and volume increment, based on increment cores sampled at breast height and on stem analysis, were made in a young balsam fir stand that had been defoliated by spruce budworm. Use of increment cores is not recommended to estimate individual tree growth, because large errors, ranging from 20.9 to 57.2%, and error variability can be expected. The inability, when using increment cores, to estimate basal area is the major source of this variation. Although large uncertainties are associated with future growth predictions, on a per ha basis, changes over time based on increment cores may in some instances give comparable results to those based on stem analysis due to the canceling effect of trees being approximately equally overestimated and underestimated. However, a prerequisite is that the defoliation history and the year of individual tree death are known in detail to aid in the correct dating of ring widths. North. J. Appl. For. 13(2):73-78.

Evaluation of Ground Plane Detection for Estimating Breast Height in Stereo Images

2020 ◽  
Vol 66 (5) ◽  
pp. 612-622
Author(s):  
Lucas A Wells ◽  
Woodam Chung
Keyword(s):  
Measurement Error ◽  
Mean Squared Error ◽  
Ground Plane ◽  
Stem Density ◽  
Diameter Measurement ◽  
Height Measurement ◽  
Individual Tree ◽  
Height Estimation ◽  
Diameter At Breast Height ◽  
Breast Height

Abstract Diameter at breast height is a standard method for characterizing trees and ultimately forests over large geographical scales. Expressing the cross-section of a tree stem with a diameter measurement has inherent errors, as stems are not perfect conical frustums. Diameter suffices as an approximation, since methods for the exact cross-sectional area of a stem are infeasible in practice. There are other primary sources of error in diameter at breast height measurements: diameter measurement error and breast height measurement error. This paper addresses the latter in the context of an automated measurement system using 3D photography. We consider breast height estimation a fundamental component in such systems, as errors in measurement height can precipitate significant errors in stand-level attribute estimation as diameter changes along the height of the stem because of taper. We evaluate the efficacy of breast height estimation using stereo photogrammetry by fitting a planar surface to the ground and elevating the plane to breast height. Results from a validation test on 560 observations show that breast height can be estimated with a root mean squared error of 10.20 cm within 10 m from the camera and 13.36 cm within 20 m from the camera on flat terrain in varying levels of stem density. Study Implications Increasing the level of automation in forest operations is one approach to address workforce attrition and safety issues in the industry. Automated tree measurement and mapping systems present an opportunity to reduce operational costs by providing machine operators with necessary information to carry out silvicultural prescriptions and eliminate the need for individual tree marking in certain situations. In order to maintain trust between landowners and harvesting contractors, it is imperative that automatic measurement systems are rigorously tested to determine that measurement accuracy is within acceptable limits. Breast height measurement error is often overlooked as a source of error in estimating diameter at breast height. However, accurate breast height estimation is a necessary prerequisite for reliable, consistent, and precise diameter at breast height measurement. The capacity of machine vision systems to automate forest inventory and monitoring tasks is increasing and can help managers achieve sustainable forestry objectives on more acres in less time.

Stem Volume and Site Index Equations for European Larch in Maine

1993 ◽  
Vol 10 (2) ◽  
pp. 70-74 ◽  
Author(s):  
Daniel W. Gilmore ◽  
Russell D. Briggs ◽  
Robert S. Seymour
Keyword(s):  
New York ◽  
New England ◽  
Analysis Data ◽  
Site Index ◽  
Stem Volume ◽  
Prediction Equations ◽  
European Larch ◽  
Stem Analysis ◽  
Breast Height ◽  
Volume Equation

Abstract Stem analysis data collected from 101 sample trees located in 12 plantations established between 1930 and 1982 throughout central Maine were used to develop total and merchantable stem volume prediction equations, and site index prediction equations for plantation-grown European larch. The inside bark merchantable volume equation (4 in. top dob and 12 ft minimum merchantable bole) using a weighted combined variable was very similar to one for Japanese larch in Pennsylvania. Site index curves from this study were identical to those developed in southern New York and New England below a breast height (bh) age of 20 yr; after bh age 20, our curves predicted increasingly greater height growth and show a 6-12 ft superiority in height at a bh age of 50. North. J. Appl. For. 10(2):70-74.

Variance reduction in Ueno's method and cylinder sampling for forest volume estimation

1995 ◽  
Vol 25 (11) ◽  
pp. 1783-1794 ◽  
Author(s):  
Thomas B. Lynch
Keyword(s):  
Computer Simulation ◽  
Variance Reduction ◽  
Volume Estimation ◽  
Critical Height ◽  
Volume Estimate ◽  
Individual Tree ◽  
Stand Volume ◽  
Reduction Techniques ◽  
Antithetic Variates ◽  
Volume Equation

Three basic techniques are proposed for reducing the variance of the stand volume estimate provided by cylinder sampling and Ueno's method. Ueno's method is based on critical height sampling but does not require measurement of critical heights. Instead, a count of trees whose critical heights are less than randomly generated heights is used to estimate stand volume. Cylinder sampling selects sample trees for which randomly generated heights fall within cylinders formed by tree heights and point sampling plot sizes. The methods proposed here for variance reduction in cylinder sampling and Ueno's method are antithetic variates, importance sampling, and control variates. Cylinder sampling without variance reduction was the most efficient of 12 methods compared in computer simulation that used estimated measurement times. However, cylinder sampling requires knowledge of a combined variable individual tree volume equation. Of the three variance reduction techniques applied to Ueno's method, antithetic variates performed best in computer simulation.

Predicting Logging Residue Volumes in Alaska

2021 ◽  
Vol 67 (2) ◽  
pp. 119-124
Author(s):  
Erik C Berg ◽  
Eric A Simmons ◽  
Todd A Morgan ◽  
Stanley J Zarnoch
Keyword(s):  
Predictive Models ◽  
Tree Species ◽  
Timber Harvesting ◽  
Individual Tree ◽  
Growing Stock ◽  
Prediction Tools ◽  
Breast Height ◽  
Logging Residue ◽  
The Creation ◽  
Forest Managers

Abstract Alaska forest managers seek information on how timber harvesting practices change the creation of postharvest woody residues. To predict residue volumes, researchers investigated how residue ratios—growing-stock residue volume per mill-delivered volume—related to readily available data on logging site and tree attributes in Alaska. Residue ratios were not related to logging site-level variables but were related to individual tree variables with predictive models. Ratios varied widely by tree species and were predicted to increase with larger stump height and larger small-end used diameters and decline exponentially with increasing diameter breast height (dbh) to approximately 25 inches. Ratios were then predicted to increase progressively in larger dbh trees. Results from this study update previous findings in other US Northwest states and can be used to produce or improve residue prediction tools for Alaska land managers.

scholarly journals Individual Tree Volume Equations for Red Pine in Michigan

1997 ◽  
Vol 14 (2) ◽  
pp. 53-58 ◽  
Author(s):  
Gary W. Fowler
Keyword(s):  
Red Pine ◽  
Data Sets ◽  
Regression Equations ◽  
Independent Data ◽  
Data Set ◽  
Individual Tree ◽  
Standing Trees ◽  
Pine Stands ◽  
Volume Estimates ◽  
Volume Equations

Abstract New total, pulpwood, sawtimber, and residual pulpwood cubic foot individual tree volume equations were developed for red pine in Michigan using nonlinear and multiple linear regression. Equations were also developed for Doyle, International 1/4 in., and Scribner bd ft volume, and a procedure for estimating pulpwood and residual pulpwood rough cord volumes from the appropriate cubic foot equations was described. Average ratios of residual pulpwood (i.e., topwood, cubic foot or cords) to mbf were developed for 7.6 and 9.6 in. sawtimber. Data used to develop these equations were collected during May-August 1983-1985 from 3,507 felled and/or standing trees from 27 stands in Michigan. Sixteen and 11 stands were located in the Upper and Lower Peninsulas, respectively. All equations were validated on an independent data set. Rough cord volume estimates based on the new pulpwood equation were compared with contemporary tables for 2 small cruise data sets. The new equations can be used to more accurately estimate total volume and volume per acre when cruising red pine stands. North. J. Appl. For. 14(2):53-58.

Site Index Curves for Norway Spruce in Southern Ontario1

1989 ◽  
Vol 6 (1) ◽  
pp. 23-26 ◽  
Author(s):  
Andrew M. Gordon ◽  
Peter A. Williams ◽  
Edward P. Taylor
Keyword(s):  
Norway Spruce ◽  
Soil Texture ◽  
Sandy Soils ◽  
Site Index ◽  
Height Growth ◽  
Stem Analysis ◽  
Mean Values ◽  
Breast Height ◽  
Drainage Class ◽  
The Mean

Abstract Four dominant or codominant Norway spruce trees from each of 55 sites were destructively sampled and the annual height growth determined by stem analysis. The sampled sites were stratified by soil textural class (coarse, medium, and fine) and depth to distinct mottling (0-16, 16-40, and 40 in.). Two sets of an-amorphic site index curves were constructed using a total age of 30 years (SI30), and breast height age of 25 years (SIBH25) as base ages. The mean SI30 from Ontario (53 ft) was found to be 17.8% higher than the mean values published from Vermont (45 ft) and currently used in Ontario. SIBH25 values had a range of 34.6 to 74.8 ft with a mean of 55.3 ft. Analysis of variance showed significant differences in SIBH25 due to soil texture and drainage class, and in years to breast height (BH) due to drainage class. SIBH25 was highest on sites with loamy soils and distinct mottling at 16-40 in. It took an average of 6.5 years for seedlings to reach BH with a range of 3 to 12 years. Years to BH was lowest on sites with sandy soils and those with distinct mottling below 40 in. North. J. Appl. For. 6(1):23-26, March 1989.

Estimating Breast Height Diameters from Stump Measurements in British Columbia

1982 ◽  
Vol 58 (3) ◽  
pp. 143-145 ◽  
Author(s):  
Julien P. Demaerschalk ◽  
Stephen A. Y. Omule
Keyword(s):  
British Columbia ◽  
Prediction Model ◽  
Tree Species ◽  
Prediction System ◽  
Tree Diameter ◽  
Local Volume ◽  
Breast Height ◽  
Central Canada ◽  
Volume Equation ◽  
Stump Diameter

A means of estimating tree diameter at breast height from stump measurements has many applications. In this paper, metric equations are derived for estimating diameters at breast height from measured stump heights for all commercial tree species in British Columbia by age class and biogeoclimatic zones. The model found best was the same one as used by Alemdag and Honer (1977) for eleven tree species from eastern and central Canada. This prediction system can be incorporated into any local volume equation to derive a tree volume prediction model based on stump diameter and stump height.

Sign in / Sign up

Export Citation Format

Share Document