The power function as a simple stem profile examination tool

1991 ◽  
Vol 21 (2) ◽  
pp. 193-198 ◽  
Author(s):  
R. R. Forslund
Keyword(s):  
Power Function ◽  
Volume Estimation ◽  
Stem Volume ◽  
Centre Of Mass ◽  
Centre Of Gravity ◽  
Profile Characteristics ◽  
Volume Estimates ◽  
Quantitative Indicators ◽  
Form Stability ◽  
Mass Form

Formulae are presented for calculating the volume, surface area, centre of gravity, centre of mass, form, taper, and instantaneous slope of the power function. A profile plotting technique is also used that allows visual comparisons between average stem profiles independent of the size and taper of individual stems. The technique is used to demonstrate that the position near 30% of the height from the base of the stem is a position of form stability for volume estimation. Using the paracone profile model (a power function midway between a paraboloid and a cone) with the diameter at the 30% position and the total stem height, individual stem volume estimates within 10% of the true volume (95% confidence) are obtained once again using a sample of 50 yearling aspen (Populustremuloides Michx.). The plotting technique is then applied to the aspen sample, and the average profiles support the hypothesis that juvenile stems may begin life as paraboloids. The average centre of gravity, the average centre of mass, the sectional form, the average form, and the taper of the stems are also examined and are shown to be quantitative indicators of the plotted profile characteristics.

Analysis of stand density effects on the stem form of Norway spruce trees and volume miscalculation by traditional form factor equations using terrestrial laser scanning (TLS)

2020 ◽  
Vol 50 (1) ◽  
pp. 51-64 ◽  
Author(s):  
Martin Jacobs ◽  
Andreas Rais ◽  
Hans Pretzsch
Keyword(s):  
Form Factor ◽  
Norway Spruce ◽  
Laser Scanning ◽  
Terrestrial Laser Scanning ◽  
Volume Estimation ◽  
Tree Level ◽  
Stem Volume ◽  
Stem Form ◽  
Stem Wood ◽  
Volume Estimates

Tree and stand volume estimates are relevant for forest inventories, forest sales, and carbon stock evaluations. Forest practice commonly uses generalized stem-wood volume functions; however, such generalized approaches neglect the stem form in detail. Hence, trees of a given species with the same diameter at breast height (d1.3) and height (h) are always assumed to have the same form factor and thus the same volume. This case study focused on stem form variation of Norway spruce (Picea abies (L.) Karst.) due to competition effects. Using terrestrial laser scanning (TLS), we measured the stem shape of 868 trees from a long-term spacing and thinning experiment in Germany. The plots covered a broad density range. We analysed the effect of competition and compared the TLS-determined stem volume estimates with those determined conventionally. TLS-based volume estimations showed that the lower the competition was, the lower the tree volume was with a given d1.3 and h. Commonly used functions underestimated the volume stock overall by 4.2%, disregarding any levels. At plot level, underestimation varied from 0.7% to 7.0%. At tree level, the volume was under- and over-estimated by −10% to +10%, respectively. The more precise the examination was, the more suitable the application of TLS was for enhancing volume estimation.

scholarly journals Nondestructive volume estimates of 11-year-old jack pine and black spruce using the power function volume model

1994 ◽  
Vol 70 (6) ◽  
pp. 762-767 ◽  
Author(s):  
R. R. Forslund ◽  
J. M. Paterson
Keyword(s):  
Power Function ◽  
Pinus Banksiana ◽  
Black Spruce ◽  
Jack Pine ◽  
Stem Volume ◽  
Relative Height ◽  
Stem Height ◽  
Function Model ◽  
Volume Model ◽  
Volume Estimates

Two methods for estimating the total outside-bark stem volume of all trees in young plantations of jack pine (Pinus banksiana Lamb.) and black spruce (Picea mariana [Mill.] B.S.P.) were compared. The first method was time-intensive, and required destructive sampling to obtain volume estimates using many paired diameter/height measurements. The second method was nondestructive and required only two field measurements: an outside-bark diameter at either a fixed height (such as breast height) or at a relative height, and the total stem height. The results indicated that total plantation volume estimates to within ±5% can be obtained using the power function model and two stem measurements: a diameter at a relative height of 30% from the base of the stem and total stem height. The power function model offers a good alternative for accurately assessing plantation volume. Key words: black spruce, jack pine, power function volume model, paracone, upper diameters, profile shape, stem volume

scholarly journals Constructing single-entry stem volume models for four economically important tree species of Greece

2021 ◽  
Vol 48 (2) ◽  
pp. 136-146
Author(s):  
Panagiotis P. Koulelis ◽  
Kostas Ioannidis
Keyword(s):  
Tree Species ◽  
National Level ◽  
Sustainable Use ◽  
Information Criterion ◽  
Cost Effective ◽  
Volume Estimation ◽  
Stem Volume ◽  
Nonlinear Regression Models ◽  
Cubic Polynomial ◽  
Two Parameter

Abstract Three different nonlinear regression models were tested for their ability to predict stem volume for economically important native tree species in Greece. Τhe models were evaluated using adjusted R square (Adj Rsqr) root mean square error (RMSE) and Akaike information criterion (AICc), where necessary. In general, the quadratic polynomial and cubic polynomial models and the two-parameter power models fit the data well. Although the two-parameter power function fit best for fir, oak, and beech trees, the cubic polynomial model produced the best fit statistics for black pine. Making forest inventory estimates often involves predicting tree volumes from only the diameter at breast height (DBH) and merchantable height. This study covers important gaps in fast and cost-effective methods for calculating the volume of tree species at national level. However, the increasing need for reliable estimates of inventory components and volume changes requires more accurate volume estimation techniques. Especially when those estimates concern the national inventory, those models must be validated using an entire range of age/diameter and site classes of each species before their extended use across the country to promote the sustainable use of forest resources.

scholarly journals COMPATIBILITY BETWEEN THE STEM VOLUME AND TAPER EQUATIONS VOLUME FOR BLACK WATTLE TREES

FLORESTA ◽  
2020 ◽  
Vol 50 (3) ◽  
pp. 1518
Author(s):  
Marcos Behling ◽  
Henrique Soares Koehler ◽  
Alexandre Behling
Keyword(s):  
Traditional Approach ◽  
Stem Volume ◽  
System Of Equations ◽  
Data Set ◽  
Taper Function ◽  
Black Wattle ◽  
Taper Equations ◽  
Volume Estimates ◽  
Forest Engineering

A system of equations widely used in Forest Engineering by the international community of researchers consists of a combination of a volumetric function and a taper function, with the purpose of making volume estimates compatible. When using the volume function and the taper function in a system, the result of the volume estimated by the two functions should be compatible, meaning that the volume estimated by the volumetric function should not differ from the volume obtained by integrating the taper function. Thus, the purpose of this paper was to develop and present the procedures of a system of equations to make volume estimates from both volume and taper equations compatible, and then compare it to the traditional approach, which is used in forestry companies. The procedures proposed were applied to a data set on the Acacia mearnsii De Wild. (black wattle) at sites where the plantation of this species is concentrated in the state of Rio Grande do Sul. The data set included 343 trees ranging from 5 to 10.75 years of age. It was noted that the lack of volume compatibility, in absolute terms, grows exponentially with the size of the tree. The quality of the estimates using the system of compatible equations did not differ from those obtained from the traditional model, therefore, the former is preferable. Furthermore, it was noted that the residuals from the volume and taper equations are correlated, which suggests that the system of equations be fitted simultaneously.

Cubic-Foot Volume of Loblolly Pine to Any Merchantable Top Limit

1977 ◽  
Vol 1 (2) ◽  
pp. 7-9 ◽  
Author(s):  
Harold E. Burkhart
Keyword(s):  
Loblolly Pine ◽  
Stem Volume ◽  
Simple Equations ◽  
Volume Estimates ◽  
Volume Equations

Abstract Foresters commonly wish to predict tree volume for various top diameters. However, tree volume equations are generally restricted to specific top limits. Further, volume equations for various top limits often cross illogically. This study was conducted with the objective of developing logically related cubic-foot volume estimates for any desired top diameter limit. The approach taken was to predict total stem volume and to convert total volume to merchantable volumes by applying predicted ratios. Results reported here enable users to employ relatively simple equations to obtain cubic-foot volume to any top diameter limit. Volume between any two specified diameters on the stem can be obtained by subtraction.

scholarly journals Comparison of Hossfeld's Method and Two Modern Methods for Volume Estimation of Standing Trees

2011 ◽  
Vol 26 (1) ◽  
pp. 19-23 ◽  
Author(s):  
Mark J. Ducey ◽  
Michael S. Williams
Keyword(s):  
American Literature ◽  
Ponderosa Pine ◽  
Modern Method ◽  
Black Hills ◽  
Volume Estimation ◽  
The North ◽  
Modern Methods ◽  
Standing Trees ◽  
Pine Trees ◽  
Volume Estimates

Abstract Two modern methods, centroid sampling and the paracone model, have been shown to be accurate approaches for obtaining the volumes of trees and logs when taper functions are unavailable or local volume estimates are desired. We show that the equation for whole-tree volume using Hossfeld's method, an older method that has all but disappeared from the North American literature, is nearly identical to that for centroid sampling and the paracone model. Hossfeld's method may be slightly simpler to implement in the field, and like the modern methods, it can be used either for whole trees or for unmerchantable tops. In comparison with detailed measurements taken on 186 ponderosa pine trees from the Black Hills of South Dakota, the paracone model was most accurate for whole trees, but Hossfeld's method was slightly more accurate than centroid sampling. Hossfeld's method was substantially more accurate than either modern method for estimating the volume in tops.

Forest stem volume estimation using high-resolution lidar and SAR data

2003 ◽  
Author(s):  
G. Smith ◽  
A. Persson ◽  
J. Hohmgren ◽  
B. Hallberg ◽  
J.E.S. Fransson ◽  
...  
Keyword(s):  
High Resolution ◽  
Volume Estimation ◽  
Stem Volume ◽  
Sar Data

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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