scholarly journals STRATEGIES FOR STEM MEASUREMENT SAMPLING: A STATISTICAL APPROACH OF MODELLING INDIVIDUAL TREE VOLUME

CERNE ◽  
2016 ◽  
Vol 22 (3) ◽  
pp. 249-260 ◽  
Author(s):  
Hassan Camil David ◽  
Rodrigo Otávio Veiga Miranda ◽  
John Welker ◽  
Luan Demarco Fiorentin ◽  
Ângelo Augusto Ebling ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Statistical Tests ◽  
Fixed Number ◽  
Stem Volume ◽  
Diameter Class ◽  
Clear Trend ◽  
Data Set ◽  
Individual Tree ◽  
Volume Estimates ◽  
Volume Equations

ABSTRACT The aim of this paper was to evaluate different criteria for stem measurement sampling and to identify the criterion with best performance for developing individual tree volume equations. Data were collected in eucalyptus stands 58 to 65 months old. Schumacher-Hall model was applied using five sampling criteria with nine variations (45 in total): 1) number of trees per diameter class, being (a) fixed number, (b) proportional to the diameter class of the sample, or (c) proportional to the standard deviation of the sample; and 2) the width of the diameter class, which ranged from 1.0 up to 5.0 cm. We used the equations generated from each of the five sampling criteria to estimate stem volume of trees reserved for validation. This allowed us to obtain standard errors of estimates from this data-set. In addition, residuals of volume estimates were examined by means of statistical tests of bias, autocorrelation and heteroscedasticity. Better performances of volume equations occurred when smaller diameter class widths were used, i.e., when the sample size increased. There was no clear trend in increasing/decreasing residual autocorrelation and/or heteroscedasticity. Both methods of sampling proportional to the frequency of diameter class had the best performances, inclusive using only 36 trees. The ones where choice of trees was proportional to the standard deviation had the worst. In conclusion, the selection proportional to the frequency of the diameter class, under the condition that at least two trees per class are sampled, provides models statistically better than all the other criteria.

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.

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 Taper, Volume, and Weight Equations for Red Pine in West Virginia

2008 ◽  
Vol 25 (3) ◽  
pp. 151-153 ◽  
Author(s):  
Lichun Jiang ◽  
John R. Brooks
Keyword(s):  
West Virginia ◽  
Ease Of Use ◽  
Red Pine ◽  
Seemingly Unrelated Regression ◽  
Stem Volume ◽  
West Virginia University ◽  
Individual Tree ◽  
Unrelated Regression ◽  
Taper Equation ◽  
Volume Equations

Abstract Compatible taper, volume, and weight equations were developed for planted red pine in West Virginia. The data were based on stem analysis of 26 trees from West Virginia University Research Forest, located in northern West Virginia. A commonly used segmented polynomial taper equation was chosen because of its balance between prediction accuracy and ease of use. Seemingly unrelated regression was used to simultaneously fit the system of equations for inside and outside bark data. When compared with existing total stem volume equations developed by Fowler (Fowler, G.W., 1997, Individual tree volume equations for red pine in Michigan, North. J. Appl. For. 14:53–58) and by Gilmore et al. (Gilmore, D.W., et al., 2005, Thinning red pine plantations and the Langsaeter hypothesis: A northern Minnesota case study. North, J. Appl. For. 22:19–25), a positive bias was evident that increased directly with stem diameter for trees from this region.

Incorporating crown ratio into prediction equations for Douglas-fir stem volume

1987 ◽  
Vol 17 (1) ◽  
pp. 17-22 ◽  
Author(s):  
David W. Hann ◽  
David K. Walters ◽  
John A. Scrivani
Keyword(s):  
Statistical Significance ◽  
Linear Equations ◽  
Douglas Fir ◽  
Stem Volume ◽  
Validation Data ◽  
Data Set ◽  
Component Approach ◽  
Modeling Data ◽  
Volume Equations

Crown ratio was incorporated into four Douglas-fir (Pseudotsugamenziesii (Mirb.) Franco) total-stem cubic volume equations as a nonlinear multiplier. Two of the equations are traditional linear equations, one is nonlinear, and one is a new component approach that divides stem volume into that above and that below breast height. These equations, with and without crown ratio terms, were fitted to a modeling data set, and the statistical significance of the crown ratio terms was examined. All equations were then applied to a validation data set for comparison of their predictive abilities. The crown ratio term proved to be highly significant in the component approach, and component equations that included crown ratio had the smallest bias and the greatest prediction precision of all equations examined. That form was therefore selected as the most accurate characterization of Douglas-fir stem volume.

scholarly journals Evaluation of Alternative Approaches for Predicting Individual Tree Volume Increment

2010 ◽  
Vol 25 (3) ◽  
pp. 120-126 ◽  
Author(s):  
David W. Hann ◽  
Aaron R. Weiskittel
Keyword(s):  
Direct Method ◽  
Analysis Data ◽  
Stem Volume ◽  
Prediction Errors ◽  
Data Set ◽  
Individual Tree ◽  
Diameter Increment ◽  
Volume Increment ◽  
Alternative Approaches ◽  
Taper Equation

Abstract The volume increment of individual trees is often inferred from a volume or taper equation and predicted or observed diameter and height increments. Prediction errors can be compounded with this type of approach because of the array of equations used and differences in their accuracy. The consequences of several alternative approaches for indirectly or directly estimating individual tree volume increment were examined using an extensive stem analysis data set of Douglas-fir (Pseudotsuga menziesii [Mirb.] Franco) in southwest Oregon. The data were used to construct new stem volume, taper, and volume increment equations, which were then used to compare predicted and observed 5-year volume increments. The results of this analysis suggest that the indirect prediction of volume increment is sensitive to both the approach used for estimating stem volume and the use of actual versus predicted diameter and height increment, especially diameter increment. In addition, using the indirect method of volume and taper equations was found to have a slightly lower level of accuracy in predicting stem volume increment than the direct method. It was found that the use of local calibration procedures could help to mitigate possible problems with the bias incurred by using predicted rather than actual diameter increment.

scholarly journals Effects of Measurement Errors on Individual Tree Stem Volume Estimates for the Austrian National Forest Inventory

2014 ◽  
Vol 60 (1) ◽  
pp. 14-24 ◽  
Author(s):  
Ambros Berger ◽  
Thomas Gschwantner ◽  
Ronald E. McRoberts ◽  
Klemens Schadauer
Keyword(s):  
Forest Inventory ◽  
Measurement Errors ◽  
National Forest Inventory ◽  
Stem Volume ◽  
National Forest ◽  
Individual Tree ◽  
Volume Estimates ◽  
Tree Stem

New Form-class Equations Improve Volume Estimates

1973 ◽  
Vol 3 (3) ◽  
pp. 338-341
Author(s):  
F. Evert
Keyword(s):  
Ground Level ◽  
Red Pine ◽  
Stem Diameter ◽  
Individual Tree ◽  
Stand Volume ◽  
Above Ground Level ◽  
Form Class ◽  
New Form ◽  
Volume Estimates ◽  
Volume Equations

Three form-class volume equations involving the upper stem diameter at 19.5 ft (5.94 m) above ground level and three standard volume equations based on d.b.h. and height were tested for accuracy in estimating both tree and stand volume in different stands of red pine (Pinusresinosa Ait.). All three form-class equations met the required 10% accuracy in estimating individual tree volumes; the three standard volume equations failed to meet this accuracy. All three form-class equations also met the required 5% accuracy in estimating stand volume, but none of the standard equations did.

scholarly journals Differences in Computed Individual-Tree Volumes Caused by Differences in Field Measurements

2008 ◽  
Vol 25 (4) ◽  
pp. 195-201 ◽  
Author(s):  
James A. Westfall
Keyword(s):  
Field Measurements ◽  
Accurate Estimation ◽  
Statistical Bias ◽  
Full Data ◽  
Data Set ◽  
Individual Tree ◽  
Forest Inventory And Analysis ◽  
Species Groups ◽  
Input Variables ◽  
Volume Equations

Abstract Individual-tree volumes are primarily predicted using volume equations that rely on measured tree attributes. In the northeastern United States, the Forest Inventory and Analysis program determines tree volume using dbh, bole height, proportion of cull, and species information. These measurements are subject to variability due to a host of factors. The sensitivity of the volume equations were assessed in relation to changes in each of the input variables. Additionally, data from 3,345 trees that were independently remeasured were used to assess differences in gross and net volumes between operational and audit measurements. Evaluations were conducted for dbh, bole height, and proportion of cull classes, across 18 different species groups. Differences in bole height and proportion cull measurements were found to contribute the most to volume differences. Surprisingly, trees with relatively short bole heights were affected more than trees having taller bole heights. Differences in dbh and species identification contributed little to the volume differences. An analysis of the full data set across all realized volume differences showed no statistical bias in either gross or net volume. These results show the influence that specific field measurements have on accurate estimation of volume, which may be useful for targeting specific attributes where additional training or refined measurement protocols could improve consistency.

Two new height models for volume estimation of lodgepole pine stands

1988 ◽  
Vol 18 (2) ◽  
pp. 195-201 ◽  
Author(s):  
W. T. Zakrzewski ◽  
I. E. Bella
Keyword(s):  
Lodgepole Pine ◽  
Tree Height ◽  
Practical Method ◽  
Volume Estimation ◽  
Data Set ◽  
Individual Tree ◽  
Pine Trees ◽  
Quadratic Mean Diameter ◽  
The Cost ◽  
Volume Estimates

To reduce the cost and increase the efficiency of obtaining individual tree height information required for sample plot volume estimation, two general height–diameter (H/D) regression models were developed using two-stage regression analysis and data from 96 lodgepole pine (Pinuscontorta Dougl. var. latifolia Engelm.) sample plots. The derived models were examined using an independent data set of 28 plots. In addition to diameter at breast height (D), these models also included two easily measurable stand parameters as independent variables: quadratic mean diameter (Dq) and the height of a tree with diameter Dq (Hq). With a practical method to estimate Hq (from up to three heights measured) and using these two new H/D models in conjunction with available regional standard volume equations (V = f (D,H)), the stand volume estimates, on the average, were 0.003% higher (SD 4.1%) for the first model and 1.081% lower (SD 4.6%) for the second model than those obtained using traditional H/D curves for each plot based on 30 or more height measurements. The new models are therefore recommended for use in height estimation of lodgepole pine trees within the range of conditions of the data. This approach may be applied to other species and regions.

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