scholarly journals COMPATIBILITY BETWEEN THE SPURR FUNCTION VOLUME AND THE KOZAK’S TAPER FUNCTION AND QUINTIC POLYNOMIAL VOLUMES FOR BLACK WATTLE TREES

FLORESTA ◽  
2021 ◽  
Vol 51 (2) ◽  
pp. 521
Author(s):  
Marcos Behling ◽  
Henrique Soares Koehler ◽  
Alexandre Behling
Keyword(s):  
Stem Volume ◽  
System Of Equations ◽  
Acacia Mearnsii ◽  
Data Set ◽  
Taper Function ◽  
Quintic Polynomial ◽  
Black Wattle ◽  
Taper Equation ◽  
Volume Estimates ◽  
Taper Models

When modeling the taper and volume, it is desired that the volume estimates obtained by using these two methods are compatible, where the total stem volume estimates shall not differ when using a total volume equation and the volume calculated by integrating the taper equation. There are several of such systems proposed in the literature, in which modifications in the volume and taper models were made to obtain compatible systems. This paper introduces an idea to obtain compatibility in a simpler way, without the need to modify the volume and taper models. Thus, the overall objective of this study was to develop and present a procedure to obtain compatibility between the Spurr function volume and the Kozak’s taper function and quintic polynomial volumes for Acacia mearnsii De Wild trees and compare the results to the traditional method of the same system of equations. The procedures proposed were applied on data on the Acacia mearnsii De Wild (black wattle) species in the towns of Cristal, Piratini, and Encruzilhada in the south of the state of Rio Grande do Sul, Brazil. The data set included 343 trees ranging from 5 to 10.75 years of age. The quality of the fitting for the volume and taper equations fitted using procedures 1 and 2 is similar, and both are compatible. The system of equations presented in procedure 2 is simpler to be applied when compared to procedure 1.

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.

What factors should be accounted for when developing a generalized taper function for black wattle trees?

2020 ◽  
Vol 50 (11) ◽  
pp. 1113-1123
Author(s):  
Mateus Niroh Inoue Sanquetta ◽  
John Paul McTague ◽  
Henrique Ferraço Scolforo ◽  
Alexandre Behling ◽  
Carlos Roberto Sanquetta ◽  
...  
Keyword(s):  
Solid Wood ◽  
Auxiliary Variables ◽  
Stem Form ◽  
Mixed Effect ◽  
Individual Tree ◽  
Taper Function ◽  
Black Wattle ◽  
Taper Equation ◽  
Total Tree ◽  
Mixed Effect Modeling

Taper functions have been widely used for various purposes. Several functions were developed and successfully applied; however, most of these functions fail to account for the influence of stand-level and individual-tree effects of variation on the stem profile. Hence, we aimed in this study to assess how these factors influence the stem profile of black wattle (Acacia mearnsii De Wild.) trees in southern Brazil. There is a notable necessity for developing a domestic market for black wattle solid wood. The database was composed of 218 black wattle trees at age 10 years distributed across the state of Rio Grande do Sul, Brazil. A dimensionally compatible taper equation combined with the mixed-effect modeling approach was used. Additionally, auxiliary variables were included to build a generalized taper function that explains stem form variations. In general, all variables showed a significant influence on the stem profile, except the crown ratio. The inclusion of relative spacing and tree hierarchical position in the taper function resulted in higher accuracy when estimating stem diameters and total tree volume. This study indicates that accounting for attributes at the stand and individual-tree levels may improve stem profile predictions, as well as the biological soundness of the taper function.

Stem volume models with random coefficients for Pinus kesiya in Tanzania, Zambia, and Zimbabwe

2001 ◽  
Vol 31 (5) ◽  
pp. 879-888 ◽  
Author(s):  
Kalle Eerikäinen
Keyword(s):  
Variable Exponent ◽  
Generalized Least Squares ◽  
General Assumption ◽  
Random Coefficients ◽  
Stem Volume ◽  
Random Parameters ◽  
Pinus Kesiya ◽  
Taper Equation ◽  
Volume Models ◽  
Taper Models

The aim of the study was to estimate stem volume and taper models for Pinus kesiya (Royle ex Gordon). The volume function provides a simple prediction model for the stem volume. Taper models were developed for over- and under-bark diameters. The under-bark taper curve was determined with the variable-exponent taper equation, whereas the over-bark taper curve was derived from the predicted under-bark taper model using the variable-exponent form of the bark-thickness model. Because of the spatial correlation structures of the data, the general assumption of uncorrelated residuals did not hold. In addition, the models were assumed to contain random parameters that vary from stand to stand and from tree to tree. Therefore, the fixed and random parameters of the models were estimated with the generalized least squares technique. The results of the study show that the mixed models for stem volume and taper are more reliable volume and diameter predictors for P. kesiya than earlier taper and volume functions.

Modelling and localizing a stem taper function for Pinus radiata in Spain

2015 ◽  
Vol 45 (6) ◽  
pp. 647-658 ◽  
Author(s):  
Manuel Arias-Rodil ◽  
Ulises Diéguez-Aranda ◽  
Francisco Rodríguez Puerta ◽  
Carlos Antonio López-Sánchez ◽  
Elena Canga Líbano ◽  
...  
Keyword(s):  
Random Effects ◽  
Pinus Radiata ◽  
Mixed Model ◽  
Mixed Effects ◽  
Stem Diameter ◽  
Mixed Effects Models ◽  
Stem Volume ◽  
Diameter Measurement ◽  
Data Set ◽  
Taper Function

The parsimonious taper function proposed by Riemer et al. (1995. Allg. Forst.- Jagdztg. 166(7): 144–147) was fitted for radiata pine (Pinus radiata D. Don) stems in Spain by using a nonlinear mixed modelling approach. Eight candidate models (all possible expansion combinations of the three fixed parameters with random effects) were assessed, and the mixed model with three random effects performed the best according to the goodness-of-fit statistics. An evaluation data set was used to assess the performance of these models in predicting stem diameter along the bole, as well as total stem volume. Four prediction approaches were compared: one subject (tree) specific (SS) and three population specific (ordinary least squares (OLS), mean (M), and population averaged (PA)). The SS responses for a tree were estimated from a prior stem diameter measurement available for that tree, whereas OLS, M, and PA were obtained from the fixed-effects model, from the fixed parameters of mixed-effects models, and by computing mean predictions from the mixed-effects models over the distribution of random effects, respectively. Prediction errors were greater for the M and PA responses than for the OLS response, and therefore, from the prediction point of view, the use of the mixed-effects models is not recommended when an additional stem diameter measurement is not available. The mixed model with three random effects was also selected as the best model for SS estimations. Measurement of an additional stem diameter at a relative tree height of approximately 0.5 provided the best calibrations for stem diameters along the bole and total stem volume predictions. The SS approach increased the flexibility and efficiency of the selected mixed-effects model for localized predictions and thus improved the overall predictive capacity of the base model.

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 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.

Compatible taper equation for loblolly pine

1986 ◽  
Vol 16 (6) ◽  
pp. 1272-1277 ◽  
Author(s):  
J. P. McClure ◽  
R. L. Czaplewski
Keyword(s):  
Loblolly Pine ◽  
Volume Estimation ◽  
Main Stem ◽  
Stem Volume ◽  
Model Parameters ◽  
Data Set ◽  
Fit Statistics ◽  
Estimation Formula ◽  
Volume Equation ◽  
Taper Equation

Cao's compatible, segmented polynomial taper equation (Q. V. Cao, H. E. Burkhart, and T. A. Max. For. Sci. 26: 71–80. 1980) is fitted to a large loblolly pine data set from the southeastern United States. Equations are presented that predict diameter at a given height, height to a given top diameter, and volume below a given position on the main stem. All estimates are inside bark. A condition is given that forces the Cao model to be exactly compatible with any total main stem volume equation. An exact volume estimation formula is derived. Twelve benchmarks, which represent realistic utilization criteria, are used to describe expected errors in actually applying the taper equation rather than the more common fit statistics that describe errors encountered when estimating model parameters. Errors in using the fitted model are very similar to errors using Cao's estimates.

scholarly journals Accuracy of common stem volume formulae using terrestrial photogrammetric point clouds: a case study with savanna trees in Benin

2021 ◽  
Author(s):  
Hospice A. Akpo ◽  
Gilbert Atindogbé ◽  
Maxwell C. Obiakara ◽  
Arios B. Adjinanoukon ◽  
Madaï Gbedolo ◽  
...  
Keyword(s):  
Point Clouds ◽  
Stem Volume ◽  
Individual Tree ◽  
Volume Calculation ◽  
Tropical Regions ◽  
Solid Of Revolution ◽  
Taper Function ◽  
Geometric Solids ◽  
Traditional Approaches ◽  
Tree Stem

AbstractRecent applications of digital photogrammetry in forestry have highlighted its utility as a viable mensuration technique. However, in tropical regions little research has been done on the accuracy of this approach for stem volume calculation. In this study, the performance of Structure from Motion photogrammetry for estimating individual tree stem volume in relation to traditional approaches was evaluated. We selected 30 trees from five savanna species growing at the periphery of the W National Park in northern Benin and measured their circumferences at different heights using traditional tape and clinometer. Stem volumes of sample trees were estimated from the measured circumferences using nine volumetric formulae for solids of revolution, including cylinder, cone, paraboloid, neiloid and their respective fustrums. Each tree was photographed and stem volume determined using a taper function derived from tri-dimensional stem models. This reference volume was compared with the results of formulaic estimations. Tree stem profiles were further decomposed into different portions, approximately corresponding to the stump, butt logs and logs, and the suitability of each solid of revolution was assessed for simulating the resulting shapes. Stem volumes calculated using the fustrums of paraboloid and neiloid formulae were the closest to reference volumes with a bias and root mean square error of 8.0% and 24.4%, respectively. Stems closely resembled fustrums of a paraboloid and a neiloid. Individual stem portions assumed different solids as follows: fustrums of paraboloid and neiloid were more prevalent from the stump to breast height, while a paraboloid closely matched stem shapes beyond this point. Therefore, a more accurate stem volumetric estimate was attained when stems were considered as a composite of at least three geometric solids.

scholarly journals Analytical approaches for modeling tree crown volume in black wattle (Acacia mearnsii De Wild.) stands

2016 ◽  
Vol 11 (49) ◽  
pp. 4979-4989
Author(s):  
C. Cadori Guilherme ◽  
R. Sanquetta Carlos ◽  
Pellico Netto Sylvio ◽  
Behling Alexandre ◽  
Costa Junior Sergio ◽  
...  
Keyword(s):  
Tree Crown ◽  
Acacia Mearnsii ◽  
Crown Volume ◽  
Black Wattle ◽  
Analytical Approaches

scholarly journals MODELOS DE AFILAMENTO PARA Pinus elliottii EM DIFERENTES IDADES, NA REGIÃO DE CAÇADOR, SC

FLORESTA ◽  
2013 ◽  
Vol 43 (3) ◽  
pp. 439 ◽  
Author(s):  
Saulo Jorge Téo ◽  
Alan Marcon ◽  
Tiago Ehlers ◽  
Júlio César Bianchi ◽  
Adriano Peloso ◽  
...  
Keyword(s):  
Pinus Elliottii ◽  
Degree Polynomial ◽  
Stem Form ◽  
Taper Function ◽  
Different Ages ◽  
Polynomial Models ◽  
Old Trees ◽  
Taper Models ◽  
Best Estimates

Os objetivos deste trabalho foram ajustar e selecionar modelos de afilamento para estimar diâmetros a várias alturas e volume total, com e sem casca, de árvores de Pinus elliottii Engelm., na região de Caçador, SC, para estudar a forma dos fustes das árvores de diferentes idades. Ao todo, 78 árvores, com idades de 10, 18 e 27 anos, foram abatidas, cubadas rigorosamente e tiveram os seus volumes obtidos por meio do método de Smalian. Os modelos de afilamento testados foram os Polinômios de 2º e de 5º Graus e o Polinômio de Potências Fracionárias de Hradetzky. A função de afilamento que apresentou melhor desempenho para estimar o diâmetro com e sem casca ao longo do fuste das árvores foram baseadas no Polinômio de Potências Fracionárias de Hradetzky, para as idades de 10, 18 e 27 anos. O Polinômio de 2º Grau propiciou as melhores estimativas de volume total com casca para as idades de 10 e 27 anos e de volume total sem casca para as idades de 18 e 27 anos. Já o Polinômio de Potências Fracionárias apresentou melhores estimativas de volume com casca para 18 anos e de volume sem casca para árvores de 10 anos. Os fustes das árvores de Pinus elliottii apresentam melhor forma nas idades mais avançadas. AbstractTaper models for Pinus elliottii, at different ages, in the region of Caçador - SC. The research aims to fit and select taper models in order to estimate diameters at different heights and total volumes, inside and outside bark, of Pinus elliottii Engelm. trees, in the region of Caçador - SC, Brazil, as well as to analyze  behavior of stem form for trees at different ages. Altogether, 78 trees at 10, 18 and 27 years of age, had been cut and their volumes obtained by Smalian method. The taper models tested were the 2nd and 5th Degree Polynomial and the Hradetzky Polynomial of Fractioned Potencies. The best performance taper function for estimate diameters inside and outside bark throughout the stem were based on the Hradetzky Polynomial of Fractioned Potencies, for 10, 18 and 27 years of age. The 2nd Degree Polynomial provided the best estimates of outside bark volume for 10 and 27 years of age, and of inside bark volume for 18 and 27 years of age, although the Hradetzky Polynomial presented the best estimates of outside bark volume for 18 years of age and of inside bark volume for 10 years old trees. The stems of the Pinus elliottii trees present better form for the oldest tress.Keywords: Polynomial models; profile models; stem form.

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