Compatible Taper Equations Research Articles

Developing fully compatible taper and volume equations for all stem components of Eucalyptus globoidea Blakely trees in New Zealand

Background: Individual-tree taper and volume equations are essential for forest management. They provide estimates of volume that are incorporated into plot-level volume equations and also into growth and yield models to estimate volumes per hectare in forest crops. Moreover, taper equations allow forest managers to estimate dimensions of logs that can be cut from stems in their forests when they have measured diameters at breast height and heights of trees in inventories. Compatible taper and volume equations have the property that the same individual tree volume can be estimated either from the tree volume equation or by integrating the taper equation. Durable eucalypt species such as Eucalyptus globoidea Blakely, however, have especially valuable heartwood and so managers require estimates of the volumes and shapes of heartwood zones within trees. Simple overall wood taper and volume equations would therefore be inadequate. Methods: 74 Eucalyptus globoidea trees were destructively sampled in 8 different trial plots throughout New Zealand. Tree ages were 7 to 29 years old, the DBHs were 11 to 67.6 cm and the heights were 7.2 to 35.4 m. All trees were felled and lengths and taper diameters outside bark were measured. To measure taper diameters of heartwood and sapwood, discs were cut at irregular intervals along the stems. Heartwood and sapwood components were identified by applying methyl orange dye and quantified using image analysis. In this study we extended compatibility so that sums of estimated volumes of separate components of stems, bark, sapwood and heartwood, would equal overall tree volume estimates. In addition, taper equations were made for outside bark, inside bark and heartwood that were compatible with their respective volume equations. Parameters of five volume equations for whole stem, whole wood, bark, sapwood, and heartwood were simultaneously estimated. Compatible taper equations for whole stem, stem wood and heartwood were estimated so that they were compatible with the volume equations, thereby creating a fully compatible system. Results: Root mean squared error (RMSE) of volume models were 0.1248298 m3 for heartwood, 0.05496807 m3 for sapwood, 0.1539625 m3 for wood inside bark, 0.1108201 m3 for bark and 0.1439786 m3 for wood including bark. RMSE of taper models was 2.572765 cm for heartwood, 2.348552 cm for wood inside bark and 2.474088 cm for wood including bark. Conclusions: A compatible system of multiple taper and volume equations can be fitted through the simultaneous fitting of parameters with minimal bias and precision levels of ± 0.055-0.154 m3 for volume equations and ± 2.35 to 2.57 cm for taper equations. Leave-one-out cross-validation of the fitted models yielded very similar levels of precision and bias to those encountered when fitting models with the entire dataset.

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

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.

Development of compatible taper equations for brutian pine stands in Asar Forest Sub-district

Bu çalışmada, Antalya Orman Bölge Müdürlüğü, Antalya Orman İşletme Müdürlüğü, Asar İşletme Şefliği sınırları içinde yayılış gösteren kızılçam (Pinus brutia Ten.) meşcereleri için geliştirilen uyumlu gövde çapı denklemlerinin gövde çapını modellemedeki başarıları karşılaştırılmıştır. Bu amaçla, Max and Burkhart (1976), Jiang vd. (2005) ve Kozak (1988)’ın denklemi esas alınarak geliştirilen 3 denklemin oluşturduğu 5 farklı model kullanılmıştır. Başarı ölçütlerine göre yapılan karşılaştırmada, Jiang vd. (2005) tarafından geliştirilen denklemin %95.95’lik açıklayıcılığı ile kızılçamın gövde çapı gelişimlerini modellemede daha başarılı olduğu görülmüştür. Jiang vd. (2005) denkleminin uygunluğu, bağımsız bir veri grubu kullanılarak iki eş arasındaki farkın önemlilik testi ile test edilmiş ve p<0.05 önem düzeyinde denklemin çalışma alanına uygulanabileceği sonucuna varılmıştır. Bu bakımdan, bu denklemin kızılçam meşcerelerinde daha doğru ve tutarlı gövde çapı tahminlerinin yapılmasına imkan sağlayacağı söylenebilir.

Deriving compatible taper functions from volume ratio equations based on upper-stem height

A very common model for prediction of tree stem volumes to upper-stem height or diameter limits is the use of a merchantable to total volume ratio function multiplied by a total stem volume function. Many users of these prediction systems also desire taper equations that can predict heights to upper-stem diameters. While taper equations compatible with volume ratio equations have been used for many years, compatible taper equations from volume ratio equations that are functions of upper-stem height have been used infrequently. Yet many studies have indicated that height-based ratio equations perform well and frequently have statistics of fit that are comparable with diameter-based volume ratio equations. Compatible taper equations derived from height-based ratio equations are presented here. The methodology that uses height-based merchantable to total volume ratios does not require the solution of a differential equation after differentiating the height-based volume ratio, as is necessary when using the method of deriving taper equations from diameter-based merchantable to total volume ratios. This could be an advantage depending on the complexity of the ratio function. Example taper equations fitted to loblolly pine (Pinus taeda L.) data from the southeastern USA and the state of Oklahoma, USA, indicate good fit to these data, whether fitted directly to taper data or implicitly by using parameters fitted to volume ratio data.

Volume and Taper Equations for P. taeda (L.) and E. grandis (Hill ex. Maiden)

We compared several taper and volume equations with emphasis in testing the suitability of compatible taper equations, so that they can be used in forest inventories or decision support systems. We used data from 863 and 932 trees of Pinus taeda and Eucalyptus grandis respectively, collected from the Departments of Rivera, Tacuarembó, Paysandú, and Río Negro in Uruguay. In general, rankings of the candidate models were consistent for both species. For volume estimation the most accurate equations were the models presented by Clutter et al. (1983) and Schumacher and Hall (1933) for P. taeda and E. grandis respectively, while for describing stem profiles the most accurate model was a variable exponent equation presented by Muhairwe (1999) and modified by Methol (2001). The best compatible taper equation tested remained in an intermediate ranking position, but represented a satisfactory option for foresters seeking to use the advantages of this class of equations.

Comparison of model forms for estimating stem taper and volume in the primary conifer species of the North American Acadian Region

• The performance of ten commonly used taper equations for predicting both stem form and volume in balsam fir [ Abies balsamea (L.) Mill], red spruce[ Picea rubens (Sarg.)], and white pine[ Pinus strobus (L.)] in the Acadian Region of North America was investigated.• Results show that the Kozak () and Bi () equations were superior to the other equations in predicting diameter inside bark for red spruce and white pine, while the Valentine and Gregoire () equation performed slightly better for balsam fir.• For stem volume, the Clark et al. () equation provided the best predictions across all species when upper stem diameter measurements were available, while the Kozak () and compatible taper equation of Fang et al. () performed well when those measurements were unavailable.• The incorporation of crown variables substantially improved stem volume predictions (mean absolute bias reduction of 7–15%; root mean square error reduction of 10–15%) for all three species, but had little impact on stem form predictions.• The best taper equation reduced the predicted root mean square error by 16, 39, and 45% compared to estimates from the widely used Honer (1965) regional stem volume equations for balsam fir, red spruce, and white pine, respectively.• When multiple taper equations exist for a certain species, the use of the geometric mean of all predictions is an attractive alternative to selecting the “best”equation.

Scaling Taper Relationships from Miniature-Scale to Operational-Scale Stands of Loblolly Pine

Abstract Taper relationships for trees grown in miniature- and operational-scale stands of loblolly pine were established using stem analysis data from 106 and 173 trees, respectively. Tree taper was modeled using segmented polynomial and dimensionally compatible taper equations. The relationship was then scaled from miniature to operational scale using the profiles obtained from these taper equations. Stump diameter was used in the taper equations instead of dbh in scaling the relationship. A simple linear regression equation described well the taper relationship between trees grown at miniature and operational scales. The fit statistics for both the segmented polynomial and dimensionally compatible taper equations were comparable at both scales. In terms of predictive accuracy, however, the segmented polynomial taper equation was superior to the dimensionally compatible taper equation in scaling the taper relationship for trees from miniature- to operational-scale plots.

Compatible volume-taper equations for predicting merchantable volume to variable merchantable limits for &lt;i&gt;Cupressus lusitanica&lt;/i&gt;, Ethiopia

Compatible systems of merchantable total tree cubic volume and stem taper equations are derived by integrating an existing volume equation. The systems are developed to yield volume at any merchantable length, total volume and for any merchantable top diameter. It is also demonstrated that the most common types of volume equation can be converted to compatible taper equation. Key words/phrases: Merchantable volume, compatible volume, taper equations SINET: Ethiopian Journal of Science Vol. 28 (1) 2005: 15–22

Variable-exponent taper equations for jack pine, black spruce, and balsam fir in eastern Canada

A variable-exponent taper equation was developed for jack pine ( Pinus banksiana Lamb.), black spruce ( Picea mariana (Mill.) B.S.P.) and balsam fir ( Abies balsamea (L.) (Mill.)) trees grown in eastern Canada. The equation was derived from the dimensionally compatible taper equation. Stem analysis data from several of Forintek’s research projects on these tree species grown across eastern Canada were used to fit the taper equation, and the equation was then evaluated with independent data collected by Forintek and other organizations in eastern Canada. The taper equation presented in this paper was superior to the segmented polynomial, variable-exponent, and variable-form taper equations developed for different tree species in estimating diameters along the bole. Moreover, stand density or thinning effect on the taper of these tree species was examined, and the taper equation was modified in order to incorporate this effect.

Compatible taper equation for loblolly pine

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.

Integrated Systems for the Estimation of Tree Taper and Volume

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.

Converting Volume Equations to Compatible Taper Equations

Converting Volume Equations to Compatible Taper Equations