Merchantable Volume Equations Research Articles

Improving Volume and Biomass Equations for Pinus oocarpa in Nicaragua

We present a new set of equations for tree level volume and aboveground biomass estimation for ocote pine (Pinus oocarpa Schiede ex Schltdl). These equation systems are the first developed for this species in Nicaragua. The first system includes a taper function, a merchantable volume equation, and volume equations for stem, coarse branches, and whole trees. The second system estimates whole tree and individual tree component biomass (stem wood, bark, branches, and needles). Data from 112 sampled trees were used for models’ development. Seemingly Unrelated Iterative Regression and the Generalized Method of Moments were used to simultaneously fit the volume and biomass equations systems, respectively; both methods ensure additivity and compatibility between equations. Weighted regression and a second-order continuous autoregressive error structure were used to correct heteroscedasticity and autocorrelation within the hierarchical dataset. The predictive power of the new proposed equations is higher than the currently used models for P. oocarpa in the country. These equation systems represent a scientific advancement that will enhance forest inventories, optimize timber management of the species, and facilitate accurate monitoring of forest carbon dynamics. Additionally, the new equations will contribute to a more precise accounting of CO2 emissions from the country’s forestry sector.

Total and Merchantable Volume Equations for 25 Commercial Tree Species Grown in Canada and the Northeastern United States

Accurate estimates of tree bole volume are fundamental to sustainable forest management. Total inside and outside bark and merchantable volume equations were developed for 25 major commercial tree species grown in natural stands in eastern and central Canada and the northeastern United States. Data used to develop these equations was collected from 9647 trees sampled from natural stands across the study area. The number of trees sampled varied among species. Jack pine (Pinus banksiana Lamb.) had the most observations (1648 trees) and American basswood (Tilia americana) and red oak (Quercus rubra L.) had the fewest (28 trees each). Two mathematically consistent volume equations (dimensionally compatible and combined variable) were fitted to inside and outside bark and merchantable tree volume data from these tree species. The final volume equation was selected based on fit statistics, predictive accuracy, and logical consistency. Its predictive accuracy was compared with a volume equation previously developed by Honer. Both (total and merchantable) volume equations were fitted using a nonlinear mixed-effects modelling approach. However, random effects were significant for total volumes for only four tree species. A weight (power function) was used to address heteroscedasticity in the data. The modified form of the dimensionally compatible volume equation outperformed the combined variable volume equation in terms of fit statistics and predictive accuracy and was selected as the total inside and outside bark and merchantable volume equations for all tree species. This equation produced logically consistent estimates of total and merchantable volumes and was more accurate than that previously developed by Honer to estimate volumes for most of the tree species used in this study. This new equation can be used to estimate total inside and outside bark and merchantable volumes of major commercial tree species in eastern and central Canada and the northeastern United States.

An algorithm for the automatic parametrization of wood volume equations from Terrestrial Laser Scanning point clouds: application in Pinus pinaster

ABSTRACT The parametrization of wood volume equations has traditionally been carried out with destructive samplings, which are highly resource-intensive. These equations must be specifically set up for each species and set of conditions, meaning that, in many cases, they are unfeasible or non-existent. Here, we present a nondestructive and fully automated methodology for the parametrization of merchantable volume equations from terrestrial laser scanning (TLS) data, which aims at being applicable to any species and stand typology. It is based on the estimation of diameters along the stem and the height of each tree, including a robust system for the automatic identification and correction of anomalous values. The implementation considers several types of volume equations, the most suitable equation being selected and parameterized using the diameter and height estimations. The methodology was tested in a Pinus pinaster plot with 428 trees, steep slopes, low branches and dense understory. The results showed that 97% of trees were automatically detected, and RMSE of the height and diameter estimations was 1.52 m and 1.14 cm, respectively. A volume ratio equation was automatically selected as the best option for the test dataset. RMSE in automatic volume estimations was 0.0233 m3, and 0.0149 m3 using diameters reviewed by an operator.

Cumulative Merchantable Stem Volume Equations for Poplar Plantations on Farmland in Sweden

Cumulative Merchantable Stem Volume Equations for Poplar Plantations on Farmland in Sweden

Ahusamiento y volumen comercial de pinos tropicales en plantaciones forestales de Veracruz, México

En los últimos años, en el sureste de México se han establecido plantaciones forestales de Pinus caribaea, que tienen como propósito la extracción de resina y la producción de madera. Ambas variables se han correlacionado positivamente con características morfológicas como la forma del fuste. Generalmente, para la descripción del perfil fustal se utilizan dos expresiones: factor de forma y ahusamiento. En este sentido, el objetivo del presente estudio fue construir un sistema de cubicación para estimar el ahusamiento y el volumen comercial de tres progenies de pinos tropicales establecidos en una plantación forestal en las Choapas, Veracruz, México, así como evaluar sus diferencias en la geometría del fuste a través de enfoque de variables indicadoras. Por medio del modelo de la variable combinada lineal y la utilización de variables indicadoras, se analizó el efecto de la procedencia en el factor de forma, encontrándose que el híbrido entre Pinus caribaea y Pinus elliotti presenta una geometría cercana al paraboloide. Se probaron diferentes modelos de ahusamiento, de los cuales, el de Demaerschalk presentó el mejor ajuste y, a partir de su integración matemática, se derivó una ecuación de volumen comercial variable, que se ajustó de manera simultánea con la de ahusamiento para generar un sistema compatible de ahusamiento-volumen comercial. Los resultados indican que el híbrido es superior en la geometría del fuste y en el volumen comercial maderable frente a las otras dos procedencias de Pinus caribaea.

Compatible taper-volume systems for major tropical species in Mexico

A compatible system consisting of stem taper, merchantable-, stem-, branch-and stem and coarse branch tree volume equations was developed for 11 major tropical species in southeast Mexico. A database corresponding to 6187 felled trees was used to develop the system of equations. Iterative seemingly unrelated regression was used to fit the system in two steps: The stem volume, branch volume and stem and coarse branch tree volume equations were first fitted simultaneously and the common estimated parameters were substituted in the stem taper and merchantable volume equations. In the second step, the remaining parameters were estimated by fitting the stem taper and merchantable volume equations simultaneously. Weighted regression and a second order autoregressive model were used in the model fitting to account for heteroscedasticity and autocorrelation. To assess whether the compatible system differs between ecoregions for the same species, a system with the same set of parameters for all the ecoregions was compared with a system with a different set of parameters for each ecoregion. The results of the comparisons indicated the need to fit a different system for each ecoregion and species. The proposed equations can be used to estimate stem-, branch-and merchantable volume at any upper diameter and height, as well as stem and coarse branch tree volume. If classification of the products by merchantable sizes is not required, the stem and coarse branch volume equation is preferred, thereby simplifying the calculations and making it more suitable for practical purposes.

Taper and Volume Systems Based on Ratio Equations for Pinus pseudostrobus Lindl. in Mexico

Studies on functional relationships between relative stem diameter and height to estimate timber yield are useful in the management of commercial forest plantations. With taper analysis data of 42 Pinus pseudostrobus Lindl. trees in the indigenous community of Nuevo San Juan Parangaricutiro , Michoacan, Mexico, six compatible systems for predicting taper (d), merchantable volume (Vm), stem volume (Vs), total tree volume (Vt) and branch volume (Vb) were fitted and evaluated. The compatible taper and merchantable volume equations were based on volume ratio equations. Three Vs equations were tested in each system. In general, the compatible systems presented statistical accuracy in the d, Vm, Vs and Vt components but were less accurate in Vb. Three compatible systems were selected, according to their more efficient goodness-of-fit statistics, and a different total volume equation was incorporated into each system. The compatible systems based on volume ratio equations are simple, reliable tools for estimation of stand timber stocks and product classification of P. pseudostrobus in commercial forest plantations in Mexico.

Estimating upper stem diameters and volume of Douglas-fir and Western hemlock trees in the Pacific northwest

BackgroundVolume and taper equations are essential for obtaining estimates of total and merchantable stem volume. Taper functions provide advantages to merchantable volume equations because they estimate diameter inside or outside bark at specific heights on the stem, enabling the estimation of total and merchantable stem volume, volume of individual logs, and a height at a given diameter.MethodsUsing data collected from 1218 trees (1093 Douglas-fir (Pseudotsuga menziesii (Mirbel) Franco) and 125 western hemlock (Tsuga heterophylla)), we evaluated the performance of one simple polynomial function and four variable-exponent taper functions in predicting upper stem diameter. Sample trees were collected from different parts of the states of Oregon, Washington, and California. We compared inside-bark volume estimates obtained from the selected taper equation with estimates obtained from a simple logarithmic volume equation for the data obtained in this study and the equations used by the Forest Inventory and Analysis program in the Pacific Northwest (FIA-PNW) in the state of California and western half of the states of Oregon and Washington.ResultsVariable exponent taper equations were generally better than the simple polynomial taper equations. The FIA-PNW volume equations performed fairly well but volume equations with fewer parameters fitted in this study provided comparable results. The RMSE obtained from taper-based volume estimates were also comparable with the RMSE of the FIA-PNW volume equations for Douglas-fir and western hemlock trees respectively.ConclusionsThe taper equations fitted in this study provide added benefit to the users over the FIA-PNW volume equations by enabling the users to predict diameter at any height, height to a given diameter, and merchantable volume in addition to cubic volume including top and stump (CVTS) of Douglas-fir and western hemlock trees in the Pacific Northwest. The findings of this study also give more confidence to the users of FIA-PNW volume equations.

New Variable-Top Merchantable Volume and Weight Equations Derived Directly from Cumulative Relative Profiles for Loblolly Pine

New Variable-Top Merchantable Volume and Weight Equations Derived Directly from Cumulative Relative Profiles for Loblolly Pine

New Variable-Top Merchantable Volume and Weight Equations Derived Directly from Cumulative Relative Profiles for Loblolly Pine

New Variable-Top Merchantable Volume and Weight Equations Derived Directly from Cumulative Relative Profiles for Loblolly Pine

Development of a Compatible Taper Function and Stand-Level Merchantable Volume Model for Chinese Fir Plantations.

Chinese fir (Cunninghamia lanceolata [Lamb.] Hook) is one of the most important plantation tree species in China with good timber quality and fast growth. It covers an area of 8.54 million hectare, which corresponds to 21% of the total plantation area and 32% of total plantation volume in China. With the increasing market demand, an accurate estimation and prediction of merchantable volume at tree- and stand-level is becoming important for plantation owners. Although there are many studies on the total tree volume estimation from allometric models, these allometric models cannot predict tree- and stand-level merchantable volume at any merchantable height, and the stand-level merchantable volume model was not seen yet in Chinese fir plantations. This study aimed to develop (1) a compatible taper function for tree-level merchantable volume estimation, and (2) a stand-level merchantable volume model for Chinese fir plantations. This “taper function system” consisted in a taper function, a merchantable volume equation and a total tree volume equation. 46 Chinese fir trees were felled to develop the taper function in Shitai County, Anhui province, China. A second-order continuous autoregressive error structure corrected the inherent serial autocorrelation of different observations in one tree. The taper function and volume equations were fitted simultaneously after autocorrelation correction. The compatible taper function fitted well to our data and had very good performances in diameter and total tree volume prediction. The stand-level merchantable volume equation based on the ratio approach was developed using basal area, dominant height, quadratic mean diameter and top diameter (ranging from 0 to 30 cm) as independent variables. At last, a total stand-level volume table using stand basal area and dominant height as variables was proposed for local forest managers to simplify the stand volume estimation.

Total Stem and Merchantable Volume Equations of Norway Spruce (Picea abies (L.) Karst.) Growing on Former Farmland in Sweden

An equation was constructed to estimate the stem volume of Norway spruce (Picea abies (L.) Karst.) in 145 stands growing on former farmland in Sweden (Latitude 56–63° N). The mean total age was 40 ± 13 (range 17–91) years, the mean diameter at breast height (ob) was 15 ± 4 (range 5–27) cm and the mean density was 1621 ± 902 (range 100–7600) stems ha−1. The equation which fits the data best used the diameter at breast height and total stem height as predictive variables. Merchantable volume equations for the estimation of commercial volume for any top diameter and bole length were developed. Soil types in the stands were sediments (coarse sand, fine sand and silt and heavy, medium and light clay), tills (sandy, fine sandy and silty) and peat. The standing volume was calculated; the mean was 253 ± 103 (range 26–507) m3 ha−1 with a MAI (mean annual increment) of 6.9±3.5 (range 1.3–16.7) m3 ha−1 year−1. There were statistically significant differences between MAI and coarse sand, sand and silt, light clay, peat and silty till soils. Spruce stands growing on silty tills had the lowest MAI (4.94 ± 2.27 m3 ha−1 year−1) and light clay, fine sand and silt and peat the highest (7.62 ± 4.24, 7.46 ± 3.33 and 8.67 ± 2.83 m3 ha−1 year−1).

Stem taper function for sweet chestnut (Castanea sativa Mill.) coppice stands in northwest Spain

Despite the economic importance of Castanea sativa Mill. in northwest Spain, studies of its growth and yield are practically non-existent. A compatible system formed by a taper function, a total volume equation, and a merchantable volume equation was developed for chestnut (C. sativa Mill.) coppice stands in northwest Spain. Data from 203 destructively sampled trees were used for the adjustment. Outliers were removed with a non-parametric local adjustment, providing a final data set of measurements taken from 3,188 sections which was used to test five taper models (compatible and non-compatible). A second-order continuous autoregressive error structure was used to model the error term and account for autocorrelation. Presence of multicollinearity was evaluated with the condition number. Comparison of the models was carried out using overall goodness-of-fit statistics and graphical analysis. Results show that the models developed by Fang et al. in For Sci 46: 1–12, 2000 and Kozak in For Chron 80, N 4: 507–515, 2004 were superior to other equations in predicting diameter for chestnut coppice stands. The compatible volume system developed by Fang et al. in For Sci 46: 1–12, 2000 was finally selected as it provided the best compromise between describing stem profile and also estimating merchantable height, merchantable volume, and total volume and therefore provides the first specific tool for more effective management of chestnut coppice stands.

Total and Merchantable Volume Equations for Tectona grandis Linn. f. Plantations in Karnataka, India

Tectona grandis (teak) is one of the most important timber species worldwide and India is one of the major teak growing countries. Though some volume equations were developed in the past in India, merchantable volume equations (any top diameter or bole length) are not available. Moreover, the models developed were neither quantitatively and qualitatively evaluated nor validated with independent data sets. Hence, the objective of this study was to develop appropriate volume equations to predict total tree volume and merchantable volume for teak in Karnataka. Linear and non-linear equations were used to model the relationship of the volume with respect to diameter at breast height (dbh) and total height. Merchantable volume equations for estimating merchantable volume to any minimum top diameter or bole length have also been constructed. The equations tested mostly fitted well to the data. Other models developed elsewhere tended to underestimate the volume, especially at dbh ≥ 23 cm. The geometric cylinder volume equation, in combination with a stem form factor of .40, is widely used for teak in Karnataka but they were found to be less precise compared to regression equations when applied to the present data set. Model validation indicated that models should be calibrated with local data for greater accuracy in the prediction.

Variable-top merchantable volume equations for Scots pine (Pinus sylvestris) and Sitka spruce (Picea sitchensis (Bong.) Carr.) in Northern Britain

Summary In this study, data collected from stands in Scotland and Northern England were used to develop variable-top merchantable volume equations for plantation-grown Scots pine (Pinus sylvestris) and Sitka spruce (Picea sitchensis). After fitting and evaluating a number of total volume and volume ratio equations, the Schumacher and Hall (1933) equation (Schumacher, F.X. and Hall, F.S. 1933 Logarithmic expression of timber tree volume. J. Agric. Res. 47, 719–734) gave the best results for total volume, while the Van Deusen et al. (1981) and Cao and Burkhart (1980) models (Van Deusen, P.C., Sullivan, A.D. and Matney, T.G. 1981 A pre diction system for cubic foot volume of loblolly pine applicable through much of its range. South. J. Appl. For. 5, 186–189; Cao, Q.V. and Burkhart, H.E. 1980 Cubic-foot volume of loblolly pine to any height limit. South. J. Appl. For. 4, 166–168) gave the best fits for volume ratio equations to variable-top diameter and height limits, respectively. Variable-top merchantable volume equations were jointly estimated as a product of total volume and volume ratio equations. The final models, obtained using a non-linear mixed-effects modelling approach, showed considerable improvements compared with their fixed-effects counterparts. Even though further modelling of serial correlation using a banded toeplitz error structure improved model fits, it also led to an increase in the residual variance of the models and could degenerate the predictive ability of the models. We therefore recommend the use of mixed models with simple ‘iid’ error structure. However, in situations where additional data are not available to predict the random effects, we recommend the use of the models based on non-linear least squares.

Total and Merchantable Wood Volume Equations for Eucalyptus hybrid Trees in Gujarat State, India

Eucalyptus hybrid is one of the most important tree species adopted for large-scale commercial plantations by State Forest Departments, nongovernmental organizations (NGOs), and farmers in India. But accurate volume equations are not available. The aim of this study was to develop equations for predicting individual tree total volume and merchantable volume for E. hybrid. A total of 114 trees with ages between 1 and 19 yr and breast height diameter (dbh) between 4.7 and 33.1 cm were felled for model fitting and analysis. Linear and nonlinear equations were used to model the relationship of total volume with dbh, and with dbh and total height of the trees. Merchantable volume equations for estimating merchantable volume to any minimum bole height are also presented. For this, diameters were measured at different heights along the stem including height to the base of crown. The equations tested fitted the data well. The adjusted R2 and root mean squared error indicated that for estimation of V0 from dbh, and from dbh and total height, non-linear equations performed better. These equations may also be recommended for use because of their simplicity and ease of use in the field. In general, nonlinear models only with diameter and with diameter & height overestimated total volume with a mean difference between measured and predicted values of 0.48% and 0.15%, respectively. The variable top-height volume equation tended to underestimate the merchantable volume with an average difference of 1.74% between measured and predicted volume. Model validation with an independent data set indicated that for greater accuracy models should be calibrated with local data. Based on the model validation with sample data and on the models biological logic (volume depends on tree diameter as well as on height), model incorporating diameter as well as height was considered to be more appropriate for general volume estimations.

Compatible taper function for Scots pine plantations in northwestern Spain

A compatible system for estimation of individual tree volume was developed for Scots pine (Pinus sylvestris L.) in northwestern Spain. The system comprises a merchantable volume equation, a total volume equation, and a taper function. The use of the volume equation allows rapid estimation of tree volume, and stand volume by summing individual tree volumes, which is equal to the volume obtained by integrating the taper equation. The volume equation is very easy to use and is therefore preferred when classification of the products by merchantable sizes is not required. Data from 228 destructively sampled trees were used for model development. Fourteen compatible volume equations were evaluated, 13 of these equations were taken from the available literature, and the other was developed in the present study. A modified second-order continuous autoregressive error structure was used to correct the autocorrelation of the hierarchical data used. The model developed by Fang et al. (Z. Fang, B.E. Borders, and R.L. Bailey. 2000. For. Sci. 46: 1–12) best described the data. There model is therefore recommended for the estimation of diameter at a specific height, merchantable volume, and total volume of Scots pine stems in the area of study.

Parsimonious and Completely Compatible Taper, Total, and Merchantable Volume Models

Abstract A parsimonious and compatible system of taper, total, and merchantable volume equations sharing a common vector of three parameter estimates was derived from Clark and Saucier's (1990) volume ratio model. Clark and Saucier's model expresses volume inside bark as a function of outside bark diameter and is itself not compatible with the derived taper equation. To ensure compatibility, models were fit to express volume outside bark as functions of diameter outside bark. By constraining the limits of integration of the taper function to go from the tip to groundline diameter, a completely compatible system of taper, total, and merchantable volume equations were developed. Systems of equations were fit using nonlinear seemingly unrelated regressions with nonlinear cross-equation constraints to account for contemporaneous correlations in the data. The system fit was found to account for at least 96% of the variation in diameter outside bark, total, and merchantable outside bark volume. FOR. SCI. 51(6):578–584.

Dendrometria de espécies nativas em plantios homogêneos no estado de Roraima: andiroba (Carapa guianensis Aubl), castanha-do-Brasil (Bertholletia excelsa Bonpl.), ipê-roxo (Tabebuia avellanedae Lorentz ex Griseb) e jatobá (Hymenaea courbaril L.)

Estudou-se o crescimento e a seleção de equações para quatro espécies florestais nativas visando identificar espécies promissoras para o plantio em programas de reflorestamentos e em sistemas agroflorestais no Estado de Roraima. O crescimento da andiroba (Carapa guianensis Aubl.), da castanha-do-brasil (Bertholletia excelsa Bonpl.), do ipê-roxo (Tabebuia avellanedae Lorentz ex Griseb.) e do jatobá (Hymenaea courbaril L.), aos sete anos de idade, mostrou-se promissor atingindo incrementos médios anuais em volume comercial de 6.3; 14.6; 6.0 e 2.3 m³.ha-1.ano-1, respectivamente. Em relação ao crescimento em diâmetro, todas as espécies apresentaram incrementos médios anuais em diâmetro maiores do que 1 cm, sendo superiores aos observados para árvores crescendo em florestas naturais. A análise estatística, indicou a equação hipsométrica de Prodan como a de melhor ajuste para estimar a altura em função do diâmetro para as quatro espécies analisadas. No entanto, a análise gráfica indicou que a forma da curva altura/diâmetro variou com a espécie sendo necessário o ajuste em separado. O ajuste de equações de volume comercial com casca e fator de forma comercial mostraram ser necessário o ajuste de diferentes equações em função da espécie. A análise gráfica das curvas de volume comercial e fator de forma indicaram que as espécies diferiram em ambos os parâmetros, indicando que a utilização de um fator de forma médio para todas as espécies deve ser evitado, como forma de aumentar a precisão nas estimativas volumétricas.

Comparing stem taper functions and analysis the taper ratio of three poplar clones (Populus x euramericana) in Navarre

The present work analyzes three stem taper functions on three clones of Populus x euramericana (Canadá Blanco, I-214 and MC) in Navarre to elaborate a merchantable volume equation. To minimize the effect of the autocorrelation a continuous autoregressive error structure CAR(2) or CAR(3), depending the clone analyzed, is used. On the other hand, the local form exponent of the three clones is compared by two methods: the analysis of variance of the individual estimation of the local form exponent, and contrasting the maximum likelihood statistic between adjustments. The Canadá clone is the more conical clone of the three clones analyzed. The data come from 143 poplars in even-aged stands with the same frame of plantation (real frame at 4,5 × 4,5 m).