FORM FACTORS AND VOLUME MODELS FOR ESTIMATING TREE BOLE VOLUME OF MAHOGANY AT COMMUNITY FORESTS IN CENTRAL JAVA

Form factors and volume models are often be used in the estimation of tree volumes. However, a few studies have developed and evaluated the accuracy of form factors and volume models for estimating tree volumes of community forests. This study aimed to formulate form factors and volume models and assess their prediction accuracy for estimating tree bole volumes of mahogany at community forests in Central Java. This study used 120 sample trees with diameters of 6–38 cm to formulate artificial and absolute form factors and to develop tree bole volume models. These form factors coupled with bole height and total height were used in simple volume equations. Regression analyses were used to develop volume models using the diameter and total height as predictors. The simple volume equations and volume models' prediction accuracy was evaluated using a cross-validation dataset and independent dataset (30 sample trees). The artificial form factor (0.68 ± 0.11) of mahogany, which was higher than the absolute form factor (0.46 ± 0.09), provided accurate estimates of tree bole volumes when it was used with the bole height instead of the total height. The volume model that uses diameter and total height produced the most accurate estimates, while the volume model that uses diameter alone provided the most practical yet reliable tool for estimating tree bole volumes of mahogany. The results of this study are useful for improving community forest management.

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.

Form Factor of Eucalyptus Saligna Species in a Commercial Forest Plantation

The present investigation proposes to determine the form factor of the species Eucalyptus saligna in a commercial forest plantation of the Tambillo bajo sector, of the Colta canton, Chimborazo province. For this purpose, 100 individual specimens with straight shafts and without bifurcations were taken as a sample, and each individual’s commercial and total height, diameter at breast height, and diameters along the stem were measured, to determine the real volume of the wood using the Smalian and Newton formulas, the graphical method, and with a form factor of 0.70. Based on the measured data, a comparative analysis of the calculation of real volume by the method used was performed; the results obtained showed significant differences between calculation methods. In addition, five potential volume equations that presented the highest adjusted coefficient of determination and the lowest mean square error were selected. To verify the commercial volume calculated with the estimated form factors against the volume equations, the commercial volume was recalculated based on the form factors and equations found. The calculation of the commercial volume by the Smalian formula is taken as the exact value, and the other methods are taken as approximated values. Keywords: dasometry, form factor, forest plantation, volumen equations, commercial volume. Resumen La presente investigación propone: determinar el factor de forma de la especie Eucalyptus saligna en una plantación forestal comercial; para lo cual se toma como muestra 100 individuos con fustes rectos y sin bifurcaciones, a cada individuo se midió la altura comercial y total, diámetro a la altura del pecho y diámetros a lo largo del fuste, para determinar el volumen real de madera utilizando la fórmula de Smalian, Newton, método gráfico y con un factor de forma de 0,70. En base a los datos medidos, se realiza un análisis comparativo del cálculo de volumen real por método empleado, los resultados obtenidos mostraron diferencias significativas entre métodos de cálculo empleados. Además, se seleccionó 5 ecuaciones de volumen potenciales los cuales presentaron mayor coeficiente de determinación ajustado y menor error cuadrático medio. Para la verificación del volumen comercial calculado con los factores de forma estimados frente a las ecuaciones de volumen se vuelve a calcular el volumen comercial a partir de los factores de forma y ecuaciones encontrados, se toma como valor exacto el cálculo de volumen comercial por la fórmula de Smalian y como valor de aproximación los demás métodos. Palabras clave: dasometría, ecuaciones de volumen, factor de forma, plantación forestal, volumen comercial.

USE OF QUANTILE REGRESSION AND RANSAC ALGORITHM IN FITTING VOLUME EQUATIONS UNDER THE INFLUENCE OF DISCREPANT DATA

The objective of this study was to evaluate three estimation methods to fit volume equations in the presence of influential or leverage data. To do so, data from the forest inventory carried out by the Centro Tecnológico de Minas Gerais Foundation were used to fit the Schumacher and Hall (1933) model in its nonlinear form for Cerradão forest, considering the quantile regression (QR), the RANSAC algorithm and the nonlinear Ordinary Least Squares (OLS) method. The correlation coefficient ( ) between the observed and estimated volumes, root-mean-square error (RMSE), as well as graphical analysis of the dispersion and distribution of the residuals were used as criteria to evaluate the performance of the methods. After the analysis, the nonlinear least squares method presented a slightly better result in terms of the goodness-of-fit statistics, however it altered the expected trend of the fitted curve due to the presence of influential data, which did not happen with the QR and the RANSAC algorithm, as these were more robust in the presence of discrepant data.

Compatible Taper and Volume Systems Based on Volume Ratio Models for Four Pine Species in Oaxaca Mexico

Estimating tree volume components is an essential element in sustainable forest management. Compatible taper and merchantable outside-bark volume systems based on volume ratio models were globally fitted to four pine species (reduced models) with the aim to select the best reduced model and to fit it with dummy variables and additive effects using Pinus pseudostrobus Lindl as a base species. The study was carried out in the northern mountains of Oaxaca, Mexico. To fit the taper, merchantable volume, stem volume, branch volume, and total tree volume (stem volume and branch volume) equations, a taper dataset of 222, 230, 245, and 333 trees of Pinus douglasiana Martínez (Pd), Pinus oaxacana Mirov (Po), Pinus patula Schltd (Pp), and Pinus pseudostrobus Lindl (Pps), respectively, was used. In general, the compatible systems explained more than 97% in the observed variability for the four studied components: outside-bark diameter (d), merchantable outside-bark volume (Vm), stem outside-bark volume (Vs), and total tree volume (Vt). Alternatively, more than 52% of the observed variability for branch volume (Vb) was also explained. The developed compatible systems based on volume ratio models are a simple and consistent alternative for estimating the outside-bark diameter and variable outside-bark volume, as well as the components of commercial species for uneven-age and mixed-species forests in Oaxaca, Mexico.