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Taper equations are indispensable tools for characterizing the stem profile of trees, providing valuable insights for forest management, timber inventory, and optimal assortments allocation. The recent progress in Terrestrial Laser Scanning (TLS) has revolutionized forest inventory practices by enabling non-destructive data collection. In this study, four taper models from three different model categories were established based on point cloud data of 219 Pinus nigra trees. The taper equations fitted with TLS data were used to predict the diameter at specific stem heights and the total stem volume. The results show that among fitted models, the Max and Burkhart segmented model calibrated by the means of a mixed-effects approach provided the best estimate of the diameter at different heights and the total stem volume evaluated for different diameter at breast height (DBH) classes. In numerical terms, this model estimated the diameter and the volume with a respective overall error of 0.781 cm and 0.021 m3. The predicted profile also shows that above a relative height of 0.7, the diameter error tends to increase due to the low reliability of data collected beyond the base of the crown primarily caused by interference from branches and leaves. Nevertheless, this study shows that TLS technology presents a compelling opportunity and a promising non-destructive alternative for generating taper profiles and estimating tree volume.

As a complement to traditional estimates of stem dimensions from numerical models, terrestrial light detection and ranging (Lidar) provides direct stem diameter and volume values using cylindrical models constructed from point clouds. This study used two approaches to estimate total stem volume using Lidar and compared them with two empirical equations, one used by the Forest Inventory Analysis in the Pacific Northwest (FIA-PNW) and one based on a taper equation. We fitted point clouds of 10 Douglas-fir with three sets of cylinder models that are distinguished by their segment length (i.e. 0.5 m, 1 m, and 2 m), then developed three taper equations based on the point-cloud-based diameter estimated previously. We estimated the total stem volume of the tree with eight models: six-point cloud-based (i.e. three taper and three cylinders) and two empirical. Finally, we used simulations to extrapolate the volume estimations of various methods for different diameters at breast height (DBH) classes. We found that all the point-cloud-based taper equations were similar in their performance (R2=0.94, RMSE = 4.6 cm) and produced mean volume estimates greater than mean estimates of the existing models. The cylinder models produced 11–16% greater mean volume estimates than the FIA-PNW estimate, with the 0.5 m segment length producing the greatest values, followed by the 1 m and 2 m segment length. The simulated data suggested that the mean volume estimates of a given DBH class are different when using different computation methods. ANOVA revealed a combined effect of the computation methods and the DBH class on the mean volume estimates. We conclude that the point-cloud-based taper equations, after being symmetrically calibrated, would be consistent with the regional stem volume estimates, whereas the cylinder models would be better in estimating individual stem volume. When constructing Lidar-based cylinder models in future applications, cylinder segment length would need to be adjusted to the length and DBH of the stem, as well as to the objectives of the research.

The diameter at breast height (DBH) is the most important independent variable in biomass allometry models based on metabolic scaling theory (MST) or geometric theory. However, the fixed position DBH can be misleading in its use of universal scaling laws and lead to some deviation for the biomass model. Therefore, it is still an urgent scientific problem to build a high-precision biomass model system. A dataset of 114 trees was destructively sampled to obtain dry biomass components, including stems, branches, and foliage, and taper measurements to explore the applicability of biomass components to allometric scaling laws and develop a new system of additive models with the diameter in relative height (DRH) for each component of a Larch (Larix principis-rupprechtii Mayr) plantation in northern China. The variable exponential taper equations were modelled using nonlinear regression. In addition, applying nonlinear regression and nonlinear seemingly unrelated regression (NSUR) enabled the development of biomass allometric models and the system of additive models with DRH for each component. The results showed that the Kozak's (II) 2004 variable exponential taper equation could accurately describe the stem shape and diameter in any height of stem. When the diameters in relative height were D0.2, D0.5, and D0.5 for branches, stems, and foliage, respectively, the allometric exponent of the stems and branches was the closest to the scaling relations predicted by the MST, and the allometric exponent of foliage was the most closely related to the scaling relations predicted by geometry theory. Compared with the nonlinear regression, the parameters of biomass components estimated by NSUR were lower, and it was close to the theoretical value and the most precise at forecasting. In the study of biomass process modelling, utilizing the DRH by a variable exponential taper equation can confirm the general biological significance more than the DBH of a fixed position. [ABSTRACT FROM AUTHOR]

Stem form is the shape of the trunk, differs among tree species and mainly affected by stand density factor. Accurate taper equations are crucial for estimating the stem diameter, form and tree volume, which is conducive to timber utilization and sustainable forest management and planning. Larch (Larix principis-rupprechtii Mayr.) is a valuable afforestation species under large-scale development in North China, but no study on the effect of density on its stem taper has been reported yet. The dataset included 396 analytical trees from 132 standard plots of larch plantation in Saihanba, Hebei Province. Based on 12 different forms of models, we explored the optimal basic equation for plantations and the effects of the stand density, basal area, canopy density and different forms of stand density on the prediction accuracy of the variableexponent models. The variable-exponent taper equation that includes Sd (stand density) was constructed by using nonlinear regression, a nonlinear mixed effect model and the nonlinear quantile regression method. The results indicate that the Kozak's 2004 variable-exponent taper equation was the best basic model for describing changes in the stem form of larch plantations, and the density factor in the form of Sd improved the prediction accuracy of the basic model. Among the three regression methods, the quantile regression method had the highest fitting accuracy, followed by the nonlinear mixed effect model. When the quantile was 0.5, the nonlinear quantile regression model exhibited the best performance which provides a scientific basis for the rational management of larch plantations. [ABSTRACT FROM AUTHOR]

Ten systems of compatible taper and outside-bark volume equations derived from upper-height-based volume ratio equations were compared with a used segmented-stem system of compatible taper and volume equations. All the systems were simultaneously fitted to cumulative volume data and taper data for Arizona pine, Aztec pine, Durango pine, Mexican white pine, and Smooth-leaved pine species in naturally regenerated mixed-species forests in Mexico. The systems derived from volume ratio equations performed better than the segmented-stem system for most species. The resultant top systems might be easier to implement than the segmented-stem system for predicting upper-stem height, upper-stem diameter, merchantable volume, and total stem volume for considered species. [ABSTRACT FROM AUTHOR]

The diameter at breast height (DBH) is the most important independent variable in biomass allometry models based on metabolic scaling theory (MST) or geometric theory. However, the fixed position DBH can be misleading in its use of universal scaling laws and lead to some deviation for the biomass model. Therefore, it is still an urgent scientific problem to build a high-precision biomass model system. A dataset of 114 trees was destructively sampled to obtain dry biomass components, including stems, branches, and foliage, and taper measurements to explore the applicability of biomass components to allometric scaling laws and develop a new system of additive models with the diameter in relative height (DRH) for each component of a Larch ( Larix principis-rupprechtii Mayr) plantation in northern China. The variable exponential taper equations were modelled using nonlinear regression. In addition, applying nonlinear regression and nonlinear seemingly unrelated regression (NSUR) enabled the development of biomass allometric models and the system of additive models with DRH for each component. The results showed that the Kozak's (II) 2004 variable exponential taper equation could accurately describe the stem shape and diameter in any height of stem. When the diameters in relative height were D 0.2 , D 0.5 , and D 0.5 for branches, stems, and foliage, respectively, the allometric exponent of the stems and branches was the closest to the scaling relations predicted by the MST, and the allometric exponent of foliage was the most closely related to the scaling relations predicted by geometry theory. Compared with the nonlinear regression, the parameters of biomass components estimated by NSUR were lower, and it was close to the theoretical value and the most precise at forecasting. In the study of biomass process modelling, utilizing the DRH by a variable exponential taper equation can confirm the general biological significance more than the DBH of a fixed position., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Wang, Zhang, Zhang and Huang.)

Stem form is the shape of the trunk, differs among tree species and mainly affected by stand density factor. Accurate taper equations are crucial for estimating the stem diameter, form and tree volume, which is conducive to timber utilization and sustainable forest management and planning. Larch ( Larix principis-rupprechtii Mayr.) is a valuable afforestation species under large-scale development in North China, but no study on the effect of density on its stem taper has been reported yet. The dataset included 396 analytical trees from 132 standard plots of larch plantation in Saihanba, Hebei Province. Based on 12 different forms of models, we explored the optimal basic equation for plantations and the effects of the stand density, basal area, canopy density and different forms of stand density on the prediction accuracy of the variable-exponent models. The variable-exponent taper equation that includes Sd (stand density) was constructed by using nonlinear regression, a nonlinear mixed effect model and the nonlinear quantile regression method. The results indicate that the Kozak's 2004 variable-exponent taper equation was the best basic model for describing changes in the stem form of larch plantations, and the density factor in the form of S d improved the prediction accuracy of the basic model. Among the three regression methods, the quantile regression method had the highest fitting accuracy, followed by the nonlinear mixed effect model. When the quantile was 0.5, the nonlinear quantile regression model exhibited the best performance which provides a scientific basis for the rational management of larch plantations., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Xu, Wang, Liu, Zhang, Zhang and Huang.)

Five non-segmented taper functions were modeled for Tectona grandis, which has increased significantly their planted area in Coastal Ecuador were formulations of this type are unknown. A process of nonlinear regression (maximum likelihood) was performed to a sample of 125 trees with fit evaluation. Subsequently, an independent validation process were performed, non parametric tests and a relative height analysis in order to identify strengths and weaknesses in each part of the shank was also applied. The fifth grade polynomial function showed the best fit (Absolute Bias = 1.009, Fit Index = 0.962), for that reason, the integrated form of this equation was calculated. It is expected that these developed models and their application benefits could be useful for the forestry comunity in Ecuador. [ABSTRACT FROM AUTHOR]

Throughout the northeastern United States, thinning is a common management practice in stands of eastern white pine (Pinus strobus L.), but foresters lack clear information as to whether conventional B-line or low-density thinning will best achieve their growth and financial objectives. Conventional management consists primarily of light crown thinning, whereas low-density management uses heavy crown thinning to isolate selected crop trees. To better inform silviculturists of the effects of these thinning regimes on volume growth and taper of white pine, we compared the lower bole taper- quantified as Girard form class (GFC)-and volume growth between the two thinning regimes and a nonthinned control. Over the 17-year study period, GFC increased among all treatments from an overall average of 0.77 ± 0.01 (±SE) to 0.82 ± 0.00. Trees under the B-line thinning regime had the most taper (lowest GFC), owing to a thinning-induced growth response at breast height but not at the top of the butt log. Low-density thinning, on the other hand, resulted in substantially larger, less tapered butt logs with significantly higher growth rates at both breast height and the top of the butt log. The volume growth of low-density trees was significantly higher than that of trees in the other treatments. At the stand level, however, the overall volume growth of the low-density treatment was significantly lower than that of the B-line treatment. Thus, this study reveals that when implementing low-density thinning, there is a tradeoff between overall stand growth and larger, less tapered individual trees. [ABSTRACT FROM AUTHOR]

Segmented taper equation was selected to model stem profile of Dahurian larch ( Larix gmelinii Rupr.). The data were based on stem analysis of 74 trees from Dailing Forest Bureau in Heilongjiang Province, Northeastern China. Two taper equations with crown ratio and stand basal area were derived from the Max and Burkhart's (1976) taper equation. Three taper equations were evaluated: (1) the original equation, (2) the original equation with crown ratio, and (3) the original equation with basal area. SAS NLIN and SYSNLIN procedures were used to fit taper equations. Fit statistics and cross-validation were used to evaluate the accuracy and precision of these models. Parameter estimates showed that the original equation with inclusion of crown ratio and basal area variables provided significantly different parameter estimates with lower standard errors. Overall fit statistics indicated that the root mean square error (RMSE) for diameter outside and inside bark decreased respectively by 10% and 7% in the original model with crown ratio and by 12% and 7.2% in the original model with basal area. Cross-validation further confirmed that the original equation with inclusion of crown ratio and basal area variables provided more accurate predictions at the lower section (relative heights, <10%) and upper section (relative heights, >50%) for both outside and inside bark diameters. [ABSTRACT FROM AUTHOR]

Taper equations are useful for estimating the diameter of a tree at any height on its trunk or bole. Then a more precise tree volume can be calculated based on these diameters and the corresponding heights. However, these equations may bias estimates of tree volume, if the sample size is determined arbitrarily. In this paper, an alternative method was applied to determine the sample size for optimizing taper equations fitting. In this method, the sample size required is not referred to the number of sampled trees, but to the total number of diameters estimated in the sampled trees. The analysis showed that this method is efficient from a validity standpoint. Since this method has the advantage of decreased cost (it costs much more to incrementally sample another tree than it does to make another diameter measurement on an already sampled tree), is suggested for sample size estimation. [ABSTRACT FROM AUTHOR]

Tree bole volumes of 89 Scots pine (Pinus sylvestris L.), 96 Brutian pine (Pinus brutia Ten.), 107 Cilicica fir (Abies cilicica Carr.) and 67 Cedar of Lebanon (Cedrus libani A. Rich.) trees were estimated using Artificial Neural Network (ANN) models. Neural networks offer a number of advantages including the ability to implicitly detect complex nonlinear relationships between input and output variables, which is very helpful in tree volume modeling. Two different neural network architectures were used and produced the Back propagation (BPANN) and the Cascade Correlation (CCANN) Artificial Neural Network models. In addition, tree bole volume estimates were compared to other established tree bole volume estimation techniques including the centroid method, taper equations, and existing standard volume tables. An overview of the features of ANNs and traditional methods is presented and the advantages and limitations of each one of them are discussed. For validation purposes, actual volumes were determined by aggregating the volumes of measured short sections (average 1 meter) of the tree bole using Smalian's formula. The results reported in this research suggest that the selected cascade correlation artificial neural network (CCANN) models are reliable for estimating the tree bole volume of the four examined tree species since they gave unbiased results and were superior to almost all methods in terms of error (%) expressed as the mean of the percentage errors. [Copyright &y& Elsevier]

Abstract: Volume ratio method is one of the methods used for estimating merchantable volume of a stem between a pre-specified stump height and top diameter. Volume ratios of merchantable volume to total volume were expressed as a function of the ratio of merchantable top diameter to breast height diameter (d m/D) and as a function of merchantable height to total tree height (h m/H). A number of mathematical equations were developed using d m/D and h m/H as independent variables for its estimation for Cupressus lusitanica. Fit index and standard error of estimate were used to evaluate and chose the best equations for each explanatory variable. The predictive abilities of the selected equations for estimating merchantable volume ratios were then examined using a test data. The results showed that the selected equations had an overall mean bias of −0.0111 and −0.0052, respectively. Development of merchantable volume ratio equations led to stem taper equations that predict diameter on a stem at any height and height at any diameter, based on given D and H. The performances of the derived taper equations were also tested. The overall absolute biases were 0.2276cm and 0.2438m for predicting merchantable top diameter and height at various relative heights and varying merchantable top diameters, respectively. [Copyright &y& Elsevier]