Taper Equations Research Articles

Taper functions to predict the upper stem diameter of Chir pine (Pinus roxburghii) in the mid-hills of Nepal

A function that predicts the upper stem diameters of an individual tree is helpful in better quantifying the volume and devising sustainable management of commercially and ecologically important species. This study compares three forms of the taper equation (single, variable-exponent, and segmented) using destructive sample data collected from 80 Chir pine (Pinus roxburghii Sarg.) trees across three adjacent stands in the Mid hills of Nepal. A mixed-effects modeling approach was used to evaluate the 13 different taper functions, selecting the best parameter association with the random effect to avoid overparameterization. Additionally, these models were fitted to minimize errors by modeling correlation structure with continuous autoregressive correlation structure of order 1 (corCAR1) and variance with a power variance function. All models were statistically significant at 5% level in the likelihood ratio test when compared with the models fitted without these error minimization. Furthermore, model performance (root mean square error, mean absolute error, and pseudo-R2) was evaluated using k-fold cross-validation procedure. Although all taper functions described more than 95% of the variation in upper stem diameter prediction, the single-form models of Bennett and Swindel (1972) and Amidon (1984), the variable-exponent model form of Sharma and Zhang (2004), and the segmented model form of Max and Burkhart (1976) explained more than 98% percent of the variability. Residual diagnostics indicated that Sharma and Zhang's (2004) model provided better constant and minimum errors in predicting the upper stem diameter along the 8 to 20 m stem length, whereas other models exhibited higher residual errors. Despite model's better performance, variability along the upper stem diameter prediction would affect its applicability in estimating the volume at any merchantable height of individual trees.

Regional differences in stem form between southern and northern red spruce (Picea rubens Sarg.) populations

Abstract Red spruce (Picea rubens Sarg.) is a commercially and ecologically important conifer species that primarily exists at northern latitudes of eastern North America and extends southward following the Appalachian Mountains into North Carolina and Tennessee. Due to a warming climate and human-caused disturbances, only fragmented, sky-island populations remain at the highest peaks of the southern Appalachians where their habitat continues to be threatened. While they have been recognized for the rare wildlife habitat they provide in the region, these populations remain understudied. This work aimed to examine differences in stem form between the northern and southern populations of red spruce and to provide additional quantitative methods for managing red spruce stands through providing regionally fitted stem taper models. First, we examined differences in stem form using two methods: a sectional rate of change in diameter and a region variable added to the Kozak (2004) Model 02 taper model. The sectional taper comparison showed significant differences (P < .05) in taper rate throughout the stem that were most pronounced below breast height and above the midpoint. The nested model comparison also showed a significant difference after performing a likelihood ratio test. These results agreed that significant differences in stem form between the two populations exist and supported the idea that localized taper models would provide the best results. Next, we evaluated four stem taper models for their ability to predict upper stem diameters and total volume in southern Appalachian red spruce: a quadratic polynomial, a segmented, a variable exponent, and a geometric model. Fitting data came from a 1992 study across three southern Appalachian spruce-fir sites. Validation data came from a new dataset collected in 2022 at Unaka Mountain, Tennessee. Based on past studies and our results, we found that the Kozak (My last words on taper equations. For Chron 2004;80:507–15. https://doi.org/10.5558/tfc80507-4.) Model 02 variable exponent and the Max and Burkhart (Segmented polynomial regression applied to taper equations. For Sci 1976;22:283–9.) segmented polynomial models performed equally well. The choice of the final model should depend on the users’ objectives and practical limitations (i.e. programming ability, availability of fitting data, error tolerance).

Developing stem taper of Shorea robusta in the far-western Terai of Nepal

Tree taper functions expressed in terms of height and diameter at breast height (BDH) can provide accurate and timely information on current growing stock. Taper equations are very important for calculation of growing stock in forest inventories, however, in the context of Nepal, these are still unavailable at the required level. The study aimed to develop taper equations, so that those can be used to predict the diameter anywhere along the stem, and estimate tree volumes at desired sections. The input data was a destructive sampling method of 81 sample trees of Shorea robusta distributed in ten locations of the far western Terai of Nepal (Kailali and Kanchanpur districts).
 Using two independent B-Spline and 5th-degree polynomial taper models, the upper stem diameters were imputed. Both models were applied on the whole dataset, irrespective of DBH size, to get common fitted taper models. Later, the same models were tested for three different DBH classes to compare and evaluate the best-fit model. 
 Taper models, developed under the B-spline polynomial model of 3rd degree, were found to be highly dependent on the tree (DBH) sizes. Thus, better models could be developed by classifying the whole dataset based on different DBH classes. On the other hand, developed models under the 5th degree polynomial taper model did not exhibit their dependency on the tree (DBH) sizes and a better model was found for the unclassified datasets, i.e. for all DBH sizes.

Developed of Taper Equation and Volume for Eucalyptus camaldulensis Dem. in the Nineveh Region

This study aimed to estimate a taper equation for eucalyptus trees growing in Nineveh Governorate, it is used in forest inventory or management planning systems, giving information about the diameter at any point along the main stem of the tree. Data were collected from three naturally growing trees for diameter at breast height, total height, and diameter at different levels, starting from 0.5 m above ground level, with distances of half a meter along the main stem, using computer and regression methods. different. Linear and non-linear. In the preparation of the taper equation, as well as the use of statistical measures, namely, the coefficient of determination R2, the standard error attributed to the S.E rate, in the test of the best taper equation, and through the comparison between equations through statistical measures, we were able to obtain the following taper equation: d = 14.2299 * hi -0.1873 And by taking the integration of the taper equation, we got an equation for estimating the size of eucalyptus trees, which is:V1 = 0.02542(hi)0.6254.

Stem Profile Patterns ofPinus nigraandPinus sylvestrisGrowing in Mixed Stands

AbstractTaper equations provide one of the most successful approaches of calculating tree volume to specified top diameters from standing tree measurements. This study assessed the stem profile patterns of Black pine (Pinus nigra Arnold.) and Scots pine (Pinus sylvestris L.) trees growing in mixed stands in northwestern Türkiye using a segmented polynomial taper equation. Models were fitted with the continuous second-order autoregressive structure to correct for the autocorrelation. The models fit the data well, describing more than 99%, 98%, and 97% of variation in diameter, merchantable volume, and total stem volume, respectively. However, the prediction errors were slightly larger for black pine than for Scots pine. Results also revealed that the model coefficients for these species were significantly different. Models developed in this study should provide more accurate upper stem diameter and volume estimates when the objective is to estimate such attributes for black pine and Scots pine growing in the mixed stands.Study Implications: Estimates of total and merchantable tree volume in a stand are essential for forest management and planning. Taper models are one of the most accurate approaches to estimating upper stem diameters and volume to any merchantability limit. There has been an increasing interest in managing mixed-species stands but limited work has been done on taper equations for trees growing in mixed stands. This study assessed the stem profile patterns of black pine and Scots pine trees growing in mixed-species stands in northwestern Türkiye. As has been reported for pure stands, species-specific taper equations were more accurate upper stem diameter and volume estimations in mixed-species stands. The developed taper models should play an important role in planning and inventorying mixed Black pine and Scots pine stands in Türkiye.

Extraction of Forest Structural Parameters by the Comparison of Structure from Motion (SfM) and Backpack Laser Scanning (BLS) Point Clouds

Forest structural parameters are key indicators for forest growth assessment, and play a critical role in forest resources monitoring and ecosystem management. Terrestrial laser scanning (TLS) can obtain three-dimensional (3D) forest structures with ultra-high precision without destruction, whereas some shortcomings such as non-portability and cost-consuming can limit the quick and broad acquisition of forest structure. Structure from motion (SfM) and backpack laser scanning (BLS) technology have the advantages of low-cost and high-portability while obtaining 3D structure information of forests. In this study, the high-overlapped images and the BLS point cloud, combined with the point cloud registration and individual tree segmentation to extract the forest structural parameters and compared with the TLS for assessing the accuracy and efficiency of low-cost SfM and portable BLS point clouds. Three plots with different forest structural complexity (coniferous, broadleaf and mixed plot) in the northern subtropical forests were selected. Firstly, portable photography camera, BLS and TLS were used to acquire 3D SfM and LiDAR point clouds, and spatial co-registration of different-sourced point cloud datasets were carried out based on the understory markers. Secondly, the point clouds of individual tree trunk and crown were segmented by the comparative shortest-path algorithm (CSP), and then the height and position of individual tree were extracted based on the tree crown point cloud. Thirdly, the trunk diameter at different heights were calculated by point cloud slices using the density-based spatial clustering of applications with noise (DBSCAN) algorithm, and combined with the stem curve of individual tree which was constructed using four Taper equations to estimate the individual tree volume. Finally, the extraction accuracy of forest structural parameters based on SfM and BLS point clouds were verified and comprehensively compared with field-measured and TLS data. The results showed that: (1) the individual tree segmentation based on SfM and BLS point clouds all performed quite well, among which the segmentation accuracy (F) of SfM point cloud was 0.80 and the BLS point cloud was 0.85; and (2) the accuracy of DBH and tree height extraction based on the SfM and BLS point clouds in comparison with the field-measured data were relatively high. The root mean square error (RMSE) of DBH and tree height extraction based on SfM point cloud were 2.15 cm and 4.08 m, and the RMSE of DBH and tree height extraction based on BLS point cloud were 2.06 cm and 1.63 m. This study shows that with the adopted image capture method, terrestrial SfM photogrammetry can be applied quite well in extracting DBH.

Optimal bucking of stems from terrestrial laser scanning data to maximize forest value

ABSTRACT An optimal bucking strategy that allocates cutting patterns to forest stands based on the individual characteristics of each stem is critical for maximizing value recovery. However, cutting patterns are usually excluded from bucking algorithms due to the difficulties associated with capturing tree quality features when collecting forest inventory data (e.g. branchiness and tree shape). This paper presents a non-destructive and fully automated methodology for the optimal bucking of stems based on terrestrial laser scanning (TLS) point clouds that aims to maximize the economic value of trees in a forest stand. It is based on the three-dimensional modelling of stems and includes the diameter and curvature of each log. The bucking algorithm also considers several timber products and calculates the most valuable log combination for each tree. The methodology was tested in a Pinus radiata plot with 120 trees, and the results were compared with those obtained with input data that do not take curvature into account: i.e. only diameters from TLS and taper equations. The analysis of the results suggests that not including curvature in the algorithm for optimal bucking results in an overestimation of the commercial value of timber products.

Biomass allometric models for Larix rupprechtii based on Kosak's taper curve equations and nonlinear seemingly unrelated regression.

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.

Taper equations for eight major forest tree species in flat land Ukraine

Abstract Stem taper equations are crucial for forest management allowing to reliably estimate merchantable wood volume. Their main benefit is the ability to predict stem diameters at a certain height of the stem. Ukraine has recently adopted European Union standards for round wood classification, which prompted the necessity to model stem taper and updates all reference data to conform with the new standards. This study is a systematic attempt to develop a set of taper equations for the most common forest tree species in the Polissia and Forest steppe of Ukraine. For this purpose, we used a data set of 1994 sample trees representing eight tree species collected on 238 sample plots. The Kozak A. (2004, My last words on taper equations. For. Chron. 80, 507–515) model was chosen to fit the taper equations. To characterize the variability in stem shape among tree species, mixed-effect models were calibrated for this equation. In this model, random-effect parameters were selected based on their coefficients of variation through a bootstrapping process. This is a novel feature we suggest for the process of calibrating taper models. The Kozak A. (2004, My last words on taper equations. For. Chron. 80, 507–515) equation showed a good performance in predicting diameters outside bark and estimating the total stem volume. Our mixed-effect modelling approach accurately characterizes the variation in stem form for different tree species based on adequately chosen random-effect parameters. The stem volumes derived from the developed taper models were compared with existing volume equations outputs (divergence up to 0.5 per cent). A deviation up to 5 per cent was found between the values of fitted and observed cylindrical form factors for the studied tree species. We expect that our taper equations will complement the future steps towards the development of reliable merchantable volume distribution models for the main tree species in the forests of flat land Ukraine, thus, contributing to transparency, reliability and sustainability of forest management and markets in Europe.

Incorporating stand density effects and regression techniques for stem taper modeling of a Larix principis-rupprechtii plantation.

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 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.

Laser Caliper Reliability in Upper-Stem Diameter Measurements by Multiple Users

Considering the uncertainty of upper-stem diameter measurements and the fact that there are few studies on the accuracy of diameters using the Mantax Black caliper with Gator Eyes (Haglöf, Långsele, Sweden), the aim of this research is to check laser caliper reliability in upper-stem diameter measurements. The study was conducted in Parc Aventura Braşov (Romania), where a target tree was marked with visible signs at 1 m, 3 m, 5 m, 7 m, 9 m, and 13 m above the ground, and the diameters of the six sections were measured using a conventional caliper and climbing equipment. Later on, 14 forest mensurationists used a laser caliper to measure the diameters of the marked sections 13 m away from the tree, maintaining the direction of measurement. Each user performed repeated independent measurements of the upper-stem diameters, resulting in 14 data sets with 10 values for every section and a total number of 840 observations. Applying ANOVA for all the sections, we found that there are significant differences between the data sets collected by many users, and the pairwise t-test and the Benjamini-Hochberg method showed significant differences. Taking into account the analysis of the individual errors in measuring the upper-stem diameters using a laser caliper, we were able to identify the data sets affected by abnormal errors. By measuring the diameters along the stem up to 13 m above the ground using a laser caliper, one out of 2.4 measurements up to one out of approximately 1.5 was determined with an error below 2 cm. At heights above 5 m, a maximum of one out of five measurements was affected by errors above 4 cm. In addition, it was noted that there is generally a tendency to underestimate the upper-stem diameter and volume estimate when the laser caliper is used for the measurements. The absolute mean error varied between 1.46 cm and 2.52 cm along the stem and the root mean squared error varied between 1.84 cm and 3.04 cm. Nevertheless, general uncertainty about this subject remains, because if we measure upper-stem diameters without contact with the trunk, we will never know whether a single reading shows a negligible error to be used for calibrating taper equations or for increasing volume estimation accuracy. Consequently, we recommend that when used for this purpose, diameters should be measured several times, by experienced users who have proven their skill in measurements that yield smaller errors.

입목수간재적표 기반의 입목재적 추정의 불확실성과 이에 따른 탄소축적 추정의 편향: 강원도 홍천군을 대상으로

The purpose of this study was to quantify the uncertainty in the estimation of forest growing stock and carbon stock that occurs as DBH(Diameter at Breast Height) and HT (Height) are rounded when locating stem volumes in a stem volume table, and to present a case study using the Hongcheon-gun NFI (National Forest Inventory) data. We quantified the uncertainty of the estimated value of the stem volume obtained from the stem volume table, assuming that the stem volume calculated by the stem taper equation is the true value, and the resulting bias in carbon stock estimation, using two indicators. In all the indices, as DBH and HT increased, a trend was observed in which the absolute values of these indicators increased. BIAS appeared as a positive value in all sections, which means that the stem volume table with rounding DBH and HT underestimated stem volumes. BIAS was found to range from 0.0134m³ to 0.0178m³ depending on the species. RMSE (Root Mean Square Error) was about 4 ~ 7 times greater than BIAS with the same tree sizes. The increase rate of stem volume was almost constant regardless of HT, but increased as DBH increased. This indicates that DBH is more effective in reducing rounding-induced uncertainty when using stem volume tables. Note that rounding DBH combined with this characteristic led to systematic underestimation of stem volume. As a result of estimating the growing stock in the forests of Hongcheon-gun, Gangwon-do using the stem taper equation and the stem volume table, it was confirmed that the stem volume table underestimated the growing stock by 1,475,606m³, and accordingly, did the carbon stock by 860,232 tC. Even if the figure was limited to Hongcheon-gun, it was difficult to consider it a small value. As projects related to greenhouse gas reduction are expected to become more active in the future compared to the past, uncertainty in such estimates may affect the reliability of such projects. Therefore, it is necessary to provide a tool that can calculate stem volume and carbon stock by directly inputting DBH or HT values.

Taper and individual tree volume equations of Eucalyptus varieties under contrasting irrigation regimes

Background: Compatible taper and volume equations are key for traditional growth and yield and current process-based or hybrid models. However, most equations do not consider variables such as genotype, water regime and their interaction, limiting the development of general equations for species or regions. Our research investigated taper and individual tree volume equations for eight Eucalyptus genotypes (E. nitens, E. badjensis, E. smithii, E. camaldulensis x globulus and two varieties of low and high productivity of E. globulus and E. nitens x globulus), all materials are growing under summer irrigated vs. no irrigated conditions. Methods: A 7-year old Eucalyptus plantation experiment was sampled considering four representative trees per genotype x water regime combination treatment. Four non-linear taper equations were evaluated: Kozak (2004), Kozak et al. (1969), Ormerod (1973) and Max and Burkhart (1976). In addition, total and merchantable volume was evaluated with the Schumacher and Hall (1933) equation. The effect of genotype, irrigation regime and interaction were evaluated for each equation. Then, the best taper equation was selected from adjusted coefficient of determination, mean square error, and AIC and BIC parameters. Finally, the validation of evaluations was carried out with the Leave-One-Out Jackknife method. Results: Genotype, irrigation regime, or the interaction were not statistically significant for all evaluated taper - volume equations and a generalised model equation was obtained. The best taper equation was Kozak (2004) which showed the best fit and adaptation to irregular boles. Regarding volume equations, all showed a trend to underestimate volume (total and merchantable) in trees with a volume greater than 0.22 m3. Validation of the equations showed reduced bias suggesting that the equations can be used to predict taper and volume regardless of Eucalyptus genotype x irrigation regimen combinations. Conclusions: Our results suggest a negligible or minor effect of irrigation (water resource availability) and genotype (for tested taxas and genotypes) on taper and individual tree volume equations. A generalised taper and volume equation (total and merchantable) may be used for all tested genotypes, regardless of water regime (site water availability). This generalised model would simplify Eucalyptus estimates required for stand management and projection.

Comparison of stem volume estimates from terrestrial point clouds for mature Douglas-fir (Pseudotsuga menziessi (Mirb.) Franco)

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.

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.

Predicting the upper stem diameters and volume of a tropical dominant tree species

Predicting upper stem diameters and individual tree volumes is important for product quantification and can provide important information for the sustainable management of forests of important commercial tree species (Shorea robusta) in Nepal. The aim of this study was to develop a taper equation for S. robusta. Fifty-four trees were selected and felled in the southern low land of Nepal. A mixed effect modelling approach was used to evaluate 17 different taper functions. ‘Leave-one-out cross-validation’ was used to validate the fitted taper functions. The variable exponent taper function best fitted our data and described more than 99% of the variation in upper stem diameters. Results also showed significant effects of stand density on tree taper. Individual tree volume prediction using the local volume model developed in this study was more accurate compared to the volume predicted through the taper function and existing volume model. The taper function developed in this study provides the benefit of predicting upper stem diameter and can be used for predicting volume to any merchantable height of individual trees. It will have implications in estimates of volume, biomass, and carbon and thus may be a potential supporting tool in carbon trade and revenue generation.

Construction of the additive model system for heartwood, sapwoodand bark taper of Pinus koraiensis plantation in different regions of Heilongjiang Province, China

With the commonly used variable-exponent taper models developed by Kozak (1988), Muhairwe (1999), Lee (2003) and Kozak (2004), we aimed to develop taper functions of diameter outside bark (DOB), heartwood diameter (HD), sapwood width (SW), and bark thickness (BT) based on the data of 2977 discs from 103 sample trees of Pinus koraiensis plantations under different conditions in Mengjiagang Forest Farm, Dongjingcheng and Linkou Forestry Bureau in Heilongjiang Province. We selected the optimal basic model after comparison. By using seemingly unrelated regression (SUR) method in the PROC MODEL of SAS software, we established an additive model system for the taper equations of DOB, HD, SW and BT. By introducing the region as a dummy variable, the models were evaluated by coefficient determination (Radj2), root mean square error (RMSE), Akaike information criterion (AIC) and Bayesian information criterion (BIC). The results showed that the taper model developed by Kozak (2004) was the optimal one for the DOB, HD, SW and BT. When satisfying the additivity of each component and total amount, the additivity model system got better prediction effect, with a prediction precision of more than 98%. The additive model system with dummy variables improved the prediction ability to varying degrees, especially the prediction precision of HD and SW models. Minor differences existed in DOB and BT among different regions, while enormous differences in HD and SW. The additive model system with dummy variables not only had high prediction accuracy but also satisfied the additive logic of DOB, HD, SW and BT, which provided a basis for accurate estimation of heartwood, sapwood and bark volume of P. koraiensis.

Semi-empirical estimation of log taper using stem profile equations

In January 2019 the forest industry in Ukraine adopted European standards for measuring and grading of round wood based on mid-point diameters, which caused major discrepancies from traditionally used estimates of timber volume using top diameters. To compare methods of merchantable wood volume estimation, we investigated the stem form inside bark for two dominant tree species in Ukraine, i.e. Scots pine (Pinus sylvestris L.) and common oak (Quercus robur L.). We used tree stem measurements to fit stem profile equations, whereas simulation was applied to derive log taper. We found that Newnham's (1992) variable-exponent taper equation performed well for predicting stem taper for both tree species. Then, we simulated the structure of harvested wood, so that it replicated annual distribution of logs by their length and diameters. As a result, the average log taper was estimated at 0.836 ÷ 0.855 cm·m<sup>–1</sup> and 1.180 ÷ 0.121 cm·m<sup>–1</sup> for pine and oak, respectively. The study also indicated that log taper varied along stems. The higher rates of diameter decrease were found for butt logs, for which the taper was 2.5–3.5 times higher than its average for the whole stem. The results of our study ensure the stacked round wood volume conversion between estimates obtained using top and mid-point diameters.

Global Tree Taper Modelling: A Review of Applications, Methods, Functions, and Their Parameters

Taper functions are important tools for forest description, modelling, assessment, and management. A large number of studies have been conducted to develop and improve taper functions; however, few review studies have been dedicated to addressing their development and parameters. This review summarises the development of taper functions by considering their parameterisation, geographic and species-specific limitations, and applications. This study showed that there has been an increase in the number of studies of taper function and contemporary methods have been developed for the establishment of these functions. The reviewed studies also show that taper functions have been developed from simple equations in the early 1900s to complex functions in modern times. Early taper functions included polynomial, sigmoid, principal component analysis (PCA), and linear mixed functions, while contemporary machine learning (ML) approaches include artificial neural network (ANN) and random forest (RF). Further analysis of the published literature also shows that most of the studies of taper functions have been carried out in Europe and the Americas, meaning most taper equations are not specifically applicable to tropical tree species. Developing well-conditioned taper functions requires reducing the variation due to species, measurement techniques, and climatic conditions, among other factors. The information presented in this study is important for understanding and developing taper functions. Future studies can focus on developing better taper functions by incorporating emerging remote sensing and geospatial datasets, and using contemporary statistical approaches such as ANN and RF.

Developing taper equations for planted teak (Tectona grandis L.f.) trees of central lowland Nepal

Foresters rely on taper models to estimate total and merchantable volume for commercial species. While there is an abundance of literature in taper modeling for many softwood and hardwood species, little is known of teak tree stem form. Taper modeling is in early stage for the forestry sector in Nepal. Currently, no publicly available taper equations exist for teak trees in Nepal. Therefore, the main goal of this study was to develop a taper equation for valuable teak trees of lowland Nepal. Destructive sampling was carried out in teak plantations in the Sagarnath Forestry Development Project. Five common taper equations (simple, segmented, and variable exponent types) from the literature as well as one dynamic taper equation were considered as candidate models. Our results showed that the nonlinear dynamic taper equation performed best in terms of fit and cross-validation statistics with least error and bias. This new taper model can be considered as a step forward for hardwood forest management in Nepal. It is expected that this equation will assist forest managers to predict stem volume and diameters to any merchantable limit for teak growing in similar site conditions.