Taper Model Research Articles

Response of Douglas-fir stem profile to operational nitrogen fertilization in western Oregon

Nitrogen (N) fertilizer is a commonly applied silvicultural treatment intended to promote growth of intensively managed coast Douglas-fir [Pseudotsuga menziesii (Mirb.) Franco var. menziesii] plantations in the Pacific Northwest region of the US (PNW) and adjacent areas of Canada. Because responses have been geographically variable, fertilization trials were established in the Coast Range of northwestern Oregon to enhance general understanding of Douglas-fir growth response and test the economic viability of operational N applications in this subregion. Twenty-three operational stands comprising the trials were dominated by Douglas-fir, had an initial total age of 16–24 years, had been pre-commercially thinned 7–10 years prior to establishment of the fertilization trials, and started with 387–1260 trees ha−1. Nitrogen fertilizer was applied aerially as pelletized urea (46% N) at a rate of 224 kg N ha−1 to half of each stand during the dormant season of 2009–2010. In the dormant season of 2016–2017, seven growing seasons following fertilizer application, forty sample trees were felled in ten randomly selected stands to assess the influence of N-fertilization on stem form. A variable exponent taper model was developed using a nonlinear mixed-effects modelling approach. A tree-level random effect and a first-order continuous autoregressive [CAR(1)] error process were incorporated into the model to facilitate accurate tests of significance on model parameter estimates. The variable exponent taper model captured significant variation in stem form resulting from fertilization based on interaction with a crown variable, suggesting that the N-fertilization influence on stem form was mediated by initial crown length of trees with given diameter and height. Volume predictions from the resulting taper model were compared to those from the regional growth model ORGANON, which assumes no influence of fertilization on stem form. The regional growth model ORGANON significantly (p < 0.01) under-predicted fertilized tree volume by 3.6%. Results are being incorporated into individual-tree growth models to improve site-specific predictions of growth response. Improved understanding and modeling of mechanistic responses of foliage, growth, and stem form to fertilization may help discriminate between sites with high and low growth response potential. Mechanistic insights coupled with better site characterization should help improve the understanding of economic and environmental performance of fertilized Douglas-fir stands.

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.

Evaluation of four regression techniques for stem taper modeling of Dahurian larch (Larix gmelinii) in Northeastern China

Estimating stem volume and biomass in forests is fundamental to both economic and ecological assessments of forest ecosystem structure and function. Stem taper models were widely used to calculate stem volume and biomass, but it can be challenging to get an accurate and convenient technique for taper models in practice. This study evaluated ordinary nonlinear least squares (ONLS), fixed-effects model (FIXED), quantile regression (QR), and generalized additive model (GAM) to predict tree diameter, volume, and merchantable height of Dahurian larch (Larix gmelinii) in Northeastern China. As far as we know, a comprehensive analysis of these four techniques is limited for taper data. Therefore, our main objectives were to compare these four techniques at an equitable level without calibration and select a single and widely applied technique for the taper model. The dataset comprising 1372 felled-trees from Dahurian larch natural forest were used to evaluate the techniques with a leave-one-out cross-validation approach. Evaluation statistics and box plots showed that the GAM performed better than other techniques for stem profile description and volume estimation. Results also revealed that all techniques had a bias in estimating merchantable height. However, this limitation does not significantly affect the overall performance and applied use of the GAM for diameter and volume prediction. When intuitive interpretations are not needed, the GAM can serve as an accurate and convenient technique for prediction.

Evaluation of Compatible Taper and Volume Models for Combretum hartmannianum and Lonchocarpus laxiflorus Tree Species.

This paper developed and evaluated the performance of the current functional tree taper and volume models. The models were applied to some selected economically important natural tree species common to central Sudan, namely, Combretum hartmannianum and, Lonchocarpus Laxiflorus. The tree variables measured were the diameter at breast height (DBH, cm), diameter at the base of the tree (d0, cm), upper stem diameters (di), total tree height (H), and height to the base of the crown (Hb). In total, 19 taper and 32 volume models were tested and evaluated (22 models were two-variable models (Diameter at breast height and total tree height or bole height) and 10 were three-variable models (Diameter at ground level, Diameter at breast height and total tree height or bole height). The model goodness of fit was evaluated in terms of adjusted coefficient of determination (Ra2), standard error (SE), mean absolute residual (MAR), bias (BI) Akaike’s information criterion (AIC), homogeneity of the residuals and significance of the regression parameters. As far as taper models is concerned, Models, some of the models were found to yield satisfactory results for the tow selected species with R2 range of 0.94 – 0.96. For the within species variation of models on the basis of the AIC values, the ranking of the models (smaller AIC first) were in consistant with the rankings due to SE and Ra2 values although AIC penalizes models in proportion to the number regression parameters. In general the results of the study indicated that higher residuals valuse are in most of the cases associated with the lower parts of the bole, the butress portion of the stem. This suggests that care should be taken during the application of such models for hardwood species, especially in open woodlands where butress is a common characteristic.The results for volume models revealed differences in the behaviour of different models for each species as the degree of significance of the regression parameters varies between tree species. However, the replacement of the total tree height by the bole height (merchantable height) improves both the level of parameter significance and the coefficient of determination. The results also reveal that inclusion of diameter at grown level to the original two variables (DBH, Ht) and the replacement of the original model total height with the bale height results in quite significant improvement of the Ra2 values. In general, the study concluded that taper and volume models can provide precise and accurate estimation of tree growth variables for the studied species with reasonable cost and time, but care should be taken when dealing with same model for the same species across varying growth and management condition, or when dealing with different species. country.

Modeling of stem taper evolution using stochastic differential equations

Stochastic differential equations (SDEs) were developed at the beginning of the twentieth century to quantify all aspects of stochastic processes. This study focusses to evaluate the applicability and efficiency of the SDEs for modeling tree diameter over bark at any particular height and total stem volume for birch tree species in the boreal forests of Lithuania. Newly developed models of the stem taper development are based on well-defined diffusion processes, such as the symmetric Vasicek type diffusion process, and asymmetric geometric type diffusion process. The stem taper models with the fixed- and mixed-effect parameters are examined. The fixed- and mixed-effect parameters of the SDEs stem are evaluated using maximum likelihood procedure. Results are illustrated using birch trees longitudinal measurements. These models are compared with traditionally used regression type stem taper models using statistical measures and residual analysis. Overall, the best goodness-of-fit statistics for tree diameter and volume predictions produced the SDEs stem taper models. All results are implemented in the Maple software.

The Effect of Crown Dimensions on Stem Profile for Dahurian Larch, Korean Spruce, and Manchurian Fir in Northeast China

Crown architecture has long been evaluated for its impact on taper modeling. However, most of the research has focused on a limited number of crown dimensions. This study examined the effect of adding several crown dimensions in improving the diameter and volume estimates of Dahurian larch, Korean spruce, and Manchurian fir in northeast China. The crown dimensions included crown length, crown ratio, crown width, height to live crown base, diameter at the crown base, and crown shape. A well-known taper model of Clark et al. (1991) was fitted to the data of 276 trees from natural stands. To adjust the inherent autocorrelation in the data, we added a third-order continuous-time error structure in the model fit. Model fitting was carried out with the NLMIXED procedure (Non-linear Mixed Procedure), followed by the MODEL procedure of SAS using the generalized nonlinear least-squares method. Fit statistics and graphical assessments were used to evaluate the original and modified models. Above 98% of the total variance of d was explained by the models for all species. The addition of crown variables showed slight improvements for root mean square error (RMSE) values in the analyzed species. The RMSE plots indicated that the models with crown variables slightly improved the diameter and volume predictions for the species but only for the upper stem (&gt;50%–90%). The study demonstrated that crown dimensions influence the stem taper, but the original model of Clark et al. (1991) reasonably realized that effect.

Stem taper functions for white birch (Betula platyphylla) and costata birch (Betula costata) in the Xiaoxing’an Mountains, northeast China

AbstractWhite birch (Betula platyphylla Sukaczev) and costata birch (Betula costata Trautv.) are valuable hardwood tree species growing in northeast China. Several taper studies have analysed birch species in the countries harbouring the boreal forests. However, this study presents an initial attempt to develop stem taper models using the fixed- and mixed-effects modelling for white birch and costata birch in Xiaoxing’an Mountains, northeast China. Ten commonly used taper models were evaluated by using 228 destructively sampled trees of both tree species comprising of 4582 diameter and height measurements. The performance of these models was tested in predicting diameter at any height, total volume and merchantable volume (10 and 20 cm top diameters). We incorporated a second-order continuous-time error structure to adjust the inherent autocorrelation in the data. The segmented model of Clark best predicted the diameter and total or merchantable volume when the upper stem diameter at 5.3 m was available. When diameter measurements at 5.3 m were not available, the models of Kozak and Max and Burkhart were superior to other models for white birch and costata birch, respectively. After model comparison, the best model of Clark was refitted as the NLME model.

COMPATIBILITY BETWEEN THE SPURR FUNCTION VOLUME AND THE KOZAK’S TAPER FUNCTION AND QUINTIC POLYNOMIAL VOLUMES FOR BLACK WATTLE TREES

When modeling the taper and volume, it is desired that the volume estimates obtained by using these two methods are compatible, where the total stem volume estimates shall not differ when using a total volume equation and the volume calculated by integrating the taper equation. There are several of such systems proposed in the literature, in which modifications in the volume and taper models were made to obtain compatible systems. This paper introduces an idea to obtain compatibility in a simpler way, without the need to modify the volume and taper models. Thus, the overall objective of this study was to develop and present a procedure to obtain compatibility between the Spurr function volume and the Kozak’s taper function and quintic polynomial volumes for Acacia mearnsii De Wild trees and compare the results to the traditional method of the same system of equations. The procedures proposed were applied on data on the Acacia mearnsii De Wild (black wattle) species in the towns of Cristal, Piratini, and Encruzilhada in the south of the state of Rio Grande do Sul, Brazil. The data set included 343 trees ranging from 5 to 10.75 years of age. The quality of the fitting for the volume and taper equations fitted using procedures 1 and 2 is similar, and both are compatible. The system of equations presented in procedure 2 is simpler to be applied when compared to procedure 1.

Equações de perfil do tronco avaliados para Corymbia citriodora Hill & Johnson

Equações de perfil do tronco das árvores viabilizam quantificar diferentes usos que se possam destinar a produção madeireira de um determinado povoamento florestal. São advindas do ajuste de modelos de taper, referenciados como: modelos de afilamento, adelgaçamento, forma e, ou de perfil do tronco ou do fuste. Como não se encontram estudos sobre o emprego de equações de perfil do tronco em plantios brasileiros com Corymbia citriodora, esse trabalho objetivou verificar o ajuste de uma grande quantidade de modelos para esta importante espécie florestal. Foram utilizadas 35 árvores cubadas com medições diretas do diâmetro do tronco nas posições: 0,2 m, 0,4 m, 0,7 m, 1,3m, 2,7 m e a cada 2 metros até um valor aproximado de 1,0 cm com casca. Como critérios estatísticos de avaliação das equações de perfil do tronco geradas para C. citriodora, foram considerados: coeficiente de determinação ajustado, erro padrão da estimativa, distribuição gráfica dos resíduos, média dos desvios absolutos, desvio padrão das diferenças, soma dos quadrados dos resíduos relativos, média dos desvios percentuais, raiz quadrada do erro médio, viés e coeficiente de correlação linear múltipla. Concluiu-se que, para descrever o perfil do tronco de C. citriodora, as equações geradas por modelos muito difundidos no Brasil apresentaram desempenho insatisfatório e que se destacaram seis modelos ainda pouco testados ou sem aplicação no país.

Development of a Taper Equation for Teak (Tectona grandis L.f.) Growing in Western Thailand

Teak is an important and valuable tropical hardwood species. In this study, we developed and evaluated suitable taper equations for teak growing in Western Thailand using a formulation of Goodwin cubic polynomial model combined with a bark thickness model. The best taper model calibration was selected based on goodness-of-fit and leave-one-out cross validation statistical testing. In total, 12 different model calibrations were tested, with Thong Pha Phum (TPP) 2 being the most suitable for teak in Western Thailand. The mean prediction error of three validation statistics: (prediction of diameter under bark given height; prediction of height given diameter under bark; and prediction of under bark volume given log length) were within 10% and the overall validation index was 5.454, which was the lowest when compared to other calibrations. A comparison of TPP 2 with a teak taper equation developed for Northern Thailand, using a graphical analysis of the stem shape and bark thickness, indicated that the teak trees growing in the two regions have similar stem shapes, but the trees in Western Thailand tend to have a thicker bark. These results will also help in further work as they indicate that bark thickness equations are particularly important.

Voxel-Based Automatic Tree Detection and Parameter Retrieval from Terrestrial Laser Scans for Plot-Wise Forest Inventory

This paper presents a fully automatic method addressing tree mapping and parameter extraction (tree position, stem diameter at breast height, stem curve, and tree height) from terrestrial laser scans in forest inventories. The algorithm is designed to detect trees of various sizes and architectures, produce smooth yet accurate stem curves, and achieve tree height estimates in multi-layered stands, all without employing constraints on the shape of the crown. The algorithm also aims to balance estimation accuracy and computational complexity. The method’s tree detection combines voxel operations and stem surface filtering based on scanning point density. Stem diameters are obtained by creating individual taper models, while tree heights are estimated from the segmentation of tree crowns in the voxel-space. Twenty-four sample plots representing diverse forest structures in the south boreal region of Finland have been assessed from single- and multiple terrestrial laser scans. The mean percentages of completeness in stem detection over all stand complexity categories are 50.9% and 68.5% from single and multiple scans, respectively, while the mean root mean square error (RMSE) of the stem curve estimates ranges from ±1.7 to ±2.3 cm, all of which demonstrates the robustness of the algorithm. Efforts were made to accurately locate tree tops by segmenting individual crowns. Nevertheless, with a mean bias of −2.9 m from single scans and −1.3 m from multiple scans, the algorithm proved conservative in tree height estimates.

Variable-Exponent Taper Equation Based on Multilevel Nonlinear Mixed Effect for Chinese Fir in China

A variable-exponent taper equation was developed for Chinese fir (Cunninghamia lanceolate (Lamb.) Hook.) trees grown in southern China. Thirty taper equations from different groups of models (single, segmented, or variable-exponent taper equation) were compared to find the excellent basic model with S-plus software. The lowest Akaike information criteria (AIC), Bayesian information criteria (BIC), and -2loglikelihood (-2LL) was chosen to determine the best combination of random parameters. Single taper models were found having the lowest precision, and the variable-exponent taper equations had higher precision than the segmented taper equations. Four variable-exponent taper models that developed by Zeng and Liao, Bi, Kozak, Sharma, and Zhang respectively, were selected as basic model and had no difference in fit statistics between them. Compared with the model without seldom parameter, the nonlinear mixed-effects (NLME) model improves the fitting performance. The plot-level NLME model was found not to remove the residual autocorrelation. The tree-level and two-level NLME model had better simulation accuracy than the plot-level NLME model, and there were no significant differences between the tree-level and two-level NLME model. Variable-exponent taper model developed by Kozak showed the best performance while considering two-level or tree-level NLME model, and produced better predictions for medium stems compared to lower and upper stems.

A Taper Equation for Loblolly Pine Using Penalized Spline Regression

Abstract Stem profile needs to be modeled with an accurate taper equation to produce reliable tree volume assessments. We propose a semiparametric method where few a priori functional form assumptions or parametric specification are required. We compared the diameter and volume predictions of a penalized spline regression (P-spline), P-spline extended with an additive dbh-class variable, and six alternative parametric taper equations including single, segmented, and variable-exponent equation forms. We used taper data from 147 loblolly pine (Pinus taeda L.) trees to fit the models and make comparisons. Here we show that the extended P-spline outperforms the parametric taper equations when used to predict outside bark diameter in the lower portion of the stem, up to 40% of the tree height where the more valuable wood products (62% of the total outside bark volume) are located. For volume, both P-spline models perform equal or better than the best parametric model, with taper calibration, which could result in possible savings on inventory costs by not requiring an additional measurement. Our findings suggest that assuming a priori fixed form in taper models imposes restrictions that fail to explain the tree form adequately compared with the proposed P-spline.

Segmented taper models form for Manchurian fir and Korean spruce in northeastern China

ABSTRACT Background: Manchurian fir (Abies nephrolepis Maxim) and Korean spruce (Picea koraiensis Nakai) are primary conifer species of economic and ecological importance in northeast China. Several taper studies have analyzed for fir and spruce species in the countries harboring the boreal forests. However, taper models do not exist for Manchurian fir and Korean spruce in China or abroad. This study aimed to develop stem taper models for these species. A dataset of 188 destructively sampled trees (Manchurian fir 123 and Korean spruce 65) was used to evaluate eight well-known taper models. These models were fitted with generalized non-linear least squares by using 3,570 diameter and height measurements. We incorporated a first-order continuous-time error structure to adjust the inherent autocorrelation. Results: The form-class segmented model of Clark et al. (1991) best predicted the diameter, merchantable volume, and stem volume of the species when the upper stem diameter at 5.3 m was available or predicted. Conclusion: When diameter measurements at 5.3 m were not available, the Kozak (2004) and Max and Burkhart (1976) models were superior to other models in estimating the diameter of both species and volume of Korean spruce. For Manchurian fir, the Fang et al. (2000) model was more accurate in volume estimates.

New proposal for flexural strengthening of a continuous I-steel beam using FRP laminate under thermo-mechanical loading

Construction materials such as composites are used recently for the reinforcement and rehabilitation of structures subject to risks of partial or total degradation during their service, which are due to either poor design, overload or a charge assignment. The use of fibers is a new technique which gives additional rigidity and resistance to structures. In this research, we develop an approach which makes it possible to analyze the interfacial constraints which are the cause of the delamination phenomenon at the level of the structure, for a continuous steel beam bonded by a FRP laminate plate, under thermo-mechanical loading coupled with the shear lag model. In such plated beams, shear forces develop in the bonded beam and these will be transferred to the FRP plate via the adhesion technique. Thus, the interfacial shear stress and normal stress will develop consequently, and debonding may occur at the FRP plate ends due to high interfacial stress values in this area. This original research aims to study the debonding phenomenon using an analytical model, in order to identify the interfacial stresses of a continuous steel beam strengthened by the FRP plate with taper model, taking into account a new coupled approach of thermomechanical loading effect. Finally, numerical comparisons between the existing solutions and the present solution enable a clear appreciation of the effects of various parameters. This article explores the effects of various parameters related to the subject, such as the effect of thermal loading, geometrical and physical properties, on the stress behavior of FRP composites. This solution is intended for application to beams made of all kinds of materials bonded with a thin composite plate. For steel I-beam section, a geometrical coefficient q is determined to show the effect of the adherend shear deformations. This research is helpful for the understanding on mechanical behaviour of the interface and design of such structures.

Stem taper models for maritime pine plantations in Istanbul Sarıyer Region

Maritime pine (Pinus pinaster Ait.) is one of the most important tree species in Turkey for establish industrial plantations. In this study, stem taper models were developed for maritime pine plantations in Istanbul-Sariyer region. For this aim, two commonly used and well-known taper models belonging to different groups (segmented and variable-form) were evaluated. In this frame, totally 194 destructively sampled trees were used. The equations were fitted with ordinary nonlinear least squares method. We incorporated a second-order continuous-time autoregressive error structure (CAR(2)) to address of autocorrelation problem and used condition numbers to detect presence of multicollinearity. The predictive performance of the taper models was evaluated using five different evaluation criteria (R2, RMSE, AIC, BIC, and AAE). According to evaluation statistics, Fang et al. (2000) model provided better results than the Kozak (2004) model for height at a specific diameter, merchantable volume and total volume predictions except for diameter at a specific height. However, there are no significant differences among both models in terms of prediction performance of the models. Therefore, it will be more reasonable for the decision maker to decide which model will be preferred in maritime pine plantations.

Equações hipsométricas, volumétricas e funções de afilamento para Pinus spp.

O emprego de ferramentas como a modelagem florestal torna-se cada vez mais importantes no planejamento florestal pois geram estimativas acuradas da produção dos povoamentos. O objetivo do estudo foi realizar o ajuste de modelos hipsométricos, volumétricos e de afilamento para quatro espécies de Pinus na Região Serrana de Santa Catarina. As espécies utilizadas foram Pinus taeda, Pinus elliottii, Pinus greggii e Pinus patula todas implantadas e conduzidas sobre o mesmo plano de manejo florestal. O povoamento está localizado no município de Correia Pinto, Santa Catarina, com 14 anos de idade. Para as análises foram ajustados modelos matemáticos com base nos dados do censo florestal. Para a escolha do melhor modelo utilizaram-se os critérios estatísticos: o coeficiente de determinação ajustado (R²aj), erro padrão da estimativa (Syx%), análise gráfica dos resíduos. As equações hipsométricas apresentaram R² ajustado relativamente baixos, com valores variando entre 0,14 e 0,35 para as espécies e Syx% variando entre 7,67% a 4,86%. Em relação as equações volumétricas, o R² ajustado ficou acima de 0,91 e o Syx% foi inferior a 10%. No que diz respeito as funções de afilamento o melhor modelo para descrever o perfil do fuste das espécies foi Hradetzky, com R² ajustado acima de 0,96 e Syx% inferior a 10%. Os modelos de Naslund, Spurr I e II e Naslund modificado foram selecionados para estimar a volumetria das espécies e; o modelo de afilamento de Hradetzky, foi superior aos demais, sendo selecionado para descrever o perfil do fuste das espécies na área de estudo.

Stem taper modeling equation for dahurian larch based on nonparametric regression methods

Stem taper modeling equation for dahurian larch based on nonparametric regression methods

FITTING AND CALIBRATING A MIXED-EFFECTS SEGMENTED TAPER MODEL FOR BRUTIAN PINE

Taper models are one of several necessary tools in modern forest inventory, giving information on diameter at any point along the tree stem and this information can also be used to estimate stem volume. In this study, we used nonlinear mixed-effects (NLME) modeling approach to minimize existing statistical problems in constructing taper equations. A segmented taper model of Max and Burkhart (1976) was fitted using this approach to consider for within- and between-tree variation in brutian pine (Pinus brutia Ten.) stem taper. Based on evaluation statistics, the model including random-effects parameters β 1, β 3 and β 4 were found to be the best. Inclusion of random parameters were not completely eliminated heterogenous variance and autocorrelation in residuals. Incorporating variance function and a continuous autoregressive error structure (CAR(1)) to NLME Max and Burkhart model removed the heteroscedasticity and autocorrelation in residuals. Upper stem diameters were used to localized stem taper model to individual tree. For this, two different measurement scenarios were evaluated as one and two upper stem diameter measurements. Inclusion of random parameters were improved the predictive capability of taper model in particularly the middle and lower sections of stem based on upper stem diameter measurements. The calibration using upper stem diameter measurements can improve the tree-level accuracy of stem taper model is therefore recommended.

Stem taper equations for diameter and volume predictions of Abies cilicica Carr. in the Taurus Mountains, Turkey

Taper equations are an important tool in estimating stem volumes at a multi-product level for sustainable forest management. Nine taper equations are tested from three categories to estimate diameter at specified point on the stem, height at specified diameter, volumes of any desired portion of the stem, and whole tree volume of Taurus fir in Taurus Mountains of Turkey. To account for autocorrelation and multicollinearity present among multiple stem data observations collected from the same tree, proper statistical approaches were used in model fitting. Comparisons are made to determine which equation provides the best overall fit to all data based on four goodness-of-fit statistics, Coefficient of determination (R2); Root mean square error (RMSE), Akaike’s Information Criterion (AIC), and Bayesian information criterion (BIC). Results indicated that all taper equations tested could be used to accurately estimate section diameter at given height and stem volume. Clark et al.’s taper equation provided better results than the others for Taurus fir when an additional stem diameter observation at 5.30 m was available. Segmented and variable-form taper models consistently provided better results than the simple taper models except for Max and Burkhart’s model. Fang et al.’s and Kozak’s taper models showed equally good performance to describe stem taper and to predict tree stem volume. Therefore, these taper equations are able to be used to estimate diameter and volume for Taurus fir trees, if an upper stem diameter measurement was not available.