A merchantable volume system for major pine species in El Salto,Durango (Mexico)

A compatible volume system for the major pine species in El Salto, Durango (Mexico) was developed from data corresponding to 1930 destructively sampled trees. Several well-known taper functions were evaluated and compared against the model selected in a previous study of these pine species in the same area. Appropriate statistical procedures were used in model fitting to account for the problems of autocorrelation and multicollinearity that are associated with the construction of taper functions. A compatible segmented model best described the experimental data and was found to be better than the previously selected model. It is therefore recommended for estimating diameter at a specific height, height to a specific diameter, merchantable volume, and total volume for the five species analyzed. The non-linear extra sum of squares method indicated differences in species-specific taper functions. A different taper function should therefore be used for each pine species.     

Comparison of taper functions between two planted and coppiced eucalypt clonal hybrids, South Africa

In addition to regeneration through seed, certain eucalypts are able to regenerate via the production of coppice shoots following felling, which can then be selectively thinned over time and managed as a coppice stand for the commercial production of timber. Little information could be found if tree form differs between coppiced (where one or two stems had been left per stump) and planted eucalypts, or whether different volume taper models would need to be developed. To determine if this was necessary, rotation-end stem taper data was collected from an Eucalyptus grandis × E. urophylla and an E. grandis × E. camaldulensis trial to compare volume taper equations for planted versus coppiced commercially grown Eucalyptus clonal hybrids. For treatment comparisons, taper data were collected from the parent crop (1R), the replanted crop (2R), as well as from coppiced stands where either a single (Cop_Sngl) or double stem (Cop_Dbl) had been left per stump. Stem taper functions used for treatment comparisons indicated differences between clones, as well as between treatment, with the models based on single stems (1R, 2R or Cop_Sngl) being significantly different from those containing two stems (Cop_Dbl). Despite any non-significant model differences (for example between 1R, 2R and Cop_Sngl single stem crops) the percentage magnitude of any bias in utilizable volume differences when comparing the individual models (between a 6.31% over-prediction to a 3.8% under-prediction) still needs to be taken into account as these differences may have importance in terms of the volume and product prediction.     

A set of models for individual tree merchantable volume prediction for <Emphasis Type="Italic">Pinus pinaster</Emphasis> Aiton in central inland of Portugal

The study purpose selected among several candidate models for best individual tree, over bark, total volume model, volume ratio model to any top height limit and taper model for maritime pine (Pinus pinaster Aiton) in the regions of Pinhal Interior Sul and Beira Interior Sul, Portugal. The data used in the study were collected from 144 felled trees, corresponding to 995 diameter/height measurements. To select among the best models, several statistics were computed during model fitting, and the independent validation procedure was used to evaluate model fitting, collinearity and prediction performance. A ranking index was used to support the final decision. The analysis of models studentized residuals distribution showed that some regression model assumptions, such as normality and homogeneity, were not met. To overcome this unideal situation, the models selected were then fitted again using robust regression and weighted regression techniques. The set of adjusted models will allow the prediction of individual tree, over bark, total volume and merchantable volume to any merchantable limit, for both species and region to support management decisions.     

A taper function for Pseudotsuga menziesii plantations in Spain

Five stem taper models belonging to three different taper function categories were fitted to data corresponding to 282 Pseudotsuga menziesii trees. The trees were selected in the area surrounding 61 research plots installed in Galicia, Asturias and the Basque Country, northern Spain. The models were simultaneously fitted to observed values of diameter outside bark and inside bark. A third-order continuous-time autoregressive error structure was used to account for autocorrelation. Selection of the best model was based on both numerical (goodness-of-fit statistics) and graphical analysis (plots of residuals against position along the stem and against tree size). The three-segmented taper model finally selected has the advantage of being compatible with both a merchantable and a total stem volume equation.     

Segmented taper equations with crown ratio and stand density for Dahurian Larch (<Emphasis Type="Italic">Larix gmelinii</Emphasis>) in Northeastern China

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 a...     

A merchantable volume system for Pinus sylvestris L. in the major mountain ranges of Spain

? Accurate estimation of stem volume makes it possible to estimate the monetary value of one of the many commodities and services that forests provide to society, i.e. timber.

? In the present study a compatible volume system for Scots pine in the major mountain ranges of Spain (the Pyrenees, Southern Iberian Range, Northern Iberian Range, Soria and Burgos Mountains, Central Range and Galician Mountains) was developed with data from 2 682 destructively sampled trees. Several well-known taper functions were evaluated. A second-order continuous-time autoregressive error structure was used to correct the inherent autocorrelation in the hierarchical data, allowing the model to be applied to irregularly spaced and unbalanced data.

? The compatible segmented model of Fang et al. (2000) best described the experimental data. It is therefore recommended for estimating diameter at a specific height, height to a specific diameter, merchantable volume, and total volume for the six mountain ranges analyzed.

? The non-linear extra sum of squares method indicated differences in mountain range-specific taper functions. A different taper function should therefore be used for each mountain range in Spain.

     

Volume estimation of Cryptomeria japonica logs in southern Brazil using artificial intelligence models

This study aimed to test taper functions and artificial intelligence (AI) models in order to estimate merchantable volumes of Japanese cedar (Cryptomeria japonica) trees in a homogenous plantation in southern Brazil. A total of 30 individuals were rigorously scaled and their total volumes were calculated, including those of the following log assortments: veneer, sawn, pulp and energy. Three AI models, i.e. two variants of k-nearest neighbours (KNN) instance-based classification (one and three nearest neighbours) and an artificial neural network (ANN) approach, were compared with three traditional taper models: fifth-order polynomial, fractional powers and the Garay model. The estimated volumes were compared with the actual volumes by means of the standard error (S_yx), bias, precision and accuracy. Total volume estimates proved to be unbiased (maximum bias 5.42%), precise (maximum precision 9.28%) and accurate (maximum accuracy 10.79%) with all of the investigated models. The tested models tended to give lower bias, better precision and accuracy in the middle portion of the stems, but worse estimates at the base and tip (maximum bias ?12.41%). In general, the KNN models improved merchantable volume estimation, particularly KNN1, which is a straightforward and simple method. We conclude that AI techniques have appeal for application in forest inventories and that KNN is a particularly interesting alternative for tree volume estimation.     

Tree taper models for Cupressus lusitanica plantations in Ethiopia

To provide a taper model for planning and management of Cupressus lusitanica plantations in Ethiopia, seven taper models were compared. Four performance indicator statistics were used for comparing the models in their ability to estimate tree diameter, and total and merchantable volumes. For the selected species, Kozak (1988) was found to be the best, followed by modified Lee et al. (2003) and Kozak (2004) as second and third best taper models, respectively. Both the Kozak (Kozak, 1988, 2004) and the modified Lee et al. (2003) models were very flexible in capturing the different shapes of trees. In particular, Kozak (2004) proved to be best of all models in diameter estimation even though it was found to be inferior to the Kozak (1988) and modified Lee et al. (2003) models for total and merchantable volume estimation. To understand the influence of the inflection point p in the Kozak (1988) model, Monte Carlo simulation was used to examine sensitivity of the model performance against inflection point p. In this effort, slightly lower standard errors were observed for p between 0.1 and 0.3. Mixed effects modeling was also used to further study the inflection point p as a random effect. The empirical Bayes estimates of the random effects were found to vary from tree to tree and also appear to depend on tree size. The results from both the Monte Carlo and mixed effects modeling study seem to indicate the need to estimate p from the data.     

Developing a taper model for the Pinus elliottii × P. caribaea var. hondurensis hybrid in South Africa

A relatively new hybrid, Pinus elliottii × P. caribaea var. hondurensis (Pexc), for which a taper model does not exist, is being planted commercially in South Africa. This study primarily focused on developing a taper model for Pexc in South Africa. Taper data were collected from a total of 363 trees, in the Mpumalanga and Limpopo provinces, using a random sampling method. A subsample was selected to determine if altitude, rainfall, temperature or soil have a significant influence on the taper of Pexc. Only rainfall significantly influenced the overall taper. The Max and Burkhart segmented polynomial taper model, as well as the Kozak88, Kozak01 and Kozak02 variable exponent taper models, were fitted, compared and tested using the statistical analysis system (SAS). The predictive ability of the models was evaluated based on the results from the mean bias, standard deviation, the standard error of prediction and the average percentage deviation. The Kozak02 model had the best fit overall followed by the Max and Burkhart model (MB76). The MB76 model, however, predicted the volumes more accurately than the Kozak02 model.     

Mixed-effect non-linear modelling for diameter estimation along the stem of Tectona grandis in mid-western Brazil

This study evaluated the efficiency of taper functions and the application of mixed-effect modelling for diameter estimation along the stems of Tectona grandis. We sampled 266 trees of Tectona grandis, measuring the diameter at relative heights for volume determination, grouping the data according to three form-factor classes. Six taper functions were fitted, selecting the function with better fit performance. Six taper functions were fitted, selecting the function with better fit performance. The selected function was fitted in its basic formulation, and with the mixed non-linear modelling technique in different scenarios, and for the stem stratified in three portions of the total height. The precision and selection of the adjusted models were evaluated regarding the coefficient of determination, standard error of estimate, the Akaike information criterion, bias, quadratic error and absolute bias. According to the statistical criteria used, the model of Kozak was selected for the adjustments. For diameter estimation, the scenario with two coefficients as random effects provided an accuracy increase of 11.91%, and the mixed non-linear modelling better estimated the stem diameter for the stratified stems. In conclusion, the model of Kozak can be used to describe the stem shape of Tectona grandis, and the mixed-effect non-linear model approach was the best technique to estimate diameter along the stem of Tectona grandis.     

A flexible stem taper and volume prediction method based on mixed-effects B-spline regression

Modelling stem taper and volume is crucial in many forest management and planning systems. Taper models are used for diameter prediction at any location along the stem of a sample tree. Furthermore, taper models are flexible means to provide information on the stem volume and assortment structure of a forest stand or other management units. Usually, taper functions are mean functions of multiple linear or nonlinear regression models with diameter at breast height and tree height as predictor variables. In large-scale inventories, an upper diameter is often considered as an additional predictor variable to improve the reliability of taper and volume predictions. Most studies on stem taper focus on accurately modelling the mean function; the error structure of the regression model is neglected or treated as secondary. We present a semi-parametric linear mixed model where the population mean diameter at an arbitrary stem location is a smooth function of relative height. Observed tree-individual diameter deviations from the population mean are assumed to be realizations of a smooth Gaussian process with the covariance depending on the sampled diameter locations. In addition to the smooth random deviation from the population average, we consider independent zero mean residual errors in order to describe the deviations of the observed diameter measurements from the tree-individual smooth stem taper. The smooth model components are approximated by cubic spline functions with a B-spline basis and a small number of knots. The B-spline coefficients of the population mean function are treated as fixed effects, whereas coefficients of the smooth tree-individual deviation are modelled as random effects with zero mean and a symmetric positive definite covariance matrix. The taper of a tree is predicted using an arbitrary number of diameter and corresponding height measurements at arbitrary positions along the stem to calibrate the tree-individual random deviation from the population mean estimated by the fixed effects. This allows a flexible application of the method in practice. Volume predictions are calculated as the integral over cross-sectional areas estimated from the calibrated taper curve. Approximate estimators for the mean squared errors of volume estimates are provided. If the tree height is estimated or measured with error, we use the “law of total expectation and variance” to derive approximate diameter and volume predictions with associated confidence and prediction intervals. All methods presented in this study are implemented in the R-package TapeR.     

兴安落叶松树干去皮直径预测模型

利用兴安落叶松解析木数据,比较了树干去皮直径预测的3种类型模型:Grosenbaugh的比率方程式、回归模型和削度方程。Grosenbaugh的比率方程式有很大的灵活性,没有参数不需要模型拟合。总体评价和模型分段比较表明,回归模型有较小的预测误差,尤其是Cao and Pepper提出的含有带皮直径、树高、相对树高、胸径处的带皮直径和去皮直径变量的模型。由于削度模型不含有带皮直径变量,因此产生较大的去皮直径预测误差。不同类型的模型在森林经营过程中都有一定的适应性。     

A stem taper equation compatible to volume equation for <Emphasis Type="Italic">Paraserianthes falcataria </Emphasis>in Pare,East Java,Indonesia: its implications for the plantation management

A stem taper equation compatible to the volume equation was derived from the data of 172 trees sampled in the three plantations of Paraserianthes falcataria in Pare, East Java. The stem taper equation in this study was based on a conventional logarithmic volume equation, with the addition of one free parameter that minimized the standard errors of estimate to the observed diameter of stems at 1.0-m intervals. The derived equation was able to predict the stem taper of P. falcataria reasonably well, while it was not flexible enough to describe delicate changes of the taper in the upper portion of stem. The equation was able to predict bole length and the volume up to the top diameter 20 cm, the diameter size merchantable for sawn timber in Indonesia, with reasonable accuracy. An appropriate rotation age for sawn-timber production was found to be 8–9 years old, at which the mean annual increment of sawn timber would be maximized.     

Stem taper equation analysis for Larix kaempferi species in the Central Region of South Korea

Taper equation was developed to predict diameters at specific height for Larix kaempferi species in the Central Region of South Korea. The sampled trees that were collected through destructive sampling ranged from 0.60 to 47.90 cm DBH with total height ranging from 2.00 to 33.00 m. The dataset was randomly split into two: 80% for initial model fitting and 20% for model validation. The combined that means 100% dataset was used for final model fitting. Statistics of fit were used as criteria, including the coefficient of determination (R²), standard error of the estimate (SEE), bias (ē), the absolute mean difference (AMD), and the Akaike information criterion (AIC) values and weight (AICw), with a rank analysis being applied. Initial model fitting utilized a total of nine taper equations, with the three segmented taper equations and another three non-segmented determined for model validation and final model fitting. Kozak02 equation, which had not yet been evaluated for L. kaempferi species, indicated the best performance for the species in the Central Region of South Korea. Upon comparison, the ability of this study to predict diameters at specific height and stem volume was better than the existing taper equation for L. kaempferi in South Korea.     

Stem taper functions for Betula platyphylla in the Daxing'an Mountains,northeast China

Accurate prediction of stem diameter is an important prerequisite of forest management.In this study,an appropriate stem taper function was developed for upper stem diameter estimation of white birch(Betula platyphylla Sukaczev) in ten sub-regions of the Daxing'an Mountains,northeast China.Three commonly used taper functions were assessed using a diameter and height dataset comprising 1344 trees.A first-order continuous-time error structure accounted for the inherent autocorrelation.The segmented model of Max and Burkhart(For Sci 22:283-289,1976.https://doi.org/10.1093/forestscience/22.3.283) and the variable exponent taper function of Kozak(For Chron 80:507-515,2004.https://doi.org/10.5558/tfc80507-4) described the data accurately.Owing to its lower multicollinearity,the Max and Burkhart(1976) model is recommended for diameter estimation at specific heights along the stem for the ten sub-regions.After comparison,the Max and Burkhart(1976) model was refitted using nonlinear mixed-effects techniques.Mixed-effects models would be used only when additional upper stem diameter measurements are available for calibration.Differences in region-specific taper functions were indicated by the method of the non-linear extra sum of squares.Therefore,the particular taper function should be adjusted accordingly for each sub-region in the Daxing'an Mountains.     

Nonlinear mixed-effects modeling of variable-exponent taper equations for lodgepole pine in Alberta,Canada

Four variable-exponent taper equations and their modified forms were evaluated for lodgepole pine (Pinus contorta var. latifolia Engelm.) trees in Alberta, Canada. A nonlinear mixed-effects modeling approach was applied to account for within- and between-tree variations in stem form. Even though a direct modeling of within-tree autocorrelation by a variance–covariance structure failed to achieve convergence, most of the autocorrelation was accounted for when random-effects parameters were included in the models. Using an independent data set, the best taper equation with two random-effects parameters was chosen based on its ability to predict diameter inside bark, whole tree volume, and sectioned log volume. Diameter measurements from various stem locations were evaluated for tree-specific calibrations by predicting random-effects parameters using an approximate Bayesian estimator. It was found that an upper stem diameter at 5.3 m above ground was best suited for calibrating tree-specific predictions of diameter inside bark, whole tree volume, and sectioned log volume.     

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

? Context

Despite the economic importance of Castanea sativa Mill. in northwest Spain, studies of its growth and yield are practically non-existent.

? Aims

A compatible system formed by a taper function, a total volume equation, and a merchantable volume equation was developed for chestnut (C. sativa Mill.) coppice stands in northwest Spain.

? Methods

Data from 203 destructively sampled trees were used for the adjustment. Outliers were removed with a non-parametric local adjustment, providing a final data set of measurements taken from 3,188 sections which was used to test five taper models (compatible and non-compatible). A second-order continuous autoregressive error structure was used to model the error term and account for autocorrelation. Presence of multicollinearity was evaluated with the condition number. Comparison of the models was carried out using overall goodness-of-fit statistics and graphical analysis.

? Results

Results show that the models developed by Fang et al. in For Sci 46: 1–12, 2000 and Kozak in For Chron 80, N 4: 507–515, 2004 were superior to other equations in predicting diameter for chestnut coppice stands.

? Conclusion

The compatible volume system developed by Fang et al. in For Sci 46: 1–12, 2000 was finally selected as it provided the best compromise between describing stem profile and also estimating merchantable height, merchantable volume, and total volume and therefore provides the first specific tool for more effective management of chestnut coppice stands.     

Representation of tree stem taper curves and their dynamic, using a linear model and the centroaffine transformation

One main task of forestry is a reliable estimation of the stem form and its development applied in calculating total and log volume. As long as process-oriented models are not available for this practical use, empirical models must serve instead. Taper curve data of trees within stands normally show a rank maintenance,i.e., a tree which has a greater diameter than another one at a certain height, is most probably bigger at any other height, too. This property also applies to the analysed tree species, sugi (Cryptomeria japonica) and hinoki (Chamaecyparis obtusa), and will be well-represented by a linear model formulation. As model parameter sets of single stands have a very limited time validity, two approaches for future stem form prediction are discussed. The one, the centroaffine transformation of a linear taper curve function, is not suitable for representing the time-depending change of the stem form. However, this can be done by a linear unit taper curve model, the parameters of which are based on sample trees of stands of several age classes. Temporary unit parameter sets are derived for sugi and hinoki and the estimated stand volumes are compared to the real ones to evaluate the model performance, which turned out to be very good. We would like to express our gratitude to the Japan Science and Technology Corporation for the financial promotion, which enabled this research work.     

Development and validation of stem volume models for Pinus kesiya in Benguet province,Philippines

Stem volume equations (overbark) were developed, using established volume equation forms, and validated using a subset of the data collected for Pinus kesiya in Benguet province, Philippines. A total of 481 trees from Pinus kesiya stands in Benguet were measured through non-destructive sampling. The data set was randomly split into two subsets for initial model development (80% of the data set) and validation (20% of the data set). The performance of the different models was evaluated using evaluation statistics: fit index (FI), root mean square error (RMSE), bias (ē), absolute mean difference (AMD) and coefficient of variation (CV%). The best model forms were selected for final model development using the combined data set (100%). Overall, volume models with two independent variables (DBH and total height) performed better than models with only one (DBH). In the validation of the models, it was observed that AMD of the models converged in the DBH classes with higher sample size. Furthermore, one of the best models in this study, Model 2, also performed better when compared to the general single volume equation developed for the non-dipterocarp species in regions 1, 2, 3 and the Cordillera Administrative Region (CAR) of the Philippines. The models developed in this study may assist forest managers acquire improved stem volume predictions of Pinus kesiya in the forests of Benguet, Philippines.     

Regional estimation of Japanese cedar (<Emphasis Type="Italic">Cryptomeria japonica</Emphasis> D. Don) productivity by use of digital terrain analysis

Digital terrain modeling and spatial climatic data have been used to estimate the spatial distribution of Japanese cedar (Cryptomeria japonica D. Don) forest productivity on a regional-scale. The study was conducted on Japanese cedar forests in Himi city, Oyabe city, Takaoka city, and Imizu city (a total area of 683 km²) in northwestern Toyama Prefecture. On the basis of data from 146 sample stands, above-ground net primary productivity (ANPP) was calculated from tree height, age, and density using existing ANPP conversion equations for Japanese cedar stands. Six topographic factors (slope, profile curvature, plan curvature, openness, wetness index, and topographic radiation index) were calculated from a 10-m cell size digital elevation model. Three climatic factors (annual mean temperature, annual total precipitation, and annual maximum snow depth) were obtained from an existing spatial data set. Relationships between ANPP and environmental factors were analyzed by regression tree models. For the tree model with ANPP as a dependent variable, four environmental factors (annual mean temperature, wetness index, openness, topographic radiation index) were adopted as independent variables. Annual mean temperature was the first split variable in this model and explained 25.5% of the total deviance in ANPP. Wetness index, which represents soil moisture variation caused by lateral flow, explained 11.5% of the total deviance in ANPP. The resulting tree model explained approximately half of the total deviation in ANPP and indicated that the spatial distribution of Japanese cedar productivity was controlled by regional-scale interactions between climatic and topographic processes. A high-resolution map of productivity was prepared by use of the ANPP prediction model and vegetation information obtained from satellite data.