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 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.     

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...     

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.     

Improving harvester estimates of bark thickness for radiata pine (Pinus radiata D.Don)

Harvesters estimate bark thickness primarily from diameter over bark (DOB) and use it to estimate log volume and value. Harvester bark thickness estimation errors can reduce returns through poor bucking optimisation and out-of-specification logs. Radiata pine bark thickness data from harvested logs and permanent sample plots (PSP) were analysed to determine best-fit coefficients for current and potential future harvester bark thickness models. The most suitable current harvester bark thickness model for radiata pine is: double bark thickness = b ₀ + b ₁*DOB (the ‘DOB model’). This describes a straight line, whereas radiata pine bark relative to DOB is thicker near the stem base and consistent over the remainder. PSP data set coefficients for this model overestimated upper stem bark thickness and underestimated lower stem values. The harvester model for Scots pine bark fitted better than the DOB model for diameters <400 mm but performed poorly for larger logs, as it is restricted to trees with a diameter at breast height <590 mm. Two better models were identified: (1) a model using relative height to account for bark thickness changes with height, and (2) implementing separate DOB models for the bottom 10% and top 90% of the stem split by relative height. These approaches require approval by the StanForD committee to be implemented. Prior to approval, the upper 90% model coefficients could be applied to the entire stem to improve upper 90% stem volume and value predictions at the expense of the lower 10%. Further research will determine if this approach produces acceptable results when optimising bucking. Increasing variability of bark thickness estimates with increasing DOB in the PSP data set may reflect manual measurement errors with thicker bark or may show that additional explanatory variables are needed. Efforts to identify new variables would need to be weighed against additional returns and probable reductions in numbers of larger trees by as the clearfell age is reduced.     

黑龙江东部地区落叶松人工林削度方程研究

文章以佳木斯孟家岗林场的不同年龄、不同密度及不同立地条件的落叶松人工林为研究对象，选取130株样木，测定每株样木15个相对高处的带皮直径，采用非线性回归模型的参数估计方法拟合5个削度方程，根据所计算各削度方程的拟合统计量和残差分析，选择最佳削度方程。研究结果表明，模型V-修正Kozak（1994）式为拟合效果最好的落叶松人工林可变参数削度方程。该模型拟合精度高，而且预测误差低、预估精度高，可以很好地估计落叶松不同林木大小任意部位的去皮直径或任意小头直径时的材长，为编制落叶松人工林材种出材率表提供基础。     

Non-destructive measurement techniques for taper equation development: a study case in the Spanish Northern Iberian Range

In recent years, the technology for measuring the diameter and height of standing trees has improved significantly. These enhancements allow estimation of the volume of standing trees using stem taper equations, which traditionally have been constructed with data from felled trees, in an accurate and economically feasible way. A non-destructive method was evaluated with data from 38 pines and was validated with data from another 38 pines, both in the Northern Iberian Range (Spain). The electronic dendrometer Criterion RD1000 (Laser Technology Inc.) and the laser hypsometer TruPulse (Laser Technology Inc.) were used due to their accuracy and interoperability. The methodology was valid (unbiased and precise) measuring from a distance similar to the height of the tree. In this distance, statistical criteria and plots based on the residuals showed no clear advantage in volume estimation with models fitted with data from destructive methods against models fitted with data from the proposed non-destructive technique. This methodology can be considered useful for individual volume estimation and for developing taper equations.     

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.     

Modeling stem profile of Lebanon cedar,Brutian pine,and Cilicica fir in Southern Turkey using nonlinear mixed-effects models

The Max and Burkhart segmented taper model was fitted using nonlinear mixed-effects modeling techniques to account for within- and between-individual stem profile variation for Lebanon cedar (Cedrus libani A. Rich.), brutian pine (Pinus brutia Ten.), and cilicica fir (Abies cilicica Carr.) in Turkey. About 75% of the trees were randomly selected for model development, with the remainder used for model validation. Diameter measurements from various heights were evaluated for tree-specific calibrations by predicting random-effects parameters using an approximate Bayesian estimator. The procedure was tested with a validation dataset. Predictive accuracy of the model was improved by including random-effects parameters for a new tree based on upper stem diameter measurements. Prediction in stem diameter was less biased and more precise across the all sections of bole when compared to predictions based only on fixed-effects parameters. In the future, the proposed mixed models can be applied to region wide three species stands by fitting the model to a larger data set that more closely represents regional variation.     

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.     

Pine needle consumption and bark stripping by sheep grazing annual pastures in young stands of widely spaced Pinus radiata and P. pinaster

The consumption of the pine needles and the stripping of bark by sheep grazing annual pastures in three open stands of P. radiata and one of P. pinaster were measured. The P. radiata were four years old and the densities were 250, 500 and 750 trees ha^-1. The P. pinaster included two, three and four year-old trees and the density was 440 trees ha^–1.Needles were eaten immediately after the sheep were admitted and this continued throughout the year. Within ten weeks of the start of winter grazing, sheep stocked at 7–10 ha^–1 had eaten about half of the accessible needles on both species where densities were less than500 trees ha^–1. The estimated consumption was about 260 g sheep^–1 day^–1 for the P. radiata. Bark stripping then commenced and continued throughout spring and summer on most plots. In some plots at low tree density, bark was stripped from more than 35% of the trees. In denser stands, needle consumption per tree was less and bark was stripped from less than 5% of the trees.Bark damage was most common on the smaller trees, and severity of stripping was negatively correlated with tree size. Of all the trees with bark damage, 22% of the P. pinaster and 14% of the P. radiata had more than half of the stem circumference stripped. A number of these will probably suffer both stem distortion and growth retardation, and some may die.Methods of reducing the incidence of bark damage are discussed.     

桂西南米老排人工林单株生物量回归模型

通过对桂西南大青山林区28a生米老排(Mytilaria laosensis)人工林林分进行每木检尺和生物量的测定,建立了米老排各器官生物量与胸径、树高和胸径平方乘树高(D2 H)的相关关系;分别选用幂函数等5种模型,用回归分析方法对米老排人工林单株生物量模型进行了拟合。结果表明:树叶和树根生物量分别与胸径和树高的相关关系最显著,而树干、树枝、树皮和全株的生物量都与D2 H的相关关系最为显著。胸径、树高和D2 H与各器官生物量拟合的模型中,全株、树干和树皮的拟合效果最好,树叶和树根的拟合效果中等,树枝的拟合效果较差。除树皮外,各器官均以幂指数模型的拟合效果最好。     

An evaluation of the conical approximation as a generic model for estimating stem volume, biomass and nutrient content in young Eucalyptus plantations

Accurately and non-destructively quantifying the volume, mass or nutrient content of tree components is fundamental for assessing the impact of site, treatment, and climate on biomass, carbon sequestration, and nutrient uptake of a growing plantation. Typically, this has involved the application of allometric equations utilising diameter and height, but for accurate results, these equations are often specific to species, site, and silvicultural treatment. In this study, we assessed the value of incorporating a third piece of information: the height of diameter measurement. We derived a more general volume equation, based on the conical approximation, using a diameter projected to the base of the tree. Common equations were developed which allowed an accurate estimate of stem volume, dry weight and nutrient content across two key plantation grown eucalypt species, Eucalyptus grandis W. Hill ex Maiden and Eucalyptus globulus (Labill.). The conical model was developed with plantation-grown E. grandis trees ranging from 0.28 to 15.85 m in height (1.05 g to 80.3 kg stem wood dry weight), and E. globulus trees ranging from 0.10 to 34.4 m in height (stem wood dry weight from 0.48 g to 652 kg), grown under a range of contrasting cultural treatments, including spacing (E. grandis), site (E. globulus) and fertilization (nitrogen and phosphorus) for both species. With log transformed data the conical function (V_con) was closely related to stem sectional volume over bark and stem weight (R² = 0.996 and 0.990, respectively) for both E. grandis and E. globulus, and the same regressions can be applied to both species. Back transformed data compared with the original data yielded modelling efficiencies of 0.99 and 0.97, respectively. Relationships between V_con and bark dry weight differed for the two species, reflecting differing bark characteristics. Young trees with juvenile foliage had a different form of relationship to older trees with intermediate or adult foliage, the change of slope corresponding to heights about 1.5 m for E. grandis and age 1 year for E. globulus. The V_con model proved to be robust, and unlike conventional models, does not need additional parameters for estimating biomass under different cultural treatments. More than 99% of the statistical variance of the logarithm of biomass was accounted for in the model. V_con captures most of the change in stem taper associated with cultural treatments and some of the change in stem form that occurs after the crown base has lifted appreciably. Fertilization increased N and P concentrations in stem wood and bark, and regressions to estimate N and P contents (the products of biomass and concentration) were dependent on treatment. For instance, there was a large growth response to N fertilization in E. globulus corresponding with a change (P < 0.05) in the intercept of the regression to estimate N content.     

Stem taper functions for maritime pine (<Emphasis Type="Italic">Pinus pinaster</Emphasis> Ait.) in Galicia (Northwestern Spain)

A total of 31 taper functions from 3 different groups of models (single, segmented and variable-form taper functions) were fitted to diameter-height data from 203 Pinus pinaster trees sampled across even-aged stands in Galicia (northwestern Spain). Most of the taper functions analyzed showed problems of multicollinearity as indicated by the condition number. A second-order autoregressive CAR(2) error process was incorporated into the models to minimize the effect of autocorrelation inherent in the longitudinal data used, and to provide valid tests of significance for model parameter estimates. In general, variable-form taper functions provided the most accurate predictions. The flexibility and predictive performance of the variable-form model developed by Kozak (For Chron 80(4):507–515, 2004) indicated its usefulness for estimating diameter at a specific height, merchantable volume, and total volume of Maritime pine in the study area.     

Estimation of taper curve using stand variables and sample tree measurements

The aim of the study was to develop methods for estimating the taper curves for trees tallied in a forest inventory. The average stem form in a stand was described by the principal components of the stand effects in the stem dimensions measured in the polar coordinate system. Measurements of diameter at breast height, diameter at a height of 6 meters, and height taken from trees on the sample tree plots were used for determining the first four principal components. Regression models were derived to predict the principal components from the site and growing stock variables. These models were used to estimate the taper curves of the tallied trees. Use of the principal components estimated by the regression models gave less reliable results than use of the principal component estimates based on measurement of the height of one randomly chosen tree on the sample plot. The best result was found with combined use of the principal component estimates and one height measurement per sample plot.     

Stem taper equations for poplars growing on farmland in Sweden

We developed a simple polynomial taper equation for poplars growing on former farmland in Sweden and also evaluated the performance of some well-known taper equations. In Sweden there is an increasing interest in the use of poplar. Effective management of poplar plantations for high yield production would be facilitated by taper equations providing better predictions of stem volume than currently available equations. In the study a polynomial stem taper equation with five parameters was established for individual poplar trees growing on former farmland. The outputs of the polynomial taper equation were compared with five published equations. Data for fitting the equations were collected from 69 poplar trees growing at 37 stands in central and southern Sweden (lat. 55-60° N). The mean age of the stands was 21 years (range 14-43), the mean density 984 stems ha -1 (198 3,493), and the mean diameter at breast height (outside bark) 25 cm (range 12-40). To verify the tested equations, performance of accuracy and precision diameter predictions at seven points along the stem was closely analyzed. Statistics used for evaluation of the equations indicated that the variable exponent taper equation presented by Kozak (1988) performed best and can be recommended. The stem taper equation by Kozak (1988) recommended in the study is likely to be beneficial for optimising the efficiency and profitability of poplar plantation management. The constructed polynomial equation and the segmented equation presented by Max & Burkhart (1976) were second and third ranked. Due to the statistical complexity of Kozak’s equation, the constructed polynomial equation is alternatively recommended when a simple model is requested and larger bias is accepted.     

Characterization of Douglas-fir grown in Portugal: heartwood,sapwood, bark,ring width and taper

Douglas-fir (Pseudotsuga menziesii) is one of the best timber conifers providing long sawnwood components. Original from North America, it has been planted in Europe on approximately 550 thousand ha. Twenty Douglas-fir trees growing in two sites in Portugal were studied regarding ring analysis, heartwood, sapwood and bark development, and taper. The radial growth rate was 7.1 and 6.6 mm year⁻¹ at stem base for 45- and 50-year-old trees, respectively, in the two sites. Initial growth rate was slower, increasing until about 20 years and decreasing afterwards. Heartwood proportion represented on average 49% of the cross section in the lower part of the stem and decreased upwards. Heartwood formation was estimated to start at a cambial age of 8–9 years and increasing by 0.7–0.9 rings year⁻¹. Sapwood width was on average 75 mm at stem base, decreasing upwards. Bark was 26–27 mm thick at stem base, where it represented 15% of the cross-sectional area and decreased to 3–5 mm at the top. Stemwood and heartwood tapers were on average 15 mm m⁻¹ in the lower stem part and 21 and 18 mm m⁻¹, respectively, in the upper part. Douglas-fir showed a good potential for the mountain areas of Portugal, and under the silvicultural conditions of both stands the trees presented ring homogeneity, small conicity and low taper suitable for long wood components.

     

A simple stem taper model with mixed effects for boreal black spruce

We simplified Kozak’s taper model by setting the inflection point at 1.3 m (dbh) without losing accuracy and precision. The simplification was required to facilitate the estimation of the covariance parameters when using a mixed-effects method. This method was necessary to take into account the correlation among multiple diameter measurements on an individual stem. The simple stem taper model was fitted to an extended data set collected across the province of Quebec, Canada. Comparison of the predicted stem taper and the derived stem volume with those obtained using existing models showed a comparable predictive power for the simple model. Including a prediction of the tree random effects based on supplementary diameter measurements of the bole improves the predictive ability of the model around the extra diameter observation. This model offers welcome simplicity as a means of predicting tree taper at coarse resolution for planning tree harvesting.     

广西马尾松经济材出材率表编制研究

以马尾松人工林作为研究对象,用伐倒木样木数据,经干形分析和多指标精度比较,选定最佳的削度方程;通过树皮率方程和树高曲线方程进行计算机理论造材,依据各经济材种规格,编制出马尾松胸径树高二元经济材出材率表。经检验,以该方法编制的出材率表达到林业数表模型编制的精度要求。     

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.