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。     

苍梧县杉木削度方程与材积比方程研究

在苍梧县共青林场等集体林场的伐区,随机量测样木548株,年龄为20～21年,直径分布6～26cm,树高6～16m,按2m区分段,量测各段中央处的带皮直径、去皮直径,并现场造材,记录不同材种的出材率。并选择模型7为最适宜削度方程,方程11为最适宜材积方程,确定了不同材种不同材长的出材率,编制了苍梧县杉木出材率表。     

油松正形数f_(0.15h)的性质及其应用

陕西的油松林分或单株木用正形数f_(0.15h)与胸高形数、实验形数相比,其带、去皮值相对差异最小。应用关系式f_(0.15h)(带皮)≈f_(0.15h)(去皮),得到新的树皮率计算公式,并可根据带皮材积导算出去皮材积和树皮材积。当树高小于10m时,直接测定0.15h处带、去皮直径;当树高大于10m时,根据带、去皮胸径导算0.15h处带、去皮直径。     

苍梧县杉木削度方程与材积比方程研究

在苍梧县并青林场等集体林场的伐区，随机量测样木５４８株，年龄为２０～２１年，直径分布６～２６ｃｍ，树高６～１６ｍ按２ｍ区分段，量测各段中央处的带皮直径，去皮直径，并现场造材，记录不同材种的出材率，并选择模型７为最适宜削度方程，方程１１为最适宜材积方程，确定了不同材种不同材长的出材率，编制了苍梧县杉木出材率表。     

燕山山地华北落叶松不同测树因子之间的关系研究

华北落叶松(Larix principis-rupprechtii Mayr.)是华北地区森林类型的主要优势树种,本文通过对华北落叶松各测树因子的(胸径和树高)的调查,利用树干解析,建立带皮胸径和去皮胸径、带皮胸径和树高之间的相关关系,并对其结果进行双变量方差分析。结果显示,30年生的华北落叶松树高和胸径都存在极显著相关,而12、15年生差异并不显著;中坡由于处于上下坡位的交界位置,所以胸径树高差异均不明显。     

海南省松树、橡胶树削度方程模型研建

以海南省松树、橡胶树为研究对象,利用Ormerod提出的基本削度方程模型结构,并在此基础上构建可变参数削度方程模型。通过对固定参数与可变参数削度方程模型的比较分析,可知:所建立的松树、橡胶树带皮和去皮削度方程拟合效果均很好,模型确定系数均达到0.93以上,预估精度在99%以上;而可变参数模型要明显优于固定参数模型,是生产中的首选模型。     

用主成份分析确定南方松的干形(续二)

多变量统计方法中之主成份分析法被用于确定美国路易斯安那之火炬松及湿地松树干削度。用了四组资料(三组火炬松、一组湿地松)。资料包括单木在地面基部,0.02、0.04、0.06、0.08处及树高每隔0.1处的直径。这样每组(ⅰ)包括ni株数,每株有14个直径测定值。主成份分析用于每组资料在各个情况下单一的特征超过总方差99％。与主要特征值相关的特征向量元素图,代表了该组资料中的树木干削度的平均值。同组资料在胸径或树高级之间反映在干形上未发现有差别,但具有冠比大于0.51的树木在其树干0.3的上部有较大的削度。不同范围内生长的树木之间在干形上可见明显的差别,生长在同一范围内的两种树种间也有明显差异。同不同方法将第一特征向量内插以获得干削度模型。我们用回归技术,把第一特征向量当作因变量,相应的位置高及它们的幂次当作自变量。这样得到的方程式用于确定材积。我们相信第一主成份特征向量曲线至少是描述干削度规律的近似值。     

湖北省湿地松立木二元材积表的编制

湖北省湿地松栽培区只有少数单位编制出了立木材积表,而且大多具有临时性和偏差性,不仅精度达不到要求,应用范围也相当狭小,且各地区标准不一,可比性差。为此,本研究根据在“七·五”、“八·五”期间对全省湿地松栽培区的抽样调查资料中,挑选出有代表性的118根解析木材料,对每根解析木的年龄、树高、区分龄阶数、区分圆盘数和各圆盘年轮数、各龄阶检尺直径分别整理检算。通过解析计算,求算出各解析木的带皮直径、皮厚、带皮材积、去皮材积,用直接法编制出我省湿地松立木二元材积表。1回归模型的拟合在多个模型的比较上,选择山本…     

云杉落叶松二元材积表的编制

本文利用在管涔林区经营采伐标地内的伐倒木,按2cm 区分段实测各部分带皮去皮直径和稍端长度,计算带皮和去皮材积,按2cm 一个径阶进行归类,用Ⅴ=aD~bH~c分别对云杉和落叶松进行回归,求各径阶对应树高的材积,进而编制成管涔林区云杉落叶松二元材积表。通过对相关系数,单株材积检验,认为该表可在管涔林区使用。     

基于分位数回归和哑变量模型的大兴安岭兴安落叶松树高-胸径模型

【目的】基于Richards方程比较分位数回归和哑变量模型对树高-胸径方程预测精度的影响,为林业树高-胸径模型的构建提供新的思路和方法。【方法】利用大兴安岭4个区域的兴安落叶松Larix gmelinii伐倒木胸径/树高实测数据,采用分位数回归和哑变量模型构建树高-胸径模型,并与基本模型进行对比分析。评价指标采用平均绝对误差(MAE)、均方根误差(RMSE)、确定系数(R2)、赤池信息量(AIC)、贝叶斯信息量(BIC)、平均预测误差百分比(MPE)、平均绝对百分比误差(MAPE)、均方根百分比误差(RMSPE),同时利用非线性额外平方和法进行区域性检验。【结果】1)Richards树高-胸径模型在9个不同的分位点(τ=0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9)都能收敛,且每个区域都有其对应的最优分位数模型,区域1、2、3和4的最优分位数模型所对应的分位数分别是τ=0.7、τ=0.3、τ=0.5和τ=0.3,各区域最优分位数模型与哑变量模型所得结果差异不大,都优于基本模型。2)F检验结果表明哑变量模型的构造是有必要的,区域2和区域4没有显著不同,其他5对区域都有显著不同。3)模型检验结果表明区域1、3、4的最优分位数回归模型都要优于哑变量模型,区域2的哑变量模型没有通过正态性检验(P=0.028 6),因此区域2的最优模型仍然为τ=0.3时的分位数模型。【结论】分位数回归模型和哑变量模型都能够反映不同区域树高-胸径关系的变化,在拟合和检验统计量等方面都表现较好,适合于大兴安岭落叶松树高预测。在进行方法选择时,可以根据数据特征和研究目的进行选择。     

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 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.     

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.     

Estimating and predicting bark thickness for seven conifer species in the Acadian Region of North America using a mixed-effects modeling approach: comparison of model forms and subsampling strategies

In many situations, information on stem diameters inside bark (dib) are more desirable than on diameters outside bark (dob). However, obtaining dib measurements is usually expensive, time-consuming, and prone to significant measurement errors when done on standing trees. Many bark thickness equations have been proposed to estimate the dibs of standing trees. In this study, we compared several commonly used bark thickness equations for seven conifer species in the Acadian Region of North America. Mixed-effects modeling techniques were employed to fit linear and non-linear bark thickness equations. We found the equation proposed by Cao and Pepper (South J Appl Forestry 10:220?C224, 1986; Eq. 5) performed significantly better than other equations for most of our study species. The Cao and Pepper (South J Appl Forestry 10:220?C224, 1986) equation is a function of dob, relative height in the stem, tree height, and the ratio of dib to dob at breast height. The mean absolute bias was found to be reduced up to 74% compared with using a fixed ratio approach employed in the widely used Northeastern variant of the Forest Vegetation Simulator (FVS-NE) growth and yield model. Leave-one-out cross validation was further performed to determine the location of suitable prior measurements in the prediction process for three of the most well-behaved equations. Results show that no unified prior measurement can provide best predictive abilities across all species as the choice of prior dib measurements depends on both species and bark thickness equations.     

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.     

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.     

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.     

A flexible regression model for diameter prediction

We present a functional regression model for diameter prediction. Usually stem form is estimated from a regression model using dbh and height of the sample tree as predictor. With our model additional diameter observations measured at arbitrary locations within the sample tree can be incorporated in the estimation in order to calibrate a standard prediction based on dbh and height. For this purpose, the stem form of a sample tree is modelled as a smooth random function. The observed diameters are assumed as independent realizations from a sample of possible trajectories of the stem contour. The population average of the stem form within a given dbh and height class is estimated with the taper curves applied in the national forest inventory in Germany. Tree deviation from the population average is modelled with the help of a Karhunen–Loève expansion for the random part of the trajectory. Eigenfunctions and scores of the Karhunen–Loève expansion are estimated through conditional expectations within the methodological framework of functional principal component analysis (FPCA). In addition to a calibrated estimation of the stem form, FPCA provides asymptotic pointwise or simultaneous confidence intervals for the calibrated diameter predictions. For the application of functional principal component analysis modelling the covariance function of the random process is crucial. The main features of the functional regression model are discussed informally and demonstrated by means of practical examples.     

Aboveground biomass estimation of small diameter woody species of tropical dry forest

Estimation of accurate biomass of different forest components is important to estimate their contribution to total carbon stock. There is lack of allometric equations for biomass estimation of woody species at sapling stage in tropical dry forest (TDF), and therefore, the carbon stored in this forest component is ignored. We harvested 46 woody species at sapling stage in a TDF and developed regression models for the biomass estimation of foliage, branch, bole and the total aboveground part. For foliage and branch biomass, the models with only stem diameter as estimator showed greater R ². For bole and aboveground biomass, the models including wood specific gravity or wood density exhibited higher R ² than those without wood density. Also, the model consisting of wood density, stem diameter and height had the lowest standard error of estimate for bole and aboveground biomass. Moreover, the R ² values are very similar among models for each component. The measurement error of height and the use of a standard value of wood density together may introduce more than 2 % error into the models. Therefore, we suggest using diameter-only model, which may be more practical and equally accurate when applied to stands outside our study area.     

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.