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 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.     

Comparison of model forms for estimating stem taper and volume in the primary conifer species of the North American Acadian Region

? The performance of ten commonly used taper equations for predicting both stem form and volume in balsam fir [Abies balsamea (L.) Mill], red spruce[Picea rubens (Sarg.)], and white pine[Pinus strobus (L.)] in the Acadian Region of North America was investigated.

? Results show that the Kozak (2004) and Bi (2000) equations were superior to the other equations in predicting diameter inside bark for red spruce and white pine, while the Valentine and Gregoire (2001) equation performed slightly better for balsam fir.

? For stem volume, the Clark et al. (1991) equation provided the best predictions across all species when upper stem diameter measurements were available, while the Kozak (2004) and compatible taper equation of Fang et al. (2000) performed well when those measurements were unavailable.

? The incorporation of crown variables substantially improved stem volume predictions (mean absolute bias reduction of 7–15%; root mean square error reduction of 10–15%) for all three species, but had little impact on stem form predictions.

? The best taper equation reduced the predicted root mean square error by 16, 39, and 45% compared to estimates from the widely used Honer (1965) regional stem volume equations for balsam fir, red spruce, and white pine, respectively.

? When multiple taper equations exist for a certain species, the use of the geometric mean of all predictions is an attractive alternative to selecting the “best” 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.     

河南省杨树材种出材率表的研编

用削度方程和单株带皮—去皮胸径的转换关系式两个模型对河南省杨树进行计算机理论造材．经精度检验，满足要求，方法可行，依此编制了河南省杨树材种出材率表。     

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。     

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.     

理论造材:削度方程和出材率表的编制

本文提出了计算机理论造材仅根据削度方程和单株带,去皮胸径的转换关系式两个模型,可不必由削度方程推导材长方程和材积比方程。比相关指数,均方程为指标,结合残差图分析,选择了杉木、落叶松的削度方程;结合标准树高曲线,是可仅根据优势高为任一具体林分编制（一元）单株出材率表（特称之为自动调整出材率表）。     

Crown area allometries for estimation of aboveground tree biomass in agricultural landscapes of western Kenya

Classical allometries determine biomass from measurements of diameter at breast height or volume. Neither of these measurements is currently possible to be derived directly from remote sensing. As biomass estimates at larger scales require remotely sensed data, new allometric relations are required using crown area and/or tree height as predictor of biomass, which can both be derived from remote sensing. Allometric equations were developed from 72 trees semi-randomly selected for destructive sampling in three 100?km² sentry sites in western Kenya. The equations developed fit the data well with about 85?% of the observed variation in aboveground biomass explained by crown area. Addition of height and wood density as second predictor variables improved model fit by 6 and 2?% and lowered the relative error by 7 and 2?%, respectively. The equation with crown area in combination with height and wood density estimated representative aboveground biomass carbon to be about 20.8?±?0.02?t?C?ha^?1; which is about 19?% more than the amount estimated using an allometry with diameter at breast height as predictor. These results form the basis for a new generation of allometries using crown area as a predictor of aboveground biomass in agricultural landscapes. Biomass predictions using crown area should be supported by height and wood density and the application of crown area equations for remote sensing based up-scaling should consider crown interactions with competing or coexisting neighboring trees.     

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.     

Within crown variation in the relationship between foliage biomass and sapwood area in jack pine

The relationship between sapwood area and foliage biomass is the basis for a lot of research on eco-phyisology. In this paper, foliage biomass change between two consecutive whorls is studied, using different variations in the pipe model theory. Linear and non-linear mixed-effect models relating foliage differences to sapwood area increments were tested to take into account whorl location, with the best fit statistics supporting the non-linear formulation. The estimated value of the exponent is 0.5130, which is significantly different from 1, the expected value given by the pipe model theory. When applied to crown stem sapwood taper, the model indicates that foliage biomass distribution influences the foliage biomass to sapwood area at crown base ratio. This result is interpreted as being the consequence of differences in the turnover rates of sapwood and foliage. More importantly, the model explains previously reported trends in jack pine sapwood area at crown base to tree foliage biomass ratio.     

Allometric equations for estimating the foliage biomass of Scots pine

The research described in this paper was performed in the Niepolomice Forest (Southern Poland) in 2001 as part of the Forest Environmental Monitoring and Management System (FOREMMS; 5FP IST) project. The material for the present study consisted of the measurement results of the biomass of Scots pine shoots with needles and needles alone carried out on 113 felled sample trees. The purpose of this study was to construct empirical equations for estimating the foliage biomass of Scots pine from easy to measure parameters. To achieve this aim, the dependence of the foliage biomass of Scots pine on stem diameter, height, age, crown length, basal area increment of the trees was analyzed. Using the biometric characteristics such as: tree diameter at breast height (dbh), basal area increment, age, height, and crown length empirical equations for estimating the foliage biomass of Scots pine reasonably precisely have been established. The created empirical equation gives accurate foliage biomass estimates. The explained variability varies between 65 and 85%, it depends on the number of variables applied in the equation. The equations presented in this paper were created with a view to their possible use in ecological studies where biomass quantity may be used, for example, in modeling carbon circulation in the forest ecosystem. From the point of view of forestry practice, these equations may help to assess biomass production in Scots pine stands.     

云南省云杉立木生物量模型研建

以云南云杉为研究对象,对云杉地上生物量和地下生物量模型进行研建。建立云杉地上总生物量、树干、树冠、干材、干皮、树枝、树叶独立模型与材积相容模型,采用分级联合控制和度量误差模型方法,建立地上总生物量和所有分量相容的立木生物量模型,建立根茎比模型对云杉地下生物量进行估计。结果表明：建立的云杉地上总生物量、树干、干材生物量二元模型预估精度均达95％以上,干皮生物量模型预估精度达94％以上,树冠、树叶、树枝生物量的预估精度均在92％以上,地下生物量模型预估精度在88％以上;所建立的模型可以用于云杉生物量的估计。     

Crown architecture of stand-grown sugar maple (Acer saccharum Marsh.) in the Adirondack Mountains

Leaf and crown morphology of shade-tolerant sugar maple (Acer saccharum Marsh.) were examined to test the hypotheses (1) that leaf area exhibits significant plasticity both within and between crown classes and individual tree crowns and (2) that leaf area is accurately predicted from estimates of crown volume. A total of 18 trees, ranging from 3.3 to 43.4 cm dbh, were felled and dissected into upper, middle, lower, and below-crown layers, for measurements of leaf, bark, and xylem dimensions. For dominant trees only, bark thickness and xylem radii were higher within the crown than below the crown. Cumulative leaf area index increased with decreasing stratum height at similar rates in all trees, except for two trees that were located in the understory. Area leaf weight declined with decreasing stratum height within the crown of all except four overstory trees. These four trees showed an increase with decreasing stratum height, i.e., leaves were heavier per unit area in the lower crown stratum and below the crown than they were at mid-crown. Within-tree leaf area density was usually higher in the upper crown of overstory trees and in the lower crown of understory trees. Total crown volume was the best predictor of whole-tree leaf area, but it was only slightly better than dbh.     

Integrated individual tree biomass simultaneous equations for two larch species in northeastern and northern China

Forest biomass estimation at large scale has become an important topic in the background of facing global climate change, and it is fundamental to develop individual tree biomass equations suitable for large-scale estimation. Based on the measured data of biomass components and stem volume from 100 sample trees of two larch species (Larix gmelinii and L. principis-rupprechtii) in northeastern and northern China, an integrated equation system including individual tree biomass equations, stem volume equation and height–diameter regression model were constructed using the dummy variable model and error-in-variable simultaneous equations. In the system, all the parameters of equations were estimated simultaneously, so that the aboveground biomass equation was compatible to stem volume equation and biomass conversion factor (B_CF) function; the belowground biomass equation was compatible to root-to-shoot ratio (R_SR) function; and stem wood, stem bark, branch and foliage biomass equations were additive to aboveground biomass equation. In addition, the system also ensured the compatibility between one- and two-variable models. The results showed that: (1) whether aboveground biomass equations or belowground biomass equations and stem volume equations, the estimates for larch in northeastern China were greater than those in northern China; (2) B_CF of a larch tree decreased with the growing diameter while R_SR increased with the growing diameter; (3) the proportion of stem wood biomass to aboveground biomass increased with the growing diameter while those of stem bark, branch, and foliage biomass decreased.     

雷州尾叶桉树冠指标与抚育间伐关系的探讨

通过对雷州尾叶桉树冠有效受光面积、树冠比率、树冠投影面积进行调查研究,分别用树冠有效受光面积、树冠比率、投影面积与胸径建立一元幂函数回归方程进行研究与分析,结果表明树冠有效受光面积公式对指导培育中径材较好;树冠比率与树冠投影面积公式的回归效果基本一致,对指导培育小径材较为理想,并利用上述回归公式编制单株营养面积、公顷立木株数和公顷基面积表为尾叶桉人工林的抚育间伐设计与施工提供理论依据。     

Development of equations for predicting Puerto Rican subtropical dry forest biomass and volume

Carbon accounting, forest health monitoring and sustainable management of the subtropical dry forests of Puerto Rico and other Caribbean Islands require an accurate assessment of forest aboveground biomass (AGB) and stem volume. One means of improving assessment accuracy is the development of predictive equations derived from locally collected data. Forest inventory and analysis (FIA) measured tree diameter and height, and then destructively sampled 30 trees from 6 species at an upland deciduous dry forest site near Ponce, Puerto Rico. This data was used to develop best parsimonious equations fit with ordinary least squares procedures and additive models fit with nonlinear seemingly unrelated regressions that estimate subtropical dry forest leaf, woody, and total AGB for Bucida buceras and mixed dry forest species. We also fit equations for estimating inside and outside bark total and merchantable stem volume using both diameter at breast height (d.b.h.) and total height, and diameter at breast height alone for B. buceras and Bursera simaruba. Model fits for total and woody biomass were generally good, while leaf biomass showed more variation, possibly due to seasonal leaf loss at the time of sampling. While the distribution of total AGB into components appeared to remain relatively constant across diameter classes, AGB variability increased and B. simaruba and B. buceras allocated more carbon into branch biomass than the other species. When comparing our observed and predicted values to other published dry forest AGB equations, the equation developed in Mexico and recommended for areas with rainfall >900 mm/year gave estimates substantially lower than our observed values, while equations developed using dry forest data from forest in Australia, India and Mexico were lower than our observed values for trees with d.b.h. <25 cm and slightly higher for trees with d.b.h. >30 cm. Although our ability to accurately estimate merchantable stem volume and live tree AGB for subtropical dry forests in Puerto Rico and other Caribbean islands has been improved, much work remains to be done to sample a wider range of species and tree sizes.     

Shoot allometry of Jatropha curcas

The South African government has banned planting of Jatropha curcas L. (Jatropha), potentially a multipurpose tree and biofuel source, owing to insufficient knowledge about the species. Use of allometry as a non-destructive method of monitoring growth and biomass attributes of Jatropha was investigated. The objectives were to examine: reliability of allometry between above-ground variables and basal diameter and crown depth of Jatropha; effects of below-ground interspecies competition and tree spacing on allometry; and validity of these relationships with independent data. The study site was Ukulinga Research Farm, South Africa. Destructive sampling was carried out in March 2008, and tree height and basal diameter were measured periodically during March 2005 to April 2007. Regression analysis and analyses of covariance were used to analyse the data. The height-diameter equation developed by destructive sampling was validated using independent data. Highly significant allometric regressions resulted from using basal diameter (r ≥ 0.89) and crown depth (r ≥ 0.94). Stem diameter had linear relationships with wood and foliage biomass percentages (r = 0.91). Height-diameter equations were equivalent across competition and tree spacing treatments. Predicted and measured tree heights were linearly related (r > 0.97). It could be concluded that above-ground allometry of Jatropha was very reliable and not significantly affected by either below-ground interspecies competition or tree spacing. The site-specific allometric equations are useful for accurate and non-destructive estimations of Jatropha growth under various growing and (non-pruning) tree management conditions. The equations presented here are, however, not universally applicable.     

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.     

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.