抚育间伐对栓皮栎人工林直径和树高分布的影响

【目的】以河南登封林场栓皮栎人工林为研究对象,研究抚育间伐对林分不同生长阶段林木株数、林木直径分布和树高分布的影响,为制定科学合理的抚育经营措施奠定理论和技术基础。【方法】在株数强度为31.55%的间伐林分和条件基本一致的未间伐林分内,分别设置1个1 hm2样地,间伐作业2 a后获取每木检尺数据,分别利用Normal分布、Gamma分布、Lognormal分布、Weibull分布、Logistic分布函数对间伐样地和对照样地栓皮栎人工林林木个体直径分布、树高分布进行拟合,并应用Kolmogorov-Smirnov(KS)拟合优度检验,选择拟合效果最好的分布模型。【结果】1)间伐和对照样地幼树、小树和大树林木株数比例分别是9:642:582和229:978:585。相比对照样地,间伐样地林木小树和大树生长阶段株数比重较高。2)间伐样地林木直径分布范围主要集中在8~18 cm,高于对照样地的4~16 cm。KS拟合优度检验结果表明,间伐样地林木直径分布采用Weibull分布拟合效果最好,Normal和Logistic分布次之;对照样地林木直径分布采用Weibull分布拟合效果最好,Normal和Gamma分布次之。3)间伐样地和对照样地林木树高级分别为8~16 m和4~14 m,但KS拟合优度检验结果表明,5种分布函数对间伐样地和对照样地树高分布拟合优度排序一致,说明抚育间伐对林分树高分布的影响不明显。【结论】抚育间伐调整了栓皮栎人工林林分的直径结构,林分直径分布向较大径阶方向偏移,使林分直径分布结构更趋于对称分布,但对树高分布影响不明显。     

Characterising the diameter distribution of Sal plantations by comparing normal,lognormal and Weibull distributions at Tilagarh Eco-park,Bangladesh

For many years foresters have been using statistical probability density functions to describe and characterise stand structure. Predicting the current and future yields of a stand is essential for successful stand and timber management. Implicit prediction of current yield is accomplished by using diameter distribution methods. All diameter distribution yield systems predict the number of trees per unit area by diameter class. In this study, the normal, lognormal and the three-parameter Weibull probability density function were compared to characterise the diameter distributions of Sal (Shorea robusta) plantations grown at Tilagarh Eco-park, Bangladesh. Data from 70 plots, established in three plantations, were used for this study. The Weibull parameters were estimated by the maximum likelihood and moments estimator methods. A one-sample Kolmogorov–Smirnov test was used for the goodness of fit for all models. The Kolmogorov–Smirnov test results showed that both lognormal and Weibull distributions were suitable to characterise the diameter distributions of Sal plantations in the study area and may be applicable for other Sal forests in Bangladesh.     

Applying age-based mortality analysis to a natural forest stand in Japan

Mortality analysis of tree populations is widely applied to forest science studies. When mortality analysis is applied to forest inventories, the use of the variable of tree age is not common due to the difficulty of measuring age data censored in successive observations. The purpose of this study is to apply age-based mortality analysis, i.e., survival analysis, to the individual tree populations in a natural forest. The study site was the secondary natural stand of 0.26 ha dominated by fir (Abies firma), hemlock (Tsuga sieboldii), and oak (Quercus serrata) in the Boso peninsula, Japan. First, we measured the ages of the trees with diameter at breast height greater than or equal to 5 cm using a RESISTOGRAPH. Then, tree mortality probabilities of both non-parametric Kaplan–Meier estimates and parametric probability distributions of Gamma and Weibull were estimated by applying survival analysis techniques to the tree age data. The results implied that the survival analyses could be implemented not only by the non-parametric estimates in any cases but also by the common parametric distributions of Gamma and Weibull in cases in which the tree mortality probability distribution had a monotonously decreasing shape as observed in the immature natural stand in the study site.     

辽东山区天然次生林林分直径分布模型研究

以峰度、偏度和变动系数为指标研究了辽东山区天然次生林直径株数分布特征。运用Johnson’s SB分布、Gamma分布、3参数和2参数Weibull分布等4种概率密度函数研究了辽东山区天然次生林直径株数分布规律,同时利用Kolmogorov-Smirnov(KS)检验法来检验4种概率分布的拟合效果,结果表明:林分直径的株数分布以Johnson’s SB分布拟合效果最好,Weibull分布(包括2参数和3参数)仅仅适合中度区和弱度区,但不是最好。所有的分布模型均通过了优势度检验,说明均适用于直径株数分布的拟合。     

Comparison of beta,Johnson’s SB,Weibull and truncated Weibull functions for modeling the diameter distribution of forest stands in Catalonia (north-east of Spain)

The purpose of this study was to compare the beta, Johnson SB, Weibull and truncated Weibull functions in describing the diameter distributions of forest stands in Catalonia. The data consisted of permanent sample plots from the Spanish National Forest Inventory in Catalonia. The empirical data represent left-truncated distributions, as the smallest diameter measured in the field was 7.5 cm. A total of 1,242 plots were used to fit the functions and analyze their performance. The distribution functions were fitted to the diameter distributions of the number of stems (DD_N) and stand basal area (DD_G). The performance of the candidate functions was compared by means of their bias and RMSE for different diameter sums measuring the difference between the empirical and fitted distributions. The leftmost part (from 0 to 7.5 cm) of the non-truncated functions was ignored in this analysis. Sensitivity analyses were conducted to check whether the results depended on the number of trees measured in the stand, or the main species of the stand. The truncated Weibull function for the diameter distribution of stand basal area appeared to be in all cases the most accurate and consistent function. Generally, functions describing the distribution of stand basal area performed better than functions that described the distribution of the number of trees. Of the basal area distributions, beta and Johnson’s SB were the second best and nearly equally good with each other. The order of precision of the tested functions was: truncated Weibull for DD_G, truncated Weibull for DD_N, Johnson’s SB for DD_G, beta for DD_G, beta for DD_N and Weibull for DD_G, Weibull for DD_N, and Johnson’s SB for DD_N.     

Use of Gumbel and Weibull functions to model extreme values of diameter distributions in forest stands

Context

Families of the Gumbel (type I), Fréchet (type II) and Weibull (type III) distributions can be combined in the generalized extreme value (GEV) family of distributions. Maximum and minimum values of diameters in forest stands can be used in forest modelling, mainly to define parameters of the functions used in diameter class models as well as in some practical cases, such as modelling maximum diameters for sawing and processing purposes.

Aims

The purpose of this study was to examine and compare two extreme value distribution functions (the Gumbel and the Weibull functions) in modelling the distribution of the minimum and the maximum values of representative sets of tree diameter samples. Both of these functions were applied to the lower and upper values of the diameter distributions of the main forest species in northwest Spain: Quercus robur L., Betula pubescens Ehrh., Pinus radiata D. Don, Pinus pinaster Ait. and Pinus sylvestris L.

Methods

Parameters of the Gumbel function were estimated using the mode and the moments of the distributions, and parameters of the Weibull function were estimated using the moments method.

Results

In general, the Weibull distribution was the most suitable model for describing the maximum diameters. The mode method of the Gumbel yielded the best results for minimum diameters of birch and Monterrey pine. The Gumbel distribution, fitted by either the mode- or moments-based methods, proved more suitable than the Weibull distribution for describing the minimum diameters in maritime pine and Scots pine stands.

Conclusion

In some cases, better results were obtained with the Gumbel than the Weibull distribution for describing the distribution of extreme diameter values in forest stands in northwest Spain. This is the first example of the application of the Gumbel distribution in forest modelling.     

Modeling diameter distribution of Austrian black pine (<Emphasis Type="Italic">Pinus nigra</Emphasis> Arn.) plantations: a comparison of the Weibull frequency distribution function and percentile-based projection methods

The main purpose of the present investigation is to examine and compare three methods for diameter distribution modeling in terms of their fitness to predict from stand level variables the diameter distributions of even-aged Austrian black pine (Pinus nigra Arn.) plantations in Bulgaria. The percentile-based projection method involving empirical probability density function based on 12 percentiles was the first method tested. A new modified approach based on the first method was proposed as the second alternative. The third method was the 2-parameter Weibull functional model in which parameters were recovered from the first and the second raw moments and the second central moment of the empirical distributions. The Kolmogorov–Smirnov test was applied to compare the experimental distributions with the predicted ones, and estimation of the error indices was employed to evaluate the total absolute deviation of the predicted numbers from the actual ones by diameter class. The two-parameter Weibull function proved superior to the examined alternative percentile-based projection methods and the newly proposed percentile method, without a driver percentile showed improved precision compared to the classical percentile method (with a driver percentile). The parameters of the Weibull frequency distribution function can be easily recovered from the stand quadratic mean diameter. Consequently, this diameter distribution model could be incorporated as a sub-model for stand horizontal structure characterization within the Stand Density Management Diagram modeling framework.     

落叶松人工林林分因子模型的建立

利用落叶松人工林所设标准地的观测数据, 求算各标准地的威布尔分布参数a、b、c, 并将其与林分因子: 平均直径、上层平均树高、株数密度结合, 建立了Richards3种林分因子模型。经检验其精度达到96 7 % ~97 7%, 通过进一步检验表明, 密度、上层高、直径模型优于其他两种模型, 可在森林经营上应用。     

Comparing normal,lognormal and Weibull distributions for fitting diameter data from Akashmoni plantations in the north-eastern region of Bangladesh

Statistical probability density functions are widely used to model tree diameter distributions and to describe stand structure. The objective of this study was to compare the performance of normal, logarithmic-normal and three-parameter Weibull distributions for fitting diameter data from Akashmoni (Acacia auriculiformis A. Cunn. ex Benth.) plantations grown in the north-eastern region of Bangladesh. Data from 96 plots, established in 24 plantations in north-eastern Bangladesh and ranging in age from 1 to 6 years, were used for this study. The parameters of the Weibull distribution were calculated using maximum likelihood estimation (MLE) and moment estimation (ME) methods. The goodness of fit of normal, lognormal, Weibull MLE and Weibull ME were tested using one-sample Kolmogorov-Smirnov (KS) tests. The KS test results showed that both lognormal and Weibull distributions were equally effective for describing the diameter distributions of these Akashmoni plantations grown in the north-eastern region of Bangladesh.     

A growth model for Pinus radiata D. Don stands in north-western Spain

A dynamic whole-stand growth model for radiata pine (Pinus radiata D. Don) stands in north-western Spain is presented. In this model, the initial stand conditions at any point in time are defined by three state variables (number of trees per hectare, stand basal area and dominant height), and are used to estimate total or merchantable stand volume for a given projection age. The model uses three transition functions derived with the generalized algebraic difference approach (GADA) to project the corresponding stand state variables at any particular time. These equations were fitted using the base-age-invariant dummy variables method. In addition, the model incorporates a function for predicting initial stand basal area, which can be used to establish the starting point for the simulation. Once the state variables are known for a specific moment, a distribution function is used to estimate the number of trees in each diameter class by recovering the parameters of the Weibull function, using the moments of first and second order of the distribution. By using a generalized height-diameter function to estimate the height of the average tree in each diameter class, combined with a taper function that uses the above predicted diameter and height, it is then possible to estimate total or merchantable stand volume.     

北京西山油松人工林结构特征研究

以西山试验林场近自然经营试点区建立的11块中龄油松人工林样地为依据,对油松林分的结构特点、表达模型和树种多样性格局进行了分析。结果表明：油松人工林林分平均密度为1069株／hm^2,平均胸径为13．7cm,平均高为8．6m,蓄积量为86．36m3／hm^2。应用正态分布、Weibull分布、对数正态分布、Gamma分布和Beta分布拟合直径和树高结构,发现正态分布拟合直径分布和树高分布效果最好,也符合人工林的林分结构规律;油松人工林层次结构简单,物种多样性较低,乔木层、灌木层和草本层的Shannon—wiener指数、均匀度指数分别为0．355、0．726、0．160和0．372、0．651、0．266;幼苗更新各高度级均以构树和栾树为主,他们分别占总体更新树种的72．2％和10．2％。     

林木最近距离分布模型的研究

林木距离分布是森林结构的重要体现，林木最近距离分布的估计是应用与距离有关的单木生长模型、林分空间结构模拟与重现以及森林可视化经营的重要基础。研究提出了模拟林木最近距离分布的新途径，指出林木距离分布遵从Weibull分布。结构丰富天然林的林木最近距离分布仅用2参数的Weibull分布函数足以很好地表达。研究提出的描述林木最近距离分布模型是进一步用非耗时费力的因子预测距离分布的前提。     

A model for predicting log yield from stand characteristics

A method for forecasting the log‐class distribution resulting from harvesting forest stands is investigated. The diameter distribution of a stand is approximated by a two‐parameter Weibull density function, the parameters of which are recovered from stand level characteristics. Theoretical bucking is performed for actual and simulated distributions and the resulting log yields are compared. An application to 40 stands indicates that an accurate prognosis can be expected, given a good approximation of the diameter distribution. For cases with multimodal diameter distributions or many small trees, the prognosis is unreliable.     

火炬松人工林直径分布收获模型的研究

搜集福建省火炬松人工林各30株林分平均木和优势木的树干解析数据，运用正态分布、对数正态分布、Weibull分布、B分布、Γ分布函数来拟合福建省火炬松人工林的直径分布规律。结果表明：Weibull分布的拟合效果好，标准地接受率为80％，用参数回收技术建立火炬松人工林直径分布收获模型，经检验，每公顷材积平均相对误差8．37％，每公顷胸高断面积平均相对误差6．72％。因此该模型可以用来估测福建省火炬松人工林的林分结构和产量。     

Modelling stand structure in young Scots pine dominated stands

The purpose of this study was to construct models for predicting the structure of young Scots pine (Pinus sylvestris L.) stands. The two-parameter Weibull function characterized the height distribution of the stands. In young stands height was preferred to dbh as a random variable because of its continuous feature. Tree diameters were predicted using a multiplicative model, fitted as a linearized mixed-effect model. The modelling data consisted of repeatedly measured Scots pine dominated juvenile stands, carried out on a sub-sample of the 7th National Forest Inventory. The data covered a dominant height range from 0.2 up to 17 m. Two independent data sets were used to validate the models. The Weibull function was fitted using the maximum likelihood method. Four methods for predicting the distributions were compared: (1) parameter prediction models (PPM) consisting of seemingly unrelated regression equations, (2) a generalized linear model (GLM) which was a one-stage distribution and model fitting procedure, (3) a hybrid method including PPM for the shape parameter together with moment-based parameter recovery for the scale parameter, and (4) inclusion of moment-based parameter recovery for the scale parameter in the estimated GLM. Goodness-of-fit were tested in terms of Kolmogorov–Smirnov and error index statistics. Parameter recovery showed no improvement when used with PPM, but it improved GLM and gave the overall best performance for this new method. The constructed diameter–height model showed quite flexible and unbiased behaviour. Models are recommended as practical tools for Finnish forest management planning purposes.     

A flexible modeling of irregular diameter structure for the volume estimation of forest stands

Simple distribution models (SDMs) have deficiencies in portraying irregular forest diameter structure. This paper introduces mixture distribution models (MDMs) to improve the estimation accuracy of stand volume of Siberian larch (Larix sibirica Ledeb.) forests. Stand volume was estimated by combining the suitable diameter mixture model and diameter–height model. Appropriate mixture models are derived by integrating multiple SDMs of Burr III and XII, Johnson S_B, Weibull or lognormal probability density functions (pdf) that satisfied the criteria of goodness of fit tests. Results showed that the average bias of volume estimation for all of the study plots using SDM and MDM approaches are underestimated by 6.93 and 2.42 m³, respectively. Each of the estimates is equivalent to an estimation error of 25.59 ± 18.18 and 7.08 ± 2.97 %. This suggests that the MDM approach is a more flexible and suitable modeling technique for forest volume estimation, in particular for forests that have been frequently disturbed by natural events.     

Tree growth-competition relationships in thinned Eucalyptus plantations vary with stand structure and site quality

Growth responses to thinning can vary with site quality and age, however, the direction of the response varies. An understanding of the mechanisms behind thinning responses could help forest managers optimise production as well as inform modellers and ecologists about the functioning of tree stands. Thinning was used to create a range of stand densities in eleven Eucalyptus plantation stands on seven sites in south-eastern Australia. Basal area periodic annual increment (PAI; cm² year^?1) of individual dominant and codominant trees was then related to competition, such that PAI = a + b ln(Competition). Competition was defined as the sum of the basal area of neighbouring trees within a radius of 6.5 m. The relative (%) and absolute (cm² year^?1) responses to competition were quantified using b, which was correlated with site quality and stand structure of unthinned stands. Stand structure was quantified using statistics or parameters that describe the diameter distribution for the given age, species and site, including skewness, the coefficient of variation and parameters of the Weibull probability distribution. Relative and absolute responses both increased with increasing site quality and in stands with more negatively skewed diameter distributions (higher proportion of larger trees) or lower coefficients of variation. Absolute thinning responses often increased with increasing size class, while relative thinning responses often decreased. Variables describing diameter distributions (size-class structure) were able to describe some of the variation in competition responses that site quality could not. This indicates why stands on similar site qualities but with different stand structures can have correspondingly different thinning responses. Stand structural variables may be more useful predictors of thinning responses in stands that experience large temporal changes in diameter distributions compared with site quality, which is a more static variable. Thus, knowledge about the development of diameter distributions might help to refine thinning regimes.     

Biomass, basic density and biomass expansion factor functions for European beech (Fagus sylvatica L.) in Denmark

The objective of this study was to analyse the within-tree allocation of biomass and to develop biomass functions for above- and below-ground components of European beech in Denmark. Separate functions were developed for stem, branches, below-ground stump and root system, total above-ground biomass and total tree biomass. For each of these components or aggregate components, models were also developed for the average basic density of wood and bark. To enhance the versatility of the models, a function for estimating the biomass expansion factor (BEF) was also developed. The functions were based on 66 trees measured for total biomass. Model performance was evaluated based on 74 trees measured only for above-ground biomass. The trees were sampled in 18 different forest stands covering a wide range of tree sizes and stand treatments. Models were estimated using a linear mixed-effects procedure to account for within-stand correlations. The functions for biomass and BEFs included only diameter at breast height and total tree height for individual trees as predictor variables. Inclusion of additional variables reflecting site quality or stand density did not improve model performance. The functions for basic density included individual tree diameter, tree height and quadratic mean diameter as predictor variables, indicating an effect of stand density on the basic density of wood and bark.     

西藏天然林直径分布模型及其应用研究

以西藏自治区2006年森林资源连续清查的479个天然林实测样地资料为基础,利用相对直径和累积概率的概念,借鉴相对树高曲线模型的建模方法,研究建立了冷杉、云杉、柏木、松类、栎类、桦类、阔叶类、针阔类等8个树种（组）的直径分布累积概率模型。通过与常用于天然异龄林直径分布结构的Weibull分布函数的拟合结果进行对比分析,表明所建模型效果良好。所建的直径分布累积概率模型为预估林分直径分布结构提供了参考依据,尤其为2006年西藏森林资源连清遥感样地和目测样地的样木模拟提供了定量依据。