Stand Diameter Distribution Modelling and Prediction Based on Richards Function

The objective of this study was to introduce application of the Richards equation on modelling and prediction of stand diameter distribution. The long-term repeated measurement data sets, consisted of 309 diameter frequency distributions from Chinese fir (Cunninghamia lanceolata) plantations in the southern China, were used. Also, 150 stands were used as fitting data, the other 159 stands were used for testing. Nonlinear regression method (NRM) or maximum likelihood estimates method (MLEM) were applied to estimate the parameters of models, and the parameter prediction method (PPM) and parameter recovery method (PRM) were used to predict the diameter distributions of unknown stands. Four main conclusions were obtained: (1) R distribution presented a more accurate simulation than three-parametric Weibull function; (2) the parameters p, q and r of R distribution proved to be its scale, location and shape parameters, and have a deep relationship with stand characteristics, which means the parameters of R distribution have good theoretical interpretation; (3) the ordinate of inflection point of R distribution has significant relativity with its skewness and kurtosis, and the fitted main distribution range for the cumulative diameter distribution of Chinese fir plantations was 0.4∼0.6; (4) the goodness-of-fit test showed diameter distributions of unknown stands can be well estimated by applying R distribution based on PRM or the combination of PPM and PRM under the condition that only quadratic mean DBH or plus stand age are known, and the non-rejection rates were near 80%, which are higher than the 72.33% non-rejection rate of three-parametric Weibull function based on the combination of PPM and PRM.     

三种直径分布拟合模型在长白落叶松林分的实际应用

基于长白落叶松中龄纯林样地调查,采用相对直径法、指数函数法和Weibull分布函数法三种常用方法拟合林分胸径分布规律.结果表明,三种方法均能有效描述林分直径分布规律,特别是指数函数简单易行、拟合精度高、适用性强,可视为长白落叶松中龄林直径分布拟合的最优模型.     

樟子松沙地人工林直径分布模拟

利用反 Weibull函数模拟了章古台沙地樟子松人工林的直径分布规律 .结果表明 ,反 Weibull分布函数模拟樟子松人工林的直径分布效果好 ,具有精度高、适应性强等特点 .分别建立了反 Weibull分布函数 3个参数与林分年龄及密度之间的关系方程以及直径分布与 3个参数的回归方程 ,这些方程可用来预估林分产量、出材量以及评价经营效果     

麻城黄山松天然林直径分布

为研究黄山松天然次生林直径分布特征,以麻城市黄山松天然次生林为研究对象,采用标准样地调查,计算林分直径的偏度、峰度,林分直径分布的Shannon-Weiner和Simpson指数,运用负指数分布、normal分布、lognormal分布、logistic分布和Weibull分布等5种概率密度函数对黄山松天然次生林林分直...     

Development of a Compatible Taper Function and Stand-Level Merchantable Volume Model for Chinese Fir Plantations

Chinese fir (Cunninghamia lanceolata [Lamb.] Hook) is one of the most important plantation tree species in China with good timber quality and fast growth. It covers an area of 8.54 million hectare, which corresponds to 21% of the total plantation area and 32% of total plantation volume in China. With the increasing market demand, an accurate estimation and prediction of merchantable volume at tree- and stand-level is becoming important for plantation owners. Although there are many studies on the total tree volume estimation from allometric models, these allometric models cannot predict tree- and stand-level merchantable volume at any merchantable height, and the stand-level merchantable volume model was not seen yet in Chinese fir plantations. This study aimed to develop (1) a compatible taper function for tree-level merchantable volume estimation, and (2) a stand-level merchantable volume model for Chinese fir plantations. This “taper function system” consisted in a taper function, a merchantable volume equation and a total tree volume equation. 46 Chinese fir trees were felled to develop the taper function in Shitai County, Anhui province, China. A second-order continuous autoregressive error structure corrected the inherent serial autocorrelation of different observations in one tree. The taper function and volume equations were fitted simultaneously after autocorrelation correction. The compatible taper function fitted well to our data and had very good performances in diameter and total tree volume prediction. The stand-level merchantable volume equation based on the ratio approach was developed using basal area, dominant height, quadratic mean diameter and top diameter (ranging from 0 to 30 cm) as independent variables. At last, a total stand-level volume table using stand basal area and dominant height as variables was proposed for local forest managers to simplify the stand volume estimation.     

基于混合效应的大别山地区杉木树高-胸径模型比较

基于安徽省大别山区马鬃岭林场杉木人工林30块样地1087组数据,选用7个常用树高-胸径(H-D)模型(线性模型、Chapman-Richards模型、Logistic模型等),采用最小二乘法拟合并选出最优基础模型(式11,只含D变量的Chapman-Richards模型),然后基于该模型构建含林分变量优势木平均高度、密度的H-D模型(式12),同时考虑样地水平的随机效应,分别基于式11、12构建混合模型(式13、14),并用幂函数、指数函数消除误差异方差,利用决定系数(R²)、均方根误差(RMSE)、平均绝对误差(MAE)和平均相对误差绝对值(MAPE)等指标来评价模型的拟合与预测能力,最终获取最优树高预测模型.结果表明:含林分变量的模型的拟合精度(式12,R²=0.863、RMSE=1.381、MAE=0.971)优于基础模型(式11,R²=0.827、RMSE=1.554、MAE=0.101).对于误差方差,幂函数、指数函数均能较好地消除异方差,但幂函数相对最好.混合模型的拟合与预测能力均优于式11、12,但混合模型(式13、14)之间的拟合与预测精度相差不大.基于混合效应的H-D模型(式13)能够较好地描述不同林分间H-D关系的差异,实际运用中可选用该模型来预测杉木树高,具有较高的预测精度.     

基于抚育间伐效应的落叶松人工林直径分布动态模拟

基于黑龙江省孟家岗林场长白落叶松人工林5块固定样地(其中1块为对照样地,4块为抚育间伐样地,断面积强度为3.7%~49.7%)1974—2014年(林龄为19～59 a)复测的31次胸径数据,采用三参数Weibull分布函数拟合5块样地各年份直径分布,研究了直径分布曲线随林龄的动态变化规律,并分析了抚育间伐对林分直径分布曲线及Weibull分布参数的动态影响.构建了基于抚育间伐效应的Weibull分布参数预测的联立方程组模型,分别采用三阶段最小二乘法及度量误差法估计了模型的参数.结果表明: 未间伐林分(对照)直径分布曲线随林龄增加由“高峰狭窄”(林木直径分布集中)状态逐渐向“低峰宽广”(林木直径分布分散)状态过渡;抚育间伐后,林木直径分布曲线均较抚育间伐前右偏加剧,峰度变高,径阶变窄,对称性下降;间伐强度越大,伐除的中小径阶树木越多,直径分布曲线较间伐前左侧截尾明显,峰度增高,径阶分布范围变小.低强度抚育间伐使得参数a值变大,b值变小,对参数c的影响不明显;高强度抚育间伐使得参数a的增量变大,b值变小,参数c值变小.参数预测联立方程组模型的拟合结果表明,参数b的预测模型拟合效果最好,R²>0.98;参数c预测模型拟合效果稍差,但R²>0.91;三阶段最小二乘法拟合结果与度量误差联立方程组方法区别不大,两种方法检验结果均较好,模型精度都>97%,拟合效率均>0.92.所建立的模型能够较好地模拟抚育间伐效应下落叶松人工林直径分布动态变化,为科学合理经营森林提供了依据.     

基于经验模型和机理模型的杉木人工林生物量估测对比研究

为了揭示间伐干扰下杉木人工林生物量的变化规律,研究利用江西省吉水县石阳林场的36块杉木人工林样地的实测数据和研究区气候数据,通过基于经验的引入地位指数(SI)的生物量生长方程组和基于机理的3-PG模型,模拟并预估林分生物量,分析在间伐和非间伐的情况下,不同立地的林分其生物量0-50a的变化。结果表明:(1)构建了生物量生长方程组,并在参数a、b、c中引入地位指数SI,发现改进后的模型对于基础模型拟合精度更高,且对数似然比检验表明,改进效果显著(P<0.05)。(2)通过对3-PG模型预测精度验证发现,预估值和实测值之间有很高的一致性,各因子的决定系数(R²)在0.65-0.96之间,其中,胸径和树高的R²均高于0.92;各因子的平均相对误差(MRE)不超过26%。(3)通过比较经验模型和机理模型的生物量预测发现,经验模型的预测误差MRE为16.50%,机理模型为23.52%,经验模型预估精度更高。进一步对未来预测对比分析表明,机理模型预估值高于经验模型。(4)两个模型模拟的杉木人工林生物量规律一致,即随着林龄的增加,杉木人工林林分总生物量均表现出先快速增加,后逐渐平稳的趋势;并且间伐不会改变这种趋势,但间伐林分在间伐后的生物量生长速率高于无间伐林分。此外,由于SI对经验模型影响显著,改进模型拟合效果更好,更具有生态学意义。参数化后的3-PG模型模预估精度较高,能够为江西杉木人工林生长规律研究提供依据。虽然经验模型和机理模型在对研究区杉木人工林生物量的预估上均具有较好的表现,但各具特点和局限性。经验模型参数较易获得,且经验模型预测生物量、林分胸高断面积和林分平均树高的R²、MRE均优于机理模型;但模型对于建模数据内的评价效果较好,对于建模数据外的应用具有局限性,即经验模型更适合模拟生长期间的某一阶段的林分生物量。机理模型虽然需要的参数较多,但是考虑了生态学原理,弥补了经验模型的不足,可较好解释和模拟环境因子对树木生长的影响,对校正数据之外生长阶段的林分生物量预测更有优势。     

长白山东北红豆杉生境内针阔混交林直径结构分布研究

选择能够拟合长白山自然保护区东北红豆杉生境内针阔混交林的直径结构分布模型,为该区林分经营管理提供参考。以长白山自然保护区龙荒沟林场15块东北红豆杉林分内针阔混交林为研究对象,采用负指数函数和三参数Weibull分布函数2种直径分布模型拟合和χ^2检验,分析了15块样地的直径结构分布规律。15块样地的密度为400~981株·hm^-2,平均胸径变化范围为10.5~19.9 cm,各样地林分的直径分布的偏度均为正值,直径分布函数曲线均往左偏,除了9~11号样地的直径分布用三参数Weibull分布模型效果较好外,其他样地均适合用负指数模型拟合。两种模型均能有效描述直径结构分布规律,三参数Weibull分布模型用来拟合不规则直径分布时效果较好,而负指数分布模型拟合近似“反J”型曲线时效果好。该区东北红豆杉林分内针阔混交林直径结构分布不合理,应加强该林区经营技术措施。     

Tree Biomass Estimation of Chinese fir (Cunninghamia lanceolata) Based on Bayesian Method

Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) is the most important conifer species for timber production with huge distribution area in southern China. Accurate estimation of biomass is required for accounting and monitoring Chinese forest carbon stocking. In the study, allometric equation was used to analyze tree biomass of Chinese fir. The common methods for estimating allometric model have taken the classical approach based on the frequency interpretation of probability. However, many different biotic and abiotic factors introduce variability in Chinese fir biomass model, suggesting that parameters of biomass model are better represented by probability distributions rather than fixed values as classical method. To deal with the problem, Bayesian method was used for estimating Chinese fir biomass model. In the Bayesian framework, two priors were introduced: non-informative priors and informative priors. For informative priors, 32 biomass equations of Chinese fir were collected from published literature in the paper. The parameter distributions from published literature were regarded as prior distributions in Bayesian model for estimating Chinese fir biomass. Therefore, the Bayesian method with informative priors was better than non-informative priors and classical method, which provides a reasonable method for estimating Chinese fir biomass.     

不同林龄杉木人工林土壤团聚体磷素分布特征

探究不同林龄杉木人工林土壤团聚体各形态磷素的分布特征有利于提升杉木人工林土壤磷素有效性。本研究选取位于广西融水县的幼龄(9 a)、中龄(17 a)、成熟(26 a)杉木人工林和邻近撂荒地(CK),利用干筛法将采集到的表层(0～20 cm)原状土壤分为4个粒级团聚体(>2、1～2、0.25～1和<0.25 mm),测定各粒级团聚体中不同形态磷组分。结果表明: 1)不同林龄杉木人工林土壤团聚体组成差异显著,CK和各林龄杉木人工林中>2 mm粒级团聚体含量显著较高,随林龄的增长先增后减,在17 a时最高;土壤平均重量直径(MWD)和几何平均直径(GMD)的变化趋势与>2 mm粒级团聚体一致。2)CK和各林龄杉木人工林中各粒级土壤团聚体全磷、无机磷和有机磷含量差异均不显著,而土壤有效磷含量在>2 mm粒级团聚体中显著较高,达1.23～7.33 mg·kg^-1;不同林龄杉木人工林土壤团聚体及全土全磷、有效磷和无机磷含量均显著高于CK,并随杉木林龄的增长先增后减,全土总磷和有效磷含量在9 a时最高,分别为322.40和7.33 mg·kg^-1,全土无机磷含量在17 a时最高,为114.05 mg·kg^-1;全土有机磷含量随杉木林龄的增长先增再减再增,在9 a时最高,为210.00 mg·kg^-1。3)不同粒级土壤团聚体磷储量与土壤团聚体组成比例显著相关。CK和各林龄杉木人工林中>2 mm粒级团聚体各形态磷储量较高。除有机磷外,各形态土壤磷储量均随杉木林龄的增长先增后减。综上,林龄17 a之前,杉木人工林的种植有利于提升土壤团聚体稳定性,促进土壤磷素水平的提升;林龄17 a后,>2 mm粒级团聚体的破碎导致土壤团聚体稳定性和土壤磷素供应水平逐渐下降。因此,在杉木人工林培育栽种17 a以后应重视土壤中>2 mm粒级团聚体的保护,以保障土壤质量,维持土壤供磷水平。     

A Hierarchical Bayesian Model to Predict Self-Thinning Line for Chinese Fir in Southern China

Self-thinning is a dynamic equilibrium between forest growth and mortality at full site occupancy. Parameters of the self-thinning lines are often confounded by differences across various stand and site conditions. For overcoming the problem of hierarchical and repeated measures, we used hierarchical Bayesian method to estimate the self-thinning line. The results showed that the self-thinning line for Chinese fir (Cunninghamia lanceolata (Lamb.)Hook.) plantations was not sensitive to the initial planting density. The uncertainty of model predictions was mostly due to within-subject variability. The simulation precision of hierarchical Bayesian method was better than that of stochastic frontier function (SFF). Hierarchical Bayesian method provided a reasonable explanation of the impact of other variables (site quality, soil type, aspect, etc.) on self-thinning line, which gave us the posterior distribution of parameters of self-thinning line. The research of self-thinning relationship could be benefit from the use of hierarchical Bayesian method.     

Crown profile of foliage area characterized with the Weibull distribution in a hinoki (Chamaecyparis obtusa) stand

Summary Thirten sample trees of various sizes in a 29-year-old hinoki [Chamaecyparis obtusa (Sieb, et Zucc.) Endl.] plantation were felled and subjected to the stratified clip technique. Crown profile of foliage area fitted well with the Weibull distribution. The crown profile tended to be more skewed toward the top of crowns in smaller trees than in larger trees. This tendency was reflected in the value of the shape parameter of the Weibull distribution. The shape parameter ranged from 1.73 to 3.23 and gradually increased up to an asymptotic value with an increase of stem diameter at breast height. The scale parameter of the distribution ranged from 1.0 to 4.2 and tended to increase in proportion to stem diameter at breast height. Foliage area of a tree correlated well with stem diameter at breast height through an ordinary allometric equation. Tree height could be approximated fairly well by a generalized allometric equation as a function of stem diameter at breast height. On the basis of the census of stem diameter at breast height, canopy profile could be constructed synthesizing crown profiles of foliage area for individual trees in the stand. Leaf area index was estimated to be 6.6 ha ha^–1.     

Muscle endurance time estimation during isometric training using electromyogram and supervised learning

Constant-force isometric muscle training is useful for increasing the maximal strength , rehabilitation and work-fatigue assessment. Earlier studies have shown that muscle fatigue characteristics can be used for evaluating muscle endurance limit. Study Objective: To predict muscle endurance time during isometric task using frequency spectrum characteristics of surface electromyography signals along with analysis of frequency spectrum shape and scale during fatigue accumulation. Method: Thirteen subjects performed isometric lateral raise at 60% MVC of deltoid (lateral) till endurance limit. Time windowed sEMG frequency spectrum was modelled using 2-parameter distributions namely Gamma and Weibull for spectrum analysis and endurance prediction. Results: Gamma distribution provided better spectrum fitting (P < 0.001) than Weibull distribution. Spectrum Distribution demonstrated no change in shape but shifted towards lower frequency with increase of magnitude at characteristic mode frequency. Support Vector Regression based algorithm was developed for endurance time estimation using features derived from fitted frequency spectrum. Time taken till endurance limit for acquired dataset 38.53 ± 17.33 s (Mean ± Standard Deviation) was predicted with error of 0.029 ± 4.19 s . R-square: 0.956, training and test sets RMSE was calculated as 3.96 and 4.29 s respectively. The application of the algorithm suggested that model required 70% of sEMG signal from maximum time of endurance for high prediction accuracy. Conclusion: Endurance Limit prediction algorithm was developed for quantification of endurance time for optimizing isometric training and rehabilitation. Our method could help personalize and change conventional training method of same weight and duration for all subjects with optimized training parameters, based upon individual sEMG activity.     

Comparing Different Models of the Development of Verb Inflection in Early Child Spanish

How children acquire knowledge of verb inflection is a long-standing question in language acquisition research. In the present study, we test the predictions of some current constructivist and generativist accounts of the development of verb inflection by focusing on data from two Spanish-speaking children between the ages of 2;0 and 2;6. The constructivist claim that children’s early knowledge of verb inflection is only partially productive is tested by comparing the average number of different inflections per verb in matched samples of child and adult speech. The generativist claim that children’s early use of verb inflection is essentially error-free is tested by investigating the rate at which the children made subject-verb agreement errors in different parts of the present tense paradigm. Our results show: 1) that, although even adults’ use of verb inflection in Spanish tends to look somewhat lexically restricted, both children’s use of verb inflection was significantly less flexible than that of their caregivers, and 2) that, although the rate at which the two children produced subject-verb agreement errors in their speech was very low, this overall error rate hid a consistent pattern of error in which error rates were substantially higher in low frequency than in high frequency contexts, and substantially higher for low frequency than for high frequency verbs. These results undermine the claim that children’s use of verb inflection is fully productive from the earliest observable stages, and are consistent with the constructivist claim that knowledge of verb inflection develops only gradually.     

Normal and Extreme Wind Conditions for Power at Coastal Locations in China

In this paper, the normal and extreme wind conditions for power at 12 coastal locations along China’s coastline were investigated. For this purpose, the daily meteorological data measured at the standard 10-m height above ground for periods of 40–62 years are statistically analyzed. The East Asian Monsoon that affects almost China’s entire coastal region is considered as the leading factor determining wind energy resources. For most stations, the mean wind speed is higher in winter and lower in summer. Meanwhile, the wind direction analysis indicates that the prevalent winds in summer are southerly, while those in winter are northerly. The air densities at different coastal locations differ significantly, resulting in the difference in wind power density. The Weibull and lognormal distributions are applied to fit the yearly wind speeds. The lognormal distribution performs better than the Weibull distribution at 8 coastal stations according to two judgement criteria, the Kolmogorov–Smirnov test and absolute error (AE). Regarding the annual maximum extreme wind speed, the generalized extreme value (GEV) distribution performs better than the commonly-used Gumbel distribution. At these southeastern coastal locations, strong winds usually occur in typhoon season. These 4 coastal provinces, that is, Guangdong, Fujian, Hainan, and Zhejiang, which have abundant wind resources, are also prone to typhoon disasters.     

Density effect, self-thinning and size distribution in Pinus densiflora Sieb. et Zucc. stands

The competition-density (C-D) effect for given times and self-thinning over time in even-aged, natural, pure stands of Pinus densiflora Sieb. et Zucc. were analyzed with the reciprocal equation of the C-D effect in self-thinning stands, and the equation describing the time-trajectory of mean stem volume and stand density. The C-D effect and self-thinning were consistently well explained by the two equations. Differences in mean stem volume and in stand density among the stands tended to merge with increasing stand age. The self-thinning line with a slope of approximately –3/2 was reached by the higher density stand prior to the medium and lower density stands. The skewness of tree height distribution showed positive values, which means that the distribution is more or less L-shaped, and in addition the skewness decreased with increasing mean tree height, which indicates that smaller trees died as the stands grew. This trend is consistent with the asymmetric (one-sided) competition hypothesis that self-thinning is driven by competition for light. The tree height distribution was analyzed using the Weibull distribution. The location parameter h _min of the Weibull distribution increased with increasing stand age, and the scale parameter a tended to increase slightly with increasing stand age. The range of the shape parameter b of the Weibull distribution corresponded to that of the skewness.     

Intrinsic units of growth for teak trees

Attempts were made to evaluate intrinsic biological units of growth of teak trees, which were identified as age and size at inflection point of diameter at breast height. The observations were further utilized in estimating fractal dimension of the tree crown, which is an important eco-physiological characteristic of the species. A total of 38 teak plantations belonging to different age groups and site quality classes were selected for estimating the intrinsic units. Altogether, 57 stumps were identified for gathering information on age and size at inflection point at stump level (10 cm above ground) from the selected plantations. Photographs of the upper surface of the selected stumps were taken using a digital camera. Counting of annual rings/ring age and recording the radial distance from pith to each of the annual rings were done directly (visually) by using Photoshop and CorelDRAW software in a computer. Thus the age and size at inflection point at stump level were estimated. The values of intrinsic units at breast height level were estimated using allometric relations. The present study revealed that these units viz., (namely) age and size (diameter) at inflection point were 6 years and 6 cm at stump level, respectively. The corresponding values at breast-height level were estimated as 8 years and 10.6 cm including the bark. Fractal dimension was calculated based on the growth parameters, which were estimated through stump analysis. The fractal dimension worked out to 2.13 for the species. The value of fractal dimension obtained was biologically justifiable considering the light demanding nature of the species.     

Modelling and predicting the spatial distribution of tree root density in heterogeneous forest ecosystems

Background and Aims In mountain ecosystems, predicting root density in three dimensions (3-D) is highly challenging due to the spatial heterogeneity of forest communities. This study presents a simple and semi-mechanistic model, named ChaMRoots, that predicts root interception density (RID, number of roots m^–2). ChaMRoots hypothesizes that RID at a given point is affected by the presence of roots from surrounding trees forming a polygon shape.Methods The model comprises three sub-models for predicting: (1) the spatial heterogeneity – RID of the finest roots in the top soil layer as a function of tree basal area at breast height, and the distance between the tree and a given point; (2) the diameter spectrum – the distribution of RID as a function of root diameter up to 50 mm thick; and (3) the vertical profile – the distribution of RID as a function of soil depth. The RID data used for fitting in the model were measured in two uneven-aged mountain forest ecosystems in the French Alps. These sites differ in tree density and species composition.Key Results In general, the validation of each sub-model indicated that all sub-models of ChaMRoots had good fits. The model achieved a highly satisfactory compromise between the number of aerial input parameters and the fit to the observed data.Conclusions The semi-mechanistic ChaMRoots model focuses on the spatial distribution of root density at the tree cluster scale, in contrast to the majority of published root models, which function at the level of the individual. Based on easy-to-measure characteristics, simple forest inventory protocols and three sub-models, it achieves a good compromise between the complexity of the case study area and that of the global model structure. ChaMRoots can be easily coupled with spatially explicit individual-based forest dynamics models and thus provides a highly transferable approach for modelling 3-D root spatial distribution in complex forest ecosystems.     

Modelling the distribution of diameter growth along the stem in Scots pine

This paper presents an empirical model for the distribution of diameter growth along the stem in Scots pine (Pinus sylvestris L.) and for the consequent stem form over time. First, the distribution of annual mass growth in the stem is determined as a function of the total annual growth in stem mass, current stem mass and the distribution of the latter along the stem. Second, the distribution of diameter growth is obtained by converting the fraction of annual growth in the stem mass at a given height in the stem into the thickness of the annual ring at the same height. Application of the model to Scots pine data sets including both young and mature trees not used in parameter estimation showed that the model was capable of reconstructing the distribution of diameter growth from the stem butt to the apex and from the pith to the stem surface at any height in the stem in both young and mature trees. The resulting empirical model was also linked to a physiological, process-based model in order to study its performance in a simulated stand. Simulations representing trees grown in unthinned and thinned Scots pine stands with trees of different status (from dominant to suppressed) showed that the response in tree growth to thinning in terms of the distribution of diameter growth along the stem was quite realistic relative to measured data.