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.     

Estimating Stem Volume Using QuickBird Imagery and Allometric Relationships for Open Populus xiaohei Plantations

There has been a great deal of interest in studying the crown of trees using remote sensing data. In this study, crown width was extracted from high-resolution QuickBird images for open Populus xiaohei plantations. Regression models for predicting the individual stem volumes of Populus xiaohei were established using extracted crown width, as well as estimated tree parameters （i.e. diameter at breast height [DBH] and tree height） as predictors. Our results indicated that crown width could be accurately extracted from QuickBird images using a multi-scale segmentation approach with a mean relative error of 5.74%, especially for wide-spacing stands. Using either extracted crown width alone or with estimated DBH and tree height can successfully estimate individual stem volume of Populus xiaohei with the R2 value ranging from 0.87 to 0.92 depending on different model forms. In particular, the two second-order polynomial models （model 2 and model 6）, based on QuickBird image-derived crown widths and estimated DBH and tree heights, respectively, were the best at describing the relationship between stem volume and tree characteristics.     

Estimating Stem Volume Using QuickBird Imagery and Allometric Relationships for Open Populus xiaohei Plantations

There has been a great deal of interest in studying the crown of trees using remote sensing data.In this study,crownwidth was extracted from high-resolution QuickBird images for open Populus xiaohei plantations.Regression modelsfor predicting the individual stem volumes of Populus xiaohei were established using extracted crown width,as well asestimated tree parameters(i.e.diameter at breast height[DBH]and tree height)as predictors.Our results indicated thatcrown width could be accurately extracted from QuickBird images using a multi-scale segmentation approach with a meanrelative error of 5.74%,especially for wide-spacing stands.Using either extracted crown width alone or with estimatedDBH and tree height can successfully estimate individual stem volume of Populus xiaohei with the R~2 value ranging from0.87 to 0.92 depending on different model forms.In particular,the two second-order polynomial models(model2 andmodel 6),based on QuickBird image-derived crown widths and estimated DBH and tree heights,respectively,were the bestat describing the relationship between stem volume and tree characteristics.     

A Study of Stand Growth Model for Pinus yunnanensis (Pinaceae) Based on Plots Data——A Case Study in Yangliu Township,Baoshan, Yunnan Province

Pinus yunnanensis is one of most important timber species in Yunnan Province, and widely distributed in southwest China. Studies on growth model have been reported, however, most of which focused on a specific part of growth model. To build detailed, easily used and accurate empirical stand growth model from the same dataset, a case study was conducted in Yangliu Township, Baoshan, Yunnan Province. A total of 86 sample plots data were collected using two stages sampling design. Several popular non-linear growth functions were fitted and compared, including Chapman-Richards, Mitscherlich, Schumacher, Gompertz, Logistic, Korf and Allometric function. Models of site index, density index, average diameter at breast height (DBH) and stock volume growth model were fitted respectively. The different models performed more or less similarly in terms of coefficients of determination and root mean square error (RMSE). However, empirical growth function “Schumacher” had lower coefficient of variation for all parameters than other models. Schumacher function was the most suitable one for site index, average DBH and stock volume growth model in all alternative functions.     

北京地区侧柏人工林密度效应

密度是影响森林尤其是人工林生长的重要因素,林冠层是森林生态系统与其他系统进行能量和物质交换的重要场所,树木及树冠生长对林分密度的响应关系可以看作是生物对环境变化产生的适应性现象。林分密度效应是生态学和森林培育学的重要研究内容之一。以23块8种不同密度梯度的北京山区侧柏人工幼龄林林分为研究对象分析其树木生长及树冠生长对密度的响应关系,其中树冠指标使用了参照了美国林务局(USDA)的树冠调查指标。研究结果表明:(1)林分平均胸径、平均树高和平均冠幅生长均随密度增大而减小,林分密度大于3000株/hm2时各指标减小的趋势变缓,使用异速生长模型可以很好地拟合这种变化关系;(2)随密度增加,树冠水平方向和垂直方向生长均到显著地抑制作用,树冠外形表现出由饱满冠型向狭长冠型变化的适应性现象;(3)使用树冠二维、三维指标与密度进行相关性分析可知树冠长度、树冠率等指标与林分密度呈负相关关系,树冠圆满度及树冠生产效率与密度表现出极显著正相关关系;(4)采用枝解析的方法研究了树枝长度、材积的平均生长量、连年生长量与密度的关系,结果表明幼龄期各生长量差异不大;(5)在建立冠幅模型时考虑了自变量间的多重共线性问题,所建的胸径单自变量二次方模型能够很好地预测侧柏人工幼龄林冠幅生长过程,模型相关系数R2为0.961。     

基于随机效应的兴安落叶松材积生长模拟

基于黑龙江省带岭林业局大青川林场80株人工兴安落叶松解析木数据和Logistic生长模型,分别考虑单木效应和样地效应,利用S-PLUS软件中的NLME过程拟合非线性材积生长模型,采用赤池信息准则(AIC)、贝叶斯信息准则(BIC)、对数似然值和似然比检验等模型评价指标对不同模型的精度进行比较.结果表明：当考虑单木效应影响时,b₁、b₂、b₃（分别代表Logistic模型中的渐进、尺度和形状的随机参数）同时作为随机参数时模型拟合效果最好; 当考虑样地效应影响时,b₁作为随机参数时模型拟合效果最好.基于单木效应和样地效应的混合模型的拟合精度高于基本模型（Logistic生长模型）,考虑单木效应影响的混合模型的精度高于考虑样地效应影响的模型.模型检验结果表明,随机效应模型不但能反映单木材积的总体平均变化趋势,还能反映个体之间的差异;随机效应模型通过校正随机参数值能提高模型的预测精度.     

苹果果实生长的数学模型及各生长指标间的相关性分析

以富士苹果(Malus domestica‘Fuji’)为试材,测定其果实生长发育期间各生长指标的动态变化,选择5种理论生长方程对纵径、横径、单果重、体积、干重进行拟合,并根据拟合结果确定合适的生长方程建立各生长指标的数学模型,采用多项式拟合建立果形指数变化的数学模型,同时对果实各生长指标之间进行相关性分析。结果表明,果实纵径、横径生长适合选择Logistic方程,单果重、体积、干重适合选择Gompertz方程,果形指数的变化适合采用多项式拟合;果实纵径、横径、单果重、体积、干重两两之间均呈显著正相关,果形指数、果实干物质相对含量均与纵径、横径、单果重、体积、干重之间呈显著负相关,果实密度与纵径、横径、单果重、体积、干重之间呈显著负相关,而与果形指数、果实干物质相对含量之间呈显著正相关。     

人工红松树干内部节子体积预测模型

基于黑龙江省林口林业局林场和东京城林业局林场29块标准地中49株人工红松1207个节子数据,使用图片处理软件Digimizer对节子纵剖面图片数据进行提取,将节子形状用一个二维散点图表示。根据节子二维形状散点图,把人工红松节子分为3种类型: 活节(整个节子为健全节)、未包藏死节(节子由健全节和疏松节组成)和包藏死节(节子的健全节和疏松节部分被树干包藏)。3个类型节子的健全节体积通过对健全节形状参数方程求积得到;疏松节体积利用圆柱体的体积计算得到;节子总体积等于健全节体积与疏松节体积之和。最后,基于节子变量(节子直径、节子相对高、节子总长度)和树木变量(胸径),采用样地和树木水平的线性混合模型建立了红松人工林健全节体积、疏松节体积和节子总体积的预测模型。与基础模型相比,考虑样地和树木水平的混合效应所建立的健全节体积、疏松节体积和节子总体积预测模型,其参数估计更精准,残差分布更均匀,拟合精度明显提高。检验结果表明,基础模型预估精度均在90%以上,引入样地和树木效应的混合模型的预估精度均在93%以上,说明所建模型可以很好地预测红松人工林节子体积大小。     

青藏高原典型人工林幼树生物量模型构建

森林生物量计算是全球碳储量估算的基础,现已纳入全球国家森林清单项目。普遍的森林碳汇计量采用的材积源生物量法针对胸径5 cm以上的树木,幼树(胸径<6 cm,树高>0.3 m)的碳汇量并未被完整计入其中,导致生态系统碳汇能力被低估。基于青藏高原137株5种典型人工林幼树的实测生物量数据,以地径代替胸径作为预测变量,采用加权广义最小二乘法建立独立生物量模型,选择比例总量直接控制及代数和控制2种结构形式的相容性生物量模型,并通过加权非线性似乎不相关回归进行方程组估算,建立了整株及各组分的相容性生物量方程。结果表明: 二元相容性模型优于一元以及独立模型,对整株生物量来说,R²达到0.90～0.99,两种相容性模型对于不同树种来说各有优势但精度差距可以忽略,从林业生产实践角度考虑,比例总量直接控制生物量模型更有实践意义,从遥感技术的变量提取角度考虑,本研究构建了更适于遥感估算的幼树生物量模型,其整体上拟合精度高,可以准确地进行类似气候环境中的幼树整株和各组分生物量的估算。     

Growth, biomass yield and biomass functions for plantation-grown Nauclea diderrichii (de wild) in the humid tropical rainforest zone of south-western Nigeria

Adequate management of forest plantation requires estimation of growth and biomass yield and consequently, the fitting of functions for estimating biomass. Growth, biomass yield and biomass functions for estimating biomass of Nauclea diderrichii plantations in Omo forest reserve, Nigeria are described. Data were obtained from 30 temporary sample plots selected from stands that are 5-30 years old. A total of 81 trees were harvested for biomass estimation. Mean tree diameter at breast height (dbh), total height and stand bole volume ranged from 9.6 to 29.3 cm; 9.0 to 23.6m and 23.27 to 535.52 m(3)ha(-1), respectively while Total Above Ground Biomass (TAGB) varied from 32.5 t ha(-1) to 287.5 t ha(-1) between 5 and 30 years. Biomass allocations to stem, branch and foliage were 84.5%, 13.5% and 3%, respectively. All biomass components could be described precisely by dbh alone (R(adj)(2)>0.97), with very low standard errors of estimates. Little improvement in the precision of the functions was achieved by including total height. In addition, the residuals of regression functions with only dbh were generally more constrained than those that included total height. Consequently, the functions with dbh alone and its derivative as independent variables were recommended for estimating biomass of opepe in Nigeria.     

间伐对日本落叶松人工林林下更新木本植物组成和生长影响的时间效应

明确间伐对针叶人工林林下更新阔叶木本植物组成和生长影响的时间效应,可为促进人工纯林向针阔混交林转化、进而解决纯林生产与生态功能无法兼顾的问题提供参考。本研究以我国北方重要针叶人工林——日本落叶松人工林为例,比较间伐后短期(1～3年)、中期(4～9年)和长期(>9年)人工林林下更新木本植物组成的差异;并选择具有较高重要值且与落叶松互惠共生的3种更新树种蒙古栎、色木槭、糠椴,分析不同间伐时期人工林内光照(郁闭度)与更新木本植物生长的关系。结果表明: 在间伐样地内更新的阔叶木本植物达46种,不同间伐时期样地内共有且占据优势的乔木树种为色木槭,灌木树种为忍冬和卫矛。随间伐后时间的推移,更新物种数逐渐减少,但乔灌比呈增大的趋势;中性树种占据优势地位。间伐对更新树种生长影响的时间效应受树种耐荫性的影响,糠椴的基径和树高均高于蒙古栎和色木槭。随间伐后时间的延长,糠椴的基径、色木槭的树高对光照响应较敏感,分别倾向于采用“耐荫策略”和“避荫策略”以适应间伐后变化的环境。间伐对日本落叶松人工林林下更新阔叶木本植物组成和生长的影响具有明显的时间效应;在制定以促进人工林林下树种更新为目标的间伐措施时,应该考虑适当延长间伐间隔,从而保证糠椴和色木槭等阔叶树幼苗的生长,使其进入林冠层,促进形成针阔混交林,实现人工林的可持续发展。     

Potential density and basal area prediction equations for unthinned Eucalyptus hybrid plantations in the Gujarat state of India

The aim of this paper is to present equation for estimating potential stand density and basal area projection model for unthinned pure even-aged plantations of Eucalyptus hybrid in Gujarat State of India. Relationships between quadratic mean diameter and stems ha(-1) were developed, which was used to establish the limiting density line. Eight different stand level models, belonging to the path invariant algebraic difference form of a non-linear growth function, were compared for projecting basal area. They can be used to predict future basal area as a function of stand variables like dominant height and stem number per hectare and are crucial for evaluating different silvicultural treatment options. The performance of the models was evaluated using different statistical criteria. The model proposed by Pienaar and Shiver performed best and hence is recommended for projecting the basal area in E. hybrid stands.     

黑龙江不同区域人工红松心边材及树皮削度可加性模型系统构建

基于黑龙江省孟家岗林场、东京城林业局和林口林业局不同林分条件下103株人工红松解析木的2977个圆盘数据,结合林业研究中常见的Kozak(1988)、Muhairwe(1999)、Lee(2003)、Kozak(2004)可变指数削度方程,构建带皮直径、心材直径、边材宽度、树皮厚度的削度方程,并对比选出最优基础模型;采用SAS软件PROC MODEL模块中似乎不相关回归(SUR),建立带皮直径、心材直径、边材宽度和树皮厚度削度方程的可加性模型系统,同时将区域作为哑变量引入模型中,通过调整确定系数(R_adj²)、均方根误差(RMSE)、赤池信息准则(AIC)、贝叶斯信息准则(BIC)等模型评价指标,对模型进行综合评价。结果表明: 带皮直径、心材直径、边材宽度和树皮厚度最优基础模型均为Kozak(2004);可加性模型系统在满足各分量与总量可加性的基础上,也得到较好的预测效果,预估精度均达到98%以上,引入哑变量后,可加性模型系统预测能力均有不同程度的提升,尤其心材直径和边材宽度预测能力提升更显著;不同区域带皮直径和树皮厚度削度差异较小,而心材直径、边材宽度的削度存在明显差异。本研究构建的包含哑变量可加性模型系统,不但模型预测精度较高,还满足带皮直径、心材直径、边材宽度和树皮厚度之间的可加性逻辑,为人工红松心边材及树皮材积的准确估测提供了基础。     

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.     

Spatio-temporal change in forest cover and carbon storage considering actual and potential forest cover in South Korea

This study analyzes change in carbon storage by applying forest growth models and final cutting age to actual and potential forest cover for six major tree species in South Korea. Using National Forest Inventory data, the growth models were developed to estimate mean diameter at breast height, tree height, and number of trees for Pinus densiflora, Pinus koraiensis, Pinus rigida, Larix kaempferi, Castanea crenata and Quercus spp. stands. We assumed that actual forest cover in a forest type map will change into potential forest covers according to the Hydrological and Thermal Analogy Groups model. When actual forest cover reaches the final cutting age, forest volume and carbon storage are estimated by changed forest cover and its growth model. Forest volume between 2010 and 2110 would increase from 126.73 to 157.33 m3 hm-2. Our results also show that forest cover, volume, and carbon storage could abruptly change by 2060. This is attributed to the fact that most forests are presumed to reach final cutting age. To avoid such dramatic change, a regeneration and yield control scheme should be prepared and implemented in a way that ensures balance in forest practice and yield.     

Phenomenological models of the forest plantations growth

Phenomenological models of the forest plantations growth are analyzed. Those derived from the Verhulst's model are shown to fail describing qualitative effects reflecting tree growth, phytomass withdrawals, and plantation restoration. The method of phase portraits is used for exploration of the forest ecosystem dynamics, which allows to describe regulatory mechanisms of the growth processes, regulation delay, and feedback types. A bistable phenomenological model is suggested herewith to characterize dynamic processes in the forest ecosystems. Principal patterns of formation of the forest plantations at different stages of the forest generation processes are considered on the basis of that model, and ecological effects responsible for the plantation dynamics are revealed.     

六盘山南坡不同密度华北落叶松水源林生长过程比较

以六盘山南侧的华北落叶松水源涵养林为研究对象,利用标准木树干解析法,研究了21年生低、中、高3种密度(1200、1500和2000 株·hm^-2)华北落叶松人工林的生长过程和直径结构.结果表明：华北落叶松3种密度林分在10年生前各项生长指标差异不显著;10年生后的林木直径、单株材积和林分蓄积生长过程明显不同;21年生时,低密度林分的生长状况明显优于中、高密度林分,但树高生长受密度影响不显著;3种密度林分直径分布的偏度系数(S_k)差异较大,高密度林分的S_k（0.338)大于中密度(0.072)和低密度林分(0.015).前者直径分布偏离正态分布,呈现顶峰偏左的现象;后者的直径分布接近正态分布,密度结构较合理;中密度林分直径分布的峰度系数(K,1.691)大于高密度(1.532)和低密度林分(0.665).说明中密度林分的林木分化程度比高、低密度林分小;林龄为21年的华北落叶松人工林的合理保留密度应为1200 株·hm^-2.     

利用混合模型分析地域对国内马尾松生物量的影响

开展全国森林生物量监测和评估,建立适合较大区域范围的通用性立木生物量模型是一项重要的基础工作,而分析森林生物量受不同地域的影响并保证不同尺度范围森林生物量估计值的可靠性,是必须面临的问题。以南方马尾松(Pinus massoniana)地上生物量数据为例,介绍了如何利用混合模型理论来分析地域对马尾松地上生物量的影响以及利用混合模型构建全国通用性立木生物量模型,为得到不同区域尺度范围内可靠的森林生物量评价和估计提供了有效途径。结果表明,混合模型不仅提高了模型的精度和通用性,并且模型中每个参数都有特定的数学含义,通过这些参数很容易分析出随机因子对生物量的影响程度。因此混合模型方法具有较大的灵活性和适应性,可推广到其它通用性模型(如材积方程)的建立。     

不同间伐措施对乳源木莲生长的影响

由于间伐措施不同,杉木与乳源木莲混交林中的乳源木莲生长差异显著。间伐适时,乳源木莲的胸径、树高生长量明显增加,材积速生期延长,且17年生仍处在速生期;而逾期间伐,林分密度偏大,则混交林中乳源木莲生长受抑制,速生期提早结束,生长不良。作者认为,为提高杉莲混交林的经营效果,适时间伐、密度合理至关重要。     

Relationship between Modelling Accuracy and Inflection Point Attributes of Several Equations while Modelling Stand Diameter Distributions

In this study, seven popular equations, including 3-parameter Weibull, 2-parameter Weibull, Gompertz, Logistic, Mitscherlich, Korf and R distribution, were used to model stand diameter distributions for exploring the relationship between the equations’ inflection point attributes and model accuracy. A database comprised of 146 diameter frequency distributions of Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) plantations was used to demonstrate model fitting and comparison. Results showed that the inflection points of the stand diameter cumulative percentage distribution ranged from 0.4 to 0.6, showing a 1/2 close rule. The equation’s inflection point attribute was strongly related to its model accuracy. Equation with an inflection point showed much higher accuracy than that without an inflection point. The larger the effective inflection point interval of the fitting curve of the equation was, and the closer the inflection point was to 0.5 for the equations with fixed inflection points, the higher the equation’s accuracy was. It could be found that the equation’s inflection point had close relationship with skewness of diameter distribution and stand age, stand density, which provided a scientific basis for model selection of a stand diameter distribution for Chinese fir plantations and other tree species.