基于混合模型的落叶松微纤丝角模型

以黑龙江省七台河市林业局金沙林场9株人工落叶松2 790个样品数据为例,选择6个常用方程进行非线性回归分析,把拟合精度最高的修正Logistic模型作为微纤丝角基础模型y=b1/[1+ exp(b2x)]+b3,然后,利用S-PLUS软件中的NLME过程,拟合非线性微纤丝角模型.采用AIC、BIC、对数似然值和似然比检验等模型评价统计指标对不同模型的精度进行比较分析.结果表明:当对微纤丝角-年龄关系进行拟合时,b1,b2,b3同时作为混合参数时模型拟合效果最好.把相关性结构包括复合对称结构(CS)、一阶自回归结构AR(1)、一阶移动平均结构MA(1)及一阶自回归与移动平均结构[ARMA(1,1)]加入到微纤丝角最优混合模型中,一阶自回归与移动平均模型[ ARMA(1,1)]显著提高了微纤丝角混合模型的拟合精度.模型检验结果表明:混合模型通过校正随机参数值能提高模型的预测精度.因此,混合模型在应用上不仅能反映总体微纤丝角预测,而且能通过方差协方差结构和误差相关性结构校正随机参数来反映个体微纤丝角差异.     

基于非线性混合模型的落叶松树干削度模型

以黑龙江省带岭林业局大青川林场84株人工落叶松解析木数据为例,采用Max和Burkhart分段削度模型作为基础模型,利用SAS软件中的似乎不相关回归过程得到该分段削度模型的4个参数和2个拐点参数同时估计。参数估计显著性检验(P<0.000 1)以及模型检验(F=31 392.30,P<0.000 1)都证明该分段模型能较好地描述落叶松树干干形变化。然后以该分段模型为基础模型,采用非线性混合模型的方法,建立落叶松人工林树干削度混合效应模型。结果表明:当考虑样地效应影响时,b1,b2同时作为混合参数时模型拟合最好;当考虑树木效应影响时,b2,b4同时作为混合参数时模型拟合最好。无论考虑样地效应影响还是考虑树木效应影响,混合模型的拟合精度都比基本模型的拟合精度高,并且考虑树木效应影响要比考虑样地效应影响的精度更高。模型检验结果表明:混合模型通过校正随机参数值能提高模型的预测精度。     

改进栓皮栎树高预测混合效应模型研究

树高与胸径是森林资源调查中2个重要的测树因子。鉴于树高测量相对不易实现的问题,以金华市永康市西溪镇的94株栓皮栎树为研究对象,在比较林业上常用的10个树高曲线模型拟合效果的基础上,改进了传统的Gompertz树高曲线模型,提出并构建了含有立地因子的Gompertz混合效应树高预测改进模型。实验表明:1)当对Gompertz混合效应模型拟合时,引入随机参数b_1,b_3时模型拟合最好;当对Gompertz混合效应改进模型拟合时,引入随机参数b_1,b4时模型拟合最好。2)构建的Gompertz混合效应改进模型决定系数达到0. 779,Gompertz混合效应模型决定系数为0. 553,Gompertz模型决定系数为0. 542,即仅凭混合效应方法构建模型对提高模型预测精度并不明显。实验证明了本文构建的Gompertz混合效应改进模型大大提高了栓皮栎的树高预测精度,为研究树种树高-胸径关系模型提供了一种新方法。     

基于线性混合模型的落叶松枝条长度和角度模型

以黑龙江省五营林业局丽林林场30株人工落叶松2190个枝条长度和角度数据为例,利用逐步回归技术建立落叶松枝条长度和角度模型:BL=b1+b2DINC+b3DINC2+b4DBH·DINC2,BA=b1+b2DINC+b3DINC2+b4DBH·DINC。利用S-PLUS软件中的LME模块,考虑树木效应拟合线性枝条长度和角度模型。采用AIC、BIC、对数似然值和似然比检验等模型评价统计指标对不同模型的拟合效果进行比较分析。结果表明:当拟合枝条长度和角度模型时,b1,b2,b3同时作为混合参数时模型拟合最好。为了描述混合模型构建过程中产生的异方差现象,把幂函数和指数函数加入到枝条长度和角度混合模型中。指数函数显著提高了枝条长度混合模型的拟合效果,幂函数显著提高了角度混合模型的拟合效果,并且消除了异方差现象。模型检验结果表明:混合模型通过校正随机参数值能提高模型的预测精度。因此,混合模型在应用上不但能反映总体枝条长度和角度预测,而且能通过方差协方差结构校正随机参数来反映树木之间的差异。     

利用2种非线性混合效应模型(2水平)对杉木林胸径生长量的分析

选择2种2水平非线性混合模型对杉木林胸径生长量进行分析,其中模型1为一般的2水平非线性混合模型,模型2在模型1的基础上进一步考虑固定效应参数随某一特定因子水平变化而变化。本文通过对这2种模型的分析,首先确定构建2水平非线性混合模型的基础模型,然后对模型1衍生出的665种模型及模型2衍生出的2703种模型进行计算和比较:对于模型1,有57种模型计算收敛,当形参b0同时考虑区组和样地效应、而b4和b5只考虑区组效应时,模型拟合效果最好,因此把该模型作为模型1的最佳拟合模型;对于模型2,有24种模型计算收敛,当形参b5同时考虑区组和样地效应、b1只考虑区组效应并且固定效应b0的取值与各区组水平有关时,模型拟合效果最好,因此把该模型作为模型2的最佳拟合模型。最后对传统的非线性回归模型、模型1及模型2进行比较:模型1和模型2的拟合效果都比传统的非线性回归模型好,且模型2的拟合效果最好。     

基于纵向数据非线性混合模型的杉木林优势木平均高研究

以江西省大岗山实验局不同初植密度的杉木林为研究对象,选择修改的Richards模型形式,考虑样地效应,采用SAS软件进行非线性混合效应模型的模拟,利用AIC和BIC值评价模型模拟效果。在此基础上考虑优势木平均高连续观测数据的时间序列相关性,并把初植密度以哑变量形式考虑进去,再进行混合模型的模拟。最后,利用验证数据对混合模型方法与传统的非线性回归模拟方法进行精度比较。研究结果表明,修改的Richards形式的优势木平均高与林龄关系的非线性混合效应模型,其估计精度比传统的回归模型估计精度明显提高,增加随机效应参数个数能够提高模型的估计精度。一阶自回归误差结构矩阵模型在解释优势木平均高的时间序列相关性时不仅提高了混合模型的模拟精度,而且能够很好的表达连续观测数据间误差分布情况;同时考虑样地的随机效应、观测数据的时间序列相关性及不同初植密度的混合模型模拟精度比传统的非线性回归方法模拟精度高。     

木荷最优树高曲线基础模型的比较选择

以福建将乐国有林场不同立地、不同林龄的木荷林分标准地调查数据为基础,采用2参数和3参数的非线性模型对木荷的树高估算模型进行拟合、比较分析,选择较优树高估算模型。结果表明,Schumacher(1939)的2参数的树高曲线模型:H=1.3+a×exp(-b/D)和Curtis(1967)的3参数的树高曲线模型:H=1.3+exp(a+b×D~c)的拟合精度最高,且2个模型的拟合精度差异不明显,若采用传统非线性模型、人工神经网络和非线性混合效应模型等方法对比研究木荷树高曲线,可选择2个参数的Schumacher(1939)模型拟合即可。     

基于ICESat-GLAS波形估测平均树高的研究

以吉林省汪清林业局经营区域为例,基于星载激光雷达ICESat-GLAS回波参数,构建了平均树高回归模型,预估精度为84.05%;利用反距离加权法,对ICESat-GLAS光斑平均树高估测值进行差值运算,得到初始CHM(Canopy Height Model),实现了平均树高空间连续分布制图;再利用坡度校正和3×3移动窗口差分滤波平滑初始CHM,得到研究区平均树高修正CHM,预估精度达到91.52%。研究结果表明,坡度校正和移动窗口差分滤波方法能有效削弱坡度影响,剔除异常点,提高平均树高估测精度。     

基于非线性混合模型的杉木优势木平均高

从理论上介绍一阶线性化算法和一阶条件期望线性化算法求解非线性混合效应模型参数,并利用这2种算法分别对杉木优势木平均高进行拟合(选用常用的Logistic模型作为基础模型,把区组作为随机效应因子)。结果表明:2种算法对杉木优势木平均高进行拟合时精度都很高。通过对2种线性化算法进一步比较可得,在分析单木水平非线性混合效应优势木平均高模型时,2种算法拟合效果非常接近,因此在实际应用中可以选择其中任意一种算法对杉木优势木平均高进行拟合。     

塞罕坝华北落叶松人工林树冠外部轮廓模型

【目的】构建树冠最大外部轮廓非线性混合效应模型和非线性分位数回归模型,为准确预测树冠生长发育规律及预估生产力提供科学依据。【方法】以河北省塞罕坝机械林场华北落叶松人工林为研究对象,基于58株解析木数据和1 789个枝条解析数据,利用幂函数、修正Kozak方程、修正Weibull方程选取基础模型,构建华北落叶松人工林树冠外部轮廓非线性混合效应模型和非线性分位数回归模型。【结果】在幂函数、修正Kozak方程和修正Weibull方程中,幂函数拟合树冠外部轮廓效果较好,作为树冠外部轮廓基础模型;林分年龄(Age)、冠长(CL)、胸径(DBH)、树高(HT)、冠高比(CHR)、高径比(HDR)对树冠外部轮廓影响较大。在混合效应模型中,两水平混合效应模型优于单水平混合效应模型,可明显提高模型拟合精度,HDR相关的参数a6考虑样地效应,相对着枝深度(RDINC)、CHR相关的参数a4、a5考虑样木效应,模型确定系数(R2)为0.873,均方根误差(RMSE)为0.319 m,平均相对误差(MRE)为6.642 m。在分位数回归模型中,当分位数q=0.90时模型曲线最接近树冠最大外部轮廓,R2为0.672。【结论】混合效应模型拟合精度较高,可准确描述树冠最大枝条的平均趋势。分位数回归模型可确定树冠最外部轮廓,在预测条件均值之外的研究中发挥重要作用。     

Modeling Microibril Angle with Mixed Models for Dahurian Larch

In this study,the sample data was based on 2 790 samples of 9 trees from dahurian larch （Larix gmelinii） plantations located in Qitaihe Forest Bureau in Heilongjiang Province.The modified Logistic model y = b₁ /[1 + exp（b₂ x）]+ b₃ was selected to modeling microfibril angle from six models based on nonlinear regression.Then,the logistic model was fitted using nonlinear mixed-effect modeling approach based on NLME of S-PLUS software.Evaluation statistics,such as AIC,BIC, Log Likelihood and Likelihood ratio test were used for model comparisons.The results showed that the Logistic model with parameters b₁,b₂,b₃ as mixed effects showed the best performance.Correlation structures included compound-symmetry structure （CS）,first-order autoregressive correlation structure AR（1）,moving average correlation structure MA（1） and autoregressive-moving average correlation structure[ARMA（1,1）]were incorprated into the best microfibril angle mixed model.[ARMA（1,1）]significantly improved the precision of mixed model.Validation confirmed that the mixed model with calibration of random parameters could provide more accurate and precise prediction.Therefore,the application of mixed model not only showed the mean trends of microfibril angle,but also showed the individual difference based on variance-covariance structure and correlation structure.     

Modeling Branch Length and Branch Angle with Linear Mixed Effects for Dahurian Larch

In this study,the sample data was based on 2 190 branch length and angle samples of 30 trees from dahurian larch（Larix gmeiinii） plantations located in Wuying Forest Bureau in Heilongjiang Province.The stepwise regression techniques were used to develop branch length and branch angle models:BL= b₁ + b₂ DINC + b₃ DINC² + b₄ DBH·DINC²,BA = b₁ + b₂ DINC + b₃ DINC² + b₄ DBH·DINC.Then,the developed models were fitted using linear mixed-effects modeling approach based on LME procedure of S-PLUS software.Evaluation statistics,such as AIC,BIC, Log Likelihood and Likelihood ratio test were used for model comparisons.The results showed that the branch length and branch angle models with parameters b₁,b₂,b₃ as mixed effects showed the best performance.Exponential and power functions were incorporated into mixed branch length and branch angle model.The addition of the exponential and power functions significantly improved the mixed-effects model.The plots of standardized residuals indicated that the mixed-effect model with exponential and power functions showed more homogeneous residual variance than the mixed-effects model.Validation confirmed that the mixed model with calibration of random parameters could provide more accurate and precise prediction.Therefore,the application of mixed model not only showed the mean trends of branch length and branch angle,but also showed the individual difference based on variance-covariance structure.     

基于线性混合模型的落叶松枝条基径模型

以黑龙江省五营林业局丽林林场30株人工落叶松2 190个枝条基径数据为例,利用逐步回归技术建立了落叶松枝条基径模型:BD=b1+b2DINC+b3DINC2+b4DBH.DINC2。然后,利用S-PLUS软件中的LME过程,拟合线性枝基径模型。采用AIC、BIC、对数似然值和似然比检验等模型评价统计指标对不同模型的拟合效果进行比较分析。结果表明:当拟合枝条基径模型时,b1、b2、b3同时作为混合参数时模型拟合最好。为了矫正混合模型构建过程中产生的异方差现象,把幂函数和指数函数加入到枝条基径混合模型中。指数函数显著提高了枝条基径混合模型的拟合效果,并且消除了异方差现象。模型模拟表明:对于大小相同树木,枝条基径随着着枝深度(DINC)的增加而增大,对于大小不同的树木,枝条基径随着胸径(DBH)的增加而增大。林木的胸径变量很好地反映了不同大小树木的枝条基径的变化。在不知道详细林分信息的前提下,可以利用树木变量合理地预测兴安落叶松人工林的枝条基径的变化规律。     

GROWTH AND YIELD MODELS FOR DAHURIAN LARCH PLANTATIONS

Growth and yield models were developed for individual tress and stands based on336 temporary plots with 405 stem analysis trees of dahurian larch(Larix gmelinii(Rupr.)Rupr.)plantations throughout Daxing’anling mountains.Several equations were selected using nonlinearregression analysis.Results showed that the Richards equation was the best model for estimatingtree height,stand mean helght and stand dominant height from age; The Power equation was thebest model for prediction tree volume from DBH and tree height; The logarithmic stand volumeequation was good for predicting stand volume from age,mean height,basal area and other standvariables.These models can be used to construct the volume table, the site index table and other for-estry tables for dahurian larch plantations.     

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。     

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.     

Models for predicting tree and stand development on larch plantations in Hallormsstaður,Iceland

The aim was to model the growth of Siberian larch (Larix sibirica Ledeb.) and Russian larch (Larix sukaczewii Dyl., syn. L. sibirica var. sukaczewii) plantations in Hallormsstaeur, Iceland. The field inventory was carried out in eastern Iceland in June 2006. Models were constructed for predicting dominant height, total tree height and 5-year diameter increment. Several linear and non-linear forms of models were tested in preliminary analyses to find the equations that fitted the modelled characteristics best. Due to the spatially hierarchical correlation structure of the data (stands, plots and trees), the assumption of non-correlated error terms did not hold. Therefore, a random parameter modelling approach was adopted using mixed models when the estimates obtained for the random effects were statistically significant. The variance estimates for the random effects can be further used to calibrate the models. The models generated here performed well with independent test data and were consistent with the forest growth theory. They can be used to evaluate site quality and to estimate the growth and yield of larch stands in eastern Iceland in connection with forest planning.     

Modelling primary branch growth based on a multilevel nonlinear mixed‑effects model: a Pinus koraiensis plantation case study in north‑east China

On the basis of a multilevel nonlinear mixed?effects model approach, branch diameter and length growth models were developed for a Pinus koraiensis plantation in north?east China. The models developed were able to better capture the residual variation successfully by partitioning the residual variance into plot?, tree? and branch? level variations via random parameter modeling at the three levels. In addition to random effects, various time series correlation structures were evaluated to account for residual autocorrelation, and the AR(1) and ARMA(1,1) structures were selected for the branch diameter and length growth models, respectively. Model validation results using an independent data set confirmed that multilevel mixed models with an appropriate correlation structure produced more accurate and precise branch?specified diameter and length predictions. Overall, the models were suitable in describing the trends and inherent variability of crown profile and good enough to be included in growth simulation systems for Pinus koraiensis plantations.     

基于多水平非线性混合效应蒙古栎林单木断面积模型

以吉林省汪清林业局184块样地中的10 111株蒙古栎为例,首先选用线性函数、Richards函数、Logistic 函数、指数函数等7种常用函数形式,分析4个因变量(后期胸径、后期胸高断面积、直径增量和胸高断面积增量)与前期胸径的影响,确定一个用于构建混合效应模型的基础模型。然后确定同时考虑林场效应和林场与样地交互效应时基础模型中最优的形式参数构造形式,利用逐步回归方法确定模型中所包含的林分变量,并分析和比较用来消除异方差的3种常用残差方差函数(指数函数、幂函数和常数加幂函数),最后检验模型预测效果。结果表明:Wykoff模型且因变量为后期胸高断面积拟合效果较好,故作为基础模型;除前期胸高直径(D)外,当考虑坡度正切(ST),对象木胸高直径与样地算术平均直径的比(RAD),样地胸高总断面积(TBA),样地中大于对象木直径所有树木的胸高断面积和(GSBA),对象木胸高断面积与样地算术平均胸高断面积的比 (RABA)和对象木胸高断面积与样地胸高总断面积的比(RBA)等林分变量时能进一步提高模型预测精度;对于残差方差,指数函数、幂函数和常数加幂函数都能消除异方差,但幂函数效果最好;当模型同时考虑林场效应和林场与样地交互效应时预测精度最高。