湖南楠木次生林生长与收获预估模型

[目的]建立湖南省楠木次生林林分断面积与蓄积相容性生长收获预估模型,为林分的生长预测和经营决策提供理论依据.[方法]以湖南省1989—2014年6期一类清查样地中的楠木次生林为研究对象,建立其林分断面积和蓄积生长的联立方程组,在此基础上,加入样地效应,构建基于混合效应的联立方程系统.[结果]基础模型包括3个含林分变量的...     

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。     

利用非线性混合模型模拟杉木林优势木平均高

介绍国内外利用非线性混合效应模型方法模拟林分优势木平均高的研究进展情况。以江西省大岗山实验局不同初植密度的人工杉木为研究对象,考虑初植密度的随机效应,选择常用的Richards和Logistic形式,通过变换混合效应参数个数来构造优势木平均高和林龄关系的非线性混合效应模型。采用确定系数、均方误差和平均绝对残差等模型评价指标对不同模型的精度进行比较分析。结果表明:无论是Richards形式还是Logistic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;但是增加随机效应参数个数并不一定绝对提高模型的估计精度,相反估计精度有可能下降。以(4)式为基础的Logistic方程中,3个参数都作为混合模型的模拟精度最高。     

基于两层次线性混合效应模型的杉木林单木胸径生长量模型

基于两层次线性混合效应模型方法,建立江西省杉木人工林单木胸径生长量模型.研究所用数据来自于长期观测的固定样地数据,数据库包括82个区域、365个样地、5416株树木共计16248条记录.为了解决不同区域及不同样地之间的差异,本文构建的混合模型分别考虑样地层次、区域层次及两层次的随机参数效应.针对数据存在的重复测量及嵌套结构特性,在模拟时选择合适的异方差和自相关模型矩阵来解决此类问题.最后利用独立的抽样验证数据对模拟结果进行验证.结果表明:林分断面积、对象木胸径、林分内大于对象木的断面积之和与对象木胸径的比值以及海拔对单木胸径生长量有显著影响.与林业中常用的传统最小二乘方法相比,采用混合效应模型方法后模型的模拟精度和验证精度均有提高.选择适合的异方差和自相关函数后,模型比只考虑参数的随机效应有更好的适应性,并体现出了混合效应模型的灵活性和准确性.     

基于机载激光雷达数据估计林分蓄积量及平均高和断面积

基于东北林区191个红松林(Pinus koraiensis)样地的机载激光雷达数据和地面实测数据,首先,通过多元线性回归和非线性回归估计方法,确定林分蓄积量及平均高、断面积的基础回归模型;然后,利用误差变量联立方程组方法,建立基于激光雷达变量的林分蓄积量与平均高、断面积的模型系统。结果显示:建立的多元线性、多元和二元非线性林分蓄积量回归模型,其确定系数R~2分别为0.858,0.846和0.821,平均预估误差MPE分别为2.57%,2.66%和2.85%,平均百分标准误差MPSE分别为26.35%,16.35%和17.88%;利用模型系统对林分平均高、断面积和蓄积量进行估计,其R~2分别为0.597,0.750和0.822,MPE分别为1.90%,2.52%和2.84%,MPSE分别为10.85%,15.28%和17.73%。结果表明:基于机载激光雷达数据估计林分蓄积量、平均高等主要森林参数,非线性模型优于线性模型,而且基于点云高度变量(中位数)和强度变量(75%分位数)的二元非线性模型就能达到比较理想的预估效果;误差变量联立方程组方法,是建立林分蓄积量与平均高、断面积回归模型系统的一种可行方法;所建立的东北红松林平均高、断面积和蓄积量联立模型,其预估精度达到森林资源调查相关技术规定要求,可以在实践中推广应用。     

基于非线性混合模型的落叶松云冷杉林分断面积模型

以吉林省汪清林业局金沟岭林场20块落叶松云冷杉样地为研究对象.首先选择传统的回归方法从4个常用的断面积模型中找出模拟精度最高的模型作为基础模型,利用基础模型及模拟数据构建非线性混合模型,考虑样地效应,采用SAS软件进行模拟,选择模型收敛及其对数似然值、AIC和BIC值最小的混合模型作为最优模型;然后,在此基础上考虑断面积连续观测数据的时间序列相关性,并把间伐强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.结果表明:林分密度指数作为自变量的Schumacher式的模拟精度最高,而考虑样地效应的混合模型模拟精度优于传统的回归模型方法;一阶自回归误差结构矩阵模型在解释断面积的时间序列相关性时不仅提高了混合模型的模拟精度,而且能够很好地表达连续观测数据问误差分布情况;同时考虑样地的随机效应、观测数据的时间序列相关性及间伐强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.     

华北落叶松人工林林分枯损株数随机效应预测模型

【目的】构建能够准确预测华北落叶松林分枯死木的计数模型,探究影响华北落叶松林中林木枯死数量的主要原因,为冬奥会核心区的华北落叶松人工林科学经营与管理提供决策依据。【方法】以张家口市崇礼冬奥核心区45块华北落叶松人工林样地为研究对象,构建华北落叶松林分枯死数量Poisson回归模型、负二项回归模型、零膨胀Poisson回归模型和零膨胀负二项回归模型、Hurdle-Poisson回归模型、Hurdle负二项回归模型,根据AIC值选出最优计数模型。基于最优计数模型,考虑不同随机效应水平和作用在截距和协变量上的随机参数,根据模型收敛情况和AIC值确定最优的随机效应水平和随机参数组合,构建最优林分枯死数量混合效应模型。【结果】林分平均直径、林分优势木平均高、林龄、林分断面积和林分胸径Gini系数为影响林分枯死的林分因子,立地因子对林分枯死的影响并不大。未考虑零膨胀现象时,负二项回归模型拟合效果优于Poisson回归模型;考虑零膨胀现象后,Hurdle-Poisson回归模型拟合效果优于零膨胀Poisson回归模型。最终几种考虑零值过多的计数模型的拟合精度表现为：Hurdle负二项回归模型(HNB...     

湖南楠木次生林断面积生长模型研究

建立湖南楠木次生林断面积生长预测模型,为林分的生长预测和经营决策提供理论依据和科学指导。以湖南省1989—2014年6期森林资源连续清查样地中的楠木次生林为对象,以5个有生物学意义的理论模型构建断面积生长基础模型;在此基础上,加入与林分生长密切相关的立地指数,构建立地指数模型;为提高模型预测精度,加入含林分密度的随机参数,构建湖南楠木次生林断面积生长混合效应模型。选择5个有生物学意义的理论模型中确定系数(R~2=0.2410)和预估精度(P=98.8213%)最高、残差平方和最小(SSE=2986.1492)的Logistic生长模型作为基础模型;在参数b_1处加入立地指数,构建了湖南楠木次生林立地指数模型,其确定系数提升到0.331 2;以林分密度划分密度等级,构建以林分密度为随机效应的混合效应模型,结果显示,在参数b_4处加入随机参数的模拟,其AIC和BIC值最小,拟合效果显著优于其他模拟(ρ<0.0001);相比基础模型,混合效应模型的ME,MAE,RME,RMAE值均明显降低,确定系数提升到0.946 2,预测精度有所提升。所构建的混合效应模型能够提升林分断面积生长的预估精度,消除林分不同密度等级间的差异,为湖南楠木次生林的合理经营提供了科学依据。     

基于立地因子的杉木人工林断面积生长混合效应模型研究

基于湖南省150块杉木人工林样地数据,采用方差分析、回归分析、非线性混合效应模型、K-means聚类等方法,构建了含立地因子的杉木人工林断面积生长混合效应模型。结果显示:1)海拔(HB)、坡度(PD)、坡位(PW)、土壤厚度(TH)、土壤类型(TL)对林分断面积的生长具有显著影响,其显著性顺序为TLTHPDPWHB;2)在8种常用的理论生长方程中,Schumacher(M5)的确定系数最高(R~2=0.7636),被选为林分断面积生长模拟的基础模型;3)将不同立地因子组合的107个立地类型(ST)作为随机效应,构建了非线性混合效应模型,其确定系数(R~2)提高至0.895 1;4)将107个立地类型(ST)聚类为5个立地类型组(STG),进一步构建了杉木断面积生长混合效应模型,其确定系数(R~2)提高至0.920 2。研究表明:基于立地因子的非线性混合效应模型,客观解释了立地因子对杉木人工林断面积生长的影响,提高了林分断面积生长模型的模拟精度。     

基于混合效应的杉木人工林冠幅模型

构建杉木(Cunninghamia lanceolata)人工林单木冠幅模型,可以提高杉木冠幅的预测精度,并为杉木人工林的科学经营提供参考依据。以杉木为研究对象,基于江西省崇义县杉木人工林57个样地的7 198株单木数据,对基础模型进行扩展,并构建含林分因子和单木因子的冠幅非线性混合效应模型;采用十折交叉验证方法,以调整后的决定系数(R²_adj)、均方根误差(E_RMS)和平均绝对误差(E_MA)模型评价指标对各模型的预测效果进行评价。结果表明:(1)备选模型中,Logistic模型的预测效果最佳。(2)除胸径以外,有6个指标对冠幅有显著影响(P<0.05)。6个指标分别是地位指数、林龄、基尼系数(Gini系数)、林分密度指数、枝下高和大于对象木的断面积之和。添加协变量构建的广义模型较基础模型更优,R²_adj增加了28.53%,E_RMS和E_MA分别下降了17.80%和15.72%。(3)考虑样地水平随机效应的混...     

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。     

Comparison of nonspatial and spatial approaches with parametric and nonparametric methods in prediction of tree height

Nonparametric modelling has been popular in recent forestry applications. However, nonparametric modelling methods usually assume independent observations, that is, do not acknowledge the spatial relationships of most forest data sets. For these situations, mixed model and kriging approaches have been used. The aim of this paper was to compare accuracy of spatial parametric and nonparametric approaches, namely mixed models and a combination of k-nn method and mixed models, in prediction of tree height. The spatial approaches were compared to a nonspatial parametric model and k-nn method. Tree height was first modelled using either mixed model or k-nn. The residual error was divided into plot and tree effects. A nonspatial prediction was obtained using the fixed part of the models. The spatial prediction was obtained when this prediction was further adjusted using the estimates of within-plot correlation of errors and best linear predictor. The influence of the quality of modelling data was also considered. The adjustment of nonspatial estimates of both parametric and nonparametric approaches markedly improved the predictions in all study cases. For many applications, the combination of the nonparametric k-nn method for the fixed component of the model, along with random effects for spatial correlations to create a mixed model, could be used. This would allow for spatial prediction, which would likely provide improved predictions, as shown for predicting height in this paper. Also, there is the added benefit that the nonparametric k-nn does not require a particular model form.     

基于混合效应的湖南马尾松次生林单木生长模型

[目的]建立湖南省马尾松次生林单木断面积与材积生长模型,为林木的生长预估提供理论依据.[方法]以湖南省2014年一类清查样地中的20块马尾松次生林为研究对象,选取5个具有生物学意义的生长方程,建立马尾松断面积和材积随年龄变化的基础模型,在此基础上,加入以样地为随机效应的随机参数,构建基于混合效应的湖南马尾松次生林单木断...     

Development of a linear mixed-effects individual-tree basal area increment model for masson pine in Hunan Province,South-central China

ABSTRACT

An individual-tree basal area increment model was developed for masson pine based on 26276 observations of 13,138 trees in 987 sample plots from the 7th (2004), 8th (2009), and 9th (2014) Chinese National Forest Inventory in Hunan Province, South-central China. The model was built using a linear mixed-effects approach with sample plots included as random effects since the data have a hierarchical stochastic structure and biased estimates of the standard error of parameter estimates could be a consequence of applying ordinary least square (OLS) for regression. In addition, within-plot heteroscedasticity and autocorrelation were also considered. The final mixed-effects model was determined according to the Akaike information criterion (AIC), Bayesian information criterion (BIC), log-likelihood (Loglik), and the likelihoodratio test (LRT). The results revealed that initial diameter (DBH), the sum of the basal area (m²/ha) in trees with DBHs larger than the DBH of the subject tree (BAL), number of trees per hectare (NT), and elevation (EL) had a significant impact on individual-tree basal area increment. The mixed-effects model performed much better than the basic model produced using OLS. Additionally, the variance structure of the model errors was successfully modeled using the power function. However, the autocorrelation structures were not defined because there was no autocorrelation amongst the data. It is believed that the final model will contribute to the scientific management of the masson pine.     

A flexible stem taper and volume prediction method based on mixed-effects B-spline regression

Modelling stem taper and volume is crucial in many forest management and planning systems. Taper models are used for diameter prediction at any location along the stem of a sample tree. Furthermore, taper models are flexible means to provide information on the stem volume and assortment structure of a forest stand or other management units. Usually, taper functions are mean functions of multiple linear or nonlinear regression models with diameter at breast height and tree height as predictor variables. In large-scale inventories, an upper diameter is often considered as an additional predictor variable to improve the reliability of taper and volume predictions. Most studies on stem taper focus on accurately modelling the mean function; the error structure of the regression model is neglected or treated as secondary. We present a semi-parametric linear mixed model where the population mean diameter at an arbitrary stem location is a smooth function of relative height. Observed tree-individual diameter deviations from the population mean are assumed to be realizations of a smooth Gaussian process with the covariance depending on the sampled diameter locations. In addition to the smooth random deviation from the population average, we consider independent zero mean residual errors in order to describe the deviations of the observed diameter measurements from the tree-individual smooth stem taper. The smooth model components are approximated by cubic spline functions with a B-spline basis and a small number of knots. The B-spline coefficients of the population mean function are treated as fixed effects, whereas coefficients of the smooth tree-individual deviation are modelled as random effects with zero mean and a symmetric positive definite covariance matrix. The taper of a tree is predicted using an arbitrary number of diameter and corresponding height measurements at arbitrary positions along the stem to calibrate the tree-individual random deviation from the population mean estimated by the fixed effects. This allows a flexible application of the method in practice. Volume predictions are calculated as the integral over cross-sectional areas estimated from the calibrated taper curve. Approximate estimators for the mean squared errors of volume estimates are provided. If the tree height is estimated or measured with error, we use the “law of total expectation and variance” to derive approximate diameter and volume predictions with associated confidence and prediction intervals. All methods presented in this study are implemented in the R-package TapeR.     

A mixed nonlinear height–diameter model for pyrenean oak (Quercus pyrenaica Willd.)

A nonlinear mixed-effects modelling approach was used to model the individual tree height–diameter relationship in pyrenean oak (Quercus pyrenaica Willd.). A set of 24,627 pairs of height–diameter measurements were used to fit the model. These were taken at 950 Spanish National Forest Inventory plots embracing six different biogeoclimatic strata. Eleven biparametric nonlinear height–diameter equations were evaluated to find a local model, which only includes the dimensions of the tree as explanatory variables. After selecting the local model, a regional or generalized model was studied. The following stand variables were tested for inclusion in the model as fixed effects: stand density, quadratic mean diameter, arithmetic mean diameter, dominant diameter, arithmetic mean height, dominant height and basal area. Dominant height and basal area of the stand were found to produce the most satisfactory fits in the stand model. Interregional variability was studied by including strata effects as dummy categorical variables and was analysed using the non-linear extra sum of squares method and the Lakkis–Jones test. Height–diameter models were found to be similar for the six biogeoclimatic strata. Finally, a mixed nonlinear model technique was applied to fit the definitive model. By calibrating the model it is possible to predict random components of definitive model from height measurements previously taken from a subsample of trees. The different alternatives tested reveal that only two or three trees are necessary to calibrate the model.     

云冷杉阔叶混交过伐林林分优势高估计方法的研究

[目的]以云冷杉阔叶混交林为对象,比较混交林优势高的估计方法,为混交林立地质量评价提供依据。[方法]在吉林省汪清林业局金沟岭林场,调查53块云冷杉阔叶混交林样地,样地为圆形,面积600 m^2。在每个样地实测6株针阔叶树种优势木的树高和年龄,并采用针叶树的优势高、阔叶树的优势高、算术平均优势高、加权平均优势高4种方法估计林分优势高,通过不同优势高的相关分析、与林分年龄、蓄积量、生产力和密度的关系进行比较。[结果]4种方法得到的林分优势高有显著的相关性,相关系数在0.434~0.980之间;但单用针叶或阔叶树得到的优势高与二者平均高的差别较大,算术及加权平均方法的结果非常接近;4种方法得到的林分优势高与林分蓄积量具有中等的相关性,相关系数在0.358~0.577之间,以断面积加权林分优势高最大,但与林分生产力无显著的相关性;林分优势高受到林分密度的显著影响,与年龄的关系很弱。[结论]对于云冷杉阔叶异龄混交林,4种林分优势高都不能反映立地生产力,需要更多的验证和发展新的立地质量评价指标。     

Thinning intensity and growth response in SW-European Scots pine stands

The effect of different thinning intensities on growth and yield was studied in Pinus sylvestris L. stands at the south-western limit of its distribution area (Central Spain), using five long-term thinning trials. Data were analysed collectively considering several factors (trial, block, plot and period) as random effects. Total volume and volume increment decreased with thinning intensity, this loss being more significant in the case of moderate and heavy thinning. No difference was found among treatments for total basal area or the increment in basal area. The results revealed an optimum basal area (Assmann’s definition) between 85 and 100% of the basal area in unthinned plots. Volume growth loss associated with heavy thinnings (reduction of 18% in volume increment) was smaller than that reported in Central and Northern European regions (greater than 25%). Height increment was not influenced by thinning, whereas dominant and quadratic mean diameter increments increased with the thinning intensity. The response of diameter growth to thinning was greater at younger ages (less than 50 y) and in medium-sized trees.