Mixed-effects modeling for tree height prediction models of Oriental beech in the Hyrcanian forests

Height–diameter relationships are essential elements of forest assessment and modeling efforts.In this work,two linear and eighteen nonlinear height–diameter equations were evaluated to find a local model for Oriental beech（Fagus orientalis Lipsky） in the Hyrcanian Forest in Iran.The predictive performance of these models was first assessed by different evaluation criteria： adjusted R^2（R^2_（adj））,root mean square error（RMSE）,relative RMSE（%RMSE）,bias,and relative bias（%bias） criteria.The best model was selected for use as the base mixed-effects model.Random parameters for test plots were estimated with different tree selection options.Results show that the Chapman–Richards model had better predictive ability in terms of adj R^2（0.81）,RMSE（3.7 m）,%RMSE（12.9）,bias（0.8）,%Bias（2.79） than the other models.Furthermore,the calibration response,based on a selection of four trees from the sample plots,resulted in a reduction percentage for bias and RMSE of about 1.6–2.7%.Our results indicate that the calibrated model produced the most accurate results.

Innovative deep learning artificial intelligence applications for predicting relationships between individual tree height and diameter at breast height

Background:Deep Learning Algorithms(DLA)have become prominent as an application of Artificial Intelligence(Al)Techniques since 2010.This paper introduces the DLA to predict the relationships between individual tree height(ITH)and the diameter at breast height(DBH).Methods:A set of 2024 pairs of individual height and diameter at breast height measurements,originating from 150 sample plots located in stands of even aged and pure Anatolian Crimean Pine(Pinus nigra J.F.Arnold ssp.pallasiana(Lamb.)Holmboe)in Konya Forest Enterprise.The present study primarily investigated the capability and usability of DLA models for predicting the relationships between the ITH and the DBH sampled from some stands with different growth structures.The 80 different DLA models,which involve different the alternatives for the numbers of hidden layers and neuron,have been trained and compared to determine optimum and best predictive DLAs network structure.Results:It was determined that the DLA model with 9 layers and 100 neurons has been the best predictive network model compared as those by other different DLA,Artificial Neural Network,Nonlinear Regression and Nonlinear Mixed Effect models.The alternative of 100#neurons and 9#hidden layers in deep learning algorithms resulted in best predictive ITH values with root mean squared error(RMSE,0.5575),percent of the root mean squared error(RMSE%,4.9504%),Akaike information criterion(AIC,-998.9540),Bayesian information criterion(BIC,884.6591),fit index(Fl,0.9436),average absolute error(AAE,0.4077),maximum absolute error(max.AE,2.5106),Bias(0.0057)and percent Bias(Bias%,0.0502%).In addition,these predictive results with DLAs were further validated by the Equivalence tests that showed the DLA models successfully predicted the tree height in the independent dataset.Conclusion:This study has emphasized the capability of the DLA models,novel artificial intelligence technique,for predicting the relationships between individual tree height and the diameter at breast height that can be required information for the management of forests.

New approach to calculating tree height at the regional scale

Background:Determining the spatial distribution of tree heights at the regional area scale is significant when performing forest above-ground biomass estimates in forest resource management research.The geometric-optical mutual shadowing(GOMS)model can be used to invert the forest canopy structural parameters at the regional scale.However,this method can obtain only the ratios among the horizontal canopy diameter(CD),tree height,clear height,and vertical CD.In this paper,we used a semi-variance model to calculate the CD using high spatial resolution images and expanded this method to the regional scale.We then combined the CD results with the forest canopy structural parameter inversion results from the GOMS model to calculate tree heights at the regional scale.Results:The semi-variance model can be used to calculate the CD at the regional scale that closely matches(mainly with in a range from-1 to 1 m)the CD derived from the canopy height model(CHM)data.The difference between tree heights calculated by the GOMS model and the tree heights derived from the CHM data was small,with a root mean square error(RMSE)of 1.96 for a 500-m area with high fractional vegetation cover(FVC)(i.e.,forest area coverage index values greater than 0.8).Both the inaccuracy of the tree height derived from the CHM data and the unmatched spatial resolution of different datasets will influence the accuracy of the inverted tree height.And the error caused by the unmatched spatial resolution is small in dense forest.Conclusions:The semi-variance model can be used to calculate the CD at the regional scale,together with the canopy structure parameters inverted by the GOMS model,the mean tree height at the regional scale can be obtained.Our study provides a new approach for calculating tree height and provides further directions for the application of the GOMS model.

Comparing Tree Heights among Montane Forest Blocks of Kenya Using LiDAR Data from GLAS

This study was designed to use LiDAR data to research tree heights in montane forest blocks of Kenya. It uses a completely randomised block design to asses if differences exist in forest heights: 1) among montane forest blocks, 2) among Agro ecological zones (AEZ) within each forest block and 3) between similar AEZ in different forest blocks. Forest height data from the Geoscience Laser Altimeter System (GLAS) on the Ice Cloud and Land Elevation Satellite (ICE-SAT) for the period 2003-2009 was used for 2146 circular plots, of 0.2 - 0.25 ha in size. Results indicate that, tree height is largely influenced by Agro ecological conditions and the wetter zones have taller trees in the upper, middle and lower highlands. In the upper highland zones of limited human activity, tree heights did not vary among forest blocks. Variations in height among forest blocks and within forest blocks were exaggerated in regions of active human intervention.

Formulae of Tree Height Curve and Volume Curve Derived from Theory of Column Buckling

In this paper, the new formulae of tree height curve and volume cdrie were derived from the theory of column buckling. They were applied to artificial Pine (Pinus sylvestris var. mongolica) and Larch (Larix principis rupprechtii). The results demonsed that the new formulae wee more effeCtive and precise than conventional formulae of height curve and volume curve.

Estimating Pinus palustris tree diameter and stem volume from tree height,crown area and stand-level parameters

Accurate and efficient estimation of forest growth and live biomass is a critical element in assessing potential responses to forest management and environmental change. The objective of this study was to develop models to predict longleaf pine tree diameter at breast height （dbh） and merchantable stem volume （V） using data obtained from field measurements. We used longleaf pine tree data from 3,376 planted trees on 127 permanent plots located in the U.S. Gulf Coastal Plain region to fit equations to predict dbh and V as functions of tree height （H） and crown area （CA）. Prediction of dbh as a function of H improved when CA was added as an additional independent variable. Similarly, predic- tions of V based on H improved when CA was included. Incorporation of additional stand variables such as age, site index, dominant height, and stand density were also evaluated but resulted in only small improvements in model performance. For model testing we used data from planted and naturally-regenerated trees located inside and outside the geographic area used for model fitting. Our results suggest that the models are a robust alternative for dbh and V estimations when H and CA are known on planted stands with potential for naturally-regenerated stands, across a wide range of ages. We discuss the importance of these models for use with metrics derived from remote sensing data.

Predicting the Growth in Tree Height for Building Sunshine in Residential District

Residential greening constitutes a significant portion of the urban environment. Trees, as the largest entities in the tree-shrub-herb greening system, are the best choice for residential afforestation. Hence, tree arrangement in green space between buildings is significant, for which may exert negative impact on building sunshine. This study takes He Qingyuan residential area in Beijing as a case study to predict the growth in tree height between buildings to meet good sunshine requirements. The procedures were draw as follows: 1) models including building layout and trees were built using computer-aided design (Auto CAD). Afterwards, according to tree crown shape, tree height limits were determined for the same building layout;2) and after that, the growth in tree height was predicted using the nonlinear height-diameter functions to meet the good sunshine requirements. The results allow us to determine which trees to plant between buildings in that the designers can predict the effects of future tree growth on building sunshine.

An approach to estimate tree height using PolInSAR data constructed by the Sentinel-1 dual-pol SAR data and RVoG model

We estimate tree heights using polarimetric interferometric synthetic aperture radar(PolInSAR)data constructed by the dual-polarization(dual-pol)SAR data and random volume over the ground(RVoG)model.Considering the Sentinel-1 SAR dual-pol(SVV,vertically transmitted and vertically received and SVH,vertically transmitted and horizontally received)configuration,one notes that S_(HH),the horizontally transmitted and horizontally received scattering element,is unavailable.The S_(HH)data were constructed using the SVH data,and polarimetric SAR(PolSAR)data were obtained.The proposed approach was first verified in simulation with satisfactory results.It was next applied to construct PolInSAR data by a pair of dual-pol Sentinel-1A data at Duke Forest,North Carolina,USA.According to local observations and forest descriptions,the range of estimated tree heights was overall reasonable.Comparing the heights with the ICESat-2 tree heights at 23 sampling locations,relative errors of 5 points were within±30%.Errors of 8 points ranged from 30%to 40%,but errors of the remaining 10 points were>40%.The results should be encouraged as error reduction is possible.For instance,the construction of PolSAR data should not be limited to using SVH,and a combination of SVH and SVV should be explored.Also,an ensemble of tree heights derived from multiple PolInSAR data can be considered since tree heights do not vary much with time frame in months or one season.

Extraction and analysis of tree canopy height information in high-voltage transmission-line corridors by using integrated optical remote sensing and LiDAR

Traditional inspection methods cannot quickly and accurately monitor tree barriers and safeguard the transmission lines.To solve these problems,in this study,we proposed a rapid canopy height information extraction method using optical remote sensing and LiDAR,and used UAV optical imagery with LiDAR to monitor the height of trees in a university and a high-voltage transmission line corridor in the Ningxia region.The results showed that the relative error of tree height extraction using UAV optical images was less than 5%,and the lowest relative error was 0.11%.The determination coefficient R^(2) between the optical image tree height extraction results and the measured tree height was 0.97,thus indicating a high correlation for both.In the field of tree barrier monitoring,the determination coefficient R^(2) of tree height extracted using airborne LiDAR point cloud,and canopy height model(CHM)and of the measured tree height were 0.947 and 0.931,respectively.The maximum and minimum relative error in tree height extraction performed using point cloud was 2.91%and 0.2%,respectively,with an extraction accuracy of over 95%.The experimental results demonstrated that it is feasible to use UAV optical remote sensing and LiDAR in monitoring tree barriers and tree height information extraction quickly and accurately,which is of great significance for the risk assessment and early warning of tree barriers in transmission-line corridors.

适于GlobalAllomeTree国际数据平台的标准化中国主要树种树高-胸径方程研建

GlobalAllomeTree作为共享异速方程的国际网络平台,逐渐受到全球高度关注。当前,为促进该项国际合作,针对当前该平台缺乏中国主要树种生长异速方程的现状,系统性更新标准化中国主要树种树高-胸径方程。由于树冠和下部灌木及草丛遮挡,树高相对于胸径测量具有一定的难度,因此需要使用数学工具进行计算。选取了36个树种为材料构建树高-胸径关系方程,以全国主要树种的二元材积模型、各地区一元材积表为基础材料,以取样径阶为1 cm间隔所生成1692组树高-胸径数据作为建立方程样本,1238组外业调查数据为验证样本。建模结果表明:36个主要树种的1692组树高-胸径数据建立的全国通用性树高-胸径方程拟合相关系数(R2)为0.801,方程拟合结果较好,说明可以通过测定胸径,带入树高(H,m)-胸径(D,cm)方程(H=aDb)预估树高;对36个主要树种的树高-胸径方程进行拟合,决定系数R2值均大于0.916,平均误差(ME)、平均绝对误差(MAE)和均方根误差(RMSE)相对较小,方程整体精度较高,可广泛推广;将外业采集的1238组树高-胸径数据,根据36个主要树种树高-胸径方程拟合公式及参数估计值a、b进行方程精度验证,方程预测的平均相对误差为16.86%,在误差允许范围内,并且模型形式规范,可为GlobalAllomeTree平台用户提供科学参考。

Fine-resolution forest tree height estimation across the Sierra Nevada through the integration of spaceborne LiDAR, airborne LiDAR, and optical imagery

Forests of the Sierra Nevada(SN)mountain range are valuable natural heritages for the region and the country,and tree height is an important forest structure parameter for understanding the SN forest ecosystem.There is still a need in the accurate estimation of wall-to-wall SN tree height distribution at fine spatial resolution.In this study,we presented a method to map wall-to-wall forest tree height(defined as Lorey’s height)across the SN at 70-m resolution by fusing multi-source datasets,including over 1600 in situ tree height measurements and over 1600 km^(2) airborne light detection and ranging(LiDAR)data.Accurate tree height estimates within these airborne LiDAR boundaries were first computed based on in situ measurements,and then these airborne LiDAR-derived tree heights were used as reference data to estimate tree heights at Geoscience Laser Altimeter System(GLAS)footprints.Finally,the random forest algorithm was used to model the SN tree height from these GLAS tree heights,optical imagery,topographic data,and climate data.The results show that our fine-resolution SN tree height product has a good correspondence with field measurements.The coefficient of determination between them is 0.60,and the root-mean-squared error is 5.45 m.

Effects of climate factors on the height increment of poplar protec-tion forest in the riverbank field

Based on the data of stand investigation and stem analysis, the effects of climate factors on the poplar protection forest increment in the riverbank field of the Dalinghe and Xiaolinghe rivers of Liaoning Province, China were studied by step-wise regression procedure and grey system theories and methods. A regression model reflecting the correlation between the height increment of poplar protection forest and climatic factors was developed. The order of grey relevance for the effect of climatic factors on the height increment of poplar protection forest is: light>water>heat, and it could be interpreted that the poplar increment was mainly influenced by light factor, water factor, and heat factor. This result will provide scientific basis for the in-tensive cultivation and regeneration of the poplar protection forest in riverbank field in similar regions in China.

Analysis on the Growth Condition of Cunninghamia lanceolata Plantation in Lingnan Forest Farm

[Objectives]This study was conducted to provide good basic research data for Cunninghamia lanceolata plantations in southern Anhui,so as to improve local ecological,economic and social benefits.[Methods]A 22-year-old near-mature C.lanceolata plantation in Lingnan Forest Farm,Xiuning County,Huangshan City,Anhui Province was investigated and analyzed by sample plot survey.[Results]The average DBH value of the C.lanceolata plantation at the lower slope was the largest,24.7%and 19.2%higher than those at the upper and middle slopes,respectively.The average single plant wood volume at the lower slope was 47.6%and 49.1%higher than those in the upper and middle slopes,respectively.However,the average tree heights at various slope positions showed little difference.Meanwhile,all the indexes showed the phenomenon of semi-shady slope>sunny slope>shady slope under different slope directions.Among them,the effect of slope position on DBH was extremely significant,but the effect of slope direction on DBH was not significant,and slope position,slope direction and the interaction of slope direction and slope position had no significant effects on the tree height of the C.lanceolata plantation.In addition,slope direction and slope position had extremely significant effects on single plant wood volume.From the overall growth situation of the C.lanceolata plantation in Lingnan Forest Farm,the slope position factor had greater effects on various indexes of forest growth than the slope direction factor,mainly manifested in that the lower slope was better than the middle slope,and the middle slope position was better than the upper slope,while although slope direction had some effect on the growth of the C.lanceolata plantation,the influence degree was not as significant as that of slope position.[Conclusions]This study provides some reference for the adjustment and optimization,development and renewal of C.lanceolata plantation structure in the later period in this area,as well as some data support for other theoretical research on economic forests.

基于无人机低空遥感数据的时序动态生物量计算研究

为解决林分自然生长和人工剪伐修枝引起的单木特征参数变化所造成的生物量变化问题,采用地基激光雷达数据(TLS)和无人机激光雷达数据(UAV-LS)为数据源,通过单木分割的方法,以地基激光雷达数据提供的高精度数字高程模型为基础,提升无人机激光雷达数据的单木召回率;基于无人机激光雷达数据进行单木树高的提取及一致性评定,通过优化的生物量模型,利用树高参数计算2022年和2023年各树种单木生物量。结果表明,联合地面激光雷达数据可以将无人机激光雷达数据的单木召回率从60.0%提升至73.1%;对2022年、2023年树高参数提取得到近两年树木自然生长、修剪状况;对树高一致性评定得到一致性相关系数(Concordance correlation coefficient,CCC)为0.98,均方根误差(RMSE)为1.12 m;对生物量计算得到近两年各树种单木生物量、林分生物量,2022年、2023年单位面积生物量分别为77.39、81.56 t/hm^(2)。研究证实在研究区通过无人机低空遥感数据获取树高时序动态计算各树种单木生物量可行,可以掌握林分自然生长和人工修剪引起的生物量变化。

基于混合效应和分位数回归的温带针阔混交林树高与胸径关系研究

【目的】基于非线性回归和广义模型构建不同分位数回归和混合效应的树高预测方程,并对比分析非线性模型、不同分位点(τ=0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9)模型、广义模型及非线性混合效应模型的拟合效果和预测精度,为研究林分生长和收获提供理论依据。【方法】本研究以吉林蛟河地区针阔混交林的主要树种(红松、色木槭、紫椴和水曲柳)为研究对象,基于21.12 hm2样地数据,首先在11个广泛使用的树高方程基础模型中选定基础模型;其次探究林分变量对树高的影响并构建含林分变量的广义模型;最后在基础模型和广义模型的基础上,构建分位数模型,同时考虑样方效应对树高的影响,构建混合效应模型。【结果】(1)各树种均以Richards模型拟合精度更高,且具有生物学意义,选定为基础模型;考虑林分变量与树高的相关性以及模型收敛性,加入优势木高建立的广义模型能显著提高拟合效果。(2)各树种均为中位数τ=0.5时模型拟合效果最佳,且与非线性回归预测精度相近,红松、色木槭、紫椴和水曲柳最高R^(2)值分别为0.811、0.809、0.724和0.617,广义中位数回归预测能力得到进一步提高,R^(2)值分别为0.891、0.874、0.858和0.627。(3)混合效应模型相对其他模型能显著提高预测精度,其中基础混合模型略优于广义混合模型,4个树种R^(2)值达到0.937、0.919、0.906和0.643,表明包含样方效应的混合模型能得到更准确更稳定的预测结果。【结论】与传统方法建立的基础模型和广义模型以及两者的中位数回归模型相较,基于非线性混合效应构建的树高-胸径模型预测精度更高,其中基于基础混合效应构建的吉林蛟河地区混交林树高-胸径模型更具优越性和稳定性。

南疆阿拉尔垦区密植棉花株高模拟研究

【目的】探讨新疆阿拉尔垦区密植条件下不同模型对棉花株高的预测效果。【方法】以株型差异较大的新陆中81号和塔河2号为试验材料,在阿拉尔垦区16000株·hm^(-2)密植条件下开展大田试验,用Python语言建立株高生长的逻辑斯谛(logistic)、冈珀茨(Gompertz)、理查德(Richards)方程和决策树机器学习预测模型,并对模型的预测精度进行分析。【结果】Logistic、Gompertz和Richards模型中,新陆中81号株高的均方根误差(root mean square error,RMSE)分别为8.38%、7.49%和7.52%,平均绝对误差(mean absolute error,MAE)分别为6.80%、5.79%和5.82%;塔河2号株高的RMSE分别为6.09%、4.77%和4.85%,MAE分别为4.52%、3.34%和3.36%。决策树机器学习方法中,新陆中81号与塔河2号株高的RMSE分别为6.91%和3.27%,MAE分别为5.04%和2.16%。Logistic、Gompertz和Richards生长方程以及决策树机器学习方法均能较好地预测密植条件下棉花株高的生长,但在预测精度上决策树机器学习方法总体上优于生长方程。【结论】基于决策树的机器学习方法不需要用数理统计知识解释模型,训练模型需要的数据量也较少,模拟精度更高,在模拟棉花株高方面有一定优势,是对传统生长方程的有益补充。

红松半同胞家系生长性状变异及优良家系和单株的筛选

在辽宁省本溪满族自治县清河城实验林场国家红松良种基地,以2007年营建的15年生红松半同胞子代测定林为研究对象,选择参试家系171个(其中包括当地生产苗作为对照),造林株行距2 m×3 m,设计为10株小区,9次重复;2022年11月份,测定试验林所有存活木的树高、胸径,以树高、胸径、单株材积等生长性状为评价指标,计算各指标的变异系数、家系遗传力、遗传增益、现实增益;采用多目标决策法、隶属函数法筛选优良家系和优良单株。结果表明:参试家系各测定指标差异均达极显著水平(P<0.01),各指标变异系数变化范围为9.69%~35.01%、家系各指标遗传力变化范围为0.64~0.78、家系单株遗传力变化范围为0.14~0.45,说明参试家系具有较大的性状变异和较高的遗传力。利用隶属函数法筛选出优良家系17个,入选家系的胸径均值5.69 cm、树高均值12.92 m、单株材积均值0.04 m^(3),分别是当地生产苗(对照)胸径的1.14倍、树高的1.13倍、单株材积的1.44倍;17个优良家系的现实遗传增益,胸径为3.21%、树高为4.54%、单株材积为9.37%。在优良家系的基础上筛选出50株优良单株,入选单株胸径平均值为6.6 cm、树高平均值为15.1 m、单株材积平均值为0.0573 m^(3)。

基于机载激光雷达点云数据和Catboost算法的杉木单木蓄积量估测研究

选取福建顺昌县洋口国有林场6块杉木标准地内200株杉木的激光雷达点云数据和地面调查数据,基于机载激光雷达点云数据生成的冠层高度模型,运用局域极大值算法检测树冠顶点,提取树高;采用标记极值的分水岭算法估测冠幅面积,将估测的树高和冠幅面积结合单木蓄积量真值,构建基于Catboost算法的单木蓄积量估测模型。结果表明:使用局域极大值算法估测树高,R^(2)为0.91,RMSE为0.81 m;采用标记极值的分水岭算法估测冠幅面积,R^(2)为0.81,RMSE为1.18 m^(2);采用Catboost算法构建单木蓄积量估测模型R^(2)为0.934。因此,机载激光雷达点云数据可以有效估测树高和树冠面积,采用Catboost算法能够实现杉木单木蓄积量的估测,为高精度反演森林蓄积量提供新的思路。

基于地基雷达数据构建红松人工林树高、枝下高及接触高模型

采用地面激光雷达(Terrestrial Laser Scanning,TLS)扫描10块人工红松林所得到的数据,与实地调查数据相结合,构建红松树高曲线模型、枝下高预估模型与接触高预估模型,并建立联立方程组。首先,从所选择的5种树高曲线模型中,选择出拟合效果较好的2个模型作为联立方程组的备选模型。然后再从5个枝下高基础模型中选出1个拟合效果好,并且适用程度高的模型作为基础模型,运用再参数化和最优子集回归的方法将林分因子(林分平均胸径、林分断面积、高径比、优势木平均胸径和优势木平均高)代入基础模型,选择拟合效果较好的模型作为枝下高备选模型。相同的方法选择拟合效果好的接触高备选模型。最后将树高曲线模型、枝下高备选模型与接触高备选模型分别两两联立,建立联立方程组。通过似不相关回归(Seemingly Unrelated Regression Estimation,SVR或SURE),根据拟合优度与检验结果选择最优秀的方程组,并对联立方程组进行评价。最终得到结果最优联立方程组预估树高时,决定系数R^(2)=0.896,均方根误差RMSE=0.612 m;当方程组预估枝下高时,R^(2)=0.575,RMSE=0.850 m;当方程预估接触高时,R^(2)=0.719,RMSE=0.791 m,而且各种检验指标都较好。综合来看,方程组对树高、枝下高与接触高拟合精度与检验效果较好,可以解决树高、枝下高与接触高的内在相关性问题,为进一步研究红松树冠结构与动态变化提供基础。

含竞争指标的广义可加混合效应树高-胸径模型

广义可加混合效应模型(GAMM)兼具参数模型与非参数模型的优点,同时适于处理多层次分组数据。通过运用广义可加混合效应模型模拟胸径及树高之间关系,加入竞争因子作为辅助变量,并与传统非线性混合效应模型进行比较,能够为建立树高曲线及提高模型精度提供新方法。根据吉林省汪清林业局金沟岭林场2块100 m×100 m次生混交林样地中的实测单木数据,按照7∶3比例随机划分建模与验证数据。随机效应设定为林木分级,辅助变量选择大于对象木胸高断面积之和(B_(AL))或简单竞争指数(Hegyi指数,H_(EG)),根据随机效应的设定位置共构建15个广义可加混合效应模型,对照模型以Logistic及Richard方程为基础模型,共构建6个非线性混合效应树高-胸径模型。结果表明:所有广义可加混合效应模型均能较好地描述自变量与树高之间的关系,决定系数(R^(2))为0.8897~0.8998,相对均方根误差(R_(RMSE))为17.87%~18.74%,平均绝对误差(M_(AE))为1.7881~1.8745 m,赤池信息量(A_(IC))为4120.42~4162.23,均优于相同自变量下的非线性混合模型,R^(2)平均提高0.005,相对均方根误差、平均绝对误差、赤池信息量分别平均降低0.46%、0.0587 m、41.49。对于验证数据的预测可以看出,模型5具有最小的预测相对均方根误差,为20.28%,同时具有最小的预测平均绝对误差,为2.1038 m。但部分广义可加混合效应模型的预测表现略差于非线性混合模型。综合考虑参数与非参数估计显著性、模型估计精度及预测能力,所有模型中的最优模型为模型5,即以B_(AL)为辅助变量,考虑唯一全局平滑函数并以具有相同扭曲程度的分组水平平滑函数为基础添加随机效应。竞争因子选择B AL作为辅助变量能够提升树高模型的精度,而选择Hegyi指数为辅助变量的促进效果不明显。研究建立的广义可加混合效应树高胸径模型相较于传统非线性混合效应模型具有更高的估计精度及预测效果,B AL适宜作为树高模型的辅助变量来反映林木竞争状况的影响。