塞罕坝华北落叶松人工林树冠外部轮廓模型

doi:10.11707/j.1001-7488.20210510

Abstract

Abstract:

Objective: The crown of a tree is an important organ for material exchange and energy conversion. The nonlinear mixed effect model and the nonlinear quantile regression model of the maximum crown outline were constructed to provide a scientific basis for accurately predicting the growth and development law of the crown and its productivity. Method: Taking Larix principis-rupprechtii plantation of Saihanba forest farm in Hebei Province as the research object, based on 1 789 branches data of 58 trees, the power equation, modified Kozak and modified Weibull equation were selected as the basic models to construct a mixed effect model and a nonlinear quantile regression model for predicting the crown shape of L. principis-rupprechtii plantation. Result: Among the power function, modified Kozak equation and modified Weibull equation, the power function equation had the best fitting effect of tree crown profile. The power function equation was chosen as the basic model of tree crown profile. Stand age (Age), diameter at breast height(DBH), height of the tree (HT), crown height ratio (CHR), and height to diameter ratio (HDR) had significant effects on fitting crown contour. In the mixed effect model, the two-level mixed effect model considering both plot and tree effects was superior to the single-level mixed effect model. The random effect of the plot was added to the HDR parameter, and the random effect of the sample was added to the RDINC(relative depth into crown) and CHR parameters. The model determination coefficient (R²) was 0.873, the root mean square error (RMSE) was 0.319 m, and the mean relative error (MRE) was 6.642 m. In the quantile regression model, when q=0.90, the model curve model was the closest to the crown maximum profile, R² was 0.672. Conclusion: The mixed-effect model might be a better fitting accuracy and could accurately describe the average trend of the largest branches of the canopy. The quantile regression model could determine the outermost contour of the canopy and may play an important role in research beyond the prediction of conditioned mean.

Key words: Saihanba, Larix principis-rupprechtii, nonlinear mixed effect model, nonlinear quantile regression model, crown profile

CLC Number:

S757

Tingting Zhao,Dongzhi Wang,Dongyan Zhang,Li Guo,Xuanrui Huang. Crown Prediction Model of Larix principis-rupprechtii Plantation in Saihanba of Hebei Province, Northern China[J]. Scientia Silvae Sinicae, 2021, 57(5): 108-118.

Figures/Tables 12

Table 1

Table 2

Table 3

Table 4

Table 5

Table 6

Table 7

Table 8

Table 9

Fig.1

Fig.2

Fig.3

References 0

	符利勇, 李永慈, 李春明, 等. 两水平非线性混合模型对杉木林优势高生长量研究. 林业科学研究, 2011, 24 (6): 48- 54.
	Fu L Y , Li Y C , Li C M , et al. Study of the dominant height for Chinese fir plantation using two-level nonlinear mixed effects model. Forest Research, 2011, 24 (6): 48- 54.
	符利勇, 李永慈, 李春明, 等. 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. 林业科学, 2012, 48 (5): 39- 46.
	Fu L Y , Li Y C , Li C M , et al. Analysis of the basal area for Chinese fir plantation using two kinds of nonlinear mixed effects model(two levels). Scientia Silvae Sinicae, 2012, 48 (5): 39- 46.
	符利勇, 唐守正, 张会儒, 等. 基于多水平非线性混合效应蒙古栎林单木断面积模型. 林业科学研究, 2015, 28 (1): 27- 35.
	Fu L Y , Tang S Z , Zhang H R , et al. Multilevel nonlinear mixed-effects basal area models for individual trees of Quercus mongolica. Forest Research, 2015, 28 (1): 27- 35.
	高慧淋. 2017. 东北林区针叶树树冠外部轮廓及特征因子模拟. 哈尔滨: 东北林业大学博士学位论文.
	Gao H L. 2017. Modelling crown profile and characteristic attributes of coniferous tree species in northeast China. Harbin: PhD thesis of Northeast Forestry University. [in Chinese]
	高慧淋, 董利虎, 李凤日. 基于混合效应的人工落叶松树冠外部轮廓模型. 林业科学, 2017, 53 (3): 84- 93.
	Gao H L , Dong L H , Li F R . Crown shape model for Larix olgensis plantation based on mixed effect. Scientia Silvae Sinicae, 2017, 53 (3): 84- 93.
	高慧淋, 董利虎, 李凤日. 黑龙江省红松和长白落叶松人工林树冠外部轮廓模拟. 南京林业大学学报: 自然科学版, 2018, 42 (3): 10- 18.
	Gao H L , Dong L H , Li F R . Modelling outer crown profile for planted Pinus koraiensis and Larix olgensis trees in Heilongjiang Province, China. Journal of Nanjing Forestry University: Natural Sciences Edition, 2018, 42 (3): 10- 18.
	高慧淋, 董利虎, 李凤日. 基于修正Kozak方程的人工樟子松树冠轮廓预估模型. 林业科学, 2019, 55 (8): 84- 94.
	Gao H L , Dong L H , Li F R . Crown profile prediction model for Pinus sylvestris var. mongolica plantation based on modified Kozak model. Scientia Silvae Sinicae, 2019, 55 (8): 84- 94.
	郭孝玉. 2013. 长白落叶松人工林树冠结构及生长模型研究. 北京: 北京林业大学博士学位论文.
	Guo X Y. 2013. Crown structure and growth model of Larix olgensis plantation. Beijing: PhD thesis of Beijing Forestry University. [in Chinese]
	郭艳荣, 吴保国, 郑小贤, 等. 杉木不同龄组树冠形态模拟模型研究. 北京林业大学学报, 2015, 37 (2): 40- 47.
	Guo Y R , Wu B G , Zheng X X , et al. Simulation model of crown profile for Chinese fir(Cunninghamia lanceolata)in different age groups. Journal of Beijing Forestry University, 2015, 37 (2): 40- 47.
	贾炜玮, 朱飞燕, 李凤日. 长白落叶松人工林心材变化规律. 应用生态学报, 2018, 29 (7): 2277- 2285.
	Jia W W , Zhu F Y , Li F R , et al. Change pattern of heartwood of Larix olgensis plantation. Chinese Journal of Applied Ecology, 2018, 29 (7): 2277- 2285.
	李春明. 混合效应模型在森林生长模型中的应用. 林业科学, 2009, 45 (4): 131- 138. doi: 10.3321/j.issn:1001-7488.2009.04.022
	Li C M . Application of mixed effects models in forest growth model. Scientia Silvae Sinicae, 2009, 45 (4): 131- 138. doi: 10.3321/j.issn:1001-7488.2009.04.022
	李春明, 张会儒. 利用非线性混合模型模拟杉木林优势木平均高. 林业科学, 2010, 46 (3): 91- 97.
	Li C M , Zhang H R . Modeling dominant height for Chinese fir plantation using a nonlinear mixed-effects modeling approach. Scientia Silvae Sinicae, 2010, 46 (3): 91- 97.
	李凤日. 长白落叶松人工林树冠形状的模拟. 林业科学, 2004, 40 (5): 16- 24. doi: 10.3321/j.issn:1001-7488.2004.05.003
	Li F R . Modeling crown profile of Larix olgensis trees. Scientia Silvae Sinicae, 2004, 40 (5): 16- 24. doi: 10.3321/j.issn:1001-7488.2004.05.003
	刘兆刚, 郭承亮, 袁志强. 落叶松人工林树冠形状的预估. 东北林业大学学报, 1996, 24 (6): 15- 21.
	Liu Z G , Guo C L , Yuan Z Q . Estimation of crown form for Larix olgensis plantation. Journal of Northeast Forestry University, 1996, 24 (6): 15- 21.
	吴丹子, 王成德, 李倞, 等. 福建杉木树冠外轮廓和树冠体积相容性模型. 浙江农林大学学报, 2020, 37 (1): 114- 121.
	Wu D Z , Wang C D , Li J , et al. Crown profile and volume compatibility model of Cunninghamia lanceolata in Fujian Province. Journal of Zhejiang A&F University, 2020, 37 (1): 114- 121.
	吴明钦. 2014. 福建杉木人工林树冠结构研究. 北京: 北京林业大学博士学位论文.
	Wu M Q. 2014. A study crown structure of Cunninghamia lanceolata plantation in Fujian. Beijing: PhD thesis of Beijing Forestry University. [in Chinese]
	Baldwin Jr V C , Peterson K D . Predicting the crown shape of loblolly pine trees. Canadian Journal of Forest Research, 1997, 27 (1): 102- 107. doi: 10.1139/x96-100
	Bohora S B , Cao Q V . Prediction of tree diameter growth using quantile regression and mixed-effects models. Forest Ecology and Management, 2014, 319, 62- 66. doi: 10.1016/j.foreco.2014.02.006
	Cade B S , Noon B R . A gentle introduction to quantile regression for ecologists. Frontiers in Ecology and the Environment, 2003, 1 (8): 412- 420. doi: 10.1890/1540-9295(2003)001[0412:AGITQR]2.0.CO;2
	Cadori G C , Sanquetta C R , Netto S P , et al. Analytical approaches for modeling tree crown volume in black wattle(Acacia mearnsii De Wild.)stands. African Journal of Agricultural Research, 2016, 11 (49): 4979- 4989. doi: 10.5897/AJAR2016.11747
	Crecente-Campo F , Marshall P , LeMay V , et al. A crown profile model for Pinus radiata D. Don in northwestern Spain. Forest Ecology and Management, 2009, 257 (12): 2370- 2379. doi: 10.1016/j.foreco.2009.03.038
	Crecente-Campo F , Álvarez-González J G , Castedo-Dorado F , et al. Development of crown profile models for Pinus pinaster Ait.and Pinus sylvestris L. in northwestern Spain. Forestry, 2013, 86 (4): 481- 491. doi: 10.1093/forestry/cpt019
	Dong C , Wu B , Wang C , et al. Study on crown profile models for Chinese fir(Cunninghamia lanceolata)in Fujian Province and its visualization simulation. Scandinavian Journal of Forest Research, 2016a, 31 (3): 302- 313. doi: 10.1080/02827581.2015.1081982
	Dong L , Liu Z , Bettinger P . Nonlinear mixed-effects branch diameter and length models for natural Dahurian larch(Larix gmelinii)forest in northeast China. Trees, 2016b, 30 (4): 1191- 1206. doi: 10.1007/s00468-016-1356-y
	Doruska P F , Mays J E . Crown profile modeling of loblolly pine by nonparametric regression analysis. Forest Science, 1998, 44 (3): 445- 453.
	Ducey M J , Knapp R A . A stand density index for complex mixed species forests in the northeastern United States. Forest Ecology and Management, 2010, 260, 1613- 1622. doi: 10.1016/j.foreco.2010.08.014
	Ferrarese J , Affleck D , Seielstad C . Conifer crown profile models from terrestrial laser scanning. Silva Fenn, 2015, 49, 1106. doi: 10.14214/sf.1106
	Fu L , Sharma R P , Hao K , et al. A generalized interregional nonlinear mixed-effects crown width model for Prince Rupprecht larch in northern China. Forest Ecology and Management, 2017, 389, 364- 373. doi: 10.1016/j.foreco.2016.12.034
	Gao H , Bi H , Li F . Modelling conifer crown profiles as nonlinear conditional quantiles: an example with planted Korean pine in northeast China. Forest Ecology and Management, 2017, 398, 101- 115. doi: 10.1016/j.foreco.2017.04.044
	Garber S M , Maguire D A . Vertical trends in maximum branch diameter in two mixed-species spacing trials in the central Oregon Cascades. Canadian Journal of Forest Research, 2005, 35 (2): 295- 307. doi: 10.1139/x04-164
	Hemery G E , Savill P S , Pryor S N . Applications of the crown diameter-stem diameter relationship for different species of broadleaved tree. Forest Ecology and Management, 2005, 215 (1/3): 285- 294.
	Jahnke L S , Lawrence D B . Influence of photosynthetic crown structure on potential productivity of vegetation, based primarily on mathematical models. Ecology, 1965, 46 (3): 319- 326. doi: 10.2307/1936335
	Koenker R , Bassett Jr G . Regression quantiles. Econometrica: Journal of the Econometric Society, 1978, 46 (1): 33- 50. doi: 10.2307/1913643
	Koenker R , Park B J . An interior point algorithm for nonlinear quantile regression. Journal of Econometrics, 1996, 71 (1/2): 265- 283.
	Koenker R. 2019. Quantreg: quantile regression. R package version 5. 40. https://CRAN.R-project.org/package=quantreg.
	Mehtätalo L , Gregoire T G , Burkhart H E . Comparing strategies for modeling tree diameter percentiles from remeasured plots. Environmetrics: The Official Journal of the International Environmetrics Society, 2008, 19 (5): 529- 548.
	ÖzçelikR, CaoQ V, TrincadoG, 等. Predicting tree height from tree diameter and dominant height using mixed-effects and quantile regression models for two species in Turkey. Forest Ecology and Management, 2018, 419, 240- 248.
	Parente P M D C , Silva J M C S . Quantile regression with clustered data. Journal of Econometric Methods, 2016, 5 (1): 1- 15. doi: 10.1515/jem-2014-0011
	Sadono R . Crown model for perhutani's teak plus from clonal seed garden aged 6 to 11 years in madiun forest district, East Java, Indonesia. Australian Journal of Basic and Applied Sciences, 2015, 9 (5): 151- 160.
	Sterck F J , Bongers F , Newbery D M . Tree architecture in a bornean lowland rain forest: intraspecific and interspecific patterns. Plant Ecology, 2001, 153 (1/2): 279- 292. doi: 10.1023/A:1017507723365
	Sun Y , Gao H , Li F . Using linear mixed-effects models with quantile regression to simulate the crown profile of planted Pinus sylvestris var.mongolica trees. Forests, 2017, 8 (11): 446. doi: 10.3390/f8110446
	Tanabe S I , Toda M J , Vinokurova A V . Tree shape, forest structure and diversity of drosophilid community: comparison between boreal and temperate birch forests. Ecological Research, 2001, 16 (3): 369- 385. doi: 10.1046/j.1440-1703.2001.00402.x
	Wang F, Wu D, Yamamoto H, et al. 2016. Digital image analysis of different crown shape of Platycladus orientalis. Ecological Informatics, 34: 146-152. http://dx.doi.org/10.1016/.
	Weiskittel A R , Hann D W , Kershaw Jr J A , et al. Forest growth and yield modeling. John Wiley & Sons, 2011,
	Zang H , Lei X , Zeng W . Height-diameter equations for larch plantations in northern and northeastern China: a comparison of the mixed-effects, quantile regression and generalized additive models. Forestry, 2016, 89 (4): 434- 445. doi: 10.1093/forestry/cpw022
	Zhang L , Bi H , Gove J H , et al. A comparison of alternative methods for estimating the self-thinning boundary line. Canadian Journal of Forest Research, 2005, 35 (6): 1507- 1514. doi: 10.1139/x05-070

样地号 Sample plot No.	林分年龄 Stand age/a	密度Stand density/(tree·hm^-2)	平均胸径 Mean DBH/cm	平均树高 Mean HT/m	平均冠幅 Mean CW/m	平均冠长 Mean CL/m
1	17	2 680	12.167	9.467	1.416	6.818
2	43	1 200	22.667	19.450	2.213	9.533
3	43	1 500	20.317	17.067	1.537	8.950
4	30	1 580	15.650	14.803	1.363	6.508
5	45	825	20.150	18.000	1.677	9.317
6	22	2 190	13.733	12.067	1.475	7.300
7	44	757	27.625	18.175	1.935	11.550
8	23	2 495	15.433	12.017	1.516	6.583
9	38	735	23.458	17.500	2.445	9.625
10	14	2 240	9.833	8.500	1.270	4.667

样木及枝条属性 Sample trees and branch attributes	建模样本Fitting data				检验样本Validation data
样木及枝条属性 Sample trees and branch attributes	最小值 Min.	最大值 Max.	平均值 Mean	标准差 Std.	最小值 Min.	最大值 Max.	平均值 Mean	标准差 Std.
树木变量Tree variables	n=44				n=14
年龄Age/a	11	46	11	46	11	46	11	46
胸径DBH/cm	7.812	32.222	7.812	32.222	7.812	32.222	7.812	32.222
树高HT/m	6.532	20.443	6.532	20.443	6.532	20.443	6.532	20.443
高径比HDR	0.654	1.187	0.654	1.187	0.654	1.187	0.654	1.187
冠幅CW/m	1.089	3.454	1.089	3.454	1.089	3.454	1.089	3.454
冠长CL/m	4.434	12.765	4.434	12.765	4.434	12.765	4.434	12.765
冠长率CLR	0.421	0.809	0.421	0.809	0.421	0.809	0.421	0.809
枝条变量Branch variables	n=1 371				n=418
枝龄Branch age/a	1	28	1	28	1	28	1	28
着枝角度BA/(°)	10	90	10	90	10	90	10	90
基径BD/mm	2.524	119.424	2.524	119.424	2.524	119.424	2.524	119.424
枝长BL/m	0.123	4.562	0.123	4.562	0.123	4.562	0.123	4.562

模型Model	函数表达式Function expression	函数形式Function form	来源Source
M1	${\rm{CR}} = {a_1}{\rm{RDIN}}{{\rm{C}}^a}2{{\rm{e}}^{{a_3}{\rm{RDINC}}}}$	幂函数Power	Sun et al., 2017
M2	${\rm{CR}} = {a_1}{\left[ {\frac{{1 - {{(1 - {\rm{RDINC}})}^{0.5}}}}{{1 - {P^{0.5}}}}} \right]^{{a_2}}}$	修正Kozak方程Modified Kozak equation	高慧淋等，2018
M3	${\rm{CR}} = {a_3}\left({\frac{{{a_2}}}{{{a_1}}}} \right){\left({\frac{{{\rm{RDINC}}}}{{{a_1}}}} \right)^{{a_2} - 1}}{{\rm{e}}^{ - {{\left({{\rm{RDINC}}/{a_1}} \right)}^{{a_2}}}}}$	修正Weibull方程Modified Weibull equation	高慧淋等，2018

函数形式Function form	参数Parameter	估计值Estimates	标准误SE	R²	RMSE	MRE
幂函数Power	a₁	8.528	1.570	0.712	0.495	15.388
	a₂	1.183	0.103
	a₃	-1.252	0.204
修正Kozak方程 Modified Kozak equation	a₁	2.172	0.030	0.690	0.890	19.450
	a₂	0.300	1.700
	a₃	0.470	0.210
修正Weibull方程 Modified Weibull equation	a₁	1.266	0.102	0.711	0.497	15.424
	a₂	1.929	0.055
	a₃	3.678	0.389

变量Variables	统计量Statistics	Age	Sd	CL	DBH	HT	CHR	CW	HDR
MCR	相关系数Correlation coefficient	0.561 8	-0.534 3	0.626 4	0.713 5	0.565 6	0.739 5	0.019 0	-0.564 7
MCR	P	< 0.000 1	0.000 2	< 0.000 1	< 0.000 1	< 0.000 1	< 0.000 1	0.902 5	< 0.000 1
MRDINC	相关系数Correlation coefficient	-0.131 1	0.060 8	-0.122 3	-0.024 9	-0.024 3	-0.057 7	-0.101 0	-0.044 0
MRDINC	P	0.428 0	0.695 0	0.429 2	0.872 6	0.875 8	0.710 0	0.514 1	0.776 9

Crown Prediction Model of Larix principis-rupprechtii Plantation in Saihanba of Hebei Province, Northern China

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 12

References 0

Related Articles 15

Recommended Articles

Metrics

Comments

模型 Model	方差结构 Structure of variance		样地效应 Plot effect	样木效应 Tree effect	AIC	BIC	logLik	LRT	P
模型 Model	ψ₁	ψ₂	样地效应 Plot effect	样木效应 Tree effect	AIC	BIC	logLik	LRT	P
15.1	无None	无None	无None	a₄，a₅	408.175 5	450.341 5	-194.087 7
15.2	无None	无None	a₅	a₅	373.277 3	412.644 6	-178.347 6	32.898 1	< 0.000 1
15.3	无None	无None	a₆	a₄，a₅	350.050 7	396.433 4	-164.025 4	27.226 6	< 0.000 1
15.4	对角矩阵 Diagonal matrix	无None	a₄，a₆	a₄，a₅	352.050 7	402.650 0	-164.025 4	< 0.000 1	0.998 5
15.5	对角矩阵 Diagonal matrix	无None	a₁，a₄，a₆	a₄，a₅	354.056 5	408.872 4	-164.028 3	0.005 8	0.939 5

方差函数Variance function	AIC	BIC	-2logLik	LRT	P
指数函数Exponential function	250.073 2	304.889 0	-112.036 6
广义幂函数Generalized power function	230.319 1	285.135 0	-102.159 6	19.754 0	< 0.000 1
幂函数Power function	227.724 9	286.757 7	-99.862 4	4.594 2	0.032 1

项目Items	a₁	a₂	a₃	a₄	a₅	a₆
估计值Estimates	0.407	-0.058	3.880	1.166	0.266	-1.805
标准误SE	0.085	0.029	0.882	0.059	0.201	0.176
样地协方差结构 Covariance structure of plot	ψ₁=0.008
样木协方差结构 Covariance structure of tree	${\psi _2} = \left\{ {\begin{array}{*{20}{l}}{0.018}&{0.012}\\{0.012}&{0.029}\end{array}} \right\}$
R²	0.873
RMSE	0.319
MRE	6.642

分位数Quantile point	a₁	a₂	a₃	a₄	a₅	a₆	R²
0.50	0.569	-0.113	2.323	1.113	0.291	-1.571	0.732
0.55	0.563	-0.110	2.480	1.111	0.281	-1.580	0.739
0.60	0.508	-0.094	2.901	1.097	0.197	-1.521	0.745
0.65	0.488	-0.085	2.811	1.077	0.305	-1.534	0.754
0.70	0.488	-0.087	2.849	1.059	0.304	-1.511	0.749
0.75	0.457	-0.078	2.725	1.027	0.280	-1.415	0.747
0.80	0.382	-0.062	2.668	0.948	0.316	-1.256	0.732
0.85	0.343	-0.049	2.252	0.872	0.416	-1.175	0.716
0.90	0.340	-0.058	2.404	0.842	0.507	-1.148	0.672
0.95	0.500	-0.094	2.601	0.883	0.135	-1.113	0.478

[1]	Ping She,Bing Cao,Yanhui Wang,Zhijia Yu,Zheng Wang,Jie Ma,Baoguang Jia. Effect of Forest Floor Treatments on Density of the First-Year Seedlings in Larix principis-rupprechtii Plantation [J]. Scientia Silvae Sinicae, 2021, 57(3): 18-28.
[2]	Wenbo Li,Zhengang Lü,Xuanrui Huang,Zhidong Zhang. Predicting Spatial Distribution of Site Index for Larix principis-rupprechtii Plantations in the Northern Hebei Province [J]. Scientia Silvae Sinicae, 2021, 57(3): 79-89.
[3]	Han Xinsheng, Wang Yanhui, Li Zhenhua, Wang Yanbing, Yu Pengtao, Xiong Wei. Daily Forest Floor Evapotranspiration of Larix principis-rupprechtii Plantation and Its Influencing Factors in the Semi-Arid Area of Liupan Mountains [J]. Scientia Silvae Sinicae, 2019, 55(9): 11-21.
[4]	Zheng Conghui, Zhang Hongjing, Wang Yuzhong, Dai Jianfeng, Dang Lei, Du Zichun, Liu Jianting, Gao Yunru. An Analysis of a Regional Trial of Larix principis-rupprechtii Families Based on BLUP and GGE Biplot [J]. Scientia Silvae Sinicae, 2019, 55(8): 73-83.
[5]	Gao Huilin, Dong Lihu, Li Fengri. Crown Profile Prediction Model for Pinus sylvestris var. mongolica Plantation Based on Modified Kozak Model [J]. Scientia Silvae Sinicae, 2019, 55(8): 84-94.
[6]	Zhengang Lü,Wenbo Li,Xuanrui Huang,Zhidong Zhang. Larix principis-rupprechtii Growth Suitability Based on Potential NPP under Climate Change Scenarios in Hebei Province [J]. Scientia Silvae Sinicae, 2019, 55(11): 37-44.
[7]	Mengmei Hu,Long Tian,Yanan Wu,Jinyu Yang,Xiaocui Lü,Xuanrui Huang. Influences of Thinning and Mixed Transformation of Larix principis-rupprechtii Plantations on the Community Structure of Soil Macro Faunal in Saihanba Area [J]. Scientia Silvae Sinicae, 2019, 55(11): 153-162.
[8]	Wang Yanbing, Wang Yanhui, Xiong Wei, Yao Yiqiang, Zhang Tong, Li Zhenhua. Variation in the Sap Flow Velocity of Larix principis-rupprechtii and Its Impact Factors in Different Slope Positions in a Semi-Arid Region of Liupan Mountains [J]. Scientia Silvae Sinicae, 2017, 53(6): 10-20.
[9]	Gao Huilin, Dong Lihu, Li Fengri. Crown Shape Model for Larix olgensis Plantation Based on Mixed Effect [J]. Scientia Silvae Sinicae, 2017, 53(3): 84-93.
[10]	Cui Shimeng, Xiang Wei. Effects of Thinning and Climate Factors on Larix olgensis Tree-Ring Width [J]. Scientia Silvae Sinicae, 2017, 53(12): 1-11.
[11]	Wang Dongzhi, Zhang Dongyan, Zhang Zhidong, Huang Xuanrui. Height-Diameter Relationship for Conifer Mixed Forest Based on Nonlinear Mixed-Effects Model [J]. Scientia Silvae Sinicae, 2016, 52(1): 30-36.
[12]	Fu Liyong;Zhang Huiru;Tang Shouzheng. Dominant Height for Chinese Fir Plantation Using Nonlinear Mixed Effects Model Based on Linearization Algorithm [J]. Scientia Silvae Sinicae, 2012, 48(7): 66-71.
[13]	Li Chunming;Zhang Huiru. Modeling Dominant Height for Chinese Fir Plantation Using a Nonlinear Mixed-Effects Modeling Approach [J]. Scientia Silvae Sinicae, 2010, 46(3): 89-95.
[14]	Li Fengri. Modeling Crown Profile of Larix olgensis Trees [J]. Scientia Silvae Sinicae, 2004, 40(5): 16-24.
[15]	Ruide Lei,Kunliang Dang,Shuoxin Zhang,Fanglin Tan. EFFECT OF A LARlX PRlNCIPlS-RUPPRECHTII FOREST PLANTATION ON SOIL IN MIDDLE ZONE OF SOUTH—FACING SLOPE OF THE QINLING MOUNTAINS [J]. Scientia Silvae Sinicae, 1997, 33(5): 463-470.