相容性单木生物量模型估计方法的比较——以青冈栎为例

doi:10.11707/j.1001-7488.20200918

Abstract

Abstract:

Objective: Biomass model is an effective method to estimate forest biomass,and nonlinear simultaneous equations are common method to construct compatible biomass model. This article takes Cyclobalanopsis glauca as an example to compared two common biomass model construction method and three parameter estimation algorithms,so as to select the best biomass model construction method and algorithms,and provide technical support for model construction and biomass studies. Method: Based on abore-ground biomass data of 25 trees of C.glauca. In South China,the compatible biomass models of controlling directly by proportion functions and controlling by the sum of equations were selected,and ordinary least square (OLS),two-stage least square (2SLS) and three-stage least square (3SLS) were used as estimation algorithms. Establishing the compatibility model of the above-ground biomass and the biomass of each component,and comparing the fitting effect of various compatible biomass models. Result: Under three kinds of parameter estimation algorithms,these two biomass models both can guarantee the compatibility between above-ground biomass and biomass of stem,branch and leaf components.The determination coefficient of each component biomass model is above 0.8,the determination coefficient of above-ground biomass model is the highest,and the determination coefficient of the leaf biomass model is the lowest. Using the same parameter estimation algorithm,there is not much difference in the fitting effect of compatible biomass between the two structures. Comparing three parameter estimation algorithms,parameter estimation values and evaluation indexes of compatible biomass model,that indicated by two-stage least square and three-stage least-squares are consistent respectively. However,the result obtained by ordinary least square are quite different which is distinguished by a higher fitting accuracy and a simpler calculation process. Conclusion: Considering the main purpose in forestry practice is usually to calculate above-ground biomass,the controlling directly by proportion functions based on the ordinary least square can immediately calculate the above-ground biomass with high estimation accuracy,and has good application prospects.

Key words: least square, compatible biomass models, Cyclobalanopsis glauca secondary forest, controlling directly by proportion functions, controlling by the sum of equations

CLC Number:

S758.1

Xiuhong Liu,Chunqian Jiang,Rui Xu,Xiao He,Mengjuan Qi. Comparison of Methods to Construct Compatible Individual Tree Biomass Models — A Case Study of Cyclobalanopsis glauca[J]. Scientia Silvae Sinicae, 2020, 56(9): 164-173.

Figures/Tables 7

Table 2

Table 3

Table 4

Table 5

Table 6

Table 7

References 0

	曹磊, 李海奎. 广东省樟树相容性生物量模型的构建. 森林与环境学报, 2018. 38 (4): 458- 465.
	Cao L , Li H K . Establishment and analysis of compatible biomass model for Cinnamomum camphora in Guangdong Province. Journal of Forest and Environment, 2018. 38 (4): 458- 465.
	陈振雄, 贺东北, 肖前辉, 等. 西藏冷杉立木生物量和材积模型研建. 中南林业科技大学学报, 2018. 38 (1): 16- 21.
	Chen Z X , He D B , Xiao Q H , et al. Establishment of biomass and tree volume equations for Abies in Tibet. Journal of Central South University of Forestry Science & Technology, 2018. 38 (1): 16- 21.
	董利虎, 李凤日. 三种林分生物量估算方法的比较. 应用生态学报, 2016. 27 (12): 3862- 3870.
	Dong L H , Li F R . Comparison of three stand-level biomass estimation methods. Journal of Applied Ecology, 2016. 27 (12): 3862- 3870.
	董利虎, 李凤日, 宋玉文. 东北林区4个天然针叶树种单木生物量模型误差结构及可加性模型. 应用生态学报, 2015a. 26 (3): 704- 714.
	Dong L H , Li F R , Song Y W . Error structure and additivity of individual tree biomass model for four natural conifer species in northeast China. Journal of Applied Ecology, 2015a. 26 (3): 704- 714.
	董利虎, 张连军, 李凤日. 立木生物量模型的误差结构和可加性. 林业科学, 2015b. 51 (2): 28- 36.
	Dong L H , Zhang L J , Li F R . Error structure and additivity of individual tree biomass model. Scientia Silvae Sinicae, 2015b. 51 (2): 28- 36.
	董玉峰, 匡星星, 秦乃花, 等. 造林配置对杨树人工林生长和地上生物量的影响. 东北林业大学学报, 2015. 43 (9): 30- 33.
	Dong Y F , Kuang X X , Qin N H , et al. Effects of initial planting spacing on growth and above-ground biomass of poplous plantation. Journal of Northeast Forestry University, 2015. 43 (9): 30- 33.
	杜沔, 邵欢, 万欢. 公司治理机制与公司价值内生性实证研究. 汕头大学学报:人文社会科学版, 2014. 30 (6): 62- 72, 96.
	Du M , Shao H , Wan H . Endogenous empirical study about the mechanisms of corporate governance and firm value. Shantou University Journal:Humanities & Social Sciences Bimonthly, 2014. 30 (6): 62- 72+96.
	范德成. 联立方程计量经济学模型ILS和2SLS估计等价性的证明. 哈尔滨工程大学学报, 2000. 21 (3): 90- 92.
	Fan D C . Proof that ILS estimator equals 2SLS estimator to simultaneous equations econometrics model. Journal of Harbin Engineering University, 2000. 21 (3): 90- 92.
	符利勇, 雷渊才, 孙伟, 等. 不同林分起源的相容性生物量模型构建. 生态学报, 2014. 34 (6): 1461- 1470.
	Fu L Y , Lei Y C , Sun W , et al. Development of compatible biomass models for trees from different stand origin. Acta Ecologica Sinica, 2014. 34 (6): 1461- 1470.
	符利勇, 雷渊才, 曾伟生. 几种相容性生物量模型及估计方法的比较. 林业科学, 2014. 50 (6): 42- 54.
	Fu L Y , Lei Y C , Zeng W S . Comparison of several compatible biomass models and estimation methods. Scientia Silvae Sinicae, 2014. 50 (6): 42- 54.
	韩文轩, 方精云. 幂指数异速生长机制模型综述. 植物生态学报, 2008. 32 (4): 951- 960.
	Han W X , Fang J Y . Review on the mechanism models of all ometric scaling laws:3/4 VS. 2/3 power. Journal of Plant Ecology, 2008. 32 (4): 951- 960.
	黄贤松. 2011.杉木与马尾松碳收获量模型研究.福州:福建农林大学硕士学位论文.
	Huang X S. 2011. Study on the carbon gain model in fir and pine. Fuzhou: MS thesis of Fujian Agricultural and Forestry University.[in Chinese]
	黄兴召, 王泽夫, 徐小牛. 生物量转换因子连续函数的拟合方法比较. 浙江农林大学学报, 2017. 34 (5): 775- 781.
	Huang X Z , Wang Z F , Xu X N . Comparison of fitting approaches with biomass expansion factor equations. Journal of Zhejiang A & F University, 2017. 34 (5): 775- 781.
	李海奎, 宁金魁. 基于树木起源、立地分级和龄组的单木生物量模型. 生态学报, 2012. 32 (3): 740- 757.
	Li H K , Ning J K . Individual tree biomass model by tree origin, site classes and age groups. Acta Ecologica Sinica, 2012. 32 (3): 740- 757.
	李建明, 曲成毅. 隐变量交互作用分析建模方法——两阶段最小二乘法(2SLS)及其在SAS软件上的实现. 数理医药学杂志, 2011. 24 (6): 631- 634.
	Li J M , Qu C Y . Modeling latent variable interaction effect analysis-2SLS and its realization by SAS software. Journal of Mathematical Medicine, 2011. 24 (6): 631- 634.
	李树生. 2008.基于广义线性模型的森林植物多样性估测的研究.哈尔滨:东北林业大学博士学位论文.
	Li S S. 2008. Estimating forest plant diversity based on generalized linear model. Harbin: PhD thesis of Northeast Forestry University.[in Chinese]
	刘坤, 曹林, 汪贵斌, 等. 银杏生物量分配格局及异速生长模型. 北京林业大学学报, 2017. 39 (4): 12- 20.
	Liu K , Cao L , Wang G B , et al. Biomass allocation patterns and allometric models of Ginkgo biloba. Journal of Beijing Forestry University, 2017. 39 (4): 12- 20.
	刘盛. 2007.森林生态效益模型及GIS空间分析系统开发.哈尔滨:东北林业大学博士学位论文.
	Liu S. 2007. The development of a GIS spatial analysis and model system of forest ecological benefits. Harbin: PhD thesis of Northeast Forestry University.[in Chinese]
	刘薇祎, 邓华锋, 黄国胜, 等. 云南松不同区域相容性生物量模型的构建. 西北农林科技大学学报:自然科学版, 2018. 46 (7): 13- 20.
	Liu W Y , Deng H F , Huang G S , et al. Establishment of compatible biomass models for Pinus yunnanensis in different regions. Journal of Northwest University of Agriculture and Forestry Science and Technology:Natural Science Edition, 2018. 46 (7): 13- 20.
	骆期邦, 曾伟生, 贺东北, 等. 立木地上部分生物量模型的建立及其应用研究. 自然资源学报, 1999. 14 (3): 271- 277.
	Luo Q B , Zeng W S , He D B , et al. Establishment and application of compatible tree above ground biomass models. Journal of Natural Resources, 1999. 14 (3): 271- 277.
	马克西, 曾伟生, 李智华. 新疆云杉一体化立木生物量模型系统研建. 林业科学研究, 2018. 31 (6): 105- 113.
	Ma K X , Zeng W S , Li Z H . Integrated individual tree biomass systems for Picea spp. in Xinjiang. Forest Research, 2018. 31 (6): 105- 113.
	彭娓, 董利虎, 李凤日. 基于可加性生物量模型的大兴安岭东部主要林型森林植被碳储量及其分配. 应用生态学报, 2016. 27 (12): 3749- 3758.
	Peng W , Dong L H , Li F R . Carbon storage of forest vegetation and allocation for main forest types in the east of Daxing'an mountains based on additive biomass model. Journal of Applied Ecology, 2016. 27 (12): 3749- 3758.
	彭娓, 李凤日, 董利虎. 黑龙江省长白落叶松人工林单木生长模型. 南京林业大学学报:自然科学版, 2018. 42 (3): 019- 27.
	Peng W , Li F R , Dong L H . Individual tree diameter growth model for Larix olgensis plantation in Heilongjiang Province, China. Journal of Nanjing Forestry University:Natural Science Edition, 2018. 42 (3): 19- 27.
	彭小勇. 2007.闽北杉木人工林地上部分生物量模型的研究.福州:福建农林大学硕士学位论文.
	Peng X Y. 2007. Study on the biomass bodel of Cunninghamia lanceolata plantations in northern Fujian. Fuzhou: MS thesis of Fujian Agricultural and Forestry University.[in Chinese]
	苏瑞兰. 异速生长模型估算不同林龄杉木人工林生物量. 福建林业科技, 2017. 44 (2): 105- 108.
	Su R L . Allometric equations to estimate biomass of different age-sequence of chinese fir (Cunninghamia lanceolata) plantations. Fujian Forestry Science and Technology, 2017. 44 (2): 105- 108.
	唐守正, 张会儒, 胥辉. 相容性生物量模型的建立及其估计方法的研究. 林业科学, 2000. 36 (zk): 19- 27.
	Tang S Z , Zhang H R , Xu H . Study on establish and estimate of compatible biomass model. Scientia Silvae Sinicae, 2000. (zk): 19- 27.
	王维枫, 雷渊才, 王雪峰, 等. 森林生物量模型综述. 西北林学院学报, 2008. 23 (2): 58- 63.
	Wang W F , Lei Y C , Wang X F , et al. A review of forest biomass models. Journal of Northwest Forestry College, 2008. 23 (2): 58- 63.
	邢海涛, 陆元昌, 刘宪钊, 等. 海南岛东北部木麻黄立木生物量建模. 南京林业大学学报:自然科学版, 2017. 41 (2): 103- 110.
	Xing H T , Lu Y C , Liu X Z , et al. Modeling above-ground and below-ground biomass of Casuarina equisetifolia in the northeast of Hainan Province. Journal of Nanjing Forestry University:Natural Science Edition, 2017. 41 (2): 103- 110.
	杨宪龙, 魏孝荣, 邵明安. 黄土高原北部典型灌丛枝条生物量估算模型. 应用生态学报, 2016. 27 (10): 3164- 3172.
	Yang X L , Wei X R , Shao M A . Stem biomass estimation models for dominant shrubs on the northern Loess Plateau of China. Journal of Applied Ecology, 2016. 27 (10): 3164- 3172.
	曾伟生. 2011.全国立木生物量方程建模方法研究.北京:中国林业科学研究院博士学位论文.
	Zeng W S. 2011. Methodology on modeling of single-tree biomass equations for national biomass estimation in China. Beijing: PhD thesis of Chinese Academy of Forestry Sciences.[in Chinese]
	曾伟生. 利用误差变量联立方程组建立南方杉木一元立木材积模型和胸径地径回归模型. 中南林业调查规划, 2012. 31 (4): 1- 4.
	Zeng W S . Using error-in-variable simultaneous equations approach to construct one-way tree volume models and diameter at breast height-diameter on root collar regression model for chinese fir (Cunninghamia lanceolata) in southern China. Central South Forestry Survey Planning, 2012. 31 (4): 1- 4.
	曾伟生, 骆期邦, 贺东北. 论加权回归与建模. 林业科学, 1999. 35 (5): 5- 11.
	Zeng W S , Luo Q B , He D B . Research on weighting regression and modelling. Scientia Silvae Sinicae, 1999. 35 (5): 5- 11.
	曾伟生, 唐守正. 东北落叶松和南方马尾松地下生物量模型研建. 北京林业大学学报, 2011a. 8 (2): 1- 6.
	Zeng W S , Tang S Z . Establishment of below-ground biomass equations for larch in northeastern and Masson pine in southern China. Journal of Beijing Forestry University, 2011a. 8 (2): 1- 6.
	曾伟生, 唐守正. 非线性模型对数回归的偏差校正及与加权回归的对比分析. 林业科学研究, 2011b. 24 (2): 137- 143.
	Zeng W S , Tang S Z . Bias correction in logarithmic regression and comparison with weighted regression for non-linear models. Forest Research, 2011b. 24 (2): 137- 143.
	曾伟生, 唐守正. 立木生物量方程的优度评价和精度分析. 林业科学, 2011c. 47 (11): 106- 113.
	Zeng W S , Tang S Z . Goodness evaluation and precision analysis of tree biomass equations. Scientia Silvae Sinicae, 2011c. 47 (11): 106- 113.
	曾伟生, 肖前辉, 胡觉, 等. 中国南方马尾松立木生物量模型研建. 中南林业科技大学学报, 2010. 30 (5): 50- 56.
	Zeng W S , Xiao Q H , Hu J , et al. Establishment of single-tree biomass equations for Pinus massoniana in southern China. Journal of Central South University of Forestry Science and Technology, 2010. 30 (5): 50- 56.
	张宇, 岳祥华, 漆良华, 等. 利用异速生长关系和地统计方法估算武夷山南麓毛竹林生物量. 生态学杂志, 2016. 35 (7): 1957- 1962.
	Zhang Y , Yue X H , Qi L H , et al. Estimation of Phyllostachys edulis forest biomass in southern Wuyishan mountain using allometric equation and geostatistical technique. Journal of Ecology, 2016. 35 (7): 1957- 1962.
	张仲礼,林甫生,朱根. 2008.探索·创新当代经济新学科新方法新流派(第三卷).上海:上海社会科学院出版社.
	Zhang Z L, Lin F S, Zhu G. 2008. Exploration and Innovation of New Approaches and Schools of Contemporary Economic New Disciplines. Shanghai: Shanghai Academy of Social Sciences Press.[in Chinese]
	赵娜, 洪广彬. 多项分布内生回归元计数模型的两阶段估计方法研究. 统计与信息论坛, 2018. 33 (8): 19- 30.
	Zhao N , Hong G B . Research on two-stage estimation method for endogenous regression model of multiple distribution. Statistics & Information Forum, 2018. 33 (8): 19- 30.
	郑冬梅, 夏朝宗, 王海宾, 等. 基于SPOT-7影像的马尾松生物量估测模型研究. 中南林业科技大学学报, 2018. 38 (9): 82- 88.
	Zheng D M , Xia C Z , Wang H B , et al. Study on biomass estimation model of masson pine based on SPOT-7 image. Journal of Central South University of Forestry & Technology, 2018. 38 (9): 82- 88.
	周海川. 空气质量与公共健康:以森林吸收烟粉尘为例. 林业科学, 2017. 53 (8): 120- 131.
	Zhou H C . Air pollution and public health:evidence from forests absorb smoke and dust emission in China. Scientia Silvae Sinicae, 2017. 53 (8): 120- 131.
	Berk K N . Validating regression procedures with new data. Technometrics, 1984. 26 (4): 331- 338. doi: 10.1080/00401706.1984.10487985
	Bi H , Turner J , Lambert M J . Additive biomass equations for native eucalypt forest trees of temperate Australia. Trees Structure and Function, 2004. 18 (4): 467- 479.
	Bi H Q , Long Y S , Turner J , et al. Additive prediction of aboveground biomass for Pinus radiata (D. Don) plantations. Forest Ecology & Management, 2010. 259 (12): 2301- 2314.
	Castedodorado F , Gómezgarcía E , Diéguezaranda U , et al. Aboveground stand-level biomass estimation:a comparison of two methods for major forest species in northwest Spain. Annals of Forest Science, 2012. 69 (6): 735- 746. doi: 10.1007/s13595-012-0191-6
	Dong L H , Zhang L J , Li F R . A three-step proportional weighting system of nonlinear biomass equations. Forest Science, 2015. 61 (1): 35- 45. doi: 10.5849/forsci.13-193
	González garcía M , Hevia A , Majada J , et al. Above-ground biomass estimation at tree and stand level for short rotation plantations of Eucalyptus nitens (Deane & Maiden) Maiden in Northwest Spain. Biomass & Bioenergy, 2013. 54, 147- 157.
	Hasenauer H , Monserud R A , Gregoire T G . Using simultaneous regression techniques with individual-tree growth models. Forest Science, 1998. 44 (1): 87- 95.
	Kozak A , Kozak R . Does cross validation provide additional information in the evaluation of regression models?. Canadian Journal of Forest Research, 2003. 33 (6): 976- 987. doi: 10.1139/x03-022
	Li H K , Zhao P . Improving the accuracy of tree-level above-ground biomass equations with height classification at a large regional scale. Forest Ecology and Management, 2013. 289 (1): 153- 163.
	Merino A , Rodriguez R , Balboa M A . Temporal variations and distribution of carbon stocks in aboveground biomass of radiata pine and maritime pine pure stands under different silvicultural alternatives. Forest Ecology & Management, 2006. 237 (1/3): 29- 38.
	Paré D , Bernier P , Lafleur B , et al. Estimating stand-scale biomass, nutrient contents, and associated uncertainties for tree species of Canadian forests. Canadian Journal of Forest Research, 2013. 43 (7): 599- 608. doi: 10.1139/cjfr-2012-0454
	Parresol B R . Additivity of nonlinear biomass equations. Canadian Journal of Forest Research, 2001. 31 (5): 865- 878. doi: 10.1139/x00-202
	Patricia A , Jari H , Isabel C , et al. Individual-tree diameter growth model for Rebollo oak (Quercus pyrenaica Willd. ) coppices. Forest Ecology & Management, 2008. 255 (3/4): 1011- 1022.
	Ritchie M W , Hamann J D . Individual-tree height-, diameter-and crown-width increment equations for young Douglas-fir plantations. New Forests, 2008. 35 (2): 173- 186. doi: 10.1007/s11056-007-9070-7
	Shao J . Linear model selection by cross-validation. Publications of the American Statistical Association, 1993. 88 (422): 486- 494. doi: 10.1080/01621459.1993.10476299
	Tang S Z , Li Y , Wang Y H . Simultaneous equations, error-in-variable models, and model integration in systems ecology. Ecological Modelling, 2001. 142 (3): 285- 294. doi: 10.1016/S0304-3800(01)00326-X

项目 Item	DBH/ cm	树高 Tree height/ m	树龄 Tree age/a	冠长 Crown length/m	地上生物量 Above ground biomass/kg	树干生物量 Stem biomass/kg	树枝生物量 Branch biomass/kg	树叶生物量 Leaf biomass/kg
最小值Min.	5.5	6.6	14	1.7	7.4	5.9	0.6	0.1
最大值Max.	19.0	16.6	31	11.0	292.4	224.0	57.5	10.9
平均Mean	9.9	12.5	22	6.2	62.8	50.0	10.4	2.4
SD	3.7	2.4	5	2.8	66.2	50.5	13.9	2.7
CV(%)	37.37	19.20	22.73	45.16	105.33	101.04	133.85	112.50

组分 Component	a	b	R²	SEE	TRE	ASE	MPE	MPSE
树干Stem	1.190 4×10^-1	2.530 9	0.956 3	10.79	0.07	8.58	7.39	16.09
树枝Branch	3.563 0×10^-3	3.284 4	0.925 7	3.88	0.44	5.32	12.70	32.35
树叶Leaf	3.961 0×10^-3	2.672 2	0.842 4	1.10	0.09	1.86	15.75	34.37
地上Aboveground	1.085 0×10^-1	2.656 9	0.971 7	11.37	0.15	7.59	6.19	15.73

参数估计算法 Parameter estimation algorithm	a₀	a₁	b₀	b₁	c₀	c₁
OLS	1.131 5×10^-1	2.641 0	3.547 2×10^-2	6.898 7×10^-1	3.456 4×10^-2	1.264 8×10^-1
2SLS	8.996 3×10^-2	2.732 2	2.806 6×10^-2	7.836 0×10^-1	3.873 5×10^-2	8.487 7×10^-2
3SLS	8.996 3×10^-2	2.732 2	3.718 4×10^-2	6.728 2×10^-1	3.872 7×10^-2	8.492 7×10^-2

组分 Component	模型构建方法 Model building method	R²	SEE	TRE	ASE	MPE	MPSE
树干 Stem	比例总量直接控制 Controlling directly by proportion functions	0.955 6	11.96	0.00	8.71	8.19	16.02
树干 Stem	代数和控制 Controlling by the sum of equations	0.956 3	10.79	－0.02	8.58	7.39	16.11
树枝 Branch	比例总量直接控制 Controlling directly by proportion functions	0.924 3	4.30	－0.01	5.39	14.10	31.02
树枝 Branch	代数和控制 Controlling by the sum of equations	0.924 0	3.92	0.10	5.42	12.84	30.40
树叶 Leaf	比例总量直接控制 Controlling directly by proportion functions	0.842 2	1.21	0.00	1.86	17.34	34.23
树叶 Leaf	代数和控制 Controlling by the sum of equations	0.842 4	1.10	0.03	1.86	15.75	34.29
地上 Aboveground	比例总量直接控制 Controlling directly by proportion functions	0.971 4	11.42	0.00	7.64	6.22	15.63
地上 Aboveground	代数和控制 Controlling by the sum of equations	0.971 9	12.46	0.01	7.51	6.79	15.68

组分 Component	模型构建方法 Model building method	R²	SEE	TRE	ASE	MPE	MPSE
树干 Stem	比例总量直接控制 Controlling directly by proportion functions	0.955 7	11.95	－0.05	8.68	8.18	15.87
树干 Stem	代数和控制 Controlling by the sum of equations	0.954 9	10.96	－0.04	8.85	7.51	16.68
树枝 Branch	比例总量直接控制 Controlling directly by proportion functions	0.923 8	4.32	－1.66	5.33	14.14	34.10
树枝 Branch	代数和控制 Controlling by the sum of equations	0.922 1	3.97	0.45	5.58	13.01	29.61
树叶 Leaf	比例总量直接控制 Controlling directly by proportion functions	0.842 0	1.21	－0.91	1.84	17.35	34.46
树叶 Leaf	代数和控制 Controlling by the sum of equations	0.841 5	1.10	－0.40	1.86	15.79	35.30
地上 Aboveground	比例总量直接控制 Controlling directly by proportion functions	0.971 7	11.37	－0.35	7.55	6.20	16.07
地上 Aboveground	代数和控制 Controlling by the sum of equations	0.970 5	12.76	0.03	7.88	6.95	15.78

Comparison of Methods to Construct Compatible Individual Tree Biomass Models — A Case Study of Cyclobalanopsis glauca

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 7

References 0

Related Articles 7

Recommended Articles

Metrics

Comments

参数估计算法 Parameter estimation algorithm	a₂	b₂	a₃	b₃	a₄	b₄
OLS	1.196 4×10^-1	2.529 2	4.566 1×10^-3	3.190 5	4.009 3×10^-3	2.667 6
2SLS	1.385 0×10^-1	2.471 6	5.217 4×10^-3	3.137 8	3.303 2×10^-3	2.745 2
3SLS	1.387 2×10^-1	2.470 9	5.225 4×10^-3	3.137 2	3.304 5×10^-3	2.745 0

[1]	Xie Wen, Zhao Xiaomin, Guo Xi, Ye Yingcong, Sun Xiaoxiang, Kuang Lihua. Spectrum Based Estimation of the Content of Soil Organic Matters in Mountain Red Soil Using RBF Combination Model [J]. Scientia Silvae Sinicae, 2018, 54(6): 16-23.
[2]	Cao Zhengbin, Zhou Shiyu, Liu Xiaoping, Gao Chuang, Du Guangyue, Zhou Yucheng. Modeling of Natural Convection Temperature Field Produced by Wood Floor with Geothermal System Based on LS-SVM [J]. Scientia Silvae Sinicae, 2018, 54(11): 29-36.
[3]	Ren Hong, Shen Wenwen, Bai Jieyun, Guan Jun. Mathematical Models and Analysis of Particle Size of Coniferous Wood Flour Based on the Least Squares Method [J]. Scientia Silvae Sinicae, 2015, 51(4): 164-170.
[4]	Xu Xiaojun;Zhou Guomo;Du Huaqiang;Dong Dejin;Cui Ruirui;Zhou Yufeng;Shen Zhenming. Estimation of Aboveground Biomass of Phyllostachys praecox Forest Based on Landsat Thematic Mapper Image [J]. Scientia Silvae Sinicae, 2011, 47(9): 1-6.
[5]	Ju Cunyong;Di Xueying;Cai Tijiu. Comparing Impact of Two Selecting Variables Methods on Canopy Closure Estimation. [J]. Scientia Silvae Sinicae, 2007, 43(12): 33-38.
[6]	Li Yongci;Tang Shouzheng. A Study on Impact of Measurement Error on Whole Stand Model [J]. Scientia Silvae Sinicae, 2005, 41(6): 166-169.
[7]	Li Rongwei. STUDIES ON TIME-DEPENDENT MARKOV MODEL OF DIAMETER GROWTH [J]. , 1994, 30(4): 338-345.