我国8个松属树种林木树冠因子与胸径树高回归建模

doi:10.13466/j.cnki.lczyyj.2025.02.015

摘要/Abstract

摘要： 树冠形态是反映林木生长活力的关键因素,其主要特征因子为冠幅和冠长。林木冠幅、冠长与胸径、树高之间存在紧密的相关关系,但相关研究成果多基于局部地区数据,基于大范围数据的研究极少。为此,利用在全国范围内采集的8个松属树种的1 354株代表性样木调查数据,采用非线性回归估计、混合模型和哑变量模型方法,探究冠幅和冠长与林木胸径、树高之间的关系。结果表明:1)林木冠幅与胸径呈正相关,与林木的高径比呈负相关,仅基于胸径的线性模型即可解释冠幅变动的80%,如果再增加树高或高径比,对提高冠幅预测的精度作用甚微;2)幼树阶段冠径比相对较高,随着胸径的增加而快速降低,在胸径10 cm以上趋于稳定;3)林木冠长与胸径、树高呈非线性相关,其R²高于0.75,冠长率与胸径呈正相关,与树高呈负相关;4)各个径阶的平均冠长率变化不大,在胸径10 cm以下随胸径的增加而降低,但在胸径超过10 cm时又缓慢回升,在同一径阶内,冠长率随树高的增加而降低。对于上述变化规律,8个松属树种间存在一定差异。所建立的林木冠幅和冠长与胸径和树高之间的回归模型,对进一步研究林木竞争和指导森林科学经营具有现实意义。

关键词: 冠幅, 冠径比, 冠长, 冠长率, 混合模型, 哑变量模型

Abstract:

Crown condition may be viewed as the determinant of the growth vigor of trees,and the two key characteristic factors are crown width and crown length.There is a close relationship between crown width(CW)or crown length(CL)and diameter at breast height(DBH)and/or height of trees,but most of the studies in this area were based on local data,and few studies were carried out based on large-scale data.Using the measurement data of 1 354 representative sample trees of eight pine species collected throughout the whole country of China,the relationships between CW or CL and DBH and/or tree height were studied by using nonlinear regression estimation,mixed model and dummy variable model methods.The results showed:1)CW was positively correlated with DBH and negatively correlated with ratio of tree height to DBH;the linear model based on DBH alone can explain 80% of the variation of CW,but adding tree height or ratio of tree height to DBH has little effect on the prediction accuracy of CW.2)The ratio of CW to DBH of young trees was relatively high,but it decreased rapidly with the increase of DBH,and began to stabilize when the DBH reached 10 cm or more.3)CL had a nonlinear correlation with DBH and height,with R² of ≥0.75;and the ratio of CL to height was positively related to DBH and negatively related to tree height.4)The average ratios of CL to height in all diameter classes had little variation,and decreased with the increase of DBH below 10 cm,but increased slowly when the DBH exceeded 10 cm;and in the same diameter class,the ratio of CL to height decreased with the increase of tree height.There are some differences among the eight pine species in the above relationships.The correlation between CW,CL,DBH and tree height is of practical significance to further study forest competition and guide scientific forest management.

Key words: crown width, ratio of crown width to stem diameter, crown length, ratio of crown length to tree height, mixed model, dummy variable model

中图分类号:

S711

邹文涛, 曾伟生, 温雪香. 我国8个松属树种林木树冠因子与胸径树高回归建模[J]. 林草资源研究, 2025,(2): 141-150.

ZOU Wentao, ZENG Weisheng, WEN Xuexiang. Modeling the relationships between tree crown and DBH and tree height for eight pine species in China[J]. Forest and Grassland Resources Research, 2025,(2): 141-150.

图/表 8

表1

图1

表2

表3

表4

混合模型随机参数和哑变量模型特定参数估计值及对各树种的评价指标

模型	模型编号	树种	随机或特定参数	树种效应	评价指标
模型	模型编号	树种	$a 1 i$ 或 $b 3 i$	$b 1 i$ 或 $c 3 i$	R²	SEE/m	TRE/%	ASE/%	MPE/%	MPSE/%
混合模型	(1)	马尾松	0.422 9	-0.016 0	0.810	1.09	0.27	-0.70	2.80	19.62
		油松	-0.117 1	-0.002 9	0.813	0.98	-0.22	0.81	4.13	19.41
		云南松	0.210 5	-0.013 5	0.803	1.18	0.25	-1.35	4.42	19.96
		思茅松	-0.249 9	0.055 0	0.910	1.03	-0.09	-1.23	3.34	14.14
		高山松	-0.355 6	-0.013 3	0.834	1.06	-0.69	-1.21	4.58	21.14
		黄山松	-0.131 0	-0.024 6	0.829	0.98	-0.38	-0.57	4.31	23.22
		樟子松	0.475 4	0.011 9	0.773	1.38	0.69	1.11	4.49	21.94
		湿地松	-0.255 2	0.003 4	0.896	0.73	-0.40	-0.76	3.03	14.39
	(3)	马尾松	0.042 2	-0.066 1	0.757	1.71	1.55	3.37	3.16	20.90
		油松	-0.220 2	0.326 4	0.844	1.32	1.18	3.43	3.57	18.82
		云南松	-0.197 7	0.260 2	0.813	1.77	0.45	1.56	4.67	18.74
		思茅松	0.149 9	-0.178 5	0.867	1.32	-0.57	-1.91	3.40	14.85
		高山松	0.329 0	-0.405 7	0.766	1.65	1.21	0.37	4.21	19.28
		黄山松	-0.003 1	-0.058 5	0.785	1.40	-5.52	-9.07	4.76	21.66
		樟子松	0.019 7	-0.015 5	0.660	2.29	-0.48	-2.01	6.09	26.08
		湿地松	-0.119 8	0.137 7	0.834	1.12	-0.29	1.62	3.36	18.12
	(1)
哑变量模型		马尾松	0.470 1	-0.018 0	0.810	1.09	0.00	-1.30	2.80	19.63
		油松	-0.130 0	-0.002 5	0.813	0.98	0.00	1.28	4.13	19.54
		云南松	0.260 3	-0.015 8	0.803	1.18	0.00	-2.01	4.42	20.08
		思茅松	-0.325 9	0.059 4	0.910	1.02	0.00	0.01	3.33	14.06
		高山松	-0.399 7	-0.012 2	0.834	1.06	0.00	0.31	4.58	21.71
		黄山松	-0.127 6	-0.025 6	0.829	0.98	0.00	-0.20	4.31	23.28
		樟子松	0.552 8	0.009 3	0.773	1.38	0.00	-0.14	4.49	21.70
		湿地松	-0.300 0	0.005 4	0.896	0.73	0.00	0.41	3.03	14.42
	(3)	湿地松	-0.300 0	0.005 4	0.896	0.73	0.00	0.41	3.03	14.42
		马尾松	0.048 1	-0.073 8	0.757	1.71	1.63	3.46	3.16	20.92
		油松	-0.262 8	0.383 7	0.844	1.32	0.98	4.12	3.57	19.24
		云南松	-0.207 7	0.272 4	0.813	1.77	0.61	2.07	4.67	18.96
		思茅松	0.184 8	-0.220 7	0.867	1.32	-0.94	-2.53	3.40	14.92
		高山松	0.356 7	-0.440 3	0.767	1.65	0.77	-0.18	4.21	19.32
		黄山松	-0.007 7	-0.057 5	0.786	1.40	-4.29	-7.91	4.75	21.63
		樟子松	0.028 8	-0.026 4	0.660	2.29	-0.62	-2.15	6.09	26.05
		湿地松	-0.140 2	0.162 6	0.834	1.12	0.19	2.48	3.36	18.50

表4

图2

图3

图4

参考文献 35

[1]	ZHANG Jian, GOU Zhonghua, ZHANG Fan, et al. A study of tree crown characteristics and their cooling effects in a subtropical city of Australia[J]. Ecological Engineering, 2020,158:106027.
[2]	CATTANEO N, SCHNEIDER R, BRAVO F, et al. Inter-specific competition of tree congeners induces changes in crown architecture in Mediterranean pine mixtures[J]. Forest Ecology and Management, 2020,476:118471.
[3]	和璐璐, 张萱, 章毓文, 等. 辽东山区不同坡向长白落叶松人工林树冠特征与林木生长的关系[J]. 植物生态学报, 2023, 47(11):1523-1539. doi: 10.17521/cjpe.2022.0390
[4]	HUMMEL S. Height,diameter and crown dimensions of Cordia alliodora associated with tree density[J]. Forest Ecology and Management, 2000, 127(1-3):31-40. doi: 10.1016/S0378-1127(99)00120-6
[5]	XU Hao, SUN Yujun, WANG Xinjie, et al. Linear mixed-effects models to describe individual tree crown width for China-fir in Fujian province,southeast China[J]. Plos One, 2015, 10(4):e0122257. doi: 10.1371/journal.pone.0122257
[6]	THORPE H C, ASTRUP R, TROWBRIDGE A, et al. Competition and tree crowns:A neighborhood analysis of three boreal tree species[J]. Forest Ecology and Management, 2010, 259(8):1583-1596.
[7]	王艳, 王迪海, 张剑南, 等. 黄土区不同密度侧柏人工林树冠二维特征的差异[J]. 西北林学院学报, 2014, 29(3):125-128.
[8]	PRETZSCH H. Canopy space filling and tree crown morphology in mixed-species stands compared with monocultures[J]. Forest Ecology and Management, 2014,327:251-264.
[9]	BUCHACHER R, LEDERMANN T. Interregional crown width models for individual trees growing in pure and mixed stands in Austria[J]. Forests, 2020, 11(1):114. doi: 10.3390/f11010114
[10]	GILL S J, BIGING G S, MURPHY E C. Modeling conifer tree crown radius and estimating canopy cover[J]. Forest Ecology and Management, 2000, 126(3):405-416. doi: 10.1016/S0378-1127(99)00113-9
[11]	BECHTOLD W A. Largest crown width models for 53 species in US[J]. Western Journal of Applied Forestry, 2004, 19(4):245-251. doi: 10.1093/wjaf/19.4.245
[12]	CONDÉS S, STERBA H. Derivation of compatible crown width equations for some important tree species of Spain[J]. Forest Ecology and Management, 2005, 217(2-3):203-218. doi: 10.1016/j.foreco.2005.06.002
[13]	董晨, 吴保国, 韩焱云, 等. 基于修正函数的杉木人工林单木冠幅预测模型[J]. 东北林业大学学报, 2015, 43(5):49-53.
[14]	符亚健, 吕飞舟, 朱光玉, 等. 华北落叶松天然次生林单木冠幅模型构建[J]. 林业资源管理, 2016(5):65-70.
[15]	SHARMA R P, VACEK Z, VACEK S. Individual tree crown width models for Norway spruce and European beech in Czech Republic[J]. Forest Ecology and Management, 2016,366:208-220.
[16]	COOMBES A, MARTIN J, SLATER D. Defining the allometry of stem and crown diameter of urban trees[J]. Urban Forestry & Urban Greening, 2019,44:126421.
[17]	杨阳, 彭浩贤, 潘萍, 等. 基于混合效应的飞播马尾松林单木冠幅预测模型[J]. 江西农业大学学报, 2020, 42(5):990-1001.
[18]	马爱云, 李凤日, 董利虎. 应用混合效应法建立的杂种落叶松人工林单木冠幅预测模型[J]. 东北林业大学学报, 2021, 49(3):9-14.
[19]	邱思玉, 孙玉军. 长白落叶松人工林单木冠幅模型[J]. 东北林业大学学报, 2021, 49(2):49-53.
[20]	张晓芳, 郭旭展, 洪亮, 等. 冬奥核心区华北落叶松和白桦单木冠幅预测模型:组级贝叶斯模型、加性模型和混合效应模型比较[J]. 林业科学, 2022, 58(10):89-100.
[21]	TIAN Dongyuan, HE Pei, JIANG Lichun, et al. Developing crown width model for mixed forests using soil,climate and stand factors[J]. The Journal of Ecology, 2024, 112(2):427-442. doi: 10.1111/jec.v112.2
[22]	QIN Yangping, WU Biyun, LEI Xiangdong, et al. Prediction of tree crown width in natural mixed forests using deep learning algorithm[J]. Forest Ecosystem, 2023,10:100109.
[23]	卢军, 李凤日, 张会儒, 等. 帽儿山天然次生林主要树种冠长率[J]. 林业科学, 2011, 47(6):70-76.
[24]	BIANCHI S, SIIPILEHTO J, HYNYNEN J. How structural diversity affects Norway spruce crown characteristics[J]. Forest Ecology and Management, 2020,461:117932.
[25]	贺梦莹, 董利虎, 李凤日. 长白落叶松-水曲柳混交林不同混交方式单木冠长预测模型[J]. 南京林业大学学报(自然科学版), 2021, 45(4):13-22. doi: 10.12302/j.issn.1000-2006.202005043
[26]	夏杰, 周根苗, 易烜, 等. 基于混合效应的华北落叶松次生林单木冠长模型[J]. 中南林业科技大学学报, 2022, 42(5):44-53.
[27]	刘奇峰, 陈东升, 冯健, 等. 辽东山区人工红松冠长率影响因子研究[J]. 林业科学研究, 2022, 35(6):127-134.
[28]	RAUTIAINEN M, STENBERG P. Simplified tree crown model using standard forest mensuration data for Scots pine[J]. Agricultural and Forest Meteorology, 2005, 128(1-2):123-129. doi: 10.1016/j.agrformet.2004.09.002
[29]	TROXEL B, PIANA M, ASHTON M S, et al. Relationships between bole and crown size for young urban trees in the northeastern USA[J]. Urban Forestry & Urban Greening, 2013, 12(6):144-153.
[30]	PRETZSCH H, BIBER P, UHL E, et al. Crown size and growing space requirement of common tree species in urban centres,parks,and forests[J]. Urban Forestry & Urban Greening, 2015, 14(3):466-479.
[31]	李应涛, 刘时良, 孙海龙, 等. 云冷杉针阔混交林单木枝下高和冠幅模型构建[J]. 森林与环境学报, 2022, 42(3):2890296.
[32]	国家林业和草原局. 中国森林资源报告(2014-2018)[M]. 北京: 中国林业出版社,2019:275-277.
[33]	WANG Mingliang, BORDERS B E, ZHAO Dehai. An empirical comparison of two subject-specific approaches to dominant heights modeling the dummy variable method and the mixed model method[J]. Forest Ecology and Management, 2008, 255(7):2659-2669. doi: 10.1016/j.foreco.2008.01.030
[34]	ZENG Weisheng. Using nonlinear mixed model and dummy variable model approaches to construct origin-based single tree biomass equations[J]. Trees, 2015, 29(1):279.
[35]	唐守正, 郎奎建, 李海奎. 统计和生物数学模型计算(ForStat教程)[M]. 北京: 科学出版社, 2008.

树种	胸径/cm			树高/m			冠幅/m			冠长/m
树种	最小值	最大值	平均值± 标准差	最小值	最大值	平均值± 标准差	最小值	最大值	平均值± 标准差	最小值	最大值	平均值± 标准差
马尾松	1.2	47.2	16.5±11.9	1.6	30.3	12.1±7.2	0.60	11.73	4.43±2.50	0.7	17.5	6.14±3.46
油松	1.2	32.9	15.3± 9.9	1.6	20.1	9.4±4.8	0.75	10.42	3.85±2.25	0.9	13.3	5.99±3.33
云南松	1.8	47.1	16.7±12.4	1.8	33.3	10.7±6.9	0.75	12.59	4.31±2.64	0.8	26.1	6.10±4.07
思茅松	1.6	46.2	16.7±12.1	1.9	26.4	11.4±6.8	0.75	14.15	4.96±3.39	1.1	17.2	6.26±3.60
高山松	1.5	53.0	16.9±12.1	1.9	31.3	10.2±6.3	0.15	11.75	3.74±2.59	0.9	15.4	6.32±3.39
黄山松	1.2	41.8	16.3±11.8	1.6	24.1	10.6±6.0	0.45	10.05	3.67±2.35	0.3	15.6	4.74±3.01
樟子松	1.5	38.7	16.4±11.7	1.9	27.7	10.9±6.3	0.78	13.44	4.95±2.87	0.9	19.1	6.07±3.91
湿地松	1.2	33.9	15.5± 9.8	1.6	20.0	9.8±4.8	0.85	9.00	3.85±2.21	1.0	12.0	5.32±2.66
合计	1.2	53.0	16.3±11.6	1.6	33.3	10.8±6.4	0.15	14.15	4.24±2.65	0.3	26.1	5.90±3.49

模型	模型参数					评价指标
模型	a_i	b_i	c_i	d_i		R²		SEE/m		TRE/%		ASE/%		MPE/%		MPSE/%
(1)	0.896	0.205			0.800		1.18		0.00		-0.53		1.49		21.59
(2)	1.202	0.200	-0.285		0.801		1.18		0.00		-0.31		1.49		21.57
(3)	0.551	0.477	0.410		0.756		1.73		0.02		-0.13		1.56		21.21
(4)	-1.129	-0.011 3	0.045 0	0.770	0.750		1.75		1.56		5.95		1.58		24.27
(5)	1.229	0.754			0.764		3.09		-0.80		-3.52		1.53		23.11

模型	模型编号	固定或全局参数			评价指标
模型	模型编号	a_i	b_i	c_i	R²	SEE/m	TRE/%	ASE/%	MPE/%	MPSE/%
混合模型	(1)	0.852 8	0.206 8	/	0.840	1.07	0.00	-0.51	1.34	19.26
	(3)	0.468 4^*	0.464 4	0.477 5	0.787	1.62	0.00	0.09	1.47	19.92
	(5)	1.277 0^*	0.735 6	/	0.787	2.97	-0.94	-3.93	1.46	22.47
哑变量模型	(1)	0.846 7	0.207 1	/	0.840	1.07	0.00	-0.33	1.34	19.32
	(3)	0.467 5^*	0.459 1	0.484 9	0.787	1.62	0.08	0.32	1.46	20.05
	(5)	1.280 8^*	0.734 2	/	0.787	2.95	-0.92	-3.91	1.46	22.47