The Relationship Between Height-to-diameter Ratio and DBH and Tree Height in Typical Natural Broad-leaved Forests in Mid-subtropical Zone

YAN Ming-hai; WANG Jin-chi; HUANG Qing-lin; ZHUANG Chong-yang; ZHENG Qun-rui; ZHUO Ming-xiu; GUAN Xiao-hui

doi:10.13275/j.cnki.lykxyj.2022.005.009

Volume 35 Issue 5

Oct. 2022

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The Relationship Between Height-to-diameter Ratio and DBH and Tree Height in Typical Natural Broad-leaved Forests in Mid-subtropical Zone

1.
Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing　100091, China
2.
Key Laboratory of Forest Management and Growth Modelling, National Forestry and Grassland Administration, Beijing　100091, China
3.
Forestry College of Fujian Agriculture and Forestry University, Fuzhou　350002, Fu jian, China
4.
Administrative Office of Jian’ou Wanmulin Provincial Nature Reserve, Jian’ou　353105, Fu jian, China

Corresponding author: HUANG Qing-lin, huangql@caf.ac.cn ;
Received Date: 2022-01-14
Accepted Date: 2022-02-17

Abstract

Objective To provide a typical reference in the aspect of height-to-diameter ratio of broad-leaved trees for the sustainable management of artificial broad-leaved forest, semi-natural broad-leaved forest and natural broad-leaved forest in mid-subtropical zone, the relationship between tree height-to-diameter ratio and DBH and tree height were revealed in each stratum of typical natural broad-leaved forests. Method In Jian’ou Wanmulin Provincial Nature Reserve, 50 m × 50 m plots were set up in 5 most typical natural broad-leaved forest in mid-subtropical zone respectively. Spearman rank correlation coefficient was used to analyze the correlation between tree height-to-diameter ratio and DBH and tree height in each stratum, and exponential function and hyperbola equation were chosen to fit the relationship between height-to-diameter ratio and DBH in each stratum. Results The variation range of the average value of the height-to-diameter ratio in each stratum was not large. The average height-to-diameter ratio of the stand in the 5 sample plots was 103.1. The mean height-to-diameter ratio in stratum Ⅲ(112.7) was the largest, followed by stratum Ⅱ (89.0) and stratum Ⅰ(66.9), as well as in the minimum and maximum values. The height-to-diameter ratio of each stratum showed a significant negative correlation with DHB and the correlation coefficient was high. The absolute value of correlation coefficient was the highest in stratum Ⅰ(0.896～0.961) and stratum Ⅱ(0.912～0.971), the middle in the stand(0.613～0.749), and the lowest in stratum Ⅲ(0.415～0.596).The relationship between tree height-to-diameter ratio and tree height in each stratum was complex and the absolute value of correlation coefficient was low (< 0.480). The stand showed extremely negative correlation, but the absolute value of correlation coefficient was low (0.283～0.458). The R²of the tree height-to-diameter ratio and DBH in stratum Ⅰ and stratum Ⅱ fitted by exponential function were 0.852～0.906 and 0.830～0.914, respectively, while the R²of the stand and stratum Ⅲ were 0.465～0.575 and 0.202～0.399, respectively. The R²of the height-to-diameter ratio and DBH in stratum Ⅰ and stratum Ⅱ fitted by hyperbolic curve were 0.874～0.937 and 0.856～0.968, respectively, while the R² of the stand and stratum Ⅲ were 0.387～0.536 and 0.186～0.350, respectively. Exponential function fitting stand and stratum Ⅰ relationship of DBH than height-to-diameter ratio of R² was relatively high, and RMSE and AMR was relatively small. hyperbola from fitting relationship of DBH than height-to-diameter ratio stratum Ⅰ and stratum Ⅱ fitted by hyperbola equation had relatively high R² and small RMSE and AMR was values. Conclusion The tree height/diameter ratio of typical natural broad-leaved forest in mid-subtropical zone varies with the stratum. The tree height/diameter ratio in the same stratum also varies with DBH. The height-to-diameter ratio and DBH in each stratum shows a very significant negative correlation and the correlation coefficient is high, and the curve fitting of the relationship is significant. Hyperbolic function can well describe the relationship between height-to-diameter ratio and DBH in the stratum Ⅰ and stratum Ⅱ, while exponential function is more suitable to describe the relationship between height-to-diameter ratio and DBH in the stand and the stratum Ⅲ. The relationship between tree height-to-diameter ratio and tree height in each stratum is complex and the correlation coefficient is low. In the typical natural broad-leaved forest of the mid-subtropical zone, the characteristics of tree height/diameter ratio can be expressed by the relationship curve between tree height to diameter and DBH of each stratum.

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高径比是衡量林分稳定性、密度和竞争的重要指标^[1-5]，可用于评估林木活力和健康状况^[5-8]，也可用于编制立木材积表以及确定立木生长率，还可在各种森林模型中作为描述竞争效应的显著预测因子^[9]。高径比还是反映林木干形和林木生长的指标^[10-12]，它的大小直接影响木材的质量和经济价值^[12]。高径比因林木大小、林木年龄、生长资源的可得性、林分密度和物种组成而异^[5]，研究高径比对于提升森林质量和木材产品价值有重要意义^[5-8,12]，同时对于更好地理解森林生态过程至关重要^[3]。

为了更好地表征林木高径比特征，林木高径比与胸径及树高的关系引起了国内外一些学者的重视^[13-15]，林木高径比与胸径密切相关，其随林木胸径的增大而减小^[15-17]，其关系可用指数函数和双曲线函数来拟合^[17-19]，而林木高径比与树高的相关性通常不高，有时呈负相关^[17]，有时呈正相关^[4]。但目前对林木高径比与胸径及树高关系的研究多是针对整个乔木层，很少基于各亚层 ^[3,16]，且多是集中在结构简单、单层同龄的人工纯林，很少研究天然针阔混交林^[17]，未见针对结构复杂、复层异龄多树种混交的天然阔叶林的相关研究。对于中亚热带天然阔叶林的林层划分，目前已有科学的、在野外操作简单易行的和具有一定的生物学意义的林层定量划分新方法可供选用^[20-26]。因此，本研究以典型中亚热带天然阔叶林为对象，研究各林层（包括乔木层和各乔木亚层）林木高径比与胸径及树高的关系，旨在揭示典型中亚热带天然阔叶林各林层林木高径比与胸径及树高的关系特征，为中亚热带人工阔叶林、半天然林和天然阔叶林可持续经营提供阔叶林木高径比方面的参照。

1. 研究区概况

建瓯万木林省级自然保护区是1957年划定的全国首批19个天然森林禁伐区（自然保护区）之一，是继鼎湖山之后我国建立的第二个自然保护区^[27]。保护区位于闽北建瓯市境内，属武夷山南坡低山丘陵，海拔230～556 m，地理坐标为27°02′28″ ～ 27°03′32″ N，118°08′22″～118°09′23″ E，气候属中亚热带海洋性季风气候，年平均气温18.7 ℃，极端最低气温−5.9 ℃，极端最高气温40.7 ℃。年平均降水量1 700 mm，6月最多，雨日年平均166 d。土壤为中生代燕山运动侵入的花岗岩为主要成土母岩的红壤，立地类型以Ⅱ类地为主。

2. 材料与方法

2.1. 样地设置与调查

在建瓯万木林省级自然保护区内选择5个最典型中亚热带天然阔叶林^[22-23,28]，在5个试验林分内分别设置50 m × 50 m的样地，对样地内胸径≥5.0 cm的林木进行每木调查，准确调查测定并记录每株林木的位置、树种、胸径、树高、枝下高、冠长、冠幅和冠形等因子，采用最大受光面法进行林层划分^[22-23]。各样地概况见表1，5个样地各林层的相关信息详见《中亚热带天然阔叶林林层特征》^[24]、《基于林层的典型中亚热带天然阔叶林树种组成与多样性》^[25]。

样地号 Sample plot	群落类型 Community type	种丰富度 Species brichness	平均胸径 Mean DBH/cm	平均树高 Mean height/m	密度 Density/ (individual·hm⁻²)	蓄积量 Volume/ (m³·hm⁻²)
1	木荷 + 光叶山矾（Schima superba + Symplocos lancifolia）	36	21.0	26.8	1 164	481.7
2	猴欢喜 + 木荷（Sloanea sinensis + Schima superbar）	50	25.7	27.9	952	591.5
3	木荷 + 新木姜子（Schima superba + Neolitsea aurata）	49	22.0	23.9	1 076	435.4
4	木荷 + 浙江桂（Schima superba + Cinnamomum chekiangense）	45	23.6	24.1	1 056	493.3
5	浙江桂 + 木荷（Cinnamomum chekiangense + Schima superba）	45	21.9	25.2	1 056	443.0

Table 1. General situation of sample plots

2.2. 研究方法

采用Spearman秩相关系数分析高径比与胸径及树高的相关性，运用指数函数和双曲线函数拟合林木高径比与胸径关系，参考前人的研究^[17-19]，选择以下2种模型对各林层（包括全林分和各亚层）林木高径比与胸径关系曲线进行拟合。具体表达式如下：

式中：y表示高径比的大小，x表示胸径大小，a和b是该模型的参数，（1）式中b表示林木高径比在连续的径阶中减小的速率；（2）式中a表示双曲线函数的上下限（b > 0时，a为下限；b < 0时，a为上限）。

选用均方根误差（RMSE）、决定系数（R²）和平均绝对误差（AMR）等作为模型评价指标。

4. 讨论

在研究各亚层高径比与胸径关系曲线时，由于第Ⅰ、Ⅱ亚层林木相对较少，可能会对研究结果产生影响，本研究尝试将相对位置较近、树种组成类似的2和3号样地、4和5号样地合成2个新的样地，用以分析第Ⅰ、Ⅱ亚层高径比与胸径关系，结果表明，新样地第Ⅰ、Ⅱ亚层高径比与胸径关系特征与原样地的一致。

本研究结果表明，中亚热带典型天然阔叶林各林层林木高径比与胸径均呈现极显著负相关，这与其他学者对人工针叶林全林林木高径比^[4,15]和天然针叶林全林林木高径比^[13]的研究结论基本一致，也与其他学者对天然针阔混交林主要树种的林木高径比研究结论基本一致^[17]。典型中亚热带天然阔叶林各林层林木高径比与树高的关系较为复杂且相关系数绝对值都较低（即相关性不高），这与其他学者对人工针叶林林木高径比^[4]的研究结论基本一致，也与其他学者对天然针阔混交林主要树种的林木高径比研究结论基本一致^[17]。目前对人工针叶林全林林木高径比与树高关系的研究有正相关^[4]，对天然针阔混交林主要树种的林木高径比与树高关系的研究有负相关^[17]，而本研究各亚层林木高径比与树高的关系较为复杂，有负相关、也有正相关，有不显著相关、显著相关、也有极显著相关，这种林木高径比与树高关系的复杂性是否正是典型天然阔叶林所特有的特征有待进一步深入研究。

5. 结论

典型中亚热带天然阔叶林林木高径比会因所属亚层的不同而变化，因此有必要分亚层来探讨林木高径比与胸径及树高关系；同一亚层的林木高径比也会因胸径不同而变化，各林层林木高径比与胸径均呈现极显著负相关且相关系数都较高，其关系曲线拟合是有意义且必要的，双曲线函数能很好地描述第Ⅰ亚层和第Ⅱ亚层的关系曲线，指数函数更适合描述全林分和第Ⅲ亚层的关系曲线；各林层林木高径比与树高的关系较为复杂且相关系数都较低，其关系曲线拟合是没有意义的；典型中亚热带天然阔叶林林木高径比特征需要且可以采用各林层林木高径比与胸径的关系曲线来表达。

Reference (28)

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[2]	丁良忱, 别克. 天山云杉人工幼林生长规律的初步研究[J]. 八一农学院学报, 1988(2):38-45.
[3]	Sharma R P, Vacek Z, Vacek S, et al. A nonlinear mixed-effects height-to-diameter ratio model for several tree species based on Czech National Forest Inventory Data[J]. Forests, 2019, 10(1): 70.
[4]	Oyebade B A, Eguakun F S, Egberibin A. Tree slenderness coefficient (TSC) and tree growth characteristics (TGCS) for Pinuscaribaea in Omo Forest Reserve, Nigeria[J]. Journal of Environmental Science, 2015, 9(3): 56-62.
[5]	Hess A F, Minatti M, Costa E A, et al. Height-to-diameter ratios with temporal and dendro/morphometric variables for Brazilian pine in south Brazil[J]. Journal of Forestry Research, 2021, 32(1): 191-202.
[6]	Opio C, Jacob N, Coopersmith D. Height to diameter ratio as a competition index for young conifer plantations in northern British Columbia, Canada[J]. Forest Ecology and Management, 2000, 137(1-3): 245-252.
[7]	Adeyemi A A, Adesoye P O. Tree slenderness coefficientand percent canopy cover in Oban Group Forest, Nigeria[J]. Journal of Natural Sciences Research, 2016, 6(4): 9-17.
[8]	Adeyemi A A, Ugo-Mbonu N A. Tree slenderness coefficients and crown ratio models for Gmelina arborea (ROXB) stand in afi river forest reserve, cross river state, Nigeria[J]. Nigerian Journal of Agriculture, Food and Environment, 2017, 13(1): 226-233.
[9]	Yang Y, Huang S. Effects of competition and climate variables on modelling height to live crown for three boreal tree species in Alberta, Canada[J]. European Journal of Forest Research, 2018, 137: 153-167.
[10]	黄旺志, 赵剑平, 王昌薇, 等. 不同造林密度对杉木生长的影响[J]. 河南农业大学学报, 1997, 31(4):379-385.
[11]	蔡坚, 潘文, 王保华, 等. 林分密度对湿地松林木干形影响的研究[J]. 广东林业科技, 2006, 22(2):6-10.
[12]	丁贵杰, 周政贤, 严仁发, 等. 造林密度对杉木生长进程及经济效果影响的研究[J]. 林业科学, 1997, 33(A1):67-75.
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样地号 Sample plot	平均林木高径比 Mean tree height-to-diameter ratio				林木高径比分布范围 Treeheight-to-diameter ratio range
样地号 Sample plot	S	Ⅰ	Ⅱ	Ⅲ	S	Ⅰ	Ⅱ	Ⅲ
1	108.0	78.2	101.4	116.2	42.5～175.9	42.5～135.0	56.4～157.3	55.7～175.9
2	97.2	58.1	82.2	107.4	27.5～242.5	27.5～109.2	37.2～138.2	43.5～242.5
3	103.8	62.8	77.7	114.0	34.5～202.9	36.8～108.2	34.5～140.5	47.8～202.9
4	102.2	69.4	97.8	112.0	32.2～209.0	35.9～123.2	32.2～181.1	47.3～209.0
5	104.1	66.1	85.9	114.0	32.5～198.8	38.4～94.0	32.5～148.4	54.2～198.8
注：S表示全林分；Ⅰ表示第Ⅰ亚层；Ⅱ表示第Ⅱ亚层；Ⅲ表示第Ⅲ亚层。下同。　　Note: S means stand, Ⅰ mean stratum Ⅰ, Ⅱ mean stratum Ⅱ, Ⅲ mean stratum Ⅲ. The same below.

样地号 Sample plot	高径比与胸径的相关系数 Correlation coefficient between height-to-diameter ratio and DHB				高径比与树高的相关系数 Correlation coefficient between height-to-diameter ratio and tree height
样地号 Sample plot	S	Ⅰ	Ⅱ	Ⅲ	S	Ⅰ	Ⅱ	Ⅲ
1	−0.613**	−0.961**	−0.912**	−0.436**	−0.283**	−0.286	−0.169	0.208*
2	−0.749**	−0.958**	−0.953**	−0.596**	−0.456**	−0.311	−0.408**	−0.020
3	−0.742**	−0.896**	−0.942**	−0.560**	−0.458**	−0.051	−0.211	−0.046
4	−0.729**	−0.957**	−0.971**	−0.560**	−0.431**	−0.310*	0.119	−0.022
5	−0.657**	−0.928**	−0.923**	−0.415**	−0.330**	−0.262	−0.480**	0.233**
注：表示高径比与树高或与胸径有显著相关；表示高径比与树高或与胸径有极显著相关。　　Note: means that the height-to-diameter ratio is significantly correlated with tree height or with DBH;** means that the height-to-diameter ratio is extremely significantly correlated with tree height or with DBH.

样地号 Sample plot	层属 Stratum	指数函数 Exponential function					双曲线函数 Hyperbolic curve
		参数 Parameters		评价指标 Evaluation indicators			参数 Parameters		评价指标 Evaluation indicators
		a	b	R²	RMSE	AMR	a	b	R²	RMSE	AMR
1	S	135.6	−0.015 55	0.465	20.60	16.08	75.42	326.7	0.387	22.06	18.07
	Ⅰ	196.1	−0.022 83	0.906	7.48	5.91	12.11	2 508.7	0.930	6.46	4.68
	Ⅱ	221.6	−0.038 50	0.830	9.79	8.06	18.15	1 622.2	0.856	9.01	7.12
	Ⅲ	154.9	−0.033 07	0.217	21.95	17.94	81.27	276.1	0.201	22.17	18.07
2	S	132.8	−0.019 68	0.514	22.24	16.94	58.81	411.2	0.511	22.30	17.04
	Ⅰ	139.0	−0.014 82	0.893	6.38	4.33	11.27	2 553.8	0.924	5.35	4.31
	Ⅱ	185.0	−0.032 70	0.878	7.90	6.39	18.61	1 484.1	0.914	6.62	5.11
	Ⅲ	157.1	−0.039 64	0.356	23.75	17.84	62.37	377.2	0.341	24.04	18.26
3	S	142.4	−0.022 14	0.575	21.02	15.80	61.48	418.6	0.536	21.97	17.45
	Ⅰ	155.0	−0.019 05	0.862	6.45	5.23	10.83	2 354.9	0.909	5.25	4.18
	Ⅱ	193.0	−0.032 93	0.875	8.95	6.82	10.11	1 760.3	0.916	7.34	5.77
	Ⅲ	160.0	−0.036 57	0.359	22.23	16.99	71.59	344.4	0.326	22.79	17.94
4	S	138.3	−0.019 87	0.568	21.41	15.83	61.83	406.5	0.504	22.93	17.75
	Ⅰ	167.8	−0.021 87	0.905	6.63	5.48	11.20	2 203.9	0.937	5.39	4.38
	Ⅱ	280.4	−0.051 90	0.914	11.35	9.40	0.51	1 879.3	0.968	6.88	5.63
	Ⅲ	158.1	−0.037 91	0.399	21.83	16.35	65.24	372.4	0.350	22.72	17.68
5	S	135.3	−0.018 33	0.488	22.21	17.05	66.58	363.9	0.428	23.46	18.57
	Ⅰ	145.7	−0.017 10	0.852	7.00	5.12	12.28	2 351.2	0.874	6.46	4.46
	Ⅱ	175.9	−0.028 64	0.890	7.99	6.31	21.07	1 502.1	0.897	7.75	6.20
	Ⅲ	152.7	−0.034 07	0.202	24.70	19.72	77.25	284.6	0.186	24.94	19.93

The Relationship Between Height-to-diameter Ratio and DBH and Tree Height in Typical Natural Broad-leaved Forests in Mid-subtropical Zone