基于地面激光扫描数据的马褂木材积建模与出材率研究

陈军; 孙圆; 刘晨曦; 姚睿涵; 于嘉辉; 曹福亮; 余鹏飞

doi:10.12171/j.1000-1522.20210296

基于地面激光扫描数据的马褂木材积建模与出材率研究

陈军^{1, 2,},
孙圆^{1, 2, ,},
刘晨曦¹,
姚睿涵¹,
于嘉辉¹,
曹福亮^{1, 2},
余鹏飞³

1.
南方现代林业协同创新中心，南京林业大学，江苏南京 210037
2.
南京林业大学林学院，江苏南京 210037
3.
睢宁县润企投资有限公司，江苏睢宁 220122

基金项目: 江苏省科技厅自然科学面上基金项目（BK20191388），南京林业大学大创项目（2020NFUSPITP0235），江苏省高校优势学科建设工程自助项目（PAPD）

详细信息

作者简介:
陈军，博士生。研究方向：森林培育。Email：763502609@qq.com　地址：210037江苏省南京市玄武区龙蟠路159号南京林业大学林学院

责任作者:
孙圆，博士，副教授。研究方向：森林资源管理、林业遥感、森林精准培育。Email：yuan.sun@njfu.edu.cn　地址：同上

中图分类号: S792.21
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出版历程
- 收稿日期: 2021-08-04
- 修回日期: 2022-11-22
- 录用日期: 2023-05-27
- 网络出版日期: 2023-05-29
- 发布日期: 2023-06-24

Volume modeling and yield for Liriodendron tulipifera based on terrestrial laser scan data

Chen Jun^{1, 2,},
Sun Yuan^{1, 2, ,},
Liu Chenxi¹,
Yao Ruihan¹,
Yu Jiahui¹,
Cao Fuliang^{1, 2},
Yu Pengfei³

1.
Co-Innovation Center for Sustainable Forestry in Southern China, Nanjing Forestry University,Nanjing 210037, Jiangsu, China
2.
College of Forestry, Nanjing Forestry University, Nanjing 210037, Jiangsu, China
3.
Suining County Run Enterprises Investment Co., Ltd., Suining 220122, Jiangsu, China

摘要

摘要:
目的马褂木是优良的用材树种，研究其材积模型并分析多种密度种植下的径级材种造材出材率，旨在为马褂木人工林高效培育提供重要的指导。
方法在马褂木多密度人工林试验区获取全样地地面激光雷达数据。通过点云提取单木结构参数，对4种造林密度（株行距配置：2 m × 2 m、3 m × 3 m、4 m × 4 m、5 m × 5 m）马褂木试验林测树因子（胸径DBH，树高H，材积V）进行分析，建立一元材积方程、削度方程模型，并应用削度方程计算各密度林分材种出材率。
结果研究得到的一元二次式 $V=0.000\;3 {D}^{2} + 0.006\;5 D-0.036\;9$ 为研究区马褂木最优一元材积式，该模型的决定系数（R²）为0.884，经过剩余标准差（S_EE）、系统误差（T_RE）、平均相对误差（M_SE）、预估精度（ρ）等评价指标检验，无明显系统偏差，可用于研究区马褂木材积估计。研究选定改进的舒马赫方程式作为不同密度马褂木的削度方程，该模型R²为0.924，经检验方程均方根误差为1.454，平均相对误差为0.050，预估精度达到0.910。进一步采用削度方程为多密度马褂木试验林进行多径级材造材，得到疏林地4 m × 4 m密度种植下的大径材出材率最大（39.582%），密林地2 m × 2 m密度种植下的小径材出材率最大（81.250%），而综合出材率最大的是4 m × 4 m密度（98.650%）。
结论马褂木多密度经营下，疏林地大径材出材率最大，密林则以小径材为主要径级材种。基于地面激光点云获取的单木参数可以直观地进行森林经理研究，对提升人工林的生产经营水平以及提高林业工作者的工作效率均有积极影响。
- 地面激光扫描 /
- 点云 /
- 测树因子 /
- 一元材积表 /
- 削度方程 /
- 材种出材率
Abstract:
Objective Liriodendron tulipifera is an excellent timber species. It is of great significance to study the volume model of L. tulipifera wood and analyze the yield of merchantable timber under different densities for the efficient cultivation of L. tulipifera plantation.
Method In this study, the terrestrial laser scan (TLS) data was obtained in the multi-density L. tulipifera plantation area in Jiangsu Province of eastern China. The single tree parameters (DBH, tree height H, volume V) were extracted for the various densities (2 m × 2 m, 3 m × 3 m, 4 m × 4 m, 5 m × 5 m) of the L. tulipifera sample stand. The single entry volume model was conducted and the taper equation model was established. The timber yield of each density stand was calculated by the taper equation.
Result The quadratic formula with one variable: ${V}=0.000\;3 {{D}}^{2} +$ $0.006\;5 {D}-0.036\;9$ was obtained as the single entry volume model for L. tulipifera wood in the study area. The model’s coefficient of determination (R²) was 0.884. After the test of residual standard deviation (S_EE), systematic error (T_RE), mean relative error (M_SE), precision estimation (ρ) and other indicators, there was no obvious systematic deviation, so the model can be used to estimate the volume of L. tulipifera in the study area. This study selected the improved Schumacher’s equations as taper equation for different afforestation densities, the model’s R² was 0.924, root mean square error (RMSE) was 1.454, and M_SE was 0.050, ρ was 0.910, etc. Furtherly, the taper equation was used to make multi-diameter grade wood in the multi-density afforestation forest sample plots. It was found that the output rate of large-diameter timber was the highest (39.582%) under 4 m × 4 m density planting forest, the output rate of small-diameter timber was the highest (81.250%) under 2 m × 2 m density planting forest, and the maximum composite yield was 4 m × 4 m density planting forest (98.650%).
Conclusion For L. tulipifera plantation under the multi-density management, the yield of large-diameter timber in the open forest is the largest, while the small-diameter wood is the main diameter class in the dense forest. The single tree parameters obtained based on the ground laser point cloud could be intuitively studied for the forest manager, which has a positive impact on the improvement of the production and management level of the plantation and the improvement of the work efficiency of the forestry workers.
- terrestrial laser scan /
- point cloud /
- mensuration factor /
- unary volume table /
- taper equation /
- yield of merchantable timber

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图 1 研究区域位置和数据概览图

Figure 1. Overview of research place and data

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图 2 马褂木立木切片示意图

Figure 2. Schematic diagram of standing wood section in Liriodendron tulipifera

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图 3 胸径点云提取值与实测值拟合散点图

Figure 3. Scatter plot fitting of extracted and measured values from DBH point cloud

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图 4 一元材积方程拟合情况

Figure 4. Fitting condition of univariate volume equations

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表 1 材积方程模型一览表

Table 1 List of volume equation models

公式 Formula	编号 No.
$y={a}_{0} + {a}_{1}x$	V1
$y={a}_{0} + {a}_{1}x + {a}_{2}{x}^{2}$	V2
$y={a}_{0}\mathrm{l}\mathrm{n}x + {a}_{1}$	V3
$y={a}_{0}{x}^{{a}_{1}}$	V4
$y={a}_{0}{{\rm{e}}}^{ {a}_{1}x}$	V5
注：y. 立木材积（m³）；x. 直径（cm）；a_i. 参数（i = 0，1，2）。Notes: y, standing volume (m³); x, diameter (cm); a_i, parameter (i = 0, 1, 2).

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表 2 削度方程模型一览表

Table 2 List of taper equation models

公式 Formula	编号 No.
$d=D{\left(\dfrac{H-h}{H-1.3}\right)}^{ {a}_{0} } \setlength{\voffset}{0pt}$	T1
${\left(\dfrac{d}{D}\right)}^{2}={a}_{0} + {a}_{1}{\left(\dfrac{H-h}{H-1.3}\right)}^{{a}_{2}} \setlength{\voffset}{0pt}$	T2
${d}^{2}={a}_{0}{D}^{ {a}_{1} }\dfrac{ {(H-h)}^{ {a}_{2} } }{ {H}^{ {a}_{3} } } \setlength{\voffset}{0pt}$	T3
${d}^{2}={a}_{0}D{\left(\dfrac{H-h}{H-1.3}\right)}^{{a}_{1}} \setlength{\voffset}{0pt}$	T4
${d}^{2}={D}^{2}{\left(\dfrac{H-h}{H-1.3}\right)}^{{a}_{0}} \setlength{\voffset}{0pt}$	T5
注：d为树干h高处的带皮直径（cm）；D为带皮胸径（cm）；H为全树高（m）；h为距地面的高度（m）； ${a}_{0}$ 、 ${a}_{1}$ 、 ${a}_{2}$ 、 ${a}_{3}$ 为待定参数。下同。Notes: d is the diameter (cm) of the bark at h height of the trunk; D is DBH (cm) with bark; H is the total tree height (m); h is the height (m) above the ground; ${a}_{0}$ , ${a}_{1}$ , ${a}_{2}$ , ${a}_{3}$ are undetermined parameters. The same below.

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表 3 点云测定马褂木测树因子概况

Table 3 General situation of mensuration factors of Liriodendron tulipifera forest with point cloud

样地密度 Sample plot density	株数 Plant number	平均地径 Average ground diameter/cm	平均DBH Average DBH/cm	平均树高 Average tree height/m	平均材积 Average volume/m³
2 m × 2 m	79	23.200	16.200	17.860	0.184
3 m × 3 m	79	27.820	20.570	17.220	0.213
4 m × 4 m	48	29.000	20.890	16.520	0.184
5 m × 5 m	18	30.870	21.920	16.570	0.213
总计/平均 Total/mean	224	27.723	19.895	17.043	0.198

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表 4 一元材积模型拟合结果

Table 4 Fitting results of univariate volume models

模型编号 Model No.	公式 Formula	${R}^{2}$	${S}_{\mathrm{E}\mathrm{E}}$	${T}_{\mathrm{R}\mathrm{E}}$ /%	${M}_{\mathrm{S}\mathrm{E}}$ /%
V1	V = 0.016 4D − 0.122 3	0.873	0.009	0.004	−184.440
V2	V = 0.000 3 ${D}^{2}$ + 0.006 5D − 0.036 9	0.884	0.008	0.003	−1.279
V3	V = 0.026 6lnD − 0.581 2	0.798	0.112	0.001	−20.018
V4	V = 0.000 6 ${D}^{1.945\;7}$	0.902	0.017	−0.066	39.572
V5	V = 0.019 5 ${\mathrm{e} }^{0.109\;6D}$	0.823	0.056	0.271	−56.163
注：R². 决定系数；S_EE. 剩余标准差；T_RE. 系统误差；M_SE. 平均相对误差。Notes: R², determination coefficient; S_EE, residual standard deviation; T_RE, systematical error; M_SE, average relative error.

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表 5 不同造林密度削度方程模型参数

Table 5 Model parameters of taper equations with different afforestation densities

密度 Density	模型 Model	a₀	a₁	a₂	a₃	R²	RMSE	AIC
2 m × 2 m	T1	0.625				0.945	0.940	−3479.60
	T2	0.141	0.887	1.694		0.950	0.901	−3501.80
	T3	3.237	2.130	1.247	1.761	0.949	0.904	−3499.70
	T4	16.887	1.193			0.793	1.829	−3115.20
	T5	1.250				0.945	0.940	−3479.60
3 m × 3 m	T1	0.824				0.907	1.674	−4348.70
	T2	0.063	0.930	1.903		0.911	1.636	−4362.30
	T3	10.648	2.262	1.584	2.665	0.914	1.603	−4375.30
	T4	21.401	1.557			0.815	2.357	−4101.80
	T5	1.648				0.907	1.674	−4348.70
4 m × 4 m	T1	1.006				0.872	2.746	−2098.50
	T2	0.042	0.866	2.053		0.886	2.662	−2110.00
	T3	9.253	1.706	1.775	2.220	0.899	2.580	−2121.10
	T4	20.367	1.766			0.865	2.792	−2087.10
	T5	2.011				0.872	2.746	−2093.40
5 m × 5 m	T1	0.961				0.952	1.416	−817.72
	T2	0.010	0.993	1.981		0.952	1.414	−817.01
	T3	0.094	1.482	1.914	0.456	0.964	1.226	−840.86
	T4	22.732	1.860			0.859	2.429	−724.96
	T5	1.923				0.930	1.594	1641.07
整体 Total	T1	0.866				0.952	1.504	1641.07
	T2	0.025	0.965	1.822		0.931	1.504	1642.55
	T3	2.758	1.861	1.618	1.783	0.954	1.454	1505.00
	T4	20.409	1.522			0.825	2.214	3192.55
	T5	1.643				0.922	6.887	7747.51

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表 6 不同造林密度削度方程模型的适用性检验结果

Table 6 Applicability test results of taper equation models with different afforestation densities

密度 Density	模型 Model	S_EE	T_RE/%	M_SE/%	$\;\rho$
2 m × 2 m	T1	0.117	−4.001	−4.20	0.862
	T2	0.061	−3.772	−3.90	0.862
	T3	0.052	−3.438	−1.10	0.863
	T4	0.154	1.112	−3.20	0.873
	T5	0.117	−4.000	−4.20	0.862
3 m × 3 m	T1	0.051	1.250	−3.20	0.846
	T2	0.058	0.626	−0.80	0.847
	T3	0.057	0.087	−0.02	0.849
	T4	0.207	7.415	−9.50	0.831
	T5	0.051	1.250	−0.01	0.846
4 m × 4 m	T1	0.057	14.805	21.50	0.681
	T2	0.058	16.523	21.40	0.689
	T3	0.047	6.600	10.70	0.701
	T4	0.055	12.481	12.30	0.697
	T5	0.056	14.327	16.30	0.699
5 m × 5 m	T1	0.014	5.544	7.90	0.972
	T2	0.015	5.511	7.80	0.996
	T3	0.014	1.561	7.90	0.996
	T4	0.118	11.530	12.70	0.994
	T5	0.017	8.240	10.90	0.995

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表 7 不同密度马褂木人工林材种出材率

Table 7 Yield of artificial Liriodendron tulipifera plantations with different densities

项目 Item		密度 Density
项目 Item		5 m × 5 m	4 m × 4 m	3 m × 3 m	2 m × 2 m
株数 Plant number		18	48	79	79
蓄积 Volume/cm³		5.002	13.236	20.948	14.955
胸径 DBH/cm	平均 Average	21.918	20.959	17.046	16.413
	最大 Max.	33.300	30.300	33.370	26.050
	最小 Min.	10.370	8.100	9.480	5.820
树高 Tree height/m	平均 Average	16.569	16.456	17.046	16.063
	最大 Max.	18.810	20.470	19.520	16.840
	最小 Min.	13.680	10.220	11.030	7.540
造材材积 Merchantable wood volume/cm³	大径 Big	1.245	1.266	2.003	0.143
	中径 Middle	1.552	5.239	6.752	2.331
	小径 Small	1.914	6.552	11.878	12.151
出材率 Yield/%	大径 Big	24.885	9.568	9.563	0.957
	中径 Middle	31.020	39.582	32.232	15.588
	小径 Small	38.269	49.500	56.704	81.250
合计Total		94.174	98.650	98.499	97.796

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参考文献(22)

[1]	贾忠奎. 我国人工林长期生产力维持技术研究进展[J]. 世界林业研究, 2012, 25(1): 49−54. doi: 10.13348/j.cnki.sjlyyj.2012.01.014 Jia Z K. Research progress of maintenance technology of long-term productivity of plantation in China[J]. World Forestry Research, 2012, 25(1): 49−54. doi: 10.13348/j.cnki.sjlyyj.2012.01.014
[2]	李增元, 庞勇, 刘清旺, 等. 激光雷达森林参数反演技术与方法[M]. 北京: 科学出版社, 2015: 204−234. Li Z Y, Pang Y, Liu Q W, et al. LiDAR forest parameter retrieval technology and method[M]. Beijing: Science Press, 2015: 204−234.
[3]	Liang X L, Hyyppä J, Kaartinen H, et al. International benchmarking of terrestrial laser scanning approaches for forest inventories[J]. ISPRS Journal of Photogrammetry and Remote Sensing, 2018, 144(10): 137−179.
[4]	Ekaterina B, Oscar P P, Tarek S M, et al. Using terrestrial laser scanning for characterizing tree structural parameters and their changes under different management in a Mediterranean open woodland[J]. Forest Ecology and Management, 2021, 486(4): 118945−118961.
[5]	Sun Y, Lin X Y, Gong Y L, et al. Multi-station LiDAR scanning-based hierarchical features for generation of an allometric stem volume model[J]. Journal of Applied Remote Sensing, 2021, 15(2): 028503.
[6]	Wang Y S, Pyörälä J, Liang X L, et al. In situ biomass estimation at tree and plot levels: what did data record and what did algorithms derive from terrestrial and aerial point clouds in boreal forest[J]. Remote Sensing of Environment, 2019, 232(10): 111309.
[7]	Chen J H, Hao Z D, Guang X M, et al. Liriodendron genome sheds light on angiosperm phylogeny and species−pair differentiation[J]. Nature Plants, 2019(5): 18−25.
[8]	郝自远, 李火根, 康昊, 等. 北美鹅掌楸人工林生长规律及早期选择可行性探究[J]. 林业科学研究, 2017, 30(5): 878−885. Hao Z Y, Li H G, Kang H, et al. Growth pattern and early selection of Liriodendron tulipifera[J]. Forest Research, 2017, 30(5): 878−885.
[9]	蔡伟建. 杂交马褂木人工林培育技术研究[D]. 南京: 南京林业大学, 2011. Cai W J. Research on cultural technology of Liriodendron chinense × L. tulipifera plantation[D]. Nanjing: Nanjing Forestry University, 2011.
[10]	李淑娟. 下蜀实习林场地理信息系统建立与应用[D]. 南京: 南京林业大学, 2007. Li S J. Establishment and application of geographic information system in Xiashu Forestry Centre[D]. Nanjing: Nanjing Forestry University, 2007.
[11]	Mcgaughe R J. FUSION/LDV: softwaare for LIDAR data analysis and visualization[M]. Washington: USDA Forest Service, 2022.
[12]	汪献义, 邢艳秋, 尤号田, 等. 基于近邻几何特征的TLS林分点云分类研究[J]. 北京林业大学学报, 2019, 41(6): 138−146. Wang X Y, Xing Y Q, You H T, et al. TLS point cloud classification of forest based on nearby geometric features[J]. Journal of Beijing Forestry University, 2019, 41(6): 138−146.
[13]	刘鲁霞, 庞勇, 李增元. 基于地基激光雷达的亚热带森林单木胸径与树高提取[J]. 林业科学, 2016, 52(2): 26−37. Liu L X, Pang Y, Li Z Y. Individual tree DBH and height estimation using terrestrial laser scanning (TLS) in a subtropical forest[J]. Scientia Silvae Sinicae, 2016, 52(2): 26−37.
[14]	蒋佳文, 温小荣, 顾海波, 等. 基于多站扫描的点云特征参数与材积结构动态分析[J]. 南京林业大学学报(自然科学版), 2019, 3(6): 83−90. Jiang J W, Wen X R, Gu H B, et al. Dynamic analysis of point cloud characteristic parameters and volume structure based on multi-station scan[J]. Journal of Nanjing Forestry University (Natural Sciences Edition), 2019, 3(6): 83−90.
[15]	孟宪宇. 测树学[M]. 北京: 中国林业出版社, 2006. Meng X Y. Forest measurement[M]. Beijing: China Forestry Publishing House, 2006.
[16]	靳晓东, 姜立春. 基于树干不同形率的樟子松立木材积方程研建[J]. 北京林业大学学报, 2020, 42(3): 78−86. doi: 10.12171/j.1000-1522.20190047 Jin X D, Jiang L C. Equation construction on standing tree volume of Pinus sylvestris var. mongolica based on different form quotients of trunk[J]. Journal of Beijing Forestry University, 2020, 42(3): 78−86. doi: 10.12171/j.1000-1522.20190047
[17]	Sun Y, Liang X L, Liang Z Y, et al. Deriving merchantable volume in poplar through a localized tapering function from non-destructive terrestrial laser scanning[J]. Forests, 2016, 7(12): 87−95. doi: 10.3390/f7040087
[18]	Li Y M, Guo Q H, Su Y J, et al. Retrieving the gap fraction, element clumping index, and leaf area index of individual trees using single-scan data from a terrestrial laser scanner[J]. ISPRS Journal of Photogrammetry and Remote Sensing, 2017, 130(8): 308−316.
[19]	Cao L, Coops N, Sun Y, et al. Estimating canopy structure and biomass in bamboo forests using airborne LiDAR data[J]. ISPRS Journal of Photogrammetry and Remote Sensing, 2019, 148: 114−129. doi: 10.1016/j.isprsjprs.2018.12.006
[20]	黄星旻, 孙圆, 刘慧倩, 等. 多回波点云数据解算单株木叶面积指数[J]. 遥感学报, 2018, 22(6): 1042−1050. Huang X W, Sun Y, Liu H Q, et al. Resolving leaf area index of individual trees based on multi-return terrestrial laser point cloud data[J]. Journal of Remote Sensing, 2018, 22(6): 1042−1050.
[21]	Shen X, Cao L, Chen D, et al. Prediction of forest structural parameters using airborne full-waveform LiDAR and hyperspectral data in subtropical forests[J]. Remote Sensing, 2018, 10(11): 1729. doi: 10.3390/rs10111729
[22]	Schumacher F X, Hall F S. Logarithmic expression of timber tree volume[J]. Journal of Agricultural Research, 1993, 47: 719−734.

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