基于激光雷达的北京市主要林分因子联立模型构建与应用

doi:10.11707/j.1001-7488.LYKX20250309

摘要/Abstract

摘要：

目的: 探索基于激光雷达数据构建主要林分因子模型估计乔木林小班因子的可行性，为推进激光雷达技术在全国林草综合监测中的应用提供示范。方法: 基于北京市1 966块乔木林样地激光雷达点云参数和地面实测数据，应用误差变量联立方程组方法，分13种森林类型构建林分平均胸径、平均高、优势高、每公顷株数、断面积、蓄积量、生物量和碳储量共8项林分因子预估模型；利用全市乔木林小班范围内按25 m×25 m网格单元提取的激光雷达点云参数，采用所建8项林分因子预估模型完成对所有乔木林小班因子的估计。结果: 1）对估计主要林分因子贡献最大的激光雷达点云参数为累计高度80%分位数和点云高度中位数，其次为叶面积指数；2）所建13种森林类型的8项林分因子预估模型，自检和交叉检验的平均预估误差（MPE）均在15%以内；3）以森林为总体进行评价，8项林分因子预估模型的确定系数（R²）均达0.7以上（每公顷株数除外），MPE均在3%以内，平均百分标准误差（MPSE）均在40%以内，其中平均胸径、平均高和优势高模型的MPSE达15%左右；4）根据模型反演得出的乔木林小班蓄积量累计值与全市综合监测得到的森林蓄积量相比仅差?1.79%，3个副总体范围内的乔木林小班蓄积量与综合监测结果相比也仅分别相差1.04%、?3.91%和?5.44%，均在抽样调查允许误差范围内。结论: 1）对估计主要林分因子贡献最大的激光雷达点云参数为累计高度80%分位数和点云高度中位数，其次为叶面积指数，点云强度和密度参数的作用不显著；2）应用误差变量联立方程组方法构建主要林分因子联立模型，可同时解决不同模型参数的相容性和不同林分因子估计的误差传递问题；3）所建13种森林类型的8项林分因子预估模型，可用于对全市乔木林小班主要林分因子的估计；4）基于激光雷达点云参数构建主要林分因子模型，其预估精度能够满足森林资源调查监测技术要求，可在生产实践中推广应用。

关键词: 激光雷达数据, 主要林分因子, 误差变量, 联立模型, 北京

Abstract:

Objective: The purpose of this study is to explore the feasibility of establishing models for major stand characteristics based on LiDAR data to estimate the factors of forest patches, providing a demonstration for promoting the application of LiDAR technology in integrated monitoring of the national forest and grassland. Method: Based on the LiDAR point cloud metrics and ground measured data of 1 966 forest plots in Beijing, the error-in-variable simultaneous equations were used to construct 8 forest factor estimation models for 13 forest types, including mean diameter at breast height (DBH), mean height, dominant height, stem number, basal area, stock volume, biomass and carbon storage. Additionally, based on the LiDAR point cloud metrics extracted from the 25 m×25 m grid cells within the forest patches in Beijing, the eight prediction models were used to estimate major stand characteristics of all forest patches. Result: 1) The LiDAR point cloud metrics that contributed the most to the estimation of major stand characteristics were 80% quantile of cumulative height and median point cloud height, followed by leaf area index. 2) The mean prediction errors (MPEs) of eight major stand characteristics models for 13 forest types were less than 15% in either self-validation or cross-validation. 3) Taking the forest as a whole, the determination coefficient (R²) of all eight prediction models were all above 0.7 (excluding the stem number per hectare), the MPEs were less than 3%, and the mean percentage standard errors (MPSEs) were less than 40%, among which the MPSEs of the mean DBH, mean height and dominant height models were about 15%. 4) According to the model inversion, the cumulative value of stock volume in all forest patches estimated by the volume model differed only by ?1.79% from that obtained by the integrated monitoring of the municipality. The differences between the stock volume of forest patches and the integrated monitoring results in the three sub-populations were only 1.04%, ?3.91% and ?5.44%, respectively, which were all within the allowable error range of sampling survey. Conclusion: 1) The LiDAR point cloud metrics that contribute the most to estimating the major stand characteristics are percentile 80 of heights distribution and median height, followed by leaf area index. However, the point cloud intensity and density metrics have no significant effect. 2) The method of error-in-variable simultaneous equations can be applied to construct the simultaneous models of major stand characteristics, which is able to solve both compatibility of different model parameters and error propagation of different stand characteristic estimates. 3) The eight prediction models for 13 forest types can be used to estimate the major stand characteristics of forest patches in Beijing. 4) The prediction accuracy of the major stand characteristics models based on LiDAR point cloud metrics can meet the technical requirements of forest resource inventory and monitoring, and the models can be applied in practice.

Key words: LiDAR data, major stand characteristics, error-in-variable, simultaneous models, Beijing

中图分类号:

S757

曾伟生,温雪香,付涵,孙乡楠,吕康梅,刘樯漪,王甜. 基于激光雷达的北京市主要林分因子联立模型构建与应用[J]. 林业科学, 2026, 62(4): 68-80.

Weisheng Zeng,Xuexiang Wen,Han Fu,Xiangnan Sun,Kangmei Lü,Qiangyi Liu,Tian Wang. Establishment and Application of Simultaneous Models for Estimating Major Stand Characteristics in Beijing Based on LiDAR Data[J]. Scientia Silvae Sinicae, 2026, 62(4): 68-80.

图/表 7

图1

表1

表2

13种森林类型的联立模型参数估计值①"

森林类型 Forest type	林分因子 Stand factor	解释变量 Explanatory variable	参数估计值Parameter estimates
森林类型 Forest type	林分因子 Stand factor	解释变量 Explanatory variable	a₀~g₀	a₁~f₁	a₂~c₂	a₃~c₃	a₄~c₄
油松林 Pinus tabuliformis forest (n=200)	D	X₁、X₃、X₅	10.213 0	0.202 2	0.187 6	0.037 8
	H_d	X₁、X₃	2.238 1	?0.099 2	0.795 9
	G	X₄、X₅	2.433 3	0.586 0	0.663 5
	V	X₁、X₃、X₅	11.427 0	0.690 2	0.364 9	0.682 1
	H		0.031 7	0.836 1
	B		0.474 7	0.988 2
	C		0.509 3
侧柏林 Platycladus orientalis forest (n=100)	D	X₁、X₃、X₅	4.912 8	0.679 5	0.271 0	?0.097 9
	H_d	X₁、X₃	4.914 1	0.441 9	0.230 5
	G	X₄、X₅	0.684 0	1.470 0	0.473 1
	V	X₄、X₅	1.612 7	1.864 2	0.438 7
	H		?0.149 7	0.861 4
	B		0.981 3	1.329 7
	C		0.484 3
针叶混交林 Coniferous mixed forest (n=100)	D	X₁、X₂、X₅	4.100 4	0.396 0	0.313 4	?0.104 4
	H	X₂、X₄	2.874 4	0.111 6	0.444 2
	G	X₁、X₅	2.128 2	1.039 6	0.472 6
	V	X₁、X₅	5.514 7	1.444 9	0.507 1
	H_d		0.290 5	1.244 1
	B		2.441 4	1.180 1
	C		0.489 9
栎树林 Quercus spp. forest (n=200)	D	X₂、X₅	4.273 6	0.561 0	?0.124 6
	H_d	X₂、X₄	2.878 6	0.895 1	?0.346 7
	G	X₃、X₅	8.005 4	1.120 4	0.081 3
	V	X₃、X₄	22.55 7	1.185 6	0.305 7
	H		0.345 2	0.767 9
	B		3.072 4	1.350 2
	C		0.480 3
桦木林 Betula spp. forest (n=88)	D	X₁、X₂	1.307 4	?0.229 7	1.121 6
	H_d	X₂	2.197 8	0.707 4
	G	X₃、X₄	1.013 2	0.121 3	1.253 8
	V	X₃、X₄	3.389 6	0.380 7	1.376 5
	H		0.058 6	0.817 9
	B		3.776 8	1.098 0
	C		0.484 1
杨树林 Populus spp. forest (n=200)	D	X₁、X₂	3.925 5	0.110 7	0.572 5
	H_d	X₂	5.228 9	0.446 9
	G	X₂	0.558 3	1.198 6
	V	X₂	2.066 6	1.495 0
	H		?0.582 8	0.926 8
	B		1.304 9	0.802 5
	C		0.472 5
榆树林 Ulmus spp. forest (n=100)	D	X₂、X₅	2.488 9	0.806 9	?0.031 4
	H_d	X₂	2.129 4	0.744 5
	G	X₄、X₅	0.446 3	1.428 0	0.161 8
	V	X₄、X₅	1.055 4	1.778 8	0.153 7
	H		?0.133 1	0.871 9
	B		0.895 1	1.100 1
	C		0.449 4
刺槐林 Robinia pseudoacacia forest (n=100)	D	X₂、X₅	2.774 1	0.762 0	?0.033 7
	H	X₂	2.952 8	0.566 8
	G	X₂	0.222 2	1.625 1
	V	X₂	0.772 8	1.838 0
	H_d		0.125 2	1.144 2
	B		1.434 7	1.341 0
	C		0.482 9
柳树林 Salix spp. forest (n=88)	D	X₁、X₂	1.296 6	?0.198 0	1.103 0
	H	X₂	1.775 8	0.713 7
	G	X₃、X₄	1.159 0	0.262 9	1.144 8
	V	X₃、X₄	4.007 4	0.501 8	1.259 7
	H_d		0.027 6	1.216 7
	B		2.998 3	1.107 9
	C		0.484 2
乔木经济林 Economic forest of trees (n=90)	D	X₃、X₅	13.525 0	0.561 5	?0.105 3
	H_d	X₃	8.457 3	0.369 2
	G	X₃	6.283 6	1.003 0
	V	X₃	24.672 0	1.225 4
	H		0.941 4	0.739 9
	B		2.849 4	1.782 5
	C		0.483 7
其他硬阔林 Other hard broad-leaved forest (n=300)	D	X₂、X₅	3.595 5	0.695 9	?0.010 3
	H_d	X₂	2.870 8	0.594 4
	G	X₂、X₄	0.389 2	0.323 5	1.297 2
	V	X₂、X₄	0.857 8	0.542 9	1.434 9
	H		0.116 4	0.878 1
	B		2.198 5	1.512 5
	C		0.483 5
其他软阔林 Other soft broad-leaved forest (n=100)	D	X₁、X₂、X₄、X₅	2.268 1	0.644 6	1.380 1	?1.149 3	?0.106 3
	H_d	X₂、X₅	1.885 4	0.774 4	?0.071 5
	G	X₂	0.102 6	2.060 6
	V	X₂	0.202 3	2.436 3
	H		0.460 6	0.796 8
	B		1.944 9	1.259 6
	C		0.480 8
阔叶混交林 Broad-leaved mixed forest (n=300)	D	X₁、X₂、X₄、X₅	2.860 9	0.242 6	1.044 8	?0.583 1	?0.131 5
	H	X₂、X₅	2.487 6	0.593 4	?0.037 7
	G	X₁、X₃、X₅	2.400 7	0.722 5	0.676 3	0.225 8
	V	X₁、X₃、X₅	7.772 3	0.923 4	0.899 9	0.206 3
	H_d		?0.520 6	1.286 7
	B		4.350 3	1.181 6
	C		0.478 8

表2

表3

图2

图3

图4

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特征数 Statistics	平均胸径 Mean diameter at breast height (D)/cm	平均高 Mean height (H)/m	优势高 Dominant height (H_d)/m	株数 Stem number (N)/ (tree·hm^?2)	断面积 Basal area (G)/(m²·hm^?2)	蓄积量 Stock volume (V)/(m³·hm^?2)	生物量 Biomass (B)/(t·hm^?2)	碳储量 Carbon storage (C)/ (t·hm^?2)
平均数Mean	14.0	8.8	10.3	771	10.8	59.0	68.8	33.2
最小值Min.	5.0	1.9	2.0	15	0.1	0.1	0.1	0.1
最大值Max.	44.8	27.4	28.1	4110	43.9	435.4	338.6	163.7
标准差Standard deviation （SD）	6.1	3.9	4.4	598	7.8	57.5	54.9	26.5
变动系数Coefficient of variation （CV）（%）	43.6	44.2	42.4	77.6	72.8	97.4	79.7	79.7

森林类型 Forest type	林分因子 Stand factor	自检结果Self-validation results						交叉检验结果Cross-validation results
森林类型 Forest type	林分因子 Stand factor	R²	SEE	TRE	ASE	MPE	MPSE	R²	SEE	TRE	ASE	MPE	MPSE
森林 Forest	D	0.731	3.20	1.97	1.75	1.01	15.52	0.715	3.27	2.05	2.05	1.03	15.88
	H	0.773	1.87	0.13	?0.71	0.94	15.27	0.760	1.91	0.13	?0.52	0.96	15.58
	H_d	0.766	2.14	0.08	?0.88	0.92	15.79	0.755	2.18	0.18	?0.60	0.93	15.94
	G	0.726	4.14	0.40	0.47	1.70	31.50	0.708	4.30	1.10	1.94	1.73	31.64
	N	0.536	416	3.55	3.70	2.39	38.73	0.517	430	4.48	5.11	2.42	39.38
	V	0.767	28.0	1.22	?2.43	2.10	34.28	0.752	28.9	1.61	?0.93	2.12	34.29
	B	0.703	30.4	?0.30	0.90	1.95	34.38	0.684	31.7	0.28	2.38	1.99	34.49
	C	0.701	14.7	?0.35	0.98	1.96	34.42	0.682	15.4	0.23	2.46	2.00	34.53
针叶林 Coniferous forest	D	0.683	2.15	1.06	1.33	1.74	13.35	0.662	2.22	1.00	1.35	1.80	13.81
	H	0.752	1.44	?0.31	?1.55	2.01	14.19	0.733	1.49	?0.16	?1.32	2.08	14.55
	H_d	0.723	1.84	?0.37	?1.81	2.12	15.80	0.705	1.89	?0.23	?1.58	2.18	16.10
	G	0.839	3.22	?0.98	1.05	2.79	21.42	0.832	3.29	?1.13	0.99	2.84	21.58
	N	0.538	368	2.85	4.45	3.83	31.05	0.511	379	2.83	4.81	3.95	31.83
	V	0.837	23.6	1.49	?1.43	4.06	23.59	0.829	24.1	1.32	?1.36	4.16	23.88
	B	0.806	22.4	?2.77	1.23	3.61	24.62	0.792	23.2	?3.01	1.25	3.73	25.05
	C	0.808	11.2	?2.81	1.20	3.61	24.40	0.794	11.6	?3.05	1.22	3.74	24.82
阔叶林 Broadleaved forest	D	0.727	3.41	2.17	1.85	1.17	16.07	0.712	3.49	2.28	2.23	1.19	16.41
	H	0.762	1.96	0.21	?0.50	1.06	15.55	0.748	2.01	0.18	?0.32	1.07	15.84
	H_d	0.761	2.21	0.17	?0.64	1.01	15.79	0.749	2.24	0.26	?0.35	1.02	15.90
	G	0.696	4.34	0.78	0.33	2.03	34.07	0.676	4.52	1.71	2.18	2.05	34.21
	N	0.524	427	3.79	3.50	2.92	40.69	0.508	442	5.02	5.18	2.94	41.31
	V	0.749	29.0	1.16	?2.68	2.42	37.01	0.732	30.0	1.68	?0.82	2.44	36.95
	B	0.680	32.1	0.26	0.82	2.25	36.87	0.659	33.5	1.01	2.67	2.27	36.91
	C	0.677	15.5	0.24	0.92	2.27	36.98	0.656	16.2	0.99	2.78	2.29	37.02

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