基于UAV-LiDAR的长白落叶松人工林单木断面积生长量估测模型研建

doi:10.11707/j.1001-7488.LYKX20250679

摘要/Abstract

摘要：

目的: 基于高密度无人机激光雷达（UAV-LiDAR）数据构建长白落叶松人工林单木胸高断面积生长量（$ \text{BAI} $）估测模型，评估UAV-LiDAR技术在单木水平生长建模中的应用潜力，为森林精准经营与碳汇动态评估提供新的技术方案和决策依据。方法: 以黑龙江省孟家岗林场不同年龄、密度和立地条件下的长白落叶松人工林为对象，提取UAV-LiDAR数据中的树冠结构和竞争指标作为主要变量，结合147株解析木断面积生长数据，采用相关性分析、前向逐步回归、共线性诊断与混合效应模型建模方法，建立基于UAV-LiDAR数据的单木生长量估测模型，同时构建基于实测数据的生长量估测模型，通过10折交叉验证比较两模型的预测精度。结果: UAV-LiDAR衍生的冠层竞争指标和树冠结构指标均与$ \text{BAI} $显著相关，其中光竞争指数（$ \text{LCI} $）和暴露冠表面积（$ \text{ECA} $）分别作为相关性最高的竞争和树冠结构变量，优于传统实地测量的胸径和竞争指标。基于UAV-LiDAR的单木断面积生长量估测模型拟合效果良好，调整后决定系数（$ R_{\mathrm{a}}^{2} $）达0.846，均方根误差（$ \text{RMSE} $）为1.35 cm²·a^–1，交叉验证结果显示，模型具有较好的稳健性和预测能力，其平均绝对误差（$ \text{MAE} $）和平均绝对百分比误差（$ \text{MAPE} $）分别为1.26 cm²·a^–1和25.7%，均低于基于实测数据构建的模型。结论: 单时相UAV-LiDAR数据在单木生长预测中展现出良好潜力，完全基于点云提取的变量能够有效量化驱动树木生长的树冠结构和冠层竞争机制，所构建的模型可为单木水平的生长预测和经营决策提供可靠的理论依据和技术支持。

关键词: 无人机激光雷达, 冠层竞争, 树冠结构, 单木生长量估测模型, 长白落叶松人工林

Abstract:

Objective: This study aims to construct a breast height basal area increment (BAI) estimation model for individual trees of Larix olgensis plantations by using high-density UAV-LiDAR data, in order to evaluate the application potential of UAV-LiDAR in individual tree growth modeling. Method: The study was conducted in L. olgensis plantations with various ages, densities, and site conditions in Mengjiagang Forest Farm in Heilongjiang Province. The crown structure and competition indices derived from UAV-LiDAR data served as primary variables, integrated with $ \text{BAI} $ data obtained from 147 stem-analyzed trees. A modeling method based on correlation analysis, forward stepwise regression, collinearity diagnostics, and mixed-effects model was employed to develop an UAV-LiDAR-based individual tree growth model. A field-measurement-based model was also constructed for comparison. Predictive accuracy of the two models was evaluated and compared using 10-fold cross-validation. Result: There were significant correlations between the UAV-LiDAR-derived canopy competition and crown structure variables and $ \text{BAI} $. Among them, the light competition index ($ \text{LCI} $) and exposed crown surface area ($ \text{ECA} $) were the highest correlated variables of competition and canopy structure, respectively, outperforming traditional field-measured diameter at breast height and competition indices. The UAV-LiDAR-based individual BAI estimation model achieved a satisfactory goodness-of-fit, with adjusted coefficient of determination ($ R_{\mathrm{a}}^{2} $) of 0.846 and a root mean square error ($ \text{RMSE} $) of 1.35 cm²·a^–1. The results of cross validation showed that the UAV-LiDAR-based model possessed good robustness and predictive capability, yielding a mean absolute error ($ \text{MAE} $) of 1.26 cm²·a^–1 and a mean absolute percentage error ($ \text{MAPE} $) of 25.7%, which were lower than those of the field-measurement-based model. Conclusion: The uni-temporal UAV-LiDAR data has shown great potential in accurately predicting individual tree growth. Variables entirely derived from UAV-LiDAR can effectively quantify the crown structure and competition mechanisms driving tree growth. The developed model provides a theoretical foundation and technical support for individual tree-level growth prediction and forest management decision-making.

Key words: unmanned aerial vehicle light detection and ranging (UAV-LiDAR), canopy competition, crown structure, individual tree growth model, Larix olgensis plantation

中图分类号:

S758

刘鑫,郝元朔,董利虎,赵颖慧,李凤日. 基于UAV-LiDAR的长白落叶松人工林单木断面积生长量估测模型研建[J]. 林业科学, 2026, 62(8): 11-20.

Xin Liu,Yuanshuo Hao,Lihu Dong,Yinghui Zhao,Fengri Li. Development of a Basal Area Growth Estimation Model for Individual Trees of Larix olgensis Plantations based on UAV-LiDAR Data[J]. Scientia Silvae Sinicae, 2026, 62(8): 11-20.

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参数Parameters	规格Specification
激光雷达传感器LiDAR sensor	RIEGL VUX-1UAV
无人机平台Unmanned aerial vehicle platform	DJI Matrice 600 Pro
激光脉冲频率Laser frequency/kHz	550
最大回波数Maximum echo number	5
视场角Field of view/(°)	330
扫描速度scanning speed/(scans·s^–1)	200
距地面飞行高度Flying altitude/m	80
飞行速度Flying speed/(m·s^–1)	8
航带重叠宽度Strip interval/m	80
扫描角Scan angle/(°)	± 45
平均点云密度Mean point density/(pt·m^–2)	1 000

变量类型Variable type	变量Variable	均值Mean	标准差SD	最小值Min.	最大值Max.
单木变量 Individual tree variables	胸径Diameter at breast height ($ D $)/cm	16.4	7.0	5.5	33.4
	树高Tree height ($ H $)/m	17.3	6.2	6.9	28.8
	冠幅Crown width ($ \text{CW} $)/m	2.6	1.1	0.7	6.9
	枝下高Height to crown base ($ \text{HCB} $)/m	4.8	2.2	0.5	14.3
	断面积增量Basal area increment ($ \text{BAI} $)/(cm²·a^–1)	4.88	3.51	0.27	16.59
林分变量 Stand variables	林分年龄Stand age ($ \text{Age} $)/a	36	16	13	62
	林分密度Stand density ($ \text{SD} $)/(tree·hm^–2)	1 406	732	249	3 033
	林分平均胸径Mean diameter at breast height (D_g)/cm	17.5	5.8	8.8	31.5
	林分断面积Stand basal area ($ \text{BAS} $)/(m²·hm^–2)	36.8	11.5	15.7	64.8
	林分优势高Dominant height (H_d)/m	22.3	5.5	12.5	32.0
竞争指标 Competition indices	大于对象木断面积和Basal area in larger trees ($ \text{BAL} $)/(m²·hm^–2)	24.1	12.5	0.0	60.4
	Hegyi竞争指数Hegyi competition index ($ \text{Hegyi} $)	7.4	5.2	0.0	21.6
	基于高差的竞争指数 Height-difference-based competition index （($ \text{HCI} $)	24.2	16.6	0.0	63.7

参数 Parameter		基于UAV-LiDAR 数据的模型 UAV-LiDAR- based model	基于实测数据的模型 Field-measured- based model
固定效应参数估计值（标准误） Fixed-effects parameter estimates (standard errors)	$ {\beta }_{0} $	3.62 (0.866)	0.976 (0.364)
	$ {\beta }_{1} $	–0.772 (0.252)	8.52×10^–2 (1.32×10^–2)
	$ {\beta }_{2} $	2.69×10^–3 (8.59×10^–4)	–0.108 (1.59×10^–2)
	$ {\beta }_{3} $	–1.42 (0.267)	–1.40×10^–2 (4.57×10^–3)
	$ {\beta }_{4} $	–2.78×10^–2 (6.81×10^–3)	–6.63×10^–4 (1.03×10^–4)
	$ {\beta }_{5} $	4.47×10^–2 (1.22×10^–2)	3.91×10^–2 (1.61×10^–2)
	$ {\beta }_{6} $	–3.02 (1.35)	—
随机效应参数方差估计值 Variance of random effects parameter estimates	$ \sigma _{{u}_{0}}^{2} $	0.226	7.38×10^–2
	$ \sigma _{{u}_{1}}^{2} $	0.193	4.23×10^–5
	$ {\sigma }_{{{u}_{0}}{{,u}_{1}}} $	–0.207	–1.48×10^–3
	$ \gamma $	–0.216	–8.76×10^–2
	$ \text{CF} $	1.06	1.06
拟合统计量 Fitting statistics	$ {R}_{\mathrm{a}}^{2} $	0.846	0.741
	$ \text{RMSE} $/ (cm²·a^–1)	1.35	1.76
	$ \text{AIC} $	178	215

检验指标 Validation metrics	基于UAV-LiDAR 数据的模型 UAV-LiDAR-based model	基于实测数据的模型 Field-measured-based model
$ \text{ME} $	–0.11	0.01
$ \text{MAE} $	1.26	1.51
$ \text{MPE}(\% ) $	–2.2	0.2
$ \text{MAPE}(\% ) $	25.7	30.9

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