赣中天然闽楠单木冠幅预测模型的研究

doi:10.12302/j.issn.1000-2006.202006045

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南京林业大学学报（自然科学版） ›› 2022, Vol. 46 ›› Issue (1): 88-96.doi: 10.12302/j.issn.1000-2006.202006045

赣中天然闽楠单木冠幅预测模型的研究

单凯丽(), 臧颢, 潘萍, 宁金魁, 欧阳勋志^*()

鄱阳湖流域森林生态系统保护与修复国家林业和草原局重点实验室,江西农业大学林学院,江西南昌 330045

收稿日期:2020-06-26 接受日期:2020-09-24 出版日期:2022-01-30 发布日期:2022-02-09
通讯作者: 欧阳勋志
基金资助:
国家林业公益性行业科研专项项目(201504301);国家自然科学基金项目(31760207)

Individual tree crown width prediction models for natural Phoebe bournei in central Jiangxi Province

SHAN Kaili(), ZANG Hao, PAN Ping, NING Jinkui, OUYANG Xunzhi^*()

Key Laboratory of National Forestry and Grassland Administration for the Protection and Restoration of Forest Ecosystem in Poyang Lake Basin, College of Forestry, Jiangxi Agricultural University, Nanchang 330045, China

Received:2020-06-26 Accepted:2020-09-24 Online:2022-01-30 Published:2022-02-09
Contact: OUYANG Xunzhi

摘要/Abstract

摘要：

【目的】探讨竞争指标和建模方法对天然闽楠(Phoebe bournei)单木冠幅预测模型的影响,以期为精准预测天然闽楠单木的冠幅提供参考。【方法】以江西省赣中25块闽楠天然次生林典型样地中的1 011株闽楠为研究对象,采用普通最小二乘法(OLS模型)、仅考虑样地水平的混合效应模型、增强回归树和随机森林4种建模方法建立单木冠幅模型,分别添加林分每公顷断面积、大于对象木的断面积之和、林分密度指数和简单竞争指数4种竞争指标,分析竞争指标对冠幅模型的影响,采用决定系数(R²)、均方根误差(RMSE)、平均相对误差绝对值(RMA)和平均绝对误差(MAE)确定最佳模型。【结果】不添加竞争指标时,模型的预测能力表现为:混合效应模型>OLS模型>增强回归树>随机森林;添加竞争指标时,最优模型表现为:混合效应模型>OLS模型>随机森林>增强回归树。OLS模型中添加大于对象木的断面积之和竞争指标时预测能力最佳;增强回归树中添加固定半径为7 m的简单竞争指数时预测能力最佳;随机森林中添加林分每公顷断面积竞争指标时预测能力最佳;混合效应模型不添加竞争指标时预测能力最佳(RMSE为0.846 0,RMA为0.211 1,MAE为0.650 1),并且都优于其他模型。【结论】研究结果可对天然闽楠单木冠幅生长进行精准预测,并为提高闽楠天然次生林的林分质量提供理论依据。

关键词: 闽楠, 冠幅模型, 竞争指标, 混合效应模型, 刀切法

Abstract:

【Objective】 The influence of competitive indices and modeling methods on the prediction of individual tree crowns of natural Phoebe bournei in Jiangxi Province was discussed to provide a reference for accurately predicting the crown width of natural Phoebe bournei.【Method】An individual crown width model was developed based on a dataset comprising 1 011 Phoebe bournei from 25 typical plots of natural secondary Phoebe bournei forest located in Jiangxi Province. The individual tree crown width model was established using four modeling methods: ordinary least squares (OLS) model, mixed effects model, boosted regression trees, and random forest. Four competitive indices, namely, basal area, basal area of larger trees, stand density, and simple competition, were added to reflect the influence of competition on the crown width model. The model evaluation criteria included determination coefficient (R²), root-mean-square error (RMSE), relative mean absolute error (RMA) and mean absolute error (MAE).【Result】The results demonstrated that when no competition index was added, the order of model accuracy was mixed effects model > OLS model > boosted regression trees > random forest; when the competition index was added, the optimal model was as follows: mixed effects model > OLS model> random forest > boosted regression trees (BRT). The OLS model had the best predictive ability when the basal area of larger trees was added; the BRT had the best predictive ability when a simple competition index with a fixed radius of 7 m was added; the random forest had the best predictive ability when the basal area was added. The mixed effects model had the best predictive ability when no competitive index was added (RMSE is 0.846 0, RMA is 0.211 1, MAE is 0.650 1), and it was superior to the other models. 【Conclusion】The results of this study accurately predicted the growth of Phoebe bournei individual tree crowns, thereby providing a theoretical basis for improving the forest quality of natural secondary Phoebe bournei forest.

Key words: Phoebe bournei, crown width model, competitive index, mixed effect model, Jack knife

中图分类号:

S758.5

单凯丽,臧颢,潘萍,等. 赣中天然闽楠单木冠幅预测模型的研究[J]. 南京林业大学学报（自然科学版）, 2022, 46(1): 88-96.

SHAN Kaili, ZANG Hao, PAN Ping, NING Jinkui, OUYANG Xunzhi. Individual tree crown width prediction models for natural Phoebe bournei in central Jiangxi Province[J].Journal of Nanjing Forestry University (Natural Science Edition), 2022, 46(1): 88-96.DOI: 10.12302/j.issn.1000-2006.202006045.

图/表 6

表1

表2

备选基础模型"

模型 model	模型表达式 model equation	模型形式 model form	模型 model	模型表达式 model equation	模型形式 model form
M1	C_W=a₀+b₀D_BH	线性 Linear	M7	C_W=exp(a₀+b₀D_BH)	Growth
M2	C_W=a₀+b₀D_BH+c₀ $D BH 2$	二次型 Quadratic	M8	C_W=a₀[1-exp(-b₀D_BH) $] c 0$	Richards
M3	C_W=a₀ $D BH b 0$	幂函数 Power	M9	C_W=a₀/[1+b₀exp(-c₀D_BH)]	Logistic
M4	C_W=a₀[1-exp(-b₀D_BH)]	Monomolecular	M10	C_W=a₀/[1+exp[b₀+β₂ln(D_BH+1)]]	Logistic
M5	C_W=[D_BH/(a₀+b₀D_BH)]²	Hossfeld 1	M11	C_W=a₀[1-exp(-b₀ $D BH c 0$ )]	Weibull
M6	C_W=a₀( $b 0 D BH$ )	Compound

表2

表3

表4

图1

表5

模型参数、方差估计值及评价指标"

项目 item	参数 parameter	OLS模型 OLS model	混合效应模型 mixed effect model
固定参数 fixed parameter	a₀	1.431 366	1.222 190
	b₀	0.134 100	0.222 282
	b₁	0.022 591	—
	c₀	0.001 121	-0.002 181
方差组成 composition of variance	$σ a 0$	—	0.192 855
	$σ b 0$	—	0.011 628
	$σ c 0$	—	0.000 010
	$σ a 0 b 0$	—	-0.027 466
	$σ a 0 c 0$	—	0.000 925
	$σ b 0 c 0$	—	-0.000 313
评价指标 evaluation indexes	R²	0.727 9	0.851 0
	σ(RMSE)	1.149 1	0.850 3
	σ(RMA)	0.281 3	0.217 5
	σ(MAE)	0.829 9	0.614 5

表5

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统计量 statistic quantity	闽楠单木 Phoebe bournei individual			林分 stand
统计量 statistic quantity	胸径/cm DBH	树高/m height	冠幅/m crown width	平均胸径/cm average DBH	平均树高/m average height	平均冠幅/m average crown width	密度/ (株·hm^-2) density
平均值 mean	10.10	8.20	2.60	11.80	9.20	3.30	1 657.70
标准差 SD	8.84	3.92	1.93	3.85	1.92	1.22	733.12
最小值 min.	2.00	1.90	0.50	6.60	6.20	1.70	50.00
最大值 max.	69.60	32.00	22.50	24.10	15.00	7.50	2 800.00

模型 model	建模数据 fitting data												检验数据 validation data
	R²			σ(RMSE)			σ(RMA)			σ(MAE)			σ(RMSE)			σ(RMA)			σ(MAE)
	平均值 mean	标准差 SD	平均值 mean		标准差 SD	平均值 mean		标准差 SD	平均值 mean		标准差 SD	平均值 mean		标准差 SD	平均值 mean		标准差 SD	平均值 mean		标准差 SD
M1	0.718 5	0.011 9	1.167 4		0.020 6	0.281 1		0.003 5	0.833 6		0.016 7	1.258 7		0.499 4	0.279 7		0.093 9	0.950 6		0.359 2
M2	0.722 7	0.012 8	1.158 6		0.020 7	0.280 1		0.003 5	0.832 1		0.016 7	1.255 6		0.518 3	0.279 7		0.093 1	0.944 3		0.353 0
M3	0.692 7	0.010 9	1.220 1		0.025 2	0.303 4		0.004 9	0.855 3		0.019 0	1.338 3		0.582 9	0.301 7		0.127 9	1.006 9		0.421 0
M4	0.627 0	0.015 9	1.343 9		0.028 5	0.462 7		0.018 4	0.973 8		0.025 6	1.494 5		0.666 2	0.435 6		0.245 1	1.145 0		0.476 2
M5	0.562 9	0.010 8	1.455 6		0.040 1	0.460 3		0.026 0	1.001 0		0.030 4	1.547 2		0.815 8	0.442 4		0.269 9	1.181 9		0.546 7
M6	0.664 8	0.016 9	1.273 8		0.022 9	0.310 8		0.003 6	0.959 1		0.015 4	1.309 4		0.548 0	0.294 2		0.097 7	0.980 7		0.381 1
M7	0.664 8	0.016 9	1.273 8		0.022 9	0.310 8		0.003 6	0.959 1		0.015 4	1.309 4		0.548 0	0.294 2		0.097 7	0.980 7		0.381 1
M9	0.708 8	0.013 1	1.187 4		0.020 7	0.291 1		0.003 3	0.866 1		0.015 7	1.277 3		0.540 5	0.284 1		0.092 9	0.957 8		0.344 6

模型类型 model	竞争指标 competitive index	σ(RMSE)		σ(RMA)		σ(MAE)
模型类型 model	竞争指标 competitive index	平均值 mean	标准差 SD	平均值 mean	标准差 SD	平均值 mean	标准差 SD
OLS模型 OLS model	无	1.255 6	0.518 3	0.279 7	0.093 1	0.944 3	0.353 0
	A_B	1.284 3	0.490 6	0.280 6	0.097 0	0.956 9	0.338 2
	A_BL	1.230 1	0.521 3	0.276 6	0.101 5	0.926 8	0.359 5
	I_SD	1.267 4	0.462 3	0.278 9	0.093 8	0.943 2	0.308 4
	H_egyi(N=1)	1.259 0	0.524 8	0.280 6	0.095 0	0.946 3	0.356 7
	H_egyi(R=1)	1.261 1	0.524 6	0.280 9	0.094 7	0.954 4	0.012 9
混合效应模型 mixed effects model	无	0.846 0	0.321 8	0.211 1	0.056 5	0.650 1	0.258 1
	A_B	0.894 8	0.331 0	0.219 0	0.052 8	0.690 9	0.263 6
	A_BL	0.846 4	0.314 9	0.211 7	0.054 4	0.649 2	0.251 4
	I_SD	0.895 7	0.333 7	0.218 9	0.052 5	0.691 8	0.266 8
	H_egyi(N=1)	0.848 6	0.322 2	0.211 4	0.055 5	0.652 1	0.255 6
	H_egyi(R=1)	0.839 1	0.317 6	0.210 8	0.056 6	0.649 0	0.263 8
增强回归树 BRT	无	1.502 0	0.627 8	0.311 5	0.113 2	1.067 6	0.446 5
	A_B	1.555 2	0.595 3	0.349 9	0.115 8	1.133 8	0.429 5
	A_BL	1.526 1	0.621 1	0.323 6	0.114 3	1.084 9	0.430 1
	I_SD	1.539 4	0.553 4	0.351 2	0.112 0	1.131 4	0.403 4
	H_egyi(N=4)	1.476 3	0.574 6	0.306 6	0.112 0	1.057 4	0.420 1
	H_egyi(R=7)	1.459 9	0.536 9	0.305 2	0.113 2	1.051 5	0.416 4
随机森林 RF	无	1.567 6	0.656 8	0.340 2	0.109 3	1.140 9	0.465 9
	A_B	1.400 6	0.468 3	0.320 2	0.074 8	1.058 2	0.281 0
	A_BL	1.488 8	0.606 6	0.319 2	0.099 2	1.090 4	0.387 5
	I_SD	1.529 4	0.645 8	0.335 8	0.101 4	1.111 4	0.361 6
	H_egyi(N=8)	1.455 1	0.650 2	0.330 4	0.109 5	1.094 4	0.518 3
	H_egyi(R=6)	1.460 1	0.687 6	0.331 9	0.108 3	1.110 1	0.547 7

赣中天然闽楠单木冠幅预测模型的研究

Individual tree crown width prediction models for natural Phoebe bournei in central Jiangxi Province

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