长白落叶松-水曲柳混交林单木叶面积预估模型

doi:10.12302/j.issn.1000-2006.202311012

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南京林业大学学报（自然科学版） ›› 2024, Vol. 48 ›› Issue (5): 235-245.doi: 10.12302/j.issn.1000-2006.202311012

长白落叶松-水曲柳混交林单木叶面积预估模型

王越(), 苗铮, 郝元朔, 刘鑫, 董利虎^*()

东北林业大学林学院,黑龙江哈尔滨 150040

收稿日期:2023-11-13 修回日期:2024-01-17 出版日期:2024-09-30 发布日期:2024-10-03
通讯作者: * 董利虎(lihudong@nefu.edu.cn),教授。
作者简介:
王越(1109364622@qq.com)。
基金资助:
国家重点研发计划(2022YFD2201001)

A single tree leaf area prediction model in the Larix olgensis and Fraxinus mandshurica mixed forest

WANG Yue(), MIAO Zheng, HAO Yuanshuo, LIU Xin, DONG Lihu^*()

Colleage of Forestry,Northeast Forestry University,Harbin 150040,China

Received:2023-11-13 Revised:2024-01-17 Online:2024-09-30 Published:2024-10-03

摘要/Abstract

摘要：

【目的】构建长白落叶松-水曲柳单木叶面积模型,以提升长白落叶松-水曲柳人工混交林单木叶面积的预测精度,了解模型变量与叶面积关系,为进一步研究林分生产力和树冠结构提供理论基础。【方法】选取黑龙江省尚志市不同混交比例长白落叶松-水曲柳混交林中111株落叶松以及113株水曲柳,测量其叶面积。采用全子集回归法建立两树种的非线性单木叶面积预估模型。通过相对权重法分析各变量对模型的贡献,同时考虑样地对叶面积的随机影响,构建混合效应模型,并对模型进行评价。【结果】相对权重计算结果显示,在最优模型中,胸径(D_BH)对长白落叶松和水曲柳单木叶面积的影响最大。考虑样地层次随机效应的最优长白落叶松单木叶面积混合效应模型包括冠长率(P_CR)、D_BH、林木树高与林分优势木平均高之比(P_HDH),模型调整后的决定系数( $R a d j 2$ )为0.89,均方根误差(RMSE)为11.68 m²,平均偏差(ME)为-0.202 7 m²,平均绝对偏差(MAE)为7.943 0 m²,预测精度(P_a)为99%;考虑样地层次随机效应的最优水曲柳单木叶面积混合效应模型包含P_CR、D_BH、P_HDH及冠幅(P_CW),模型的 $R a d j 2$ 为0.87,RMSE为13.61 m²,平均偏差(ME)为-0.281 7 m²,MAE为9.397 6 m²,P_a为99%,具有较好的拟合和预测效果。【结论】考虑样地水平的混合效应模型提升了两树种单木叶面积预测准确性,D_BH是影响单木叶面积最重要的变量,且在混交林叶面积模型中考虑林木竞争变量是有必要的,建立的模型可为准确预测长白落叶松和水曲柳单木叶面积提供技术支持,同时有助于深入研究林分的生长发育和树冠结构。

关键词: 长白落叶松-水曲柳混交林, 相对权重, 混合效应, 经验线性无偏最优预测法, 叶面积

Abstract:

【Objective】 Using tree-level variables and single-tree competition indicators, a nonlinear mixed-effects model was used to construct a single-tree leaf area model of Larix olgensis-Fraxinus mandshurica, providing a theoretical basis for further research on stand productivity and canopy structure.【Method】 A total of 111 Larix olgensis plants and 113 Fraxinus mandshurica plants were selected from different mixing proportions of Larix olgensis-Fraxinus mandshurica mixed forest in Shangzhi City, Heilongjiang Province, and their leaf areas were measured. The whole subset regression method was used to establish a nonlinear single-tree leaf area prediction model for the two tree species. The contribution of each variable to the model was analyzed through the relative weight method. Simultaneously, the random influence of the sample plot on leaf area was considered, a mixed effect model was constructed, and the model was evaluated.【Result】 The optimal mixed effect model of larch single-tree leaf area considering random effects at the plot level was composed of P_CR (crown ratio), D_BH (diameter at breast height, DBH), and P_HDH (ratio of forest tree height to the average height of dominant trees in the forest stand), including one random effect parameter. The $R a d j 2$ of the model was 0.89, root mean square error (RMSE) was 11.68 m², mean deviation (ME) was -0.202 7 m², mean absolute deviation (MAE) was 7.943 0 m², and prediction accuracy (P_a) was 99%. The optimal mixed effect model of ash single-tree leaf area considering the random effect at the plot level consists of P_CR, D_BH, P_HDH, and P_CW (crown width), including one random effect parameter, The $R a d j 2$ of the model was 0.87, RMSE was 13.61 m², ME was -0.281 7 m², MAE was 9.397 6 m², and P_a was 99%, all of which had good fitting effects. The relative weight calculation results showed that in the optimal model, D_BH was the variable that has the greatest impact on the single-tree leaf area of Larix olgensis and Fraxinus mandshurica. 【Conclusion】 The mixed effect model considering the plot level improves the accuracy of predicting the leaf area of single trees of the two tree species. DBH is the variable that has the greatest impact on the leaf area of a single tree. It is necessary to consider tree competition variables in leaf area models of mixed forests. The model constructed in this study can provide technical support for accurately predicting the leaf area of single trees of Larix olgensis-Fraxinus mandshurica and can help with conducting in-depth research on the growth, development, and crown structure of the forest stand.

Key words: Larix olgensis(larch)-Fraxinus mandshurica(ash) mixed forest, relative weight, mixed effect, empirical linear unbiased optimal prediction method, leaf area

中图分类号:

S758

王越,苗铮,郝元朔,等. 长白落叶松-水曲柳混交林单木叶面积预估模型[J]. 南京林业大学学报（自然科学版）, 2024, 48(5): 235-245.

WANG Yue, MIAO Zheng, HAO Yuanshuo, LIU Xin, DONG Lihu. A single tree leaf area prediction model in the Larix olgensis and Fraxinus mandshurica mixed forest[J].Journal of Nanjing Forestry University (Natural Science Edition), 2024, 48(5): 235-245.DOI: 10.12302/j.issn.1000-2006.202311012.

图/表 11

表1

表2

图1

图2

表3

长白落叶松与水曲柳单木叶面积备选模型表达式"

树种 species	模型编号 model No.	模型 model	调整后决定系数 $R a d j 2$	均方根误差/m² RMSE
长白落叶松 larch	1	S_CLA=1.4953 $P C R 0.9173 D B H 1.5534 P H D H 0.8080$	0.89	11.56
	2	S_CLA=14.655 7 $C L 0.4097 P R D B H 1.6628 P H D H 0.7934$	0.88	12.06
	3	S_CLA=0.716 3 $C L 0.9151 D B H 0.8979 P H D R - 0.9377$	0.88	12.07
	4	S_CLA=0.702 2 $P C R 0.9241 D B H 1.8228$	0.88	12.01
	5	S_CLA=57.322 2 $P C R 0.0459 P H D R - 1.9479 P H D H 2.6974$	0.86	12.62
水曲柳ash	6	S_CLA=2.372 8 $P C R 0.6330 D B H 1.3886 P H D H 0.7371 P C W 0.3144$	0.87	13.61
	7	S_CLA=1.593 4 $P C R 0.5771 D B H 1.4941 P C W 0.3881$	0.87	13.94
	8	S_CLA=1.894 4 $P C R 0.7249 D B H 1.5568 P H D H 0.9593$	0.87	13.97
	9	S_CLA=0.662 8 $C L 0.8338 D B H 1.1190 P H D R - 0.3027$	0.85	14.36
	10	S_CLA=8.976 4 $C L 0.9507 P H D R - 1.0210 P H D H 1.0996 P C W 0.4025$	0.86	14.44

表3

表4

图3

表5

图4

表6

长白落叶松与水曲柳单木叶面积模型评价"

项目 item	参数 parameter	模型(12) model(12)	模型(14) model(14)	模型(13) model(13)	模型(15) model(15)
	β₀	1.495 3	1.701 1	—	—
	β₁	0.917 3	0.989 9	—	—
	β₂	1.553 4	1.522 2	—	—
	β₃	0.808 0	1.088 8	—	—
固定参数	β₄	—	—	2.372 8	2.372 8
fixted parameter	β₅	—	—	0.633 0	0.633 0
	β₆	—	—	1.388 6	1.388 6
	β₇	—	—	0.737 1	0.737 1
	β₈	—	—	0.314 4	0.314 4
随机效应的方差-协方差矩阵 variance-covariance matrix for random effects	$σ b 2 2$	—	0.001 6	—	—
误差方差 variance of error	$σ b 8 2$	—	—	—	0.051 3
	σ₂	131.395 1	131.395 1	179.659 7	184.299 4
拟合优度 goodness of fit	RMSE/m²	11.68	11.68	13.71	13.61
	$R a d j 2$	0.88	0.89	0.87	0.87

表6

表7

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变量 variable	平均值 mean	标准差 SD	最小值 min	最大值 max
林龄/a stand age	18.20	3.41	11.00	25.00
林分密度/(株·hm^-2) stand density	2 150.00	492.00	1 580.00	3 600.00
平均胸径/cm mean DBH	11.39	2.10	7.35	15.73
平均树高/m mean HT	12.29	2.15	7.96	15.80
优势木平均树高/m mean HT of dominant tree	14.34	2.79	8.19	20.42
优势木平均胸径/cm mean DBH of dominant tree	14.12	3.00	8.48	17.81

变量 variable	长白落叶松 Larix olgensis				水曲柳Fraxinus mandshuria
变量 variable	平均值 mean	标准差 SD	最小值 min	最大值 max	平均值 mean	标准差 SD	最小值 min	最大值 max
胸径/cm DBH	12.67	5.09	2.00	23.60	10.73	4.36	1.80	20.70
树高/m HT	12.88	3.88	3.60	20.15	12.31	3.33	3.64	17.95
冠长/m CL	6.87	2.08	2.25	12.26	5.94	2.35	1.35	13.55
冠幅/m CW	1.22	0.33	0.57	2.03	1.30	0.48	0.23	2.80
冠长率CR	0.56	0.16	0.24	0.93	0.48	0.14	0.15	0.84
高径比HDR	1.09	0.25	0.71	2.20	1.25	0.31	0.70	2.24
相对树高RH	1.04	0.19	0.44	1.46	1.00	0.16	0.45	1.28
相对胸径RDBH	1.17	0.40	0.27	1.90	1.00	0.34	0.24	1.63
林木胸径与林分优势木胸径之比DDH	0.88	0.31	0.17	1.50	0.75	0.27	0.15	1.35
林木树高与林分优势木树高之比HDH	0.88	0.18	0.36	1.28	0.85	0.15	0.37	1.11
树冠叶面积/m² CLA	44.84	34.45	0.42	139.86	45.20	38.01	0.76	171.53

变量 values	相对权重/% weights
变量 values	模型(12) model (12)	模型(13) model (13)
P_CR	5.09	12.02
D_BH	52.95	36.45
P_HDH	41.96	29.75
P_CW	—	21.78

树种 species	模型 model	随机效应参数 random-effects parameters	参数个数 parameters numbers	赤池信息准则 AIC	贝叶斯信息准则 BIC	对数似然值 LogLik	似然比值 LRT	P
长白落叶松 larch	(12)		4	864.277 1	877.824 7	-427.138 5
	(12-1)	b₂	5	848.207 4	864.464 6	-418.103 7	18.069 7	<0.000 1
	(12-2)	b₂、b₃	6	850.931 0	872.607 2	-417.465 5	1.276 5	0.528 2
	(12-3)	b₁、b₂、b₃	7	852.534 5	882.339 4	-415.267 3	4.396 4	0.221 7
	(13)		5	917.574 5	933.938 9	-452.787 3
水曲柳ash	(13-1)	b₈	6	892.456 4	911.548 1	-439.228 2	27.118 1	<0.000 1
	(13-2)	b₅、b₆	7	894.092 9	918.639 4	-438.046 5	2.363 4	0.306 8

模型 model	平均误差/ m² ME	平均绝对误差/m² MAE	预估精度/% P_a
长白落叶松模型(12) CLA model of larch(12)	-0.587 3	8.325 9	98
长白落叶松最优混合效应模型(14) optimal mixed-effect model of larch(14)	-0.202 7	7.943 0	99
水曲柳单木叶面积模型(13) CLA model of ash(13)	0.134 6	9.918 7	99
水曲柳最优混合效应模型(15) optimal mixed-effect model of ash(15)	-0.281 7	9.397 6	99

长白落叶松-水曲柳混交林单木叶面积预估模型

A single tree leaf area prediction model in the Larix olgensis and Fraxinus mandshurica mixed forest

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