Tree crown length prediction models for Larix olgensis and Fraxinus mandshurica in mixed plantations with different mixing methods

doi:10.12302/j.issn.1000-2006.202005043

JOURNAL OF NANJING FORESTRY UNIVERSITY ›› 2021, Vol. 45 ›› Issue (4): 13-22.doi: 10.12302/j.issn.1000-2006.202005043

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Tree crown length prediction models for Larix olgensis and Fraxinus mandshurica in mixed plantations with different mixing methods

HE Mengying¹^,²(), DONG Lihu¹, LI Fengri¹^,^*()

1. Key Laboratory of Sustainable Forest Ecosystem Management-Ministry of Education, School of Forestry, Northeast Forestry University, Harbin 150040, China
2. Forestry Investigation and Planning Institute of Jilin Province, Changchun 130022, China

Received:2020-05-25 Accepted:2020-08-06 Online:2021-07-30 Published:2021-07-30
Contact: LI Fengri E-mail:hemy1994@126.com;fengrili@126.com

Abstract

Abstract:

【Objective】 To accurately predict the crown length of Larix olgensis and Fraxinus mandshurica trees mixed by rows with four different mixing methods (1∶1, 2∶2, 3∶3, 5∶5), crown length models for L. olgensis and F. mandshurica were developed using simultaneous equation models. 【Method】 The data for sample trees of L. olgensis and F. mandshurica in mixed stands were collected from 54 permanent sample plots in the Shangzhi Administrative Bureau of National Forestry Centers in Heilongjiang Province. The best crown length model was selected from three nonlinear basic models, and the Mitscherlich model was selected as the basic model of the height-diameter model. The mixed proportion (Z_i) and the tree position (K) in mixed rows were taken as dummy variables. Other tree variables, as well as stand variables and competition factors were also added. Based on the optimal crown length and height-diameter model, the simultaneous equations model of the crown length and height were developed, respectively. The nonlinear seemingly uncorrelated regression (NSUR) method was used to estimate the parameters, and the fitting effects of the models was evaluated. 【Result】The ratio of the total tree height to DBH was negatively correlated with the crown length of L. olgensis, and the ratio of tree height to dominant tree height was positively correlated with the crown length of L. olgensis. The height-diameter ratio was negatively correlated with the crown length of F. mandshurica and the ratio of tree diameter at breast height to dominant tree diameter was positively correlated with the crown length of F. mandshurica. The average stand height of L. olgensis was positively correlated with the height of L. olgensis, while the dominant tree height of F. mandshurica was positively correlated with the height of F. mandshurica. For the simultaneous equations, the adjusted coefficients of determination ( $R a 2$ ) of the crown length and height of L. olgensis were 0.478 1 and 0.821 6, respectively. For the simultaneous equations, the $R a 2$ of the crown length and height of F. mandshurica were 0.395 8 and 0.752 9, respectively. 【Conclusion】 Constructing a simultaneous equation system for the crown length and tree height not only has good fitting effects and prediction accuracy, but also solves the problem of the inherent correlation between the crown length and height. Therefore, the crown length models established in this study can accurately predict the crown length of L. olgensis and F. mandshurica in the rows of mixed plantations, thereby providing a basis for a further study on the crown structure in mixed plantations.

Key words: mixed plantation, Larix olgensis, Fraxinus mandshurica, simultaneous equation, crown length model

CLC Number:

S758

HE Mengying, DONG Lihu, LI Fengri. Tree crown length prediction models for Larix olgensis and Fraxinus mandshurica in mixed plantations with different mixing methods[J]. JOURNAL OF NANJING FORESTRY UNIVERSITY, 2021, 45(4): 13-22.

Figures/Tables 10

Table 1

Table 2

Table 3

Candidate models of crown length"

模型编号 No. of model	表达式 expression	模型形式 model form	因变量的范围 range of dependent variable
Ⅰ	L_C= H $1 - exp (- aX)$	单分子式	(-∞, H)
Ⅱ	L_C= H $1 - c exp (- aX)$	单分子式	(-∞, H)
Ⅲ	L_C= H/ $1 + exp (- aX)$	Logistic形式	(0, H)

Table 3

Table 4

Table 5

Results of goodness of fit and validation of crown length and height-diameter models for Larix olgensis and Fraxinus mandshurica"

模型 models	拟合优度 goodness of fitting		检验结果 validation result
模型 models	$R a 2$	σ(RMSE)/ m	σ(ME)/ m	σ(MAE)/ m	σ(TRE)/ %
(12)	0.481 7	1.188 5	0.302 0	0.939 8	0.197 4
(13)	0.395 2	2.016 9	0.025 0	1.158 6	-2.089 6
(14)	0.821 4	1.142 8	-0.064 3	0.851 5	-0.293 7
(15)	0.752 9	1.181 5	0.027 2	0.925 3	-0.288 5

Table 5

Table 6

Table 7

Results of goodness of fit and validation of simultaneous equations model (16) and model (17)"

模型 models	变量 variable	拟合优度 goodness of fitting		检验结果 validation result
模型 models	变量 variable	$R a 2$	σ(RMSE)/ m	σ(ME)/ m	σ(MAE)/ m	σ(TRE)/ %
(16)	L_Lar	0.478 1	1.192 7	0.298 1	0.942 4	0.134 6
	H_Lar	0.821 6	1.143 1	-0.062 6	0.851 4	-0.283 6
(17)	L_Fra	0.395 8	1.424 6	0.022 0	1.159 9	-2.098 0
	H_Fra	0.752 9	1.181 5	0.035 0	0.925 8	-0.268 8

Table 7

Fig.1

Fig.2

Fig.3

References 25

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变量 variable	最小值 min.	最大值 max.	平均值 mean	标准差 SD	变异系数/% CV
D_g/cm	7.35	14.73	10.91	1.92	17.63
H_g/m	7.96	15.80	12.47	2.24	17.97
H_gLar/m	7.17	15.87	11.75	2.16	18.37
H_gFra/m	6.67	15.79	10.39	2.00	19.22
D_0Lar/cm	8.47	21.14	15.73	2.74	17.39
D_0Fra/cm	9.36	21.13	14.43	2.65	18.34
H_0Lar/m	7.78	19.37	14.39	2.52	17.51
H_0Fra/m	9.41	19.07	14.81	2.50	16.91
N/(株·hm^-2)	1 207	3 600	2 060	460	22
N_Lar/(株·hm^-2)	240	1 727	763	335	44
N_Fra/(株·hm^-2)	380	2 667	1 220.25	388	32
A_Lar/a	11	26	19	4	21
A_Fra/a	11	26	19	4	21

树种 species	数据类型 data type		变量 variable		最小值 min.		最大值 max.		平均值 mean		标准差 SD		变异系数/% CV
长白落叶松 L. olgensis	拟合数据 fitting data		D_BH/cm		5.00		25.10		11.31		3.27		28.94
			H/m		4.20		19.40		11.82		2.71		22.90
			L_C/m		0.90		13.30		4.90		1.65		33.74
			r_HD		0.48		2.46		1.08		0.20		18.21
			C_R		0.09		0.90		0.42		0.13		30.24
			H_CBLar/m		0.90		14.00		6.92		2.27		32.72
	检验数据 validation data		D_BH/cm		5.00		25.60		11.66		3.43		29.38
			H/m		5.00		20.60		12.02		2.87		23.86
			L_C/m		0.80		11.60		5.25		1.61		30.73
			r_HD		0.51		2.32		1.06		0.20		18.47
			C_R		0.08		0.86		0.45		0.14		30.84
			H_CBLar/m		1.10		14.40		6.77		2.54		37.52
树种 species		数据类型 data type		变量 variable		最小值 min.		最大值 max.		平均值 mean		标准差 SD	变异系数/% CV
水曲柳 F. mandshurica		拟合数据 fitting data		D_BH/cm		5.00		25.30		10.26		2.87	27.99
				H/m		5.70		20.00		12.79		2.38	18.59
				L_C/m		0.60		14.80		5.69		1.83	32.21
				r_HD		0.60		2.69		1.29		0.24	18.36
				C_R		0.06		0.94		0.45		0.12	27.37
				H_CBFra/m		0.60		14.00		7.10		2.06	29.02
		检验数据 validation data		D_BH/cm		5.00		22.20		9.81		2.83	28.83
				H/m		4.10		18.90		12.46		2.53	20.29
				L_C/m		0.70		14.40		5.57		1.88	33.82
				r_HD		0.61		2.42		1.32		0.24	18.58
				C_R		0.07		0.90		0.45		0.13	28.74
				H_CBFra/m		0.80		12.40		6.89		2.16	31.39

模型 models	参数 parameter
模型 models	b₁	b₂	b₃	p	s₁	s₂	s₃	s₄
(12)	-0.092 6 (0.004 2)	-1.340 5 (0.053 9)	2.349 6 (0.092 6)	0.014 2 (0.015 9)	0.441 9 (0.078 3)	0.326 9 (0.077 7)	0.255 3 (0.077 0)	0.070 7 (0.076 3)
(13)	-0.030 8 (0.004 0)	0.080 8 (0.044 4)	1.267 6 (0.083 8)	0.062 6 (0.015 9)	-0.766 6 (0.101 2)	-0.936 4 (0.102 4)	-0.802 9 (0.099 2)	-1.046 7 (0.100 0)
(14)	5.303 1 (0.215 7)	0.096 6 (0.006 7)	0.936 9 (0.022 9)	0.013 7 (0.009 2)	-0.169 1 (0.030 8)	-0.219 0 (0.026 8)	-0.164 0 (0.028 7)	-0.172 5 (0.028 3)
(15)	25.123 6 (0.978 2)	0.037 8 (0.003 2)	-0.037 3 (0.002 7)	0.016 4 (0.004 0)	0.212 9 (0.029 3)	0.208 0 (0.029 0)	0.234 2 (0.030 8)	0.216 7 (0.030 3)

模型 models	变量 variable	b₁	b₂	b₃	p	s₁	s₂	s₃	s₄
(16)	L_Lar	-0.088 3 (0.004 2)	-1.436 4 (0.054 2)	2.038 2 (0.092 0)	0.012 4 (0.015 9)	0.761 4 (0.078 4)	0.643 3 (0.077 8)	0.567 2 (0.077 1)	0.386 1 (0.076 4)
	H_Lar	5.101 3 (0.207 6)	0.103 1 (0.006 7)	0.929 5 (0.021 2)	0.014 4 (0.009 8)	-0.141 9 (0.032 8)	-0.196 6 (0.028 8)	-0.139 7 (0.030 6)	-0.147 2 (0.030 4)
(17)	L_Fra	-0.030 2 (0.004 0)	0.116 1 (0.044 4)	1.300 4 (0.083 8)	0.062 8 (0.015 9)	-0.840 7 (0.101 2)	-1.012 1 (0.102 3)	-0.875 5 (0.099 2)	-1.121 4 (0.100 0)
	H_Fra	25.194 6 (0.989 6)	0.037 6 (0.003 2)	-0.037 1 (0.002 7)	0.016 3 (0.004 0)	0.210 4 (0.029 2)	0.205 7 (0.028 9)	0.231 8 (0.030 7)	0.214 2 (0.030 2)

Tree crown length prediction models for Larix olgensis and Fraxinus mandshurica in mixed plantations with different mixing methods

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