Bark thickness prediction models for larch plantation

doi:10.3969/j.issn.1000-2006.201810024

JOURNAL OF NANJING FORESTRY UNIVERSITY ›› 2019, Vol. 43 ›› Issue (6): 97-104.doi: 10.3969/j.issn.1000-2006.201810024

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Bark thickness prediction models for larch plantation

JIA Weiwei(), LIANG Yuzhao, LI Fengri^*()

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

Received:2018-10-15 Revised:2019-04-21 Online:2019-11-30 Published:2019-11-30
Contact: LI Fengri E-mail:JIAWW2002@163.com;fengrili@126.com

Abstract

Abstract:

【Objective】The prediction model of bark factor and bark thickness at any height of larch plantation was established in order to predict bark thickness more accurately and provide more accurate prediction model and guidance for actual wood production and forest management.【Method】Based on 1 186 disk data of 49 artificial larch trees in Mengjiagang Forest Farm of Jiamusi City, Heilongjiang Province in 2015, the bark thickness (bark factor, bark thickness at any height) of larch plantation linear mixed effects prediction model was constructed using the MIXED module in SAS 9.4 software. The model evaluation indicators were Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), -2 log likelihood (-2LL) and likelihood ratio test (LRT). 【Result】For the bark factor model, the bark factor model with b₁,b₂, b₄ and random parameter combination is the optimal mixed model based on the tree effect, and the model with b₁, b₂ random parameter combination is the optimal model based on the plot effect. For the bark thickness model at any height, the combination of b₁, b₂ is the optimal mixed model based on the tree effect, and the combination of b₀,b₂,b₃ is the optimal model based on the plot effect. All the optimal models have the best fitting effect when they have unstructured (UN) variance-covariance matrix. 【Conclusion】The tree effect has the greatest influence on the model whether it is the bark factor or the bark thickness model. The prediction accuracy of the mixed-effect model is significantly improved compared with the traditional regression model.

Key words: larch plantation, bark factor, bark thickness, linear mixed model, the prediction model, disk of larch tree

CLC Number:

S758

JIA Weiwei, LIANG Yuzhao, LI Fengri. Bark thickness prediction models for larch plantation[J]. JOURNAL OF NANJING FORESTRY UNIVERSITY, 2019, 43(6): 97-104.

Figures/Tables 8

Table 1

Fig.1

Table 2

Table 3

Table 4

Table 5

Estimated values, variance components and fitted statistics for each model"

变量 variable	参数 parameter	树皮因子 bark thickness factor			树皮厚度 bark thickness
变量 variable	参数 parameter	基础模型(A) based model	混合模型(B) (树木) mixed model (tree)	混合模型(C) (样地) mixed model (plot)	基础模型(D) based model	混合模型(E) (树木) mixed model (tree)	混合模型(F) (样地) mixed model (plot)
固定参数 fixed parameter	β₀	0.554 7	0.399 4	0.516 5	0.110 6	-0.028 0	0.065 8
	β₁	0.264 1	0.272 1	0.266 8	-0.071 3	0.092 5	-0.001 4
	β₂	-0.388 2	-0.399 5	-0.392 5	0.030 7	0.045 6	0.036 7
	β₃	0.003 0	0.001 4	0.002 4	0.073 9	0.024 6	0.045 8
	β₄	0.313 4	0.509 1	0.365 0	-	-	-
方差组成 variance component	σ₂	3.318 2	0.001 0	0.001 1	42.978 4	0.007 2	0.008 8
	$σ b 0 2$		-	-		-	0.016 1
	$σ b 1 2$		0.010 8	0.001 5		0.000 7	-
	$σ b 2 2$		0.014 3	0.001 6		0.000 1	0.000 0
	$σ b 3 2$		-	-		-	0.020 3
	$σ b 4 2$		0.000 0	-		-	-
	$σ b 0 b 1 2$		-	-		-	-
	$σ b 0 b 2 2$		-	-		-	-0.000 2
	$σ b 0 b 3 2$		-	-		-	-0.018 0
	$σ b 0 b 4 2$		-	-		-	-
	$σ b 1 b 2 2$		-0.012 3	-0.001 5		-0.000 1	-
	$σ b 1 b 3 2$		-	-		-	-
	$σ b 1 b 4 2$		-0.001 1	-		-	-
	$σ b 2 b 3 2$		-	-		-	0.000 1
	$σ b 2 b 4 2$		0.001 4	-		-	-
	$σ b 3 b 4 2$		-	-		-	-
拟合统计量 fitting parameter	R²	0.675 8	0.733 5	0.695 7	0.786 1	0.857 5	0.820 4
	σ(MAE)	0.023 0	0.021 6	0.022 1	0.066 7	0.052 8	0.061 4
	σ(RMSE)	0.034 6	0.031 5	0.033 7	0.102 0	0.082 9	0.093 1

Table 5

Fig.2

Table 6

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数据 data	变量 variable	样本数 sample size	平均值 mean	最大值 maximum	最小值 minimum	标准差 SD
建模数据 fitting data	年龄/a age	891	21.8	33.0	9.0	9.2
	胸径/cm DBH	891	13.0	27.0	2.0	6.3
	H_T/m	891	13.1	21.5	3.8	4.9
	D_ib/cm	891	7.2	29.2	0.2	5.3
	D_ob/cm	891	8.0	31.9	0.3	5.6
检验数据 variation data	年龄/a age	295	18.5	23.0	14.0	6.4
	胸径/cm DBH	295	10.5	18.0	4.5	4.4
	H_T/m	295	10.9	17.2	6.6	2.9
	D_ib/cm	295	6.0	25.8	0.2	4.2
	D_ob/cm	295	6.6	28.4	0.3	4.6

模型 model	参数估计值 parameter estimate					拟合统计量 good-of-fit statistics
模型 model	a₀	a₁	a₂	a₃	a₄	决定系数 R²	均方误差 MSE	均方根误差 RMSE
(1)	0.554 7	0.264 1	-0.388 23	0.003 0	0.313 4	0.675 8	0.001 2	0.034 6
(2)	0.110 6	-0.071 3	0.030 69	0.073 8	-	0.786 1	0.010 4	0.102 0

随机效应 random effects	模型 model	模型形式 model form	随机参数 random parameter	参数个数 parameters number	赤池信息准则 AIC	贝叶斯信息准则 BIC	对数似然值 -2LL	似然比检验 LRT	P
树木效应 tree effect	树皮因子 bark factor	(1)	无 none	6	-3 410.3	-3 405.6	-3 412.3
		(1.1)	b₂	7	-3 473.5	-3 470.4	-3 477.5	65.18	<0.000 1
		(1.2)	b₁,b₂	9	-3 490.4	-3 484.2	-3 498.4	20.90	<0.000 1
		(1.3)	b₁,b₂,b₄	12	-3 503.8	-3 494.5	-3 515.8	17.40	0.001 0
	树皮厚度 bark thickness	(2)	无 none	5	-1 510.3	-1 505.5	-1 512.3
		(2.1)	b₂	6	-1 722.3	-1 719.2	-1 726.3	213.98	<0.000 1
		(2.2)	b₁,b₂	8	-1 724.9	-1 718.7	-1 732.9	6.60	0.037 0
		(2.3)	b₁,b₂,b₃	11	-1 724.1	-1 713.2	-1 738.1	5.20	0.158 0
样地效应 plot effect	树皮因子 bark foctor	(3)	无 None	6	-3 410.3	-3 405.6	-3 412.3
		(3.1)	b₁	7	-3 437.8	-3 438.6	-3 441.8	29.45	<0.000 1
		(3.2)	b₁,b₂	9	-3 440.7	-3 442.3	-3 448.7	6.90	0.032 0
	树皮厚度 bark thinkness	(4)	无 None	5	-1 510.3	-1 505.5	-1 512.3
		(4.1)	b₂	6	-1 596.3	-1 597.0	-1 600.3	87.97	<0.000 1
		(4.2)	b₀,b₃	8	-1 598.3	-1 599.9	-1 606.3	6.00	0.050 0
		(4.3)	b₀,b₂,b₃	11	-1 622.3	-1 625.1	-1 636.3	30.00	<0.000 1

随机效应 random effect	模型 model	方差-协方差结构 variance- covariance	参数个数 parameters number	赤池信息准则 AIC	贝叶斯信息准则 BIC	对数似然值 -2LL	似然比检验 LRT	P
树木效应 tree level	树皮因子 bark thickness factor	UN	12	-3 503.8	-3 494.5	-3 515.8
		CS	8	-3 462.9	-3 458.2	-3 468.9	46.9	<0.000 1
		UN(1)	7	-3 473.9	-3 469.2	-3 479.9	11	0.000 9
	树皮厚度 bark thickness	UN	8	-1 724.9	-1 718.7	-1 732.9	-	-
		CS	7	-1 723.6	-1 718.9	-1 729.6	3.3	0.069 0
		UN(1)	7	-1 722.7	-1 718.1	-1 728.7	0.9	-
样地效应 plot level	树皮因子 bark thickness factor	UN	9	-3 440.7	-3 442.3	-3 448.7	-	-
		CS	8	-3 442.7	-3 443.8	-3 448.7	0	1.000 0
		UN(1)	8	-3 436.3	-3 437.5	-3 442.3	6.4	-
	树皮厚度 bark thickness	UN	11	-1 622.3	-1 625.1	-1 636.3	-	-
		CS	7	-1 596.5	-1 597.7	-1 602.5	33.8	<0.000 1
		UN(1)	8	-1 609.8	-1 611.3	-1 617.8	15.3	<0.000 1

拟合统计量 fitting parameter	树皮因子bark thickness factor			树皮厚度 bark thickness
拟合统计量 fitting parameter	基础模型 based model	混合模型 (树木) mixed model (tree)	混合模型 (样地) mixed model (plot)	基础模型 based model	混合模型 (树木) mixed model (tree)	混合模型 (样地) mixed model (plot)
R²	0.598 8	0.610 6	0.606 8	0.716 3	0.745 1	0.729 1
σ(MAE)	0.025 3	0.025 0	0.025 0	0.071 4	0.065 1	0.071 4
σ(RMSE)	0.039 4	0.038 8	0.039 0	0.117 3	0.111 1	0.114 6

Bark thickness prediction models for larch plantation

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