基于胸高处边材面积、胸径和冠基部直径的杉木单木叶生物量预测模型

doi:10.11707/j.1001-7488.LYKX20210732

Abstract

Abstract:

Objective: The tree leaf biomass models of Chinese fir plantations were developed based on multiple variables, and the best model was selected to provide reference for accurate prediction of leaf biomass of Chinese fir. Method: Besides the three variables of sapwood area at breast height, diameter at breast height and diameter at crown base using 63 trees from 21 plots of different forest ages, the other variables related to leaf biomass were also considered. The nonlinear mixed model was considering the random effect of plot. In addition, exponential function, power function, and constant plus power function were used to eliminate the heteroscedasticity among the data. The best model was selected according to the model evaluation index AIC (Akaike information criterion), BIC(Bayesian information criterion), and Log Likelihood. The mixed model with different parameters was tested by likelihood ratio test. Finally, the leave-one-out cross-validation method was used to calculate coefficient of determination (R²), total relative error (TRE), and mean absolute error (MAE) to test the models. Result: The mixed models considered power function as heteroscedasticity structure performed the best among the three types of models. In addition, all the mixed models were better than the basic models, and the leaf biomass model developed based on diameter at crown base performed the best. Conclusion: The nonlinear mixed effect model (Model 16) based on diameter at crown base with R² values of 0.805 1 was used as the final model for individual leaf biomass of Chinese fir plantations, which was consistent with the pipe model theory. All the variables had certain biological and statistical significance and were easy to obtain in the field work (non-destructive). In addition, this study can also provide a reference for other tree species in predicting individual leaf biomass.

Key words: Chinese fir, leaf biomass, pipe model theory, diameter at crown base, sapwood area at breast height, diameter at breast height

CLC Number:

S758

Yancheng Qu,Yihang Jiang,Yanyan Jiang,Jianguo Zhang,Anli Luo,Xiongqing Zhang. Tree Leaf Biomass Models of Chinese fir Plantations Based on Sapwood Area and Diameter at Breast Height and Diameter at Crown Base[J]. Scientia Silvae Sinicae, 2023, 59(7): 106-114.

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因子类型 Attribute type	因子 Attribute	样本数 Number	最小值 Min.	最大值 Max.	平均值 Mean	标准差 Std.	变异系数 CV(%)
单木因子 Tree attributes	叶生物量 Leaf biomass (LB) / kg	63	0.41	21.15	6.99	5.57	79.73
	树高 Tree height(H) / m	63	3.40	20.70	12.63	4.96	39.25
	胸径 Diameter at breast height(DBH) / cm	63	3.70	26.20	14.73	6.39	43.37
	冠基部直径 Diameter at crown base(DCB) / cm	63	4.70	21.80	11.66	4.65	39.84
	胸高处边材面积 Sapwood area at breast height(SABH)/ cm²	63	37.13	332.42	118.75	68.38	57.58
	冠幅 Crown width(CW) / m	63	1.17	4.40	2.94	0.85	28.86
	冠长 Crown length(CL) / m	63	2.80	13.80	7.17	2.66	37.10
	冠长率 Crown ratio(CR)	63	0.32	0.93	0.61	0.16	25.84

林分因子 Stand attributes	林龄 Stand age(A) / a	21	3	49	20.71	15.05	72.63
	林分密度 Stand density(N) /(trees·hm^?2)	21	533	3 550	1 731.81	1 113.99	64.33
	每公顷断面积 Basal area per hectare(BA) /(m²·hm^?2)	21	4.27	35.16	22.60	8.74	38.67
	优势木平均高 Dominant tree mean height(H_d) / m	21	5.15	20.85	15.11	5.30	35.05

变量 Variable	模型 Model	随机参数 Random parameter	参数个数 Number of parameters	AIC	BIC	Loglik	LRT	P
胸高处边材面积 Sapwood area at breast height(SABH)	11.1	b₁	6	319.028 2	331.887 0	?153.514 1
	11.2	b₂, b₃	8	310.105 7	327.250 8	?147.052 9	12.922 5	0.001 6
	11.3	b₁, b₂, b₃	11	316.110 2	339.684 7	?147.055 1	0.004 5	0.999 9
胸径 Diameter at breast height(DBH)	12.1	b₁	6	309.181 4	322.040 2	?148.590 7
	12.2	b₁, b₃	8	313.181 4	330.326 5	?148.590 7	0.000 0	1.000 0
	12.3	b₁, b₂, b₃	11	306.027 2	329.601 7	?142.013 6	13.154 2	0.022 0
	12.4	b₀, b₁, b₂, b₃	15	314.027 2	346.174 2	?142.013 6	0.000 0	1.000 0
冠基部直径 Diameter at crown base(DCB)	13.1	b₀	7	295.749 3	310.751 2	?140.874 7
	13.2	b₀, b₁	9	299.749 3	319.037 5	?140.874 7	0.000 0	1.000 0
	13.3	b₂, b₃, b₄	12	296.098 9	321.816 6	?136.0495	9.650 4	0.085 8
	13.4	b₁, b₂, b₃, b₄	16	297.0968	331.387 0	?132.5484	16.652 5	0.054 4

变量 Variable	异方差结构 Heteroscedasticity structure	参数个数 Number of parameters	AIC	BIC	Loglik	LRT	P
胸高处边材面积 Sapwood area at breast height(SABH)	无 None	8	310.105 7	327.250 8	?147.052 9
	指数函数 Exponential function	9	不收敛 No convergence
	幂函数 Power function	9	271.213 7	290.5019	?126.606 8	40.892 1	<0.000 1
	常数加幂函数 Constant plus power function	10	273.213 7	294.6450	?126.606 8	0.000 0	0.999 6
胸径 Diameter at breast height(DBH)	无 None	11	306.027 2	329.6017	?142.013 6
	指数函数 Exponential function	12	265.331 6	291.0492	?120.665 8
	幂函数 Power function	12	253.975 4	279.6930	?114.987 7	54.051 8	<0.000 1
	常数加幂函数 Constant plus power function	13	255.975 0	283.8357	?114.987 5	0.000 4	0.983 3
冠基部直径 Diameter at crown base(DCB)	无 None	7	295.749 3	310.7512	?140.874 7
	指数函数 Exponential function	8	257.680 5	274.8256	?120.840 2
	幂函数 Power function	8	239.787 7	256.9328	?111.893 9	57.961 6	<0.000 1
	常数加幂函数 Constant plus power function	9	241.791 4	261.0796	?111.895 7	0.003 7	0.951 3

项目 Item	参数 Parameter	胸高处边材面积 Sapwood area at breast height		胸径 Diameter at breast height		冠基部直径 Diameter at crown base
项目 Item	参数 Parameter	基础模型 Basic model	混合模型 Mixed model	基础模型 Basic model	混合模型 Mixed model	基础模型 Basic model	混合模型 Mixed model
固定效应参数 Fixed effect parameter	β₀	0.000 2	0.029 9	0.103 4	0.081 6^*	0.067 6	0.034 6^*
	β₁	0.386 9^*	0.219 1	1.825 2^*	1.678 6^*	1.983 6^*	1.652 2^*
	β₂	1.115 1^*	0.929 4^*	0.738 9^*	0.556 3	0.885 3^*	0.719 3^*
	β₃	2.606 8^*	1.184 9^*	?0.542 5^*	?0.262 9^*	?1.335 1^*	?0.695 9^*
	β₄					?0.700 7^*	?0.027 2
随机效应方差 Random effect variance	$ {\sigma }_{{b}_{0}}^{2} $						7.59×10^?13*
	$ {\sigma }_{{b}_{1}}^{2} $				0.020 5
	$ {\sigma }_{{b}_{2}}^{2} $		0.040 8^*		0.005 6
	$ {\sigma }_{{b}_{3}}^{2} $		1.46×10^?11*		0.027 9
	$ {\sigma }_{{b}_{1}{b}_{2}} $				0.010 7
	$ {\sigma }_{{b}_{1}{b}_{3}} $				?0.023 9
	$ {\sigma }_{{b}_{2}{b}_{3}} $		7.71×10^?10*		?0.012 5
误差方差 Error variance	σ²	7.833 3	0.088 6	6.679 2	0.072 5	5.195 9	0.076 0
异方差 Heteroscedasticity	λ		1.061 5^*		1.069 7		1.042 0^*
评价指标 Evaluation index	AIC	318.164 9	271.213 7	307.465 9	253.975 4	293.749 3	239.787 7
	BIC	328.880 5	290.501 9	318.181 5	279.693 0	306.608 1	256.932 8
	Loglik	?154.082 4	?126.606 8	?148.732 9	?114.987 7	?140.874 6	?111.893 8

变量 Variable	模型类型 Model type	留一交叉验证 Leave-one-out cross-validation
变量 Variable	模型类型 Model type	R²	TRE(%)	MAE
胸高处边材面积 Sapwood area at breast height(SABH)	基础模型 Basic model	0.645 4	0.14	2.472 6
胸高处边材面积 Sapwood area at breast height(SABH)	混合模型 Mixed model	0.650 0	0.17	2.367 3
胸径 Diameter at breast height(DBH)	基础模型 Basic model	0.732 1	0.11	1.892 8
胸径 Diameter at breast height(DBH)	混合模型 Mixed model	0.753 7	0.11	1.849 6
冠基部直径 Diameter at crown base(DCB)	基础模型 Basic model	0.773 2	0.09	1.925 3
冠基部直径 Diameter at crown base(DCB)	混合模型 Mixed model	0.805 1	0.06	2.461 1

Tree Leaf Biomass Models of Chinese fir Plantations Based on Sapwood Area and Diameter at Breast Height and Diameter at Crown Base

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