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

摘要/Abstract

摘要：

目的: 基于多个变量分别构建杉木单木叶生物量预测模型，并选择出预测效果最佳的模型，为杉木叶生物量的精准预测提供参考。方法: 以21块不同林龄样地共63株解析木为例，分别基于胸高处边材面积、胸径和冠基部直径3个变量，考虑其他与叶生物量相关的单木和林分因子，以样地为随机效应因子构建非线性混合模型，采用指数函数、幂函数和常数加幂函数消除数据间的异方差性。根据模型评价指标赤池信息准则（AIC）、贝叶斯信息准则（BIC）和对数似然值（Log Likelihood）选择最佳模型，并对不同参数的混合模型进行似然比检验。采用留一交叉验证法，计算模型决定系数（R²）、总相对误差（TRE）和平均绝对误差（MAE），对模型预测效果进行检验。结果: 基于3个变量以幂函数为异方差结构构建的混合模型效果最好，混合模型均优于基础模型，且基于冠基部直径构建的模型预测效果最佳。结论: 以基于冠基部直径构建的非线性混合效应模型（模型16）作为预测杉木单木叶生物量的最佳模型，符合管道模型理论。各变量均具有一定生物学和统计学意义，野外调查较易获取（非破坏性）。模型具有一定实用性，且预测精度较高（R² = 0.805 1）。本研究结果可为其他树种构建单木叶生物量模型提供参考。

关键词: 杉木, 叶生物量, 管道模型理论, 冠基部直径, 胸高处边材面积, 胸径

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

中图分类号:

S758

屈彦成,江怡航,姜彦妍,张建国,罗安利,张雄清. 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[J]. 林业科学, 2023, 59(7): 106-114.

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