兴安落叶松可加性树干削度和树皮厚度联立方程组研建

doi:10.11707/j.1001-7488.20201207

摘要/Abstract

摘要：

目的: 研建兴安落叶松可加性树干削度和树皮厚度模型系统，为一致性估算兴安落叶松树干带皮、去皮材积和树皮材积提供参考。方法: 运用Kozak（2004）模型和多元回归技术构建兴安落叶松树干带皮直径（DOB）、去皮直径（DIB）和树皮厚度（BT）模型，并与以往构建的树干削度和树皮厚度模型进行比较。基于所构建的单模型，采用单模型估计、总量控制方法及2种逻辑关系变形和总量分解法分别研建可加性树干削度和树皮厚度模型系统。利用SAS软件PROC MODEL的SUR（似乎不相关回归）方法拟合各可加性模型系统，不同可加性方法使用赤池信息准则（AIC）、贝叶斯信息准则（BIC）、均方根误差（RMSE）和调整决定系数（R_a²）4个指标进行评价，采用平均误差（ME）、平均误差绝对值（MAE）、总体相对误差（TRE）和平均相对误差绝对值（MAPE）4个指标对模型进行独立检验。结果: 1）运用Kozak（2004）模型和多元回归技术构建的兴安落叶松树干带皮直径、去皮直径和树皮厚度模型优于其他模型，且条件数（CN）均小于30，不存在多重共线性，可用于构建最优模型系统；2）5种可加性方法拟合结果对比表明，采用总量控制方法的各评价指标综合表现最优，且独立检验与拟合结果基本一致。结论: 基于总量控制方法的最优模型系统在拟合、检验兴安落叶松树干带皮直径、去皮直径、树皮厚度和残差分布等方面表现出一致性，推荐其作为兴安落叶松材积和树皮材积的一致性预测模型系统。

关键词: 可加性联立方程组, 削度方程, 树皮厚度, 兴安落叶松

Abstract:

Objective: The paper focused on studying and developing the additive model systems of stem taper and bark thickness of dahurian larch(Larix gmelinii), which was expected to provide the bases for consistent estimation of the stem and bark volume of dahurian larch. Method: The equations of diameter outside bark (DOB), diameter inside bark (DIB) and bark thickness (BT) of dahurian larch were developed based on Kozak (2004) model and multiple regression technique, and they were compared with former models of taper and bark thickness. In addition, the five methods and the developed individual models were combined to construct the optimal additive taper and bark thickness model systems, respectively. Five methods included the single model estimation, total amount control and two of its logistic transformation, and total decomposition methods. All additive model systems were fitted by the PROC MODEL of SAS packages with the seemingly unrelated regression (SUR) method. Four indexes of Akaike information criterion(AIC), Bayesian information criterion(BIC), root mean square error(RMSE) and adjusted coefficient of determination(R_a²) were used to evaluate different additivity methods. Mean error (ME), mean absolute error (MAE), total relative error (TRE) and mean absolute percentage error (MAPE) were employed to evaluate the prediction precision of different model systems. Result: 1) The developed single models Kozak (2004) of DOB, DIB and BT were better than the other selected taper and bark thickness models, and the condition number (CN) values were all less than 30. It was generally believed that if the CN value is less than 30, there is no multicollinearity existed in the models, so they were used to establish the optimal system. 2) The fitting results of the five additive models showed that in general, four indexes of the total amount control performed better than the rest, and the results of validation were in accordance with the fitting results. Conclusion: The fitting and validation results, and the residual graphics of additive equation systems of DOB, DIB and BT with the total amount control showed consistent performances, therefore, the total amount control was selected as consistent prediction model system of stem and bark volume of dahurian larch in Daxing'anling.

Key words: additive equation systems, taper equations, bark thickness, dahurian larch

中图分类号:

S757

许延丽,何培,辛士冬,姜立春. 兴安落叶松可加性树干削度和树皮厚度联立方程组研建[J]. 林业科学, 2020, 56(12): 60-66.

Yanli Xu,Pei He,Shidong Xin,Lichun Jiang. Study on Additive Equation Systems of Stem Taper and Bark Thickness of Dahurian Larch[J]. Scientia Silvae Sinicae, 2020, 56(12): 60-66.

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分组 Group	变量 Variable	样木数 Number	平均值 Mean	最小值 Min.	最大值 Max.	标准差 Std.	变异系数 CV
建模数据 Fitting data	带皮直径 Diameter outside bark/cm	100	19.99	5.4	38.8	8.17	40.85
	去皮直径 Diameter inside bark/cm	100	17.56	4.2	35.7	7.14	40.66
	树皮厚度 Bark thickness/cm	100	2.43	0.3	10.0	1.75	71.84
	树高 Tree height/m	100	15.38	5.0	23.9	4.29	27.89
检验数据 Validation data	带皮直径 Diameter outside bark/cm	35	19.95	5.1	32.7	7.46	37.41
	去皮直径 Diameter inside bark/cm	35	17.29	4.6	28.4	6.37	36.83
	树皮厚度 Bark thickness/cm	35	2.65	0.3	5.8	1.57	59.40
	树高 Tree height/m	35	15.42	4.5	23.5	4.28	27.77

模型 Models		RMSE	R_a²	CN
带皮直径 DOB	模型(1)Model(1)	1.410 8	0.975 7	29
	模型(4)Model(4)	1.596 0	0.966 4	6 208
	模型(5)Model(5)	1.677 9	0.965 8	50
	模型(6)Model(6)	1.588 3	0.969 1	66
去皮直径 DIB	模型(2)Model(2)	1.598 5	0.957 0	25
	模型(4)Model(4)	1.663 6	0.950 6	7 166
	模型(5)Model(5)	1.763 9	0.947 5	52
	模型(6)Model(6)	2.385 8	0.904 1	16
树皮厚度 BT	模型(3)Model(3)	1.117 5	0.646 0	21
	模型(7)Model(7)	1.352 7	0.481 3	6
	模型(8)Model(8)	1.158 1	0.619 8	3
	模型(9)Model(9)	1.230 4	0.570 9	13

方法 Methods	变量 Variable	RMSE	R_a²	AIC	BIC
方法1 Method 1	DOB	1.461 9	0.973 7	508	517
	DIB	1.598 5	0.957 0	623	630
	BT	1.117 5	0.646 0	157	164
方法2 Method 2	DOB	1.409 7	0.975 7	461	469
	DIB	1.616 4	0.956 0	637	644
	BT	1.092 6	0.661 6	127	134
方法3 Method 3	DOB	1.414 1	0.975 5	465	473
	DIB	1.621 2	0.955 7	641	648
	BT	1.096 4	0.659 3	132	139
方法4 Method 4	DOB	1.417 4	0.975 4	468	476
	DIB	1.622 1	0.955 7	642	649
	BT	1.125 7	0.640 8	166	173
方法5 Method 5	DOB	1.410 8	0.975 7	462	470
	DIB	1.640 3	0.954 7	656	663
	BT	1.104 5	0.654 2	141	148

方法 Methods	变量 Variable	b₁	b₂	b₃	b₄	b₅	b₆
方法2 Method 2	DIB	0.982 2(0.022 6)	0.967 7(0.007 3)	0.466 5(0.018 4)	-0.370 0(0.049 8)	0.406 2(0.016 3)	0.002 3(0.001 0)
方法2 Method 2	BT	0.036 6(0.003 0)	1.345 6(0.025 6)	-0.700 4(0.055 9)	2.198 4(0.263 7)	1.264 7(0.059 2)	-7.265 1(0.604 0)

方法 Methods	变量 Variable	ME	MAE	TRE(%)	MAPE(%)
方法1 Method 1	DOB	0.29	1.02	12.85	8.56
	DIB	-0.22	1.12	16.17	11.06
	BT	0.50	0.71	80.99	40.01
方法2 Method 2	DOB	0.03	0.95	11.47	8.47
	DIB	-0.43	1.16	17.23	11.71
	BT	0.46	0.70	72.20	39.49
方法3 Method 3	DOB	0.03	0.96	11.57	8.45
	DIB	-0.44	1.17	17.20	11.73
	BT	0.47	0.70	73.14	39.56
方法4 Method 4	DOB	0.05	0.96	11.71	8.37
	DIB	-0.42	1.18	17.54	11.65
	BT	0.47	0.73	80.45	42.75
方法5 Method 5	DOB	-0.06	0.96	11.45	8.53
	DIB	-0.54	1.20	17.56	11.85
	BT	0.48	0.70	77.79	39.71