天然樟子松和兴安落叶松树干削度方程4种建模方法比较

doi:10.11707/j.1001-7488.LYKX20200889

摘要/Abstract

摘要：

目的: 基于樟子松和兴安落叶松干形数据，比较分析最小二乘法（ONLS）、分位数回归（QR）、混合效应模型的固定效应法（FIXED）以及广义加性模型（GAM）对树干不同位置直径和树干总材积的预测精度，为树木干形和材积精准预测提供参考。方法: 以大兴安岭漠河林业局不同林分条件下的187株樟子松和283株兴安落叶松为研究对象，拟合林业上常用的33个削度方程，选出精度较高的削度方程作为ONLS、QR和FIXED的基础模型。基于描述干形的常用变量，同时考虑变量转换，如平方和开根号等变量转换构建GAM。应用R软件对4种建模方法进行拟合，选取平均误差（ME）、均方根误差（RMSE）、百分比均方根误差（RMSE%）和确定系数（R²）对比分析4种建模方法，采用留一交叉检验法对不同建模方法进行检验，比较各方法预测树干不同位置直径和树干总材积的精度。为更直观展示各建模方法效果，分别从2种树种中随机抽取2株不同大小树木进行树干模拟。结果: 1）基于Kozak（2004）模型的ONLS、QR和FIXED以及构建的GAM拟合结果表明，4种建模方法均能较好拟合樟子松和兴安落叶松干形数据；2）留一交叉检验结果显示，GAM对樟子松和兴安落叶松树干直径的预测精度优于ONLS、QR和FIXED；3） GAM预测2种树种材积时与估计直径一致，即GAM预测精度优于其他建模方法；相较ONLS，樟子松和兴安落叶松GAM材积预测的RMSE分别下降5.6%和11.3%；4） 2种树种不同大小树木树干模拟发现，对于大树树干，ONLS、QR、FIXED和GAM模拟效果相似，且均能较好模拟樟子松和兴安落叶松树干干形；对于小树树干，ONLS、QR、FIXED和GAM模拟效果差异较大，其中GAM能较好模拟樟子松和兴安落叶松树干干形。结论: GAM预测树干不同位置直径和树干总材积时精度最高。当以预测为主要目的时，GAM通过简单编程能够实现对樟子松和兴安落叶松树干直径和材积的估计，可作为一种精度较高的树干干形预测方法。

关键词: 削度方程, 最小二乘法, 分位数, 固定效应, 广义加性模型

Abstract:

Objective: Based on the taper data of Pinus sylvestris var. mongolica and Larix gmelinii, the ordinal nonlinear least squares method (ONLS), quantile regression (QR), the fixed part of mixed effects model (FIXED) and generalized additive model (GAM) were compared by prediction accuracy of the diameter and total volume. Method: The data of 187 Pinus sylvestris var. mongolica and 283 Larix gmelinii with different stands in Mohe Forestry Bureau, Daxing'an Mountains, were studied. 33 commonly used taper equations in forestry were fitted. The taper equation with higher accuracy was selected as the basic model of ONLS, QR and FIXED. In addition, the commonly used variables for describing the stem shape were used to construct GAM. At the same time, transformed variables such as square, square root and other conversions were considered. The four methods were fitted using R software. And they were compared by mean error (ME), root mean square error (RMSE), percentage root mean square error (RMSE%) and coefficient of efficiency (R²). A leave-one-out cross-validation method was used to validate the prediction accuracy of diameter and total volume of different modelling methods. In order to show the effects of each modelling method more intuitively, two trees with different sizes were randomly selected from the two tree species for stem simulation. Result: 1) The fitting results showed that ONLS, QR and FIXED based on Kozak (2004) as well as constructed GAM could fit Pinus sylvestris var. mongolica and Larix gmelinii stem well. 2) The results of cross-validation showed that the GAM is better than ONLS, QR and FIXED for two species. 3) The GAM for volume estimation of the two tree species was consistent with diameter, that is, the accuracy of GAM estimation is better than other methods. Compared with the ONLS, the RMSE of volume prediction of the GAM decreased by 5.6% and 11.3% for Pinus sylvestris var. mongolica and Larix gmelinii, respectively. 4) The ONLS, QR, FIXED and GAM had similar simulation effects for large trees after simulating the stem of these two species with different sizes, and they can simulate the large stem form well for both species. For small trees, ONLS, QR, FIXED and GAM were quite different. The GAM can simulate the small tree stem well for these two species. Conclusion: The GAM has the highest accuracy for diameter and volume prediction. When prediction is the main purpose, the GAM constructed in this study can be used for diameter and volume prediction for Pinus sylvestris var. mongolica and Larix gmelinii by simple programming. It can be used as an accurate method to predict stem shape.

Key words: taper equation, least squares method, quantile regression, fixed effects, generalized additive model

中图分类号:

S758

何培,王君杰,辛士冬,张兹鹏,姜立春. 天然樟子松和兴安落叶松树干削度方程4种建模方法比较[J]. 林业科学, 2023, 59(6): 28-35.

Pei He,Junjie Wang,Shidong Xin,Zipeng Zhang,Lichun Jiang. Comparison of Four Methods on Modelling Stem Taper Function for Natural Pinus sylvestris var. mongolica and Larix gmelinii[J]. Scientia Silvae Sinicae, 2023, 59(6): 28-35.

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树种 Species	样木数 Number	变量 Variable	最小值 Min.	最大值 Max.	平均值 Mean	标准差 SD
樟子松 Pinus sylvestris var. mongolica	187	胸径 DBH/cm	15.4	55.9	39.1	9.78
樟子松 Pinus sylvestris var. mongolica	187	树高 Tree height/m	11.4	25.4	20.3	2.62
兴安落叶松 Larix gmelinii	283	胸径 DBH/cm	5.1	58.9	35.7	12.70
兴安落叶松 Larix gmelinii	283	树高 Tree height/m	7.3	31	22.3	4.83

方法 Methods	樟子松 Pinus sylvestris var. mongolica				兴安落叶松 Larix gmelinii
方法 Methods	ONLS	QR	FIXED	GAM	ONLS	QR	FIXED	GAM
β				0.793 5 (0.000 9)				0.801 1 (0.000 9)
b₁	0.981 2 (0.035 3)	0.967 3 (0.016 3)	1.015 9 (0.018 6)		0.775 8 (0.026 1)	0.934 2 (0.018 5)	0.952 3 (0.027 9)
b₂	0.976 5 (0.007 2)	0.987 3 (0.003 6)	0.987 8 (0.003 9)		0.917 4 (0.007 8)	0.977 3 (0.006 6)	0.978 6 (0.008 3)
b₃	0.034 7 (0.015 1)	0.025 1 (0.007 9)	0.009 8 (0.007 9)		0.173 5 (0.016 0)	0.044 9 (0.012 7)	0.040 9 (0.016 4)
b₄	0.556 2 (0.017 3)	0.596 9 (0.022 8)	0.603 3 (0.015 4)		0.541 5 (0.016 2)	0.600 6 (0.019 2)	0.659 2 (0.008 8)
b₅	0.252 8 (0.084 4)	0.164 1 (0.146 3)	0.406 5 (0.160 2)		?0.119 8 (0.060 9)	?0.418 2 (0.068 1)	?0.504 2 (0.087 5)
b₆	0.440 4 (0.011 1)	0.407 1 (0.019 0)	0.421 5 (0.020 6)		0.376 7 (0.011 0)	0.388 5 (0.016 1)	0.348 0 (0.015 9)
b₇	?4.547 4 (0.677 6)	?3.320 6 (0.945 6)	?5.424 7 (1.209 5)		?1.940 9 (0.349 1)	?0.255 1 (0.298 3)	0.381 0 (0.373 5)
b₈	?0.007 9 (0.001 6)	?0.010 2 (0.002 1)	?0.014 0 (0.001 8)		?0.003 6 (0.001 3)	0.000 4 (0.002 3)	?0.013 7 (0.001 5)
b₉	0.117 9 (0.023 7)	0.151 4 (0.030 9)	0.197 9 (0.024 5)		0.339 1 (0.022 9)	0.277 8 (0.034 9)	0.491 7 (0.026 6)

树种 Species	方法 Methods	ME	RMSE	RMSE%	R²
樟子松 Pinus sylvestris var. mongolica	ONLS	0.001 8	2.017 2	6.743 3	0.977 3
	QR	0.166 1	2.030 5	6.787 6	0.977 0
	FIXED	0.070 0	2.029 2	6.783 3	0.977 1
	GAM	?0.000 008	1.941 8	6.491 3	0.978 9
兴安落叶松 Larix gmelinii	ONLS	?0.022 6	2.400 2	9.081 4	0.972 7
	QR	0.090 2	2.439 2	9.229 1	0.971 8
	FIXED	?0.025 4	2.485 9	9.405 7	0.970 7
	GAM	0.000 2	2.268 1	8.581 7	0.975 6

树种 Species	方法 Methods	ME	RMSE	RMSE%	R²
樟子松 Pinus sylvestris var. mongolica	ONLS	0.000 9	2.039 4	6.817 3	0.976 8
	QR	0.170 5	2.068 0	6.913 2	0.976 2
	FIXED	0.068 9	2.046 7	6.841 9	0.976 7
	GAM	0.000 6	2.014 0	6.732 5	0.977 3
兴安落叶松 Larix gmelinii	ONLS	?0.024 3	2.417 3	9.146 1	0.972 3
	QR	0.087 0	2.449 0	9.266 2	0.971 6
	FIXED	?0.025 4	2.485 9	9.405 7	0.970 7
	GAM	0.003 3	2.305 5	8.723 1	0.974 8

树种 Species	方法 Methods	ME	RMSE	RMSE%	R²
樟子松 Pinus sylvestris var. mongolica	ONLS	0.009 9	0.085 3	6.217 3	0.978 4
	QR	0.019 7	0.087 0	6.342 2	0.977 6
	FIXED	0.014 4	0.085 6	6.240 7	0.978 3
	GAM	0.007 3	0.080 5	5.868 4	0.980 8
兴安落叶松 Larix gmelinii	ONLS	0.009 2	0.093 9	7.6889	0.977 3
	QR	0.011 1	0.098 7	8.079 5	0.974 9
	FIXED	0.003 7	0.091 7	7.507 3	0.978 3
	GAM	0.000 2	0.083 3	6.816 1	0.982 1