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

Abstract

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

CLC Number:

S758

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.

Figures/Tables 8

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References 0

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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

Comparison of Four Methods on Modelling Stem Taper Function for Natural Pinus sylvestris var. mongolica and Larix gmelinii

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