Stem Shape Curves Simulation for Larixprincipis-rupprechtii Using Quantile Regressions

doi:10.13466/j.cnki.lyzygl.2020.01.019

Abstract

Abstract:

Stem shape is an important index to reflect the external shape of stem and it is also an important basis for evaluating the value of trunk.The taper equation is an important quantitative index to describe the quality of tree stem shape.The accuracy of its simulation of stem shape directly determines the estimation of trunk volume and forest volume.In this study,four simple taper equations were used to estimate the stem shape of planted Larixprincipis-rupprechtii and the model fit and validation were assessed byadjusted determination coefficient(R_a²),root mean square error(RMSE),mean error(ME)and absolute mean error(MAE).The optimal model was selected and the taper shape of Larixprincipis-rupprechtii was modelled by using quantile regression technology.Result showed that Kozak equation has the best fitting result(R_a²=0.934, RMSE=1.985cm)and the validation result(ME=0.125cm, MAE=1.212cm)on the stem shape among the four simple taper equations.Thus,the taper shape of Larixprincipis-rupprechtii was established by using quantile regression technology based on Kozak equation.Compared with the basic model,the goodness-of-fit of quantile regression model was improved.When the quantile is set to 0.1,the model has a better fitting effect on the stem shape near the lower and upper part of trunk,when the quantile is set to 0.5,the model has a better fitting effect on the trunk at the middle part of trunk,and when the quantile is set to 0.9,the model has a better fitting effect on the base of trunk.It can be seen that quantile regression technology makes the model more flexible.

Key words: quantile regression, taper curve, Saihanba machinery forest farm, Larixprincipis-rupprechtii

CLC Number:

S758

Lihua FU, Jinchao HOU, He SUN, Hezhi WANG, Qiang LIU, Shun CHENG. Stem Shape Curves Simulation for Larixprincipis-rupprechtii Using Quantile Regressions[J]. FOREST RESOURCES WANAGEMENT, 2020, (1): 151-157.

Figures/Tables 7

Tab.1

Tab.2

Basic model forms

模型	表达式	来源
M1	d=a₁ $D a 2 H - h a 3 H a 4$	Demaerschalk^[19]
M2	d²/D²=b₁+b₂ $h / H$ +b₃ $h / H 2$	Kozak^[20]
M3	d/D= $1 - h / H c 1 1 / c 2$	Forslund^[21]
M4	d=D $e - d 1 h - 1.3$	Metcalf^[22]

Tab.2

Tab.3

Results of the estimations of parameters and goodness-of-fitting

模型	参数	估计值	置信区间95%		P 值	决定系数 ( $R a 2$ )	均方根误差 (RMSE/cm)
M1	a₁	1.7565(0.0921)	1.5677	1.9254	<0.001	0.888	5.080
	a₂	0.8658(0.0198)	0.8269	0.9045	<0.023
	a₃	0.7929(0.0077)	0.7778	0.0808	<0.001
	a₄	-0.7926(0.0242)	-0.8402	-0.7451	0.028
M2	b₁	1.5607(0.0125)	1.5362	1.5853	<0.001	0.934	1.985
	b₂	-3.2744(0.0663)	-3.4045	-3.1444	<0.001
	b₃	1.8807(0.0725)	1.7384	2.0229	<0.001
M3	c₁	1.3738(0.0216)	1.3313	1.4162	0.047	0.893	2.319
M3	c₂	1.3039(0.0201)	1.2645	1.3434	0.031	0.893	2.319
M4	d₁	0.0774(0.0009)	0.0754	0.0793	<0.001	0.905	2.417

Tab.3

Tab.4

Validations of the models

模型	模型形式	平均误差(ME /cm)	平均误差绝对值(MAE/cm)
M1	d=1.7565D⁰^.⁸⁶⁵⁸ $H - h 0.7929$ H^-0^.⁷⁹²⁶	0.237	1.452
M2	d²/D²=1.5607-3.2744 $h / H$ +1.8807 $h / H 2$	0.125	1.212
M3	d/D= $1 - h / H 1.3738 1 / 1.3039$	-0.618	1.345
M4	d=D $e - 0.0774 h - 1.3$	-0.729	1.741

Tab.4

Tab.5

Fig.1

Fig.2

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数据	统计量	树龄/a	数量/株	树高/m	胸径/cm
建模数据	最小值	41~43	195	8.95	7.76
	最大值			20.93	26.96
	平均值			14.94	17.98
	标准差			2.60	3.58
检验数据	最小值	41~43	65	9.28	9.61
	最大值			20.50	26.39
	平均值			15.01	17.80
	标准差			2.64	3.84