塞罕坝华北落叶松人工林树冠外部轮廓模型

doi:10.11707/j.1001-7488.20210510

摘要/Abstract

摘要：

目的: 构建树冠最大外部轮廓非线性混合效应模型和非线性分位数回归模型，为准确预测树冠生长发育规律及预估生产力提供科学依据。方法: 以河北省塞罕坝机械林场华北落叶松人工林为研究对象，基于58株解析木数据和1 789个枝条解析数据，利用幂函数、修正Kozak方程、修正Weibull方程选取基础模型，构建华北落叶松人工林树冠外部轮廓非线性混合效应模型和非线性分位数回归模型。结果: 在幂函数、修正Kozak方程和修正Weibull方程中，幂函数拟合树冠外部轮廓效果较好，作为树冠外部轮廓基础模型；林分年龄（Age）、冠长（CL）、胸径（DBH）、树高（HT）、冠高比（CHR）、高径比（HDR）对树冠外部轮廓影响较大。在混合效应模型中，两水平混合效应模型优于单水平混合效应模型，可明显提高模型拟合精度，HDR相关的参数a₆考虑样地效应，相对着枝深度（RDINC）、CHR相关的参数a₄、a₅考虑样木效应，模型确定系数（R²）为0.873，均方根误差（RMSE）为0.319 m，平均相对误差（MRE）为6.642 m。在分位数回归模型中，当分位数q=0.90时模型曲线最接近树冠最大外部轮廓，R²为0.672。结论: 混合效应模型拟合精度较高，可准确描述树冠最大枝条的平均趋势。分位数回归模型可确定树冠最外部轮廓，在预测条件均值之外的研究中发挥重要作用。

关键词: 塞罕坝, 华北落叶松, 非线性混合效应模型, 非线性分位数回归模型, 树冠外部轮廓

Abstract:

Objective: The crown of a tree is an important organ for material exchange and energy conversion. The nonlinear mixed effect model and the nonlinear quantile regression model of the maximum crown outline were constructed to provide a scientific basis for accurately predicting the growth and development law of the crown and its productivity. Method: Taking Larix principis-rupprechtii plantation of Saihanba forest farm in Hebei Province as the research object, based on 1 789 branches data of 58 trees, the power equation, modified Kozak and modified Weibull equation were selected as the basic models to construct a mixed effect model and a nonlinear quantile regression model for predicting the crown shape of L. principis-rupprechtii plantation. Result: Among the power function, modified Kozak equation and modified Weibull equation, the power function equation had the best fitting effect of tree crown profile. The power function equation was chosen as the basic model of tree crown profile. Stand age (Age), diameter at breast height(DBH), height of the tree (HT), crown height ratio (CHR), and height to diameter ratio (HDR) had significant effects on fitting crown contour. In the mixed effect model, the two-level mixed effect model considering both plot and tree effects was superior to the single-level mixed effect model. The random effect of the plot was added to the HDR parameter, and the random effect of the sample was added to the RDINC(relative depth into crown) and CHR parameters. The model determination coefficient (R²) was 0.873, the root mean square error (RMSE) was 0.319 m, and the mean relative error (MRE) was 6.642 m. In the quantile regression model, when q=0.90, the model curve model was the closest to the crown maximum profile, R² was 0.672. Conclusion: The mixed-effect model might be a better fitting accuracy and could accurately describe the average trend of the largest branches of the canopy. The quantile regression model could determine the outermost contour of the canopy and may play an important role in research beyond the prediction of conditioned mean.

Key words: Saihanba, Larix principis-rupprechtii, nonlinear mixed effect model, nonlinear quantile regression model, crown profile

中图分类号:

S757

赵婷婷,王冬至,张冬燕,郭立,黄选瑞. 塞罕坝华北落叶松人工林树冠外部轮廓模型[J]. 林业科学, 2021, 57(5): 108-118.

Tingting Zhao,Dongzhi Wang,Dongyan Zhang,Li Guo,Xuanrui Huang. Crown Prediction Model of Larix principis-rupprechtii Plantation in Saihanba of Hebei Province, Northern China[J]. Scientia Silvae Sinicae, 2021, 57(5): 108-118.

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样地号 Sample plot No.	林分年龄 Stand age/a	密度Stand density/(tree·hm^-2)	平均胸径 Mean DBH/cm	平均树高 Mean HT/m	平均冠幅 Mean CW/m	平均冠长 Mean CL/m
1	17	2 680	12.167	9.467	1.416	6.818
2	43	1 200	22.667	19.450	2.213	9.533
3	43	1 500	20.317	17.067	1.537	8.950
4	30	1 580	15.650	14.803	1.363	6.508
5	45	825	20.150	18.000	1.677	9.317
6	22	2 190	13.733	12.067	1.475	7.300
7	44	757	27.625	18.175	1.935	11.550
8	23	2 495	15.433	12.017	1.516	6.583
9	38	735	23.458	17.500	2.445	9.625
10	14	2 240	9.833	8.500	1.270	4.667

样木及枝条属性 Sample trees and branch attributes	建模样本Fitting data				检验样本Validation data
样木及枝条属性 Sample trees and branch attributes	最小值 Min.	最大值 Max.	平均值 Mean	标准差 Std.	最小值 Min.	最大值 Max.	平均值 Mean	标准差 Std.
树木变量Tree variables	n=44				n=14
年龄Age/a	11	46	11	46	11	46	11	46
胸径DBH/cm	7.812	32.222	7.812	32.222	7.812	32.222	7.812	32.222
树高HT/m	6.532	20.443	6.532	20.443	6.532	20.443	6.532	20.443
高径比HDR	0.654	1.187	0.654	1.187	0.654	1.187	0.654	1.187
冠幅CW/m	1.089	3.454	1.089	3.454	1.089	3.454	1.089	3.454
冠长CL/m	4.434	12.765	4.434	12.765	4.434	12.765	4.434	12.765
冠长率CLR	0.421	0.809	0.421	0.809	0.421	0.809	0.421	0.809
枝条变量Branch variables	n=1 371				n=418
枝龄Branch age/a	1	28	1	28	1	28	1	28
着枝角度BA/(°)	10	90	10	90	10	90	10	90
基径BD/mm	2.524	119.424	2.524	119.424	2.524	119.424	2.524	119.424
枝长BL/m	0.123	4.562	0.123	4.562	0.123	4.562	0.123	4.562

模型Model	函数表达式Function expression	函数形式Function form	来源Source
M1	${\rm{CR}} = {a_1}{\rm{RDIN}}{{\rm{C}}^a}2{{\rm{e}}^{{a_3}{\rm{RDINC}}}}$	幂函数Power	Sun et al., 2017
M2	${\rm{CR}} = {a_1}{\left[ {\frac{{1 - {{(1 - {\rm{RDINC}})}^{0.5}}}}{{1 - {P^{0.5}}}}} \right]^{{a_2}}}$	修正Kozak方程Modified Kozak equation	高慧淋等，2018
M3	${\rm{CR}} = {a_3}\left({\frac{{{a_2}}}{{{a_1}}}} \right){\left({\frac{{{\rm{RDINC}}}}{{{a_1}}}} \right)^{{a_2} - 1}}{{\rm{e}}^{ - {{\left({{\rm{RDINC}}/{a_1}} \right)}^{{a_2}}}}}$	修正Weibull方程Modified Weibull equation	高慧淋等，2018

函数形式Function form	参数Parameter	估计值Estimates	标准误SE	R²	RMSE	MRE
幂函数Power	a₁	8.528	1.570	0.712	0.495	15.388
	a₂	1.183	0.103
	a₃	-1.252	0.204
修正Kozak方程 Modified Kozak equation	a₁	2.172	0.030	0.690	0.890	19.450
	a₂	0.300	1.700
	a₃	0.470	0.210
修正Weibull方程 Modified Weibull equation	a₁	1.266	0.102	0.711	0.497	15.424
	a₂	1.929	0.055
	a₃	3.678	0.389

变量Variables	统计量Statistics	Age	Sd	CL	DBH	HT	CHR	CW	HDR
MCR	相关系数Correlation coefficient	0.561 8	-0.534 3	0.626 4	0.713 5	0.565 6	0.739 5	0.019 0	-0.564 7
MCR	P	< 0.000 1	0.000 2	< 0.000 1	< 0.000 1	< 0.000 1	< 0.000 1	0.902 5	< 0.000 1
MRDINC	相关系数Correlation coefficient	-0.131 1	0.060 8	-0.122 3	-0.024 9	-0.024 3	-0.057 7	-0.101 0	-0.044 0
MRDINC	P	0.428 0	0.695 0	0.429 2	0.872 6	0.875 8	0.710 0	0.514 1	0.776 9