华北落叶松人工林直径分布预测模型构建

doi:10.3969/j.issn.1000-2006.201812012

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南京林业大学学报（自然科学版） ›› 2020, Vol. 44 ›› Issue (2): 117-124.doi: 10.3969/j.issn.1000-2006.201812012

华北落叶松人工林直径分布预测模型构建

周泽宇¹(), 杨绕华², 张玉珍¹, 黄选瑞¹, 张志东¹, 王冬至¹^,^*(), 李大勇²

1.河北农业大学林学院,河北省林木种植资源创新与保护实验室, 河北保定 071000
2.河北省木兰围场国有林场管理局, 河北承德 068450

收稿日期:2018-12-06 修回日期:2019-02-27 出版日期:2020-03-30 发布日期:2020-04-01
通讯作者: 王冬至
基金资助:
国家重点研发计划(2017YFD0600403);河北省教育厅资助科研项目(QN2018125);国家林业公益性行业科研专项项目(20150430304)

Prediction model construction of diameter distribution of Larix principis-rupprechtii plantation

ZHOU Zeyu¹(), YANG Raohua², ZHANG Yuzhen¹, HUANG Xuanrui¹, ZHANG Zhidong¹, WANG Dongzhi¹^,^*(), LI Dayong²

1. College of Forestry Agricultural University of Hebei, Forest Resources Innovation and Protection Laboratory of Hebei, Baoding 071000, China
2. Mulan Weichang State-owned Forest Farm Administration Bureau of Hebei Province, Chengde 068450, China

Received:2018-12-06 Revised:2019-02-27 Online:2020-03-30 Published:2020-04-01
Contact: WANG Dongzhi

摘要/Abstract

摘要：

【目的】基于不同直径分布预测模型(Weibull分布模型、Gamma分布模型、Lognormal分布模型),构建包含华北落叶松林分因子的直径分布线性混合效应模型,有助于分析直径分布对林分因子动态变化的响应。【方法】利用塞罕坝华北落叶松人工林标准地调查数据,应用最大似然估计法(Maximum Likelihood Estimation, MLE)估计模型参数,通过K-S(Kolmogorov-Smirnov)检验、C-V(Cramer-von Mises)检验、A-D(Anderson-Darling)检验对模型适用性进行检验,基于最优模型构建华北落叶松人工林直径分布线性混合效应模型。【结果】塞罕坝华北落叶松人工林直径分布最优模型为Weibull分布;基于最优模型,构建了包含优势高、断面积、对数密度的线性混合效应模型,当3个参数随机效应方差-协方差结构和误差项结构均为对角矩阵结构[UN(1)]时,模型的拟合效果最好。包含位置、尺度、形状3参数随机效应项模型的决定系数R²分别为0.895、0.888、0.801,均方误差(MSE)分别为5.365、1.724、1.151,均方根误差(RMSE)分别为2.316、1.313、1.073,拟合结果均较好。【结论】线性混合效应模型具有较好的预测直径分布能力,可为精准预测华北落叶松人工林直径分布提供理论依据和技术参数。

关键词: 华北落叶松, 动态直径分布模型, 最大似然估计, 线性混合模型

Abstract:

【Objective】 Based on different diameter distribution prediction models(Weibull distribution, Gamma distribution, Lognormal distribution), linear mixed-effects model including the main stand factors are constructed to help to reflect the response of diameter distribution to stand dynamics. 【Method】 Using the survey data of typical Larix principis-rupprechtii plantation, the model parameters were estimated by using the Maximum Likelihood Estimation (MLE), and the adaptability of the established model was evaluated via K-S (Kolmogorov-Smirnov)test, C-V (Cramer-von Mises) test, and A-D (Anderson-Darling) test. Based on the optimal model, a linear mixed-effects model of diameter distribution of Larix principis-rupprechtii plantation was constructed. 【Result】 The optimal model for the diameter distribution ofLarix principis-rupprechtii plantation was the 3-parameter Weibull distribution. Based on the optimal model, a linear mixed-effect model with inputs of stand dominant height, stand basal area and logarithmic density was constructed and the mixed-effect model had the best fitting result as the variance-covariance structure of random-effect and the error term variance-covariance structure was both Diagonal matrix UN(1). The R ² of linear mixed-effect model of Weibull distribution of parameter a, b, and c were estimated at 0.895, 0.888, and 0.801 respectively. The MSE were at 5.365, 1.724, 1.151 and RMSE were at 2.316, 1.313, 1.073. the fitting result was relatively accurate. 【Conclusion】 Linear mixed-effects model has the capability to accurately predict stand diameter distribution. The model can provide theoretical basis and technical parameters for accurately predicting the diameter distributions ofLarix principis-rupprechtii plantation.

Key words: Larix principis-rupprechtii, dynamic diameter distribution model, Maximum Likelihood Estimation(MLE), linear mixed-effect model

中图分类号:

S758.5⁺7

周泽宇,杨绕华,张玉珍,等. 华北落叶松人工林直径分布预测模型构建[J]. 南京林业大学学报（自然科学版）, 2020, 44(2): 117-124.

ZHOU Zeyu, YANG Raohua, ZHANG Yuzhen, HUANG Xuanrui, ZHANG Zhidong, WANG Dongzhi, LI Dayong. Prediction model construction of diameter distribution of Larix principis-rupprechtii plantation[J].Journal of Nanjing Forestry University (Natural Science Edition), 2020, 44(2): 117-124.DOI: 10.3969/j.issn.1000-2006.201812012.

图/表 8

表1

表2

表3

表4

表5

表6

表7

线性混合模型参数估计"

参数 parameter	位置参数 location parameter				尺度参数 scale parameter				形状参数 shape parameter
参数 parameter	估计值 estimation	标准差 SD	t	P	估计值 estimation	标准差 SD	t	P	估计值 estimation	标准差 SD	t	P
截距interept	-4.723	1.554	-3.04	0.081	-10.456	1.822	-5.73	0.010	1.733	2.390	3.23	0.012
H_d	1.029	0.081	12.77	<0.001	0.812	0.051	15.86	<0.001	0.023	0.057	9.74	<0.001
G	0.072	0.028	2.53	0.020	0.002	0.016	6.96	0.052	0.026	0.021	4.28	0.032
log s	-0.089	0.162	-3.66	0.041	0.734	0.239	-3.06	0.081	0.048	0.329	-2.61	0.018
$σ u 1 2$	0.032	0.069	3.26	0.007	0.001	0.524	6.28	0.025	0.001	0.007	2.00	0.023
$σ u 2 2$	0.150	0.393	4.08	0.049	0.031	0.338	3.87	0.047	0.058	0.284	5.23	0.008
e_ij	0.017 28	0.020	2.98	0.090	0.287	0.614	1.52	0.073	1.799	1.569	3.51	0.101
R²	0.895	0.888	0.801
σ_MSE	5.365				1.724				1.151
σ_RMSE	2.316				1.313				1.073

表7

图1

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数据类型 data type	变量 variable	平均胸径/ cm DBH	林分平均高/m height	林分密度/ (株· hm^-2) stand density	年龄/a age	林分断面积/ (m²·hm^-2) stand basal area	优势高/m dominant height	海拔/m elevation	坡度/ (°) slope
建模数据 modeling data	最小值min.	6.70	5.0	267	10	6.42	6.4	953	1
	最大值max.	31.30	21.9	3 014	53	41.98	23.5	1 429	37
	均值mean	19.39	14.9	769	35	20.58	16.2	1 184	17
	标准差SD	4.29	3.1	499	7	9.28	3.1	258	8
检验数据 validation data	最小值min.	7.80	5.0	258	11	8.79	6.4	930	2
	最大值max.	31.30	20.7	2 980	45	35.23	21.9	1 423	40
	均值mean	21.44	15.9	772	36	20.49	17.1	1 162	18
	标准差SD	4.10	2.9	501	7	5.51	2.9	260	8

模型 model	通过率/% pass rate	未通过率/% unpass rate
3-Gamma	58.7	41.3
3-Weibull	100.0	0.0
3-Lognormal	52.6	47.4

参数 parameter	Weibull分布 Weibull distribution					拟合优度 fitting goodness
参数 parameter	最大值max.	最小值min.	均值mean	标准差SD	D		W²		A²
a	23.02	0.69	10.43	4.63		0.072 (P<0.01)		0.266 (P<0.001)		1.756 (P<0.001)
b	20.75	3.01	8.98	4.27
c	9.81	1.00	3.03	1.47

变量 variable	1	2	3	4	5	6
D_g	0.487 2	-0.172 1	0.267 9	-0.197 5	-0.495 4	0.613 9
D_d	0.459 1	-0.175 9	0.262 4	0.786 6	0.257 3	-0.067 5
H_d	0.483 0	0.054 2	0.036 7	-0.511 5	0.707 3	0.022 0
A	0.423 8	0.120 6	-0.873 9	0.123 6	-0.163 5	-0.013 3
G	0.344 5	0.572 7	0.305 9	-0.107 6	-0.355 1	-0.567 5
log s	-0.142 6	0.770 7	0.026 5	0.232 0	0.187 9	0.543 9

主成分 principle component	特征值 eigenvalue	方差贡献率 variance contribution	累积贡献率 cumulative contribution
1	3.638 3	0.606 4	0.606 4
2	1.511 9	0.252 0	0.858 4
3	0.414 5	0.069 1	0.927 5
4	0.237 1	0.039 5	0.967 0
5	0.168 1	0.028 0	0.995 0
6	0.030 1	0.005 0	1.000 0

华北落叶松人工林直径分布预测模型构建

Prediction model construction of diameter distribution of Larix principis-rupprechtii plantation

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参数类别 parameter category	随机效应 random-effect	AIC	BIC	-2Log- Like	LRT	P
位置参数 location parameter	截距 intercept	566.9	583.8	554.9	0.05	0.950
	H_d、log s	544.2	566.7	528.2	7.86	0.005
	H_d	593.7	585.2	572.7	2.62	0.450
	log s	583.7	591.6	582.7	1.58	0.640
尺度参数 scale- parameter	截距 intercept	429.9	446.8	417.9	0.01	0.998
	H_d、log s	443.6	426.8	414.8	3.17	0.075
	H_d	529.8	545.6	517.8	1.05	0.560
	log s	527.8	541.1	517.8	1.21	0.510
形状参数 shape parameter	截距 intercept	431.3	451.0	417.3	0.02	0.920
	H_d、log s	425.6	436.8	417.6	4.73	0.193
	H_d	429.8	445.6	417.8	3.54	0.420
	log s	427.8	441.1	417.8	3.62	0.380

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