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

doi:10.3969/j.issn.1000-2006.201812012

JOURNAL OF NANJING FORESTRY UNIVERSITY ›› 2020, Vol. 44 ›› Issue (2): 117-124.doi: 10.3969/j.issn.1000-2006.201812012

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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 E-mail:2291818678@qq.com;wangdz@126.com

Abstract

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

CLC Number:

S758.5⁺7

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, 2020, 44(2): 117-124.

Figures/Tables 8

Table 1

Table 2

Table 3

Table 4

Table 5

Table 6

Table 7

Parameter estimation of linear mixed model"

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

Table 7

Fig.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

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

[1]	WANG Yunni, CAO Gongxiang, XU Lihong, CHEN Shengnan. Evapotranspiration characteristics of Larix principis-rupprechtii plantation and its impact factors in the Daqing Mountains of Inner Mongolia [J]. JOURNAL OF NANJING FORESTRY UNIVERSITY, 2023, 47(4): 148-156.
[2]	NIE Luyi, DONG Lihu, LI Fengri, MIAO Zheng, XIE Longfei. Construction of taper equation for Larix olgensis based on two-level nonlinear mixed effects model [J]. JOURNAL OF NANJING FORESTRY UNIVERSITY, 2022, 46(3): 194-202.
[3]	LIU Zixuan, JIA Cun, QIN Zhiqiang, LI Yongning. Effects of light conditions on the growth of understory Picea meyeri sapling in Larix principis-rupprechtii forest [J]. JOURNAL OF NANJING FORESTRY UNIVERSITY, 2020, 44(6): 111-117.