Research on Growth Mixed Effect Model for Basal Area of Cunninghamia lanceolata Plantation Based on Site Factors

doi:10.13466/j.cnki.lyzygl.2021.02.011

Abstract

Abstract:

Based on data of 150 Cunninghamia lanceolata Plantation plots in Central China's Hunan Province,this study attempt to construct a mixed effect model of Cunninghamia lanceolata Plantation growth with site factors through using methods such as variance analysis,regression analysis,nonlinear mixed effects model and K-means clustering.The results show that:(1)Altitude (HB),slope (PD),slope position (PW),soil thickness (TH) and soil type (TL)have a significant impact on the growth of the basal area,and the order of significance is TL>TH>PD> PW>HB.(2)Among the eight commonly used theoretical growth equations,Schumacher (M5)has the highest coefficient of determination (R²=0.7636),and was selected as the basic model for forest basal area growth simulation.(3)A nonlinear mixed effects model was constructed by taking 107 site types (ST)of different site factor combinations as random effects and the coefficient of determination (R²)increased to 0.895 1.(4)The 107 site types (ST)were clustered into 5 site type groups (STG),and the mixed effect model of Cunninghamia lanceolata cross-sectional basal area growth was further constructed,and the determination coefficient (R²)increased to 0.920 2.Studies have shown that the nonlinear mixed effect model based on site factors objectively explains the impact of site factors on the growth of Cunninghamia lanceolata Plantation,which helps improve the simulation accuracy of the stand growth model.

Key words: Cunninghamia lanceolata, basal area, site typ, mixed effect model, cluster analysis

CLC Number:

S791.27
S711

WU Xuping, LV Yong, ZHANG Xiongqing, YI Xuan, ZHU Guangyu. Research on Growth Mixed Effect Model for Basal Area of Cunninghamia lanceolata Plantation Based on Site Factors[J]. FOREST RESOURCES WANAGEMENT, 2021, (2): 75-82.

Figures/Tables 11

Tab.1

Tab.2

Tab.3

Basic models candidates

序号	模型名称	表达式
M1	理查德(Richards)	G=a×(1-e^(-^b^×^T⁾)×(SDI/1000)^c
M2	理查德(Richards)	G=a×(1-e^(-^b^×^T⁾)×(N/1000)^c
M3	舒马克(Schumacher)	G=a×e^(-^b^×^T⁾)×(SDI/1000)^c
M4	舒马克(Schumacher)	G=a×e^(-^b^×^T⁾)×(N/1000)^c
M5	舒马克(Schumacher)	G=HT⁽^a⁺^b/T⁾×(SDI/1000)⁽^c⁺^d/T⁾×e⁽^q⁺^w/T⁾
M6	舒马克(Schumacher)	G=HT⁽^a⁺^b/T⁾×(N/1000)⁽^c⁺^d/T⁾×e⁽^q⁺^w/T⁾
M7	舒马克(Schumacher)	G=e⁽^a⁺^b/T⁾×(SDI/1000)^c+d/T
M8	单分子(Mitscherlish)	G=a×(1- $e (- b × (SDI / 1000) c)$ ×T)

Tab.3

Tab.4

Tab.5

Tab.6

Tab.7

Tab.8

Tab.9

Fig.1

Fig.2

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因子	断面积(G)/(m²/hm²)	年龄(Age)/a	密度指数(SDI)	单位面积株数(N)/株/hm²)	海拔(HB)/m
平均值	26.78	18	2079	2580	469
标准差	8.95	3	974	1000	268
最小值	9.63	11	969	780	49
最大值	52.91	27	5536	5175	1250

立地因子	符号	等级划分
海拔	HB	100m为一级
坡度	PD	缓坡	斜坡	陡坡	急坡	险坡
坡位	PW	上坡	中坡	下坡
坡向	PX	阳坡	阴坡
土壤类型	TL	红壤	黄壤	山地黄壤
土壤厚度	TH	薄	中	厚

因子组	平方和	自由度	均方	F值	Pr>F	备注
HB	1182.38	11	107.49	2.12	0.02300	显著
PD	966.22	4	241.55	4.77	0.00128	显著
PW	461.26	2	230.63	4.56	0.01228	显著
PX	11.75	1	11.74	0.23	0.63084	不显著
TH	730.34	2	365.17	7.21	0.00108	显著
TL	1196.30	2	598.15	11.82	0.00002	显著

模型	a	b	c	d	q	w	R²	P/%	MAE	RMSE
M1	12.455	473.41	0.8146	—	—	—	0.6376	97	3.61	4.85
M2	20.551	472.66	0.3863	—	—	—	0.2187	95	6.16	8.01
M3	19.143	9.3464	0.8945	—	—	—	0.7118	97	3.63	4.86
M4	33.455	9.9705	0.4674	—	—	—	0.2982	95	5.76	7.59
M5	1.4039	-17.978	0.8222	0.8792	-0.3722	33.868	0.7636	97	3.08	4.40
M6	1.7490	-20.861	0.0382	8.3653	-0.3535	34.106	0.4226	95	5.12	6.88
M7	2.9448	-9.9929	0.9145	10.881	—	—	0.7119	97	3.62	4.86
M8	61.762	0.0088	1.3313	—	—	—	0.7014	97	3.84	4.95

随机效应	添加位置	a	b	c	d	q	w	AIC	BIC	R²
ST	a	1.205	-13.66	0.731	2.906	0.175	22.03	877.41	901.49	0.8857
ST	b	1.254	-14.49	0.772	2.324	0.035	24.29	877.91	901.99	0.8794
ST	c	1.212	-13.81	0.762	2.566	0.119	22.90	872.41	896.50	0.8951
ST	d	1.286	-15.12	0.818	1.686	-0.091	26.51	873.88	897.97	0.8871
ST	q	1.256	-14.68	0.749	2.594	0.044	24.62	879.17	903.26	0.8785
ST	w	1.306	-15.57	0.786	2.037	-0.099	27.07	879.65	903.74	0.8713