A Crown Ratio Model for Cunninghamia lanceolata Plantations Based on Mixed Effect in Hubei

doi:10.11924/j.issn.1000-6850.casb2020-0023

Abstract

Abstract:

The paper aims to study the relationship between crown ratio and stand factors, and analyze the effects of different factors on crown ratio. 715 dominant trees and average trees in 181 sample plots were established in Chinese fir planting areas in Hubei Province. Tree height, diameter at breast height, height to diameter ratio, stand density and basal area per hectare for trees larger than the subject tree closely associated with crown ratio were selected among tree and site factors. The basic model of crown ratio was constructed by adding correlation factors as variables in the form of logistic equation, and the single-level mixed effect model of sample plot was further established. By comparing the AIC, BIC and likelihood ratio test, the mixed model with random parameters a and f has the best fitting effect compared with the model without random parameters. The results of independent sample test show that the root mean square errors and average error of the mixed model are reduced, respectively -0.0095 and 0.1175, and the residual range is smaller. Compared with the basic model, R² of the mixed model increased from 0.3231 to 0.5417, but RMSE and Bias decreased. Based on the goodness of fit and test index of the model, the mixed model can significantly improve the fitting accuracy of the model, and can be used to predict the crown length.

Key words: crown ratio, Cunninghamia lanceolata, logistic equation, mixed effect, model

CLC Number:

S750

Yuan Hui, Du Chaoqun, Zhao Xiaotao, Xiao Zhiming, Zhao Hu. A Crown Ratio Model for Cunninghamia lanceolata Plantations Based on Mixed Effect in Hubei[J]. Chinese Agricultural Science Bulletin, 2021, 37(4): 31-37.

Figures/Tables 10

References 24

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数据	变量	极小值	极大值	平均值	标准差
建模数据(n=500)	胸径/cm	7.5	39.10	16.88	5.56
	树高/m	6.70	23.90	13.18	3.15
	海拔/m	36	1462	632.71	496.36
	坡度/°	3	47	19.85	10.05
	树龄/年	6	59	23.84	10.89
	每公顷株数/(株/hm²)	500	7050	1963.51	1168.01
	冠长/m	1.3	17.1	6.41	2.67
	冠长率	0.12	0.92	0.48	0.14
	大于对象树木每公顷断面积/(m²/hm²)	0	45.58	15.99	10.79
	高径比	0.46	1.14	0.81	0.12
检验数据(n=215)	胸径/cm	7.60	34.40	14.11	6.03
	树高/m	6.80	21.50	11.55	2.99
	海拔/m	12	1694	345.78	602.50
	坡度/°	2	30	10.09	9.28
	树龄/年	8	39	16.37	10.35
	每公顷株数/(株/hm²)	1250.00	6467.00	3965.09	1797.37
	冠长/m	1.90	15.10	5.81	2.45
	冠长率	0.16	0.89	0.50	0.13
	大于对象树木每公顷断面积/(m²/hm²)	0	44.13	19.36	12.45
	高径比	0.52	1.17	0.87	0.15

数据	变量	极小值	极大值	平均值	标准差
建模数据(n=500)	胸径/cm	7.5	39.10	16.88	5.56
	树高/m	6.70	23.90	13.18	3.15
	海拔/m	36	1462	632.71	496.36
	坡度/°	3	47	19.85	10.05
	树龄/年	6	59	23.84	10.89
	每公顷株数/(株/hm²)	500	7050	1963.51	1168.01
	冠长/m	1.3	17.1	6.41	2.67
	冠长率	0.12	0.92	0.48	0.14
	大于对象树木每公顷断面积/(m²/hm²)	0	45.58	15.99	10.79
	高径比	0.46	1.14	0.81	0.12
检验数据(n=215)	胸径/cm	7.60	34.40	14.11	6.03
	树高/m	6.80	21.50	11.55	2.99
	海拔/m	12	1694	345.78	602.50
	坡度/°	2	30	10.09	9.28
	树龄/年	8	39	16.37	10.35
	每公顷株数/(株/hm²)	1250.00	6467.00	3965.09	1797.37
	冠长/m	1.90	15.10	5.81	2.45
	冠长率	0.16	0.89	0.50	0.13
	大于对象树木每公顷断面积/(m²/hm²)	0	44.13	19.36	12.45
	高径比	0.52	1.17	0.87	0.15

随机参数	参数个数	AIC	BIC	log-likelihood	LRT	P
无	6	-975.154	-867.5326	489.7412
a	7	-1005.499	-961.0544	510.7494	10.32	0.0221
a、f	9	-1006.777	-968.92	513.3886	9.46	0.0314
b、c、e	12	-1000.393	-940.9538	513.1967
a、b、c、e	16	-991.157	-913.4282	512.5785

随机参数	参数个数	AIC	BIC	log-likelihood	LRT	P
无	6	-975.154	-867.5326	489.7412
a	7	-1005.499	-961.0544	510.7494	10.32	0.0221
a、f	9	-1006.777	-968.92	513.3886	9.46	0.0314
b、c、e	12	-1000.393	-940.9538	513.1967
a、b、c、e	16	-991.157	-913.4282	512.5785

方差协方差矩阵	AIC	BIC	log-likelihood	LRT	P
广义正定矩阵	-1006.778	-961.053	513.3879
对角矩阵	-1003.499	-962.3483	510.3879	5.28	0.0216