An Improved Hight Prediction Mixed Effect Model for Quercus variabilis

doi:10.13466/j.cnki.lyzygl.2018.05.010

Abstract

Abstract:

Tree height and DBH are two important tree-building factors in the survey of forest resources.In view of the relatively difficulty for height measurement,in this article we took 94 cork oaks from Xixi Town,Jinhua City as the research object and compared the fitting effects of 10 tree height curve models commonly used in forestry,improved the traditional Gompertz tree height curve model,proposed and constructed a Gompertz mixed effect tree high prediction model with site factors.The results show that:(1) The model fits best when the random parameters b₁ and b₃ are introduced for Gompertz mixed effect model.The model fits best when the random parameters b1 and b4 are introduced for Gompertz mixed effect improvement model.(2) The Gompertz mixed effect improvement model constructed in this paper has a coefficient of determination of 0.779 with 0.553 Gompertz mixed effect model,and with 0.542 for Gompertz model.That is building the model only by the mixed effect method is not obvious for improving the accuracy of the prediction model.(3) Experiments show that the Gompertz mixed effect improvement model constructed in this paper greatly improves the prediction accuracy of the height of Quercus variabilis,and provides a new method for studying the relationship between tree height and diameter at breast height.

Key words: Cork oak, tree height prediction, site factor, Gompertz model, mixed effect

CLC Number:

S758
S792.18

HUANG Feng, XU Aijun, TANG Lihua. An Improved Hight Prediction Mixed Effect Model for Quercus variabilis[J]. FOREST RESOURCES WANAGEMENT, 2018, (5): 54-62.

Figures/Tables 11

Tab.1

Tab.2

Tree height curve empirical model

序号	模型形式	作者/文献
(1)	$H = β 0 - β 1 × exp (- β 2 × DBH)$	Banin (2012)/[8]
(2)	$H = β 0 + β 1 / (β 2 + DBH)$	Tang(1991)/[11]
(3)	$H = β 0 × (1 - exp - β 1 × DBH)$	Meyer(1940)/[3]
(4)	H=β₀×exp(-β₁×exp $- β 2 × DBH$ )	Gompertz(1992)/[9]
(5)	$H = β 0 × exp (- β 1 × DB H β 2)$	Lundqvist-Korf(1939)/[12]
(6)	$H = β 0 + β 1 × (1 - exp - β 2 × DBH)$	Mitscherlish(1919)/[13]
(7)	$H = 10 β 0 + β 1 DBH$	Schumacher(1939)/[14]
(8)	$H = β 0 × exp (β 1 / (DBH + β 2))$	Ratkowsky(1990)/[11]
(9)	H=DBH²/(β₀+β₁×DBH+β₂×DBH²)	Curtis(1967)/[11]
(10)	$H = β 0 × exp (- β 1 / DBH)$	寺崎(1915)/[13]

Tab.2

Fig.1

Tab.3

Estimation values and fitting statistics of 10 tree height curve models of Quercus variabilis

参数、统计量/指标	模型编号
参数、统计量/指标	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
$β 0$	18.656	22.376	18.642	18.350	0.005	0.073	1.340	22.253	0.001	21.859
$β 1$	18.584	-4.582	3.465	1.543	-8.280	18.583	-0.077	-0.196	0.007	0.178
$β 2$	3.449	0.146	—	4.325	0.045	3.449	—	0.021	0.047	—
RMSE	2.906	2.945	2.906	2.887	3.113	2.906	2.912	2.942	2.938	2.912
SSE	264.4	268.0	264.4	262.7	283.2	264.4	267.8	267.8	267.4	267.8
R²	0.539	0.533	0.539	0.542	0.506	0.539	0.533	0.533	0.534	0.533

Tab.3

Fig.2

Fig.3

Tab.4

Tab.5

Gompertz mixed effect model simulation

模拟次数	随机参数	参数个数	AIC	BIC	R²
基本模型	无	3	0.184	-3.375	0.542
模拟1	$b 1$	4	0.159	-3.500	0.553
模拟2	$b 2$	4	0.159	-3.500	0.553
模拟3	$b 1, b 3$	5	0.159	-3.500	0.553
模拟4	$b 2$ , $b 3$	5	-0.257	-3.816	0.468
模拟5	$b 1, b 2, b 3$	6	-0.256	-3.816	0.468

Tab.5

Tab.6

Improved Gompertz mixed-effect model simulation

模拟次数	随机参数	参数个数	AIC	BIC	R²
基本模型	无	4	22.570	-0.569	0.596
模拟1	$b 3$	5	26.430	3.291	0.777
模拟2	$b 4$	5	26.881	3.742	0.709
模拟3	$b 1, b 3$	6	26.931	3.793	0.703
模拟4	$b 1, b 4$	6	26.471	3.333	0.779
模拟5	$b 2, b 3$	6	26.465	3.327	0.726
模拟6	$b 3, b 4$	6	22.589	-0.550	0.598
模拟7	$b 1, b 2, b 3$	7	26.921	3.782	0.702
模拟8	$b 1, b 3, b 4$	7	21.994	-1.144	0.512
模拟9	$b 2, b 3, b 4$	7	26.921	3.782	0.702
模拟10	$b 1, b 2, b 3, b 4$	8	26.454	3.315	0.778

Tab.6

Tab.7

Model parameters,variance estimates and fitting statistics

参数/ 统计量	参数	Gompertz 模型	Gompertz混合效应模型	本文改进的Gompertz 混合效应模型
固定参数	$β 1$	18.35	-33.039	3.853
	$β 2$	1.543	30.984	13.263
	$β 3$	4.325	-168.259	4.643
	$β 4$	—	—	0.053
拟合统计量	Bias	-0.0009	0.0001	0.4542
	RMSE	2.887	2.911	1.118
	R²	0.542	0.553	0.779

Tab.7

Fig.4

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变量	最小值	最大值	标准差	均值	偏度	峰度
坡度/(°)	20.73	42.73	3.21	36.05	-1.50	5.76
坡向	1	3	1.01	1.98	0.04	-2.04
坡位	1	3	0.70	1.51	1.02	-0.25
海拔/m	169	521	41.70	475.89	-4.49	30.99
树高(H)/m	8	19	2.48	14.50	-0.28	-0.63
胸径(DBH)/cm	25	100	16.40	47.17	1.19	1.37

检验指标	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
ME	0.0001	-0.0003	0.0002	0.0057	-0.3003	-0.00008	-0.0390	1.4600	0.0070	-0.0036
MAE	1.1996	1.2168	1.1995	1.1907	1.2804	1.1996	1.2108	1.9769	1.3922	1.2152
M%E	-0.0162	-0.0164	-0.0162	-0.0161	-0.0389	-0.0162	-0.0191	-0.0156	-0.0245	-0.0166
MA%E	0.0910	0.0920	0.0910	0.0904	0.0985	0.0910	0.0920	0.0920	0.0927	0.0920