改进栓皮栎树高预测混合效应模型研究

doi:10.13466/j.cnki.lyzygl.2018.05.010

摘要/Abstract

摘要：

树高与胸径是森林资源调查中2个重要的测树因子。鉴于树高测量相对不易实现的问题,以金华市永康市西溪镇的94株栓皮栎树为研究对象,在比较林业上常用的10个树高曲线模型拟合效果的基础上,改进了传统的Gompertz树高曲线模型,提出并构建了含有立地因子的Gompertz混合效应树高预测改进模型。实验表明:1)当对Gompertz混合效应模型拟合时,引入随机参数b₁,b₃时模型拟合最好;当对Gompertz混合效应改进模型拟合时,引入随机参数b₁,b₄时模型拟合最好。2)构建的Gompertz混合效应改进模型决定系数达到0.779,Gompertz混合效应模型决定系数为0.553,Gompertz模型决定系数为0.542,即仅凭混合效应方法构建模型对提高模型预测精度并不明显。实验证明了本文构建的Gompertz混合效应改进模型大大提高了栓皮栎的树高预测精度,为研究树种树高-胸径关系模型提供了一种新方法。

关键词: 栓皮栎树, 树高预测, 立地因子, Gompertz模型, 混合效应

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

中图分类号:

S758
S792.18

黄峰, 徐爱俊, 唐丽华. 改进栓皮栎树高预测混合效应模型研究[J]. 林业资源管理, 2018,(5): 54-62.

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

图/表 11

表1

表2

树高曲线经验模型

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]

表2

图1

表3

栓皮栎10种树高曲线模型参数估计值及拟合统计量

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

表3

图2

图3

表4

表5

Gompertz混合效应模型模拟

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

表5

表6

本文改进的Gompertz混合效应模型模拟

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

表6

表7

各模型参数估计值及拟合统计量

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

表7

图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