基于气候因子的杉木单木胸径生长模型构建

doi:10.12302/j.issn.1000-2006.202108030

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南京林业大学学报（自然科学版） ›› 2023, Vol. 47 ›› Issue (1): 47-56.doi: 10.12302/j.issn.1000-2006.202108030

所属专题：智慧林业之森林参数遥感估测

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基于气候因子的杉木单木胸径生长模型构建

郭常酉¹(), 郭宏仙², 王宝华²^,^*()

1.国家林业和草原局宣传中心,北京 100013
2.宁夏大学农学院,宁夏银川 750021

收稿日期:2021-08-15 接受日期:2021-10-13 出版日期:2023-01-30 发布日期:2023-02-01
通讯作者: 王宝华
基金资助:
国家自然科学基金项目(31470592)

Study on increment model of individual-tree diameter of Cunninghamia lanceolata in consideration of climatic factors

GUO Changyou¹(), GUO Hongxian², WANG Baohua²^,^*()

1. Propaganda Center, State Forestry and Grassland Administration, Beijing 100013, China
2. Agricultural College of Ningxia University, Yinchuan 750021, China

Received:2021-08-15 Accepted:2021-10-13 Online:2023-01-30 Published:2023-02-01
Contact: WANG Baohua

摘要/Abstract

摘要： 【目的】 为准确预测湖南杉木的生长及制定经营管理措施,构建了考虑气候因子的杉木单木胸径生长混合效应模型。【方法】 基于湖南省第七、八次全国森林资源连续清查中73块样地的3 638株杉木数据,运用多元逐步回归的方法,考虑林木大小、竞争、立地和其他林分因子以及气候因子对杉木胸径生长的影响,分别以5年胸径增长量(D₂-D₁)、5年胸径增长量的自然对数[ln(D₂-D₁+1)]、5年胸径平方增长量的自然对数[ln(D²₂-D²₁+1)]、胸径平方增长量(D²₂-D²₁)为因变量构建模型,选择最优基础模型。在最优模型的基础上,引入样地随机效应,构建单水平线性混合效应模型,并引入3种常用的异方差函数和3种常用的自相关结构来消除模型的异方差和自相关,最后采用十折交叉验证的方法对模型的预估效果进行检验。【结果】 与其他3种因变量相比,因变量为ln(D²₂-D²₁+1)时模型表现最好,因此,因变量为ln(D²₂-D²₁+1)的模型为最优基础模型。根据模型结果可以看出,显著影响杉木胸径生长的变量主要包括期初胸径、大于对象木胸高断面积之和与期初胸径之比、每公顷断面积、坡向正弦值与海拔自然对数之积、年平均降雨量和1月平均最低温度。与最优基础模型相比,混合效应模型显著提高了模型的预测精度。同时,异方差函数和自相关矩阵的加入也明显改善了模型的拟合效果,其中以指数函数(exponent)和自回归移动平均结构[ARMA(1,1)]表现最好。在模型十折交叉检验中,混合效应模型也表现出较好的拟合效果。【结论】 气候因子对于湖南杉木单木胸径的生长有显著影响。与基础模型相比,引入样地随机效应构建单水平线性混合效应模型可以显著提高模型效果,所构建的模型可以为该区域杉木的科学经营提供支持。

关键词: 杉木, 单木胸径生长, 气候因子, 混合效应模型, 十折交叉验证

Abstract:

【Objective】 To accurately predict growth and formulate forest management strategies for Cunninghamia lanceolata in Hunan Province, a mixed-effects individual tree diameter increment model for Cunninghamia lanceolata was developed considering climatic factors. 【Method】 Based on the data of 3 638 observations in 73 plots from the 7^th and 8^th Chinese National Forest Inventory in Hunan Province, this study used the multiple stepwise regression method to introduce tree size, competition, site conditions, other stand variables, and climate factors as independent variables, and developed and evaluated four different dependent variables: i.e. 5-year diameter increment (D₂-D₁), the natural logarithm of 5-year diameter increment [ln(D²₂-D²₁+1)], the natural logarithm of 5-year squared diameter increment [ln(D²₂-D²₁+1)], and 5-year squared diameter increment (D²₂-D²₁). An optimal basic model was selected. A linear mixed-effects model with sample plots as random effects was then fitted. In addition, three commonly used variance functions and correlation structures were introduced to remove the heteroscedasticity of the residuals and autocorrelation. Finally, the 10-fold cross-validation method was used to assess predictive ability. 【Result】 Compared with the other three dependent variables, the model performed best with ln(D²₂-D²₁+1) as the dependent variable. Therefore, the model in which the dependent variable was ln(D²₂-D²₁+1) was selected as the optimal basic model. According to the results of the optimal basic model, the initial diameter, the ratio of the sum of the basal area of trees with diameters larger than the subject tree’s diameter to the initial diameter, stand basal area per hectare, the product of the sine of the slope and the natural logarithm of the altitude, mean annual precipitation, and mean minimum temperature in January significantly affected the increase in the diamteter of Cunninghamia lanceolata. Compared with the optimal basic model, the mixed-effects model showed a significantly improved prediction accuracy. Additionally, the introduction of variance functions and correlation structures also significantly improved the model’s performance, of which the exponent function (exponent) and ARMA(1,1) performed the best. In the 10-fold cross-validation, the mixed-effects model also showed better performance. 【Conclusion】 Climatic factors have a significant effect on the increase of diameter in Cunninghamia lanceolata. Compared with the basic model, the linear mixed-effects model with sample plots as random effects could greatly improve the model’s performance, and we hope that the model could provide support for the scientific management of Cunninghamia lanceolata in Hunan Province.

Key words: Cunninghamia lanceolata, individual-tree diameter increment, climate factor, mixed-effects model, 10-fold cross-validation

中图分类号:

S757

郭常酉,郭宏仙,王宝华. 基于气候因子的杉木单木胸径生长模型构建[J]. 南京林业大学学报（自然科学版）, 2023, 47(1): 47-56.

GUO Changyou, GUO Hongxian, WANG Baohua. Study on increment model of individual-tree diameter of Cunninghamia lanceolata in consideration of climatic factors[J].Journal of Nanjing Forestry University (Natural Science Edition), 2023, 47(1): 47-56.DOI: 10.12302/j.issn.1000-2006.202108030.

图/表 9

表1

表2

表3

不同因变量的杉木单木胸径生长模型拟合结果"

因变量 dependent variable	自变量 independent variable	参数估计值 estimate	标准差 SD	t	P	BIAS	RMSE	R²
	截距intercept	3.451	0.609	5.671	<0.05
	1/D₁	9.320	0.585	15.922	<0.05
	N₁	-1.132×10^-4	3.382×10^-5	-3.348	<0.05
D₂-D₁	S_BAL1/D₁	-12.570	0.406	-30.989	<0.05	1.041	1.318	0.277
	T_max07	-0.108	2.090×10^-2	-5.158	<0.05
	T_min01	0.285	3.204×10^-2	8.907	<0.05
	P_MA1	8.965×10^-4	1.192×10^-4	7.519	<0.05
	S_LN	4.669×10^-2	5.118×10^-3	9.123	<0.05
	截距intercept	2.406	0.172	13.966	<0.05
	1/D₁	2.726	0.167	16.315	<0.05
	S_BAL1/D₁	-4.280	0.103	-41.491	<0.05
ln(D₂-D₁+1)	T_min01	0.098	0.011	8.572	<0.05	1.007	1.339	0.325
	T_growth	-0.070	0.008	-8.612	<0.05
	P_PT01	0.002	0.000	4.166	<0.05
	S_LN	0.007	0.001	4.452	<0.05
	截距intercept	2.783	1.096×10^-1	25.389	<0.05
	D₁	4.745×10^-2	4.283×10^-3	11.080	<0.05
	S_BAL1/D₁	-7.575	3.112×10^-1	-24.342	<0.05
ln( $D 22$ - $D 12$ +1)	S_BA1	-8.268×10^-3	2.233×10^-3	-3.702	<0.05	1.006	1.341	0.471
	P_MA1	6.473×10^-4	6.153×10^-5	10.520	<0.05
	T_min01	8.088×10^-2	1.356×10^-2	5.966	<0.05
	S_LN	1.349×10^-2	2.605×10^-3	5.178	<0.05
	截距intercept	1.054×10²	19.040	5.538	<0.05
	1/D₁	68.550	21.850	3.138	<0.05
	N₁	-1.679×10^-2	8.305×10^-4	-20.212	<0.05
D²₂-D²₁	D_R1	90.800	3.140	28.919	<0.05	1.045	1.326	0.348
	T_min01	7.397	1.171	6.316	<0.05
	T_growth	-5.979	-0.831	-7.193	<0.05
	P_PT07	3.278×10^-2	1.506×10^-2	2.177	<0.05
	S_LN	1.116	0.147	7.579	<0.05

表3

图1

表4

表5

图2

表6

图3

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统计值 statistics	胸径/cm DBH			林分密度/ (株·hm^-2) stand density	胸高断面积/ (m²·hm^-2) basal area	海拔/m elevation	坡度/ (°) slope	坡向/ (°) aspect	林龄/a stand age	树高/m tree height
统计值 statistics	期初 initial	期末 after a 5-year growth	林分平均 quadratic mean	林分密度/ (株·hm^-2) stand density	胸高断面积/ (m²·hm^-2) basal area	海拔/m elevation	坡度/ (°) slope	坡向/ (°) aspect	林龄/a stand age	树高/m tree height
平均值 mean	10.64	12.89	10.94	1 668.60	12.62	430.00	28.98	169.78	16.45	8.40
标准差 SD	4.75	4.94	3.39	854.77	10.56	305.45	9.84	107.08	7.99	2.91
最小值 min	5.00	5.10	6.30	313.00	2.09	60.00	5.00	0.00	4.00	1.50
最大值 max	34.80	36.70	24.78	3 209.00	40.38	1 555.00	48.00	315.00	40.00	18.00

统计值 statistics	气温/℃ temperature		降水量/mm precipitation		生长季平均气温/℃ mean annual growing season temperature	年平均气温/℃ mean annual temperature	年平均降水量/mm mean annual precipitation
统计值 statistics	1月 Jan.	7月 Jul.	1月 Jan.	7月 Jul.	生长季平均气温/℃ mean annual growing season temperature	年平均气温/℃ mean annual temperature	年平均降水量/mm mean annual precipitation
平均值 mean	1.38	26.11	61.04	182.80	22.48	17.03	1 480.00
标准差 SD	1.00	1.40	16.32	42.60	1.35	1.20	230.25
最小值 min	-2.25	21.35	35.20	116.20	17.90	12.74	1 152.00
最大值 max	3.32	28.68	139.60	333.40	24.61	18.86	2 429.00

模型 model	随机效应参数 random parameters	AIC	BIC	-2LL	LRT	P
基础模型 basic model	无	7 497	7 547	7 481
Model.1	b₄	6 381	6 437	6 363	1 118.15	<0.000 1
Model.2	b₂、b₄	6 221	6 289	6 199	164.07	<0.000 1
Model.3	b₁、b₂、b₄	6 210	6 297	6 182	17.09	0.000 7
Model.4	b₂、b₃、b₅、b₆	6 209	6 320	6 173	9.39	0.052 1
Model.5	b₀、b₁、b₂、b₃、b₆	6 209	6 352	6 163	—	—
Model.6	—	未收敛	—	—
Model.7	—	未收敛	—	—

模型 model	异方差函数 variance function	自相关结构 correlation structure	AIC	BIC	-2LL	LRT	P
Model.3	无	无	6 210	6 297	6 182	—	—
Model.3.1	power	无	6 104	6 197	6 074	108.28	<0.000 1
Model.3.2	exponent	无	6 084	6 176	6054	128.66	<0.000 1
Model.3.3	ConstPower	无	6 106	6 205	6 074	108.27	<0.000 1
Model.3.2.1	exponent	CS	—	未收敛	—	—	—
Model.3.2.2	exponent	AR(1)	5 988	6 087	5 956	97.43	<0.000 1
Model.3.2.3	exponent	ARMA(1,1)	5 914.99	6 020	5 881	172.51	<0.000 1

模型model	R²	-2LL	AIC	BIC	LRT	P	NMSE	PRESS
基础模型 basic model	0.471 3	7 481	7 497	7 547			0.075 1	656.201 6
混合效应模型 mixed-effects model	0.676 5	5 928	5 962	6 068	15 553.27	<0.001	0.047 4	414.736 8

基于气候因子的杉木单木胸径生长模型构建

Study on increment model of individual-tree diameter of Cunninghamia lanceolata in consideration of climatic factors

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