冀北山地杨桦次生混交林地位指数模型构建

doi:10.13466/j.cnki.lczyyj.2024.03.009

摘要/Abstract

摘要：

在多树种、结构复杂的阔叶混交林中,如何基于优势木胸径构建高精度地位指数模型是混交林立地质量评价中亟待解决的科学问题。以河北省木兰围场山杨与白桦阔叶混交林为研究对象,基于70块标准地调查数据(每块标准地面积为0.06 hm²),利用非线性最小二乘法、BP神经网络、非线性混合效应3种参数估计方法分别构建山杨与白桦阔叶混交林地位指数模型,采用均方误差(MSE)、均方根误差(RMSE)、平均偏差百分比(MPB)、决定系数(R²)、调整后的决定系数($R_{\mathrm{adj}}^{2}$)、Akaike信息准则(AIC)、贝叶斯信息准则(BIC)和负2倍对数似然值(-2LL),比较不同参数估计方法对模型预测精度的影响。结果表明:1)在5个候选方程中,以优势木胸径为自变量的Logistic方程是山杨与白桦阔叶混交林的最优地位指数基础模型,其模型的MSE、RMSE、MPB、R²、$R_{\mathrm{adj}}^{2}$分别为9.071 7、2.269 6、11.972 9、0.583 8、0.569 9;2)与非线性最小二乘和BP神经网络相比,基于非线性混合效应构建的山杨与白桦阔叶混交林地位指数模型具有更高的预测精度,其模型的MSE、RMSE、MPB、R²、$R_{\mathrm{adj}}^{2}$分别为5.477 4、1.779 4、9.161 4、0.782 8、0.761 7。以优势木胸径为自变量构建的地位指数模型可用于评价混交林立地质量。

关键词: 地位指数, BP神经网络, 非线性混合效应模型, 阔叶混交林

Abstract:

In broad-leaved mingled forest with multiple tree species and complex structures,constructing a high-precision site index model based on the diameter at breast height of dominant trees is a key scientific challenge in evaluating the site quality of these forests.The Populus davidiana and Betula platyphylla broad-leaved mingled forest in Mulan Weichang,Hebei Province is selected as the research object.Based on the survey data from 70 standard plots(each standard land area is 0.06 hm²),using the nonlinear least squares method,BP neural network,and nonlinear mixed-effects model,three parameter estimation methods are used to construct the site index models of P.davidiana and B.platyphylla broad-leaved mingled forest.Using Mean Square Error(MSE),Root Mean Square Error(RMSE),Mean Percentage Bias(MPB),Coefficient of Determination(R²),Adjusted Coefficient of Determination($R_{\mathrm{adj}}^{2}$),Akaike Information Criterion(AIC),Bayesian Information Criterion(BIC),and Negative Twice the Log-Likelihood(-2LL),the impact of different parameter estimation methods on model prediction accuracy is compared.The results show that:1)Among the five candidate equations,the logistic equation with the diameter at breast height of dominant trees as the independent variable is the optimal site index base model for the mingled P.davidiana and B.platyphylla broad-leaved forest,and the MSE,RMSE,MPB,R²,$R_{\mathrm{adj}}^{2}$ of its model are 9.071 7,2.269 6,11.972 9,0.583 8,0.569 9,respectively.2)Compared with the nonlinear least squares method and BP neural network,the site index model of P.davidiana and B.platyphylla broad-leaved mingled forest based on the nonlinear mixed-effects has higher prediction accuracy.The MSE,RMSE,MPB,R²,$R_{\mathrm{adj}}^{2}$ of the model are,5.477 4,1.779 4,9.161 4,0.782 8,0.761 7,respectively.The site index model constructed with the diameter at breast height of dominant trees as the independent variable can be used to evaluate the site quality of mingled forests.

Key words: site index, BP neural network, nonlinear mixed-effects model, broad-leaved mingled forest

中图分类号:

S758.1

董自华, 李大勇, 梁宇, 梁媛娜, 王冬至, 刘强. 冀北山地杨桦次生混交林地位指数模型构建[J]. 林草资源研究, 2024,(3): 70-78.

DONG Zihua, LI Dayong, LIANG Yu, LIANG Yuanna, WANG Dongzhi, LIU Qiang. Construction of the Site Index Model of Secondary Populus Davidiana×Betula Platyphylla Mingled Forest in Northern Hebei Mountains[J]. Forest and Grassland Resources Research, 2024,(3): 70-78.

图/表 10

表1

表2

非线性地位指数候选模型

模型	方程名称	表达式
M₁	舒马赫方程 Schumacher	H_D=a× $e x p - b / D D$
M₂	双曲线方程 Hyperbolic curve	H_D=a+b/D_D
M₃	抛物线方程 Parabola	H_D=a+b×D_D+c× $D D 2$
M₄	逻辑斯蒂方程 Logistic	H_D= $a (1 + b × e x p - c × D D)$
M₅	坎派兹方程 Gompertz	H_D=a×exp[-c×exp(-b×D_D)]

表2

图1

表3

候选模型拟合与评价

模型	a	b	c	MSE	RMSE	MPB	R²	$R a d j 2$
M₁	29.135 3^***	12.056 7^***		9.388 5	2.450 5	12.228 8	0.578 2	0.571 3
M₂	23.620 9^***	-150.710 0^***		9.955 2	2.417 5	12.470 3	0.513 6	0.505 6
M₃	-0.151 3^*	1.008 6^*	-0.014 4^*	9.786 3	2.325 4	12.064 2	0.577 3	0.563 3
M₄	21.533 0^***	4.932 3^*	0.131 7^**	9.071 7	2.269 6	11.972 9	0.583 8	0.569 9
M₅	23.398 6^***	0.084 6^*	2.124 8^**	9.506 0	2.335 9	11.977 6	0.578 0	0.563 9

表3

表4

表5

表6

表7

不同参数估计方法精度比较

参数估计方法	MSE	RMSE	MPB	R²	$R a d j 2$
非线性最小二乘法	9.071 7	2.269 6	11.972 9	0.583 8	0.569 9
BP神经网络	6.364 0	1.997 2	10.820 6	0.620 8	0.609 5
非线性混合效应	5.477 4	1.779 4	9.161 4	0.782 8	0.761 7

表7

图2

图3

参考文献 40

[1]	孟宪宇. 测树学[M]. 北京: 中国林业出版社, 2011.
[2]	LIU Xianzhao, DUAN Guangshuang, CHHIN S, et al. Evaluation of potential versus realized site productivity of Larix principis-rupprechtii plantations across northern China[J]. Forest Ecology and Management, 2021, 479:118608.
[3]	王冬至, 张冬燕, 蒋凤玲, 等. 塞罕坝华北落叶松人工林地位指数模型[J]. 应用生态学报, 2015, 26(11):3413-3420.
[4]	KOIRALA A, MONTES C R, BULLOCK B P. Modeling dominant height using stand and water balance variables for loblolly pine in the Western Gulf,US[J]. Forest Ecology and Management, 2021, 479:118610.
[5]	SOCHA J, SOLBERG S, TYMIńska-CZABAńSKA L, et al. Height growth rate of Scots pine in Central Europe increased by 29% between 1900 and 2000 due to changes in site productivity[J]. Forest Ecology and Management,2021, 490:119102.
[6]	ZHU Guangyu, HU Song, CHHIN S, et al. Modelling site index of Chinese fir plantations using a random effects model across regional site types in Hunan province,China[J]. Forest ecology and management, 2019, 446:143-150. doi: 10.1016/j.foreco.2019.05.039
[7]	巩垠熙, 何诚, 闫飞, 等. 人工神经网络结合多光谱遥感数据用于立地质量评价[J]. 光谱学与光谱分析, 2013, 33(10):2815-2822.
[8]	WANG Mingliang, MONTE C R, BULLOCK B P, et al. An empirical examination of dominant height projection accuracy using difference equation models[J]. Forest Science, 2020, 66(3):267-274. doi: 10.1093/forsci/fxz079
[9]	CHEN Jiaxin, YANG Hongqiang, MAN Rongzhou, et al. Using machine learning to synthesize spatiotemporal data for modelling DBH-height and DBH-height-age relationships in boreal forests[J]. Forest ecology and management, 2020, 466:118104.
[10]	CARMEAN W H. Forest site quality evaluation in the United States[J]. Advances in agronomy, 1975, 27:209-269.
[11]	MOLINA-VALERO J A, DIéGUEZ-ARANDA U, ÁLVAREZ-GONZáLEZ J G, et al. Assessing site form as an indicator of site quality in even-aged Pinus radiata D.Don stands in north-western Spain[J]. Annals of forest science, 2019, 76(4):1-10.
[12]	BELTRAN H A, CHAUCHARD L, VELáSQUEZ A, et al. Diametric site index:An alternative method to estimate site quality in Nothofagus obliqua and N.alpina forests[J]. Cerne, 2016, 22:345-354.
[13]	马建路, 宣立峰, 刘德君. 用优势树全高和胸径的关系评价红松林的立地质量[J]. 东北林业大学学报, 1995,(2):20-27.
[14]	沈剑波, 雷相东, 雷渊才, 等. 长白落叶松人工林地位指数及立地形的比较研究[J]. 北京林业大学学报, 2018, 40(6):1-8.
[15]	HUANG Songming, TITUS S J. An index of site productivity for uneven-aged or mixed-species stands[J]. Canadian Journal of Forest Research, 1993, 23(3):558-562.
[16]	梁万君, 何怀江, 李岩, 等. 东北地区天然水曲柳地位指数表和立地形表的编制[J]. 吉林林业科技, 2023, 52(1):23-28.
[17]	李清顺, 金万洲, 王得军, 等. 利用多树种立地形指数对林地质量进行综合评价[J]. 南京林业大学学报(自然科学版), 2021, 45(6):81-89. doi: 10.12302/j.issn.1000-2006.202103007
[18]	ZOBEL J M, SCHUBERT M R, GRANGER J J. Shortleaf Pine(Pinus echinata)Site Index Equation for the Cumberland Plateau,USA[J]. Forest Science, 2022, 68(3):259-269.
[19]	ZOU Kailun, DUAN Guangshuang, WU You, et al. Site index model for Southern Subtropical Masson Pine forests using stand dominant height[J]. Forests, 2023, 15(1):87.
[20]	沈剑波, 王应宽, 雷相东, 等. 基于BP神经网络的广东省针阔混交异龄林立地质量评价[J]. 北京林业大学学报, 2019, 41(5):38-47.
[21]	LIU Yongkai, WANG Dongzhi, ZHANG Zhidong, et al. Modeling free branch growth with the competition index for a Larix principis-rupprechtii plantation[J]. Forests, 2023, 14(7):1495.
[22]	董云飞, 孙玉军, 许昊. 3种标准树高曲线建立方法的比较[J]. 西北农林科技大学学报(自然科学版), 2015, 43(11):82-90.
[23]	WANG Yanlin, WANG Dongzhi, ZHANG Dongyan, et al. Predicting carbon storage of mixed broadleaf forests based on the finite mixture model incorporating stand factors,site quality,and aridity index[J]. Forest Ecosystems, 2024, 11(3):276-286.
[24]	SOCHA J, TYMIńSKA-CZABAńSKA L, GRABSKA E, et al. Site index models for main forest-forming tree species in Poland[J]. Forests, 2020, 11(3):301.
[25]	HE Haimei, ZHU Guangyu, MA Wu, et al. Additivity of stand basal area predictions in canopy stratifications for natural Oak forests[J]. Forest Ecology and Management, 2021, 492:119246.
[26]	沈剑波, 雷相东, 王虎威, 等. 针阔混交异龄林林分优势高的确定方法[J]. 林业与环境科学, 2019, 35(1):43-48.
[27]	REYES-HERNANDEZ V, COMEAU P G, BOKALO M. Static and dynamic maximum size-density relationships for mixed Trembling aspen and White spruce stands in western Canada[J]. Forest ecology and management, 2013, 289:300-311.
[28]	陈永富, 杨彦臣, 张怀清, 等. 海南岛热带天然山地雨林立地质量评价研究[J]. 林业科学研究, 2000(2):134-140.
[29]	TEMESGEN H,ZHANG Caihong,ZHAO Xiuhai. Modelling tree height-diameter relationships in multi-species and multi-layered forests:A large observational study from Northeast China[J]. Forest Ecology and Management, 2014, 316:78-89.
[30]	MUTLU A C, BOYACI I H, GENIS H E, et al. Prediction of wheat quality parameters using near-infrared spectroscopy and artificial neural networks[J]. European food research and technology, 2011, 233:267-274.
[31]	段光爽, 李学东, 冯岩, 等. 华北落叶松天然次生林树高曲线的混合效应模型[J]. 南京林业大学学报(自然科学版), 2018, 42(2):163-169. doi: 10.3969/j.issn.1000-2006.201703014
[32]	AERTSEN W, KINT V, VAN Orshoven J, et al. Comparison and ranking of different modelling techniques for prediction of site index in Mediterranean mountain forests[J]. Ecological modelling, 2010, 221(8):1119-1130.
[33]	吴恒, 党坤良, 田相林, 等. 秦岭林区天然次生林与人工林立地质量评价[J]. 林业科学, 2015, 51(4):78-88.
[34]	CICŞA A, TUDORAN G M, BOROEANU M, et al. Estimation of the productivity potential of mountain sites(mixed beech-coniferous stands)in the Romanian Carpathians[J]. Forests, 2021, 12(5):549.
[35]	DăNESCU A, ALBRECHT A T, BAUHUS J, et al. Geocentric alternatives to site index for modeling tree increment in uneven-aged mixed stands[J]. Forest Ecology and Management, 2017, 392:1-12.
[36]	YANG Yuqing, HUANG Shongming, VASSOV R, et al. Climate-sensitive height-age models for top height trees in natural and reclaimed oil sands stands in Alberta,Canada[J]. Canadian journal of forest research, 2020, 50(3):297-307. doi: 10.1139/cjfr-2019-0293
[37]	王冬至, 胡雪娇, 李大勇, 等. 基于非线性混合效应模型的针阔混交林地位指数研究[J]. 南京林业大学学报(自然科学版), 2020, 44(4):159-166. doi: 10.3969/j.issn.1000-2006.201907010
[38]	金星姬, 贾炜玮, 李凤日. 基于BP人工神经网络的兴安落叶松天然林全林分生长模型的研究[J]. 植物研究, 2008(3):370-374. doi: 10.7525/j.issn.1673-5102.2008.03.025
[39]	车少辉, 张建国, 段爱国, 等. 杉木人工林胸径生长神经网络建模研究[J]. 西北农林科技大学学报(自然科学版), 2012, 40(3):84-92.
[40]	XU Anyang, WANG Dongzhi, LIU Qiang, et al. Incorporating stand density effects and regression techniques for stem taper modeling of a Larix principis-rupprechtii plantation[J]. Frontiers in Plant Science, 2022, 13:902325.

变量	最大值	最小值	标准差	平均值
海拔/m	1 530.00	1 233.00	79.98	1 359.86
坡度/(°)	23.70	5.00	3.88	13.36
平均胸径/cm	24.24	6.96	3.90	15.10
平均树高/m	18.88	7.87	2.76	13.15
密度/(株/hm²)	2 817.00	233.00	577.95	1 158.33
郁闭度/%	0.80	0.55	0.71	0.09
胸径/cm	32.31	7.15	4.84	16.73
树高/m	22.72	7.14	3.84	14.53
冠幅/m	6.54	1.45	4.15	3.63
枝下高/m	5.26	1.25	4.97	3.41

类别	传递函数
输入层到隐含层	H₁=tansig(-4.1D_D+4.2)
	H₂=tansig(-3.9D_D)
	H₃=tansig(4D_D+4.5)
隐含层到输出层	H_D=purelin(-0.618 3H₁+0.904 2H₂+ 0.540 5H₃+0.633 1)

随机效应参数位置	AIC	BIC	-2LL
a	1 038.7	1 057.4	1 028.7
b	1 030.4	1 049.2	1 020.4
a、b	1 033.0	1 051.7	1 022.9
b、a	1 037.9	1 056.6	1 027.8

参数	估计值	标准差	95%置信区间		P值
a	21.947 8	3.472 4	18.439 7	32.052 3	<0.000 1
b	3.338 1	0.252 0	3.066 9	3.694 6	<0.000 1
c	0.108 3	0.007 3	0.129 3	0.137 8	0.001 3
μ_i	0.001 4	0.002 1	0.000 1	0.002 8	0.000 5
σ²	0.106 8	0.011 8	0.031 0	0.109 7	0.001 0