长白落叶松人工林优势高广义代数差分生长模型

doi:10.11707/j.1001-7488.LYKX20230534

摘要/Abstract

摘要：

目的: 以长白落叶松人工林为研究对象，探究不同立地类型的立地质量差异，实现从立地分类到立地分级，精准评价长白落叶松人工林立地质量。方法: 基于吉林省一类调查和二类调查固定样地数据，采用广义代数差分法构建林分优势高生长差分模型。通过偏相关分析筛选对长白落叶松优势高生长具有显著影响的主导立地因子并形成立地类型（ST），应用K-Means算法对立地类型聚类形成立地类型组（STG），分别以ST、STG作为随机效应构建优势高生长混合效应模型，引入指数函数、幂函数、常数加幂函数消除异方差，采用一阶自回归、复合对称和自回归移动平均3种结构考虑自相关性，选出最优混合效应模型，根据立地类型组30年生的优势高进行立地分级。结果: 最优差分模型M1.1的调整决定系数（$ {R}_{\mathrm{a}}^{2} $）为0.865，相对均方根误差（rRMSE）为7.756%。对林分优势高具有显著影响（P<0.01）的立地因子（偏相关系数）为海拔（0.379）、土层厚度（?0.247）、腐殖质层厚度（0.190）、坡位（0.113）、坡度（0.067），前3项为主导立地因子，形成45个立地类型。45个立地类型聚类形成5个立地类型组，考虑立地类型组的混合效应模型M1.7最优，赤池信息准则（AIC）为4 402.492、贝叶斯信息准则（BIC）为4 451.014，相较M1.1的AIC和BIC分别下降7.42%、7.04%。利用M1.7将5个立地类型组划分为5个立地等级，30年生的优势高依次为18.7、17.6、16.2、14.4和12.8 m。结论: Richards、Korf、Hossfeld较其他基础模型更适宜推导差分模型；海拔、土层厚度、腐殖质层厚度是影响长白落叶松优势高生长的主导立地因子；获得立地类型与立地等级的对应表。

关键词: 广义代数差分法, 长白落叶松, 混合效应模型, 立地质量评价

Abstract:

Objective: Taking Larix olgensis plantations as the research object, this study aims to explore the difference of site quality between different site types, grade division of site from classification of site types is realized, and accurately evaluate the site quality of L. olgensis plantations. Method: Based on the sample plot data by the national forest inventory and the forest management inventory in Jilin Province, a difference model for stand dominant height growth was constructed by generalized algebraic difference approach. The dominant site factors significant affecting dominant height growth of L. olgensis were screened by partial correlation analysis and formed the site types (ST). Site type groups (STG) is formed by clustering site types based on K-Means algorithm, and the ST and STG are taken as random effects to construct the dominant high growth mixed effect model respectively, adding exponential function, power function and constant plus power function to eliminate heteroscedasticity, autocorrelation of order 1, compound symmetry and autocorrelation-moving average, three structures were used to consider the autocorrelation, the optimal mixed effect model was selected and carried out the site rank according to the site type groups corresponding to the dominant height at 30 years. Result: The optimal difference model M1.1 evaluation index adjusted coefficient of determination ($ {R}_{\mathrm{a}}^{2} $) = 0.865, relative root mean square error (rRMSE) = 7.756%. The site factors that had significant effect on stand dominant height (P<0.01) and their partial correlation coefficients were elevation 0.379, soil thickness ?0.247, humus thickness 0.190, slope position 0.113, slope degree 0.067, respectively, the first three factors were identified as dominant site factors, and 45 site types were formed. 5 site type groups were obtained from 45 site type clusters, the optimal mixed effect model M1.7 considering site type groups, AIC (Akaike information criterion) is 4 402.492 and BIC (Bayesian information criterion) is 4 451.014, decreased by 7.42% and 7.04% compared with AIC and BIC of M1.1 respectively. Divided into 5 site grades by using M1.7, the dominant height at 30 years are 18.7, 17.6, 16.2, 14.4, 12.8 m in turn. Conclusion: Richards, Korf and Hossfeld are more suitable than other base models to derive difference models. Elevation, soil thickness and humus thickness are the dominant site factors affecting the growth of dominant height for L. olgensis. The corresponding table of site types and site grade is obtained.

Key words: generalized algebraic difference approach, Larix olgensis, mixed effect model, site quality evaluation

中图分类号:

S758

罗光成,何潇,雷相东,吴璧芸,向玮. 长白落叶松人工林优势高广义代数差分生长模型[J]. 林业科学, 2024, 60(12): 1-12.

Guangcheng Luo,Xiao He,Xiangdong Lei,Biyun Wu,Wei Xiang. Generalized Algebraic Differential Growth Model of Dominant Height for Larix olgensis Plantations[J]. Scientia Silvae Sinicae, 2024, 60(12): 1-12.

图/表 12

表1

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备选差分模型"

编号 No.	参考文献 References	差分模型 Difference model	X的解 Solution for X	自由参数 Free parameter	基础模型 Base model
M1	Scolforo et al., 2016	$ H={\rm e}^{X}{\left(1-{\rm e}^{-bT}\right)}^{{d}_{1}+{d}_{2}X} $	$ X=\dfrac{\mathrm{l}\mathrm{n}{H}_{0}-{d}_{1}\mathrm{ln}\left(1-{\rm e}^{-b{T}_{0}}\right)}{1+{d}_{2}\mathrm{ln}\left(1-{\rm e}^{-b{T}_{0}}\right)} $	$ a={\rm e}^{X} $ $ c={d}_{1}+{d}_{2}X $	Richards $ H=a{\left(1-{\rm e}^{-bT}\right)}^{c} $
M2	Ercanli et al., 2014	$ H={\rm e}^{X}{\left(1-{\rm e}^{-bT}\right)}^{{d}_{1}+{d}_{2}/X} $	$ X=0.5\left(\mathrm{l}\mathrm{n}{H}_{0}-{d}_{1}F+\sqrt{{\left({d}_{1}F-\mathrm{l}\mathrm{n}{H}_{0}\right)}^{2}-4{d}_{2}F}\right) $ $ F=\mathrm{ln}\left(1-{\rm e}^{-b{T}_{0}}\right) $	$ a={\rm e}^{X} $ $ c={d}_{1}+{d}_{2}/X $
M3	Ercanli et al., 2014	$ H={\rm e}^{X}{\left(1-{\rm e}^{-bT}\right)}^{{d}_{1}+1/X} $	$ X=0.5\left(\mathrm{l}\mathrm{n}{H}_{0}-{d}_{1}F+\sqrt{{\left({d}_{1}F-\mathrm{l}\mathrm{n}{H}_{0}\right)}^{2}-4F}\right) $ $ F=\mathrm{ln}\left(1-{\rm e}^{-b{T}_{0}}\right) $	$ a={\rm e}^{X} $ $ c={d}_{1}+1/X $
M4	赵磊等, 2012	$ H={\rm e}^{X-\left({d}_{1}+{d}_{2}/X\right){T}^{-c}} $	$ X=0.5\left({d}_{1}{t}_{0}^{-c}+\mathrm{l}\mathrm{n}{H}_{0}+F\right) $ $ F=\sqrt{{\left({d}_{1}{T}_{0}^{-c}+\mathrm{l}\mathrm{n}{H}_{0}\right)}^{2}+4{d}_{2}{T}_{0}^{-c}} $	$ a={\rm e}^{X} $ $ b={d}_{1}+{d}_{2}/X $	Korf $ H=a{\rm e}^{-b{T}^{-c}} $
M5	赵磊等, 2012	$ H={\rm e}^{X-\left({d}_{1}/X\right){T}^{-c}} $	$ X=0.5\left(\mathrm{l}\mathrm{n}{H}_{0}+\sqrt{{\left(\mathrm{l}\mathrm{n}{H}_{0}\right)}^{2}+4{d}_{1}{T}_{0}^{-c}}\right) $	$ a={\rm e}^{X} $ $ b={d}_{1}/X $
M6	牛亦龙, 2021	$ H={\rm e}^{X-\left({d}_{1}+{d}_{2}X\right){T}^{-c}} $	$ X=(\mathrm{l}\mathrm{n}{H}_{0}+{d}_{1}{T}_{0}^{-c})/(1-{d}_{2}{T}_{0}^{-c}) $	$ a={\rm e}^{X} $ $ b={d}_{1}+{d}_{2}X $
M7	Scolforo et al., 2016	$ \mathrm{l}\mathrm{n}H=X+\left({d}_{1}+{d}_{2}X\right)\mathrm{ln}\left(-{\rm e}^{-{T}^{c}}\right) $	$ X=\dfrac{\mathrm{l}\mathrm{n}{H}_{0}-{d}_{1}\mathrm{ln}\left(1-{\rm e}^{-{T}_{0}^{c}}\right)}{1+{d}_{2}\mathrm{ln}\left(1-{\rm e}^{-{T}_{0}^{c}}\right)} $	$ a=X $ $ b={d}_{1}+{d}_{2}X $	修正Weibull Adjusted Weibull $ \mathrm{l}\mathrm{n}H=a+b\mathrm{l}\mathrm{n}\left(1-{\rm e}^{-{T}^{c}}\right) $
M8	曹元帅等, 2017	$ H={(d}_{1}+X)/[1+\left({d}_{2}/X\right){T}^{-c}] $	$ X=0.5\left({H}_{0}-{d}_{1}-\sqrt{{\left({H}_{0}-{b}_{1}\right)}^{2}+4{d}_{2}{H}_{0}{T}_{0}^{-c}}\right) $	$ a={d}_{1}+X $ $ b={d}_{2}/X $	Hossfeld $ H=a/(1+b{T}^{-c}) $
M9	王冬至等, 2016	$ H={(d}_{1}+X)/(1+{d}_{2}X{T}^{-c}) $	$ X=({H}_{0}-{d}_{1})/(1+{d}_{2}{H}_{0}{T}_{0}^{-c}) $	$ a={d}_{1}+X $ $ b={d}_{2}X $
M10	牛亦龙, 2021	$ H=({d}_{1}+X)/[1+\left({d}_{2}+{d}_{3}/X\right){T}^{-c}] $	$ X=0.5\left({H}_{0}+{H}_{0}{d}_{2}{T}_{0}^{-c}-{d}_{1}+\sqrt{F}\right) $ $ F={\left({H}_{0}+{H}_{0}{d}_{2}{T}_{0}^{-c}\right)}^{2}+4{H}_{0}{d}_{2}{T}_{0}^{-c} $	$ a={d}_{1}+X $ $ b={d}_{2}+{d}_{3}/X $
M11	Scolforo et al., 2016	$ \mathrm{l}\mathrm{n}H=X+X\left({d}_{1}/T\right) $	$ X=\mathrm{l}\mathrm{n}{H}_{0}/\left(({T}_{0}+{d}_{1})/{T}_{0}\right) $	$ a=X $ $ b={d}_{1}X $	Schumacher $ \mathrm{l}\mathrm{n}H=a+b/T $
M12	牛亦龙, 2021	$ H={\rm e}^{X}{\rm e}^{-\left({d}_{1}+{d}_{2}X\right){\rm e}^{-cT}} $	$ X=(\mathrm{l}\mathrm{n}{H}_{0}+{d}_{1}{\rm e}^{-c{T}_{0}})/(1-{d}_{2}{\rm e}^{-c{T}_{0}}) $	$ a={\rm e}^{X} $ $ b={d}_{1}+{d}_{2}X $	Gompertz $ H=a{\rm e}^{-b{\rm e}^{-cT}} $
M13	牛亦龙, 2021	$ H={\rm e}^{X}{\rm e}^{-\left({d}_{1}+{d}_{2}/X\right){\rm e}^{-cT}} $	$ X=0.5\left(\mathrm{l}\mathrm{n}{H}_{0}+{d}_{1}{\rm e}^{-c{T}_{0}}+\sqrt{F}\right) $ $ F={\left(\mathrm{l}\mathrm{n}{H}_{0}+{d}_{1}{\rm e}^{-c{T}_{0}}\right)}^{2}+4{d}_{2}{\rm e}^{-c{T}_{0}} $	$ a={\rm e}^{X} $ $ b={d}_{1}+{d}_{2}/X $	Gompertz $ H=a{\rm e}^{-b{\rm e}^{-cT}} $

表2

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表4

表5

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表8

图2

图3

表9

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林分因子Stand variables	平均值Mean	标准差Standard deviation	最小值Min.	最大值Max.
林分平均年龄Stand mean age/a	27.0	9.7	5	65
林分优势高Stand dominant height/m	14.5	3.0	5.6	23.0
林分平均胸径Stand average DBH/cm	13.0	3.8	5.7	28.1
林分断面积Stand basal area/(m2·hm^?2)	13.41	7.23	0.79	37.13
林分蓄积Stand volume/(m3·hm^?2)	81.73	52.68	2.53	284.31
林分密度指数Stand density index/(tree·hm^?2)	498.1	246.1	40	1 285

立地因子 Site factors	等级范围（样本量） Level range (sample size)
海拔 Altitude/m	Ⅰ: 0~200 (8); Ⅱ: 201~400 (539); Ⅲ: 401~600 (566); Ⅳ: 601~800 (310); Ⅴ: 801~1 000 (160); Ⅵ: 1 001~1 200 (35); Ⅶ: 1 201~1 400 (4)
坡度 Slope degree/(°)	平坡Conservative slope: 0~4 (401); 缓坡Gentle slope: 5~14 (786); 斜坡Incline slope: 15~24 (379); 陡坡Steep slope: 25~34 (45); 急坡Acute slope: 35~44 (11)
坡向（方位角） Slope aspect (azimuth)/(°)	北坡North slope: 338~22 (186); 东北坡Northeast slope: 23~67 (142); 东坡East slope: 68~112 (136); 东南坡Southeast slope: 113~157 (205); 南坡South slope: 158~202 (135); 西南坡Southwest slope: 203~247 (122); 西坡West slope: 248~292 (147); 西北坡Northwest slope: 293~337 (148); 无坡向No aspect: 坡度<5的地段Slope degree <5 (401)
坡位 Slope position	脊部Ridge (28); 上坡Up slope (386); 中坡Middle slope (640); 下坡Down slope (418); 山谷Valley (53) ;平地Flat (97)
土层厚度 Soil thickness/cm	厚Thick: ≥60 (201); 中Middle: 30~59 (1 290); 薄Thin: <30 (131)
腐殖质层厚度 Humus thickness/cm	厚Thick: ≥5.0 (328); 中Middle: 2.0~4.9 (1 018); 薄Thin: <2.0 (276)

编号 No.	与立地无关参数 Site independent parameter (SIP)		差分模型参数 Difference model parameter			$ {R}_{\mathrm{a}}^{2} $	RMSE/m	rRMSE(%)
编号 No.	b	c	d₁	d₂	d₃	$ {R}_{\mathrm{a}}^{2} $	RMSE/m	rRMSE(%)
M1	0.054		5.085	?1.353		0.865	1.093	7.756
M2	0.054		?3.054	12.211		0.864	1.095	7.770
M3	0.033		0.423			0.849	1.156	8.203
M4		0.540	?2.756e+04	9.866e+04		0.846	1.166	8.277
M5		0.381	16.459			0.864	1.095	7.770
M6		0.659	76.297	?20.469		0.862	1.106	7.852
M7		0.318	38.912	?9.535		0.830	0.091	3.484
M8		1.050	27.604	6.110e-06		0.858	1.119	7.940
M9		2.801	12.149	122.262		0.449	2.206	15.661
M10		1.213	0.336	?156.340	4 513.895	0.864	1.095	7.774
M11			?2.527			0.652	0.131	4.993
M12		0.079	7.639	?1.967		0.864	1.095	7.770
M13		0.079	?3.923	16.943		0.864	1.096	7.778

立地因子 Site factors	偏相关系数 Coefficient of partial correlation (R_p)	P	贡献度 Contribution (%)
海拔Altitude	0.379	<0.001	37.790
坡度Slope degree	0.067	0.007	6.703
坡向Slope aspect	0.006	0.799	0.632
坡位Slope position	0.113	<0.001	11.249
土层厚度Soil thickness	?0.247	<0.001	24.634
腐殖质层厚度 Humus thickness	0.190	<0.001	18.992

混合参数 Mixed parameter	参数估计Parameter estimation					模型评价Model evaluation
混合参数 Mixed parameter	b	d₁	d₂	d₁₁	d₁₂	AIC	BIC	$ {R}_{\mathrm{a}}^{2} $
d₁₁	0.051	3.014	?0.683	5.584	?1.533	4 752.506	4 790.245	0.879
d₁₂	0.051	3.032	?0.689	5.561	?1.525	4 753.599	4 791.339	0.879
d₁₁, d₁₂	不收敛Nonconvergence