湖南栎类-马尾松天然混交林单木生长模型研究

doi:10.13466/j.cnki.lyzygl.2020.02.015

摘要/Abstract

摘要：

建立湖南栎类-马尾松天然混交林单木材积和断面积生长模型,为该林分的提质增量提供科学指导。选取湖南省9个地区共23块栎类-马尾松天然混交林,构建栎类、马尾松单木材积和断面积生长模型。通过分析可知:两种树种的材积和断面积生长模型均以Richards生长模型为最优,其确定系数(R²)最高,残差平方和(SSE)最小;混合效应模型模拟结果显示,栎类单木材积和断面积生长模型的随机效应在参数a₁处最好,而马尾松的材积和断面积生长模型的随机参数分别为b₁和a₁+b₁;相比基础模型,混合效应模型的拟合精度(P)、确定系数均有所提高,平均误差(ME)、平均误差绝对值(MAE)、相对平均误差(RME)和相对平均误差绝对值(RMAE)均大幅降低。结果表明,天然林林木的材积和断面积生长受树种与立地类型差异的影响较大,而混合效应模型能够充分考虑立地之间的差异,可以很好地解决这一难题。

关键词: 栎类-马尾松混交林, 生长模型, 断面积, 材积, 混合效应

Abstract:

In order to provide scientific guidance for the increment of quality of the mixed Oak and Pinus massoniana natural forest,establishing the growth model of individual volume and basal area.Twenty-three mixed Oak and Pinus massoniana natural forests in nine areas of Hunan province were selected to construct the growth models of individual volume and basal area.Through analysis,we can know that Richards model was the best model for volume and basal area growth of the two tree species,the determining coefficients (R ²) were the highest and the sum of squares of residuals (SSE) were the smallest.The result of mixed effect models show that the random effects of the Oak single-wood volume and basal area growth model are best at parameter a₁,while the volume and basal area growth model of Pinus massoniana are best at parameter b₁ and a₁+b₁.Compared with the basic model,the fitting precision (P) and determination coefficients of the mixed effect model are improved.Mean error (ME),mean absolute error (MAE),mean percent error (RME) and mean absolute percent error (RMAE) are all slumped substantially.The results show that wood volume and basal area growth of natural forests are greatly affected by the differences between tree species and site types.Mixed-effect model can take full account of the differences between sites,and solve this problem well.

Key words: mixed Oak and Pinus massoniana forest, growth model, basal area, stem volume, mixed effect

中图分类号:

S758

彭其龙, 陈哲夫, 陈端吕. 湖南栎类-马尾松天然混交林单木生长模型研究[J]. 林业资源管理, 2020,(2): 94-102.

ENG Qilong, CHEN Zhefu, CHEN Duanlv. A Study on the Growth Model of Individual Trees in Natural Mixed Forests of Oak and Pinus Massoniana in Hunan[J]. FOREST RESOURCES WANAGEMENT, 2020,(2): 94-102.

图/表 12

表1

表2

表3

基础模型与混合效应模型表达式

序号	模型	基础模型	混合效应模型
1	对数 Logarithm	$V (G) = a · ln (A) + b$	$V (G) = (a + a 1) · ln (A) + (b + b 1)$
2	指数Exponentin	$V (G) = a · A b$	$V (G) = (a + a 1) · A (b + b 1)$
3	二次函数Quadratic function	$V (G) = a · A 2 + b · A + c$	$V (G) = (a + a 1) · A 2 + (b + b 1) · A + (c + c 1)$
4	舒马赫Schunacher	$V (G) = a · e - b A$	$V (G) = (a + a 1) · e - (b + b 1) A$
5	理查德Richards	$V (G) = a · (1 - e - b · A) c$	$V (G) = (a + a 1) · (1 - e - (b + b 1) · A) (c + c 1)$
6	坎派兹Compertz	$V (G) = a · e - b · e - c · A$	$V (G) = (a + a 1) · e - (b + b 1) · e - (c + c 1) · A$
7	修正威布尔 Weibull modified	$V (G) = a · (1 - e - b · A c)$	$V (G) = (a + a 1) · (1 - e - (b + b 1) · A (c + c 1))$
8	逻辑斯蒂Logistic	$V (G) = a 1 + b · e - c · A$	$V (G) = a + a 1 1 + (b + b 1) · e - (c + c 1) · A$

表3

表4

表5

表6

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表8

表9

表10

图1

图2

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树种	株数/株	年龄(A)/a			直径(D)/cm			单株材积(V)/m³			单株断面积(G)/m²
树种	株数/株	最大值	最小值	平均值	最大值	最小值	平均值	最大值	最小值	平均值	最大值	最小值	平均值
柏木	6	20	36	31(±8.28)	7.3	15.0	12.6(±3.16)	0.011	0.074	0.051(±0.024)	0.004	0.018	0.013(±0.005)
枫香	15	15	57	29(±12.31)	5.5	16.6	9.7(±5.15)	0.008	0.108	0.037(±0.090)	0.002	0.022	0.008(±0.013)
栎类	1636	15	110	27(±12.04)	5.0	44.9	9.3(±5.11)	0.006	1.295	0.038(±0.085)	0.002	0.158	0.008(±0.013)
柳树	13	16	42	27(±11.69)	5.2	13.4	8.6(±3.73)	0.007	0.063	0.024(±0.039)	0.002	0.014	0.006(±0.007)
马尾松	796	10	95	25(±12.06)	5.1	43.0	12.8(±5.11)	0.005	1.146	0.072(±0.085)	0.002	0.145	0.016(±0.013)
杉木	104	5	67	21(±12.48)	5.0	26.2	10.4(±5.23)	0.005	0.396	0.048(±0.092)	0.002	0.054	0.010(±0.013)
油桐	10	24	43	32(±23.86)	8.7	14.8	11.3(±5.99)	0.022	0.081	0.045(±0.195)	0.006	0.017	0.010(±0.024)
樟树	43	14	50	25(±12.02)	5.0	17.6	9.5(±5.14)	0.006	0.125	0.035(±0.086)	0.002	0.024	0.008(±0.013)

特征项	柏木	枫香	栎类	柳树	马尾松	杉木	油桐	樟树	合计
株数/株	6(0.23)	15(0.57)	1636(62.35)	13(0.50)	796(30.34)	104(3.96)	10(0.38)	43(1.64)	2624(100)
总材积/m³	0.303(0.27)	0.554(0.43)	62.837(48.89)	0.318(0.25)	57.601(44.82)	4.959(3.86)	0.447(0.35)	1.511(1.18)	128.53(100)
总断面积/m²	0.078(0.28)	0.127(0.46)	13.57(48.99)	0.081(0.29)	12.35(44.59)	1.037(3.74)	0.104(0.38)	0.35(1.26)	27.698(100)

树种	林分变量	建模数据
树种	林分变量	样本量			最大值		最小值	平均值		标准差		样本量	最大值			最小值		平均值	标准差
栎类	年龄(A)/a		1088	135		15			26	10.896	548			91	16		27			10.692
	直径(D)/cm		1088	35.4		5.0			9.1	4.111	548			30.2	5.0		9.4			4.155
	材积(V)/m³		1088	0.721		0.006			0.035	0.057	548			0.485	0.006		0.037			0.054
	断面积(G)/m²		1088	0.098		0.002			0.008	0.009	548			0.072	0.002		0.008			0.009
马尾松	年龄(A)/a		528	95		10			25	11.315	268			50	11		23			8.873
	直径(D)/cm		528	43.0		5.1			13.1	5.950	268			27.0	5.1		12.2			5.178
	材积(V)/m³		528	1.146		0.005			0.078	0.116	268			0.347	0.005		0.061			0.068
	断面积(G)/m²		528	0.145		0.002			0.016	0.017	268			0.057	0.002		0.014			0.012

树种	方程序号		参数					指标
树种	方程序号		a		b	c		R²	SSE
栎类	1	0.16866(±0.00372)		-0.50288(±0.01202)			0.557			4.198
	2	0.00007(±0.00000)		1.90001(±0.01248)			0.873			1.199
	3	0.00003(±0.00000)		0.00194(±0.00012)		-0.03960(±0.00247)	0.885			1.090
	4	1.91577(±0.03867)		126.10227(±1.34834)			0.840			1.515
	5	1.20318(±0.10381)		0.01369(±0.00111)		3.09178(±0.12107)	0.887			1.068
	6	1.42190(±0.03881)		6.21277(±0.06351)		0.18458(±0.00396)	0.873			1.205
	7	1.67263(±0.10172)		0.00232(±0.00010)		2.18514(±0.02864)	0.883			1.112
	8	1.05344(±0.01917)		104.31849(±3.69011)		0.47873(±0.00722)	0.836			1.554
马尾松	1	0.18573(±0.00630)		-0.50742(±0.01984)			0.523			4.004
	2	0.00005(±0.00001)		2.20912(±0.03073)			0.804			1.647
	3	0.00013(±0.00000)		-0.00072(±0.00046)		-0.00562(±0.00720)	0.805			1.632
	4	2.62627(±0.11859)		103.20307(±2.00159)			0.768			1.948
	5	7.28237(±3.99675)		0.00715(±0.00252)		2.66767(±0.18742)	0.805			1.631
	6	2.07629(±0.21976)		6.55694(±0.12845)		0.02431(±0.00146)	0.799			1.683
	7	2.12563(±0.36265)		140.98612(±40.10094)		1.11202(±0.09743)	0.759			2.022
	8	1.10377(±0.05014)		107.47063(±7.02958)		0.07316(±0.00230)	0.784			1.814

树种	方程序号		参数						指标
树种	方程序号		a		b		c		R²	SSE
栎类	1	0.02711(±0.00045)		-0.07872(±0.00147)				0.685			0.063
	2	0.00004(±0.00000)		1.59895(±0.01066)				0.860			0.028
	3	0.00002(±0.00000)		0.00060(±0.00002)		-0.00917(±0.00036)		0.879			0.024
	4	1.75671(±0.00322)		88.52108(±0.89458)				0.839			0.032
	5	0.12090(±0.00710)		0.17403(±0.01143)		2.80860(±0.09905)		0.884			0.023
	6	0.14740(±0.00384)		5.34338(±0.05482)		2.17172(±0.04515)		0.865			0.027
	7	0.17380(±0.00076)		0.57425(±0.03849)		1.92531(±0.02449)		0.876			0.025
	8	0.11690(±0.00219)		56.22297(±1.80148)		51.00943(±0.83070)		0.826			0.035
马尾松	1	0.03096(±0.00079)		-0.08112(±0.00250)				0.657			0.064
	2	0.00005(±0.00001)		1.74066(±0.02481)				0.815			0.034
	3	0.00001(±0.00000)		0.00059(±0.00007)		-0.00650(±0.00103)		0.816			0.034
	4	0.20645(±0.00806)		68.32779(±1.43521)				0.779			0.041
	5	0.66325(±0.30482)		0.65953(±0.23592)		2.03500(±0.12000)		0.819			0.034
	6	0.19207(±0.01438)		5.24315(±0.10016)		0.07682(±0.00144)		0.809			0.035
	7	0.64705(±0.20216)		26.59188(±3.52349)		0.66159(±0.06525)		0.805			0.036
	8	0.12868(±0.00518)		48.29720(±2.73098)		0.07029(±0.00213)		0.792			0.038