基于3-PGmix过程模型的落叶松人工林生长过程表编制

doi:10.11707/j.1001-7488.LYKX20220837

摘要/Abstract

摘要：

目的: 编制落叶松人工林生长过程表，为落叶松人工林经营管理提供科学依据。方法: 以我国东北华北七省（市、区）——北京市、河北省、山西省、辽宁省、吉林省、黑龙江省和内蒙古自治区落叶松人工林为研究对象，基于第5~8次全国森林资源连续清查552块固定样地数据和气象数据，运用3-PG_mix过程模型编制落叶松人工林不同立地等级生长过程表。结果: 通过校验得到4种落叶松人工林3-PG_mix过程模型参数，林分各变量模型预测值与实测值一致性较高（R²在0.71~0.96之间），兴安落叶松、长白落叶松、华北落叶松和日本落叶松林分蓄积量的平均误差分别为5.70%、0.95%、4.70%和?4.56%，均方根误差分别为14.88、12.00、16.74和13.11 m³·hm^?2。编制的林分生长过程表能够描述林分平均胸径、平均高、株数密度、公顷蓄积量、公顷生物量以及蓄积量和生物量的公顷年均生长量和连年生长量等随林龄增加的动态变化规律，4种落叶松人工林生长过程存在差异，其原因是适生条件、物候期、生长期等生物学特性不同所致，结果具有一定的统计可靠性和生物合理性。结论: 3-PG_mix过程模型模拟结果可用于编制落叶松人工林生长过程表，为生长过程表的编制提供一种新的方法。

关键词: 落叶松人工林, 3-PG_mix过程模型, 生长过程表

Abstract:

Objective: Larch is the main tree species for afforestation in northeast and north China. Growth and yield tables of larch plantations were compiled to provide the basis for scientific management. Method: Based on the data of 552 permanent sample plots of larch plantations from the fifth to the eighth national forest inventory and meteorological data in 7 provinces of northeast and north China (Beijing, Hebei, Shanxi, Liaoning, Jilin, Heilongjiang and Inner Mongolia), growth and yield tables were produced for larch plantations with different site levels using 3-PG_mix model. Result: The model parameters of larch plantations were obtained by calibration and validation. The simulated and measured values of stand variables were consistent with each other (R² was between 0.71 and 0.96). The mean relative errors in terms of stand volume were 5.70%, 0.95%, 4.70%, and ?4.56% for Larix gmelinii, Larix olgensis, Larix principis-rupprechtii and Larix kaempferi, respectively. The RMSE (root mean square error) values were 14.88, 12.00, 16.74 and 13.11 m³·hm^?2, respectively. The growth and yield tables could describe the change of stand variables with age, including stand average DBH, average height, stem density, stock volume, stand biomass, periodical and mean annual increment etc. Results showed the differences in the growth of the four larch species, owing to the difference in suitable conditions, phenological period, growth period and other biological characteristics. The model results are statistically reliable and biologically rational. Conclusion: The simulation results of the 3-PG_mix process-based growth model can be used to produce the growth and yield table of larch plantations, and the study provided a novel way for forest growth and yield table.

Key words: larch plantation, 3-PG_mix process-based growth model, growth and yield table

中图分类号:

S757

解雅麟,雷相东,曾伟生. 基于3-PG_mix过程模型的落叶松人工林生长过程表编制[J]. 林业科学, 2023, 59(12): 87-104.

Yalin Xie,Xiangdong Lei,Weisheng Zeng. Compilation of Growth and Yield Table for Larch Plantations Based on 3-PG_mix Model[J]. Scientia Silvae Sinicae, 2023, 59(12): 87-104.

图/表 10

表1

表2

表3

落叶松人工林3-PGmix模型参数"

参数Parameters	符号Symbol	单位Unit	确定方法Methods
当胸径为2 cm时的叶干质量比Foliage∶stem partitioning ratio @ D=2 cm	p₂	—	拟合Fitted
当胸径为20 cm时的叶干质量比Foliage∶stem partitioning ratio @ D=20 cm	p₂₀	—	拟合Fitted
干质量与胸径的关系常数Constant in the stem mass v. diam. relationship	a_S	—	拟合Fitted
干质量与胸径的幂指数Power in the stem mass v. diam. relationship	n_S	—	拟合Fitted
NPP分配到根的最大比例Maximum fraction of NPP to roots	η_Rx	—	拟合Fitted
NPP分配到根的最小比例Minimum fraction of NPP to roots	η_Rn	—	拟合Fitted
最大叶凋落速率Maximum litterfall rate	γ_Fx	month^?1	拟合Fitted
叶凋落速率达1/2时林龄Age at which litterfall rate has median value	t_γF	month	Xie et al. 2017
月均根周转率Average monthly root turnover rate	γ_R	month^?1	优化Adjust
叶子长出月If deciduous, leaves are produced at end of this month	leaf_P	month	王战，1992
叶子脱落月If deciduous, leaves all fall at start of this month	leaf_L	month	王战，1992
生长最低温度Minimum temperature for growth	T_min	℃	王战，1992
生长最适温度Optimum temperature for growth	T_opt	℃	王战，1992
生长最高温度Maximum temperature for growth	T_max	℃	王战，1992
最大林龄Maximum stand age used in age modifier	t_x	a	Xie et al.2020a; 2020b
林龄最大时死亡率Mortality rate for large age	γ_Nx	%·a^?1	拟合Fitted
死亡率达到1/2时林龄Age at which mortality rate has median value	t_γN	a	拟合Fitted
死亡率响应指数Shape of mortality response	n_γN	—	拟合Fitted
当林分密度为1 000 株·hm^?2时单株最大干质量Max. stem mass per tree @ 1 000 trees·hm^?2	w_{Sx1 000}	kg·tree^?1	实测Observed
初期比叶面积Specific leaf area at age 0	σ₀	m²·kg^?1	实测Observed
冠层量子效率Canopy quantum efficiency	αC_x	mol·mol^?1	优化Adjust
茎高关系常数Constant in the stem height relationship	a_H	—	拟合Fitted
胸径在茎高关系中的幂指数Power of DBH in the stem height relationship	n_HB	—	拟合Fitted
竞争在茎高关系中的幂指数Power of competition in the stem height relationship	n_HC	—	拟合Fitted
材积关系常数Constant in the stem volume relationship	a_V	—	拟合Fitted
胸径在材积关系中的幂指数Power of DBH in the stem volume relationship	n_VB	—	拟合Fitted
胸径的平方及树高在材积关系中的幂指数 Power of DBH² and height in the stem volume relationship	n_VH	—	拟合Fitted
胸径的平方×树高在材积关系中的幂指数 Power of DBH²×height in the stem volume relationship	n_VBH	—	拟合Fitted

表3

表4

各林分因子实测值与3-PGmix模型预测值的校准和验证"

林分因子 Stand factor	统计量 Statistic	校准 Calibration				验证 Validation
林分因子 Stand factor	统计量 Statistic	长白落叶松Larix olgensis	兴安落叶松Larix gmelinii	华北落叶松 Larix principis-rupprechtii	日本落叶松Larix kaempferi	长白落叶松Larix olgensis	兴安落叶松Larix gmelinii	华北落叶松 Larix principis-rupprechtii	日本落叶松Larix kaempferi
林分平均高 Average height	R²	0.84	0.82	0.74	0.94	0.76	0.79	0.71	0.90
	MAE/m	1.17	1.49	1.08	1.04	1.43	1.61	1.22	1.21
	MRE(%)	1.69	7.64	?2.08	3.60	0.32	0.30	?1.93	?3.92
	RMSE/m	1.60	1.91	1.34	1.24	1.93	2.03	1.46	1.51
	RRMSE(%)	14.27	19.09	17.15	11.57	14.32	16.98	15.28	9.07
林分平均胸径 Average DBH	R²	0.84	0.89	0.78	0.93	0.79	0.88	0.73	0.90
	MAE/cm	2.65	1.80	1.97	1.36	2.33	1.54	2.03	1.82
	MRE(%)	20.85	17.25	7.25	3.18	11.91	6.90	?4.52	?7.14
	RMSE/cm	3.18	2.18	2.83	1.65	2.94	1.97	3.58	2.50
	RRMSE(%)	26.90	24.69	27.62	15.73	20.52	17.85	28.17	14.76
林分公顷蓄积量 Stand volume	R²	0.93	0.93	0.92	0.96	0.94	0.91	0.91	0.95
	MAE/(m³·hm^?2)	12.03	7.02	7.65	8.61	7.73	9.18	10.54	10.34
	MRE(%)	13.53	11.04	2.06	8.49	0.95	5.70	4.70	?4.56
	RMSE/(m³·hm^?2)	17.07	10.62	12.43	11.44	12.00	14.88	16.74	13.11
	RRMSE(%)	21.88	28.54	26.96	17.71	12.55	27.02	25.32	10.01
叶公顷生物量 Foliage biomass	R²	0.85	0.78	0.78	0.91	0.77	0.84	0.70	0.90
	MAE/(t·hm^?2)	0.45	0.40	0.52	0.28	0.39	0.42	0.65	0.29
	MRE(%)	?11.45	1.68	?5.57	?3.74	?4.09	11.75	12.91	5.11
	RMSE/(t·hm^?2)	0.59	0.54	0.70	0.37	0.56	0.61	1.01	0.34
	RRMSE(%)	23.96	28.68	32.61	13.05	17.76	31.04	40.58	11.51
干公顷生物量 Stem biomass	R²	0.86	0.92	0.93	0.95	0.80	0.93	0.94	0.94
	MAE/(t·hm^?2)	5.92	4.03	5.67	2.82	7.13	4.17	6.58	3.54
	MRE(%)	23.92	15.17	15.16	10.27	20.25	13.95	15.04	5.96
	RMSE/(t·hm^?2)	7.85	6.03	8.50	3.62	10.03	6.74	10.21	5.26
	RRMSE(%)	34.78	32.84	32.23	16.64	33.45	27.29	27.41	13.82
根公顷生物量 Root biomass	R²	0.91	0.91	0.94	0.94	0.89	0.93	0.92	0.95
	MAE/(t·hm^?2)	3.57	1.90	1.54	2.28	3.83	2.24	2.05	2.29
	MRE(%)	10.56	?0.78	?8.11	?9.44	6.07	11.24	9.16	1.74
	RMSE/(t·hm^?2)	5.19	2.73	2.21	2.92	5.87	3.55	3.08	2.84
	RRMSE(%)	21.82	25.44	23.42	17.44	17.79	26.40	25.08	9.76
总公顷生物量 Total biomass	R²	0.90	0.94	0.95	0.97	0.87	0.96	0.95	0.96
	MAE/(t·hm^?2)	9.74	4.62	5.73	3.86	10.85	6.04	8.54	6.24
	MRE(%)	19.08	8.78	8.28	4.40	15.55	12.90	13.86	6.78
	RMSE/(t·hm^?2)	13.68	7.33	9.07	5.45	15.65	9.57	13.25	7.91
	RRMSE(%)	28.02	23.69	23.88	12.76	23.65	23.86	25.39	10.96
株数密度 Stem density	R²	0.78	0.91	0.75	0.93	0.76	0.81	0.77	0.84
	MAE/(trees·hm^?2)	247.02	84.77	186.02	153.54	183.11	78.73	210.26	106.62
	MRE(%)	?11.00	5.55	9.82	?7.04	?7.30	5.65	19.80	?3.20
	RMSE/(trees·hm^?2)	348.02	237.93	367.87	218.21	278.26	237.18	354.61	153.79
	RRMSE(%)	29.01	20.81	29.61	15.99	29.98	32.07	36.31	19.83
净初级生产力 Net primary productivity	R²	0.80	0.80	0.82	0.87	0.73	0.86	0.86	0.84
	MAE/(t·hm^?2a^?1)	1.11	1.69	1.64	1.24	0.93	1.40	1.19	1.02
	MRE(%)	?4.12	?23.04	?23.53	?10.28	?7.21	?19.03	?14.59	?7.10
	RMSE/(t·hm^?2a^?1)	1.55	2.26	2.16	1.76	1.44	1.95	1.55	1.56
	RRMSE(%)	20.57	37.93	35.81	19.98	16.85	32.62	24.85	17.33

表4

图1

图2

表5

基于3-PGmix过程模型的华北落叶松生长过程表"

林龄 Stand age/a	立地等级Site level
	Ⅰ（9.02 ≤ SI < 13.51, n=35）											Ⅱ（7.37 ≤ SI < 9.02, n=35）
	胸径 Diameter at breast height/cm	树高 Height/ m	株数 The number of trees/ (tree·hm^?2)	林分公顷蓄积 Stand volume/ (m³·hm^?2)	年均生长量 Mean annual increment of stand volume/ (m³·hm^?2a^?1)	连年生长量 Current annual increment of stand volume/ (m³·hm^?2a^?1)	公顷生物量Biomass/ (t·hm^?2)	年均生长量Mean annual increment of biomass/ (t·hm^?2a^?1)	连年生长量Current annual increment of biomass/ (t·hm^?2a^?1)	枯死株数Number of dead trees/ (tree·hm^?2)	净初级生产力Net primary productivity/ (t·hm^?2a^?1)	胸径 Diameter at breast height/cm	树高 Height/ m	株数 The number of trees/ (tree·hm^?2)	林分公顷蓄积 Stand volume/ (m³·hm^?2)	年均生长量 Mean annual increment of stand volume/ (m³·hm^?2a^?1)	连年生长量 Current annual increment of stand volume/ (m³·hm^?2a^?1)	公顷生物量Biomass/ (t·hm^?2)	年均生长量Mean annual increment of biomass/ (t·hm^?2a^?1)	连年生长量Current annual increment of biomass/ (t·hm^?2a^?1)	枯死株数Number of dead trees/ (tree·hm^?2)	净初级生产力Net primary productivity/(t·hm^?2a^?1)
5	1.29	2.81	3 129	2.39	0.48	1.62	2.27	0.45	1.48	51	2.16	0.80	2.20	3 129	0.62	0.13	0.46	0.77	0.15	0.52	51	0.43
10	4.62	5.62	2 802	28.16	2.82	6.83	23.64	2.36	5.41	85	11.39	3.30	4.67	2 821	12.90	1.32	4.01	11.77	1.18	3.24	66	4.79
15	7.48	7.28	2 324	59.78	3.99	6.21	46.22	3.08	4.22	104	13.60	5.56	6.17	2 477	35.49	2.42	4.97	27.62	1.84	3.16	69	7.61
20	10.31	8.62	1 835	86.50	4.32	4.59	63.10	3.16	2.69	94	12.37	7.48	7.23	2 133	58.81	3.00	4.44	41.04	2.05	2.30	71	7.98
25	13.69	9.99	1 332	108.72	4.35	4.24	77.57	3.10	2.75	91	12.80	9.48	8.18	1 741	79.56	3.25	3.83	52.30	2.09	1.95	85	8.26
30	17.31	11.30	997	128.82	4.29	3.85	90.51	3.02	2.46	57	11.86	11.73	9.14	1 357	96.60	3.28	3.21	61.25	2.04	1.61	67	7.70
35	21.16	12.57	763	147.93	4.23	3.77	103.01	2.94	2.45	40	11.33	14.11	10.06	1 066	111.97	3.26	2.97	69.44	1.98	1.55	52	8.06
40	25.08	13.74	600	165.77	4.14	3.52	114.80	2.87	2.38	29	10.75	16.53	10.93	853	125.96	3.20	2.80	77.04	1.93	1.56	38	7.62
45	28.83	14.80	487	181.67	4.04	3.12	124.90	2.78	2.00	20	9.54	18.83	11.71	700	138.11	3.12	2.37	83.23	1.85	1.24	27	6.73
50	32.38	15.74	404	195.16	3.90	2.35	133.09	2.66	1.34	15	7.83	21.03	12.42	583	148.09	3.01	1.74	88.05	1.76	0.76	21	5.58
55	35.88	16.63	338	206.17	3.75	1.97	139.89	2.54	1.19	12	7.20	23.21	13.08	487	155.81	2.88	1.35	91.85	1.67	0.62	18	4.99
60	39.44	17.49	282	214.32	3.57	1.37	144.82	2.41	0.81	10	6.18	25.42	13.72	407	161.11	2.73	0.85	94.32	1.57	0.35	15	4.12
65	43.11	18.34	236	220.22	3.39	1.04	148.45	2.28	0.63	9	5.52	27.69	14.36	340	164.53	2.57	0.54	95.91	1.48	0.24	12	3.73
70	46.92	19.19	197	223.97	3.20	0.63	150.86	2.16	0.43	7	4.89	30.03	14.99	284	166.24	2.41	0.25	96.70	1.38	0.14	10	3.26
75	50.82	20.02	164	225.25	3.00	0.14	151.58	2.02	0.08	6	4.04	32.42	15.60	237	166.11	2.25	?0.13	96.40	1.29	?0.09	9	2.63
80	54.81	20.85	137	224.24	2.80	?0.44	150.75	1.88	?0.35	5	3.04	34.85	16.21	198	164.37	2.08	?0.51	95.22	1.19	?0.34	7	1.91
85	58.90	21.67	114	221.42	2.60	?0.70	148.87	1.75	?0.47	4	2.54	37.35	16.82	165	161.34	1.93	?0.71	93.45	1.10	?0.41	6	1.49
90	63.13	22.48	95	217.13	2.41	?0.97	146.06	1.62	?0.64	4	1.96	39.91	17.42	137	157.33	1.77	?0.89	91.18	1.01	?0.50	5	1.08

表5

表6

基于3-PGmix过程模型的兴安落叶松生长过程表"

林龄 Stand age/a	立地等级Site level
	Ⅰ（11.17 ≤ SI < 20.08, n=47）											Ⅱ（9.03 ≤ SI < 11.17, n=47）
	胸径 Diameter at breast height/cm	树高 Height/ m	株数 The number of trees/ (tree·hm^?2)	林分公顷蓄积 Stand volume/ (m³·hm^?2)	年均生长量 Mean annual increment of stand volume/ (m³·hm^?2a^?1)	连年生长量 Current annual increment of stand volume/ (m³·hm^?2a^?1)	公顷生物量Biomass/ (t·hm^?2)	年均生长量Mean annual increment of biomass/ (t·hm^?2a^?1)	连年生长量Current annual increment of biomass/ (t·hm^?2a^?1)	枯死株数Number of dead trees/ (tree·hm^?2)	净初级生产力Net primary productivity/(t·hm^?2a^?1)	胸径 Diameter at breast height/cm	树高 Height/ m	株数 The number of trees/ (tree·hm^?2)	林分公顷蓄积 Stand volume/ (m³·hm^?2)	年均生长量 Mean annual increment of stand volume/ (m³·hm^?2a^?1)	连年生长量 Current annual increment of stand volume/ (m³·hm^?2a^?1)	公顷生物量Biomass/ (t·hm^?2)	年均生长量Mean annual increment of biomass/ (t·hm^?2a^?1)	连年生长量Current annual increment of biomass/ (t·hm^?2a^?1)	枯死株数Number of dead trees/ (tree·hm^?2)	净初级生产力Net primary productivity/(t·hm^?2a^?1)
5	0.72	1.82	3 146	0.42	0.12	0.44	1.26	0.25	0.12	45	1.23	0.46	1.32	3 146	0.14	0.03	0.08	0.61	0.12	0.03	45	0.68
10	2.99	4.91	2 876	9.81	1.09	3.10	15.67	1.57	1.09	58	8.26	2.13	3.77	2 876	5.09	0.48	1.13	9.93	0.99	0.48	58	6.61
15	4.95	7.07	2 564	28.18	2.01	4.15	33.59	2.24	2.01	66	11.23	3.82	5.81	2 577	17.82	1.13	1.98	23.08	1.54	1.13	60	10.29
20	6.59	8.68	2 242	48.12	2.56	4.14	47.15	2.36	2.56	62	10.83	5.31	7.46	2 270	33.92	1.65	2.34	33.31	1.67	1.65	60	10.64
25	8.38	10.25	1 885	69.43	2.98	4.67	59.91	2.40	2.98	72	11.54	6.78	9.00	1 974	52.41	2.12	2.94	42.91	1.72	2.12	58	11.53
30	10.22	11.74	1 566	89.45	3.22	4.52	69.49	2.32	3.22	60	10.66	8.19	10.40	1 700	70.67	2.47	3.12	49.86	1.66	2.47	54	10.75
35	12.22	13.25	1 292	109.72	3.41	4.58	78.49	2.24	3.41	51	10.24	9.71	11.80	1 440	89.63	2.79	3.39	56.43	1.61	2.79	49	10.27
40	14.36	14.79	1 062	129.93	3.55	4.41	86.83	2.17	3.55	40	9.67	11.29	13.19	1 217	108.43	3.07	3.51	62.22	1.56	3.07	41	9.69
45	16.46	16.24	887	149.01	3.64	4.22	93.77	2.08	3.64	31	8.88	12.80	14.50	1 040	126.28	3.30	3.59	66.78	1.48	3.30	32	8.71
50	18.39	17.55	756	165.96	3.67	3.58	98.79	1.98	3.67	23	7.27	14.19	15.69	899	142.05	3.47	3.32	69.67	1.39	3.47	26	7.02
55	20.31	18.82	650	182.34	3.68	3.69	104.00	1.89	3.68	20	7.00	15.54	16.84	781	156.91	3.62	3.57	72.60	1.32	3.62	22	6.52
60	22.11	19.99	564	196.38	3.64	3.16	107.46	1.79	3.64	16	5.95	16.85	17.94	678	169.39	3.72	3.36	74.06	1.23	3.72	19	5.41
65	23.94	21.16	489	208.96	3.59	2.82	110.32	1.70	3.59	14	5.30	18.19	19.03	589	180.83	3.80	3.32	75.29	1.16	3.80	17	4.67
70	25.82	22.33	425	220.08	3.52	2.33	112.57	1.61	3.52	12	4.68	19.54	20.12	512	190.76	3.86	3.11	76.00	1.09	3.86	15	4.00
75	27.71	23.48	369	228.79	3.42	1.85	113.52	1.51	3.42	11	3.98	20.88	21.19	444	198.74	3.89	2.89	75.88	1.01	3.89	13	3.26
80	29.57	24.59	320	234.62	3.30	1.13	112.95	1.41	3.30	9	2.97	22.21	22.23	385	204.39	3.89	2.42	74.86	0.94	3.89	11	2.34
85	31.45	25.70	278	238.78	3.17	0.89	112.00	1.32	3.17	8	2.55	23.55	23.27	334	208.52	3.86	2.32	73.66	0.87	3.86	10	1.90
90	33.33	26.79	241	240.64	3.02	0.40	110.03	1.22	3.02	7	1.90	24.89	24.29	290	210.82	3.81	1.98	71.95	0.80	3.81	8	1.35

表6

表7

基于3-PGmix过程模型的长白落叶松生长过程表"

林龄 Stand age/a	立地等级Site level
	Ⅰ（12.76 ≤ SI < 18.23, n=47）											Ⅱ（10.00 ≤ SI < 12.76, n=47）
	胸径 Diameter at breast height/cm	树高 Height/ m	株数 The number of trees/ (tree·hm^?2)	林分公顷蓄积 Stand volume/ (m³·hm^?2)	年均生长量 Mean annual increment of stand volume/ (m³·hm^?2a^?1)	连年生长量 Current annual increment of stand volume/ (m³·hm^?2a^?1)	公顷生物量Biomass/ (t·hm^?2)	年均生长量Mean annual increment of biomass/ (t·hm^?2a^?1)	连年生长量Current annual increment of biomass/ (t·hm^?2a^?1)	枯死株数Number of dead trees/ (tree·hm^?2)	净初级生产力Net primary productivity/ (t·hm^?2a^?1)	胸径 Diameter at breast height/cm	树高 Height/ m	株数 The number of trees/ (tree·hm^?2)	林分公顷蓄积 Stand volume/ (m³·hm^?2)	年均生长量 Mean annual increment of stand volume/ (m³·hm^?2a^?1)	连年生长量 Current annual increment of stand volume/ (m³·hm^?2a^?1)	公顷生物量Biomass/ (t·hm^?2)	年均生长量Mean annual increment of biomass/ (t·hm^?2a^?1)	连年生长量Current annual increment of biomass/ (t·hm^?2a^?1)	枯死株数Number of dead trees/ (tree·hm^?2)	净初级生产力Net primary productivity/ (t·hm^?2a^?1)
5	0.74	3.52	3 169	0.86	0.21	0.62	3.56	0.71	2.14	50	3.09	0.55	2.88	3 169	0.48	0.12	0.33	2.18	0.44	1.28	50	1.94
10	3.26	6.87	2 890	17.06	1.87	4.76	27.46	2.75	5.63	61	11.31	2.54	5.76	2 890	10.45	1.17	3.24	19.65	1.97	4.42	61	8.86
15	5.33	8.90	2 568	41.65	2.97	4.71	53.21	3.55	5.09	68	13.61	4.37	7.63	2 580	28.75	2.10	3.80	41.41	2.76	4.45	62	11.75
20	7.18	10.58	2 206	65.20	3.45	4.46	73.82	3.69	3.57	80	12.27	5.92	9.00	2 276	47.71	2.58	3.78	59.68	2.98	3.17	59	10.95
25	9.26	12.44	1 797	86.87	3.67	4.46	93.40	3.74	3.79	81	13.16	7.38	10.27	1 986	66.07	2.85	4.03	77.66	3.11	3.53	58	11.88
30	11.68	14.38	1 437	106.85	3.76	4.18	110.70	3.69	3.58	65	12.72	8.96	11.57	1 691	83.78	3.01	3.86	93.24	3.11	3.15	62	11.56
35	14.34	16.35	1 156	126.20	3.81	4.13	126.81	3.62	3.37	48	12.34	10.77	12.97	1 392	100.28	3.10	3.63	106.82	3.05	2.85	53	11.35
40	17.34	18.44	933	146.06	3.87	4.16	142.96	3.57	3.10	37	11.71	12.83	14.47	1 142	116.86	3.18	3.55	120.09	3.00	2.46	44	10.85
45	20.39	20.46	767	164.69	3.89	3.77	157.47	3.50	2.97	29	11.37	14.98	15.95	940	131.76	3.20	3.19	131.46	2.92	2.34	35	10.57
50	23.41	22.32	642	182.09	3.88	3.56	169.57	3.39	2.13	20	9.43	17.12	17.31	787	145.61	3.20	3.00	140.57	2.81	1.51	25	8.71
55	26.38	24.16	545	198.13	3.85	3.67	181.61	3.30	2.39	17	9.40	19.23	18.65	669	158.43	3.18	3.08	149.64	2.72	1.80	21	8.74
60	29.39	25.93	466	213.29	3.81	3.38	192.28	3.20	2.19	14	8.67	21.36	19.94	574	170.59	3.15	2.84	157.46	2.62	1.62	18	8.02
65	32.43	27.68	401	227.09	3.76	3.02	201.39	3.10	1.87	12	8.05	23.54	21.22	493	181.72	3.11	2.56	164.03	2.52	1.37	15	7.47
70	35.64	29.48	345	240.16	3.70	2.79	209.79	3.00	1.49	10	7.34	25.86	22.55	424	192.35	3.07	2.37	170.09	2.43	1.05	13	6.82
75	38.92	31.27	296	250.74	3.62	2.13	215.88	2.88	1.17	9	6.79	28.22	23.87	365	201.11	3.01	1.86	174.28	2.32	0.82	11	6.31
80	42.27	33.05	255	258.82	3.52	1.63	219.07	2.74	0.33	8	5.31	30.65	25.18	314	207.92	2.92	1.43	176.08	2.20	0.07	9	4.91
85	45.69	34.85	219	264.37	3.39	1.39	221.01	2.60	0.30	7	4.91	33.12	26.50	270	212.78	2.82	1.22	177.00	2.08	0.11	8	4.57
90	49.22	36.67	188	268.08	3.26	0.90	221.15	2.46	?0.02	6	4.16	35.67	27.83	232	216.19	2.72	0.83	176.48	1.96	?0.13	7	3.86

表7

表8

基于3-PGmix过程模型的日本落叶松生长过程表"

林龄 Stand age/a	立地等级Site level
	I（13.64 ≤ SI < 16.83, n=10）											Ⅱ（11.50 ≤ SI < 13.64, n=9）
	胸径 Diameter at breast height/cm	树高 Height/ m	株数 The number of trees/ (tree·hm^?2)	林分公顷蓄积 Stand volume/ (m³·hm^?2)	年均生长量 Mean annual increment of stand volume/ (m³·hm^?2a^?1)	连年生长量 Current annual increment of stand volume/ (m³·hm^?2a^?1)	公顷生物量Biomass/ (t·hm^?2)	年均生长量Mean annual increment of biomass/ (t·hm^?2a^?1)	连年生长量Current annual increment of biomass/ (t·hm^?2a^?1)	枯死株数Number of dead trees/ (tree·hm^?2)	净初级生产力Net primary productivity/ (t·hm^?2a^?1)	胸径 Diameter at breast height/cm	树高 Height/ m	株数 The number of trees/ (tree·hm^?2)	林分公顷蓄积 Stand volume/ (m³·hm^?2)	年均生长量 Mean annual increment of stand volume/ (m³·hm^?2a^?1)	连年生长量 Current annual increment of stand volume/ (m³·hm^?2a^?1)	公顷生物量Biomass/ (t·hm^?2)	年均生长量Mean annual increment of biomass/ (t·hm^?2a^?1)	连年生长量Current annual increment of biomass/ (t·hm^?2a^?1)	枯死株数Number of dead trees/ (tree·hm^?2)	净初级生产力Net primary productivity/ (t·hm^?2a^?1)
5	1.08	1.62	3 110	0.73	0.35	1.10	3.45	0.87	2.35	55	4.43	0.99	1.52	3 110	1.23	0.19	1.09	3.60	0.52	2.49	55	2.75
10	4.99	5.75	2 784	21.12	3.38	8.02	32.08	3.80	6.53	70	16.02	3.87	4.66	2 784	23.47	2.49	8.30	34.90	2.84	7.13	70	12.98
15	8.18	8.67	2 183	58.55	5.73	10.70	60.29	4.62	5.51	157	18.03	6.49	7.12	2 421	59.06	4.49	10.83	65.21	3.68	5.56	79	15.37
20	11.42	11.40	1 599	99.20	7.22	9.94	80.70	4.57	3.24	87	15.01	9.67	9.83	1 922	99.20	5.71	10.49	85.96	3.70	3.33	93	13.19
25	15.33	14.49	1 189	147.55	8.62	13.13	100.75	4.53	3.78	78	15.82	13.55	12.92	1 491	148.15	6.80	13.79	105.99	3.68	3.69	81	13.83
30	19.80	17.84	835	201.22	9.85	14.98	118.72	4.44	3.48	59	14.66	18.12	16.43	1 151	202.82	7.72	15.44	122.85	3.56	3.33	69	12.91
35	24.68	21.37	624	256.84	10.81	15.51	133.64	4.27	3.06	36	13.75	22.83	19.89	876	259.85	8.45	16.00	137.20	3.42	2.94	48	12.07
40	29.96	25.05	483	317.84	11.69	15.44	148.22	4.14	2.62	23	12.23	27.79	23.42	686	320.81	9.13	15.73	150.92	3.29	2.41	32	10.80
45	35.02	28.47	392	376.41	12.28	15.52	160.04	3.96	2.37	16	11.12	32.44	26.63	558	378.43	9.59	15.47	161.48	3.14	2.10	23	9.83
50	39.78	31.62	326	427.82	12.54	11.56	167.77	3.73	0.90	12	8.22	36.76	29.54	464	428.60	9.79	11.47	167.78	2.94	0.61	17	7.30
55	44.73	34.83	272	476.17	12.64	11.96	173.64	3.50	0.97	10	7.65	41.23	32.48	387	474.28	9.87	11.59	172.10	2.75	0.66	14	6.81
60	49.91	38.13	226	519.98	12.60	10.91	177.11	3.26	0.58	8	6.42	45.87	35.49	322	514.25	9.84	10.35	174.04	2.56	0.26	12	5.74
65	55.28	41.48	189	557.02	12.41	9.12	177.90	3.02	0.10	7	5.43	50.66	38.53	268	547.08	9.69	8.53	173.36	2.36	?0.18	10	4.84
70	60.97	44.97	157	590.42	12.15	7.37	177.47	2.78	?0.31	6	4.37	55.69	41.68	223	575.36	9.49	6.72	171.57	2.17	?0.56	8	3.91
75	66.84	48.50	130	616.24	11.79	5.94	174.85	2.55	?0.59	5	3.53	60.88	44.88	186	596.34	9.21	5.20	167.79	1.99	?0.81	7	3.16
80	72.84	52.07	108	633.72	11.33	3.17	170.14	2.32	?1.17	4	2.28	66.19	48.11	154	609.98	8.85	2.60	162.24	1.81	?1.30	6	2.04
85	79.10	55.72	90	645.82	10.84	2.43	164.58	2.11	?1.18	3	1.80	71.74	51.44	128	618.64	8.46	1.84	156.09	1.64	?1.27	5	1.61
90	85.63	59.49	75	653.12	10.33	1.37	158.35	1.91	?1.27	3	1.26	77.53	54.86	107	623.03	8.06	0.84	149.56	1.49	?1.31	4	1.13

表8

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林分因子 Stand variables	统计指标 Indicators	长白落叶松 Larix olgensis	兴安落叶松 Larix gmelinii	华北落叶松 Larix principis-rupprechtii	日本落叶松 Larix kaempferi
平均胸径 Mean DBH/cm	区间Range	5.0~29.1	5.0~32.5	5.2~26.2	5.5~27.3
平均胸径 Mean DBH/cm	平均值Mean	12.8 (4.7)	10.6 (4.7)	11.3 (4.1)	13.3 (4.8)
平均树高 Mean height/m	区间Range	4.1~24.0	3.3~22.8	3.2~17.4	4.0~23.5
平均树高 Mean height/m	平均值Mean	12.0 (4.0)	11.0 (4.0)	8.5 (2.7)	12.7 (4.7)
株数密度 Stem density/（trees·hm^?2）	区间Range	217~3267	200~3150	210~3169	288~3122
株数密度 Stem density/（trees·hm^?2）	平均值Mean	1116 (607)	1051 (637)	1185 (644)	1217 (700)
公顷蓄积量 Stand volume/（m³·hm^?2）	区间Range	10.15~231.81	10.15~226.38	10.01~222.78	10.45~282.25
公顷蓄积量 Stand volume/（m³·hm^?2）	平均值Mean	86.55 (51.37)	57.56 (42.24)	60.77 (48.60)	88.99 (58.81)
总公顷生物量 Total stand biomass/（t·hm^?2）	区间Range	8.15~169.30	8.04~172.89	8.03~177.49	8.26~162.13
总公顷生物量 Total stand biomass/（t·hm^?2）	平均值Mean	56.65 (33.21)	41.66 (30.52)	47.38 (39.01)	53.85 (30.95)
林龄 Stand age/a	区间Range	7~52	6~52	6~60	8~41
林龄 Stand age/a	平均值Mean	26 (10)	25 (9)	26 (9)	22 (7)
净初级生产力 Net primary productivity/（t·hm^?2a^?1）	区间Range	1.74~14.26	1.03~12.00	1.36~12.66	2.23~15.33
净初级生产力 Net primary productivity/（t·hm^?2a^?1）	平均值Mean	7.96 (2.28)	6.42 (2.40)	6.33 (2.38)	8.87 (2.70)

树种Tree species	立地等级 Site level	地位指数范围 Site index（SI）
日本落叶松 Larix kaempferi	Ⅰ	13.64 ≤ SI < 16.83
	Ⅱ	11.50 ≤ SI < 13.64
	Ⅲ	8.26 ≤ SI < 11.50
	Ⅳ	4.40 ≤ SI < 8.26
华北落叶松 Larix principis-rupprechtii	Ⅰ	9.02 ≤ SI < 13.14
	Ⅱ	7.37 ≤ SI < 9.02
	Ⅲ	6.08 ≤ SI < 7.37
	Ⅳ	3.15 ≤ SI < 6.08
兴安落叶松 Larix gmelinii	Ⅰ	11.17 ≤ SI < 20.08
	Ⅱ	9.03 ≤ SI < 11.17
	Ⅲ	7.68 ≤ SI < 9.03
	Ⅳ	2.49 ≤ SI < 7.68
长白落叶松 Larix olgensis	Ⅰ	12.76 ≤ SI < 18.23
	Ⅱ	10.00 ≤ SI < 12.76
	Ⅲ	8.21 ≤ SI < 10.00
	Ⅳ	3.06 ≤ SI < 8.21

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