基于3-PGmix过程生长模型和优化算法的长白落叶松人工林潜在生产力估计

doi:10.11707/j.1001-7488.LYKX20250384

摘要/Abstract

摘要：

目的: 提出一种基于过程生长模型和优化算法估计林分潜在生产力的新方法，为立地质量评价和森林经营提供科学依据。方法: 基于长白落叶松纯林连续观测样地数据校准3-PG_mix模型，应用决定系数（R²）、平均绝对误差（MAE）、均方根误差（RMSE）和相对均方根误差（rRMSE）评价模型性能；设置蓄积连年生长量和5年定期平均生长量最大2种目标情景，采用粒子群优化算法求解不同立地等级下林分蓄积生产力最大值和对应的最优林分密度，在此基础上通过Weibull分布函数的尺度和形状参数模型得到对应的最优直径结构。结果: 1）在校准数据和验证数据中，3-PG_mix模型模拟的长白落叶松人工林的平均胸径、株数密度、蓄积量和地上生物量与样地实测值一致性较好，决定系数均大于0.86，相对均方根误差均小于16%。2）基准年龄30年时，长白落叶松人工林连年生长量和5年定期平均生长量最大时5个立地等级的蓄积潜在生产力分别为4.50~8.11和4.53~8.18 m³·hm^?2a^?1。3）达到蓄积潜在生产力时的径阶数量随林龄增加单调递增，径阶香农指数在生长前期经波动变化后也呈现出增加趋势，且立地等级越高二者数值越大。结论: 结合过程模型3-PG_mix与粒子群优化算法可以实现蓄积潜在生产力的估计，弥补传统方法未考虑林分自稀疏和气候因素影响的不足，为林分潜在生产力估计提供了一种新的方法。

关键词: 立地质量评价, 3-PG_mix模型, 潜在生产力, 粒子群优化

Abstract:

Objective: This study aims to develop a novel method for estimating stand potential productivity based on a process-based model and optimization algorithm, thereby providing a scientific basis for site quality assessment and forest management. Method: The 3-PG_mix model was calibrated using continuous observation data from pure stands of Larix olgensis obtaied from China’s national forest inventory. The model was evaluated by the coefficient of determination (R²), mean absolute error (MAE), root mean square error (RMSE) and relative root mean square error (rRMSE). Two target scenarios were set: maximization of annual volume increment and 5-year periodic mean increment. A particle swarm optimization (PSO) algorithm was applied to estimate the maximum stand volume productivity and corresponding optimal forest density under five different site quality grades. Based on these results, the optimal diameter structure was derived using the scale and shape parameter models of the Weibull distribution. Result: 1) In the calibrated and validated data, the mean diameter at breast height (DBH), stem density, stand volume, and stem biomass of L. olgensis plantations simulated by the 3-PGmix model were consistent with the measured values in the plot, with R² values greater than 0.86 and rRMSE less than 16%. 2) At the base age of 30 years, the potential volume productivity of L. olgensis plantations at the maximum annual and periodic average growth increment for the five site grades ranged from 4.50 to 8.11 m³·hm^?2a^?1 and from 4.53 to 8.18 m³·hm^?2a^?1, respectively. 3) The number of diameter classes, which reached the potential productivity of accumulation, increased monotonically with stand age, and the Shannon index of diameter classes exhibited an increasing trend after a fluctuating pattern at the early growth stage. The two indicators showed higher values under better site quality conditions. Conclusion: The integration of the process-based 3-PG_mix model and the PSO algorithm enables effective estimation of volume potential productivity, compensating for the limitations of traditional methods that do not account for self-thinning and climatic factors, and thereby provides a new approach for potential productivity estimation of forest stands.

Key words: site quality assessment, 3-PG_mix model, potential productivity, particle swarm optimization

中图分类号:

S757

黄宏超,雷相东,国红,罗光成,何潇. 基于3-PG_mix过程生长模型和优化算法的长白落叶松人工林潜在生产力估计[J]. 林业科学, 2026, 62(7): 38-49.

Hongchao Huang,Xiangdong Lei,Hong Guo,Guangcheng Luo,Xiao He. Estimation of Potential Productivity of Larix olgensis Plantations Based on 3-PG_mix Process-Based Model and Optimization Algorithm[J]. Scientia Silvae Sinicae, 2026, 62(7): 38-49.

图/表 8

表1

表2

长白落叶松人工林3-PGmix模型参数"

参数 Parameters	符号 Symbol	单位 Unit	参数值 Values	方法 Methods
当胸径为2 cm时的树叶和地上生物量比 Foliage:stem partitioning ratio at DBH=2 cm	p₂	—	0.69	优化 Optimization
当胸径为20 cm时的树叶和地上生物量比 Foliage:stem partitioning ratio at DBH=20 cm	p₂₀	—	0.14	优化 Optimization
地上生物量与胸径的关系常数 Constant in the stem mass and DBH relationship	a_S	—	0.11	拟合 Fitting
地上生物量与胸径的幂指数 Power in the stem mass and DBH relationship	n_S	—	2.429	拟合 Fitting
NPP分配到根的最大比例 Maximum fraction of NPP to roots	η_Rx	—	0.67	优化 Optimization
NPP分配到根的最小比例 Minimum fraction of NPP to roots	η_Rn	—	0.44	优化 Optimization
最大叶凋落速率 Maximum litterfall rate	γ_Fx	每月Month^?1	0.03	优化 Optimization
叶凋落速率达1/2时林龄 Age at which litterfall rate has median value	t_γF	月数 Months	24	Xie et al. 2017
月均根周转率 Average monthly root turnover rate	γ_R	每月 Month^?1	0.023	优化 Optimization
叶生长月份 If deciduous， leaves are produced at end of this month	leaf_P	月 Month	5	王战，1992
叶凋落月份 If deciduous， leaves all fall at start of this month	leaf_L	月 Month	10	王战，1992
生长最低温度 Minimum temperature for growth	T_min	℃	?5	王战，1992
生长最适温度 Optimum temperature for growth	T_opt	℃	16	王战，1992
生长最高温度 Maximum temperature for growth	T_max	℃	38	王战，1992
霜冻损失生产力天数Days production lost per frost day	k_F	天数 Days	0.3	优化 Optimization
肥力为0时m的值Value of m when FR = 0	m₀	—	0.1	优化 Optimization
肥力为0时f_N的值Value of f_N when FR = 0	f_N0	—	0.8	优化 Optimization
最大林龄 Maximum stand age used in age modifier	t_x	年 Years	160	Xie et al. 2020a
林龄最大时死亡率 Mortality rate for large age	γ_Nx	%·a^?1	2	优化 Optimization
当林分密度为1000株·hm^?2时单株最大地上生物量 Maximum stem biomass per tree at 1000 trees·hm^?2	w_Sx_{1 000}	kg·tree^?1	144	拟合 Fitting
自稀疏幂指数 Power in self-thinning rule	n_m	—	1.22	拟合 Fitting
初期比叶面积 Specific leaf area at age 0	σ₀	m²·kg^?1	8.4	优化 Optimization
成熟林比叶面积 Specific leaf area for mature leaves	σ₁	m²·kg^?1	4.6	优化 Optimization
比叶面积达（σ₀ +σ₁）/2时林龄 Age at which specific leaf area = （σ₀ +σ₁）/2	t_σ	年 Years	10	优化 Optimization
冠层量子效率 Canopy quantum efficiency	α_Cx	mol·mol^?1	0.048 5	优化 Optimization
树高关系常数 Constant in the stem height relationship	a_H	—	1.1	拟合 Fitting
胸径在树高关系中的幂指数 Power of DBH in the stem height relationship	n_HB	—	0.83	拟合 Fitting
材积关系常数 Constant in the stem volume relationship	a_V	—	0.000 2	拟合 Fitting
胸径在材积关系中的幂指数 Power of DBH in the stem volume relationship	n_VB	—	2.434	拟合 Fitting

表2

图1

表3

图2

表4

表5

图3

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统计量 Statistics	林龄 Stand age/a	平均胸径 Mean DBH/cm	平均树高 Mean height/m	株数密度 Stem density/ （trees·hm^?2）	林分蓄积量 Stand volume/ （m³·hm^?2）	地上生物量 Stem biomass/ （t·hm^?2）	树叶生物量 Foliage biomass/ （t·hm^?2）	树根生物量 Root biomass/ （t·hm^?2）
平均值 Mean	30	14.2	13.9	1 203	124.96	67.79	3.68	12.16
标准差 Standard deviation	9	3.8	3.8	693	55.86	30.31	1.40	10.94
最小值 Minimum	9	6.5	5.0	317	15.68	8.43	0.68	1.62
最大值 Maximum	56	26.5	26.1	4 033	281.53	152.12	7.20	26.53

数据类型 Datasets	林分因子 Stand factors	决定系数 Determination coefficient （R² ）	平均绝对误差 Mean absolute error （MAE）	均方根误差 Root mean square error （RMSE）	相对均方根误差 Relative root mean square error （rRMSE）
校准数据 Calibration data	平均胸径Mean DBH	0.88	0.61	1.20	7.80
	株数密度Stem density	0.99	0.18	52.36	4.81
	蓄积量Stand volume	0.88	1.43	17.87	12.89
	地上生物量Stem biomass	0.88	1.52	9.99	13.25
	叶生物量Foliage biomass	0.72	3.93	0.74	18.90
	根生物量Root biomass	0.86	1.70	3.85	13.92
验证数据 Validation data	平均胸径Mean DBH	0.90	0.61	1.19	7.76
	株数密度Stem density	0.99	0.04	26.54	2.39
	蓄积量Stand volume	0.87	2.03	21.10	14.86
	地上生物量Stem biomass	0.86	2.12	11.67	15.19
	叶生物量Foliage biomass	0.62	5.76	0.87	21.83
	根生物量Root biomass	0.81	2.90	5.03	17.86

方案情景Scenario	指标 Indicator	立地等级 Site class
方案情景Scenario	指标 Indicator	Ⅰ	Ⅱ	Ⅲ	Ⅳ	Ⅴ
逐年优化 Annual optimization scenario	蓄积潜在生产力Potential volume productivity/（m³·hm^?2a^?1）	8.11	7.49	6.83	5.72	4.50
	株数密度Stand density/（trees·hm^?2）	920	885	884	1 107	1 721
	单木材积Individual tree volume/m³	0.20	0.19	0.18	0.12	0.066
每5年优化 Five-year optimization scenario	蓄积潜在生产力Potential volume productivity/（m³·hm^?2a^?1）	8.18	7.57	6.94	5.85	4.53
	株数密度Stand density/（trees·hm^?2）	1 294	1 282	1 295	1 426	1 808
	单木材积Individual tree volume/m³	0.14	0.12	0.11	0.092	0.062
自然生长 Natural growth	蓄积连年生长量Annual volume increment/（m³·hm^?2a^?1）	7.26	7.06	6.60	5.68	4.56
	株数密度Stand density/（trees·hm^?2）	2 414	2 437	2 437	2 437	2 437
	单木材积Individual tree volume/m³	0.079	0.070	0.065	0.055	0.047

目标变量 Target variable	参数 Parameter	估计值 Estimated value	调整决定系数 Adjusted R²	目标变量 Target variable	参数 Parameter	估计值 Estimated value	调整决定系数 Adjusted R²
尺度参数 Scale parameter	b₀	15.994 9^***	0.91	形状参数 Shape parameter	c₀	9.907 4^***	0.25
	b₁	7.746 1^***			c₁	?0.245 2^***
	b₂	1.530 2^***			c₂	?0.209 2^***
	b₃	?8.166 3e-4^*			c₃	6.908 3e-3^***
	—	—			c₄	?7.192 9e-4^***

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