利用经验-过程混合建模方法优化华山松过程模型的参数

doi:10.11707/j.1001-7488.20210903

摘要/Abstract

摘要：

目的: 以基于碳平衡的过程模型CROBAS为例，提出一种结合经验模型与过程模型的混合建模方法，优化华山松过程模型CROBAS-PA的参数，探索在建模数据不足情况下预估复杂过程模型参数的有效途径。方法: 参数优化模型的目标函数设为过程模型CROBAS-PA与经验模型QUASSI 1.0在树高和生物量预测上的离差，优化模型的决策变量选取过程模型中10个随气候和树种调整的参数（树冠树叶分形维数、消光系数、比叶面积、最大光合速率、树叶衰老率、叶表面积密度、自然整枝参数、树枝边材率、树干边材衰老率和树枝边材衰老率），约束条件为过程模型参数的可行域。选用差分演化算法，采用Sobol一阶灵敏度和全局灵敏度系数进行参数敏感性分析与评估，利用平均误差（ME）、平均绝对误差（MAE）和平均相对误差（MRE）进行模型检验。结果: 经参数优化后的华山松过程模型CROBAS-PA的有效预测时间可达20年，树高和胸径预测值平均绝对误差分别小于1.03 m和1.19 cm，平均相对误差分别低于5.59%和2.59%。灵敏度分析显示，最大光合速率、比叶面积、消光系数、树冠树叶分形维数对树高和胸径的生长变化有明显影响，而叶表面积密度对胸径和树高的生长变化影响较小。结论: 经参数优化后的华山松过程模型CROBAS-PA可以较准确预测华山松的树高和胸径生长以及林木各器官中的碳分配，基于经验-过程混合建模方法在复杂过程模型参数预估中具有一定应用潜力。

关键词: 生物量, 差分演化算法, 参数预估, 华山松, 过程模型, 林分生长

Abstract:

Objective: Process-based models often consist of photosynthesis, respiration, and carbon allocation modules. This leads to a higher dimensionality of variables than empirical models. Thus, it is prone to the problem of insufficient data for traditional biological modelling. Based on a carbon balance model CROBAS, the study applied a hybrid modelling approach to optimize the parameters of CROBAS-PA for Pinus armandii, to explore an effective way to parameterize complex process-based models under the condition of sparse data. Method: The objective function of the parametric optimization model was set as the deviation of the process model CROBAS-PA from the empirical model QUASSI 1.0 for tree height and biomass predictions. The decision variables for the optimization model were selected from the process model with ten parameters that vary with climate and species: the "fractal dimension" of foliage in crown, the extinction coefficient, the specific leaf area, the maximum rate of canopy photosynthesis per unit area, the specific senescence rate of foliage, the "surface area" density of foliage, the parameter relative to self-pruning, the form factor of sapwood in branches, the form factor of senescent sapwood in stem inside crown, and the form factor of senescent sapwood in branches. The constraints are the feasible domains of the process-based model parameters. A differential evolution algorithm was chosen for the optimization. A sensitivity analysis for parameters was implemented with Sobol's first-order indices and total-effect indices. Model performance was judged by mean error(ME), mean absolute error(MAE), and mean relative error(MRE). Result: Model simulations showed that the effective prediction period of the process-based CROBAS-PA could reach 20 years. The average absolute errors of tree height and diameter at breast height were less than 1.03 m and 1.19 cm, respectively; The average relative errors were less than 5.59% and 2.59%, respectively. The sensitivity analysis showed that the maximum rate of canopy photosynthesis per unit area, the specific leaf area, the extinction coefficient, and the "fractal dimension" of foliage in crown had apparent effects on the growth of height and DBH, while the effect of "surface area" density of foliage was negligible. Conclusion: The parameter-optimized CROBAS-PA can accurately predict or explain tree diameter and height growth, as well as the carbon allocation in each organ of Pinus armandii. This indicates that the hybrid modelling technique has a promising potential for the parameter estimation of complex process-based models.

Key words: biomass, differential evolution, parameterization, Pinus armandii, process-based model, stand development

中图分类号:

S757

薛海连,田相林,曹田健. 利用经验-过程混合建模方法优化华山松过程模型的参数[J]. 林业科学, 2021, 57(9): 21-33.

Hailian Xue,Xianglin Tian,Tianjian Cao. Optimizing Parameters of a Process-Based Model for Pinus armandii: A Compromise between Empirical and Process-Based Modelling Approaches[J]. Scientia Silvae Sinicae, 2021, 57(9): 21-33.

图/表 11

表1

表2

表3

华山松过程模型CROBAS-PA参数估计值"

参数 Parameter	生理学意义 Meaning of biology	参数值Parameter values	参数化方法 Method of parameterization
φ_s	冠基树干边材率 Form factor of sapwood in stem below crown	1.0	基于PIPE理论假设的理论值Theoretical value based on the assumption of pipe theory
Ψ_s	冠基树干边材衰老率 Form factor of senescent sapwood in stem below crown	1.0	基于PIPE理论假设的理论值Theoretical value according to pipe theory
φ_c	冠层树干边材率 Form factor of sapwood in stem within crown	0.75	基于椎体形式理论值Based on the conical form
φ′_t	运输根边材率(粗根没有心材) Form factor of sapwood in transport roots (no heartwood in coarse roots)	1.0	Mäkelä, 1997
ρ_s	树干部分木材密度 Density of wood in stem	400 kg·m^-3	梁保松等，2008
ρ_b	树枝部分木材密度 Density of wood in branch	400 kg·m^-3	梁保松等，2008
ρ_t	运输根部分木材密度 Density of wood in transport roots	400 kg·m^-3	梁保松等，2008
c_t	运输根长/干长 Ratio of transport root length to stem length	1.0	Mäkelä, 1997
α_s	树干边材面积/叶生物量 Ratio of sapwood area in stem to foliage weight	1.2×10^-3 m²·kg^-1	陈存根等，1996
α_b	树枝边材面积/叶生物量 Ratio of sapwood area in branches to foliage weight	5×10^-3 m²·kg^-1	陈存根等，1996
α_t	运输根边材面积/叶生物量 Ratio of sapwood area in transport roots to foliage weight	4.0×10^-4 m²·kg^-1	陈存根等，1996
r₁	树叶细根呼吸率 Specific maintenance respiration rate of foliage + fine roots	0.1 kg C·kg^-1DW a^-1	Mohren, 1987
r₂	木质部呼吸率 Specific maintenance respiration rate of wood	0.01kg C·kg^-1DW a^-1	Mohren, 1987
s_r	细根衰老速率 Specific senescence rate of fine roots	1.0 a^-1	张小全，2001
d_s0	树干部分整枝边材面积转化率 Specific sapwood area turnover rate per unit relative pruning in stem	1.0	Mäkelä, 1997
d_b0	树枝部分整枝边材面积转化率 Specific sapwood area turnover rate per unit relative pruning in branch	1.0	Mäkelä, 1997
d_t0	传输根部分整枝边材面积转化率 Specific sapwood area turnover rate per unit relative pruning in transport root	1.0	Mäkelä, 1997
d_s1	树干部分无整枝边材面积转化率 Specific turnover rate of sapwood area in case of no pruning in stem	0.01	Mäkelä, 1997
d_b1	树枝部分无整枝边材面积转化率 Specific turnover rate of sapwood area in case of no pruning in branch	0.01	Mäkelä, 1997
d_t1	传输根无整枝边材面积转化率 Specific turnover rate of sapwood area in case of no pruning in transport root	0.01	Mäkelä, 1997
Ψ′_t	运输根边材衰老率(运输根无心材) Form factor of senescence sapwood in transport roots(no heartwood in coarse roots)	0	Mäkelä, 1997
α_r	细根/叶生物量 Ratio of fine root to foliage weight	0.2	Vanninen et al., 1996
a_σ	单位冠长对应光合作用下降率 Decrease of photosynthesis per unit crown length	0.02 m^-1	Yoder et al., 1994
c_b	树冠半径/冠长 Ratio of crown radius to crown length	0.3	本研究This study
q	冠幅自然整枝度 Degree of control by crown coverage of self-pruning	0.35	预估值Estimate value
Y	碳有效利用率 Carbon use efficiency	0.65 kg C·kg^-1 DW	刘华等，2007
s_f	树叶衰老率(针叶生命周期3~5 a) Specific senescence rate of foliage(based on needle lifetime of 3-5 a)	0.193 6 [0.2, 0.333] a^-1	本研究This study
A_n	比叶面积 Specific leaf area	5.219 1 [4.765 1, 6.543] m²·kg^-1	时忠杰等，2009
P	最大光合速率 Maximum rate of canopy photosynthesis per unit area	3.498 3 [1.0, 5.074 5] kgC·m^-2a^-1	梁军生等，2009
k	消光系数 Extinction coefficient	0.117 4 [0.01, 0.18]	宋子炜等，2009
a_q	自然整枝参数 Parameter related to self-pruning	0.461 4 [0.45, 0.8]	本研究This study
φ′_b	树枝边材率 Form factor of sapwood in branches	2.0 [0.1, 2.0]	本研究This study
z	冠层树叶分形维数 Fractal dimension of foliage in crown	3.0 [2.0, 3.0]	Zeide et al., 1991
x	叶表面积密度 Surface area density of foliage	0.198 7 [0.03, 0.2] kg·m^-z	陈存根等，1996
Ψ_c	树干边材衰老率 Form factor of senescence sapwood in steminside crown	0.945 5 [0.5, 1.0]	本研究This study
Ψ′_b	树枝边材衰老率 Form factor of senescence sapwood in branches	3.0 [0.9, 3.0]	本研究This study

表3

图1

图2

图3

图4

图5

图6

表4

表5

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调查年份 Inventory year	样地类型 Plot type	样地数量 Number of plots	林龄 Stand age/a	林分密度 Stand density/hm^-2	平均胸径 Mean DBH/cm	平均树高 Mean tree height/m	林分断面积 Stand basal area/(m²·hm^-2)
1990	临时样地Temporary plots	244	20~60	113~2 324	10.0~32.0	6.5~22.0	5.0~33.0
2005	临时样地Temporary plots	143	16~67	92~2 190	7.6~33.8	5.3~22.5	5.0~37.0
2013	临时样地Temporary plots	70	20~81	181~2 254	11.2~29.6	6.0~19.0	7.0~30.0
2014	固定样地Permanent plots	31	20~52	289~4 616	6.2~22.9	6.7~16.0	6.9~28.6

公式 Equation	因变量 Dependent variable	样本量 Sample size	拟合参数 Parameter estimate	决定系数 Determination coefficient (R²)
(1)	H	387	a₁=24.994；a₂=42.728；a₃=1.032	0.382
(2)	SDI	85	β=1.662	0.811
(3)	G	387	b₁=16.132；b₂=0.233；b₃=6.572；b₄=1.475	0.781
(4)	D	387	c₁=22.717；c₂=0.182；c₃=24.893；c₄=0.182	0.482

地位级 Site class	样本量 Sample size	ME		MAE		MRE(%)
地位级 Site class	样本量 Sample size	树高 Tree height/m	DBH/cm	树高 Tree height/m	DBH/cm	树高 Tree height/m	DBH/cm
Ⅰ	30	1.03	0.33	1.03	0.74	5.59	2.59
Ⅱ	30	0.61	0.36	0.61	0.81	4.80	1.84
Ⅲ	30	0.06	0.12	0.27	1.19	0.59	0.60

参数Parameter	树高Tree height		DBH
参数Parameter	一阶灵敏度系数 The first order sensitivity index	总灵敏度系数 The total sensitivity index	一阶灵敏度系数 The first order sensitivity index	总灵敏度系数 The total sensitivity indiex
树叶衰老率Specific senescence rate of foliage(s_f)	0.020 4	0.002 4	0.030 5	0.003 4
比叶面积Specific leaf area(A_n)	0.077 9	0.301 0	0.052 2	0.343 3
最大光合速率Maximum rate of canopy photosynthesis per unit area(P)	0.153 0	0.444 3	0.099 0	0.500 3
消光系数Extinction coefficient(k)	0.079 2	0.312 9	0.073 0	0.359 6
自然整枝参数Parameter related to self-pruning(a_q)	0.029 6	0.033 3	0.034 0	0.025 0
树枝边材率Form factor of sapwood in branches(φ_b)	0.020 0	0.000 2	0.038 4	0.048 8
冠层树叶分形维数Fractal dimension of foliage in crown(z)	0.128 4	0.3610	0.110 5	0.402 6
叶表面积密度Surface area density of foliage(x)	0.029 1	0.033 8	0.033 6	0.028 0
树干边材衰老率Form factor of senescence sapwood in steminside crown(Ψ_c)	0.020 8	0.004 0	0.031 2	0.000 0
树枝边材衰老率Form factor of senescence sapwood in branches(Ψ′_b)	0.041 1	0.067 0	0.031 2	0.000 1
细根/叶生物量Fine root: foliage weight ratio(α_r)	0.023 8	0.026 0	0.023 0	0.038 6
细根衰老速率Specific senescence rate of fine roots(s_r)	0.023 3	0.022 2	0.031 9	0.033 1

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