近似贝叶斯法在光合模型参数估计中的应用

doi:10.17521/cjpe.2016.0067

摘要/Abstract

摘要：

长期以来, 光合作用机理模型中参数的确定都是一个难点。该文提出一种参数反演的方法, 称为近似贝叶斯法(APMC), 用来确定Farquhar光合模型的生理参数。通过将整个冠层抽象为一片大叶的思维抽象, 笔者进一步将APMC应用到冠层尺度的生理参数求解, 使直接求算冠层尺度生理参数成为可能。该文详细介绍了使用APMC估算光合模型参数的具体算法, 并用实测数据进行了验证。结果表明, APMC可以很好地应用于冠层光合模型参数的估计, 估计所得的参数落在参数生理上下限值之间, 应用1 948个实测数据进行检验, 得到决定系数0.75。模拟值和实测值的线性回归曲线斜率为1.04, 与理论上的1.0非常接近。这个方法对光合模型参数的获取或许有积极的意义。

关键词: 蒙特卡洛, 大叶模型, Farquhar光合模型, 净生态系统交换

Abstract:

We developed a method, namely Adaptive Population Monte Carlo Approximate Bayesian Computation (APMC), to estimate the parameters of Farquhar photosynthesis model. Treating the canopy as a big leaf, we applied this method to derive the parameters at canopy scale. Validations against observational data showed that parameters estimated based on the APMC optimization are un-biased for predicting the photosynthesis rate. We conclude that APMC has greater advantages in estimating the model parameters than those of the conventional nonlinear regression models.

Key words: Monte Carlo, big-leaf model, Farquhar photosynthesis model, net ecosystem exchange

曾继业, 谭正洪, 三枝信子. 近似贝叶斯法在光合模型参数估计中的应用. 植物生态学报, 2017, 41(3): 378-385. DOI: 10.17521/cjpe.2016.0067

Ji-Ye ZENG, Zheng-Hong TAN, Nobuko SAIGUSA. Using approximate Bayesian computation to infer photosynthesis model parameters. Chinese Journal of Plant Ecology, 2017, 41(3): 378-385. DOI: 10.17521/cjpe.2016.0067

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链接本文: https://www.plant-ecology.com/CN/10.17521/cjpe.2016.0067

https://www.plant-ecology.com/CN/Y2017/V41/I3/378

图/表 6

参考文献 34

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符号 Symbol	单位 Units	注释 Remark	参考值 Reference value
A	μmol·m^-2·s^-1	净光合速率 Net photosynthesis rate
A_c	μmol·m^-2·s^-1	Rubisco酶限制下的光合速率 Rubisco activity limited net photosynthesis rate
A_j	μmol·m^-2·s^-1	RuBP再生限制的光合速率 Electron transport limited net photosynthesis rate
R_d	μmol·m^-2·s^-1	呼吸速率 Respiration rate
C_i	μbar	胞内CO₂分压 Intercellular CO₂ partial pressure
C_a	μbar	大气CO₂分压 Air CO₂ partial pressure
C_s	μbar	叶面CO₂分压 Leaf-surface CO₂ partial pressure
Γ^*	μbar	CO₂补偿点 CO₂ compensation point
V_cmax	μmol·m^-2·s^-1	最大羧化速率 Maximal rubisco carboxylase rate
J_max	μmol·m^-2·s^-1	最大电子传输速率 Maximal electronic transport rate
J	μmol·m^-2·s^-1	电子传输速率 Electronic transport rate
I₂	μmol·m^-2·s^-1	电子传输速率 Electronic transport rate through photosystem II
I₀	μmol·m^-2·s^-1	光照强度 Photon flux density
f		光谱校正常数 Fraction of effective photon flux	0.15
α		转化率 Conversion efficiency	0.15
O_i	mbar	胞内氧分压 Intercellular O₂ partial pressure	210
K_o	mbar	氧化酶的动力学常数 Michaelis-Menten constant of Rubisco for O₂
K_c	μbar	羧化酶的动力学常数 Michaelis-Menten constant of Rubisco for CO₂
g_b	mol·m^-2·s^-1	边界层导度 Boundary-layer conductance
g_s	mol·m^-2·s^-1	气孔导度 Stomatal conductance
g₀	mol·m^-2·s^-1	气孔最小导度 Minimum stomatal conductance	0.01
g₁		气孔导度常数 Sensitivity coefficient of stomatal conductance	10.0
h_s		叶面相对湿度 Relative humidity on leaf surface
WS	m·s^-1	风速 Wind speed
LeafW	m	叶片宽度 Leaf width
V₂₅, J₂₅, K_c25, K_o25, R_d25, Γ^*₂₅		相应参数在25 ℃的值 Values at 25 °C	分别为80, 160, 260, 165, 1, 38 respectively
E_a	J·mol^-1	活化能 Activation energy	分别为58 500, 37 000, 59 400, 36 000, 66 400, 23 400 respectively
TK	K	温度 Temperature
TC	°C	温度 Temperature
R	J·K^-1·mol^-1	气体常数 Gas constant	8.314
S	J·K^-1·mol^-1	电子传输速率的温度参数 Entropy term	650
H	J·mol^-1	曲率参数 Deactivation energy	200 000
C_m	°C^-1	温度修正参数 Temperature modification constant
T_m	°C	温度修正参数 Temperature modification constant
V_Tm	μmol·m^-2·s^-1	羧化速率参数 Rubisco carboxylase rate
J_Tm	μmol·m^-2·s^-1	电子传输速率参数 Potential rate of electron transport
NEE	μmol·m^-2·s^-1	有效净生态系统CO₂交换率 Net ecosystem exchange
PPFD	μmol·m^-2·s^-1	有效光量子流密度 Photosynthetic photon flux density
P₂	kPa	大气压 Air pressure
LAI		叶面积指数 Leaf area index

符号 Symbol	单位 Units	注释 Remark	参考值 Reference value
A	μmol·m^-2·s^-1	净光合速率 Net photosynthesis rate
A_c	μmol·m^-2·s^-1	Rubisco酶限制下的光合速率 Rubisco activity limited net photosynthesis rate
A_j	μmol·m^-2·s^-1	RuBP再生限制的光合速率 Electron transport limited net photosynthesis rate
R_d	μmol·m^-2·s^-1	呼吸速率 Respiration rate
C_i	μbar	胞内CO₂分压 Intercellular CO₂ partial pressure
C_a	μbar	大气CO₂分压 Air CO₂ partial pressure
C_s	μbar	叶面CO₂分压 Leaf-surface CO₂ partial pressure
Γ^*	μbar	CO₂补偿点 CO₂ compensation point
V_cmax	μmol·m^-2·s^-1	最大羧化速率 Maximal rubisco carboxylase rate
J_max	μmol·m^-2·s^-1	最大电子传输速率 Maximal electronic transport rate
J	μmol·m^-2·s^-1	电子传输速率 Electronic transport rate
I₂	μmol·m^-2·s^-1	电子传输速率 Electronic transport rate through photosystem II
I₀	μmol·m^-2·s^-1	光照强度 Photon flux density
f		光谱校正常数 Fraction of effective photon flux	0.15
α		转化率 Conversion efficiency	0.15
O_i	mbar	胞内氧分压 Intercellular O₂ partial pressure	210
K_o	mbar	氧化酶的动力学常数 Michaelis-Menten constant of Rubisco for O₂
K_c	μbar	羧化酶的动力学常数 Michaelis-Menten constant of Rubisco for CO₂
g_b	mol·m^-2·s^-1	边界层导度 Boundary-layer conductance
g_s	mol·m^-2·s^-1	气孔导度 Stomatal conductance
g₀	mol·m^-2·s^-1	气孔最小导度 Minimum stomatal conductance	0.01
g₁		气孔导度常数 Sensitivity coefficient of stomatal conductance	10.0
h_s		叶面相对湿度 Relative humidity on leaf surface
WS	m·s^-1	风速 Wind speed
LeafW	m	叶片宽度 Leaf width
V₂₅, J₂₅, K_c25, K_o25, R_d25, Γ^*₂₅		相应参数在25 ℃的值 Values at 25 °C	分别为80, 160, 260, 165, 1, 38 respectively
E_a	J·mol^-1	活化能 Activation energy	分别为58 500, 37 000, 59 400, 36 000, 66 400, 23 400 respectively
TK	K	温度 Temperature
TC	°C	温度 Temperature
R	J·K^-1·mol^-1	气体常数 Gas constant	8.314
S	J·K^-1·mol^-1	电子传输速率的温度参数 Entropy term	650
H	J·mol^-1	曲率参数 Deactivation energy	200 000
C_m	°C^-1	温度修正参数 Temperature modification constant
T_m	°C	温度修正参数 Temperature modification constant
V_Tm	μmol·m^-2·s^-1	羧化速率参数 Rubisco carboxylase rate
J_Tm	μmol·m^-2·s^-1	电子传输速率参数 Potential rate of electron transport
NEE	μmol·m^-2·s^-1	有效净生态系统CO₂交换率 Net ecosystem exchange
PPFD	μmol·m^-2·s^-1	有效光量子流密度 Photosynthetic photon flux density
P₂	kPa	大气压 Air pressure
LAI		叶面积指数 Leaf area index

参数 Parameter		参数值下限 Lower value	参数值上限 Upper value	实际模拟值 Inversed value
V_cmax	V_opt	10	500	374
V_cmax	E_a	10 000	70 000	21 287
J_max	J_opt	10	500	310
J_max	E_a	10 000	50 000	10 000
R_d	R_d25	0	10	10
R_d	E_a	10 000	70 000	10 033
C_m		0.25	0.50	0.28
T_m		20.0	50.0	26.9
g₁		0.0	10.0	3.7

参数 Parameter		参数值下限 Lower value	参数值上限 Upper value	实际模拟值 Inversed value
V_cmax	V_opt	10	500	374
V_cmax	E_a	10 000	70 000	21 287
J_max	J_opt	10	500	310
J_max	E_a	10 000	50 000	10 000
R_d	R_d25	0	10	10
R_d	E_a	10 000	70 000	10 033
C_m		0.25	0.50	0.28
T_m		20.0	50.0	26.9
g₁		0.0	10.0	3.7