Chin J Plan Ecolo ›› 2017, Vol. 41 ›› Issue (3): 378-385.doi: 10.17521/cjpe.2016.0067

• Method and Technology • Previous Articles    

Using approximate Bayesian computation to infer photosynthesis model parameters

Ji-Ye ZENG1, Zheng-Hong TAN2,*(), Nobuko SAIGUSA1   

  1. 1National Institute for Environmental Studies, Tsukuba 305-8506, Japan
    and
    2Department of Environmental Science, Hainan University, Haikou 570228, China
  • Online:2017-04-12 Published:2017-03-10
  • Contact: Zheng-Hong TAN E-mail:dr.tan.zhenghong@gmail.com
  • About author:

    KANG Jing-yao(1991-), E-mail: kangjingyao_nj@163.com

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

Fig. 1

Comparison of the temperature correction models. Solid line is the curve of von Caemmerer et al. (2009) when S = 710 and H = 220 000; dotted line is the curve when S is increased by 10% (S=790, H=220 000); dashed line is the curve calculated according to our new response curve (Cm = 0.3, Tm = 37)."

Table 2

Variables and parameters used in the photosynthesis model and their reference values mainly from Caemmerer et al. (2009)"

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
Ac μmol·m-2·s-1 Rubisco酶限制下的光合速率 Rubisco activity limited net photosynthesis rate
Aj μmol·m-2·s-1 RuBP再生限制的光合速率 Electron transport limited net photosynthesis rate
Rd μmol·m-2·s-1 呼吸速率 Respiration rate
Ci μbar 胞内CO2分压 Intercellular CO2 partial pressure
Ca μbar 大气CO2分压 Air CO2 partial pressure
Cs μbar 叶面CO2分压 Leaf-surface CO2 partial pressure
Γ* μbar CO2补偿点 CO2 compensation point
Vcmax μmol·m-2·s-1 最大羧化速率 Maximal rubisco carboxylase rate
Jmax 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
Oi mbar 胞内氧分压 Intercellular O2 partial pressure 210
Ko mbar 氧化酶的动力学常数 Michaelis-Menten constant of Rubisco for O2
Kc μbar 羧化酶的动力学常数 Michaelis-Menten constant of Rubisco for CO2
gb mol·m-2·s-1 边界层导度 Boundary-layer conductance
gs 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
hs 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, Kc25,
Ko25, Rd25, Γ*25
相应参数在25 ℃的值 Values at 25 °C 分别为80, 160, 260, 165, 1, 38 respectively
Ea
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
Cm °C-1 温度修正参数 Temperature modification constant
Tm °C 温度修正参数 Temperature modification constant
VTm μmol·m-2·s-1 羧化速率参数 Rubisco carboxylase rate
JTm 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

Table 3

Initial parameter ranges and modeled values"

参数
Parameter
参数值下限
Lower value
参数值上限
Upper value
实际模拟值
Inversed value
Vcmax Vopt 10 500 374
Ea 10 000 70 000 21 287
Jmax Jopt 10 500 310
Ea 10 000 50 000 10 000
Rd Rd25 0 10 10
Ea 10 000 70 000 10 033
Cm 0.25 0.50 0.28
Tm 20.0 50.0 26.9
g1 0.0 10.0 3.7

Fig. 2

Relationship between modeled and observed net ecosystem exchange (NEE). The solid line indicates that model outputs equal observations."

Appendix I

Model entity in the APMC"

对每一个APMC粒子 For all particles
for k = 1 to Nobs do(对所有的观测数据) For all observations
用APMC粒子选定的V25, J25, Rd25, g1, Ea, Cm, Tm Use parameter values selected by AMPC
计算Vcmax, Jmax, Rd, gb Estimate target model parameters
t = 1 (Ci的迭代计算次数) At initial time
设\(C_i^0=0.7C_a\) Set the intercellular CO2 equal to 70% of air CO2
设\(\Delta C_i >1\) Set the intercellular CO2 not in equilibrant While \(\Delta C_i >1 \) do
计算 Ac, Aj
Compute the two rate.
计算\(A=\frac{A_c+A_j-\sqrt{(A_c+A_j)^2-4\times 0.98A_cA_j}}{2\times 0.98} \\ Compute the joint rate 计算\\ C_i^t=C_a-\frac{A}{g_b}-\frac{g_bC_aA-A^2}{g_bg_1h_sA-g_0A+g_0Ag_bg_oC_a}\) Compute the intercellular CO2
\( \Delta C_i=|C_i^t-C_i^{t-1}|\) Check equilibrant state
t = t + 1 Advance time
end while
end for
将|A-NEE|的平均值作为APMC粒子的r Calculate the difference between modeled photosynthesis rate and the observed rate
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