Table 1.
Summary of selected small dynamic leaf-level photosynthesis models.
(Ordinary differential equations abbreviated as ODEs).
Fig 1.
Parameter estimation data set: Model inputs measured on 8 September 2021.
(a) Measured irradiance (I) μmolm−2s−1 (b) Measured leaf temperature (Tl) K.
Fig 2.
Global optimisation results for the stomatal parameter ku in expression 15.
(a) The range of potential ku values considered is shown along with the optimised ku distribution. The genetic algorithm converged to a parameter value on the interval [170, 180], with the optimised ku = 179.4 s. (b) Objective function values: computed profile likelihood for a range of ku values. The 95% confidence interval is shown in red as [157.5, 202.5] s.
Fig 3.
Global optimisation results for the stomatal parameter kd in expression 16.
(a) The range of potential kd values considered is shown along with the optimised kd distribution. The genetic algorithm converged to a parameter on the interval [800, 850], with the optimised kd = 830.3 s. (b) Objective function values: computed profile likelihood for a range of kd values. The 95% confidence interval is shown in red as [735.6, 927.5] s.
Fig 4.
Global optimisation results for parameter c3 in expression 10 used in 18.
(a) The range of potential c3 values considered is shown along with the optimised c3 distribution. The genetic algorithm converged to an optimal parameter value on the interval [37.9,38] as c3 = 37.96. (b) Objective function values: computed profile likelihood for a narrow range of c3 values. The 95% confidence interval is shown in red as [37.95, 37.98] s.
Table 2.
Values of the model parameters in expressions 15 and 16.
Parameters of the steady-state target function G(I(t),ca(t)), computed under ca = 400ppm and ca = 800ppm, respectively, are also included. Estimated unknown system parameters are given with accompanying confidence intervals.
Table 3.
Values of the model parameters in expression 18.
A priori estimated parameters of function J(I(t)) and the respective steady-state parameters Vcmax and Rd are given. The unknown system parameter and its confidence interval is also shown. Finally, the parameters related to the temperature dependence of key FvCB model parameters are also given.
Fig 5.
Results obtained after parameter estimation.
(a) Total stomatal conductance to CO2 diffusion molm−2s−1. (b) Net photosynthetic rate μmolm−2s−1 (c) min(Wc,Wj) μmolm−2s−1, indicates whether photosynthesis is limited by the carboxylation or electron transport rate.
Fig 6.
Results obtained after parameter estimation.
The correlation between An and the electron transport rate (J(I(t)) is shown for both measured and simulated data sets.
Table 4.
Greenhouse data measured under natural fluctuating irradiance.
Summary of RMSEs computed to assess the accuracy of An. Here , with the measured output denoted by An,m. Results comparing the use of the optimised parameter c3 = 37.96 to the original c3 = 38.28 [28] are shown. Experiments were conducted under 2 sets of ambient CO2 concentrations, 400ppm and 800ppm, respectively. R2 values are given in [].
Fig 7.
Model validation results obtained for measurements taken on 6 Sept 2021 with ca = 400ppm.
(a) Measured irradiance μmolm−2s−1. (b) Net photosynthetic rate μmolm−2s−1 (c) min(Wc,Wj) μmolm−2s−1, indicates whether photosynthesis is limited by the carboxylation or electron transport rate.
Fig 8.
Model validation results obtained for measurements taken on 7 Sept 2021 with ca = 800ppm.
(a) Measured irradiance μmolm−2s−1. (b) Net photosynthetic rate μmolm−2s−1 (c) min(Wc,Wj) μmolm−2s−1, indicates whether photosynthesis is limited by the carboxylation or electron transport rate.
Fig 9.
Results obtained for the validation data set measured on 7 Sept 2021 under elevated ca = 800ppm.
The correlation between An and the electron transport rate (J(I(t)) is shown for both measured and simulated data sets.