Biochemically-based model for photosynthetic parameter estimation using Bayesian method and its application in grapes in arid region

The response of photosynthesis to CO₂ concentration can provide a number of important parameters related to environmental factors. Using white seedless grape as the tested material in this study, net photosynthetic rates of leaves were measured for different intercellular CO₂ concentrations during two typical growing seasons from June to September in 2014 and 2015. A widely used biochemical model (FvCB model) in the simulation of CO₂ and H₂O gas exchange at the leaf scale was parameterized using data obtained from situ leaf-scale observations. In order to obtain the photosynthetic parameters values, to explore seasonal variations in the photosynthetic parameters in different seasons and to discuss the feasibility and advantage of the Bayesian method in solving high dimensional and complex model parameters estimation, the Bayesian approach was used to estimate the parameters of the FvCB model. In order to generate the Bayesian posterior probability distribution, a version of the Markov Chain Monte Carlo (MCMC) technique was used. In contrast, the least square procedure was used in the application of the same set of observational data. The results showed that maximum ribulose 1.5-bisphosphate carboxylase/oxygenase (Rubisco) carboxylation rate (V_cmax), potential light-saturated electron transport rate (J_max) and the rate of use of triose-phosphates utilization (TPU) had evident seasonal variations which increased from June to August, and then decreased in September. The maximum values were observed in August (54.30 μmol·m^-2·s^-1, 88.45 μmol·m^-2·s^-1 and 6.56 μmol·m^-2·s^-1, respectively) and minimum values in September (34.66 μmol·m^-2·s^-1, 58.86 μmol·m^-2·s^-1 and 4.38 μmol·m^-2·s^-1, respectively). The trend in mesophyll conductance (g_m) was relatively stable in different months, with respective values of 5.16 μmol·m^-2·s^-1·Pa^-1, 5.29 μmol·m^-2·s^-1·Pa^-1, 5.39 μmol·m^-2·s^-1·Pa^-1, 5.41 μmol·m^-2·s^-1·Pa^-1 from June to September. In comparison with traditional least square method, the values of V_cmax estimated by the Bayesian method were relatively small and those of J_max, TPU and g_m had no obvious difference. Also because the estimated parameters by the Bayesian method were obtained after adequate consideration of prior information, each parameter was in biological sense obviously more meaning. As a consequence, it indicated that the Bayesian approach combined with Markov Chains and Monte Carlo (MCMC) sampling algorithm was an effective way of estimation of the parameters in the FvCB model. As the parameters in the FvCB model were different in different seasons, it was necessary to consider these variations in using the parameters in the FvCB model.