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Title: Parameter estimation of the Farquhar-von Caemmerer-Berry biochemical model from photosynthetic carbon dioxide response curves

item WANG, QINGGUO - Apec Climate Center (APCC)
item CHUN, J - Apec Climate Center (APCC)
item Fleisher, David
item Reddy, Vangimalla
item Timlin, Dennis
item RESOP, JONATHAN - University Of Maryland

Submitted to: Sustainability
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 7/19/2017
Publication Date: 7/24/2017
Citation: Wang, Q., Chun, J.A., Fleisher, D.H., Reddy, V., Timlin, D.J., Resop, J. 2017. Parameter estimation of the Farquhar-von Caemmerer-Berry biochemical model from photosynthetic carbon dioxide response curves. Sustainability. 9:1288.

Interpretive Summary: Scientists use mathematical equations to describe how plant growth responds to differences in climate. For example, equations for photosynthesis are used that predict responses to light, temperature, and carbon dioxide concentration. These equations need to be calibrated using experimental data before they can be applied for different studies. There is uncertainty regarding how well these calibration methods actually work which can impact their accuracy. This research used mathematical approaches to evaluate the differences between two curve fitting methods. We discovered that both methods were flawed when used with datasets that contained a limited number of datapoints. However, one method was shown to provide better calibration results when given more datapoints with higher quality data. The results are expected to help improve the accuracy of the photosynthesis equations used by scientists. This research can help crop model users have more confidence in the quality of their results.

Technical Abstract: The methods of Sharkey and Gu for estimating the eight parameters of the Farquhar-von Caemmerer-Berry (FvBC) model were examined using generated photosynthesis versus intercellular carbon dioxide concentration (A/Ci) datasets. The generated datasets included data with (A) high accuracy, (B) normal accuracy, (C) normal accuracy and measurement error, (D) high accuracy with variable data point distributions, and (E) variable accuracy among the different data points. Nonlinear regression was utilized to estimate the parameters using these datasets according to procedures described by the two methods. By comparing these estimated parameters against their true values, we concluded that the Sharkey method was unable to correctly estimate any parameter, while the Gu method was unable to correctly estimate any parameter using a dataset with less than five datapoints or when the data had an accuracy of four or fewer decimal places. The Gu method was also unable to correctly estimate all eight parameters when the number of data points was eight or fewer. The majority of estimated parameters VCMAX, KCO, GM and G* were underestimated, and RD and ALPHA values overestimated, using the Gu approach with datasets that had the same measurement errors and accuracies as those obtained experimentally from a typical open gas exchange system (B), (C), and (E). Correlation coefficients larger than 0.9 were obtained between estimated and true values for TP and JMAX. Using the Sharkey approach, JMAX was overestimated, VCMAX and GM were underestimated, TP showed even distributions between estimated and true values with correlation coefficients again larger than 0.9, and many values of RD were over their upper limit of 5.000 micromoles per meter square per second. The poor estimates for these parameters occurred from both methods because (i) not enough data points were used to satisfy the statistical assumptions required for nonlinear regression, (ii) there were intrinsic problems inherent with using the nonlinear regression approach for this type of application, and (iii) the curve-fitting implementations for both schemes as specified by the original authors were flawed. However, despite these mathematical limitations, the parameters obtained by both methods still remained useful to predict photosynthetic rates.