## 4 Materials and Methods
### Estimation of \(\Gamma^{*}\), \(R_{d}\), and \(C_{c}\)  
[PERSON] et al. [76] and [PERSON] et al. [77] showed that \(\Gamma^{*}\) can be estimated as a function of \(T_{\rm air}\):  
\[\Gamma*=36.9+1.18\times(T_{\rm air}-25)+0.036\times(T_{\rm air}-25)^{2}, \tag{18}\]  
Here, we used air temperature as measured in the LI-6800 leaf chamber. \(R_{\rm d}\) is described as [78]:  
\[R_{\rm d}=0.015\times V_{\rm cmx,0}, \tag{19}\]  
Mesophyll conductance to CO\({}_{2}\) was assumed to be infinite and thus \(C_{\rm c}\) was considered to be equal to intercellular CO\({}_{2}\) partial pressure \(C_{\rm i}\), [53]. \(C_{\rm i}\) is estimated as [79]:  
\[C_{\rm i}=C_{\rm a}-\frac{A_{\rm net}}{G_{\rm c}}, \tag{20}\]  
where \(C_{\rm a}\) is the ambient air CO\({}_{2}\) partial pressure (\(\mu\)mol mol\({}^{-1}\)), and \(G_{\rm c}\) is the stomatal conductance for CO\({}_{2}\) (mol m\({}^{-2}\) s\({}^{-1}\)). \(A_{\rm net}\) is the minimum of \(A_{\rm C}\) and \(A_{\rm J}\) (Equation (14)). Because \(C_{\rm i}\), \(A_{\rm net}\), and \(G_{\rm c}\) are coupled to each other, the estimation of \(A_{\rm net}\) and \(G_{\rm c}\) has to be resolved iteratively over \(C_{\rm i}\) given an initial value, which is \(C_{\rm i}\) = 0.7 \(\times\)\(C_{\rm a}\) for C3 winter wheat [80]. The iterative loop stops when the difference in \(C_{\rm i}\) between two successive iterations is less than 0.1 umol mol\({}^{-1}\). The biochemical model of photosynthesis proposed by [PERSON], [PERSON] and [PERSON] [64] was used to estimate \(A_{\rm net}\) as the minimum of the Rubisco-limited CO\({}_{2}\) assimilation rate and the electron-transport-limited CO\({}_{2}\) assimilation rate.  
\(G_{\rm c}\) is estimated using a modified Ball-Woodrow-Berry model BWB [81]:  
\[G_{\rm s}=G_{0}+\frac{a\times\beta_{\rm s}\times A_{\rm net}}{C_{\rm s}\times( 1+\rm VPD/D_{0})}, \tag{21a}\]  
\[G_{\rm c}=0.64\times G_{\rm s} \tag{21b}\]  
where \(G_{0}\) is the residual conductance (mol m\({}^{-2}\) s\({}^{-1}\)), assumed to be 0.01 [81]; \(C_{\rm s}\) is the CO\({}_{2}\) concentration at the leaf surface (umol mol\({}^{-1}\)), assumed to be the product of \(a/(a-1)\) and \(C_{\rm j}\); VPD is the vapor pressure deficit (kPa); D\({}_{0}\) (kPa) is an empirical parameter related to stomatal sensitivity to VPD, assumed to be 1.5 [81]; \(a\) is a parameter related to \(C_{\rm j}\), assumed to be 11.0 [81]; \(0.64\) is a factor used to convert the molecular diffusivity of water vapor to CO\({}_{2}\)[79]; \(\beta_{\rm S}\) is the normalized soil-moisture-dependent stress function which accounts for the reduction in \(G_{\rm S}\) under water stress. \(\beta_{\rm S}\) and \(\beta_{\rm B}\) (Equation (17)) can be defined as:  
\[\beta_{i}=\left\{\begin{array}{cc}0&\theta_{\rm SWC}<\theta_{\rm WP}\\ \left[\frac{\theta_{\rm SWC}-\theta_{\rm WP}}{\theta_{\rm FC}-\theta_{\rm WP }}\right]^{\rm q}\theta_{\rm WP}\leq\theta_{\rm SWC}\leq\theta_{\rm FC}\\ 1&\theta_{\rm SWC}>\theta_{\rm FC}\end{array},\right. \tag{22}\]  
where \(\beta_{\rm i}\) ranges between 1 (for plants not suffering from drought) and 0 (transpiration is zero); the subscripts i = B and S are for biochemical and stomatal limitations, respectively [75]; \(\theta_{\rm FC}\) and \(\theta_{\rm WP}\) represent \(\theta_{\rm SWC}\) at the field capacity (24%) and wilting point (9%); the fitting parameter q\({}_{\rm j}\) is a measure of the nonlinearity of the effects of water stress on the biochemical and stomatal limitations, and j takes the values B and S for i = B and S, respectively [75,82]. q\({}_{\rm B}\) (Equation (17)) and q\({}_{\rm S}\) in (Equation (21)) were determined by minimizing a cost function, \(C\) = \((M-S)^{2}\), where \(M\) represents the measurement and \(S\) is the corresponding simulated value (\(V_{\rm cmx}\) for q\({}_{\rm B}\), and Gs for q\({}_{\rm S}\)).