## 2 Materials and Methods
### Settings of FQE Values  
Two different FQE settings were adopted for the SIF simulations, as follows:  
1. Fixed FQE, simulations with fixed FQE values as the literature suggested values: 0.01 for fqe2 and 0.2 for fqe1/fqe2.
2. Variable FQE, simulations with variable FQE values, which were estimated by fitting the SIF simulations to the observed SIF data and minimizing the systematic deviations in SIF\({}_{\rm{A}}\) and SIF\({}_{\rm{B}}\) simulations with the LUT of changing values of FQE.  
As mentioned previously, the fqe2 and fqe1 are directly proportional to PSII and PSI fluorescence, respectively, and the PSII fluorescence spectra cover both the red and far-red bands, while the PSI fluorescence spectra cover only the far-red band. Thus, the fqe2 and fqe1/fqe2 are directly proportional to the simulated SIF\({}_{\rm{B}}\) and SIF\({}_{\rm{A}}\)/SIF\({}_{\rm{B}}\), respectively. In other words, if the simulated SIF\({}_{\rm{B}}\) and SIF\({}_{\rm{A}}\)/SIF\({}_{\rm{B}}\) values have systematic deviation, it is likely to be caused by the unsuitable FQE values. Adjusting FQE should find the optimal (fqe2, fqe1/fqe2) setting that makes the systematic deviation of diurnal SIF\({}_{\rm{A}}\) and SIF\({}_{\rm{B}}\) simulations minimum for each fieldwork day (hereafter denoted as the daily FQE values). According to the literature [28], the measured SIF normalized by PAR has a weak diurnal cycle for unstressed crops in a steady state. Therefore, the FQE values during one day are regarded as invariable in this study.  
First, the SCOPE model was run with an LUT of different fqe2 and fqe1/fqe2 values at half-hour time steps corresponding to each diurnal experiment. The fqe2 was set from 0.005 to 0.02 with a step of 0.001, and the fqe1/fqe2 was set to 0.05-0.5 with a step of 0.05. Then, for every fieldwork day, 120 sets of half-hour SIF\({}_{\rm{A}}\) and SIF\({}_{\rm{B}}\) data under 120 different (fqe2, fqe1/fqe2) conditions were collected from the SCOPE model outputs. For each (fqe2, fqe1/fqe2) condition, the bias in daily averages of diurnal SIF\({}_{\rm{A}}\) and SIF\({}_{\rm{B}}\) simulations was adopted to describe the systematic deviation of diurnal SIF\({}_{\rm{A}}\) and SIF\({}_{\rm{B}}\) simulations, as defined in Equation (6)  
\[bias_{\rm{SIF_{B}}}=\frac{\overline{\rm{SIF_{B,sim}}}-\overline{\rm{SIF_{B, mea}}}}{\overline{\rm{SIF_{B,mea}}}},bias_{\rm{SIF_{A}}}=\frac{\overline{\rm{SIF_{A, sim}}}-\overline{\rm{SIF_{A,mea}}}}{\overline{\rm{SIF_{A,mea}}}} \tag{6}\]  
in which \(\overline{\rm{SIF}}\) represents the daily average of diurnal SIF during one fieldwork day, the subscripts 'B' and 'A', respectively, represent the O\({}_{2}\)-B and O\({}_{2}\)-A bands, and the subscripts'sim' and'mea', respectively, represent the simulated and measured data. The computation of the daily average of diurnal SIF is necessary, because the diurnal variations in SIF are dominated by the diurnal cycles of irradiance, making it more difficult to reflect FQE effects. The absolute value of \(bias_{\rm{SIF_{B}}}\) and can simultaneously reach their minimum value by adjusting the two FQE values, because fqe2 and fqe1/fqe2 separately governs the simulated \(\mathrm{SIF_{B}}\) and \(\mathrm{SIF_{A}}\)/\(\mathrm{SIF_{B}}\). Finally, the two FQE values that provide a minimum sum of the absolute value of \(\mathit{bias_{\mathrm{SIF_{B}}}}\) and \(\mathit{bias_{\mathrm{SIF_{A}}}}\) (\(\left|\mathit{bias_{\mathrm{SIF_{B}}}}\right|+\left|\mathit{bias_{\mathrm{SIF _{A}}}}\right|\)) were selected as the daily FQE values for each fieldwork day.