## 3 Results
### Responses of the SIF-IWUE Relationship to the Environmental Factors
#### 3.3.2 Effects of Solar Radiation on IWUE-SIF Correlations  
The intensity of SIF emission depends on incoming solar radiation. However, excessive light may cause plants to invoke various protection mechanisms to release excessive energy as NPQ [42], which tends to weaken SIF-GPP correlations [40]. Also, too strong solar radiation may also result in lower \(R^{2}\) between SIF and \(T\)[32]. So, it is necessary to investigate how changes in radiation regime affect the SIF-IWUE relationship. Based on the relationship of PAR-GPP (Figure S1), we used 1300 umol photons/m\({}^{2}\)/s as the threshold to separate all hourly data into two groups: (1) PAR saturation group and (2) no PAR saturation group. Our results show that the PAR saturation has a negative effect on the SIF-IWUE correlations but with limited impacts. The highest \(R^{2}\) provided by SIF\({}_{761}\) is 0.50 under no PAR saturation, whereas it only has a small decrease to 0.41 under the PAR saturation (Figure 4). Further, the SIF band combinations seem to provide a strong resistance to radiation stress. Under the no saturation condition, the combination of SIF\({}_{687}\), SIF\({}_{720}\), and SIF\({}_{761}\) can explain 54% and 66% variance in IWUE for the LR and GPR models, respectively (Figure 4). When PAR reaches saturation, its performance only has a minimal decline with 48% and 63%, respectively (Figure 4). Figure 3: The effect of vapor pressure deficit (VPD, kPa) on the coefficients of determination (\(R^{2}\)) between inherent water use efficiency (IWUE) and the selected single SIF bands and their combinations by using (**a**) linear regression analysis and (**b**) Gaussian processes regression, respectively. The blue, yellow, and red bars represent \(R^{2}\) for data with VPD \(\leq\) 0.5 kPa, 0.5 kPa \(<\) VPD \(\leq\) 1.0 kPa, and VPD \(>\) 1.0 kPa, respectively. All data have an hourly time resolution and belong to the period between 7 a.m. and 5 p.m. local time. Considering the fact that remotely-sensed datasets typically use cloud fractions to select high-quality data, we calculate the clearness index (\(K\)) [43] at the site level (Figure S2) and only use data with \(K>0.8\) to analyze the SIF-IWUE correlations (Table 3). Our results show that all the SIF-IWUE correlations only have moderate decreases. Under the clear sky condition, for example, SIF\({}_{761}\) has a small decrease in its \(R^{2}\) with IWUE of 0.05 and 0.06 for LR and GPR, respectively (Table 3). Again, the band combinations produce a more stable performance, especially when the nonlinear GPR models are used. Combining SIF emission at the three absorption lines can still determine 46% and 60% of variance in hourly IWUE (Table 3). \begin{table}
\begin{tabular}{c c c} \hline \hline
**SIF bands** & **LR** & ** GPR** \\ \hline SIF\({}_{687}\) & 0.04 (0.17) & 0.04 (0.17) \\ SIF\({}_{720}\) & 0.27 (0.48) & 0.30 (0.48) \\ SIF\({}_{761}\) & 0.39 (0.44) & 0.46 (0.52) \\ SIF\({}_{687}\), SIF\({}_{761}\) & 0.43 (0.49) & 0.54 (0.62) \\ SIF\({}_{687}\), SIF\({}_{720}\), SIF\({}_{761}\) & 0.46 (0.59) & 0.60 (0.65) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The correlation coefficient (\(R^{2}\)) between the SIF bands and inherent water use efficiency (IWUE) by using the linear regression analysis (LR) and Gaussian processes regression (GPR), respectively. All the datasets had an hourly time step and were measured between 7 a.m. and 5 p.m. local time with clearness index (K) higher than 0.8. The numbers in the parentheses are the \(R^{2}\) calculated from all the hourly data acquired between 7 a.m. and 5 p.m. local time. Figure 4: The effect of intensity of Photosynthetically Active Radiation (PAR) on the coefficients of determination (\(R^{2}\)) between inherent water use efficiency (IWUE) and the selected single SIF bands and their combinations by using (**a**) linear regression analysis and (**b**) Gaussian processes regression, respectively. The blue/red bars represent \(R^{2}\) from data with PAR less/more than 1300 μmol photons/m\({}^{2}\)/s.