## 3 Results
### Overall Performance of SIF Emission in Predicting Hourly and Daily WUEs
#### 3.2.2 Performance in Predicting Daily WUEs  
Longer time steps, such as daily, are more suitable in many applications. A recent model-based study [41] showed that SIF-GPP correlations were enhanced at both leaf and canopy scales when longer time steps were considered. Therefore, we also calculated SIF-WUEs' correlations at a daily time scale by using the LR and GPR models. Because the number of valid daily observations is much smaller, we used a cross-validation to test for possible overfit in the regressions. Specifically, all daily measurements (55) were randomly split into two groups: (a) a training group containing 60% of all daily measurements, used to develop the regression models, and (b) a testing group containing the other 40% that were used to test the performance of the predictions. We did not find an obvious difference in the \(R^{2}\) from the two groups (see the Supplementary Materials), which confirms no overfitting in building the regression models. The below results, describing the relationships between SIF and WUEs at a daily time step, were derived from all the daily measurements. Overall, our results show that all the SIF-WUEs' correlations are enhanced after aggregating from hourly to daily scale (Table 2). \(\text{SIF}_{687}\) is still the weakest predictor for all the four WUEs, and its best \(R^{2}\), 0.41, is achieved when it is used to predict daily IWUE (Table 2). It shows this negative effect due to the (re)absorption in red SIF emission, which is still strong at a daily time step. In contrast, \(\text{SIF}_{720}\) and \(\text{SIF}_{761}\) exhibit much higher correlations with the WUEs after the temporal aggregation, especially when the GPR models are used (Table 2). Again, \(\text{SIF}_{761}\) produces the strongest correlations with the WUEs among the three single SIF bands, as it captures 62% and 65% variance in daily IWUE for the LR and GPR, respectively (Table 2). \(\text{SIF}_{761}\) can also explain 44%, 47%, and 57% of the variance in daily WUE, \(\text{WUE}_{\text{i}}\), and uWUE, respectively (Table 2). Although \(\text{SIF}_{720}\) is not as strong a predictor as \(\text{SIF}_{761}\), it is still superior to \(\text{SIF}_{687}\). For example, \(\text{SIF}_{720}\) accounts for 53% and 62% of the variability in daily IWUE by using the LR and GPR models, respectively (Table 2). At a daily time step, the band combinations demonstrate further improvements in their correlations with the WUEs. The combination of \(\text{SIF}_{687}\) and \(\text{SIF}_{761}\) can explain more than 50% variance in all WUEs when the GPR models were used (Table 2), and can also explain more than 60% of the variance in IWUE and uWUE, respectively (Table 2). The combination using all the three single SIF bands provided modest improvements, as it can explain 70% and 63% of the variance in daily IWUE and uWUE with the GPR models (Table 2). Also, the combination of \(\text{SIF}_{687}\), \(\text{SIF}_{720}\), and \(\text{SIF}_{761}\) is a fairly good predictor of daily WUE and \(\text{WUE}_{\text{i}}\), which provides \(R^{2}\) of 0.58 and 0.65, respectively (Table 2). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**SIF bands**} & \multicolumn{2}{c}{**WUE**} & \multicolumn{2}{c}{**WUE\({}_{\text{i}}\)**} & \multicolumn{2}{c}{**IWUE**} & \multicolumn{2}{c}{**uWUE**} \\ \cline{2-10}  & **LR** & **GPR** & **LR** & **GPR** & **LR** & **GPR** & **LR** & **GPR** \\ \hline \(\text{SIF}_{687}\) & 0.00 & 0.00 & 0.08 & 0.00 & 0.21 & 0.41 & 0.11 & 0.37 \\ \(\text{SIF}_{720}\) & 0.17 & 0.38 & 0.30 & 0.34 & 0.53 & 0.62 & 0.43 & 0.47 \\ \(\text{SIF}_{761}\) & 0.17 & 0.44 & 0.37 & 0.47 & 0.62 & 0.65 & 0.49 & 0.57 \\ \(\text{SIF}_{687}\), \(\text{SIF}_{761}\) & 0.19 & 0.51 & 0.51 & 0.53 & 0.64 & 0.65 & 0.52 & 0.60 \\ \(\text{SIF}_{687}\), \(\text{SIF}_{720}\), \(\text{SIF}_{761}\) & 0.24 & 0.58 & 0.52 & 0.65 & 0.67 & 0.70 & 0.58 & 0.63 \\ \hline \hline \end{tabular}
\end{table}