## 4 Discussion  
Overall, we find that SIF emission has the potential to predict the carbon-water exchange process through stomata. Among the four different WUE formulations, SIF emission shows a good performance in estimating IWUE and uWUE. The likely explanation is that the consideration of VPD in IWUE and uWUE largely remove the nonlinear effect of VPD on \(T\). In contrast, SIF emission shows weaker correlations with WUE and WUE\({}_{i}\), especially at an hourly time step. Because variations in the traditional WUE (ET/GPP) still contain impacts of VPD, which cannot be tracked by SIF, the correlations between WUE and SIF are typically low. Although WUE\({}_{i}\) is derived from the physical-based model, it involves numerous not-easily measured environmental variables, which makes it difficult to use at a large scale. Also, the simplification assumptions needed in inverting the P-M equation likely bring strong noises in its time series, which tends to undermine the performance of SIF emission in predicting WUE\({}_{i}\). When the daily daytime data are used, SIF emission demonstrates a more powerful predictive capability of all these four WUEs. The recent studies [32; 41] have shown that SIF emission has a better performance in estimating both GPP and \(T\) at a longer time step. More field- and model-based works are needed to analyze the reason for stronger SIF-IWUE correlations under a longer temporal resolution. Combining different SIF bands provides stronger correlations with IWUE than those when single SIF bands were used individually. SIF emission at different spectra contains information on the physiological status of plants. For example, most of red SIF emission comes from the photosystem II (PSII) [48]. SIF emission in the near-infrared region contains contributions from both PSI and PSII [49] and it was found to be closely correlated with GPP at both global [50; 51] and local scales [52]. Thus, SIF band combination should contain more complete information on plant physiological conditions. In this study, we only used the combination of SIF emission at the three absorption lines. Full exploitation of the complete SIF spectrum may provide further better performance of SIF emission in predicting WUEs [32; 39]. It is important to note that the performance of the full SIF spectrum depends on: (1) the accuracy of the sensor, and (2) the approach used to reconstruct full SIF emission. Our spectrometer is not the newest. Furthermore, the SCOPE model [39], which is currently used to build full SIF, may not be the best option. More efforts are highly needed in better extracting the potential of full SIF. The combinations of different SIF bands may bring more nonlinear behaviors. Also, our results show that IWUE-SIF correlations show more non-linear behaviors when plants are under stressful conditions. In both cases, nonlinear regression models such as GPR should be used. We find that a variety of physiological and environmental factors affect SIF-IWUE relationships. The interactions of these factors further complicate the link between SIF emission and IWUE. Among them, VPD is found to have less of an effect on the SIF-IWUE correlations (Figure 3). The stable SIF-IWUE correlations under different VPD values show that (1) incorporation of VPD into IWUE largely removes impacts of VPD on GPP and \(T\), and (2) VPD in 2014 showed no clear negative effect on SIF-GPP and SIF-\(T\) correlations. However, it is important to note that the precipitation at the study site in 2014 was higher than the multi-year average precipitation. The relatively wet condition in 2014 did not allow us to fully analyze variations in SIF-IWUE relationships under severe water stress. SIF-IWUE correlations may further deteriorate when more severe drought conditions occur. Thus, more field experiments are needed to evaluate SIF-IWUE relationships under stronger water stress. Our results show too high or too low LAI values that tend to deteriorate SIF-IWUE correlations.