## 5 Conclusions  
By using continuous records of SIF measurements, carbon and latent heat fluxes, this study shows that SIF emission can serve as a good predictor of IWUE and uWUE, two WUE formulations with consideration of VPD effect, in a temperate deciduous forest. However, SIF emission has weaker correlations with WUE and WUE\({}_{\rm i}\). The predictive capability of SIF emission is dependent on a variety of environmental, biogeophysical, and biogeochemical factors including solar radiation, LAI,observation time, and air temperature. In particular, we find that (1) the models using SIF band combinations provide more a powerful capacity to estimate IWUE than the models using single SIF bands, (2) a temporal aggregation to the daily scale can further enhance the SIF-IWUE correlations, especially when SIF band combination and non-linear models are considered, (3) PAR saturation shows a limited negative effect on the SIF-IWUE correlations, but more experiments are highly needed, (4) too high LAIs largely reduce the SIF-IWUE correlations due to (re)absorption and scattering of SIF emission, (5) large nontranspiration flux due to soil and dew evaporation significantly reduces the SIF-IWUE correlations, and (6) it is desirable to use SIF emission measured in the afternoon for retrieving IWUE when dew evaporation is low.  
This study provides a new SIF application in understanding the nexus between carbon uptake and transpiration loss in terrestrial ecosystems. In comparison to physical models that are inputs demanding and complex, a SIF-based approach offers a simple but powerful way to investigate carbon uptake and water loss in plants at a large spatial scale.  
The following are available online at [[http://www.mdpi.com/2072-4292/10/5/796/s1](http://www.mdpi.com/2072-4292/10/5/796/s1)]([http://www.mdpi.com/2072-4292/10/5/796/s1](http://www.mdpi.com/2072-4292/10/5/796/s1)). **Figure S1**: The responses of hourly daytime (a) gross primary production (GPP, umol CO\({}_{2}\) m/s) and (b) transpiration (\(T\), mm/hour) to incident photosynthetically active radiation (PAR, umol photons/m\({}^{2}\)/s) during the growing season in 2014. **Figure S2**: The hourly clearness index at the Harvard site in 2014. **Table S1**: The correlation coefficient (\(R^{2}\)) of the training and testing groups in predicting and daily WUEs by using the linear regression analysis (LR) and Gaussian processes regression (GPR), respectively. This section also describes the details in estimating SIF emission from irradiance and radiance measurements.  
[PERSON] and [PERSON] conceived and designed the study, and interpreted the results; [PERSON] carried out the analyses and wrote the paper; [PERSON], [PERSON] and [PERSON] contributed to the manuscript revision. [PERSON] and [PERSON] made important contributions to the field experiments.  
We would like to thank Harvard Forest for providing site and logistic support during our research. The water flux data were downloaded from the Harvard Forest data archive (PI: [PERSON]). This research was supported by U.S. Department of Energy Office of Biological and Environmental Research Grant DE-SC0006951, National Science Foundation Grants DBI 959333 and AGS-1005663, and the University of Chicago and the MBL Lillie Research Innovation Award to [PERSON]. This study was also supported by the open project grant (LBKF201701) of Key Laboratory of Land Surface Pattern and Simulation, Chinese Academy of Sciences.  
The authors declare no conflict of interest.