## 5 Conclusions  
The SIF product becomes the emerging proxy to estimate GPP with a higher accuracy globally along with the launch of OCO-2. Moreover, several previous studies in the field of botany had mentioned that the atmospheric CO\({}_{2}\) concentration is a critical factor in determining the photosynthesis efficiency. In this study, we proposed a SIF-CO\({}_{2}\)-GPP model to take the effect of the atmospheric CO\({}_{2}\) concentration on photosynthesis into considerations of estimating GPP, aiming at better modeling of GPP by means of satellite products. This study confirms that the effect of atmospheric CO\({}_{2}\) concentrations on the photosynthesis efficiency can be also observed at a larger spatial scale, which is a promising feature to estimate GPP using remotely sensed products. Our results showed that the SIF-CO\({}_{2}\)-GPP linear model (R\({}^{2}\) = 0.63 - 0.90, \(p\) < 0.001) is more suitable to estimate GPP comparing with the linear SIF-GPP model (R\({}^{2}\) = 0.41 - 0.87, \(p\) < 0.001). In addition, the concentration of CO\({}_{2}\) in the surface atmosphere is one of the key factors affecting GPP because it is the raw material for photosynthesis. We use the SCOPE model to prove that the atmospheric CO\({}_{2}\) concentration is a factor affecting the modeling of GPP. A reasonable mechanism could be that the increment of CO\({}_{2}\) concentration at leave's surface would induce intercellular CO\({}_{2}\) concentration and the CO\({}_{2}\) assimilation rate raise. That eventually would cause a rise of GPP and vice versa. Moreover, there is a strongly linear relationship between XCO\({}_{2}\) of OCO-2 and surface CO\({}_{2}\) mixing ratio of EC Flux towers (R = 0.54 - 0.87, \(p\) < 0.001), laying the foundation for utilizing the SIF-CO\({}_{2}\)-GPP model to monitor global distributions of GPP using OCO-2 or other similar satellites. The availability of intensive OCO-2 products surrounding the US-PFa site allows us to generate grid SIF and XCO\({}_{2}\) and then to estimate gridded GPP at the landscape scale for different seasons using SIF-CO\({}_{2}\)-GPP model and SIF-GPP model. Taking results of the SIF-CO\({}_{2}\)-GPP model as a benchmark, the traditional SIF-GPP model underestimates GPP in spring and winter and overestimates GPP in summer and autumn. Besides, we also confirmed that daily SIF is more suitable for estimating GPP than instantaneous SIF. In addition, SIF757 is also more strongly correlated with GPP than SIF771 for most forests. In future works, investigations on relationships among SIF, XCO\({}_{2}\) and GPP should be deepened for more vegetation types and more latitude zones after obtaining more in situ measurements of EC flux towers. Furthermore, along with forthcoming products from GOSAT-3, OCO-3 and FLEX, we believe that the SIF-CO\({}_{2}\)-GPP model would help obtain accurate GPP estimates with high spatial resolution and large coverage, providing better data and new prospects for climate change and carbon cycle studies.  
Figure 9: The spatial coverage of the OCO-2 satellite in October 2014; the color of the footprint indicates the magnitude of the chlorophyll fluorescence value, yellow indicates a high value and blue indicates a low value.  
**Author Contributions:** Conceptualization, R.Q. and G.H.; methodology, R.Q. and G.H.; software, R.Q.; validation, R.Q.; writing--original draft preparation, R.Q. and G.H.; writing--review and editing, R.Q., G.H., X.M., H.X., T.S. and M.Z. Investigation, Z.S. and H.X.; Resources, Z.S. and M.Z. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was supported by the National Natural Science Foundation of China (Grant No. 41971283, 41801261, 41827801, 41801282), the National Key Research and Development Program of China (2017 YFC0212600), Postdoctoral Science Foundation of China (2017T100580).  
**Acknowledgments:** We thank the OCO-2 and Ameriflux teams for making the SIF and GPP data.  
**Conflicts of Interest:** The authors declare no conflict of interest.