## Discussions  
### Reasons for Differences between SIF-GPP and SIF-CO\({}_{2}\)-GPP Model  
Previous studies had shown that the atmospheric CO\({}_{2}\) concentration is a non-negligible driving factor of GPP. The influence of the atmospheric CO\({}_{2}\) concentration on ecosystems could even exceed the temperature and precipitation [41; 42]. Under the environment of the surging atmospheric CO\({}_{2}\) concentration, the photosynthesis of vegetation would be enhanced, which is the so-called CO\({}_{2}\) fertilization effect [34]. When the CO\({}_{2}\) concentration rises, the CO\({}_{2}\) concentration between plant cells increases, which is the main factor affecting the photosynthetic rate of vegetation [43]. Therefore, the increase in the atmospheric CO\({}_{2}\) concentration would effectively promote the improvement of ecosystem productivity. In the meantime, it is also illustrated that when the atmospheric CO\({}_{2}\) concentration is elevated to a very high level, the photosynthesis of vegetation will be in turn reduced to the original efficiency [44; 45; 46]. Therefore, we believe it is necessary to consider the effects of atmospheric CO\({}_{2}\) concentrations when trying to estimate GPP using SIF products as key driven factor. There is a significant seasonal change in CO\({}_{2}\) in the forest, peaking before the spring and dropping to troughs at the end of the summer [35]. Figure 7a,e shows that GPP\({}_{\text{M}}\) is higher than GPPs in the spring, and we calculated the monthly average CO\({}_{2}\) concentration for four selected months using in situ CO\({}_{2}\) measurements from the US-PFa flux tower. The monthly surface average CO\({}_{2}\) concentration of EC tower in April is 407.84 ppm, which is the second higher, second only to that in winter. Spring is often accompanied by a surge in CO\({}_{2}\) concentration to promote the germination of vegetation. We speculate that SIF-GPP model does not take the atmospheric CO\({}_{2}\) concentration into account and thus ignore the CO\({}_{2}\) fertilization effect. That could explain why GPP\({}_{\text{M}}\) is higher than GPPs at this stage. Actually, the fact that the increasing CO\({}_{2}\) concentration in a short term promotes photosynthesis of vegetation has been reported widely [30; 47]. It is thus implied that the vegetation carbon sequestration capacity could be underestimated in spring if GPP was estimated using SIF data alone. Figure 7b,f shows that GPP\({}_{\text{M}}\) is lower than GPPs in summer. The monthly surface concentration is 402.25 ppm for June. The vegetation is lush, and daytime is long in summer. Strong photosynthesis in summer reduces CO\({}_{2}\) concentration in the canopy to lower than that in the free atmosphere [35]. Relatively lower CO\({}_{2}\) concentration inhibits the effect of vegetation photosynthesis [48]. That could explain why GPP\({}_{\text{M}}\) is lower than GPP\({}_{\text{S}}\) in summer. Figure 7c,g shows that GPP\({}_{\text{M}}\) is lower than GPP\({}_{\text{S}}\) in autumn. The monthly surface concentration is 401.52 ppm for September. The CO\({}_{2}\) concentration in the early autumn is lower than that in summer. Low concentrations of CO\({}_{2}\) and gradual deciduous vegetation reduce the photosynthetic rate of vegetation, limiting the fertilization effect of CO\({}_{2}\). Therefore, the value of GPP\({}_{\text{M}}\) is lower compared with GPP\({}_{\text{S}}\). The value of GPP\({}_{\text{M}}\) is closer to the measured GPP of the EC Flux Towers, which supports the above discussion to some extent. Figure 7d,h shows that the mean GPP\({}_{\text{M}}\) is higher than the mean GPP\({}_{\text{S}}\) in winter. In temperate forests, GPP should drop to an extremely low level in winter. The monthly surface CO\({}_{2}\) concentration in November is 411.73 ppm. CO\({}_{2}\) concentration increases rapidly during the winter. A surge in CO\({}_{2}\) concentration promotes photosynthesis of vegetation [49]. That could partly explain why SIF-CO\({}_{2}\)-GPP model overestimate GPP comparing with the SIF-GPP model.