## 3 Results
### Mechanism of CO\({}_{2}\) Affecting Modeling of GPP  
Our results have shown that considering atmospheric CO\({}_{2}\) concentrations can improve the accuracy of the GPP estimates. However, it is uncertain whether this improvement is statistically  
Figure 7: Gridded GPP estimated by means of the SIF-CO\({}_{2}\)-GPP model for four seasons, (**a**)–(**d**). Gridded GPP estimated by means of SIF-GPP model for four seasons, (**e**)–(**h**). The value underneath the date represents the mean modeled GPP data in selected regions and the unit of GPP is g C m\({}^{-2}\)d\({}^{-1}\).  
artificial or driven by real ecological processes. Therefore, we used the SCOPE model to explore the possible mechanisms behind the statistical results. SIF of two bands were included in this experiment. Figure 8 shows relationships between SIF and simulated GPP. To highlight the effect of the atmospheric CO\({}_{2}\) concentration, each dot is colored according to its atmospheric CO\({}_{2}\) concentration. Two main conclusions can be drawn from Figure 8. Firstly, there is a non-linear relationship between SIF and simulated GPP within half an hour. Current researchers usually applied an adjustment factor to convert instantaneous SIF to daily SIF, then built linear relationships with daily GPP. However, some researches have shown that the relationship between SIF and GPP could be non-linear. At present, there is no uniform conclusion as to whether SIF and GPP are linear or non-linear. Therefore, if we represent the nonlinear relationship in terms of linear relationship, it tends to lead to overestimation and underestimation of the GPP. The same phenomenon is shown in Figure 8. From Figure 7, we can conclude that CO\({}_{2}\) corrects for the SIF-GPP linear model overestimating GPP in summer and fall and underestimating GPP in spring and winter. Therefore, adding CO\({}_{2}\) to the SIF-GPP linear model may result in an equilibrium between the linear and non-linear relationship of SIF and GPP. Second, linear regression models are not sufficient to accurately link SIF and GPP when atmospheric CO\({}_{2}\) concentrations change. It is clear that the simulated GPP at high CO\({}_{2}\) concentrations is higher than that at low CO\({}_{2}\) concentrations, and the higher the SIF intensity, the greater the difference in the simulated GPP at different CO\({}_{2}\) concentrations, and the results of the SCOPE simulation are consistent with the previous statistical results. These results re-emphasize that the effects of atmospheric CO\({}_{2}\) concentrations should be considered when modelling GPP using SIF as a key driver. A plausible explanation for this result is that atmospheric CO\({}_{2}\) concentration is a key constraint on photosynthetic efficiency.  
Photosynthesis consists of light reactions and dark reactions. Light reactions are chlorophyll's conversion of light energy into electrical energy and then into active chemical energy, which is finally stored in ATP (ATP adenosine triphosphate). The essence of the dark reaction is the assimilation of  
Figure 8: Sensitivity analysis of the effects of different levels of atmospheric CO\({}_{2}\) concentrations on SIF-GPP relationship. (**a**) SIF757 versus GPP; (**b**) SIF771 versus GPP.  
CO\({}_{2}\) to CH\({}_{2}\)O under the action of various enzymes in the chloroplast stroma. Therefore, CO\({}_{2}\) is the main raw material for photosynthesis and an important factor affecting the intensity of photosynthetic. GPP is the amount of organic carbon fixed by green plants per unit area through photosynthesis per unit time. CO\({}_{2}\) assimilation rate refers to the amount of dry matter added to plants per unit time and per unit assimilated area. If the CO\({}_{2}\) assimilation rate increased, then the amount of fixed organic carbon per unit time would increase simultaneously.