## 3 Results
### Mapping GPP using OCO-2 SIF and XCO\({}_{2}\) Products  
Finally, we have mapped the gridded GPP based on the traditional SIF-GPP model and SIF-CO\({}_{2}\)-GPP model to explore new features of the proposed model. In this experiment, we used SIF757 and XCO\({}_{2}\) products of OCO-2 spanning from 2015 to 2016, which are around 20 km of US-PFa, to generate GPPM and GPPS products with a spatial resolution of 1 km (14 April 2015, 1 June 2015, 14 September 2016, 1 November 2016). Though the data amount of SIF and XCO\({}_{2}\) products around US-PFa is the largest in all 12 sites, there are still considerable missing data, especially for 1 November 2016, which results in blank parts in Figure 7.  
Figure 7 shows gridded GPPS and GPPM on 4 representative days of different seasons around US-PFa EC flux tower. Overall, GPPS and GPPM products exhibit similar seasonality, i.e., high GPP in summer and fall and low GPP in spring and winter. In the spring, the vegetation begins to grow along with the rising temperature. Hence, GPP in spring is higher than GPP in winter. The mean GPP of summer is the highest in all seasons because the driven parameter of GPP-estimating model, SIF, reaches peak in summer along with the strong effect of photosynthesis. The date we chose for autumn belongs to early autumn in this study. The vegetation has not completely withered, resulting in a  
Figure 6: Linear relationships between XCO\({}_{2}\) of OCO-2 and measured surface CO\({}_{2}\) mixing ratio of EC flux towers. Dots indicate CO\({}_{2}\) of EC towers and XCO\({}_{2}\) fit points at the flux towers, and black lines indicate the fit line.  
higher GDP in the fall simulation than in the spring. In winter, the photosynthesis of vegetation becomes weak because of the low temperature. The mean annual temperature of US-PFa is 4.33 \({}^{\circ}\)C in winter. Hence, the mean GPP drops to the lowest. We averaged all the GPP grids data estimated by SIF-CO\({}_{2}\)-GPP model and SIF-GPP model within 20 \(\times\) 20 km for each day. Then, we compared the modeled GPP and measured GPP. The measured GPP of flux towers are 2.09, 7.03, 4.15 and 1.59 for four representative days (Apr 14, 2015, Jun 1, 2015, Sep 14, 2016, and Nov 1, 2016). The unit is g Cm\({}^{-2}\)d\({}^{-1}\). The mean GPP\({}_{\rm M}\) estimated by SIF-CO\({}_{2}\)-GPP model are 2.09, 6.90, 4.33 and 1.61. The mean GPP\({}_{\rm S}\) estimated by SIF-GPP model are 1.84, 7.93, 4.45 and 1.43. Therefore, it is concluded that the SIF-CO\({}_{2}\)-GPP model is more suitable for estimating GPP and yields a higher precision than the SIF-GPP model.  
On the whole, there are evident differences between GPP\({}_{\rm S}\) and GPP\({}_{\rm M}\) in spring, summer, autumn, and winter. The SIF-CO\({}_{2}\)-GPP model leans to overestimate GPP in spring and winter, but underestimate GPP in summer and autumn, comparing with the SIF-GPP model. The value of GPP\({}_{\rm M}\) is closer to the measured GPP value of the flux tower, which indicates to some extent that the SIF-CO2-GPP model is able to estimate GPP with higher accuracy. Therefore, we can conclude that the effect of CO\({}_{2}\) is not simply shrinking or amplifying estimated GPP. The introduction of CO\({}_{2}\) helps reduce estimated GPP in some conditions but helps increase estimated GPP in other conditions. This is why we argue that negative coefficients of CO\({}_{2}\), as shown in Table 3, should not be attributed to a high CO\({}_{2}\) concentration causing a decrease in GPP or vice versa. We should notice that the level of CO\({}_{2}\) concentration is regulated by the intensity of the photosynthesis. Consequently, it is impossible to keep the CO\({}_{2}\) concentration at a constant level under natural conditions when the intensity of SIF is varying. To explore and explain the correction effect of the CO\({}_{2}\) concentration on GPP, we carried out extra simulation experiments using the SCOPE model in the next section.