## 3 Results
### Relations between GPP and SIF and Its Application to Calculate GPP
Furthermore, the annual sums of GPP were also obtained, and both simulation performances were significantly improved. The relative errors were 5.20% (0-15.33%) and 4.88% (0.15-13.23%) when using linear and non-linear Equations (1) and (2), respectively. Therefore, both GPP/SIF methods captured the annual sums of GPP and can be used as an additional tool, and the non-linear GPP/SIF method showed a slightly better performance than the linear method (for monthly and annual GPP). It was due to \(\mathrm{GPP_{cal3}}\)/SIF or  
Figure 11: Relationships between the estimated monthly sums of GPP (\(\mathrm{GPP_{cal1}}\), \(\mathrm{GPP_{cal2}}\), \(\mathrm{GPP_{cal3}}\), **left**, **middle**, and **right**) and monthly mean solar-induced chlorophyll fluorescence (SIF) from 2003–2017. The lines show linear fits to the data for GPP and SIF. Figure 12: Relationships between the estimated monthly sums of GPP (\(\mathrm{GPP_{cal1}}\), \(\mathrm{GPP_{cal2}}\), \(\mathrm{GPP_{cal3}}\), **left**, **middle**, and **right**) and monthly mean solar-induced chlorophyll fluorescence (SIF) from 2003–2017. The lines show non-linear fits to the data for GPP and SIF. GPP\({}_{\text{cal31}}\) providing a more detailed description of the direct and diffuse PAR roles related to canopy structure, while the EMGPP expressed the multiple interactions between PAR and absorbing and scattering GLPs, and the reflections between canopy, land, and the atmosphere from sunrise to sunset [40]. However, most of the SIF obtained by popular methods were limited to these important factors that were not well-described, as many factors affect the accurate SIF quantification contributed by the whole canopy, e.g., observation angle, light absorption, multiple light scattering, and canopy structure [91; 95; 96; 97; 98; 99]. It should also be noted that the non-linear relationship better revealed the inherent connections between the low GPP and low SIF, corresponding to the winter season and low solar zenith angle during the day. Under these specific conditions, the diffuse radiation and high atmospheric GLPs play significant roles in GPP, which can be seen from the sensitivity tests using EMGPP and larger GPP changes with the change in S/Q (representing atmospheric GLPs) at high S/Q levels compared to that at low S/Q [40]. The hourly processes of GPP, light absorption, and scattering (i.e., the GPP, photochemical, and scattering terms) in the atmosphere, as well as the canopy, are described in empirical models of GPP, Re, and NEP, especially using the optical air mass to describe the optical length and its hourly changes from sunrise to sunset. All of these calculations describe the light distributions of absorption and scattering under all sky conditions [40; 41]. The above non-linear relationship was mainly caused by PAR transferring in relative curve lines in the realistic atmosphere, especially around the early morning and late afternoon. The long-term variations of the annual sums of GPP and annual mean SIF from 2003-2017 were investigated. They shared a similar increase trend of 2.00%, 1.97%, and 1.04% per year for the calculated GPP\({}_{\text{cal31}}\), GPP\({}_{\text{cal3}}\), n, and GPP\({}_{\text{cal3}}\), respectively, and 0.93% for GPP\({}_{\text{obs}}\). The increase in GPP was mainly caused by the increase in water vapor (0.87% per year), which was consistent with the sensitivity analyses using EMGPP. GPP increases/decreases with the decrease/increase in PAR and GPP increases/decreases with the increase/decrease in water vapor [40]. The annual mean PAR and air temperature were decreased by 0.30% and 0.02% per year from 2003-2017, respectively. It is reported that global solar radiation decreased at JiAn city (\(\sim\)20 km away from the Qianyanzhou station) from 2003-2015 [100].