## 3 Results
### Relations between GPP and SIF and Its Application to Calculate GPP  
The strong relationships (most linear) between GPP and satellite SIF are found in various forests and can be used to estimate GPP [91; 92; 93; 94; 95; 96]. For example, the square of the correlation coefficient (R\({}^{2}\)) is in the range of 0.62-0.92 in evergreen forests [91]. The relationships between GPP and SIF were studied using the calculated monthly GPP (GPP\({}_{\text{call}}\), GPP\({}_{\text{cal2}}\), and GPP\({}_{\text{cal3}}\), representing relatively clean, realistic, and polluted atmospheric conditions, respectively) and monthly SIF at this subtropical coniferous forest. Firstly, strong linear correlations were found (Figure 11). Stronger correlations were obtained between GPP\({}_{\text{cal2}}\), GPP\({}_{\text{cal3}}\), and SIF (R\({}^{2}\) = 0.912, 0.900) than between GPP\({}_{\text{call}}\) and SIF (R\({}^{2}\) = 0.599), indicating that better correlations existed between GPP and SIF for realistic and polluted atmospheric conditions, revealing that (1) the representative atmosphere in this subtropical coniferous forest was the atmospheric conditions at S/Q \(\geq\) 0.5, and the atmosphere had very high GLP loads (more aerosols, clouds, misty, etc.). For example, the hourly average of S/Q was 0.85 from May 2013 to December 2016 [40]; (2) the estimated GPP and satellite SIF have better temporal and spatial consistency under realistic and polluted atmospheric conditions. In addition, the linear correlation between the observed monthly GPP and monthly SIF was 0.8460, which was lower than that between GPP\({}_{\text{cal2}}\), GPP\({}_{\text{cal3}}\), and SIF, indicating that the calculated GPP (GPP\({}_{\text{cal2}}\), GPP\({}_{\text{cal3}}\)) using EMGPP can provide more reasonable estimates of GPP, as the SIF was derived from another independent data source, and some advantages to solve unavoidable shortages in GPP measurements (e.g., in 2016) [40]. Secondly, larger correlations were found for non-linear correlations between calculated monthly GPP and monthly SIF (Figure 12). R\({}^{2}\) was 0.618, 0.915, and 0.914 between GPP\({}_{\text{cal1}}\)  
Figure 10: Annual averages of observed air temperature (T) and water vapor pressure (E), and hourly sums of observed PAR from 2003–2017. \(\mathrm{GPP_{cal2}}\), \(\mathrm{GPP_{cal3}}\), and SIF. Similarly, higher non-linear correlations were also obtained between \(\mathrm{GPP_{cal2}}\), \(\mathrm{GPP_{cal3}}\), and SIF than those between \(\mathrm{GPP_{cal1}}\) and SIF. The \(\mathrm{R^{2}}\) values between the observed monthly GPP and monthly SIF were 0.895 for the non-linear relationship and 0.846 for the linear relationship. These values were smaller than the corresponding \(\mathrm{R^{2}}\) between \(\mathrm{GPP_{cal2}}\), \(\mathrm{GPP_{cal3}}\), and SIF. This indicates that the non-linear GPP/SIF can better describe the inherent interactions associated with the processes of GPP and SIF than the linear \(\mathrm{GPP/SIF}\). Using Equations (4) and (5) determined by linear and non-linear fitting of the monthly estimated GPP (\(\mathrm{GPP_{cal3}}\), \(\mathrm{L}\) and \(\mathrm{GPP_{cal3}}\), \(\mathrm{n}\)) and the monthly SIF, the monthly sums of GPP were calculated (Figure 13). Generally, the GPP estimates were in reasonable agreement with those calculated using EMGPP. The ratio of \(\mathrm{GPP_{cal3}}\)/SIF was 1.29 (range from 0.52-10.16), and \(\mathrm{GPP_{cal3}}\)/SIF was 1.07 (\(-\)1.97-7.61). The estimated GPP using \(\mathrm{GPP/SIF}\) and EMGPP methods can better reproduce the seasonal variations in GPP. Their GPP simulations with the larger ratios appeared in winter seasons (December and January), and this was mainly caused by low GPP. \[\mathrm{GPP}=739.21\times\mathrm{SIF}+40.585\mathrm{\ (R^{2}=0.903)} \tag{4}\]  
\[\mathrm{GPP}=87.439\times\mathrm{In(SIF)}+354.09\ \mathrm{\ (R^{2}=0.914)} \tag{5}\]  
where GPP and SIF are the monthly sums of GPP and monthly mean SIF, respectively.