## 2 Materials and Methods
### Statistical Analysis of the SIF\({}_{760}\)-GPP Relationship  
To avoid the impact of low solar illumination, measurements that were collected at a solar zenith angle (SZA) \(>80^{\circ}\) were excluded from the analysis. Raw SIF data that were negative or had values higher than 2 mW/m\({}^{2}\)/nm/sr were also not used in the subsequent data processing and analysis. In addition, outliers (measurements outside the range \(\mu\pm 3\sigma\)) were also excluded from the diurnal relationship analysis (\(\mu\) and \(\sigma\) are the mean and standard deviation, respectively). Some studies have reported that the relationship between the canopy SIF and GPP exhibits a non-linear tendency and depends on the environmental variables [39], especially the light conditions. In this study, we evaluated the performance of canopy estimates based on the linear and non-linear regression model based on \(\mathit{SIF}_{760}\) and explored the effects of the CI on the linear and non-linear relationship between \(\mathit{SIF}_{760}\) and GPP. The linear and hyperbolic regression models characterizing the relationships between GPP and \(\mathit{SIF}_{760}\) are [61]:  
\[\mathit{GPP}_{L}=f_{L}(\mathit{SIF})=a\times\mathit{SIF}_{760}, \tag{8}\]  
Figure 2: A sample of the irradiance, radiance, and apparent reflectance measured by the automatic observation system at about 13:30 on June 15, 2017 at the DaMan (DM) site. The four gray shaded regions indicate the H\(\alpha\) absorption centered around 656 nm, the O\({}_{2}\)-B absorption at around 688 nm, the water vapor absorption band at around 720 nm, and the O\({}_{2}\)-A absorption region around 760 nm. The O\({}_{2}\)-A absorption band, which more clearly strengthened the weak reflected signal, was used to extract the canopy solar-induced chlorophyll fluorescence (SIF) of maize.  
\[GPP_{NL}=f_{NL}(SIF)=a\times\frac{SIF_{760}}{SIF_{760}+b}, \tag{9}\]  
where \(GPP_{L}\) is the GPP predicted by the linear model; \(GPP_{NL}\) is the GPP predicted by the non-linear model; \(a\) and \(b\) are the fitting parameters [38]; and \(f_{L}\) and \(f_{NL}\) represent the linear regression model and the non-linear regression model, respectively.  
Previous studies have reported that the weather conditions can influence GPP estimates made using the light-use efficiency model [62; 63]. As CI influences the relationship between SIF and GPP, we added CI into the SIF-based GPP estimation models (both linear and non-linear), which are expressed as  
\[\mathrm{GPP_{L-CI}}=f_{L}(\mathrm{SIF})\times g_{L}(\mathrm{CI}), \tag{10}\]  
\[\mathrm{GPP_{NL-CI}}=f_{NL}(\mathrm{SIF})\times g_{NL}(\mathrm{CI}), \tag{11}\]  
where \(\mathrm{GPP_{L-CI}}\) is the GPP predicted by the linear model considering the effects of CI, \(\mathrm{GPP_{NL-CI}}\) is the GPP predicted by the non-linear model considering the effects of CI, \(g_{L}(\mathrm{CI})\) describes the relationship between GPP/GPP\({}_{\mathrm{L}}\) and CI for the linear SIF\({}_{760}\)-based GPP model, and \(g_{NL}(\mathrm{CI})\) represents the relationship between GPP/GPP\({}_{\mathrm{NL}}\) and CI for the non-linear SIF\({}_{760}\)-based GPP model. Therefore, \(g_{L}(\mathrm{CI})\) or \(g_{NL}(\mathrm{CI})\) can be fitted using the ratio between the measured GPP (true values of GPP) and estimated GPP by \(f_{L}(\mathrm{SIF})\) or \(f_{NL}(\mathrm{SIF})\).