## 2 Materials and Methods
### Analysis  
We first examined the effects of VZA at Glint mode on the SIF values and their relationship with tower GPP. We further compared the consistency of Glint and Nadir SIF observations with the tower SIF, which was retrieved from the spectrum measurements during the growing period of summer maize on a daily timescale. Then, we optimized the parameters of the SIF model, the SL-LUE model, and the TL-LUE model with different temporal aggregation levels to examine the stability of their key parameters. SL-LUE was developed based on the concept of radiation transformation efficiency [59] and can be defined as:  
\[GPP=\varepsilon_{\text{max}}\times APAR\times f(VPD)\times g(T_{\text{a}}), \tag{5}\]  
where \(\varepsilon_{\text{max}}\) means the maximum LUE (gC MJ\({}^{-1}\)), depending on different plant functional types, and \(\varepsilon_{\text{max}}\times APAR\) is the potential GPP. \(g(T_{a})\) and \(f(VPD)\) are efficiencies and range from 0 to 1. They represent the adjusting scalars of the minimum air temperature (\(T_{\text{a}}\)) and vapor pressure deficit (\(VPD\)), which are used to constrain \(\varepsilon_{\text{max}}\) to the real LUE value. They can be expressed as:  
\[g(T_{\text{a}})=\left\{ \begin{array}{cc}0&T_{\text{a}}\leq T_{\text{min}}\\ \frac{T_{\text{a}}-T_{\text{min}}}{T_{\text{max}}-T_{\text{min}}}&T_{\text{min }}<T_{\text{a}}<T_{\text{max}}\\ 1&T_{\text{a}}\geq T_{\text{max}}\end{array} \right., \tag{6}\]  
\[f(VPD)=\left\{ \begin{array}{cc}0&VPD\geq VPD_{\text{max}}\\ \frac{VPD_{\text{max}}-VPD}{VPD_{\text{max}}-VPD_{\text{min}}}&VPD_{\text{min }}<VPD<VPD_{\text{max}}\\ 1&VPD\leq VPD_{\text{min}}\end{array} \right., \tag{7}\]  
where \(VPD_{\text{max}}\), \(VPD_{\text{min}}\), \(T_{\text{max}}\), and \(T_{\text{min}}\) are biome-dependent parameters [11; 27]. SIF can be likewise calculated as:  
\[SIF=SIF_{\text{yield}}\times APAR\times f_{\text{esc}}, \tag{8}\]where \(SIF_{\text{yield}}\) is the LUE for SIF, and \(f_{\text{esc}}\) denotes the proportion of SIF photons that escapes from the canopy in the viewing angle of the satellite sensor [19]. By combining Equations (5) and (8), a linear GPP-SIF model can be theoretically expressed as:  
\[GPP=\varepsilon/\big{(}SIF_{\text{yield}}\times f_{\text{esc}}\big{)}\times SIF \approx\varepsilon/SIF_{\text{yield}}\times SIF, \tag{9}\]  
where \(f_{\text{esc}}\approx 1\) can be set when far-red SIF data are used from cropland and grassland [54] because these land types have a lower leaf absorptance in the far-red waveband, a higher LAI, and a simpler canopy structure compared with other ecosystems [19; 60]. The TL-LUE model divides GPP into two components, sunlit and shaded leaves, by combining the algorithm of the SL-LUE model and the new generation of the dynamic land model (DLM) [32]:  
\[GPP=(\varepsilon_{\text{msu}}\times APAR_{\text{su}}+\varepsilon_{\text{msh}} \times APAR_{\text{sh}})\times f(VPD)\times g(T_{\text{a}}), \tag{10}\]  
where \(\varepsilon_{\text{msu}}\) and \(\varepsilon_{\text{msh}}\) represent the maximum LUE of sunlit and shaded leaves, respectively. \(APAR_{\text{su}}\) and \(APAR_{\text{sh}}\) denote the \(PAR\) absorbed by sunlit and shaded leaves. They are calculated as:  
\[APAR_{\text{sh}}=(1-\alpha)\times[(PAR_{\text{diff}}-PAR_{\text{diff,u}})/LAI+C] \times LAI_{\text{sh}}, \tag{11}\]  
\[APAR_{\text{su}}=(1-\alpha)\times(PAR_{\text{dir}}\times\cos(\beta)/\cos( \theta)+(PAR_{\text{diff}}-PAR_{\text{diff,u}})/LAI+C)\times LAI_{\text{su}}, \tag{12}\]  
where \(\alpha\) is the canopy albedo related to a given vegetation type and was set to 0.23 for cropland in this study [11]; \(PAR_{\text{diff}}\) and \(PAR_{\text{dir}}\) are the diffuse and direct components of incoming \(PAR\), respectively.