## 3 Results
### Performance of the PRI-Based LUE Model and SIF-Based Linear Model for GPP Estimation  
The PRI-based LUE model and SIF-based linear model for GPP estimation were compared at different time scales. The summary statistics of both models are shown in Table 1. Significant relationships were found between \(\mathrm{LUE_{PRI}}\times\mathrm{APAR}\) and \(\mathrm{GPP_{EC}}\) at these three-time scales. The R\({}^{2}\) between \(\mathrm{LUE_{PRI}}\times\mathrm{APAR}\) and \(\mathrm{GPP_{EC}}\) at the \"daily mean\" scale and the \"30 min\" scale was lower than that at the \"day-by-day\" scale (R\({}^{2}\) = 0.71 \(\pm\) 0.22, \(p\) \(<\) 0.01). This indicated that \(\mathrm{LUE_{PRI}}\times\mathrm{APAR}\) tracked the diurnal variations of \(\mathrm{GPP_{EC}}\) better than the seasonal variations of \(\mathrm{GPP_{EC}}\). Compared to \(\mathrm{SIF_{can}}\), the \(\mathrm{LUE_{PRI}}\times\mathrm{APAR}\) was higher R\({}^{2}\) with \(\mathrm{GPP_{EC}}\) at the short-term time scale, especially at the \"day-by-day\" scale. However, the R\({}^{2}\) between \(\mathrm{SIF_{can}}\) and \(\mathrm{GPP_{EC}}\) at the \"daily mean\" scale (R\({}^{2}\) = 0.50, \(p\) \(<\) 0.001) was highest among the three time scales and higher than the R\({}^{2}\) between \(\mathrm{LUE_{PRI}}\times\mathrm{APAR}\) and \(\mathrm{GPP_{EC}}\) (R\({}^{2}\) = 0.44, \(p\) \(<\) 0.001) at the same time scale. Figure 4 showed the day-by-day variation of R\({}^{2}\) between \(\mathrm{LUE_{PRI}}\times\mathrm{APAR}\) and \(\mathrm{GPP_{EC}}\) (R\({}^{2}\)\({}_{\mathrm{PRI}}\)), and between \(\mathrm{SIF_{can}}\) and \(\mathrm{GPP_{EC}}\) (R\({}^{2}\)\({}_{\mathrm{SIF}}\)) and their relative frequency. There was some data loss (Figure 4) because of instrument failure. Significant correlations (\(p\) \(<\) 0.05) between \(\mathrm{LUE_{PRI}}\times\mathrm{APAR}\) and \(\mathrm{GPP_{EC}}\) occurred on all 51 available days with an R\({}^{2}\) ranging from 0.23-0.96. \(\mathrm{SIF_{can}}\) showed significant relationships with \(\mathrm{GPP_{EC}}\) on 81% of the 79 available days (R\({}^{2}\): 0.18-0.85). The highest frequency of \(\mathrm{R^{2}_{PRI}}\) was 0.8-0.9, much higher than that of \(\mathrm{R^{2}_{SIF}}\) (0.2-0.5). In summary, \(\mathrm{LUE_{PRI}}\times\mathrm{APAR}\) tracked the diurnal variations of \(\mathrm{GPP_{EC}}\) better than \(\mathrm{SIF_{can}}\) for individual days. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Explanatory Terms for GPP** & \multicolumn{3}{c}{\(\mathrm{LUE_{PRI}}\times\mathrm{APAR}\): \(\mathrm{GPP_{EC}}\) *} & \multicolumn{3}{c}{\(\mathrm{SIF_{can}}\): \(\mathrm{GPP_{EC}}\) **} \\ \cline{2-7}
**Regression Model** & \multicolumn{1}{c}{**R\({}^{2}\)**} & \(p\) & RMSE & \(\mathrm{R^{2}}\) & \(p\) & RMSE \\ \hline daily mean & 0.44 & \(<\)0.001 & 12.25 & 0.50 & \(<\)0.001 & 11.75 \\
30 min & 0.47 & \(<\)0.001 & 15.28 & 0.45 & \(<\)0.001 & 16.12 \\ day-by-day *** & 0.71 \(\pm\) 0.22 & 0.00 \(\pm\) 0.01 & 4.59 \(\pm\) 3.08 & 0.38 \(\pm\) 0.23 & 0.08 \(\pm\) 0.19 & 8.90 \(\pm\) 5.51 \\ \hline \end{tabular}  
* \(\mathrm{LUE_{PRI}}\) = a \(\times\)\(\mathrm{PRI_{can}}\) + b, where a and b were fitted linearly using \(\mathrm{LUE_{BC}}\) and \(\mathrm{PRI_{can}}\) over the half-hourly values from 6:00 to 18:00 each day during the entire growing season in 2018. \(\mathrm{GPP_{EC}}\) represented the EC measured GPP. ** SI\(\mathrm{F_{can}}\) represented the canopy SIF. *** The results of “day-by-day” were the averages \(\pm\) standard deviations of the statistical variables (coefficient of determination (R\({}^{2}\)), significant level (\(p\)), and root mean square error (RMSE)).  
\end{table} 
Table 1: Summary statistics of the photochemical reflectance index (PRI)-based light use efficiency (LUE) model and solar-induced fluorescence (SIF)-based linear model for gross primary production (GPP) estimation at different time scales.