## 3 Results
### Temporal Relationship between \(\mathrm{GPP_{VI}}\) and \(\mathrm{GPP_{EC}}\)
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**TUM (N = 60)**} & \multicolumn{6}{c}{**WOM (N = 36)**} & \multicolumn{6}{c}{**CUM (N = 56)**} \\ \cline{2-13}  & \(\mathbf{R^{2}}\) & **RMSE** & **rRMSE** & **a** & **b** & \(\mathbf{R^{2}}\) & **RMSE** & **rRMSE** & **a** & **b** & \(\mathbf{R^{2}}\) & **RMSE** & **rRMSE** & **a** & **b** \\ \hline Clr & 0.53 & 2.35 & 0.25 & 0.36 & 5.01 & 0.87 & 0.96 & 0.14 & 0.30 & 2.88 & **0.53** & **1.05** & **0.21** & 0.31 & \(-\)0.13 \\ Clg & 0.08 & 3.33 & 0.35 & 0.01 & 8.32 & 0.90 & 0.78 & 0.11 & 0.04 & 2.75 & **0.53** & **1.01** & **0.21** & 0.04 & 1.90 \\ MTCI & **0.75** & **1.70** & **0.18** & 0.32 & 2.89 & 0.83 & 0.98 & 0.14 & 0.21 & 2.47 & 0.36 & 1.25 & 0.25 & 0.18 & 0.47 \\ NDARE1 & 0.73 & 1.77 & 0.19 & 0.36 & 3.28 & 0.89 & 0.82 & 0.12 & 0.24 & 2.58 & 0.45 & 1.15 & 0.23 & 0.21 & 0.60 \\ NDARE2 & 0.70 & 1.86 & 0.20 & 0.29 & 3.52 & 0.87 & 0.86 & 0.12 & 0.19 & 2.65 & 0.46 & 1.14 & 0.23 & 0.18 & 0.42 \\ EVI & **0.76** & **1.67** & **0.18** & 2.48 & 2.83 & **0.91** & **0.74** & **0.11** & 1.85 & 2.54 & 0.38 & 1.23 & 0.25 & 1.15 & 1.85 \\ NIRv & 0.70 & 1.89 & 0.20 & 5.40 & 3.67 & **0.91** & **0.75** & **0.11** & 4.17 & 2.52 & 0.43 & 1.17 & 0.24 & 2.92 & 1.59 \\ NDVI & 0.69 & 1.92 & 0.20 & 1.06 & 4.26 & 0.90 & 0.78 & 0.11 & 0.81 & 2.60 & 0.38 & 1.23 & 0.25 & 0.58 & 1.46 \\ MODI72 AH & 0.66 & 1.76 & 0.30 & - & - & 0.85 & 0.93 & 0.18 & - & - & 0.28 & **0.97** & 0.28 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The algorithm results for 16-day average daytime gross primary productivity (GPP) estimated at evergreen broadleaf forest (EBF) sites, with the determination coefficient (\(R^{2}\)), root-mean-square error (RMSE; unit in gC\(-\)m\({}^{-2}\)-day\({}^{-1}\)), and relative RMSE (rRMSE) presented. We employed the equation GPP\({}_{\rm EC}\) = a \(\times\) V1\(\times\) PAR + b here, where the vegetation index (VI) is the rebuilt time series, and PAR is the photosynthetic active radiation. The number of samples at each site is presented in parentheses after the site name. The numbers in bold represent the highest \(R^{2}\), lowest RMSE, and lowest rRMSE values. Both non-red-edge-related GPP\({}_{\text{EVI}}\) and red-edge-related GPP\({}_{\text{CIF}}\) showed robust correspondence with the GPP\({}_{\text{EC}}\) across all sites, with an average \(R^{2}>\) 0.70 and RMSE \(<\) 1.5 gC\(\cdot\)m\({}^{-2}\cdot\)day\({}^{-1}\). The red-edge-based GPP\({}_{\text{CIF}}\) coupled with PAR showed high correspondence with GPP at the GRA sites. The highest correlation with GPP\({}_{\text{EC}}\) was observed in CIr \(\times\) PAR, with an average \(R^{2}\) greater than 0.75 and rRMSE less than 0.39 (Table 4). The relationship between GPP\({}_{\text{CIF}}\) and GPP\({}_{\text{EC}}\) had rRMSE values that were 0.15 and 0.05 lower than those for GPP\({}_{\text{EVI}}\) at RIG and YNC, respectively. At some EBF sites, EVI \(\times\) PAR had low rRMSE values with GPP\({}_{\text{EC}}\) compared with the other red-edge-based VIs. At TUM and WOM, GPP\({}_{\text{EVI}}\) had a lower uncertainty than GPP\({}_{\text{EC}}\), with an average RMSE of 1.42 gC\(\cdot\)m\({}^{-2}\cdot\)day\({}^{-1}\) and an rRMSE that was 0.03 less than that for GPP\({}_{\text{CIF}}\). However, the red-edge-based VIs, including CIr and CIg, coupled with PAR\({}_{\text{in}}\), had lower RMSE values than the other VI-based models at CUM (Table 3). The red-edge-related GPP\({}_{\text{CIF}}\) and GPP\({}_{\text{CIg}}\) and the non-red-edge-related GPP\({}_{\text{EVI}}\) and GPP\({}_{\text{NIRV}}\) corresponded well with GPP\({}_{\text{EC}}\) at all sites. Figure 4 shows the time-series relationship between GPP\({}_{\text{VI}}\) and GPP\({}_{\text{EC}}\) during the study period. These four VIs showed similar trends with GPP\({}_{\text{EC}}\) from November 2015 to November 2016 at RIG. When the GPP\({}_{\text{EC}}\) was high in the summer, the GPP\({}_{\text{VI}}\) showed a robust relationship with GPP\({}_{\text{EC}}\) in these four VIs at YNC.