## 3 Results
### Multiple Linear Regression Models of GPP  
Based on the general relationships shown in Table 2, and with the aim of fitting models that had the same formulation for the three satellite data sets at each site, \(T_{a}\) was chosen as input environmental variables into the final linear GPP regression model:  
\[GPP=a\times EVI2\times T_{a}+b. \tag{6}\]  
We tested three models at all sites, and the RMSEs, MAEs, and R\({}^{2}\) of satellite-derived GPP and flux data-derived GPP were calculated (Table 1). We found that the differences of RMSE, MAE, and R\({}^{2}\) due to the differences in the model were greater than those due to \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **EVI2\({}_{\rm 10m}\)** & **EVI2\({}_{\rm 250m}\)** & **EVI2\({}_{\rm 90m}\)** & **T\({}_{a}\)** & **PPFD** & **VPD** \\ \hline SE-Sto & 0.77 & 0.81 & 0.83 & 0.69 & 0.04 & 0.24 \\ SE-Svb & 0.74 & 0.73 & 0.79 & 0.86 & 0.51 & 0.41 \\ SE-Deg & 0.59 & 0.58 & 0.63 & 0.68 & 0.28 & 0.34 \\ FI-Hy & 0.73 & 0.83 & 0.86 & 0.87 & 0.54 & - \\ SE-Nor & 0.81 & 0.67 & 0.72 & 0.82 & 0.74 & 0.53 \\ SE-Lnn & 0.89 & 0.93 & 0.90 & 0.31 & 0.49 & 0.23 \\ SE-Htm & 0.78 & 0.45 & 0.56 & 0.75 & 0.82 & 0.43 \\ DK-Sor & 0.93 & 0.87 & 0.89 & 0.79 & 0.76 & 0.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Coefficient of determination, R\({}^{2}\), of environmental variables/satellite EVI2 versus EC derived GPP in daily time step. No VPD data were available at FI-Hy site. the difference in the satellite data. Referring to the RMSEs from the three models at each site (Table A1), we used the model that generated the highest R\({}^{2}\) at each site for the final GPP estimation results (Table 3). Therefore, we applied the model driven by \(T_{a}\) (Equation (5)) at all sites. The slopes and intercepts of the regression models are similar within the same site (Table 3). The largest differences of slopes and intercepts among the different satellite EVI2 data were found at the three southern sites, SE-Lnn, SE-Htm, and DK-Sor. RMSEs, MAEs, and R\({}^{2}\) had similar patterns across sites, satellite data sets and model formulations, which means that the low RMSE values usually coincided with low MAE and high R\({}^{2}\) values. There was no single satellite dataset that always generated the lowest RMSE, lowest MAE, or highest R\({}^{2}\). RMSE, as well as MAE and R\({}^{2}\), differed mostly across sites, and the smallest differences were found between the EVI2 variables from the different satellite datasets (Table A1). All the \(p\)-values shown in Table 4 from Wilcoxon signed-rank tests are over 0.10, which means that the test failed to reject the null hypothesis of zero medians for the difference of RMSE/MAE/R\({}^{2}\) between paired sample sites. Separately averaging RMSE, MAE, and R\({}^{2}\) across sites, it was seen that there was almost no difference in the results generated from Sentinel-2 MSI data and MODIS data (Table 5). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **RMSE** & & **MAE** & & \multicolumn{2}{c}{**R\({}^{2}\)**} \\ \hline  & **250 m** & **500 m** & & **250 m** & **500 m** & & **250 m** & **500 m** \\ \hline
10 m & 0.547 & 0.313 & 10 m & 0.250 & 0.313 & 10 m & 0.461 & 0.461 \\ \hline
500 m & 0.195 & - & 500 m & 0.250 & - & 500 m & 0.195 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Paired \(p\)-values of RMSE, MAE and R\({}^{2}\) over 8 sites from Wilcoxon signed-rank test. All \(p\)-values of 0.10 over fail to reject the null hypothesis.