## 3 Results
### Model Performance in Evaluation Site-years
#### 3.3.2 Model Performance at the Daily Scale  
TL-LUEn showed better performance than TL-LUE at the daily scale when 58 validation site-year data was lumped together (Figure 4c,d). The average RMSE of GPP simulated by TL-LUEn and TL-LUE was both 1.7 g C m\({}^{-2}\) day\({}^{-1}\). The average R\({}^{2}\) of GPP simulated by TL-LUEn was slightly larger than that of TL-LUE. Results of the paired \(t\) test on the differences in average RMSE value between TL-LUEn and TL-LUE were not significant (_p_ = 0.75), as well as the differences in average R\({}^{2}\) value between the two models (_p_ = 0.60) (Table 4). The average RMSE value of MOD17 was 1.9 g C m\({}^{-2}\) day\({}^{-1}\). The average R\({}^{2}\) value of MOD17 was smaller than the corresponding values of TL-LUEn and TL-LUE by 0.046 and by 0.045, respectively. In addition, the differences in average RMSE value and R\({}^{2}\) value between TL-LUEn and MOD17, and TL-LUE and MOD17 were significant, with \(p\) values were all smaller than 0.0001.  
In 58 validation site-years, MOD17 produced larger RMSE and lower R\({}^{2}\) than TL-LUE and TL-LUEn at most sites. The RMSE of GPP simulated using MOD17, TL-LUE, and TL-LUEn was larger than 2.0 g C m\({}^{-2}\) day\({}^{-1}\) at 28, 15, and 15 sites, respectively. The values of R\({}^{2}\) above 0.9 occurred at only 3 sites for MOD17, at 13 sites for TL-LUE, at 16 sites for TL-LUEn, respectively (Figure 4c,d). TL-LUEn showed better ability to simulate GPP than TL-LUE at 29 sites. MOD17 only outperformed TL-LUEn and TL-LUE at 12 and 8 sites, respectively, mainly CROP, SHRUB and GRASS sites (Table A2 in the Appendix).  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & & \multicolumn{3}{c}{**RMSE**} & \multicolumn{3}{c}{**R\({}^{2}\)**} \\ \cline{3-10}  & & **TL-LUEn –** & **TL-LUEn –** & **TL-LUE –** & **TL-LUE –** & **TL-LUEn –** & **TL-LUE –** & **TL-LUE –** \\  & & **TL-LUE** & **MOD17** & **MOD17** & **TL-LUE** & **MOD17** & **MOD17** \\ \hline \hline \multirow{3}{*}{**MODEL**} & \(t\) & \multirow{3}{*}{–0.75} & \multirow{3}{*}{–4.33} & \multirow{3}{*}{–5.09} & \(t\) & \multirow{3}{*}{1.12} & \multirow{3}{*}{6.10} & \multirow{3}{*}{7.13} \\  & stat & & & & & stat & & \\  & \(p\) & 0.45 & 0.00 & 0.00 & \(p\) & 0.27 & 0.00 & 0.00 \\ \hline \multirow{3}{*}{**MODEL**} & \(t\) & \multirow{3}{*}{0.33} & \multirow{3}{*}{–4.88} & \multirow{3}{*}{–7.63} & \(t\) & \multirow{3}{*}{0.53} & \multirow{3}{*}{7.61} & \multirow{3}{*}{9.30} \\  & stat & & & & stat & & & \\  & \(p\) & 0.75 & 0.00 & 0.00 & \(p\) & 0.60 & 0.00 & 0.00 \\ \hline \multirow{3}{*}{**MODEL**} & \(t\) & \multirow{3}{*}{2.24} & \multirow{3}{*}{–1.35} & \multirow{3}{*}{–5.96} & \(t\) & \multirow{3}{*}{0.98} & \multirow{3}{*}{4.70} & \multirow{3}{*}{0.98} \\  & stat & & & & stat & & & \\  & \(p\) & 0.03 & 0.18 & 0.00 & \(p\) & 0.33 & 0.00 & 0.33 \\ \hline \end{tabular}
\end{table}
Table 4: Statistics of the Paired \(t\) Tests on the differences between TL-LUEn and TL-LUE, TL-LUEn and MOD17, and TL-LUE and MOD17 in RMSE and R\({}^{2}\) for model validation when all vegetation types lumped together at half-hourly, daily and 8-day scale.  
As to MF, NF and SHRUB, TL-LUEn performed with a higher RMSE and R\({}^{2}\) than TL-LUE. TL-LUEn only outperformed TL-LUE for BF, but performed poorer for CROP and GRASS (see Figure 5). Overall, TL-LUEn and TL-LUE outperformed MOD17 for forests and SHRUB. For three forest types, both TL-LUEn and TL-LUE outperformed MOD17. The average RMSE of both TL-LUEn and TL-LUE was 0.4 g C m\({}^{-2}\) day\({}^{-1}\) smaller than that of MOD17 while the average R\({}^{2}\) of TL-LUEn and TL-LUE was 0.063 and 0.057 higher than that of MOD17, respectively. As to CROP and GRASS, both average RMSE and R\({}^{2}\) of GPP simulated by TL-LUEn were higher than those of MOD17, while TL-LUE outperformed MOD17 with a smaller RMSE and a higher R\({}^{2}\) (see Figure 5).