## 3 Results
### Model Performance in Evaluation Site-years  
#### 3.3.1 Model Performance at the Half-hourly Scale  
Model evaluation shows that TL-LUEn performed slightly better than TL-LUE in simulating half-hourly GPP when data in all 58 validation site-years was lumped together (Figure 4a,b). The RMSE and R\({}^{2}\) of GPP simulated using TL-LUE against measurements averaged 64.3 mg C m  
Figure 3: Average RMSE and R\({}^{2}\) of GPP simulated using calibrated TL-LUEn, TL-LUE and MOD17 in the calibration site-years at half-hourly (the first and second columns), daily (the third and fourth columns), and 8-day (the last two columns) scales for individual vegetation types. Note: Broadleaf forest (BF); Mixed forest (MF); Needleleaf forest (NF); Crop (CROP); Grass (GRASS); Shrub (SHRUB). Solid black circles are the means and horizontal error bars denote standard deviations.  
(30 min)\({}^{-1}\) and 0.732, respectively, while the corresponding values of TL-LUEn were 63.9 mg C m\({}^{-2}\) (30 min)\({}^{-1}\) and 0.735, respectively. However, the differences in RMSE value between TL-LUEn and TL-LUE were not significant (\(p\) = 0.45) as well as the differences in R\({}^{2}\) between the two models (\(p\) = 0.27) (Table 4). The performance of MOD17 was the poorest, with average RMSE and R\({}^{2}\) values equaled to 70.1 mg C m\({}^{-2}\) (30 min)\({}^{-1}\) and 0.690, respectively. In addition, the differences in both the two statistics (RMSE, R\({}^{2}\)) between TL-LUEn and MOD17, and TL-LUE and MOD17 were significant, with \(p\) values smaller than 0.0001 (Table 4).  
In 58 evaluation site-years, the RMSE of GPP simulated using TL-LUEn, TL-LUE, and MOD17 was larger than 80 mg C m\({}^{-2}\) (30 min)\({}^{-1}\) at 10, 11 and 17 sites, respectively. The R\({}^{2}\) of GPP simulated using MOD17 mostly ranged from 0.5 to 0.8 (at 42 sites) while the R\({}^{2}\) of GPP simulated using TL-LUEn and TL-LUE was in the range from 0.7 to 0.9 at 39 and 40 sites, respectively (Figure 4a,b). TL-LUEn performed better than TL-LUE at 31 sites. The poorer performance of TL-LUEn relative to TL-LUE occurred at CROP, GRASS, SHRUB and NF sites. MOD17 only performed better than TL-LUE and TL-LUEn at 9 sites (Table A1 in the Appendix).  
Figure 4: The number of site-years within different RMSE and R\({}^{2}\) classes (**left**) and the averages of RMSE and R\({}^{2}\) (**right**) of gross primary productivity (GPP) simulated using the TL-LUEn, TL-LUE, and MOD17 models in 58 validation site-years at half-hourly (**a**,**b**), daily (**c**,**d**), and 8-day (**e**,**f**) temporal scales, respectively.  
Overall, TL-LUEn performed better than TL-LUE for BF, GRASS, MF and SHRUB, but poorer than TL-LUE for CROP and NF (see Figure 5). TL-LUEn and TL-LUE outperformed MOD17 for all vegetation types but CROP. The improvement of TL-LUE and TL-LUEn over MOD17 was most significant for forests (BF, MF and NF). Averaged over all forest sites, the RMSE of MOD17 was larger than those of TL-LUEn and TL-LUE by 10.1 mg C m\({}^{-2}\) (30 min)\({}^{-1}\) and 8.8 mg C m\({}^{-2}\) (30 min)\({}^{-1}\), respectively. The corresponding average R\({}^{2}\) of MOD17 was 0.063 and 0.060 lower than those of TL-LUEn and TL-LUE, respectively.