## 4 Results
### Spatial and Temporal Patterns of GPP across North America  
#### 4.3.1 GPP Difference between the TL-CLUE and TL-LUE Models  
In the leaf-on season, the difference in GPP simulation between the TL-CLUE model and the TL-LUE model was less than 0 on the entire North American continent (Figure 8a), indicating that the TL-CLUE model can decrease GPP overestimation. The difference was approximately \(-\)50\(-\)0 g C m\({}^{-2}\) yr\({}^{-1}\) in the Rocky Mountains and in high latitude regions north of 55\({}^{\circ}\)N (Figure 8a). With decreasing latitude and elevation, the difference increased to \(-\)100\(-\)50 g C m\({}^{-2}\) yr\({}^{-1}\) in the central and eastern regions between 30 and 50\({}^{\circ}\)N. The difference was only \(-\)200 g C m\({}^{-2}\) yr\({}^{-1}\) less than that in coastal areas south of 30\({}^{\circ}\)N (Figure 8a). The spatial difference in GPP simulation showed that the reduction in the error of GPP simulation from the TL-CLUE model exhibited definite spatial heterogeneity in the leaf-on season. In the leaf-gathering and leaf-scattering seasons, the differences in GPP simulation between the TL-CLUE model and the TL-LUE model were less than those in the leaf-on season. Even this difference ranged from \(-\)50 to 0 g C m\({}^{-2}\) yr\({}^{-1}\) across most of North America in the leaf-scattering season (Figure 8c). In the leaf-gathering season, this difference could be roughly classified into two areas in North America: ranging from \(-\)50 to 0 g C m\({}^{-2}\) yr\({}^{-1}\) in the Rocky Mountains and the north of 52\({}^{\circ}\)N regions and ranging from \(-\)100 to \(-\)50 g C m\({}^{-2}\) yr\({}^{-1}\) in the others (Figure 8b). These results indicate that the spatial heterogeneity of GPP simulation in the TL-CLUE model is similar to that of the other two \(\Omega\)s.  
Figure 7: \(R_{\rm bias}\) difference of eight-day GPP estimation between the TL-CLUE model and the TL-LUE model. The TL-CLUE model adopts 2 (yellow par) and 3 (light blue par) \(\Omega\)s from different seasons. in the TL-LUE model in the leaf-gathering and leaf-scattering seasons, particularly with the term of the leaf-scattering season. Figure 8: The spatial difference in GPP simulation between the TL-CLUE and TL-LUE models in the leaf-on season (**a**), leaf-gathering season (**b**), leaf-scattering season (**c**), leaf-off season (**d**), and one-year cycle (**e**) in different vegetation types (**f**) obtained from the MODIS Year Land Cover (MCD12Q1.061) across North America during 2002–2020. The magnitude and spatial characteristics of the difference in GPP simulation between the TL-CLUE and TL-LUE models in the leaf-on season are similar to those in the OYC for most areas of North America. The difference is less than 0, approximately from \(-100\) to \(0\) g C m\({}^{-2}\) yr\({}^{-1}\), in the leaf-on season and OYC across North America. In the leaf-off season, the above difference values were 10 g C m\({}^{-2}\) yr\({}^{-1}\) within most of North America (Figure 8d). The difference was only greater than 0 for SAV, MF, and other special regions (Figure 8d,f), which is attributed to the fact that the real CI is higher than the default CI currently used in the TL-LUE model in these regions. The difference was \(-\)10-0 g C m\({}^{-2}\) yr\({}^{-1}\) in the majority of areas other than SAV and lower than that in the eastern coastal belt south of 35\({}^{\circ}\)N (Figure 8d). For the OYC, the difference in the yearly GPP simulation between the TL-CLUE model and the TL-LUE model showed great spatial heterogeneity. The difference was approximately \(-\)150--100 g C m\({}^{-2}\) yr\({}^{-1}\) in the central regions from 30-50\({}^{\circ}\)N (Figure 8e) and \(-\)100--50 g C m\({}^{-2}\) yr\({}^{-1}\) in low-latitude and low-elevation regions, mainly including the eastern and central regions and some northwestern areas north of 50\({}^{\circ}\)N (Figure 8e).