## 5 Discussion  
Recently, the majority of land surface models (LSM) have adopted the different photosynthesis rates of sunlit and shaded leaves to improve GPP estimation [69; 70; 71]. Previous studies have reported that there is an obvious seasonal difference in CI, with higher values during the leaf-off season and lower values during the leaf-on season, particularly for DBF and MF [42]. The seasonal changes in CI have the potential to reflect the variation of the vegetation canopy [32; 43; 52]. Unfortunately, numerous LSMs only use the simple climatology CI [72; 73], which most likely leads to uncertainties in GPP modeling. With the improvement of long-term global CI products, it is feasible to incorporate the temporal variation of CI into the study of remote sensing and land surface simulation [60]. The MODIS LSP product is widely used for the studies of the seasonal patterns and interannual variations of global land surface [68], and contains seven vegetation phenology metrics determined by the EVI2, of which the Greenup, MidGreenup, MidGreenup, and Dormancy are used for dividing the one-year cycle of leaf growth into two or three seasons  
Figure 10: The annual spatial pattern of GPP simulated by the TL-CLUE model across North America during 2002–2020. The magnitude and spatial patterns of the annual GPP are close to those of the leaf-on season shown in Figure 9a, which could be attributed to the fact that GPP is mainly generated by vegetation in the leaf-on season. in the study. The Enhanced Vegetation Index 2 (EVI2) is a vegetation index derived from remote sensing data, often satellite imagery, used to monitor and assess the health and growth of vegetation, particularly with respect to phenological events. In the MODIS LSP product, Greenup is the Date when EVI2 first crossed 15% of the segment EVI2 amplitude, meaning vegetation begins to turn green and leaves begin to grow. Therefore, it is rational that Greenup acted as the start date of the leaf-on season in this study. However, vegetation indices retrieved from remote sensing data do not always directly reflect the physiological processes of vegetation [74], and variations of vegetation structures are not immediately detected by relative vegetation indices. Therefore, it was a clever strategy to select MidGreenup from the MODIS LSP product as the start date of the leaf-gathering season instead of Maturity in this study. Previous studies have revealed that leaves generally reach the clumping state first, but the leaf greenness, represented by chlorophyll concentration, gradually increases [75; 76]. The corresponding \(\Omega\)s in different seasons are estimated based on the MODIS CI with the long temporal resolution by averaging. Compared to the CI with shorter temporal resolutions such as daily and eight-day, CI with the longer temporal resolution decreases to some extent the influences of low-quality data and fugacious changes in ambient reflectance such as rainstorms by averaging, which offers relatively reasonable CI to zonal and global simulation of ecology and meteorology CI [42], even though some useful information may be lost along with noise in the process of CI averaging. Numerous factors affect the seasonal patterns of the CI. For instance, snow cover decreases the accuracy of CI retrievals by the main algorithm, resulting in a noticeably higher CI in snow-covered areas than in snow-free areas, with an average CI bias of \(\sim\)0.13 for needleleaf forests and \(\sim\)0.32 for the other vegetation types [77]. Therefore, it is suggested that CI values determined through quality screening and averaging should be used to more accurately characterize the seasonal change in surface CI, even though the consistency of C6 CI data retrieved from MODIS BRDF (MCD43 V006) (R\({}^{2}\) = 0.89, RMSE = 0.05, bias = 0.02) with field measurement is better than that of C5 CI data retrieved from MODIS BRDF (MCD43 V005) (R\({}^{2}\) = 0.80, RMSE = 0.07, bias = 0.03) [42].