## 5 Discussion
Although the MODIS CI applied in the study is extremely improved, with very little extreme outlier value relative to other CI products, by the hotspot-adjusted model and a backup algorithm [47], the CI data retrieved from remote sensing directional observations tend to remain highly uncertain. First, the use of BRDF information, particularly reconstructed BRDF information, is insufficient in the inversion of key land surface parameters of the carbon cycle and energy balance due to an incomplete viewing angle, which poses a large challenge for the precise retrieval of CI based on the linear relationship between the CI and NDHD. Furthermore, CI data with a vast spatial range retrieved from remote sensing are more susceptible to changes in ambient and background reflectivity in theory [32]. For example, high soil moisture leads to diminished soil reflectance in the red band, and vegetation growth below the forest further reduces the total background reflectance of the red band just after the start of the rainy season in sparse sites [78]. The daily CI in the ENF and MF shows a short increase during August and September in southeastern North America. These short-term fluctuations could be attributed to the local tropical storm that affected the retrieval values of the main algorithm by destroying the canopy and disturbing the background reflectance [79; 80]. Another source of uncertainty is the abnormal land surface shadow caused by landscape relief [81; 82]. Additionally, there is a difference in scattering characteristics and distribution structures for heterogeneous cells with different land cover types, which would introduce some uncertainties to the linear extension of BRDF in space [83; 84]. To better understand the structure and temporal variation in global vegetation [43], further studies are required to reduce the retrieval uncertainties of the eight-day CI, especially from the trajectory of daily BRDF. The results of the sensitivity analysis demonstrate that there is an obvious influence of the CI on the estimation of GPP. In this study, eight-day GPP overestimation could be reduced by 8.97 and 9.76% in the TL-CLUE model depending on two and three \(\Omega\)s from different seasons, which may be attributed to the fact that the estimation of seasonal CI would smooth the fluctuation resulting from the low-quality data and short-term variations in background reflectance by quality screening and averaging. It can therefore be suggested that the seasonal \(\Omega\) can provide relatively credible information on the CI seasonal changes for ecological and meteorological modeling at global or regional scales. Additionally, the CI is a vital parameter to estimate LAI, of which seasonal change is a key factor in controlling the GPP of vegetation [85]. The study found that the TL-LUE model generally overestimated the GPP for each vegetation type, which might be explained by the fact that the \(\Omega\) that is presently used in the TL-LUE model is far greater than the actual CI of the vegetation, which leads to a much higher GPP estimation of sunlit leaves with a higher CI than the GPP estimation of shaded leaves with a lower CI, particularly during peak vegetation growth. When other conditions remain unchanged, the higher the \(\Omega\) is, the more scattering leaves will lead to the absorption of more radiation and a larger LUE [86]; thus, vegetation can transfer more solar energy to generate more GPP. There is an apparent seasonal difference in CI, with lower values in the leaf-on season than in the leaf-off season, which is in agreement with previous studies of field measurements [87; 88; 89] and remote sensing estimations at regional scales [32; 90]. This study is in accord with previous research that found a larger CI in the growing season and a smaller CI in the dormancy season. Moreover, the seasonal difference in CI is also caused by canopy cover and arrangement, vegetation under the trees, and background reflectance [32; 42; 43].