## 4 Results
### Development of the Global MODIS Time-Share Two-Stage CI Product  
#### 4.2.1 Comparison of CIs for Different Phenological Stages  
The analysis of these studies indicates that the CI exhibits distinct phenological variations, similar to those of the NDVI, although some differences between them deserve further research. Based on this finding, the global mean CIs for different phenological stages in 2020 were calculated and analyzed via ANOVA followed by [PERSON]'s post hoc test. The results (Table 3) indicated that there were highly significant differences (\(p<0.001\)) in the CIs \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Band** & **Vegetation Cycle** & **Stage** & **Value** & **Range** \\ \hline
1 & 1 & LOS & CI & 3300–10,000, 32,767 \\
2 & & LFS & CI & 3300–10,000, 32,767 \\ \hline
3 & 2 & LOS & CI & 3300–10,000, 32,767 \\
4 & 2 & LFS & CI & 3300–10,000, 32,767 \\ \hline
5 & 1 & LOS & QA & 0–4, 32,767 \\
6 & 1 & LFS & QA & 0–4, 32,767 \\ \hline
7 & 2 & LOS & QA & 0–4, 32,767 \\
8 & 2 & LFS & QA & 0–4, 32,767 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Band settings for the MODIS time-share two-stage CI product. across different phenological stages within the same IGBP class globally. [PERSON]'s post hoc test further revealed that, except for CL\({}_{\text{LOS}}\) (the CI in the LOS) and CI\({}_{\text{LGS}}\) (the CI in the LGS) in EBF and CI\({}_{\text{LFS}}\) (the CI in the LFS) and CI\({}_{\text{LSS}}\) (the CI in the LSS) in UB, the differences in CIs between phenological stages in all other IGBP classes were highly significant (\(p<0.001\)). This confirms once again that CI exhibits significant seasonal variations. In addition, except for EBF and MF, where CI\({}_{\text{LFS}}\) is smaller than CI\({}_{\text{LOS}}\), the other IGBP classes presented CI\({}_{\text{LFS}}\) values greater than CI\({}_{\text{LOS}}\) values, with CI\({}_{\text{LGS}}\) being the smallest. For EBF, which is mainly distributed in the tropics, seasonal variations are less pronounced, and frequent cloud cover often interferes with CI inversion, possibly explaining why the CI\({}_{\text{LFS}}\) is smaller than the CI\({}_{\text{LOS}}\). According to the IGBP classification system, mixed forests (MFs) are defined as combinations of deciduous needleleaf forests (DNFs), evergreen needleleaf forests (ENFs), deciduous broadleaf forests (DBFs), and evergreen broadleaf forests (EBFs) [54]. However, in the inversion process, the CI of the MF did not account for the differences between needleleaf and broadleaf forests in the mixed pixels. Instead, the broadleaf forest CI-NDHD equation was directly applied for estimation, neglecting the influence of needleleaf forests in MF pixels [66]. This resulted in higher CIs, particularly for LOS, leading to the observed pattern of CI\({}_{\text{LFS}}\) being smaller than the CI\({}_{\text{LOS}}\) for MF. [PERSON] applied two or three CIs of LFS, LOS, LGS, and LSS to light use efficiency (LUE) models. The results demonstrated that the improvement in the estimated GPP depending on two CIs (8.97%) of the leaf-on season and the leaf-off season is nearly as high as the estimated GPP that relies on three CIs (9.76%) of the leaf-scattering, leaf-gathering, and leaf-off seasons, which may be due to the rapid growth of leaves at the beginning of the growing season, which has already developed the appearance of the canopy. Consequently, the CIs of the LGS and LSS exhibited only minor differences [65]. This is consistent with the results of our study. Therefore, based on the impact of different numbers of time-share two-stage CIs on improving GPP estimation accuracy, we decided to divide a vegetation cycle into two stages, the leaf-on season (LOS) and the leaf-off season (LFS), to make the seasonal variations in the CI more concise and effective for various meteorological and ecological models. A global MODIS time-share two-stage CI product was developed, considering the quality assurance band of the MODIS 8-day CI product.