## 5 Discussion  
### Seasonal Variability in the Global CI  
Quantitative research on CI started relatively late, resulting in considerable debate concerning conclusions concerning its seasonal variations. To address these issues, this study focuses on resolving two current controversies regarding CI: (1) whether CI exhibits seasonal variations, and (2) based on the conclusions, MODIS time-share two-stage CI products were developed to further explore the specific seasonal variation characteristics of the CI.  
The results indicate that although constrained by the inversion process, the CI has a large uncertainty relative to the NDVI in capturing the precise growth status of vegetation. However, CI still exhibits more pronounced seasonal variations, aligning with previous findings [27, 35, 47, 68, 69, 70], making it a valuable parameter for phenological monitoring. Building on these conclusions and those of previous studies [65], this study used the MODIS LSP product to divide the vegetation cycle into LOS and LFS, taking into account both the seasonal variation characteristics of CI and reducing the influence of low-quality data and background reflectance changes through quality screening and averaging. The global 500 m MODIS time-share two-stage CI product from 2001 to 2020 was then derived from the MODIS 8-day CI product. This approach provides reliable CI values with seasonal variations for global- and regional-scale modeling of ecological, meteorological, and other surface processes, ultimately improving the accuracy of various models. Globally, the CIs of different land cover types exhibit a strong clumping effect during the LOS and a weak clumping effect during the LFS. Needleleaf forests have the lowest CI values, with a slight difference between the CIOS and CIIF. Broadleaf forests have slightly higher CI values than do needleleaf forests, with more distinct seasonal variations. Shrublands presented the largest CI values, with the most pronounced seasonal variations. Thus, the seasonal variations in the CI are sensitive to land cover type, suggesting that the CI may assist in the accurate classification of land cover.  
Additionally, some scholars [71, 72] tend to assume that the BRDF varies slowly over time and even consider it constant throughout the year in their applications. In contrast, the MODIS 8-day CI product, used in this study to derive the MODIS time-share two-stage CI product, is produced based on the NDHD-CI relationship. Since NDHD is calculated via reflectance in the directions of hotspots and darkspots--two typical features of BRDF shapes in the principal plane--the results of this study imply that the BRDF exhibits seasonal variations.  
Moreover, there are still some limitations when validating whether CI exhibits seasonal variation characteristics. Ground-based phenological observation data provides accuracy and objectivity and is an important part of the validation method, ensuring the reliability of the conclusions. However, due to various constraints, ground-based phenological observation data cannot be applied on a large scale, and continuous long-term ground-based phenological observation data is difficult to obtain. Furthermore, it is challenging to find ground-based phenological observation data that matches the typical pixels selected in this study under conditions such as land cover restrictions. Therefore, this study uses the MODIS LSP product for indirect validation. Studies have shown that this product can effectively monitor vegetation phenology and is widely used as a direct application or auxiliary validation data in various phenology monitoring studies [1, 2]. Nevertheless, we hope that in the future, the results obtained from CI can be compared with ground-based observed phenological data to better understand and validate the seasonal variation characteristics of CI.