## 6 Conclusions  
In this study, we attempted to decrease the uncertainty of the GPP estimation of the TL-LUE model by considering the seasonal differences in CI (TL-CLUE). The TL-CLUE model depends on different \(\Omega\)s values from different seasons to adjust the distribution of APAR between sunlit leaves and shaded leaves among different seasons. Although the GPP estimations from the TL-LUE and TL-CLUE models are both in line with the observed GPP at EC flux sites, the regression analysis shows that the fluctuation in GPP estimation from the TL-CLUE model (RMSE = 2.46 g C m\({}^{-2}\) d\({}^{-1}\)) is lower than that from the TL-LUE model (RMSE = 2.75 g C m\({}^{-2}\) d\({}^{-1}\)). When three and two \(\Omega\)s from different seasons are used in the TL-CLUE model, the eight-day GPP overestimation could be reduced by approximately 9.76 and 8.97%, respectively, of which two \(\Omega\)s from the leaf-off and leaf-on seasons are recommended to optimize the TL-LUE model out of consideration for shrinking computing costs and simplifying the model. We anticipate that the proposed method will be incorporated into the MODIS GPP algorithms to improve GPP estimation in the future. The result of the GPP simulation shows that GPP has an obvious seasonal difference, with much larger GPP in the leaf-on season than in the leaf-off season, and spatial heterogeneity, with GPP increases with decreasing latitude and elevation across North America. Greater efforts and challenges are needed to enhance the quality of the CI, particularly at higher temporal scales such as weekly and daily relative to monthly. Future research is required to better understand the role that other key parameters of the TL-LUE model, such as the maximum LUE, play in the estimation of GPP.  
Conceptualization, Z.L. and Z.J.; Data curation, Z.L., C.W. and J.G.; Formal analysis, Z.L. and G.G.; Funding acquisition, Z.J.; Methodology, Z.L., Z.J. and C.W.; Software, Z.L.; Supervision, Y.T. and S.C.; Validation, Z.L. and S.Y.; Visualization, Z.L. and Z.T.; Writing--original draft, Z.L.; Writing--review & editing, Z.J., C.W. and J.G. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Major Program of the Natural Science Foundation of China (42090013) and the General Program of the Natural Science Foundation of China (41971288).  
The FLUXNET2015 dataset and AmeriFlux dataset can be downloaded from [[https://fluxnet.org/data/download-data/](https://fluxnet.org/data/download-data/)]([https://fluxnet.org/data/download-data/](https://fluxnet.org/data/download-data/)), accessed on 17 May 2023 and [[https://AmeriFlux.lbl.gov/data/download-data/](https://AmeriFlux.lbl.gov/data/download-data/)]([https://AmeriFlux.lbl.gov/data/download-data/](https://AmeriFlux.lbl.gov/data/download-data/)), accessed on 17 May 2023, respectively. Both MODIS Year Land Cover, land surface phenology, and eight-day leaf area index with 500 m of the spatial resolution can be downloaded from [[https://lpdaac.usgs.gov/product_search/?view=cards&amp:sort=title](https://lpdaac.usgs.gov/product_search/?view=cards&amp:sort=title)]([https://lpdaac.usgs.gov/product_search/?view=cards&amp:sort=title](https://lpdaac.usgs.gov/product_search/?view=cards&amp:sort=title)), accessed on 20 May 2023. Meteorological data from NASA MERRA-2 can be downloaded from [[https://disc.gsfc.nasa.gov/](https://disc.gsfc.nasa.gov/)]([https://disc.gsfc.nasa.gov/](https://disc.gsfc.nasa.gov/)), accessed on 20 May 2023.  
The analysis data for this study includes FLUXNET2015 and AmeriFlux datasets, MODIS products, and NASA MERRA-2 data. We Sincerely appreciate contributors to these data. We thank [PERSON] for generously sharing this MERRA-2 data. We are grateful for the insight criticism and suggestions from all anonymous reviewers and the editor.  
The authors declare no conflict of interest.