## 5 Conclusions  
In this study, we first simulated Sentinel-2 satellite reflectance based on ground ASD data and compared the correlation between commonly used vegetation indices and photosynthetically active radiation at different observation dates. Secondly, we constructed an index correlation model based on MNDVI throughout the critical growth period and validated the accuracy of the \(f\)PAR estimation using the model under different crop varieties, observation dates, and water stress conditions. Finally, we compared it with the commonly used vegetation index NDVI and carried out a sensitivity analysis. The main conclusions of this study are as follows: (1) due to differences in observation conditions and crop characteristics, the correlation between vegetation indices and \(f\)PAR can vary; (2) the index model based on MNDVI is the most stable and accurate model, with a coefficient of determination for \(f\)PAR throughout the critical growth period of winter wheat reaching 0.6649. Under different cultivars, observation dates, and water stress conditions, the highest coefficients of determination can reach 0.918, 0.881, and 0.830, with the lowest RMSE being 0.088, 0.096, and 0.089. At the satellite scale, the highest coefficient of determination is 0.8321; (3) MNDVI is more sensitive to changes in winter wheat growth and less prone to saturation compared to NDVI. In conclusion, using MNDVI for \(f\)PAR estimation during the critical growth period of winter wheat can provide good estimation results, and the estimation accuracy is less affected by internal and external factors. This study's results demonstrate the feasibility of using high spatial resolution \(f\)PAR estimation for winter wheat based on Sentinel-2 vegetation indices. By using MNDVI, it is possible to quickly and accurately obtain \(f\)PAR data with a spatial resolution of 10 m. This can assist in near real-time agricultural monitoring and provide a reference for rapid crop yield estimation. Conceptualization, Z.S. and L.S. ; methodology, Z.S. and L.S. ; data acquisition, Y.L. ([PERSON]) and Y.L. ([PERSON]); data analysis, Z.S., Y.L. ([PERSON]), Y.L. ([PERSON]), R.C., and D.W.; writing, Z.S. and L.G.T.C. ; revision, L.S., Y.L. ([PERSON]), Y.L. ([PERSON]), L.G.T.C., R.C., and D.W All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the National Key Research and Development Program of China, grant number 2023 YFD2000104, and the National Key Research and Development Program of China, grant number 2022 YFD2001102. **Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy. **Acknowledgments:** The authors are thankful to the Institute of Dryland Agriculture, Hebei Academy of Agricultural and Forestry Sciences, for providing the experimental site. **Conflicts of Interest:** Author [PERSON] was employed by the company Embrapa Soja (National Soybean Research Center--Brazilian Agricultural Research Corporation). The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. * _[PERSON] et al. (2015)_ [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Estimating the fraction of absorbed photosynthetically active radiation from the MODIS data based GLASS leaf area index product. _Remote Sens. Environ._**2015**, _171_, 105-117. [CrossRef]
* _[PERSON] et al. (2019)_ [PERSON]; [PERSON]; [PERSON]; [PERSON] Examining interactions between and among predictors of net ecosystem exchange: A machine learning approach in a semi-arid landscape. _Sci. Rep._**2019**, \(9\), 2222. [CrossRef] [PubMed]
* _[PERSON] et al. (2020)_ [PERSON]; [PERSON] MODIS/Terra+Aqua Leaf Area Index/FPAR 4-Day L4 Global 500 m SIN Grid.