## 5 Conclusions and Recommendations  
In this study, to identify a robust hybrid inversion model to improve the canola FPAR retrieving accuracy, the PROSAIL model was recompiled to simulate FPAR variations, and a total of 29 VIs and two machine learning algorithms were devoted to retrieving the FPAR. Three VIs of OSAVI, mSR and WDRVI had better capability in revealing the variations in the FPAR than the other VIs across both datasets. OSAVI, in particular, exhibited greater resistance to changes in the leaf and canopy parameters. The hybrid inversion model revealed that ANN-OSAVI exhibited the best performance for the canola FPAR retrieval, with whole R\({}^{2}\) and RMSE values of 0.65 and 0.051, respectively. In specific growth stages, the model achieved R\({}^{2}\) and RMSE values of 0.78 and 0.043 in the seedling stage, 0.63 and 0.047 in the flowering stage, and 0.61 and 0.050 in the mature stage, respectively.  
This study highlights the potential of hybrid model methods in retrieving the canola FPAR during each growth stage. An accurately estimated FPAR could provide more veritable crop growth information for biomass prediction and vegetation productivity model (e.g., gross primary production (GPP)). For example, [PERSON] [102] estimated the time series of the FPAR of sugar beet and used it to calibrate the SUCROS model to achieve crop dry matter and yield predictions. Although these are encouraging results, further improvements are warranted. For instance, considering the internal structure of leaves, in addition to the woody part, there are other components that do not participate in photosynthesis but still absorb PAR, such as pigments, leaf veins and cell walls. The energy absorbed by these components accounts for 20% to 30% of the total leaf absorption [103]. Solar radiation absorbed by the non-photosynthetic part holds no practical significance for crop growth and development. [PERSON] et al. [2] investigated the impact of the LUE and FPAR changes on GPP estimation and proposed that the chlorophyll FPAR exhibited seasonal dynamics more similar to the flux tower than the canopy FPAR. [PERSON] et al. [104] studied the solar radiation absorption characteristics of trembling aspen forests to estimate the chlorophyll FPAR and canopy FPAR and suggested that the vegetation productivity had a strong correlation with the chlorophyll FPAR, but a weak correlation with the canopy FPAR. Therefore, future efforts should be devoted to developing and refining the FPAR from the canopy scale to the leaf scale to achieve higher accuracy in vegetation productivity estimations.  
Writing--original draft preparation, J.K.; methodology, J.K.; writing--review and editing, C.Z. and M.T.; data curation, Z.L. and R.L.; software, Z.X.; funding acquisition, C.Z. and S.F. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (51909228, 52209071), the China Postdoctoral Science Foundation (2023T160552, 2020M671623), \"Chunhui Plan\" Cooperative Scientific Research Project of Ministry of Education of China (HZKY20220115) and the \"Blue Project\" of Yangzhou University.  
The data that supported this study cannot be publicly shared due to ethical or privacy reasons and may be shared upon reasonable request to the corresponding author if appropriate.  
The authors would like to acknowledge the Agricultural Water and Hydrological Ecology Experiment Station, Yangzhou University, for providing the experimental facilities.  
The authors declare no conflict of interest.