## 3 Results
### Evaluation of Best Time-Series Phenological Estimation  
This section delves into the comprehensive evaluation of our time-series phenological estimation portfolio, encompassing preprocessing steps, modeling techniques, and transition characterization methods. The aim is to gauge the accuracy of the best phenological estimation portfolio. Given the objective of evaluating the efficacy of SIF data in crop growth stage estimation within the agronomic framework, and the observations made in Section 3.2.1, highlighting the advantages of SIF data over EVI data, this section concentrates solely on SIF data in this evaluation. The best portfolio comprises a harmonious amalgamation of several components, including the data-measured time period (if necessary), compositing methods, phenologi  
Figure 9: Average of \(R^{2}\) for key growth stage identification accuracy using different phenological modeling and transition characterization datasets. Each subfigure uses distinct colors to represent specific phenological modeling methods, with solid lines for maize and dotted lines for winter wheat results. The \(x\)-axis lists the four phenological transition characterization methods. cal curve-fitting models and transition characterization methods, all chosen to optimize accuracy for each (KGS). However, selecting a universal compositing or transition characterization method suitable for all KGSs is fraught with difficulty. Therefore, this study only chose the appropriate data-measured time period (e.g., 'Morning' for maize and 'Afternoon' for winter wheat, according to the results elaborated in Section 3.2.2 and Figure 5) and the Gu model as the better-picked scheme (named after 'bp'), together adopted with different compositing methods and transition characterization methods. These methods adopted by the 'bp' scheme have been listed in Table 5. Notably, the measured times and compositing methods of in situ SIF for maize and winter wheat are consistent with the results elaborated in Sections 3.2.2 and 3.2.3. Figures 10 and 11 offer insights into the accuracy of our estimations for maize and winter wheat, respectively, utilizing SIF data processed by both the best possible portfolios and the 'bp' schemes. Notably, there are only three data points for each growth stage in Figure 11a,b, as explained in Section 2, due to the limited observations available. The distribution of dots along the horizontal axis reflects the precision of the ground-observed data, while their distribution along the vertical axis indicates the precision of the estimation results. Moreover, the distance of these dots from the fitting line serves as an indicator of the accuracy of the estimation. Notably, the \(R^{2}\) presented in these figures quantify the accuracy of the estimation relative to the fitting line, rather than the ground observations. However, the observations can be integrated with the estimations using the provided formulas in the figures. Thus, the \(R^{2}\) still serve as a comprehensive measure of the overall accuracy of our KGS estimation framework. In general, all estimation results exhibit remarkable distinctions in both precision and accuracy, underscoring the robust capabilities of SIF data in KGS estimation. Additionally, the accuracy of estimations involving TROPOMI SIF data slightly surpasses that of estimations utilizing in situ SIF data. With regard to the 'bp' schemes, the accuracy gap between estimations processed by best portfolios and 'bp' schemes is very narrow. Even the lowest 'bp' accuracy, standing at 0.81 in \(R^{2}\) (in situ SIF--'bp' for maize in Figure 10b), underscores the substantial similarity between the 'bp' schemes and the best portfolios. Consequently, our estimation framework can be streamlined with the 'bp' schemes, preserving accuracy and reducing complexity.