## 3 Results
### Comparison between Time-Series Phenological Estimation Portfolios for Crop Growth Stages
#### 3.2.4 Phenological Modeling and Transition Characterization  
In this critical section, the impact of phenological modeling and transition characterization methods on the accuracy of our crop growth stage identification framework is thoroughly examined. Notably, these choices can significantly influence the precision of our entire approach. Additionally, EVI datasets were excluded from comparisons concerning winter wheat due to their previously established performance limitations.  
Figure 9b,d clearly illustrate that, for both EVI and TROPOMI SIF datasets, the models perform best when ranked as follows: the Gu model, Spline model and Beck model. However, when applied to in situ SIF data (Figure 9a), the situation differs between maize and winter wheat. For maize, the model ranking aligns with the general trend, but for winter wheat, the Beck model yields the highest accuracy, followed by the Gu model and the Spline model. Moving to the realm of phenological transition characterization methods, in situ EVI and TROPOMI SIF tend to favor the CU (curvature-based) method, whereas the MODIS EVI dataset leans towards the TR (threshold-based) or DB (derivative-based) methods. Notably, regarding in situ SIF in Figure 9a, none of the four phenological transition characterization methods exhibit significant superiority. As for the absolute average value of \(R^{2}\), in situ SIF dataset exhibits superiority over the other three datasets. This superiority can be attributed to the more adequate measurements compared with TROPOMI SIF and advantage of SIF data over EVI data in terms of estimation accuracy as discussed in previous sections.  
Figure 8: Accuracy assessment of estimations with different composited values (MVC and AVC). (**a**) focuses on maize, while (**b**) pertains to winter wheat. The circular arcs in two radar charts are \(R^{2}\) of each estimation, ranging from 0 to 1. In this figure, the lines with square nodes indicate the use of AVC, while the lines with diamond nodes represent MVC.  
The average \(R^{2}\) values presented in Figure 8 are relatively lower compared to other figures. This is because the average \(R^{2}\) here represents the mean of \(R^{2}\) values for each individual key growth stage (KGS) using different phenological modeling and transition characterization datasets. As illustrated in Figures 5, 6 and 8, estimations with a specific dataset may exhibit decent accuracy for certain crop growth stages while showing lower accuracy for others. Consequently, this variability contributes to a relatively lower average \(R^{2}\). Furthermore, the relatively low average \(R^{2}\) in Figure 9 underscores the complexity of selecting an optimal approach suitable for all situations. The challenge lies in the fact that different phenological modeling and transition characterization methods may perform differently across various crop growth stages, making it difficult to identify a one-size-fits-all solution.  
In summary, the Gu model appears to be the most suitable choice for most crop key growth stage (KGS) estimations, with the notable exception of the in situ SIF curve of winter wheat, where the Beck model could yield superior results. However, there is not a one-size-fits-all solution when it comes to phenological transition characterization methods. The choice of optimal approach is complex, which often involves a tailored combination of models, methods and even source data for each specific KGS. This complexity may, in part, explain the relatively low mean \(R^{2}\) values observed in both this section and the previous sections, as the average \(R^{2}\) alone may not fully capture the nuanced performance of our phenological metrics in estimating KGSs.