## 4 Results
### Validation of Phenological Estimates  
The accuracy of the retrievals of phenophases using the optimal thresholds detected was further assessed against ground observation data from a separate year to assess the plausibility of the thresholds and the proposed approach. Figure 6 shows boxplots of the median of \(\Delta t\) between the phenophases derived from S2 using random thresholds (upper part) and the optimal ones (bottom part) compared to in situ measurements from DWD data in 2021 for the three crops under study. It can be observed that the phenological phases obtained using our proposed method and optimal thresholds correlate well with the phenophases reported by the DWD observations. This is in contrast to the results obtained  
Figure 5: Bar plots representing the median of absolute \(\Delta t\) values across the obtained optimal \(NDVI\) amplitude thresholds, ranging from 0 to 1 and indicated by a purple point. The pink bar represents the start of the season (SOS) and the grey bar represents the end of the season (EOS). using random or unoptimized thresholds. The interquartile range of the boxplots for optimum thresholds generally falls within the 10-day error range. Only three phenophases (emergence and milk ripeness of corn and harvest of sugar beet) have boxplots that extend slightly beyond the 10-day lines, yet their medians remain within this error range. To better understand and evaluate the performance of thresholds obtained, we conducted an ECDF analysis. Figure 7 presents the comparisons of the ECDF graphs in different types of crops and phenophases, accompanied by the results of the K-S test. From the ECDF results, it is evident that the estimated DOVs align well with the reference minimum bias predicted DOVs, highlighting a strong agreement in the estimation approach. This is reflected in the K-S test values, which are considerably lower for almost all types of crops and phenophases investigated, except for the stem elongation phase of corn, which has a slightly higher KS value of 0.54. It should be noted that the lack of spatially explicit field locations, with only station locations available, may be the reason for influencing the error values. To address this, we validated the phenological estimates derived using optimal thresholds against ground-truth field phenological observations. Figure 8 shows the scatterplots of the dates of phenophases obtained from field observations with those derived from satellite data. Each point represents a BBCH record of an agricultural field. For all crop phenophases considered here, the scatterplots show that the data points are closely aligned with the 1:1 line, with most falling within the \(\pm 10\) days range. This distribution indicates that the optimal thresholds perform well in estimating field-level phenophase dates. The RMSE values are just under 10 days, specifically 9.39 days for winter wheat, 9.53 days for corn, and 9.69 days for sugar beet. Additionally, the R-squared values are relatively high, 0.97 for winter wheat, 0.96 for corn, and 0.89 for sugar beet, reflecting a strong correlation between predicted and actual phenophase dates. The retained optimal thresholds were subsequently used to identify and map all crop-phenophase fields for the three years under study. Due to space constraints, Figure 9 illustrates the spatial distribution of the estimated DOY of only three phenological stages at the parcel level in the LS federal state. Figure 6: Boxplots of statistical agreement metrics median of \(\Delta t\) between satellite-derived phenophases dates and in-situ DWD dates across the three major crops for a separate year (2021). The top row of results was obtained using a fixed threshold approach, while the bottom set was derived after optimising thresholds. Figure 7: ECDF plot comparison of the reference DOYs with the aggregated minimum bias predicted DOYs for (**a**) winter wheat (**b**) corn, and (**c**) sugar beet.