# A Python Framework for Crop Yield Estimation Using Sentinel-2 Satellite Data
## 3 Results
### Yield Estimation
For durum wheat, the Root Mean Square Error (RMSE) ranges from 40 to 60 kg per strermma (1 strermma = 1000 m\({}^{2}\)), with the best performance observed for the GNDVI during the subset of the growing season (Tillering to Stem Elongation through Grain Filling), achieving a Mean Absolute Percentage Error (MAPE) of 11.9% and an RMSE of 41.35. The second-best performance was recorded for the NDVI during the subset period,  
Figure 6: Regression analysis plots for soft wheat: subset period (**left**) and entire growing season (**right**). followed by the GNDVI for the entire growing season. These findings emphasize the strong predictive capacity of GNDVI, particularly when focused on critical phenological stages, and the reliability of NDVI during the same subset period for yield estimation. In the case of soft wheat, the Root Mean Square Error (RMSE) spans from 59 to 102 kg per stremma (kg per 1000 m\({}^{2}\)). The most accurate predictions were achieved using the LAI during the subset of the growing season (Tillering to Stem Elongation through Grain Filling), which yielded a Mean Absolute Percentage Error (MAPE) of 10.3% and an RMSE of 59.13. The EVI during the same subset period ranked as the second-best predictor, reflecting its close relationship with LAI, as the latter is derived from EVI. Following this, the NDVI for the subset period also demonstrated strong predictive performance. These results highlight the robustness of LAI and related indices when focused on critical growth stages for soft wheat yield estimation. Across both wheat types, models based on the subset of the growing season consistently outperform those utilizing the full growing season in terms of predictive accuracy. This underscores the significance of focusing on critical phenological stages, where crop growth and yield formation are most responsive to environmental and management factors. Furthermore, the models for durum wheat demonstrate relatively lower prediction errors, indicating a more consistent and robust relationship between AUC values and yield. These findings highlight the potential for subset period models to enhance yield prediction accuracy while emphasizing the distinct physiological and agronomic characteristics influencing each wheat type. By examining the best-performing index, GNDVI (durum wheat), in relation to phenological stages, as illustrated in Figure 7, it becomes evident that fields with larger yields, such as Field 1 (425.59 kg/stremma) and Field 4 (367.79 kg/stremma), when compared to lower-yielding fields such as Field 2 (290 kg/stremma) and Field 3 (258.73 kg/stremma), exhibit greater GNDVI values during the Stem Elongation to Booting stages. This finding suggests that these phenological stages are particularly critical for yield prediction. Moreover, Field 1 shows notably higher GNDVI values during the Booting and Heading stages than Field 4, which may highlight the additional, albeit less pronounced, importance of these stages in supporting yield potential. Field 6, with a yield of 339.34 kg/stremma, performs slightly better than Fields 2 and 3. This advantage persists despite Field 6 having lower GNDVI values during the Stem Elongation to Booting stages. The increased GNDVI values observed in Field 6 from the end of Booting to Flowering likely contribute to its performance, as Fields 2 and 3 display a slight decline in GNDVI during the same period, particularly at the Heading stage. This trend underscores the potential impact of later phenological stages on yield outcomes when earlier growth stages are less optimal. The evaluation of the best-performing index, LAI (soft wheat), in relation to phenological stages, as depicted in Figure 8, reveals that fields with higher yields, such as Field 3 (636 kg/stremma), Field 4 (605 kg/stremma), and Field 2 (598 kg/stremma), tend to maintain elevated LAI values during the critical period spanning from Stem Elongation to Flowering.