# A Python Framework for Crop Yield Estimation Using Sentinel-2 Satellite Data
## 3 Results  
### Yield Estimation  
In this study, we investigated the relationship between the Area Under the Curve (AUC) of mean values of Vis (NDVI; GNDVI; EVI; LAI; and RE-PAP) during the growing season as well as within a specific time period (3 March 2024 to 27 May 2024), corresponding to key phenological stages from Tillering to Stem Elongation and continuing through Grain Filling, and the measured yield at the field scale. AUC values were computed using the trapezoidal rule, complemented by regression analysis conducted within a Python environment. The predicted yield (Ypred) is expressed in Kg/stremma, where stremma is an area measurement unit corresponding to 1000 square meters, which is officially used in Greece. The results are presented in the following tables: Table 8 for durum wheat and Table 9 for soft wheat. The regression plots are illustrated in the subsequent figures, Figures 5 and 6, corresponding to durum wheat and soft wheat, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Vegetation Index** & **Time Period** & **Reg. Equation** & **R2** & **MAPE (\%)** & **RMSE** \\ \hline GNDVI & Growing season & Ypred = 116.035 \(\times\) AUC & 0.97 & 18.8 & 102.22 \\ \hline GNDVI & Subset of growing season (from & & & & \\ Tillering to Stem Elongation through & Ypred = 169.039 \(\times\) AUC & 0.98 & 14.7 & 81.17 \\  & Grain Filling) & & & & \\ \hline LAI & Growing season & Ypred = 31.814 \(\times\) AUC & 0.98 & 13.9 & 77.83 \\ \hline LAI & Subset of growing season (from & & & \\ Tillering to Stem Elongation through & Ypred = 46.913 \(\times\) AUC & 0.99 & 10.3 & 59.13 \\  & Grain Filling) & & & & \\ \hline NDVI & Growing season & Ypred = 98.754 \(\times\) AUC & 0.98 & 14.3 & 79.24 \\ \hline NDVI & Subset of growing season (from & & & \\ Tillering to Stem Elongation through & Ypred = 154.527 \(\times\) AUC & 0.99 & 10.9 & 62.16 \\  & Grain Filling) & & & & \\ \hline RE-PAP & Growing season & Ypred = 17.233 \(\times\) AUC & 0.98 & 11.1 & 78.51 \\ \hline RE-PAP & Subset of growing season (from & & & \\ Tillering to Stem Elongation through & Ypred = 21.972 \(\times\) AUC & 0.98 & 11.8 & 86.21 \\  & Grain Filling) & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: _Cont._  
Figure 5: _Cont._Figure 5: Regression analysis plots for durum wheat: subset period (**left**) and entire growing season (**right**). Figure 6: _Cont_. The regression analysis conducted for both durum and soft wheat yields demonstrates exceptionally high Coefficient of Determination (R\({}^{2}\)) values, indicative of a strong linear relationship between yield and the AUC of vegetation indices. However, these high R\({}^{2}\) values may partly reflect overfitting, which can be attributed to several factors. Firstly, the relatively small dataset examined in this study may limit the generalizability of the results and amplify the appearance of a strong fit. Secondly, the characteristics of the data itself, including the variability and distribution of the AUC values, most likely contribute to the observed trends. Lastly, the use of a zero-intercept model was deliberately chosen due to its physical relevance as a scenario where AUC = 0 logically corresponds to yield = 0. This approach ensures that the regression equation is rooted in agronomic reality. By modeling yield as a function of AUC rather than directly using vegetation index values, this study aims to establish a predictive framework grounded in an independent variable with clear temporal and physiological significance. While the results highlight the potential of the models, further validation with larger datasets and additional variables is necessary to confirm their predictive reliability and broader applicability.