# A Python Framework for Crop Yield Estimation Using Sentinel-2 Satellite Data
###### Abstract
Various studies have demonstrated the effectiveness of different VIs in monitoring diverse crops such as potatoes, wheat, cotton, sugarcane, and corn [12; 13; 14; 15; 16; 17; 18]. For instance, the Normalized Difference Vegetation Index (NDVI) is frequently used across multiple studies for its ability to predict yield and monitor crop growth stages effectively. In potato cultivation, the NDVI, along with the red-edge chlorophyll index and optimized soil-adjusted vegetation index, is particularly useful during the tuber initiation stage for yield prediction and growth monitoring [15]. Similarly, in wheat, NDVI combined with machine learning models like Random Forests has shown promise in predicting yield with high accuracy, especially when used at key growth stages such as jointing and Flowering [19]. For cotton, the integration of VIs with texture features derived from UAV-based RGB images has enhanced yield prediction accuracy, highlighting the potential of combining different data types for improved monitoring [17]. In sugarcane, RGB-based VIs such as GLI and MGRVI, when used with machine learning models, have provided accurate growth predictions, demonstrating the utility of low-cost UAV platforms in crop management [18]. The use of Sentinel-2 data and VIs like GNDVI has been effective in assessing the within-field variability of corn yield, with machine learning techniques further enhancing prediction accuracy [20]. Despite the advantages, challenges remain, such as the need for selecting appropriate VIs and growth stages for specific crops, and the difficulty in differentiating crops with similar spectral signatures [21]. Overall, the integration of VIs with advanced remote sensing technologies and machine learning models offers a robust framework for dynamic crop monitoring and yield estimation, aiding precision agriculture practices across various crop types [15; 17; 18; 19; 20; 21]. Crop growth models like WOFOST (World Food Studies) [22] are pivotal in simulating crop development and predicting yields, which are essential for precision agriculture and food security. The WOFOST model, a process-based model, simulates the mechanistic processes of crop growth and yield production, and has been enhanced through various integrations and adaptations to improve its accuracy and applicability across different crops and environmental conditions. For instance, the integration of remote sensing data, such as UAV-derived vegetation indices, with the WOFOST model using the ensemble Kalman filter algorithm has significantly improved the accuracy of maize yield predictions, achieving a relative error of less than 5% when assimilating historical meteorological data [23]. Similarly, the coupling of WOFOST with other models, such as the WHEAT-GROW [24] and FROSTOL [25] models, has enhanced its ability to simulate winter wheat growth under low-temperature stress, improving simulation accuracy by 8.03% in frost years [26]. Sensitivity analyses using methods like EFAST [27] have further refined the model's parameters, enhancing its adaptability and accuracy in specific regions, such as the Yellow River Irrigation Area in China [28]. Additionally, the integration of deep learning techniques with WOFOST has shown promise in improving yield prediction accuracy at various growth stages, particularly during the reproductive phase of crops like corn [29]. The assimilation of high-resolution remote sensing data, such as Sentinel-2, into WOFOST has also been explored, demonstrating improved yield estimation accuracy at finer spatial resolutions [30; 31]. Moreover, the development of the WOFOST-N model, which incorporates nitrogen dynamics, has expanded the model's applicability to fruit trees, such as the Korla Fragrant pear, by accurately simulating growth and nitrogen use efficiency [32]. Despite these advancements, challenges remain, such as accurately simulating agricultural stresses like lodging, which can affect yield estimates [31].