## 2 Materials and Methods
### Calculation of Vegetation Indices from Sentinel-2 Images  
The study utilized Sentinel-2 Level-2A bottom-of-atmosphere (BOA) surface reflectance images acquired between 2019 and 2022 [24]. These multispectral images were preprocessed through the Google Earth Engine platform [47], which enabled efficient handling of large geospatial datasets across the four-year study period. The Level-2A  
Figure 2: A display of ground truth crop yield samples used for yield potential prediction from the QDANN dataset.  
products provided atmospherically corrected surface reflectance values with an initial spatial resolution ranging up to 10 m depending on the spectral band [24]. To achieve the same spatial resolution as the input crop yield data from QDANN, all bands were resampled to a 30 m resolution using the bilinear interpolation method. Both crop yield values and surface reflectance time-series values from Sentinel-2 were obtained based on raster-vector overlay from the preprocessed data. The cloud masking procedure employed a multi-layered approach combining the scene classification layer (SCL) with probabilistic cloud and snow masks. Pixels were retained for analysis only when meeting all of the following criteria: a cloud probability below 5% (MSK_CLDPRB), the absence of cirrus clouds (SCL \(\
eq\) 10), and no cloud shadow effects (SCL \(\
eq\) 3).  
Seven vegetation indices were calculated from the processed Sentinel-2 imagery. For each sample point, a complete time-series was generated by aggregating all available cloud-free observations within each study year. The temporal density of observations varied depending on cloud cover conditions but typically included 35-40 total scenes per study year. The extraction process automatically flagged and removed invalid values and eliminated duplicate observations that might occur when multiple scenes covered the same location within a short timeframe. The selected vegetation indices represented a combination of established metrics and innovative approaches designed to address the saturation effect in crop monitoring [26]. The NDVI [48] was included as a baseline reference due to its widespread use in agricultural remote sensing, despite its recognized saturation effects in dense canopies. Additionally, the EVI [49] was included, which introduces a soil adjustment factor and atmospheric resistance through inclusion of the blue band. The two-band EVI2 [50] was also included, as it maintains similar advantages to EVI while eliminating dependence on the blue band, making it compatible with a wider range of sensors. Besides these well-known indices, the wide dynamic range vegetation index (WDRVI) [51] incorporated a weighting coefficient to the near-infrared band, effectively extending the dynamic range and reducing saturation effects in high-biomass conditions. The inverted difference vegetation index (IDVI) [52] was implemented as a linear alternative to the NDVI, emphasizing absolute NIR reflectance rather than normalized ratios to maintain sensitivity across all growth stages. The three red-edge vegetation index (NDVI3 RE) [53] utilized three of Sentinel-2's red-edge bands to enhance discrimination in crops with a high leaf area index, where traditional NDVI underperforms. Finally, the plant phenology index (PPI) [54] was included specifically for its ability to track photosynthetic activity and vegetation phenology through unique band combinations.