## 2 Materials and Methods
### Initial Data  
The estimation process was anchored in the methodology outlined in [29], encompassing a substantial dataset of 10,883,214,548 pixel-based CSH predictions. These predictions, pertaining to 100 m\({}^{2}\) square pasture pixels on specific test dates, were documented between 2018 and 2021, covering 194,656 parcels situated in the Walloon region of Belgium. The overarching procedure involved retrieving S1 GRD products from the European Space Agency API. While the Scihub version [45] initially facilitated this operation, it was subsequently replaced by the Copernicus dataspace ecosystem [46]. The retro diffusivity of VV and VH polarization from S1 data was geocoded and computed to serve as inputs in the CSH prediction model. Simultaneously, S2 data in L2A format were obtained from the Theia [46] platform. Both the prepared S1 and S2 data underwent resampling to a 10 m resolution defined over the entire Walloon region of Belgium, with a specific mask applied to parcels designated as pastures in 2018. Subsequently, daily meteorological data encompassing air temperature (\({}^{\circ}\)C), wind speed (m/s), solar radiation (J/cm\({}^{2}\)), precipitation (mm), relative air humidity (%), and potential evapotranspiration (mm/day) were retrieved from the Agromet platform [47]. Additionally, degree days, with a lower threshold of 0 \({}^{\circ}\)C and an upper threshold of 35 \({}^{\circ}\)C, were calculated. Cumulative degree days and precipitation over 3, 7, and 15 days were also computed. Employing a data augmentation strategy based on the prior use of data for up to 4 days in the past, with S2 acquisition serving as the reference for data aggregation initiation, both S1 and S2 data were aggregated. Following this, meteorological data were incorporated, associating parcels with the nearest meteorological station. Once the dataset was assembled for each acquisition date, predictions were executed at a pixel level using a Cubist prediction model, resulting in an estimated accuracy of approximately 20 mm [27].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**R** & & & **Python** & \\ \hline
**Software** & **Version** & **Reference** & **Software** & **Reference** \\ \hline R & 4.1.1 & [31] & os v3.9 & [35] \\ raster & 3.4-13 & [36] & Re v3.9 & [37] \\ sf & 1.0-2 & [38] & Pandas v1.4.1 & [39] \\ data.table & 1.14.0 & [40] & Numpy v1.21.5 & [41] \\ caret & 6.0-93 & [42] & Dask v2023.4.1 & [43] \\  & & & scikit-learn v1.0.1 & [44] \\ \hline \hline \end{tabular}
\end{table}
Table 1: List of packages used.  
Figure 1: General workflow of the study.  
Records with CSH predictions falling outside the defined calibration range, specifically [0;250] mm, were systematically removed to confine extrapolation (resulting in the deletion of 0.02% of records). Subsequently, records associated with parcels possessing an area smaller than 4900 m\({}^{2}\) were excluded to enhance the probability that most pixels constituting the parcel fully align with its boundaries (leading to the removal of 24.89% of parcels). The final filtering step involved retaining only records with more than three CSH predictions per parcel for the computation of descriptive statistics (resulting in the deletion of 0.004%). The cleaned dataset encompassed 39,578,872 pixels and 145,724 parcels. To conclude, these pixel-based data were aggregated per parcel and date to calculate the mean (MEAN_DAY) and standard deviation (SD_DAY). The descriptive statistics for this refined dataset are detailed in Table 2. Both MEAN_DAY and SD_DAY offer a straightforward yet effective means to differentiate potential groups based on predicted CSH.