## 2 Materials and Methods
### NDVI-Based Clear Pixel Procedure (NDVI-CPP)  
Once the S2 collection was properly preprocessed, a cloud probability (CP) function was created with the CP threshold as the variable of the cloud mask. The CP threshold was made to vary from 1 to 100. Within the CP function, firstly, the cloud mask using the CP collection was applied to the entire S2 collection. Then, the function for calculating the NDVI was programmed and mapped on the entire S2 collection. At this point, a new collection of NDVI scenes with a 5-day revisit frequency and 10 meters' spatial resolution was obtained. Figure 2 shows an example of an NDVI index map created in false colors (red, yellow, and green). Thus, a series of MVC scenes on a monthly basis was composed. Following this, for each monthly MVC (mMVC), the spatial average of the entire field (FmMVC) was calculated. The aim of the FmMVC computation was to use it as an optimization criterion for the cloud probability threshold setting. When using the Sentinel-2 Cloud Mask, setting a CP threshold  
Figure 2: Example of NDVI map made in the Google Earth Engine environment (scene of 29 March 2020). that is too high leads to a cloud omission error (cloudy pixels not masked), and setting a CP threshold that is too low leads to a cloud commission error (clear pixels masked). The application of the monthly MVC procedure protects from cloud commission errors (no pixels are masked), but cloud omission errors are still possible (in the case of persistent adverse weather conditions for the entire monthly sequence). However, knowing that the NDVI index takes values close to 0 in the presence of clouds and higher values in the presence of vegetation, we assume that, for each monthly MVC collection (or NDVI collection), as CP threshold increases, starting from 0 (all pixels masked), the FmMVC (or F-NDVI, i.e., the field NDVI spatial mean) increases until a maximum is reached, which represents the CP value for which all clear pixels are shown. A possible subsequent decrease in FmMVC (F-NDVI) indicates the presence of (unmasked) pixels compromised by atmospheric conditions. Then, the best balance between omission and commission errors (optimal CP threshold) can be found by setting the value corresponding to the maximum FmMVC as the CP threshold (see Figure 3). To illustrate this point with an example, consider a cloudy monthly dataset under investigation and examine how the Maximum Value Composite (MVC) changes as the cloud probability (CP) threshold is adjusted. For this analysis, the month of March 2018 is selected, and for simplicity, the CP threshold is varied in increments of 10 (see Table 2). In the proposed example, the optimal CP threshold value is 60%. Lower values reveal the masking of clear pixels within the MVC, while higher values correspond to the inclusion of pixels compromised by atmospheric conditions. Thus, to extend the procedure to all the periods under investigation and determine a valid CP threshold for \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**FmMVC as CP Threshold Varies**} \\ \hline CP threshold (\%) & 10\% & 20\% & 30\% & 40\% & 50\% & **60\%** & 70\% & 80\% & 90\% & 100\% \\ FmMVC & No Data (entire 2018-03 & field masked) & 0.2965 & 0.3262 & 0.3441 & 0.4064 & **0.4725** & 0.4700 & 0.4515 & 0.4275 & 0.3368 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: FmMVC variation according to the CP threshold variation in March 2018. Figure 3: The theoretical FmMVC variation as the CP threshold varies and the optimal setting of the CP threshold as a function of FmMVC (by taking the maximum value). MVC collection, we calculated the temporal mean FmMVC value by averaging the already calculated FmMVC values temporally over the three seasons under investigation. The months from January to May were considered months for which we were certain that there was sufficient plant cover. We call this synthetic value the t-mean FmMVC (temporal-mean FmMVC).