## 2 Materials and Methods
### Methods  
The data were analyzed using different approaches, organized into three sections. **Section 1:** Study of the within-field variability of yield and area comparison. In the first section, the within-field yield variability provided by the combine was analyzed using the pixel yield anomaly by field and field area. The pixel yield anomaly by field represents the yield losses or increases inside each field in kg\(\cdot\)ha\({}^{-1}\). Thus, the difference between each 10 m pixel yield of the postprocessed yield map and the mean yield at each field was calculated. The mathematical function is described in Equation (7). To assess the variability importance at each field, the yield field anomaly was compared with each area by location and year. This section aims to characterize the within-field variability. The mean yield for each field is the parameter farmers use to evaluate the campaign results; the deviation \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Vegetation Index** & **Equation** & **Equation Number** & **Reference** \\ \hline Normalized Difference Vegetation Index (NDVI) & B08\(-\)B04 & (1) & [59] \\ Land Surface Water Index (LSWI) & B08\(-\)B04 & (2) & [60] \\ Green NDVI (GNDVI) & B08\(-\)B03 & (3) & [61] \\ Normalized Difference Red Edge 1 (NDRE1) & B08\(-\)B05 & (4) & [62] \\ Normalized Difference Red Edge 2 (NDRE2) & B07\(-\)B05 & (5) & [62] \\ Normalized Crop Management Index (NCMI) & B08\(-\)B03 + B04 & (6) & [55] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Vegetation Indices used in the study; each parameter in the equation (Eq.) represents the surface reflectance for each spectral band in Sentinel-2 nomenclature. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c c c} \hline \hline
**DAS** & **0** & **5** & **10** & **15** & **20** & **25** & **30** & **35** & **40** & **45** & **50** & **55** & **60** & **65** & **70** & **75** & **80** & **85** & **90** & **95** & **100** & **15** & **110** & **115** & **120** & **125** & **130** & **All** \\ \hline
**Stage** & \mulvalues from the field mean are a suitable reference to identify the fields that require more PA practices. \[\text{Pixel yield anomaly}_{\text{ij}}=\text{Pixel yield}_{\text{ij}}-\text{ Mean yield}_{\text{j}} \tag{7}\]  
where Pixel yield anomaly\({}_{\text{ij}}\) is the yield anomaly for each pixel i at each field j; Pixel yield\({}_{\text{ij}}\) is the yield acquired by the combine for each pixel i at each field j; and Mean yield\({}_{\text{j}}\) is the mean yield acquired by the combine at each field j. **Section 2:** Study of linear correlations among the yield, all bands, and VIs in the three main growth stages. At each main growth stage (Vegetative, Reproductive, and Ripening), a critical moment was defined as a rice growth substage inside each main stage when crop management can improve yields. Yield components were used as a reference to select the three moments [63]:  
* 1 st yield component, vegetative stage: number of fillers, one date per location and year corresponding to Mid Tillering (MT). * 2 nd yield component, reproductive stage: grain number per panicle, one date per location and year corresponding to Panicle Initiation (PI). * 3 rd yield component, ripening stage: grain weight, one date per location and year corresponding to half of Grain Filling (GF). The scheme in Figure 3 summarizes the conceptualization. Rice farms were monitored year by year at each location, and following our previous research [45; 48; 55; 58], a DAS reference was used to determine the growth stages and the related yield components. Twenty-four dates were studied (three per year and location). Selected dates for MT were 35 DAS in all locations and years except location 1 in year 4 when the date was 40 DAS (no available image at 35 DAS). For PI, the images at 55 DAS were available in all locations and years.