## 2 Materials and Methods
### Data
#### 2.1.5 Polygons  
The agricultural parcels delineations were obtained from Sistema de Informacion Geografica de Parcelas Agricolas (SIGPAC), a Spanish governmental application ([[http://sigpac.mapa.gob.es/](http://sigpac.mapa.gob.es/)]([http://sigpac.mapa.gob.es/](http://sigpac.mapa.gob.es/))) that allows identifying specific declared agricultural fields subjected to Common Agricultural Policy (CAP) subsidies. GPS coordinates were recorded to delineate the 39 fields used for training and validating the grain yield model. Crop type points were coordinated in fields throughout the three zones (Figure 3) by obtaining GPS coordinates from each of the classified types (wheat, bare soil, and other crops). The whole regional agricultural parcels polygons were downloaded for the attributes herbaceous crops and rain-fed for the three agrarian areas under study within Navarre. Furthermore, fields were 10-m-buffered with the ArcGis Pro 2.3.0 _buffer_ tool in order to reduce edge effects.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**MSI Band** & **Spatial Resolution (m)** & **Central Wavelength (nm)** \\ \hline B1: Coastal Aerosol & 60 & 443 \\ B2: Blue & 10 & 490 \\ B3: Green & 10 & 560 \\ B4: Red & 10 & 665 \\ B5: Red-Edge & 20 & 705 \\ B6: Red-Edge & 20 & 740 \\ B7: Red-Edge & 20 & 783 \\ B8: NIR & 10 & 842 \\ B8A: Vegetation RE & 20 & 865 \\ B9: Water Vapour & 60 & 945 \\ B10: SWIR Cirrus & 60 & 1375 \\ B11: SWIR & 20 & 1610 \\ B12: SWIR & 20 & 2190 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Spectral bands and spatial resolutions of the Sentinel-2 Multispectral Instrument (MSI). Novelty in spectral coverage includes three red-edge spectral bands and the vegetation red-edge (RE) at 20 m as well as improved SWIR (Short-Wave InfraRed) coverage at 20 and 60 m spatial resolutions. Broadband spectral coverage of the visible and near infrared are provided at 10 m spatial resolution.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **S-2 Formula** & **Measures** & **Reference** \\ \hline
**CI Green** & (B7/B3) \(-1\) & Chl content & [PERSON] et al. (2003) \\
**CI Red Edge** & (B7/B5) \(-1\) & Chl content & [PERSON] et al. (2003) \\ \hline
**NDWI** & (B8 - B11)(B8 + B11) & Water content & [PERSON] et al. (1996) \\ \hline
**OSAVI** & 1.16 (B8 - B4)(B8 + B4 + 0.16) & Vegetation cover & [PERSON] et al. (1993) \\
**MSAVI** & [2-B8 + 1 – \(\surd\) (2- (B8 + 1)\({}^{2}\) - \(\surd\) (B8 - B4))]/2 & Vegetation cover & [PERSON] et al. (1994) \\ \hline
**MSR** & (B8/B4 - 1)/[v(B8/ B4 + 1)] & Biomass & [PERSON] et al. (1996) \\
**NDVI** & (B8 - B4)(B8 + B4) & Biomass & Rouse Lr. (1974) \\
**GNDVI** & (B8 - B3)(B8 + B3) & Biomass & Louhaichi (2001) \\
**RDVI** & (B8 - B4)/v(B8 + B4) & Biomass & Roujean (1995) \\
**RV1** & B8/B4 & Biomass & Jordan (1969) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Vegetation indices calculation regarding Sentinel-2 bands, B refers a specific band, among those reported in Table 4. The acronyms refer to: chlorophyll index green (CI green), chlorophyll index red edge (CI red edge), normalized difference water index (NDWI), the modified soil-adjusted vegetation index (MAVI), optimized soil adjusted vegetation index (OSAVI), renormalized difference vegetation index (RDVI), ratio vegetation index (RVI), modified simple ration (MSR), normalized difference vegetation index (NDVI), and the normalized difference vegetation index (GNDVI).