## 3 Results
### eLUE Models Using Sentinel-2  
The models were built as the MODIS ones for the spatial average of the pixels mentioned above, which had a temporal resolution of 5 days. The first model was based on the relationship between eLUE (GPP/PAR\({}_{\rm TOA}\)) and NDVI, as Figure 12 shows:  
The linear regression model showed a higher R\({}^{2}\) value (R\({}^{2}\) = 0.51) than the MODIS one, and it is shown in Equation (12):  
\[eLUE=0.886\times NDVI+0.0395 \tag{12}\]  
Therefore, the GPP_S1 model for Sentinel-2 for obtaining GPP is shown in Equation (13):  
\[GPP\_S1=(0.886\times(NDVI-Soil_{bg})+0.0395)\times PAR_{TOA} \tag{13}\]  
Being \(Soil_{bg}\) the soil background coefficient (\(Soil_{bg}=-0.05\)) obtained from the linear regression model between Sentinel-2 NDVI and GPP. The soil background coefficient was the intercept of the line, that is, the value of NDVI when GPP was zero.  
The time series obtained for this model (GPP_S1) from January 2018 to July 2020 versus the tower GPP (GPP_T) is shown in Figure 13. As it is observed, this model adjusted better than GPP_M, underestimating the spring GPP maxima and overestimating the GPP minima during summer and winter. The RMSE for the study period was quite lower than the MODIS model (GPP_M1), and it was 0.93 g C m\({}^{-2}\) day\({}^{-1}\).  
Figure 12: Relationship between eLUE (GPP/PAR\({}_{\rm TOA}\)) and Sentinel-2 NDVI from January 2018 to December 2019 in the Mediterranean grassland (\(n=146\), R\({}^{2}\) = 0.51, ANOVA \(p\)-value = 0.00).  
The validation of the model was obtained using the year 2020, obtaining an R\({}^{2}\) = 0.87 and a RMSE of 0.99 g C m\({}^{-2}\) day\({}^{-1}\). Figure 14 shows the values of GPP_S1 versus the values of GPP_T:  
The second model (GPP_S2) was a multiple linear regression model with three parameters as the second MODIS model (GPP_M2): (1) NDVI \(\times\) PAR\({}_{\rm TOA}\), (2) T\({}_{\rm min}\), and (3) SWC, as Equation (14) shows. The result of the analysis of variance (ANOVA) is shown in Table 4.  
Figure 14: Values for the Gross Primary Production Sentinel-2 model 1 (GPP_S1) versus the tower Gross Primary Production (GPP_T) for the year 2020 (January to July) in the Mediterranean grassland of La Herreria (\(n\) = 40, R\({}^{2}\) = 0.87, ANOVA \(p\)-value = 0.00).  
Figure 13: Time series obtained for the Gross Primary Production Sentinel model (GPP_S1) from January 2018 to July 2020 versus the tower Gross Primary Production (GPP_T) in the Mediterranean grassland of La Herreria.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Source** & **Sum of** & **Degrees of** & & \\
**Squares** & **Freedom** & **Mean Square** & **F-Statistic** & _p-Value_ \\ \hline Model & 901.512 & 3 & 300.504 & 476.88 & 0 \\ Residual & 89.4805 & 142 & 0.630145 & & \\ TOTAL & 990.992 & 145 & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Analysis of variance (ANOVA) of the multiple regression model: \(GPP\_S2=a_{0}+b\times(NDVI\times PAR_{TOA})+c\times T_{min}+d\times SWC\) from January 2018 to December 2019 in the Mediterranean grassland.  
Figure 15: Time series obtained for the Gross Primary Production Sentinel-2 multiple linear regression model (GPP_S2) from January 2018 to July 2020 versus the tower Gross Primary Production (GPP_T) in a Mediterranean grassland.  
The validation of the model was obtained using the year 2020 with an R\({}^{2}\) = 0.87 and a RMSE of 1.06 g C m\({}^{-2}\) day\({}^{-1}\). Figure 16 shows the values of GPP_S2 versus the values of GPP_T: