## 3 Results
### eLUE Models Using MODIS  
The MODIS models were built for the pixel of the tower with a spatial resolution of 250 m and a temporal resolution of 8 days. The first model (GPP_M1) was based on the relationship between eLUE (GPP_T/PARTOA) and MODIS NDVI, as Figure 4 shows:  
Figure 4: Relationship between eLUE (GPP_T/PARTOA) and MODIS NDVI from January 2018 to December 2019 in the Mediterranean grassland of La Herreria (\(n=92\), R\({}^{2}=0.347\), ANOVA \(p\)-value = 0.00). Figure 3: Time series obtained for MODIS Gross Primary Production product (MODIS_GPP) from January 2018 to July 2020 versus the tower Gross Primary Production (GPP_T) in the Mediterranean grassland of La Herreria. The linear regression model (\(n=92\), R\({}^{2}=0.347\), ANOVA \(p\)-value = 0.00) obtained is shown in Equation (9):  
\[eLUE=1.152\times NDVI-0.162 \tag{9}\]  
Therefore, the _GPP_M1_ model for obtaining _GPP_ is shown in Equation (10):  
\[GPP\_M1=(1.152\times(NDVI-Soil_{bg})-0.162)\times PAR_{TOA} \tag{10}\]  
Being \(Soil_{bg}\) the soil background coefficient (\(Soil_{bg}=0.161\)) obtained from the linear regression model between MODIS _NDVI_ and _GPP_. The soil background coefficient was the intercept of the line, that is, the value of _NDVI_ when GPP was zero. Although the linear regression model showed a poor adjustment, we believe that this coefficient was important to compare the model proposed by [PERSON] et al. (2017). The time series obtained for this model (_GPP_M1_) from January 2018 to July 2020 versus the tower GPP (GPP_T) is shown in Figure 5. As it is observed, the model underestimated the GPP during the study period. The RMSE for the study period was 2.78 g C m\({}^{-2}\) day\({}^{-1}\). The validation of the model was performed using the year 2020, obtaining an R\({}^{2}=0.78\) and a RMSE of 2.66 g C m\({}^{-2}\) day\({}^{-1}\). Figure 6 shows the values of GPP_M1 versus the values of GPP. T:  
Figure 5: Time series obtained for the Gross Primary Production MODIS model (GPP_M1) from January 2018 to July 2020 versus the tower Gross Primary Production (GPP_T) in the Mediterranean grassland of La Herreria. The second model (GPP_M2) was a multiple linear regression model with three parameters: (1) NDVI \(\times\) PAR\({}_{\text{TOA}}\), (2) T\({}_{\text{min}}\), and (3) SWC, as Equation (7) shows. The result of the analysis of variance (ANOVA) is shown in Table 2.  
Table 3 shows the estimated coefficients of the model and their significance according to the T-statistic: \begin{table}
\begin{tabular}{c c c c c c} \hline
**Source** & **Sum of** & **Degrees of** & **Mean Square** & **F-Statistic** & _p-Value_ \\  & **Squares** & **Freedom** & **Mean Square** & **F-Statistic** & _p-Value_ \\ \hline Model & 560.466 & 3 & 186.822 & 325.84 & 0 \\ Residual & 50.4555 & 88 & 0.573 & & \\ TOTAL & 610.921 & 91 & & & \\ \hline \end{tabular}
\end{table} 
Table 2: Analysis of variance (ANOVA) of the multiple regression model: \(GPP\_M2=a_{0}+b\times(NDVI\times PAR_{TOA})+c\times T_{min}+d\times SWC\) from January 2018 to December 2019 in the Mediterranean grassland. Figure 6: Values for the Gross Primary Production MODIS model 1 (GPP_M1) versus the tower Gross Primary Production (GPP_T) for the year 2020 (January to July) in the Mediterranean grassland of La Herreria (\(n=25\), R\({}^{2}=0.78\), ANOVA _p_-value = 0.00). \begin{table}
\begin{tabular}{c c c c c} \hline
**Coefficient** & **Estimation** & **Standard Error** & **T-Statistic** & _p-Value_ \\ \hline Constant (a\({}_{0}\)) & \(-5.148\) & 0.541 & \(-9.522\) & 0 \\ NDVI \(\times\) PAR\({}_{\text{TOA}}\) (b) & 1.214 & 0.047 & 25.951 & 0 \\ T\({}_{\text{min}}\) (c) & 0.091 & 0.025 & 3.609 & 0.001 \\ SWC (d) & 12.859 & 1.617 & 7.951 & 0 \\ \hline \end{tabular}
\end{table} 
Table 3: Estimated coefficients of the multiple regression model: \(GPP\_M2=a_{0}+b\times(NDVI\times PAR_{TOA})+c\times T_{min}+d\times SWC\), standard error of the coefficients and T-statistic from January 2018 to December 2019 in the Mediterranean grassland.