# Assimilation of Earth Observation Data Over Cropland and Grassland Sites into a Simple GPP Model
## Results
### Overall Agreement between Modelled and Observed GPP  
Density scatter plots of EC measured GPP vs. the GPP estimated by the Sim model and MOD17 are shown Figures 7 and 8 while main statistics are compared Table 4.  
Figure 7: Scatter plots of EC GPP versus GPP estimated by the Sim model for all sites (**A**), crop sites (**B**), and grassland sites (**C**). The dashed line is the 1:1 line while the continuous line is the ordinary least square linear regression. The following statistics are reported: coefficient of determination (R\({}^{2}\)), [PERSON]’s correlation coefficient (r), \(p\)-value of the linear regression, gain and offset of the linear regression line, Root Mean Square Error (RMSE), Mean Bias Error (MBE), and total number of data points (n). GPP estimated by the Sim model (Figure 7) tracks well the EC GPP with a RMSE of \(2.45\,\mathrm{gC}\,\mathrm{m}^{-2}\,\mathrm{d}^{-1}\) and a small bias (MBE) of \(-0.16\) when all sites are considered together. When considering the two ecosystem types separately, we observed that the RMSE error is slightly larger for crops (\(2.7\,\mathrm{gC}\,\mathrm{m}^{-2}\,\mathrm{d}^{-1}\)) than for grasslands (\(2.20\,\mathrm{gC}\,\mathrm{m}^{-2}\,\mathrm{d}^{-1}\)). The MBE is small, positive for crops (\(0.26\,\mathrm{gC}\,\mathrm{m}^{-2}\,\mathrm{d}^{-1}\)) and negative grasslands (\(-0.53\,\mathrm{gC}\,\mathrm{m}^{-2}\,\mathrm{d}^{-1}\)). The regression line is in all cases below the 1:1 line indicating a reduction of the variability of estimated GPP as compared to the measured one. Such an effect is larger for MOD17 estimates (Figure 8). Overall, Sim model estimates appears to overestimate EC GPP al low GPP levels and underestimate it at high GPP levels. It is noted that EC GPP can be negative, representing an obvious artifact of the partitioning algorithm (i.e., processing to determine total respiration). Nevertheless, we opted for keeping the EC measurements untouched. The agreement with EC measurements of GPP is larger for the Sim model with respect to MOD17. Sample scatter and deviation from the 1:1 line is in all cases smaller for the Sim model. Agreement statistics of the Sim Model and MOD 17 are reported in Table 4.  
Figure 9 shows the model reliability to predict the total annual GPP and confirms that the Sim model outperforms MOD17. Maize sites-years are highlighted in green to evaluate whether a negative bias exists for C4 crops (maize in our sample) as consequence of using a fixed value of \(\vare \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & \multicolumn{8}{c}{**Modelled vs. Observed**} \\ \hline  & \multicolumn{3}{c}{**All sites**} & \multicolumn{3}{c}{**Crops**} & \multicolumn{3}{c}{**Grasslands**} \\ \hline
**Model** & \(\mathbf{R^{2}}\) & **RMSE** & **MBE** & \(\mathbf{R^{2}}\) & **RMSE** & **MBE** & \(\mathbf{R^{2}}\) & **RMSE** & **MBE** \\ \hline MOD17 & \(0.53\) & \(3.15\) & \(-1.08\) & \(0.53\) & \(3.52\) & \(-0.97\) & \(0.55\) & \(2.79\) & \(-1.17\) \\ \hline Sim model & \(0.67\) & \(2.45\) & \(-0.16\) & \(0.68\) & \(2.70\) & \(0.26\) & \(0.68\) & \(2.20\) & \(-0.53\) \\ \hline \%variation & \(+26.42\) & \(-22.2\) & \(-85.19\)* & \(+28.3\) & \(-23.3\) & \(-73.2\)* & \(+23.64\) & \(-21.2\) & \(-54.7\)* \\ \hline \end{tabular}
\end{table} 
Table 4: Summary statistics of GPP estimation performances. \(\mathbf{R^{2}}\), RMSE, and MBE are derived from the scatter plots of Figures 7 and 8 and represent the coefficient of determination of the ordinary least square linear regression, the Root Mean Square Error and the Mean Bias Error, respectively. The percent variation refers to the statistic of the Sim model as compared to that of MOD17. * The percent variation on MBE is computed on absolute values. Figure 8: Scatter plots of EC GPP vs. GPP estimated by MOD17 for all sites (**A**), crop sites (**B**), and grassland sites (**C**).