## 3 Results
### Surface Soil Moisture and FAPAR  
We calculated the cost function, \(J\), over the simulation period both for the prior and the various posterior results to have a quantitative measure for the improvements obtained by the different assimilation experiments. We used the cost function as a performance metric for the assimilation because the cost function also considers the observation uncertainty (Equation (1)). Therefore, it was more suitable for quantifying the model performance with respect to the different variables. Table 3 summarizes the cost function values for soil moisture (denoted as \(J_{sm}\) hereafter). Generally, the assimilation of the satellite datasets improved the model performance with respect to soil moisture. However, improvements differed between sites and depended sensitively on the assimilated dataset. As shown in Table 3, assimilation of soil moisture alone or simultaneously with FAPAR achieved the best performance in simulating soil moisture as indicated by the smallest \(J_{sm}\) values. Assimilating FAPAR only ('fapar') resulted in a larger \(J_{sm}\), and thus inferior results for the simulated soil moisture than the other experiments for both single-site and multi-site cases. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **sm** & **fapar** & **sm+fapar** \\ \cline{2-4}
**Site** & **Cost Function Reduction** & **Cost Function Reduction** & **Cost Function Reduction** \\  & **(\%)** & **(\%)** & **(\%)** \\ \hline AU-DaS & 55.58 & 0 & 53.84 \\ CA-Gro & 22.39 & 26.83 & 21.78 \\ CN-Sw2 & 65.61 & 57.82 & 69.28 \\ DK-Sor & / & 55.04 & / \\ ES-LMa & 40.92 & 34.46 & 35.52 \\ FI-Sod & / & 54.65 & / \\ FR-Pue & 16.88 & 1.38 & 32.59 \\ NL-Loo & 15.3 & 19.88 & 16.37 \\ US-Kfs & 51.88 & 86.12 & 52.79 \\ US-Wkg & 31.07 & 7.74 & 31.2 \\ Multi-site * & 35.27 & 55.06 & 49.49 \\ \hline \hline \end{tabular}  
* ‘Multi-site’ denotes multi-site assimilation.  
\end{table} 
Table 2: Summary of optimization results on cost function and gradient reduction for different assimilation experiments, ‘sm’ denotes soil moisture dataset, ‘fapar’ denotes FAPAR dataset, ‘sm+fapar’ denotes simultaneous assimilation soil moisture and FAPAR. In addition, we validated the posterior surface soil moisture values against in-situ soil moisture observations at eight sites from the FLUXNET2015 dataset and calculated the relative changes in R\({}^{2}\) (determination coefficient) and RMSE (Root Mean Squared Error), shown in Table 4. For seven of the sites, either the R\({}^{2}\) was improved (positive relative change values), or RMSE was improved (negative relative change values), or both R\({}^{2}\) and RMSE were improved (four sites). As shown in Figure 2, at the site, US-Wkg, the RMSE for soil moisture reduced from 2.51 mm in the prior case to 1.92 mm in the posterior case. For the site, FI-Sod, located at high latitudes, with very limited observations available (427 observations during 2010-2015), both R\({}^{2}\) and RMSE were not improved in the posterior case compared to the prior. The simultaneous assimilation of SMOS soil moisture and JRC-TIP FAPAR in the multi-site case was shown to improve not only carbon fluxes, but also, as expected, the soil moisture content in the surface layer.