## 3 Results
### Surface Soil Moisture and FAPAR
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Site Name**} & \multicolumn{2}{c}{**Prior**} & \multicolumn{2}{c}{**sm+fapar (Multi)**} & \multirow{2}{*}{**Data Duration**} & \multirow{2}{*}{**Observations**} \\ \cline{2-2} \cline{5-6}  & **R\({}^{2}\)** & & & & & \\ \hline AU-DaS & 0.58 & 6.02 & 1.72 & \(-51.50\) & 2010–2014 & 1826 \\ CA-Gro & 0.02 & 2.95 & 350.00 & 64.41 & 2010–2012 & 151 \\ CN-Sw2 & 0.25 & 2.72 & 112.00 & \(-25.37\) & 2011 & 260 \\ DK-Sor & 0.001 & 1.79 & 7900.00 & \(-6.15\) & 2014 & 306 \\ ES-LMa & 0.51 & 1.93 & \(-23.53\) & \(-22.80\) & 2010–2011 & 418 \\ FI-Sod & 0.06 & 2.18 & \(-16.67\) & 6.42 & 2010–2014 & 427 \\ FR-Pue & / & / & / & / & / & / \\ NL-Loo & 0.16 & 3.31 & 106.25 & 105.14 & 2010–2014 & 1826 \\ US-Kfs & / & / & / & / & / & / \\ US-Wkg & 0.07 & 2.51 & 100.00 & \(-23.51\) & 2010–2014 & 1826 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: R\({}^{2}\) and RMSE relative changes (%) to prior simulation for site soil moisture calculated against in-situ observations when SMOS soil moisture and FAPAR were assimilated simultaneously in multi-site case, denoted as sm+fapar (multi). \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Site**} & \multirow{2}{*}{**Prior**} & \multicolumn{2}{c}{**sm**} & \multirow{2}{*}{**sm**} & \multirow{2}{*}{**fapar**} & \multirow{2}{*}{**sm+fapar**} & \multirow{2}{*}{**sm+fapar**} \\  & & **(Single)** & **(Multi)** & **(Single)** & **(Multi)** & **(Single)** & **(Multi)** \\  & & \(\mathbf{J_{sm}}\)/\(\mathbf{J_{p}}\) & \(\mathbf{J_{sm}}\)/\(\mathbf{J_{p}}\) & \(\mathbf{J_{sm}}\)/\(\mathbf{J_{p}}\) & \(\mathbf{J_{sm}}\)/\(\mathbf{J_{p}}\) & \(\mathbf{J_{sm}}\)/\(\mathbf{J_{p}}\) \\ \hline AU-DaS & 6427.59 & 1709.51/ & 2327.26/ & 6427.50/ & 5441.92/ & 1995.35/ & 2362.50/ \\  & & 686.77 & 420.94 & \(4.09\times 10^{-7}\) & 61.23 & 103.94 & 855.25 \\ CA-Gro & 2337.51 & 1710.34/ & 2467.87/ & 2232.91/ & 2376.47/ & 2788.61/ & 2514.53/ \\  & & 71.84 & 420.94 & 1.65 & 61.23 & 73.95 & 855.25 \\ CN-Sw2 & 173.31 & 58.08/ & 150.37/ & 91.81/ & 117.14/ & 74.86/ & 119.34/ \\ DK-Sor & / & 4.26 & 420.94 & 10.12 & 61.23 & 11.22 & 855.25 \\ DK-Sor & / & / & / & / & / & / \\ ES-LMa & 3250.70 & 1387.87/ & 1531.16/ & 2693.86/ & 2652.02/ & 1430.91/ & 1587.30/ \\ FI-Sod & / & 17.42 & 420.94 & 6.08 & 61.23 & 68.65 & 855.25 \\ FI-Sod & / & / & / & / & / & / \\ FR-Pue & 78.90 & 30.02/ & 30.49/ & 79.42/ & 79.43/ & 27.88/ & 34.06/ \\  & & 46.75 & 420.94 & \(1.78\times 10^{-2}\) & 61.23 & 68.82 & 855.25 \\ NL-Loo & 1086.33 & 993.63 & 1481.05/ & 1074.89/ & 1073.81/ & 1114.38/ & 1463.87/ \\  & & 39.62 & 420.94 & 0.32 & 61.23 & 671.33 & 855.25 \\ US-Kfs & 3860.16 & 2059.81/ & 2250.26/ & 3124.62/ & 5556.66/ & 2147.11/ & 2372.94/ \\  & & 27.34 & 420.94 & 9.85 & 61.23 & 51.93 & 855.25 \\ US-Wkg & 4500.40 & 2370.63/ & 2443.57/ & 4542.53/ & 4472.81/ & 2371.58/ & 2352.95/ \\  & & 22.16 & 420.94 & \(5.07\times 10^{-2}\) & 61.23 & 21.13 & 855.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Cost function values for soil moisture (\(J_{sm}\)) and parameters (\(J_{p}\)) for prior and different assimilation experiments, ‘sm’ with soil moisture only, ‘fapar’ with FAPAR only, ‘sm+fapar’ with soil moisture and FAPAR data combined, ‘multi’ denotes multi-site assimilation, and ‘single’ denotes single-site assimilation. Similarly, \(J_{ippar}\) values are shown in Table 5. In the'sm' experiment, \(J_{ippar}\) values did not decrease much or even increase in comparison to the prior simulation. The smallest \(J_{ippar}\) values among the three experiments were achieved for the single-site assimilation, except for sites, FR-Pue, NL-Loo, and US-Wkg. For these sites, the cost function values for parameters (\(I_{p}\)) were much smaller, which resulted in smaller total cost function values (\(J_{total}\)) in the single-site optimizations. In the 'fapar' case, single-site assimilation achieved smaller \(J_{fapar}\) than multi-site assimilation.