## 3 Results
### Spatial Downscaling of the SM Dataset  
Table 6 shows the explanatory power of three regression models for TC estimation. Similar to the Landsat dataset, the highest \(R^{2}\) value was obtained via RF across almost all months. LR achieved the lowest explanatory power and also showed very low \(R^{2}\) values for some months (e.g., October 2015 and 2017). The \(R^{2}\) values of LR and RF were negatively correlated with the mean of the actual observation values (\(-0.568\) for both models), which means that auxiliary variables were insufficient to account for humid soil conditions. In contrast, SVR showed a positive correlation with the mean of observation values (0.591), which affected the predictive performance of the spatial downscaling results. Table 7 presents the MAE values of all comparison cases between 2015 and 2017. The accuracy values of the input AMSR-2 SM data are also presented to compare the impact of input errors on prediction accuracy. All cases showed negative mean error values (not shown here), which indicates an underestimation of the observation values. This underestimation resulted from the direct comparison of areal values with point observations, as well as the actual underestimation of satellite products. The TC estimates with SVR (C1_SVR) achieved the best prediction accuracy for most months (13 out of 18 months). This result is similar to the result of the Landsat dataset, that is, the TC estimat \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Year** & **Month** & **LR** & **RF** & **SVR** \\ \hline \multirow{8}{*}{2015} & May & 32.67 & 88.31 & 75.61 \\  & June & 46.59 & 91.69 & 84.22 \\  & July & 33.81 & 90.48 & 84.99 \\  & August & 30.57 & 89.68 & 91.87 \\  & September & 39.36 & 90.00 & 79.25 \\  & October & 6.24 & 85.56 & 83.26 \\ \hline \multirow{8}{*}{2016} & May & 22.57 & 86.11 & 79.01 \\  & June & 44.82 & 90.68 & 76.79 \\ \cline{1-1}  & July & 22.29 & 88.56 & 79.58 \\ \cline{1-1}  & August & 28.02 & 88.53 & 82.20 \\ \cline{1-1}  & September & 28.13 & 90.13 & 84.85 \\ \cline{1-1}  & October & 28.21 & 90.80 & 90.45 \\ \hline \multirow{8}{*}{2017} & May & 22.80 & 85.71 & 72.40 \\ \cline{1-1}  & June & 46.88 & 89.90 & 69.28 \\ \cline{1-1}  & July & 28.35 & 91.13 & 89.47 \\ \cline{1-1}  & August & 17.09 & 86.85 & 89.22 \\ \cline{1-1}  & September & 29.39 & 87.69 & 73.65 \\ \cline{1-1}  & October & 14.06 & 89.34 & 87.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Coefficient of determination (\(R^{2}\)) values of three regression models for the SM dataset (unit: %). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Error Level** & **Case** & **MAE** & **MRAE** & **Error Level** & **Case** & **MAE** & **MRAE** \\ \hline \multirow{8}{*}{E1} & C1\_LR & 0.019 & 13.88\% & & C1\_LR & 0.019 & 13.91\% \\  & C2\_LR & 0.015 & 11.21\% & & C2\_LR & 0.033 & 24.61\% \\  & C1\_RF & 0.016 & 11.59\% & & C1\_RF & 0.020 & 13.42\% \\  & C2\_RF & 0.015 & 10.86\% & & C2\_RF & 0.027 & 20.24\% \\  & C3\_RF & 0.015 & 10.98\% & & C3\_RF & 0.035 & 25.97\% \\  & C1\_SVR & 0.015 & 11.06\% & & C1\_SVR_ & **0.015** & **11.22\%** \\  & C2\_SVR & 0.015 & 10.78\% & & C2\_SVR & 0.033 & 24.44\% \\  & **C3\_SVR** & **0.014** & **10.46\%** & & C3\_SVR & 0.033 & 24.60\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._the input data contained severe errors. The following best predictions were produced by the TC estimates with RF (3 out of 18 months). In most cases, LR-based ATPRK (C2_LR) and RF-based ATPRK with TC normalization (C3_RF) showed the worst accuracy. For example, C2_LR and C3_RF for August 2016 exhibited decreases of 86% and 61% in MAE, respectively, compared to the best case (C1_SVR). In particular, the MAE values of those predictions were worse than those of the input data, indicating that input errors were amplified after spatial downscaling. The MRAE was found to be more effective than the MAE because it allowed for relative comparisons of SM values that vary over time. Figure 3 presents the variations of MRAE values for all comparison cases over the considered period.