## 3 Results
### Spatial Downscaling of the SM Dataset
The superior prediction accuracy of C1_SVR is clearly shown over time. The next best prediction was obtained by C2_SVR (12 out of 18 months). It is noteworthy that the accuracy values of most predictions, except for C3_RF and C2_LR, were superior to those of input AMSR-2 data when considering that spatial downscaling aims to predict fine-scale attribute values, not to produce results with superior accuracy to the input coarse resolution data. For the LR-based prediction, ATPRK had worse predictions than the TC estimate. When comparing three RF-based prediction results, the difference in MRAE between C1 and C3 was the largest. A relatively smaller difference was obtained between C1 and C2, indicating the lack of contribution of residual correction to the improvement in accuracy. Like the LR-based prediction, the accuracy of the TC estimation (C1) was better than the two ATPRK predictions (C2 and C3). Similar results were also observed for the SVR-based prediction. These results indicate that residual correction did not always improve prediction performance, particularly when the input data contained severe errors. Furthermore, ATPRK with the TC normalization degraded the prediction accuracy, compared to conventional ATPRK prediction. The impacts of both the explanatory power of regression models and input errors on predictive performance were further analyzed using correlation coefficients between accuracy values, and \(R^{2}\) and input errors were calculated for all prediction cases. All correlation coefficients between input errors and predictive accuracy values were statistically significant at the significance level of 1%. However, the correlation between accuracy and \(R^{2}\) values was not significant at the significance level of 5%, except for LR-based predictions \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Year**} & **Month** & **Input** & **C1\_LR** & **C1\_RF** & **C1\_SVR** & **C2\_LR** & **C2\_RF** & **C2\_SVR** & **C3\_RF** & **C3\_SVR** \\ \hline \multirow{4}{*}{2015} & May & 11.73 & 11.03 & 10.87 & **10.02** & 11.10 & 11.09 & 10.03 & 11.84 & 10.61 \\  & Jun. & 5.55 & 4.62 & **4.31** & 4.79 & 5.76 & 4.69 & 4.97 & 5.71 & 4.75 \\  & Jul. & 8.01 & 9.27 & **5.52** & 6.81 & 10.25 & 5.97 & 7.79 & 7.88 & 7.30 \\  & Aug. & 12.41 & 12.13 & 11.28 & **8.43** & 12.87 & 11.48 & 8.59 & 12.85 & 10.69 \\  & Sep. & 12.95 & 12.02 & 12.16 & **9.51** & 12.19 & 12.33 & 9.53 & 13.48 & 11.16 \\  & Oct. & 12.14 & 11.03 & 10.98 & **9.87** & 11.63 & 11.22 & 9.98 & 12.54 & 11.23 \\ \hline \multirow{4}{*}{2016} & May & 14.67 & 14.63 & 14.42 & 14.30 & 14.21 & 14.21 & **13.91** & 14.47 & 14.18 \\  & Jun. & 7.75 & 7.90 & 6.65 & **6.23** & 8.18 & 6.78 & 6.29 & 7.76 & 6.87 \\  & Jul. & 13.62 & 12.70 & 10.89 & **9.37** & 13.47 & 11.38 & 9.99 & 13.06 & 11.91 \\  & Aug. & 9.46 & 9.62 & 7.90 & **6.10** & 10.42 & 8.43 & 6.18 & 9.83 & 8.18 \\  & Sep. & 14.64 & 12.09 & 12.84 & **9.26** & 13.26 & 12.95 & 9.29 & 15.06 & 12.87 \\  & Oct. & 16.07 & 14.91 & 14.29 & **12.76** & 16.16 & 14.29 & 12.81 & 16.31 & 14.78 \\ \hline \multirow{4}{*}{2017} & May & 10.27 & 8.79 & 9.40 & **7.38** & 9.16 & 9.60 & 7.50 & 10.67 & 8.74 \\  & Jun. & 6.08 & 5.80 & **5.26** & 5.66 & 6.74 & 5.93 & 6.16 & 6.63 & 6.34 \\  & Jul. & 11.89 & 10.34 & 8.44 & **7.78** & 12.64 & 9.51 & 8.35 & 12.21 & 10.63 \\  & Aug. & 13.69 & 11.45 & 9.87 & **8.39** & 12.33 & 10.34 & 8.74 & 13.69 & 11.78 \\  & Sep. & 14.78 & **12.30** & 13.78 & 12.55 & 13.09 & 13.84 & 12.53 & 14.88 & 14.38 \\  & Oct. & 14.88 & 12.62 & 13.51 & **12.58** & 13.70 & 13.56 & 12.71 & 15.32 & 13.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Mean absolute error values of all comparison cases for the SM dataset. The best case per month is shown in bold. The case name can be referred to in Table 2.  
(C1_LR and C2_LR). Hence, only correlation coefficients between accuracy measures and errors of input SM data were considered (Figure 4). Strong correlations were observed between the input errors and predictive accuracy for all cases (Figure 4).