## 4 Results and Discussion
### Accuracy Assessment Under the Best Parameters Setting  
For the green band at the optimal window size (\(W\) = 31 \(\times\) 31), the \(\gamma\) = 0.91 of the USTARFM method is higher than those of the STARFM (0.89) and the unmixing method (0.82); meanwhile, USTARFM shows the lowest error (RMSE = 0.0116) compared to the prediction of the STARFM (RMSE = 0.0127) and the unmixing method (RMSE = 0.0182); ERGAS shows the same trend (1.1502 \(vs.\) 1.2559 \(vs.\) 1.8052, respectively).  
Figure 3 shows the scatterplots between reflectance estimate from USTARFM, STARFM and unmixing based method, with the optimized parameter setting, (\(W\), \(k\)) and \(w\), and the corresponding reference bands of Landsat 8 image. USTARFM inspired from STARFM improves the performance of central pixel reflectance estimation by weighting the neighboring similar pixels within the moving window, which reflected the spatial variability well, producing scatter point distributions close to 1:1. The \(\gamma\) of each band of images generated by USTARFM and STARFM is superior to that of the unmixing method, by about 0.02. The reason is that the reflectance calculated by the unmixing method is the mean reflectance of each clustered class within the window, which blurs the spatial heterogeneity and makes the scatterplot appear in \"stripe\" pattern (Figure 3g-i). Generally, the images at Landsat-like image predicted by the USTARFM are more accurate than those derived from the STARFM and the unmixing methods.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**Window Size \(\varpi\)**} & \multicolumn{2}{c}{\(\gamma\)} & \multicolumn{2}{c}{**RMSE**} & \multicolumn{2}{c}{**ERGAS**} \\ \cline{2-10}  & \(\mathbf{n\times n\) OLI Pixels} & **Green** & **Red** & **NIR** & **Green** & **Red** & **NIR** & **Green** & **Red** & **NIR** \\ \hline \multirow{6}{*}{STARFM} & 7 & 0.8822 & 0.8926 & 0.9416 & 0.0130 & 0.0172 & 0.0373 & 1.2823 & 1.8061 & 0.8088 \\  & 11 & 0.8880 & 0.8987 & 0.9394 & 0.0130 & 0.0172 & 0.0351 & 1.2865 & 1.8129 & 0.7611 \\  & 31 & 0.8895 & 0.9000 & 0.9489 & 0.0127 & 0.0170 & 0.0300 & **1.2599** & **1.7916** & **0.6507** \\  & 61 & 0.8844 & 0.8948 & 0.9490 & 0.0131 & 0.0176 & 0.0302 & 1.2968 & 1.8498 & 0.6553 \\ \cline{2-10}  & 101 & 0.8804 & 0.8931 & 0.9474 & 0.0133 & 0.0177 & 0.0309 & 1.3117 & 1.8673 & 0.6702 \\  & 151 & 0.8792 & 0.8912 & 0.9475 & 0.0133 & 0.0179 & 0.0310 & 1.3147 & 1.8782 & 0.6735 \\ \hline \multirow{6}{*}{USTARFM} & 7 & 0.9116 & 0.9226 & 0.9600 & 0.0118 & 0.0151 & 0.0260 & 1.1678 & 1.5876 & 0.5654 \\  & 11 & 0.9129 & 0.9229 & 0.9631 & 0.0116 & 0.0151 & 0.0249 & **1.1502** & **1.8550** & 0.5416 \\ \cline{1-1}  & 31 & 0.9121 & 0.9192 & 0.9650 & 0.0117 & 0.0154 & 0.0245 & 1.1550 & 1.6242 & **0.5317** \\ \cline{1-1}  & 61 & 0.9106 & 0.9171 & 0.9650 & 0.0117 & 0.0156 & 0.0245 & 1.1564 & 1.6437 & 0.5326 \\ \cline{1-1}  & 101 & 0.9094 & 0.9158 & 0.9650 & 0.0117 & 0.0158 & 0.0246 & 1.1615 & 1.6572 & 0.5334 \\ \cline{1-1}  & 151 & 0.9083 & 0.9145 & 0.9650 & 0.0118 & 0.0159 & 0.0246 & 1.1671 & 1.6700 & 0.5341 \\ \hline \hline \end{tabular} Note: Underlined bold values indicate the best value to determine the optimal window size (\(p\)-value < 0.001).  
\end{table}
Table 3: The accuracy of the STARFM and USTARFM at different window size scales.