## 4 Results and Discussion  
### Algorithm Performance Analysis Influenced by W, k and w  
We tested whether USTARFM is an improved STARFM algorithm and compared the results with STARFM to determine whether improvements could be obtained from this algorithm.  
The unmixed image as traditional Unmixing model is also produced during the USTARFM process, so we put the three fusion methods together to achieve a more comprehensive understanding of the synthetic image performance. Table 2 shows the performances of the three fused methods with varying \(W\) and \(k\) settings using the metrics of \(\gamma\), RMSE and ERGAS as benchmarks to determine the optimal combination of window size and class number for unmixing MODIS images (the best options are underlined and bold in Table 2). For the green and red bands, the optimal combination of window size (\(W\)) and class number is 31 \(\times\) 31 and 10, and for NIR, the window size (\(W\)) and class number are 31 \(\times\) 31 and 5, respectively. Considering that the metrics for the NIR band are similar to the green and red band, and more classes are feasible to guarantee class features uniform, we chose the window size  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Date**} & \multirow{2}{*}{\(W\)} & \multirow{2}{*}{\(k\)} & \multicolumn{3}{c}{\(\gamma\)} & \multicolumn{3}{c}{RMSE} & \multicolumn{3}{c}{ERGAS} \\ \cline{3-11}  & & & **Green** & **Red** & **NIR** & **Green** & **Red** & **NIR** & **Green** & **Red** & **NIR** \\ \hline \multirow{8}{*}{\(7\)} & \multirow{8}{*}{\(7\)} & \multirow{8}{*}{\(15\)} & 0.69 & 0.74 & 0.92 & 0.0204 & 0.0233 & 0.0378 & 2.0467 & 2.6494 & 0.7457 \\  & & & 10 & 0.64 & 0.70 & 0.86 & 0.0218 & 0.  
of 31 \(\times\) 31 MODIS pixels and the class number of 10 as the optimal combination for further unmixing MODIS data acquired Sept. 4.  
From the above analysis, the \(W\) and \(k\) were determined. The next step was to focus on how to calculate \(w\) for USTARFM. Table 3 shows the performance of the USTARFM and STARFM methods at different window sizes (\(w\)) to search the similar pixels for the central pixel. The USTARFM algorithm achieves the optimal effect when the window size \(w\) is 11 \(\times\) 11 OLI pixels for red and green bands, and 31 \(\times\) 31 OLI pixels for the NIR band. Compared to 31 \(\times\) 31 for the STARFM, the difference of optimal window size between NIR and visible bands may be caused by their reflectance characteristics which affect the similar pixels search efficiency. Relative to NIR, the green and red are the short-wave bands, which are sensitive to weather related factors, such as haze.  
Though the atmosphere process has been applied for MODIS data, the atmosphere effects cannot be entirely removed [38]. For the other two bands, the indices for the three methods have the same trend as the green band. Table 3 also illustrates that the best window size of USTARFM is smaller than that of STARFM, and at the same window size, the three indices of USTARFM are also better than those of STARFM. This is mainly because the unmixing data used in USTARFM is efficient to reflect the surface reflectance comparing to the directed resampled data used in STARFM.