## 3 Algorithm Test
### Implementation Procedure  
The ISODATA algorithm was applied to cluster a Landsat image collected August 19, generating land cover component maps with class number (\(k\)) as [5; 10; 15; 20; 25; 30]. Two kinds of window scales which have pronounced impacts on the performance of the USTARFM method are concerned: the optimized window (\(W\), MODIS pixel) for unmixing MODIS spectrum and the window (\(w\), Landsat pixel) of searching the similar pixels for STARFM and USTARFM. For the \(W\), a series of window size scales, [\(5\times 5\), \(7\times 7\), \(11\times 11\), \(15\times 15\), \(21\times 21\), \(31\times 31\), \(41\times 41\)], are used to unnix the MODIS data acquired on Aug. 19 at different class numbers, respectively. Next, the correlation coefficient (\(\gamma\)), RMSE and ERGAS were iteratively tested to unmix MODIS images to achieve the best results. This was completed as the popular benchmark to measure the difference between the reference Landsat 8 image and the unmixing data at different window sizes (\(W\)) and class number (\(k\)), and the optimal combination of the two parameters. An assumption considered here was that the relationship between land surface and landscape derived from the Landsat data are stable under the condition of the same area and same sensor [31]. So, the optimal window size determined from the 19 August 2014 images was inherited and further used to unmix the MODIS data acquired on 4 September 2014. The unmixing data for 19 August 19 and 4 September 2014 and the base date Landsat 8 data for 19 August 2014 were used together to predict the Landsat-like images on 4 September 2014 by weighting the similar pixels within a certain window size. The window sizes \(w\) (Landsat OLI pixel) were set as [\(7\times 7\), \(11\times 11\), \(31\times 31\), \(61\times 61\), \(101\times 101\), \(151\times 151\)].  
The performance of the synthetic images were assessed using the correlation coefficient (\(\gamma\)) and \(p\)-value, RMSE, and ERGAS metrics [20; 22]. The \(\gamma\) indicates the linear correlativity between fusion data and the reference data, and higher \(\gamma\) values represent better correlation between synthetic images and reference images; lower RMSE values show the lower fusion errors of synthetic images. In addition, ERGAS is a common comprehensive evaluation index for assessing the quality of a synthetic image which is able to quantity the spatial similarity degree of the fusion image and reference image [18; 37]. These assessment metrics have different focus to show the performance of the synthetic images as shown in Equations (4)-(6):  
\[\gamma=\frac{\sum\limits_{j=1}^{N}\left(x_{j}-\overline{x}\right)\left(y_{j} -\overline{y}\right)}{\sqrt{\sum\limits_{j=1}^{N}\left(x_{j}-\overline{x} \right)^{2}\cdot\sum\limits_{j=1}^{N}\left(y_{j}-\overline{y}\right)^{2}}} \tag{4}\]  
\[\text{RMSE}=\sqrt{\frac{\sum\limits_{j=1}^{N}\left(x_{j}-y_{j}\right)^{2}}{N}} \tag{5}\]  
where \(N\) refers to the pixels number of fine-resolution image; \(x_{j}\) and \(y_{j}\) refer to the \(j_{th}\) pixel values of the synthetic and reference images, respectively; and \(\overline{x}\) and \(\overline{y}\) are the mean value of synthetic data and reference data, respectively. ERGAS is calculated as:  
\[\text{ERGAS}=100\frac{H}{L}\sqrt{\frac{1}{N_{ban}}\sum\limits_{i=1}^{N_{ban}} \left(RMSE_{i}/M_{i}\right)^{2}} \tag{6}\]  
where \(H\) is the fine-resolution pixel size, such as 30 m; \(L\) is the coarse-resolution pixel size (480 m); \(N_{ban}\) refers to the band number; \(RMSE\) refers to the \(i_{th}\) band between the synthetic and reference data; and \(M_{i}\) refers to the mean spectrum value of reference data in \(i_{th}\) band.