## 4 Results and Discussion
### Landscape Heterogeneity Impact on USTARFM Performance  
The heterogeneity over the regions where complex mixtures of land-cover type commonly exist represents a big challenge for STARFM to identify pure pixels [25; 30]. To analyze the performance of the USTARFM algorithm in a complex landscape, the MODIS pixel scale, 480 m \(\times\) 480 m, was defined as a grid to divide the study area, and each grid was marked according to its heterogeneous degree. Here, we developed the degree of heterogeneity (\(h\)) metric using the clustered of thematic map from the Landsat 8 image as described in Equation (7). This idea is based on the quantity of land cover classes in one grid. More than one class type in one grid implies a higher degree of heterogeneity. If (\(N_{c}>0\)) (\(N_{c}\) is the pixel number of class \(c\)) is a determinant function to judge whether class \(c\) appears in the grid. \(P\) is marked as 1 if \(N_{c}\) is more than 1:  
\[h=\sum_{c=1}^{Num}\left(P,if(N_{c}>0)\right) \tag{7}\]  
_Num_ is the total class in the thematic map, here maximum number of the land cover type is 10. From this definition of the heterogeneity metric, the heterogeneity level of a grid with only one class is defined as 1 which represents the lowest heterogeneous degree. Otherwise, the higher the number of classes that appear in a pixel, the higher the degree of heterogeneity. The highest level of heterogeneity assigned was 10 (Figure 4). From Figures 2 and 4 it can be seen clearly that the areas  
Figure 3: Scatterplots of the real reflectance and the predicted product produced by the three algorithms for the green, red and NIR-infrared bands. of higher heterogeneity are distributed from the north east to south west area where fragmented cultivated land is common. The areas of lower heterogeneous grids were concentrated in the northwest which is dominated by larger cultivated fields. Figure 5 shows the RMSE and \(\gamma\) of Green, Red and NIR data generated by the three fused methods at different heterogeneity levels. For the three bands, the change trend decreases is accompanied by the heterogeneity degree increases, highlighting that the heterogeneity is a sensitive variable for the STARFM and has side-effects on the performance of the proposed method. However, an interesting result is that higher performance was achieved from USTARFM than those of STARFM at each heterogeneity level, except for level one (Figure 5a-d). Figure 4: The distribution of different heterogeneity levels in the study area. (**a**) class types within a grid (MODIS pixel scale), (**b**) the heterogeneity levels of MODIS pixels. Table 4 analyzes the relationship of the unmixing and resampled MODIS data at different heterogeneity levels to the Landsat reference data on 4 September 2014, which illustrates why USTARFM is superior to the STARFM. The relationship was obviously higher from 2 to 10 level, consistent with the trend of USTARFM trend. This is because the unmixing data instead of directed sampling data as basis for USTARFM can describe the mixed landscape clearly, especially in the higher heterogeneity level area, while the resampled method just offer the STARM uniform spot without reflecting the land cover heterogeneous characteristics. However, the areas at the heterogeneity level of 1 are special as the most homogeneous region, where STARFM has better performance. The USTARFM precedes the unmixing method but is inferior to STARFM for the green and red bands. Taking the result of the green band as an example, the RMSE and \(\gamma\) of the green band predicted by the STARFM are better than those for USTARFM (for green, RMSE: 0.0097 _vs._ 0.0102; \(\gamma\): 0.82 _vs._ 0.79). This is because the accuracy of the directly resampled data in the homogeneous area for the STARFM is better than the unmixing data for USTARFM (for green, \(\gamma\): 0.89 _vs._ 0.77; RMSE: 0.0102 _vs._ 0.0128) (Table 4), resulting in the lower accuracy of the proposed method. Figure 5: \(\gamma\) and RMSE of the three methods at different heterogeneity levels.