## 5 Discussion
### Effect of Land Surface Heterogeneity  
We then focused the analysis on tower located pixel for each site. For each scene, the semivariogram was calculated, from 15 \(\times\) 15 to 77 \(\times\) 77 TM pixels at a step of 2 TM pixels. Figure 6 shows the heterogeneous number of scenes at each step (sill value larger than 0.001). On average, 257 scenes were heterogeneous on 42 sites.  
We divided the heterogeneous landscape into three types. Figure 7 shows the general land surfaces and their spatial variations. Figure 7A shows a cropland from US-Ne3 site, located at the center of a rain-fed maize-soybean rotation field. The crop had been harvested, and only bare soil was explored in the scene. The trend in the variation in sill value was not significant with increasing scale. This meant that although the landscape was heterogeneous, the magnitude of heterogeneity at the scales was stable. The difference between the MODIS and the TM values decreased with increasing scale. In this case, with the scale enlarged, the influence of land surface heterogeneity diminished. The MODIS pixel represents an area much larger than its nominal resolution.  
Figure 7B shows a US-Fmf site. This was an evergreen needleleaf forest site. The land surface heterogeneity was mainly due to the snow in the upper-right corner. With increasing scale, the land surface became more heterogeneous and the sill value increased from 0.0034 to 0.0059. The discrepancy between MODIS and aggregated TM pixels increased accordingly. For this situation, we may conclude that the more heterogeneous the land surface is, the greater the discrepancy is.  
Figure 7C is CA-Fuf site. It is an evergreen needleleaf forest site not far from the US-Fmf site. The land surface heterogeneity was much higher than in the former two scenes, mainly due to the irregular surface and snow. The discrepancy between MODIS and TM albedo was correspondingly significant. In this case, we can hardly determine the effective spatial representativeness of the pixel.  
Land surface heterogeneity is a key factor affecting effective spatial representativeness. In general, the more heterogeneous the land surface is, the larger the effective spatial representativeness is. When the magnitudes of land surface heterogeneity at different scales are similar, with the scale increased, land surface homogeneity increases.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Scale** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** \\ \hline TM pixels & 15 \(\times\) 15 & 21 \(\times\) 21 & 23 \(\times\) 23 & 29 \(\times\) 29 & 31 \(\times\) 31 & 39 \(\times\) 39 & 47 \(\times\) 47 & 61 \(\times\) 61 \\ \(R^{2}\) & 0.944 & 0.9437 & 0.943 & 0.9404 & 0.9395 & 0.9354 & 0.9309 & 0.9207 \\ RMSE & 0.0239 & 0.0238 & 0.0238 & 0.024 & 0.0241 & 0.0243 & 0.0245 & 0.0248 \\ BIAS & 0.0117 & 0.0117 & 0.0116 & 0.0115 & 0.0114 & 0.011 & 0.0103 & 0.0081 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparative accuracy of MODIS albedo and TM data aggregated with PSF.  
Figure 6: Number of heterogeneous scenes at each scale from 15 \(\times\) 15 to 77 \(\times\) 77 TM pixels at a step of 2 TM pixels.