**4. Results**

#### *4.1. Spatial Representativeness Determined by Sill Value*

A paired t-test was performed on the sill value for each set of paired TM and MODIS data. The spatial variation was determined according to the criterion that if the *p*-value was zero, it confirmed the null hypothesis—land surface variation at adjacent scales was not different, and the pixel can represent the larger scale scape. For all data pairs, the histogram of spatial variation is shown in Figure 2. The median value was also used as the indicator of effective spatial resolution, as in Campagnolo et al. [41]. In this situation, the median value was 2, which suggests that the variation in the land surface was subtle within the 21 × 21 TM scale, and the proper aggregation scale for TM albedo data was 21 × 21 pixels. The 21 × 21 aggregation scale represented a 630 m spatial scale, which is consistent with the result of [41].

Table 3 shows the proper aggregation scale for every land cover type of AmeriFlux sites. For most land cover types, the land surface was stable within 21 × 21 TM pixels, and for mixed forest and croplands, the proposed effective spatial resolution was 690 m (approximately 23 × 23 TM pixels).

**Table 3.** Spatial representativeness of MODIS 500 m albedo product for different land cover types.


*4.2. Spatial Representativeness Determined by Relative Coefficient of Variation*

Figure 3 shows the histogram of the *RCV* at each scale. To depict the spatial variation at adjacent scales, the *RCV* was computed from the CV values at each adjacent scale. The median value was calculated as in Figure 3 to describe the integral spatial variation at each scale. From Figure 3, we can see that *RCV*1, which represents the *RCV* of the first scale, was the largest for all scales. This means that the spatial variation between scale 1 (15 × 15 TM pixels) and scale 2 (21 × 21 TM pixels) was significant. The median values of *RCV*2 and *RCV*4 were small, which means that the effective spatial resolution should have been 630 m or 870 m. The conclusion was partly consistent with that of the t-test on the sill values. However, the step sizes of the scales were different: for scales 1 and 2, the step was 6 TM pixels, but for scales 2 and 3, it was only 2. Hence, the low level of the variation in the sill value and the small value of the *RCV* could have been deduced from the small step size. To verify this conclusion, we then reduced the analysis step size and aggregated the TM data at different scales to explore the proper representative scale.

**Figure 3.** Histogram of *RCV* at (**a**)–(**h**): scale 1–scale 8. The median is the median value of *RCV* at each scale.

#### *4.3. Spatial Representativeness Determined by Direct Comparison*

We refined the step size to find the highest correlation coefficient between TM and MODIS to determine the proper aggregation scale and use it as the representative spatial scale of MODIS data. The step size was set to 2 TM pixels. Figure 4 shows that the coefficient varied with aggregation scale. TM data were aggregated from 15 × 15 to 61 × 61 TM pixels. From Figure 4 we can see that when 23 × 23 TM pixels were aggregated, the correlation coefficient was the highest and the root mean squared error was the lowest compared with MODIS data. This corresponds to the results in Table 3 in some degree.

**Figure 4.** *R*<sup>2</sup> variation with aggregation scale.

We then checked the comparative accuracy of different land cover types. Table 4 shows the accuracy of comparison in different land cover types at the suggested aggregation scale according to Table 3. For all the land cover types, the RMSE was less than 0.03 and bias less than 0.018. The *R*<sup>2</sup> of evergreen broadleaf forests was the lowest, mainly because the land surface of this type was snow free, and all albedo values clustered together. For all other land cover types, the *R*<sup>2</sup> value was higher than 0.86, and for croplands, it reaches 0.965.


