**5. Discussion**

#### *5.1. Errors Induced by Landsat Albedo Estimation and Spatial Discrepancy*

The Landsat albedo estimation algorithm has been validated on a variety of sensors and land cover types [15,16,44,58]. In this study, it was first calibrated using field observations. The errors induced by the estimation algorithm were hence eliminated.

In most cases, the sites were not located at the center of a MODIS pixel. Comparing the MODIS product with field observations or high-resolution data at the site tends to induce errors due to spatial discrepancy. In this study, high-resolution data were first calibrated with the field observations. When evaluating the spatial representativeness of the MODIS product, Landsat pixels located at the center of the MODIS pixels were selected, so the analysis focused on this area could guarantee the spatial agreemen<sup>t</sup> to the greatest extent.

#### *5.2. Difference Deduced by Upscaling Methods*

When upscaling finer-resolution data to a coarser resolution, the simple average method is generally used. Mira et al. [10] assessed an equivalent PSF based on image correlation analysis using an aggregated albedo convolved with PSF over an agricultural landscape. The results indicated that convolving the PSF can reduce uncertainty by up to 0.02 (10%). We checked the difference deduced by the upscaling method.

## 5.2.1. Simple Average Method

The TM value was first averaged then compared directly with the MODIS data. Figure 5 shows a comparison between the MODIS daily albedo data and the TM data. The results indicate that these datasets agreed well with RMSE less than 0.03 and *R*<sup>2</sup> greater than 0.92. Although the recommended aggregation scales were scale 2 and 3 (21 × 21 and 23 × 23 TM pixels), the difference in accuracy between the scales was not significant (*R*<sup>2</sup> ranged from 0.9341 to 0.9442; RMSE ranged from 0.0239 to 0.0249; the biases were nearly identical).

**Figure 5.** Comparison between MODIS albedo data with TM data aggregated at (**a**) 15 × 15, (**b**) 21 × 21, (**c**) 23 × 23, (**d**) 29 × 29, (**e**) 31 × 31, (**f**) 39 × 39, (**g**) 47 × 47, and (**h**) 61 × 61 scales.

## 5.2.2. Aggregation with PSF

MODIS gridded products are the outputs of a sampled image system that combines an imaging system with a sampling procedure. The imaging system used was characterized by the sensor PSF, which is considered as the convolution of line spread functions in the along-scan and the along-track directions [10,40]. The FWHM is an important parameter in characterizing pixel resolution. We implemented the PSF function to TM data upscaling. The FWHM was set as the first eight scale values in Table 2, and a weight smaller than 20% was neglected [10].

Table 5 shows a comparison between MODIS data and the TM albedo aggregated with the PSF. The first aggregation scale (15 × 15 TM pixels) has a high *R*<sup>2</sup> value (0.944), while the second and third aggregation scales (21 × 21 and 23 × 23 TM pixels) has the lowest RMSE (0.0239).

Comparing the results of aggregation with the simple average and those obtained by convolving them with the PSF, the highest *R*<sup>2</sup> value appeared when the aggregation scale was 23 × 23 TM pixels. The RMSE of the simple average and those obtained through the convolution of the PSF were nearly identical (0.0239 and 0.0238, respectively), indicating that for all datasets, the difference deduced by the aggregation method was not significant.


**Table 5.** Comparative accuracy of MODIS albedo and TM data aggregated with PSF.

#### *5.3. 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 × 15 to 77 × 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.

**Figure 6.** Number of heterogeneous scenes at each scale from 15 × 15 to 77 × 77 TM pixels at a step of 2 TM pixels.

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.

(**C**) US-Fuf Year: 2009 DOY: 014 

**Figure 7.** Three heterogeneous land surface types at (**A**) US-Ne3 cropland site, (**B**) US-Fmf evergreen needleleaf forest site and (**C**) CA-Fuf evergreen needleleaf forest site. For each site, the left figure is a false color composition of TM data, the middle figure is albedo from TM data, the right figure shows the aggregated TM albedo values at each scale, MODIS albedo, and sill value from scales 1 (15 × 15 TM pixels) to 32 (77 × 77 TM pixels) at a step of 2 TM pixels.
