## 4 Results
### Estimating and Verifying Single-Point Time Series Albedo  
We included five vegetated land surface types in this study: Deciduous broadleaf forest, evergreen broad-leaved forest, evergreen coniferous forest, grassland, and farmland. Three sites were subjected to validation for each land surface type. The results are shown in Figure 5.  
The algorithm starts with cloudless TM albedo data spanning the whole year. The starting days for each site are different, so the MODIS albedo data for different land surface types have different degrees of overestimation and underestimation; however, they are relatively continuous in time and all reflect the variation characteristics of surface albedo in snow-free periods. The EnKF algorithm combines the advantages of MODIS and TM sensors. The estimated results were very close to the directly calculated TM albedo data when adequate TM data were included. When TM data is absent, the albedo background is used as the final estimation to maintain a complete time series. Our results also showed that with the continuous introduction of TM observations, the errors induced by MODIS background data could be corrected by EnKF. The albedo background is generated by resampling MODIS albedo data.  
We also evaluated the heterogeneity of the test sites (Section 4.1) within the entire MODIS 500 m spatial scale. The results indicated that the proposed algorithm can adapt to heterogeneous surfaces (Figure 5e,h,o).  
Figure 6 shows scatter plots of the estimated albedos and ground measurements. Different colors represent the three different sites for each land surface type.  
As shown in Figure 6, RMSEs of the estimated albedos in deciduous broadleaf forest (DBF), evergreen broadleaf forest (EBF), evergreen needleleaf forest (ENF), cropland (CRO), and grassland (GRA) were 0.0152, 0.0085, 0.0087, 0.0152, and 0.0109; the R\({}^{2}\) values were 0.5980, 0.7061, 0.9190, 0.8191, and 0.6911, respectively. The RMSEs for all land surface types were less than 0.02, which meets the requirements of global and regional climate models [53]. The correlation coefficients between the estimated surface albedos and the surface measurements were high (R\({}^{2}\) > 0.6). The estimation results were close to the line \(y=x\). The accuracies of ENF and CRO were the highest among all land surface types with R\({}^{2}\) values of 0.9190 and 0.8191, respectively. The lowest R\({}^{2}\) value was 0.5980 for DBF, which can be attributed to the dispersion of TM data (Figure 1). At ENF and CRO sites, the distribution of TM data was more uniform across the whole time series. At the DBF site, there was a slightly longer period of missing data which prevented the albedo from being updated in a timely manner. The estimation accuracy depended on the temporal distribution of the available TM data at a certain degree, as temporally uniform distributed TM data led to higher estimation accuracy. Nevertheless, the proposed algorithm greatly improves the estimation accuracy compared to field observation alone.  
Figure 5: _Cont._Figure 5: Time series albedo estimations based on EnKF for DBF (**a–c**), EBF (**d–f**), ENF (**g–i**), CRO (**j–l**), GRA (**m–o**); three sites for each surface type. Grey vertical line represents error between estimated and measured values.