## 3 Methods
### Validation Site Land Surface Heterogeneity  
Previous researchers have verified the consistency of global land surface albedo products against ground measurement data at MODIS 500 m spatial scales at SURFRAD, Atmospheric Radiation Measurement Southern Great Plains (ARM/SGP) [34], and Cloud and Radiation Testbed-Southern Great Plains (CART/SGP) sites [35]. The MODIS albedo product has high accuracy with RMSE of 0.013-0.018. However, these verifications are based on homogeneous sites using point observations. In heterogeneous surface areas, site observations do not represent the MODIS pixels area, and thus the remote sensing products cannot be fully verified. As such, we must analyze site representativeness before validation with remote sensing data [36]. The heterogeneity of surface space describes the extent of surface heterogeneity within a certain range and reflects the heterogeneity in the area around FluxNet sites [37; 38]. In this study, we used variogram model parameters and the relative coefficient of variation (R\({}_{\text{CV}}\)) to analyze the effect of heterogeneity in the area around FluxNet sites according to Roman [39].  
Figure 2: Real-time albedo inversion based on ensemble Kalman Filter (EnKF).  
The isotropic spherical variogram model was used to evaluate landscape heterogeneity with 1.0 km\({}^{2}\), 1.5 km\({}^{2}\), and 2.0 km\({}^{2}\) TM albedo subsets. The TM albedo was obtained using the direct estimation approach proposed by [PERSON] [18]. The spherical model formula is:  
\[\gamma_{\rm sph}(h)=\left\{\begin{array}{ll}c_{0}+c\cdot(1.5\cdot\frac{\rm h}{ \rm a}-0.5(\frac{\rm h}{\rm a})^{3})&\mbox{for $0\leq\rm h\leq a$}\\ c_{0}+c&\mbox{for $\rm h>a$}\end{array}\right. \tag{3}\]  
The range a defines the distance from a point beyond which there is no further correlation of a biophysical property associated with that point. It has also been described as the average patch size of the landscape when the curve reaches the high-level distance [40]. The data are correlated within the range of a. Otherwise, the data are not correlated with each other; that is, the observations outside the range do not affect the estimation results. For a 1.0 km\({}^{2}\) subset a\({}_{\rm max}\) = 690 m, for a 1.5 km\({}^{2}\) subset a\({}_{\rm max}\) = 1050 m, and for a 2.0 km\({}^{2}\) subset a\({}_{\rm max}\) = 1410 m. The sill c is the variation of ordinates when the abscissa is greater than the variable range. The nugget c\({}_{0}\) is the variation of the abscissa at 0, which describes the variability of the data at the microcosmic level.  
The coefficient of variation (CV) is the ratio of the standard deviation to the mean. It is independent of spatial scale and can provide an estimate of the overall variability of data. The relative CV is:  
\[\rm R_{cv}=\frac{CV_{1.5x}-CV_{x}}{CV_{x}};x=1.0\leavevmode\
obreak\ \mbox{km}^{2} \tag{4}\]  
where \(\rm R_{cv}\) is the relative CV, \(\rm CV_{1.5x}\) is the CV calculated from a 1.5 km\({}^{2}\) TM albedo subset at the center of a given observation station, and \(\rm CV_{x}\) is the CV calculated from a 1.0 km\({}^{2}\) TM albedo subset at the center of the given observation station. If a site is more representative, it has a weaker spatial heterogeneity, a similar landscape around the site, and \(\rm R_{cv}\) closer to 0.