# A New Methodology for Estimating Surface Albedo in Heterogeneous Areas from Satellite Imagery
## 4 Methods
### Evaluation and Comparison of Surface Albedo's Methods
#### 4.3.2 Evaluation and Comparison with SURFRAD  
The surface albedo of the SURFRAD stations is calculated thanks to the pyranometer at the highest position in each platform (about 10 m). In this way, the surface albedo value measured is representative of a circular footprint, of approximately 60 m radius [60], the size of which varies depending on the height of the tower where the instrument is located [61]. In order to use the surface albedo data from SURFRAD stations for comparison, the heterogeneity of the land cover has to be investigated. Four different geostatistical attributes are used for this purpose: the relative coefficient of variation (RCV), the index of scale requirements (RSE), the relative strength of spatial correlation (RST), and the relative proportion of structural variation (RSV). RCV is a useful measure of the relative dispersion of the data and provides an estimate of the overall variability, and hence heterogeneity, of the data, regardless of spatial scale. RSE examines the range of variograms using two spatial thresholds with respect to the true spatial extent of a given measurement site. RST provides a spatially explicit representation of where the most different sources of surface albedo variability are likely to be found. RSV is used to assess the importance of spatial structure in the total variability of the data. The four geostatistical attributes are combined into an equation, resulting in the \(ST_{SCORE}\) (Equation (15)), which represents a spatial representativeness rating. If the spherical variogram model does not provide a good fit, another indicator, the \(RAW_{SCORE}\) (Equation (16)), can be used to provide a new spatial representativeness score. Both ratings are directly proportional to the representativeness of the location, and the zones are considered heterogeneous or with large land cover differences if both ratings have a value below 2. \[ST_{SCORE}=\left(\frac{|R_{CV}|+|R_{ST}|+|R_{SV}|}{3}+R_{SE}\right)^{-1}, \tag{15}\]  
\[RAW_{SCORE}=|2R_{CV}|^{-1}, \tag{16}\]  
Table 4 shows the results of [PERSON] et al. [59], which correspond to the SURFRAD stations selected for this project. The ratings show that the surroundings of the FPK and PSU stations are not always homogeneous since in these stations both \(ST_{SCORE}\) and \(RAW_{SCORE}\) are below 2 either in the leaf-off or in the leaf-on period. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Code** & **Footprint (m)** & **Season Period** & **RCV(\%)** & **RSE(\%)** & **RST(\%)** & **RSV(\%)** & \(ST_{\text{SCORE}}\) & \(RAW_{\text{SCORE}}\) \\ \hline \multirow{2}{*}{BND} & \multirow{2}{*}{126} & Leaf-off & 5.24 & 42.63 & \(-\)5.17 & 59.16 & 1.52 & 9.54 \\  & & Leaf-on & \(-\)4.56 & 48.50 & 2.84 & 37.10 & 1.58 & 10.9 \\ \hline \multirow{2}{*}{FPK} & \multirow{2}{*}{126} & Leaf-off & 7.01 & 19.5 & \(-\)2.03 & \(-\)1.25 & 4.37 & 7.13 \\  & & Leaf-on & 42.27 & 23.5 & 3.36 & 69.44 & **1.62** & **1.18** \\ \hline \multirow{2}{*}{PSU} & \multirow{2}{*}{126} & Leaf-off & 66.21 & 24.94 & 12.73 & 61.96 & **1.39** & **0.76** \\  & & Leaf-on & 5.06 & 22.86 & 3.16 & \(-\)14.45 & 3.29 & 9.89 \\ \hline \multirow{2}{*}{SXF} & \multirow{2}{*}{32} & Leaf-off & 7.33 & 75.5 & 1.56 & \(-\)6.74 & 1.24 & 6.82 \\  & & Leaf-on & 21.08 & 49.5 & 7.29 & 104.41 & 1.07 & 2.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Characteristics of the SURFRAD sites providing data during the 2014–2018 period. In bold are highlighted \(ST_{score}\) and \(RAW_{score}\), where both have values less than 2 and are therefore considered heterogeneous areas. Based on these data, Penn. State Univ., Pennsylvania (PSU) should not be used to assess the accuracy during the leafless season, and Fort Peck, Montana (FPK) should be discarded during the leaf season. These values represent the reality of the surroundings of the SURFRAD stations, so if the surrounding is heterogeneous, the ABOVE value cannot be compared to the SURFRAD data because of the presence of different vegetation cover in the pixel footprint and therefore a contaminated result.