# A New Methodology for Estimating Surface Albedo in Heterogeneous Areas from Satellite Imagery
## 4 Methods
### Evaluation and Comparison of Surface Albedo's Methods
#### 4.3.1 Evaluation and Comparison with ABOVE  
To examine Landsat images versus surface albedo ABOVE images, an algorithm is necessary for the pixel-by-pixel comparison. In this way, the value of each Landsat pixel (30 m) is compared with the value of the ABOVE pixel (500 m) where the center of the Landsat pixel falls. This comparison is made through the automation of the image processing by the Matlab(r) 9.3.0.713579 (R2017b) software, making a pixel-by-pixel statistical study of the Root Mean Squared Error (RMSE) between the ABOVE value and the different methodologies. The results of the various methods examined for the same data are shown in Table 3. The results are arranged according to their mean values of the BOA Normalized Difference Vegetation Index (NDVI) [57] obtained from Equation (14) with Landsat 8 data, since this parameter has proved to have an influential role on the determination of the surface albedo [58; 59]. \[NDVI=\frac{\rho_{IRC}-\rho_{RED}}{\rho_{IRC}+\rho_{RED}}\, \tag{14}\] \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Time**} & \multirow{2}{*}{**Code**} & **Mean** & **Mean Albedo** & **Pressure** & _T min_ & **RMSE** & **RMSE** & **RMSE** & **RMSE** \\  & & **NDVI** & **ABOVE** & **(KPa)** & (°C)** & **A-V01** & **A-V02** & **A-V03** & **A-V04** \\ \hline
1 November 2015 & FPK & 0.2141 & 0.2091 & 93.06 & 5.8 & 0.0381 & 0.0423 & 0.0268 & 0.1394 \\
13 November 2015 & BND & 0.2464 & 0.1671 & 99.66 & 1.3 & 0.0488 & 0.0408 & 0.0458 & 0.1098 \\
13 October 2014 & FPK & 0.2515 & 0.2174 & 94.28 & 0 & 0.0454 & 0.0537 & 0.0272 & 0.1212 \\
13 August 2015 & FPK & 0.2785 & 0.1983 & 94.15 & 17.5 & 0.0524 & 0.0410 & 0.0517 & 0.1801 \\
28 March 2015 & SXF & 0.3119 & 0.1807 & 96.4 & \(-3.7\) & 0.0751 & 0.0800 & 0.0749 & 0.1437 \\
24 September 2013 & FPK & 0.3197 & 0.2038 & 93.92 & 3.8 & 0.0432 & 0.044 & 0.0355 & 0.1332 \\
13 April 2015 & SXF & 0.331 & 0.1841 & 96.65 & 3.3 & 0.0400 & 0.0434 & 0.0645 & 0.1072 \\
8 October 2016 & SXF & 0.3653 & 0.2139 & 96.76 & 1.3 & 0.0729 & 0.0766 & 0.0458 & 0.0992 \\
15 November 2016 & BND & 0.3778 & 0.1684 & 98.85 & 3.3 & 0.0689 & 0.0429 & 0.0558 & 0.1474 \\
7 November 2015 & SXF & 0.3794 & 0.2076 & 97.24 & \(-1.8\) & 0.0545 & 0.0475 & 0.0403 & 0.1160 \\
9 November 2016 & SXF & 0.3806 & 0.2123 & 97.04 & \(-1.5\) & 0.0530 & 0.0499 & 0.0387 & 0.1082 \\
25 October 2014 & BND & 0.3843 & 0.2096 & 99.07 & 10.4 & 0.0646 & 0.0613 & 0.0457 & 0.1287 \\ \hline
23 May 2016 & BND & 0.3854 & 0.1785 & 99.08 & 13.1 & 0.0523 & 0.0532 & 0.0801 & 0.0794 \\
30 July 2016 & FPK & 0.4150 & 0.1796 & 93.68 & 9.3 & 0.0309 & 0.0310 & 0.0431 & 0.1463 \\
20 April 2016 & PSU & 0.4364 & 0.1360 & 98.14 & 1.4 & 0.0399 & 0.0454 & 0.0794 & 0.1686 \\
25 July 2014 & FPK & 0.4576 & 0.1862 & 93.66 & 10.6 & 0.0355 & 0.0359 & 0.0348 & 0.1341 \\
26 June 2015 & FPK & 0.4891 & 0.1697 & 94.6 & 10.1 & 0.030 & 0.0309 & 0.0604 & 0.1701 \\
8 June 2016 & BND & 0.5233 & 0.1672 & 99.18 & 11.6 & 0.0568 & 0.0595 & 0.0875 & 0.1088 \\
23 September 2014 & BND & 0.5472 & 0.1938 & 100.19 & 8.1 & 0.0579 & 0.0601 & 0.0824 & 0.1101 \\
14 November 2016 & PSU & 0.5542 & 0.1523 & 97.39 & \(-4\) & 0.0432 & 0.0436 & 0.0477 & 0.1497 \\
4 May 2015 & PSU & 0.5627 & 0.1435 & 97.85 & 7.2 & 0.0446 & 0.0482 & 0.0775 & 0.1862 \\ \hline
12 September 2016 & BND & 0.5630 & 0.1765 & 99.48 & 12.3 & 0.0460 & 0.0470 & 0.0433 & 0.1255 \\
11 October 2015 & PSU & 0.6146 & 0.1595 & 97.17 & 2.4 & 0.0419 & 0.0440 & 0.0355 & 0.1246 \\
21 October 2013 & PSU & 0.6209 & 0.1611 & 97.39 & 0.8 & 0.0416 & 0.0452 & 0.0338 & 0.1379 \\
21 August 2016 & SXF & 0.7440 & 0.1942 & 96.2 & 10.4 & 0.0433 & 0.0449 & 0.0314 & 0.0827 \\
12 July 2013 & SXF & 0.7762 & 0.1857 & 95.79 & 18.7 & 0.0250 & 0.0205 & 0.0566 & 0.1380 \\
4 September 2013 & BND & 0.8049 & 0.1962 & 99.6 & 11.5 & 0.0396 & 0.0418 & 0.0307 & 0.0903 \\ \hline \hline \multicolumn{1}{c}{**Mean RMSE**} & \multicolumn{1}{c}{0.0461} & \multicolumn{1}{c}{0.0459} & \multicolumn{1}{c}{0.0464} & \multicolumn{1}{c}{0.1262} \\ \hline \hline \end{tabular}
\end{table}