## 3 Calibration of MODIS-Compatible VIIRS EVI Using Global Data
### Optimization Results
The averages of \(K_{i}\) (\(\overline{K}_{i}\)) using these averages can be computed as: \(\overline{K}_{1}=\overline{A}_{r}/\overline{A}_{n}=1.026\), \(\overline{K}_{2}=\left(\overline{D}_{n}-\overline{D}_{r}\right)/\overline{A} _{n}=0.010\), \(\overline{K}_{3}=\overline{A}_{b}/\overline{A}_{n}=0.888\), and \(\overline{K}_{4}=(C_{1}\overline{D}_{r}+\overline{D}_{n}-C_{2}\overline{D}_{ b}+L)/\overline{A}_{n}=1.107\). These values are very similar to \(K_{i}^{\bullet}\); especially they are the same for \(K_{1}\). Therefore, the optimized, best coefficients \(K_{i}^{\bullet}\) can be reasonable. Thus, the calibrated MODIS-compatible EVI (\(\phi_{m}^{\bullet}\)) is written as  
\[\phi_{m}^{\bullet}=G\frac{\rho_{v,n}-K_{1}^{\bullet}\rho_{v,r}+K_{2}^{\bullet}} {\rho_{v,n}+K_{1}^{\bullet}C_{1}\rho_{v,r}-K_{3}^{\bullet}C_{2}\rho_{v,p}+K_{4 }^{\bullet}} \tag{10}\]  
Figure 3b shows MODIS-compatible VIIRS EVI minus MODIS EVI (\(\xi_{2}^{\bullet}\)) and that the MODIS-compatible VIIRS EVI with optimized coefficients resulted in a lower error magnitude than VIIRS EVI, _i.e._, a reduction of the mean difference from 0.019 (\(\delta_{1}\)) to 0.002 (\(\delta_{2}^{\bullet}\)). The STD of \(\delta_{2}^{\bullet}\) (0.028) was the same as that of \(\delta_{1}\) (0.028) because the errors were included in both sensors, especially in VIIRS. The RMSE of \(\delta_{2}^{\bullet}\) (0.028) was lower than that of \(\delta_{1}\) (0.034) because of the reduction in the systematic differences. Figure 4a,b show the spatial distributions of \(\delta_{1}\) and \(\delta_{2}^{\bullet}\), respectively. In plotting \(\delta_{1}\) and \(\delta_{2}^{\bullet}\) in map format, when multiple error values were found for a single grid, their average value is plotted for the grid. Errors were not measured over all of the grids because the MODIS and VIIRS sun-target-view geometry matchup were found over limited geographic areas. Note that the size of the colored dots is larger than the actual grid size (0.05\({}^{\circ}\)-by-0.05\({}^{\circ}\)) for improved visualization. Fewer samples seen in tropical forests and high northern latitude regions were due to frequent cloud cover and snow/ice cover. Generally, large negative values in \(\delta_{1}\) were found everywhere, especially in the southeast area of the South American continent, India, West Europe, the western and southern part of Africa, and the northern part of the Eurasian continent. Positive errors were found in the regions that also showed large negative errors and where vegetation are found. Such samples might have been impacted by factors other than spectral bandpasses as mentioned before. Positive errors were also observed in the regions showing lower magnitudes of negative and positive values in \(\delta_{1}\) (-0.03-0.01) such as \begin{table}
\begin{tabular}{c c c c} \hline \hline \(K_{1}^{\bullet}\) & \(K_{2}^{\bullet}\) & \(K_{3}^{\bullet}\) & \(K_{4}^{\bullet}\) \\ \hline
1.026 & \(-0.001\) & 0.874 & 1.022 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Values of optimized coefficients obtained using the sample data. sparsely/less vegetated areas and desert including Australia, northern Africa, the central part of Asia, and the southern part of South American continent. Figure 4b shows the spatial distribution of \(\delta_{2}^{*}\). The negative values in \(\delta_{1}\) were corrected over the globe by the MODIS-compatible EVI. Areas that showed negative errors in Figure 4a resulted in smaller magnitude of errors. However, positive errors were not properly corrected and remained or increased in their magnitude, in particular, over the southeast of South America and Europe. Clusters of negative errors (approximately \(-0.01\)) were observed in Africa, Australia, east South America, and the northern Eurasian continent (the areas heavily impacted by either persistent cloud cover or winter snow cover).