## 3 Calibration of MODIS-Compatible VIIRS EVI Using Global Data
### Data Extraction
Spectral data pairs were rejected if EVIs were lower than \(-\)0.05 or greater than 1.0. This is because, some VIIRS EVI exceeded the upper value of the valid range of MODIS EVI used in MOD13 series [32], _i.e._, 1.0, due probably to cloud leakage and/or residual snow/ice contamination. In addition, when VIIRS M3 surface reflectance exceeded 0.3 (possible cloud leakage or residual snow/ice contamination),  
Figure 1: Variability in rate of change in the mean absolute difference (MAD) between MODIS-compatible EVI and MODIS EVI (\(d_{n}\)) as a function of the number of sample data. A vertical dashed line corresponds to the number of sample 41,754.  
the pair was removed. If \(\delta_{1}<\text{median}\left(\delta_{1}\right)-\sigma\) or \(\delta_{1}>\) median \(\left(\delta_{1}\right)+\sigma\) (\(\delta_{1}\) is MODIS EVI minus VIIRS EVI (see Equation (8)); \(\sigma\) is 0.09, the STD of \(\delta_{1}\)), the pair was removed as an outlier. The value of \(\sigma\), 0.09 was considered large enough since the maximum difference between MODIS and VIIRS EVI calculated from model-simulated (noise free) data was less than 0.02 for nadir view [17] and less than 0.03 for off-nadir (60 degrees) view (results not shown here). The possible causes of these outliers as identified are discussed in next subsection. In this study, sample data were selected in order for the EVI frequencies to be as uniform as possible. Also, the data were selected to be more uniform with respect to sun-target-sensor viewing geometry. First, 200,000 pairs of MODIS and VIIRS spectra, which satisfied the conditions for the data extraction described above, were randomly selected and extracted from each of the 14 angular bins (seven variations in view zenith angle and two variations in relative azimuth angle), and then 2,800,000 pairs of data were created by combining the 14 data sets. The sample data were then selected randomly from the 2,800,000 pairs but to be uniform with respect to the EVI value. The relative frequency of EVI of the 2,800,000 data is shown by the blue line in Figure 2 whereas the frequency of sample data that were used in the optimization is shown by the red line in Figure 2. The total number of reflectance pairs was 137,278, which is greater than the minimum necessary number of sample (41,754) and computationally-acceptable for the optimization. The percentage of the pair of reflectances in respective angular ranges is shown in Table 1. Since the angular distribution in each EVI bin (e.g., 0.01 in EVI unit) would not be identical, the resultant values of the percentages were not uniform. The number of samples for backward scattering tended to increase with increasing view angle. On the contrary, it decreased as view angle increased in the forward scattering direction when the view angle was larger than 32.0. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Relative Azimuth Angle**} \\ \cline{3-4}  & & \(-\)**90.0 \(<\) 0\(\mu\)s \(<\) 90.0** & \(-\)**180.0 \(<\) 0\(\mu\)s \(<\) \(-\)90.0**, 90 \(<\) 0\(\mu\)s \(<\) 180 \\  & **(Backward Scattering)** & **(Forward Scattering)** \\ \hline  & 0.0 \(<\) 0\(\mu\)s \(<\) 8.0 & 6.7 & 6.3 \\  & 8.0 \(<\) 0\(\mu\)s \(<\) 16.0 & 6.9 & 6.3 \\ View zenith angle & 16.0 \(<\) 0\(\mu\)s \(<\) 24.0 & 7.7 & 6.5 \\ View zenith angle & 24.0 \(<\) 0\(\mu\)s \(<\) 32.0 & 9.3 & 6.4 \\  & 32.0 \(<\) 0\(\mu\)s \(<\) 40.0 & 10.4 & 5.1 \\  & 40.0 \(<\) 0\(\mu\)s \(<\) 48.0 & 9.6 & 4.3 \\  & 48.0 \(<\) 0\(\mu\)s \(<\) 56.0 & 10.7 & 3.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Percentage for the number of pairs of MODIS and VIIRS reflectance spectra in each angular condition. Figure 2: Relative frequency of MODIS EVI extracted from the climate modeling grid (CMG) data with the limited conditions regarding view zenith and azimuth angles and time period, denoted by blue line and that of data used for optimization (sample data), denoted by red line.