## 3 Calibration of MODIS-Compatible VIIRS EVI Using Global Data
### Optimization Results  
The errors between MODIS EVI and VIIRS EVI are written as \(\delta_{1}\), and errors between MODIS EVI and MODIS-compatible EVI with the optimized coefficients (\(K_{i}^{*}\), \(i=1,2,3,4\)) are written as \(\delta_{2}^{*}\),  
\[\delta_{1}=v_{m}-v_{v} \tag{8}\]  
\[\delta_{2}^{*}=v_{m}-\hat{v}_{m}^{*}\left(K_{1}^{*},K_{2}^{*},K_{3}^{*},K_{4}^{ *}\right) \tag{9}\]  
where \(v_{m}\), \(v_{v}\), and \(\hat{v}_{m}^{*}\) are MODIS EVI, VIIRS EVI, and MODIS-compatible VIIRS EVI with the optimized set of coefficients. In Figure 3a, MODIS EVI minus VIIRS EVI (\(\delta_{1}\)) are plotted as a function of MODIS EVI. On average, \(\delta_{1}\) was the smallest at EVI = 0, decreased until approximately EVI = 0.2, and remained nearly the same for higher EVI values (Figure 3a). The mean, STD, and root mean square error (RMSE) of \(\delta_{1}\) were \(-\)0.019, 0.028, and 0.034, respectively (Table 2). The mean values of MODIS minus VIIRS reflectances were \(-\)0.009, \(-\)0.003, and \(-\)0.011 for the blue, red, and NIR bands, respectively. In general, higher VIIRS blue and NIR reflectances contributed to higher VIIRS EVI values than the MODIS counterparts. The effect of spectral bandpasses and additional uncertainties caused by radiometric calibration could add systematic errors to surface reflectances. While \(\delta_{1}\) had less scattering about the trend at lower (0 to 0.2) EVI values, large positive values in \(\delta_{1}\) were observed with increasing EVI values (Figure 3a). This indicates that VIIRS EVI shows relatively smaller values than MODIS EVI, which can likely be attributed to cloud leakage in VIIRS Cloud Mask (VCM). Other sources of systematic and random errors arise from differences in the maturity of the atmospheric correction algorithms, including aerosol optical properties, relative geolocation errors between the sensors, and influences associated with differences in spatial compositing for generating CMG data. Although the input reflectance pairs were carefully selected to have the same sun-target-view geometric conditions, subtle differences in the geometric conditions remained in many pairs, being an additional source of random/systematic errors that are inevitable for this cross-sensor comparison. Figure 3: Density plots of EVI differences using the data for the calibration. (**a**) Density plot of MODIS EVI minus VIIRS EVI (\(\delta_{1}\)) _vs._ MODIS EVI; (**b**) Density plot of MODIS EVI minus MODIS-compatible VIIRS EVI (\(\delta_{2}^{*}\)) _vs._ MODIS EVI. The optimization was performed using the extracted data and resultant coefficients are summarized in Table 3. \(K_{1}^{\bullet}\) and \(K_{4}^{\bullet}\) were close to unity and \(K_{2}^{\bullet}\) was close to zero, whereas \(K_{3}^{\bullet}\) were 0.874. The validity of these values can be evaluated based on the slope and offset calculated from the linear regression between MODIS and VIIRS reflectances. The slope and offset of the linear regression between the VIIRS blue reflectance (x-axis) and MODIS counterpart (y-axis) were 0.813 and 0.0032, respectively, and similarly, 0.934 and 0.0039 for the VIIRS red reflectance and MODIS counterpart, and 0.915 and 0.013 for the VIIRS NIR reflectance and MODIS counterpart. We consider the slopes of the regressions as the averages of the slope of the vegetation isoline equations in Equations (2a-c) for the MODIS-VIIRS CMG data, \(\overline{A}_{b}\), \(\overline{A}_{r}\), and \(\overline{A}_{n}\) (= 0.813, 0.915, and 0.939) and consider the offsets of the regressions as the average values of offsets of the isoline equations, \(\overline{D}_{b}\), \(\overline{D}_{r}\), and \(\overline{D}_{n}\) (= 0.0032, 0.0039, and 0.013).