## 3 Calibration of MODIS-Compatible VIIRS EVI Using Global Data
### Data Extraction  
Aqua MODIS (Collection 5) and S-NPP VIIRS (Archive Set (AS) 3001) global daily 0.05-degree (climate modeling grid, CMG) resolution surface reflectance data were obtained for a one-year period of 1 August 2012 through 31 July 2013 for the calibration/optimization exercise. This VIIRS surface reflectance dataset (AS 3001) was produced at the NASA Science Investigator-led Processing System (SIPS), formerly known as the VIIRS Land Product Evaluation and Analysis Tool Element (Land PEATE), using the Joint Polar Satellite System (JPSS) near-real-time Interface Data Processing Segment (IDPS) software. The products of AS 3001 from SIPS should match the corresponding product from IDPS [30]. The VIIRS CMG surface reflectance algorithm was based on the MODIS Collection 5 CMG surface reflectance product generation algorithm [31]. The MODIS and VIIRS data were screened for cloud, cloud shadow, high aerosol loading, and snow/ice using quality assessment (QA) information and land quality flags (QF), respectively. The spectral data employed in the calibration/optimization consisted of pairs of MODIS and VIIRS reflectances that were obtained on the same dates at the same CMG locations for the same specific angle bins. Seven view zenith angle bins were defined as \(\theta_{j}\leqslant\theta_{v}<\theta_{j}+8.0\) where \(\theta_{v}\) is the view zenith angle in degrees and \(\theta_{j}\)'s for \(j=1\), \(2\), \(\cdots\), \(7\) were 0.0, 8.0, 16.0, 24.0, 32.0, 40.0, 48.0, respectively. The two relative azimuth angle (\(\theta_{a}\)) bins in degree were defined, corresponding to the backward scattering (\(-90.0<\theta_{a}<90.0\)) and forward scattering (\(-180.0<\theta_{a}-<90.0\), \(90.0<\theta_{a}<180.0\)directions. The mean and standard deviation (STD) of solar zenith angle differences between MODIS and VIIRS (MODIS minus VIIRS) were \(-\)1.2 and 1.8, respectively, and differences between relative azimuth angles were 1.9 and 5.7, respectively. More than 6 million pairs were found in and extracted from the one-year data. The calibration/optimization exercise of the MODIS-compatible VIIRS EVI would have been too computationally intensive if all the pairs had been used. Thus, the minimum necessary number of sample pairs was determined by a numerical experiment in which the number of sample pairs for the optimization was increased from \(10^{2}\) to \(10^{6}\) with a logarithmic increment in the sample size. MAD between MODIS-compatible EVI and MODIS EVI, represented by \(p_{n}\) (\(n=1\), \(2\), \(\cdots\), \(30\)), was computed for the \(n\)-th dataset. Differences between adjacent MADs (\(d_{n}\)), or between \(p_{n}\) and \(p_{n+1}\), were computed to provide information regarding the rate of change in MAD for \(n=1\), \(2\), \(\cdots\), \(29\),  
\[d_{n}=p_{n+1}-p_{n} \tag{7}\]  
A random sample of the size of \(10^{2}\) reflectance pairs were selected from the extracted pairs in the above step, from which \(p_{1}\) was computed. An additional number of randomly selected reflectance pairs were added to the first random sample to create a sample for \(p_{2}\) from which first \(p_{2}\) and then \(d_{1}\) were computed. Likewise, \(d_{n}\) were computed until \(n=29\). This procedure was repeated 10 times to provide 10 sets of \(d_{n}\). To evaluate variability in \(d_{n}\), \(d_{n}\) was plotted as a function of the sample size (Figure 1). \(d_{n}\) changed by \(\pm\)0.0003 when the sample size was equal to or greater than 41,754 highlighted by the vertical dashed line in Figure 1. This converges to zero when the number of samples is further increased. The threshold of 0.0003 was qualitatively determined after computing \(d_{n}\), but the change in MAD was small enough or nearly independent of the sample size when it was equal to or greater than 41,754. The minimum necessary number of samples in this study, therefore, was assumed to be equal to or greater than 41,754. Prior to data extraction for the optimization, we eliminated anomalies in the sample data.