## 3 Methodology and Data
### Data Processing and Analysis  
The following steps are used in the data processing: (1) For each lunar cycle, a scatterplot is generated by pairing the lunar phase angle (LPA, or moon phase angle MPA, used interchangeably in this study) and the mode of the VIIRS DNB DCC reflected lunar radiances for each near-nadir-sample aggregated from a granule. (2) The scatterplot shows a correlation between the DCC reflected lunar radiances and the lunar phase angle. This relationship is further quantified by fitting a polynomial to the data. (3) The measurements from both Suomi NPP and NOAA-20 are compared. (4) Lunar irradiance models are used to generate predicted lunar irradiances to compare the DNB observations with the model predicted values. (5) The agreement between the model and the DNB observations are evaluated, and uncertainties in both the DNB observations and models are also discussed. The results will be presented in the next section.  
The lunar irradiance models generate the spectral lunar irradiance at the given time and observation geometry at the top of the atmosphere for the DNB. In the case of MT2009 [7], the generated hyperspectral lunar irradiance is convolved with the DNB spectral response function and converted to the top of atmosphere radiance in the unit of nW/(cm\({}^{2}\)-sr), which matches the radiance unit for the VIIRS DNB. The following equation is used to compute the radiance:  
\[L=\frac{I\,\cos\omega}{\pi}\rho(\omega,\theta,\phi) \tag{2}\]  
where: \(L\) is the lunar radiance at the top of DCC (nW/cm\({}^{2}\)-sr); \(I\) is the model predicted lunar irradiance for the DNB band (W/cm\({}^{2}\)); \(\omega\) is the lunar zenith angle (degrees); \(\pi\) is the solid angle of hemisphere (sr); \(\rho(\omega,\theta,\phi)\) is the angle dependent DCC reflectance from the Angular Distribution Model (ADM) [33]; \(\theta\) is the view zenith angle (degrees); and \(\phi\) is the relative azimuth angle (degrees).  
The physical process described by Equation (2) is as follows. The lunar irradiance (\(I\)) incident on the DCC at the lunar zenith angle \(\omega\) is reflected with the reflectance of \(\rho(\omega,\ \theta,\phi)\) into hemisphere (\(\pi\) sr solid angle), and observed by VIIRS DNB. At near nadir, \(\rho\) is mainly a function of \(\omega\). Here, the reflectivity of the DCC depends primarily on the lunar zenith angle and to a lesser degree on the view zenith angle because it is near nadir view. Note that in Equation (2), the lunar zenith angle has two separate effects: the cosine effect which affects the unit area lunar irradiance incident on the DCC surface; and the bi-directional reflectance effect of the DCC which can be estimated using the Angular Distribution model (ADM) [33]. Similarly, the GIRO model takes as inputs the date, time, location, and VIIRS DNB spectral response function. It generates averaged spectral lunar irradiance in the unit of W/m\({}^{2}\)-um. This is then converted to radiance with the unit of nW/(cm\({}^{2}\)-sr) given the DNB band equivalent width. In this study, the same data processing and analysis procedures are used for both NOAA-20 and Suomi NPP VIIRS DNB observations.