## 2 Background and Previous Studies
Extensive studies of vicarious calibration using  
Figure 1: VIIRS DNB Spectral Response Functions (SRF) shows spectral shift occurred on-orbit for Suomi NPP VIIRS DNB due to RTA Mirror throughput degradation (Prelaunch vs. modeled on-orbit in April 2013). DCC have been performed in the past for many satellite instruments [9; 10; 11; 12; 13; 14]. However, most of the previous studies were for day time DCC observations with reflected solar radiance, for example, for the VIIRS reflective solar bands (RSB) [11; 12], or VIIRS DNB but again at day time with its Low Gain Stage (LGS) [10]. A more relevant study was found in [29], in which vicarious calibration of SNPP/VIIRS DNB was performed using DCC at night under lunar illumination. It demonstrated the viability, advantages and disadvantages of this approach. It concluded that for a one year period from August 2012 to July 2013, the DNB calibration is \(-4.9\%\) with \(\pm\) 8.8% uncertainty range \"near full moon.\" While this study demonstrated the value of DCC for vicarious calibration for the VIIRS DNB, there are several limitations. First, it uses daily averaged data based on \"a 2.5 by 2.5 latitude by longitude grid for four seasonal months\" for comparisons. Second, the comparison was performed in reflectance instead of radiance, in which all data were converted to reflectance, thus requiring the conversion of all data to reflectance, which depends on models and associated uncertainties, while both the original DNB product and the lunar model output are in irradiance/radiance. Third, previous studies have shown that lunar irradiance \"near full moon\" have greater uncertainties due to opposition effects [30]. For example, the GIRO lunar irradiance model is unable to generate irradiance near full moon due to large uncertainties [31]. Fourth, the lunar model used in that study is known to have uncertainties on the order of 7-12% [7]. Thus, the authors [29] concluded that their study is not an absolute calibration, but \"more of a consistency check between the simulated values and the DNB calibration.\"  
In contrast to the previous efforts, the current study made new advances in the following areas: (1) A unique dataset was developed in our study with a much finer temporal sampling interval, at every 86 seconds (or 48 VIIRS scan lines) when the satellite passes over the DCC. This allows us to investigate the lunar phase angle dependent calibration. Given the fact that the lunar phase angle changes only 0.012 degrees at this sampling rate, the uncertainties associated with lunar irradiance changes due to temporal sampling is eliminated. This DNB-DCC lunar dataset can potentially be available continuously for the next decades with the planned launch of two more VIIRS DNB for a variety of studies; (2) Our study compared the lunar phase angle dependent radiances between VIIRS DNB on two satellites: Suomi NPP and NOAA-20, which had not been done before; 3) We compared the Suomi NPP VIIRS DNB measurements with the latest state-of-the-art GIRO model predictions, and also characterized its differences from MT2009 by lunar phase angle. The range of radiances in our current comparison study is between \(\sim\)0.5 and \(\sim\)60 nanowatts (nW)/(cm\({}^{-2}\).sr) (for reference, the minimum radiance specification (L\({}_{\rm min}\)) for VIIRS DNB is 3 nW/(cm\({}^{-2}\)-sr) [19]. With this unique dataset and methodology presented in this paper, there are several fundamental science questions can be asked: can VIIRS DNB measure the lunar radiances as a function of lunar phase angle? What physical/mathematical functions does this relationship follow? How does the bi-directional reflection of the DCC affect the functions? Is the function dependent on waning and waxing phases of the moon? How does the function compare to existing lunar models? Finally, can the long-term observations from the VIIRS DNB be used to improve the GIRO as well as the DCC bi-directional reflectance models.