## 4 Results and Discussion
### VIRS DNB Observed DCC Reflected Lunar Radiance as a Function of Lunar Phase Angle  
Figure 4 provides an example of the relationship between VIIRS DNB observed lunar radiance reflected from DCC vs. lunar phase angle. The data shown here are from 7 November 2019 to 7 December 2018 (also referred to as the November-December 2018 lunar cycle) which covers a full lunar cycle from new moon to full moon and then to new moon again. From the figure we can see that the lunar radiance increases during waxing with decreasing lunar phase angle from new moon (lunar phase angle \(\sim\) 180 degrees) to full moon (lunar phase angle approaching 0 degree), while in the waning phase, the lunar radiance decreases from full moon towards new moon. The change in radiance is approximately two orders of magnitude, with \(\sim\)5 0 \(\times\) 10\({}^{-9}\) W/(cm\({}^{2}\cdot\)sr) near full moon, and down to \(\sim\)0.5 \(\times\) 10\({}^{-9}\) (W/cm\({}^{2}\cdot\)sr) at lunar phase angle of 110 degrees. In the analysis, we experimented with different methods such as using mean vs. mode radiance in generating the \"near-nadir-samples\". Our findings confirmed previous studies that the mode values better represented the granule values compared to the mean values because the mean values are prone to a few but extreme values that are out of range due to the nature of DCC reflectance variability as discussed earlier. Therefore, in the analysis, we only use the near-nadir-samples with mode radiance values for the lunar radiance study. It is also noted that few data points are available for lunar phase angles near zero, i.e., full moon, although this varies month by month. This is because the SNPP/NOAA-20 have an orbital period of \(\sim\)101 minutes and the DCC samples are taken only in the tropical regions, while the lunar phase angle changes \(\sim\)0.51 degrees/hour. As a result, not all months capture the DCC during full moon (within 2 degrees lunar phase angle). However, we found that when the full moon data were present in the near-nadir-samples, the curve near the full moon becomes extremely nonlinear, again due to lunar opposition surge [30]. Therefore, in this study we selected the November-December 2018 lunar cycle which does not have such full moon samples and focused on the data points between 7-90 degrees in lunar phase angle. Figure 4: Suomi NPP VIIRS DNB observed radiance (nW/(cm\({}^{2}\cdot\)sr)) versus Lunar phase angle (November-December 2018 Lunar cycle, data source: [[http://www.class.noaa.gov](http://www.class.noaa.gov)]([http://www.class.noaa.gov](http://www.class.noaa.gov))). Figure 4 also shows that although there is a general relationship between VIIRS DNB observed radiance and the lunar phase angle, waxing and waning phases appear to follow different patterns. A more detailed analysis reveals that this large difference between waxing and waning lunar radiances is primarily due to the lunar zenith angle changes that occurred in the Suomi NPP orbit between waxing and waning phases of the moon. It is understood that there are lunar irradiance differences in the waxing and waning phase according to a previous study in which a separate correction had to be made to the MT2009 model for waxing and waning effects [27], but that difference is much smaller than what we see here, as further discussed in Section 4.3. Figure 5 shows that at the same value for lunar phase angle, the lunar zenith angles at satellite nadir can be very different between lunar waxing and waning phases. For example, at 50 degree lunar phase angle, the lunar zenith angle is about 70 degrees in the waxing phase, while it is about 40 degrees during the waning phase. According to Equation (2), the lunar zenith angle plays a large role in the reflected radiances. In this specific case, the latter is 2.24 times of the former (cosine of 70 degrees vs. cosine of 40 degrees), even if the lunar irradiances are the same. Another feature shown in Figure 5 is that during the waxing phase, the lunar zenith angle change is in sync with the lunar phase angle change.