## 4 Results and Discussion
### VIIRS DNB Direct Lunar Radiance Comparison between Suomi NPP and NOAA-20  
Based on the discussion in the previous section, the Suomi NPP and NOAA-20 VIIRS DNB observations of DCC reflected lunar radiance can be directly compared as a function of lunar phase angle, and the results can be quantified. It is assumed that this function is relatively stable due to the stability of both the deep convective cloud reflectance and the Suomi NPP VIIRS DNB instrument calibration as discussed earlier for the period of study. Changes in this function would be primarily due to the lunar irradiance changes from month to month and the lunar zenith angle variations at the time of observation. It is also noted that this lunar-DCC curve can not only be used to quantify the calibration biases between VIIRS DNB on different satellites, but also can potentially be used to monitor the calibration changes over time for the same instrument once a long-term time series over several years is established. Figure 6 compares the lunar-DCC radiance curves from both VIIRS DNB on Suomi NPP and NOAA-20. The data used here are from 7 November 2018 to 6 December 2019. Visual inspection of Figure 6 suggests that the VIIRS DNB calibration between Suomi NPP and NOAA-20 agree very well at all lunar phase angles if the data are grouped by waxing and waning phases separately. Apparently there are two separate patterns depending on the lunar phase, as discussed in Section 4.1, primarily due to lunar zenith angles in each phase. Further quantitative comparison is also performed by generating a polynomial regression for each data set with equation (3), and the coefficients for the polynomials are provided in Table 1.  
\[L=C_{0}+C_{1}x+C_{2}x^{2}+C_{3}x^{3}+C_{4}x^{4} \tag{3}\]  
where: \(L\) is the DNB measured lunar radiance (nW/(cm\({}^{-2}\cdot\)sr)); \(x\) is the lunar phase angle; and \(C_{0}\)_to_\(C_{4}\) are coefficients (see Table 1). Figure 6: Inter-calibration of VIIRS DNB between Suomi NPP and NOAA-20 using lunar radiances reflected from DCC (November-December 2018 lunar cycle). It should be noted that although the 4 th order polynomial function forms remain valid overall from month to month, the coefficients do not remain the same because the lunar irradiance varies from month to month due to such factors as lunar phase angle and lunar zenith angle variations relative to the sun-synchronous satellite orbit, and earth-moon distance variations. This is further discussed in Section 4.3 where a time series is shown. Based on the above coefficients, the radiometric biases between VIIRS DNB on NOAA-20 vs. Suomi NPP can be calculated and plotted as shown in Figure 7.  
It can be seen in Figure 7 that the lunar radiance measured by VIIRS DNB on NOAA-20, in general, has a lower value (up to \(\sim\)5%) relative to Suomi NPP for both waxing and waning phases of the moon, especially at low lunar phase angles. There are several factors that might have contributed to the biases here. First, the half orbit separation between the NOAA-20 and Suomi NPP leads to small lunar phase and lunar zenith angle differences in the observing the DCC pixels. However, this effect is mitigated by the polynomial function through interpolation which addresses this observation time differences. Also, since Suomi NPP is always trailing the NOAA-20, the lunar phase angle effect for the near-nadir-samples would have opposite effects in the bias during waxing and waning phases, which contradicts to the consistent bias shown in Figure 7. The lunar zenith angle difference at the time of observation between SNPP and NOAA-20 might introduce biases due to the bi-directional reflection of the DCC as discussed in Section 4.3. However, Figure 5 showed that they have nearly identical lunar phase vs. zenith angle patterns. This is further confirmed through orbital simulations. Identifying the root cause of the bias is beyond the scope of the current study. However, we have identified two sources of biases and both lead to a high in-band solar irradiance in the Suomi NPP