## 4 Results and Discussion
### Comparison between Observed and Lunar Irradiance Model Predicted Radiances  
Despite the good agreement between the VIRIS DNB measurements from the two satellites, Suomi NPP and NOAA-20, the comparison made in the previous section does not give any indication of the absolute accuracy of the radiance values from the DNB measurements. To address this issue, in this section we compare the Suomi NPP VIIRS DNB measured radiances with lunar irradiance model output results. It is recognized that there are uncertainties in both lunar irradiance model predictions (GIRO and MT2009) and VIIRS DNB observations. For the GIRO model, no official uncertainty statement is found but it has been demonstrated in previous studies that the uncertainty in the absolute lunar irradiance produced by the model is estimated to be within 10% [6], although the stability is much better, on the order of \(<\)1%. For the DNB observations, the uncertainty is mainly caused by a number of factors in the earth view observations. This includes but is not limited to: (1) variabilities in the DCC reflectance depend on the view geometry, cloud optical thickness, cloud fraction, and small regional differences in the cloud properties, and (2) lunar zenith angle variations leads to bidirectional reflectance effects. A brief review of the two lunar models is necessary here to clarify the differences between them. The GIRO is a joint effort among different institutions, including the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT), the United States Geological Survey (USGS), the Centre National d'Etudes Spatiales (CNES), the Japan Aerospace Exploration Agency (JAXA), and the National Aeronautics and Space Administration (NASA). The effort is led by EUMETSAT, with an objective to make the lunar model publicly available, verified and validated, uncertainties characterized, and to establish traceability for the predicted irradiances [5; 38]. There is also discussion of further improvements from the baseline model, based on new observations such as from the CNES mission Pleiades-HR (High Resolution) satellite constellation [39]. In contrast, the MT2009 [7] is an independent model developed for a different application. It was originally developed to compute the lunar spectral irradiance for the VIIRS DNB for geophysical retrievals under lunar illumination. The model produces 1-nm resolution irradiance spectra over the spectral interval [0.3, 1.2 um] for a given date and time. The model itself is based on multiple sources of lunar observations. The model takes into account of the lunar phase angle, Sun-to-Moon, and Moon-to-Earth distances. The model output is actually interpolated based on lunar irradiance samples from the pre-calculated database, for lunar phase angles ranging from 0 degrees to 180 degrees. However, neither lunar libration nor waxing/waning effects are considered in this model. The uncertainty of the MT2009 model is estimated to be 7%-12% [7]. The purpose of using this model in the current study is that it provides an independent comparison with the VIIRS DNB observed lunar radiances such that any differences or discrepancies would be uncorrelated with the other model for the validation. In addition, since the MT2009 does not treat waning vs. waxing separately in the model predictions, it helps us diagnose the patterns between the waxing and waning phases of the VIIRS DNB data used in this study. The lunar models generate lunar irradiance at top of the atmosphere given the time, location and view geometry of the observation. The lunar irradiance values are then converted to DNB in-band radiance by convolving with the DNB spectral response function and with Equation (2). For both models used, the unit required conversion to make the comparison consistent. Several observations can be made from Figure 8. First, predicted lunar radiances matched very well with the DNB observations.