## 4 Discussion
Lastly, regarding the atmospheric conditions for AOD, total ozone, and column water vapor, using state-of-art Microtops II(r) resulted in valid accuracy values for each piece of atmospheric information. According to the user manual of Microtops II(r), the precision of the instruments is approximately 1-2%. Furthermore, the sensitivity due to these error propagations to the TOA radiance of the radiative transfer model is substantially less than 2%. In the case of AOD, there is no channel at 550 nm, which is used in the 6S radiative transfer model. Therefore, we used the Angstrom exponent law to interpolate that an aerosol optical depth of 550 nm, with two neighboring 440 and 870 nm channels. The accuracy of the Angstrom exponent law depends mainly on the size and composition of particles and degree of mixing ratio. Under benign weather conditions such as those in Mongolia, it is assumed that the uncertainty due to interpolation based on the Angstrom exponent law would be fairly low, and could be used as a generally accepted true value that is used generally [50]. Accurate atmospheric measurement with precise sunphotometers are needed to obtain more specific aerosol optical properties. Therefore, it is expected to have an error of less than 1% when using the current atmospheric instrument to simulate TOA radiance. To conclude, the combined errors of the vicarious calibration for KOMPSAT-3 and-3A sensors, approximately 5.7%, were based on the assumption that each of the manifested error sources was independent. We know that each of the mentioned error terms is not independent since each error may be offset or amplified during absolute radiometric calibration; some of the errors may or may not also be propagated into others. However, it is difficult to interpret these complicated effects. Therefore, this study simply provides worst-case uncertainty regarding the calculated error budget as a reminder that these radiometric errors exist. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Factors**} & \multicolumn{2}{c}{**Radiance Error (\%)**} \\ \cline{2-3}  & **KOMPSAT-3** & **KOMPSAT-3A** \\ \hline Relative radiometric correction & 5 & 5 \\ Solar irradiance data & 1 & 1 \\ Laboratory-based BRDF measurements & \textless{}1 & \textless{}1 \\ Surface reflectance measurement & 1 & 1 \\ ASD FieldSpec® 3 instrument & \textless{}1 & \textless{}1 \\
6S Radiative transfer & 1 & 1 \\ AOD from Microtops II® Sunphotometer & \textless{}1 & \textless{}1 \\ Total ozone from Microtops II® Ozonometer & \textless{}1 & \textless{}1 \\ Column water vapor from Microtops II® Sunphotometer & \textless{}1 & \textless{}1 \\ Combined error & \textless{}5.7 & \textless{}5.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Approximate error budget for the vicarious calibration of KOMPSAT-3 and -3A. Despite efforts to reduce the uncertainties of vicarious radiometric calibration, there are still issues to be addressed in future work. Laboratory-based BRDF measurements were used to normalize the satellite sensor geometry to the nadir direction, but they showed limitations for correcting the BRDF effects of the radiometric tarp. The hyperspectral gonioreflectometer was designed to measure two-dimensional BRDFs, meaning that only the critical plane measurement is available and it is difficult to measure the BRDF effects of azimuth angle. However, the satellite observation geometry has 3-D coordinate measurements. According to [PERSON] and [PERSON] [38], the higher the viewing zenith angle, the higher the BRDF effects in the azimuth angle direction. Future research should consider developing a new three-dimensional gonioreflectometer to determine the BRDF effects of azimuth direction. In addition, due to the characteristic of polar orbiting KOMPSAT satellites that are observing the world area, most of it is observed with the optimized sensor specifications used in this study.