## 4 Discussion  
In this study, we officially updated the DN to radiance coefficients for KOMPSAT-3 and -3A to ensure that accurate and quantitative images are available for practical use, as the imaging sensor needs to be calibrated both geometrically and radiometrically [27; 28]. Because the accuracy of radiometric calibration ultimately influences all relevant fields utilized by KOMPSAT-3 and -3A, it is essential to determine the variations of KOMPSAT-3 and -3A due to TDI adjustments and sensor degradation over time. We acquired the four scale factors during the study period in 2017. However, the first two scale factors of KOMPSAT-3, which were acquired on 14 May 2017 and 27 July 2017, respectively (Table 4), differed from the last Mongolia case. The main reason for this was that BRDF effects of the surface radiometric tarps were mostly caused by tilted satellite geometry. In the first case alone,  
Figure 10: Scatterplots between KOMPSAT-3 DN and simulated TOA radiance fine all multispectral bands acquired on 20 September 2017; (**a**–**d**) represent the blue, green, red, and NIR bands, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Bands**} & \multicolumn{2}{c}{**KOMPSAT-3**} & \multicolumn{2}{c}{**KOMPSAT-3A**} \\ \cline{2-5}  & **Previous** & **Updated** & **Previous** & **Updated** \\ \hline Blue & 0.0185 & 0.0275 & 0.0301 & 0.0362 \\ Green & 0.0248 & 0.0382 & 0.0438 & 0.0249 \\ Red & 0.0214 & 0.0294 & 0.0443 & 0.0229 \\ NIR & 0.0141 & 0.0192 & 0.0235 & 0.0130 \\ \hline \end{tabular}
\end{table} 
Table 5: Comparison of previous and updated DN to radiance coefficients of KOMPSAT-3 and -3A. laboratory-based BRDF correction could be applied to normalize tilted satellite viewing zenith angle geometry to the nadir direction because the illuminator and detector sensors could be overlapped for the second case, as mentioned. In Table 4, the values in parentheses in the first column are the BRDF corrected scale factors using ANIF values of laboratory BRDF measurements for the sampled tarps. The BRDF corrected scale factors tended to approach the value of the last column scale factors of KOMPSAT-3, but differences remained. We inferred that two-dimensional laboratory BRDF measurements could not reflect the BRDF effect of an azimuth angle direction because the actual satellite and the sun's position were approximately 90\({}^{\circ}\) from each other. In other words, it is effective if the position of the satellite, tarps, and the sun were similar to those with 2D hyperspectral gonioreflectometers; however, BRDF uncertainty increases as these are out of the principle plane, and the uncertainty magnitude is unknown. A common problem of radiometric calibration of optical sensors is how to reduce the expected error factors in order to calculate hypothetical TOA radiance; this can be achieved by carefully preparing the input parameters of the radiative transfer model, especially for atmospheric and ground measurement conditions. We have already shown how radiometric conversion coefficients can be adjusted by simply correcting the variation of satellite geometry using laboratory BRDF measurements, indicating the importance of input parameters for considering the BRDF effects of the radiometric tarp. To report detailed radiometric calibration results, in this study the relative error budgets of various calibrations of KOMPSAT-3 and -3A were analyzed considering the expected error factors. When analyzing the approximate error budget of vicarious calibrations, even worst-case conditions were simply provided to inform readers that these radiometric errors exist. Table 6 shows the estimated error budgets induced by the vicarious calibration of KOMPSAT-3 and -3A during the study periods. They have the same combined error budget values because the sensor specifications for AEISS and AEISS-A and the vicarious calibration algorithm are the same. Among the causes of error, a relative radiometric correction such as non-uniformity and pixel burst contributes the most to total budgets.