## 4 Results and Discussion  
The vital step in determining CI is the pixel normalization to compensate for backscatter and air mass effects, which often create bias in images. Thus, the normalization provides the \"true\" brightness of the earth's surface. Note that the digital number for COMS pixels varies from 0 to 1023. Figure 4 presents box-and-whisker plots of the pixel values after the normalization of each model was conducted. The normalized pixels were expected to demonstrate a constant dynamic range of the upper and lower boundaries. In all the models, the lower boundary was relatively constant, except at low backscatter angles. In other words, when the backscatter angle reached 0\({}^{\circ}\), i.e., the sun was close to the satellite, the lower boundary tends to become slightly increased. The constant lower boundary indicates that the albedo for the earth's surface had not change significantly. The upper boundaries, which represent overcast conditions, were also expected to remain constant. The variations of the upper boundaries were larger than those of the lower boundaries. Moreover, large maximums and some outliers beyond the maximum appeared. Consequently, the determination of the upper boundaries is more uncertain, and the GHI estimation under overcast conditions tends to be less accurate. Compared to the other three models, the [PERSON] model exhibited large deviations in terms of the interquartile range and the maximum. Based on the range of the normalized pixel counts, as shown in Figure 4, CI was determined according to Equation (1). CI indicates an attenuation factor from clear-sky GHI. Figure 4: Normalized COMS satellite pixel against backscatter angle; (**a**) [PERSON], (**b**) [PERSON], (**c**) [PERSON], (**d**) [PERSON], and (**e**) hybrid models. The backscatter angle, \(\psi\), was divided into nine classes with the interval of 10\({}^{\circ}\). In the box-and-whisker plot, the box height is the distance between the first and the third quartiles, and the maximum and minimum is determined by the interquartile range. The derivations of \(\mathrm{GHI_{c}}\) against \(\gamma\) are visualized in Figure 5. In general, all the models showed similar trends, where \(\mathrm{GHI_{c}}\) escalated along with \(\gamma\). However, each model also yielded different dispersions due to their basic formulas. As previously discussed, the [PERSON] model does not consider atmospheric conditions via \(T_{L}\). Consequently, the dispersion of the [PERSON] model results was the smallest among the models. The [PERSON] and [PERSON] models produced a similar trend, while the latter showed slightly larger dispersions. Contrarily, the dispersion in the Perez and hybrid models was significantly wide. Note that a small or large dispersion does not imply that the \(\mathrm{GHI_{c}}\) has good accuracy. Instead, it indicates that \(T_{L}\) has significant effects in those two models. The maximum and minimum values of \(\mathrm{GHI_{c}}\) also varied among the models. The [PERSON] model yielded the smallest range, from 70.22 to 859.54 \(\mathrm{W/m^{2}}\). The hybrid and Perez models produced broader ranges, of 10.12-1021.77 \(\mathrm{W/m^{2}}\) and 5.86-998.23 \(\mathrm{W/m^{2}}\), respectively. The Hammer model obtained the largest \(\mathrm{GHI_{c}}\), where it achieved from 50.78 \(\mathrm{W/m^{2}}\) to 1092.52 \(\mathrm{W/m^{2}}\). Figure 5: Clear-sky irradiance against the sun elevation angle; (**a**) [PERSON], (**b**) [PERSON], (**c**) [PERSON], (**d**) [PERSON], and (**e**) hybrid models. The sun elevation angle, \(\gamma\), was divided into eight classes with the interval of \(10^{\circ}\). Based on CI and clear-sky irradiance, as shown in Figures 4 and 5, GHI values under all sky conditions were derived and compared with the measurement data in Figure 6. The comparison was distinguished on different levels of the clearness index \((k_{T}=\mathrm{GHI}_{\mathrm{model}}/I_{0}\cos\theta_{x})\).