## 3 Results
### Quantitative Evaluation of Fog Detection
#### 3.1.3 Fog Detection Performance by Solar Zenith Angle  
Figure 5 illustrates the annual mean fog detection frequency of the GK2A_FDA and surface-based fog observations, stratified by SZA in 4\({}^{\circ}\) intervals. The distribution of monthly SZA varies seasonally, with smaller values in summer and larger values in winter due to the Earth's axial tilt. The GK2A_FDA generally reports higher fog detection frequencies than surface observations. Under nighttime conditions, however, the two distributions converge, indicating relatively stable detection performance without solar radiation. Previous studies [41; 45] have shown that nighttime fog detection algorithms--which rely  
\begin{table}
\begin{tabular}{c c c c} \hline
**Season** & **POD** & **FAR** & **Bias** \\ \hline Spring & 0.61 & 0.87 & 4.72 \\ Summer & 0.47 & 0.93 & 6.44 \\ Autumn & 0.61 & 0.75 & 2.48 \\ Winter & 0.65 & 0.90 & 6.43 \\ \hline \end{tabular}
\end{table}
Table 7: Summary of GK2A fog detection performance by season.  
primarily on infrared brightness temperature differences such as DCD--tend to yield lower POD than daytime algorithms that utilize visible channels. However, these nighttime algorithms also result in lower FAR and bias values, indicating a relatively reduced rate of false or over-detections under nighttime conditions compared to daytime scenes.  
Detection performance tends to degrade during twilight, making fixed threshold-based approaches, typically applied during daytime or nighttime, less effective. Thus, the GK2A_FDA relies mainly on fog detection outcomes from the preceding observation, and while twilight POD is relatively lower than during daytime or nighttime, the corresponding  
Figure 5: Monthly distribution of GK2A fog detection and ground fog occurrence frequency according to SZA at 4\({}^{\circ}\) intervals. The range of SZA changes with the month because SZA changes with the season. Daytime is defined as SZA < 80\({}^{\circ}\), twilight as 80\({}^{\circ}\)\(\leq\) SZA < 88\({}^{\circ}\), and nighttime as SZA \(\geq\) 88\({}^{\circ}\). The data represent the annual frequency at 10 min intervals from 2021 to 2023. Missing bias values in low SZA bins indicate either no ground fog observations or values exceeding the axis range.  
FAR and bias values are also lower. Seasonal changes in the SZA, notably the transition from winter to summer, combined with cloud shadows and navigation errors, degrade the quality of the 30-day minimum value composition of visible channel reflectance during daytime [31]. This degradation leads to false detection of clear-sky regions as fog when the daytime algorithm is applied over inland areas and causes discontinuities in detection results with twilight conditions. The discontinuities in fog detection become most pronounced in June when SZA reaches its annual minimum. This pattern is clearly illustrated in the spring and early summer graphs in Figure 5, where bias increases and the GK2A fog detection frequency rises sharply as the SZA drops below 80\({}^{\circ}\). At SZA values below 60\({}^{\circ}\), most fog has dissipated, resulting in very low ground-based fog occurrence [11; 12]. During this low-SZA period, although the GK2A daytime algorithm applies stricter thresholds, Bias still tends to increase noticeably as the SZA decreases.