## 3 Results  
### Quantitative Evaluation of Fog Detection  
#### 3.1.1 Overall Fog Detection Performance  
Figure 3 presents the seasonal frequency of annual average fog observations at 176 visibility meter stations used to validate the GK2A_FDA. Depending on the season and location, the number of foggy days shows substantial spatiotemporal variability, ranging from 0 to approximately 40 days. Along the west coast, fog occurrences are most frequent during spring and summer, whereas in inland regions, they are more prominent in autumn [33; 34; 35]. In contrast, the east coast exhibits a lower overall frequency of fog and, at specific stations, no ground-based fog observations during the winter season [12; 35].  
The evaluation using the nearest-pixel method yielded a three-year average POD of 0.59, a FAR of 0.86, and a bias of 4.25. In contrast, the evaluation based on the neighborhood pixel led to improved detection performance, with a POD of 0.70, FAR of 0.81, and Bias of 3.73. Year-to-year variation in the metrics was relatively small, although 2022 showed a slightly higher bias (Table 5).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Flag** & **0** & **1–13** & **14** & **15** \\ \hline Proportion [\%] & 52.90 & 0.02 & 3.73 & 43.34 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Proportion of quality flags in GK2A fog detection product at visibility meter stations, 2021–2023 (Flag 0: nominal, Flags 1–13: some channel data or previous time data missing, Flag 14: snow-contaminated, Flag 15: cloud-contaminated). The total scene count is 156,369.  
Regardless of the validation method, the POD of the GK2A_FDA was generally acceptable in the context of satellite fog detection, indicating a reasonable fog detection rate. However, the relatively high FAR and bias values suggest a tendency toward over-detection. To more conservatively assess the detection performance, this study primarily applied the nearest-pixel approach rather than the 3 \(\times\) 3 neighborhood pixel method. Therefore, the fog detection performance presented in this study reflects a minimum estimate rather than the maximum potential capability of the GK2A_FDA.  
Figure 3: The average annual number of fog occurrence days by season during 2021–2023 at 176 visibility meter stations. The quartered circular markers represent the seasonal fog frequency at each observation site. Each quadrant corresponds to a specific season in a clockwise order, starting from the top right corner: spring, summer, autumn, and winter.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**GK2A Fog** & **Year** & **POD** & **FAR** & **Bias** \\ \hline \multirow{3}{*}{The nearest pixel} & 2021 & 0.58 & 0.84 & 3.61 \\ \cline{2-5}  & 2022 & 0.59 & 0.88 & 5.13 \\ \cline{2-5}  & 2023 & 0.59 & 0.86 & 4.14 \\ \cline{2-5}  & Ave. & 0.59 & 0.86 & 4.25 \\ \hline \multirow{3}{*}{\(3\times 3\) neighborhood pixel} & 2021 & 0.69 & 0.77 & 3.04 \\ \cline{2-5}  & 2022 & 0.71 & 0.85 & 4.61 \\ \cline{2-5}  & 2023 & 0.70 & 0.81 & 3.70 \\ \cline{2-5}  & Ave. & 0.70 & 0.81 & 3.73 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Overall performance of the GK2A fog detection algorithm by year (2021, 2022, 2023) and validation method (nearest pixel, 3 \(\times\) 3 neighborhood pixel).