## 3 Results
### Case Studies of Fog Detection
#### 3.2.3 Performance According to the Fog Frequency  
Figure 9 presents the distributions of POD, FAR, and Bias grouped into ten quantile-based categories according to the daily frequency of ground fog observed by visibility meters. This analysis defines a foggy day as a day with six or more fog observations recorded at 10 min intervals [12]. In the nearest-pixel method, the first group, representing the highest fog occurrence frequency, shows a POD of 0.72, FAR of 0.65, and bias of 2.08, accounting for 45.3% of the total foggy days. As fog frequency decreases, POD gradually declines while FAR increases, reducing detection performance. POD drops to 0.28 in the lowest-frequency group, while FAR reaches 0.99 and bias increases to 24.06. When the \(3\times 3\) neighborhood pixel method is applied, the first group exhibits improved detection performance with a POD of 0.82, FAR of 0.59, and bias of 2.02, representing 45.8% of all fog observation days. In the lowest-frequency group, the performance similarly deteriorates, with a POD of 0.35, FAR of 0.99, and bias of 26.99, indicating a strong tendency  
Figure 8: A time series analysis of low stratus cases at Seoul using (**a**) GK2A fog detection imagery, (**b**) fog detection result and ground visibility data, (**c**) GK2A cloud-top height and ceilometer observations, and (**d**) ASOS meteorological data (period: 18:00 LST on 20 January 2021 to 09:00 LST on 21 January 2021).  
for false detection by the nearest-pixel method. These results align with [PERSON] et al. [31], which reported that the GK2A_FDA performs better when fog events are stronger and spatially extensive.  
According to [PERSON] et al. [28], the GK2A_FDA achieved a POD of 0.82 (0.80), FAR of 0.29 (0.37), and bias of 1.16 (1.28) for 11 validation (12 training) fog event days during algorithm development, based on the nearest-pixel method. However, the three-year average performance, which reflects all weather conditions, not just fog cases, shows lower POD and markedly higher FAR and bias than the individual validation cases.  
Figure 10 presents the monthly fog frequency of GK2A_FDA alongside ground-based fog observation frequencies. The ground fog frequency is calculated as the annual average number of fog observations per month divided by the number of stations in each region. Multiplying the satellite detection frequency by 10 min estimates each site's average annual fog duration. In inland regions, fog occurrence is highest during autumn (September-November), when radiation fog frequently forms [11; 12]. During this period, favorable conditions for fog development are established due to strong nocturnal stability, weak winds, clear skies, and dry air, which enhance longwave radiative cooling at the surface [42]. In coastal areas, fog occurs most frequently in early spring (March) and during the summer months of June and July, when sea fog is prevalent [12; 33]. Due to the influence of the Siberian High, the inland atmosphere tends to be dry and stable during winter (January-February), leading to low fog frequencies [35]. Coastal regions also show low fog frequencies in winter and August, with minimal air-sea temperature difference [33]. Although the GK2A_FDA consistently shows higher fog detection frequencies than ground-based observations across all months, the overall seasonal variation pattern is generally similar. Notably, June in inland regions shows a relatively high fog detection frequency, comparable to the autumn months.  
Figure 9: The distribution of GK2A_FDA POD, FAR, and bias based on the 10% quantiles of daily ground fog occurrences from 2021 to 2023. The dashed and solid lines indicate that validation was performed by the nearest pixel and 3 \(\times\) 3 neighborhood pixel methods, respectively.