Probability Index of Low Stratus and Fog at Dawn using Dual Geostationary Satellite Observations from COMS and FY-2D near the Korean Peninsula

We developed a new remote sensing method for detecting low stratus and fog (LSF) at dawn in terms of probability index (PI) of LSF from simultaneous stereo observations of two geostationary-orbit satellites; the Korean Communication, Ocean, and Meteorological Satellite (COMS; 128.2◦E); and the Chinese FengYun satellite (FY-2D; 86.5◦E). The algorithm was validated near the Korean Peninsula between the months of April and August from April 2012 to June 2015, by using surface observations at 45 meteorological stations in South Korea. The optical features of LSF were estimated by using satellite retrievals and simulated data from the radiative transfer model. The PI was calculated using the combination of three satellite-observed variables: (1) the reflectance at 0.67 μm (R0.67) from COMS, and (2) the FY-2D R0.67 minus the COMS R0.67 (4R0.67) and (3) the FY-2D-COMS difference in the brightness temperature difference between 3.7 and 11.0μm (∆BTD3.7-11). The three variables, adopted from the top three probability of detection (POD) scores for their fog detection thresholds: 4R0.67 (0.82) > ∆BTD3.7-11 (0.73) > R0.67 (0.70) > BTD3.7-11 (0.51). The LSF PI for this algorithm was significantly better in the two case studies compared to that using COMS only (i.e., R0.67 or BTD3.7-11), so that this improvement was due to 4R0.67 and ∆BTD3.7-11. Overall, PI in the LSF spatial distribution has the merits of a high detection rate, a specific probability display, and a low rate of seasonality and variability in detection accuracy. Therefore, PI would be useful for monitoring LSF in near-real-time, and to further its forecast ability, using next-generation satellites.


Introduction
Improved sensing of low stratus and fog (LSF) has important implications for safety in ground, sea, and air transportation, because of reduced visibility [1]. Fog occurs frequently in South Korea, particularly during the dawn and dusk rush hours, so that accurate fog detection is of vital importance in risk management, to reduce potential life and economic losses. Ground-based and satellite-based observations are commonly used for fog detection. The accuracy of ground-based observations by the naked-eye is high (80.8%), and is at 70.5% using a visibility meter [2]. However, the range is mostly limited to inland and coastal areas (or islands), making it difficult to monitor fog over larger areas, such as the open sea [3,4]. To supplement the spatial limit of ground-based observations, satellite-based

Materials and Methods
The near-simultaneous observations of the dual satellites (COMS and FY-2D) for the LSF detection at dawn near the Korean Peninsula are defined as the differences between their stereoscopic views. For this study's purpose, 'dawn' is within two hours after sunrise (67 • < SZA < 86 • ). Ground-based fog observations and associated numerical experiments were used to validate the satellite-derived LSF detections.

Satellite and Ground-Based Observations
The data from three channels (R 0.67 , BT 3.7 , and BT 11 ) in each satellite were utilized for the LSF detection. The satellite information is summarized in Table 1, and their locations are shown in Figure 1. The COMS data were linearly interpolated onto the FY-2D dataset for comparison at the same spatial resolutions. The maximum time difference allowed between COMS and FY-2D observations for this study was 15 minutes. We derived R 0.67 , BTD 3.7-11 , ∆R 0.67 , and ∆BTD 3.7-11 from these datasets. The differences in R 0.67 and BTD 3.7-11 between the satellites can be defined as follows: spatial resolutions. The maximum time difference allowed between COMS and FY-2D observations for this study was 15 minutes. We derived R0.67, BTD3.7-11, ΔR0.67, and ΔBTD3.7-11 from these datasets. The differences in R0.67 and BTD3.7-11 between the satellites can be defined as follows:  Here, R FY−2D and R COMS are the R 0.67 values of the FY-2D and COMS satellites, respectively. Similarly, BTD FY−2D and BTD COMS are the BTD 3.7-11 values of the corresponding satellites. The ∆R 0.67 threshold for LSF detection from the dual satellites in [8] was shown to be superior to the existing R 0.67 and BTD 3.7-11 thresholds of the COMS satellite alone. In our study, we introduce ∆BTD 3.7-11 as an additional variable to improve the spring (April and May) and summer LSF detection accuracy. The dual satellite observations (i.e., ∆R 0.67 and ∆BTD 3.7-11 ), as well as R 0.67 , are utilized as three components in the PI formulation. This provides a more accurate detection and specific display for the weather phenomenon, than the individual thresholds described in previous studies (e.g., [8,19]). It is because the ∆BTD 3.7-11 in (2) has less seasonality in the LSF detection than the ∆R 0.67 in (1), and because it is useful, particularly in April-May, over the Yellow Sea [31]. The R 0.67 values of less than 0.001 were excluded in the process of data quality control in this study.
Ground-based fog and clear-sky observations [32] were used to derive and validate PI for LSF detection at dawn in South Korea from April to August between April 2012 and June 2015. There are 45 meteorological ground stations located in the country's inland and coastal regions ( Figure 2 and Table A2). Ground observations included data on the cloud amount, visibility, rain, and mist at a one-hour interval. In most cases, visibility and cloud altitude are determined by an automatic weather system, but some stations still operate by utilizing human observers. A total of 754 fog and 433 clear-sky cases from the ground-based observations were used to derive the LSF thresholds and the PI for the detection ( Table 2). The fog and clear-sky data were subdivided into two periods, control data during 2012-2013 and experimental data during 2014-2015. Relatively optically thick fog cases were investigated in this study. Therefore, fog cases with a duration of at least 30 minutes were selected to exclude optically thin fog cases. The clear-sky, in contrast with the fog, was defined in this study as a cloud amount of less than 10% during the dry period (i.e., September to April). These months were chosen because clear-sky occurrences are rare between May and August, due to persistent rain and yellow dust, possibly resulting in cloud or aerosol contamination. In order to compare satellite-derived higher cloud classifications above the LSF layer with the ground-based observations, the cloud type and height data from the reports of both ground stations and surface synoptic observations (SYNOP) were used [33]. Cloud-type data were often described as being 'missing' or omitted from the reports, especially for middle and high clouds. The 'missing' cases were excluded in this study.

Probability Index Formulation from Past Fog Observations
The PI formulation converts the long-term LSF probabilities to the near real-time LSF probabilities. To make the long-term LSF probabilities, we have counted the frequencies of LSF occurrences in a grid for the 18 months. The LSF occurrences are those detected by the three threshold tests: ΔR0.67, ΔBTD3.7-11, and R0.67. Observations of ΔR0.67 and ΔBTD3.7-11 are taken from the two-satellites that are collocated in ~5 km × ~5 km grids, while R0.67 from the COMS satellite pixels. As we will show later, these three tests have been selected, as they make higher probability of detection (POD) scores in LSF detection than other tests.
Seven LSF classes have been divided from a combination of the three threshold tests (Figure 3a). Each class has a long-term probability of fog detection at the 45 stations, as indicated by the frequency of each fog class, normalized by the total frequency ( Figure 3b). Data from 754 fog and 433 clear-sky observations have been used for this calculation. Using the higher cloud criteria, the fog data have been categorized into two types of LSF cases (473 LSF1 and 281 LSFhighclouds, refer to Table A1 for the acronyms and Figure A1 for the detailed meaning). Since the three tests are not entirely independent of each other in their optical properties for detection, their information is partially overlapped. For instance, the 'Class 1' indicates the fog occurrences detected by the all three threshold tests. Each class provides information on the normalized frequency that is succeeded by the threshold tests ( Figure  3b). In Figure 3b, there is no FAR for Class 1. For instances, Class 2 and Class 5 successfully detected fog by using the two tests (ΔR0.67 and ΔBTD3.7-11) and only the R0.67 test, respectively. The LSF cases that failed the threshold tests are indicated by 'Miss'. The Normalized Frequency of LSF (NFL) in Figure 3b is summarized in Table 3.
With the same 18-month fog records, we estimated PI (PI est ) to be equivalent to the POD values (0.816 ± 0.02 for total LSF) of the best threshold test using ΔR0.67 (later shown in Table 4). This is because the PI est is PI that is estimated for the upper-limit condition of LSF detection accuracy, and it should not exceed the maximum POD value. The condition is assumed conservatively, to prevent excessive PI values. Since each threshold test has an inherently independent portion for LSF detection, the PI value (which has comprehensively been obtained from the three tests) would be better than the POD from one threshold test. Finally, the seven weighting factors ( WF(Class i ) ) in the PI formulation have to be determined, in order to satisfy the following relation:

Probability Index Formulation from Past Fog Observations
The PI formulation converts the long-term LSF probabilities to the near real-time LSF probabilities. To make the long-term LSF probabilities, we have counted the frequencies of LSF occurrences in a grid for the 18 months. The LSF occurrences are those detected by the three threshold tests: ∆R 0.67 , ∆BTD 3.7-11 , and R 0.67 . Observations of ∆R 0.67 and ∆BTD 3.7-11 are taken from the two-satellites that are collocated in~5 km ×~5 km grids, while R 0.67 from the COMS satellite pixels. As we will show later, these three tests have been selected, as they make higher probability of detection (POD) scores in LSF detection than other tests.
Seven LSF classes have been divided from a combination of the three threshold tests (Figure 3a). Each class has a long-term probability of fog detection at the 45 stations, as indicated by the frequency of each fog class, normalized by the total frequency ( Figure 3b). Data from 754 fog and 433 clear-sky observations have been used for this calculation. Using the higher cloud criteria, the fog data have been categorized into two types of LSF cases (473 LSF1 and 281 LSF highclouds , refer to Table A1 for the acronyms and Figure A1 for the detailed meaning). Since the three tests are not entirely independent of each other in their optical properties for detection, their information is partially overlapped. For instance, the 'Class 1' indicates the fog occurrences detected by the all three threshold tests. Each class provides information on the normalized frequency that is succeeded by the threshold tests ( Figure 3b). In Figure 3b, there is no FAR for Class 1. For instances, Class 2 and Class 5 successfully detected fog by using the two tests (∆R 0.67 and ∆BTD 3.7-11 ) and only the R 0.67 test, respectively. The LSF cases that failed the threshold tests are indicated by 'Miss'. The Normalized Frequency of LSF (NFL) in Figure 3b is summarized in Table 3. Normalized frequency distributions of the classes. Table 3. Normalized Frequency of LSF (NFL) and weighting factor (WF) values for each class of the DSM. The terms 'NFL' and 'WF' are defined in the text. 'WF*' has been obtained from the frequency ratio of fog cases to the whole data (i.e., fog and clear-sky) to include the false alarm rate (FAR) effect. where WF(Class i ) is the weighting factor; subscript 'i' is the ith class of LSF (i = 1 to 7); NFL i and PI est are pre-calculated values by the 18-month fog records. LSF 'Miss' could be considered as an eighth class, although it was not included in (3). The WF(Classi) values were determined, considering the three priority conditions: a high POD ranking (ΔR0.67 > ΔBTD3.7-11 > R0.67) based on observations from 45 stations, common detection from two or more threshold tests, and low FAR. Table 3 shows that the WF(Class i ) for seven classes ranges from 0.5 to 1. WF(Class i ) for 'Miss' is zero. Since the WF(Class i ) is related to fog detection from at least one of the three thresholds, it is assumed to be greater than ~0.5, in view of a reasonable probability of detection. Thus, the lowest WF is set to 0.5 ( Table 3). The values of 'NFL of clear-sky' and 'WF*' have also been presented in the table, to analyze the clear-sky (or FAR) effect on LSF detection. The effect does not exceed 10% in each class. Also, the WF* (i.e., PI), which includes the effect, is higher in each class than 0.55. However, the effect is likely to increase over the real-time satellite scene, due to various weather conditions (e.g., clear-sky, overcast, and fog, etc.).

The Near-Realtime LSF PI Retrieval Scheme
The flowchart shows the entire PI calculation process for the LSF PI retrieval at dawn, using the DSM (Figure 4). It begins with the pre-process reading data (Section 2.1) and then it requires the PI formulation (Section 2.2). In the pre-process, we collocated 45 ground station sites onto ~5 km × 5 km satellite observation grids, and satellite data were collected when fog occurred at the ground stations. The optimum thresholds were derived from this information, to discriminate between fog and clear-sky cases, based on the skill score test of the variables (ΔR0.67, R0.67, and ΔBTD3.7-11).  Table 3. Normalized Frequency of LSF (NFL) and weighting factor (WF) values for each class of the DSM. The terms 'NFL' and 'WF' are defined in the text. 'WF*' has been obtained from the frequency ratio of fog cases to the whole data (i.e., fog and clear-sky) to include the false alarm rate (FAR) effect. With the same 18-month fog records, we estimated PI (PI est ) to be equivalent to the POD values (0.816 ± 0.02 for total LSF) of the best threshold test using ∆R 0.67 (later shown in Table 4). This is because the PI est is PI that is estimated for the upper-limit condition of LSF detection accuracy, and it should not exceed the maximum POD value. The condition is assumed conservatively, to prevent excessive PI values. Since each threshold test has an inherently independent portion for LSF detection, the PI value (which has comprehensively been obtained from the three tests) would be better than the POD from one threshold test. Finally, the seven weighting factors (WF(Class i )) in the PI formulation have to be determined, in order to satisfy the following relation:

a) Seven classes of LSF
where WF(Class i ) is the weighting factor; subscript 'i' is the ith class of LSF (i = 1 to 7); NFL i and PI est are pre-calculated values by the 18-month fog records. LSF 'Miss' could be considered as an eighth class, although it was not included in (3). The WF(Class i ) values were determined, considering the three priority conditions: a high POD ranking (∆R 0.67 > ∆BTD 3.7-11 > R 0.67 ) based on observations from 45 stations, common detection from two or more threshold tests, and low FAR. Table 3 shows that the WF(Class i ) for seven classes ranges from 0.5 to 1. WF(Class i ) for 'Miss' is zero. Since the WF(Class i ) is related to fog detection from at least one of the three thresholds, it is assumed to be greater than~0.5, in view of a reasonable probability of detection. Thus, the lowest WF is set to 0.5 ( Table 3). The values of 'NFL of clear-sky' and 'WF*' have also been presented in the table, to analyze the clear-sky (or FAR) effect on LSF detection. The effect does not exceed 10% in each class. Also, the WF* (i.e., PI), which includes the effect, is higher in each class than 0.55. However, the effect is likely to increase over the real-time satellite scene, due to various weather conditions (e.g., clear-sky, overcast, and fog, etc.).

The Near-Realtime LSF PI Retrieval Scheme
The flowchart shows the entire PI calculation process for the LSF PI retrieval at dawn, using the DSM ( Figure 4). It begins with the pre-process reading data (Section 2.1) and then it requires the PI formulation (Section 2.2). In the pre-process, we collocated 45 ground station sites onto~5 km × 5 km satellite observation grids, and satellite data were collected when fog occurred at the ground stations. The optimum thresholds were derived from this information, to discriminate between fog and clear-sky cases, based on the skill score test of the variables (∆R 0.67 , R 0.67 , and ∆BTD 3.7-11 ).
higher cloud exists above the fog layer: BT11 standard deviation in 3  3 grids ( 11 ), BT11max-BT11, and R0.67-Rmin [8]. The values of BT11 and R0.67 were determined from the COMS observations. BT11max and Rmin were the values of the BT11 maximum and R0.67 minimum, respectively, in the vicinity of the Korean Peninsula (122-132E, 32.5-42.5N). Of the 754 total fog observations that occurred at the ground stations during 2012-2015, 473 were categorized as LSF1, and 281 were categorized as LSFhighclouds.  The pre-process also minimizes the effects of the higher clouds above a fog layer on the satellite-derived LSF PI retrieval. By these means, we performed RTM simulations to constructed a look-up table (LUT) for the three variables (∆R 0.67 , ∆BTD 3.7-11 , and R 0.67 ). The RTM of the Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART) was used to compute the plane-parallel radiative transfer for clear and cloudy conditions in the atmosphere and at the surface [34]. The RTM of SBDART was utilized to derive the thresholds for the fog detection and its optical characteristics for daytime [35] and nighttime [4], and at dawn [8]. The initial conditions for the RTM input were various degrees of cloudiness (i.e., clear-sky, LSF1, and LSF highclouds ) and cloud optical properties (phase, size, and optical thickness). LSF1 can be defined as being either fog or low stratus, while LSF highclouds can be defined as the LSF1 accompanying higher clouds above it. A schematic diagram on the two types of LSF is shown in Figure A1. Details about the RTM input are in Table A4. Results for the various weather conditions were saved in the LUT for the time-saving purposes before being applied to an almost real-time satellite scene. The near-simultaneous satellite observations for the three thresholds, and LUT were analyzed with the ground-based observations.
In addition, the following three conditions were used in a grid to remove the instances where higher cloud exists above the fog layer: BT 11 standard deviation in 3 × 3 grids (σ T 11 ), BT 11max -BT 11 , and R 0.67-R min [8]. The values of BT 11 and R 0.67 were determined from the COMS observations. BT 11max and R min were the values of the BT 11 maximum and R 0.67 minimum, respectively, in the vicinity of the Korean Peninsula (122-132 • E, 32.5-42.5 • N). Of the 754 total fog observations that occurred at the ground stations during 2012-2015, 473 were categorized as LSF1, and 281 were categorized as LSF highclouds .
For the determination of near-real-time LSF PI, we used the WF(Class i ) values in Table 3 from PI formulation (Section 2.2). Once the class of LSF is determined from the threshold tests for each grid-point near-real-time satellite data, the LSF PI is simply set to be one of the seven WF(Class i ) values (Table 3), which correspond to the LSF class determined from the satellite observations (Class obs ). Thus, the near-real-time LSF PI is 0, or 0.5 to 1.0. Above all, this LSF PI can be readily presented on a 2D map. This 2D map is especially useful for the west coast of the country and the Yellow Sea, where the ground observations are rare, despite frequent fog occurrences [16,28].

Results
The simulated and satellite-observed LSF detection results are described in this section to demonstrate its remote sensing skills. The RTM simulation was carried out over three time ranges, dawn, noon, and dusk. This was done in order to address the usefulness of the dual satellite observations at dawn. The pre-process for improved LSF detection is shown in Sections 3.1 and 3.2, based on the long-term observations and the RTM simulation. Spatial PI distributions from the case study are presented in Section 3.3.

RTM Simulation for LSF
The simulation gives insight for fog detection at dawn, utilizing the three thresholds (∆R 0.67 , R 0.67 , and ∆BTD 3.7-11 ) from the dual satellite observations ( Figure 5). The optical characteristics of LSF can be estimated by both their simulations and observations. Since direct and diffuse radiation varies with the diurnal variation of SZA [36], the simulated ∆R 0.67 was largest at dawn (06:00 local standard time; LST). These significantly large differences (∆R 0.67 or ∆BTD 3.7-11 ) can be used as indicators for LSF detection (Figure 5a,b). They are greater at dawn than at the other time ranges, due to the angle difference between the two satellites, compared to the spectral response function (SRF) [8]. Remote Sens. 2019, 11, x FOR PEER REVIEW 9 of 24  Table A4. Each simulation on 18 July 2014 was shown in the dual-satellite relationship of FY-2D and COMS at three different times: 06:00 LST (for dawn), 12:00 LST (noon), and 18:00 LST (for dusk). The reflectance and BTD3.7-11 simulations are presented in the left-and righthand columns, respectively. The clear-sky value is shown in the leftmost one (red square) in each figure.

Optimum Thresholds for LSF Detection
In satellite-based LSF detection, the optimum thresholds are important for distinctly separating the clear-sky and LSF phenomena. After co-locating the ground-based and dual-satellite observations, the satellite data related to these weather phenomena (754 fog and 433 clear-sky occurrences) were collected in terms of reflectance (R0.67 and ΔR0.67) and brightness temperature (BTD3.7-11 and ΔBTD3.7-11) for each grid. To determine the optimum LSF thresholds for the variables ΔR0.67, R0.67, ΔBTD3.7-11, and BTD3.7-11, the frequency distributions of LSF (green), LSF1 (red), and clear-sky (blue) were presented, respectively ( Figure 6). Here, LSF means total LSF (LSF1 and LSFhighclouds). The dashed lines in pink indicate the upper and lower thresholds between total LSF and clear-sky. There is no overlap with clear-sky in the upper-limit condition. However, it is necessary to filter the optically thick convective clouds without accompanying LSF (e.g., Yoo et al. [22]). The individual threshold was obtained iteratively until its total LSF POD reached a maximum under the limiting condition FAR ≤ 0.15, as shown in Table 4. This limitation is needed for the practical purpose of LSF detection. The POD The four colors (red, green, blue, and black) and four symbols (circle, asterisk, triangle, and rectangle) in Figure 5 denote the effective radii (ER: 2, 4, 8, 16 µm) and heights (FH or CH: 2, 4-6, 8-10 km) of the fog and cloud particles, respectively. RTM details are given in Table A4. The figures on the left show the relationship between ∆R 0.67 and R 0.67 at dawn, noon, and dusk (Figure 5a,c,e). The relationship between ∆BTD 3.7-11 and BTD 3.7-11 is presented on the right (Figure 5b,d,f). The ∆R 0.67 and ∆BTD 3.7-11 values from the dual-satellite relationship at dawn are about three times as large as those at noon and dusk, regardless of the various input conditions (e.g., high clouds above the fog layer, effective radii of fog or cloud, and their phase). In other words, the values at dawn under the LSF conditions (see also Figure A1 for the LSF definition) are substantially large compared to those at noon and dusk. However, there is a significant difference in seasonal variation between ∆R 0.67 and ∆BTD 3.7-11 (later shown in Figure 11).
While the ∆R 0.67 value at a given location was largest in the summer, the ∆BTD 3.7-11 was less sensitive to seasonality, and it was possibly useful for the other seasons (e.g., spring). The simulation implies that the dual satellite-derived thresholds for LSF sensing near the Korean Peninsula are best at dawn (Figure 5a,b) and worst at noon (Figure 5c,d). The values of ∆R 0.67 and ∆BTD 3.7-11 at dusk were relatively small and opposite to each other, compared to their values at dawn (Figure 5e,f). The relationship between ∆BTD 3.7-11 and BTD 3.7-11 is similar to that of ∆R 0.67 and R 0.67 , except at noon. Fog detection in the former relationship was less useful than in the latter, because their variations with LSF height and ER were less systematic and included more detection uncertainties. Since the simulated differences (∆R 0.67 and ∆BTD 3.7-11 ) at dawn were remarkably larger in the LSF situations than when the sky was clear, they can provide good thresholds for LSF detection from the dual-satellite observations.
The simulated ∆R 0.67 values near the Korean Peninsula at dawn need to be larger than 0.35, to separate the weather phenomena of LSF and clear-sky ( Figure 5). Since the values under the LSF condition at dusk and noon did not generally reach the threshold, these dual-satellite observations were less useful. These results were caused by the angles made by the sun and the satellites in the space (i.e., SZA and RAA), which affect direct and diffuse radiation in radiative transfer. For these reasons, the dual-satellite relationship focused only on detection at dawn.

Optimum Thresholds for LSF Detection
In satellite-based LSF detection, the optimum thresholds are important for distinctly separating the clear-sky and LSF phenomena. After co-locating the ground-based and dual-satellite observations, the satellite data related to these weather phenomena (754 fog and 433 clear-sky occurrences) were collected in terms of reflectance (R 0.67 and ∆R 0.67 ) and brightness temperature (BTD 3.7-11 and ∆BTD 3.7-11 ) for each grid. To determine the optimum LSF thresholds for the variables ∆R 0.67 , R 0.67 , ∆BTD 3.7-11 , and BTD 3.7-11 , the frequency distributions of LSF (green), LSF1 (red), and clear-sky (blue) were presented, respectively ( Figure 6). Here, LSF means total LSF (LSF1 and LSF highclouds ). The dashed lines in pink indicate the upper and lower thresholds between total LSF and clear-sky. There is no overlap with clear-sky in the upper-limit condition. However, it is necessary to filter the optically thick convective clouds without accompanying LSF (e.g., Yoo et al. [22]). The individual threshold was obtained iteratively until its total LSF POD reached a maximum under the limiting condition FAR ≤ 0.15, as shown in Table 4. This limitation is needed for the practical purpose of LSF detection. The POD maxima for the thresholds of the variables in the detection of either the total LSF or LSF1 during the study period were estimated to be ∆R 0.67 (0.82-0.90) > ∆BTD 3.7-11 (0.73-0.74) > R 0.67 (0.70-0.73) > BTD 3.7-11 (0.33-0.51). This indicates that the ∆R 0.67 threshold was best for both the total LSF and LSF1 detection (Figure 6a), while the BTD 3.7-11 threshold was worst ( Figure 6d). maxima for the thresholds of the variables in the detection of either the total LSF or LSF1 during the study period were estimated to be ΔR0.67 (0.82-0.90) > ΔBTD3.7-11 (0.73-0.74) > R0.67 (0.70-0.73) > BTD3.7-11 (0.33-0.51). This indicates that the ΔR0.67 threshold was best for both the total LSF and LSF1 detection (Figure 6a), while the BTD3.7-11 threshold was worst (Figure 6d).
Based on their frequency distributions, all of the thresholds (ΔR0.67, ΔBTD3.7-11, and R0.67) except for BTD3.7-11 were useful for LSF detection. This means that the LSF phenomena was reasonably well detected by using the dual satellite thresholds on the satellite-observed scene, where the LSF and clear-sky cases coexist. Thus, both of the satellite observation variables ΔR0.67 and ΔBTD3.7-11 are included in the PI formulation of this study, while only R0.67 was utilized in previous studies. The higher clouds above the LSF1 layer had a large effect on LSF and clear-sky classification in the ΔR0.67 domain (Figure 6a), compared to R0.67 in Figure 6b. In other words, the LSF detection from the ΔR0.67 threshold was more accurate in the LSF1 cases (red line) without the accompanying higher clouds, than for the total LSF (green line), which is composed of both LSF1 and LSFhighclouds. LSFhighclouds included the clouds above the LSF1 layer, which were a hindrance to the LSF detection [22]. The ΔBTD3.7-11 threshold was less sensitive to the higher clouds than the ΔR0.67 threshold (Figure 6a), showing similar patterns of LSF (green line) and LSF1 (red line). In summary, the accuracy of LSF detection by the satellite-derived thresholds was affected by the clouds, and the seasonal and diurnal variations of the satellite observations. Statistical verification on total LSF and LSF1 was performed with respect to the six threshold variables, ΔR0.67, R0.67, RKMA, ΔBTD3.7-11, BTD3.7-11, and BTDKMA, and the verification used fog and clearsky data at 45 ground stations in South Korea at dawn during the study period. Five skill indices Based on their frequency distributions, all of the thresholds (∆R 0.67 , ∆BTD 3.7-11 , and R 0.67 ) except for BTD 3.7-11 were useful for LSF detection. This means that the LSF phenomena was reasonably well detected by using the dual satellite thresholds on the satellite-observed scene, where the LSF and clear-sky cases coexist. Thus, both of the satellite observation variables ∆R 0.67 and ∆BTD 3.7-11 are included in the PI formulation of this study, while only R 0.67 was utilized in previous studies. The higher clouds above the LSF1 layer had a large effect on LSF and clear-sky classification in the ∆R 0.67 domain (Figure 6a), compared to R 0.67 in Figure 6b. In other words, the LSF detection from the ∆R 0.67 threshold was more accurate in the LSF1 cases (red line) without the accompanying higher clouds, than for the total LSF (green line), which is composed of both LSF1 and LSF highclouds . LSF highclouds included the clouds above the LSF1 layer, which were a hindrance to the LSF detection [22]. The ∆BTD 3.7-11 threshold was less sensitive to the higher clouds than the ∆R 0.67 threshold (Figure 6a), showing similar patterns of LSF (green line) and LSF1 (red line). In summary, the accuracy of LSF detection by the satellite-derived thresholds was affected by the clouds, and the seasonal and diurnal variations of the satellite observations. Statistical verification on total LSF and LSF1 was performed with respect to the six threshold variables, ∆R 0.67 , R 0.67 , R KMA , ∆BTD 3.7-11 , BTD 3.7-11 , and BTD KMA , and the verification used fog and clear-sky data at 45 ground stations in South Korea at dawn during the study period. Five skill indices [37,38] were used for statistical analysis: HSS (Heidke Skill Score), CSI (Critical Success Index), POD (Probability of Detection), PC (Percentage Correct), and FAR (False Alarm Ratio). Table 4 shows the verification in terms of the skill scores for Period 1 (2012-2013), Period 2 (2014Period 2 ( -2015, and the entire time span (2012)(2013)(2014)(2015). The data from Period 1 denote the control case, and the fog detection thresholds were developed from these satellite observations. The data from Period 2 are the experimental case applied to the threshold quality evaluation. Other than FAR, the higher the skill indices, the higher the detection efficiency; the lower the FAR, the higher the accuracy. The thresholds R KMA and BTD KMA , used for daytime (SZA ≤ 60 • ) fog detection in KMA [19], were included with the other four thresholds, to allow for a comparison among the available conventional thresholds. Table 4 shows that the HSS values of the total LSF for the whole period were in a descending magnitude order of R 0.67 (0.699) > R 0.67 (0.588) > BTD 3.7-11 (0.585) > R KMA (0.489) > BTD 3.7-11 (0.369) > BTD KMA (0.104). This means that the ∆R 0.67 threshold was the most effective at detecting fog at dawn. In addition, ∆R 0.67 and ∆BTD 3.7-11 (the dual satellite-observations) were at least 6-21% more accurate than the conventional COMS-only R KMA or BTD KMA thresholds [19]. The POD skill scores descend in the order of ∆R 0.67 > ∆BTD 3.7-11 > R 0.67 > R KMA > BTD 3.7-11 > BTD KMA . The results for Period 2 were similar to those for Period 1 (Figure 7a,b and Table 4), although, due to interannual variations, the scores were somewhat higher for the experimental data than those for the control. Compared to KMA [19], the ∆R 0.67 and ∆BTD 3.7-11 thresholds were excellent detection indicators overall.
The accuracy of ΔR0.67 and R0.67 in LSF1 was higher by 9-11% compared to the total LSF (Table 4). This indicates that the higher clouds above the LSF1 layer resulted in a significant hindrance to the detection by the reflectance thresholds. The LSF1 scores from the reflectance-based thresholds (i.e., ΔR0.67, R0.67, and RKMA) were higher than for total LSF, suggesting that they were more sensitive to the clouds than to the brightness temperatures (ΔBTD3.7-11, BTD3.7-11, and BTDKMA). The BTD-based thresholds did not show significant improvements over the LSF1, compared to the total LSF, probably due to their low sensitivities to the clouds. Scatter diagrams in two dimensions (2D) and three dimensions (3D) were presented by using the top three thresholds of the variables (ΔR0.67, ΔBTD3.7-11 and R0.67) in the POD scores (Table 4 and Figures 7 and 8). In total, the cases of 473 LSF1 (red asterisk), 281 LSFhighclouds (green triangle), and 433 clear-sky (blue cross) were used. The LSF1 and LSFhighclouds cases are shown for Period 1 and Period 2, respectively, in Table A5. The ratio values of LSF1 to total LSF case are 62-63% for the two periods. The dashed-line boundaries in the 2D figures indicate the threshold values of the coordinate variables (Figure 8a-c). If the satellite observations in a grid that were co-located with the ground observed fog occurrences within their threshold boundaries, the LSF detection was regarded as a 'success.' LSF and clear-sky separation in the ΔR0.67 versus R0.67 diagrams (Figure 8a) and ΔR0.67 versus ΔBTD3.7-11 diagrams (Figure 8b) were excellent.
The LSF detection value of R0.67 (69.6%) was obtained from 525 LSF cases out of 754 fog occurrences. The LSF1 detection value (73.2%) was obtained from 346 LSF1 cases out of 473 fog occurrences. Also, the POD scores of the ΔR0.67 threshold in the ordinate were 81.6% for the total LSF, and 90.1% for LSF1, respectively. ΔR0.67 from the dual satellite observations was 12.0-16.9% better at detecting the total LSF and LSF1 than the R0.67 from the single COMS observations. The POD values of ΔR0.67 compared to R0.67 were enhanced by 12.0% for the total LSF and by 16.9% for LSF1. In other words, the ΔR0.67 threshold was more accurate for LSF1 in the absence of higher clouds. In Figure 7b and Table 3, the POD values of ΔBTD3.7-11 were 73.1-74.2% for the total LSF and LSF1, and somewhat higher than those of R0.67 (69.6-73.2%). However, the FAR values of ΔBTD3.7-11, 7.2-10.9%, were higher by 4-5% than those of R0.67 (3.9-5.7%). Among the top three thresholds, ΔR0.67 was the best indicator of LSF detection; the others were close. The accuracy of ∆R 0.67 and R 0.67 in LSF1 was higher by 9-11% compared to the total LSF (Table 4). This indicates that the higher clouds above the LSF1 layer resulted in a significant hindrance to the detection by the reflectance thresholds. The LSF1 scores from the reflectance-based thresholds (i.e., ∆R 0.67 , R 0.67 , and R KMA ) were higher than for total LSF, suggesting that they were more sensitive to the clouds than to the brightness temperatures (∆BTD 3.7-11 , BTD 3.7-11 , and BTD KMA ). The BTD-based thresholds did not show significant improvements over the LSF1, compared to the total LSF, probably due to their low sensitivities to the clouds.
Scatter diagrams in two dimensions (2D) and three dimensions (3D) were presented by using the top three thresholds of the variables (∆R 0.67 , ∆BTD 3.7-11 and R 0.67 ) in the POD scores (Table 4 and Figures 7 and 8). In total, the cases of 473 LSF1 (red asterisk), 281 LSF highclouds (green triangle), and 433 clear-sky (blue cross) were used. The LSF1 and LSF highclouds cases are shown for Period 1 and Period 2, respectively, in Table A5. The ratio values of LSF1 to total LSF case are 62-63% for the two periods. The dashed-line boundaries in the 2D figures indicate the threshold values of the coordinate variables (Figure 8a-c). If the satellite observations in a grid that were co-located with the ground observed fog occurrences within their threshold boundaries, the LSF detection was regarded as a 'success.' LSF and clear-sky separation in the ∆R 0.67 versus R 0.67 diagrams (Figure 8a) and ∆R 0.67 versus ∆BTD 3.7-11 diagrams (Figure 8b) were excellent. distinguishable in the 3D depictions than in the 2D ones (Figure 8a,b). The thresholds derived from the three variables inherently had their own merits in the distinction of either LSF1 or LSFhighclouds from clear-sky phenomena, as follows; ΔR0.67 (LSF1 from clear-sky), R0.67 (LSFhighclouds from clear-sky), and ΔBTD3.7-11 (the mixed feature of ΔR0.67 and R0.67). Rather than just using the two variables (ΔR0.67 and R0.67) proposed in Yoo et al. [8], this study used the top three variables for LSF detection.
We conducted a case study on fog occurrence at the island of Ulleungdo (130.9° E, 37.48° N; orange circles) at 06:15 LST on 17 April 2014, to estimate the optical properties of LSF in the 2D and 3D coordinates. These estimations were made using both the dual satellite observations and the RTM simulation ( Figure 9). Regardless of the weather, the dual satellite observations (ΔR0.67 and ΔBTD3. [7][8][9][10][11] are shown in grey circles in the background of Figure 9a-c. The R0.67 and BTD3.7-11 values were observed by using COMS data. Fog (orange circles) is also denoted in the 3D simulation (Figure 9d). According to ground-based reports at 06:00 LST, there were typical fog conditions (surface temperature = 11 °C, air temperature = 10.3 °C, humidity = 93% and visibility = 300 m). The fog type was classified as LSF1, based on this study's higher cloud criteria (i.e., CA, CB, and CC). The groundbased observations also reported meteorological conditions that were consistent with the higher cloud estimation calculated from the satellite-derived criteria (total cloud amount = 10, amount of low and middle clouds = 10, and ceiling = 300 m). The cloud amount is scaled from 0 to 10. The LSF detection value of R 0.67 (69.6%) was obtained from 525 LSF cases out of 754 fog occurrences. The LSF1 detection value (73.2%) was obtained from 346 LSF1 cases out of 473 fog occurrences. Also, the POD scores of the ∆R 0.67 threshold in the ordinate were 81.6% for the total LSF, and 90.1% for LSF1, respectively. ∆R 0.67 from the dual satellite observations was 12.0-16.9% better at detecting the total LSF and LSF1 than the R 0.67 from the single COMS observations. The POD values of ∆R 0.67 compared to R 0.67 were enhanced by 12.0% for the total LSF and by 16.9% for LSF1. In other words, the ∆R 0.67 threshold was more accurate for LSF1 in the absence of higher clouds. In Figure 7b and Table 3, the POD values of ∆BTD 3.7-11 were 73.1-74.2% for the total LSF and LSF1, and somewhat higher than those of R 0.67 (69.6-73.2%). However, the FAR values of ∆BTD 3.7-11 , 7.2-10.9%, were higher by 4-5% than those of R 0.67 (3.9-5.7%). Among the top three thresholds, ∆R 0.67 was the best indicator of LSF detection; the others were close.
Discrimination between the clear-sky and LSF cases at the BTD 3.7-11 axis (Figure 8c) was worse than for ∆R 0.67 , R 0.67 , or ∆BTD 3.7-11 . This discrimination can be better seen in the 3D relationship depicted in Figure 8d. The LSF1, LSF highclouds , and clear-sky weather phenomena were more distinguishable in the 3D depictions than in the 2D ones (Figure 8a,b). The thresholds derived from the three variables inherently had their own merits in the distinction of either LSF1 or LSF highclouds from clear-sky phenomena, as follows; ∆R 0.67 (LSF1 from clear-sky), R 0.67 (LSF highclouds from clear-sky), and ∆BTD 3.7-11 (the mixed feature of ∆R 0.67 and R 0.67 ). Rather than just using the two variables (∆R 0.67 and R 0.67 ) proposed in Yoo et al. [8], this study used the top three variables for LSF detection.
We conducted a case study on fog occurrence at the island of Ulleungdo (130.9 • E, 37.48 • N; orange circles) at 06:15 LST on 17 April 2014, to estimate the optical properties of LSF in the 2D and 3D coordinates. These estimations were made using both the dual satellite observations and the RTM simulation ( Figure 9). Regardless of the weather, the dual satellite observations (∆R 0.67 and ∆BTD 3.7-11 ) are shown in grey circles in the background of Figure 9a-c. The R 0.67 and BTD 3.7-11 values were observed by using COMS data. Fog (orange circles) is also denoted in the 3D simulation (Figure 9d). According to ground-based reports at 06:00 LST, there were typical fog conditions (surface temperature = 11 • C, air temperature = 10.3 • C, humidity = 93% and visibility = 300 m). The fog type was classified as LSF1, based on this study's higher cloud criteria (i.e., CA, CB, and CC). The ground-based observations also reported meteorological conditions that were consistent with the higher cloud estimation calculated from the satellite-derived criteria (total cloud amount = 10, amount of low and middle clouds = 10, and ceiling = 300 m). The cloud amount is scaled from 0 to 10. The optical fog features at the island were investigated by simulating (Table A4) a) ∆R0.67 versus R0.67, b) ΔR0.67 versus ΔBTD3.7-11, and c) ΔBTD3.7-11 versus R0.67 (Figure 9a-c). The symbols and colors represent various fog or cloud conditions: i) just a fog layer (black for 0-1 km and sky-blue for 0-2 km), ii) fog with mid-level (4-6 km) clouds of different phases (red for water, blue for ice), and iii) fog with high-level (8-10 km) clouds (green). Clear-sky is denoted by pink. Similarly to Figure 8, the satellite observations inside the dashed-line rectangle were within the LSF detection threshold ranges for the same spatiotemporal conditions as for fog. Figure 9a-c show that the higher cloud effect above the fog layer (i.e., the difference between LSF1 and LSFhighclouds) varied systematically with cloud height inside the dashed-line threshold rectangle. This was derived from any two of the three variables, ΔR0.67, R0.67, and ΔBTD3.7-11. The simulated results of the middle clouds (blue for ice and red for water) showed they were mixed with each other, and difficult to separate. The simulated optical information, estimated from individual variables, did not necessarily agree with the estimates from the other variable, indicating that it was not unique. Overall, the RTM simulation (asterisks) for the case study agreed with the satellite-based observations (grey circles) and the ground-based fog observations (yellow). The 2D simulations for the case study used the optical characteristics of the top three LSF detection variables. The actual fog case (orange circles) in the 3D simulation (Figure 9d) demonstrated three kinds of LSF optical features: i) a 1 km-height fog layer (i.e., LSF1) for ΔR0.67 versus R0.67 ( Figure  9a), ii) a 2 km-height fog layer (i.e., LSF1) for ΔR0.67 versus ΔBTD3.7-11 (Figure 9b), and iii) fog (i.e., LSFhighclouds) with water-phase middle (4-6 km) clouds for ΔBTD3.7-11 vs R0.67 (Figure 9c). The clear-sky The optical fog features at the island were investigated by simulating (Table A4) a) ∆R 0.67 versus R 0.67 , b) ∆R 0.67 versus ∆BTD 3.7-11 , and c) ∆BTD 3.7-11 versus R 0.67 (Figure 9a-c). The symbols and colors represent various fog or cloud conditions: i) just a fog layer (black for 0-1 km and sky-blue for 0-2 km), ii) fog with mid-level (4-6 km) clouds of different phases (red for water, blue for ice), and iii) fog with high-level (8-10 km) clouds (green). Clear-sky is denoted by pink. Similarly to Figure 8, the satellite observations inside the dashed-line rectangle were within the LSF detection threshold ranges for the same spatiotemporal conditions as for fog. Figure 9a-c show that the higher cloud effect above the fog layer (i.e., the difference between LSF1 and LSF highclouds ) varied systematically with cloud height inside the dashed-line threshold rectangle. This was derived from any two of the three variables, ∆R 0.67 , R 0.67 , and ∆BTD 3.7-11 . The simulated results of the middle clouds (blue for ice and red for water) showed they were mixed with each other, and difficult to separate. The simulated optical information, estimated from individual variables, did not necessarily agree with the estimates from the other variable, indicating that it was not unique. Overall, the RTM simulation (asterisks) for the case study agreed with the satellite-based observations (grey circles) and the ground-based fog observations (yellow).
The 2D simulations for the case study used the optical characteristics of the top three LSF detection variables. The actual fog case (orange circles) in the 3D simulation (Figure 9d) demonstrated three kinds of LSF optical features: (i) a 1 km-height fog layer (i.e., LSF1) for ∆R 0.67 versus R 0.67 (Figure 9a), (ii) a 2 km-height fog layer (i.e., LSF1) for ∆R 0.67 versus ∆BTD 3.7-11 (Figure 9b), and (iii) fog (i.e., LSF highclouds ) with water-phase middle (4-6 km) clouds for ∆BTD 3.7-11 vs R 0.67 (Figure 9c). The clear-sky is shown as a pink circle in Figure 9d. The LSF1 estimation for ∆R 0.67 vs R 0.67 (Figure 9a) was the most reliable, based on the top two POD scores (Table 4), though the simulated fog information from each relationship, in terms of the LSF types was not unique (Figure 9).

Probability Index for Improved LSF Detection
For validation, the PI method derived from the control data of the total LSF for Period 1 was applied to the experimental data for Period 2. We compared two methods: DSM* PI, using two variables (∆R 0.67 and R 0.67 ) versus DSM PI, based on three variables (∆R 0.67 , ∆BTD 3.7-11 , and R 0.67 ). The FAR value (13.5%) of DSM PI was relatively high, compared to those of other variables (4-9%) in Table 5. However, the value seems to be acceptable in view of the results from previous studies (FAR ≤~15%) [4,39]. In addition, the POD values of DSM and DSM* were 0.982 and 0.947, respectively. Monthly average time series for the PODs of three thresholds (∆R 0.67 , R KMA , and BTD KMA ) were investigated in terms of the monthly average for the 18 months between April 2012 and June 2015 ( Figure 10). The number of fog occurrences per month varied from 17 to 75 for the period. The 18-month average values of the PODs were ∆R 0.67 (0.81), R KMA (0.55), and BTD KMA (0.14). The accuracy of the LSF detection was estimated in the order of ∆R 0.67 POD > R KMA POD > BTD KMA POD. Table 5. POD values (∆R 0.67 , ∆BTD 3.7-11 , and R 0.67 ), and the PI est values of DSM and DSM* for the LSF detection validation during Period 2 (2014-2015) using the thresholds of the satellite-observed variables for Period 1 (2012-2013). The FAR values of the five methods are also given. **The ∆R 0.67 values within ±2% have been used as the upper limit condition of PI est . The POD values of DSM and DSM* have been obtained from the NFL data, not from WF(Class i ).  In Figure 11, DSM PI derived from three variables (ΔR0.67, ΔBTD3.7-11, and R0.67) tends to be less variability within a month or season than DSM* PI. For reference, three WF values (1.0, 0.8, 0.6) have been used for DSM* PI, although the details about DSM* PI are beyond the scope of this study. The difference between DSM PI and DSM* PI was clear in the variability (one standard deviation) of the In Figure 11, DSM PI derived from three variables (∆R 0.67 , ∆BTD 3.7-11 , and R 0.67 ) tends to be less variability within a month or season than DSM* PI. For reference, three WF values (1.0, 0.8, 0.6) have been used for DSM* PI, although the details about DSM* PI are beyond the scope of this study. The difference between DSM PI and DSM* PI was clear in the variability (one standard deviation) of the LSF detection accuracy, indicating that ∆BTD 3.7-11 resulted in less variability. The LSF detection variability of DSM PI was 23-25% less than that of DSM* PI. Although ∆R 0.67 was utilized as one of the three components in the PI calculation, it has a more seasonal dependence in the detection than the PI, showing the lowest POD in April 2014. The DSM PI, however, derived from both the reflectance and brightness temperatures, was less influenced by seasonality than the ∆R 0.67 threshold. This tendency was clear in April, showing that the averages of DSM PI and POD of ∆R 0.67 were 0.776 and 0.597, respectively (Figures 10 and 11). This resulted from the low sensitivity of ∆BTD 3.7-11 to the seasonality, compared to ∆R 0.67 . In summary, compared to an individual threshold, the PI was useful for LSF detection because of its high skill level, and the low seasonality and variability in the detection accuracy.

POD
For the validation, the thresholds of three satellite-observed variables for Period 1 have been applied to the PI derivation for Period 2 ( Figure 11). The optimum thresholds for Period 1 were 0.40 < ∆R 0.67 < 0.995, 12.0 K < ∆BTD 3.7-11 < 34.0 K, and 0.20 < R 0.67 < 0.55. Note that the thresholds in Table 4 were derived from the whole period (2012-2015) data. A monthly time series of DSM PI in Period 2 (black solid line) was approximately similar to that of DSM PI (blue solid line), derived from the whole-period thresholds. The PI average and the FAR values in Period 2 were 0.853 and 0.135, respectively ( Table 5).
The DSM PI was applied to two cases of fog occurrences, to analyze its usefulness for monitoring LSF on 2D maps ( Figure 12). The PI in the LSF spatial distribution can provide more specified probability values than 2-3 steps of KMA [19]. The two cases where there were at least four fog occurrences, based on ground observations, occurred at springtime and summertime dawn in 2014, one at 06:30 LST on April 17, and the other at 06:15 LST on August 30. Fog detection on the map was presented in two stages, fog and no fog, in the R KMA threshold (Figure 12a,b); three stages, fog, possible fog, and no fog, in the KMA COMS operational algorithm [19,23] (Figure 12c,d); and with the seven PI values (no fog, 50%, 60%, 70%, 80%, 90%, and 100%) of this study (Figure 12e,f). These threshold values of KMA [19] were not accurate for actual fog cases [23], because they incorrectly detected fog areas as cloud-contamination pixels, and underestimated fog occurrence. reflectance and brightness temperatures, was less influenced by seasonality than the ΔR0.67 threshold. This tendency was clear in April, showing that the averages of DSM PI and POD of ΔR0.67 were 0.776 and 0.597, respectively (Figures 10 and 11). This resulted from the low sensitivity of ΔBTD3.7-11 to the seasonality, compared to ΔR0.67. In summary, compared to an individual threshold, the PI was useful for LSF detection because of its high skill level, and the low seasonality and variability in the detection accuracy. For the validation, the thresholds of three satellite-observed variables for Period 1 have been applied to the PI derivation for Period 2 ( Figure 11). The optimum thresholds for Period 1 were 0.40 < ΔR0.67 < 0.995, 12.0 K < ΔBTD3.7-11 < 34.0 K, and 0.20 < R0.67 < 0.55. Note that the thresholds in Table 4 were derived from the whole period (2012-2015) data. A monthly time series of DSM PI in Period 2 (black solid line) was approximately similar to that of DSM PI (blue solid line), derived from the whole-period thresholds. The PI average and the FAR values in Period 2 were 0.853 and 0.135, respectively ( Table 5).
The DSM PI was applied to two cases of fog occurrences, to analyze its usefulness for monitoring LSF on 2D maps ( Figure 12). The PI in the LSF spatial distribution can provide more specified probability values than 2-3 steps of KMA [19]. The two cases where there were at least four fog occurrences, based on ground observations, occurred at springtime and summertime dawn in 2014, one at 06:30 LST on April 17, and the other at 06:15 LST on August 30. Fog detection on the map was presented in two stages, fog and no fog, in the RKMA threshold (Figure 12a,b); three stages, fog, possible fog, and no fog, in the KMA COMS operational algorithm [19,23] (Figure 12c,d); and with the seven PI values (no fog, 50%, 60%, 70%, 80%, 90%, and 100%) of this study (Figure 12e,f). These threshold values of KMA [19] were not accurate for actual fog cases [23], because they incorrectly detected fog areas as cloud-contamination pixels, and underestimated fog occurrence. The figures in the left column of Figure 12 were used to investigate the fog-detection accuracy of the thresholds, and PI for seven fog occurrences at springtime dawn. The foggy stations in Figure 12a are denoted as pink triangles (see also Figure 2 and Table A2). The station numbers in South Korea are the west coast (2, 3, and 29), inland (25, 26, and 31), and the island of Ulleungdo (24). The R KMA threshold failed fog detection in all of the stations except on the island (Figure 12a). In the COMS operational algorithm [19], three fog occurrences at the inland sites were classified as 'possible fog,' and only the fog event on Ulleungdo island was detected. The algorithm was unsuccessful at the west coast's three stations. Two international airports, station 29 at Gimpo and station 3 at Incheon, are located in the region, and accurate fog monitoring is required for aviation. Most of the fog occurrences were successfully detected by the PI. The LSF possibility value was 100% at Ulleungdo, and it was 80% at the other six stations (Figure 12e). The PI was substantially better at springtime fog detection than the threshold for either R KMA or the operational algorithm.  [19], (c) the operational algorithm with a COMS image [19], and (e) the PI of this study. (b) As in Figure 12a [19], (c) the operational algorithm with a COMS image [19], and (e) the PI of this study. (b) As in Figure 12a The fog-detection case at summertime dawn is presented in the right-hand column of Figure 12, which also shows four fog occurrences at ground stations 10, 27, 38, and 45. While none of the fog occurrences were detected by the R KMA threshold or the COMS operational algorithm (Figure 12b,d), the PI was generally successful in the detection. The PI values were 0.9, except at ground station 45 (Sunchon), where it was a relatively value low (0.6) (Figure 12f). The four-station PI detection average (0.83) was remarkably high, in contrast with the detection failures of both the R KMA and the operational algorithms. In both of the above case studies, the DSM PI was able to detect fog and determine its spatial distribution better than the KMA [19] single GEO of COMS threshold and algorithm methods.

Discussion
The previous study [8] that emphasized ∆R 0.67 was limited to the LSF detection in summer only. Based on the dual satellite method proposed in Yoo et al. [8], this study has attempted to extend the study period to spring and summer, and to develop the probability index (PI) of LSF utilizing ∆R 0.67 with additional satellite-observed variables, ∆BTD 3.7-11 and R 0.67 . Compared to the threshold test (e.g., either fog or no fog) in Yoo et al. [8], PI in this study can visualize the LSF possibility into seven stages, and provides the practical application to LSF detection in its spatial distribution. Table 6 summarizes the differences between the two studies; the study period, the satellite variables for LSF detection, LSF probability classes, LSF spatial distribution, and the variability in the LSF detection accuracy for a month or season. The differences between this study and Yoo et al. [8] have been summarized in Table 6. Using the dual satellite method (DSM), we have derived the probability index (PI) of low stratus and fog (LSF) from 18-month satellite and ground-based observations near the Korean Peninsula at dawn during the warm season. More climatological database values may help to provide more accurate PIs. The LSF retrieval was most effective in summer, based on the BRDF values of Yoo et al. [8]. We were able to extend the previous study period from June-August (summer) to the April-August (warm season) by deriving PI from additional satellite-observed variables ( BTD 3.7-11 and R 0.67 ) to R 0.67 , as recommended by Yoo et al. [8]. The BTD 3.7-11 test tends to reduce the variability of LSF PI accuracy in a month or season, but to raise the FAR to some extent. Overall, the LSF detection methods of DSM PI, DSM* PI and ∆R 0.67 are found to have their own merits of LSF detection skill in view of POD, FAR, and favorable seasons, etc. Also, the dual satellite-observed methods may be selectively utilized for an operational purpose, for instance, considering seasons of LSF occurrence seasons and the acceptable FAR limit.
Thus, the current LSF PI retrieval algorithm is expected to be less useful for non-warm seasons and at dusk, and this may need to be investigated in future studies. The validation for DSM PI has was carried out using at 45 ground stations in South Korea, including some island stations. However, the validation was not performed over the open sea, due to the lack of these stations. Two case studies have been selected to validate DSM PI, but the LSF signals over the sea (Figure 12e,f) needs to be verified in the future for whether they were fog or low stratus, and furthermore, LSF1 or LSF highclouds . Although PI values in the case of middle/high clouds without fog have not been investigated in this study, the clouds are expected to lower the PI value, based on the LSF highclouds values out of thresholds. In addition, the visibility meter data may be utilized, particularly in the coastline. Also, there may be a case study limitation to some degree.

Conclusions
A new method for LSF detection, called DSM, was developed in terms of the LSF probability index (PI) determined from the nearly simultaneous observations of dual geostationary-orbit satellites (COMS and FY-2D) and ground station observations during the warm season of 18 months. The ground-based observations yielded 754 fog and 433 clear-sky occurrences that were utilized to validate the satellite-observed LSF detection. An RTM simulation demonstrated that LSF detection and optical properties were generally consistent with the dual-satellite observations. The POD values of six detection thresholds were ranked in a descending order of magnitude: R 0.67 > BTD 3.7-11 > R 0.67 > R KMA > BTD 3.7-11 > BTD KMA . The DSM PI was derived from a combination of observations (∆R 0.67 and ∆BTD 3.7-11 from the dual satellites; R 0.67 from a single GEO of COMS) in association with the top three POD scores for detection probability. The PI accuracy was analyzed with respect to the fog detection rates of the conventional thresholds (R KMA and BTD KMA ) and the KMA [19] operational algorithm from COMS.
Two case studies using maps of spatial fog distribution at springtime and summertime dawn addressed the PI's improved method of fog detection. Compared to the conventional methods of KMA [19] and single threshold (∆R 0.67 ; [8]), the PI has three merits: (i) a high LSF detection rate, (ii) more specified (seven classes) LSF spatial distribution, and (iii) variability of the detection accuracy in a month or season. The BTD 3.7-11 component in PI was found to lead to the trend of low variability, based on the comparison of the DSM PI with the DSM* PI, which was derived from the two reflectance variables ( R 0.67 and R 0.67 ) The PI has timely implications for LSF detection, because the newly available satellite-based observations from the advanced GEOs (e.g., GK-2A launched on December 5, 2018 [40]; FY-4A [41] and Himawari-8 [42]) have additional multi-channels with higher spatiotemporal resolution than do previous satellites. The DSM technique can be applied to other meteorological/environmental variables (e.g., cloud and dust) and satellite calibration, as well as near real-time LSF monitoring.     Figure A1. Schematic diagram describing the two types of LSF (LSF1 and LSFhighclouds). The diagram has been modified from Figure 5 of Yoo et al. [8] using different CA, CB, and CC criteria. Details of the criteria are explained in the text.