Sea fog occurs frequently around the Korean Peninsula during April to July and is considered a major marine meteorological disaster, causing serious transport accidents and socioeconomic losses. Fog-related marine accidents represent 29.5% of the total marine accidents in Korea, which mainly occur along domestic ship routes during night time. In this study, an algorithm for sea fog monitoring using information technologies was developed to reduce fog-related marine accidents and to manage marine transportation, offshore and coastal fisheries, and naval operations.
Sea fog is considered a major marine meteorological disaster in spring and summer around the Korean Peninsula (Cho et al., 2000; Heo and Ha, 2010). It often contributes to serious transport accidents and socioeconomic losses in the ocean and coastal regions: sea fog may have many impacts such as automobile accidents, problems with aviation, and marine accidents due to visibility problems. The monitoring of sea fog contributes to improving traffic management and safety from the viewpoints of commercial shipping, operational planning of passenger ships, and flight planning and operations. It is also important for managing marine transportation, offshore and coastal fisheries, and naval operations. In addition, sea fog is one of the immediate causes of property damage, public health problems and financial losses (Forthun et al., 2006).
Previous studies have shown that the occurrence of sea fog around Korea is characterized by significant seasonal variations, with a maximum in June to July mainly due to air–sea temperature differences, as a result of warm air advection over a cold pool (Cho et al., 2000; Fu et al., 2006; Heo and Ha, 2010). This advection-type fog is characterized by dense, widespread and long-duration fogs that may begin to extend toward the coast with sufficient advection of warmer moist air (Croft et al., 1997). In recent years, dense sea fogs have caused severe disasters resulting in great economic losses in Korea. For instance, between 1981 and 2010, about 800 sea fog-related ship collisions occurred: over 50% of these occurred in the Yellow Sea. In particular, in November 2011, a commercial vessel and a fishing boat collided, killing at least eight people. The collision was attributed to the sea fog along the mid-west coast of Korea. In October 2003, cars and trucks crashed into each other in thick sea fog along the Seohae Grand Bridge on the West Coast Expressway, and at least 11 people were killed and more than 50 injured in a massive pile up involving about 30 vehicles on an expressway along the western coast of Korea. In addition, more than 20 flights are cancelled each year because of sea fog at Incheon International Airport, which is a major airport located on the west coast of Korea. Furthermore, in July 2010 a fighter jet crashed off the eastern coast of Korea on its way back from a training mission: the crash was attributed to limited visibility due to sea fog.
Marine traffic, including both cargo and passenger vessels, around the Korean Peninsula has increased continuously. The number of small commercial fishing boats has decreased since the 1980s. However, accidents involving small commercial fishing boats have increased. When small commercial fishing boats sail their way through sea fog, they send their own alarm to alert others to their location, using the out-of-date method of blowing their horns. This is because their boats are not equipped with instruments such as radar or navigation and communication systems owing to the high cost and the lack of obligation. As a result, there is a high probability of exposure to danger. Therefore, reliable near real-time information on the spatiotemporal distribution of sea fog can mitigate the danger of marine accidents for sea-going ships that recognize the distribution of sea fog associated with their position and sailing route in advance. Such near real-time information can only be obtained from satellite data; station measurements are limited because of the lack of an observation network, and the interpolation of point visibility data is impractical due to the complex nature of spatial visibility distribution. Eyre et al. (1984) and Park et al. (1997) introduced a method using dual-channel radiometers with two infrared channels, short wave IR (SWIR, 3.7 µm) and long wave IR (LWIR, 11 µm) from the National Oceanic and Atmospheric Administration (NOAA) Advanced Very High Resolution Radiometer (AVHRR), to detect nocturnal fog and low stratus. Bendix et al. (2005) and Cermak and Bendix (2005) presented a ground fog detection scheme that compares the terrain height and cloud base height computed from cloud top height and considers the cloud geometrical thickness obtained from a Moderate Resolution Imaging Spectroradiometer (MODIS) satellite. However, owing to the low Earth orbit of the NOAA and MODIS satellites their detection scheme was limited to monitoring the temporal variation of a fog event. Since July 2005, the Multi-functional Transport Satellite (MTSAT) data has been available operationally; Heo et al. (2008) examined the combined method of dual-channel difference (DCD) and a Laplacian expression using the 3.9 and 10.7 µm images from the MTSAT to detect sea fog around the Korean Peninsula, with MTSAT data comprising snapshots taken at 30 min intervals. The Laplacian expression is used to remove noise and low cloud after fog and low cloud detection using the DCD method. The development of the DCD technique using MTSAT data can be carried over to the Communications, Ocean, and Meteorological Satellite (COMS-1), which was launched in June 2010, because it uses similar IT channels to MTSAT. The MTSAT and COMS-1 are geostationary satellites.
The purpose of this study is to build an algorithm for the detection of sea fog around the Korean Peninsula and to develop a sea fog warning algorithm using information technologies to reduce marine accidents related to sea fog. Two fundamental aspects of the sea fog warning algorithm are addressed here: (1) accuracy of sea fog detection, and (2) identification of the geometric relationship between sea fog area and sea-going ships. To keep the ship away from the sea fog area, the sea fog warning algorithm provides information on the geometric relationship between the sea fog and the ship using current positions and sailing routes of ships from marine navigation by means of an application for smart phones and tablet personal computers. Section 2 briefly describes the data used. Section 3 introduces the seasonal cycles of the frequency of sea fog occurrence and statistics for marine accidents related to sea fog occurrence. In Section 4, the algorithm for detecting sea fog is presented. Section 5 describes the sea fog warning algorithm, and Section 6 gives a final discussion and summary.
2.1. Meteorological data
To investigate the characteristics of sea fog occurrence around the Korean Peninsula, fog measurements from island stations were employed in the present study. Table 1 lists 20 island stations where sea fog observations were made from 1983 to 2008. The island stations are lighthouses that observe fog, air temperature and sea surface temperature. These stations report fog when visibility is 1 km or less. Observations were made every 3 h from 0600 to 1800 local standard time (LST, = UTC + 9 h). Following Cho et al. (2000), a fog day was defined as a day where there were one or more observations of fog. The Korean Meteorological Administration classifies fog as the reduction in horizontal visibility to ≤1 km except when precipitation is observed. Thus, days where fog was accompanied by rain were excluded from the data. The hourly visibility data measured by the Korea Meteorological Administration (KMA) at 16 coastal weather stations across the Korean Peninsula from 2000 to the present were used in this study. Information about the coastal weather stations is presented in Table 2. The satellite data from the MTSAT with the SWIR (3.8 µm) and LWIR (10.8 µm) channels to monitor the area of fog over time have been used. The MTSAT has five channels that consist of four infrared window channels and one visible window channel, and makes observations using a 4 km IR resolution, which is sufficient for monitoring sea fog.
Table 1. Location of island stations
Northern west coast
Western south coast
Eastern south coast
Southern west coast
Western south coast
Table 2. Location of coastal stations
38.0 °N, 124.6 °E
Northern west coast
37.5 °N, 126.6 °E
36.8 °N, 126.5 °E
36.0 °N, 126.7 °E
34.8 °N, 126.4 °E
Southern west coast
34.7 °N, 125.5 °E
34.5 °N, 126.3 °E
Western south coast
33.5 °N, 126.5 °E
33.2 °N, 126.6 °E
34.8 °N, 128.4 °E
Eastern south coast
35.1 °N, 129.0 °E
38.3 °N, 128.6 °E
37.5 °N, 129.1 °E
37.8 °N, 128.9 °E
37.0 °N, 129.4 °E
37.5 °N, 130.9 °E
2.2. Marine accident data
The marine accident data presented in this study are derived from the investigations of marine traffic accidents by the Korean Maritime Safety Tribunal (KMST, http://www.kmst.go.kr), an organization responsible for investigating marine accidents relating to ships or other marine craft and determining their circumstances and causes. During the period 1981–2010, the total number of marine traffic accidents that occurred around the Korean Peninsula was 3207. Identification of accident location is based on the accident co-ordinates. Only accident location data for 5 years, from 2004 to 2008, are available. The KMST classifies marine accidents as collision, contact, stranding/grounding, foundering/sinking, fire/explosion, capsize, machinery failure, damage to equipment, missing vessel, and structural failure. Marine accidents are also classified according to visibility, wave height and weather events including clear skies, rain, fog, snow, cloud cover, and unknown weather along with the location and time of the accidents.
2.3. Marine transportation data
The Automatic Identification System (AIS) and Electronic Chart Display and Information System (ECDIS) are two new and very helpful technologies used in marine transportation. The AIS enables ships and vessel traffic services (VTS) to exchange information electronically on very high frequency (VHF) channels. The AIS is an automated tracking system used on ships for identifying and locating other ships. The AIS is intended to assist a ship's officers and allow maritime authorities to track and monitor vessel movements. Position-reporting data from AIS include navigational status, speed over ground, position accuracy, longitude, latitude and ground track. The AIS improves marine safety as crews have more information about the courses, speeds, positions and dimensions of other ships. In addition, the system enables the transmission of short safety-related messages. The sailing route including direction, position and speed of the ship can be estimated from the AIS dataset. However, information from the AIS is simple and text-based, which imposes great constraints on data mining of such information. Furthermore, the AIS information is not available when an AIS receiver falls out of an AIS transmitter's working range.
The ECDIS is a computer-based navigation information system that complies with International Maritime Organization (IMO) regulations and can be used as an alternative to paper nautical charts. IMO refers to similar systems that do not meet its regulations as Electronic Chart Systems (ECSs). The ECDIS system displays information from electronic navigational charts (ENCs) and integrates position information from the Global Positioning System (GPS) and other navigational sensors, such as radar and AIS. It may also display additional navigation-related information, such as sailing directions and sea depths.
3. Sea fog occurrences and its relationship to marine accidents
3.1. Seasonal cycle of the frequency of sea fog occurrence
To examine the seasonal variation of sea fog occurrence, monthly mean fog days were averaged for six groups of adjacent stations for the period 1983–2008. The occurrence of sea fog around the Korean Peninsula tends to increase in frequency from April to July and to decrease rapidly in August (Figure 1). The average of fog days over the Yellow Sea is higher than that over the South Sea and over the East Sea (Sea of Japan) throughout the year. This difference may result from distinctly cooler sea surface temperatures (SSTs) over the Yellow Sea, particularly over the northern and southern parts of the west coast of Korea (Cho et al., 2000). The cooler SST regions are characterized by shallow water (5–10 m depth) with strong tidal mixing during the warm season from May to July. The seasonal increase of frequency of advection fog over the Yellow Sea from June to July arises primarily from strong warm air advection over the cooler water, which is mainly due to persistent southerly flow. Gao et al. (2007) emphasized the importance of southerly winds for the formation of advection fog. Although the numbers of fog days over the south and east coasts of Korea are relatively lower than those over the west coast, Ekman upwelling resulting from surface currents moving to the northeast due to persistent southwesterly winds during summer generates cold water over the southeast coast of Korea, which contributes to sea fog occurrence. During the fog season, 76% (42%) of the fog observations over the northern (southern) part of the west coast of Korea report visibility of less than 300 m, with the average duration of sea fog events lasting about 9 h (Figure 2). Dense and long-duration sea fogs and coastal fogs of 9 h or longer occur predominantly over the northern and southern parts of the west coast of Korea. Strong tidal mixing and temporal variations of SST are important factors associated with the formation and dissipation of advection fog over the Yellow Sea in summer (Heo and Ha, 2010). The prevailing surface winds are south-southwesterlies with speeds of 2–10 m s−1, advecting warm and moist air from the south (Heo and Ha, 2004).
3.2. Statistics of marine accidents related to sea fog occurrence
The KMST statistics show that 805 of the 3207 marine accidents (29.5%) during the 30 year period 1981–2010 occurred during sea fog events: this is the greatest single cause of accidents related to severe weather. Fog-related accidents are difficult to prevent due to the deficiency of information for sea fog monitoring. Ships are restricted from sailing during severe weather warnings such as typhoons and high seas but not during sea fog occurrence. Figure 3 shows a main domestic and international ship route around the Korean Peninsula and the locations of marine accidents such as collisions and ship groundings associated with sea fog for the period from 2004 to 2008. According to the KMST statistics regarding the causes of marine accidents, 119 marine accidents occurred due to sea fog during this period, with 45.1% of the marine accidents occurring off the west coast. The number of total accidents was 462 during this period. Therefore, 25.8% of total accidents are related to sea fog events. The geographical distribution of marine accidents suggests that they were mainly associated with the routes of domestic ships. Figure 3 also shows that most of the marine accidents occurred in coastal regions, which indicates a need for strengthened safety management in such regions. The fog-related marine accidents predominantly involved stranding/grounding, collision, foundering, and fire, and thus they pose an increased risk in terms of marine casualties. The temporal distribution of rescued ships and injured people associated with the sea fog is depicted in Figure 4(a). Compared to the previous 10 year period the rate of marine accidents and injuries associated with sea fog increased during the period 2000–2010, due to increases in the marine leisure industry and marine transportation. In addition, the marine accidents associated with sea fog mainly occurred during the period from night time to early morning (before 0800 LST). This suggests that it is important to provide information on night time sea fog (Figure 4(b)).
4. Sea fog detection algorithm
In the present study, the DCD method using MTSAT, SWIR, and LWIR was used to detect areas of fog. Usually, fog occurs during night time, when satellite IR channels are available. During night time, the detection of fog using IR images is difficult since the temperatures of fog and the underlying surfaces are similar (Scorer, 1986) and a surface inversion can also induce an inverse temperature profile near the surface (Anthis and Cracknell, 1999). As a result, a dual-channel method for the detection of fog or low stratus has been in widespread use since it was first presented by Eyre et al. (1984) and Ellrod (1995, 2000). The DCD method uses the difference in emissivity between SWIR and LWIR bands for opaque water clouds. It has been shown that the DCD method provides accurate detection of small-droplet clouds with clear separations of fog or low stratus from cloud-free regions (Cermak and Bendix, 2007). In the LWIR band, the brightness temperature (BT) is almost equal to the cloud-top temperature because opaque water clouds emit radiation as a black body (ε ≈ 1). In the SWIR band, the BT is significantly lower than the cloud-top temperature due to a lower emissivity of 0.8–0.9 µm (Hunt, 1973; Eyre et al., 1984; Park et al., 1997). Therefore, the difference in BTs between SWIR and LWIR is sensitive to the presence of fog or low clouds (Anthis and Cracknell, 1999).
It should be noted that the primary characteristic of fog is the homogeneity in the horizontal distribution of the BT. Fog can be distinguished from low clouds by its relative smoothness and the divergence of the BT gradient can be used as a measure of uniformity. This is defined by the following equation:
where BTi, j is some value at position (i, j). It is known that the BT in a cloudy region is more variable than that in a cloudless region (Coakley and Bretherton, 1982). The Laplacian operator is useful for detecting variable BT regions, or cloudy regions (Sakaida and Kawamura, 1996). The Laplacian method can be used to differentiate between low clouds and sea fog under fog conditions determined by the DCD method. The threshold value of the Laplacian operator, set to 0.1, is determined empirically to discriminate sea fog from low clouds. The verification of the combined DCD and Laplacian methods and the determination of the threshold values are presented in detail in Heo et al. (2008) who showed that this method provides a 5–6% improvement in detection accuracy when compared to use of the DCD method alone. Figure 5 shows the horizontal Laplacian expression of LWIR brightness temperature over the region where DCD is less than − 2.0. At 0533 LST 15 April and 0500 LST 13 June 2011, the combined method well detected advection fogs that were observed over the south coast and the west coast, respectively. In the first case, low visibilities of 100 and 600 m are observed with sea fogs at the Huksando (47169) and Jindo (47175) stations, respectively. In the other case, sea fogs were observed at the six coastal stations on the west coast, at the Jindo (47175) and Tongyeong (47162) stations on the south coast, and at the Gangneung (47105) station on the east coast. The synoptic condition was characterized by a southerly wind that supplied warm, moist air over the region. In Appendix A, the accuracy of sea fog detection using the algorithm is discussed.
5. Sea fog warning algorithm
An algorithm is presented that provides safety information for sailing with regard to sea fog, providing warnings when ships are in the sea fog area or are sailing towards it. The danger facing a sea-going ship is obtained using the position-reporting data of the AIS and the sailing route provided by ECDIS, together with information on the sea fog area produced by the sea fog detection algorithm. This involves analysing the geometric relationship between the sea fog area and relevant information about a ship such as its location, direction of movement, speed and sailing route, since the geometric relationship can indicate whether the ship is in the sea fog area or sailing toward the sea fog area.
5.1. Geometric relationship between the current position of a ship and the sea fog area
The geometric relationship between the sea fog area and the position of the ship is defined in order to calculate the danger due to the fog. The sea fog detection algorithm detects the sea fog area, and the position of a sea-going ship is extracted from the AIS position-reporting data. Based on the geometric relationship between a point representing the position of the sea-going ship and a polygon representing the sea fog area, it can be checked whether the ship is in the sea fog area (Figure 6). The geometric relationship is determined by the winding number method (Hormann and Agathos, 2001), which accurately determines if a point is inside a non-simple closed polygon. Each side of the polygon is assumed to have directionality. Using a clockwise sweep around each of the sides it can then be estimated whether the position of the sea-going ship is located on the right side of each edge of the polygon. The winding number of such a curve is defined using the polar co-ordinate system. A curve in a 2D plane can be defined by parametric equations in polar form as follows:
where r is distance between the point and the edge of polygon, and θ is angle between the edge and the positive horizontal axis. If the parameter t is time, then these equations specify the motion of an object in the plane between t = 0 and t = 1. This curve is closed as long as the position of the object is the same at t = 0 and t = 1. The functions r(t) and θ(t) are required to be continuous, with r > 0. Because the initial and final positions are the same, θ(0) and θ(1) must differ by an integer multiple of 2π. The integer is the winding number:
If the position of the sea-going ship is on the right side of all edges of the polygon, the sea-going ship is in the polygon (winding number > 0), which means that the sea-going ship is located in the sea fog area (Figure 6(a)). If the position of the sea-going ship is on the left side of some edges of the polygon (winding number = 0), the sea-going ship is located outside of the sea fog area (Figure 6(b)).
5.2. Warning based on the geometric relationship between the route of a ship and the sea fog area
If a sea-going ship is located outside the sea fog area, it is necessary to determine whether the ship will pass through the sea fog area. The sailing route of the ship can be derived from information on current position and direction of movement of the ship using position-reporting data from the AIS. Alternatively, the route of a ship can be obtained from the ECDIS. Sailing routes based on the AIS or the ECDIS are represented as straight lines. Therefore, a ship will pass through the sea fog if a straight line with direction starting from the current position of a ship intersects the polygon representing the sea fog area. First, an idealized bounding box of the polygon is considered because the sea fog area is usually shown as a complicated polygon. If the line does not intersect the bounding box (Figure 7(a)), the sailing route of the ship will not pass through the sea fog area. If the line intersects the polygon, then the points of contact of the line and the polygon are determined, and the angle between two tangent lines calculated (Figure 7(b)). If the angle between the straight line representing the course of the ship and one of tangent lines is less than that between the two tangent lines, it is considered that if the ship continues to follow its current course it will go into the sea fog area. In this case, the time and distance from the ship to the sea fog area is calculated and the relevant information provided to the ship's captain.
5.3. Procedure of the sea fog warning algorithm
The procedure to provide a sea fog warning to sea-going ships is shown in Figure 8. In the first step, using real-time position tracking of sea-going ships from AIS and near real-time information about sea fog detected from satellite imagery, the sea fog warning algorithm checks the geometric relationship between the current position of a ship and the sea fog area. If the ship is located in the sea fog area, the algorithm provides a warning to the ship and recommends that it changes its route. In the second step, if the ship is located outside of the sea fog area, the algorithm checks the geometric relationship between the direction of movement of the ship and the sea fog area. The algorithm then calculates the distance and time between the ship and the sea fog area. If the sailing route intersects the sea fog area, the algorithm provides a warning to the ship and recommends changing its route. In the third step, if the algorithm determines in the second step that the ship is not going toward the sea fog area, the algorithm checks the geometric relationship between the sea fog area and the direction of movement and sailing route of the ship from the ECDIS again. The sea fog warning algorithm is currently being developed as an application for smart phones and tablet personal computers. The application, which is based on marine navigation software and the ECDIS, will provide useful information concerning sea fog areas for pre-input sailing routes through a mobile network over the coastal region. The 50 stations of the communication system are located at lighthouse stations around the coastal region. The practical range for the mobile phone network is up to 20 km from the coast. Therefore, most small fishing vessels can use the application because they usually fish within a range of about 10 km from the coast. Figure 9 shows an example of the execution of the application in which marine navigation (ECDIS) overlaps the sea fog area. The sea-going ships can recognize the near real-time information about the spatiotemporal distribution of sea fog using the application and avoid potential marine accidents.
6. Results and discussion
Sea fog frequently occurs during April to July around the Korean Peninsula due to the formation of advection fog by strong warm air advection over cooler water. The dense and long-duration advection fog predominantly occurs over the northern and southern parts of the west coast of Korea. As a result, over the 30 year period from 1981 to 2010, fog-related accidents represented 29.5% of all marine accidents around the Korean Peninsula, about 45% of which occurred off the west coast. The fog-related marine accidents mainly occurred along domestic ship routes during night time and before sunrise. From a safety perspective, sea fog detection and warning algorithms seem to meet marine transportation needs. To reduce fog-related marine accidents, this study has developed an algorithm for sea fog monitoring using information technologies.
The DCD method using the SWIR and LWIR channels of MTSAT is used to detect the sea fog area. The present study shows that a combined method using a texture-related measurement as well as the DCD method improves the detection method. The threshold value of the DCD method is − 2.0 K, with values below the threshold indicating areas of sea fog and low cloud. A Laplacian calculation in the horizontal distribution of brightness temperature was proposed as a measure of homogeneity for sea fog as opposed to low cloud. The threshold value of the Laplacian expression of LWIR brightness temperature was set to 0.1, as in Heo et al. (2008).
The present paper discusses the development of an algorithm that gives warnings to sea-going ships faced with potential danger caused by sea fog. The algorithm uses information on sea fog areas and on a sea-going ship, including its current position, sailing direction and speed, and sailing route from the AIS and ECDIS. The algorithm checks the geometric relationship between the ship's route and the sea fog area using the winding number method. If the ship is sailing in the sea fog area or going toward the sea fog area, the algorithm provides a warning and recommends changing the route. Future developments include dealing with forecasting for sea fog. Future work will also analyse sea fog using multiple data sources collected by satellites and numerical weather forecasting to provide more assistance regarding sea fog warnings.
This research was supported by a grant from 'Construction of Ocean Research Stations and their Application Studies’ funded by the Ministry of Land, Transport, and Maritime Affairs of the Korean government and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No.2011-0021927, GRL).
Appendix A. Validation statistics of skill scores
To measure the accuracy of the sea fog detection algorithm in determining foggy area, we used the validation statistics of skill scores for 10 cases of sea fog during 2004–2007 (Table A.1). In the event of estimated fog occurrence (fog detected: Yes) and real fog occurrence (fog observed: Yes), the case it is classified as a hit (H); otherwise (fog observed: No), the case is classified as a miss (M). In the event of estimated fog non-occurrence (fog detected: No) and real fog occurrence (fog observed: Yes), the case is classified as a false alarm (F); otherwise (fog observed: Yes) it is classified as a correct negative (C).
Table A1. Sea fog cases for the verification of the sea fog
A, advection fog; S, steam fog.
7 April 2004
9 June 2004
9–10 June 2004
8 July 2004
8–9 July 2004
10 July 2004
5 June 2006
25 June 2006
26–27 June 2006
28–29 June 2006
2–3 July 2006
The first type, exemplified by the Heidke skill score (HSS), tests the effectiveness in specifying the occurrence of fog. It can be written in the following form:
The range of HSS is − 2FM/(F2 + M2) to one; a perfect score = 1, and no skill forecast = 0. Therefore, the HSS is 0.45, which means a 45% improvement in detection accuracy when compared to random chance (Table A.2). In the second type, probability of detection (POD) and probability of false detection (POFD) are fractions of observed events that were correctly predicted to exist and estimated events that are non-events, respectively:
Table A2. Verification score formulates for the sea fog detection algorithm
(a) HSS = 0.45, (b) POD = 0.57, (c) POFD = 0.13, (d) TSS = 0.44, (e) OR = 9.0.
Hits (H) : 102
Misses (M) : 67
False alarms (F) : 78
Correct negatives (C) : 462
The range of POD is zero to one, a perfect score = 1.
The range of POFD is one to zero; a perfect score = 0. Almost 57% of fogs that occurred were correctly detected to occur (POD = 0.57) and 13% of fog detections turned out to be false detection (no fog observed) (POFD = 0.13). The third type, the true skill score (TSS) (Hanssen and Kuipers discriminant, Pierce's skill score) examines the ability of the checklist to separate fog events from non-fog events and is defined as follows:
The range of TSS is minus one to one; a perfect score = 1, and no skill forecast = 0. The TSS is 0.44, which means that 44% of fog detections were able to separate the ‘yes’ cases from the ‘no’ cases (Table A.2). Because the correct negative term dominates the others in the table, the TSS tends toward the POD when ‘yes’ events are rare. In the last type, the odds ratio (OR) is greater than one when the hit rate (POD/1–POD) exceeds the false alarm rate (POFD/1–POFD):
The range of OR is zero to infinity; a perfect score yields infinity, and no skill system = 1, i.e., the ratio is greater than one when POD exceeds the false alarm rate. The odds of a ‘yes” detection being correct are over 9.0 times greater than the odds of a ‘yes’ detection being incorrect in this result (Table A.2). We investigate the causes of the bad performance cases of 67 misses and 78 false alarms using the KMA observation data. These cases seem to be associated with a low ceiling height, an overcast sky, light rain and drizzle, and mist.