The Climatological Analysis of Typhoon Tracks, Steering Flow, and the Pacific Subtropical High in the Vicinity of Taiwan and the Western North Pacific

Taiwan frequently suffers from typhoon hits in the boreal summer and fall. The location of Taiwan makes it vulnerable to the pathways of typhoons mainly determined by the position of the Pacific subtropical high. In order to clarify the linkage between typhoon invasion and associated large-scale environments from a climatological perspective, this study counts the historical typhoon invasion days for each month in the typhoon season to establish analyzed cases and then categorizes them with statistical thresholds. Besides, the categorized cases with less typhoon invasion are further sorted to distinguish different movements of tropical cyclones. Therefore, corresponding composites are applied for each category. The results reveal that when the subtropical high retreats eastward, the accompanying steering flow guides typhoons to make an early recurvature toward Japan and South Korea. While the subtropical high further extends its property to the west covering Taiwan, the steering flow on the south transfers typhoons moving westward to the South China Sea. However, when the subtropical high lies in areas between the above two scenarios, the steering flow along the periphery of the subtropical high continuously sends typhoons toward Taiwan and the vicinity, which greatly increases the threat to the island.


Introduction
The Western North Pacific features the most frequent tropical cyclone (typhoon) activity in the world. According to statistics from 1961 to 1990, the average annual number of typhoons over that region (100 • E to 180 • E in the Northern Hemisphere) is 27.8, accounting for about one-third of global tropical cyclone genesis [1]. Because Taiwan is located in Southeast Asia, the island is frequently hit by typhoons in the boreal summer and fall, resulting in catastrophic disasters. The violent wind speed and torrential precipitation from typhoons have often caused extensive damage throughout history. For example, in 2001, typhoon Nari brought severe flooding and sorely damaged the transportation system in northern Taiwan; typhoon Morakot, which caused the well-known destructive flood in 2009, killed 681 people.
Taiwan usually suffers three to four typhoon hits annually on average, meaning the island is constantly exposed to the risk of extreme rainfall and flooding. That fact prompted the scientific community to study typhoon-related topics. Chien and Kuo (2011) [2] explored the factors that contributed to typhoon Morakot's record-breaking precipitation over southern Taiwan, and stated the amount of rainfall in Taiwan was nearly proportional to the reciprocal of the tropical cyclone translation speed. Huang et al. (2016) [3] analyzed convective systems of typhoon Fanapi, which brought considerable precipitation to the southern Taiwan plain and the central range. They argued that the cold SST anomalies between the Bay of Bengal and the Philippine Sea, and warm SST anomalies in the tropical Western and Central Pacific. The SST gradient between each forms a convergence zone through the Walker circulation over the Western North Pacific, and Matsuno-Gill-type [11,12] circulation characteristics appear. It also exhibits Pacific-Japan (PJ) pattern [13] characteristics, so more typhoons approach Taiwan. As for the typhoon-active fall, warm (cold) SST anomalies are seen in the tropical Western (Eastern) Pacific with a convergence (divergence) pattern over the same region. In the meantime, a Matsuno-Gill-type circulation driven by the convergence center is also found, which brings a cyclonic circulation southwest of Taiwan and an anticyclonic circulation extending to the northwest over the Western North Pacific. In this situation, Taiwan and its vicinity are more prone to typhoon passage.
Based on the findings proposed by the research mentioned above, one should realize that the degree of typhoon activity in Taiwan is closely related to large-scale environmental fields in the Western North Pacific or neighboring areas of Taiwan. Because of the small geographical area of Taiwan, any slight difference in the spatial configuration of the large-scale environmental field would considerably change the extent of the typhoon impact. Therefore, the frequency of typhoon invasion varies largely from year to year.
Some researchers suggested that large-scale circulations would not only exert their influences on typhoon motion but also affect the length of the typhoon impact period. Chu et al. (2012) [14] indicated the weakening of the easterly steering flow would slow down the movement of a typhoon and thus extend the period of typhoon invasion. Tu and Chou (2013) [15] also argued that the slower movement of a typhoon caused by the weaker steering flow is a factor that enhances typhoon precipitation in Taiwan. Chang et al. (2013) [16] studied 84 typhoon cases that made landfall in Taiwan from 1960 to 2011 and counted rainfall data from 21 stations operated by the Central Weather Bureau (CWB). The results also showed an increase in typhoon precipitation for the island. They attributed the findings to the weakening of the easterly steering flow that extended the periods of the typhoon impacts. In addition, the southwesterly winds not only caused the typhoons to drop more rain after the tropical cyclones left from the west coast of the island, but also affected the large-scale environment again, which weakened the easterly steering flow to slow down the motions of the typhoons.
Previously, many researchers focused on case studies when it came to analyzing factors that influence typhoon motion. Huang et al. (2011) [17] used high-resolution simulations to examine the eminent deflection of typhoon Krosa's track before its landfall over a mountainous island topography. Yeh et al. (2012) [18] studied the looping motion of typhoon Haitang prior to making landfall in Taiwan and showed the importance of a terrain-induced vortex interacting with the typhoon. However, those studies were usually confined to the scope of the mesoscale. In order to take a look at typhoon motion from a broader viewpoint, this study tries a different concept via categorizing historical typhoons that invaded Taiwan from a climatological point of view. After that, our work examines different corresponding large-scale environmental conditions for the goal of clarifying what mechanisms affect the movement of a typhoon. In addition, rather than investigating some common objects, such as typhoon rainfall and typhoon amount, this study chooses to look at things from counting the historical typhoon invasion days in Taiwan.
The following Section 2 will introduce the data used in this study for the analysis. The statistical categorization method and related formula will be detailed in Section 3. The categorized results and the corresponding large-scale environmental fields in the Western North Pacific will be presented in Section 4 to understand the role of large-scale circulations in the entire scenario. Finally, the discussion and conclusions will be provided in Section 5, where we will discuss other major factors influencing typhoon activity and go over our results, subsequently highlighting the specialties of this study.

Data
This study uses multiple datasets to investigate typhoons and their associated large-scale environmental fields. The Joint Typhoon Warning Center (JTWC) data, which has been recording Atmosphere 2020, 11, 543 4 of 20 typhoon tracks and activities within the Western North Pacific at 6-hour intervals since 1945, is obtained for the investigation of typhoon tracks. In this study, "The Best Track" from the JTWC is used as the typhoon track data to statistically count and categorize the typhoon invasion day in Taiwan as well as providing the necessary information for the analysis of typhoon motion over the Western North Pacific. The time zone of the original data is converted to UTC+8 to fit the allocated zone for Taiwan. As for precipitation data, daily observed precipitation data from two CWB synoptic weather stations, Taipei and Tainan, representing the northern and southern Taiwan, respectively, and the Taiwan Rainfall Index (TRI) [19] are adopted to verify the precipitation characteristic for each analyzed case. The sources of the TRI include 22 synoptic weather stations and 253 automatic weather stations operated by the CWB and 901 Taiwan rainfall stations (1176 stations in total), with a time span of 119 years, from 1897 to 2015. This study accesses the 1950 to 2014 segment.
In order to understand the relationship between the large-scale environmental fields over the Western North Pacific and the motion of the tropical cyclone, this study obtains the NOAA-CIRES Twentieth Century Reanalysis (V2c) dataset through the following website: https://www.esrl.noaa. gov/psd/ [20]. The time span of the monthly data is from 1851 to 2014; our analyzed period here takes the segment from 1950 to 2014. The spatial grid resolution is 2 • × 2 • , covering the whole world, including several analyzed variables such as u, v winds at each pressure level, sea level pressure (SLP), and 500 hPa geopotential height.

Establishing the Typhoon (Ty) Category
In order to select the case of typhoon invasion, determine the impact duration, and distinguish the typhoon-related precipitation, a straightforward method adopted by many studies is to identify the influence of the typhoon with a rectangular domain. In other words, when a typhoon center enters this rectangular domain, it is defined as a case of typhoon invasion. Tu et al. (2009) [21] analyzed typhoon tracks over the Western North Pacific and examined the change in typhoon activity near Taiwan by a domain ranging from 21 • N to 26 • N and from 119 • E to 125 • E. Tu and Chou (2013) [15] indicated that most of the heavy rain (30 mm h −1 to 50 mm h −1 ) appears in a range of within 500 km from the center of a typhoon, and the highest frequency of the heavy rain occurs in the range of 100 km to 300 km from the center. Based on that, for their research, a rectangular domain from 18 • N to 29.5 • N and from 116 • E to 126 • E is regarded as the area where a typhoon affects Taiwan.
Considering the typhoon storm radius defined by the CWB is about 200 km to 300 km, and the major storm radius of the typhoon mentioned in the studies above is within 300 km from the center outward, our work defines a rectangular domain centered over Taiwan. It expands the boundaries outside the island by an extra 3 degrees for both latitude and longitude. Finally, a domain ranging from 19 • N to 28 • N and from 117 • E to 125 • E is set to identify the typhoon invasion for the study.
Even though typhoons can be generated in any season over the Western North Pacific, Taiwan is mainly affected by tropical cyclones in the boreal summer and fall, with the highest probability of being invaded from July to September. According to the statistics from 1950 to 2014, the averaged typhoon invasion day in Taiwan for each month is 3.23 days in July, 4.2 days in August, and 4.48 days in September.
For each month from July to September over the investigated years from 1950 to 2014, when a typhoon's center falls into the above-defined domain, its impact day starts being counted until the center moves out of the domain. One should note that there are cases that the lifespan of a typhoon occurs during two continuous months. In that situation, its typhoon invasion days are separately counted and adjudicated for the corresponding month. Through this definition, 65 years × 3 months, all 195 analyzed cases are individually assigned a number representing the typhoon invasion day.
Rather than treating the entire typhoon season as a whole, the method adopted in this study is to statistically set thresholds for each investigated month to categorize the cases established, which Atmosphere 2020, 11, 543 5 of 20 will ensure that the qualified cases are statistically representative. This method also avoids the contamination of statistical characteristics from other months while the thresholds for each month are defined.
In order to set thresholds and categorize all the analyzed cases by the typhoon invasion day, our work first calculates the standard deviation from all the analyzed cases for each month based on the typhoon invasion day, and the results show 2.42 days in July, 3.2 days in August, and 3.77 days in September. A threshold as the upper (lower) boundary is defined as the averaged typhoon invasion day plus (minus) 0.5 standard deviations. After all, this method yields two different thresholds for each month, namely 4.44 days and 2.02 days for July, 5.8 days and 2.6 days for August, and 6.37 days and 2.6 days for September.
Therefore, a case where the number of the typhoon invasion days is more than the upper threshold is defined as "more typhoon invasion days (hereafter Ty+)". Meanwhile, a case where the number of the typhoon invasion days is less than the lower threshold is defined as "less typhoon invasion days (hereafter Ty−)". The remaining analyzed cases that do not exceed either the upper or lower thresholds stay closer to the mean state. Those cases are considered normal cases and excluded for further study. Since most of the typhoon movements in the Ty− category are found to separate in two different directions, a verification domain is delimited by high overall passing frequency areas in each direction. The way to determine the classification of the two paths from the Ty− category is to count the overall frequency within each verification domain and then select the one with more typhoon passages as the final decision based on its corresponding path. Therefore, the typhoons from the Ty− category are further subdivided into two additional subcategories: "Recurving path" and "Westbound path".

Calculating Steering Flow
In order to calculate averaged steering flow across multiple pressure layers, this study refers to the study of Kimberlain and Breman (2017) [22], who pointed out that the averaged wind across layers of the troposphere is highly correlated with the actual movement of tropical cyclones. The method to calculate this multi-layer averaged wind should adopt the concept of the mass-weighted average, as they suggested in their study.
The steering flow, which is usually adopted to analyze the typhoon movement, is based on an averaged wind field across 300 hPa to 850 hPa [23]. In this study, u and v wind data taken from the NOAA-CIRES Twentieth Century Reanalysis (V2c) are equally divided by 50 hPa, creating 11 intervals of layers between 300 hPa and 850 hPa. Based on the mass-weighted average calculation method proposed by Kimberlain and Breman (2017) [22], this study reformulates the formula and takes the following case as an example: to calculate the averaged u wind from 300 hPa to 850 hPa, the formula should be The same formula can be applied to calculate the averaged v wind by replacing u components with v. After obtaining the averaged u and v wind fields across 300 hPa to 850 hPa through the above formula, the averaged steering flow and the averaged wind speed can be obtained.

The Ty Categories
After establishing the Ty categories, the corresponding years of the categorized cases for each investigated month are listed in Table 1. Our definition avoids the contamination of statistical characteristics from a month with others because the averaged value and standard deviation are exclusively calculated from each investigated month to produce its thresholds. It allows the categorizing process to retain physical information from each analyzed case ideally, and thus secures representativeness for the categorized cases to best reflect the relevant large-scale environmental fields.
Atmosphere 2020, 11, 543 6 of 20 In Figure 1, a category is given for each analyzed case with the corresponding year and month to schematically indicate the dominating category for that period.  1952 1950 1960 1950 1956 1950 1961 1951 1961 1951 1957 1954 1962 1953 1962 1952 1959 1955 1966 1954 1972 1954 1963 1958 1968 1955 1974 1956 1966 1960 1972 1956 1982 1957 1974 1965 1973 1957 1986 1958 1977 1967 1977 1958 1990 1963 1989 1972 1979 1959 1992 1964 1990 1975 1987 1960 1994 1967 1991 1976 1990 1970 1995  1969  1992  1979  1998  1974  1997  1970  1993  1981  2000  1975  2003  1971  2001  1984  2001  1976  2004  1983  2008  1988  2002  1978  2005  1987  2010  1996  2004  1983  2007  1988  -1997  2006  1985  2008  2001  -2003  2008  1986  2010  2002  -2007  2013  1988  2012  2014  -2009  -1989  2013  --2011  -1992 For the following analyses, all the categorized cases from each investigated month will be gathered and discussed based on their corresponding category. The results will represent different typhoon-associated atmospheric conditions during the typhoon season from July to September. The relevant information of the Ty+ category, Ty− category, and normal cases are presented in Figure 2. Among the total 195 analyzed cases from July to September over the analyzed years, the Ty-category shows similarity to the normal cases in terms of the amount (Figure 2a), while the Ty+ category is considerably less than the others. Figure 2b shows the monthly typhoon invasion day for each category. The statistical results reveal that most typhoons invading Taiwan tend to stroll around the island or adjacent areas for a few days with an averaged typhoon invasion spell of about four days per month. Since the components from the normal cases do not show an obvious tendency toward any category, and do not pass the 0.5 standard deviations threshold, the number of days is very close to the climatology value as expected. Meanwhile, a massive difference in the monthly typhoon invasion days is seen between the Ty+ category and the Ty− category, with the number from the Ty+ category almost reaching eight times the number from the Ty− category, which also implies that the mechanisms affecting the two categories should be different. For the following analyses, all the categorized cases from each investigated month will be gathered and discussed based on their corresponding category. The results will represent different typhoon-associated atmospheric conditions during the typhoon season from July to September. The relevant information of the Ty+ category, Ty− category, and normal cases are presented in Figure 2. Among the total 195 analyzed cases from July to September over the analyzed years, the Tycategory shows similarity to the normal cases in terms of the amount (Figure 2a), while the Ty+ category is considerably less than the others. Generally, typhoon-related rainfall should be proportional to the duration of the invasion. Figure 2c,d, respectively, present typhoon-related precipitation conditions by the observational rainfall averaged from the CWB Taipei and Tainan stations, and the TRI. Regarding the precipitation observed at the Taipei and Tainan stations (Figure 2c), the averaged value from the normal cases, again as expected, is similar to the climatology value, and the other two categories show clearly proportional results to the typhoon invasion day. In other words, when a typhoon affects an area for longer, the rainfall rises, and vice versa [24]. A similar situation is also reflected in the analysis of the TRI (Figure 2d). One should note that the Ty+ category contributes nearly half of the total precipitation from all the analyzed cases. Considering the rather small number of cases but torrential precipitation from this category, it is reasonable to imagine that Taiwan would suffer from severe disasters.
Since Taiwan is located in the Western North Pacific, which accounts for the most substantial portion of typhoon genesis globally, one should wonder about the linkage between the level of typhoon activity over that oceanic region and the extent of typhoon invasion in Taiwan. For that, this study also investigates the relationship between the number of typhoons invading Taiwan and the number of typhoons generated over the Western North Pacific based on our categories for each investigated month.  Figure 2b shows the monthly typhoon invasion day for each category. The statistical results reveal that most typhoons invading Taiwan tend to stroll around the island or adjacent areas for a few days with an averaged typhoon invasion spell of about four days per month. Since the components from the normal cases do not show an obvious tendency toward any category, and do not pass the 0.5 standard deviations threshold, the number of days is very close to the climatology value as expected. Meanwhile, a massive difference in the monthly typhoon invasion days is seen between the Ty+ category and the Ty− category, with the number from the Ty+ category almost reaching eight times the number from the Ty− category, which also implies that the mechanisms affecting the two categories should be different.
Generally, typhoon-related rainfall should be proportional to the duration of the invasion. Figure 2c,d, respectively, present typhoon-related precipitation conditions by the observational rainfall averaged from the CWB Taipei and Tainan stations, and the TRI. Regarding the precipitation observed at the Taipei and Tainan stations (Figure 2c), the averaged value from the normal cases, again as expected, is similar to the climatology value, and the other two categories show clearly proportional results to the typhoon invasion day. In other words, when a typhoon affects an area for longer, the rainfall rises, and vice versa [24]. A similar situation is also reflected in the analysis of the TRI (Figure 2d). One should note that the Ty+ category contributes nearly half of the total precipitation from all the analyzed cases. Considering the rather small number of cases but torrential precipitation from this category, it is reasonable to imagine that Taiwan would suffer from severe disasters. According to the statistics, the results within each investigated region reveal somewhat coherent increasing or decreasing rates in both July and August. For the Ty+ category, the amount of typhoons invading Taiwan increases greatly compared to the climatology, with increasing rates of 52.05% in July and 55.43% in August; however, in the meantime, the total amount of typhoons generated over the Western North Pacific only slightly increases from the climatology by 7.98% in July and 10.54% in August. For the Ty− category, the amount of typhoons invading Taiwan reduces in comparison to the climatological mean, with largely decreasing rates of 52.68% in July and 76.2% in August. Different from the weak connection between these two investigated regions in the Ty+ category, considerable reductions in the number of typhoons are also found over the Western North Pacific in the Ty− category, with numbers noticeably lower than the climatology by 20.15% in July and 18.55% in August.
The results in September expose disparities in all aspects. For the Ty+ category, the amount of typhoons invading Taiwan shows a massive rise by 67.33% from the climatology, although the total amount of typhoons over the Western North Pacific is only slightly higher than the climatology by 7.81%. For the Ty− category, the amount of typhoons invading Taiwan decreases greatly by 60.16% from the climatology; however, over the Western North Pacific, the amount of typhoons is only 2.26% less than the climatology.
These above results point to a phenomenon as follows: Although the variation in the number of typhoons over the Western North Pacific is a possible factor affecting the number of typhoons invading Taiwan, only the Ty− category in July and August presents a simultaneous decrease in typhoon amount Atmosphere 2020, 11, 543 9 of 20 for both Taiwan and the Western North Pacific. It means the variation in the number of typhoons generated over the Western North Pacific cannot be directly applied to the extent of the typhoon invasion over Taiwan.
Previously, some studies explored factors that could alter general typhoon motion. Wang et al. (1998) [25] proposed that a wide variety of external and internal dynamical forces and their interaction would lead to the complexity of tropical cyclone motion. Tu et al. (2009) [21] suggested that the abrupt increase of typhoon frequency in the Taiwan region is due to the northward shift of typhoon movements over the Western North Pacific. Wang et al. (2011) [26] showed that the typhoon track changes are linked to global SST warming and the associated changes in large-scale steering flows. With that said, the only way to reasonably and scientifically determine the impacts of a typhoon on Taiwan is to examine the movement of the tropical cyclone. Therefore, in the scope of discussing the change of the typhoon invasion days in Taiwan, this study suggests that one should place emphasis on the linkage between the large-scale environment and the movement of the typhoon.

Typhoon Paths and Corresponding Large-Scale Environmental Fields
A considerable number of typhoons are generated over the Western North Pacific annually, and most of their tracks are traceable.   [27,28] mentioned that typhoon paths in the Western North Pacific can be roughly classified into two directions: one is going westward to the direction of Taiwan, South China, and the South China Sea; the other is going northward toward Japan and South Korea. Taiwan is at the junction between these two paths and at the turning point of the track for most typhoons over the Western North Pacific-East Asian region [29]. Hence, regardless of the path, the island encounters a high possibility of receiving a typhoon. Composites of the two defined categories, which represent the different extents of typhoon invasion over Taiwan during the typhoon season, are reserved for this section to delve into their corresponding large-scale environmental fields.

The Ty+ and Ty− Categories
In order to complete the distribution picture of the typhoon path, the passing frequency from all typhoons in the Ty+ category is shown in Figure 3a. The results clearly indicate that most of the typhoons move toward the northwest after they are generated, and finally pass through Taiwan and the vicinity, especially within the domain for identifying typhoon invasion (domain A, black box in Figure 3a) defined in Section 3.1. In our analysis, most of the areas in the domain A reach extremely high passing frequencies (over 65 times), which clearly reveals a message that Taiwan is extremely vulnerable to the typhoons in these cases. Some typhoons would either travel northward to Japan and South Korea when they approach the east coast of Taiwan or go all the way to the South China Sea through the Bashi Channel (partly through the northern part of Luzon, Philippines); however, the frequencies of these typhoon cases are much lower. Figure 3b shows the corresponding anomalous fields of the SLP and 1000 hPa streamline relative to their climatology for the Ty+ category. Since most of the typhoons in this category will pass through Taiwan and its adjacent areas, the low pressure and cyclonic circulation from the tropical cyclones create an extensive much-lower-than-average pressure area. The area is centered over Taiwan and expands to the surroundings, including South China, the South China Sea, Japan, and South Korea, with anomalous convergent flows above. It indeed suggests that the typhoons frequently pass through Taiwan and the nearby areas in the Ty+ category.
The Ty− category is investigated in the same way, while the results reveal significant differences from the other. Figure 3c shows the passing frequency from all typhoons in the Ty− category. The results contain information worthy of further discussion. For example, most of the typhoons bypass Taiwan and its nearby areas, and the paths are divided into two main routes: the recurving path to Japan and South Korea, and the westbound path to the South China Sea, characterizing as high passing-frequency (over 60 times) areas on each route, shown by the verification domains B and C mentioned in Section 3.1 (black boxes in Figure 3c). It is worth noting that the westbound path to the South China Sea seems to be more south here than those typhoon cases seen in the Ty+ category. The latter tends to pass through the Bashi Channel, yet the former seems to be mainly traveling through Luzon, Philippines.
typhoons in the Ty+ category is shown in Figure 3a. The results clearly indicate that most of the typhoons move toward the northwest after they are generated, and finally pass through Taiwan and the vicinity, especially within the domain for identifying typhoon invasion (domain A, black box in Figure 3a) defined in Section 3.1. In our analysis, most of the areas in the domain A reach extremely high passing frequencies (over 65 times), which clearly reveals a message that Taiwan is extremely vulnerable to the typhoons in these cases. Some typhoons would either travel northward to Japan and South Korea when they approach the east coast of Taiwan or go all the way to the South China Sea through the Bashi Channel (partly through the northern part of Luzon, Philippines); however, the frequencies of these typhoon cases are much lower.  Figure 3b shows the corresponding anomalous fields of the SLP and 1000 hPa streamline relative to their climatology for the Ty+ category. Since most of the typhoons in this category will pass through Taiwan and its adjacent areas, the low pressure and cyclonic circulation from the tropical cyclones create an extensive much-lower-than-average pressure area. The area is centered over Taiwan and expands to the surroundings, including South China, the South China Sea, Japan, and South Korea, with anomalous convergent flows above. It indeed suggests that the typhoons frequently pass through Taiwan and the nearby areas in the Ty+ category.
The Ty− category is investigated in the same way, while the results reveal significant differences from the other. Figure 3c shows the passing frequency from all typhoons in the Ty− category. The results contain information worthy of further discussion. For example, most of the typhoons bypass Taiwan and its nearby areas, and the paths are divided into two main routes: the recurving path to Japan The corresponding anomalous SLP and 1000 hPa streamline for the Ty− category are presented in Figure 3d. Opposite to the results from the Ty+ category, the anomalous patterns from the Ty− category show an extensive high-pressure property in a Taiwan-centered area, together with an anticyclonic circulation anomaly above. The phenomenon implies that the area experiences relatively low frequencies of passage by low-pressure systems. It is also possible that the subsidence outflowing from the typhoons would contribute to the stable atmospheric conditions in this area [30] when the tropical cyclones take the bypass. Japan and South Korea, right on one of the main typhoon paths, suffer from frequent typhoon invasions. Hence, an area with anomalous low-pressure and convergence covering these countries is expected. However, another main typhoon moving path, westbound path to the South China Sea, does not show a corresponding negative (or cyclonic) anomalous pattern. In this regard, it is because that region already has relatively low pressures in the climatological field, and thus cyclonic contributions from the typhoons are not prominent.

The Recurving and Westbound Paths
Most of the typhoons from the Ty+ category show a relatively simple motion, while there are different types of movement seen in the typhoon cases from the Ty− category. As defined in Section 3.1, the Ty− category is further subcategorized into two different routes: the recurving path and westbound path, which should arise from different large-scale configurations. Figure 4 shows the passing frequency of the typhoons from these two paths. For the recurving path (Figure 4a), the verification domain B near Kyushu, Japan reveals fairly high passing frequencies.
Another region south of the verification domain B, slightly east of the Ryukyu Islands, also frequently encounters the typhoons passing through. Although that region is outside the verification domain B, it is right on the route of those northbound typhoon cases. Hence, high typhoon passing frequencies are still in line with our expectations.
Atmosphere 2020, 11, x FOR PEER REVIEW 12 of 21 Concerning the westbound path (Figure 4b), as expected, the verification domain C at the South China Sea has fairly high typhoon passing frequencies. Same as the finding seen in Figure 3c, the typhoons here are more likely to pass through Luzon, Philippines, instead of taking the Bashi Channel as their passage. It seems to imply that in the westbound path scenario, there should be a large-scale force to push the typhoons further moving to the south. Note that there are a few exceptional typhoon tracks that do not comply with their categorized subcategory, such as going westward in the recurving path category. It is because when an analyzed case is individually categorized as the Ty− category, the path with a higher overall typhoon passing frequency within that period would be determined for the typhoon path subcategory. In other words, some exceptional typhoon cases moving in other directions or toward the other verification domain with a lower overall passing frequency are not ruled out. Concerning the westbound path (Figure 4b), as expected, the verification domain C at the South China Sea has fairly high typhoon passing frequencies. Same as the finding seen in Figure 3c, the typhoons here are more likely to pass through Luzon, Philippines, instead of taking the Bashi Channel as their passage. It seems to imply that in the westbound path scenario, there should be a large-scale force to push the typhoons further moving to the south. Note that there are a few exceptional typhoon tracks that do not comply with their categorized subcategory, such as going westward in the recurving path category. It is because when an analyzed case is individually categorized as the Ty− category, the path with a higher overall typhoon passing frequency within that period would be determined for the typhoon path subcategory. In other words, some exceptional typhoon cases moving in other directions or toward the other verification domain with a lower overall passing frequency are not ruled out.

Corresponding Large-Scale Circulations
Generally, the path of a typhoon is usually determined by the surrounding large-scale circulation before it makes landfall. Chu et al. (2012), Wang et al. (2011), and Wu et al. (2005) [14,26,31] all suggested that the steering flow is undoubtedly a vital factor in influencing typhoon motion or moving speed. According to the formula defined in Section 3.2, an averaged wind field across 300 hPa to 850 hPa is derived to represent the steering flow in a large-scale background. Thus, corresponding large-scale circulations and related mechanisms that exert influences on the typhoon path can be examined, with three analyzed groups for further study: the Ty+ category, the recurving path of the Ty− category, and the westbound path of the Ty− category.
The Ty+ category (Figure 5a) shows that the easterly flows dominate the area in the Western North Pacific (east of 150 • E and south of 24 • N). The flows west of 150 • E gradually turn into the southeasterly and point to Taiwan as well as its surroundings. Regarding the wind speed over this area, the distribution of the strong winds south of 24 • N extends from the east to the west. Its spatial pattern gradually merges toward the northwest and points to Taiwan at about 130 • E, forming clear steering flows. Since most typhoons over the Western North Pacific are generated around this area, they are likely to be steered toward Taiwan and the surroundings once they are generated. As a result, the island frequently suffers from typhoon hits.
The averaged wind field also discloses other essential messages for further discussion. The large-scale flows gradually turn into the southwesterly at about 24 • N. With the strong westerlies on the north, the flows construct an anticyclonic circulation over the Western North Pacific. The turnaround flows (the southeasterly turning into the southwesterly) on the western side of the anticyclonic circulation lie beside Taiwan, which could make northwestward-moving typhoons too late to recurve when they approach the island. Besides, the anticyclonic circulation contains an almost east-west-shaped weak and calm wind speed zone at about 28 • N. It should be considered as the ridge of the anticyclone [32].
The recurving path from the Ty− category (Figure 5b) presents a somewhat different pattern. Similar to the Ty+ category, the area east of 150 • E and south of 24 • N is dominated by the easterly flows. The flows are also gradually turning into the southeasterly, but the wind direction does not point to Taiwan. Instead, the turnaround flows of the anticyclonic circulation substantially retreat eastward to about 140 • E and 30 • N, with a relatively strong wind speed region nearby, forming bridge-like flows connecting the westerlies on the north. The connecting flows in that area play a key role in the recurvature. The steering flows first drive typhoons generated from low latitudes to that area. Sequentially, the mentioned bridge-like flows take over the job to guide the typhoons crossing the ridge at about 30 • N. Thus, the typhoons move toward Japan and then are steered away by the westerlies, completing the process of the recurvature.
In addition, there is another path of the airflow over the Bashi Channel and Luzon, Philippines, heading to the South China Sea and Hainan. From the wind speed field, the wind speed across the Bashi Channel and Luzon, Philippines, is relatively similar to the mentioned bridge-like flows south of Japan, although its spatial pattern is much more extensive than the other one. However, the re-enhancement of the wind speed over the South China Sea is not that prominent compared to the much stronger westerlies above Japan (or north of the recurving path). It consequently leads to the fact that most typhoons tend to be towed by the turnaround flows south of Japan and the strong westerlies toward the north, rather than going westward when they are guided to areas around 140 • E. Certainly, there are some exceptional typhoons cases that would instead follow the relatively weak flows south of Taiwan toward the South China Sea. As the results seen in Figure 4a, few typhoons take the westbound path through Luzon, Philippines, to the South China Sea in the recurving path scenario. Atmosphere 2020, 11, x FOR PEER REVIEW 14 of 21 The recurving path from the Ty− category (Figure 5b) presents a somewhat different pattern. Similar to the Ty+ category, the area east of 150° E and south of 24° N is dominated by the easterly flows. The flows are also gradually turning into the southeasterly, but the wind direction does not point to Taiwan. Instead, the turnaround flows of the anticyclonic circulation substantially retreat eastward to about 140° E and 30° N, with a relatively strong wind speed region nearby, forming bridge-like flows connecting the westerlies on the north. The connecting flows in that area play a key role in the recurvature. The steering flows first drive typhoons generated from low latitudes to that area. Sequentially, the mentioned bridge-like flows take over the job to guide the typhoons crossing Regarding the westbound path from the Ty− category (Figure 5c), the area south of 24 • N is still dominated by the easterly flows. However, the changing from the easterly to the southeasterly is subtle; instead, the main flows go westward through the Bashi Channel and Luzon, Philippines. After arriving over the South China Sea and South China, the flows gradually turn into the southeasterly and even the southerly, which indicates the position of the western edge of the anticyclonic circulation.
The wind speed field shows a similar spatial pattern. The strong wind zone south of 28 • N gradually merges toward areas on the west at 18 • N, including the Bashi Channel and Luzon, Philippines, while the wind speed here is higher than that in the recurving path scenario. The conspicuous bridge-like flows south of Japan seen in the recurving path scenario disappear. Besides, a weak and calm wind speed zone, which is regarded as the ridge, now extends all the way to Taiwan, blocking out most typhoons from passing by like a barrier and leading them to the South China Sea on the west. It also could be a reason why the typhoons are forced to move through Luzon, Philippines, instead of the Bashi Channel on the north, and it more or less creates a hard time for those typhoons to affect southern Taiwan. Despite the ridge across the ocean, there are some southerly flows at around 140 • E and 28 • N, which should explain why there are still few recurving typhoons in the westbound path scenario.

Typhoon Paths and the Position of the Pacific Subtropical High
In the analyses of the steering flow, the anticyclonic circulation over the Western North Pacific is certainly not a negligible feature, and obviously, most typhoons would follow the flows around the circulation of the anticyclone. The trade winds, south of the subtropical high, is responsible for the general westward motion of typhoons, and the flows on the western edge of this large-scale anticyclone take over the job for the poleward motion [33]. Given that the flows are mainly controlled by the subtropical high, this study analyzes the 500 hPa geopotential height to represent the location of the Pacific subtropical high and investigates its relationship with different typhoon routes. In order to quickly determine the margin of the subtropical high, Figure 6 highlights the 5880 m contour and 5870 m contour as a thick solid line and a thick dashed line, respectively. Figure 6a shows the 500 hPa geopotential height field for the Ty+ category. The westmost side of the 5880 m contour is located south of Honshu, Japan, at about 130 • E and 28 • N. The western edge of the 5870 m contour lies further west, about southwest of Kyushu, Japan, and northwest of the Ryukyu Islands. According to the results from the previous analyses of the steering flow, the anticyclonic circulation is roughly aligned with the 5870 m contour, with the ridge at approximately 28 • N, shown before as a weak and calm wind speed zone. Therefore, when the western margin of the Pacific subtropical high lies between Kyushu, Japan, and Taiwan, the accompanying steering flow would lead typhoons from the low latitudes toward Taiwan and its adjacent areas, leading to an increase in the typhoon invasion days.
The Pacific subtropical high considerably retreats eastward in the recurving path of the Ty− category, as shown by the 5880 m and 5870 m contours in Figure 6b. The western edge of the 5870 m contour shrinks eastward from the region between Taiwan and Kyushu, Japan, to the place south of Kyushu, Japan. Similar to the results from the Ty+ category, the position of the 5870 m contour coincides with the anticyclonic circulation seen in the analyses of the steering flow. Therefore, when the Pacific subtropical high retreats eastward and its western edge is located south of Kyushu, Japan, typhoons are likely to be transferred northward by the steering flow toward Japan without affecting Taiwan.
Regarding the westbound path of the Ty− category (Figure 6c), although the position of the 5880 m contour shrinks slightly more to the east in comparison to what it behaves in the recurving path scenario, the 5870 m contour widely extends further to the west and even covers Taiwan. The pattern of the ridge crossing over Taiwan is the same as that from the analyses of the steering flow. The stable atmospheric environment under the ridge acts as a barrier to hinder typhoons from passing by Taiwan. Once again, as seen in the previous findings, the anticyclonic circulation here is also roughly consistent with the 5870 m contour. As a result, when the property of the Pacific subtropical high dominates areas over Taiwan, typhoons are unlikely to invade the island nor to recurve. Instead, they would be led by the steering flow toward the west, heading westward to the South China Sea through Luzon, Philippines. Under this circumstance, Taiwan is more likely to avoid the threat from the typhoon.  Figure 6a shows the 500 hPa geopotential height field for the Ty+ category. The westmost side of the 5880 m contour is located south of Honshu, Japan, at about 130° E and 28° N. The western edge of the 5870 m contour lies further west, about southwest of Kyushu, Japan, and northwest of the Ryukyu Islands. According to the results from the previous analyses of the steering flow, the anticyclonic circulation is roughly aligned with the 5870 m contour, with the ridge at approximately 28° N, shown before as a weak and calm wind speed zone. Therefore, when the western margin of the Pacific subtropical high lies between Kyushu, Japan, and Taiwan, the accompanying steering

Discussion
There are certainly other factors that can influence the movement and intensity of typhoons over the Western North Pacific. The Madden-Julian Oscillation (MJO) [34][35][36] is an eastward-moving intra-seasonal phenomenon that has been well discussed in terms of its broad impacts on precipitation, surface temperature, tropical cyclones, and monsoons [37][38][39]. The northward or northwestward propagating mode in the Northern Hemisphere during the boreal summer within the intra-seasonal time scale [40][41][42], specifically named the boreal summer intra-seasonal oscillation (BSISO), has interactions with typhoon activities over the Western North Pacific [43][44][45]. Our previous study, Hung et al. (2016) [46], showed that the typhoon frequency patterns associated with heavy rainfall in Taiwan are closely related to the 10 to 30-day BSISO2 phases during the typhoon season. When the major BSISO2 convection moves northwestward from the Philippine Sea to Taiwan and adjacent areas, during phases 3 and 4, an anomalous low-level cyclonic flow and increased typhoon frequency directly contribute to larger rainfall in Taiwan.
Although the MJO has shown to be one of the prominent factors impacting on typhoon frequency in the Taiwan region, its intra-seasonal time scale signal, particularly the 10 to 30-day MJO phases, does not match the scope of the seasonal time scale examined in this study. The three-month investigated spell from July to August in this research was chosen to best reflect the typhoon-associated large-scale backgrounds during the most active period in the typhoon season for Taiwan. Therefore, the direct influences exerted by the MJO may not be crucial here.
The El Niño Southern Oscillation (ENSO) is another major factor that can extensively alter atmospheric systems over the Western North Pacific [47,48]. Kubota (2012) [49] indicated ENSO can modulate typhoon activity, including typhoon genesis location, landfall numbers, intensity, life span, and rainfall, mainly through the relocation of a monsoon trough with the eastward shift of the Walker circulation. Apart from the conventional Eastern Pacific warming El Niño events, a noncanonical El Niño type (also known as central Pacific El Niño or El Niño Modoki), which is characterized by equatorial central warming, has been recently observed [50,51].
The different types of El Niño, SST warming patterns, and vertical motions all have their mechanisms to change the behavior of atmospheric systems associated with typhoon tracks, such as the location and intensity of the subtropical high, the strength of the low-level vorticity, the monsoon trough, and large-scale circulations [21,52,53], which adds more complexity to the entire story. Therefore, to build a linkage between the above factors and our results remains the quest of further studies in the future to clarify the entire physical process. Under this consideration, the current goal of this study mainly focuses on investigating the steering flow and associated typhoon tracks from a climatological perspective.

Concluding Remarks
Typhoons generated over the Western North Pacific always make a profound impact on East and Southeast Asian countries. They become more active in the boreal summer and fall, while any deviation of their movement can bring a different result to Taiwan owing to the small geographical area of the island. This study counts the amount of the typhoon invasion days in Taiwan for each investigated month from July to September over the period of 1950 to 2014, to establish numerous analyzed cases. Those cases are classified into the Ty+ and Ty− categories by the statistical thresholds to represent the different extents of typhoon impacts on Taiwan. After investigating the corresponding typhoon paths from each category, our work demonstrates that there are two types of typhoon movements with completely different routes in the Ty− category. Therefore, the Ty− category is further subdivided into two additional subcategories. Finally, three groups for the analysis are established, namely "the Ty+ category", "the recurving path of the Ty− category", and "the westbound path of the Ty− category".
Through examining composites for each group, the large-scale environmental fields and corresponding typhoon motions can be clearly clarified, and the final results are presented in a schematic plot, as shown in Figure 7. The 5880 m and 5870 m contours of the 500 hPa geopotential height field represent the margin of the Pacific subtropical high. The variation in their positions is used to explain the mechanisms causing different typhoon motions.
"the westbound path of the Ty− category".
Through examining composites for each group, the large-scale environmental fields and corresponding typhoon motions can be clearly clarified, and the final results are presented in a schematic plot, as shown in Figure 7. The 5880 m and 5870 m contours of the 500 hPa geopotential height field represent the margin of the Pacific subtropical high. The variation in their positions is used to explain the mechanisms causing different typhoon motions. When the western edge of the Pacific subtropical high is located between Taiwan and Kyushu, Japan, the steering flow controlled by the margin of the Pacific subtropical high tends to steer typhoons generated at low latitudes directly toward Taiwan on the northwest. Alternatively, the flow When the western edge of the Pacific subtropical high is located between Taiwan and Kyushu, Japan, the steering flow controlled by the margin of the Pacific subtropical high tends to steer typhoons generated at low latitudes directly toward Taiwan on the northwest. Alternatively, the flow leads the typhoons to make a late recurvature toward Japan and South Korea while the tropical cyclones approach the east coast of Taiwan. In either way, Taiwan is likely to suffer from typhoon hits.
When the Pacific subtropical high considerably shrinks to the east, and its western edge lies southeast of Japan, typhoons generated at low latitudes are still easily guided to their northwest. However, the steering flow accompanying the retreating subtropical high would turn around at the western margin of the high and thus takes the typhoons to recurve before reaching the Ryukyu Islands. Under this circumstance, only few typhoons have a chance to impact Taiwan.
In contrast, when the Pacific subtropical high widely extends the property to its west including Taiwan, the ridge is like a barrier to block out typhoons from passing through. In this scenario, Taiwan is apparently under a stable and hot summer weather condition. The westward-extending subtropical high controls the easterly steering flow along its southern margin to flow through the Bashi Channel and Luzon, Philippines. When arriving at the South China Sea, the steering flow starts to turn clockwise over Hainan or even South China. In this scenario, the typhoons are likely to be driven by the flow, following the same route toward the west. In addition, most of the typhoons here tend to move through Luzon, Philippines, rather than taking the Bashi Channel, which certainly further reduces the threat to Taiwan.
Compared with previous typhoon-related studies, the features of this work are highlighted as follows: First, rather than directly studying each individual typhoon, our work categorizes multiple analyzed cases from a climatological perspective to understand the linkage between the different typhoon paths and their corresponding large-scale environmental fields. Secondly, in the analyses for the Ty− category, different typhoon paths are further classified to avoid compound messages from different corresponding large-scale environmental configurations. All these features demonstrate different perspectives of analysis to enrich the framework of typhoon-related topics. Therefore, our work can help to indicate noteworthy messages that have not been properly discussed through conventional study methods, and the relevant understandings from this study should provide valuable support to typhoon forecasting in the future.