Swell Source Analysis of East China Sea Under the Influence of Typical Typhoon Scenarios

The characteristics of swells within the East China Sea have been reported by Tao et al. (2017), while the question of where the swells come from remains unanswered. By using the wave model WAVEWATCH III and the swell tracking method proposed by Hanson (2001), the spatial sources of the swells are investigated during four typical typhoon scenarios, which usually affect the wave environment in the East China Sea, including the Recurving type, the Northward type, the Westward type (striking the East China Sea) and the Westward type (over the South China Sea). The numerical results show that parts of the swells are from the North West Pacific with a long-distance travelling. The moving paths of the swells are affected by the typhoon tracks, which result in various fetches. The Westward type (over the South China Sea) makes one peak in the evolution process. The landing process of the Westward type (striking the East China Sea) could result in swells with low energy. The swell energy depends on swell propagation distance, existence time and wind intensity of generation fetch. The consistent fetch and forceful wind intensity make swell carry more energy.


Introduction
Swells refer to the waves that still exist after winds stopping or steering. Sometimes the swells present without any wind since they come from other sea areas. The transmission of swells could be over 10000 km, which was initially discovered from the analysis of ocean waves (Barber and Ursell, 1948). Subsequent observations on swells have further ascertained the global nature of swell propagation. Snodgrass (1957−1958) observed that swells could propagate over very long distance and the Pacific is too small to permit such distant sources. This phenomenon was subsequently confirmed with a three-station array at San Clemente Island off California (Munk et al., 1963). Also in the south hemisphere, Cartwright et al. (1977) found that swells arrived at Saint Helena are clearly corresponding to distant storms in the north Atlantic after a long travelling. Swells could cause resonant motions of big ships and platforms. Ha et al. (2017) found that large swell waves have aroused attention from many engineers and scientists in South Korea because the eastern coast of the Korean Peninsula has been frequently damaged by large swell waves for several years during winter season. In this work, we investigate the sources of swells propagating in the East China Sea.
Swell tracking is a mathematic method used to identify spatial and temporal sources of swells, and it helps analyze the structure and generation mechanism of swells. The concept of swell tracking is firstly proposed to predict the source of swell by Munk et al. (1963). From buoy data over served at Saint Helena, Cartwright et al. (1977) had drawn local swell energy density-time contour map to present the evolution trend of wave energy. According to energy ridge lines plotted in the contour map, a best energy decay line is chosen to reveal the dissipation trend of swell energy and then identify the originated time of meteorological event and propagation direction. To probe the effect of swell on Alaska southern coast induced by super typhoon 'Flo' in the Pacific, Mettlach et al. (1994) analyzed swell data from 18 buoys around Alaska coast during typhoon processes. Based on the theory proposed by Earle et al. (1984), a postulate is set that swells recorded at two buoys are originated from the same meteorological event. Under the premise of equal frequency, approximate energy density and some conditions, the origination direction of swell is obtained. Because of the limitation caused by non-directional spectrum, the third buoy observation is needed to confirm the accurate coordinate of swell source. Since space exploration soars, SAR observation data have been introduced to track swells. SAR data of surface waves within the Atlantic during typhoon 'Josephine' are analyzed to acquire swell information by Gonzalez et al. (1986). The coordinate of typhoon center and buoy, the azimuth between swell propagation direction and typhoon radius tangential and incident angle of swell are utilized to compute the coordinate of swell source. Hanson and Phillips (2001) proposed a simple swell source identification method with wave parameters provided by buoy. This method is conducted to find sources of swells that had arrived at the Gulf of Alaska. With the maturation of directional spectra, over 40 swell events are discovered and their sources are sequentially identified on global meteorological map.
Most studies on swells in the East China Sea focus on wave characteristics. Liu et al. (1998) did a research on internal waves of the (East) China Sea based on SAR images. According to his research, wave lengths of swells spread in the sea areas surrounding Taiwan range from 250 m to 300 m. Jun et al. (2015) found that the extremely high waves evolved as a result of the superposition of distant large swells and high wind seas generated by strong winds. Pei et al. (2016) indicated that a region within the East China Sea named E3 affected by swell generated in Northwest Pacific during typhoon scenarios. The effects of these different meteorological conditions on the generation mechanisms and evolutionary characteristics of swells in the East China Sea are considered in this study. From comparisons with the simulation results provided by WAVEWATCH III, Tao and Wu (2017) identified the composition of swells in the East China Sea. It is postulated that swells in the East China Sea partly propagated from waters outside the Ryukyu Islands. These studies demonstrate that, swells generated in the Northwest Pacific or even further waters propagate in general in accordance with deep-water simplifications to linear gravity wave theory, and are likely to propagate across the Ryukyu Islands then affect the East China Sea. However, the work on swell tracking in the East China Sea is limited. Most researchers pay much attention to swell propagation using numerical simulation, but not the sources of swells. Tracking swells in the East China Sea would find out the relationship between variations of wave energy and typhoon tracks, and then explore the effect on swell propagation due to typhoon trajectories. Tracking swells provide a new way to predict swell propagation in the East China Sea according to typhoon tracks when typhoons prevail in the Northwest Pacific.
Swells generated in the Northwest Pacific basin by different moving tropical cyclones will be numerically simulated to verify whether swells generated outside the East China Sea could affect waters inside. Results from swell tracking and swell source prediction are presented to indicate the spatial and temporal sources of swells that influence the East China Sea. In addition, the comparison between swells simulated by double variety of topography is provided to ascertain the shadow effect on swell propagation resulted from Taiwan Island and the Ryukyu Islands. Furthermore, it is essential to dig out other effect factors from meteorological events which may affect swell propagation by comparison.

Methodology
2.1 Numerical model 2.1.1 Description θ WAVEWATCH III (ww3) is the third, matured wave model produced by NOAA (Tolman, 2014). The basic spectrum within WAVEWATCH III is the wavenumber-direction spectrum F(k, ) as its invariance characteristics. In WAVEWATCH III, the energy of a wave package is conserved without current considered. In contrast, the energy of a wave package is no longer conserved due to the work done by current on the mean momentum transfer of waves Stewart, 1961, 1962). Here, to keep consistence of wave energy, swell simulation is conducted without currents. To run the wave model, two optional parts have to be set, one is terrain grid, and the other is wind field.

Terrain setting
The main optional part of WAVEWATCH III is spatial grid setting. In this case, spatial grid is set as a rectangular grid ranges from 100°E to 160°E, and 0°N to 50°N, grid resolution is 0.25°×0.25° (see Fig. 1). Obstruction grids in x and y direction, which indicate terrain effect caused by topography, would be built according to the input terrain grid. Topography data come from ETOPO1 datasets (the highresolution version), and data extraction resolution is reset to correspond to optional grid resolution (Amante and Eakins, 2009).

Wind input
The wind field used as the dynamic source of the wave model is an ideal typhoon wind field. The theoretical typhoon model wielded in this study is a modified Holland typhoon model provided by Hu et al. (2012). After modification, the pressure field becomes: (1) And after gradient wind balance is applied, the tangential wind is modified as: where p is the pressure at radius r, p c is the central pressure, p n is the ambient pressure, R m is the radius of maximum wind, V g (r) is the gradient wind at r, is the air density, f is the Coriolis parameter, , is the rotational frequency of the earth, is the latitude, and B is the hurricane shape parameter. Theoretically, B can be derived from Eq.
(2) by neglecting the Coriolis parameter and is set, as shown below: V gm where is the maximum gradient wind (at R m ). Each parameter of typhoon (i.e., central pressure, maximum velocity) is provided by China Meteorological Administration Best Track (CMABST) (Ying et al., 2014).

Swell separation
The first step is to build directional spectra at specific point, searching spectral matrix and locate wave energy peak with a distinct partition. Hanson and Phillips (2001) provided that Wind seas are identified by a wave age criterion, which indicates that wind sea peaks lie within a specific boundary as: is the phase speed of the wind sea, is the 10m elevation wind speed, and is the angle between the wind and the wind sea. In terms of peak frequency , Eq. (4) can be translated to Eq. (5). (5) According to the above two equations, swells could be isolated from wind seas.
Next step is to combine adjacent swell peaks that belong to the same swell system. The distance between two peaks and the minimum value between peaks are used to consider whether swell peaks are mutual or not. After combining peaks, a threshold value e is proposed to remove swell partition whose total energy is below it.
A and B are chosen to eliminate noise in low energy regions of the spectrum. Finally, for each swell partition, a variety of statistical information would be computed.

Swell trackingfθ
a rms Several ways are available to conduct swell tracking. Here, the method based on Wave Identification and Tracking System (WITS) developed by Hanson (1996) is chosen as the tracking method. Swell tracking in WITS is a twostep process. Firstly, preliminary groups of swell are identified according to the value of , and for each swell partition. A weighted distance is introduced to determine if a new swell partition belongs to a previously identified preliminary group: θ where represents the radians. Values of d exceeding a given threshold are considered too high for a valid match. However, WAVEWATCH can only simulate significant wave height of swell instead of root mean square amplitude H m 0 and provide spectral peak period instead of mean period. The relationship between and spectral moment of zeroorder m 0 satisfies the equation: Then, Eq. (7) can be rewritten as: According to observation mentioned by Hanson and Phillips (2001), the threshold of D is set as 0.6.
The following step is to locate specific swell events within preliminary groups in frequency-time plot. The events are ascertained by searching through the preliminary wave groups for the series that obey deep-water wave dispersion relationship. The slope and variable about the bestfit line through all possible sequences of three or more simulation data are determined. After the source locations and origination time of swells are determined, source positions are located on the tropical cyclone maps to verify the credibility of each prediction.

Source identification
In linear wave theory, the dissipation of surface wave satisfies the deep water dispersion relationship.
(11) Wave propagates at the group velocity shown below according to linear wave theory.
(12) Based on basic physics, wave propagation group speed approximately equates to the travelling distance divided by the travel time. .
(13) It is easy to make a connection between frequency f and propagation distance d in accordance with Eqs. (9) and (10): The main wave frequency observed at specific station could be identified as linearly increases over time, and increase slope named is defined as: (15) According to the equation about the relationship between and distance d, the relationship between and d can be simply described as: with the wave origination time computed at f = 0 by where b is the f intercept (t = 0) for the observed shift.
The slope and intercept of the beset-fit line through the mean frequency and time pairs are calculated by Eqs. (13) and (14) from linear wave theory to determine the distance of the swell source and the swell origination time, respectively. With spherical geometry, the source position is obtained. The source latitude ( ) and longitude ( ) are given by Bartsch (1974): where = mean wave direction of specific group, = observation station latitude, = observation longitude, = angular distance to source, and = radius of the earth.

Simulation cases setup
According to previous investigations on typhoon tracks, typhoons in the Northwest Pacific could be divided into seven clusters (Kim et al., 2010). Among those clusters, four types of typhoons are able to affect the East China Sea (see Fig. 2). The first is the recurving type, which is defined as typhoons passing the east of Japan with early recurving YAN Jin et al. China Ocean Eng., 2020, Vol. 34, No. 2, P. 210-222 213 tracks. The second is the northward type, which is defined as typhoons striking the Korean Peninsula and Japan with north-oriented tracks, and those affecting Japan are included. The third is the westward type (striking the East China Sea), which is defined as typhoons hitting Taiwan Island and eastern China with west-oriented tracks. And the last is the westward type (over the South China Sea), which is defined as typhoons over the South China Sea and typhoons moving across the Philippines. Typhoons travel-ing the easternmost region over the West Northern Pacific are ignored as typhoon tracks are far away from the East China Sea. Besides, the amount of this type is small than others. Each typhoon type has its own effect on swell generation and propagation. To explore the characteristics of each typhoon type generated swells, we choose 3 typical typhoon processes for every type. The total 12 processes are listed in Table 1.
As the range of the East China Sea is too large to investigate the characteristics of typhoon induced swells, here, 11 representative stations around China coastal regions are chosen to reveal the swells characteristics. Information of these stations is shown in Table 2 (terrain data come from Etopo1) and Fig. 3, each station is located at the vertex of terrain grid and has a similar depth condition. According to the recent research, swells in the East China Sea have a peak period wave length variable in a section 100−300 m, which means that the depth condition of each station is intermediate, and the deformation of shallow water could be ignored.

Verification
The verification is conducted in two ways to investigate the feasibility of WAVEWATCH III. Observation data from three buoys named 'Xiangshui', 'Dafeng' and 'Ikitsuki' respectively are used to check the applicability. Their geographical details and location information are demonstrated in Table 3 and Fig. 4. Firstly, a comparison between significant wave heights from observation and simulation is shown to prove the accurateness of WAVEWATCH III (see Fig. 5). Observation data are from two buoys named 'Xiangshui' and 'Ikitsuki' respectively. As the content plotted in Fig. 5, simulation results are in good accordance with the observation from two distant buoys. Secondly, spectral pattern validation is implemented to check the veracity of wave spectra generated by WAVEWATCH III. In this part, the third station named 'Dafeng' is chosen to provide the actual measurement. The comparison between the observed spectra and simulated spectra from given wind input conditions are shown in Fig. 6. It is obvious that the spectra pattern of simulation fits that of the observation quite well, and the values of peak spectra frequency as well as the correspond-

Result introduction
Because of the limitation in swell system separation due to WAVEWATCH III, it is a pity that only one swell system is provided per output. Each wave system of swell evolution process has its own spatial and temporal source. The direct direction of swell system indicates that a step of typhoon is found at the predicted time and location with winds oriented toward the station. Wind fields are generated from Holland typhoon model, with rotation around low atmosphere centers in the Northwest Pacific. The regulation of CMABST is that the information about typhoon centers is recorded every six hours. Inferred swell occurrence time is seldom located on the time list of typhoon process collected by CMABST accurately. This makes allowance for slight modifications to the generation within ±12 h of the predicted occurrence time. The typhoons used to simulate swells are presented in Fig. 7, and all of them contain at least three change steps during typhoon durations, which ensures that wind fields are strong enough to generate swells to affect the East China Sea.

Recurving type typhoon induced swells
Three types of swell variation could be extracted from the swell significant wave height evolution histories (see Fig. 8). The representative station of Type 1 is ST. 1, which has a smaller value than that of other stations, and only one peak of curve during swell evolution. Type 2 is dominated in eight stations from ST. 2 to ST. 9. In this type, the curve of swell significant wave height has two peaks differing from Type 1, and both peaks of each station have similar occurrence timings. The second trait is that the significant wave height of the first peak is much larger than that of the following peak. ST. 10 and ST. 11 have the same type labeled as Type 3, which means that there is no swell at the two stations during typhoon scenarios.
From the curve of ST. 1, it can be seen that swell initially appears when swells of Type 2 almost reach their peaks, which suggests that the source is different from those of Type 2. In Type 2, swells of ST. 4 appear a bit earlier than that of other stations, which leads to a phenomenon that appearances of swells and the first peak of curve postpone northward and southward center on ST. 4. In addition, the peak of the curve at ST. 4 is the largest among the eight stations from Type 2, and ST. 3 and ST. 5 also have higher peak value than other stations. Both traits mentioned above shows that waters nearby Zhejiang Province coast are more    susceptible by swells caused by the recurving type typhoon than that of other area in the East China Sea. However, appearance sequence of the second peak is not as apparent as that of the first peak. Swell group separation method is used to identify the spatial and temporal sources of swells. The slope and intercept of each fitting line and the mean direction of every swell series are computed to predict the swell generation time and locations. The most representative swell evolution m ftΘ ϕ, φ process caused by 'Melor' at ST. 4 is illustrated as an example. The regression slope and intercept b are listed along with the mean wave propagation direction for specific group, the generation time t 0 , swells travel distance d and source geodesic coordinates ( ) are provided in Table 4. As shown in Fig. 9, swell wave height evolution process could be divided into six groups according to the separation method. Each swell group has the independent slope of the fitting line.
Specific groups 1, 2 and 3 are related to an increasepeak-decrease process of swell significant wave height with a similar spectrum peak frequency in low frequency range. Specific groups 2 and 3 have a similar occurrence time that falls in with respect to 0600 and 1200 UTC 4 October 2009 in Fig. 10. For a direct exhibition to the propagation route of swells, the great circle path that links the sources and the station are added into the chart. These are mature swell events that have travelled over 2000 km and reached ST. 4 (Table 4). Furthermore, these swell events are generated in the step 'super typhoon' that cyclonically rotating winds carry much higher energy than other steps, and generation region within Northwest Pacific basin.
In contrast to the swell groups 2 and 3 from meteorological event in the region far away from the East China Sea, group 4 appears to be a result of typhoon moving toward the East China Sea and changing direction outward the Ryukyu Islands. Having travelled approximately 1100 km before  Fig. 9. Swell group separation and swell significant wave height. Six specific swell groups are extracted from preliminary groups. Swell groups 2 and 3 are related to the process of the swell wave height increasing and reaching the first peak. Groups 4 and 5 correspond to the process of swell wave height decreasing after the first peak and then reaching the second peak. reaching the sampling point, the specific swell groups experience energy dissipation and diffraction as they propagate across many islands of the Ryukyu Islands. It is interesting that group 5 is the only swell event originated from the waters within the East China Sea. This swell event is essentially a young swell event that has travelled less than 1000 km. The predicted source position is located within the East China Sea, and not quite accurately in the region of rotating winds toward ST. 4. The typhoon step that induces swells is 'severe typhoon', which has less energy than step 'super typhoon'.

Westward type (over the South China Sea) typhoon induced swells
Swells generated by the westward type typhoon possess an evolution tendency quite different from that caused by the recurving type typhoon, with merely one peak in plot. The westward typhoon induced swells present a trend that swells increase sharply after appearing at each station, reach the peak, decrease and then dissipate slowly. Swells at ST. 4 and ST. 5 have an approximate appearance time, which lead other stations. The same as the recurving type typhoon, swell peaks center at ST. 4 and ST. 5 (see Fig. 8b), decrease southward and northward separately. In addition, swells at ST. 1 differ from those of the stations mentioned above. When swells of these stations reach their peaks, swell does not yet exist at ST. 1.
The swell evolution process at ST. 4 is chosen for its ϕ, φ prominent characteristics. The generation time t 0 , distance d that swells travelled and source geodesic coordinates ( ) are provided in Table 5. Swells reached ST. 4 in sequence during tropical cyclone effect scenario can be divided into 9 groups by separation method. The most obvious feature is that during tropical cyclone process, swells appear to be in a main tendency of increasing from low-frequency to highfrequency range. Note that swell groups within low frequency range 0.5-1.2 Hz, travelled the farthest distance among typhoon induced swells, which is similar to swells generated by 'Melor'. Such phenomenon indicates that swells generated in low frequency range may have the ability to propagate for a long distance, on the other side, swells generated in higher frequency tend to easily disperse on the way to destination. The specific group 2 has a source located in a wide region east to the low pressure center of tropical cyclone. The wind speed at the position where the source is located is high enough to support the generation of swell with wind direction toward to ST. 4. The swell event is a mature swell group caused by step 'typhoon' of 'Mirinae'.
Swells belong to groups 3 and 4 are both from distant storms located in the Northwest Pacific basin with the same temporal source. According to the predicted great circle propagation path of swells, groups 3 and 4 all pass through the gap of the Ryukyu Islands with most wave energy maintained after the long journey. Moreover, swells dominating the station are also generated from the step 'typhoon', and have been maturely developed after formation.
In contrast to the swell groups 2−4 from meteorological event in the region within the middle part of the Northwest Pacific, groups 6−8 are both generated by the rotating wind field around the Philippine Islands. The feature of the predicted sources of the three groups is similar. As portrayed in Fig. 10, these swell events move across the gap between the southern part of the islands and Taiwan Island with much smaller energy than that of groups 2−4.

Westward type (striking the East China Sea) typhoon
induced swells Swells resulted from this typhoon type have three varieties in their wave height evolution process (see Fig. 8c): the presentative stations of this type swells are ST.1−ST.6, they have double discontinuous crests, and the six stations are located in the waters near the typhoon path. Swells within the region, firstly, due to the typhoon generated swells in advance, reach the first peak during swell evolution curve; then, the typhoon propagates along the track into the East Sea and gradually approaches Chinese mainland, limited by WAVEWATCH III swell separation and wave energy computation methods. Swells in the East China Sea rapidly disappear after reaching the peak. The waters near the East China Sea are mainly affected by the typhoon induced storm waves, but swells usually do not exist. With the typhoon deepening into the mainland, the typhoon waves in the East China Sea dissipated or converted to swells. Swells in the East China Sea appear again and fast achieve the second wave peak, then due to the migration and dissipation of the typhoon, input wave energy gradually disappears. Swells within the domain continuously lose their energy and finally disappear.
From the trajectory figure (Fig. 7), the typhoon passes through ST. 3. By station swell evolution curves, it is easy to discover that swells at ST. 3 are less affected by the typhoon compared with those at other stations, and the significant wave height of swell at ST. 3 is the maximum among stations near the typhoon propagation path. In addition, for the waters near the typhoon maximum wind radius, swells are significantly affected by tropical cyclones, swells decay rapidly and keep zero for a long time. The peak value and zero duration at the station decrease as the distance to the track increases. It proves that there is a negative correlation between the distance from the target waters to the tropical cyclone path and the extent of typhoon generated swells.
Swells at ST. 7−ST. 9 have one continuous peak. Swells reach the wave height peak in a short time, and then gradually decrease to zero due to its own energy dissipation. With increase of the distance between stations and typhoon tracks, the value of the swell is reduced. This type of swells also conform to the negative correlation between the impact extent of waters and the distance from the sea areas to the center of the typhoon.
It is easy to find that swell values at ST. 10 and ST. 11 in the East China Sea can be ignored. The westward type typhoon always propagates into the East China Sea in low latitude waters, because of the terrain influence, ST. 10 and ST. 11 are usually located in the shadow region of the mainland, and the area is located in the East China Sea continental shelf. Swells are easily affected by the topography, which leads to energy dissipation.
In order to further study the sources of this type of swell, sources of swells at ST. 4 are tracked to present the source distribution. Sources of swells at ST. 4 are mainly from the stage that the westward typhoon does not enter the East China Sea. From Table 6, Group 1 with smaller swell energy comes from the tropical storm stage at the beginning of typhoon generation. When the tropical cyclone is transformed into a 'typhoon' stage, the energy of the swell is gradually enhanced with the increasing of the input energy. The origin of group 4 is the closest one to the East China Sea in the tropical cyclone process among these swell groups, which indicates that the space sources also have a great impact on the generation of swell energy. In 0000 to 1800 UTC 10 August, swells at ST. 4 contain quite low energy, and the main composition of the mixed wave is wind sea. During this scenario, the tropical cyclone propagates into the East China Sea and enters the super strong typhoon stage. The strong wind of tropical cyclone makes only typhoon waves in ocean surface. Swells arriving at the station disappear due to super typhoon or coupled with typhoon waves, and then lose swell characteristics. After that, the tropical cyclone landed inland. The wind force decreases and the effective distance of the wind area de-  China Ocean Eng., 2020, Vol. 34, No. 2, P. 210-222 219 creases. The swell generated at the former stage is transmitted to the target station. But at this time the energy of the swells has been dissipated, close to annihilation.

Northward type typhoon induced swells
From the wave evolution curves in Fig. 8d, swells generated by the northward type typhoon can be divided into two types, one is the single peak wave curve, and the other is the double peaks type wave curve. The representative sta- The single peak wave curve can be divided into two seed types. For the first seed type, swell wave height values are smaller. Stations belonging to this type are mainly distributed in the low latitude areas and high latitude areas of the East China Sea. The two areas mentioned above suffer less from the northward typhoon, and this phenomenon is resulted from the terrain and geographical reason. The representative stations of this type are ST. 1 and ST. 9−ST. 11. The feature of the second seed type is that the wave heights are smaller in the initial and late stages. While on August 27, the wave heights suddenly increased, reaching the peak value of wave height and then gradually decreased to zero. ST. 5−ST. 6 stand for this seed type.
The double peaks type swell curve can be divided into two seed types. The wave height values of the first type are small, and the first wave peak evolution process is relatively smooth. The second peak value is much higher than that of the first type, and the evolution process takes shorter time than that of the first one. Swells quickly reached the peak height in a relatively short period of time. Contrary to the first seed type, swells of the second seed type have a higher first peak value with a higher growth and decay rate. The second peak value is smaller, with faster growth rate, but then slowly decays to zero for a long time. Representative stations for this seed type are ST. 7−ST. 8.
During the process of typhoon propagation at the middle and high latitudes of the East China Sea, due to the typhoon propagation path closing, there would be zero or small values originated from the influence of the tropical cyclone effective wind coverage. This feature is quite different from that of the other three types of typhoons, indicating that swells generated by the northward type typhoon have a significant impact on the middle and high latitude waters in the East China Sea.
To further analyze the sources of this type of swell and tracking swells at ST. 4, swells appearing at ST. 4 can be divided into 12 groups (Table 7), but only 6 groups are effective. According to the 6 effective tracking results, swells at ST. 4 are mostly from regions outside the East China Sea, and only a few swells are originated from the East China Sea. The swells initially occurred at ST. 4, which came from the primary stage of the tropical cyclone. Because of the limited input wind energy, the wave energy is low, and the swell curve slowly reaches its first peak and then slowly declines. With the propagation and evolution of the tropical cyclone, the wind power of the typhoon is strengthened, the sources of the swells approach the East China Sea, and the energy of swells is enhanced. Under this condition, swells reach the second peak rapidly, and then gradually attenuate to zero due to the migration and dissipation of the typhoon. ST. 4 is located in the low latitude waters of the East China Sea, and it can be traced by the tracking results that only affected by the northward tropical cyclone in the stages within the northwest Pacific Ocean. However, swells generated by the tropical cyclone in the East China Sea do not have significant impacts on ST. 4.

Conclusions
The investigation on the swells, which are simulated in 12 typical typhoon cases, reveals the relationship between the swell energy and typhoon track, which is of significant use in swell prediction during typhoon scenarios. From the swell tracking results, we find that swell sources are mostly located outside the Ryukyu Islands, which means that swells are generated in the waters apart from the East China Sea and then can propagate across the islands to arrive at the coastal areas of China.
Based on the research on the four types of tropical cyclones, we find that typhoon path can decide the evolution characteristics of typhoon-generated swells. Different typhoon tracks result in different swell evolutions, each type with its own features. There are two peaks in swells that are caused by recurving type typhoon. The first peak is related to the consistent fetch with high wind speed while the second peak is related to the frail fetch due to the diversion of track. Swells propagating toward the East China Sea, which are caused by the westward (over the South China Sea) type typhoon, have only one but continuous peak during their evolution. Swells from the westward (striking the East China Sea) type typhoon would be affected by typhoon effective range and disappear before typhoons landing in the mainland, which makes discontinuous double peaks exist in swell evolution curve. Swells induced by the northward typhoon have a similar feature as the swells generated by the recurving type. The spatial tracking results indicate that typhoon tracks significantly influence swell generation and propagation. Swell energy depends on swell propagation distance, existence time and wind intensity of generation fetch. A consistent track with forceful wind intensity could make swell carry much more energy than that from discontinuous track or with weak wind intensity. Moreover, swell energy is positively correlated to swell propagation.