To estimate storm waves during typhoon invasions, the third-generation wave model SWAN ver. 41.31A, based on the wave action balance equation, is used to reproduce multi-directional irregular waves. The SWAN spectrum wave model can simulate the growth of wave energy by wind and wave propagation according to refraction, shallow water effects, reflection, and diffraction. It is divided into first, second, and third generations according to the source and sink terms. The governing equation is as follows: where t is the time, θ is the direction, σ is the angular wave number (=2π/f), and N is the wave action density spectrum (=E(σ,θ)/σ; E is the energy density spectrum). c_x, c_y, c_z, and c_θ are the wave energy propagation speeds for each phase (x, y, σ, and θ). S_in is the growth of wave energy by wind, S_nl is nonlinear wave-wave interaction), and S_ds is energy dissipation by white capping, nonbreaking wave dissipation, bottom friction, and depth-induced wave breaking. Details on the scientific and technical background of this wave model can be found in the SWAN Team (2020a, 2020b).

The computational domain of this study is set between latitudes 20° to 43° and longitudes 117° to 142°, considering the track of Typhoon Bolaven, to accurately estimate the waves generated and propagated by the typhoon wind. As shown in Fig. 2(a), the computational domain is composed of rectangular grids at 0.0417° (approximately 4.6 km) intervals. For the water depth of the computational domain, the underwater topography from SRTM5+V2.0 (Tozer et al., 2019), constructed based on 494 million depth survey data points selected from the latest global models CryoSat-2 and Jason-1, is applied as shown in Fig. 2(b). Spatial interpolation is performed according to the computational grid size (0.0417°) of SRTM5+V2.0, which has a resolution of 15” (approximately 450 m).

In this study, the frequency of the wave energy spectrum (0.04 to 1.0 Hz) is divided into 34 sections to utilize the JONSWAP wave spectrum and to account for the period component of long-period waves, such as storm waves. In addition, the wave energy spectrum is calculated by dividing the wave direction into 36 sections at 10° intervals (see Table 1).

The one-hour interval wind field with a resolution of 0.0625° × 0.05° provided by JMA-MSM is applied to the calculation of storm waves using the SWAN model. This field covers the area from the Shandong Peninsula, China to the west, Hokkaido, Japan to the east, Taiwan’s southern waters to the south, and Manchuria to the north, including Japan and Korea.

Typhoon Bolaven, as shown in Fig. 2(b), is considered for storm wave simulation. It represents a maximum wind speed of 36 m/s at 125.2°E and 33°N at 03:00 on August 28, 2012, as it passes through the western sea of Jeju Island. It also maintained strong winds of up to 28.29 m/s at 15:00 on August 28, 2012, when it moved north at a close distance from Taean.

SWAN ver. 41.31A was applied to estimate swell-like storm waves on the east coast of Korea in winter by Son and Do (2021). This model was found to be suitable for wave estimation in the waters around the Korean Peninsula through a comparison with observed waves. In this study, an attempt was made to verify the validity of the SWAN model and the effectiveness of the numerical results before estimating the storm waves generated by the wind of Typhoon Bolaven. The numerical results were compared with the data observed by KMA at the locations of nine wave OPs (see Fig. 3 and Table 2). Although the observation data from OP2, OP4, and OP5 had missing sections, the maximum wave height of storm waves was measured, except for OP2 and OP4.

Fig. 4 and 5 compare the calculated values of the SWAN model with the time distribution of the significant wave height (H_s ) and significant wave period (T_s ) observed at the nine points from August 14 to September 5, 2012, when Typhoon Bolaven invaded the Korean Peninsula. Table 2 shows the maximum significant wave heights at the nine OPs during the invasion of Typhoon Bolaven. In addition, the quantitative accuracy of the storm wave estimation by the SWAN model is presented using R-squared (R²), root mean square error (RMSE), and normalized root mean square error (NRMSE) in Fig. 6.

From Fig. 4 and Fig. 5, it can be seen that Typhoon Bolaven had a direct impact on the southwest and west coasts and an indirect impact on other waters beginning from Jeju Island around August 28, 2012, when it approached the Korean Peninsula. A second peak was observed as the Korean Peninsula came under the direct influence of Typhoon Tembin on August 30, 2012. At each observation point, the trends in H_s and 2, as well as the tendencies of maximum T_s and H_s, were relatively similar. When examining the maximum H_s during the typhoon invasion as shown in Table 1, it was found that the estimated maximum H_s by Typhoon Bolaven differed by more than 1 m from the observed H_s at OP10 to OP13. Among these, the values at OP11 (Oeyeondo Island on the west coast) and OP13 (Marado, Jeju Island) were errors caused by missing observations of peak H_s . Excluding these, the maximum H_s at OP12 (Chilbaldo Islet) was 1.69 m higher than the observed value, resulting in a 31% overestimation. At OP14 (Geomundo Island), where the highest H_s was observed, H_s was 0.4 m lower, showing a 4% underestimation. At OP14 to OP18, located in the South Sea and the East Sea, the estimated H_s from the SWAN model reproduced the observed values with significantly high accuracy. On average, the maximum H_s estimated by the SWAN model overestimates the observed values by 7%. Excluding OP11 and OP13, where peak H_s was not observed, the estimated maximum H_s underestimated the observed values by 3%. Fig. 6 compares the estimated and observed values. The scatter plot and the quantitative indicators (R², RMSE, and NRMSE) suggest that the validity and effectiveness of the SWAN model for storm wave analysis have been partially verified.

The accuracy of the SWAN model was secured to some extent in estimating the maximum storm wave height due to typhoon wind, but the reliability of the period is not as secured as the wave height. In this study, the maximum storm wave height is compared with the design wave height of the 50-year return period to discuss the storm wave characteristics of Typhoon Bolaven. Therefore, storm waves generated by the typhoon wind are simulated using the SWAN model, whose reliability in storm wave height prediction accuracy was confirmed through a comparison with observed values.

As shown in Fig. 2(b), which includes the track of Typhoon Bolaven, the typhoon moved to the north in the East China Sea, passed through the sea to the west of Jeju Island, moved to the north at a close distance from the west coast of Korea, and landed in Jangsu-ri, Gangnyeong-gu, Hwanghae-do (16:00 on August 28, 2012). During this period (00:00 to 21:00 on August 28, 2012), the intensity of Typhoon Bolaven did not significantly decrease before landing as can be seen from Fig. 7. Fig. 7 shows the wind fields (sea surface wind) at three-hour intervals based on the reanalysis weather fields provided by JMA-MSM for Typhoon Bolaven that directly affected the west coast of the Korean Peninsula. In the figure, the locations of the center of Typhoon Bolaven are (a) 170 km to the southwest of Seogwipo (sea), (b) 120 km to the west-southwest of Seogwipo (sea), (c) 120 km to the southwest of Mokpo (sea), (d) 100 km to the northwest of Mokpo (sea), (e) 80 km to the west of Seosan (sea), (f) 120 km to the west-northwest of Seoul (sea), (g) 120 km to the south of Pyongyang (land), and (h) 30 km to the southwest of Pyongyang (land). The typhoon information (central location, central pressure, maximum wind speed, radius of strong winds, and movement speed) provided by KMA is shown in Table 3.

Considering the radius of strong winds of Typhoon Bolaven from Table 3, Jeju Island was directly affected by the typhoon from Fig. 7(a) to 7(c). The southwest coast came under direct influence from Fig. 7(b), and the west coast was directly influenced in Fig. 7(c). As Typhoon Bolaven landed in Jangsu-ri, Gangnyeong-gu, Hwanghae-do while maintaining its strong winds, the entire west coast was directly affected as it moved north, as shown in Fig. 7(d) to 7(g). As shown in Fig. 7(h), the intensity of Typhoon Bolaven weakened after landing. It subsequently transitioned into an extratropical cyclone on land, approximately 220 km north of Ganggye, Jagang-do, North Korea, at 06:00 on August 29, 2012.

Fig. 8 demonstrates the storm wave height at three-hour intervals from 00:00 on August 28 when Jeju Island was under direct influence of Typhoon Bolaven to 16:00 when the typhoon landed in Jangsu-ri, Gangnyeong-gun, Hwanghae-do and 21:00 when it passed through the land. Table 4 shows maximum H_s and the wind speed based on JMA-MSM at time points that correspond to Fig. 7(a) to 7(h). Before the landing of Typhoon Bolaven, the location with maximum H_s was not significantly different from the center of the typhoon.

From Fig. 8, it can be seen that (a) H_s of more than 10 m occurred near the south coast of Jeju Island when Typhoon Bolaven passed through the sea at 170 km to the southwest of Seogwipo, and (b) H_s was more than 11 m when the typhoon passed through the sea at 120 km to the west-southwest of Seogwipo. (c) H_s on the south coast of Jeju Island slowly decreased as the typhoon passed through the west coast of the island and entered the sea at 120 km to the southwest of Mokpo. In addition, H_s of 7 to 8 m occurred in Shinan, an island included in Jindo, as the typhoon entered the West Sea. As the typhoon moved to the north along (d) the sea at 100 km to the northwest of Mokpo, (e) the sea at 80 km to the west of Seosan, and (f) the sea at 120 km to the west-northwest of Seoul, H_s of 6 to 7 m was observed on the adjacent west coast. After Typhoon Bolaven landed in Jangsu-ri, Gangnyeong-gun, Hwanghae-do at 16:00 on August 28, 2012, the wave height on the south coast of the Korean Peninsula, including Jeju Island, significantly decreased when the typhoon reached (g) the land at 120 km to the south of Pyongyang and (h) the land at 30 km to the southwest of Pyongyang. High waves, however, existed in the West Sea over a considerable period even after the landing of the typhoon. Meanwhile, as the typhoon slowly moved to the north, the storm wave height significantly increased on the southeast coast as well as the southwest coast. In addition, after the landing of Typhoon Bolaven, the wave height in the northern part of the East Sea tended to increase under the indirect influence of the typhoon. This is because wind waves continuously develop within the influence of Typhoon Bolaven, which has a large radius of strong winds as in Table 3.

Fig. 9 shows the spatial distribution of (a) the maximum wind speeds obtained from the JMA-MSM wind field of Typhoon Bolaven and (b) the maximum significant wave heights of storm waves simulated in the SWAN model by applying the maximum wind speeds. In other words, the figure shows the maximum wind speeds and significant wave heights between 18:00 on August 26, 2012, when the typhoon directly or indirectly affected the Korean Peninsula, to 09:00 on August 29, when it transformed into an extratropical cyclone on land.

Fig. 9 suggests that the sphere of influence of the strong winds above 20 m/s by Typhoon Bolaven almost coincides with the area where high waves of more than 5 m are distributed. H_s of more than 6 m is distributed over a very wide area in Jeju Island, the Southwest Sea, and the West Sea, which are located in the track of the typhoon. Since the area to the north of Jeju Island is a shielded area, H_s is not relatively high in Chujado, Jindo, and Haenam. Although Typhoon Bolaven moved to the north with no significant decrease in intensity, H_s ranged from 6 to 8 m due to the relatively shallow depth of the West Sea. This is also because the fetch length, duration, and wind direction were changed under the influence of land on the eastern side of the typhoon as it moved north in the West Sea. Although the intensity of the typhoon significantly decreased when it landed in Jangsu-ri, Gangnyeong-gun, Hwanghae-do at 16:00 on August 28, 2012, H_s of 5 to 5.5 m was relatively widely distributed as the northern part of the East Sea entered the sphere of indirect influence.

To assess the size of the storm waves caused by Typhoon Bolaven, they are compared with the 50-year return period deepwater design waves proposed by the Ministry of Oceans and Fisheries (MOF, 2019). These design waves are used for coastal and port planning, as well as for structure design in Korea. MOF (2019) revised the deepwater design waves in 2019 to reflect marine characteristics such as sea level rise caused by global warming, extreme weather events, changes in typhoon intensity, and the occurrence of abnormal waves. Fig. 10 shows the major coastal GPs used by MOF (2019) to provide deepwater design wave specifications around the Korean Peninsula. MOF (2019) provides deepwater design wave specifications (wave height, period, and wave direction by frequency) at a total of 210 major coastal GPs in the East Sea, the West Sea, and the South Sea, including islands.

The design wave specifications (MOF, 2019) show that GPs corresponding to the South Sea, typically passed through by typhoons invading the Korean Peninsula, range from GP63 to GP109. The average maximum wave heights among the design waves for each GP in this region is 11.67 m, which is higher compared to the East Sea. In the East Sea, corresponding to GP110 to GP152, the average maximum wave height is 9.43 m. Overall, the wave directions for maximum wave heights at GP63 to GP91, located to the west of the South Sea, are predominantly S, SSW, ESE, and SE-series, due to the presence of Jeju Island to the south. At GP92 to GP109, in the remaining area of the South Sea (the eastern part), corresponding to the Korea Strait, the S and SSW series exhibit maximum wave heights. In the southern part of the East Sea, at GP110 to GP121, the S and SSW series also show maximum wave heights, similar to the eastern part of the South Sea. In the remaining part of the East Sea (the northern part), from GP122 to GP152, N and NNE-series design waves have the maximum wave heights. For Jeju Island, GP170 has the highest design wave height of 14.5 m among the GPs, while the northern points GP180 and GP181 have heights of 7.9 m, indicating significant differences by area. Various wave directions are also observed. For Ulleungdo, the average maximum wave heights at GP203 to GP206 is 10.25 m, with N and NNE-series wave directions being dominant. For Dokdo, the average maximum wave heights at GP207 to GP210 is 10.5 m, with SSW and N-series wave directions observed. In the West Sea, corresponding to GP1 to GP62, the average maximum wave height is 8.04 m, with GP62 on the southwest coast having the highest design wave height of 11.7 m. Overall, S, SSW, and SW-series wave directions have maximum wave heights. At GP1 to GP4 in the northern part of the west coast, the NW series show maximum wave heights. At GP187 to GP190, corresponding to the islands in the northern part of the West Sea, including Nando, Seokdo, Woobaedo, and Gyeokryeolbi Yeoldo, design waves with an average height of 8.7 m are observed, with the main wave directions being SSW series. At GP191 to GP202, corresponding to the islands in the southern part of the West Sea, including Heuksando, Hongdo, and Gageodo, the design wave height at GP197 in the south is the highest at 11.9 m, with S and SSE-series wave directions being dominant.

Fig. 11 and 12 compare the maximum storm wave heights during the invasion of Typhoon Bolaven, as estimated from the SWAN model, with the design wave heights provided at the major coastal GPs around the Korean Peninsula. Fig. 11 shows the comparison results for the coastal GPs in (a) Jeju Island and (b) the South Sea of Korea, which are located in typical typhoon tracks. Fig. 12 shows the results for the coastal GPs in (a) the islands in the northern part of the West Sea, (b) the entire west coast, and (c) the islands in the southern part of the West Sea.

The storm wave heights at the coastal GPs of Jeju Island (GP153 to 186) and the South Sea (GP63 to 109) in Fig. 11 correspond to 70% to 94% and 47% to 89% of the design wave heights, respectively. In addition, the storm wave heights of Jeju Island and the south coast compared to the design waves are 83.49% and 71.14% on average. In Fig. 12, the storm surge heights for the islands in the northern part of the West Sea (GP187 to 190), the entire West Sea (GP1 to 62), and the islands in the southern part of the West Sea (GP191 to 202) are 88% to 91%, 42% to 86%, and 74% to 87%, respectively, compared to the design wave heights at the coastal GPs. The average values for these areas correspond to 89.55%, 79.55%, and 71.05% compared to the design wave heights, respectively.

Fig. 11 and 12 compare the storm waves generated by Typhoon Bolaven with the design waves. Table 5 provides the wave heights, periods, and wave directions at coastal GPs where the storm waves correspond to more than 90% of the design wave heights.

Typhoon Bolaven slowly moved north at a distance from the west coast while maintaining its strong intensity until it landed. Consequently, for the islands in the northern part of the West Sea, which have relatively low design wave heights, storm waves with an average height of 7.82 m, corresponding to approximately 90.22% of the design wave heights, occurred at GP187 to 190, except for GP188 (125.583°E, 36.5°N). During the invasion of Typhoon Bolaven, the average wave height reached 11.57 m at GP157 to 162, to the southwest of Jeju Island, which corresponds to 91.48% of the design wave heights.

The storm waves of Typhoon Bolaven that exhibit more than 90% of the design wave heights occur at the coastal GPs of the islands in the northern part of the West Sea and Jeju Island. Storm wave heights on the southern coast of Jeju Island are high because the coast is located in the dangerous semicircle of the typhoon, and thus the movement speed and rotation speed of the typhoon are combined, making the wind stronger. Moreover, the southern sea of Jeju Island has few obstacles such as islands. This further develops wind waves by ensuring the fetch length and duration of the typhoon wind. Historically, there have not been many typhoons that entered the West Sea of the Korean Peninsula, and their intensity rapidly decreased as they moved to higher latitudes. The design wave heights of the islands in the northern part of the West Sea are not high compared to the coastal GPs in other areas, possibly for this reason. Therefore, the storm waves of Typhoon Bolaven, which slowly moved north while maintaining its intensity, reached 90% of the design wave heights at the coastal GPs of the islands in the northern part of the West Sea.

Kossin (2018) reported that global warming has weakened tropical circulation in summer, thereby decreasing the movement speeds of typhoons by 10% worldwide. Accordingly, the movement speed of typhoons striking the Korean Peninsula has slowed compared to the past, leading to the development of more storm waves in the East China Sea. If these storm waves enter the waters of the Korean Peninsula, coastal areas will inevitably suffer increased typhoon damage. The World Meteorological Organization (WMO) revealed that four major climate change indicators―greenhouse gas concentrations, sea level rise, seawater temperature rise, and ocean acidification―set new records. Notably, the sea level rose by an average of 4.5 mm each year from 2013 to 2021, with the global mean sea level reaching its peak in 2021. The increase rate between 1993 and 2002 more than doubled, primarily due to the loss of ice from glaciers. This sea level rise significantly affects hundreds of millions of coastal residents and increases vulnerability to the storm surges caused by tropical cyclones (WMO, 2022). Therefore, the impact of climate change will significantly increase the vulnerability of coastal areas, considering the uncertainties of future predictions. This could have serious regional and global impacts from social and economic perspectives. Consequently, it is necessary for researchers specializing in coastal engineering to accurately analyze potential risks and develop countermeasures to reduce the damage caused by coastal disasters caused by abnormal climate conditions.