Wave Energy in Korean Seas from 12-Year Wave Hindcasting

: In this study, a numerical simulation is performed to produce wave hindcasting data from 2007 to 2018 for the assessment of wave energy resources in the sea waters of Korea. The hindcasting data are obtained with a relatively ﬁne spatial resolution of 1 / 20 ◦ covering 120–150 ◦ E longitude and 22.4–47.6 ◦ N latitude using the Simulating WAves Nearshore wave model (SWAN). Three di ﬀ erent wind ﬁelds, those of the European Centre for Medium-Range Weather (ECMWF), National Centers for Environmental Prediction (NCEP), and Japan Meteorological Agency (JMA), are used for the numerical wave simulation. It is observed that the wind ﬁeld dataset of JMA exhibits the best agreement with available ﬁeld observation data. For this reason, the wave energy resources are evaluated based on the data hindcasted using the JMA wind ﬁeld. It is found that the overall magnitudes of wave energy are larger in winter than in summer. The wave energy in August, however, is comparable to the mean wave energy during winter because of the inﬂuence of frequent high wave events caused by typhoons. The highest monthly average wave power around Yellow Sea, South Sea, East Sea, and Jeju Island are 13.3, 18.2, 13.7, and kW / m, respectively.


Introduction
Recently, the regulations on the use of fossil fuels have been made more stringent because of worsening global warming and pollution. To resolve these problems, renewable energies derived from solar heat and tidal currents and waves are suggested as appropriate alternatives to fossil fuels. In this regard, various research works have been conducted in oceans because wide spaces are available, and the potential threat to human lives is lower than when these studies are conducted on land. For the successful production of these renewable energies in oceans, however, it is necessary to understand the capacity of available power before the infrastructures are built; thus, advanced thorough investigations are crucial. For example, in the case of wave power generation, a precise comprehension of the distributions and variation patterns of wave energy and other wave characteristics in a region of interest is imperative. This is difficult to achieve, however, because of the high variability and dispersion of wave fields over time and space. To determine wave characteristics at a specific location, observational data must be gathered at different points in the area over sufficiently long periods (at least 10 years). In most ocean areas, however, such data are not available. An alternative approach to understand wave characteristics in specific regions is hindcasting. This technique employs wave models by which previous wave conditions have been represented and improved through comparisons with observational data.

Wind Data
Three wind products using the three wind datasets of the ECMWF, NCEP, and JMA are evaluated for wave hindcasting. The ECMWF and NCEP datasets are global products, whereas the JMA (Japan Meteorological Agency) dataset is a regional product for East Asia. The spatial resolutions of ECMWF, NCEP, and JMA are 0.125 • , 0.205 • , and 0.0625 • , respectively. The time interval of ECMWF is 6 h, and that of NCEP and JMA is 1 h; wind product details are listed in Table 1.  10 , i.e., wind speed (m/s) at a height of 10 m above the sea surface.

Wave Data
In this study, the data employed for model evaluation are obtained from WINK because this system provides quality-controlled observational wave data from 32 stations (16, 6, and

Theoretical Formulations
The evolution of the action density N(E/σ, where E is the wave energy density distributed over intrinsic frequencies (σ) and propagation directions (θ)) is governed by the action balance equation.
The quantities C σ and C θ are the propagation velocities in spectral space (σ, θ). The right-hand side contains S tot , which is the source/sink term that represents all physical processes which generate, dissipate, or redistribute wave energy.
These terms denote, respectively, wave growth by the wind, nonlinear transfer of wave energy through three-wave interactions [14] and wave decay due to whitecapping, bottom friction and depth-induced wave breaking. The energy transfer from wind to waves (S in ) and wave energy dissipation caused by whitecapping (S wc ) are approached with the saturation-based model of Westhuysen [15] combined with the wind input formulation proposed by Yan [16]. The energy dissipation by bottom friction (S bot ) is computed according to the formulation developed by Madsen et al. [17]. The energy dissipation due to wave breaking (S brk ) according to Battjes and Janssen [18].

Model Setup
In this study, the SWAN model version 40.91 is employed. The model has an orthogonal grid with a spatial resolution of 0.05 • and covers 120 • -150 • E longitude and 22.4 • -47.6 • N latitude. The topographic data provided by KHOA are utilized for the model grid depth (Figure 2). The initial water level is set as the approximate highest high water level (AHHWL). By fixing the sea levels in all model runs, the change in water level caused by the tide is disregarded. The AHHWL, instead of the mean sea level, is used because tidal flats are widely generated on the western coast, and a significant portion of the sea has to be treated as land if the latter is applied. The two-dimensional wave spectrum used in the model consists of direction and frequency. The wave direction is divided into 48 segments, each of which is set at 7.5 • wide. The frequency is divided into 20 bands within the (0.04-0.4)-Hz range. These 20 frequency bands may produce extremely wide bandwidths especially in long waves with lower frequency levels. To examine this, a sensitivity test with 40 bands is implemented. The model integration time usually increases with the frequency band. The computational cost can be reduced if the frequency bands are also reduced (provided that the results are stable). Figure 3 shows a comparison of wave parameters calculated in three different cases. In Case 1, 20 bands in the (0.04-0.4)-Hz frequency range are used. In Cases 2 and 3, 40 bands in the (0.04-0.4) and (0.02-0.4)-Hz frequency ranges are used and observed at the KMA-2 location, respectively. No distinct difference is found among the three cases, thus validating the use of 20 band levels to reduce computational cost.
In the model runs, only wind forcing is present, and no waves are set along the lateral boundaries, assuming that waves from the open seas do not enter the computational domain. For validation, the three wind fields of ECMWF, NCEP, and JMA are compared with the observational data measured in 2016; the setting details of the model are listed in Table 3. Other model conditions, such as ocean currents, are not considered in the experiments.

Model Setup
In this study, the SWAN model version 40.91 is employed. The model has an orthogonal grid with a spatial resolution of 0.05° and covers 120°-150 °E longitude and 22.4°-47.6 °N latitude. The topographic data provided by KHOA are utilized for the model grid depth (Figure 2). The initial water level is set as the approximate highest high water level (AHHWL). By fixing the sea levels in computational cost can be reduced if the frequency bands are also reduced (provided that the results are stable). Figure 3 shows a comparison of wave parameters calculated in three different cases. In Case 1, 20 bands in the (0.04-0.4)-Hz frequency range are used. In Cases 2 and 3, 40 bands in the (0.04-0.4) and (0.02-0.4)-Hz frequency ranges are used and observed at the KMA-2 location, respectively. No distinct difference is found among the three cases, thus validating the use of 20 band levels to reduce computational cost. In the model runs, only wind forcing is present, and no waves are set along the lateral boundaries, assuming that waves from the open seas do not enter the computational domain. For validation, the three wind fields of ECMWF, NCEP, and JMA are compared with the observational data measured in 2016; the setting details of the model are listed in Table 3. Other model conditions, such as ocean currents, are not considered in the experiments.

Comparison with Point Measurements
To evaluate the accuracy of wind datasets, the verification of three wind fields of ECMWF, NCEP, and JMA is conducted. Observational wind data from 22 stations monitored by the KMA and KHOA are used for the evaluation. Considering the spatial resolution of the model (0.05 • or~5 km), data from the six stations monitored by the MOF are excluded because these stations are close to the coast (water depths, 15-36 m).  (Table 4). For the wave by wave height evaluation, the wave height is classified as <1, 1-2, 2-3, and >3 m. The JMA data perform best among all wave levels ( Table 5). Figure 4 shows the time series of model data and observational data from Jeju-South station monitored by the KHOA. The scatter diagrams for the 22 stations are shown in Figure 5. Based on the foregoing, the JMA wind data are selected to investigate the wave energy characteristics in the seas of Korean.

Wave energy Calculation Method
Wave energy, , can be calculated by where is a significant wave height; is the specific density of water; is the gravitational acceleration; is the average wave period indicating the energy period and is usually determined as 90% of the peak wave period in the SWAN model [4,10]. Parameters and are obtained from the wave model outputs.

Spatial distribution of wave energy
In order to investigate the wave energy distribution in Korean seas, the wave energy average over a span of 12 years (2007-2018) and the yearly wave energy average are shown in Figures 6 and  7, respectively. The wave energy averages in the Yellow Sea, Korea Strait, East Sea, and the vicinity of Jeju Island are 0.6-13.3, 3-9, 3-8, and 7-12 kW/m, respectively ( Figure 6). The yearly wave energy average for 12 years shown in Figure 7 indicates that the wave energy exceeds 15 kW/m in the vicinity of Jeju Island. The high wave energy around Jeju Island appears related to the fact that more high waves occur in its vicinity than in other regions when typhoons occur in summer.

Wave Energy Calculation Method
Wave energy, P, can be calculated by where H s is a significant wave height; is the specific density of water; is the gravitational acceleration; T e is the average wave period indicating the energy period and is usually determined as 90% of the peak wave period in the SWAN model [4,10]. Parameters H s and T e are obtained from the wave model outputs.

Spatial Distribution of Wave Energy
In order to investigate the wave energy distribution in Korean seas, the wave energy average over a span of 12 years (2007-2018) and the yearly wave energy average are shown in Figures 6 and 7, respectively. The wave energy averages in the Yellow Sea, Korea Strait, East Sea, and the vicinity of Jeju Island are 0.6-13.3, 3-9, 3-8, and 7-12 kW/m, respectively ( Figure 6). The yearly wave energy average for 12 years shown in Figure 7 indicates that the wave energy exceeds 15 kW/m in the vicinity of Jeju Island. The high wave energy around Jeju Island appears related to the fact that more high waves occur in its vicinity than in other regions when typhoons occur in summer.

Inter-Annual Wave Energy Evolution
In order to examine the characteristic features of wave energy distribution, the monthly wave energies in four regions (Yellow Sea, South Sea, East Sea, and Jeju Island vicinity) are listed in Tables 6  and 7; the distribution map is shown in Figure 8. The time series of monthly wave energy for 12 years is shown in Figure 9. Figure 10 shows the monthly wave energy over 12 years. Figure 9 and the list in Table 7 suggest that the monthly wave energy is highly variable. The Yellow Sea has high variabilities: 3.2-8.6, 0.7-5.0, and 1.9-10.9 kW/m in February, June, and August, respectively. In May, however, the wave energy is at a minimum (0.6-2.5 kW/m) and with low variability. The wave energies in the Yellow Sea, South Sea, East Sea, and Jeju Island vicinity are 0.6-13.3, 1.1-18.2, 0.7-13.7, and 1.6-40 kW/m, respectively, suggesting high monthly variations. Generally, the wave energy reaches the maximum value and variability in winter and the minimum in summer (except for August). The high variability in August compared with the other months is possibly the effect of typhoons.
The results in Table 7 and Figure 9 represent the average wave energy in each region. If the wave energy average of the entire area is calculated, however, the result will not be relevant for wave energy exploitation because various depths are encountered. Figure 11 and the list in Table 8 are, therefore, included to compare the time series of wave energy computed at two selected locations in each region. The wave energy increases with the distance from the shore, except for the Yellow Sea, where the discrepancies among different locations are smaller than in other regions. In general, the magnitude of wave energy in the Yellow Sea, South Sea, and East Sea are similar, and the temporal variation is not significant. The wave energy in Jeju Island, however, is approximately two times greater than those in other regions; the magnitude is greatest in summer.

Seasonal Evolution of Wave Energy
In order to investigate the seasonal variation of wave energy, the monthly averaged wave energy over 12 years from 2007 to 2018 is used, as shown in Figure 12. Figure 13 shows the monthly averaged wave energy in February and August in 2007, 2012, and 2018. As shown in Figure 11, the wave energy is generally high in December and January and low in May and June. The lower energy during summer (except for August when typhoons and tropical storms cross the region) gradually increases with time and again peaks in December. The wave energy variability in the South Sea shown in Figure 13 is influenced by the occurrence of typhoons.

Wave Height, Period, and Direction
In Section 4.3, the analyzed data are presented in terms of wave energy distribution because the study aims to provide information for designing the wave power generation in the regions around the Korean Peninsula. In this section, additional hindcast data on other wave parameters, such as height, period, and direction, are described. Figures 14 and 15 show the distributions of monthly mean wave height and period, respectively. The wave height distribution is similar to that of wave energy because it significantly increases in winter from December to February in all four regions. In December, the monthly mean wave heights increase to as high as 2 m in the East Sea and Jeju Island. The wave height decreases after winter and reaches the minimum in May. In August, however, the wave height near Jeju Island increases to~1.5 m probably because of tropical storms that occasionally cross this region. On the other hand, the monthly variation in wave period is less significant because the spatial-temporal variations are not as distinct as the changes in wave height. The pattern, nevertheless, is generally similar to that of wave height because it increases in December, January, and February; in August, a significant increase in wave period is also observed near Jeju Island.
To understand the wave propagation directions, the rose diagrams of wave height and direction at eight selected locations in the four regions are presented in Figure 16. The wave direction exhibits distinct differences among the regions. In Jeju Island and the Yellow Sea, the waves generally approach the shore from the northwest. On the other hand, in the East and South Seas, they approach from the northeast. These patterns indicate that the waves developed in the Yellow Sea generally approach the coast from the northwest, whereas those generated in the East Sea approach from the northeast. It should be noted that the wave directions at P3 and P7 are clearly distinguishable although the distance between these two locations is only~50 km.

Extreme Storm Events
In this section, the investigation of model performance under extreme wave conditions is presented. The Korean Peninsula is influenced by tropical storms because some of the typhoons that develop southwest of the North Pacific Ocean cross the East China Sea and East Sea. Table 9 Figure 17 shows the paths of these 23 typhoons. All the storms that moved to the west below 30 °N latitude passed over the East China Sea. Some of them, thereafter, changed directions toward the east and crossed the East Sea, thus impacting the southern and eastern coasts of the

Extreme Storm Events
In this section, the investigation of model performance under extreme wave conditions is presented. The Korean Peninsula is influenced by tropical storms because some of the typhoons that develop southwest of the North Pacific Ocean cross the East China Sea and East Sea. Table 9 Figure 17 shows the paths of these 23 typhoons. All the storms that moved to the west below 30 • N latitude passed over the East China Sea. Some of them, thereafter, changed directions toward the east and crossed the East Sea, thus impacting the southern and eastern coasts of the Korean Peninsula. The other storms continued to the north and passed through the Yellow Sea, thereby affecting the west coast.  In running the models for hindcasting, the impact of these typhoons is evaluated by means of the wind fields. In calculating the wave parameters and energy, however, it is found that the contributions of storms are indistinct.
The model performances using the wind fields during some of the tropical storms are compared. It is found that the outcomes of JMA best agree with observational data. In Figure 18, the model performance comparisons during Typhoons GONI (2015) and CHABA (2016) are provided for additional information.

Discussion
In this study, the SWAN wave model is employed for hindcasting. In reality, other wave models, such as WAM (wave model), can be used for similar purposes. For example, Kim et al. [10] used the HYPA and WAM for hindcasting in the seas around the Korean Peninsula. Their research motivated the present study. The SWAN model has been widely employed in hindcasting in other oceans and seas [1,3,4,6,7,8,9] but not in the seas around the Korean Peninsula. Apparently, it would be

Discussion
In this study, the SWAN wave model is employed for hindcasting. In reality, other wave models, such as WAM (wave model), can be used for similar purposes. For example, Kim et al. [10] used the HYPA and WAM for hindcasting in the seas around the Korean Peninsula. Their research motivated the present study. The SWAN model has been widely employed in hindcasting in other oceans and seas [1,3,4,[6][7][8][9] but not in the seas around the Korean Peninsula. Apparently, it would be advantageous to use SWAN for hindcasting around this area. It should be noted, however, that the present study aims to determine the wind fields that are most appropriate for wave hindcasting in specific regions around the peninsula. Kim et al. [10] only utilized the ECMWF data for wind field hindcasting. It is, therefore, necessary to examine whether these data are indeed the best choice for wind field hindcasting or a better alternative dataset is available.
The results show that the JMA data better agree with measurements. Moreover, the hindcast model in the present study employs a finer resolution compared with that in Kim et al. [10]-the horizontal grid size in the latter is 1/6 • , whereas 1/20 • is employed in the experiments of the present study. A finer resolution is typically regarded as indicating that derived results are more accurate; consequently, the model outcomes may be deemed more credible by readers and potential users of published data. Although sensitivity tests among various hindcast models have not been performed in this study, these would have yielded valuable outcomes as well. The conduct of these tests is thus proposed in future studies. Among the deficiencies of the present research is the absence of lateral boundary conditions for the model and the assumption that no waves enter the computational domain simply because there is a dearth of information. In the low-frequency bands, however, long waves could propagate over extended distances and possibly affect wave conditions and distributions in the regions considered in this study. This aspect, therefore, also requires thorough consideration in future experiments.

Conclusions
It is advantageous to use wave data observed over a period of at least 10 years to determine the wave power generation in a particular location. In reality, however, it is difficult to continuously measure wave data over a 10-year period in the ocean; hence, such field datasets are rarely obtained. Alternatively, wave information could be obtained from hindcast simulations using wave models. Based on the foregoing, the present study is designed to derive information on the distributions of wave energy and other relevant parameters in the four regions around the Korean Peninsula-Yellow Sea, South Sea, East Sea, and Jeju Island.
Before hindcasting is conducted, the reproducibility of wave fields between the wind products of ECMWF, NCEP, and JMA is evaluated through comparisons with observational data from 21 stations. The results show that the differences among the wind fields are statistically significant. Furthermore, because the JMA wind field exhibits the highest correlation coefficient and the lowest root mean square and bias error, it is considered the best dataset among the three. Based on these results, the JMA wind data are selected for the conduct wave hindcasting using the SWAN model over a 12-year period (2007-2018) to investigate the characteristic patterns of wave energy distributions in the four regions.
Among the four regions, it is found that the wave energy near Jeju Island is the highest then followed by that in the South Sea; the lowest is observed in the Yellow Sea. The seasonal variability of wave energy is also observed to be high around Jeju Island. Its maximum is reached in December and January, and its minimum occurs in May. In August, the wave energy near Jeju Island sharply increases because of the occasional occurrence of typhoons that pass through this region. Around the island, the other wave parameters, such as wave height, period, and direction, also exhibit a pattern similar to that of wave energy. The wave height and period reach the maximum in December, January, and February and thereafter gradually decrease (except for August, when these parameters increase). The wave direction also exhibits severe spatial discrepancies because the waves in the Yellow Sea and near Jeju Island generally approach the shore from the northwest, whereas those in the South and East Seas approach from the northeast. The foregoing indicates that the waves in the coasts along the Korean Peninsula mainly develop in the northern parts of the Yellow Sea and East Sea.
The regions considered in the present study have been influenced by the occasional occurrence of typhoons. Accordingly, it is necessary to examine the performance of the hindcast model under extreme conditions. Through comparisons, it is confirmed that among the three wind fields, the JMA wind field dataset best agrees with observational data measured during major typhoons (such as GONI (2015) and CHABA (2016)). Although it is found that the energy generated by the waves in the seas around the Korean Peninsula (specifically near Jeju Island) may be sufficiently high for wave power generation, further investigations are necessary because the results of the present study only focused on determining the most appropriate wind field for hindcast simulations. Model validations through comparisons with additional observational data and other wave models are thus suggested for future investigations.