atmosphere

Article Propagation of a from the Yellow to the Strait in April 2019

Kyungman Kwon 1, Byoung-Ju Choi 2,* , Sung-Gwan Myoung 2 and Han-Seul Sim 2

1 Jeju Marine Research Center, Korea Institute of Science & Technology, Jeju 63349, Korea; [email protected] 2 Department of , Chonnam National University, Gwangju 61186, Korea; [email protected] (S.-G.M.); [email protected] (H.-S.S.) * Correspondence: [email protected]; Tel.: +82-62-530-3471

Abstract: A meteotsunami with a height of 0.1–0.9 m and a period of 60 min was observed at gauges along the on 7 April 2019, while a train of two to four disturbances with disturbance heights of 1.5–3.9 hPa moved eastward from the to the Korea Strait. Analysis of observational data indicated that isobar lines of the atmospheric pressure disturbances had angles of 75–83◦ counterclockwise due east and propagated with a velocity of 26.5–31.0 m/s. The generation and propagation process of the meteotsunami was investigated using the Regional Ocean Modeling System. The long ocean were amplified due to Proudman

 resonance in the southwestern Yellow Sea, where the water is deeper than 75 m; here, the long  ocean waves were refracted toward the coast on the shallow coastal region of the northern Korea

Citation: Kwon, K.; Choi, B.-J.; Strait. Refraction and reflection by offshore islands significantly affect the wave heights at the Myoung, S.-G.; Sim, H.-S. coast. To investigate the effects of an eastward-moving velocity and angle of atmospheric pressure Propagation of a Meteotsunami from disturbance on the height of a long ocean wave, sensitivity simulations were performed. This result the Yellow Sea to the Korea Strait in will be useful for the real-time prediction system of in the Korea Strait. April 2019. Atmosphere 2021, 12, 1083. https://doi.org/10.3390/atmos Keywords: meteotsunami; Proudman resonance; atmospheric pressure disturbance; long ocean c12081083 wave; Korea Strait

Academic Editors: Antonio Ricchi, Giovanni Liguori, Rossella Ferretti, Alvise Benetazzo and 1. Introduction Francesco Barbariol A meteotsunami, a -like long ocean wave, is generated by atmospheric pres- sure disturbances, atmospheric gravity waves, and squalls propagating over the ocean Received: 25 June 2021 Accepted: 20 August 2021 surface [1,2]. Long ocean waves are induced in the process of rapid change and restoration Published: 23 August 2021 of by this atmospheric forcing. The long ocean waves are amplified by Proud- man [3], Greenspan [4], shelf, and harbor resonances depending on the region, and it has

Publisher’s Note: MDPI stays neutral been suggested that Proudman resonance is the main cause of meteotsunami amplifica- with regard to jurisdictional claims in tion worldwide [5]. Proudman resonance occurs when the propagation speed (C) of the published maps and institutional affil- generated ocean wave is close to the movement speed (U) of pressure perturbations [1,6–9]: iations. p C = gH (1)

where g is gravitational acceleration and H is the water depth. When the Froude number (Fr = U/C) is close to 1.0, a strong amplification of the long ocean wave occurs by absorbing Copyright: © 2021 by the authors. the energy of moving atmospheric pressure disturbances (i.e., Proudman resonance) [10]. Licensee MDPI, Basel, Switzerland. The long ocean waves propagating along the coast are also amplified due to Greenspan This article is an open access article resonance; the amplification depends on the wave period and bottom topographic slope [4]. distributed under the terms and However, these external resonances alone do not make a destructive meteotsunami. The conditions of the Creative Commons long ocean waves generated by external resonance are amplified as they propagate into Attribution (CC BY) license (https:// semienclosed bays, and water depth becomes shallower; the amplification strength of the creativecommons.org/licenses/by/ 4.0/). waves varies depending on the size, shape, and depth of the water body. The long ocean is

Atmosphere 2021, 12, 1083. https://doi.org/10.3390/atmos12081083 https://www.mdpi.com/journal/atmosphere Atmosphere 2021, 12, 1083 2 of 16

further amplified due to harbor resonance in a long narrow bay when the period of the long ocean wave is close to the natural resonant periods of a bay [11–14]. If these long ocean waves reach the shore during high tide, even in calm weather, they can cause coastal flooding by high sea level oscillations and become a devastating natural disaster [15,16]. The causes and damage conditions of meteotsunami events known around the world are summarized in [2]. There have been several reports of disasters caused by meteot- sunamis in the Yellow Sea and East Sea [2,17]. On 31 March 1979, a meteotsunami occurred in Nagasaki Bay, , with a maximum sea level anomaly of 4.8 m [1,18]. Meteotsunamis induced a strong current, making severe damage to cargo vessels and fishing boats by tearing their lines in Nagasaki Bay. Due to the meteotsunami on 25 February 2009, with a maximum of 2.9 m, 30 vessels were capsized and damaged in western Kyushu, and eight residences were inundated below floor level [19]. A meteotsunami caused by a pressure disturbance moving southeast from the eastern Yellow Sea resulted in the death of three people along the west coast of Korea on 31 March 2007 [15,20]. The meteotsunami overlapped with high tide, causing severe inundation along the coast and capsizing more than 90 vessels along the west coast of Korea [15]. Recently, a real-time pressure disturbance monitoring system was developed for the pre- vention of meteotsunami disasters based on the available atmospheric pressure data from 89 automatic weather stations (AWS) along the Korean coastline [21]. There were 42 events of sea level oscillations due to the arrival of long ocean waves with wave heights higher than 40 cm in Jinhae- Bay (128.4–128.8◦ E, 34.9–35.3◦ N) in the Korea Strait from 2013 to 2017, and the periods of the long ocean waves were 48–125 min [22]. The abnormal observed at MS in the past resulted in wave heights of up to 80 cm, and when it overlaps with high , flooding of low-lying regions may occur [22]. On 7 April 2019, long ocean waves with a wave height of 0.9 m arrived at MS in the Korea Strait, and there was a flood threat due to the high sea level oscillations in Jinhae-Masan Bay. However, there is no explanation for the generation mechanism of the long ocean waves that were observed in the Korea Strait on 7 April 2019. In this study, the generation mechanism and propagation process of the long ocean waves that were observed on 7 April 2019, in the Korea Strait were investigated using observational data and numerical simulations. Observational data and two-dimensional numerical simulations are introduced in Section2. In Section3, the of the observed atmospheric pressure and sea level data in the Korea Strait are analyzed, and two-dimensional numerical simulations are performed to determine the generation and propagation processes of the long ocean waves that occurred on 7 April 2019. In Section4, possible amplification mechanisms for long ocean waves in the Korea Strait are discussed, the role of offshore islands on the refraction and reflection of long ocean waves toward Jinhae-Masan Bay is examined, the resonance effects due to local features are explained, and numerical model simulations are performed to find the angle and speed at which Proudman resonance can occur most effectively. Finally, conclusions are drawn in Section5.

2. Materials and Methods 2.1. Observational Data To understand the generation and propagation of meteotsunamis in the Korea Strait, the time series of atmospheric pressure and sea level data observed at meteorological stations and stations were used. Data were obtained from a total of 10 stations: CJ, SGP, GM, GH, YS, GJ, GD, MS, SSB, and HKT (Figure1b). In this study, atmospheric pressure and sea level data from 7 to 8 April 2019 were analyzed, and local standard time (UTC + 9 h) was used. Atmospheric pressure data were supplied by the Korea Meteorological Administration (KMA) and Japan Meteorological Agency (JMA), and the data intervals were 1 and 10 min, respectively. Sea level data were provided by the Korea Hydrographic and Oceanographic Agency (KHOA) and Japan Oceanographic Data Center (JODC), and the data intervals were 1 and 10 min, respectively. Atmospheric pressure data Atmosphere 2021, 12, x FOR PEER REVIEW 3 of 17

Atmosphere 2021, 12, 1083 tervals were 1 and 10 min, respectively. Sea level data were provided by the Korea3 Hy- of 16 drographic and Oceanographic Agency (KHOA) and Japan Oceanographic Data Center (JODC), and the data intervals were 1 and 10 min, respectively. Atmospheric pressure datawere were obtained obtained with with automatic automatic weather weather station station (AWS) (AWS) and and automated automated surface surface observing observ- ingsystems systems (ASOS), (ASOS), and and sea sea level level was was measured measured using using float-type float-type tide tide gauges. gauges.

(a) (b)

FigureFigure 1. 1. ((aa)) The The red red dashed dashed rectangle rectangle represents represents the the study study area area covering covering the the Korea Korea Strait Strait between between the the Yellow Yellow Sea, Sea, East East ChinaChina Sea, Sea, and and East East Sea. Sea. (b (b) )Observation Observation stations stations for for atmospheric atmospheric pressure pressure (red) (red) and and sea sea level level (yellow) (yellow) in in the the Korea Korea Strait. Strait. CJ, SGP, GM, GH, YS, GJ, GD, MS, SSB, and HKT stand for Chujakdo, Seogwipo, Geomundo, Goheung, Yeosu, , CJ, SGP, GM, GH, YS, GJ, GD, MS, SSB, and HKT stand for Chujakdo, Seogwipo, Geomundo, Goheung, Yeosu, Geojedo, Gadeokdo, Masan, Sasebo, and Hakata, respectively. Contours represent the bottom topography (m). and Tsu- Gadeokdo, Masan, Sasebo, and Hakata, respectively. Contours represent the bottom topography (m). Jeju Island and shima Island are located at 126.8° E, 33.4◦ ° N and◦ 129.5° E, 34.5◦ ° N, respectively,◦ in the Korea Strait. MS is located in Jinhae- MasanTsushima Bay Island(128.4– are128.8° located E, 34.9 at– 126.835.3° N).E, 33.4 N and 129.5 E, 34.5 N, respectively, in the Korea Strait. MS is located in Jinhae-Masan Bay (128.4–128.8◦ E, 34.9–35.3◦ N). By analyzing the time series of atmospheric pressure and sea level data in the Korea By analyzing the time series of atmospheric pressure and sea level data in the Korea Strait, the movement direction and speed of atmospheric pressure disturbances and long Strait, the movement direction and speed of atmospheric pressure disturbances and long ocean waves (meteotsunami) were estimated. The horizontal movement of squall lines ocean waves (meteotsunami) were estimated. The horizontal movement of squall lines was traced from the rainfall intensity radar images provided by the KMA. A high-pass was traced from the rainfall intensity radar images provided by the KMA. A high-pass filter with a cutoff period of 180 min was used to remove tide signals in the sea level data filter with a cutoff period of 180 min was used to remove tide signals in the sea level data and low-frequency variability in the atmospheric pressure data. Wavelet analysis was per- and low-frequency variability in the atmospheric pressure data. Wavelet analysis was formedperformed on the on thetime time series series of atmospheric of atmospheric pressure pressure and and sea sea level level data data to to find find peak peak energy energy periodsperiods and and event event durations durations in in the the data. data.

2.2.2.2. Numerical Numerical Model Model Simulation Simulation ToTo reproduce reproduce the the generation generation of of a a meteot meteotsunamisunami in in the the Korea Korea Strait Strait and and analyze analyze the the propagationpropagation process, process, two two-dimensional-dimensional numerical numerical modeling modeling experiments experiments were were conducted conducted usingusing the the Regional Regional Ocean Ocean Modeling Modeling System System (ROMS) (ROMS) [23,24]. [23,24]. The The model model domain domain encom- encom- passedpassed the the shelf shelf sea sea region region of of 32.0 32.0–35.3–35.3°◦ N,N, 122. 122.4–129.64–129.6°◦ E,E, including including the the Korea Korea Strait, Strait, whichwhich is is located located between between the the Yellow Yellow Sea, Sea, East East China China Sea, Sea, and and East East Sea Sea (Figure (Figure 11b).b). The horizontalhorizontal grid grid spacing spacing of of the the model model was was approximately approximately 300 300 m. m. The The bottom bottom topography topography datadata were were obtained obtained from from the the Korbathy Korbathy 30s 30s bath bathymetryymetry dataset dataset [25], [25], and and the the minimum minimum waterwater depth depth was was 0.1 0.1 m. m. The numerical model was forced only by a train of moving atmospheric pressure disturbances.The numerical The movement model was direction, forced only speed, by angle, a train and of wavemoving period atmospheric of the atmospheric pressure disturbances.pressure forcing The were movement estimated direction, based onspeed, the analysisangle, and results wave of period the KMA of the and atmospheric JMA obser- pressurevation data. forcing The were initial estimated temperature, based salinity, on the andanalysis sea levelresults in theof the numerical KMA and model JMA were ob- servationuniform, data. set as The 15 initial◦C, 30 temperature, psu, and 0 m, salinity, respectively. and sea Windlevel in forcing the numerical was not model considered were uniform,because theset windas 15 speed°C, 30 atpsu, the and time 0 ofm, the respectively. meteotsunami Wind event forcing was was weak not (<3 considered m/s). For the open boundaries of the numerical model, Chapman [26] and Flather [27] conditions were used for sea level and velocity, respectively. The time step of the model was 3 s, and the simulation was performed for 24 h. The numerical simulations in this study were

Atmosphere 2021, 12, 1083 4 of 16

performed with an analytical forcing and initial condition. In order to quantify the role of offshore islands on the refraction and reflection of long ocean waves and the amplitude of sea level oscillations at the coastal tide gauge stations, an additional numerical experiment was performed without the offshore islands. To find the critical movement speed and angle of atmospheric pressure disturbances that are optimal to induce the largest sea level oscillations by Proudman resonance in the Korea Strait, a range of movement speeds of 20–40 m/s and angles of 60–120◦ were applied in sensitivity experiments.

3. Results 3.1. Atmospheric and Ocean Observation On 7 April 2019, convective rain clouds were observed moving from west to east in the Korea Strait (Figure2). A zonal band of rain clouds moved eastward along the northern coast of the Korea Strait, and a southern branch of rain clouds to the west of Jeju Island headed toward the island at 15:00 on 7 April. Atmospheric pressure disturbances propagated ahead of the southern branch of rain clouds (Figures2 and3). It could be observed that the atmospheric pressure jumps were tilted spatially, and the titling angle was approximately 80◦ counterclockwise due east (Figure3). The trains of atmospheric pressure disturbances arrived at CJ at 13:49 on 7 April, and moved over SGP, GM, and MS at 14:29, 14:50, and 15:46, respectively (Figure3a,c and Table1). The arrival times of the atmospheric pressure disturbances were defined as the time of the lowest elevation point of the first anomaly peak. The movement angle and time were spatially inferred using the arrival time of the atmospheric pressure disturbances at each station (red dashed line in Figure3c). The line of atmospheric pressure jumps was inclined at approximately 75–83◦ counterclockwise due east in the Korea Strait. The angle gradually increased as it moved from west to east, because the eastward-moving speed of atmospheric pressure disturbances was faster in the south than the north from 13:30 to 14:30 on 7 April (Figures2 and3c). Once the disturbances passed the GH and GM stations, the angle was maintained at 75–80◦. The speeds of the atmospheric pressure disturbances were calculated using differences in the arrival times and distances between each station in the east–west direction based on the observed data. The speeds of the atmospheric pressure disturbances along the northern coastal stations (GH–GD), central stations (CJ–GM), and southern stations (SGP–HKT) of the Korea Strait were approximately 31.0, 26.5, and 30.4 m/s, respectively (Figure3c and Table1). The height of atmospheric pressure disturbances from trough to crest was approximately 1.5–3.9 hPa (Table1). Atmospheric pressure disturbances consisting of two to four waves moved eastward along the Korea Strait (Figure3a).

Table 1. Start time and maximum height (∆P) of atmospheric pressure disturbances at the coastal stations on 7 April 2019. ∆t is the corresponding elapsed time in the change of atmospheric pressure (∆P). Intervals of atmospheric pressure data at SSB and HKT are 10 min and their station name, arrival time, ∆t, and ∆P are in italics.

Arrival Times Station ∆t (Minutes) ∆P (hPa) (Hour:Minute) CJ 13:49 59 3.9 SGP 14:29 34 2.6 GH 14:15 17 2.1 GM 14:50 17 2.0 YS 14:33 12 2.1 GJ 15:58 29 1.9 MS 15:46 26 1.5 GD 16:21 33 2.5 SSB 17:35 71 2.7 HKT 18:15 66 2.7 Atmosphere 2021, 12, x FOR PEER REVIEW 5 of 17

SSB 17:35 71 2.7 Atmosphere 2021, 12, 1083 5 of 16 HKT 18:15 66 2.7

(a) (b)

(c) (d)

FigureFigure 2. 2. RainfallRainfall intensity intensity (mm/h) (mm/h) estimated estimated from from rainfall rainfall radar radar at at (a ()a 15:00,) 15:00, (b (b) 16:30,) 16:30, (c ()c 18:00,) 18:00, and and (d(d) )19:30 19:30 on on 7 7April April 2019. 2019.

DuringDuring the the passage passage of of atmospheric atmospheric pressure pressure disturbances, disturbances, the the sea sea level level oscillations oscillations werewere observed observed along along the the Korea Korea Strait Strait (Figure (Figure 3b).3b). The The sea sea level level oscillation oscillation started started at at 13: 13:5959 atat CJ CJ and and arrived arrived at GH at GH and and MS MSat 15:07 at 15:07 and and17:48, 17:48, and the and maximum the maximum wave heights wave heights from troughfrom troughto crest towere crest 38.1, were 42.5, 38.1, and 42.5, 91.9 cm, and respectively 91.9 cm, respectively (Figure 3b (Figureand Table3b and2). The Table high-2). estThe wave highest height wave was heightobserved was at observed MS. The t atidal MS. range The of tidal sea rangelevel at of the sea MS level tide at observation the MS tide stationobservation is from station 120 cm is fromduring 120 the cm neap during tide the to neap240 cm tide during to 240 the cm spring during tide. the springThe tidal tide. rangeThe tidal at MS range was at188 MS cm was on 1887 April cm on2019. 7 April The 2019.start time The startof sea time level of oscillation sea level oscillation was defined was asdefined the time as of the the time highest of the point highest of the point first of peak the firstin sea peak level in variations. sea level variations. The wave height The wave at theheight offshore at the stations offshore in stationsthe western in the Korea western Strait, Korea such Strait,as CJ, suchSGP, asand CJ, GM, SGP, was and relatively GM, was small,relatively from small,16.3 to from 38.1 cm, 16.3 and to 38.1 the cm,sea level and theoscillations sea level started oscillations 8–15 min started after 8–15 the minpassage after ofthe an passageatmospheric of an atmosphericpressure disturba pressurence. disturbance.However, at However,the GH, YS, at the GJ, GH, MS, YS,GD, GJ, SSB, MS, and GD, HKTSSB, stations and HKT, located stations, on located the coast on or the in coast a bay or of in the a bay eastern of the Korea eastern Strait, Korea the Strait, wave the height wave inheight sea level in seaoscillations level oscillations was relatively was relatively large, but large, the sea but level the oscillations sea level oscillations started approxi- started matelyapproximately 40–115 min 40–115 after min the afterpassage the passageof atmospheric of atmospheric pressure pressure disturbances. disturbances. The spatial The propagationspatial propagation patterns patternsof the waves of the were waves inferred were inferredusing the using arrival the times arrival of times the long of the ocean long ocean waves at each station (blue dashed lines in Figure3d). Propagation analysis of the observed sea level data revealed that the long ocean waves propagate from the southwest to the northeast of the Korea Strait.

Atmosphere 2021, 12, x FOR PEER REVIEW 6 of 17

waves at each station (blue dashed lines in Figure 3d). Propagation analysis of the ob- Atmosphere 2021, 12, 1083 6 of 16 served sea level data revealed that the long ocean waves propagate from the southwest to the northeast of the Korea Strait.

(a) (b)

(c) (d)

FigureFigure 3. Variations 3. Variations of of(a ()a atmospheric) atmospheric pressure pressure (hPa) (hPa) and and (b) sea levelslevels (cm),(cm), which which were were high-pass-filtered high-pass-filtered with with a cutoff a cutoff periodperiod of of180 180 min min.. (c) ( cArrival) Arrival times times (hour:minute) (hour:minute) of of atmospheric atmospheric pressurepressure disturbancesdisturbances and and ( d()d the) the long long ocean ocean waves waves (meteotsunami)(meteotsunami) along along the the Korea Korea Strait Strait on on 7 April 2019.2019. TheThe contour contour intervals intervals are are 30 30 min. min The. The dashed dashed green green contour contour lines li innes in ((cc), dand) are (d the) are extrapolated the extrapolated locations locations of atmospheric of atmospheric pressure pressure disturbance disturbance and long and ocean long wave, ocean respectively, wave, respectively, based on thebased on the patterns of nearby observation data. patterns of nearby observation data.

Table 2. Arrival times and maximum wave heights of long ocean waves at the tide gauge stations Table 2. Arrival times and maximum wave heights of long ocean waves at the tide gauge stations in in the Korea Strait. the Korea Strait. Station Arrival Time (Hour:Minute) Maximum Wave Height (cm) Station Arrival Time (Hour:Minute) Maximum Wave Height (cm) CJ 13:59 38.1 CJ 13:59 38.1 SGP SGP14:14 14:14 26.626.6 GH GH15:07 15:07 42.542.5 GM GM14:56 14:56 16.316.3 YS YS15:48 15:48 29.729.7 GJ 16:47 30.1 GJ MS16:47 17:48 91.930.1 MS GD17:48 17:05 30.191.9 GD SSB17:05 17:18 38.630.1 HKT 20:08 39.0

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Atmosphere 2021, 12, 1083 7 of 16

SSB 17:18 38.6 HKT 20:08 39.0 To determine the dominant periods and duration of atmospheric pressure and the sea level oscillations,T waveleto determine spectrum the dominant analysis periods was and performed duration of on atmospheric the time series pressure of and the atmospheric pressuresea level and oscillations, sea level wavelet data at spectrum SGP, GH, analysis and MS.was performed The SGP, on GH, theand time MSseries of at- stations are locatedmospheric in the southwest, pressure and north, sea level and data northeast at SGP, ofGH, the and Korea MS. The Strait, SGP, respectively. GH, and MS stations The dominant periodsare located of atmospheric in the southwest, pressure north, fluctuations and northeast were of 40–115 the Korea min Strait, and lasted respectively. for The 7–19 h (Figure4a).dominant The sea level periods oscillations of atmospheric at SGP pressure and GH fluctuations had relatively were 40 large–115 min energy and lasted in for 7– the periods of 10–9019 andh (Figure 10–160 4a). min The andsea level lasted oscillations for approximately at SGP and 7GH and had 12 relatively h, respectively. large energy in the periods of 10–90 and 10–160 min and lasted for approximately 7 and 12 h, respectively. The sea level oscillations at MS had relatively distinct periods of 35–90 min. The sea level The sea level oscillations at MS had relatively distinct periods of 35–90 min. The sea level oscillation was relativelyoscillation strong was relatively for the firststrong 5 for h, andthe first it lasted 5 h, and approximately it lasted approximately 14 h. The 14 h. The durations of sea leveldurations oscillation of sea werelevel oscillation longer at were the GHlonger and at MSthe GH stations, and MS which stations, are which located are located in shallow and coastalin shallow regions, and thancoastal at region the SGPs, than station, at the whichSGP station, is in anwhich offshore is in an area. offshore area.

(a) Atmospheric pressure (b) Sea level

FigureFigure 4. Wavelet 4. Wavelet spectrum spectrum of (a) atmospheric of (a) atmospheric pressure and pressure (b) sea level and time (b) seaseries level at the time SGP, series GH, and at the MS SGP, stations GH, from 12:00 on 7 April to 12:00 on 8 April 2019. and MS stations from 12:00 on 7 April to 12:00 on 8 April 2019.

3.2. Numerical Simulations3.2. Numerical Simulations The generation and propagation process of long ocean waves in the Korea Strait was The generationinvestigated and propagation using a two process-dimensional of long numerical ocean waves model. in theA simple Korea form Strait of wasatmospheric investigated usingpressure a two-dimensional forcing was constructed numerical based model. on the A observational simple form data of atmosphericfor the numerical sim- pressure forcing wasulations. constructed An ensemble based of onatmospheric the observational pressure disturbances data for the with numerical different sim- amplitudes, ulations. An ensemblemoving of speeds, atmospheric angles, shapes, pressure and disturbancesperiods was tested with to differentreproduce amplitudes,the observed sea level moving speeds, angles,oscillations shapes, along and the periods coast in was the testedKorea toStrait. reproduce In this study, the observed a single realization, sea level which oscillations along thefitted coast the insea the level Korea oscillations Strait. along In this the study, Korea a Strai singlet on realization, 7 April 2019, which is presented. fitted Atmos- the sea level oscillationspheric pressure along the disturbances Korea Strait propagated on 7 April eastward 2019, is along presented. the Korea Atmospheric Strait and consisted pressure disturbancesof three propagated sinusoidal eastwardplane waves along based the on Koreathe observation Strait and data consisted (Figure 5). of The three amplitude, period, movement speed (U), and angle (θ) of the atmospheric pressure disturbances were sinusoidal plane waves based on the observation data (Figure5). The amplitude, period, assumed to be 1 hPa, 60 min, 30 m/s, and 80° counterclockwise due east, respectively. The movement speed (Ushape), and of angleatmospheric (θ) of thedisturbances atmospheric changes pressure in time disturbances and space, an wered idealized assumed sinusoidal ◦ to be 1 hPa, 60 min,waves 30 m/s, were and used 80 in thecounterclockwise numerical experiment due east,(Figures respectively. 2 and 3a,c). TheMost shape of other of previous atmospheric disturbances changes in time and space, and idealized sinusoidal waves were used in the numerical experiment (Figures2 and3a,c). Most of other previous studies also used approximate disturbances (i.e., idealized shapes, such as step function, triangle, and sinusoidal wave) [15,18,28,29]. Their shape and moving speed do not change in time like in our study. However, they are localized disturbances moving in time. When one or two sinusoidal waves of atmospheric disturbances were propagated eastward, the duration of the long ocean wave event was shorter, and the number of long ocean waves was smaller than the observation data. When four sinusoidal waves of atmospheric disturbances were Atmosphere 2021, 12, x FOR PEER REVIEW 8 of 17

studies also used approximate disturbances (i.e., idealized shapes, such as step function, triangle, and sinusoidal wave) [15,18,28,29]. Their shape and moving speed do not change in time like in our study. However, they are localized disturbances moving in time. When Atmosphere 2021, 12, 1083 one or two sinusoidal waves of atmospheric disturbances were propagated eastward,8 of the 16 duration of the long ocean wave event was shorter, and the number of long ocean waves was smaller than the observation data. When four sinusoidal waves of atmospheric dis- moving,turbances the were duration moving, of the the long duration ocean of wave the long event ocean was longerwave event than the was observation. longer than The the periodobservation. of the The long period ocean of waves the long increased ocean withwaves the increase perioddof with the the sinusoidal period of atmospheric the sinusoi- disturbances,dal atmospheric whereas disturbances, the amplitude whereas of the longamplitude ocean of waves the long was ocean nearly waves invariant was exceptnearly atinvariant the MS tide except observation at the MS station. tide observation The numerical station. simulations The numerical in this study simulations are idealized in this onesstudy in are terms idealized of atmospheric ones in terms forcing of atmospheric and initial conditions. forcing and initial conditions.

FigureFigure 5.5. EastwardEastward propagationpropagation ofof atmosphericatmospheric pressurepressure disturbancesdisturbances with with a a moving moving speed speed ( U(U)) and and angleangle (θ(θ)) at at 13:00 13:00 on on 7 April7 April 2019. 2019. The The angle angle of aof moving a moving isobar isobar was was measured measured counterclockwise counterclockwise due east.due east. The arrowThe arrow represents represents the moving the moving direction direction of the atmosphericof the atmospheric pressure pressure disturbances. disturbances. The waves The underwaves the under arrow the represent arrow represent a schematic a schematic sinusoidal sinusoidal form of form the atmospheric of the atmospheric pressure pressure disturbances. disturb- ances. The time series of the atmospheric pressure forcing used for the numerical simulations and thoseThe time of the series observed of the atmosphericatmospheric pressure dataforcing were used compared for the numerical at SGP, GH, simula- and MStions (Figure and those6a). Theof the atmospheric observed at pressuremospheric forcing pressure at SGP data and were GH, compared which are at located SGP, GH, to theand southwest MS (Figure and 6a). north The atmospheric of the Korea pressure Strait, respectively, forcing at SGP had and two GH, and threewhich peaks are located from 13:50to the to southwest 17:10 on and 7 April. north The of the amplitude Korea Strait, and respectively, phase of the had first two peaks and were three different peaks from at SGP,13:50 although to 17:10 on the 7 April. second Th ande amplitude third peaks and hadphase a similarof the first amplitude peaks were and different phase. Atat SGP, GH, thealthough phases the of the second first and peak third were peaks coincident had a but similar the amplitudes amplitude were and phase. different, At andGH, thethe amplitudesphases of the of first the peak second were and coincident third waves but the were amplitudes similar but were the different, model forcing and the lagged ampli- behindtudes of the the observed second a atmosphericnd third waves pressure were similar variation. but the The model atmospheric forcing pressurelagged behind anomaly the hadobserved similar atmospheric wave amplitudes pressure at variation. MS but wasThe atmospheric out of phase pressure between anomaly the model had forcing similar andwave the amplitudes observation. at MS The but atmospheric was out of phase pressure between disturbances the model from forcing the observation and the observa- kept changingtion. The atmosphe in time andric spacepressure (Figure disturbances3a); therefore, from thethe simpleobservation sinusoidal kept changing form of modelin time atmosphericand space (Figure pressure 3a); forcing therefore, could the not simple match sinusoidal the irregular form observed of model atmospheric atmospheric pressure pres- disturbances.sure forcing could However, not match the packets the irregular or trains observed of atmospheric atmospheric pressure pressure disturbances disturbances. were relativelyHowever, similar the packets at SGP, or GH, trains and of MSatmospheric in terms of pressure beginning disturbances time, end time, were and relatively amplitude sim- (Figureilar at SGP,6a). GH, and MS in terms of beginning time, end time, and amplitude (Figure 6a). The simulated sea level variations were compared with sea level observation data that were high-pass-filtered with a cutoff period of 180 min (Figure6b). The numerical model reproduced the amplitude and phase of sea level oscillations similar to the observation at SGP, GH, and MS. There were time lags between the simulated and the observed sea level anomalies. The lags of simulated sea level variations were −1, −4, and +3 min compared with the observations at SGP, GH, and MS, respectively. The time-lagged correlation coefficients over 6 h were 0.53, 0.37, and 0.89 at SGP, GH, and MS, respectively, and the RMSEs were 5.38, 10.78, and 19.70 cm at SGP, GH, and MS, respectively. As the pressure disturbances moved to the east (black solid lines in Figure7), long ocean waves were generated due to Proudman resonance in the southwestern Yellow Sea. The amplitude of the long ocean waves kept growing while they propagated, in addition to pressure disturbances in the relatively deep region of 122.5–126.0◦ E and 33.5–35.0◦ N (Figure7a,c). The long ocean waves were refracted due to the bottom topography, where the water depth was less than about 75 m (Fr ≤ 0.9), and lagged behind the pressure disturbances (Figure7c,d). However, the long ocean waves propagated ahead of the atmospheric pressure disturbances where the water depth was deeper than 108 m (Fr ≥ 1.1) (Figure7d). Reflected waves were generated and propagated westward, while the forced long ocean waves (meteotsunami) propagated eastward (Figure7d,e). As the long ocean waves reached Atmosphere 2021, 12, 1083 9 of 16

the shallow coastal region or islands, they refracted and reflected (Figure7c,e). Even after the pressure disturbances moved out of the model domain, the sea level continued to oscillate due to the waves reflecting from the coast (Figure7g,i). The start times of sea level oscillations at SGP were similar to the arrival times of the trains of atmospheric pressure disturbances, whereas sea level oscillations started 1–3 h after the arrival times of atmospheric pressure disturbances at GH and MS (Figure6). The reason the arrival of long Atmosphere 2021, 12, x FOR PEER REVIEW 9 of 17 ocean waves was delayed at GH and MS is that the propagation of long ocean waves is slowed down as they refract in the coastal region due to the shallow water (Figure7c,d).

(a) (b)

FigureAtmosphereFigure 6. Comparison 206.21 Comparison, 12, x FOR of PEER of (a )(a atmosphericREVIEW) atmospheric pressurepressure anomalies anomalies and and (b) ( bsea) sea level level variations variations from fromobservations observations and numerical and numerical 10 of 17 simulations at SGP, GH, and MS from 12:00 on 7 April to 06:00 on 8 April 2019. simulations at SGP, GH, and MS from 12:00 on 7 April to 06:00 on 8 April 2019. The simulated sea level variations were compared with sea level observation data that were high-pass-filtered with a cutoff period of 180 min (Figure 6b). The numerical model reproduced the amplitude and phase of sea level oscillations similar to the obser- vation at SGP, GH, and MS. There were time lags between the simulated and the observed sea level anomalies. The lags of simulated sea level variations were −1, −4, and +3 min compared with the observations at SGP, GH, and MS, respectively. The time-lagged cor- relation coefficients over 6 h were 0.53, 0.37, and 0.89 at SGP, GH, and MS, respectively, and the RMSEs were 5.38, 10.78, and 19.70 cm at SGP, GH, and MS, respectively. As the pressure disturbances moved to the east (black solid lines in Figure 7), long ocean waves were generated due to Proudman resonance in the southwestern Yellow Sea. The ampli- tude of the long ocean waves kept growing while they propagated, in addition to pressure disturbances in the relatively deep region of 122.5–126.0° E and 33.5–35.0° N (Figure 7a,c). The long ocean waves were refracted due to the bottom topography, where the water depth was less than about 75 m (Fr ≤ 0.9), and lagged behind the pressure disturbances (Figure 7c,d). However, the long ocean waves propagated ahead of the atmospheric pres- sure disturbances where the water depth was deeper than 108 m (Fr ≥ 1.1) (Figure 7d). Reflected waves were generated and propagated westward, while the forced long ocean waves (meteotsunami) propagated eastward (Figure 7d,e). As the long ocean waves reached the shallow coastal region or islands, they refracted and reflected (Figure 7c,e). Even after the pressure disturbances moved out of the model domain, the sea level con- tinued to oscillate due to the waves reflecting from the coast (Figure 7g,i). The start times of sea level oscillations at SGP were similar to the arrival times of the trains of atmospheric pressure disturbances, whereas sea level oscillations started 1–3 h after the arrival times of atmospheric pressure disturbances at GH and MS (Figure 6). The reason the arrival of long ocean waves was delayed at GH and MS is that the propagation of long ocean waves FigureFigure 7. Spatial 7. Spatial distribution distributionis of slowed modeledof modeled down sea sea as level level they elevation elevation refract in (colors) the coastal in in the the region Yellow Yellow due Sea Sea toand the and Korea shallow Korea Strait Straitwater every every (Figure 1.5 h 1.5from 7c,d). h from 11:00 to11:00 23:00 to 23:00 on 7 on April 7 April 2019. 2019. Colors Colors represent represent sea sea level level anomalies.anomalies. Black Black straight straight lines lines represent represent 1024 1024hPa isobars hPa isobars in in atmosphericatmospheric pressure pressure that that propagate propagate eastward eastward (Figure (Figure5). 5). 4. Discussion 4.1. Proudman and Greenspan Resonances Long ocean waves are amplified by three resonance processes in the shallow coastal ocean: Proudman, Greenspan, and shelf resonances [3,4]. When a long ocean wave enters a bay or an estuary, its wave height may be amplified due to shoaling and harbor reso- nance. As atmospheric disturbances move eastward with speeds of 20.0–31.0 m/s over the southern Yellow Sea toward the Korea Strait (Figure 2 and Table 1), Proudman resonance amplifies long ocean waves, where the bottom depth is between 40.1 and 91.7 m (Figures 1 and 7). These eastward-moving atmospheric pressure disturbances amplify long ocean waves by Proudman resonance in an offshore region deeper than 45 m in the southern Yellow Sea (Figure 7). As the long ocean waves cross 126° E and enter the Korea Strait, they lag behind the atmospheric pressure disturbances, moving eastward in the shallow region near the coast, and the wave crests tend to become parallel to the coast due to re- fraction (Figures 7 and 8). However, the long ocean waves offshore and deeper than 100 m keep accompanying the moving atmospheric pressure disturbances and grow in am- plitude. Greenspan resonance occurs when the propagation speed of an atmospheric disturb- ance is close to that of edge waves, coastal trapped waves over a sloping shelf that prop- agate along the coast [30]. The speed of an (퐶푒푤) is given as:

퐶푒푤 = 𝑔푇 tan[(2푛 + 1)훽]/2휋 (2)

where 𝑔 is the acceleration due to gravity, 푛 is an integer for each mode, 훽 is the bottom slope, and 푇 is the wave period [31]. Based on the bottom slope (훽) of 0.00103–0.00224 from CJ to GD along the 50 m isobath in the northern Korea Strait and the observed wave period of 60 min, the estimated edge wave speeds are 6–13 m/s for 푛 = 0 and 17.0–38.0

Atmosphere 20212021,, 1212,, 1083x FOR PEER REVIEW 1110 of 17 16

푛 m/s4. Discussion for = 1. It may be possible that the eastward propagation speed (21–31 m/s) of the atmospheric pressure disturbances is close to the trapped edge wave speeds, and the long 4.1. Proudman and Greenspan Resonances waves grow by Greenspan resonance [4,28]. Long ocean waves are amplified by three resonance processes in the shallow coastal 4.2.ocean: Refraction Proudman, and Reflection Greenspan, by Offshore and shelf Islands resonances [3,4]. When a long ocean wave enters a bay or an estuary, its wave height may be amplified due to shoaling and harbor The sea level oscillations at MS in Jinhae-Masan Bay had relatively large amplitudes resonance. As atmospheric disturbances move eastward with speeds of 20.0–31.0 m/s from both observations and numerical simulations among the tide gauge stations in the over the southern Yellow Sea toward the Korea Strait (Figure2 and Table1), Proudman Korearesonance Strait amplifies (Figures long 3 and ocean 7 and waves, Table where2). The the superposition bottom depth of iswaves between propagating 40.1 and 91.7north- m eastward(Figures1 alongand7). the These coast eastward-movingof the Korea Strait atmospheric and waves refracted pressure and disturbances reflected by amplify bottom topographylong ocean wavesand Tsushima by Proudman Island resonance increased inthe an wave offshore energy region entering deeper Jinhae than- 45Masan m in Bay the (Figuresouthern 7e Yellow,g). To examine Sea (Figure the7 effects). As the of refraction long ocean andwaves reflection cross due 126◦ toE bottom and enter topography the Korea andStrait, Tsushima they lag behindIsland theon the atmospheric waves entering pressure Jinhae disturbances,-Masan movingBay, a numerical eastward inmodel the shallow simu- lationregion was near performed the coast, and without the wave the crests islands tend under to become the same parallel atmospheric to the coast pressure due to refraction forcing (NOI(Figures expe7 andriment).8). However, After removing the long the ocean islands waves from offshore the model and domain, deeper the than bottom 100 m topog- keep raphyaccompanying where the the islands moving had atmospheric been was made pressure similar disturbances to the surrounding and grow in region amplitude. (Figure 8).

(a) CON (b) NOI

Figure 8. SpatialSpatial distributions distributions of of bottom bottom depth depth (m) (m) for ( a)) the the control control (CON) experiment and ( b) no offshore islands (NOI) experiment. The c contourontour intervals of the isobaths are 50 m.

TheGreenspan distribution resonance of the sea occurs level when at 16:30 the indicated propagation that speedwave heights of an atmospheric between GJ and dis- Tsushimaturbance isIsland close were to that higher of edge in the waves, control coastal (CON) trapped experimen wavest than over in the a sloping NOI experiment shelf that (Figurepropagate 9b). along A trough thecoast of long [30 ocean]. The waves speed propagated of an edge wave through (Cew the) is mouth given of as: Jinhae-Masan Bay at 16:30. The long ocean wave refracted and reflected by the islands formed a wave crest parallel to the coast in theCew CON= gT experimenttan[(2n + 1 at)β ]16:45,/2π whereas the wave crest was(2) perpendicular to the coast in the NOI experiment (Figure 9b). Then, the crest of the long oceanwhere waveg is the entered acceleration the mouth due of to Jinhae gravity,-Masann is an Bay integer at 17:00 for (Figures each mode, 7e andβ is 9) the and bottom prop- agatedslope, andtowardT is MS the at wave 17:15. period The [distribution31]. Based onof thesea bottomlevel at slope16:15 (wasβ) of similar 0.00103–0.00224 to that at 17:15,from CJbut to had GD an along opposite the 50 phase m isobath to that in at the 16:45 northern in both Korea numerical Strait simulations. and the observed In the wave NOI experiment,period of 60 min,most the of estimatedthe long ocean edge wavewave speedsenergy are propagated 6–13 m/s forto then = east 0 and along17.0–38.0 the coast m/s n insteadfor = 1of. entering It may be Jinhae possible-Masan that Bay the (Figure eastward 9b). propagation speed (21–31 m/s) of the atmospheric pressure disturbances is close to the trapped edge wave speeds, and the long waves grow by Greenspan resonance [4,28].

4.2. Refraction and Reflection by Offshore Islands The sea level oscillations at MS in Jinhae-Masan Bay had relatively large amplitudes from both observations and numerical simulations among the tide gauge stations in the Korea Strait (Figures3 and7 and Table2). The superposition of waves propagating northeastward along the coast of the Korea Strait and waves refracted and reflected by bottom topography and increased the wave energy entering Jinhae-

Atmosphere 2021, 12, 1083 11 of 16

Masan Bay (Figure7e,g). To examine the effects of refraction and reflection due to bottom topography and Tsushima Island on the waves entering Jinhae-Masan Bay, a numerical model simulation was performed without the islands under the same atmospheric pressure forcing (NOI experiment). After removing the islands from the model domain, the bottom topography where the islands had been was made similar to the surrounding region (Figure8). The distribution of the sea level at 16:30 indicated that wave heights between GJ and Tsushima Island were higher in the control (CON) experiment than in the NOI experiment (Figure9b). A trough of long ocean waves propagated through the mouth of Jinhae-Masan Bay at 16:30. The long ocean wave refracted and reflected by the islands formed a wave crest parallel to the coast in the CON experiment at 16:45, whereas the wave crest was perpendicular to the coast in the NOI experiment (Figure9b). Then, the crest of the long ocean wave entered the mouth of Jinhae-Masan Bay at 17:00 (Figures7e and9) and propagated toward MS at 17:15. The distribution of sea level at 16:15 was similar to that at Atmosphere 2021, 12, x FOR PEER REVIEW17:15, but had an opposite phase to that at 16:45 in both numerical simulations. In12 the of 17 NOI

experiment, most of the long ocean wave energy propagated to the east along the coast instead of entering Jinhae-Masan Bay (Figure9b).

(a)

(b)

Figure 9. Spatial distributions of surface elevation every 15 min from 16:15 to 17:15 on 7 April 2019. The upper and lower panelsFigure are 9. (a Spatial) surface distributions elevation fromof surface the original elevation topography every 15 min (CON) from and 16:15 (b to) no 17:15 offshore on 7 April island 2019. (NOI) The models, upper and respectively. lower Thepanels contour are intervals(a) surface of elevation surface elevationfrom the original are 5 cm. topography (CON) and (b) no offshore island (NOI) models, respectively. The contour intervals of surface elevation are 5 cm. To examine the role of the refracted and reflected waves on sea level variation in Jinhae-MasanTo examine Bay, the sea role level of variations the refracted from and the reflected numerical waves simulations on sea werelevel comparedvariation in with theJinhae observed-Masan sea Bay, level sea variations level variations at GJ, GD, from and the MS numerical (Figure 10simulations). The sea levelwere oscillationscompared in thewith CON the experimentobserved sea started level variations at 16:46, 17:05, at GJ, andGD, 17:48and MS at GJ,(Figure GD, and10). The MS, sea respectively. level oscil- The sealations level in oscillations the CON experiment in the NOI started experiment at 16:46, started 17:05, atand 16:38, 17:48 16:57, at GJ, andGD, 17:40,and MS, respectively, respec- whichtively. were The sea 8 min level earlier oscillations than thosein the inNOI the experiment CON experiment. started at When16:38, 16:57, the amplitudes and 17:40, of searespectively, level oscillations which were were 8 comparedmin earlier over than 6 th hose from in the CON beginning experiment. of the longWhen wave the am- event, plitudes of sea level oscillations were compared over 6 h from the beginning of the long the wave amplitudes at GJ, GD, and MS were 34.2%, 67.8%, and 72.7% larger in the CON wave event, the wave amplitudes at GJ, GD, and MS were 34.2%, 67.8%, and 72.7% larger experiment than those in the NOI experiment, respectively. The numerical experiments in the CON experiment than those in the NOI experiment, respectively. The numerical revealed that the refraction and reflection of waves by the offshore island and bottom experiments revealed that the refraction and reflection of waves by the offshore island topography affect amplitudes and arrival times of the long wave in Jinhae-Masan Bay. and bottom topography affect amplitudes and arrival times of the long wave in Jinhae- In [15], it is suggested that the interaction between long waves and tides in the Yellow Masan Bay. In [15], it is suggested that the interaction between long waves and tides in Sea affects the arrival time and amplitude of long ocean waves. Therefore, the interaction the Yellow Sea affects the arrival time and amplitude of long ocean waves. Therefore, the betweeninteraction long between waves long and waves tidesmay and tides need may to be need considered to be considered to increase to increase the accuracy the accu- in the predictionracy in the of prediction amplitudes of amplitudes and arrival and times arrival of long times ocean of long waves ocean in the waves Korea in Strait.the Korea Strait.

AtmosphereAtmosphere 20202121, 1,212, x, 1083FOR PEER REVIEW 1312 of of 17 16

FigureFigure 10. 10. SeaSea level level variations variations from from the the observation observation (black (black line), line), original original topography topography model model (CON; (CON; redred line), line), and and no no offshore offshore island island model model (NOI; (NOI; blue blue dotted dotted line) line) at GJ, at GJ,GD, GD, and and MS MS from from 15:00 15:00 on 7 on April7 April to 06:00 to 06:00 on 8 on April 8 April 2019. 2019.

4.3.4.3. Local Local Topographic Topographic Effects Effects AsAs a along long ocean ocean wave wave generated generated by by Proudman Proudman resonance resonance propagate propagate in in the the ocean, ocean, it it cancan be be amplified amplified by by Greenspan, Greenspan, shelf, shelf, and and harbor harbor resonances resonances due due to to local local bathymetric bathymetric characteristicscharacteristics [5]. [5 SGP]. SGP and and GH GHare located are located in the in west the, west,and MS and is MSin the is east in the of the east Korea of the StraitKorea (Figure Strait 1). (Figure The long1). Thewaves long arriving waves at arriving SGP and at GH SGP were and amplified GH were in amplified the southeast- in the ernsoutheastern Yellow Sea Yellow, whereas Sea, the whereas long theocean long waves ocean arriving waves arriving at MS propagated at MS propagated through through the Koreathe Korea Strait Straitand entered and entered Jinhae Jinhae-Masan-Masan Bay (Figures Bay (Figures 3 and3 11).and T11he). t Theide observation tide observation sta- stations at SGP and GH are located at an open coast. However, the MS tide observation tions at SGP and GH are located at an open coast. However, the MS tide observation sta- station is located in an elongated bay, Jinhae-Masan Bay. Before the long ocean waves tion is located in an elongated bay, Jinhae-Masan Bay. Before the long ocean waves en- entered Jinhae-Masan Bay, they were amplified and refracted in the Korea Strait. After the tered Jinhae-Masan Bay, they were amplified and refracted in the Korea Strait. After the long waves entered Jinhae-Masan Bay, their amplitudes were increased by shoaling and long waves entered Jinhae-Masan Bay, their amplitudes were increased by shoaling and harbor resonance [18,22]. MS is almost in the innermost part of the elongated narrow bay harbor resonance [18,22]. MS is almost in the innermost part of the elongated narrow bay (Figure 11). The distance and average depth from the 40 m isobath offshore to the MS tide (Figure 11). The distance and average depth from the 40 m isobath offshore to the MS tide observation station are approximately 40 km and 24 m, respectively. The periods of natural observation station are approximately 40 km and 24 m, respectively. The periods of natu- harbor resonance for a semienclosed bay are given as: ral harbor resonance for a semienclosed bay are given as: 4l4푙 Tn = n = 1, 2, 3, . . . (3) 푇푛 = p 푛 = 1, 2, 3, … (3) (2(n2푛−−1)1) √gh𝑔ℎ where T is the resonant harbor oscillation period of the n-th mode for a semienclosed where 푇푛 nis the resonant harbor oscillation period of the n-th mode for a semienclosed bay.bay. 푙 landand ℎh areare the the length length and and average average depth depth of of a abay, bay, respectively. respectively. 𝑔 gisis gravitational gravitational acceleration.acceleration. The The resonance resonance periods periods (푇 (푛T) nin) in Jinhae Jinhae-Masan-Masan Bay Bay are are 174, 174, 58, 58, and and 35 35 min min for for 푛 n== 1, 1, 2, 2, and and 3, 3, respectively. respectively. T Thehe theoretical theoretical periods periods of of the the second second and and third third modes modes (푛 ( n== 2 2 andand 3) 3) in in sea sea level level oscillations oscillations are are within within the the observed observed periods periods of of 35 35–90–90 min min at at the the MS MS tide tide observationobservation station station (Figure (Figure 4).4). In In [22] [ 22, ],it itis isassumed assumed that that the the length length and and averaged averaged depth depth of of ◦ thethe inner inner bay bay from from 35.08 35.08° NN to to the the MS MS tidal tidal station station are are 13.1 13.1 km km and and 10.6 10.6 m, m, respectively respectively (Figure(Figure 11c). 11c). They They suggested suggested that that the the natural natural resonance resonance periods periods of of the the inner inner bay bay are are 85.6 85.6 andand 28.5 28.5 min min for for 푛n == 1 1 and and 2. 2.

Atmosphere 2021, 12, x FOR PEER REVIEW 14 of 17 Atmosphere 2021, 12, 1083 13 of 16

(a) (b) (c)

FigureFigure 11. 11. EnlargedEnlarged topographic topographic maps maps of of the the (a (a) )SGP, SGP, ( (bb)) GH, GH, and and (c (c) )MS MS tide tide observation observation stations. stations. Colors Colors represent represent bottom bottom depthsdepths in in meter. meter. The The b bottomottom topography topography is is contoured contoured at at depths depths of of 10, 10, 20, 20, 50 50 and and 100 100 m. m.

4.4.4.4. Effects Effects of of Speed Speed and and Angle Angle of of the the Atmospheric Atmospheric Pressure Pressure Disturbances Disturbances EvenEven if if the the amplitude amplitude of ofatmospheric atmospheric pressure pressure disturbance disturbance is the is same, the same, the amplitude the ampli- oftude a long of aocean long wave ocean generated wave generated by the moving by the atmospheric moving atmospheric pressure disturbance pressure disturbance depends ondepends the propagating on the propagating speed and speed angle and of atmospheric angle of atmospheric pressure pressurejumps in jumps a coastal in a region coastal [15,28,29]region [15. Changes,28,29]. Changes in long ocean in long wave ocean amplitude wave amplitude are caused are by causedthe refraction, by the reflection refraction,, andreflection, shoaling and of shoalingpropagating of propagating long ocean waves long ocean due to waves variations due toin variationsbottom topography in bottom andtopography the coastline. and theTo estimate coastline. changes To estimate in the changes amplitude in the of amplitudelong ocean ofwaves long with ocean respect waves towith the respectpropagation to the speed propagation and angle speed of atmospheric and angle of pressure atmospheric disturbances pressure in disturbances the Korea Straitin the (Figure Korea Strait5), numerical (Figure 5 experiments), numerical forced experiments by atmospheric forced by pressureatmospheric disturbances pressure ◦ movingdisturbances with speeds moving of with 20–40 speeds m/s and of 20–40angles m/s of 60 and–120° angles were of performed 60–120 were (Figure performed 12). In these(Figure experiments, 12). In these atmospheric experiments, disturbance atmospheric was disturbanceassumed as wasan idealized assumed sine as anwave idealized prop- agatingsine wave eastward propagating with an eastward amplitude with of an 1 hPa amplitude and a period of 1 hPa of and 60 min a period. When of such 60 min. air Whenpres- suresuch jumps air pressure move from jumps the move west from to the the east west along to the the east Korea along Strait, the Koreathe ranges Strait, of the long ranges ocean of wavelong oceanamplitudes wave amplitudesat SGP, GH, at SGP,and MS GH, are and 3 MS–12, are 4–19, 3–12, and 4–19, 17– and76 cm, 17–76 respectively. cm, respectively. The The eastward-moving atmospheric pressure jumps with velocities of 27–34 m/s and angles eastward-moving atmospheric pressure jumps with velocities of 27–34 m/s and angles of of 80◦–118◦ make the amplitude of the long ocean wave higher than other atmospheric 80°–118° make the amplitude of the long ocean wave higher than other atmospheric pres- pressure jumps. The amplitude of long ocean waves arriving at SGP and GH is less sen- sure jumps. The amplitude of long ocean waves arriving at SGP and GH is less sensitive sitive to the moving speed and angle of atmospheric pressure disturbances than that at to the moving speed and angle of atmospheric pressure disturbances than that at MS. MS. When the speed of eastward-moving atmospheric pressure disturbances is between When the speed of eastward-moving atmospheric pressure disturbances is between 24 24 and 30 m/s, Proudman resonance effectively enhances the long wave amplitude in the and 30 m/s, Proudman resonance effectively enhances the long wave amplitude in the southwestern Yellow Sea and , and the amplitude of long waves observed southwestern Yellow Sea and East China Sea, and the amplitude of long waves observed at SGP and GH increases. However, the amplitude of long waves observed at MS would at SGP and GH increases. However, the amplitude of long waves observed at MS would reach a maximum when the eastward-moving speed and angle of atmospheric pressure reach a maximum when the eastward-moving speed and angle of atmospheric pressure disturbance are 30 m/s and 85–100◦, respectively. Such selective and sensitive responses of disturbance are 30 m/s and 85–100°, respectively. Such selective and sensitive responses the sea level at MS may be related to the bottom topography of the Korea Strait and harbor ofresonance the sea level within at Jinhae-MasanMS may be related Bay. to the bottom topography of the Korea Strait and harborThe resonance expected within amplitude Jinhae of-Masan long wavesBay. at each station in Figure 12 can be used to predictThe the expected amplitude amplitude of long oceanof long waves waves when at each the eastward-movingstation in Figure speed12 can and be directionused to predictof atmospheric the amplitude pressure of isobarslong ocean are detected waves when in the the real-time eastward monitoring-moving system.speed and For direc- future tionstudy, of atmospheric it will be necessary pressure to isobars investigate are detect the generationed in the real of-time meteotsunamis monitoring insystem. the Korea For futureStrait whenstudy, atmospheric it will be necessary pressure to disturbances investigate propagatethe generation from of south meteotsunamis to north across in the the Koreastrait, Straitsuch as when in a long atmospheric ocean wave pressure event in disturbances March 2014 propagate [22], using from observation south to data north and acrossnumerical the strait, experiments. such as in a long ocean wave event in March 2014 [22], using observation data and numerical experiments.

Atmosphere 20202121, 1122, x 1083 FOR PEER REVIEW 1514 of of 17 16

(a) SGP (b) GH (c) MS

FigureFigure 12. ExpectedExpected amplitudes amplitudes (cm) (cm) of of the the long long ocean ocean waves waves at at ( (aa)) SGP, SGP, ( (bb)) GH, GH, and and ( (cc)) MS MS in in the the Korea Korea Strait Strait if if an an atmosphericatmospheric pressure disturbancedisturbance propagatedpropagated eastwardeastward with with various various isobar isobar angles angles (θ (θin in Figure Figure5) and5) and traveling traveling speeds speeds ( U) (U) from 20 to 40 m/s. from 20 to 40 m/s.

5.5. Conclusions Conclusions InIn this work, work, long long ocean ocean waves waves (meteotsunami) (meteotsunami) propagating propagating from from southwest southwest to north- to northeasteast along along the Korea the Korea Strait Strait were observed,were observed while, atmosphericwhile atmospheric pressure pressure disturbances disturbances moved movedfrom west from to west east to on east 7 April on 7 April 2019. 2019. The amplification The amplification of long of long ocean ocean waves waves by Proudmanby Proud- manresonance resonance in the in Korea the Korea Strait Strait was demonstrated was demonstrated in this in study this forstudy the firstfor the time. first The time. moving The movingspeed of speed atmospheric of atmospheric pressure pressure disturbances disturbances was 26.5–31.0was 26.5– m/s31.0 m/s with with an an inclination inclination of ◦ of75–83 75–83°in in the the counterclockwise counterclockwise direction. direction. The The average average height height of theof the atmospheric atmospheric pressure pres- suredisturbance disturbance was was 2.4 hPa, 2.4 hPa, and twoand totwo four to four waves waves passed passed in succession. in succession. TheThe two-dimensionaltwo-dimensional numerical numerical simulation simulation reproduced reproduced the propagationthe propagation of long of ocean long oceanwaves waves in the in Korea the Korea Strait. Strait. The arrival The arrival time, phase,time, phase, and period and period of the of simulated the simulated long ocean long oceanwaves wave weres appropriatelywere appropriately estimated estimated to within to within a few a minutes. few minutes. The long The oceanlong ocean waves waves were weregenerated generated due to due Proudman to Proudman resonance resonance as the atmosphericas the atmospheric pressure pressure disturbances disturbances moved movedover the over Yellow the SeaYellow and EastSea and China East Sea. China The maximumSea. The maximum amplitude amplitude of sea level of fluctuation sea level fluctuationwas 16.3–91.9 was cm. 16.3 The–91.9 amplification cm. The amplification of sea level of oscillations sea level wasoscillations highest was at Masan highest (MS) at Masandue to reflection(MS) due fromto reflection an island from and an the island shoaling and effect. the shoaling After the effect. long After wave the hit thelong coast wave of hitthe the Korea coast Strait, of the the Korea sea level Strait, oscillated the sea continuouslylevel oscillated for continuously 7–19 h with 10–160for 7–19 min h with periods. 10– 16The0 min long periods. ocean waves The long responded ocean waves immediately responded to atmosphericimmediately pressureto atmospheric disturbances pressure in disturbancesthe open sea, in but the they open reacted sea, but 1–3 they h later reacted in the 1 coasts–3 h later and in bays the ofcoasts the Korea and bays Strait. of Thethe Koreapropagation Strait. The speed propagation of a long oceanspeed waveof a long was ocean slowed wave down was by slowed shallow down topography by shallow in ttheopography coast, and in refractionthe coast, wasand causedrefraction by complexwas caused topography, by complex coastlines, topography, and islands. coastlines, The andreason islands. for the The small reason amplitude for the ofsmall sea levelamplitude oscillations of sea inlevel coastal oscillations areas except in coastal for MS areas was that a long ocean wave propagated parallel to the isobath; thus, the shoaling effect was except for MS was that a long ocean wave propagated parallel to the isobath; thus, the small. At MS, the amplitude of sea level fluctuation was largest due to the combination of shoaling effect was small. At MS, the amplitude of sea level fluctuation was largest due to the refraction, the reflection by the islands, harbor resonance, and the shoaling effect as the combination of the refraction, the reflection by the islands, harbor resonance, and the energy entered the bay. The contribution of reflected waves by islands was 72.7% for sea shoaling effect as energy entered the bay. The contribution of reflected waves by islands level oscillations of MS. We could determine the high sea level oscillation conditions in the was 72.7% for sea level oscillations of MS. We could determine the high sea level oscilla- Korea Strait through sensitivity experiments with different moving velocities and angles. tion conditions in the Korea Strait through sensitivity experiments with different moving These results will be useful for the development of real-time monitoring and prediction velocities and angles. These results will be useful for the development of real-time moni- systems for meteotsunami. toring and prediction systems for meteotsunami. Author Contributions: Conceptualization, B.-J.C. and K.K.; methodology, B.-J.C. and S.-G.M.; valida- Author Contributions: Conceptualization, B.-J.C. and K.-M.K.; methodology, B.-J.C. and S.-G.M.; tion, K.K., S.-G.M., and H.-S.S.; formal analysis, B.-J.C. and S.-G.M.; data curation, H.-S.S.; writing— validation,original draft K.- preparation,M.K., S.-G.M. K.K.;, and writing—review H.-S.S.; formal analysis, and editing, B.-J.C. B.-J.C. and andS.-G.M.; K.K.; data visualization, curation, H. S.-G.M.-S.S.; writingand H.-S.S.;—original supervision, draft preparation, B.-J.C. All K. authors-M.K.; havewriting read—review and agreed and editing, to the published B.-J.C. and version K.-M.K.; of vis- the ualization,manuscript. S.-G.M. and H.-S.S.; supervision, B.-J.C. All authors have read and agreed to the pub- lished version of the manuscript.

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Funding: This research was part of a project titled “Improvements of ocean prediction accuracy using numerical modeling and artificial intelligence technology” funded by the Ministry of and Fisheries, Korea, and supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2020R1A2C1014678). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: The authors would like to thank the Korea Meteorological Administration (KMA) and the Korea Hydrographic and Oceanographic Agency (KHOA) for the dataset. Conflicts of Interest: The authors declare no conflict of interest.

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