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Article Type:
Research Article

Wave Spectra Analysis on the Spatiotemporal Variability of Sea States under Distinct Typhoon Tracks in a Semienclosed Sea

Jie Peng aCAS Key Laboratory of Coastal Environmental Processes and Ecological Remediation, Yantai Institute of Coastal Zone Research, Chinese Academy of Sciences, Yantai, Shandong, China
bShandong Key Laboratory of Coastal Environmental Processes, Yantai, Shandong, China
cUniversity of Chinese Academy of Sciences, Beijing, China

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Miaohua Mao aCAS Key Laboratory of Coastal Environmental Processes and Ecological Remediation, Yantai Institute of Coastal Zone Research, Chinese Academy of Sciences, Yantai, Shandong, China
bShandong Key Laboratory of Coastal Environmental Processes, Yantai, Shandong, China
cUniversity of Chinese Academy of Sciences, Beijing, China

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https://orcid.org/0000-0002-3013-4849
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Meng Xia dDepartment of Natural Sciences, University of Maryland Eastern Shore, Princess Anne, Maryland

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Online Publication:
27 Feb 2024
Print Publication:
01 Mar 2024
DOI:
https://doi.org/10.1175/JPO-D-23-0066.1
Page(s):
783–807
Free access

Abstract

The dynamics of typhoon-induced waves in semienclosed seas become an interesting topic with the increase of typhoon intensity. Based on the calibrated Simulating Waves Nearshore (SWAN) model, wave dynamics were investigated under distinct typhoon tracks [e.g., Matmo (2014), Rumbia (2018), and Lekima (2019)] in the Bohai Sea. Distributions of significant wave heights (SWHs) are affected by the typhoon wind fields and are directly related to the typhoon tracks. The classical JONSWAP wave spectra were adopted for the analysis of sea states (e.g., wind seas or swells) to further explain variations in wave heights. Results indicate that the dominant sea state with higher energy experiences significant spatiotemporal variability under distinct tracks. For typhoons passing through the central part of the Bohai Sea (e.g., Rumbia), high-energy waves are observed under swell-dominated and mixed sea states, which are subjected to the fetch limitation in the semienclosed sea and rapid changes in typhoon winds. The high energy waves induced by other typhoons passing along the edges of the Bohai Sea correspond to the wind-sea-dominated sea state. Spatiotemporal variability of the sea state exhibits a high correlation with its position relative to the typhoon center. Therefore, a reference frame based on the radius of the maximum wind speed was established to discuss the sea states in this semienclosed sea. Further investigations reveal that swells (wind seas) dominate the regions within the radius of the maximum wind speed (elsewhere), and the double-peaked wave spectra tend to appear in the left quadrants.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Miaohua Mao, mhmao@yic.ac.cn

Abstract

The dynamics of typhoon-induced waves in semienclosed seas become an interesting topic with the increase of typhoon intensity. Based on the calibrated Simulating Waves Nearshore (SWAN) model, wave dynamics were investigated under distinct typhoon tracks [e.g., Matmo (2014), Rumbia (2018), and Lekima (2019)] in the Bohai Sea. Distributions of significant wave heights (SWHs) are affected by the typhoon wind fields and are directly related to the typhoon tracks. The classical JONSWAP wave spectra were adopted for the analysis of sea states (e.g., wind seas or swells) to further explain variations in wave heights. Results indicate that the dominant sea state with higher energy experiences significant spatiotemporal variability under distinct tracks. For typhoons passing through the central part of the Bohai Sea (e.g., Rumbia), high-energy waves are observed under swell-dominated and mixed sea states, which are subjected to the fetch limitation in the semienclosed sea and rapid changes in typhoon winds. The high energy waves induced by other typhoons passing along the edges of the Bohai Sea correspond to the wind-sea-dominated sea state. Spatiotemporal variability of the sea state exhibits a high correlation with its position relative to the typhoon center. Therefore, a reference frame based on the radius of the maximum wind speed was established to discuss the sea states in this semienclosed sea. Further investigations reveal that swells (wind seas) dominate the regions within the radius of the maximum wind speed (elsewhere), and the double-peaked wave spectra tend to appear in the left quadrants.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Miaohua Mao, mhmao@yic.ac.cn
Keywords: Hurricanes/typhoons; Ocean dynamics; Wind waves; Numerical analysis/modeling; Ocean models; Spectral analysis/models/distribution

1. Introduction

Typhoons (in the northwest Pacific) and hurricanes (in the North Atlantic and northeast Pacific) are derived from tropical cyclones. They can induce extreme waves, which impact navigational safety, destroy marine infrastructure (e.g., ports, seawalls, and oil platforms) and coastal habitats (Chen et al. 2019), modulate nearshore currents (Lin et al. 2021; Wu et al. 2021; Wang et al. 2022), intensify transport processes and bay–shelf exchanges (Xia et al. 2008; Gao et al. 2018; Song et al. 2021; Dobbelaere et al. 2022; Liang et al. 2023), and increase storm surges through the wave-induced setup (Huang et al. 2010; Mao and Xia 2018; Marsooli and Lin 2018). Owing to global climate change, rising sea surface temperature could provide more energy for the development of more intense typhoons in the western North Pacific (Webster et al. 2005; Knutson et al. 2010; Emanuel 2013; Guan et al. 2018; Mei and Xie 2016). Statistical analysis of previous tropical cyclones indicates that the typhoon size increased recently (Kossin 2018), which resulted in more extreme winds and waves (Moon et al. 2003; Young and Vinoth 2013; Chen et al. 2019; Inagaki et al. 2021). Most studies of typhoon and hurricane waves have been conducted in open sea areas, while the dynamics in semienclosed seas are seldom investigated. Due to the irregular geometry and nonlinear shallow-water dynamics, the mechanism of the typhoon waves is complex in the semienclosed sea. Additionally, typhoons that intensify in nearshore regions pose a critical threat to coastal communities (Emanuel 2017; Balaguru et al. 2022). Therefore, it is of great theoretical and practical significance to provide a broad overview and comprehensive analysis of the typhoon induced wave dynamics in semienclosed seas.

Wind fetch is a prominent factor in the development of waves in geographically limited waters with finite depths (Young and Verhagen 1996a,b; Benetazzo et al. 2013; Fisher et al. 2017; Kukulka et al. 2017; Chen et al. 2018; Qi and Wang 2020; Peng et al. 2023). Longer fetches accompanied by mature waves often occur in open terrain and deep oceans. Due to the proximity to land and shallow waters, the available fetches are significantly reduced in semienclosed and enclosed basins, lakes and lagoons, such as the Chesapeake Bay (Chen et al. 2018), Delaware Bay (Kukulka et al. 2017), Maryland coastal bays (Mao and Xia 2018, 2023), Long Island Sound (Shin et al. 2021), Lake Michigan (Mao et al. 2016), Lake Erie (Niu and Xia 2016), the west coast of Norway (Christakos et al. 2020), the southwest reef lagoon of New Caledonia (Jouon et al. 2009), and the southern Catalan coast (Alomar et al. 2014). These studies indicate that wave generation depends mostly on the wind fetch but need more in-depth analysis of the fetch differences caused by wind direction changes and the corresponding sea states. This study focused on the dynamics of the fetch-limited waves in semienclosed seas during typhoon events, considering the variations of the wind fetch and dominated sea state due to changes in typhoon winds.

Due to the variations in internal mechanisms and external characteristics, it is vital to investigate the dynamics of wind seas and swells independently (Li et al. 2020b). Separation and identification of the wind seas and swells are conducive to an accurate description of the sea states, especially for the typhoon waves with rapid spatial changes and temporal evolutions. To analyze wave characteristics and distinguish various sea states, the method of wave spectra analysis has been used widely. Recently, the double-peaked wave spectra containing both wind-sea and swell peaks have been reported in the Gulf of Oman (Adibzade et al. 2021), the Gulf of Mexico (Hu and Chen 2011; Esquivel-Trava et al. 2015), and Tokyo Bay (Tamura et al. 2021), especially during typhoon and hurricane events. However, most of the swell components in these double-peaked spectra are generated in open seas before propagating into the bays. It is an unresolved question whether double-peaked wave spectra can be generated due to the typhoon wind changes in semienclosed seas. The classical JONSWAP spectra (Hasselmann et al. 1973) have been used for wave studies in numerous sea areas around the world (Kumar et al. 2014a,b; Amurol and Ewans 2019; Mazaheri and Imani 2019; Craciunescu and Christou 2020), and the sea waters of China (Yang et al. 2015; Shi et al. 2017; Mo et al. 2019). Therefore, research on the sea state determination, energy analysis, and directional distinction of the JONSWAP wave spectra can be further explored.

During the transit of typhoon events, the waves are highly impacted by the radius of the maximum wind speed (Rmax) and their distances from the typhoon center (Young and Burchell 1996; Moon et al. 2003; Zhou et al. 2008; Collins et al. 2018). Based on the Rmax, establishing a reference frame will be beneficial for discussing the wave characteristics and sea states in each quadrant. Similar reference frameworks have been employed in open seas, including the Philippine Sea (Collins et al. 2018), the Gulf of Mexico (Hu and Chen 2011), and the South China Sea (Xu et al. 2017). The scale of the reference frame reached 5–10 times that of the Rmax in these areas, and the dominant sea state is dependent upon the typhoon characteristics and the relative location to the typhoon center in each quadrant. Given that the limited topography of the semienclosed seas leads to complex physical processes (e.g., wave reflection, refraction, and diffraction), it is worthwhile to investigate the sea states in such reference frames to deepen the understanding of fetch-limited waves in semienclosed seas.

Considering the recent poleward migration trends of typhoon tracks in the northwest Pacific (Shan and Yu 2020; Feng et al. 2021; Studholme et al. 2022), it is worthy of attention for the semienclosed seas located at higher latitudes. The Bohai Sea is the northernmost semienclosed sea in China with an area of 77 000 km2. This shallow water body (e.g., mean water depth of 18 m) is surrounded by lands on its three sides with a complex coastal topography. The maximum typhoon-induced wave height from 1979 to 2018 in the Bohai Sea is around 3 m (Li et al. 2020a). According to the statistics of typhoon tracks released by the Central Meteorological Observatory, the Bohai Sea experienced 19 typhoon events from July to September during 1992–2022 (Fig. 1a), and the occurrence numbers are unevenly distributed among different years (e.g., 2–3 times in 1994, 2011, and 2018). Therefore, the Bohai Sea is an ideal study domain for deepening the understanding of typhoon wave dynamics in the typical semienclosed seas.

Fig. 1.
Fig. 1.

(a) The 19 typhoons that affected the Bohai Sea in 1992–2022, (b) tracks and the maximum wind speed of Matmo (2014), Rumbia (2018), and Lekima (2019), (c) computational meshes for the Bohai Sea, and (d) bathymetry and locations of wind and wave observations.

Citation: Journal of Physical Oceanography 54, 3; 10.1175/JPO-D-23-0066.1

The tracks of typhoons and hurricanes have critical impacts on nearshore hydrodynamics (Xia et al. 2008), and the spatial variability of the wave field has been proven to be highly sensitive to the typhoon track (Li et al. 2020a; N. Wang et al. 2019). Among the two types of typhoons affecting the Bohai Sea, the first one makes landfall on the Shandong Peninsula before entering the Bohai Sea, accounting for 11 of the 19 typhoons, such as Typhoons Rumbia (2018) and Lekima (2019), which directly crossed over and wandered around the Bohai Sea, respectively. The second type moves northward through the North Yellow Sea and then affects the Bohai Sea, such as the track of Typhoon Matmo (2014) (Fig. 1b).

This work investigates the spatial and temporal variability of wave distributions and sea states during these three typhoon events, aiming to understand typhoon wave dynamics in semienclosed seas with complex geographic features. Three main questions are addressed during three typical typhoon events: 1) What are the spatial distributions and temporal evolutions of the significant wave heights (SWHs)? 2) How do the distinct typhoon tracks impact the spatiotemporal variations of sea states? 3) What are the sea states in each quadrant with distinct distances from the typhoon center? The remaining sections of this manuscript are organized as follows. Section 2 introduces the methodology, which includes the study domain, model description, data sources, skill metrics, study methods, and cases. In section 3, the quality of three wind field data is examined and the wave model is validated against observations. In section 4, the spatiotemporal variations of sea states are thoroughly discussed using wave spectra analysis. Major conclusions are summarized and concluded in section 5.

2. Methodology

a. Bathymetry and study domain

The Bohai Sea is a semienclosed sea with a shallow water body (e.g., the mean and maximum water depths of 18 and 80 m, respectively), and the bathymetry gradually deepens from the coast to the Bohai Strait. It is surrounded by lands on three sides with a total coastline length of 3700 km and includes three bays from the north to the south, namely, Liaodong Bay, Bohai Bay, and Laizhou Bay. The model domain consists of the entire Bohai Sea and part of the North Yellow Sea (e.g., the longitude of 117.2°–122.5°E and latitude of 37°–41.2°N) (Peng et al. 2023). The bathymetry data are obtained from the Global Multi-Resolution Topography (GMRT) with a resolution of 244 m (Fig. 1d). The coastline used for the model is based on satellite imagery from Google Earth in 2016, which could adapt to the complex coastline changes in the Bohai Sea in recent years (Chu et al. 2006; Pelling et al. 2013; Xu et al. 2016). The complex coastline and bathymetry are well resolved by using a total of 26 205 unstructured grids, and their grid sizes are reduced from 10 km along the open boundary and the central Bohai Basin to 1 km near the coast and islands (Fig. 1c; Peng et al. 2023).

b. Model description

Wave generation and propagation in the Bohai Sea were investigated using the unstructured-grid version of the third-generation Simulating Waves Nearshore (SWAN) (Booij et al. 1999; SWAN Group 2022a,b). It is challenging to predict the development and evolution of typhoons, which leads to the complexity in estimating typhoon waves. The SWAN model has been widely used to hindcast and forecast typhoon-generated waves in the South China Sea (Li et al. 2020), Tampa Bay (Huang et al. 2010), the Gulf of Mexico (Huang et al. 2013), and the U.S. East and Gulf Coasts (Marsooli and Lin 2018). To resolve the complex coastline and bathymetry in the Bohai Sea, the developed unstructured version of SWAN (Zijlema 2010) is adopted.

Equation (1) represents the spectral action balance equation, where temporal and spatial evolutions of the wave action density N˜ are on the left side, and the total wave energy source and sink term Stot is on the right side. The Stot in Eq. (1) consists of wind input Sin, wave dissipation Sds due to whitecapping, bottom friction, and wave breaking, and three-wave and four-wave nonlinear interactions Snl:
∂N˜∂t+∂cλN˜∂λ+cos−1φ∂cφcosφN˜∂φ+∂cσN˜∂σ+∂cθN˜∂θ=Stotσ, and
Stot=Sin+Sds+Snl.
The equation is integrated using the finite difference method, and the model is executed in a nonstationary mode. It is computed at 36 equally spaced propagation directions with an interval of 10° and 27 frequencies f between 0.04 and 0.5 Hz. The wind input and whitecapping dissipation setting developed by Komen et al. (1984) and the JONSWAP bottom friction setting by Hasselmann et al. (1973) are adopted.
The Komen package calculates the wind linear and exponential growths according to Cavaleri and Malanotte-Rizzoli (1981) and Komen et al. (1984):
Sin,KOMEN(σ,θ)=max{0,0.25ρaρw[28u*ccos(θ−θw)−1]}×σE(σ,θ),
in which c is the wave phase speed, ρa and ρw are the air and water densities. The term θ is the direction of spectral wave component, and θw is the wind direction. The friction velocity u* is given as
u*=τρa,
in which τ is the wind stress. The whitecapping dissipation uses the pressure pulse model of Hasselmann (1974), formulated by Komen et al. (1984):
Sds,KOMEN(σ,θ)=−Cds,KOMEN[(1−δ)+δkk˜](S˜S˜PM)p×σ˜kk˜E(σ,θ),
in which δ and p are tuning parameters, k is the wavenumber, and S˜=k˜Etot is the mean spectral steepness. The term Etot is the total energy of the wave spectrum; k˜ and σ˜ are the mean wavenumber and circular frequency, respectively. The term S˜PM corresponds to the mean spectral steepness of the Pierson–Moskowitz spectrum with S˜PM=3.02×10−3. The term Cds,KOMEN is the coefficient for determining the rate of whitecapping dissipation at 2.36 × 10−5.
The JONSWAP (Hasselmann et al. 1973) bottom friction energy dissipation term is computed as
Sds,b=−Cbσ2g2sinh2(kd)E(σ,θ),
in which d is the water depth, and g is the gravity acceleration. The term Cb is the bottom friction coefficient with default value Cb,JONSWAP = 0.038.

The depth-induced breaking and nonlinear wave–wave interactions (e.g., quadruplets and triads) adopt default settings, which achieve an optimum solution for wave simulations during cold wave events in the Bohai Sea (Peng et al. 2023).

c. Wind forcing data and observations

Recent studies indicate that the quality of wind data is essential for simulating waves accurately (Mao et al. 2016; Christakos et al. 2020; He et al. 2020; Wu et al. 2020), especially under typhoon conditions (Appendini et al. 2013; Chen et al. 2019). Due to the cyclonic feature of typhoon winds, accurate representations of the wind vector pose significant impacts on wave simulations. Three reanalysis datasets including ERA5; the Climate Forecast System, version 2 (CFSv2); and the Cross-Calibrated Multi-Platform (CCMP) were intercompared against observations from coastal oceanic stations and buoys herein.

The ERA5 is the latest atmospheric reanalysis data produced by the European Centre for Medium-Range Weather Forecasts (ECMWF), which replaced the ERA-Interim product since June 2018. The temporal and horizontal resolutions have been improved from 6 to 1 h and from 79 to 31 km, respectively (Hersbach et al. 2020; Wu et al. 2020). Compared to the ERA-Interim, ERA5 is produced with the 4DVar method and incorporates more historical observations with an upgraded assimilation system. The CFSv2 is an improved version of the Climate Forecast System (CFS) that has updated physics and better resolution since March 2011. It is a fully coupled model representing the interactions among the ocean, land, sea ice, and atmosphere with advanced physics, increased resolution, and refined initialization to improve seasonal climate forecasts. The temporal interval of CFSv2 winds is 1 h and the grid spacing is ∼33 km. The most recent version CCMPv2 was carried out by Remote Sensing Systems (RSS), which combines satellite observations and in situ wind measurements with background wind fields at 10-m height from the ERA-Interim reanalysis to produce 6-hourly global maps at 25-km spatial resolution (Bian et al. 2021).

The wind observation data are from buoys (e.g., QF104 and QF114) and oceanic stations (e.g., Laohutan, Zhifudao, Huanghua, and Huanghegang). The observed waves are from four buoys (e.g., QF104, QF114, DYG, and BHC) (Fig. 1c and Table 1). Additionally, Jason-3, which provided the Ku-band SWH data used herein, was launched on 17 January 2016 as a joint effort involving CNES, NASA, EUMETSAT, and NOAA. It has a non-sun-synchronous orbit of 1336 km, a 66° inclination on a Proteus platform, and a cycle of 10 days. Periods of the observations cover these three typhoon events.

Table 1.

Locations, water depths, available durations, and data sources for the wind and wave observations.
Table 1.

d. Skill metrics

Skill metrics includes the mean deviation (MD), Pearson correlation coefficient (CC), root-mean-square error (RMSE), and scatter index (SI). These expressions are given as follows:
MD=∑n=1N(rn−fn)N,
RMSE=[1N∑n=1N(rn−fn)2]1/2,
CC=1N−1∑n=1N(rn−r¯)(fn−f¯)σrσf,
SI=[1N∑n=1N(rn−fn)2]1/21N∑n=1Nfn, and
NRMSE=[1N∑n=1N(rn−fn)2]1/2fmax,
where f¯ and r¯ are the mean values of observations fn and simulations rn, respectively, in a sample of size N; fmax is the maximum values of fn; σf and σr are the corresponding standard deviations.

e. The JONSWAP wave spectra

The expression of the JONSWAP spectral form S(f) given by Hasselmann et al. (1973) is as follows:
S(f)=αg2(2π)4f−5exp[−54(ffp)−4]γexp[−(f−fp)2/(2σ2fp2)]
in which fp is the spectral peak frequency, and γ is the peak enhancement factor with a default value of 3.3. The fetch-dependent expression for α and the nondimensional peak frequency f˜p [f˜p=(U10/g)fp, in which U10 is the wind speed at 10-m elevation] is a function of the nondimensional fetch X˜ [X˜=(g/U102)X, in which X is the fetch]. Thus, S(f) is determined by the wind speed and fetch:
α=0.075X˜−0.22, and
f˜p=3.5X˜−0.33.

f. Division of sea state

Wave spectra for sea states are separated into swell ES and wind sea EW (Smedman et al. 2003):
ES=∫0fSS(f)df,
EW=∫fS∞S(f)df, and
fS=g2πβU10
in which S(f) is the one-dimensional (1D) wave spectrum, f is frequency, fS is the separation frequency (Sahlée et al. 2012). The wave age β=Cp/U10=gTp/(2πU10) (in which Cp is the wave phase speed, U10 is the10-m height wind speed, and Tp is the peak period of the 1D frequency spectrum) (Geernaert et al. 1987; Hanley et al. 2010) is set to 1.2 (Pierson and Moskowitz 1964; Donelan et al. 1985; Smith et al. 1992; Zou et al. 2019; Li et al. 2020; Peng et al. 2023). In the original definition, the calculation of β contains the included angle between the wind and wave directions at the peak of the wave spectrum. Because swell effects are similar for perpendicular and following angles (e.g., 90° and 0°) (Högström et al. 2009; Smedman et al. 2009), the calculation methods that include the cosine term of the included angle could lead to an erroneous classification of the sea state (Högström et al. 2011). The wind-wave ratio used to classify the type of sea states is defined as Ew/Es (Potter 2015; Lin 2021), and sea states are classified into wind-sea, mixed-sea, and swell conditions when Ew/Es > 2.0, (0.5 ≤ Ew/Es ≤ 2.0 and Ew/Es < 0.5, respectively.

g. Calculation of the radius of the maximum wind speed

The radius of the maximum wind speed (Rmax) is the distance between the typhoon center and its band of the strongest winds. It is a key factor in describing typhoon winds and has a significant influence on the typhoon structure and wind speeds (Zhou et al. 2008; Collins et al. 2018). Based on the measured data, Knaff et al. (2007) provided an empirical equation:
Rmax=m0+m1υmax+m2(φ−25)
in which φ is the latitude of the typhoon center, and υmax is the maximum wind speed. The terms m0, m1, and m2 are empirical parameters whose values depend on the typhoon location and vary among different basins (e.g., western Pacific, eastern Pacific, or North Atlantic). According to the updates for the western North Pacific (Knaff et al. 2018), they were set to 56.92 (n mi; 1 n mi = 1.852 km), −0.1541 (n mi kt−1; 1 kt ≈ 0.51 m s−1), and 0.7372 (n mi per degree), respectively.

h. Study cases

Typhoon Matmo was generated in the northwest Pacific Ocean east of the Philippines at 1800 UTC 17 July 2014, and then moved northwesterly. It strengthened into a strong typhoon and weakened into a strong tropical storm when it landed along the southeast coast of China. After continuing northward on land, it entered the Yellow Sea and moved from the southwest to the northeast. At 2100 UTC 24 July, the tropical storm landed again with a maximum wind speed of 18 m s−1 in the center. It continuously moved to the northeast but never entered the Bohai Sea, and eventually weakened in the North Yellow Sea.

Typhoon Rumbia was developed near the East China Sea at 0000 UTC 15 August 2018. It moved to the northwest and landed from the southeast of Shanghai City. Before moving to the northeast, it changed from a tropical storm to a tropical depression. It turned into a tropical storm again and entered the Bohai Sea from the Yellow River estuary at 2300 UTC 19 August with a maximum wind speed of 18 m s−1. Then it moved from southwest to northeast, passed through the Bohai Strait and entered the North Yellow Sea, and its intensity decreased until dissipation.

Typhoon Lekima was generated over the oceanic area to the east of the Philippines at 0600 UTC 4 August 2019. After formation, it moved northwestward and gradually strengthened into a supertyphoon. At 1250 UTC 11 August, it landed along the west coast of the Yellow Sea and moved northwestward. The maximum wind speed near the center was 23 m s−1 (tropical storm level). Around 1800 UTC, it entered the Bohai Sea through Laizhou Bay, with an intensity maintained at a tropical storm level. It stayed in Laizhou Bay and turned into a tropical depression with a maximum wind speed of 18 m s−1 at 2300 UTC 11 August. After 0000 UTC 12 August, it had an eastward movement track in Laizhou Bay and finally weakened and dissipated in the eastern part. Lekima has a high intensity, long impact time, and wide impact range. Especially after it made landfall at the Shandong Peninsula and went northwesterly, its moving speed slowed down and wandered around Laizhou Bay, resulting in serious disasters along the Bohai Sea (Fu et al. 2021; Li et al. 2021).

To make simulations more stable and accurate, one week was reserved as the model stabilization time before the typhoon center entered the study domain (Table 2).

Table 2.

The time when the typhoon center enters the study domain, and the start and end times of the simulation during study cases.
Table 2.

3. Model validation

a. Data quality of various sources of wind fields

Comparisons of the three wind datasets (ERA5, CCMP, and CFSv2) with the observed wind during typhoon events are shown in Figs. 2a and 2b. Statistical analysis (Table 3) indicated that the mean CCs of ERA5 and CCMP were better than those of CFSv2 (e.g., 0.84 and 0.85 vs 0.79), while the absolute mean deviation (AMD) and RMSE between the ERA5 and observations were better than those of CCMP (e.g., 1.44 vs 1.49 m s−1 for AMD; 2.94 vs 2.95 m s−1 for the mean RMSE). In addition, the ERA5 performs better than CCMP and CFSv2 against the observations for wind directions (e.g., 0.67 vs 0.58 and 0.61 for CC; 2.03° vs 6.32° and 3.17° for AMD; 0.55 vs 0.61 and 0.57 for SI). With fine horizontal resolution, enhanced methods of data assimilation, and improved model physics, the ERA5 wind data excel in representing extreme atmospheric events like typhoons and tropical cyclones (Hersbach et al. 2020; Bian et al. 2021). Considering that the irregular coastline significantly impeded the coastal winds, the rapid changes of nearshore winds are the possible reason for the model-to-data deviations (Mao et al. 2016; Christakos et al. 2020). Based on the above advantages, the ERA5 wind data are used to drive the wave model in this work.

Fig. 2.
Fig. 2.

Time series of observed and modeled (a) wind speeds and (b) wind directions at the oceanic stations and buoys.

Citation: Journal of Physical Oceanography 54, 3; 10.1175/JPO-D-23-0066.1

Table 3.

The MD, CC, RMSE, and SI of three wind sources against observations.
Table 3.

b. Verification of simulated waves

The settings used in this model perform well for wave simulations during typhoon events in the Bohai Sea (Li et al. 2020; Y. Wang et al. 2019), but the bottom friction term needs improvement. The bottom friction coefficient Cb = 0.038 was proposed by Hasselmann et al. (1973) with the JONSWAP results. Zijlema et al. (2012) found that a unified value of Cb = 0.038 can be used if the second-order polynomial fit for the wind drag coefficient calculation is employed. Therefore, this default value is unchanged irrespective of swell and wind-sea conditions in the Sea of Marmara (Akpınar et al. 2021), Chesapeake Bay (Fisher et al. 2017), and Black Sea (Akpınar et al. 2017). Under strong wind conditions in open oceans, a value of 0.067 was adopted (Marsooli and Lin 2018; Christakos et al. 2020). Recently, a lower value of 0.019 proposed by the NOAA operational third-generation ocean wind-wave (WAVEWATCH-III) model was applied to the Gulf of Mexico during hurricane events by Huang et al. (2013), and they found that the low Cb value improved the underestimated SWH in shallow waters. Bottom friction dissipation depends largely on bottom material compositions (Xu et al. 2013; Qian et al. 2021), and the default bed friction implemented is based on a sandy bottom (Siadatmousavi et al. 2011). Bottom sediments in the Gulf of Mexico are largely fine-grained with an average clay content of 71% (Balsam and Beeson 2003; Ellwood et al. 2006; Murawski et al. 2020). Clay and marl dominate the sediment deposited in its central part, while siliceous silt and clay dominate along its shelf. Because the accumulated sediments in the Bohai Sea are also mainly clay and silt with very limited sand and gravel (Wang et al. 2013), a low value of Cb = 0.019 was assessed against observations during typhoon events in the Bohai Sea.

Observations of SWH include buoys QF104, QF114, DYG, and BHC and Jason-3 satellite Ku-band data (Fig. 1d and Table 1). Figures 3a and 3b show that the simulated SWHs are generally acceptable (e.g., mean CC more than 0.9, see Table 4). By reducing the value of Cb from 0.038 to 0.019, the MD, RMSE, and normalized root-mean-square error (NRMSE) were improved by 18.8%, 8.1%, and 7.1%, respectively. This improvement is even higher than that in the Gulf of Mexico during Hurricane Dennis (2005) (Siadatmousavi et al. 2011), which was a 5%–10% improvement in the simulated SWH of coastal stations. This indicates that the default Cb is possibly overly high, causing more wave energy to be dissipated and estimating lower wave heights in shallow water (Y. Xu et al. 2020). However, the simulation is less sensitive to the adjustment of Cb at station BHC as it is in the sea area with a 30-m water depth and near the island. Simulation results using Cb = 0.019 driven by distinct winds are further tested using quantile–quantile (Q–Q) plots (Fig. 3c). The simulated SWHs using the ERA5 winds have the same trend as the observation, and it is more stable than those of the CCMP and CFSv2, which underestimate lower values and overestimate higher values. Therefore, it is confirmed that the ERA5 wind field is the best choice for the Bohai Sea wave simulations.

Fig. 3.
Fig. 3.

(a) Time series of observed and simulated SWHs with the bottom friction coefficient of 0.019 and 0.038, (b) scatter diagrams of significant wave heights between simulations and Jason-3 satellite Ku-band data, and (c) Q–Q plots of simulated SWHs using the bottom friction coefficient of 0.019 with distinct wind fields.

Citation: Journal of Physical Oceanography 54, 3; 10.1175/JPO-D-23-0066.1

Table 4.

The MD, CC, RMSE, and NRMSE of significant wave height simulations against observations with a bottom friction coefficient of 0.038 and 0.019. The upward arrow represents the percentage of improvement in results after changing the bottom friction coefficient to 0.019, and the downward arrow represents the percentage of deterioration in results.
Table 4.

Simulated wave spectra are compared with those from the ECMWF with 1° spatial resolution, 30 frequency bins, and 24 directions in various locations including single- and double-peaked spectra (Fig. 4). During the three typhoon events, the spectra shape and energy density values between the two sources are highly similar. Peak frequencies are mostly consistent with each other, while a slight directional deviation was detected. A pair of high-value centers in the double-peaked spectrum were found during Lekima from both models (Fig. 4d).

Fig. 4.
Fig. 4.

Wave spectra validation of ECMWF and SWAN simulations during Typhoons (a) Matmo, (b) Rumbia, and (c),(d) Lekima.

Citation: Journal of Physical Oceanography 54, 3; 10.1175/JPO-D-23-0066.1

4. Results and discussion

a. Spatial distributions and temporal evolutions of typhoon winds and waves

To show the spatial distributions and temporal evolutions of wind fields and SWHs, a time span of 12 h including the time of the maximum SWH during three typhoon events is depicted in Fig. 5. At 0000 UTC 25 July 2014, Matmo began to impact the Bohai Sea by generating more than 2-m SWHs when its center shifted from southwest to northeast in Laizhou Bay (Fig. 5a). At 0600 UTC, the sea area with large winds and high waves appeared in the southern Bohai Sea and North Yellow Sea, and the maximum wind speed reached around 16 m s−1. The maximum SWH in Laizhou Bay was 2.7 m, while it was generally less than 1 m in Liaodong Bay (Fig. 5b). The typhoon center continued to move northeast and passed through the southeast boundary of the Bohai Sea. At 1200 UTC, the maximum SWH of 3.5 m appeared in the North Yellow Sea when the maximum wind speed was 17.7 m s−1. The SWH in the Bohai Strait reached 2 m, while it was less than 1.5 m in most other regions (Fig. 5c).

Fig. 5.
Fig. 5.

(a)–(c) Temporal evolutions of the wind and wave fields from 0600 to 1800 UTC 25 Jul 2014 during Matmo, (d)–(f) from 1800 19 Aug to 0600 20 Aug 2018 during Rumbia, and (g)–(i) from 1200 UTC 11 Aug to 0000 UTC 12 Aug 2019 during Lekima. The red dots represent the typhoon center locations, and typhoon centers not marked in the figure are outside the study area.

Citation: Journal of Physical Oceanography 54, 3; 10.1175/JPO-D-23-0066.1

At 1800 UTC 19 August 2018, Rumbia reached the southwest of the Bohai Sea, and the maximum wind speed and SWH along the southwest coast reached 16.6 m s−1 and 2.2 m (Fig. 5d). At 0000 UTC 20 August, the typhoon center entered the Bohai Sea with a maximum wind speed of 16.2 m s−1. The maximum SWH near the mouth of Bohai Bay was 2.8 m, and there was another high-value area in the North Yellow Sea (Fig. 5e). The typhoon center continued to move northeast and entered the North Yellow Sea at 0600 UTC, and high waves appeared in the central Bohai Basin at the left-rear part of the typhoon center with a maximum SWH of 2.4 m (Fig. 5f).

Lekima moved northwest to the south of Laizhou Bay after landing on the Shandong Peninsula at 1200 UTC 11 August 2019, which affected the central Bohai Basin, Bohai Bay and Laizhou Bay with the 17.8 m s−1 maximum wind speed and 3.7-m SWH (Fig. 5g). Lekima wandered south of Laizhou Bay, and its moving speed slowed down, leading to the continuous strong northeast wind (e.g., the maximum wind speed of more than 20 m s−1). At 1800 UTC, the high SWH area with a maximum value of 4.5 m moved from the central Bohai Basin to the mouth of Bohai Bay (Fig. 5h). At 0000 UTC 12 August, the wind field weakened in most sea areas except for the northwest part of the Bohai Sea still experienced high winds and strong waves (e.g., the maximum wind speed and SWH of 20.2 m s−1 and 3.9 m, respectively, in Fig. 5i).

The above results demonstrate that typhoons with distinct tracks induced waves have unique spatiotemporal variations, and the SWHs are highly correlated with typhoon wind structure and tracks. For typhoons entering the Bohai Sea, the high SWH areas gradually change with the transit of typhoons, the contour lines of which show a radius distribution around the typhoon center. For typhoons passing along the eastern edge of the Bohai Sea into the North Yellow Sea, the high SWH distributions are relatively stable (Figs. 5a–c).

b. Analysis of the double- and single-peaked wave spectra

According to the wave distributions in section 4a, waves generated by Lekima are much stronger than those by Matmo and Rumbia, during which the high-value areas are located in the central and western parts of the Bohai Sea. Two observation stations are available for wave observations during Lekima with QF104 (QF114) being closer to the high (low) waves, both of which were selected to conduct the spectral analysis (Fig. 6).

Fig. 6.
Fig. 6.

Temporal spectra with a time interval of 6 h at (a) QF104 and (b) QF114. Also shown are the 1D spectra of QF104 at (c) 1200 and (d) 1800 UTC 11 Aug 2019 and (e) 0000 UTC 12 Aug 2019.

Citation: Journal of Physical Oceanography 54, 3; 10.1175/JPO-D-23-0066.1

The fp gradually shifted between 0.1 and 0.2 Hz, and the temporal variation of the peak energy density Sp(f) was quite large (Figs. 6a,b). When the typhoon center of Lekima was close to QF104, the wave spectra began to show a pair of peaks from 0000 to 0400 UTC 12 August (Fig. 6a). The double-peaked wave spectra were usually observed in the developing and decaying stages of typhoons (Fossen 2011; Mo et al. 2019; Vettor and Guedes Soares 2020). At 0000 UTC 12 August (Fig. 6e), Sp(f) ranged from 3.5 to 0.5 m2 Hz−1, and similar phenomenon was observed when Typhoon Conson (2010) passed through the northern South China Sea (Mo et al. 2019). The energy density of the double-peaked wave spectrum continued to decrease before gradually returning to a single-peaked state at 0600 UTC.

The 1D wave spectra at QF114 (Fig. 6b) were single peaked, and fp varied from 0.13 to 0.18 Hz during Lekima. Similar observations were reported under storm weather conditions in the Persian Gulf (Mazaheri and Imani 2019). From 0600 to 1200 UTC 11 August, Sp(f) increased and fp decreased with the gradual strengthening of the typhoon, and the maximum Sp(f) reached 13.59 m2 Hz−1 at 1200 UTC when the corresponding fp was 0.13 Hz. This value is lower than that in the Persian Gulf (e.g., 31.7 m2 Hz−1) (Mazaheri and Imani 2019) and the South China Sea (30.8 m2 Hz−1) (Shi et al. 2017). This is related to stronger weather conditions in the open sea area, which lead to the full development of wind seas. When the typhoon began to weaken, fp gradually moved to the higher-frequency band and Sp(f) decreased accordingly.

To further explore the directional characteristics of the double-peaked wave spectra, Fig. 7 illustrates the details of the individual directional spectra at QF104. The separation frequency [fS=g/(2πβU10); Sahlée et al. 2012; Potter 2015] is introduced to differentiate waves of distinct origins, which is the lower bound for wind-sea condition, and β is set to 1.2 (Pierson and Moskowitz 1964; Donelan et al. 1985; Smith et al. 1992). The fS is the wave frequency at which the wave phase speed approximately equals the wind speed at the surface, and waves of a lower frequency than fS with faster wave phase speed are not from the local winds input. Therefore, the part of the frequency above (below) fS originates from wind seas (swells).

Fig. 7.
Fig. 7.

Directional spectra of QF104 station during Lekima. Also shown are the direction (all using the “going to” convention) of the wind in red vertical lines, the direction of the wave in green vertical lines, and the moving direction of Lekima in orange vertical lines. The separation frequency fS (shown in yellow horizontal dashed lines) divides the wave spectrum into the wind-sea (above the yellow dashed line) part and the swell part (below the yellow dashed line), and the peak energy density of wind seas and swells are shown in white vertical lines.

Citation: Journal of Physical Oceanography 54, 3; 10.1175/JPO-D-23-0066.1

The wave spectra at QF104 were variable, which contained wind-sea-dominated single-peaked spectra (e.g., 1200 UTC 11 August), swell-dominated single (e.g., 1800 UTC 11 August) and double-peaked spectra (e.g., 0000 UTC 12 August). Initially, the peak wave energy was from the wind direction before the Lekima center approached the Bohai Sea. The waves were dominated by wind seas, and the mean wave direction was toward the southwest (Fig. 7a). Then the wind gradually shifted to the northwest when the typhoon center moved closer (Fig. 7b). Consequently, the sea state changed to swell dominated when the wind direction reached the middle of the mean wave and the typhoon moving directions (Fig. 7c). Given that the swell propagation speed is greater than the wind speed, the wave energy was concentrated in the direction of the preceding wind seas, which supported that the swell at QF104 was consistent with previous remote wind seas propagating direction. As the wind direction continued to move toward the northwest, the width of the wave spectra gradually expanded and double peaks appeared owing to the superposition of swells over local wind seas (Figs. 7e,f), which was clearly separated by fS (e.g., wind seas/swells above/below the yellow dashed lines). The wave spectrum energy is swell dominated, and the wind seas are separated from the swells by about 128°, which aligned with the wind direction but a little offset counterclockwise. Attributed to nonlinear wave–wave interactions (Young 2006), the directional misalignment between winds and waves prevailed during typhoon events including the wind-sea-dominant region (Collins et al. 2018). During this process, the wave spectra energy kept decreasing since there was no additional wind energy replenished in its original propagating direction under wind-sea conditions. Because of the high variability of winds, typhoon induced wind seas were difficult to fully grow and develop without sufficient fetch and duration. Analysis of wave spectra at QF104 during Lekima demonstrates that the shape of wave spectra shape is influenced by the swells (Mazaheri and Imani 2019; Ochi 2005; Massel 2007), and they gradually widen with the formation of a mixed sea state.

c. Spatiotemporal distributions of wave spectral characteristics

Because of the misalignment between wind and wave directions, the wave frequency varies in a wide range and the width of the double-peaked spectra gradually expanded at QF104 (Fig. 7), indicating that the spectral characteristics can reflect changes in sea states. The spectrum bandwidth provides sufficient information on the dominant sea state, degree of wave coupling and nonlinearity in this system (Liu et al. 2015; Mazaheri and Imani 2019). The spectrum width ε proposed by Cartwright and Longuet-Higgins (1956) is expressed as follows:
ε=(1−m22m0m4)0.5,
in which mi is the ith-order moment calculated by
mi=∫0∞fiS(f)df.
Time series of m0, m1, m2, m4, and ε at QF114 during Lekima are shown in Fig. 8a. Lekima gradually moved northward and approached station QF114 from 0600 to 1200 UTC 11 August, and sea states were dominated by wind seas driven by the typhoon’s frontal side, where the wave direction was concentrated and ε decreased. When Lekima moved northwest, the swell component began to increase with its direction deviation from the wind direction, leading to the directional variability of waves. Subsequently, the energy distribution in a wide range of frequency with ε being increased, similar to a previous typhoon study in the northwestern South China Sea (Shi et al. 2017). At 0000 UTC 12 August, Lekima wandered around the south of Laizhou Bay, and the wind and wave fields gradually stabilized as ε decreased. The ε at QF114 varied between 0.59 and 0.66, which is within the range of 0.5–0.9 (Liu et al. 2015; Kumar et al. 2014b).
Fig. 8.
Fig. 8.

(a) Time series of m0, m1, m2, and m4 and spectral width ε during Lekima at station QF114. The spatial distributions of spectral peakedness parameter Qp (the first row) and the partitions according to Qp (the second row) during (b) Matmo, (c) Rumbia, and (d) Lekima. The red dots represent the typhoon center locations, and typhoon centers not marked in the figure are outside the study area.

Citation: Journal of Physical Oceanography 54, 3; 10.1175/JPO-D-23-0066.1

Because ε depends on a higher moment of the energy spectrum (e.g., m ≥ 2), it is sensitive to the high-frequency spectrum portion (Mazaheri and Imani 2019). The peakedness parameter Qp is more reliable since it bases on stable quantities like m0 and S(f) in its computation (Prasada Rao 1988):
Qp=2m02∫0∞fs2(f)df.
Here, Qp > 2 and Qp < 2 are defined for narrow and broad-banded spectra, respectively, and Qp ≈ 2 represents the fully developed wind seas. A smaller (larger) value of Qp indicates wider (narrower) wave spectra, which increases (decreases) the degree of randomness [e.g., shorter (longer) wave groups]. Because Qp has been proven to perform well for the spectral shape (Goda 1970; Kumar et al. 2014a,b; Mazaheri and Imani 2019), it was used for the analysis of spatial dynamics. Spatial distributions of Qp during three typhoon events are shown in Figs. 8b–d, which are similar to those of SWH (Fig. 5), as Qp increases with SWH under wind seas conditions (Kumar et al. 2014a,b). Most sea areas are narrow-banded spectra during typhoon events, indicating that single-peaked spectra are common. The broad-banded spectra are more likely observed nearshore, showing a roughly circular distribution at a certain distance from the typhoon center, related to the radius of the maximum wind speed. By analyzing the Qp distribution, the location of the mixed sea state can be inferred. However, Qp values for wind-sea and swell-dominated broad-banded multipeaked spectra are similar (Kumar et al. 2014b). To further distinguish the dominant wave component, sea states in distinct sea areas of the Bohai Sea during typhoon events will be discussed in the following subsection.

d. Spatial and temporal variations of sea state

Due to geographical differences in various sea areas, five representative test points were selected (Fig. 2a), and their time series of wind and wave (not shown here) indicate that the durations affected by typhoons varied greatly in distinct sea areas. Sea areas far from the typhoon track were affected for only 24–36 h, while the wandering track of Lekima resulted in more than 60 h of affected duration, and the Ew/Es comparison can be found in Fig. 9. A comparison of these three typhoons shows that the wave energy is weaker during Matmo (Fig. 9a), and the sea states are usually wind sea dominated with high wave energy during Matmo except for Bohai Bay. The typhoon wind fields passing by the North Yellow Sea hardly affect Bohai Bay, and waves are mostly dominated by incoming swells from the central Bohai Basin (e.g., from 1300 UTC 25 July to 0000 UTC 26 July 2014).

Fig. 9.
Fig. 9.

The 1D wave spectra at five test points during (a) Matmo, (b) Rumbia, and (c) Lekima. Black solid lines denote the wind wave ratio (Ew/Es). Black dotted lines (Ew/Es = 2.0) denote the separation ratio between the wind-sea-dominated and mixed conditions. Black dashed lines (Ew/Es = 0.5) denote the separation ratio between the mixed and swell-dominated conditions. Red solid lines denote whether the spectrum is single peaked or double peaked.

Citation: Journal of Physical Oceanography 54, 3; 10.1175/JPO-D-23-0066.1

Wave energy during Rumbia (Fig. 9b) is more concentrated in the low frequency (0.05–0.15 Hz) (Kumar et al. 2014b), similar to the finding of Shi et al. (2017) in the South China Sea (e.g., fp of 0.063–0.217 Hz). The high wave energy is primarily found in the swell-dominated and mixed sea states before the arrival and after the passage of the typhoon center (e.g., before 20 August and after 22 August 2018). The sea state experienced alternately between wind-sea and swell conditions in Bohai and Laizhou Bays, accompanied by shifts of single or double-peaked wave spectra. Because the typhoon translation speed is superimposed over the wind around its center, the wave energy density on the right side is relatively large in open seas (Hu and Chen 2011; Fomin 2017; Collins et al. 2018; F. Xu et al. 2020). However, the wave energy density on the right side of the track (e.g., Laizhou Bay) was lower than that on the left side (e.g., Bohai Bay with a longer fetch) in the Bohai Sea. This reflects the difference in typhoon-generated waves between the semienclosed seas and open seas, and it indicates that wind fetch plays an important role in typhoon wave dynamics over geographically limited sea areas.

Lekima made landfall in Shandong Province at 1300 UTC 11 August 2019 (Fig. 9c), and high wave energy densities in each sea area corresponded to the sea state dominated by wind seas. This is due to the invasion of cold air into the typhoon center (Zhu et al. 2022) and the formation of a stable northeast wind field with high winds in the Bohai Sea, similar to the northeasterly wind during cold wave events (Peng et al. 2023). After entering the Bohai Sea from Laizhou Bay, the double-peaked wave spectrum was dominated by swells in Laizhou Bay, consistent with the situation at QF104 and the existence of broad-banded wave spectra discussed in sections 4b and 4c. The Bohai Strait showed single-peaked wind seas, consistent with the situation at QF114.

Therefore, the sea states show obvious evolutions in different stages of typhoons, predominantly dominated by wind sea for typhoons not passing through the central part of the Bohai Sea. High values of wave energy are mostly in the swell-dominated and mixed sea states before the arrival and after the departure of the typhoons passing through the central part. In this situation, the width along the northwest–southeast axis of the Bohai Sea is approximately equal to the radius of the maximum wind speed, which is not conducive to the generation and development of wind seas. The differences in distinct sea areas are highly correlated with the distance and angle to the typhoon center, which is influenced by the radius of the maximum wind speed (Rmax) (Zhou et al. 2008; Collins et al. 2018). Therefore, a reference frame is established based on Rmax, and the wave spectra in each quadrant will be investigated in the following section.

e. Reference frame based on the radius of the maximum wind speed

Centers of three typhoons are basically located between latitudes of 37°–39°N, and Rmax are between 110 and 115 km with the maximum wind speeds of 16–23 m s−1. This agrees with the statistical results of Knaff et al. (2007), in which the maximum wind speed and mean Rmax are 26.0 m s−1 and 101.8 km among 1107 typhoons in the western North Pacific. The typhoon reference frame takes the circle center, and uses the distances normalized by Rmax to determine the radius of R/2, R, and 2R. The reference frame is shown at 3-h intervals during the passage of typhoons through the Bohai Sea, and the two-dimensional (2D) wave spectra are shown in each quadrant.

Rumbia passed through the Bohai Sea from southwest to northeast (Fig. 10), and the first quadrant was soon affected by the frontal wind field. When the typhoon center entered the Bohai Sea at 0000 UTC 20 August 2018 (Fig. 10a), the first quadrant tended to show double-peaked spectra with different directions. For the double-peaked wave spectrum at R/2, the energy of the wind-sea peak was lower than the swell peak, due to the typhoon center’s weak intensity of the wind speed and the variability of the wind direction. For the wave spectrum at R and 2R, the wind-sea peak shows higher energy under the effect of the large wind speed. At 0300 (Fig. 10b), the typhoon center moved to the Bohai Strait, and the double-peaked wave spectra appeared in the second quadrant. A swell-dominated double-peaked spectrum appeared at R/2, and a wind-sea-dominated double-peaked spectrum appeared at R. The wave spectrum at 2R was dominated by wind seas, but the maximum energy density was only about 1/10 of that at R because the northerly wind induced short fetch in the shallow nearshore. The typhoon center left the Bohai Sea and entered the North Yellow Sea at 0600 (Fig. 10c), when part of the Bohai Sea was located in the second and third quadrants. The energy was concentrated in wind seas at R and 2R in the second quadrant, while there were two swell peaks in the spectrum at R/2 in the third quadrant (e.g., wave ages of 1.25 and 1.38), and swells with stronger (smaller) energy spread from the North Yellow Sea (Liaodong Bay) to the northwest (southeast). To sum up, the double-peaked wave spectra during Rumbia majorly appear at R/2 and R, and the variable wind field results in complex wave characteristics. This is because a larger translation speed greatly affects the wave direction in the left quadrant (Hu and Chen 2011), which corresponds to the double-peaked spectra in the second and third quadrants during Rumbia. The Bohai Sea is basically in the second quadrant when Matmo moves from southwest to northeast, and the results (not shown here) are consistent with that during Rumbia. It can be concluded that during the transit of typhoons from southwest to northeast, swell peaks are more likely to occur at R/2. The wind speed is high at R in each quadrant, and it is likely to have wind-sea-dominated spectra with high energy. Wind sea is dominated at 2R, but the energy density is much lower than that at R.

Fig. 10.
Fig. 10.

Directional spectra in each quadrant of the reference frame based on the radius of the maximum wind speed during Rumbia at (a) 0000 and (b) 0300 UTC 20 Aug 2018.

Citation: Journal of Physical Oceanography 54, 3; 10.1175/JPO-D-23-0066.1

Fig. 10c.
Fig. 10c.

As in (a) and (b), but at 0600 UTC 20 Aug 2018.

Citation: Journal of Physical Oceanography 54, 3; 10.1175/JPO-D-23-0066.1

Lekima is one of the few typhoons that have a moving track from southeast to northwest, and its frontal part entered Laizhou Bay at 1800 UTC 11 August 2019 (Fig. 11b). The first quadrant was in the Bohai Strait at 1800 UTC with a double-peaked wind-sea-dominated spectrum at 2R. The R/2 position in the second quadrant has a single-peaked swell, and the R position has a single-peaked wind-sea-dominated spectrum with an extremely low energy being close to the coast. In this situation, the wind and fetch reductions by lands and shallow waters affect the wave spectra (Hu and Chen 2011). The typhoon center entered Laizhou Bay at 2100 UTC (Fig. 11c), and the first quadrant has swell-dominated single-peaked (double-peaked) wave spectra at R/2 and R (2R). The swell-dominated wave spectrum at R appears because the short southeasterly wind fetch cannot facilitate wind seas development. The second quadrant has a single-peaked spectrum dominated by swells and wind seas at R/2 and 2R. Overall, the double-peaked wave spectra tend to appear at 2R in the first quadrant during Lekima. Since Lekima moved slowly and wandered around Laizhou Bay, its wind field was less variable. The double-peaked wave spectra in the first quadrant are caused by the combined effect of typhoon-induced wind seas and cold air-induced swells from the north (Zhu et al. 2022).

Fig. 11.
Fig. 11.

Directional spectra in each quadrant of the reference frame based on the radius of the maximum wind speed during Lekima at (a) 1500, (b) 1800, and (c) 2100 UTC 11 Aug 2019.

Citation: Journal of Physical Oceanography 54, 3; 10.1175/JPO-D-23-0066.1

The wave spectral analysis indicates that swells dominate within the distance of R, while wind seas prevail in other regions, consistent with N. Wang et al. (2019), which used the swell index during typhoon events in the Yellow and East China Seas. However, it is smaller than that in the South China Sea, where waves over an area within 5R were mainly dominated by wind seas (Xu et al. 2017). In the double-peaked wave spectra during typhoon events, two separate peaks induced by swell and local wind seas have large directional deviations (e.g., mean deviation of 109°). This is consistent with the tropical cyclones induced double-peaked wave spectra in the Philippine Sea, where the wind seas separated from the swell by about 100° (Collins et al. 2018). Such wave spectra generally appear close to the typhoon center (Hu and Chen 2011), in which wave energy and height are usually high in the second quadrant because of a large fetch. This corroborates with the results in section 4a that the wave energy density in Laizhou Bay (in the fourth quadrant) was lower than that in Bohai Bay (in the second quadrant). In the future, it is worthwhile including additional observations of wave spectra in the Bohai Sea to further understand wave dynamics in semienclosed seas.

5. Conclusions

Recent climate change has increased the intensity of typhoons in the northwest Pacific, which makes the typhoon waves along China’s coasts more noteworthy. As a semienclosed sea, wave dynamics in the Bohai Sea are worthy of study due to its unique geographic features. A third-generation wave model Simulating Waves Nearshore (SWAN) has been applied successfully to the Bohai Sea during Typhoons Matmo (2014), Rumbia (2018), and Lekima (2019). The SWH (significant wave height) distributions and dominant sea states exhibit spatiotemporal variability, highly correlated with the typhoon tracks and the position relative to the typhoon center. To further explore the dynamics of sea states during typhoon events in a semienclosed sea, a reference frame based on the radius of the maximum wind speed (Rmax) is established. The main findings of this work are summarized and concluded as follows:

  1. Spatiotemporal evolutions of the winds and waves are well marked during typhoon events. SWHs are highly correlated with typhoon wind structure, and the high values show a circular distribution related to Rmax. Large waves have a direct relationship with the typhoon tracks, which are relatively stable for typhoons not passing through the central part of the Bohai Sea.

  2. The dominant sea state with higher energy experiences significant spatiotemporal variability under distinct typhoon tracks, leading to corresponding variations of SWH. High energy waves are observed under swell-dominated and mixed sea states before the arrival and after the departure of the typhoons passing through the central part of the Bohai Sea, subjected to geographical limitation (e.g., the width along the northwest–southeast axis is approximately equal to Rmax) and rapid changes in typhoon winds. Otherwise, high energy waves of other tracks passing along the edges correspond to the sea state dominated by wind seas along the passage of the typhoon center. Changes in sea state were usually accompanied by shifts of single- or double-peaked wave spectra.

  3. Using the distances normalized by Rmax to determine the radius, a reference frame was established to show wave spectra in each quadrant at R/2, R, and 2R. Swells dominate within the radius of R, while wind seas prevail elsewhere. The double-peaked wave spectra with significant directional variations mostly appeared at R/2 and R in the second and third quadrants. Because the typhoon translation speed is superimposed over the wind speed, the wave energy density is larger on the right side of the typhoon track in open seas. However, this statement is not entirely applicable to the Bohai Sea, for which wind fetch plays a substantial role in typhoon waves over this geographically semienclosed sea.

Acknowledgments.

Dr. M. Mao was supported by the National Natural Science Foundation of China (42006025), the Yantai City “Double Hundred Plan” Elite Program (E039031101), and the Chinese Academy of Sciences “BRJH” Program (E129030401). The authors greatly appreciate the editor (Dr. Gregory Foltz) and anonymous reviewers for their constructive comments that significantly improve the quality of this manuscript. Numerical simulations were conducted remotely at Beijing Super Cloud Computing Center. The authors declare no conflicts of interest.

Data availability statement.

Wind data can be retrieved from ECMWF (https://apps.ecmwf.int/datasets/), CCMP (http://data.remss.com/ccmp/), and CFSR (https://hycom.org/dataserver/ncep-cfsr). The GSHHS coastline data are provided by A Global Self-consistent, Hierarchical, High-resolution Geography Database (http://www.soest.hawaii.edu/pwessel/gshhg/). The wave input information of ERA5 can be retrieved from ECMWF (https://apps.ecmwf.int/datasets/). The wave spectra of ECMWF are obtained from the ERA-Interim dataset (https://apps.ecmwf.int/data-catalogues/era-interim/). The bathymetry data are provided by the Global Multi-Resolution Topography (https://www.gmrt.org/GMRTMapTool/). The observation data in Laohutan and Zhifudao oceanic stations are provided by the National Marine Data Center (http://mds.nmdis.org.cn/). These data are also available upon request to Dr. Mao at mhmao@yic.ac.cn.

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  • <sc>Fig</sc>. 1.
    View in gallery
    Fig. 1.

    (a) The 19 typhoons that affected the Bohai Sea in 1992–2022, (b) tracks and the maximum wind speed of Matmo (2014), Rumbia (2018), and Lekima (2019), (c) computational meshes for the Bohai Sea, and (d) bathymetry and locations of wind and wave observations.

  • <sc>Fig</sc>. 2.
    View in gallery
    Fig. 2.

    Time series of observed and modeled (a) wind speeds and (b) wind directions at the oceanic stations and buoys.

  • <sc>Fig</sc>. 3.
    View in gallery
    Fig. 3.

    (a) Time series of observed and simulated SWHs with the bottom friction coefficient of 0.019 and 0.038, (b) scatter diagrams of significant wave heights between simulations and Jason-3 satellite Ku-band data, and (c) Q–Q plots of simulated SWHs using the bottom friction coefficient of 0.019 with distinct wind fields.

  • <sc>Fig</sc>. 4.
    View in gallery
    Fig. 4.

    Wave spectra validation of ECMWF and SWAN simulations during Typhoons (a) Matmo, (b) Rumbia, and (c),(d) Lekima.

  • <sc>Fig</sc>. 5.
    View in gallery
    Fig. 5.

    (a)–(c) Temporal evolutions of the wind and wave fields from 0600 to 1800 UTC 25 Jul 2014 during Matmo, (d)–(f) from 1800 19 Aug to 0600 20 Aug 2018 during Rumbia, and (g)–(i) from 1200 UTC 11 Aug to 0000 UTC 12 Aug 2019 during Lekima. The red dots represent the typhoon center locations, and typhoon centers not marked in the figure are outside the study area.

  • <sc>Fig</sc>. 6.
    View in gallery
    Fig. 6.

    Temporal spectra with a time interval of 6 h at (a) QF104 and (b) QF114. Also shown are the 1D spectra of QF104 at (c) 1200 and (d) 1800 UTC 11 Aug 2019 and (e) 0000 UTC 12 Aug 2019.

  • <sc>Fig</sc>. 7.
    View in gallery
    Fig. 7.

    Directional spectra of QF104 station during Lekima. Also shown are the direction (all using the “going to” convention) of the wind in red vertical lines, the direction of the wave in green vertical lines, and the moving direction of Lekima in orange vertical lines. The separation frequency fS (shown in yellow horizontal dashed lines) divides the wave spectrum into the wind-sea (above the yellow dashed line) part and the swell part (below the yellow dashed line), and the peak energy density of wind seas and swells are shown in white vertical lines.

  • <sc>Fig</sc>. 8.
    View in gallery
    Fig. 8.

    (a) Time series of m0, m1, m2, and m4 and spectral width ε during Lekima at station QF114. The spatial distributions of spectral peakedness parameter Qp (the first row) and the partitions according to Qp (the second row) during (b) Matmo, (c) Rumbia, and (d) Lekima. The red dots represent the typhoon center locations, and typhoon centers not marked in the figure are outside the study area.

  • <sc>Fig</sc>. 9.
    View in gallery
    Fig. 9.

    The 1D wave spectra at five test points during (a) Matmo, (b) Rumbia, and (c) Lekima. Black solid lines denote the wind wave ratio (Ew/Es). Black dotted lines (Ew/Es = 2.0) denote the separation ratio between the wind-sea-dominated and mixed conditions. Black dashed lines (Ew/Es = 0.5) denote the separation ratio between the mixed and swell-dominated conditions. Red solid lines denote whether the spectrum is single peaked or double peaked.

  • <sc>Fig</sc>. 10.
    View in gallery
    Fig. 10.

    Directional spectra in each quadrant of the reference frame based on the radius of the maximum wind speed during Rumbia at (a) 0000 and (b) 0300 UTC 20 Aug 2018.

  • <sc>Fig</sc>. 10c.
    View in gallery
    Fig. 10c.

    As in (a) and (b), but at 0600 UTC 20 Aug 2018.

  • <sc>Fig</sc>. 11.
    View in gallery
    Fig. 11.

    Directional spectra in each quadrant of the reference frame based on the radius of the maximum wind speed during Lekima at (a) 1500, (b) 1800, and (c) 2100 UTC 11 Aug 2019.

Fig. 1.

(a) The 19 typhoons that affected the Bohai Sea in 1992–2022, (b) tracks and the maximum wind speed of Matmo (2014), Rumbia (2018), and Lekima (2019), (c) computational meshes for the Bohai Sea, and (d) bathymetry and locations of wind and wave observations.
Fig. 2.

Time series of observed and modeled (a) wind speeds and (b) wind directions at the oceanic stations and buoys.
Fig. 3.

(a) Time series of observed and simulated SWHs with the bottom friction coefficient of 0.019 and 0.038, (b) scatter diagrams of significant wave heights between simulations and Jason-3 satellite Ku-band data, and (c) Q–Q plots of simulated SWHs using the bottom friction coefficient of 0.019 with distinct wind fields.
Fig. 4.

Wave spectra validation of ECMWF and SWAN simulations during Typhoons (a) Matmo, (b) Rumbia, and (c),(d) Lekima.
Fig. 5.

(a)–(c) Temporal evolutions of the wind and wave fields from 0600 to 1800 UTC 25 Jul 2014 during Matmo, (d)–(f) from 1800 19 Aug to 0600 20 Aug 2018 during Rumbia, and (g)–(i) from 1200 UTC 11 Aug to 0000 UTC 12 Aug 2019 during Lekima. The red dots represent the typhoon center locations, and typhoon centers not marked in the figure are outside the study area.
Fig. 6.

Temporal spectra with a time interval of 6 h at (a) QF104 and (b) QF114. Also shown are the 1D spectra of QF104 at (c) 1200 and (d) 1800 UTC 11 Aug 2019 and (e) 0000 UTC 12 Aug 2019.
Fig. 7.

Directional spectra of QF104 station during Lekima. Also shown are the direction (all using the “going to” convention) of the wind in red vertical lines, the direction of the wave in green vertical lines, and the moving direction of Lekima in orange vertical lines. The separation frequency fS (shown in yellow horizontal dashed lines) divides the wave spectrum into the wind-sea (above the yellow dashed line) part and the swell part (below the yellow dashed line), and the peak energy density of wind seas and swells are shown in white vertical lines.
Fig. 8.

(a) Time series of m0, m1, m2, and m4 and spectral width ε during Lekima at station QF114. The spatial distributions of spectral peakedness parameter Qp (the first row) and the partitions according to Qp (the second row) during (b) Matmo, (c) Rumbia, and (d) Lekima. The red dots represent the typhoon center locations, and typhoon centers not marked in the figure are outside the study area.
Fig. 9.

The 1D wave spectra at five test points during (a) Matmo, (b) Rumbia, and (c) Lekima. Black solid lines denote the wind wave ratio (Ew/Es). Black dotted lines (Ew/Es = 2.0) denote the separation ratio between the wind-sea-dominated and mixed conditions. Black dashed lines (Ew/Es = 0.5) denote the separation ratio between the mixed and swell-dominated conditions. Red solid lines denote whether the spectrum is single peaked or double peaked.
Fig. 10.

Directional spectra in each quadrant of the reference frame based on the radius of the maximum wind speed during Rumbia at (a) 0000 and (b) 0300 UTC 20 Aug 2018.
Fig. 10c.

As in (a) and (b), but at 0600 UTC 20 Aug 2018.
Fig. 11.

Directional spectra in each quadrant of the reference frame based on the radius of the maximum wind speed during Lekima at (a) 1500, (b) 1800, and (c) 2100 UTC 11 Aug 2019.
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