Numerical Simulations of Extratropical Storm Surge in the Bohai Bay Based on a Coupled Atmosphere–Ocean–Wave Model

Abstract

The Bohai Bay is particularly vulnerable to storm surges triggered by extratropical storms or cold-air outbreaks. A coupled atmosphere–ocean–wave model with high resolution is presented and applied to simulate a cold-air outbreak that happened in late November 2004. The surge dynamics are examined in detail. Each model component is separately validated, demonstrating that the triply coupled system can reproduce intense winds, storm surge amplitudes, and significant surface waves with high fidelity. The potential coupling effects on the simulation results are investigated. Six experiments are performed covering various coupling models, and a two-way nesting technique is utilized during simulation. After comparison it shows that there is little difference in wind speed between the three numerical models and that the reanalysis data may significantly underestimate extreme winds. The evident improvements are obtained for peak values of water level when using the atmosphere–ocean coupled configuration versus uncoupled model simulation. It also can be found that the negative surge can be captured by each of the coupled and uncoupled models. The ocean–wave coupled configuration yields significant wave heights that closely match in situ measurements, underscoring the critical role of ocean–wave interaction in storm wave prediction. Our findings confirm that the fully coupled model is well-suited for forecasting extratropical storm surge in Bohai Bay. Northeast winds emerge as the primary driver, with the western coast of Bohai Bay bearing the greatest impact.

1. Introduction

Bohai Bay, one of three embayments comprising the Bohai Gulf, is highly susceptible to storm surges driven by cold-air outbreaks, which occur primarily in spring, autumn, and winter. These surges profoundly affect a severe impact on the topography and landforms near the coast of Bohai Bay [1,2]. Furthermore, storm surges may cause significant human life losses and severe damage to coastal structures, and thus it is very important to get acquainted with the extratropical storm surges occurring in the Bohai Bay [3,4].

As a semi-enclosed, funnel-shaped inner sea at mid-latitudes, the Bohai Sea features shallow depths (average ∼18 m) and gentle slopes (Figure 1). It connects to the Yellow Sea via the Bohai Strait and consists of Bohai Bay, Liaodong Bay, and Laizhou Bay. During cold-air surges, strong easterly winds drive open seawater westward into the bay, causing rapid sea-level rise due to the bay’s restricted geometry.

Extratropical storm surge in Bohai Bay manifests as long-period waves primarily induced by cold-air outbreaks, with surge intensity governed by wind strength and direction. Numerous studies have aimed to observe, interpret, and predict severe storm surges [5,6,7,8,9,10,11], and numerical simulations have become increasingly vital for coastal planning and disaster mitigation.

Numerical models for storm surge analysis fall into three main categories. The first category, widely adopted, couples ocean models with prescribed wind fields [12,13,14]. Here, ocean models compute water levels, while wind field data, typically from reanalysis products or analytical wind models, serves as surface forcing. For example, Zhao and Jiang [12] developed 20 cold-air scenarios to evaluate the influence of storm tracks, pressure fields, and wind durations on maximum surge in the Bohai Sea using the Finite-Volume Coastal Ocean Model (FVCOM). Mo et al. [13] employed a three-dimensional model driven by Climate Forecast System Reanalysis (CFSR) data to investigate the roles of wind direction, speed, and cyclone–tide interactions.

The second category uses uncoupled atmospheric and ocean models [6,15,16,17], where winds from atmospheric simulations force separate ocean runs. Li et al. [6] used Fifth-Generation Mesoscale Model (MM5) winds to drive surge simulations, identifying wind stress as the dominant surge mechanism. Ding and Ding [15] forced FVCOM with outputs from the Weather Research and Forecasting (WRF) system to reproduce the October 2003 surge and later assessed land reclamation impacts [16]. Li et al. [17] integrated the Regional Ocean Modeling System (ROMS) with Quick Scatter Meter/National Center for Environmental Prediction (QSCAT/NCEP) wind stress to model surge and inundation along the western Bohai Gulf.

The third category encompasses fully multi-field coupled models [5,18,19,20,21,22,23]. Warner et al. [5] developed a Coupled Ocean–Atmosphere–Wave–Sediment Transport (COAWST) modeling system, combining the ocean model (ROMS), the atmosphere model (WRF), the wave model (Simulating WAves Nearshore, SWAN), and the sediment model (Community Sediment Transport Model, CSTM), demonstrating improved storm intensity prediction. The COAWST system was originally developed to evaluate model sensitivity during the simulation of Hurricane Isabel in 2003. Subsequently, it was applied to hindcast Hurricane Ivan in 2004 [18]. A series of sensitivity experiments then assessed the effects of coupling on the atmospheric, oceanic, and wave predictions during the tropical cyclone (TC). Results revealed a marked improvement in storm intensity forecasts when using the fully atmosphere–ocean–wave coupled configuration compared to uncoupled simulations. Further, to examine atmosphere–ocean–wave interactions during tropical cyclones, Hurricane Ida (November 2009) and Typhoon Kai-tak (1213) (August 2012) were simulated with COAWST [19,20]. Li et al. [21] employed a coupled atmosphere–ocean model to analyze the mid-October 2003 extratropical surge in Bohai Bay but omitted wave dynamics. However, waves play a crucial role in reshaping the bay’s seabed and coastline by lifting and redistributing sediment. Incorporating a wave component into the coupled framework is therefore essential for accurately capturing seabed and nearshore morphological changes during storm surges [3,24].

As noted above, the Bohai Bay remains highly prone to extratropical storm surges and, while numerous studies have approached the topic from various angles [3,4,6,12,15,16,17], few have used a fully coupled atmosphere–ocean–wave model. To enhance surge forecasting and mechanistic insight for Bohai Bay, we introduce such a three-way coupled system, in which each component exchanges data fields via two coupling packages. This coupled model is applied to simulate an extratropical storm surge that happened in November 2004. The potential coupling effects on the simulation results are investigated. Six experiments are performed covering different coupling ways. The calculated results are compared with observation data, which identifies whether the fully coupled model can simulate the winds and ocean hydrodynamics accurately. Section 2 describes component models, including atmospheric models, ocean models, and wave models. In addition, the coupling packages and methods are introduced. Section 3 outlines the experiment design and model settings. Section 4 presents the calculated results and discusses the impact of different coupling ways on storm surge simulation. Finally, Section 5 summarizes our findings and offers conclusions.

2. Numerical Models

2.1. WRF

The atmospheric component of the coupled system is the WRF model, a next-generation mesoscale numerical weather prediction model developed by the National Centre for Atmospheric Research (NCAR, Boulder, CO, USA) and collaborating institutes. This model has been widely employed for both real-world and idealized simulations. Numerous studies demonstrate that WRF performs reliably across scales ranging from meters to thousands of kilometers [25,26,27].

The WRF model solves the fully compressible Eulerian equations using terrain-following hydrostatic-pressure coordinates to simulate various atmospheric variables. The modeling framework in the WRF model offers flexible configuration options, allowing users to choose different parameterizations for key atmospheric processes, including microphysics, cumulus schemes, boundary-layer treatments, and radiation physics. In the present study, the WRF v3.6 is coupled with the ocean model ROMS and wave model SWAN.

The wave-induced surface roughness at the coupling interface is computed in WRF using the following relation [28]:

$$z_0=3.35H_s{\left({\displaystyle \frac{u^{*}}{c_w}}\right)}^{3.4}+0.11{\displaystyle \frac{\nu }{u^{*}}}$$

(1)

where $z_0$ is the roughness length, $H_s$ is the significant wave height, $u^{*}$ is the wind friction speed, $c_w$ is the phase speed at the peak period, and $\nu$ is the kinematic viscosity.

2.2. ROMS

The ROMS model is a free-surface, sigma-coordinate, primitive equations ocean model and widely used for numerical simulations in physical oceanography [29,30]. The ROMS ocean model solves the Reynolds-averaged Navier–Stokes equations based on the hydrostatic and Boussinesq approximations [31]. Here, ROMS v3.6 is integrated into the coupled framework.

The governing equations in Cartesian coordinates are shown as follows. The Reynolds-averaged formulation of the momentum equations in the x- and y-directions are:

$${\displaystyle \frac{\partial u}{\partial t}}+\overrightarrow{v}\cdot \nabla u-fv=-{\displaystyle \frac{\partial \varphi }{\partial x}}-{\displaystyle \frac{\partial }{\partial z}}\left(\overline{u^{\prime }{w}^{\prime }}-\nu {\displaystyle \frac{\partial u}{\partial z}}\right)+F_u+D_u$$

(2)

$${\displaystyle \frac{\partial v}{\partial t}}+\overrightarrow{v}\cdot \nabla v+fu=-{\displaystyle \frac{\partial \varphi }{\partial y}}-{\displaystyle \frac{\partial }{\partial z}}\left(\overline{v^{\prime }{w}^{\prime }}-\nu {\displaystyle \frac{\partial v}{\partial z}}\right)+F_v+D_v$$

(3)

The equation of state is:

$$\rho =\rho \left(T,S,P\right)$$

(4)

Hydrostatic balance yields:

$${\displaystyle \frac{\partial \varphi }{\partial z}}=-{\displaystyle \frac{\rho g}{{\rho }_0}}$$

(5)

Continuity for an incompressible fluid is:

$${\displaystyle \frac{\partial u}{\partial x}}+{\displaystyle \frac{\partial v}{\partial y}}+{\displaystyle \frac{\partial w}{\partial z}}=0$$

(6)

Closure is achieved by parameterizing Reynolds stresses and turbulent tracer fluxes:

$$\overline{u^{\prime }{w}^{\prime }}=-K_m{\displaystyle \frac{\partial u}{\partial z}}$$

(7)

$$\overline{v^{\prime }{w}^{\prime }}=-K_m{\displaystyle \frac{\partial v}{\partial z}}$$

(8)

where u, v, and w are the components of speed vector $\overrightarrow{v}$ in the x, y, and z directions, respectively, t is time, T is the temperature, S is the salinity and P is the pressure, g is gravity acceleration, $\rho$ is the water density, $\varphi$ is the dynamic pressure, $f$ is the Coriolis parameter, D is the diffusive term, F is the forcing term, including surface wind stress and wave radiation stress, and $K_m$ is the eddy viscosity for momentum.

2.3. SWAN

Accurate wave prediction is essential for storm surge modeling. In this study, we employ the third-generation spectral wave model SWAN (v40.91A). SWAN simulates wind-wave generation and propagation in coastal waters, incorporating key processes such as refraction, diffraction, shoaling, nonlinear wave–wave interactions, and energy dissipation [32,33]. Specifically designed for shallow-water environments, SWAN solves the action balance equation:

$${\displaystyle \frac{\partial N}{\partial t}}+{\displaystyle \frac{\partial c_{x}N}{\partial x}}+{\displaystyle \frac{\partial c_{y}N}{\partial y}}+{\displaystyle \frac{\partial c_{\sigma }N}{\partial \sigma }}+{\displaystyle \frac{\partial c_{\theta }N}{\partial \theta }}={\displaystyle \frac{S_w}{\sigma }}$$

(9)

where N is the action density spectrum, $\sigma$ is the relative radian frequency, $\theta$ is direction normal to the wave crest, x and y are coordinate space, and $c_x$ and $c_y$ are the group velocities in x- and y-directions, respectively. $c_{\sigma }$ is the propagation speed in frequency space and $c_{\theta }$ is a speed in directional space, and $S_w$ is the combined source and sink terms of wave energy density.

2.4. Coupled WRF–ROMS–SWAN Model

The WRF atmosphere model, ROMS ocean model, and SWAN wave model are coupled via the open-source Model Coupling Toolkit (MCT, https://web.cels.anl.gov/projects/climate/mct/, accessed on 1 July 2025) and the Spherical Coordinate Remapping and Interpolation Package (SCRIP, https://github.com/SCRIP-Project/SCRIP, accessed on 1 July 2025) [34]. MCT provides a fully parallelized framework using MPI for exchanging model variables, mesh regridding, and time averaging [35]. In addition, the grid points have to be interpolated for data exchange between different model grids and the SCRIP can be competent for this job. The SCRIP computes addresses and weights for remapping and interpolating fields between different grids [36].

During the ocean–atmosphere–wave coupling, model variables are exchanged as follows: ROMS receives wind stress and heat flux parameters from WRF and conversely supplies WRF with updated sea surface temperature values; the wave height, period, length, direction, and so on are passed from SWAN to ROMS; the sea surface height and depth averaged currents are passed from ROMS to SWAN; the 10 m winds are passed from WRF to SWAN; and the sea surface roughness in WRF is computed by significant wave height, length, period, and so on. Figure 2 illustrates the data-exchange pathways. All three models support parallel execution via MPI on distributed-memory architectures.

3. Model Application

We simulate the storm surge induced by a cold-air outbreak in November 2004. Arctic air masses from Siberia advected across the Bohai Sea. The coupled system runs from 20 to 27 November 2004, with all times in Coordinated Universal Time (UTC). To assess the contribution of each component, we conduct six experiments (

Table 1. Modeling experiments.

Experiment	Component
EXP1 (3-Way)	WRF–ROMS–SWAN coupling
EXP2 (2-Way)	WRF–ROMS coupling
EXP3 (2-Way)	WRF–SWAN coupling
EXP4 (1-Way)	SWAN
EXP5 (1-Way)	WRF
EXP6 (1-Way)	ROMS

). The first (EXP1) implements fully coupled WRF–ROMS–SWAN integration (three-way), exchanging fields every 10 min. Experiments 2 and 3 perform two-way coupling between WRF–ROMS and WRF–SWAN (two-way). The final three (EXP4–EXP6) run each model independently (one-way), driven by ECMWF’s ERA-Interim reanalysis.

3.1. Atmospheric Model Setup

The WRF computational domain and associated topography are depicted in Figure 3. A coarse domain of 150 × 150 grid points at 10 km spacing was configured to fully encompass the storm and minimize open-boundary effects. The domain extends roughly from 29.0° N to 42.5° N and 112.5° E to 130.5° E. A nested grid is employed at three times finer horizontal resolution. Vertical discretization consists of 44 non-uniform σ levels. Time steps of 60 s (coarse) and 20 s (nest) are applied.

The following WRF parameterizations were selected: time discretization was achieved with a third-order Runge–Kutta scheme and spatial derivatives were handled by a fifth-order scheme, Lin microphysics [37], Noah land-surface model [38], Monine–Obukhov surface-layer scheme, Rapid Radiative Transfer Model (RRTM) longwave radiation [39], Dudhia shortwave radiation [40], Yonsei University (YSU) planetary boundary-layer scheme [41], and Kain–Fritsch cumulus parameterization [42]. Initial and lateral boundary conditions were obtained from ERA-Interim reanalysis data (0.5°/6 h). Further details are provided by Skamarock et al. [43].

3.2. Ocean Model Setup

The ROMS computational domain and seafloor topography are shown in Figure 4, with open southern boundary and closed boundaries on the remaining sides. The ROMS domain is configured to encompass the entire Bohai Sea and most of the Yellow Sea (117° E–127° E, 35° N–41° N), with grid spacings of 0.04° in longitude and 0.03° in latitude. There are 250 × 200 grid points for coarse domain and the horizontal resolution ratio between the nest grid and the coarse grid is 3. Six sigma levels are used in the vertical direction. Time steps of 60 s are used in the coarse domain and one-third of that value in the nested domain.

A third-order upstream scheme is used for horizontal momentum advection, together with the Mellor-Yamada 2.5 turbulence closure for vertical mixing. Bottom friction is represented by a quadratic parameterization with a drag coefficient of 0.012. Bathymetric data were compiled from high-resolution (1 min) National Geophysical Data Center of National Oceanic and Atmospheric Administration (NOAA) and Sung Kyun Kwan University’s (SKKU) digital elevation models [44], then smoothed via a second-order Shapiro filter. Coastline information was obtained from NOAA’s World Vector Shoreline database.

Both open and closed lateral boundary conditions are implemented; open boundaries incorporate free surface dynamics, 2D momentum conservation, and 3D momentum radiation physics. Tidal forcing includes eight principal constituents (M2, S2, N2, K2, K1, O1, P1, and Q1), with water surface elevations derived from Oregon State University’s OTPS (OSU Tidal Prediction Software, https://www.tpxo.net/otps, accessed on 1 July 2025) tidal prediction system. Closed boundaries employ no-slip wall conditions for surface elevation and normal speed components. Initial conditions assume quiescent flow (zero speed) with water levels set to mean sea level.

3.3. SWAN Model Setup

SWAN executed the same grid and bathymetry as ROMS (Figure 4). Initial conditions were generated via a stationary spin-up using reanalysis wind data. The JONSWAP spectrum served as the boundary condition for the initial stationary steady-state simulation and the non-stationary simulation. The relevant parameters are derived from the solutions of the global WaveWatch 3 (WW3) model.

In this configuration, nonlinear quadruplet wave interactions were activated, and wind-wave growth was parameterized following the Komen formulation [45]. Additional wave parameters used in this study are summarized in

Table 2. SWAN parameters.

Parameters	Value
Frequency range (Hz)	0.05–1.0
Frequency bins	24
Breaking constant	0.75
Direction Full	circle
Direction bins	72
Bottom friction	Madsen formulation
Friction parameter	0.05
Minimum water depth (m)	0.05

. The model ran with a 120 s time step, and outputs of significant wave height, wave period, and wavelength were recorded every 10 min.

4. Results and Discussion

4.1. Atmosphere Results

Accuracy representation of the wind field is essential for realistic storm surge and wave state simulations. Wind vectors at 4 h intervals from 2100 UTC 23 November 2004, as produced by EXP1, are presented in Figure 5. At 2100 UTC on 23 November, easterly to northeasterly winds dominated the northern and central Bohai Sea. The wind speed increased rapidly, reaching a peak of 16.0 m/s at approximately 0100 UTC on 24 November (Figure 5b). Thereafter, wind speeds declined gradually to about 12 m/s by 0900 UTC on 24 November. Winds exceeding Beaufort force 6 persisted for over 10 h, with a prevailing northeast direction across most of the Bohai Sea (Figure 5d).

Sea level temperature and pressure at 4 h intervals are shown in Figure 6. A pronounced temperature drop was simulated, with surface temperatures in Bohai Bay falling by nearly 10 °C over 12 h. Sea level pressure decreased from north to south as a cold high-pressure system advanced southward. Prior to 2100 UTC on 23 November (Figure 6b), the intensifying pressure gradient was associated with increasing wind speeds. In summary, the southeastward movement of the northwest cold high pressure caused abrupt cooling and sustained strong winds, triggering the extratropical storm surge.

Wind speed time series at Huanghua station (0000 UTC 23 November 2004) are compared in Figure 7 for EXP1, EXP2, EXP5, and ECMWF reanalysis. It was found that the 10 m winds during the cold-air outbreak are reasonably well captured. The three numerical models produce similar results. When contrasting the three-way coupling with the two-way runs, the three-way model yields slightly lower wind speeds. This is attributed to the increased surface roughness computed via Equation (1) after SWAN was integrated into the WRF–ROMS framework. The results do suggest that wave height has notable effects on wind field and that the higher the wave height is, the larger the effect is. Through the comparison of the results between the two-way model and the WRF-only model, it can be seen that the wind velocities obtained by one-way model are systematically smaller, indicating that sea surface temperature significantly influences wind simulation.

Unfortunately, in situ wind observations are unavailable, preventing direct validation. The simulated winds tend to exceed the reanalysis dataset. Previous work has shown that WRF overestimates weak winds, whereas reanalysis data underestimates extremes [21]. The extreme value of predicted wind speed is around 16 m/s and the value extracted from ECMWF database is 12 m/s, and the difference is about 25%. It also indicates that the reanalysis data may significantly underestimate the extreme winds and the storm surge simulated based on reanalysis data may be underestimated.

Figure 8 compares 1-hourly wind vectors from the three-way model and ECMWF reanalysis data at Station Huanghua during the cold wave. As noted, the simulated winds are noticeably stronger than the winds extracted from reanalysis data. In addition, during the first several hours, the wind directions were west and the wind speeds were small. After that, the winds veered rapidly to the northeast and intensified. By ~0100 UTC 24 November, wind speeds peaked near 16 m/s. Subsequently, winds weakened and gradually shifted northwestward. The modeled wind directions exhibit a westward bias relative to reanalysis. Furthermore, after noon on 25 November, winds swung from north to west, with westerlies persisting ~20 h. These wind-field characteristics directly influence water-level simulations, as discussed in the next section.

4.2. Ocean Results

Storm surge denotes the anomalous sea level variation induced by severe meteorological disturbances. The measured and simulated water levels at Station Huanghua are compared in Figure 9. Before cold-air outbreak, sea level fluctuation primarily reflected the astronomical tide. During cold-air outbreak, the high water level within each tidal cycle rose progressively under strong winds, diverging from the astronomical tide. Maximum water elevation reached approximately 2.2 m during the high-tide event occurring at 0500 UTC on 24 November 2004. The surge peaked about four hours after the wind speed maximized, indicating a lag tied to tidal timing. Once the wind weakened and shifted direction, the elevated water levels receded rapidly. Additionally, after reaching peak water level, the high water level within a tidal cycle quickly decreased as the wind direction changed and intensity became weaker. In addition, the water level measured at Station Huanghua also showed a largely negative surge about 57 h after the peak surge arrived and each of the models can capture this negative surge accurately. The minimum water level reached nearly −2.8 m and the driving force is the sustained west wind, which lasted about 20 h (Figure 8). In Bohai Bay, extratropical storm surge is clearly governed by wind direction; offshore winds lower sea level, while onshore winds raise it.

In the one-way case, good agreement is achieved except at extreme values, where simulated peaks are slightly lower than observations. A lag of approximately 0.8 h precedes the surge maximum, attributable to bulk-flux forcing by ERA-Interim, whose winds veer more southward than predicted (Figure 8). The significant improvements are obtained for peak values when atmosphere–ocean coupling between WRF and ROMS is activated (EXP1 and EXP2), demonstrating WRF’s ability to reproduce the cold-air outbreak’s strong wind field. Peak timing was well captured, and only marginal improvements were observed when waves were included, suggesting a limited impact of wind waves on Bohai Bay water levels for this event. Xia et al. [46] developed a coupled SWAN–ADCIRC model to investigate wind waves and storm tides during extratropical surges in the Bohai Sea, finding similarly small wave effects on water level.

For validation, Root Mean Square Error (RMSE) quantifies prediction error and Normalized Root Mean Square Error (NRMSE) normalizes it across scales, which are introduced here:

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{{\displaystyle \sum _{n=1}^N{\left({\stackrel{⌢}{y}}_n-y_{ n}\right)}^2}}{N}}}$$

(10)

$$\mathrm{NRMSE}={\displaystyle \frac{\mathrm{RMSE}}{y_{\max }-y_{\min }}}$$

(11)

where N represents the number of observations. ${\stackrel{⌢}{y}}_n$ represents model simulation outputs, while $y_n$ corresponds to actual observed measurements. $y_{\max }$ and $y_{\min }$ correspond to the upper and lower bounds of the dataset, representing the highest and lowest observed values, respectively.

Table 3. Statistics between experiments and observations of the water level from 1600 UTC 22 November 2004 to 1600 UTC 25 November 2004.

Experiment	Water Level (m)
	RMSE (NRMSE)	Bias
EXP1	0.18 (4.8%)	0.025
EXP2	0.15 (4.0%)	−0.018
EXP6	0.15 (4.1%)	−0.064

summarizes RMSE, NRMSE, and bias for all experiments. All configurations achieve NRMSE values below 5%. The best agreement is achieved by two-way coupling model (EXP2) and the model can preferably reproduce the dynamic change in the water level. The model obtains the smallest NRMSE (4.0%) and is slightly negatively biased around 18 cm. Although the three-way coupling model can accurately predict the maximum water level during the period of storm surge, the model obtains the highest RMSE (18 cm) and NRMSE (4.8%), alongside a positive bias (+0.025 m), indicating a tendency to overestimate water levels. The one-way ROMS run (EXP6) maintains a low global NRMSE (4.1%) but generally underestimates the extreme surge elevation (Figure 9).

As noted in the introduction, Bohai Bay is highly susceptible to rapid and pronounced sea-level fluctuations under extreme weather. Figure 10 illustrates the spatial distribution of total sea level obtained from the ocean model. Due to the strong eastward wind, vast volumes of seawater surged into Bohai Bay and the water level in this area increased sharply during storm surge, causing a sharp rise in water level (Figure 10a). Peak elevations exceeding 2 m occurred along the bay’s western shore, whereas the northern Yellow Sea coast experienced a ~2 m depression. During the negative surge phase, westerly winds drove offshore currents from Bohai Bay, resulting in water accumulation along the northern Yellow Sea coast (Figure 10b). Wind strength and direction emerge as the primary controls on surge magnitude, with northeastern winds identified as the chief driver of extratropical storm surges in Bohai Bay, particularly along its western coasts.

Wind stress directly governs surface current velocities, as shown by the 12 h average outputs in Figure 11. Under initial surge conditions, mean surface speeds remained below 0.2 m/s in a chaotic flow regime (Figure 11a). Pre-peak surge conditions exhibited intensified inflow currents exceeding 0.5 m/s, particularly along the northeast coast, where velocities exceeded those in southern areas (Figure 11b). Post-peak, velocities declined rapidly, leaving residual higher flows concentrated nearshore (Figure 11c,d). Ahead of the pronounced negative surge, currents reversed out of Bohai Bay, again exceeding 0.5 m/s and driving increased southward flow (Figure 11e,f). Notably, strong westward currents appear during the early cold wave (Figure 11b), whereas eastward currents dominate during the negative surge (Figure 11f). These patterns underscore that average surface-current direction in Bohai Bay during a storm surge is firmly dictated by the prevailing wind direction (Figure 8).

4.3. Wave Results

One of direct consequence of sustained winds is the transfer of energy from the atmosphere to the ocean, producing surface waves. Owing to the sea-level rise induced by strong onshore wind, water depths in the nearshore zone increased during the extratropical storm surge. Consequently, bottom-boundary-layer energy dissipation diminished with greater depth, promoting storm waves of increased height and extended period. As wind-induced waves occupy a larger area, they influence the surge’s hydrodynamic [47]. Moreover, wave growth modifies sea surface roughness, amplifying wind stress effects on the surge.

The spatial distribution of significant wave heights ($H_s$) during storm surge for the fully coupled run (EXP1) is shown in Figure 12. The wave heights in the south were markedly stronger than those in the north. Due to the accumulation and propagation of energy and also because of the increase in alongshore water depths resulting from the high landward winds, which were beneficial to wave growth, the wave heights along the coasts of Bohai Bay increased. Compared with Figure 5, the significant wave heights rose with wind speed. At 0100 UTC on 24 November 2004, the maximum wave height exceeds 4 m in the central and eastern Bohai Bay. With the decrease in the wind speed, the wave height decreased correspondingly. The changes in wind velocities could lead to the changes in the significant wave heights and the results revealed a good correlation between them. In addition, the distribution of wave height is not entirely consistent with that of the wind speed, which may result from the difference in the seafloor topography.

To assess the influence of tides and storm surges on wind waves, the simulated results were compared with observations. Figure 13 compares modeled results and measured significant wave heights at Station Huanghua. Among the three configurations, the three-way coupling model achieved the closest agreement. It accurately captured the variability of $H_s$ during the surge, resolving both high and low wave events. The maximum $H_s$ peaked at 2.6 m at 0100 UTC on 24 November 2004, fell to 2.1 m at 0330 UTC on 24 November 2004, and then rose again to 2.5 m at 0630 UTC on 24 November 2004. Finally, the significant wave height dropped to 1.4 m at 1100 UTC on 24 November 2004. The three-way model can successfully depict this varied process, while the one- and two-way models fail. This demonstrates that the ocean–wave interaction is crucial to surface wave simulation and the three-way coupled model can well reflect the developing and changing process of storm wave. In addition, according to the growth process of wind waves (Figure 13), it can be seen that the duration of wave growth is short in the southwest coast of the Bohai Bay and the big waves are generated in a short period of time by strong landward winds.

Comparing the two-way and SWAN-only runs (Figure 13) reveals that the one-way model consistently underestimates wave heights. This underestimation stems from the reanalysis wind speeds being lower than those in the coupled simulations (Figure 7). Relative to the two-way run, the three-way model’s wave heights vary with tidal currents, producing more realistic patterns. Yin et al. [48] introduced a joint numerical of wave and tide-surge motion to examine the influence of interaction effects in the Bohai Sea. They reported an immediate 8% change in wave heights due to wave–tide-surge coupling. In this study, the mean interaction effect on wave height is approximately 10%, highlighting the importance of ocean–wave coupling for accurate storm wave simulation.

Table 4. Statistics between experiments and observations of the significant wave height from 2100 UTC 23 November 2004 to 1100 UTC 25 November 2004.

Experiment	Significant Wave Height (m)
	RMSE (NRMSE)	Bias
EXP1	0.26 (9.6%)	−0.01
EXP3	0.33 (12.1%)	0.17
EXP4	0.27 (9.8%)	−0.06

summarizes statistics for significant wave height. All models reproduce wave heights effectively, with NRMSE values between 9.8% and 12.1%. The three-way coupling model (EXP1) achieves a low RMSE (26 cm, 9.6%) and an almost zero bias (1 cm). The one-way uncoupled model (EXP4) also shows globally low NRMSE (9.8%) but fails to capture $H_s$ variability, resulting in slightly lower wave heights during the surge. These shortcomings persist in the two-way coupled model (EXP3), which yields the highest NRMSE of 12.1%. This model exhibits a consistent positive bias of ~0.17 m, indicating a systematic tendency of the two-way approach to overpredict wave heights.

Figure 14 illustrates the spatial distribution of mean wave period from the 2100 UTC 24 November 2004 as simulated by EXP1. The mean period values in Bohai Bay were below 5 s, with longer periods in the south than that in the north and shorter intervals near the coast. In contrast to simulated results of winds (Figure 5), it is obvious that the east–northeast (ENE) winds were more helpful to the growth of wind wave than the northeast (NE) winds for the central Bohai Bay. We can see that the significant wave heights were close to 4 m and the mean wave periods were over 5 s under ENE wind condition (Figure 12b or Figure 14b). Conversely, under NE winds, $H_s$ stayed below 3 m and mean periods dropped below 4 s (Figure 12c or Figure 14c). Notably, the highest $H_s$ and mean periods occurred just outside Bohai Bay’s mouth.

Figure 15 presents mean wave period time series at Huanghua Station. The one- and two-way models overpredicted mean periods by approximately 30% compared to the three-way simulation. Observed values ranged from 1.5 to 4.5 s, displaying significant tidal-driven fluctuations. This reinforces that ocean–wave interaction must be incorporated for accurate surface-wave modeling during storm surges.

5. Summary and Conclusions

A three-way coupled atmosphere–ocean–wave model has been developed for Bohai Bay, integrating the WRF atmospheric model, ROMS oceanic model, and SWAN wave model via the MCT and SCRIP coupling libraries. The coupled model was applied to simulate an extratropical storm surge happened in November 2004. The dynamic process of the storm surge is analyzed. The coupling effects on the simulation results are investigated with six numerical experiments. Through comparative analysis, all model components are validated independently. The key conclusions are as follows:

• Minor differences in 10 m wind speed were observed between coupled and uncoupled runs, with sea surface temperature exerting a significant influence on wind simulation.
• During the cold-air outbreak, peak water-level timing was well reproduced when WRF–ROMS coupling was enabled, with the two-way configuration achieving the closest match. Although the three-way model accurately predicted maximum surge heights, it tended to overestimate water levels.
• A time lag of ~0.75 h was noted in the one-way ROMS run before the surge peak, and this configuration generally underestimated storm-surge magnitude. Inclusion of SWAN yielded small further improvements, indicating a limited impact of waves on water-level simulations in Bohai Bay for this event.
• Wind and tidal currents strongly modulated wave growth and, in turn, wave dynamics enhanced the effective wind stress driving the surge. The three-way coupling demonstrated the greatest improvement in wave prediction.

The coupled framework establishes a robust basis for integrating sediment transport modules. Future work will focus on sediment entrainment and transport patterns during storm surges using this multi-field coupling approach.