Wind and Wave Climatic Characteristics and Extreme Parameters in the Bohai Sea

Abstract

The Weather Research and Forecasting (WRF) model is employed to conduct numerical simulations and simulated acquisition of a 30-year (1993–2022) wind field dataset for the Bohai Sea. The simulated WRF wind field is subsequently used to drive the Simulating Waves Nearshore (SWAN) model, producing a corresponding wave field dataset for the same period in the Bohai Sea. Using these datasets, we analyzed the extreme value distributions of wind speed and significant wave height in the study area. The results reveal that both the annual mean wind speed and significant wave height exhibit a ring-like spatial pattern. The highest values are concentrated in the southern Liaodong Bay to the central Bohai Sea region, with a gradual radial decrease toward the periphery. Specifically, values decline from the center outward, from southeast to northwest, and from offshore to nearshore regions. The Gumbel extreme value distribution is applied to estimate 100-year return period extremes, yielding maximum wind speeds of 37 m/s and significant wave heights of 6 m in offshore areas. In nearshore regions, the 100-year return period wind speeds range between 20–25 m/s, while significant wave heights vary from 2 to 3 m. This study provides important scientific basis and decision-making reference for the design of offshore extreme conditions.

1. Introduction

Extensive research has been conducted on the extreme environment of wind and waves, particularly in the context of the global economy and the ocean as a strategic space. The significance of the ocean for international economic development has become increasingly evident [1]. However, with the continuous deepening and expansion of marine development in fisheries, energy, and other fields, the frequency and intensity of marine disasters are also increasing significantly [2,3,4], which poses a grave threat to the economic stability and ecological security of coastal regions. The statistical analysis of the “China Marine Disaster Bulletin” found that the number of deaths or disappearances caused by marine disasters in China from 2000 to 2015 was as high as 2599, of which the loss caused by wave disasters accounted for 73.7% [5]. Statistical data indicated that the direct economic loss incurred due to marine disasters in China in 2022 amounts to approximately CNY 24 billion [6]. Consequently, there is an imperative need to undertake rigorous research on the extreme environment of wind and waves.

In marine science, a comprehensive understanding of wind–wave characteristics, accurate prediction of extreme events, and assessment of climate change impacts on marine environments are crucial. For wind–wave studies in the Bohai Sea, the Weather Research and Forecasting (WRF) model has been widely employed to simulate wind waves driven by high-resolution wind fields. For example, Luo [7] combined WRF-generated high-resolution wind fields with the Simulating Waves Nearshore (SWAN) model to investigate seasonal spatial distributions of wind and wave characteristics in the Bohai Sea. Similarly, Liu [8] utilized the WRF model for long-term simulations to examine spatiotemporal characteristics of low-level atmospheric ducts in the South China Sea. Furthermore, significant progress has been achieved in optimizing the coupling between WRF and wind–wave models. Wu et al. [9] developed a comprehensive typhoon modeling system by constructing and implementing a coupled WRF–SWAN model, demonstrating its effectiveness in supporting typhoon forecasting. Du et al. [10] systematically examined the impacts of physical parameterization schemes in the WRF model on wind speed prediction accuracy and wind energy resource assessment, subsequently optimizing the model’s performance for wind–wave prediction in the Bohai Sea. Chen [11] conducted a numerical hindcast of the most intense tropical cyclone recorded in the eastern South China Sea, quantifying extreme values of wind speed, wave height, current velocity, and water level while analyzing their characteristic patterns. Wang et al. [12] utilized the SWAN wave model to perform a numerical simulation of the wind field and waves in the Bay of Bengal and conducted an analysis of the temporal and spatial distribution characteristics and extreme parameters of wind and waves. Islek et al. [13] utilized the SWAN model to evaluate the long-term changes of wave characteristics in the Black Sea and analyzed the differences of wave characteristics in different regions. The study provided fundamental data for understanding the characteristics of wind waves in specific sea areas and demonstrated the effectiveness of the model in wind wave simulation.

Extreme wind speeds and wave conditions are critical parameters for coastal engineering design. In China’s coastal regions, statistical models utilizing meteorological station data have been conventionally employed to determine design wind speed criteria [14]. The Gumbel distribution has proven particularly effective for characterizing extreme wind and wave conditions during severe weather events [15,16,17]. Through Gumbel distribution fitting, reliable estimates of extreme wind speeds and significant wave heights can be obtained, providing essential data for structural assessment and disaster prevention strategies. However, these methods face limitations in data-scarce regions or areas with poor observational infrastructure, as they fundamentally depend on long-term, high-quality wind speed measurements. Wei [18] demonstrated successful applications in storm wave prediction by forecasting significant wave height, mean wave period, and related parameters, highlighting the practical value of extreme value analysis. Furthermore, the investigation of climate change impacts on marine environments has emerged as a significant research focus in this domain. Lobeto et al. [19] systematically investigated future trends of extreme waves under various climate change scenarios, employing a wave climate simulation ensemble to project changes in extreme significant wave heights across global ocean surfaces. Yuksel [20] conducted comprehensive wind–wave simulations in the Marmara Sea by integrating wind field data with the SWAN model, specifically analyzing extreme wave modifications and associated topographic effects. These studies collectively underscore the critical role of extreme value analysis in assessing climate change impacts on marine environments, while particularly highlighting the methodological significance of Gumbel extreme value theory applications.

The research on wind and wave modeling under specific conditions in the Bohai Sea is limited. This study is not only limited to the application of a single model, but also uses the WRF model and wind and wave models (such as SWAN), which provides a more comprehensive perspective for the simulation of the marine environment and meteorological conditions in the Bohai Sea. The traditional extreme value distribution method was optimized, which improved the accuracy and reliability of wind speed prediction. Through the simulation and prediction of extreme ocean wave and wind speed events, the prediction ability of extreme events in a complex marine environment is improved, which provides strong support for offshore areas to cope with climate change and marine disasters.

2. Data Sources and Research Methods

2.1. Numerical Simulation of Wind Field

WRF is used to simulate the wind field in the study area as shown in Figure 1a. The water depth is white, and the water depth is blue. Tropical cyclone tracks are identified through systematic screening of tropical cyclone data obtained from the China Typhoon Network (http://typhoon.weather.com.cn/, accessed on 27 March 2025), as shown in Figure 1b. To ensure simulation accuracy while maintaining computational efficiency, a two-layer nested grid configuration is implemented in the model set-up [21]. This approach optimally balances numerical precision with computational resource requirements, ensuring both reliable results and practical feasibility. The numerical simulation employs a two-domain nested grid system with horizontal resolutions of 30 km (outer domain) and 10 km (inner domain), maintaining a 3:1 refinement ratio. To ensure numerical stability, the time integration step is set to 50 s for the inner domain and correspondingly 150 s for the outer domain, consistent with the spatial resolution ratio. The computational grids consist of 63 × 75 (outer domain) and 112 × 130 (inner domain) grid points, respectively. Output frequency is configured at 3 h intervals for the outer domain (d01) and 1 h intervals for the inner domain (d02). The model utilizes a Lambert conformal projection with 37 vertical layers extending to a top pressure of 5000 Pa. As shown in Figure 1, the simulation covers geographical ranges of 25° N–46° N, 112° E–134° E (d01) and 30° N–42° N, 116° E–128° E (d02). The physical parameterization schemes, validated through previous simulation analyses and literature review, are summarized in

Table 1. WRF model parameter settings.

Name	Setting
Microphysical scheme	Lin et al. scheme [22]
Cumulus convection scheme	Kain–Fritsch (new eta) scheme
Longwave radiation scheme	rrtmg scheme
Shortwave radiation scheme	rrtmg scheme
Planetary boundary layer scheme	YSU scheme
Near-ground layer scheme	Revised MM5 Monin–Obukhov scheme
Land-surface process scheme	Unified Noah land-surface model scheme

.

2.2. Numerical Simulation of Wave Field

SWAN (Simulated Waves Nearshore) is the third generation of the nearshore shallow water wave numerical model [23,24,25,26,27]. It was first developed by the Delft University of Technology in the Netherlands and has grown after years of development and improvement. Due to the influence of the flow field, the density of the spectral energy is not conserved, but the action density, the variance density divided by the relative frequency conserved, is only changed with time and space. The equilibrium equation of wave action in a Cartesian rectangular coordinate system is expressed as follows [28]:

$${\displaystyle \frac{\partial N}{\partial t}}+{\displaystyle \frac{\partial C_{x}N}{\partial x}}+{\displaystyle \frac{\partial C_{y}N}{\partial y}}+{\displaystyle \frac{\partial C_{\sigma }N}{\partial \sigma }}+{\displaystyle \frac{\partial C_{\theta }N}{\partial \theta }}={\displaystyle \frac{S}{\sigma }}$$

(1)

where $\sigma$ is the phase frequency, and $\theta$ is the phase frequency. $C_x$ and $C_y$ are propagation velocities in the $x$ and $y$ directions; $C_{\sigma }$ and $C_{\theta }$ are the propagation velocities in the $\sigma$ and $\theta$ directions. The source term $S$ represents the impacts of the wind generation, dissipation, and non-linear wave–wave interactions. The source term $S$ consists of the following parts [29]:

$$S=S_{in}+S_{nl3}+S_{nl4}+S_{ds,w}+S_{ds,b}+S_{ds,br}$$

(2)

where $S_{in}$ represents wind energy input; $S_{nl3}$ and $S_{nl4}$ represent the energy projections of the non-linear interactive waves of three components and four components, respectively; $S_{ds,w}$ represents the white capping dissipation; $S_{ds,b}$ represents the bottom friction; and $S_{ds,br}$ represents the wave breaking due to shallow water.

The wind input term is expressed as follows [30]:

$$S_{in}\left(\sigma ,\theta \right)=A+BE\left(\sigma ,\theta \right)$$

(3)

where A represents linear growth and BE represents exponential growth [31].

$$S_{n/3}\left(\sigma ,\theta \right)=S_{n/3}^{-}\left(\sigma ,\theta \right)+S_{n/3}^{+}\left(\sigma ,\theta \right)$$

(4)

$$S_{n/4}\left(\sigma ,\theta \right)=S_{n/4}^{*}\left(\sigma ,\theta \right)+\delta S_{n/4}^{**}\left(\sigma ,\theta \right)$$

(5)

The white cap dissipation term represents the energy loss of waves in deep water, and the degree of energy dissipation is represented by wave steepness. The expression is as follows [31]:

$$S_{ds,w}\left(\sigma ,\theta \right)=-\mathrm{\Gamma }\overline{\sigma }{\displaystyle \frac{k}{\overline{k}}}E\left(\sigma ,\theta \right)$$

(6)

where $\overline{k}$ and $\overline{\sigma }$ represent the average wave number and the average frequency of waves, respectively.

The formula for bottom friction is expressed as follows [31]:

$$S_{ds,b}\left(\sigma ,\theta \right)=-C_{bottom}{\displaystyle \frac{{\sigma }^2}{g^2{\sinh }^2\left(kd\right)}}E\left(\sigma ,\theta \right)$$

(7)

where $C_{bottom}$ represents bottom friction coefficients.

Battjes and Janssen’s formula is mainly used to describe the crushing effect of shallow water in the SWAN model [31]:

$$S_{ds,br\left(\sigma ,\theta \right)}={\displaystyle \frac{D_{tot}}{E_{tot}}}E\left(\sigma ,\theta \right)={\displaystyle \frac{a_{BJ}{Q}_b\overline{\sigma }}{{\beta }^2\pi }}\left(\sigma ,\theta \right)$$

(8)

where $D_{tot}$ represents energy dissipation rate per unit horizontal area. $Q_b$ represents wave breaking factor. $\overline{\sigma }$ represents average speed.

In this study, a total of 30 years of wind field data from 1993 to 2022 were simulated by WRF, and the SWAN model is driven by the hindcast to calculate the waves in the Bohai Sea. In all cases, the SWAN model is used for non-stationary two-dimensional models to simulate wave propagation during 1993~2022. The calculation area is consistent with the WRF area, the resolution is 0.25° × 0.25°, the calculation time step is 1 h, and the output time step is 3 min. The physical process in SWAN mode is shown in

Table 2. Physical processes in the SWAN mode.

Physical Processes	SWAN Mode
Wind speed index growth part	Komen et al. [32]
White cap	Komen et al. [32]
Coefficient of friction	Hasselmann et al. [33]
Fragmentation caused by water depth	The ratio of maximum significant wave height to depth gamma = 0.73
Nonlinear wave–wave interactions	E1deberky

. The water depth required for the calculation of the SWAN model uses the water depth data of the ETOPO1 global terrain database. ETOPO1 includes land terrain data and ocean water depth data (https://ngdc.noaa.gov/mgg/global/relief/ETOPO1/tiled/, accessed on 27 March 2025).

2.3. Verification of Wind and Wave Fields

The Bohai Sea experienced an extreme wave event from 10 to 12, November 2012, triggered by the interaction between a cold air mass and a cyclonic system. This rare meteorological–oceanic phenomenon is designated as the “11·10” wave event. In the historical data, the “11·10” wave is not common, and the event is successfully simulated. We can infer that the simulation results of the model under other similar complex conditions are also reliable, so this event is selected for research. The location of the observation station is depicted in Figure 2. The observation station information is shown in

Table 3. Calculation points description.

Station	Longitude	Latitude	Data Available
P1	121°22′48″	36°12′00″	2012.11.01.00–2012.11.15.23
P2	120°09′36″	38°19′48″	2012.11.01.00–2012.11.15.23
P3	119°00′00″	38°52′48″	2012.11.01.00–2012.11.15.23
P4	120°36′00″	39°30′00″	2012.11.01.00–2012.11.15.23
P5	120°04′48″	39°02′24″	2012.11.01.00–2012.11.15.23
P6	119°51′00″	37°58′12″	2012.11.01.00–2012.11.15.23

. Utilizing the hourly wind and wave data from 1993 to 2022, derived from WRF simulations and SWAN numerical modeling, the simulated results are validated against available observational data. A comparative analysis between the simulated and measured data is conducted [34], with the results shown in Figure 3 and

Table 4. Correlation coefficient between measured data and simulated data.

r	P2	P4	P5	P6
Wind speed	0.972	0.881	0.937	0.958
Wind direction	0.942	0.934	0.887	0.963

. The findings indicate that the simulation demonstrates a high degree of accuracy, with the modeled data exhibiting strong agreement with the observational records. This validation confirms the reliability of the simulated dataset, ensuring its suitability for subsequent extreme value analysis.

3. Analysis of Long-Term Characteristics of Wind Field in Bohai Sea

3.1. Temporal and Spatial Distribution Characteristics

Studying the long-term changes of wind speed and direction is conducive to the development of offshore wind energy and the orientation of wind field location. Using the WRF wind field data from 1993 to 2022, the average wind speed of the Bohai Sea in the past 30 years was analyzed, and the spatial distribution of the annual average wind speed in the past 30 years was obtained, as shown in Figure 4. On the whole, the annual average wind speed shows a decreasing trend from the middle to the surrounding areas and from the far sea to the land. The wind speed peak is above 7 m/s from the south of Liaodong Bay to the center of Bohai Sea. The sea area is greatly affected by the winter monsoon, and the annual average wind field wind direction in most sea areas is northwestward.

The wind farm data from the study area over the past 30 years are seasonally averaged to generate the seasonal mean wind field characteristics, as illustrated in Figure 5a. The results indicate a general trend of increasing wind speed from northwest to southeast, from nearshore to offshore, and from the periphery toward the central Bohai Sea. Notable seasonal variations in wind speed distribution are observed, with the highest seasonal mean wind speeds occurring in autumn and winter. In particular, winter exhibits the most pronounced peak wind speeds, exceeding 8 m/s, whereas summer records the lowest peak values, approximately 5 m/s. The wind speed distribution in spring and summer is relatively uniform, with prevailing wind directions predominantly ranging from southeast to southwest. In contrast, autumn and winter exhibit greater spatial variability in wind speed, with prevailing winds predominantly from the northwest.

In order to analyze the wind field characteristics of the Bohai Sea in greater detail, the monthly average processing was carried out in this sea area. Figure 6b is the monthly mean wind field map of the Bohai Sea. The analysis reveals that during the months of March, April, and May, the wind speed in a substantial portion of the Bohai Sea attained speeds of 4 m/s. In the months of November, December, and January, the wind speed in the southeastern region of the Bohai Sea exceeded 7 m/s, particularly in December. The predominant wind direction is from the northwest. Conversely, the monthly average wind speed in June, July, and August is minimal, with the predominant wind direction being southeast. These summer wind field characteristics have the potential to exert a significant influence on the marine ecosystem and the organization of marine fishery production activities. The maximum wind speeds recorded during different months are primarily concentrated in the south of Liaodong Bay and the central region of the Bohai Sea. This phenomenon holds significant value in the selection of offshore wind power project sites and facilitates effective risk assessment and response measures.

In order to further analyze the distribution of wind speed and wind direction in the Bohai Sea, nine representative points were selected, covering Bohai Bay, Liaodong Bay, Laizhou Bay, Bohai Strait, and central Bohai Sea. The specific location is shown in Figure 6a, which can reflect the spatial distribution characteristics of the wind field more comprehensively. Based on the wind speed and wind direction data of 30 years from 1993 to 2022, the wind rose diagram of each feature point is drawn, as shown in Figure 6b.

As for Figure 6b, it can be concluded that the wind speed of T5 and T6 is low, and the dominant wind speed range is concentrated in 0–6 m/s. The strong wind direction is ENE. The wind speed in Laizhou Bay is mainly 3–9 m/s, the high wind speed of 6–9 m/s appears locally, and the frequency is slightly lower than that of Bohai Bay. The wind speed of T2 is higher, followed by T8, and the strong wind direction is NE and NNE. The wind speed of T9 is the highest in all regions, and the wind speed frequency and wind direction are highly consistent.

3.2. Long-Term Variation Features

Wind is one of the main driving forces of atmospheric motion. Analyzing the long-term trend of a wind field is helpful to understand the evolution law of the wind field in the Bohai Sea. Taking the Bohai Sea as the research object, four characteristic points T1, T2, T3, and T4 (Figure 7a) are selected to represent the wind field characteristics of Bohai Bay, central Bohai Sea, Liaodong Bay, and Laizhou Bay. This kind of point layout can comprehensively reflect the spatial distribution difference and long-term change trend of the wind field in the Bohai Sea.

As for Figure 7a, a general upward trend in wind speed over the 30-year period obtains, with T3 exhibiting higher speeds compared to T1, T2, and T4. The wind speed fluctuated within 0.5 m/s from 1993 to 1997, reached a 30-year high in 1998, and reached a 30-year low in 2019. Figure 7b illustrates the seasonal average trend in wind speed. The wind speed at the four characteristic points in spring fluctuated from 1993 to 1999, peaked in 2001, fluctuated from 2003 to 2013, and peaked in 2021. A notable peak in wind speed is observed in summer in 2018, marking a 30-year high. The wind speed at the characteristic points in autumn has been subject to fluctuation, reaching a peak in 1998. The winter characteristic points, conversely, reached their peak in 2010 and 2012.

The regression coefficients of each feature point are extracted as shown in

Table 5. Linear regression coefficient of annual and seasonal average wind speed change trend.

The Representative Sea Area	Bohai Bay		In the Central Bohai Sea		Liaodong Bay		Laizhou Bay
Feature Point	T1	T1 (P)	T2	T2 (P)	T3	T3 (P)	T4	T4 (P)
Annual average	0.0003	0.035	0.0004	0.0246	0.0059	0.0450	0.0025	0.0112
Winter	0.0133	0.0447	0.0074	0.0253	0.0121	0.0410	0.0038	0.0171
Spring	0.0002	0.0290	0.0098	0.0006	0.0265	0.0497	0.0053	0.0007
Summer	0.0044	0.0211	0.0048	0.0034	0.0215	0.0415	0.0129	0.0012
Autumn	0.0111	0.0006	0.0019	0.4031	−0.0104	0.0316	0.0021	0.0001

. The enhancement of the winter monsoon may lead to the increase in winter wind speed, so the regression coefficient of winter wind speed is generally high, the change in wind speed is relatively stable and slightly increases, and the coefficient of Liaodong Bay is the largest in spring, which may be due to the significant warming enhancement of sea–land breeze circulation. The wind speed regression coefficient T3 in autumn decreased slightly.

In order to conduct a more detailed study of the possible wind speed changes between different months and provide key information for the wind speed trend of a specific month, the linear trend in monthly average wind speed is shown in Figure 8 below.

It can be concluded from the

Table 6. Linear regression coefficient of monthly mean wind speed change trend.

The Representative Sea Area	Bohai Bay		In the Central Bohai Sea		Liaodong Bay		Laizhou Bay
Feature Point	T1	T1 (P)	T2	T2 (P)	T3	T3 (P)	T4	T4 (P)
Jan.	0.0114	0.0366	0.0182	0.0422	0.0218	0.0484	0.0161	0.0091
Feb.	0.018	0.0244	0.0084	0.0374	0.004	0.0428	0.0037	0.0123
March	0.024	0.0103	0.0349	0.0713	0.0352	0.0294	0.0382	0.0441
April	0.0258	0.0446	0.0267	0.015	0.0425	0.063	0.0308	0.0002
May	−0.0169	0.0475	−0.0098	0.0105	0.018	0.0506	−0.0044	0.0019
June	−0.0154	0.0123	−0.012	0.0388	0.0075	0.0439	−0.0158	0.002
July	0.0095	0.0043	0.0105	0.0046	−0.0005	0.0167	0.0211	0.0412
Aug.	0.0297	0.0417	0.0234	0.019	0.018	0.0087	0.0168	0.0174
Sept.	0.0136	0.0002	0.0072	0.0126	−0.0083	0.0414	0.0105	0.0003
Oct.	0.0061	0.0156	0.0047	0.0419	0.0054	0.0157	−0.0041	0.0457
Nov.	0.0333	0.0272	0.0221	0.0332	0.0007	0.04497	0.0237	0.0016
Dec.	−0.0105	0.0395	−0.0294	0.0498	−0.0162	0.0251	−0.0337	0.0434

that in the 12 months, the wind speed is low at most points in spring and summer, while the wind speed is higher in autumn and winter, especially at the T3 and T4 points.

The regression coefficient of each feature point is extracted as shown in Table 2. From the perspective of monthly average, the wind speed change at T1 is relatively stable, and some months (May, June and December) show a downward trend, with regression coefficients of −0.0169 m/s·year⁻¹, −0.0154 m/s·year⁻¹, and −0.0105 m/s·year⁻¹. Other months show an upward trend, with the most obvious upward trend in November. The wind speed at T2 decreased in some months (May, June, and December). On the whole, the variation in wind speed in the central Bohai Sea is relatively mild, but there are obvious seasonal fluctuations. The wind speed variation at T3 attains the maximal degree, presenting remarkable seasonal characteristics throughout the year. The wind speed variation at T4 is relatively stable. However, during the summer and autumn phases, especially in June and December, it shows a significant downward trend.

4. Analysis of Wave Characteristics in Bohai Sea

4.1. Temporal and Spatial Distribution Characteristics of Waves

Based on the wave data of 30 years from 1993 to 2022 calculated by the SWAN model, the spatial distribution of annual average significant wave height in the Bohai Sea has obvious regional characteristics after annual average processing, as shown in Figure 9.

Regarding spatial distribution, the regions with high significant wave height are chiefly concentrated in the central sea area of the Bohai Sea, and the significant wave height is about 0.8–0.9 m. This area is far away from the land, the wind speed and wind field are relatively stable, and the wave energy accumulation is strong. Especially in winter and autumn, wind and waves are strong. The regional significant wave height is annularly distributed and decreases from the center to the periphery. In places far away from the coast, the significant wave height gradually decays to 0.2–0.4 m.

In the study area, seasonal averages of wave data spanning 30 years are calculated, yielding average wave field maps for spring, summer, autumn, and winter, as depicted in Figure 10a. The spatial distribution of monthly average significant wave height and wave direction is also shown in Figure 10b.

On the whole, the seasonal average wave distribution is similar to the annual average wave distribution, which is consistent with the trend of decreasing significant wave height from the middle to the surrounding and from the open sea to the near shore, and the maximum significant wave height appears in the central and southeastern open sea areas. Because the winter monsoon is large and lasts for a long time, it provides more energy for seawater and promotes seawater to form higher waves, so the average significant wave height in autumn and winter is higher than that in spring and autumn. In spring, the significant wave height is high, and the maximum value is about 0.8 m. It is mainly concentrated in the center of the Bohai Sea and mainly propagates to the southeast. In summer, the significant wave height decreases due to the decrease in wind force, and the wave direction propagates from southeast to southwest.

The monthly mean significant wave height and wave direction distribution in the Bohai Sea show obvious seasonal changes, which are basically consistent with the seasonal mean wind field distribution characteristics. The maximum significant wave height is concentrated in the central and southeastern offshore areas, which persists throughout the year. The monthly mean wave direction is dominated by the monsoon, and the dominant wave propagation direction in different months is periodically adjusted with the change in the seasonal wind field.

In this section, the nine aforementioned feature points are selected for analysis of wave distribution characteristics. In addition, the 30-year wave observation data are extracted for detailed analysis of the spatial distribution law and long-term change trend of waves in the sea area. The data extracted are then utilized to create a wave rose diagram (illustrated in Figure 11) at each feature point. This diagram offers a visual representation of the distribution characteristics of significant wave height and wave direction in the Bohai Sea over a 30-year period.

The wave directions of the Bohai Sea are mainly concentrated in the NE~ESE and SSW~W, and the wave directions of T1 and T5 are mainly concentrated in the SSW and ESE. The dominant wave directions of T4 and T7 are NE and ENE; the dominant wind waves of T3 and T6 are NE and ENE; the dominant wind waves of T2 and T8 are ENE; the dominant wind wave of T9 is W. Except for T1 and T9, which are characteristic points near the coast, the frequency of NE~NSE and SW~W in the remaining points during the 30-year statistical period is approximately the same. The strong and sub-strong wave directions of the feature points are concentrated in the SSW~W and NE~ENE.

4.2. Long-Term Variation Characteristics of Waves

The study of four characteristic points (T1, T2, T3, T4) in the Bohai Sea (Figure 6a) reveals an upward trend in significant wave height from 1993 to 2022 (Figure 12a). The overall trend is characterized by an upward trend in volatility. The T1 significant wave height exhibited notable fluctuations, particularly in 2007 and 2011. In contrast, the T2 significant wave height exhibited a relatively stable trend, with an approximate measurement of 1 m and a marginal upward trajectory. A notable increase in significant wave height was observed in 2017 and 2011. The variation trend in T3 wave height is analogous to that of T2, but its significant wave height is marginally higher. T4 also exhibited a significant peak, particularly in 2007 and 2011, and demonstrated a discernible upward trend over the long term.

As for Figure 12b, the long-term trend in the mean value of significant wave height varies significantly between different seasons. The four feature points demonstrate a gradual upward trend. The winter period is characterized by significant fluctuations. In contrast, the significant wave height in spring maintains relative stability, though T2 and T4 demonstrate notable fluctuations during spring 2013, with an upward trend observed. The T1 significant wave height fluctuates significantly during summer, particularly in 1996, when the peak value approaches 1.5 m. The T2 significant wave height also exhibits substantial fluctuations, with a marked upward trend, especially during the peak period of 2011. T3 displays a substantial peak in summer 2012, with a significant wave height nearing 2.5 m, and exhibits significant overall fluctuations. T4, meanwhile, exhibits significant variability, ranging from 0.5 to 2.5 m. In contrast, the fluctuation in significant wave height in autumn is minimal, and the overall trend is stable.

The regression coefficient of significant wave height change at each feature point (representing the annual significant wave height change) is extracted as shown in

Table 7. Linear regression coefficients of variation trend in annual and seasonal mean significant wave height.

The Representative Sea Area	Bohai Bay		In the Central Bohai Sea		Liaodong Bay		Laizhou Bay
Feature Point	T1	T1 (P)	T2	T2 (P)	T3	T3 (P)	T4	T4 (P)
Annual average	0.0012	0.0326	0.0026	0.0412	0.0023	0.0333	0.0013	0.0267
Winter	0.0006	0.0465	0.0041	0.0148	0.0051	0.0335	−0.0552	0.0389
Spring	0.0002	0.0212	0.006	0.0453	0.007	0.0335	0.2012	0.0395
Summer	−0.0006	0.0028	0.0076	0.0427	0.0062	0.0008	0.0455	0.0063
Autumn	−0.001	0.0427	0.0084	0.0453	0.0053	0.0454	0.1145	0.0039

. In terms of the annual average, the inter-annual variability in significant wave height across the four sea areas is not consistent. T1 demonstrates a minor downward trend in significant wave height, while T2, T3, and T4 exhibit a slight upward trend.

From the perspective of seasonal changes, in summer, T1 showed a downward trend, which may be related to the weakening of the summer monsoon. Other sea areas still maintained growth, with the largest increase in the central Bohai Sea. The significant wave height of T3 increases fastest in winter, which may be related to the frequent occurrence of cold waves and strong wind in winter. The increase in the middle side of the Bohai Sea in autumn reached the peak of the whole year, which may be related to the enhancement of typhoon activity in autumn.

As for Figure 13, the months of January and February are characterized by a predominance of northwesterly winds, accompanied by relatively stable significant wave heights. The spring and autumn months (April–May and September–December) correspond to the seasonal transition period. The months of September and December undergo significant fluctuations, with a notable rise in significant wave height. From June to August, the significant wave height increases slightly due to the influence of typhoon tracks. The reclamation area along the coast of Laizhou Bay has increased from 2000 to 2025, leading to an anomalous decrease in significant wave height in September. The study reveals that the change in the wave field in the Bohai Sea is regulated by air–sea interaction, topographic forcing, and human activities, which has important guiding value for ship navigation safety and coastal engineering design.

In order to conduct a more detailed study of the possible changes in significant wave height between different months and provide key information for the wind speed trend in a specific month, the linear change trend in monthly average significant wave height is shown in Figure 13.

As for

Table 8. Average wind speed change trend linear regression coefficient.

The Representative Sea Area	Bohai Bay		In the Central Bohai Sea		Liaodong Bay		Laizhou Bay
Feature Point	T1	T1 (P)	T2	T2 (P)	T3	T3 (P)	T4	T4 (P)
Jan.	0.0006	0.0372	0.0013	0.0085	0.0027	0.0409	0.0444	0.0211
Feb.	−0.0018	0.0108	0.0042	0.0417	0.0048	0.0465	0.0261	0.0447
March	−0.0021	0.0407	0.0046	0.0423	0.0038	0.0391	0.0788	0.0338
April	−0.0017	0.0193	0.0051	0.0192	0.0029	0.0402	0.0352	0.0344
May	−0.0014	0.0414	0.0059	0.0417	0.0022	0.0323	−0.079	0.0454
June	0.0009	0.0333	0.0058	0.0494	0.0017	0.0417	0.0006	0.0353
July	0.0001	0.0465	0.0044	0.0485	0.0009	0.034	−0.0276	0.0251
Aug.	0.0016	0.0369	0.0027	0.0074	−0.0006	0.0476	0.0136	0.0209
Sept.	0.0031	0.0304	0.0014	0.0367	−0.0023	0.0296	−0.0006	0.0255
Oct.	0.0045	0.0348	0.0004	0.0471	−0.0031	0.0492	0.0296	0.0365
Nov.	0.0064	0.0222	−0.0011	0.0161	−0.0018	0.0372	0.0981	0.0383
Dec.	0.0095	0.0456	−0.002	0.0412	0.005	0.0359	0.1278	0.0271

, except that T1 showed a downward trend in February, March, April, and May, the significant wave height in other months showed an upward trend. The overall performance of T2 shows an increasing trend, and the regression coefficients in most months are positive, indicating that the significant wave height in the sea area is on the rise for a long time, especially in February–May and June–August. The change trend of T3 is more complex, with an upward trend in some months (January~July), but a downward trend in August~October, and a rebound in winter (November~December). The trend of the T4 significant wave height is stable.

5. Analysis of Gumbel Extremum Characteristics

5.1. Introduction of Gumbel Extreme Value

The Gumbel distribution is the extreme value distribution of the parameters estimated by the moment method. The probability density function of the Gumbel distribution is as follows [12]:

$$f\left(x\right)=A\exp \left\{-A\left(x-B\right)-\exp \left[-A\left(x-B\right)\right]\right\}$$

(9)

In the formula, A and B are undetermined parameters, which are generally obtained by the moment method [12]:

$$A={\displaystyle \frac{\pi }{\sqrt{6}S}}$$

(10)

$$B=\overline{X}-0.450053S$$

(11)

In the formula, 0.450053 is the Euler constant, $S$ is the standard deviation of the sample, and $x$ is the mean of the sample.

The Gumbel distribution is widely used in marine hydrography, especially for maximum wind speed and significant wave height derivation. The Gumbel distribution has a good fit when the data samples are large enough, and the fit of the Gumbel distribution is low when the data samples are missing or relatively small.

5.2. Distribution Characteristics of Annual Extreme Values of Wind Field

In this section, the WRF model is used to study the 30-year wind field in the Bohai Sea. The annual extreme value method is used to extract the annual maximum wind speed in the Bohai Sea for 30 years as the extreme wind speed data of the corresponding year. Subsequently, based on the extreme value type I distribution (Gumbel distribution) model, the return period wind speed in the study area is calculated [35,36,37]. Through statistical analysis, the return period wind speeds of 100-year, 50-year, 25-year, 10-year, five-year, and two-year return periods are calculated, and on this basis, the spatial distribution maps of wind speed fields in different return periods in the Bohai Sea are drawn in Figure 14.

As for Figure 14, the maximum wind speed value once in a year in the Bohai Sea mainly occurs in the central waters. The central waters are far away from land and are less blocked by terrain, which allows the wind to fully develop; in the western and northern waters, the wind speed during the recurrence period is relatively low, mostly concentrated between 20 m/s and 30 m/s [38]. As the recurrence period shortens, the wind speed gradually decreases, and the spatial distribution maintains the characteristics of “high in the middle and low in the surrounding areas”. These areas may be affected by local climatic conditions, such as monsoon direction, ocean circulation, etc., making the extreme wind speed value relatively low. The extreme wind speed in the Laizhou Bay waters is more prominent, especially in extreme weather events. The terrain of Laizhou Bay is relatively closed and may be strongly affected by specific meteorological conditions (such as cold air moving south, typhoons, etc.), resulting in a significant increase in the extreme wind speed.

As for

Table 9. Extreme values of wind speed at different return periods at characteristic points.

The Representative Sea Area	Bohai Bay	In the Central Bohai Sea	Liaodong Bay	Laizhou Bay
Feature Point	T1	T2	T3	T4
Once in 100 years	32.02	32.05	30.24	33.21
Once in 50 years	27.73	28.00	26.41	28.88
Once in 25 years	23.40	23.91	22.56	24.52
Once in 10 years	17.58	18.40	17.36	18.65
Once in 5 years	12.96	14.04	13.25	14.00
Once in 2 years	6.00	7.46	7.04	6.97

, the extreme value of wind speed in Laizhou Bay is more prominent, especially in extreme weather events, which should be taken more seriously. Because of the differences in wind speed extremes in different regions, it is important to strengthen the prediction and preventive measures of wind speed extremes in Bohai Bay, especially in the extreme return period (100 years, 50 years). It is also important to strengthen the wind safety design of infrastructure. At the same time, Bohai Bay, central Bohai Sea, and Liaodong Bay still need to create emergency response measures in the case of a five-year and a two-year return period.

5.3. Distribution Characteristics of Wave Extreme Values

The wind field of the WRF model is utilized as the input wind field of the SWAN model, with the objective of forecasting the 30-year waves in the Bohai Sea. The maximum value of the significant wave height in the Bohai Sea over the past 30 years (1993–2022) is extracted as the annual extreme significant wave height. The Gumbel distribution model is then employed to calculate and analyze the significant wave height of the 100-year, 50-year, 20-year, and five-year return periods in the study area [39,40,41,42]. The wave height distribution characteristics of different return periods are obtained, and the corresponding wave field distribution map of the Bohai Sea is drawn, as shown in Figure 15.

Figure 15 shows that the maximum significant wave height for 100-year and 50-year return periods is approximately 6 m and 5.5 m, respectively, in the central and southeastern sea areas. These regions are particularly susceptible to wind-driven processes, and the substantial water depth in these areas fosters the formation and development of waves. The maximum significant wave heights of the five-year and 10-year return periods are recorded as 5.2 m and 5.0 m, respectively. It is acknowledged that these areas may be subject to influence from local wind and wave conditions, including, but not limited to, variations in wind direction and wind size. The T2 sea area may be distinguished by distinctive seabed topography or hydrological conditions, including variations in water depth and the presence of seabed obstacles. These factors may promote the formation of waves and energy concentration, resulting in higher wave extremes. The extreme value of the T2 wave is significantly higher than that of other regions.

Table 10. Wave extreme values of different return periods at characteristic points.

The Representative Sea Area	Bohai Bay	In the Central Bohai Sea	Liaodong Bay	Laizhou Bay
Feature Point	T1	T2	T3	T4
Once in 100 years	3.87	5.85	3.62	5.33
Once in 50 years	3.65	5.58	3.46	5.08
Once in 25 years	3.36	5.22	3.24	4.74
Once in 10 years	3.13	4.94	3.08	4.48
Once in 5 years	2.89	4.65	2.91	4.21
Once in 2 years	2.54	4.21	2.65	3.80

shows the wave extreme values of T1, T2, T3, and T4 for different return periods. By comparison, the spatial distribution characteristics of wave extreme values in different regions and the variation law with the shortening of the return period can be observed. The wave extreme value of T2 is significantly higher than that of other regions [43]. Even at lower return periods, the wave extreme value of T2 is still 4.21 m·year⁻¹, showing that it has a significant wave advantage. The wave extreme values of T1 and T3 are relatively low and close together, and the wave extreme value of T4 is higher than that of Bohai Bay and Liaodong Bay. In the case of the lower return period, the extreme significant wave height in Laizhou Bay reaches 3.80 m annually, showing relatively strong wave characteristics.

6. Conclusions

By comparing the simulated data with the measured data in order to verify the accuracy of the model, the following conclusions are drawn:

(1) With regard to the annual average wind speed, the wind speed in the Bohai Sea shows obvious seasonal differences. The wind speed in autumn and winter is greater than that in spring and summer, which is mainly due to the frequent southward movement of cold air and the influence of monsoon. In a similar fashion, the significant wave height in the Bohai Sea displays comparable seasonal characteristics. The annual mean significant wave height exhibits a gradual decrease from the middle to the periphery, from the southeast to the northwest, and from the far sea to the land.

(2) Further analysis of the wind direction data indicates that the wind direction of the Bohai Sea exhibits a significant direction. The prevalence of strong winds and sub-strong winds is observed to be concentrated in the N~ENE direction, while the normal wind direction and sub-normal wind direction are concentrated in the S~SSW direction. This distribution of wind direction exerts a direct influence on the direction of wave generation and propagation.

(3) The long-term change trend indicates that the wind speed and significant wave height in the Bohai Sea show an upward trend as a whole. This conclusion is substantiated through comprehensive analysis of wind and wave field data spanning from 1993 to 2022. This upward trend is significant on the whole, which may be related to global climate change, marine environmental warming, and other factors.

(4) The spatial distribution of wind speed and significant wave height in different return periods is consistent with the extreme wind speed and significant wave height. The maximum wind speeds of the 100-, 50-, 25-, and 10-year return periods are primarily located in the T4 sea area, while the maximum wind speeds of the five-year and two-year return periods are situated in the T2 sea area. A similar spatial distribution of extreme significant wave height values is also evident. The maximum significant wave height that occurs once every 100 years is higher than that observed in the current T2 sea area, and the significant wave height in the nearshore area is comparatively low.

This study not only provides detailed data support for the wind and wave characteristics in the Bohai Sea but also provides an important scientific basis and decision-making reference for the design of offshore extreme conditions.