Extreme wave and storm surge characteristics in the southeastern coastal and offshore regions of China

Abstract

A numerical model is established based on the FVCOM-SWAVE wave-current coupling model to investigate the typhoon-induced wave and storm surge level in the southeastern coastal and offshore regions of China. A hindcast of 192 typhoons from 1979 to 2023 is conducted, providing insights into the distribution of significant wave height and storm surge level. The disaster zone maps are derived from the annual extreme significant wave height and storm surge level. The results show that the maximum significant wave height for the 500-year return period is observed in the southeastern region of Taiwan. The extreme wave generally decreases northward and toward the shore, and the wave contours are almost parallel to the coastlines. Extreme storm surges are observed in the nearshore regions, especially in the Qiantang River estuary, Hangzhou Bay and Pearl River estuary. As water depth decreases, the storm surge level gradually increases shoreward. The Grade I storm surge hazard zone is predominately observed in the coastal areas near the Qiantang River Estuary, Hangzhou Bay and Pearl River Estuary.

Introduction

Typhoon disasters are the most severe threat to the marine engineering in the southeastern coastal and offshore regions of China. There are at least four tropical cyclones per year made landfall along the coastal areas of China annually from 1949 to 2023¹. Over the past decade, the total direct economic losses from marine disasters in coastal cities amounted to RMB 57.6 billion yuan, with an average annual loss of RMB 5.76 billion yuan. In particular, the direct economic losses in 2023 were RMB 2.5 billion yuan². Typhoons refer to low pressure vortices that form over the ocean surface in tropical or subtropical regions, often accompanied by strong winds and low atmospheric pressures, resulting in abnormally extreme waves and storm surges. These disasters can severely impact infrastructure and cause severe socio-economic losses^3,4. Extreme waves and storm surges have been considered as a major issue for safety in both coastal and offshore regions. The development of risk assessment maps for typhoon-induced waves and storm surges, along with the delineation of potentially affected areas, is crucial for implementing disaster prevention measures in typhoon-prone regions^5,6,7,8. However, the observation data of significant wave heights and extreme water levels obtained from the ocean buoy and remote sensing systems are limited during typhoon events^9,10,11,12.

Due to the lack of observed data, numerical simulation serves as an effective approach for estimating extreme typhoon-induced waves and storm surge levels. Numerous numerical wave-current coupling methods such as ROMS (Regional Ocean Model System)-SWAN(Simulating Waves Nearshore) model¹³POLCOMS (Proudman Oceanographic Laboratory Coastal Ocean Modeling System)-WAM model^14, ADCIRC (Advanced Circulation)-SWAN model^8,15,16, Delft3D-SWAN model^17, FVCOM circulation model-FVCOM-SWAVE model^18,19 have been proposed with different grid structures, coupling methods and influencing factors to improve the understanding of wave-current interactions^{20,21,22,23,24,25,26,27,28,29}. Both the structured and unstructured grids are adopted for the couple models to simulate typhoon induced waves and storm surges^{18,20,22,23,30,31}. Compared to the structured grids, unstructured grids could allow for localized increases in resolution without the need for nested grids, adapt complex coastlines and eliminate the need for interpolation between coupled models^29,32. In general, waves alter current by modifying sea surface roughness and bottom stress¹⁹. Additionally, radiation stress also influences current²⁰. On the other hand, waves are also influenced by current, wave-current interactions lead to a transfer of wave energy towards lower frequencies. Furthermore, in nearshore areas, current velocity influenced by waves changes water levels, which affects wave propagation^21,22. Wave-current coupling modifies both sea surface morphology and current field distribution, which in turn affects the superposition mechanism of storm surge levels and also modifies wave propagation characteristics.

A large number of studies indicate that the spatial distribution characteristics of typhoon-induced waves and storm surges are related to typhoon tracks and strongly depended on the typhoon wind field^33,34. Several sources of reanalysis data such as NCEP (National Centers for Environmental Prediction), ECMWF (European Centre for Medium-Range Weather Forecasts) and CCMP (Cross-Calibrated Multi-Platform) are adopted to derive wind speed and atmospheric pressure information³⁵. ERA5 is the next-generation reanalysis dataset from ECMWF with a spatial resolution of 0.125° × 0.125° and a temporal resolution of 1-hour, it could effectively reproduce the tropical cyclones and other atmospheric features^36,37. However, under extreme conditions such as typhoons, reanalysis wind fields fail to accurately capture wind information near the typhoon center, leading to limited accuracy of the reconstructed wind fields^16,38,39,40. Many scholars have proposed that wind fields near the typhoon center should be replaced by parameterized typhoon wind fields, which are constructed using information such as the latitude and longitude of typhoon tracks, maximum wind speeds, and minimum sea level pressures^{41,42,43,44,45}. These parameterized models are statistical formulations derived from historical observations and have shown effectiveness in the analysis of storm surge levels and significant wave heights.

In recent years, the frequency and severity of disasters caused by typhoon-induced waves and storm surges associated with tropical cyclones are significantly increased⁴⁶. A series of numerical simulations have been conducted globally to evaluate the distribution characteristics of typhoon-induced waves and storm surges under extreme marine environmental conditions^{47,48,49,50,51,52,53}. It has been reported that they are influenced by various characteristics of typhoons such as intensity, translation speed and atmospheric changes. Several methods have been developed to assess storm surge levels and wave heights for different return periods. Kumar et al.⁵⁴ investigated the probable maximum typhoon cyclone parameters along the eastern and western coasts of India, and evaluated the pressure difference between the cyclone centre and its periphery ΔP as well as the maximum wind velocity V_max by the extreme value analysis method for the storm surge simulation. The probable maximum storm surge level was subsequently estimated for port and harbor facilities⁵⁵. On the other hand, many scholars have computed the storm surge levels and extreme wave heights for different return periods by simulating historical typhoons^6,26,47,49. The wave boundary layer model has been applied for wind stress evaluation in the simulation of storm surges and typhoon-induced waves^56,57, and the simulated wave parameters, with the inclusion of wave boundary condition in the model, are close to the observed field data for Cyclone Phailin (2013)⁵⁷. Some scholars have investigated the hundred-year extreme water level and significant wave height under emission reduction policies and global warming scenarios^58,59. Approximately 1.3% of the global population will face floods with a return period of one hundred years⁶⁰. The frequency of tropical storm surges in China has shown a significant upward trend, among the coastal provinces, Guangdong, Fujian and Zhejiang provinces experience the highest occurrence of storm surges⁶¹. It is of great importance to predict the extreme significant wave heights and storm surge levels for different return periods in the design, operation and maintenance of coastal and offshore engineering facilities. Numerous distribution methods such as Pearson-III, Gumbel distribution model and Generalized Extreme Value (GEV) distribution model have been widely applied to estimate the significant wave height and storm surge level at different return periods^61,62,63. The frequencies corresponding to different intensities are analyzed, and risk index zone maps are drawn based on the simulated significant wave height and storm surge level during typhoon events^64,65,66. The storm surge intensity grade is determined based on the return period level calculated using the Gumbel distribution model⁶⁴. Distinct from the conventional single-factor hazard assessments, scholars have analyzed the distributions of storm surge disasters based on three aspects, such as extreme storm surge events occurrence frequency, resulting economic losses,  and numbers of casualties and missing persons⁶⁶. Risk index zone maps can effectively provide early warnings and inform decision-making in disaster prevention and mitigation efforts. The combined effects of typhoons and typhoon-induced waves have been considered in the design of offshore wind turbine structures near the coastline of China⁶⁷. The Gumbel copula and hierarchical Archimedean copulas (HAC) are used to construct joint distribution models for multidimensional environmental contours^68,69.

Most of the previous studies are focused on the temporal and spatial distributions of typhoon-induced waves or storm surges during a single typhoon event^19,70,71. Several studies have been performed to investigate the effects of wave-current interaction on the typhoon-induced waves and storm surges for a single typhoon event^{16,19,24,26,28,29}. The results indicate that the wave-current interaction significantly improves the accuracy of wave height and wave energy spectra, particularly during the peak stages of typhoon events. Feng et al.²⁹ found that the fully coupled model, which considers wave-induced radiation stress, the effect of waves on the wind stress drag coefficient, and the modulation of current and water level on the waves, achieves the most realistic simulation compared with the observation data. The impact of wave-current interactions results in changes to the distribution of significant wave height fields during hurricanes Juan and Bill⁷⁴. Moreover, the effect of wave-current coupled model on storm surges in the shallow sea areas is significant, where wave effects contribute up to 40% to the peak surge rises during typhoon Sanba^{73. Additionally,} the effect of wave-induced radiation stress results in a significant increase in storm surge maxima along the coast during Typhoon Usagi²⁹. The increase in storm surge levels, considering the wave setup component, has also been observed in the studies of Li et al.²⁴ and Kumar et al.^55, indicating that the contribution of wave setup by typhoon-generated surface waves cannot be neglected in storm surge simulation and forecasting. However, the hazard zones of typhoon-induced waves and storm surges in the southeastern coastal and offshore areas of China have not been well understood. It is essential to consider the effects of wave-current interaction in long-term simulations to study extreme waves and surges. Therefore, the objective of this study is to investigate the distributions of extreme significant wave heights and storm surge levels for different return periods, assess the hazard zones for typhoon-induced waves and storm surges from simulations of historical typhoon events along the southeastern coastal and offshore areas of China, and provide joint probability distributions of annual maximum wind speed and significant wave height along the water depth isobaths.

Here, we used the FVCOM-SWAVE model to simulate the typhoon-induced waves and storm surges caused by 192 typhoon events affecting the southeastern coastal and offshore areas of China from 1979 to 2023. Based on the simulation results, we estimated the distributions of extreme significant wave height and storm surge levels for different return periods and further assessed the hazard zones for waves and storm surges induced by typhoons. Additionally, we conducted a joint probability distribution study of wind and waves at characteristic points with a water depth of 50 m for different return periods, providing scientific support for the design and maintenance of offshore and ocean engineering in southeastern coastal China.

Results

Estimation of extreme significant height and storm surge level

We extract the data on hourly significant wave heights and extreme water levels at each grid node from the simulated typhoon-induced waves and storm surges. The storm surge levels are derived by linearly subtracting tidal levels from extreme water levels. Therefore, the reference datum for the storm surge level is the astronomical tide level. We calculate the annual extreme series of significant wave heights and storm surge levels at each grid node for 192 typhoons and use the GEV distribution model to estimate the distributions of extreme significant wave heights and storm surge levels for different return periods.

Figure 1 shows the spatial distributions of extreme significant wave heights along the southeastern coastal and offshore region of China for 10-, 30-, 50-, 100-, 300- and 500-year return periods. The estimated significant wave heights exhibit similar spatial distributions with different return periods, where the significant wave height gradually decreases northward and shoreward. This is attributed to wave breaking as waves approach the coastline, and the influence of bottom friction becomes more pronounced with the decrease of water depth. The dominant dissipation processes of wind waves are depth-induced breaking and bottom friction^7,75. The transformation and energy dissipation of storm waves occur during the propagation of tropical cyclones in shallow water as a result of variations in both topography and bottom friction⁸. The depth-induced energy dissipation is found to be dominated wave height in the shallow water region⁵⁶. Wave breaking dominates energy dissipation, while the bottom friction plays an important role only in shallow water areas^76,77. The contributions of wave bottom friction and wave breaking are varied with different water depths and topographies⁷⁸. Wave whitecapping dominates the wave energy dissipation in deep water areas, but the bottom friction controls the major dissipation process as waves propagate toward coastal areas.

Taking the 50-year return period as an example, the maximum significant wave height of the 50-year return period reaches 20 m in the southeast of Taiwan Island. The significant wave height varies from 4 m to 20 m in the northern coastal areas of Guangdong province, and from 2 m to 16 m in the southern coastal areas of Guangdong province. A sharp decrease in significant wave height to a range of 1 m to 5 m is observed at the Pearl River Estuary. The gradient of significant wave height perpendicular to the Hainan Island coastline shows an increasing trend. The significant wave height varies from 8 m to 16 m on the southeastern side of Hainan Island. In the Beibu Gulf area, most regions have a significant wave height of 10 m, which is 3 to 5 m higher than that in shallower areas within the bay. However, typhoon events with westward and northwestward tracks are always blocked by Taiwan Island, resulting in energy dissipation during the wave propagation process. The mean significant wave height in the Taiwan Strait is 10 m, which is 2 m to 8 m lower than that on the eastern side of Taiwan Island perpendicular to the coastline. Within an offshore distance of 190 km, the significant wave height for a 50-year return period in the central region of Fujian Province varies from 2 m to 10 m, and increases to a range of 4 m ≤ H_s ≤ 12 m in the northern and southern coastal regions. The significant wave height at Qiantang River Estuary ranges from 4 m to 6 m, while in the Hangzhou Bay area, it ranges from 6 m to 8 m. The discrepancy in significant wave height may be attributed to the influence of terrain and coastline, such as bathymetric gradients, bottom roughness and reflection. For instance, the decrease in significant wave height near the Qiantang River estuary and Hangzhou Bay is due to continuous changes in seabed topography gradient as waves propagate toward the shore. When waves propagate into shallow water, changes in the bathymetric gradients trigger depth-induced wave breaking, and rough seabed topography generates bottom friction. When the wave reaches the shore, it will be reflected when it encounters obstacles. These processes lead to wave energy dissipation. The significant wave heights in the open sea area are much higher than those in the shoreline zone. Along the southern coastlines of Zhejiang Province, the maximum significant wave height reaches 16 m, which is 2 m larger than that along the northern coastlines.

The maximum significant wave height for a 50-year return period reaches 20 m in the southeast of Taiwan Island, decreases to 14 m and 18 m for the 10-year and 30-year return periods, and increases to 22 m, 28 m and 32 m for the 100-year, 300-year and 500-year return periods, respectively. Despite the coastline shielding effect on the eastern side of Taiwan Island, the significant wave height is noticeably higher than that in the shoreline zone. A similar phenomenon is also observed in Li et al.^19, they suggested that the large waves occurring in the east and southeast of Taiwan Island are attributed to a large fetch for waves development and propagation shoreward.

Fig. 1

Spatial distribution of significant wave height along the southeastern coastal region of China for different return periods. (a) 10-year; (b) 30-year; (c) 50-year; (d) 100-year; (e) 300-year; (f) 500-year. The map was created using the Mapping Toolbox in MATLAB (https://www.mathworks.com/products/mapping.html).

Figure 2 shows the spatial distributions of storm surge levels along the southeastern coastal and offshore regions of China for 10-, 30-, 50-, 100-, 300-, and 500-year return periods. The storm surge is closely related to local water depth. Opposite to the variation of significant wave height, the extreme storm surge level increases as the water depth decreases. The spatial distributions of storm surge levels exhibit similar patterns for different return periods. The maximum storm surge level during the 50-year return period occurs at the Qiantang River Estuary, Hangzhou Bay, Sanmen Bay, offshore area of Ningde in Fujian Province, Pearl River Estuary, and Leizhou Bay. The extreme storm surge level exceeds 2.6 m for the 50-year return period, and increases to 2.8 m, 3.3 m, 4.0 m for the 100-year, 300-year and 500-year return periods, respectively. The storm surge levels are relatively high in the Qiantang River, Hangzhou Bay and Sanmen Bay, due to the concentration of tidal energy and the funnel shaped coastlines. Additionally, wave divergence within the bays leads to a relatively dispersed wave energy, while currents reduce momentum loss of the waves by elevating the water surface. The combined effects of wind drag and pressure drop result in a nonlinear relationship among wind, pressure and storm surge. It is reported that the influence of wind intensity on storm surge is strongest, followed by forward speed and surface pressure^79,80,81. Wind speed exerts the significant influence on storm surges during the 12 to 18 hours preceding landfall^82, and storm surge magnitudes correlate better with prelandfall wind speeds than with wind speeds at landfall⁸³. Moreover, the combined effects of wind speed and direction have a significant effect on storm surge water levels during Typhoon Morakot, where onshore and offshore winds typically lead to an increase and decrease of water level, respectively²⁶.

Taking the 50-year return period as an example, large storm surge levels are observed along the coastal areas of Guangdong province. The extreme storm surge level exceeds 2.6 m in the Pearl River Estuary and Leizhou Bay, and decreases to 1.2 m in the northern nearshore area of the Pearl River Estuary. The gradient of storm surge level increases shoreward. In coastal areas of Fujian Province, the storm surge level reaches 2.6 m in Lianjiang, Luoyuan, and Sansha Bay, while the storm surge level in other coastal areas ranges from 1.2 m to 2 m. The average storm surge level in the Taiwan Strait is 1.6 m, where the surrounding current exerts force on waves to prevent the reduction of wave momentum, altering the average water level and resulting in new hydrostatic pressure. The inverse relationship between storm surge levels and significant wave heights in Taiwan Strait is attributed to hydrostatic pressure resulting from a reduction in wave energy⁸⁴. Waves have a certain influence on water level rise in shallow waters, where the water level gradient is proportional to the wave radiation stress and inversely proportional to the water depth. This indicates that, under constant radiation stress, shallower water depth leads to significant water level rise. The radiation stress makes a significant contribution to the increase of storm surge water levels⁸⁴. Large storm surge levels reach 1.2–1.6 m at the Qiongzhou Strait due to the frequent occurrence of typhoons and tide-wave interaction. The narrowing effect of Qiongzhou Strait may lead to increased tidal energy and extreme storm surge levels. The storm surge level ranges from 0.5 m to 1.4 m on the southeastern side of Hainan Province, while on the northern Beibu Gulf, it ranges from 0.8 m to 2.2 m.

Fig. 2

Spatial distribution of storm surge levels along the southeastern coastal region of China for different return periods. (a) 10-year; (b) 30-year; (c) 50-year; (d) 100-year; (e) 300-year; (f) 500-year. The map was created using the Mapping Toolbox in MATLAB (https://www.mathworks.com/products/mapping.html).

To better illustrate the variations in significant wave heights and storm surge levels across different locations, we have chosen Hangzhou Bay, Taiwan Strait, Pearl River Estuary, and Qiongzhou Strait for analysis. The locations of the four stations are shown in Fig. 8. Figure 3 shows the GEV plots for the annual maximum significant wave height and storm surge level at the four stations for different return periods. We fit the annual maximum significant wave height and storm surge level using the maximum likelihood method, and the simulated results almost all fall within the 90% confidence interval at the four stations, indicating a good fit of the GEV distribution. The largest RMSE of significant wave height (RMSE_Hs) is 0.39 m in the Qiongzhou Strait region, while it is below 0.25 m for the other three stations. The significant wave height exceeds 10 m for the 100-year return period and reaches 15 m for the 500-year return period at Taiwan Strait and Qiongzhou Strait. The significant wave height and storm surge level increase with the increase of return period from 1-year to 500-year. The largest RMSE of storm surge levels (RMSE_SS) is 0.09 m at Pearl River Estuary and Qiongzhou Strait, and decreases to below 0.08 for Hangzhou Bay and Taiwan Strait. In both Hangzhou Bay and Pearl River Estuary regions, the storm surge level is almost 3 m for the 100-year return period, and exceeds 4 m for the 500-year return period.

Fig. 3

GEV plots for the modelled annual maxima at four stations. (a) Hangzhou Bay; (b) Taiwan Strait; (c) Pearl River Estuary; (d) Qiongzhou Strait; (e) Southeast of Taiwan.

Wave and storm surge hazard zone

We calculate the annual average occurrence frequency of significant wave height at each grid node and assess the corresponnding wave hazard zones. Figure 4 shows the hazard zone maps for waves and storm surges along the southeastern coastal and offshore regions of China. Both the spatial distributions of wave and storm surge hazard zones are generally in parallel with the coastlines. The wave hazard disaster index decreases shoreward, however, an opposite phenomenon is observed for storm surge hazards. Level I wave hazard zones characterized by the normalized wave hazard disaster index 0.75 ≤ H_wn≤1.0 are predominantly found in the offshore areas of Guangdong and northeastern Taiwan. This is mainly due to the severe typhoon threats to the northern and eastern coastal areas of Taiwan Island⁷². Despite the coastline shielding effect on the eastern of Taiwan Island, the significant wave height is noticeably higher than that in the shoreline zone. Similar phenomenon is also observed in Li et al.^19, they suggested that the large waves occurred in the east and southeast of Taiwan Island is attributed to the large fetch for waves development and propagation shoreward. It is characterized by the offshore areas at a distance of 171 km and 284 km from the coastline of Guangdong and Fujian provinces, respectively. Level II wave hazard zones (0.5 ≤ H_wn<0.75) are observed in the offshore areas paralleled with the coastlines of Guangdong, southern Zhejiang, northern Fujian, eastern Taiwan and eastern Hainan. The Level II wave hazard zone includes sea areas with an offshore distance of 156 km in Zhejiang, 208 km and 415 km in the north and south of Fujian, 102 km in Guangdong and 76 km in the east of Hainan. The spatial distributions of Level III wave hazard zones (0.25 ≤ H_wn<0.5) are similar to those of Level II wave hazard zones. The extents are included the offshore areas with an offshore distance of 55 km in Zhejiang and northern Fujian, 168 km in southern Fujian, 16 km in Guangdong, and 7 km in the east of Hainan. Level IV wave hazard zones (0 ≤ H_wn<0.25) are observed along the southeastern coastal areas of China. When waves propagate into the shoreline zone, changes in the bathymetric gradients trigger depth-induced wave breaking, and the rough seabed topography generates bottom friction, waves will be reflected due to the presence of obstacles, leading to wave energy dissipation in the shoreline zone.

Fig. 4

Hazard zone map along the southeast coastal region of China. (a) typhoon-induced wave; (b) storm surge level. The map was created using the Mapping Toolbox in MATLAB (https://www.mathworks.com/products/mapping.html).

Four levels of storm surge hazard zones are classified based on the normalized storm surge disaster index S_wn. Grade I (0.75 ≤ S_wn≤1.0) storm surge hazard zone is found in the coastal areas of Qiantang River Estuary, Hangzhou Bay, Sanmen Bay, central Fujian Province, Leizhou Bay and Pearl River Estuary. The coastal areas of Zhejiang province are mostly affected by the storm surge. Apart from the aforementioned areas, most coastal regions are affected by Grade II storm surge hazard zone (0.5 ≤ S_wn<0.75). Grade III storm surge hazard zone (0.25 ≤ S_wn<0.5) is predominantly found in the northern Pearl River Estuary in Guangdong Province and southern Fujian Province. Within an average offshore distance of 194 km from Fujian Province, Grade III storm surge intensity occurs, with an affected area of 6.9 × 10⁴ km². The influence range of Grade III storm surge near the coastal region of Guangdong is 3.9 × 10⁴ km²significantly smaller than that of Zhejiang and Fujian provinces. The Grade III storm surge hazard zone affects a coastline length of 248 km in northern Hainan Province. Grade IV storm surge hazard zone (0 ≤ S_wn<0.25) is predominantly found in the sea areas with an offshore distance ranging from 36 km to 143 km from north to south in Guangdong Province. The Grade IV storm surge hazard zone is also observed in the eastern and southwestern offshore regions of Hainan Province.

Joint distribution of wind speed and significant wave height

The joint probability distribution of wind speed and significant wave height along the water depth isobath h = 50 m for four coastal provinces, as well as the environmental contours for different return periods, is shown in Fig. 5. The red scatter represents the original data, and the green contour indicates the magnitude of the probability density. The estimated parameter α and correlation coefficient τ are presented in each figure. More red scatters are concentrated within the darker green contours, indicating that the original data are consistent with the joint probability density distribution. The environmental contours for different return periods exhibit similar shapes, with the environmental contours of smaller return periods contained within those of larger return periods. This is because the environmental contours for different return periods are derived by transforming spheres of different radius R in U-space.

At the selected points with a water depth isobath h = 50 m in Zhejiang Province and Guangdong Province, the environmental contours of wind and wave are narrowest at low wind speeds (V_w < 15 m/s) and low significant wave heights (H_s < 8 m), gradually expanding outward at high wind speeds and significant wave heights. The environmental contours for different return periods in the offshore area of Hainan Province are approximate symmetrical. The environmental contours for different return periods in the nearshore area of Fujian Province are narrowest in the middle, and gradually expand outward on both sides, possibly due to the obstruction of the Taiwan Strait.

Taking Fujian Province as an example, at the water depth isobath of 50 m along the coast of Fujian Province, within the moderate wind speed range (15 m/s < V_w < 30 m/s), wind speed and wave height are almost proportional. The significant wave height varies from 2.2 m to 10.4 m, and the range of wind speed is from 8.2 m/s to 34.1 m/s in original data. The highest probability occurs within the range of 5.25 m < H_s < 6.9 m and 16.7 m/s < V_w < 22.0 m/s. The maximum probability density is 2.4 × 10⁻², the maximum probability is inversely proportional to the concentration. Among the four coastal provinces, Fujian Province has the most concentrated joint distribution of significant wave height and wind speed, resulting in the highest probability of occurrence. The strong winds brought by typhoons render wind waves the dominant factor. The interaction between wind and sea surface causes the energy of ocean waves to increase with wind speed within a certain range, leading to an increase in significant wave height. Due to the island barrier effect, the ocean waves in the Taiwan Strait are primarily influenced by local climate and wind force, and swell waves may be weakened around the islands⁸⁵.

Fig. 5

Bivariate joint distributions of typhoon-induced wind and wave at a water depth of 50 m.(a) Zhejiang; (b)Fujian; (c)Guangdong; (d)Hainan.

Additionally, based on the Frank copula, the joint distribution of annual maximum wind speed and significant wave height yields a correlation coefficient (Kendall’s τ), which is approximately varied from 0.65 to 0.78, indicating that the Frank copula is suitable for the joint distribution of wind speed and significant wave height.

Discussion

Here, we utilized the wave-current coupled model to simulate typhoon-induced waves and storm surges affecting the southeast coastal and offshore regions of China. From the validation results, it is evident that the extreme significant wave heights and extreme water levels are generally consistent with the field data. The mean value of root-mean-square error (RMSE) for significant wave heights at 8 validation sites during 13 typhoon events is 0.54 m, the mean relative error is 9.6%. We applied the annual maxima method and GEV distribution to obtain the distributions of significant wave height and storm surge level for the 10-, 30-, 50-, 100-, 300-, 500- year return periods in the southeastern coastal and offshore regions. This finding is consistent with previous studies^19, which indicate that extreme wave height generally decreases towards the north and towards the shore. Extreme storm surge levels appear to coincide with isobaths, and as water depth decreases, storm surge gradually increases from offshore towards the shoreline. This suggests a substantial influence of water depth on storm surge levels. The spatial distribution patterns of significant wave heights are opposite to those of storm surge levels. For instance, in the offshore areas of Fujian Province , the 50-year return period storm surge levels range from 0.5 to 1.5 m in the northern and southern regions, whereas they increase to  1.5 to 2.5 m in the northern central region. In contrast, the 50-year return period significant wave heights vary between 5 and 14 m in the northern and southern regions, and between 4 and 10 m in the northern central region . The relatively lower significant wave heights observed in the Taiwan Strait may be attributed to the shielding effect of Taiwan Island, resulting in a decrease in wave energy. The increase in storm surge levels in this region could result from the reduction in significant wave heights, as the surrounding water flow exerts forces on the waves to maintain a decrease in wave momentum, resulting the generation of new hydrostatic pressure.

Here, the typhoon-induced wave and storm surge hazard disaster indexes exhibit characteristics similar to those of distributions with different return periods. The wave hazard zone reveals a higher hazard index in Guangdong Province. This is closely related to the frequency and intensity of typhoons affecting the region⁸⁷.  Specifically, Guangdong Province experiences 30.7% of the total typhoon occurrences, the highest portion among the four coastal provinces. The western Hainan Island demonstrates a lower hazard index compared to its eastern counterpart. The storm surge zone indicates a Level I hazard index in the Qiantang River Estuary, Hangzhou Bay, Sanmen Bay, offshore areas of Ningde City in Fujian Province, the Pearl River Estuary, and Leizhou Bay, where the hazard index gradually decreases with the increase of water depth. In this study, the hazard indexes of significant wave height and storm surge level are calculated using frequency statistics based on a fifty-year storm surge return period. Although this method is widely adopted in hazard assessment, it neglects the multiple process nature of coastal hazards.

In response to the fact that marine factor disaster assessments involve multiple processes, this study constructs a Copula-based bivariate joint distribution to describe the correlations between environmental variables and provide wind-wave environmental contours for different return periods. Due to space limitations, the analysis is focused on four representative points at a depth of 50 m along the coast. The environmental contours for different return periods are nested within each other, with those corresponding to smaller return periods contained within those of the larger return periods. This article considers the extreme values of wind speed and significant wave height within a 250 km radius of typhoon influence. The previous studies have reported that the occurrence times of typhoon-induced maximum wind speed and maximum wave height are not synchronized^88,89. The time lag between typhoon-induced maximum wind speed and wave height is closely related to the site location and typhoon characteristics. The maximum wind speed and significant wave height increase slightly by 2% with the neglect of time lag^89, leading to slight overestimations of the wind and wave loads in the engineering practice, and the time lag decreases to zero with the increase of typhoon-induced maximum wind speed and wave height. Therefore, due to the slight overestimation of wind speed and wave height without consideration of time lag, this study assumes that the maximum significant wave height and maximum wind speed occur simultaneously. The effects of time lag between the typhoon-induced wind and wave on the reliability of the joint probability distributions and hazard indices require further investigation. Additionally, random samples can be generated based on existing wind-wave distribution patterns to compensate for the limited number of available typhoons for analysis.

The scatter plots of maximum wind speed and maximum storm surge level at a water depth isobath of 50 m along the coasts of Zhejiang Province, Fujian Province, Guangdong Province and Hainan Province are further analyzed (see Supplementary Fig. S8). Taking the coast of Zhejiang Province as an example, it can be seen that compared to the correlation between wind speed and significant wave height, a weaker correlation between wind speed and storm surge level is observed from the scatter plots. When the storm surge level exceeds 0.5 m, the corresponding wind speeds are represented as discrete points, ranging from 17.8 m/s to 34.2 m/s. Storm surge levels exceeding 0.5 m are observed in Fujian, Guangdong, and Hainan provinces, even when wind speeds are less than 10 m/s. Overall, the maximum storm surge in Zhejiang predominantly occurs at wind speeds of 25 ≤ V_w ≤ 35 m/s, whereas in Fujian, Guangdong, and Hainan provinces, peak storm surges are more commonly associated with lower wind speeds (V_w < 15 m/s). A similar phenomenon has also been observed by Hu et al.⁸⁶. Since the storm surges are influenced by many factors such as wind intensity, surface wave pressure, forward speed, size, angle of approach, landfall location, and local bathymetry^81, the joint distributions among wind speed, storm surge level and pressure behave more complicated than those between wind speed and significant wave height. In the future studies, the joint distributions among wind speed, storm surge level and pressure will be assessed to predict coastal surge hazards.

The present understanding of the typhoon-induced wave and storm surge hazard zones is not fully comprehensive. Special attention should be paid to the filed observations of typhoon-induced waves and storm surges during typhoon events. Establishing field observation and numerical datasets, together with high-resolution numerical simulations, is critical for the forecasting and hindcasting of typhoon-induced wave and storm surge disasters.

Data sources and methodology

A framework illustrating the modeling workflow as shown in Fig. 6. This diagram illustrates the modeling workflow from data acquisition to hazard zone mapping and the joint distributions of wind and wave for different return periods.

Fig. 6

Framework for typhoon-induced wave and storm surge hazards zones.

Data acquisition

The historical typhoon track dataset is obtained from China Meteorological Administration’s Tropical Cyclone Center database (https://tcdata.typhoon.org.cn), with a total number of 192 typhoons selected within a radius of 250 km centered around the southeast coastlines of China from 1979 to 2023. The typhoon’s central longitude and latitude, central minimum pressure and 2-min averaged maximum wind speed near the center are obtained with a temporal resolution of 6 hours and a spatial resolution of 0.1°. Figure 7 shows the historical typhoon tracks affecting the southeast coastal region of China in 1979–2023. It can be seen that the main types of typhoon paths are westward-moving, northward-moving, northwestward-moving and turning typhoons. Most of the typhoons are occurred in Guangdong, Hainan, Zhejiang and Fujian provinces, accounting for occurrence frequencies of 30.7%, 23.9%, 23.0% and 22.4%, respectively. The reanalysis wind field data for 192 typhoons are obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF) database with a spatial resolution of 0.125° × 0.125° and a temporal resolution of 1-hour (https://cds.climate.copernicus.eu/datasets/reanalysis-era5-single-levels).

Fig. 7

Historical typhoons affecting the southeast coastal region of China in 1979–2023. (a) typhoon tracks; (b) typhoon numbers. The map was created using the Mapping Toolbox in MATLAB (https://www.mathworks.com/products/mapping.html).

The coastline data is derived from the Global High-resolution Shoreline (GSHHS) dataset released by the National Geophysical Data Center (NGDC), and has been further refined and improved through correction and supplementation using Google Earth satellite maps. The offshore bathymetric data is obtained from the Global Bathymetric Chart of the Oceans (GEBCO), a global topographic dataset with a resolution of 30 arc-seconds (https://download.gebco.net/). The electronic nautical charts are used to digitize and geodetically correct the coastal seabed topography. The location of eight wave field observation stations and five tidal field observation stations in Zhejiang, Fujian and Guangzhou provinces are shown in Fig. 8, with the observed data from these stations used for the validation of simulated results.

Fig. 8

Field observation stations for tidal level and significant wave height. S1-S8 are respectively Shengsi station, Zhoushanwaihai station, Wezhou station, Nanji station, Strait No.1 station, Minjiangkou station, Strait No.2 station, Yangjiang station. T1-T7 are respectively Damen station, Dahengqin station, Denglongshan station, Hengmen station, Nasha station, Kanmen station, Dachen station. The coloured dots in the map indicate the location of the observation stations. The map was created using the Mapping Toolbox in MATLAB (https://www.mathworks.com/products/mapping.html).

Typhoon wind model

The typhoon wind field is constructed by an asymmetric Holland wind field combined with ERA5 reanalysis wind field. The analytical wind model from Holland (1980) is applied in reconstructing the wind field. The radial distribution of pressure and wind are determined as follows⁹⁰:

$${P_{}}(r)={P_c}+({P_n} - {P_c})\exp {\left( { - \frac{{{R_{\hbox{max} }}}}{r}} \right)^B}$$

(1)

$${{\text{V}}_{\text{s}}}(r)=\sqrt {({P_n} - {P_c})\frac{B}{{{\rho _a}}}{{(\frac{{{R_{\hbox{max} }}}}{r})}^B}\exp {{( - \frac{{{R_{\hbox{max} }}}}{r})}^B}+{{(\frac{{rf}}{2})}^2}} - \frac{{rf}}{2}$$

(2)

where P_c represents the sea-level atmospheric pressure at the cyclone center, P_n represents the sea-level atmospheric pressure in the background field. R_max represents the maximum wind speed radius, B represents the cyclone shape parameter. ρ_a represents the atmospheric density, f represents the Coriolis force.

The maximum wind speed radius is selected using the aviation data formula, and the shape parameter is calculated using the Vickery (2008) formula, the calculation formula is expressed as follows⁹¹:

$${R_{\hbox{max} }}=rk - 0.4({P_c} - 900)+0.01{({P_c} - 900)^2}$$

(3)

$$B=1.38 - 0.00184({P_n} - {P_c})+0.00309{R_{\hbox{max} }}$$

(4)

where rk is 40.

The transitioning wind field adopts the model proposed by Ueno Takeo (1981), and expressed as follows⁹²:

$${V_d}\left( r \right)={V_c}\exp \left( { - \frac{\pi }{4} \cdot \frac{{\left| {r - {R_{\hbox{max} }}} \right|}}{{{R_{\hbox{max} }}}}} \right)$$

(5)

where V_c is typhoon movement speed.

The expression for the asymmetric wind field around the typhoon center is as follows:

$${V_{TY}}={C_1}{V_d}\left( \begin{gathered} - \sin (\theta +\beta ) \hfill \\ \cos (\theta +\beta ) \hfill \\ \end{gathered} \right)+{C_2}{V_s}$$

(6)

where C₁ and C₂ is the correction coefficients, θ is the angle between the line connecting the calculation point and typhoon center and the positive direction of x-axis, β is the angle between the gradient wind and sea surface.

The hybrid wind field model is constructed based on the ECMWF reanalysis wind field and model-generated typhoon wind field with the weighted coefficients, expressed as follows:

$${V_e}=(1-e){V_{{\text{TY}}}}+e{V_{{\text{ECMWF}}}}$$

(7)

$$e={c^4}/\left( {1+{c^4}} \right)$$

(8)

$$c=r/n{R_{\hbox{max} }}$$

(9)

where e is the weight coefficient, r is the radial distance from the typhoon center, n is 9.

Wave-current coupled model

The wave-current coupled FVCOM (Finite Volume Community Ocean Model) model and FVCOM-SWAVE model is used to simulate the typhoon-induced waves and storm surge levels during 192 typhoons in the present study. The FVCOM model is a prognostic, unstructured-grid, finite-volume, free-surface, three-dimensional primitive equations community ocean model^93,94. The FVCOM-SWAVE model is an unstructured grid version of the surface wave model with the implementation of finite-volume algorithm in the SWAN model^18,19,95,96. The computational domain is 15.39°N − 40.92°N and 105.60°E -139.35°E, including Bohai Sea, Yellow Sea, East China Sea and South China Sea. A total of 79,774 nodes and 155,354 elements are used in the bathymetry mesh along the southeast coastal regions of China (see Supplementary Fig. S1). The numerical model is discretized into 21 sigma layers along the water depth. The mesh resolution is ranged from 50 km to 2 km.

Eight major tidal components M₂, S₂, N₂, K₂, K_l, O₁, P_l and Q_l are considered for the open-sea boundaries. The tidal variations at the open-sea boundaries are computed using the tide forecast function from the TPXO7.2 global tidal model. The model discriminates between wet and dry depths, with the threshold depth set at 0.05 m. The wave model employs a semi-implicit integration algorithm, with a time step of 600s.

In the FVCOM-SWAVE model, S_tot in the spectral action balance equation is the sum of the source terms of wave variance, defined as^18,19,95,96:

$$S_{{tot}} = S_{{in}} + S_{{nl3}} + {\text{ }}S_{{nl4}} + {\text{ }}S_{{ds,w}} + {\text{ }}S_{{ds,b}} + {\text{ }}S_{{ds,br}}$$

(10)

where S_in is the function for wind-induced wave growth, S_nl3 is the nonlinear transfer of wave energy from three-wave interactions, S_nl4 is the nonlinear transfer of wave energy from four-wave interactions, S_{ds, w} is the wave decay from white capping, S_{ds, b} is the wave decay from bottom friction, S_{ds, br} is the wave decay from depth-induced wave breaking. The bottom friction coefficient is set to 0.067m²/s³ in the present study.

For the numerical simulation, the coupled FVCOM and FVCOM-SWAVE model is performed using the data exchange between the two models. After the initialization, the data calculated from the FVCOM-SWAVE model include significant wave height, wave direction, wave length, spectral peak period, bottom orbital velocity, bottom orbital period, and wave breaking percentage are exchanged with the FVCOM model. On the other hand, the current speed and water levels calculated from the current model are further fed back to the wave model for wave-current interaction at the next time step. The time interval of data exchange between the FVCOM model and FVCOM-SWAVE model is 600s.

Model validation

The significant wave heights driven by the modified ERA5 wind field data were compared with the measured data from eight observation stations, including S1-S8 stations along the coastal regions of Zhejiang, Fujian and Guangdong provinces. The comparisons of simulated and observed significant wave heights at eight wave stations during 13 typhoon events were performed (see Supplementary Fig. S2). And the comparisons of simulated and observed storm surge levels at five tidal stations during 3 typhoon events were carried out (see Supplementary Fig. S3). The numerical results of significant wave heights and storm surge levels are generally in good agreement with the observed data. It can be seen that approximately 81% of the sites have a root-mean square error (RMSE) of significant wave height below 0.7 m, with the maximum RMSE value less than 0.9 m. 76% of the sites have a correlation coefficient larger than 0.75. For the extreme water levels, the maximum RMSE value is less than 0.66 m and the lowest correlation coefficient is larger than 0.78.

The output of the wave-current model is found to be directly related to wind input and energy dissipation⁹⁷. The discrepancies between the numerical results and field observations may be contributed to the limitations of spatial resolutions of ERA5 reanalysis wind field and Digital Elevation Model (DEM) accuracy. On one hand, there is still some discrepancies in the wind energy input due to the limitations of spatial and temporal resolutions for the reanalysis wind field. On the other hand, the energy dissipations caused by the coastal seabed topography and bottom friction have significant effects on the significant wave height and storm surge level. The accuracy of topographic elevation data obtained from DEM influences the wave decay from depth-induced wave breaking and bottom friction, leading to the discrepancies of simulated and field observed data.

We have further analyzed the discrepancies in significant wave heights and storm surge levels during Typhoon Lekima by comparing the results obtained from the uncoupled and coupled wave-current models (see Supplementary Figs. S4-S6). It can be observed that due to the wave-current interaction, the maximum discrepancy in significant wave heights between two models is about 0.8 m in deep water area, and decreases to 0.4 m in the shallow water area. During the propagation of typhoon-induced wave toward the shore, radiation stress is generated due to the wave energy transfer, which is mainly contributed to the discrepancies in storm surge levels observed between two models. As the typhoon center approaches the shore, the maximum discrepancy in storm surge levels increases from 0.1 m in deep water area to 0.3 m in shallow water area. This indicates that wave radiation stress significantly influences the storm surge in nearshore areas adjacent to the landfall position. In the Northern Hemisphere, currents on the right side of a typhoon’s path generally align with the wave direction, leading to the increase of wavelengths and decrease of wave heights. Consequently, wave-current coupled model exhibits a lower significant wave height (SWH) on the right side compared to the uncoupled model, leading to a negative difference in SWH. On the left side, the opposite effect occurs, resulting in a positive difference in SWH. A similar phenomenon has also been observed in Wang and Sheng⁹⁸ and Samiksha et al.⁹⁹ Moreover, the root mean square error (RMSE) between the wave-current coupled simulation and the observed data is 0.62 m and 0.65 m, while the RMSE between the uncoupled simulation and the observed data is 1.17 m and 0.84 m at S1 and S3 station (see Supplementary Fig. S6). The significant wave heights derived from the coupled model simulation are much closer to the observed data than those obtained from the uncoupled model. When the wave setup effect is incorporated into the simulation, the storm surge level obtained from the coupled model is reduced, showing better consistency with the observed data compared to the uncoupled model simulation, where the storm surge level is reduced, ranging from − 0.27 to 1.01 m at T6 and 0.17 m to 1.50 m at T7 station(see Supplementary Fig. S6). Therefore, the influence of wave-current interactions should be fully considered during the simulations of typhoon waves and storm surges.

Wave and storm surge hazard disaster index

Based on historical wave height data, the annual average occurrence frequency of wave heights for levels I, II, III, and IV at each grid point is calculated, represented by N₁-N₄, respectively. The wave hazard zone is obtained according to the wave hazard disaster index H_wn, which is the annual average occurrence frequency of wave heights for levels I, II, III, and IV at each grid point after weight assignment and normalization¹⁰⁰:

$${H_w}{\text{=0}}{\text{.6}}{N_{\text{1}}}{\text{+0}}{\text{.25}}{N_{\text{2}}}{\text{+0}}{\text{.1}}{N_{\text{3}}}{\text{+0}}{\text{.05}}{N_{\text{4}}}$$

(11)

$${H_w}_{n}=\frac{{{H_w}-\hbox{min} ({H_w})}}{{\hbox{max} ({H_w})-\hbox{min} ({H_w})}}$$

(12)

where N₁-N₄ represent the annual average occurrence frequencies of wave heights for level I, II, III and IV. According to the “guideline for risk assessment and zoning of wave disaster”, the weights for N₁, N₂, N₃ and N₄ are 0.6, 0.25, 0.1 and 0.05, respectively.

We divide four levels Grade I (0.75 ≤ H_wn≤1.0), Grade II (0.75 ≤ H_wn≤1.0), Grade III (0.25 ≤ H_wn<0.5) and Grade IV (0 ≤ H_wn<0.25) for the wave hazard zones according to the normalized wave hazard disaster index H_wn.

The reference datum for the storm surge level is the astronomical tide level in the present study, the storm surge level is defined as the extreme water level minus the astronomical tide level. The storm surge hazard zone is obtained according to storm surge hazard disaster index S_wn, which is calculated the normalized storm surge level of 50-year return period. Similar to the study of Wang et al.⁶⁴, the storm surge level with 50-year return period is adopted for the evaluation factor, since the defense standard for the offshore engineering such as harbours, dike reaches the 50-year return period¹⁰⁵. Four levels storm surge hazard zones Grade I (0.75 ≤ S_wn≤1.0), Grade II (0.75 ≤ S_wn≤1.0), Grade III (0.25 ≤ S_wn<0.5) and Grade IV (0 ≤ S_wn<0.25) are classified based on the normalized storm surge hazard disaster index S_wn.

Joint probability distribution model

Generalized Extreme Value Distribution (GEV) is employed to fit the marginal distributions of variables and assess the extreme significant wave height and storm surge level for a given return period. The Gumbel, Frechet and Weibull distributions are assembled as the GEV distribution family¹⁰¹, where the Gumbel distribution corresponds to Type I of the tail if ξ = 0, Frechet distribution is referred to as having a tail Type II for ξ < 0, and Weibull distribution corresponds to Type III of the tail for ξ > 0. The probability distribution function is expressed as follows:

$$G(x,\mu ,\sigma ,\xi )=\exp \left\{ { - {{\left[ {1+\xi \left( {\frac{{x - \mu }}{\sigma }} \right)} \right]}^{ - \frac{1}{\xi }}}} \right\},\left[ {1+\xi \left( {\frac{{x - \mu }}{\sigma }} \right)} \right]>0$$

(13)

For a given T-year return period, the value of X_T can be estimated using the following equation:

$${X_T}=\mu - \frac{\sigma }{\xi }\{ 1 - {\left[ { - \ln \left( {1 - \frac{1}{T}} \right)} \right]^{ - \xi }}\}$$

(14)

where µ is a location parameter, σ is a scale parameter, ξ is a shape parameter. µ, ξ∈R, σ > 0.

Similar to the studies of Li et al.¹⁹ and Menéndez et al.¹⁰², the quantile-quantile (Q-Q) plots of the significant wave heights and surge levels are analyzed for the validation of GEV method at Hangzhou Bay, Taiwan Strait, Pearl River Estuary, Qiongzhou Strait and Southeast of Taiwan in the present study(see Supplementary Fig. S7 online). It can be seen from the Q-Q plots that the theoretical GEV model fits the simulated annual extreme value data well, indicating the suitability of GEV method.

The Frank copula was adopted in the present study for the joint cumulative distribution function, as shown in Eqs. (15) and (16).

$${F_{XY}}(x,y)={C_{XY}}(u,v)$$

(15)

$$C{\text{(}}u{\text{,}}v{\text{)=}} - \frac{1}{\alpha }\ln \left[ {1+\frac{{({e^{ - \alpha u}} - 1)({e^{ - \alpha v}} - 1)}}{{({e^{ - \alpha }} - 1)}}} \right]$$

(16)

where x and y are random variables, u is the cumulative distribution function F_X(x), and v is the cumulative distribution function F_Y(y). C_XY is the Frank copula distribution function. α is the parameter of the Frank Copula, α > 0.

Environmental contour method

The environmental contour (EC) method is based on the inverse first-order reliability method (IFORM), a reliability-based approach is used to determine contours at a certain confidence level in multivariate systems. It can match corresponding environmental combination parameters along contours of a given return period. There are several challenges, for instance, the variables to be linked must be fitted as functions of independent variables, wind speed and wave height are not independent in actual sea conditions. To reflect the correlation between wind and wave, a copula function is used to link the two variables¹⁰³. The IFORM based on Rosenblatt transformation is adopted to construct two uncorrelated distribution variables U₁ and U₂ with a radius R, return period T and average annual occurrence frequency N of random events. It can be defined as follows:

$$T=\frac{1}{{N[1 - \phi (R)]}}$$

(17)

$$\phi ({U_1})={F_{{V_w}}}({V_w})$$

(18)

$$\phi ({U_2})={F_{{H_s}|{V_w}}}\left( {{H_s}|{V_w}} \right)$$

(19)

where ϕ is the standard normal cumulative distribution function, F_Vw(V_w) is the marginal cumulative distribution function of extreme wind speed, F_Hs|Vw(H_s|V_w) is the distribution of significant wave height under the extreme wind speed. Significant wave height H_s is defined as the mean wave height of the highest one-third of an irregular wave train⁵⁶. The radius R of equal probability sphere is directly related to the return period. In the uncorrelated standard normal space, the radius of equal probability sphere equals the target reliability index, which is determined by the average annual occurrence frequency and return period. The U-space is modeled as a sphere to simplify the joint distribution of random variables and analyze the behavior of multiple random variables¹⁰⁴.

The Rosenblatt transformation is used for the joint probability to achieve for the conversion between the stochastic vectors (U₁, U₂) in the standard normal U-space and environmental variables (V_w, H_s) in the physical space. Consequently, we can obtain the contour lines for wind speed and significant wave height for different return periods.

Conclusion

A series of numerical simulations for the typhoon-induced wave and storm surge are performed during the historical 192 typhoons affecting the southeast coastal and offshore regions of China from 1979 to 2023. We investigate the distributions of extreme significant wave height and storm surge level for different return periods, and propose an assessment method for wave and storm surge hazard zones. The joint probability distributions of annual maximum wind speed and significant wave height along the water depth isobaths are analyzed.

The results show that extreme waves in the study area decrease towards the north and nearshore, as the waves propagate almost parallel to the coastline. The maximum significant wave height occurs in the southeastern regions of Taiwan Island. The extreme storm surge appears to coincide with the bathymetric contours, the surge levels gradually increase from the offshore to nearshore areas as water depth decreases. Extreme storm surges are observed in the nearshore areas, particularly in Hangzhou Bay and Qiongzhou Strait. Four different levels of wave hazard zones are generally distributed parallel to the coastline, the wave hazard level decreases as wave approaches the coastline. Coastal areas are affected by Level IV wave hazards, while storm surge hazard zones exhibit the opposite pattern, where the coastal areas are affected by Level I to Level III storm surge hazards.

The joint probability distributions of wind speed and significant wave height indicate that the significant wave height increases with the increase of wind speed. Environmental contours of Zhejiang and Guangdong provinces are narrowest at low wind speeds, gradually expanded outward as wind speed increases. Environmental contours of Hainan Province are approximately symmetrical, while they are narrowest in the middle and expanded outward on both sides. The wind-wave correlation is strongest in the moderate wind speed range in Fujian Province.

This study could provide a comprehensive understanding of the temporal and spatial distributions of extreme significant wave heights and storm surge levels, it is helpful to minimize the typhoon damages, provide disaster warning and optimize emergency response measures. The hazard maps of the extreme waves and storm surges could be used to identify the extreme significant wave height and surge level for offshore and ocean engineering designs at a given longitude and latitude location, leading to the reduction of risk and investment. In the further studies, the extreme wave heights and storm surge levels will be estimated with the consideration of probable maximum typhoon cyclone parameters.