The Characteristics of Storm Wave Behavior and Its Effect on Cage Culture Using the ADCIRC+SWAN Model in Houshui Bay, China

YIN Chao , HUANG Haijun , WANG Daoru, LIU Yanxia and GUO Ziyue

1) Key Laboratory of Marine Geology and Environment, Institute of Oceanology, Chinese Academy of Sciences,Qingdao 266071, China

2) University of Chinese Academy of Sciences, Beijing 100049, China

3) Hainan Academy of Ocean and Fisheries Sciences, Haikou 571126, China

4) School of Mathematics, Sun Yat-Sen University, Zhuhai 519082, China

Abstract The current storm wave hazard assessment tends to rely on a statistical method using wave models and fewer historical data which do not consider the effects of tidal and storm surge. In this paper, the wave-current coupled model ADCIRC+SWAN was used to hindcast storm events in the last 30 years. We simulated storm wave on the basis of a large set of historical storms in the North-West Pacific Basin between 1985 and 2015 in Houshui Bay using the wave-current coupled model ADCIRC+SWAN to obtain the storm wave level maps. The results were used for the statistical analysis of the maximum significant wave heights in Houshui Bay and the behavior of wave associated with storm track. Comparisons made between observations and simulated results during typhoon Rammasun (2014) indicate agreement. In addition, results demonstrate that significant wave height in Houshui Bay is dominated by the storm wind velocity and the storm track. Two groups of synthetic storm tracks were designed to further investigate the worst case of typhoon scenarios. The storm wave analysis method developed for the Houshui Bay is significant in assisting government’s decision-making in rational planning of deep sea net-cage culture. The method can be applied to other bays in the Hainan Island as well.

Key words storm wave; ADCIRC+SWAN; maximum significant wave height; Houshui Bay; deep sea net-cage

1 Introduction

In the past decades, dozens of typhoon occur from June to November with significant impact in the Hainan Island,especially in the northern coastal areas. Coastal waves induced from typhoon have caused massive damage to deep sea net-cage in the offshore of Hainan Island. It can be evidenced by the typhoon NESAT that hit Houshui Bay in 2011, resulting in the destruction of more than 70% of the offshore net-cage. Damages from typhoon NESAT was estimated to amount to 763 million RMB, making it the most costly storm in history. In essence, most of the coastal disasters are known to be associated with extreme storm waves (Khandekar, 1994). Other recent examples include Rammasun (2014) and Kalmaegi (2014). These events produced huge waves in Houshui Bay causing significant economic losses. These events have led to the identification of storm waves as one of the most hazardous elements to deep sea net-cage in Houshui Bay.

Houshui Bay (northwest of Hainan Island) is a shallow wind sensitive semi-enclosed bay, covering an area of approximately 156 km2(Fig.1). Houshui Bay is the largest deep sea net-cage base of Hainan Province and the third largest port by total tonnage. In this paper, Houshui Bay is redefined, consisting of three sub bays: east, south, and west. Usually, typhoons develop in marine basin, propagate across the continental slope, and then interact with the near shore environment. Waves that are generated in the deeper waters are transformed in Houshui Bay as a result of the dramatic variations in both bottom friction and topography. As the shape of the wave becomes steeper,the offshore net-cage will be in greater threat. With the increasing economic issues in coastal areas, such a potential threat indicates an urgent need for accurate storm wave hazard assessment for typhoon preparedness.

Recent researches have sought to study the effect factors of storm wave features by marine modeling. For instance, Irish et al. (2006) explored the relationship between storm surge and size under the condition of changing bottom slope using ADCIRC model. The USACE Coastal and Hydraulics Laboratory run the ADCIRCSTWAVE model to offer timely emergency managements.Forbes et al. (2010) used the ADCIRC model to obtain higher efficiency and accuracy in real time forecast of storm surge. Dietrich et al. (2011a, 2011b) also successfully investigated the influence of recent hurricanes on the Southern Louisiana coastline using the ADCIRC+SWAN model. The study area is a small bay, experiencing a strong effect of the wave-current interaction. Water depths and currents affect the evolution and behavior of waves. On the one side, radiation stress gradients produced by wave transformation propel set-up and currents. There are high surface currents in the storm center that significantly affect wave heights and directions. Therefore, when using coastal models in a particular application, circulation, tide and wave processes should be considered together.The tight wave-current coupled model ADCIRC+SWAN includes almost all significant processes, such as tides,currents, atmospheric pressure, wind-waves and surges,which ensures good simulation performance.

Fig.1 The location of Houshui Bay. The gridlines represents the area of deep sea net-cage.

In the present study, we carried out a storm wave hazard assessment in Houshui Bay using ADCIRC+SWAN model, which has also been fully applied to hindcast recent hurricanes (Chen et al., 2008; Hope et al., 2013; Martyr et al., 2013; Burleson et al., 2015). This storm wave model is composed of coastal ocean model, nearshore wave model, as well as a synthetic asymmetric gradient wind vortex model. It was used with an unstructured high-resolution mesh incorporating the South China Sea and Hainan Island coastlines (Rego and Li, 2010).

In addition, the model was validated through the hindcast of typhoon Rammasun. After that, the coupled model was employed to simulate the significant historical storms that change in storm strength and track, to deduce wave heights for Houshui Bay at high resolution. We further used the results of the simulations to study the influence of factors such as wind speed, storm track and distance from storm center on the distribution of wave heights. To some extent, the distribution of maximum significant wave height along the coast of Houshui Bay reflects the physical damages level of deep-sea net cage. Therefore, we chose it as the key evaluation index. In the following section of this effort, wave hindcast results were used to derive the spatial differentiation of significant wave height for a 100 year return period in Houshui Bay. In the final section, we infer the region, over which typhoon passes,with the greatest impact on Houshui Bay. The methodology, which can be applied to other bays in Hainan Island,provides scientific basis for rational planning of deep water net-cage culture. Besides, it allows cage culture planners to exercise aggressive and effective storm wave risk management.

2 Methodology

2.1 ADCIRC Model

The adopted ADCIRC model is a two-dimensional version that encompasses features of shallow water, finite element and depth-averaged barotropic equations (Luettich and Westerink, 2004). By solving the Generalized Wave Continuity Equation, water levels can be expressed as:

Further, to obtain the depth averaged velocity, ADCIRC solves the vertically integrated momentum equations:

where U and V are the vertically integrated currents; f is the Coriolis parameter; ζ is the water surface elevation; Psrepresents the atmospheric pressure; ρ0is the reference density of water; α represents the earth elasticity factor; η is the Newtonian equilibrium tide potential; τsxand τsyare the surface stresses; H = ζ+h is the water depth; τbxand τby,are the bottom stress; g is the gravity constant; M, D and B represent lateral stress gradients, momentum dispersion and baroclinic pressure gradient respectively (Kolar et al.,1994).

2.2 SWAN Model

The SWAN model, which is based on the spectral action balance equation, is committed to solving the complicated wave process. The process includes generation,propagation, dissipation, bottom friction, refraction, and other terms. (Booij et al., 1999; Ris et al., 1999; Zijlema,2010):

Both SWAN and ADCIRC models share the same mesh.Since SWAN model has larger time steps, the time of data exchange between ADCIRC and SWAN is set to be the SWAN interval (Dietrich et al., 2011b). Wave exerts stress on the water columns, thus bringing up the water levels when they break along the shoreline. Wind speeds, water surface elevations and flow velocity, which are simulated via ADCIRC are passed every 10 min to the SWAN model.As such, the SWAN model passes the wave radiation stress gradients back to the ADCIRC model. These gradients τs,wavesare defined as:

where Sxx, Sxyand Syyare the wave radiation stresses:

Parameter n is given in terms of group velocity divided by phase velocity (Longuet-Higgins and Stewart, 1964).

2.3 Synthetic Asymmetric Vortex Wind Forcing

Synthetic asymmetric vortex wind fields coupled to ADCIRC were obtained through the gradient vortex wind formula at each computational nodal points and time step.The formulation of the asymmetric vortex wind is derived by Xie et al. (2006):

In the above equation, the surface pressure P is determined by the radius r and the azimuthal angle θ from the typhoon center. Pcrepresents the storm central surface pressure, Pnis the background surface pressure, while Rmaxrepresents the maximum wind velocity radius. The tangential velocity Vasymis obtained through the pressure field:

where f represents the Coriolis force, ρais the air density,and B is the storm shape parameter which controls the gradient of the tangential velocity and eye diameter:

where Vmaxrepresents the maximum wind velocity in the storm, VTis the movement speed of the storm, and WPBLis the wind reduction factor. Parameter B is restricted to values between 1 and 2.5.

The storm data sets used as input files were obtained from the Joint Typhoon Warning Center (JTWC). These data sets of synthetic storms are consistent with the historical records of track, intensity and size. The JTWC data have been used to test forecast errors in Northwest Pacific (Shoemaker et al., 2009).

We chose the northwest Pacific best track data of JTWC to force the ADCIRC+SWAN storm wave model.The JTWC data provide different time varying input parameters, including date and time, latitude and longitude of storm center, surface pressure at the storm center, maximum wind speed (knots), wind speed radii in four directions (NE, SE, SW, NW) at either 34, 50, 64 or 100 knots, and so on. It is notable that the simulation results of storm wave and surge are sensitive to the wind speed radii, and thus contribute to the profile and size of the storm isotachs (Mattocks and Forbes, 2008).

To compare the results computed for typhoon RAMMASUN, three cases were simulated under different wind forcing. Section 3.3 presents a comparison of the wind vortex algorithms between symmetric Holland, asymmetric Holland and generalized asymmetric wind model for typhoon Rammasun.

3 Hindcast of Typhoon Rammasun

3.1 Parameters of Hindcast

The complex bathymetry and topography are shown in Figs.2 and 3. The ADCIRC model grid domain shown in Fig.2 consists of the South China Sea, the Beibu Gulf and the Qiongzhou Strait. This mesh incorporates a significant amount of detail around Houshui Bay, with finer resolution up to 30 m in the nearshore. As well, the deep ocean basin of the South China Sea in mesh resolution ranges from 1 to 10 km, in which the waves are generated. The effects of the dissipation stress and breaking waves are substantial as a result of gentle slope and shallow water depth. Thus, higher resolution mesh is necessary in this study (Blain et al., 1994; Westerink et al., 2008; Zhao and Jiang, 2011). The bathymetry data from The Navigation Guarantee Department of the Chinese Navy Headquarters is used in the whole computation domain, with resolution of up to 50–70 m near the coast.

The Manning’s n formulation is applied to derive the parameter of the bottom friction, which changes based on the local water depth and geomorphological classification.In addition, the largest eight tidal constituents (P1, Q1, K1,O1, K2, N2, M2, S2) are used to force the open boundary in the ADCIRC model. Tidal potential terms are derived from Oregon State University’s TPXO model.

The coupling interval of this simulation and SWAN time step are all set to 10 min. The default SWAN wave frequencies range from 0.031 Hz to 0.548 Hz. The wave directions are divided into 36 sectors, with each sector representing 10˚. The wind drag coefficient Cd≤ 0.0035 is that given by Garratt (1977) and the decay coefficient of surface wind is defined as 0.9.

Fig.2 The model region and topography.

Fig.3 Bathymetry and topography (m) for Houshui Bay, including major geographic locations.

3.2 Typhoon Rammasun

Typhoon Rammasun developed in Western Pacific and moved westward before crossing the Philippines. Then it turned northwestward when it entered the South China Sea.The intensity of Rammasun increased, becoming a super typhoon with peak wind speed nearing 140 kt while passing through the northeast edge of Hainan Island and Leizhou Peninsula. It made a landfall at Fangchenggang in Guangxi Province 2310 UTC, July 19, 2014 as a strong Category (173 km h-1, 950 mb). Fig.5 illustrates the track of typhoon Rammasun. It was a large typhoon, with waves of 16 m high in the deep sea basin and surges of almost 2 m near the coast. Typhoon Rammasun had a large wind field within 280 km radius of the storm cycle.

In this paper, we investigate the behavioral characteristic of typhoon Rammasun as it passed through the South China Sea. Fig.4 shows the calculated significant wave heights in Houshui Bay at 4 hour intervals as Rammasun moves into the deep sea basin, passes through the north continental shelf, and lands in Guangxi Province.

Fig.4 displays the significant wave heights of typhoon Rammasun in Houshui Bay, hindcast by ADCIRC+SWAN model for 0400 UTC July 18 2014 to 0000 UTC July 19 2014. Waves of the two meters were first generated in the east bay. However, as the center of typhoon Rammasun moved northwestward across the Leizhou Peninsula, just the right northeast of Houshui Bay as indicated in Fig.4(d),the waves reached a height of 5 m or higher at 1600 UTC July 18. The maximum winds of 35 m s-1are derived in Houshui Bay, while the maximum wave height isoline of 5.5 m is along the north shore of Linchang reef. Besides,the barrier effect of Linchang reef and the topographic effects control the distribution of wave heights as shown in Fig.4.

Fig.4 Filled contours of the significant wave height and wind vector of typhoon Rammasun at 4 h intervals in Houshui Bay. (a),0400 UTC July 18 2014; (b), 0800 UTC July 18 2014; (c), 1200 UTC July 18 2014; (d), 1600 UTC July 18 2014; (e), 2000 UTC July 18 2014; (f), 0000 UTC July 19 2014.

Fig.5 Schematic of the South China Sea with the 3 oceanographic stations (blue dot) during typhoon Rammasun. The track of typhoon Rammasun is also shown with red line.

In regions where the water is shallow and bathymetry changes rapidly, such as in the eastern and western areas of Linchang reef, the waves transform over short distances before breaking. Meanwhile, broken waves generate radiation stress on the water column, resulting in changes in water surface elevation. As shown in Fig.4(d), it seems that the breaking wave zone is concentrated in the east and north edges of Linchang reef, which appears to be the place where maximum stress gradients is experienced. The radiation stress helped to add dozens of centimeters to the water surface elevations, contributing to over 5%–20%(Dietrich et al., 2010). In the following validation section,the results of the coupled model will be compared to the existing data.

3.3 Validation of the Coupled Model

The simulation results of typhoon Rammasun caused great damage effects to the coast of northern Hainan Island,including those in Houshui Bay. Fig.5 shows the highwater marks and significant wave height data collected at 3 buoys by The South China Sea Branch of State Oceanic Administration (SCSBSOA). The Haikou station (110˚9.6΄ E, 20˚4.5΄N) is located north of Xinhai Port, the Sanya station (109˚29.8΄E, 18˚14.7΄N) is located in the east of Sanya Bay, and the Dongfang station (108˚36.3΄E, 19˚7.0΄N)is located west of Basuo Port. However, we recognized that the observation of significant wave height was terminated at extreme value due to hardware failure in Haikou station. In this section, sea surface elevations and significant wave heights for typhoon Rammasun are employed to assess the model performance.

In Fig.6 the sea surface elevations from the ADCIRC+SWAN simulations are compared with SCSBSOA observations at Haikou/Dongfang/Sanya stations. These preliminary results depict that all the computed water surface levels have the same order of magnitude. The computational results of generalized asymmetric wind model are largely consistent with the observations. The discrepancies are likely the result of the wind velocity, radius of maximum winds, wind speed radii in four directions, and so on. Holland and Asymmetric Holland wind model were also tested, although the results did not show any noticeable improvement. The sea surface elevation produced from the generalized asymmetric wind model was slightly lower than the observations at Haikou station. Meanwhile,the Holland wind model caused larger amplitude fluctuations of sea level. The difference between Holland and generalized model in Haikou station is 0.64 m, whereas the difference between the asymmetric and generalized model is 0.32 m. The results of the three different vortex wind forcing were overlapped together for Sanya and Dongfang stations in Figs.6(b) and 6(c) due to a relatively long distance from the typhoon center.

Fig.6 Sea surface elevations computed using generalized asymmetric wind model (red line), asymmetric Holland wind model (light blue line) and Holland wind model (blue line) vs. SCSBSOA observations (black dots) for the Haikou (a) Sanya (b) Dongfang (c) stations.

The interval of the measured data is 3 h. When the typhoon strengthened or came closer to Hainan Island, the interval was shortened to 1 h. We set the interval of the SWAN outputs to 3600 s (1 h), and used spline fitting method to obtain the continuous curve. The lack of observation data in Houshui Bay makes it difficult to directly validate the simulated results. Haikou Station is 85 km away from Houshui Bay, and Dongfang is 127 km away. Haikou and Dongfang stations are located in nearshore areas with depths of approximately 10 m. They have complicated physical effects, such as wave-current interaction, bottom friction and wave breaking, etc. Fig.7 displays the significant wave height record. It demonstrates that typhoon Rammasun created a maximum wave height of 4 m at Haikou station and almost 2.4 m at Dongfang station. As indicated in Fig.7, SWAN results match the magnitude and time series of wave heights at both stations. For instance, the computed maximum height is 2.1 m at station Dongfang,which is in agreement with the measured peak value of 2.4 m.

The results obtained from different synthetic vortex wind models showed that the time series of water surface level are greatly influenced by wind field asymmetry. The accuracy of the coupled model was evaluated by computed surface elevations and wave heights during typhoon Rammasun. Thus, this model can be used as a basis for the historical storms simulation in the next section.

Fig.7 Significant wave heights (m) during typhoon Rammasun at Haikou (a) and Dongfang (b) station. The black hollow circulars represent measured data, while the blue lines denote computed results.

4 Results and Discussion

4.1 Characterizing Storm Wave Behavior in Houshui Bay

This research applies the ADCIRC+SWAN model to examine the characteristic of storm waves under different conditions of wind speed, distance and storm track in the Houshui Bay. After completion of simulations of all the historical storms, we selected the ones with a significant impact on Houshui Bay. The maximum value derived from comparing wave height values for each mesh vertex during the entire storm process was defined as the maximum significant wave height. The storm events with a long distance from Houshui Bay (beyond 200 km) or with a weak intensity, were discarded in the wave height statistics. Table 1 shows the list of the selected storms. We classified and analyzed the maximum significant wave heights of storms in orders of maximum local wind intensity, shortest distance from Houshui Bay and storm track characteristic,respectively.

Fig.8 displays the maximum significant wave heights that were ranked by Beaufort scale. It indicates that there are two big isolated peaks of wave height located at the east bay and the west bay, respectively. An oval-shaped swath of wave heights above 3 m is observable to the north-east of Linchang reef. The wave height isoline of 2.5 m is around the reef, as shown in Fig.8(a). As shown in Fig.8(b),the wave heights reached as high as 4 m to the northeast of Linchang reef and diminished rapidly closer to the shore.It is clear that the wave height gradients on the right and left sides of Linchang reef became larger with the increase of wind strength. Fig.8 depicts that there is approximately 1 m increase in significant wave height for every level increase in Beaufort scale. Fig.8(e) indicates that the storm wind over 10 degree on Beaufort scale produced waves in excess of 6.5 m to the northeast of Linchang reef and 7.5 m to the northwest. The large wave height gradients illustrate that the waves decrease in height as a result of the effects of rapid change in bathymetry, bottom friction, and wave breaking. Furthermore, it shows that the growth of wave height in the South Bay is limited since it is a semienclosed bay and sheltered by reefs. The area of 4 m isoline expanded and appeared in the South Bay when wind strength was above 10 degree on Beaufort scale. Meanwhile wave height can increase 5 m or even more, thereby threatening the structure of deep sea net cage. The south and southeast of Linchang reef experience lower risk due to the shelter effects. The results of Fig.8 indicate that there is a positive interrelated relationship between the maximum significant wave height and local wind velocity.

Table 1 Characteristics for the simulated storm

In Fig.9 the distributions of the maximum significant wave height in Houshui Bay divided by various distances are compared. The wave height in case (b) is seen to be slightly larger than that in case (a). The area of 3.5 m isoline is expanded slightly in the west bay. The maximum wave height of whole Houshui Bay is less than 4 m when the distance from storm center to Houshui Bay is beyond 100 km. As shown in Fig.9(c), the maximum wave height obviously increased, while the area of 5 m isoline extended to the edge of Linchang reef. However, the center of the storm was more than 50 km away from Houshui Bay. The computed maximum significant wave heights range from about 1.5–2 m in the coastal areas and 5 m to 6 m offshore.As shown in Fig.9(d), the highest wave is found in the northeast and west of Linchang reef. Differences are found to be low in the South Bay. The comparison between cases(a) to (d) revealed a significant increase in the risk of deep sea net-cage when the distance is within 100 km. We find similar results from the previous part: the greatest risk areas are located in the northern and middle of the east bay.

Fig.8 The maximum significant wave heights under different local wind velocities. Gridlines represent the areas of deep sea net-cage. (a), Under 8 degree on Beaufort scale; (b), 8 degree on Beaufort scale; (c), 9 degree on Beaufort scale; (d), 10 degree on Beaufort scale; (e), above 10 degree on Beaufort scale.

Fig.9 The maximum significant wave heights at different distances from Houshui Bay. (a), 150–200 km away; (b), 100–150 km away; (c), 50–100 km away; (d), within 50 km.

A classification comparison between the different tracks was used to examine the influence of storm track on maximum significant wave height. Fig.10 displays the classification results. The left column indicates the four types of historical storm tracks, while the right column shows the corresponding spatial distribution of maximum significant wave height. As shown in Fig.10, every type of storm track has its own characteristics of spatial distribution of maximum wave height. Different from the results obtained in the previous section, Fig.10 shows a large variation in the spatial distribution. In Fig.10(a), for instance,the storm turned north into Beibu Gulf with strong southerly winds on the right hand of the storm center, thus producing isolines of wave height nearly parallel to the latitudes. The storm that crossed the southern part of Hainan Island as exhibited in Fig.10(b) generated wave heights increasing gradually from the east bay to the west bay.Unlike in Fig.10(a) and Fig.10(b), Fig.10(c) and Fig.10(d)indicate that the isolines of wave height are consistent with the depth contour. Fig.10(d) depicts an enormous increase in significant wave height higher than in the other cases.Therefore, we can deduce that most hazardous waves in Houshui Bay exceeding 4 m are mainly caused by storm tracks passing through the northeast corner of Hainan Island and then entering the Beibu Gulf. The reason for this inference is that storm’s counter-clockwise winds create large waves and surge in Houshui Bay and the storm passing through Qiongzhou strait with the northerly winds in the left quadrant of the storm are the most direct factor to push waves against the shoreline. From the results of this analysis we conclude that different moving routes produce different spatial distribution of wave heights.

4.2 Probabilistic Result

To identify a probabilistic worst case in Houshui Bay for the simulated storms, we calculated the wave heights of 100-year return period in the whole computed domain(Krien et al., 2015). As a rule, the level of wave risk chosen to determine the design of coastal engineering projects is based on the wave height of 100-year return period(Dong et al., 2012). In addition, this method is applicable to deep sea net-cage. The sample consists of the highest significant wave height in each year, while the Pearson-III extreme value distribution is applied to derive the 100-year return periods. Fig.11(a) displays the expected storm wave heights in the 100-year return period in Houshui Bay.From this figure, we can clearly identify areas of extreme wave conditions in Houshui Bay. The wave heights range from 2 m in coastal areas to almost 8 m in the north of Linchang reef. The highest storm waves of Houshui Bay are found in the east and west bays. Here, there is a large amount of energy accumulated and passed through the channel because of the geographic characteristics of halfopen bay, threatening the physical structure of deep sea net-cage. The 100-year storm wave height hardly exceeds 8 m in the Houshui Bay due to the effects of water depths and bottom friction. Considering the design working life of the deep sea net cage to be 10 years, we add the results of the wave heights of 10-year return period in Fig.11(b),which generally accounts for about 60%–65% of the wave heights of 100-year return period.

4.3 Synthetic Typhoon Simulation

According to the above results, the most destructive storm track was found to be through the northeast corner of Hainan Island and into Beibu Gulf. To further establish a likely worst case typhoon scenario, two groups of typhoon tracks were designed for sensitivity analysis (Sebastian et al., 2014). We shifted the track of typhoon Rammasun along the Qiongzhou Strait to investigate the results of various landfall locations (lines N19.6–N20.6 and R01–R10 in Fig.12), while maintaining the typhoon’s moving speed, forces, and time series. The moving direction of one group was parallel to the line of latitude, while the other was parallel to typhoon Rammasun. The lines were separated from each other by 0.1˚. The two groups intersect in the north of Hainan Island and Qiongzhou Strait.For a comprehensive assessment of the risks, we chose five representative points, as shown in Fig.13 for the entire cage culture area. Point A is at the outer north edge of Houshui Bay, while points B, C and D are in the north,middle, and south of the east bay, respectively. Meanwhile,point E is in the south bay, near the Jiangyin Reef. Once all of the synthetic typhoons were simulated, the maximum significant wave height of each of the five points was extracted and the maximum significant wave height ratios for synthetic typhoons to typhoon Rammasun were listed in Table 2.

Fig.10 The maximum significant wave heights have the characteristic of storm track. (a), Along the southern coast of Hainan Island, then turning north toward Beibu Gulf; (b), across the Hainan Island from southeast to northwest; (c), landing on the land along the northeast corner of Hainan Island; (d), passing through Qiongzhou strait or Leizhou peninsula and then entering Beibu Gulf. (a’)–(d’) indicate the corresponding spatial distribution of maximum significant wave height.

Fig.11 Spatial distribution of significant wave height in Houshui Bay. (a), For a 100-year return period; (b), for a 10-year return period.

Fig.12 Twenty-one hypothetical typhoon tracks were examined. The new storm tracks are shown in red lines. The original track of typhoon Rammasun is shown in black line.

Fig.13 The area of deep sea net-cage (gridlines) with 5 selected points (A–E) used for the risk assessment of storm wave.

Table 2 The maximum significant wave height ratios for synthetic typhoons to typhoon Rammasun at 5 selected points

As displayed in Table 2, varying typhoon tracks change local wind strength and cause different distribution of the wave field. The two track groups have a similar feature in wave height variation. We realized that as track group R shifted west or group N shifted north, the wave height increased first before ultimately decreasing. The result of group R indicates that points A and B reach the maximum values in track R04, while the maximum value of point C comes from R06. Points D and E as well as the sum of the five points reach their maximum values in track R05. At the same time, points A and B reach the maximum values in tracks N19.9 and N20.1, respectively. Points C, D, E and the sum of the five points reach their maximum values in track N19.8 at the same time. Meanwhile, the sum of the five points in tracks R04, R05, and N19.8 are obviously higher than in the other tracks. Therefore, we can deduce that the area surrounded by track R04 and N19.8,as shown in Fig.14, is the range of typhoon tracks with the greatest impact on the Houshui Bay. It means that a typhoon or super-typhoon which travels from east to west across this area is likely to cause tremendous losses to deep sea net-cage in Houshui Bay.

5 Conclusions

Based on the efficiency and accuracy of the parametric synthetic vortex formulation approach for producing the wind field which could be applied directly to the high resolution mesh at each time step and element node, this study used the wave-current coupled model ADCIRC+SWAN to analyze the historical storm wave characteristics in Houshui Bay in the last 30 years. The conclusions can be summarized as follows:

1) The simulated and observed results of typhoon Rammasun are consistent with each other, which show the validity and efficacy of this method. The results indicated that the typhoon’s large wind field produced a great wave height impacting the entire Houshui Bay.

Fig.14 The area surrounded by red lines represents the range of typhoon tracks which have the greatest impact on Houshui Bay.

2) As shown by the statistics analysis of the simulated results, the maximum significant wave height had a positive correlation with the storm wind speed. On the contrary, there was a negative correlation between the distance from Houshui Bay and the maximum significant wave height. We also realized that the maximum wave height increased significantly in Houshui Bay when the distance from storm center to Houshui Bay was less than 100 km.

3) We also found that every type of storm track had its own characteristics of spatial distribution of maximum wave height. The storm tracks passing through the northeast corner of Hainan Island into Beibu Gulf caused the most hazardous wave heights in Houshui Bay. By taking a unified approach to storm wave modeling, we concluded that wave behavior in Houshui Bay is subjected to the combined effects of geographic characteristic, local wind velocity, and storm track.

4) In the last section, we calculated the 100-year return period wave height in Houshui Bay and deduced the range of typhoon tracks which had the greatest impact on Houshui Bay.

At present, the revenue of deep sea net-cage is more than 1 billion RMB in Houshui Bay, with this figure expected to approach 3 billion RMB by 2020. However, the maximum significant wave height could be as high as 7 m,exceeding the material strength of deep sea net-cage in Houshui Bay. Storm wave could further lead to the destruction of thousands of deep-sea net cages and cause severe national economic losses. Therefore, the key to preventing and reducing storm wave hazards is to understand its formation mechanism and the interaction between storm and specific sea areas. Due to the adaptability and effectiveness of this storm wave model, it could assist government managers with coastal development and aquaculture planning.

Acknowledgements

This work is supported by the Technology Development Foundation for Research Institutes of Hainan Province (No. TV45987). We would like to thank SCSBSOA for providing hydrological data sets. Many thanks also to the anonymous reviewers for offering advice on the manuscript.