The coast of China with large population and lowlying land are highly vulnerable to storm surges, which frequently suffer with extreme storm floods. In the South Yellow Sea (SYS), typhoons, or tropical storms, usually hit the coastal regions through several paths such as typhoons moving northward after landing on Zhejiang or Fujian coasts, typhoons landing with straight path, typhoons active in offshore areas, etc. (Wang et al., 2007; Xiang et al., 2008). Storm surges with high frequency and intensity cause numerous economic losses as well as serious effects on resident lives within coastal regions. For example, in August 1997, Typhoon Winnie struck the coastal area of Jiangsu province result in economics losses of USD 437 million and 200 000 people affected by the flood. In 2000, Typhoon Prapiroon destroyed seawall in coastline and caused economic losses of USD 800 million (China Marine Disaster Bulletin in 2000). Good knowledge of the mechanisms of storm surges development in SYS, therefore, is necessary for estimate of extreme sea level for coastal, and thus benefit for the coastal planning and protections in this region.
In the coastal shallow water area and estuary area, there is an apparent interaction between tide and storm surge. The interaction range can reach more than 0.2 m to 1.0 m, which has a significant impact on the generation and development of storm surge (Bernier and Thompson, 2007; Zhang et al., 2010; Idier et al., 2012). There are two major physical mechanisms for the interaction between tide and storm surges. The first is that the generation of storm surges changes the phase shifts of the tides (Olbert et al., 2013; Zhang et al., 2017). In shallow water, the storm surge makes the water depth increase, so that the friction term in the equation of motion decreases and the time of high tide advances, thereby increasing the tidal phase velocity (Proudman, 1955, 1957; Rossiter, 1961). By analyzing the shallow water equation in more detail, the different contributions of shallow water effect (water depth), advection term and bottom friction term to the interaction between tide and storm surge can be determined (Flather, 2001; Zhang et al., 2010). For example, Wolf and Flather (2005) make conclusion that the shallow water effect dominates the secondary friction when the tidal range exceeds 3 m in the shallow sea area with a water depth of 10 m with numerical simulations. Horsburgh and Wilson (2007) explained that the change of tidal phase led to the observed tidal level ahead/behind the forecast, which made the increase more concentrated in the flood stage forecast through simple numerical models.
The second interaction mechanism is the effect of tides on the magnitude of storm surge. Because the development of storm surge is related to water depth, the storm surge in shallow water is larger than that in deep water (Horsburgh and Wilson, 2007; McInnes et al., 2013), which demonstrates that the change of depth in the tidal cycle leads to the significant effect of storm surges. Prandle and Wolf (1978) found that storm surges at high tide are often limited, while they are often magnified at low tide or during flooding. Horsburgh and Wilson (2007) added that the surge at low water level was significantly larger than that at high water level. Howard et al. (2010) used this explanation to prove the existence of large surge residues in lower waters near the Thames Estuary. Surge amplification caused by the interaction is also sensitive to the shape and time profile of the surge, so as the duration of the surge decreases, the magnification increases (Prandle and Wolf, 1978). Therefore, it is of great significance to study the interaction of tide and surge in coastal waters for the prediction of extreme coastal water level.
The coastal zone of SYS consists of three parts (Fig. 1). Radial sand ridges area being famous in the world is located at the south of the coast area and plays a dominating role on the coastal hydrodynamics of the south coast of Jiangsu. More than 10 large subaqueous sand ridges distributed to the north, northeast, east and southeast directions radiate long strip with 10-100 km in length and 10-15 km in width. A very large Abandoned Huanghe (Yellow) River Delta locates in the middle of the Jiangsu coasts with relatively lower in elevation. Haizhou Bay, a semi closed bay facing to east, locates in the north of the coasts of Jiangsu. Coastline is NNW-SSE aligned in the south and NW-SE aligned in the north with the inflection point at Abandoned Huanghe River Mouth. Although a series of numerical studies have been completed for frequent storm surges in the SYS (Yu et al., 2013; Luo et al., 2014; Xu et al., 2014; Qi et al., 2016; Zheng et al., 2017a, b ), little attention has been paid to the tide-surge interaction within this area. The purpose of this work was to investigate the effect of tidal phase on storm surge by numerical simulation, which can provide a reference for determining the extreme sea level due to typhoon in different paths.
The structure of this paper is as follows: Section 2 presents the storm surge model and verification used in this work. Section 3 describes the distribution characteristics of tide-storm surge interactions along three typical typhoon tracks, which are, Typhoon Winnie (moving northward after landing), Prapiroon (active in offshore areas) and Damrey (landing straightly to the coastline). In Section 4, a series of numerical experiments were carried out to study the tide-storm interaction caused by tidal phase variation. Section 5 discusses the generation mechanism of the tide-storm surge interaction due to tidal phase variation. The conclusions are summarized in section 6.2 MATERIAL AND METHOD 2.1 ADCIRC model description
The Advanced Circulation (ADCIRC) model is employed to simulate the storm surge in South Yellow Sea. The ADCIRC model obtains the depth-averaged barotropic form of the shallow water equations for water levels and momentum (Luettich and Westerink, 2004; Westerink et al., 2008). A continuous Galerkin finite element technique is adopted and a stable and non-oscillatory solution is derived by solving the Generalized Wave Continuity Equation (GWCE) in a combined and differential form of the continuity and momentum equations. The solution technique employs the wetting and drying of elements treatment, and parallelly efficient computation as described in related publications in details. ADCIRC has been validated for various hurricanes and utilized extensively to forecast storm surge and evaluate flood risk by many users throughout the world (Westerink et al., 2008; Dietrich et al., 2010).2.2 Model grids and boundary conditions
A large model, Northwest Pacific Ocean Tide and Storm Surge Model and a local model for South Yellow Sea are coupled in the study. The local model covers the coasts of from Shandong Peninsula to Oujiang River mouth in coasts of Zhejiang, which includes coasts of Shandong Province, Jiangsu Province, the Changjiang (Yangtze) River estuary, and Hangzhou Bay (Fig. 2). High-resolution grids are placed near the coastline and tributaries, while coarse grids are placed offshore. The spatial grid resolution in the model ranges from about 0.5 to 5.0 km, and the elements are about 110 000, and the nodes are about 63 000 (Fig. 3). The Surface Water Modelling System (SMS) grid generator is used to generate the unstructured triangle grids.
The boundary conditions for the local model are the coupled water level of the astronomical tide with storm surge, which are derived from the Northwest Pacific Ocean Tide and Storm Surge Model (the big model). The improved Northwest Pacific Ocean Tide and Storm Surge Model uses the 2D vertically integrated equations in spherical coordinates for tides and storm surges incorporated a quadratic law of bottom friction with the nonlinear advective terms (Zhang et al., 2013), and the DSI method is employed to discrete the equations. The domain covers the East China Sea, South China Sea, Philippine Sea, Japan Sea, Sulu Sea, and adjacent Pacific Ocean areas. The open boundary condition for the large model is given by NAO99b, a global ocean tidal mode developed by the National Astronomical Observatory of Japan (Matsumoto et al., 2000). The results of the large model are in accordance with four main astronomical constituents (M2, S2, K1, and O1) of 435 tide gauges listed in the Admiralty Tide Table.2.3 Wind stress
The surface wind stress components are computed using the quadratic relationships as follows:
where, (τsx, τsy) are the wind stress and Cds is the coefficient of the wind stress, W10-x and W10-y are the wind speed components at east and north directions, respectively, and ρa is the air density. Cds is taken as Yelland and Taylor (1996). Based on the suggestions of Powell et al. (2003) and Donelan et al. (2004), a maximum value about 0.003 5 is taken for the surface wind stress coefficient.
The Holland parameter model was utilized to simulate the wind field and pressure field of the typhoon (Zheng et al., 2017b). The Holland model is a well-known model, which can provide wind field and pressure field of typhoon more accurately. It contains some parameters that are obtained from empirical observation or definitive meteorology knowledge. This model is widely used in risk assessment (Vickery et al., 2009). The typhoon path is obtained from the CMA-STI tropical cyclone best path data defined by the China Meteorological Administration. The background wind field was obtained from the technique of the second-generation reanalysis, i.e. Japanese 55-year reanalysis (JRA-55) carried out by the Japan Meteorological Agency (Harada et al., 2016).
The background wind field and wind field of the typhoon model can be combined as follows:
in which, VM is the wind field of the typhoon model; VQ is the background wind field; e is the weight coefficient used to smooth the two wind fields' connection.
in which, r is the distance from the typhoon center, and R is the radius to the maximum wind speed.
Data of the wind speeds and directions collected during Typhoon Winnie at Ganyu Weather Station, are used to validate the Holland wind fields. Comparisons between the observed data and calculated results are shown in Fig. 4. The Holland wind fields match the magnitude of the wind peaks, and also the oscillations in the wind speeds during the storm. It is indicated good agreement between measured and predicted data, even though there are some differences in the wind direction. The wind fields at the moment of landing or close to Jiangsu coasts are shown in Fig. 5.2.4 Model validations for astronomical tide
To testify the ADCIRC model properly reflect the characteristics of tidal wave propagation in the research region, the simulations for astronomical tides are firstly carried out without meteorological forcing. Figure 6 shows the comparisons of the observed and modelled astronomical tide in the time scale. The semi-diurnal tides are dominant in the South Yellow Sea. The tidal range reaches 5.20 m and 5.90 m at Lianyungang and Lüsi during spring tide, respectively. The result indicates that the model data are well consistent with the observed ones.2.5 Model validations for storm surge
Typhoon Winnie, No. 11th in 1997 of China, was a relatively long period storm characterized by its low pressure, high intensity, and especially its large influence domain. The strongest 2-min continuous wind speed was estimated to reach 60 m/s with 920 hPa as the lowest atmospheric pressure (Table 1). It made landfall categorized as Grade 4 (Typhoon) storm at about 13:30 in August 18, 1997 (UTC, the same in the following) along the coasts of Wenling in Zhejiang Province. Then it moved to north and entered into Bohai Sea (Fig. 2).
Prapiroon Typhoon is the No. 12th in 2000 of China. At 18:00 on August 29, 2000, the eye of Prapiroon was near 26°N, 123.9°E about 600 km southeast of the Changjiang River estuary, with the maximum wind speeds of Level 12. Then the typhoon moved northwest towards the north coasts of Zhejiang and the coast of Jiangsu.
Typhoon Damrey being the No. 10th in 2012 of China, made landfall at Chenjiagang (34.5°N, 119.9°E) in Xiangshui County, Jiangsu Province. The maximum wind speed of the center was about 35m/s with 975 hPa as the lowest atmospheric pressure.
The comparison of the computed water levels by the ADCIRC model with the measured historical data during Typhoons Winnie, Prapiroon and Damrey is depicted in Table 2 and Fig. 7, which shows that the model predicted tidal levels are basically consistent with the observed ones.
Figure 8 is the comparison of measured and simulated storm surges (water level minus astronomical tidal level) during Typhoons Winnie, Prapiroon, and Damrey. For Ocean station Lianyungang, the computed surge peaks were 1.27 m, 0.82 m, and 1.75 m for Winnie, Prapiroon, and Damrey, respectively, which closely matches with the recorded maximum storm surge (1.22 m, 0.75 m, and 1.78 m) reported by the marine monitoring bureau. For station Lüsi, the simulated surge peaks were 1.20 m and 0.81 m for Prapiroon and Damrey, respectively, also close to the recorded maximum storm surge (1.26 m and 1.07 m). There are several water level fluctuations at Qingdao during Typhoon Winnie related to the tide-surge interaction. Wave is not involved in the model to emphasize the storm surge induced by typhoons directly, which could result in the model errors. Runoff is also not included in the model boundary of the Changjiang River estuary in consideration of its minor influence on the calculated results of the coastal areas of SYS. It should be noted that it certainly brings some errors into the result in the region of the Changjiang River estuary. It can also be seen that the storm surge curve of Typhoon Winnie is a single-peak one with long duration (about 1.5 days), whereas the process of Typhoon Prapiroon is a multi-peak one with small amplitude, and for Typhoon Damrey, it is a singlepeak process with large amplitude and short duration. Figures 9-11 are the distribution of surge height during the typhoon process.3 TIDE-SURGE INTERACTION PRESENTED IN MODEL RESULT
The total water level caused by storm and tide (ηST) can be divided into non-tidal residual (ηR), surge (ηS), tide (ηT) and tide-surge interaction (ηI), which can be determined by (Horsburgh and Wilson, 2007):
Figure 12 illustrates the relationship of the maximum surge, non-tidal residual and water level increment caused by the tide-surge interaction during three typhoons at different stations in the SYS. It can be seen that under the action of Typhoon Winnie, the surge of the stations along the SYS is between 0.85 m and 1.24 m, among which those of Stations LXG, SYRM, and YWG are slightly larger and the difference is not obvious. Except for Station JG, the water level increment caused by the tide-surge interaction of each station is generally between 0.10 m and 0.30 m, and that of Station JG can reach 1.04 m. As a result, the non-tidal residuals of JG could be 1.90 m, while the results of other stations are mostly between 1.10 and 1.45 m.
Under the action of Typhoon Prapiroon, the surge of stations along the SYS is mostly between 0.55 m and 0.78 m, while that of JG is much larger with the value of 0.78 m. The water level increment caused by the tide-surge interaction of each station is also between 0.15 m and 0.35 m except for JG, and that of JG station is about 0.77 m. Similarly, the non-tidal residuals of JG stations can reach 1.55 m, which is larger than the results of other stations ranging from 0.70 m to 1.0 m.
Under the action of Typhoon Damrey, the surge of stations along the SYS is between 0.38 m and 2.13 m. It is much larger at the stations near the landing point as Stations YWG, LYG, and HT, and decreases gradually to the South. The water level increment caused by the tide-surge interaction of each station is generally between -0.03 m and 0.43 m, and the maximum occurs at Station DFG. It is much smaller at the station near the landing site and in the southern part of the radiation sandbar.
From the illustration in Fig. 13, the surge peak of Typhoon Winnie occurs 2-6 h before the high tide, while it appears 2-4 h before the high tide for Typhoon Prapiroon. That is, it mainly occurs in the tide rising stage. Under the action of Typhoon Damrey, the surge peak appears at the ebb stage, i.e. 1-4 h after the high tide in the stations approached to the landing point such as Stations HT, LYG, YWG, and XHRM; however, it occurs 1-6 h before high tide at the stations south of AYRM.4 IMPACT OF TIDAL PHASE ON SURGE AND TIDE-SURGE INTERACTION
The time of typhoon corresponding to tide is delayed by 1 to 6 h (expressed by +1 h to +6 h) or advanced 1 to 6 h (expressed by -1 h to -6 h), respectively, to change the tidal phase. About 13 groups of numerical experiments were compared with the numerical experiments without tide. Since the high sea level and surge peak are main concerns during the storm surge, the variation of the moment, magnitude of the surge peak as well as high sea level due to the tidal phase change are discussed in this section.4.1 Occurring time of the surge peak
The numerical results show that when the tidal phase changes, the time of the surge peak of each station during the action of Typhoons Winnie and Prapiroon almost remains unchanged at some stations such as YRM, SYRM, and DLP. In addition, it does not change much at the other stations, which mainly ranges in 2-4 h before the high tide in the tide rising stage (Fig. 14).
Under the action of Typhoon Damrey, when the tidal phase changes, the distribution range of the surge peak time is much wider contrary to the former two case. The surge peak of Stations XHRM, AYRM, and LDK with small tidal range in the middle of the region is evenly distributed between -5 h and +5 h. In other words, the maximum surge could occur at both stages of tide rising or falling, while at the other stations, the maximum surge mainly occurs at the stage of tide falling.4.2 Intensity change of the tide-surge interaction
The calculation results also indicate that the tidesurge interaction changes with the tidal phase variation at each station. During the period of Typhoon Winnie, except for Station JG, the maximum water level increment caused by the tide-surge interaction of each station at the time of the surge peak is between 0.22 m and 0.46 m, and the minimum is between 0.02 m and 0.29 m with the average between 0.14 m and 0.37 m (Fig. 15, Table 3). The results of Stations SYRM, LDK, and DFG are slightly large, while the results of Stations DYP and LXG are comparatively small. When the tidal phase changes, the variation range between the minimum and maximum water level increment caused by the tide-surge interaction is between 0.15 m and 0.33 m. The calculated results of each station have little relation with the tidal range in reality. The maximum value of the wave level rise caused by the tide-surge interaction is 1.09 m, the minimum is about 0.81 m, and the average is 0.97 m at Station JG in the center of the radial sandbar affected by special topography.
During Typhoon Prapiroon, except for Station JG, the tide-surge interaction of each station during the moment of the surge peak is between 0.17 and 0.50 m, the minimum is between -0.02 m and 0.33 m with the average between 0.10 m and 0.44 m. The results of Stations DFG and DLP are somewhat large, while those of DYP and LXG are slightly small. The variation range of tide-surge interaction between minimum and maximum is between 0.06 and 0.37 m. The maximum and minimum water level rise of JG caused by the tide-surge interaction are 0.90 m and 0.49 m, respectively with an average of 0.41 m.
During Typhoon Damrey, the tide-surge interaction is between -0.02 m and 0.47 m, and the minimum is between -0.27 m and 0.15 m with the average between -0.09 m and 0.28 m at the peak surge time. The variation range of the water level rise caused by the tide-surge interaction from the minimum to maximum is between 0.07 m and 0.69 m.
It can be realized that during Typhoons Winnie and Prapiroon, the trend and range of the water level rise triggered by the tide-surge interaction caused by tidal phase change are comparatively consistent, while it has a relatively larger maximum value and a negative minimum value for Typhoon Damrey. Therefore, the variation range of the interaction is large during the tidal cycle. It can be concluded from the calculation results that, there is no obviously proportional relationship between the tidal range and the interaction of the tide and storm surges along the coast of the northern part of Jiangsu Province. The tidal ranges of the stations in the abandoned Huanghe River Delta are obviously smaller than those of the stations in the north and south coasts, but there is no significant difference in the intensity.4.3 Effect on the extreme sea level
Generally, the surge peak and high sea level do not encounter at the same time. Therefore, the extreme water level in coastal areas is generally composed of (a) a moderate storm surge superposed on the hightide level or (b) an extreme storm surge superposed on a moderate tide (Olbert et al., 2013). In order to analyze the effect of the tide-surge interaction on the extreme sea level, the results of the superposition without considering their interaction and the most unpleasant combination in the course of the tidal phase variation are compared in Table 4. It can be found that the interaction has an excessive influence on the total water level, and the superposition result without considering their interaction is not always the most unfavorable situation. Thus, the tide-surge interaction must be considered in calculation of the extreme sea level.5 DISCUSSION
As mentioned above, the tide-surge interaction is mainly caused by two different physical mechanisms (Horsburgh and Wilson, 2007): the advance/lag of the tidal phase caused by the positive/negative surge; and the effect of the water depth change caused by tide on storm surge. In the process of storm surge propagation, the increasing water depth will increase the propagation speed of tides and storm surges, which leads to the tidal phase deviation of predicted and measured tides (Horsburgh and Wilson, 2007). The mathematical model proposed by Horsburgh and Wilson (2007) is shown as follows:
where θ is the phase change of non-tidal residuals, ψ is the phase change of tides, and k is the ratio of the water level rise caused by the tide-surge interaction to the tidal amplitude. Only a small tidal phase shift could trigger the calculated storm surge, and the peak value of the calculated storm surge will shift to the low tide. That is to say, the calculated maximum surge concentrates in the flood stage.
The impact of tidal changes on storm surges can be obtained by simplifying the motion equation (Pugh, 1987):
where CD is the wind stress coefficient, U10 is the wind speed in the x direction at 10 m above the sea level, ρ is the density of seawater, and D is the depth. The equation shows that the effect of the wind stress in shallow water is more likely to produce large surge.
It can be seen that for Typhoons Winnie and Prapiroon the peak of storm surge mainly appears in the flood stage, and the tide-surge interaction is dominated by the tidal phase modulation. The increase of tidal range decreases the ratio k, which reduces the possibility of the overlapping of the residual peak with high water level. In addition, the influence makes the maximum water rise appear far away from high water level. Therefore, the stations of XHRM, AYRM, and LDK in the central region have relatively small tidal range and relatively small influence of tidal phase. Thus, the maximum water level increment mainly occurs about 2-3 h before the high tide. On the contrary, the tidal range of the Haizhou Bay and radiation sandbar is larger than those of Stations HT, LYG, JG, DYP, and the maximum water level rise is closer to the low tide level. Tidal phase variation has little effect on the moment of the maximum water level rise. Meanwhile, the intensity of the tide-surge interaction at most stations is more uniform, and the amplitude of the interaction variation is more uniform when the tidal phase changes, which reflects that the effect of the storm surge and tide in the propagation process is rather stronger than the local influence. The interaction at Station JG in the central region of the radiation sandbanks during Typhoons Winnie and Prapiroon is relatively large, which is concerned with the local modulation of special topography.
From the calculation results in Section 4, it can be concluded that Typhoon Damrey directly acts on the coastal waters, and the tide has a greater impact on the storm surge, especially at the stations near the landing point, such as Stations HT, LYG, and YWG. From the Eq.5, it can be found that the scale of storm surge is significantly affected by the tide. When the tide is at the middle tidal level, the modulation effect of tide on storm surge is the smallest, when the tide is at the low tidal level, the effect is positive, whereas when the tide is at the high tidal level, it is negative. Its magnitude range is affected not only by the tidal range, but also by the topography and typhoon intensity. Since tide and wind stress are completely independent, and the water level increment caused by storm surge depends on wind stress, the appearance moment of the maximum water level increment caused by storm surge varies with tide.6 CONCLUSION
We applied the ADCIRC model to simulate storm surges South Yellow Sea triggered by typhoons in different tracks such as typhoon moving northward after landing, moving to offshore areas and landing perpendicularly to the coastline. The convinced track data from CMA by using the dynamic Holland model generate the required wind field for these typhoons, and the ADCIRC model is used to investigate the maximum surge peak within the coastal area.
The results of the numerical experiments indicate that the surge peak of Typhoons Winnie and Prapiroon appears 2-6 h before high tide, which is mainly in the tidal rising stage. When the tidal phase changes, the time of surge peak does not change so much. The tidesurge interaction is dominated by the tidal phase modulation, and the time of surge peak is insensitive to the tidal phase variation. Under the action of Typhoon Damrey, the surge peak appears at the ebbing stage, i.e. 1-4 h after the high tide at the stations near to the landing point, and it appears 1-6 h before high tide at the stations far away from the landing point. In addition, the tide-surge interaction is dominated by storm surge modulation due to the water depth varying with tide; therefore, the time of surge peak is significantly affected by tidal phase.
During the period of Typhoons Winnie and Prapiroon, except for Station JG, the maximum water level rise caused by the tide-surge interaction of each station at the time of peak surge is between 0.10 m and 0.46 m. The variation range of the minimum to the maximum is between 0.06 m and 0.37 m when tidal phase changes from -6 h to +6 h. The intensity of the tide-surge interaction is uniform for most of stations, and the interaction variation with tidal phase change is also relatively uniform due to tidal phase changes during the propagation process rather than at local position. During Typhoon Damrey, the maximum water level rise caused by the tide-surge interaction is between -0.02 m and 0.47 m at the time of surge peak, and the range from the minimum to maximum of tidesurge interaction is between 0.07 m and 0.69 m when tidal phase changes from -6 h to +6 h. The tide-surge interaction is dominated by tidal modulation, and the magnitude varies greatly with tidal phase.
The maximum water level rise triggered by the tide-surge interaction is 1.09 m and the minimum is 0.81 m with the average being 0.97 m at JG, which is concerned with the local modulation of special bathymetry in this area, and it will be further studied in the future.
Therefore, effects of tidal phase on storm surge depended on storm surge modulation and tidal modulation, which is related to typhoon tracks. The conclusions may provide useful information at the design stage of coastal protection systems.7 DATA AVAILABILITY STATEMENT
The datasets generated and analyzed during the current study are not publicly available due to relative requirements of financially supporting projects but are available from the corresponding author on reasonable request.
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