The Responses of Storm Surges to Representative Typhoons under Wave–Current Interaction in the Yangtze River Estuary

Abstract

Storm surge is one of the most remarkable natural calamities, which is shown as the abnormal sea level changes in the coastal waters during a typhoon event. To investigate the responses of storm surges to the typhoon paths, intensities and coastal dynamics, a coupled wave–current model is used to study the impacts of strong winds, considerable waves and complex currents on storm surges in the Yangtze River Estuary (YRE) during three representative typhoons of Fongwong (2014), Ampil (2018) and Lekima (2019) with different intensities and paths. The model is verified using the measured data on significant wave height and period, water level and current velocity and performs well in modeling real conditions. The numerical results demonstrate that (1) the maximum storm surge occurred in the South Channel (SC) during Fongwong and Lekima while in the North Branch (NB) during Ampil due to the typhoon path and the estuarine terrain. Among the three typhoons, Lekima presented the highest surge, with a maximum value of 1.17 m at SC2 (the inner point of the SC). There was a negative surge during Ampil, which reached −0.42 m at SC2, due to the representative path (SE to NW) and offshore wind action. (2) Tide is the main influencing factor of storm surge as the maximum or minimum value always occurs at the low or high tidal level, respectively. Meanwhile, typhoon intensity is important as it influences the variation rate of surge with higher intensity leading to a sudden increase in surge while the tidal intensity primarily affects the peak value. (3) The wave setup can counteract the wind-induced negative surge. The peak differences between storm surge isoline and wave setup isoline are 0.15, 0.2 and 0.2 m during Fongwong, Ampil and Lekima, respectively, which illustrates the impacts of the combined actions of the typhoon path and intensity on the wave setup. This research emphasizes the influences of wave–current interaction on estuarine storm surge during typhoon events and reveals the potential risks for oceanic disasters like coastal inundation.

1. Introduction

Estuaries are important for local dynamic interactions among land, river and ocean, where hydrodynamic conditions are sensitive to strong winds, waves and currents. As the most frequent disaster in coastal areas, typhoons act shortly and strongly with high wind speeds and may alter the current structure and salinity distribution [1,2,3,4,5]. During the occurrence of typhoon events, winds, waves and currents play crucial roles as the primary environmental factors within estuarine systems. Strong winds can generate considerable waves and complex current structures, which then aggravate local destratification, estuarine circulation and matter exchange [4,5,6,7,8,9].

Storm surge is a remarkable meteorological event caused by typhoon events. According to the sixth appraisal report of the IPCC (The Intergovernmental Panel on Climate Change), global warming and sea level rising raise the risk of typhoons in terms of frequency and intensity, as well as coastal inundation. A large number of studies have investigated the mechanism underlying water level variation and nonlinear interaction in estuaries. For instance, Guo and Lin [10] analyzed historical typhoon data over 20 years and obtained the concrete temporal and spatial distribution characteristics of storm surges. Yu [11] categorized storm surges into four typical forms, including normalized form, unnormalized form, undulated form and symmetric similarity form. The mechanism of storm surge is relatively complex owing to its multiple factors. Musinguzi and Akbar [12] conducted an investigation on surge responses to wind speed, atmospheric pressure, and storm passage and found that wind speed is the predominant factor. Wang et al. [13] focused on storm surges in the Pearl River mouth and observed that typhoons may cause contrary effects inside and outside the bay, which is related to their approaching speed. Thuy et al. [14] discovered a consistent trend of increasing water levels in the Beibu Gulf with the strengthened intensity of typhoons. Wang and Sheng [15] simulated three typhoon events in Canada and examined the mechanism of waves and currents during different types of storm surges. Yang et al. [16] concluded that bottom roughness and advection are prominent factors affecting the tide–storm surge interaction by analyzing nonlinear elements.

Numerical modeling has been proven to be an efficient approach in investigations of storm surges since the 1970s [17,18,19,20,21]. Among various dynamic factors, waves affect the coastal circulation and coordinate the current structure. Hence, the wave–current interaction (WCI) exhibits pronounced intensity during storms. The influence of WCI leads to a notable enhancement in the interference coefficient and, consequently, redistributes the local flow field [22,23,24,25,26,27,28]. Dietrich et al. [29] were the first to apply ADCIRC coupled with the SWAN model to simulate storm surge. This model garnered significant attention and, subsequently, found applications in storm surge studies in the United States, Korea, and China’s Zhujiang Estuary and Hangzhou Bay (HB). Mao and Xia [30,31] utilized the FVCOM coupled with the SWAN model to study the storm surge in a single-inlet lagoon system and further applied the model to oceanic systems with multiple inlets.

Estuaries in China are faced with potential hazards of tropical cyclones [32,33]. The influences of typhoons present two aspects. One involves meteorological calamities of strong wind and torrential rainfall induced by typhoon passage, and the other involves oceanic forcings of considerable waves and coastal floods [34,35]. The Yangtze River Estuary (YRE) is located between Zhejiang and Jiangsu provinces, straightly facing the East Sea (shown in Figure 1), which is considerably susceptible to frequent typhoon impacts. The main channel length of the YRE spans 232 km from Jiangyin to the river mouth and consists of two prominent branches known as the North Branch (NB) and the South Branch (SB). As it flows downstream, the SB is divided by the Changxing and Hengsha Islands into the North Channel (NC) and the South Channel (SC). According to the data from the China Meteorological Administration, typhoons generated from 5° N~22° N on the Northwest Pacific Ocean are more likely to incur coastal disasters in China, especially in summer and autumn [36,37,38]. During most typhoon events, the prevailing wind typically originates SW and possesses a subdued intensity below 5 m/s when in close proximity to the YRE [39]. Nonetheless, upon making landfall, the wind velocity may increase significantly to over 20 m/s [40].

This study aims to investigate the responses of storm surges to the three representative typhoons of Fongwong (2014), Ampil (2018), and Lekima (2019) with different intensities and paths under WCI conditions in the YRE. Figure 1 contains the major bathymetric features of the study and the paths of three typhoons. A two-dimensional hydrodynamic model is established by coupling with a wave model. The main focus of this study primarily examines the processes and distributions of storm surge in the YRE under WCI conditions. In addition, the nonlinear relationships between storm surge and tide, wind and wave are discussed by distinguishing the respective effects. The conclusions of this study have practical implications for comprehending the potential hazards of storm surges in coastal estuaries, such as the YRE. Furthermore, this study provides a valuable reference for regional risk management strategies.

2. The Three Typical Typhoon Processes

A tropical cyclone is defined as a low-pressure eddy generated above the sea surface of the tropical ocean, such as the Northwest Pacific Ocean. The value of wind center speed is used to divide the specific intensity grades of cyclones, which is as formulated by the China Meteorological Administration, as shown in

Table 1. Cyclone grades defined by China Meteorological Administration.

Maximum Center Speed (m/s)	Grade	Definition
10.8~17.1	6~7	Tropical Depression
17.2~24.4	8~9	Tropical Storm
24.5~32.6	10~11	Strong Tropical Storm
32.7~41.4	12~13	Typhoon
41.5~50.9	14~15	Strong Typhoon
≥51.0	≥16	Super Typhoon

. A typhoon is a kind of tropical cyclone once the maximum average center wind speed is above 32.7 m/s.

Figure 2 presents the variations of water level, wind velocity and significant wave height and period during Fongwong. The data on water level and wind velocity were collected from the Sheshan Station. The data on wave height and period were measured at Yangkougang station. Fongwong was generated close to the Philippines at the beginning, and it gradually became the intensity of a tropical storm (grade 8~9) when it landed in the YRE. The intensity of Fongwong was relatively low, and its maximum speed was 16.8 m/s (measured at the Sheshan station), but its variable movement directions (Figure 1) deserve a more detailed study. The exact landing moment was at 14:00 on 23 September 2014.

Figure 3 presents the variations in the main dynamics collected at Yangkougang station during Ampil. Ampil was generated over the Northwest Pacific Ocean, where the typhoon center was about 1360 km away from Zhejiang Province. Ampil landed at Chongming Island in Shanghai at 12:00 on 22 July 2018, and the maximum measured wind speed near the typhoon center was about 28 m/s. After it landed, the direction of Ampil gradually turned NW with declining wind velocity. Ampil was the strongest typhoon event to land directly in the YRE since 1990. The path of Ampil formed a cross with Fongwong (Figure 1), which is another meaningful process.

Figure 4 presents the variations in the main dynamics measured at Yangkougang station during Lekima. Lekima was generated in the Philippines and moved towards the north. It was a super typhoon landing in Taizhou with a wind intensity over Grade 16 (the wind speed of the typhoon center was ~52 m/s). As the strongest typhoon event in 2019, although it merely passed the YRE, it still caused serious damage in the adjacent regions. Meanwhile, the path of Lekima was away from the main branches of the YRE without direction changes during the process (Figure 1), so it was selected as another representative path.

3. Model Setup

A two-dimensional hydrodynamic model was established by coupling the wave model in MIKE21 for simulations of storm surges [39]. The governing equations and other parameter-setting rules can be found in the MIKE Manual [39]. The details of the present model are discussed below.

3.1. Study Area and Mesh

The domain covers the YRE from Jiangyin to the river mouth. The study area ranges from 26.9° N to 34.4° N and 120.2° E to 125.6° E, spanning 810 km in the N-S direction and 500 km in the W-E direction (Figure 1). This extensive study area covers the main center positions in typhoon paths and can reflect the regional water exchanges and current structures. The unstructured triangular mesh contains 46,066 nodes and 89,710 elements (Figure 5). The element scales decrease gradually from the east open boundary to the channel of the YRE, where the maximum value is 33,000 m in the sea boundary and the minimum value is 10 m in the inner channel. Refinement in the core research area can result in superior efficiency in simulations. Meanwhile, the position of the Deep-Water Channel Project is refined to elaborately present the dynamics variation around the complex structure.

3.2. Hydrodynamic Model

The 2D hydrodynamic model is mainly driven by the continuity equation and horizontal momentum equations.

The continuity equation is obtained as follows:

$$\frac{\partial h}{\partial t}+\frac{\partial h\overline{u}}{\partial x}+\frac{\partial h\overline{v}}{\partial y}=hS$$

(1)

where t is the time; x and y are the coordinates; h is the total water depth which is calculated based on the surface elevation and still water depth; S is the magnitude of the discharge due to point sources; and $\overline{u}$ and $\overline{v}$ are the depth-averaged velocities in the x-direction and y-direction, respectively.

The horizontal momentum equations are obtained as follows:

$$\begin{array}{l}\frac{\partial hu}{\partial t}+\frac{\partial h{u}^2}{\partial x}+\frac{\partial hvu}{\partial y}=fvh-gh\frac{\partial \eta }{\partial x}-\frac{h}{{\rho }_0}\frac{\partial p_a}{\partial x}-\frac{g{h}^2}{2{\rho }_0}\frac{\partial \rho }{\partial x}\\ +\frac{{\tau }_{sx}}{{\rho }_0}-\frac{{\tau }_{bx}}{{\rho }_0}-\frac{1}{{\rho }_0}\left(\frac{\partial s_{xx}}{\partial x}+\frac{\partial s_{xy}}{\partial y}\right)+\frac{\partial }{\partial x}\left(h{T}_{xx}\right)+\frac{\partial }{\partial y}\left(h{T}_{xy}\right)\end{array}$$

(2)

$$\begin{array}{l}\frac{\partial hv}{\partial t}+\frac{\partial huv}{\partial x}+\frac{\partial h{v}^2}{\partial y}=-fuh-gh\frac{\partial \eta }{\partial y}-\frac{h}{{\rho }_0}\frac{\partial p_a}{\partial y}-\frac{g{h}^2}{2{\rho }_0}\frac{\partial \rho }{\partial y}\\ +\frac{{\tau }_{sy}}{{\rho }_0}-\frac{{\tau }_{by}}{{\rho }_0}-\frac{1}{{\rho }_0}\left(\frac{\partial s_{yx}}{\partial x}+\frac{\partial s_{yy}}{\partial y}\right)+\frac{\partial }{\partial x}\left(h{T}_{xy}\right)+\frac{\partial }{\partial y}\left(h{T}_{yy}\right)\end{array}$$

(3)

where f is the Coriolis parameter; ρ₀ is the reference density of water; ρ is the density of water, p_a is the atmospheric pressure; τ_sx and τ_sy are the surface stress components; τ_bx and τ_by are the bottom stress components; and T_xx, T_xy and T_yy are the lateral stresses.

The three open boundaries are driven by the time-varying tidal level data from a harmonic model called the Global Tidal Model [41], which accounts for eight main astronomic components (M₂, K₂, S₂, N₂, K₁, P₁, O₁, and Q₁) and covers the entire China Sea. Apart from the open boundaries, river boundaries are driven by constant discharges for simulations. In this model, Jiangyin (as the representative station of the Yangtze River) and Cangqian (stand for Qiantangjiang) are taken as the upstream river boundaries with the discharges of 28,484 m³/s and 1000 m³/s, respectively. The threshold depths of drying, flooding and wetting are set as 0.005, 0.05 and 0.1 m, respectively. The bathymetry of the YRE and HB has been conducted by Kuang et al. [1] and Chen et al. [42], whose studies were based on the measured data obtained from the high-resolution charting of the People’s Liberation Army Navy and data obtained from remote sensing of the National Oceanic and Atmospheric Administration (NOAA). The bed resistance is described by the Manning number, which is related to the sediment grain size and the water depth as follows:

$$M=\frac{2.5\sqrt{g}\ln (\frac{30h}{k_{s}e})}{h^{1/6}}$$

(4)

where h is the water depth; g is the gravitational acceleration; and k_s is the bottom roughness height. The grain size in the YRE is 44.9~94.9 μm, with the Manning number in the range of 68~94 m^1/3/s varying in the domain.

The wind stress is obtained using the following empirical relation:

$$\overline{{\tau }_s}={\rho }_a{c}_d\left|u_w\right|\overline{u_w}$$

(5)

where ρ_a is the density of air; c_d is the drag coefficient of air; and $\overline{u_w}=(u_w,v_w)$ is the wind speed at 10 m above the sea surface. The wind data from 2014 to 2019 were downloaded from the ECMWF (European Centre for Medium-Range Weather Forecasts) with a resolution of 0.25° × 0.25°, which covers the initialization periods and simulation periods.

The shallow water equation requires the CFL (Courant–Friedrichs–Lewy) number to be within 1, so the time step was set as 30 s with the self-adaptive CFL number as 0.8.

3.3. Wave Model

The spectral wave module was launched to establish the wave model. The governing equations can be found in the MIKE 21 manual [39] and the parameter setting was in accordance with Wang et al. [43]. The relationship between the action density $N(\sigma ,\theta )$ and the energy density $E(\sigma ,\theta )$ is be defined by the following equation:

$$N(\sigma ,\theta )=\frac{E(\sigma ,\theta )}{\sigma }$$

(6)

where the $\sigma$ is relative angular frequency and $\theta$ is the wave direction.

The energy source term S is constituted for five representative components: the wave energy generated by wind ($S_{in}$), the wave energy transferred due to nonlinear wave interaction ($S_{n1}$), the dissipation of wave energy due to white capping ($S_{ds}$), the dissipation of wave energy due to bottom friction ($S_{bot}$) and the dissipation of wave energy due to surface wave breaking ($S_{\mathit{surf}}$). The calculation is as follows:

$$S=S_{in}+S_{n1}+S_{ds}+S_{bot}+S_{surf}$$

(7)

To realize the coupling process, the wave radiation stresses are the key inputs of the hydrodynamic model, which can be obtained from the numerical results of the wave model. The equations of wave radiation stresses in the three directions during the wave propagation are as follows:

$$S_{xx}=\rho g\int \left(n{\cos }^2\theta +n-\frac{1}{2}\right)Ed\sigma d\theta$$

(8)

$$S_{xy}=S_{yx}=\rho g{\displaystyle \int n\sin \theta \cos \theta Ed\sigma d\theta }$$

(9)

$$S_{yy}=\rho g\int \left(n{\sin }^2\theta +n-\frac{1}{2}\right)Ed\sigma d\theta$$

(10)

where S_xx, S_xy and S_yy are the wave radiation stresses in the xx-, xy- and yy- directions, respectively, and n is the group velocity. The wave radiation stresses are significant in coastal wave propagation, such as wave reflection and wave breaking.

According to previous studies, the wind velocity obtained from ERA5 is generally lower than the real values [44,45,46]. Fan conducted an investigation to determine the coefficient between the ECMWF data and the measured data in the Bohai Sea [45]. That study obtained a correction coefficient distribution ranging from 1.10 to 1.55. In the present study, the correction coefficient was set as 1.3, and the wind data were corrected before being input into the wave model. Other important parameters in the wave module, including the wave breaking (Gamma), the bottom friction (sand grain size, d50), and the dissipation coefficient, were set as defaults with values of 0.8, 0.00025, and 0.15, respectively [43,47].

3.4. Model Validation

Model validations are quantified based on the RMSE (Root Mean Squared Error) and the Skill number [48]. RMSE is a statistical method to judge the difference between the measured and simulated data, while the Skill number provides an index of the agreement between the model data and the real data. The equations of the two kinds of assessment are defined as follows:

$$RMSE=\sqrt{\frac{{\displaystyle \sum _i^n{({\eta }_{measured}^i-{\eta }_{simulated}^i)}^2}}{n}}$$

(11)

where ${\eta }_{measured}^i$ is the ith measured data; ${\eta }_{\mathit{simulated}}^i$ is the ith simulated data; and n is the total number of observations. A lower value of RMSE stands for better accuracy of the model. In general, 0.5 is taken as the critical value.

$$Skill=1-\frac{{\displaystyle \sum _{i=1}^N{\left|M_i-D_i\right|}^2}}{{\displaystyle \sum _{i=1}^N{(\left|M_i-\overline{D}\right|+\left|D_i-\overline{D}\right|)}^2}}$$

(12)

where M_i and D_i are the ith model result and the in situ measured data, respectively; $\overline{D}$ is the mean value of the in situ measured data; and N is the number of observations.

Figure 6, Figure 7 and Figure 8 show the validations of water level, current velocity, and wave based on our previous work [46], with the assessment values presented in the figures. The station positions are shown in Figure 1. All simulated data on the hydrodynamic factors match well with the measured data in the following figures.

According to the RMSE and the Skill numbers, the indictors are within the appropriate ranges. Meanwhile, the corresponding trend in the validations of the water level, current speed, current direction, and significant wave height and wave period illustrate the excellent performances of both the hydrodynamic model and the wave model. Therefore, the coupled model can be applied to the simulations.

4. Results

As a middle tide-dominated estuary, the typical position and coastline of the YRE are propitious to the accumulation and development of storm power. The historical maximum storm surge in the YRE exceeded 3.0 m, which caused significant risks to life and property safety in the nearby coastal cities, such as Shanghai and Hangzhou. Based on the simulations of the three typical typhoon events, the spatial and temporal distributions of storm surges were obtained for qualitative and quantitative analysis. A common calculation for storm surge is H_WCI minus H_AT, where H_WCI is the surface elevation simulated under WCI conditions and H_AT is the result when astronomic tide acts independently.

4.1. Temporal and Spatial Variation Characteristics of Fongwong

According to the measured data on typhoon Fongwong, the simulation period (20–26 September in 2014) covered the entire process, consisting of the developing, maturing and weakening stages. Figure 9 shows the variations of storm surge during Fongwong, in which the typhoon landing moment is marked by a blue arrow. It is clear that the storm surge was dominated by the tide when the typhoon was far from the YRE, and the value almost vibrated around 0. When the typhoon moved close to the estuary, all study points experienced an increase in storm surge simultaneously and gained their peak at 6:00 on 23 September, which was earlier than the landing moment due to the S-N moving direction. The maximum surge value of the inner channel was 0.90 m at NB1, which was higher than the offshore value of 0.62 m at NB2. Such a difference resulted from the narrow width and low current speed inside the NB. The maximum surge values at SC2 and NC2 were about 0.97 and 0.68 m, respectively, while the SC1 and NC1 presented values of 0.90 and 0.76 m, respectively. As the typhoon moved away from the YRE and the intensity declined, the storm surge gradually recovered and its value vibrated around 0 after 25 September. According to the typhoon process, the storm surges at different points lasted for 3–4 days. The inner point suffered a more intensive storm surge than the offshore points in the NB and NC, but the difference in the SC was relatively small.

To visualize storm surge variations directly, the distribution of storm surge at different time points (with an interval of 3 h) is shown in Figure 10. Figure 10 illustrates that during the developing stage, a strong wind initially caused high surge in the HB (Hangzhou Bay). As the typhoon moved toward the north, the surge center also moved, accompanied by an increasing value. Meanwhile, the surge center led to a complex current direction, particularly at the estuarine mouth. Additionally, the intensified flood tide current brought about more storm surge than the ebb tide current. When the typhoon moved toward NE, the surge center shifted with the wind to Jiangsu province along the coastline and decreased with declined wind speed. When the typhoon moved away from the estuary, most areas recovered to common hydrodynamic conditions. This synchronous behavior between typhoon path and storm surge variation illustrates the consistent response and recovery of surge in the channel and the offshore area. However, the storm surge in the NB failed to fade immediately due to the narrow channel, shallow depth and lower current speed.

4.2. Temporal and Spatial Variation Characteristics of Ampil

The simulation period of Ampil ranged from July 20 to 26 in 2018, and the landing moment was at 11:00 on July 22 with a center wind speed of 28 m/s. Figure 11 shows the variations in storm surge during Ampil. Similar to Fongwong, the surge vibrated around 0 before the typhoon landed and rapidly increased to the peak. The maximum value at NB1 was 0.83 m, but the SC showed a lower value due to the farther distance away from the path, so the typhoon path is important to storm surge in terms of distance. After the typhoon landing, the storm surge suddenly dropped to a negative value, and it decreased to −0.42 m (at SC2) once because all study points were located on the left side of the path and affected by the anticlockwise cyclone. After the typhoon landed, the dominant wind shifted to the offshore direction. Comparing the two typhoon events (Fongwong and Ampil), the surge variation during Ampil experienced a rapid increase and, subsequently, a rapid decrease. However, the surge peak showed a slight difference. These results indicate that typhoon intensity and astronomic tide are two significant factors among all the primary elements impacting the rise in water levels. The impacts of typhoon intensity primarily occur in the surge process, while the tide primarily affects the peak surge value.

Ampil was a special typhoon that developed during a neap tide and caused an obvious negative surge. To further investigate this rare negative surge, the distribution of storm surge from 21 to 23 July in 2018 is shown in Figure 12. At 12:00 on 22 July, the surge achieved its peak (Figure 12g) in the main branches and decreased to a negative value within 9 h. As the typhoon gradually moved landwards, the regional negative surge occurred, except at the upstream site, because the seaward wind dominated (corresponding with Figure 11), which intensified the ebb tide current further. At 12:00 on 23 July, the sea level began to recover. Additionally, the surge center path was consistent with the typhoon path, which stresses the importance of the path. The high value of the upstream surge resulted from the lifting actions of runoff.

Ampil caused a limited surge in the inner part of the estuary, and the maximum value mainly occurred in the NB. The negative surge was evident in the SB, owing to the landing position that led to a lower water level on the left side of the typhoon path where the YRE was. However, this typhoon event also resulted in significant damage to the coastal cities. A lower water depth of the Deep-Water Channel Project causes difficulties in mooring. Moreover, the SB plays a vital role in fresh water supplies because it links the Dongfengxisha, Chenxing and Qingcaosha reservoirs. If the negative surge period lasted a longer time, the water supplies might have faced considerable challenges. Therefore, the investigation of the storm surge during Ampil provides meaningful information for estuarine risk prevention.

4.3. Temporal and Spatial Variation Characteristics of Lekima

The simulation period of Lekima was from 7 to 13 August in 2019. This event never landed in the YRE, so the approaching moment was set as the moment when it crossed the upstream river of the YRE (at 15:00 on 10 August with a center wind speed of 23 m/s). Figure 13 shows the variations in storm surge during Lekima. Compared with Fongwong and Ampil, although Lekima just crossed the upstream river of the YRE, it caused the most serious surge in terms of super typhoon intensity. As shown in Figure 13, the surge value before the typhoon vibrates above 0. The maximum surge presents at SC2, and the peak might have reached 1.50 m. This event proves that typhoon intensity is one of the most significant dynamics affecting storm surge. The storm surge lasted 2–3 days, which was shorter than the Fongwong-induced surge and longer than the Ampil-induced surge, so the high surge was mainly maintained by the tide.

Figure 14 shows the surge distributions with current velocity during Lekima. As shown in the figure, the surges in the HB and SB were relatively high before the typhoon approached due to the strong wind. When the typhoon moved close to the upstream river of the YRE, the storm surge center remained in the YRE for a long time (Figure 14c–h). When the typhoon left far away, the surge tardily decreased, especially in the branches, revealing that the typhoon accumulated a significant amount of water inside the channel. The surge center path was consistent with the typhoon path from S to N. From 18:00 on 11 August, the offshore area faced a negative surge, while the channel and mouth areas presented a high surge due to the weak ebb tidal actions during the neap tide.

4.4. Summaries of Storm Surges Variations during Typical Typhoon Processes

The three representative typhoons show evident differences in terms of intensity and path. By comparing the surge characteristics during these three representative typhoons, both similarities and differences were obtained and are summarized in

Table 2. Summaries of storm surges during the three typhoon events.

Typhoon	Fongwong	Ampil	Lekima
Year	2014	2018	2019
Landing	Directly	Directly	Passed
Path
Tide	Spring tide	Neap tide	Neap tide
Intensity	Low	Middle	High
Storm surge	All positive	Positive to negative	Positive
Lasting time	3–4days	2 days	2–3days
Peak value (m)	0.97 (SC2)	0.79 (NB1)	1.17 (SC2)
Variation rate	Slow	Fast	Slow–fast

. Although the typhoon intensity of Fongwong was much lower than the other two high-intensity typhoons, it showed a longer-lasting time of storm surge for about 3–4 days at all study points due to the intensive spring tidal actions. Ampil landed north of the YRE and moved toward NW (from sea to land). It brought about a rapid increase and then a rapid decrease in storm surge. The storm surge lasted only two days, while the negative surge remained even for 3 days, and it caused the lack of water supplies. As the strongest typhoon among the three events, Lekima only passed the upstream river of the YRE, but induced the highest storm surge, which demonstrates that the storm surge is more sensitive to typhoon intensity than the landing position.

Overall, tidal intensity, typhoon intensity (wind speed), landing position and typhoon path are of great importance during a storm surge process. Their combined functions characterize the storm surge processed in the YRE.

5. Discussion

The interactions among wind, wave and tide have a vital influence on the mechanism underlying storm surge variations. Previous investigations have indicated that the nonlinear interaction between tide and wind is related to the landing moment, typhoon path, tidal intensity, water depth and location [49,50,51]. Thomas et al. [52] concluded that storm surges have a strong nonlinear relation with tide, which was consistent with the conclusion drawn by Peng et al. [53]. Furthermore, the wave–current nonlinear interaction is one of the most meaningful factors. Waves can alter the tidal level by changing the surface and bottom stresses. Meanwhile, wave radiation stresses also have distinct effects on storm surge, with a contribution of 2–5%. In this section, to figure out the key interactions between the main dynamics and storm surge, four different dynamic combinations were examined, as shown in

Table 3. Information about the dynamic conditions.

Condition	Module	Dynamics	Representative Water Level
1	Hydrodynamic	Tide	HAT
2	Hydrodynamic	Tide + wind	HWI
3	Hydrodynamic + wave	Tide + wave	HWA
4	Hydrodynamic + wave	Tide + wind + wave	HWCI

. Previous studies [54,55,56] named the storm water level (H_WCI) as the total water level (Condition 4). The storm surge H_SS is the storm water level (H_WCI) excluding the astronomic tide actions H_AT (Condition 1), which can be described as H_SS = H_WCI − H_AT. The wave setup H_WS can be obtained from the water level under the combined actions of tide and wave (Condition 3), while excluding the astronomic tide actions H_AT (Condition 1) as H_WS = H_WA − H_AT. The wind-induced surge H_WT can be gained by the water level under the combined actions of tide and wind (Condition 2), while excluding the astronomic tide actions H_AT (Condition 1) as H_WT = H_WI − H_AT. In the present study, the results of H_WS cannot exclude the influence of wind-induced waves and the interaction between current and waves on the water level, so it may overestimate the real situation of the wave setup. The nonlinear interaction of astronomic tide–storm surge–wave is calculated as H_NI = H_SS − H_WS − H_WT, which represents the residual water level.

5.1. The Effects of Different Dynamics on Surges during Typical Typhoon Events

To reflect wind, storm wave and tide functions on the surge and to find the nonlinear interactions, the surge variations under different conditions were investigated for the three typhoon events and are shown in Figure 15, Figure 16 and Figure 17.

Figure 15 shows the surge, astronomic tide and nonlinear interaction during Fongwong. The wind setup presented a positive–negative trend. The wind setup declined at a decelerating rate after the typhoon landing. Meanwhile, the wave setup was consistent with the typhoon process. During the typhoon weakening stage, this kind of surge is close to the storm surge, when it becomes the main component of storm surge. These results not only reflect that waves can counteract the negative action of seaward wind on water level but also prove the importance of waves during the storm surge. The nonlinear interactions at the inner points were slightly higher than those at the offshore points. Moreover, there was another phenomenon showing that the variation trends of surge and astronomic tide were contrary to each other. Take NB2 as an example, when the surge achieved the peak, the astronomic the tide declined to the lowest value, so tide is the main factor in generating storm surge.

Figure 16 shows the surge, astronomic tide and nonlinear interaction during Ampil. Different from Fongwong, the storm wave action during the first half of the event corresponded with the wind action, but during the last half of the event, it maintained a positive value and gradually declined to 0, while both the storm surge and wind setup showed negative values. The nonlinear interaction exhibited obvious variation after the peak of storm surge. As mentioned before, a negative surge is strongly related to the typhoon path and wind direction. All the study points were located on the left side of the typhoon path and affected by the anticlockwise cyclone. In fact, compared to Fongwong, the typhoon intensity of Ampil was much stronger, but the wave setup was almost the same. This may be explained by two aspects. On the one hand, Fongwong was coincident with the spring tide, wherein the intensive tide current might have strengthened the wave actions and weakened the wind-induced wave intensity. On the other hand, the almost perpendicular moving angle could have also contributed to the wave setup. The nonlinear interaction during Ampil was weaker than that during Fongwong. The neap tide diminished the surge with limited vibration at the beginning and at the end, so the astronomic tide affected the nonlinear interaction significantly.

Figure 17 shows the variations in storm surge, astronomic tide and nonlinear interactions during Lekima. Similar to Fongwong and Ampil, the wind setup presented a positive-to-negative phase, and there were contrary variation trends of the surge and astronomic tide. When Lekima was approaching, the offshore wave setup contributed ~50% to the total storm surge, while the inner points accounted for 30%. As the typhoon gradually moved away from the YRE, the wind setup became negative and the wave setup played a vital role in replenishing the water level. Compared to Fongwong and Ampil, the nonlinear interaction during Lekima was apparent and lasted for a long time. In addition, the surge vibration was more violent during Lekima. The reasons were that the typhoon path was far from the YRE and the astronomic tide dominated the surge.

5.2. The Mechanism of Surge Variations during the Storm Events

To compare the surge characteristics during the three representative typhoon events, the similarities and differences are summarized in this section.

Under the wind–tide condition, the wind setup during the three typhoons presented a negative surge in the last half of the process in common. The maximum wind setup increased with a rise in typhoon intensity, and both of them reached the peak simultaneously. The offshore wave setup was relatively higher than that at the inner points due to the fact that the inner channels are dominated by the runoff and tide, while the shoal area is wide and exposed to waves. In addition, wave setup is not only affected by the wind stress but also related to the astronomical tide, i.e., the spring tide brings about a higher wave setup than the neap tide. According to the results of Condition 2 and 4 (tide + wind and tide + wind + wave), the wave contributed to the predominant impact on the surge, which raised a positive storm surge at first and then diminished the negative surge. The numerical results of Condition 2 and 3, excluding astronomic tide (tide + wind and tide + wave), illustrate two similarities. One is a negative value in wind setup, and the other is that the wave setup may exceed the storm surge at the last half of the typhoon process. These similarities indicate that the wave can mitigate the excessive decrease of surge due to the offshore wind after a typhoon landing.

The multiple surge peculiarities mentioned above prove that the nonlinear interaction of astronomic tide–storm surge–wave occurs during the WCI process. Previous studies revealed that the nonlinear interaction may result from: (1) the wave radiation stress varying in water depth [57,58,59,60,61,62]; (2) the sea surface roughness affected by waves [63,64,65,66,67]. The numerical results of Condition 1 and 4 can better demonstrate that the nonlinear interaction can reduce the storm surge at high tide and, conversely, increase the storm surge at low tide. Moreover, the maximum storm surge always occurs at the low tide, while the minimum storm surge occurs at a high tide. Therefore, a conclusion can be drawn that the tide contributes to the periodic vibration of storm surge mainly. Additionally, the wind setup shows the same trend in the three typhoon events when wave actions are excluded. In the conditions with wave actions, the storm surge during Lekima is relatively high, so the wave also plays a vital role in an increase in storm surge. The three typhoon events can be sorted in descending order by the intensity of nonlinear interaction as Lekima, Fongwong and Ampil, where Lekima is characterized by the highest intensity and Fongwong is accompanied by the spring tide. Although it is difficult to distinguish the impacts of typhoon intensity or tidal period on the nonlinear interaction specifically, there is no doubt that both of them can alter the nonlinear interaction. It corresponds with the findings of Zhang et al. [68], who took typhoon Chan-Hom as the object of investigation and concluded that the higher tide height, the stronger the nonlinear interaction.

5.3. Comparision of Storm Surge and Wave Setup Distributions

Based on Section 5.1 and Section 5.2, the wave plays an impressive role in the storm surge under the WCI condition. The wave setup contributes to the storm surge in the shoal area, especially at the estuarine mouth. Figure 18, Figure 19 and Figure 20 present the distributions of storm surge and wave setup during the three typhoon events.

As shown in Figure 18, it is evident that the storm surge is generally higher than the wave setup. For example, by 0.2 m isoline, the storm surge isoline is located farther to the estuary than the wave setup isoline before 9:00 on 23 September. At the same position, the difference between the storm surge and the wave setup declines from the peak of 0.15 m. After that moment, the isoline position of wave setup coincides with the position of storm surge, but in some sea areas, the isoline of wave setup even surpasses the isoline of storm surge by 0.10 m, which is consistent with Figure 15.

In Figure 19, the wave setup lasts longer during Ampil, but its value is the same as that during Fongwong. Because of the typhoon path from SW to NW and the higher intensity, the isolines in the offshore area are denser than those during Fongwong under the same interval scale. Additionally, the wave setup is higher in the upstream river of the YRE due to the typhoon path, although the inner channels are barely affected by waves. Compared with the storm surge, the wave setup presents a small negative value in the main study area (Figure 19m–p), which is evidence that the recovery of storm surge is mainly related to the wind stress. Apart from the negative surge (Figure 19k–p), the two series of isolines during Ampil show similar characteristics as those of Fongwong, where the difference is about 0.2 m, slightly higher due to its intensity.

According to the distributions of storm surge and wave setup in Figure 20, the path of Lekima raises the storm surge at the upstream river at first, and then the shoal area out of the mouth experiences the storm surge immediately, where the storm surge lasts for a long time. The maximum wave setup occurs in the shoal area around the eastern and northern branches of Chongming Island and Jiuduansha. The strong intensity of Lekima leads to the densest isolines among the three typhoons and results in the maximum difference of 0.2 m between the two series of isolines. Among the three typhoons, a lower intensity presents relatively regular isoline distributions, whereas a higher intensity causes a larger difference between these two kinds of surges.

6. Conclusions

In the present research, a well-validated two-dimensional model based on MIKE21 was used to reproduce the temporal and spatial variations of storm surges during three typical typhoon events. To better describe the storm surge characteristics in typhoon events, the impacts of waves, winds and currents were investigated. Therefore, this study took Fongwong, Ampil and Lekima as examples to analyze the similarities and differences of the storm surges in terms of variations and distributions. Moreover, tide condition, tide–wind condition, tide–wave condition and tide–wind–wave condition were taken into account to discuss the storm surge and the nonlinear interaction in the YRE. The main conclusions are shown as follows:

During the three typhoon events, the maximum storm surge in the channel existed at NB1, with the highest value of 0.99 m during Lekima, which is resulted from the narrow channel and low current speed. The storm surge during Ampil lasted a short time because the typhoon moving direction generated a negative surge. To a certain extent, the typhoon intensity plays a more important role than the landing position in storm surge rise, which is proven by the findings regarding Lekima, the strongest typhoon that caused the highest surge even though it just crossed the upstream river. Meanwhile, the tidal period is another effective factor that can increase the peak of storm surge.

The maximum or minimum storm surge always occurs at low or high tide, respectively, indicating that tide is the main factor in the generation of storm surge. However, most study areas are dominated by wave setup after typhoon landing, especially in the shoal area outside of the estuary mouth. Therefore, the surge is also related to the geography. In fact, regardless of the wind or wave setup, there is an inverse proportion relation between storm surge and the water depth in the shoal area during typhoon processes.

The different surge peculiarities prove that a nonlinear interaction of tide–storm surge–wave occurs during the WCI process. This nonlinear interaction may reduce the storm surge at high tide and increase it at low tide, which is affected by the tidal period and typhoon intensity. Furthermore, the isolines of the storm surge and wave setup may approach after the typhoon landing, and the difference depends on typhoon intensity and tidal period.

The YRE is internationally recognized as one of the most dynamic and complex estuaries, contributing over 80% of the freshwater supplies to Shanghai. These combined actions of wind, wave and current have significant impacts on storm surges during typhoon events. Due to the complex dynamics in the YRE, it is challenging to distinguish the exact contribution of typhoon intensity, barometric pressure, tidal period, wave actions and nonlinear interaction specifically. Moreover, our research can serve as a valuable reference for other estuaries facing similar hazards. Furthermore, this investigation is practically vital in promoting sustainable development in the YRE. Typhoon-induced surges pose substantial risks to the maritime industry and the economic progress of coastal cities; therefore, more attention should be paid to risk prevention measures.