1 Introduction

Suspended sediments are carriers of nutrients, organic matter, and pollutants that impede light transmission, photosynthesis, and primary productivity and affect the marine environment and ecological processes (Fang et al. 2016; Li et al. 2016a; Zhao et al. 2018). Though there are numerous factors, typhoons are undoubtedly an important mechanism that drives drastic changes in suspended sediment concentration (SSC) in bays. The East China Sea is affected by four typhoons every year on average (Lu et al. 2018).Very high waves are generated during typhoons, these waves propagate into nearshore areas and induce phenomena such as wave reflection, refraction, and fragmentation. In recent years, the intensity and frequency of extreme events, such as typhoons, have increased, and the impact of typhoons on sediment resuspension and redistribution in coastal waters has gradually attracted increasing attention from oceanographers (Bian et al. 2010; Gong and Shen 2009; Lu et al. 2018; Palinkas et al. 2014; Xie et al. 2018). Analyzing how waves influence the sediment transport and deposition/resuspension processes in coastal bays is of critical importance to studies of coastal geomorphology or for research exploring the ecological effects of typhoons (Liu et al. 2022; Zhang et al. 2021).

In recent years, the supply of fluvial sediments to estuarine and coastal systems has been significantly reduced due to upstream dams (Syvitski et al. 2009, 2005). With the reduction of sediment entering the sea, tidal currents and waves play an important role in maintaining the SSC in coastal waters. For example, Huang et al. (2021) concluded that the main reason for the slow decline of SSC in the Changjiang Estuary and its adjacent waters is related to wave and tide-induced sediment resuspension. Luo et al. (2017) found that the bottom sediment resuspension was mainly caused by tide-induced shear stress and diffused to the surface layer by vertical mixing in winter. The waves increase the bottom shear stress through wave-current interaction, thus effectively promoting sediment resuspension (Hsu et al. 2006; Xu and You 2017). For example, Xu and You (2017) studied the effects of waves on sediment resuspension in the Oujiang Estuary, China. Zhang et al. (2021) studied wave effects on water and sediment transport in the Pearl River Estuary, China, and the results showed that the wave effects were strongest in winter and enhanced the sediment deposition in the western shoal of the Pearl River Estuary. The effect of waves on SSC is more significant during typhoons. Shen et al. (2018) and Ren et al. (2021) concluded that waves during typhoons greatly contributed to sediment resuspension in the Changjiang Estuary. Brand et al. (2010) concluded that the wave effects increased SSC from 30 mg·L−1 during calm periods to more than 100 mg·L−1 during turbulent periods at the shoals in the southern portion of San Francisco Bay, USA. In addition, waves can change the vertical stratification of the estuary and affect the distribution of suspended sediment and its transport direction (Green and Coco 2014).

Hangzhou Bay is located on the south side of the Changjiang Estuary (Fig. 1), connects to the Qiantang River in the west, and is characterized by a large irregular and semidiurnal tide, strong flow, and high SSC. Morphologically, Hangzhou Bay is an east‒west oriented trumpet shaped bay. The bay has one of the highest SSC in the world. With the development of numerical models, some researchers have used numerical models to carry out SSC research in Hangzhou Bay. Xie et al. (2009) developed a two-dimensional suspended sediment numerical model in Hangzhou Bay to obtain sediment transport directions. Du et al. (2010) used a three-dimensional suspended sediment model to analyze the temporal variation in SSC during the neap-spring tidal cycle in Hangzhou Bay. Xie et al. (2013) used the Delft3D to find that sediment transport in Hangzhou Bay was affected by tidal asymmetry. Because the bay mouth is occupied by Zhoushan Islands, it is not easy for waves from the outer sea to enter the bay. The waves in Hangzhou Bay are weak under normal weather conditions, with an annually averaged wave height of 0.2–0.5 m (Xie et al. 2013). However, Hangzhou Bay has large waves during typhoons and is affected by typhoons almost every year. Li et al. (2022a) concluded that the SSC in Hangzhou Bay was most affected by waves during Typhoon Chan-hom based on FVCOM. Li et al. (2022b) concluded that the combined wave-current bottom stress was the primary wave-current interaction that changed sediment resuspension and increased SSC. Due to the difficulty of actual observation data during typhoons, research on the SSC characteristics in Hangzhou Bay during typhoon conditions is still relatively lacking.

Fig. 1
figure 1

Map of Hangzhou Bay and Changjiang Estuary. Black triangle: the anchored ship stations; thick black line: the section from Nanhui Cape to Qiqu Archipelago; black dot: Chongming weather station

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Based on the improved ECOM-si (Estuary, Coast, and Ocean Model with semi-implicit), a high resolution three dimensional numerical model of suspended sediment in Hangzhou Bay is developed. The model takes into consideration advection, diffusion, settlement, sediment flocculation, waves, and sediment-induced stratification, to simulate the sediment transport in Hangzhou Bay under typhoon conditions. The model description and validation are presented in Sect. 2. In Sect. 3, the water and suspended sediment transport process in Hangzhou Bay during typhoons are analyzed. The sensitivity analysis for the different factors is presented in Sect. 4. Finally, the conclusion is presented in Sect. 5.

2 Materials and methods

2.1 Observations

The State Key Laboratory of Estuarine and Coastal Research, East China Normal University, conducted continuous field observations in Hangzhou Bay from August 5 to 20, 2018. Two marine research ships collected simultaneously observations at site A and site B (Fig. 1). Tripod-mounted observation systems were placed on the seafloor at each site. The instruments mounted in each tripod were positioned 0.2 m above the bottom. A 600 kHz acoustic Doppler current profiler (ADCP, RD Instruments) was used to measure the vertical current profile; an optical backscatter sensor (OBS, D&A Instrument Company) was used to measure salinity, temperature, and turbidity; a Sea-Bird SBE37 CTD was used to measure temperature and salinity; and an electromagnetic current meter (Alec, Electronics, Tokyo) was used to measure the near-bottom current inaccessible by the ADCP. The ADCP worked in upward-looking mode at a vertical resolution of 0.25 m and ensembles of 2 min at a 1-s ping interval. A diagram of the instrument positions is shown in Fig. 2. Water samples were taken at the sites and brought back to the laboratory for SSC measurements to determine the relationship between OBS turbidity and SSC. Surface data could not be obtained during typhoons Yagi and Rumbia, which impacted the site in 2018.

Fig. 2
figure 2

Tripod observation system and positions of the instruments

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At 23:00 on August 12, 2018, Typhoon Yagi made landfall on the coast of Zhejiang, China, with a maximum wind speed of 28 m/s; at 4:00 on August 17, 2018, Typhoon Rumbia directly passed through Hangzhou Bay and made landfall off the southern coast of Shanghai with a maximum wind speed of 23 m/s (Fig. 3). The tripod observation systems at sites A and B continuously recorded the variations in benthic hydrodynamics and SSC during the typhoon period from August 12 to August 18, 2018. The weather station located on Chongming Island recorded wind speed changes during typhoons. Since Chongming Island is far from the center of Typhoon Yagi, its maximum wind speed was approximately 13 m/s, while the center of Typhoon Rumbia was close to Chongming Island, and its maximum wind speed was approximately 20 m/s (Fig. 4). The impact of Typhoon Rumbia on Hangzhou Bay is more significant than that of Typhoon Yagi. The ERA5 (ECMWF Reanalysis v5) wind field data from the ECMWF (European Centre for Medium-Range Weather Forecast, https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-single-levels?tab=overview) are consistent with the actual wind speed and direction measured by the weather station and can accurately reproduce the wind speed variability during typhoons (Fig. 4). Figure 5 shows the wind field distribution at 03:00 on August 13, 2018 (Typhoon Yagi) and at 00:00 on August 17, 2018 (Typhoon Rumbia). Due to the influence of Typhoon Yagi, the wind direction in Hangzhou Bay was mainly southeast (Fig. 5a), and due to Typhoon Rumbia, the wind field in Hangzhou Bay was mainly cyclonic (Fig. 5b).

Fig. 3
figure 3

Paths of Typhoon Yagi and Typhoon Rumbia in 2018 before and after landfall

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Fig. 4
figure 4

Temporal variations in wind speed (a) and wind vector (b) at Chongming weather station. Red: observed data; black: ERA5 data

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Fig. 5
figure 5

Wind field distribution during Typhoon Yagi (a) and Typhoon Rumbia (b)

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2.2 Numerical model setup

The improved three dimensional ECOM-si includes a hydrodynamic model, a sediment module, and the SWAN (Simulating Waves Nearshore) model, which provides wave parameters for the hydrodynamic model and sediment module. The hydrodynamic model originated from the POM (Princeton Ocean Model) developed by Princeton University (Blumberg and Mellor 1987). The model uses the “Arakawa C” grid configuration variables (Arakawa and Lamb 1977). A nonorthogonal curve grid was used in the horizontal direction (Chen et al. 2004), and the sigma coordinate was adopted in the vertical direction. The level 2.5 turbulence closure model by Mellor and Yamada (1982) was used to calculate the vertical mixing coefficients, and the parameter formula of the stability function was from Kantha and Clayson (1994), while the parameterization scheme of Smagorinsky (1963) was used to calculate the horizontal mixing coefficients. A wet/dry scheme was included to describe the intertidal flat with a critical depth of 0.2 m. To reduce the numerical dissipation and improve the computational accuracy in the material transport process, Wu and Zhu (2010) developed the high order spatial interpolation at the middle temporal level coupled with a TVD limiter to solve the advection term in the material transport equation. The barotropic pressure gradient force in the momentum equation was solved by an implicit method, and the continuous equation was solved by the semi-implicit method of Casulli and Cattani (1994).

The model domain covered all of the Changjiang Estuary and Hangzhou Bay and adjacent seas from 117.5° E to 125° E longitude and 27.9° N to 33.7° N latitude (Fig. 6a). The model grid consisted of 396 × 522 cells in the horizontal dimension. Fifteen sigma levels were set in the vertical direction with five logarithmically distributed layers near the bottom (σ =  − 0.929, − 0.964, − 0.982, − 0.991, − 1.0) to distinguish the effect of high bottom SSC on the bottom friction drag coefficient, and 10 layers were established in the remaining layers (σ = 0, − 0.1, − 0.2, − 0.3, − 0.4, − 0.5, − 0.6, − 0.7, − 0.79, − 0.87). The grid resolution ranges between 200 m at the top of ​​the bay, approximately 600 m in the central part, and is 2 ⁓ 10 km near the open sea boundary (Fig. 6b).

Fig. 6
figure 6

Numerical model domain and grid (a) and an enlarged view of the model grid in Hangzhou Bay (b)

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The open sea boundary condition was specified by the tide and residual water level. The tidal signal was composed of 16 astronomical constituents, M2, S2, N2, K2, K1, O1, P1, Q1, MU2, NU2, T2, L2, 2N2, J1, M1, and OO1, which were derived from the NaoTide dataset (http://www.miz.nao.ac.jp/). The residual water level and initial salinity field were derived from the results simulated by a large domain model encompassing the Bohai Sea, Yellow Sea, and East China Sea (Wu et al. 2011). The river boundary was driven by the river discharge at the Datong hydrologic station (Changjiang Water Resources Commission) for the Changjiang River and at the Fuchunjiang hydroelectric power station for the Qiantang River. Wind data were adopted from the ERA5 dataset, with a temporal resolution of 6 h and a spatial resolution of 0.25° × 0.25°.

For a detailed introduction to the sediment module, please refer to the author’s other article (Huang et al. 2022). In the model, the sediment in the water body is considered cohesive fine grained sediment. The role of waves in sediment resuspension cannot be ignored, especially during typhoon conditions. The improved model algorithm calculates the bottom wave orbit velocity with sea surface wave parameters to obtain the bottom shear stress generated by the waves. This algorithm needs to use the significant wave height, average wave direction, and significant wave period on the sea surface. The bottom shear stress under the influence of wave-current interaction is given by (Grant and Madsen 1979):

$${\displaystyle \begin{array}{c}\tau =\left|{\tau}_w+{\tau}_c\right|=\sqrt{{\left({\tau}_w+{\tau}_c\left|\mathit{\cos}\varphi \right|\right)}^2+{\left({\tau}_c\mathit{\sin}\varphi \right)}^2}\\ {}={\tau}_w\sqrt{1+2\frac{\tau_c}{\tau_w}\left|\mathit{\cos}\varphi \right|+{\left(\frac{\tau_c}{\tau_w}\right)}^2}\end{array}}$$
(1)

where τ is the bottom shear stress considering waves and currents; \({\tau }_{w}\) is the maximum wave-induced bottom shear stress; \({\tau }_{c}\) is the tidal-induced bottom shear stress; φ is the angle between wave propagation and the current direction. \({\tau }_{c}\) and \({\tau }_{w}\) can be calculated by:

$${\tau }_{c} = \rho {C}_{d}{U}^{2}$$
(2)
$${\tau }_{w} =\frac{\rho {f}_{w}}{2}{U}_{w}^{2}$$
(3)

where ρ is the actual density of seawater with the suspended sediment; U is the bottom current velocity; \({C}_{d}\) is the bottom drag coefficient; \({f}_{w}\) is the wave fiction factor; and \({U}_{w}\) is the near-bed wave orbital velocity. A detailed calculation procedure can be found in Wiberg and Sherwood (2008). Waves affect not only the bottom shear stress but also the vertical mixing coefficient (Mellor and Blumberg 2004; Terray et al. 1999). Based on the level 2.5 turbulence closure module, Mellor and Blumberg (2004) considered the effect of waves breaking on the sea boundary layer. The sea surface boundary conditions are:

$${K}_{q}\frac{\partial {q}^{2}}{\partial z}=2{\alpha }_{CB}{u}_{\tau }^{3},\mathrm{ z }= 0$$
(4)

where \({q}^{2}\) is the turbulence kinetic energy;\({u}_{\tau }\) is the water side friction velocity;\({\alpha }_{CB}\) is a parameter related to the waves, with the following equation:

$$\alpha_{CB}=15\left(\frac{C_p}{u_\ast}\right)\exp\left[-\left(\frac{0.04C_p}{u_\ast}\right)^4\right]$$
(5)

where \({C}_{p}/{u}_{*}\) is the wave age;\({C}_{p}\) is the phase speed of waves at the dominant frequency; \({u}_{*}\) is the air side friction velocity; and \({u}_{*}=30{u}_{\tau }\). When the effect of waves is not considered, \({q}^{2}={{B}_{1}}^{2/3}{u}_{\tau }^{2}\) at z = 0, \({B}_{1}= 16.6\). When the effect of waves is considered, \({q}^{2}={(15.8{\alpha }_{CB})}^{2/3}{u}_{\tau }^{2}\) at z = 0. From measured wave heights and near-surface dissipation data, Terray et al. (1999) used the turbulence closure module to find the best fit between the turbulent mixing length (\(l)\) and the measured data.

$$l=\mathrm{max}\left(\kappa {z}_{w},{l}_{z}\right), {z}_{w}=0.85{H}_{s}$$
(6)

where \({H}_{s}\) is the significant wave height; \({l}_{z}= \kappa z\); \(\kappa = 0.4\) is the von Karman constant. When the effect of waves is not considered, \({z}_{w}= 0\).\({\text{K}}_{m}=ql{S}_{M}\) is the vertical eddy viscosity; \({\text{K}}_{\text{h}}=ql{S}_{H}\) is the vertical eddy diffusivity, where \({S}_{M}\) and \({S}_{H}\) are the stability function, please refer to Mellor and Yamada (1982).

The SWAN model (Booij et al. 1999) adopted an orthogonal mesh that covered the calculation range of the ECOM-si, with a spatial resolution of 2' × 2' and a time step of 30 min. The SWAN model outputted the significant wave height, significant wave period, and wave direction every 3 h, and these parameters were interpolated to each time step in the sediment module to calculate the bottom shear stress and vertical mixing coefficient under wave-current interactions. The wave parameters output from the SWAN model has been validated in related papers by our research group (Luo et al. 2017).

2.3 Model validation

The ECOM-si has been extensively validated in terms of water level, current speed and direction, salinity, and SSC (Chen et al. 2019; Luo et al. 2017; Lyu and Zhu 2018; Qiu and Zhu 2013; Wu and Zhu 2010; Zhu et al. 2015). This study will further validate the model in Hangzhou Bay. The following three skill assessments were used to quantify the validation of the model: correlation coefficient (CC), root mean square error (RMSE), and skill score (SS) (Murphy 1988; Warner et al. 2005; Willmott 1981):

$$\mathrm{CC}=\frac{\sum \left({\mathrm{X}}_{\mathrm{mod}}-\overline{{\mathrm{X} }_{\mathrm{mod}}}\right)\left({\mathrm{X}}_{\mathrm{obs}}-\overline{{\mathrm{X} }_{\mathrm{obs}}}\right)}{{\left[\sum {\left({\mathrm{X}}_{\mathrm{mod}}-\overline{{\mathrm{X} }_{\mathrm{mod}}}\right)}^{2}\sum {\left({\mathrm{X}}_{\mathrm{obs}}-\overline{{\mathrm{X} }_{\mathrm{obs}}}\right)}^{2}\right]}^\frac{1}{2}}$$
(7)
$$\mathrm{SS }= 1-\frac{{\sum \left({\mathrm{X}}_{\mathrm{mod}} - {\mathrm{X}}_{\mathrm{obs}}\right)}^{2}}{{\sum \left(\left|{\mathrm{X}}_{\mathrm{mod}} -\overline{{\mathrm{ X} }_{\mathrm{mod}}}\right| + \left|{\mathrm{X}}_{\mathrm{obs}} -\overline{{\mathrm{ X} }_{\mathrm{obs}}}\right|\right)}^{2}}$$
(8)
$$\mathrm{RMSE}=\sqrt{\frac{{\sum \left({\mathrm{X}}_{\mathrm{mod}}-{\mathrm{X}}_{\mathrm{obs}}\right)}^{2}}{\mathrm{N}}}$$
(9)

where X is the variable and \(\stackrel{\mathrm{-}}{\text{X}}\) is the time-averaged value. The performance levels of the modeled results and observed results were evaluated by SS where SS > 0.65 is considered excellent, 0.65–0.5 is very good, 0.5–0.2 is good, and SS < 0.2 is considered poor.

The modeled current velocity, current direction, salinity, and SSC were validated with observation data during neap tide and spring tide at site A and site B in Hangzhou Bay in August 2018; see Huang et al. (2022). This study used data that included typhoon periods to validate the model. We downloaded the real-time river discharge data for the Datong hydrological station and Fuchunjiang hydropower station, as well as the real-time wind field data from ERA5 to drive the model. The model was cold started on 1 July 2018 and ran for 62 days. The comparison between the simulated water level and the measured data from August 6 to 20, 2018, is shown in Fig. 7. Hangzhou Bay is famous for its strong tides. In terms of tidal nature, the tides outside the mouth of the bay are regular semidiurnal tides and inside the bay mouth, they are irregular semidiurnal tides. After August 12, Hangzhou Bay was impacted by Typhoon Yagi and Typhoon Rumbia. Regardless of whether it was normal or typhoon conditions, the simulated water level was consistent with the measured value, and both the SS and CC exceeded 0.95 (Table 1), indicating that the model can successfully simulate the temporal variation in water level.

Fig. 7
figure 7

Comparison of the simulated water level (black line) and measured data (red dot) at site A (a) and site B (b) in Hangzhou Bay from August 6 to 20, 2018

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Table 1 Correlation coefficients (CC), root mean square error (RMSE), and skill scores (SS) for comparison of the simulated and observed data at the measuring stations
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The simulated current velocity, direction, and SSC are compared with the observed data during typhoons in Fig. 8. Due to the effect of bottom friction, the current velocity in the bottom layer was smaller than that in the surface layer. The average SSC in the bottom layer at site A was 2.78 kg·m−3, and the average SSC in the bottom layer at site B was 2.85 kg·m−3 during typhoons. The CC, RMSE, and SS of the simulated data and the observation data are shown in Table 1. Note that the SS of the SSC is above 0.7. The model can successfully reproduce the variability in the current velocity, direction, and SSC during typhoon conditions, and can be used to study the hydrodynamic and SSC transport process in Hangzhou Bay.

Fig. 8
figure 8

Comparisons between the observed data (red dots) and simulated results (black line) at study site A (left panel) and site B (right panel). a, b surface velocity; c, d bottom velocity; e, f surface direction; g, h bottom direction; i, j bottom SSC

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3 Results

To describe the transport of water and suspended sediment, the residual unit width water flux (RUWF) and the residual unit width sediment flux (RUSF) were used to reflect the transport of water and suspended sediment, which is defined as:

$$\mathrm{RUWF }= \frac{1}{T}{\int }_{0}^{T}{\int }_{{h}_{1}}^{{h}_{2}}\overrightarrow{V}dzdt$$
(10)
$$\text{RUSF }=\frac1{\textit{T}}\int_0^\textit{T}\int_{{\textit{h}}_{1}}^{{\textit{h}}_{2}}\overset{\rightarrow}{\textit{V}}\cdot\textit{C}\cdot\,\textit{dzdt}$$
(11)

where \(\overrightarrow{V}\) is the instantaneous horizontal velocity vector; h1 and h2 are the depths at the lower and upper boundaries of a certain layer, respectively; T is one or more complete cycles; C is the SSC; and the unit width is 1 m. In this study, three semidiurnal tidal cycles were used as an averaging time window to remove the semidiurnal and diurnal tidal signals. The thickness of the surface and bottom layers was one-tenth of the total water depth over the tidal cycle. This method has been used in many studies (Chen et al. 2019; Li et al. 2016b; Lyu and Zhu 2018; Zhu et al. 2015). For the convenience of research, this paper chooses Typhoon Rumbia that directly through Hangzhou Bay as a case study, and its impact on Hangzhou Bay is more significant than that of Typhoon Yagi.

3.1 SSC

The distribution of the bottom SSC at four moments of the tidal cycle in Hangzhou Bay during Typhoon Rumbia is shown in Fig. 9. At the maximum flood, the high SSC in the bottom layer was mainly distributed in the southeastern part of Hangzhou Bay; at the flood slack, the high SSC in the bottom layer was mainly distributed in the south shore tidal flats and southeastern part of the bay, generally exceeding 10 kg·m−3. At the maximum ebb, the high SSC in the bottom layer was mainly located on the south coast and in the northern part of the bay; at the ebb slack, the high SSC in the bottom layer was mainly distributed in the leading edge of the south coast, and generally exceeded 10 kg·m−3. Through the comparison of the SSC distribution at four moments, it can be found that when the current velocity was high during the typhoon, the water mixing was stronger, and the bottom SSC was generally lower; when the current velocity was low, the southeastern part of Hangzhou Bay near the south coast was the main area for sediment fall siltation, which was also the high value area for sediment.

Fig. 9
figure 9

Modeled bottom SSC at the maximum flood (a), flood slack (b), maximum ebb (c) and maximum ebb (d) during Typhoon Rumbia

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3.2 Water flux and sediment flux

The distribution of RUWF and RUSF during Typhoon Rumbia is shown in Fig. 10. Typhoon Rumbia occurred during moderate tide and landed directly in Hangzhou Bay. The characteristics of surface RUWF (Fig. 10a) and RUSF (Fig. 10b) during the typhoon were mainly related to the shape of the local wind (Fig. 5b), with surface sediment transport in Hangzhou Bay extending all the way to the top of the bay. And surface water and suspended sediment entered from the north coast in Hangzhou Bay and was then transported to the sea from the south coast, forming a counterclockwise circulation pattern in the bay. The bottom RUWF (Fig. 10c) transported a longer distance along the north coast than the bottom RUSF (Fig. 10d), but they all converged in the central part of Hangzhou Bay. The RUWF (Fig. 10e) and RUSF (Fig. 10f) in the whole layer showed the pattern of "north-landward and south-seaward" in Hangzhou Bay, and the water and sediment mainly came from the Changjiang Estuary, which was similar to the distribution of RUWF and RUSF during the spring tide under climatic conditions (Huang et al. 2022). Although Typhoon Rumbia occurred during moderate tide, the water and suspended sediment transport volume in the whole layer were significantly greater than those during the climatological spring tide, while the surface water and suspended sediment transport were mainly determined by the wind field of the typhoon.

Fig. 10
figure 10

The distributions of RUWF (left panel) and RUSF (right panel) in the surface layer (a, b), bottom layer (c, d), and whole layer (e, f) during Typhoon Rumbia

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The net transect water flux (NTWF) and the net transect sediment flux (NTSF) across a section are calculated using the following equations:

$$\mathrm{NTWF}={\int }_{0}^{T}{\int }_{-H}^{\zeta }{\int }_{0}^{L}\overrightarrow{{V}_{n}}dldzdt$$
(12)
$$\mathrm{NTSF}={\int }_{0}^{T}{\int }_{-H}^{\zeta }{\int }_{0}^{L}C\overrightarrow{{V}_{n}}dldzdt$$
(13)

where ζ is the water level; L is the width of the transect; C is the SSC; \(\overrightarrow{{V}_{n}}\) is the velocity component normal to the transect; T is three semidiurnal tidal cycles (~ 37 h).

The water and sediment flux across the NQ section before and during the typhoon are shown in Table 2. During Typhoon Rumbia, the NTWF and NTSF across the NQ section increased by 18.13% and 265.75%, respectively, compared with those before the typhoon. It is worth noting that the sediment flux increased more significantly than the water flux, indicating that the typhoon greatly promoted sediment resuspension. Typhoons such as Typhoon Rumbia, which made direct landfall in Hangzhou Bay, can promote more suspended sediment to enter Hangzhou Bay from the mouth of the Changjiang Estuary, which played an important role in the sediment exchange between the Changjiang Estuary and Hangzhou Bay.

Table 2 NTWF and NTSF across the NQ section. Negative values indicate sediment flow into Hangzhou Bay, and positive values indicate sediment flow into the Changjiang Estuary
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4 Discussion

To discuss the effects of sediment-induced stratification, waves, and winds on suspended sediment during typhoons, three numerical sensitivity experiments were set up in this study. Exp 1 was without sediment-induced stratification, Exp 2 was without waves, and Exp 3 was without winds. The other dynamic factors were the same as the numerical model settings in Sect. 3, which was called the control experiment (Exp 0).

4.1 Effect of sediment-induced stratification

In high turbidity estuaries, sediment-induced stratification plays an important role in the trapping of bottom sediment (Huang et al. 2022; Zhu et al. 2021). Compared with other estuaries worldwide, the water in Hangzhou Bay is characterized by high turbidity. The formula for the contribution of sediment to density is as follows (Winterwerp 2001):

$$\rho=\rho_w+\left(1-\frac{\rho_w}{\rho_s}\right)C$$
(14)

where \({\rho }_{w}\) is the density of seawater without sediment, \({\rho }_{s}\) is the density of suspended sediment, and \(\rho\) is the actual density of seawater with SSC.

The comparison results of Exp 0 and Exp 1 at sites A and B during the typhoon are shown in Fig. 11. After considering sediment-induced stratification, the simulated surface SSC at sites A and B decreased by 50.8% and 58.6%, respectively; the vertical eddy diffusivity (\({\text{K}}_{\text{h}}\)) decreased by 41.0% and 36.0%, respectively, and the simulated bottom SSC decreased by 27.8% and 37.5%, respectively. The results show that the simulated SSC was much more consistent with the observed values after considering the sediment-induced stratification.

Fig. 11
figure 11

Temporal variation in surface SSC (a, b), bottom SSC (c, d), and vertical eddy diffusivity (e, f) at sites A (left panel) and B (right panel) in Exp 0 and Exp 1 during the typhoon. Red dots: measured data, same below

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The gradient Richardson number (Ri) is often used to estimate the relative strength of stratification and mixing in the water column (Galperin et al. 2007; Grant and Madsen 1986; Richardson 1920) and can be expressed as:

$${\mathrm{R}}_{\mathrm{i}}=\frac{-\frac{g}{{\rho }_{0}}\frac{\partial \rho }{\partial z}}{{\left(\partial V/\partial z\right)}^{2}}$$
(15)

where \(\rho\) is density; V is the vector horizontal velocity; g is the acceleration of gravity; \({\rho }_{0}\) is the reference density; z is the depth. Miles (1961) suggested that Ri has a critical value of 0.25, above which stable stratification tends to occur, while below this value, stratification tends to be unstable, and mixing may occur. In this study, we calculate the instantaneous value of Ri at different times to indicate the variation in water mixing intensity.

The comparison of Ri between Exp 0 and Exp 1 at sites A and B during the typhoon are shown in Fig. 12. Each point on the graph represents the relative position of Ri with and without sediment-induced stratification at a certain moment. During the typhoon, the Ri in the water column is almost always increasing after considering sediment-induced stratification (the number of blue dots is much greater than the number of black dots). Therefore, the suppression of vertical mixing by sediment-induced stratification during typhoons should not be ignored.

Fig. 12
figure 12

Comparison of Ri at site A (a) and site B (b) with and without sediment-induced stratification during the typhoon. The blue dots: Ri at the current moment of Exp 0 is greater than Exp 1; the black dots: the opposite situation; the green line: the threshold of 0.25

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4.2 Effect of waves

First, let's study the difference in the effects of waves on the water column before and during typhoons. The comparison results of Exp 0 and Exp 2 at sites A and B before the typhoon are shown in Fig. 13, taking August 5 to 8, 2018, as an example. Before the typhoon, the average significant wave height at sites A and B in Hangzhou Bay were 0.27 m and 0.26 m, respectively. After considering waves before the typhoon, the vertical eddy diffusivity (\({\text{K}}_{\text{h}}\)) at sites A and B increased by 21.1% and 28.2%, respectively, and the simulated surface SSC increased by 11.8% and 44.3%, respectively, indicating that waves significantly increased the vertical mixing in the water column before the typhoon, increasing the surface SSC. After considering waves before the typhoon, the bottom shear stress at sites A and B increased by 5.8% and 10.9%, respectively, while the simulated bottom SSC decreased by 9.3% and 5.7%, respectively, indicating that the wave-induced bottom shear stress before the typhoon is a small amount compared to the tidal-induced bottom shear stress. The upward transport of bottom sediment caused by the enhanced vertical mixing by waves is greater than the increase in sediment resuspension caused by the wave-induced bottom shear stress, thus reducing the bottom SSC. The results show that before typhoons, the effect of waves on vertical mixing is stronger than the effect of wave-induced bottom shear stress on sediment resuspension.

Fig. 13
figure 13

Temporal variation in surface SSC (a, b), bottom SSC (c, d), vertical eddy diffusivity (e, f), bottom shear stress (g, h), and significant wave height (i, j) at sites A (left panel) and B (right panel) in Exp 0 and Exp 2 before the typhoon

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The comparison results of Exp 0 and Exp 2 at sites A and B during the typhoon are shown in Fig. 14. During Typhoon Rumbia, the average significant wave height at sites A and B in Hangzhou Bay were 1.37 m and 1.17 m, respectively, which were significantly higher than those before the typhoon. After considering waves during the typhoon, the simulated surface SSC at sites A and B increased by 4.7% and 1.0%, respectively; the bottom shear stress increased by 41.5% and 52.5%, respectively; the simulated bottom SSC increased by 89.6% and 74.1%, respectively; while \({\text{K}}_{\text{h}}\) decreased by 17.5% and 7.2%, respectively. Compared with before the typhoon, it can be concluded that the effect of waves on the bottom SSC during the typhoon is more significant, while the effect on the surface SSC is less. And the effect of waves at site A is greater than that at site B during the typhoon, indicating that the effect of waves near the outside the estuary is more significant.

Fig. 14
figure 14

Temporal variation in surface SSC (a, b), bottom SSC (c, d), vertical eddy diffusivity (e, f), bottom shear stress (g, h), and significant wave height (i, j) at sites A (left panel) and B (right panel) in Exp 0 and Exp 2 during the typhoon

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Theoretically, the waves help to increase the vertical mixing in the water column, which is consistent with the results before typhoons. It is an interesting finding that \({\text{K}}_{\text{h}}\) decreases during typhoons when waves are considered. To show the effect of waves on SSC more graphically, a profile of the SSC at site A is presented, as shown in Fig. 15. Figure 15a shows that the surface and bottom SSC differ greatly during typhoons, especially the bottom SSC gradient, while Fig. 17b shows that the vertical SSC gradient decreases significantly without waves. Section 4.1 concludes that the sediment-induced stratification is highly significant, so it can be deduced that the difference in the vertical SSC caused by waves during typhoons will intensify the sediment-induced stratification effect. On the one hand, waves will directly cause vertical mixing enhancement, and on the other hand, wave-induced bottom shear stress will indirectly cause sediment-induced stratification enhancement to inhibit vertical mixing. The two is a process of mutual cancellation.

Fig. 15
figure 15

The vertical profile distributions of SSC at site A during the typhoon. a Exp 0; b Exp 2; c Exp 3

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According to the above analysis, waves further affect vertical mixing indirectly by changing the vertical SSC gradient. Before typhoons, the direct effect of waves on vertical mixing is stronger than the effect of wave-induced bottom shear stress on the sediment resuspension. While during typhoons, the wave-induced bottom shear stress greatly promotes the sediment resuspension, which indirectly makes the sediment-induced stratification (mainly in the bottom layer) stronger than the direct effect of waves on the vertical mixing in the water column.

The distribution of suspended sediment transport in Hangzhou Bay without waves in Exp 2 is shown in Fig. 16a, c, e. Compared with Fig. 10b, d, f, it can be found that the waves did not significantly change the direction of suspended sediment transport, but significantly affected the amount of suspended sediment transport in the bottom and whole layer. The NTSF across the NQ section in Exp 2 decreased by 66.10% compared to Exp 0 (Table 3), which greatly reduced the sediment transport from the Changjiang Estuary to Hangzhou Bay, indicating that waves significantly affected sediment resuspension during typhoons.

Fig. 16
figure 16

The distributions of RUSF in the surface layer (a, b), bottom layer (c, d), and whole layer (e, f) in Exp 2 (left panel) and Exp 3 (right panel) during the typhoon

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Table 3 NTSF across the NQ section. Negative values indicate sediment flow into Hangzhou Bay, and positive values indicate sediment flow into the Changjiang Estuary
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4.3 Effect of winds

To further illustrate the effect of strong winds brought by typhoons on the SSC in Hangzhou Bay, Exp 3 is set in this study. The comparison results of Exp 0 and Exp 3 at sites A and B during the typhoon are shown in Fig. 17. After considering winds during the typhoon, \({\text{K}}_{\text{h}}\) at sites A and B increased by 41.4% and 9.6%, respectively; the simulated surface SSC increased by 181.9% and 33.9%, respectively; the simulated bottom SSC increased by 74.2% and 57.0%, respectively, and the bottom shear stress decreased by only 5.4% and 5.1%, respectively. According to the analysis in Sect. 4.2, after waves were removed by Exp 2 during typhoons, the surface SSC decreased very little, while \({\text{K}}_{\text{h}}\) increases instead. When winds were removed in Exp 3, the surface SSC, bottom SSC, and \({\text{K}}_{\text{h}}\) all decreased, while the bottom shear stress increased slightly, indicating that the strong winds brought by typhoons mainly enhanced the vertical mixing, thereby increasing the surface and bottom SSC. From the SSC profile at site A (Fig. 15c), it can be seen that the vertical SSC gradient in Exp 3 is obviously stronger than that in Exp 2, but both weaker than that in Exp 0, especially in the bottom layer. The results further indicated that the effect of waves during typhoons significantly enhanced sediment-induced stratification, while winds had a stronger effect on surface SSC than waves.

Fig. 17
figure 17

Temporal variation in surface SSC (a, b), bottom SSC (c, d), vertical eddy diffusivity (e, f), and bottom shear stress (g, h) at sites A (left panel) and B (right panel) in Exp 0 and Exp 3 during the typhoon

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The distribution of suspended sediment transport in Hangzhou Bay without winds in Exp 3 is shown in Fig. 16b, d, f. Compared with Fig. 10b, d, f, it can be found that strong winds have significantly changed the amount and direction of suspended sediment transport in the surface and bottom layers of the bay, but the characteristics of " north-landward and south-seaward " of the RUSF in the whole layer in Hangzhou Bay are still the same. The NTSF across the NQ section in Exp 3 decreased by 61.80% compared to Exp 0 (Table 3), indicating that the strong winds during typhoons can promote sediment transport from the Changjiang Estuary to Hangzhou Bay.

5 Conclusion

Based on the ECOM-si three dimensional numerical model, a three dimensional suspended sediment numerical model was established to simulate and analyze the effect of typhoons on sediment transport in Hangzhou Bay, in which advection, diffusion, flocculation, settlement, waves, sediment-induced stratification, and other factors were considered. The numerical model can sufficiently reproduce the variation in SSC during typhoons. The transport of water and sediment during Typhoon Rumbia in 2018 was simulated and analyzed. During typhoons, the water and suspended sediment transport in Hangzhou Bay showed a pattern of "north-landward and south-seaward", which made the suspended sediment converge in the central part of the bay. During Typhoon Rumbia, the NTWF and NTSF across the NQ section increased by 18.13% and 265.75%, respectively, compared with those before the typhoon, prompting more suspended sediment to enter Hangzhou Bay.

For high turbidity waters, such as those in Hangzhou Bay, the simulated SSC during typhoons was much more consistent with the observed values after considering the sediment-induced stratification. The suppression of vertical mixing by sediment-induced stratification during typhoons should not be ignored. The wave-induced bottom shear stress during typhoons has a very significant impact on the bottom SSC, which greatly promotes sediment resuspension. The strong winds brought by typhoons mainly enhanced the vertical mixing, which has a stronger effect on surface SSC than waves. Before typhoons, the direct effect of waves on vertical mixing is stronger than the effect of wave-induced bottom shear stress on the sediment resuspension. While during typhoons, the wave-induced bottom shear stress greatly promotes the sediment resuspension, which indirectly makes the sediment-induced stratification stronger than the direct effect of waves on the vertical mixing.