Contrast of fine sediment dynamics between shoals and channels in a microtidal estuary with mixed semi-diurnal tides

Abstract

Estuaries usually feature complex bathymetries, where shoals and channels are co-existent. Due to the differences in water depth, current, density gradient and therefore stratification, sediment dynamics on the shoal and in the channel demonstrate significant variations. In this study, field measurements were carried out during spring and neap tides in both wet and dry seasons in the Huangmaohai Estuary, a microtidal estuary located in the southwest of the Pearl River Delta. Harmonic analysis was conducted for the timeseries data of current and suspended sediment concentration (SSC) for each deployment. Sediment transport flux was decomposed into an advective component, and tidal pumping fluxes by different tidal constituents. During the neap tides, sediment transport is primarily controlled by the advective flux, whereas during the spring tides, tidal pumping fluxes become comparable to, sometimes even exceeding, the advective one. For a 25-hr period, the M1 component of SSC usually denotes the maximum SSC associated with the highest bottom stress, while the M2 component signifies the two highs of the SSC. The M4 component is generally insignificant. The M1 and M2 components can be induced by both the advection and bottom resuspension. For the resuspension part, the M1 component is mostly induced by tidal velocity asymmetry, while the M2 component is generated by tidal straining effect. Sediment transport at the shoal is mostly controlled by the advective flux and the tidal pumping due to tidal velocity asymmetry, while that in the channel is dictated by advective transport and the tidal pumping due to tidal mixing asymmetry.

1 Introduction

Estuaries usually feature complex bathymetries, in which shoals and channels are co-existent. The hydrodynamics and sediment transport patterns are profoundly different between the shoals and channels in an estuary, due to the difference of water depth, current strength and therefore the baroclinic pressure gradient and stratification. These lateral differences control the lateral distribution of sediment transport (Ralston et al. 2012; Gong et al. 2014; McSweeney et al. 2016).

For idealized short estuaries, Pritchard (2005) and Cheng and Wilson (2008) derived analytical solutions for sediment concentration and sediment transport flux. In their studies, the importance of advection is highly recognized.

Sediment transport flux is often decomposed into several components. In an Eulerian frame, the sediment transport flux at a single vertical layer in the water column can be decomposed into:

$$F=\frac{1}{T}\int_0^T UCdt=\overline{U}\overline{C}+\overline{U\hbox{'}C\hbox{'}}$$

(1)

where U and C are water velocity and sediment concentration, respectively. The overbar means the tidally averaged, while the prime denotes the deviation from the tidally mean. U^′ and C^′ can be decomposed into different tidal components. The first term in the right of Eq. (1) is the so-called advective flux, while the second one is the tidal pumping flux.

The advective sediment flux is the multiplication of mean flow and mean suspended sediment concentration (SSC). In an estuary, the mean flow can be generated by many processes, including river discharge, horizontal density gradient, tidal rectification, tidal mixing asymmetry, Stokes return flow and wind (Cheng 2014). The mean SSC is induced by bottom resuspension of a mean bottom stress, and/or the advection of a mean horizontal SSC gradient by the mean flow (Cheng and Wilson 2008). In respect to the tidal pumping term, it is generated by the covariance between current and SSC. A quadrature phase relationship results in a zero tidal pumping, while a shift from the quadrature produces a nonzero pumping. Many physical processes have been proposed to interpret the tidal pumping, including the interaction of an oscillatory tide and a mean longitudinal SSC gradient (Cheng and Wilson 2008), settling lag and scour lag (Postma 1961), barotropic tidal asymmetry including tidal duration asymmetry, tidal velocity asymmetry and tidal acceleration asymmetry (de Swart and Zimmerman 2009; Friedrichs 2012; Gong et al., 2016), and tidal mixing asymmetry (Scully and Friedrichs 2007, herein referred to as internal tidal asymmetry by Jay and Musiak (1996)). For the tidal velocity asymmetry, an ebb (flood) dominance in velocity usually results in an ebb (flood) dominance in bottom stress, thus generating a greater resuspension during ebb (flood) than during flood (ebb), and therefore a net seaward (landward) tidal pumping flux. The asymmetry between duration of low and high water slacks also induces a tidal pumping flux. A longer duration of low water slack favors seaward sediment transport and vice versa for tidal flats (Van Maren and Winterwerp 2013). However, Sommerfield and Wong (2011) showed that in the Delaware River estuary a shorter duration of low water slack results in an incomplete settling of sediment during the ebb slack and favors a seaward sediment transport. For the internal tidal asymmetry in a partially mixed estuary, during the flood tide, the water column is more mixed and a greater bottom stress generates more sediment resuspension, which is mixed into the upper column. During the ebb tide, the water column is more stratified and less sediment is resuspended, which is more confined below the pycnocline. This pumping process generates a net landward sediment transport in the upper part of the water column and a net seaward transport near the bottom (Scully and Friedrichs 2007; Burchard et al. 2013). An opposite situation occurs for a salt wedge estuary, similar to that at a salt front (Geyer 1993).

As mentioned above, an important source of tidal pumping sediment flux is the advection of an existing horizontal SSC gradient. Weeks et al. (1993) proposed a conceptual model for the intratidal variation of SSC in a semi-diurnal continental shelf. They attributed the semi-diurnal variation of SSC to the advection by the semi-diurnal tide imposing on a mean SSC gradient, while the quarter-diurnal variation of SSC to the local resuspension. Bass et al. (2002) further analyzed the complex interactions of advection, settling and bottom erosion on the SSC variations. Incorporating a settling term can shift the phases of SSC induced by the advection and/or bottom resuspension, resulting in a deviation from the quadrature phase relationship between current and SSC, and thus a pumping flux. Yu et al. (2011) investigated the vertical distribution of SSC and the phase lag of SSC relative to tidal current by a 1DV model. By utilizing an analytical model, Pritchard (2005) studied the advection, settling and bottom resuspension on the residual sediment transport. When the tidal period is shorter than the SSC settling time scale, the advection is dominant in modulating the tidal variation of SSC and controlling the residual sediment transport. Cheng and Wilson (2008) further derived an analytical solution for the tidally induced residual sediment transport in an idealized short embayment. Yu et al. (2014) also noted that the advection of a SSC gradient generates a significant tidal pumping flux and favors the formation of turbidity maximum in well-mixed estuaries.

Sediment transport and the associated processes are different in the channel and at the shoal in an estuary. Scully and Friedrichs (2007) noted that in the York River estuary, tidal mixing asymmetry is an important mechanism generating a landward tidal pumping flux in the channel, while at the adjacent shoal, the tidal pumping sediment flux is a downstream one and is mainly induced by asymmetries in bottom stress. Sommerfield and Wong (2011) found that in the Delaware estuary, the net sediment flux in the channel is induced by the advective and tidal pumping fluxes, in which both of them are important. At the subtidal flats the net sediment fluxes are weak and dominated by tidal pumping. They proposed that the tidal pumping flux is induced by tidal asymmetry including slack water duration asymmetry, tidal mixing asymmetry, and settling and erosion lag, but the relevant contributions from these mechanisms are not clear. McSweeney et al. (2016) elucidated the role of salinity stratification on the tidal pumping sediment fluxes between the channel and flanks in the Delaware Estuary. In the channel, the stratification is induced by the tidal straining effect and generates a landward tidal pumping flux, while at the flank, the stratification is stronger during flood and weaker during ebb (a reversed tidal straining), induced by lateral circulation, and generates a seaward tidal pumping flux.

Though the tidal pumping flux has been ascribed to many different physical processes, how to quantify the contributions of individual mechanisms still remain unclear. To further understand the sediment transport mechanisms, analytical solutions have been derived for the water motion, SSC, and sediment transport in estuaries. Huijts et al. (2006) developed an analytical solution for the lateral sediment entrapment in well-mixed tidal estuaries dominated by semi-diurnal tides. The perturbation method was utilized to decompose the water motion and SSC into leading order and higher order solutions. This kind of research was further explored by Chernetsky et al. (2010), Yang et al. (2014), Kumar et al. (2017). For a semi-diurnal tidal regime, the leading order SSC is comprised of a mean SSC and a quarter-diurnal SSC by bottom resuspension. The first-order SSC is mostly a semi-diurnal one, which is induced by both the resuspension, advection and that due to the surface forcing (Kumar et al. 2017).

The above analytical studies are mainly focused on semi-diurnal tidal estuaries. For the estuaries with mixed tides, the mechanisms for sediment transport have been less studied. An exception is that conducted by Jiang et al. (2013) in the Yangtze River, China. They adopted a harmonic analysis method to decompose the variation of water elevation, velocity and SSC into different tidal constituents. The sediment flux in a single layer and the vertically integrated sediment flux were calculated. Through this method, they identified the contributions of sediment flux from different tidal constituents. Combined with the analytical solution of the residual current, the mechanisms behind the change in sediment transport fluxes before and after the Deep Waterway Project (DWP) were identified. Though encouraging results were obtained, the physics underlying the variation of SSC from different tidal constituents remains to be explored.

In this study, we conducted field measurements in a mixed semi-diurnal micro-tidal estuary, the Huangmaohai Estuary (HE), China. The observations were carried out under varying external forcing conditions, including different river discharge and wind (wet and dry seasons), tidal mixing (spring and neap tides). To reveal the difference of sediment dynamics between in the channel and at the shoal, two anchoring stations were deployed in each field survey, one was at the side shoal, and the other was in the channel. In each survey, vertical profiles of current, salinity and SSC were obtained, along with high frequency data at the bottom boundary layer through deploying a bottom tripod. The bottom stress was calculated based on the maximum log profile (Lp-Max) method after extensive tests among different methods. The observation data were subject to harmonic analysis and the associated mechanisms for each component were analyzed. Along with these observations, we derived a semi-analytical solution of the SSC for the mixed semi-diurnal regime with both the diurnal and semi-diurnal tides being important. The aims of this study are to: 1) identify the mechanisms associated with the advective and tidal pumping fluxes, especially the physics behind each tidal component; 2) distinguish the sediment dynamics between at the shoal and in the channel. In these respects, this study is much relevant to wetland restoration and navigational channel management.

2 Study site

The HE (Fig. 1) is located in the southwest of the Pearl River Delta, China. The HE composes of a bay and a tidal river. The bay is funnel shaped, with the width of the estuary narrowing from 35 km at the mouth to 1.9 km at the apex, where Hutiaomen Outlet from the east and Yamen Outlet from the north confluence. The bathymetry in the estuary is very complex, featuring several shoals and channels. For more details of the bathymetry, readers can refer to Gong et al. (2014).

Fig. 1

a The location of the HE in the Pearl River Delta; b Geometry of the HE; c Bathymetry of the estuary and the location of measurement stations

The tides in the HE are predominantly mixed, having semi-diurnal dominance and diurnal inequality. At the mouth of the estuary, the four main tidal constituents are M₂, K₁, O₁ and S₂, with tidal amplitudes of 0.49, 0.35, 0.31 and 0.17 m, respectively. The root mean square (RMS) tidal range at the estuary mouth is 1.34 m, indicating a micro-tidal regime. When the tidal wave propagates upstream, the tidal range experiences complicated changes (Gong et al. 2012). The tidal current in the estuary generally lags the water level by an almost quadrature phase, showing a characteristic that mostly resembles a standing wave. The tidal currents in the channels are on the order of 1 m/s, and can reach 1.5 m/s during spring tides, whereas the tidal currents along the peripheral shoals are less than 0.5 m/s as a whole. The total river discharge delivered to the estuary is 39.8 × 10⁸ m³ a year, of which 19.6 × 10⁸ m³ is from the Yamen Outlet. The river discharge in the estuary endures distinct seasonal variation, in which 70% of the discharge occurs in the wet season (From May to September). Because of the seasonal change in the river runoff, the estuary is in a state of partially mixed to highly stratified during the wet season and well mixed to partially mixed during the dry season (From November to March) (Huang et al. 1994).

Winds in the estuary show a distinct seasonal variation. In the dry season, winds are mainly from the northeast and, during the wet season, southwesterly winds prevail. The mean wind speeds are 4.5 m/s and 6.7 m/s, respectively, in the wet and dry seasons. Under stormy conditions, wind speeds can reach 20–30 m/s. Based on one year observation data at the mouth of the estuary, the waves also show distinct seasonal variability. The most frequent wave direction is SE, followed by S and SW. The mean significant wave height is 0.98 m, with a mean wave period of 5.3 s. The significant wave height can reach as high as 5 m under typhoon conditions.

The bottom sediment in the HE consists of a mixture of mud and sand. Most of the tidal river and the Huangmao Bay are covered by mud. In the peripheral shoals of the Bay, silty clay or clayey silt is dominant with a median diameter less than 0.008 mm. In the channel, owing to strong currents, fine- to medium-grained sands are found with a median diameter ranging from 0.05 to 0.5 mm. Offshore of the estuary mouth, sand fraction is more prevalent.

3 Methodology

3.1 Field measurements

Four field deployments were carried out to investigate the seasonal and spring-neap tidal variations of sediment dynamics: spring tide on 26–29, June, 2014 and neap tide on 5–8, July, 2014 in the wet season; neap tide on 13–16, January, 2015 and spring tide on 20–23, January, 2015 in the dry season.

The river discharge from the upstream of the Pearl River Delta during the measurement is shown in Fig. 2. In the wet season, the spring tidal period coincided with a waning period of a river pulse. The river discharge at the upstream station of Makou (the confluence of West River and North River) was approximately 10,000 m³/s. These data are roughly the multi-year mean river discharge during the wet season. The prevailing southwesterly wind was very mild with a speed less than 4 m/s. The tidal range at the mouth of the HE during the spring tide was 2.37 m while during the neap tide, the tidal range decreased to 1.01 m. In the dry season, the neap tidal period corresponded to a rising river discharge and the spring tide was during a relatively stable river discharge. The river discharge at Station Makou was between 2000 and 4000 m³/s during the measurements and represents a normal situation for the dry season. The tidal range during the neap tide was approximately 1.0 m at the estuary mouth, while it became 2.95 m during the spring tide. In the neap tide, the wind was strong, and was persistently northwesterly to northeasterly. The wind speed reached as high as 13 m/s in the deployment at the shoal, and weakened for the subsequent deployment in the channel. During the spring tide, the wind was relatively weak with a speed less than 5 m/s, and alternated between southeasterly and northeasterly.

Fig. 2

Discharge, tide and wind in the wet (left panels) and dry (right panels) seasons. Upper panels are the discharge, middle panels are the tide, and bottom panels are winds. The solid and dashed lines in (a) and (b) indicate the discharge at Stations Makou and Shijiao, respectively. The bold lines in upper and middle panels indicate the duration of observations

In each deployment, time series data were collected at 2 stations (Fig. 1c), the shoal station and the channel station. A lunar day of 25 hours was covered at the shoal and in the channel, respectively. For each deployment, an instrumented bottom tripod was installed. The tripod was equipped with an acoustic Doppler velocimeter (ADV) measuring 3D current velocities at 0.35 mab (meter above bed). The ADV collected data in burst mode at 10 min intervals and the burst duration is 5 min, with the sampling frequency within each burst being 64 Hz. Additionally, time series of turbidity, temperature and salinity were obtained at the same level as the ADV by using a nephelometer (OBS-3A, D&A Instrument Co.) and a CTD (RBR XR-420). The sampling frequency of OBS and CTD were all set as 1 Hz. During the dry season, apart from the same instruments in the bottom tripod, an additional wave recorder (AWAC) was installed for measuring wave parameters.

The near bed tripod measurements were complemented with hydrodynamic and sedimentary data collection throughout the water column from a boat anchored 50 ~ 75 m away from the tripod. Velocity profiles were obtained using a downward looking acoustic Doppler current profiler (ADP, 1000 kHz) every 3 min. The profile range extended from 0.5 m below the sea surface to near the bed with a vertical resolution (bin size) of 0.3 m. Hydrographic and in situ particle size data were also collected through the water column hourly using a profiling system consisting of a CTD, OBS and a LISST-ST. In the meantime, water samples were collected hourly from three layers in the water column (surface, middle and bottom layers). The water samples were filtered (using 0.45 μm filter) on board immediately and then subjected to laboratory analysis after returning to the university campus, for estimating the sediment concentrations.

Bed sediments at the shoal and in the channel were collected with a grab sampler. These sediments were analyzed for grain size distribution using standard techniques. A laser Malvern Mastersizer 2000 granulometer was utilized for these measurements. The results showed that the surficial sediments both at the shoal and in the channel are primarily silt with a median diameter of 6.75 in Phi units.

3.2 Data processing

The mean hydrodynamic flow conditions were measured from the ADV installed on the tripod and the ADP profile data after averaging over a period of 3 min. In addition, the ADV-collected instantaneous velocity time series were analyzed for estimation of turbulence properties and the mean bottom shear stress throughout the surveying periods. Simultaneously, regression relationship between the turbidity and SSC were obtained for converting the turbidity data into sediment concentration.

3.2.1 Bottom shear stresses estimation

Several methods to calculate the bottom shear stress were tested (Salehi and Strom 2012) in this study, including:

• 1) Mean log-profile (LP): In this method, a regression line is fit to the data in the bottom log layer, as:

$$\frac{U}{u_{\ast }}=\frac{1}{k}\ln \left(\frac{zu_{\ast }}{v}\right)+B$$

(2)

with the friction velocity, u_∗, as a regression parameter. In Eq. (2), κ is the von Karman constant (κ = 0.4) and B is a function of the dimensionless roughness, and is taken here as 5.5, as the bed is calculated as hydraulically smooth. The bed shear stress was then calculated from τ_B = ρu_∗². Here we utilized the ADV mean velocity data to calculate the friction velocity.

• 2) Maximum log-profile (LP-Max): Instead of the mean velocity, the maximum instantaneous velocity was used in Eq. (2). This method is suggested to be more suitable for estimating bed shear stress in zones with strong fluctuations in velocity. In particular, LP-max method works well in the presence of waves (Andersen et al. 2007). This method was shown to be the most appropriate in this study.

• 3) Turbulent kinetic energy (TKE): The bed shear stress is assumed to be linearly related to TKE:

$${\tau}_B={C}_0\rho q$$

(3)

where $q=\left(\overline{u{\hbox{'}}^2}+\overline{+v{\hbox{'}}^2}+\overline{+w{\hbox{'}}^2}\right)/2$ is the turbulent kinetic energy and C₀ is a coefficient set equal to 0.2 or 0.19.

• 4) Modified TKE (M-TKE): To decrease the effects of wave orbital velocity on the calculation of TKE, q was calculated using only the vertical velocity component since it is less susceptible to orbital motion. A proportionality constant of 0.9 was used in Eq. (3), therefore, the bed shear stress was calculated as:

$${\tau}_B=0.9\rho \overline{w{\hbox{'}}^2}$$

(4)

• 5) Reynolds stress (RS): Assuming there is a constant stress layer, the bed shear stress was calculated from a single point measurement within the layer as, ${\tau}_B=\rho \left(-\overline{u\hbox{'}w\hbox{'}}\right)$.

• 6) Inertial dissipation (ID): The method is valid if the measurement of turbulent spectra is done at a height above the seabed that is small enough to be within the constant stress layer. The friction velocity u∗ was calculated as:

$${u}_{\ast }={\left({\phi}_{ww}{f}^{5/3}/{\alpha}_3\right)}^{1/2}{\left(2\pi kz/\overline{w}\right)}^{1/3}$$

(5)

where ϕ_ww is the vertical energy spectrum, α₃ = 0.68, f is the frequency, z is the distance of the measurement point from the bed, $\overline{w}$ is the mean vertical velocity.

Each method mentioned above has its advantage and drawback. After extensive tests (Fig. 3), the LP-max method was shown to perform best and thus was adopted in this study. The bottom stresses derived from the LP-max method are comparable to those by M-TKE and ID, while the LP method yields a rather smaller bottom stress, and the TKE method results in a larger bottom stress during weak currents and smaller bottom stress during strong currents, the RS method produces a large fluctuation of bottom stresses, sometimes even with negative values, which is not reasonable.

Fig. 3

Comparison of the method for calculating the bed shear stress in wave (left panels) and non-wave (right panels) situations. Upper panels are the significant wave height

3.2.2 Sediment concentration estimates

The recorded signal from the OBS-3A sensors was converted to SSC using a regression relationship between turbidity (NTU) and SSC (Fig. 4). The calibration coefficient values slightly varied from deployment to deployment, probably due to different sediment characteristics that can affect the response of either the OBS, the ADV or both sensors. During the wet season, the overall correlation relationship between SSC and turbidity is SSC = 0.623NTU + 19.22, with a correlation coefficient of 0.71. During the dry season (Fig. 4), the relationship between SSC and turbidity is SSC = 0.418NTU + 34.18, with a correlation coefficient of 0.81.

Fig. 4

The correlation between SNR of ADV backscatter intensity and SSC (left panels) and between NTU of OBS and SSC (right panels) at the bottom in the wet (upper panels) and dry (bottom panels) seasons, respectively

Calibration equations were also established by fitting the converted SSC from the OBS-3A turbidity data into the range corrected ADV acoustic backscatter intensity. As the ADV backscatter data shows more fluctuations than OBS data (not shown), these data are not utilized in this study.

The LISST data was not much reliable due to unknown reasons and the data was not analyzed further.

3.2.3 Harmonic analysis, derivation of a semi-analytical solution for SSC and sediment flux decomposition

The water level, current and SSC were subject to harmonic analysis by using a standard least square method (Emery and Thomas 2001). As our study site features a mixed semi-diurnal tidal characteristic, both the diurnal and semi-diurnal tides are important. Three tidal constituents, namely, M₁, M₂and M₄are selected for the diurnal, semi-diurnal and quarter-diurnal tides, respectively. The period of the M₁ tide is the average of K₁ and O₁, thus representing a combination of these two diurnal constituents. The M₂ tide roughly represents the semi-diurnal tide as it is much stronger than S₂.

Following the method of Cheng and Wilson (2008), we derived a semi-analytical solution for the depth-integrated SSC in our study site by adding a residual flow and a M₁ tidal current for the hydrodynamic part and a M₁ component for the horizontal SSC gradient. The details are in the Appendix. For simplicity, here we assume that the horizontal SSC gradient consists of only a mean component, with higher SSC at upstream.

In our study site, the mean bottom stress is caused by the interactions between the mean flow and itself, and between other tidal current constituents and themselves, like M₁ and M₁, M₂ and M₂, and etc. The M₁ bottom stress is induced by the interactions between the mean flow and the M₁ current, and between the M₁ and M₂ currents. The M₂ bottom stress is attributed to the interactions between the mean flow and the M₂ tidal current, between the M₁ and M₁ current, and between M₂ and M₄ currents. Consequently, the mean SSC is induced by the bottom resuspension by the mean bottom stress, and by the advection of a mean horizontal SSC gradient by the mean flow. The M₁ SSC is generated by the bottom resuspension by the M₁ stress, and advection of the SSC gradient by the M₁ current. Other components of SSC are induced by the similar processes.

The sediment transport flux at each vertical layer j is thus expressed as:

$$F(j)=\overline{U\left(j,t\right)C\left(j,t\right)}=\underbrace{\overline{U_j}\overline{C_j}}_{T0}+\underbrace{U_{j,1}C_{j,1}\cos\left(\phi_{j,1}-\theta_{j,1}\right)/2}_{T1}+\underbrace{U_{j,2}C_{j,2}\cos\left(\phi_{j,2}-\theta_{j,2}\right)/2}_{T2}+\underbrace{U_{j,4}C_{j,4}\cos\left(\phi_{j,4}-\theta_{j,4}\right)/2}_{T4}$$

where φ, θ is the phase of velocity and SSC, respectively. T0 represents the advective flux, and T₁, T₂ and T₄ signifies the tidal pumping flux due to the M₁, M₂ and M₄ tides, respectively.

In this study, the water column was divided into 6 layers for the harmonic analysis, like a σ vertical grid, and the hourly current and SSC profiles were interpolated into the σ layers, same as that by Jiang et al. (2013).

4 Results

4.1 Sediment dynamics at the shoal

4.1.1 Spring and neap tides in the wet season

In the wet season, river inflow from the upstream is high (approximately 1.5 × 10⁴ m³/s). Consequently, the salinities at the shoal are relatively low. The station is located at the interface between freshwater and saline water.

During the spring tide, the amplitude of the diurnal tide is comparable to that of the semi-diurnal tide (Table 1). The tidal range is approximately 2.35 m.

Table 1 The tidal harmonic constituents of water elevation

Firstly, we examine the data of ADV, OBS, CTD at the bottom tripod (0.35 mab). The bottom stress was calculated based on the method of LP-max and shown in Fig. 5d.

Fig. 5

Measurement and calculated results at the shoal during the spring tide in the wet season. a water elevation; b, c, d, e is the velocity, salinity, shear stress and SSC at the bottom, respectively. f, g, h is the velocity in the upper, middle and bottom layers, respectively. i and j are the vertical profiles of salinity (unit: ppt) and SSC (unit: mg/l). Right panels are the harmonic analysis of axial current (k), SSC (l), phase difference between current and SSC (m) and sediment flux (n)

At the bottom layer (left column of Fig. 5), the current shows a fluctuation of two cycles of flood and ebb tides, with a smaller one followed by a greater one. The ebb duration is obviously longer than the flood one, with the peak ebb velocity larger than the peak flood velocity. The salinity is elevated during the greater flood and reaches a maximum at the high slack water. It then declines continuously and attains nearly zero at the peak ebb. The bottom stress fluctuates with the current, and is larger during the greater flood and ebb, especially at the greater ebb. The SSC is much consistent with the variations of the bottom stress, showing that bottom resuspension is mostly responsible for the fluctuations of the bottom SSC. From the harmonic analysis results of bottom stress and SSC (Table 2), it can be seen that the mean and M₁ components are the largest, while the M₂ is the smallest. The phase difference between SSC and stress is less than 90° for the M₁ and M₄ components, and larger than 90° for the M₂. The out of phase between the M₂ bottom stress and SSC is caused by the fact that two peak SSCs occur at two peak bottom stresses during flood tides. In this study, the flood current is defined as negative.

Table 2 The decomposition of bottom stress and SSC

For the vertical profiles (middle column of Fig. 5), the current shows a similar variation as at the bottom, exhibiting an asymmetry of ebb dominance. During the greater flood, there appears a subsurface maximum velocity core in the water column, while during the greater ebb, the maximum velocity is located at the water surface. This is a typical feature of the velocity profile of a salt wedge (Uncles 2002). The ebb current during the smaller tide is very weaker, with a velocity less than 0.15 m/s. The salinity variations at the station show that the station is occupied by freshwater in most of the time, except at the greater flood tide and the subsequent ebb tide, when a salinity intrusion occurs. The salinity stratification is stronger during the greater flood and ebb, showing again the feature of a salt wedge. The sediment concentrations are generally higher at peak flood and ebb velocities, showing the importance of local resuspension. However, at the peak flood velocity during the greater tide, the SSC is confined at the low water column and not as high as that during the smaller flood, suggesting the suppression of salinity stratification on the vertical mixing and sediment resuspension. During the greater ebb, the high SSC is mixed in the whole water column, indicating a reversed tidal straining effect to that by Simpson et al. (1990).

The vertical distribution of amplitudes and phases of different components of the current and SSC are depicted in the right column of Fig. 5. For the current (Fig. 5k), the mean current is a unidirectional seaward flow (0.1 m/s), and the M₁ and M₂ currents show a subsurface maximum with a magnitude of 0.4 m/s and 0.6 m/s, respectively. The M₄ current has a magnitude of 0.2 m/s, and also features a middle maximum. For the SSC (Fig. 5l), the M₀ concentration is the highest component, and shows an exponentially upward decreasing. The M₁ part is the second highest, and has two maxima, one at the bottom and the other one near the middle. The maximum SSC near the middle could be induced by a combination of horizontal advection and vertical diffusion. The M₄ part ranks the third. The smallest component is the M₂ one. The phase difference (Fig. 5m) between the current and SSC of the M₁ component shows a value mostly less than 90°, indicating that SSC and velocity are in phase. The M₂ component shows a phase difference larger than 90° in the lower water column, and smaller than 90° in the upper part. The out of phase between the bottom SSC and current has been explained above, while the in-phase at the surface could be mostly generated by the higher SSC at the greater ebb and lower SSC at the greater flood. The lower SSC at the surface during the greater flood is generated by the salinity stratification then. This reversed tidal straining effect has also been noticed by McSweeney et al. (2016) at the subtidal flanks of Delaware River estuary. The M₄ component shows an in-phase relationship between the current and SSC.

For the sediment flux (Fig. 5n), the advective flux (M₀) is seaward in the whole water column, and is the dominant contributor at the bottom and surface. The M₁ flux is mostly seaward in the water column, except at the surface. It is the main contributor of seaward flux in the middle layer. The M₂ and M₄ components are landward at the lower water column but seaward at the upper water column. The total sediment flux is seaward in the whole water column.

It is shown that during the spring tide the sediment flux is mostly controlled by the M₀, M₁ and M₂ fluxes, while the M₄ component plays a minor role.

During the neap tide (Fig. 6), the tidal range, current and sediment concentration are all decreased. From Table 1, the M₂ tide becomes the dominant tidal constitute, while the M₁ tide decreases significantly. The M₄ tide decreases by half compared to that in the spring tide. Simultaneously, the salt intrusion is enhanced and the water column becomes more stratified, with an increased estuarine circulation.

Fig. 6

The same as Fig. 5 but for the shoal during the neap tide in the wet season

At the bottom layer (left column of Fig. 6), the ebb current is still stronger than the flood one, with a longer duration of ebb than flood. The flood velocity is generally less than 0.2 m/s. The salinity is elevated compared to that in the spring tide (Fig. 6c). The salinity is increased during floods and decreased during ebbs, however, it keeps increasing in the second ebb, and reaches a maximum before the peak ebb. The reasons for such an abnormal phenomenon are unknown but could be induced by lateral circulation (Chen et al. 2020). Compared to the spring tide, the bottom stress fluctuates more greatly, while the bottom SSC does not closely follow the bottom stress. The SSC reaches a maximum near the first ebb slack. After that, it does not fluctuate much, indicating that there exists a background SSC sustained by a mean bottom stress and/or advection of a constant horizontal SSC gradient by the mean flow. Through harmonic analysis (Table 2), the M₀ bottom stress is the largest for all the components, associated with the highest SSC. The M₁ component of the bottom stress is the second largest, followed by the M₄ and M₂ components. The M₂ SSC is higher than the M₄ SSC, implying a contribution from the horizontal advection by M₂ tidal component.

For the vertical profiles (middle column of Fig. 6), the current velocity is less than 1 m/s. The surface current (Fig. 6f) shows a great fluctuation, and after Hour 18, it exhibits a consistent landward current, while the middle and bottom layers endure an ebb-flood-ebb cycle (Fig. 6g and h). We postulate that the surface southwesterly wind could be responsible for such a difference between the surface and bottom currents. The salinity variation shows that the water column is mostly occupied by freshwater, and the saline water is confined at the bottom. The sediment concentration is generally low, less than 150 mg/l. High SSCs occur at the ebb slacks (on Hour 5 and 20), and on Hour 20, high SSC occupies the upper water column and the bottom.

Harmonic analysis of the current and SSC (right column of Fig. 6) shows that the M₀ current is a unidirectional seaward flow, with the flow magnitude largest in the middle (Fig. 6k). This pattern is generated by the combined effect of baroclinic pressure gradient, bottom friction, river discharge and wind forcing. The M₂ tidal current is the largest, followed by M₁ and M₄. For the SSC (Fig. 6l), the M₀ component is the highest, and shows one maximum at the bottom and one maximum near the surface. The M₂ and M₁ SSCs are comparable. For the M₁ SSC, there are two highs in the vertical, one at the bottom and the other one at the surface. The bottom high SSC should be induced by bottom resuspension, while the surface high could be induced by horizontal advection. The phase relationship between velocity and SSC (Fig. 6m) shows that they are generally less than 90° for M₂ and M₄ components, while it is larger than 90° for M₁. This out of phase could be mostly generated by the upward diffusion of a high bed SSC from the first ebb slack (around Hour 5) to the subsequent flood tide.

For the sediment flux (Fig. 6n), the advective flux (M₀) is seaward, with a maximum in the middle water column, consistent with the vertical distribution of mean flow. The M₂ and M₄ fluxes are seaward as well. It is noted that though the M₂ current is strong and M₂ SSC is high, the phase relationship between them is nearly 90°, which results in a negligible M₂ sediment flux. This can be mostly caused by the advection of a constant horizontal SSC gradient by the M₂ current. The M₁ component becomes landward, especially near the surface. The total flux is seaward, controlled by the advective one.

4.1.2 Spring and neap tides in the dry season

In the dry season, river discharge decreases significantly (less than 4500 m³/s). Consequently, the salinity at the measurement station is increased, indicating that it is within the mesohaline regime in the estuary, and the tidal straining effect becomes more distinct.

During the spring tide, the bottom current at the shoal (left column of Fig. 7) shows a stronger ebb current than flood current, along with a longer duration of ebb. The salinity at the bottom reaches as high as 27 ppt and is elevated during floods while reaching a maximum at high water slack. The bottom stress at the spring tide is mostly controlled by the tidal current, as the wind wave is low during this period. The SSC generally follows the fluctuation of the bottom stress, with elevated SSCs at large stresses. An exception occurs on Hour 17 (Fig. 7e), when the bottom stress has declined significantly, while the SSC attains a maximum. We interpret that this can be due to the continuous erosion of the seabed as the bottom stress is still larger than the critical shear stress for erosion.

Fig. 7

The same as Fig. 5 but for the shoal during the spring tide in the dry season

Harmonic analysis of the bottom stress and SSC (Table 2) shows that the M₀ stress is the highest and relatively stronger than that in the summer, while the M₀ SSC is higher than that in the summer. The M₁component is the second largest, followed by M₂ and M₄.

For the vertical profiles (middle column of Fig. 7), the ebb duration is longer than the flood one, with a stronger ebb current (Fig. 7f ~h). The salinity is increased at flood tides, and decreased at ebb tides. The water column is highly mixed, with the salinity difference between the surface and bottom less than 5 ppt (Fig. 7i). The SSC is greatly increased during peak flood and ebb flows, showing the importance of bottom resuspension (Fig. 7j).

Harmonic analysis shows that the M₀ current is a unidirectional seaward flow with a magnitude less than 0.1 m/s. The M₂ current is the strongest component, followed by M₁ and M₄ (Fig. 7k). The decomposition of SSC indicates that the M₀ SSC is the largest component, followed by M₁, M₂ and M₄ (Fig. 7l). The phase difference between current and SSC of M₁ is less than 90°, showing that the high SSC occurs during ebb. However, the phase difference of M₂ is larger than 90°, as high SSCs of M₂ occur at floods. The phase difference of M₄ is larger than 90° near the bottom, while smaller than 90° in the rest of water column (Fig. 7m). For the sediment transport flux (Fig. 7n), the advective sediment flux is relatively small, while the total flux is primarily dominated by the M₁ flux. The M₁ flux is seaward, and is due to the fact that the highest SSC occurs on ebb tide. The M₂ component features a strong landward transport as high M₂ SSCs occur on flood tides, but is overwhelmed by the summation of the advective and M₁ fluxes. The M₄ component is insignificant.

During the neap tide, along with the reduced tidal strength, the water column becomes more stratified, and the baroclinic effect is more important. The bottom current at the shoal (Fig. 8b) is predominantly landward, possibly due to the combined effect of wind and baroclinic pressure gradient. During the measurement period, the wind is a persistently northeasterly one (Fig. 2). The salinity is kept as high as 28 ppt (Fig. 8c). It is interesting to note that on Hour 20, when the current is flood directed, the salinity decreases significantly. The reason for such a change is unknown but could be due to enhanced wave mixing with strong northeasterly wind (see Figs. 8 i and 2f). The bottom stress fluctuates largely (Fig. 8d), and is generated by the combined action of current and wave. It is high during low water when wave effect is strong, and high during the period when the current is strong. The SSC does not fluctuate much but increases under the large bottom stress (Fig. 8e). From Table 2, the bottom stress is mainly composed of a M₀ component, and the M₁ is the second strongest, followed by M₂ and M₄. The M₀ SSC is the highest, followed by M₁, M₂ and M₄.

Fig. 8

The same as Fig. 5 but for the shoal during the neap tide in the dry season

The vertical profiles of current, salinity and SSC are shown in the middle of Fig. 8. Consistent with the wind condition, the surface current at the shoal shows a predominant seaward flow (Fig. 8f), the middle current is also dominated by the seaward flow during most of the period, while from Hour 18, the landward flow prevails at the middle layer (Fig. 8g). In contrast, the bottom flow is mostly landward, except during the greater ebb tide (Fig. 8h). The flow pattern is in accordance with a wind induced circulation, where a downwind flow develops at the surface with a return flow at the bottom. Though the wind is strong in the neap tide, the wind energy does not mix the water column well, suggesting the wind straining effect is more important (Chen and Sanford 2009). The salinity stratification is strong, with a difference of 15 ppt between the surface and bottom. The salinity is increased during floods with the stratification decreased. During ebb tides, the stratification is enhanced, showing a typical tidal straining effect (Fig. 8i). The SSC is high and mixed upward in the water column during floods, while high concentration is confined at the bottom at ebbs. At Hour 17, high sediment concentration is mixed into the whole water column, induced by the wind wave effect (Fig. 8j).

The components of current, SSC, phase relationships between current and SSC, and sediment flux are shown in the right panel of Fig. 8. As the wind is strong, the mean current is a wind-induced circulation, with surface downwind flow and bottom return flow. The M₁ and M₂ tidal currents are of similar magnitudes and attain maximum at the subsurface, with the M₄ smallest (Fig. 8k). The M₀ SSC is much higher than other components and is mostly confined near the bottom (Fig. 8l). The phase differences for M₁ and M₄ are larger than 90° at the bottom, generated by strong resuspension at floods (Fig. 8m). Consequently, the sediment flux is mainly controlled by the advective flux, while other components are insignificant. The total flux is seaward (Fig. 8n).

4.2 Sediment dynamics in the channel

4.2.1 Spring and neap tides in the wet season

In the channel, the current is generally stronger than that at the shoal, and the water column is more stratified. The baroclinic effect is greatly enhanced due to the increased water depth and salinity gradient. As the bottom stress is generally stronger, sediment resuspension is expected to be higher.

During the spring tide (Fig. S1), the bottom current in the channel is stronger than at the shoal, and an ebb dominance prevails. The flood duration becomes comparable to the ebb duration while the flood velocity is smaller than the ebb one. Near the end of the measurement, the bottom flow shows a prolonged flood current (Fig. S1b). The salinity is elevated during floods and decreased during ebbs, and becomes totally fresh at ebb slack and the subsequent flood (Fig. S1c). The bottom stress is higher during peak flows (Fig. S1d), while the SSC follows closely with the bottom stress (Fig. S1e). Harmonic analysis (Table 2) shows an increase of M₂ bottom stress compared to that at the shoal. The SSC is also elevated than the shoal, especially for the M₁ and M₂ components. The M₀ SSC is the highest, while the M₁ and M₂ rank as the second and third components. The M₄ component is the lowest one.

Timeseries of vertical profiles of current, salinity and SSC profiles in the channel (middle column of Fig. S1) show some different behaviors from those at the shoal. It should be noted that the measurement date in the channel is 1 day later than at the shoal. The current in the channel is stronger than at the shoal, with a peak ebb velocity larger than 1.5 m/s at the surface (Fig. S1f). Interestingly, during the smaller tide, the bottom current exhibits a prolonged flood flow (Fig. S1h). This suggests that during the smaller tide, the baroclinic pressure gradient plays an important role in driving a landward bottom flow. The salinity in the channel exhibits a feature of salt wedge during the greater flood and ebb. Near the end of the greater ebb and at the subsequent flood, the water column is occupied by freshwater, and during the smaller tide, the water column is highly stratified (Fig. S1i). The SSC shows peak concentrations at peak flood and ebb velocities (Fig. S1j). It is noted that the sediment concentration during the spring tide is much higher, reaching 300 mg/l.

Harmonic analysis of current and SSC show that the M₀ flow is a unidirectional seaward one and is enhanced relative to that at the shoal. The M₂ current is the strongest, followed by M₁ and M₄ (Fig. S1k). There is a distinct subsurface maximum of M₂ current (Fig. S1k). The M₀ SSC is the highest, and shows an exponentially upward decreasing profile. The SSCs of M₁ and M₂ are comparable and quite high. The lowest SSC is the M₄ component (Fig. S1l). The phase difference between current and SSC of M₁ component shows a value less than 90°, indicating that SSC and current are in phase. The M₂ component shows a phase difference larger than 90° in the lower part of the water column, as high SSCs occur at flood tides near the bottom, and smaller than 90° in the upper part due to the occurrence of M₂ high SSCs at ebb tides. The M₄ component shows a similar pattern (Fig. S1m).

For the sediment flux (Fig. S1n), the advective flux is seaward in the whole water column, but becomes less important than that at the shoal. The M₁ flux is seaward in the whole water column as well. It is the most contributor of seaward flux in the middle layer. The M₂ flux is mostly landward, except near the surface. Its magnitude is comparable to those of the advective and M₁ fluxes, and largely competes against the seaward flux of these two components. The M₄ flux is relatively small, and makes little contribution to the total flux. It is shown that the sediment flux in the channel is seaward during the spring tide, and the advective, tidal pumping components of M₁ and M₂ fluxes are all important.

During the neap tide (Fig. S2), with enhanced salt intrusion, the water column becomes much stratified, and the bottom current is predominantly landward. The bottom stress keeps in pace with the change of bottom velocity (Fig. S2d), while the SSC is consistent with the bottom stress (Fig. S2e). The harmonic analysis (Table 2) indicates that the M₀ stress is the largest, followed by the M₂ component. The M₁ component becomes negligible. For the SSC, the highest is the M₀ component, followed by M₂ and M₄. The M₁ SSC is the lowest.

For the vertical profiles, the salinity stratification in the water column is greatly enhanced, with a maximum salinity difference of 20 ppt between the surface and bottom. The SSC shows that it is elevated in the peak flood current at the bottom. In the meantime, several SSC highs occur at the upper part of the water column during ebbs. These high SSCs are obviously induced by horizontal advection of high SSC from the upstream (Fig. S2j).

The harmonic analysis results show that during the neap tide, the M₀ flow becomes a typical estuarine circulation, with a surface seaward flow exceeding 0.3 m/s and a bottom landward flow of 0.1 m/s. The M₂ current is the dominant component in most of the water column. For the SSC, the M₀ component is the largest, followed by M₂ and M₄ components. The M₁ component is relatively small. The phase difference between M₂ current and SSC is larger than 90° in the lower water column, while it is smaller than 90° in the upper water column. This is induced by the fact that the lower water column is dominated by flood flow and the higher SSC occurs during floods, while the upper water column is dominated by ebb flow and higher SSC occur during ebbs.

For the sediment flux (Fig. S2n), the advective flux is the dominant component, with a landward one at the bottom and seaward one at the surface. The M₂ flux is the second largest one, sharing a similar feature to that of the advective flux. The contribution from the M₁ and M₄ components are insignificant. The total sediment flux is seaward as the magnitude of seaward flux in the upper water column is larger than the landward flux in the lower water column. This is a little different from previous studies that the sediment flux in the channel is landward during neap tides, e.g., Delaware Bay (McSweeney et al. 2016). We assume this difference could be due to the high river flow in our study period. It clearly indicates that during the neap tide, the sediment transport is controlled by the residual circulation in the channel. The tidal pumping by the M₂ component is relatively important as well.

4.2.2 Spring and neap tides in the dry season

In the dry season, the salinity is elevated and the water column is more mixed. During the spring tide (Fig. S3), the bottom current in the channel shows an ebb dominance. The bottom stress has four peaks corresponding to peak currents. The bottom SSC generally follows the bottom stress, with elevated concentrations during large stresses. From Table 2, the M₀ stress is the highest, generating a high M₀ SSC. The bottom stress of M₁ is larger than M₂ and M₄, while the SSC of M₁ is lower than M₂ but higher than M₄. Clearly, the bottom stress and SSC is not consistent and indicates a contribution from the advection by M₂ current.

During the spring tide, the water column is mostly well-mixed, and the SSC is very high during the peak floods and ebbs. At the greater ebb and the next flood, high SSCs are mixed up to the whole water column, while at the greater flood (Hour 2–4), high SSC is confined near the bottom (Fig. S3j). This pattern is consistent with the variation of salinity stratification.

Harmonic analysis results show that the M₀ current is a weak gravitational circulation, with seaward flow in most of the water column. The M₂ current component is the strongest one, followed by M₁ and M₄. The M₀ SSC is the highest, followed by M₁ and M₂.. The phase difference between current and SSC of M₁ is smaller than quadrature, while that of M₂ is larger than 90°. The result of sediment flux (Fig. S3n) shows that the advective flux is seaward in most of the water column except near the seabed, where a landward flux occurs. The M₁ flux is seaward while the M₂ flux is landward and significant. The M₄ flux is landward and small. The total sediment flux is seaward.

During the neap tide (Fig. S4), the bottom current is dominated by landward flow in most of the time, and the flood current is stronger than the ebb one. The salinity is kept much high, reaching as high as 30 ppt most of the time. The bottom stress fluctuates with the current. However, the bottom SSC does not fluctuate much. It is elevated during the first strong flood from Hour 3 to 7, and then keeps almost unchanged till the end of measurement. From Table 2, the bottom stress is mostly composed of a M₀ part and a M₂ component. The bottom SSC is controlled by a M₀ component, followed by the M₂ component.

During the neap tide, the salinity in the channel is greatly increased when compared to the wet season, and salinity stratification is more developed during ebbs. The SSC is relatively low, with a peak at the bottom at the ebb slack. There are high SSC spates in the upper part of the water column during the measurement, which could be induced by horizontal advection.

Harmonic analysis of current and SSC shows that the M₀ flow is an estuarine circulation with seaward flow of 0.4 m/s at the upper water column and landward flow of 0.1 m/s at the lower water column. The M₂ tidal current is the strongest, followed by M₁ and M₄, with the M₁ tidal current comparable to the M₂ component. The M₀ SSC is the highest, while the M₁, M₂ and M₄ components are relatively small. The phase difference between current and SSC shows that it is larger than 90° near the bottom and smaller than 90° near the surface for the M₁ component, and is smaller than 90° near the bottom and larger than 90° for the M₂ component. The advective flux is the dominant contributor for the total sediment flux, the M₁ and M₂ fluxes are in opposite directions and almost cancel out each other. The M₄ is negligible. The total sediment flux is a seaward one (Fig. S4n).

5 Discussion

5.1 The effect of tidal mixing asymmetry (tidal straining) on the generation of M ₄ tide

In our study site, the M₄ tidal components of both bottom stress and SSC are relatively small. The M₄ tidal constitute is from the propagation of offshore and/or is generated inside the estuary. Jay and Musiak (1996) proposed criteria to determine the importance of tidal straining on the generation of overtide M₄ in an estuary. Two indexes were put forward: one is the phase shift of the M₄ tidal current over the water depth, with a phase difference of 180° between the bottom and surface M₄ velocity. The other one is the ratio$R=\frac{M_{4,U}/{M}_{4,\zeta }}{M_{2,U}/{M}_{2,\zeta }}$, in which U and ζ represents the current and water elevation, respectively. When R > 1~2, the tidal mixing asymmetry can be considered as significant for generating the M₄ overtide.

We calculated the phase shift of M₄ velocity over the water depth and the ratio R. The results are listed in Table 3.

Table 3 Index values for the tidal mixing asymmetry on generating the overtide M₄

From the above results, it can be seen that the tidal mixing asymmetry in generating M₄ tide is not significant in our measurement periods. This could be owing to the following facts: 1) the criteria proposed by Jay and Musiak (1996) is for semi-diurnal tidal regime; Combinations of multiple tidal constituents may have complicated the effect of tidal mixing asymmetry in our study site; 2) Our measurement sites are not located in the region where saltwater is permanently present, and the typical tidal straining did not always occur, as shown above. It occurred in the dry season but the reversed pattern occurred in the wet season. Similar results have been noticed in the Rotterdam Waterway (de Nijs and Pietrzak 2011).

5.2 The mechanisms associated with different components of SSC

The decompositions of the bottom SSCs are shown in Fig. 9. The M₀ SSC is the largest component, showing the existence of a persistent background SSC. It is mostly induced by bottom resuspension of mean bottom stress. It can also be induced by the spatial settling lag effect (advection of a SSC gradient by the mean flow). For the four field measurements, the horizontal SSC gradient in the wet season is larger than in the dry season, as more freshwater from the upstream dumps into the estuary, together with higher SSC. The effect of spatial settling lag is thus more significant in the wet season, especially during the neap tide. The advection effect can be obviously witnessed at the vertical profiles of SSC, as high SSCs are found near the surface during ebbs (Figs. 6 and S2). During the spring tide, the bottom resuspension dominates over the advection effect, though the advection effect can still be observed by the surface high SSCs during ebbs (Fig. S1). Consequently, during the neap tide in the wet season, the vertical profile of the mean SSC (Figs. 6 and S2) features two maxima in both the shoal and channel stations, one at the bottom and one near the surface. During the spring tide in the wet season and in the dry season, the bottom resuspension is dominant, and the vertical profiles of the mean SSC all show an exponentially upward decreasing trend, with only one maximum at the bottom.

Fig. 9

The decomposition of bottom SSC into different tidal constituents. The left panel is for the shoal station. a during the spring tide in the wet season; b during the neap tide in the wet season; c during the spring tide in the dry season; d during the neap tide in the dry season. The right panel is for the channel stations. e during the spring tide in the wet season; f during the neap tide in the wet season; g during the spring tide in the dry season; h during the neap tide in the dry season. In all the figures, the tidal components of SSC have added the mean SSC for demonstration

The M₁ SSC can be generated by bottom resuspension of the M₁ bottom stress, and the advection of horizontal SSC gradient by the M₁ current (spatial settling lag). Usually, the M₁ SSC is the second largest component, next to the M₀ SSC. Sometimes it is smaller than the M₂ component, e.g. in the channel during the neap tide in the wet season and during the spring tide in the dry season (Fig. 9f and g). As M₁ means that this component has only one high in the 25-hr observation data, the peak of M₁ SSC usually coincides with the highest observed SSC. For the M₁ SSC generated by resuspension, the highest SSC occurs when the bottom stress is the largest. This occurs when the current reaches the maximum, and is associated with the tidal velocity asymmetry in the estuary (Gong et al. 2016). The highest SSC did not always coincide with the largest bottom stress, as the SSC is also influenced by the availability of erodible sediment at seabed (Huang et al. 2020). For example, during the spring tide, the highest SSC at the shoal occurs before the maximum bottom stress in the wet season (Fig. 5d and e) and after the maximum bottom stress in the dry season (Fig. 7d and e). Similar situation occurs in the channel. For the M₁ SSC induced by advection, the highest SSC occurs at the ebb slack (Weeks et al. 1993). This scenario can be greatly altered due to complex sediment transport processes (Bass et al. 2002). In our case, the highest SSC usually occurs at ebb tide, resulting in a seaward M₁ sediment flux. Similar to the M₀ SSC, in the wet season, the vertical profiles of M₁ SSC shows two maxima, one at the bottom and one near the surface or at the subsurface, coinciding with bottom resuspension and surface advection. In the dry season, the vertical profiles show an exponentially upward decreasing trend. However, during the spring tide in the dry season, the vertical profile in the channel (Fig. S3) shows a complex variation: firstly an increase from the bottom to the middle, followed by a decrease further upwards.

The M₂ SSC is induced by the advection by M₂ current, or bottom resuspension by the M₂ bottom stress. The M₂ component denotes two SSC highs during a diurnal period. In the wet season, the measurement stations are located at the front of salt intrusion and feature a reversed tidal straining effect. During the spring tide, the M₂ SSC denotes the high SSCs at the greater flood and at the subsequent prolonged ebb or at the smaller flood. High SSCs of the M₂ component occur at floods and are confined near the bottom due to the reversed tidal straining effect, resulting in a landward flux at the bottom. The variation of the surface SSC shows an opposite pattern, i.e., high M₂ SSC occurs at ebbs due to increased mixing, and exhibits a seaward flux. During the neap tide, the M₂ SSC at the shoal denotes two high SSCs near the two ebb slacks which are induced by both advection and bottom resuspension, and the M₂ flux is a seaward one. The M₂ SSC in the channel denotes two highs during floods at the bottom due to bottom resuspension and two highs during ebbs at the surface due to advection, thus the M₂ flux at the bottom and the surface is landward and seaward, respectively. In the dry season, the shoal and channel stations are within the mesohaline regime in the estuary, and feature a typical tidal straining effect. During the spring tide, the M₂ SSCs at the shoal and in the channel denote the elevated SSCs at the greater flood and the smaller flood. High SSCs occur at floods due to enhanced bottom stress and resuspension then (the tidal straining effect), and results in a landward flux. During the neap tide, the M₂ SSC at the shoal denotes the high SSC induced by wind wave on Hour 15 (at low tide) and a high SSC by ebb flow. The M₂ flux is seaward. The M₂ SSC in the channel denotes high SSCs at ebbs near the bottom and at floods near the surface generated by the tidal straining effect, and features a seaward flux near the bottom and a landward flux at the surface.

The M₄ SSC is induced by bottom resuspension of the M₄ bottom stress. In most deployments, the M₄ SSC is the smallest component and has little effect on the total sediment flux. Exception occurs at the shoal during spring tide in the wet season when it is larger than the M₄ SSC (Fig. 5l). It is interesting to note that the M₄ SSC is the leading-order component in a semi-diurnal tidal system (Huijts et al. 2006; Kumar et al. 2017), but it is rather insignificant in our study site.

Generally, the M₁ component is mostly induced by the tidal velocity asymmetry, e.g., ebb or flood dominance, while the M₂ component could be induced by both the tidal mixing asymmetry (tidal straining and/or reversed tidal straining effect) and the tidal velocity asymmetry. Quantitatively distinguishing these two effects is not feasible at this study. Numerical model simulations could resolve the contributions from the baroclinic and barotropic tidal asymmetry by turning on and off the baroclinic effect, which will be conducted in the near future.

Our results show significant difference from previous studies in the semi-diurnal tidal regime but similar to that in the mixed tidal regime, e.g. Yangtze River estuary (Jiang et al. 2013). Observations and modeling studies in the semi-diurnal tidal regimes (e.g. Weeks et al. 1993; Bass et al. 2002) have shown that the advection of a SSC gradient by M₂ tide will generate a M₂ signal in the SSC timeseries, and the bottom resuspension will induce a strong M₄ signal. In our study site, the M₁ signal is in general more significant than the M₂ and M₄ components, though the M₂ component can sometimes exceeds the M₁ component. The M₄ signal is the least important.

For the total sediment transport flux, the advective flux is dominant during the neap tides, while the tidal pumping fluxes are insignificant. When the tides get stronger (spring tides), the tidal pumping fluxes become more important. In the wet season, the M₁ flux is comparable to the advective flux to generate a seaward transport. In the dry season, the M₁ flux exceeds the advective one at the shoal and is comparable to the advective flux in the channel. The M₂ flux is the main component which drives a strong landward flux.

5.3 Difference in sediment dynamics between the shoal and the channel

Generally, the channel is deeper than the shoal, and the current is stronger in the channel. Moreover, the baroclinic effect in the channel is more significant, including stronger stratification, more developed estuarine circulation and enhanced tidal straining effect. These hydrodynamic differences result in different sediment dynamics between the shoal and channel.

During the spring tide in the wet season, the current in the channel is stronger than at the shoal, with all the tidal components being larger by 0.1–0.2 m/s. The M₀ flow in the channel is seaward and linearly increases from the bottom to the surface, stronger than that at the shoal by 0.1 m/s. Due to the great baroclinic pressure gradient in the channel, the current features a two-layer flow during smaller flood and ebb, with surface seaward flow and bottom landward flow. The flow at the shoal does not demonstrate such a vertical shear at smaller tide. The salinity intrusion in the channel is more distinct than at the shoal. Stronger stratification occurs in the channel, especially during the smaller tide. Consequently, the bottom stress in the channel is stronger than at the shoal during the greater ebb, while it is weaker than the shoal during smaller tide. SSC are generally higher in the channel than at the shoal, especially during the greater tide. The advective sediment transport is similar between the shoal and the channel, however, the tidal pumping fluxes of M₁ and M₂ components are significantly larger in the channel than at the shoal. During the spring tide, the total flux in the channel is larger, indicating that the channel is the main conduit for downstream transport of riverine sediment.

During the neap tide in the wet season, the baroclinic effect is increased. The M₀ flow in the channel shows a typical estuarine circulation with surface seaward flow and bottom landward flow. Due to the enhanced baroclinic pressure gradient, the bottom current in the channel manifests a predominantly landward flow. The mean flow at the shoal shows a unidirectional seaward flow, induced mainly by freshwater discharge. The salinity in the channel is much higher than at the shoal, and the water column is more stratified in the channel than at the shoal. The bottom stress in the channel is smaller than at the shoal in most of the time, except during the strong floods in the channel. Consequently, SSC in the channel is comparable to or lower than that at the shoal. The vertical SSC distribution at the shoal is more mixed than in the channel. It is also noted that during the neap tide, the M₂ flux at the shoal is seaward while in the channel it is landward at the bottom and seaward at the surface. This suggests that the tidal pumping M₂ flux at the shoal is more induced by tidal velocity asymmetry (ebb dominance), while the M₂ flux in the channel is more generated by tidal mixing asymmetry (reversed tidal straining effect). The total sediment flux in the channel is still larger than at the shoal.

During the spring tide in the dry season, the M₀ flow at the shoal is unidirectionally seaward, while in the channel, a two-layer flow with surface seaward current and bottom landward current develops. The flow and bottom stress in the channel are stronger than those at the shoal, along with higher SSC in the channel. The advective flux and the M₁ flux are seaward, with the advective flux being the largest, while the M₂ flux is landward in the channel. At the shoal, the M₁ flux is larger than the advective one, which are both seaward, while the M₂ flux is comparable to the M₁ flux and landward. In this case, the M₂ flux is generated by tidal mixing asymmetry with unlimited bottom sediment supply in the channel (Burchard et al. 2013) and by tidal velocity asymmetry at the shoal. During this period, the total sediment flux in the channel is similar to that at the shoal.

During the neap tide in the dry season, a strong offshore wind happened during the shoal measurement and the wind waned during the channel deployment. Both the mean flows at the shoal and in the channel present a two-layer circulation with surface seaward and bottom landward flow. However, the mechanisms are different, with the former by wind forcing while the latter by density gradient. Both the shoal and the channel show more mixed during floods and more stratified during ebbs. The bottom stress in the channel is generally larger than at the shoal, while the bottom stress at the shoal is greatly enhanced when wind wave is strong. The SSC at the shoal is higher than in the channel. During the neap tide, the total sediment flux is seaward and controlled by the advective flux, with the seaward sediment transport at the shoal being larger than in the channel. It indicates that during the neap tide in the dry season, the riverine sediment is mostly transported downstream along the western shoal. The differences between the channel and shoal are summarized in Table 4.

Table 4 The differences of sediment dynamics between the shoal and channel

Our results of sediment transport pattern with seaward flux at the shoal and bottom landward flux in the channel are consistent with the observations in the Delaware Bay (McSweeney et al. 2016) and the analytical model results by Wei et al. (2018). Combined with our findings in previous study (Chen et al. 2020) that finer sediments tend to accumulate at the west shoal while coarser sediments tend to accumulate in the channel, we can expect that finer sediment will continue to deposit in the lower part of the west shoal and coarser sediment to accumulate in the channel. This is of significant implication for the medium- to long-term morphological evolution (Gong et al. 2014).

6 Summary and conclusion

Sediment dynamics at the shoal and in the channel in a complex estuary are distinctly different. These differences can vary under varying external forcings, i.e. river discharge, tidal forcing, winds and/or waves. To reveal these variabilities, we conducted field measurements and data analysis in the HE, China, a mixed semi-diurnal micro-tidal estuary, in the wet and dry seasons, respectively.

We note that the SSC variations and mechanisms of different tidal components in a mixed semidiurnal tidal estuary are different from those in semi-diurnal tidal regimes (e.g. Weeks et al. 1993; Bass et al. 2002). In our study site, the M₁ signal is in general more significant than the M₂ and M₄ components, though the M₂ component can sometimes exceeds the M₁ component. The M₄ signal is the least important. The M₁ SSC and its transport generally represent the effect of tidal velocity asymmetry (de Swart and Zimmerman 2009), whereas the M₂ SSC and its transport flux denote the effect of both the tidal velocity asymmetry and tidal mixing asymmetry. The M₁ flux is mostly seaward in our study site, while the M₂ and M₄ fluxes are landward.

Sediment dynamics at the shoal and in the channel show different behaviors. When the tides are strong, the sediment transports at the shoal and in the channel are driven by both the advective flux and tidal pumping fluxes. With the tidal forcing decreasing, the advective flux becomes dominant in driving a seaward sediment transport. Stronger stratification occurs in the channel, especially during weak tides. Consequently, the bottom stress in the channel is stronger than at the shoal during strong tides, but becomes weaker than the shoal during weak tides. SSC are higher in the channel than at the shoal during strong tides while it becomes comparable or even lower than the shoal during weak tides. The tidal pumping fluxes of M₁ and M₂ components are significantly larger in the channel than at the shoal during strong tides. During weak tides, the M₂ flux at the shoal is seaward by tidal velocity asymmetry while in the channel it is landward at the bottom and seaward at the surface by tidal mixing asymmetry.

The individual contributions of barotropic and baroclinic tidal asymmetries in generating tidal pumping fluxes are not identified in this study. The contributions of different mechanisms in generating different components of SSC and the associated sediment transport flux are not distinguished as we could not define the erosion parameters, settling velocity and the constants in the horizontal SSC gradient. These unanswered questions warrant a future study by numerical modeling, like those conducted by Olabarrieta et al. (2018) and Zhou et al. (2020).

Appendix

1.1 A semi-analytical model

The one-dimensional depth-averaged equation describing sediment transport in the water column is given by:

$$\frac{\partial HC}{\partial t}+u\frac{\partial HC}{\partial x}={E}_r-{D}_p$$

Here, H denotes the water depth, C is the depth-averaged SSC, u is the depth-average horizontal velocity, E_r is the erosion rate, and D_r is the deposition rate.

For simplicity sake, τ_ce is assumed to be much smaller than τ_b and can be neglected (Cheng and Wilson 2008). This simplification does generate discrepancy between numerical and analytical results. Bottom shear stress, τ_b, is related to u with a drag coefficient, C_d, such that

$${E}_r=M{u}^2,M={E}_0\left(1-\varphi \right)\frac{\rho {C}_d}{\tau_{ce}}$$

Where M denotes the bed erodibility. According to the concept of continuous deposition (Sanford and Chang 1997), the deposition rate is applied as

$${D}_p={w}_s{C}_b,{C}_b= EC$$

Where C_b is the SSC near bed and E is a coefficient that adjusts C to C_b. The coefficient, E is always lager than 1 and is expected to increase with increasing settling velocity.

In the mixed semi-diurnal estuary, the depth-average horizontal velocity can be approximately expressed as:

$$u={u}_a\cos \omega t+{\varepsilon u}_a\cos \left(2\omega t+{\theta}_0\right)+{u}_b$$

Where u_a denotes the amplitude of diurnal component, mainly for the M₁ and K₁ tidal component in the HE, ε is the relative strength of the semi-diurnal tidal component compared to the diurnal tide, and θ₀ is the phase difference between diurnal tide and semi-diurnal tide, u_b denotes the residual current.

In tidally dominated estuaries, the horizontal gradient of sediment concentration follows the harmonic analysis result (Cheng and Wilson 2008), which is simply described as

$$\frac{\partial C}{\partial x}={N}_0+{N}_1\cos \left(\omega t+{\theta}_{11}\right)+{N}_2\cos \left(2\omega t+{\theta}_{12}\right)$$

Where, N₀ denotes the mean of the gradient, N₁ and N₂ are the amplitudes of the diurnal component and the semi-diurnal component, respectively, θ₁₁ is the phase difference between ∂C/∂x and the diurnal tidal current, and θ₁₂ is the phase difference between ∂C/∂x and the semi-diurnal tidal current.

The solution for the depth-averaged SSC is obtained as follows:

$${\displaystyle \begin{array}{l}C=\underset{A1}{\underbrace{\frac{M^{\prime }{u}_a^2}{2\sqrt{{E^{\prime}}^2{w}_s^2+4{\omega}^2}}}}\sin \left(2\omega t+{\theta}_2\right)\underset{A2}{\underbrace{-\frac{N_1{u}_a}{2\sqrt{{E^{\prime}}^2{w}_s^2+4{\omega}^2}}}}\sin \left(2\omega t+{\theta}_2+{\theta}_{11}\right)\\ {}\underset{A3}{\underbrace{-\frac{N_0{u}_a}{\sqrt{{E^{\prime}}^2{w}_s^2+{\omega}^2}}}}\sin \left(\omega t+{\theta}_1\right)\underset{A4}{\underbrace{+\frac{M^{\prime }{u}_a^2}{2{E}^{\prime }{w}_s}}}\underset{A5.}{\underbrace{-\frac{N_1{u}_a\cos {\theta}_{11}}{2{E}^{\prime }{w}_s}}}\\ {}\underset{A6}{\underbrace{-\frac{N_2{u}_a}{2\sqrt{{E^{\prime}}^2{w}_s^2+9{\omega}^2}}}}\sin \left(3\omega t+{\theta}_3+{\theta}_{12}\right)\ \underset{A7}{\underbrace{-\frac{N_2{u}_a}{2\sqrt{{E^{\prime}}^2{w}_s^2+{\omega}^2}}}}\mathit{\sin}\left(\omega t+{\theta}_1+{\theta}_{12}\right)\\ {}\ \underset{A8}{\underbrace{+\frac{\varepsilon^2{M}^{\prime }{u}_a^2}{2\sqrt{{E^{\prime}}^2{w}_s^2+16{\omega}^2}}}}\mathit{\sin}\left(4\omega t+{\theta}_4+2{\theta}_0\right)\underset{A9}{\underbrace{+\frac{\varepsilon^2{M}^{\prime }{u}_a^2}{2{E}^{\prime }{w}_s}}}\underset{A10}{\underbrace{-\frac{\varepsilon {N}_0{u}_a}{\sqrt{{E^{\prime}}^2{w}_s^2+4{\omega}^2}}}}\sin \left(2\omega t+{\theta}_2+{\theta}_0\right)\\ {}\ \underset{A11}{\underbrace{-\frac{\varepsilon {N}_1{u}_a}{2\sqrt{{E^{\prime}}^2{w}_s^2+9{\omega}^2}}}}\sin \left(3\omega t+{\theta}_3+{\theta}_0+{\theta}_{11}\right)\underset{A12}{\underbrace{-\frac{\varepsilon {N}_1{u}_a}{2\sqrt{{E^{\prime}}^2{w}_s^2+{\omega}^2}}}}\mathit{\sin}\left(\omega t+{\theta}_1+{\theta}_0-{\theta}_{11}\right)\ \\ {}\ \underset{A13}{\underbrace{-\frac{\varepsilon {N}_2{u}_a}{2\sqrt{{E^{\prime}}^2{w}_s^2+16{\omega}^2}}}}\sin \left(4\omega t+{\theta}_4+{\theta}_{12}+{\theta}_0\right)\underset{A14}{\underbrace{-\frac{\varepsilon {N}_2{u}_a\cos \left({\theta}_{12}-{\theta}_0\right)}{2{E}^{\prime }{w}_s}}}\\ {}\ \underset{A15}{\underbrace{+\frac{\varepsilon {M}^{\prime }{u}_a^2}{\sqrt{{E^{\prime}}^2{w}_s^2+{\omega}^2}}}}\mathit{\sin}\left(\omega t+{\theta}_1+{\theta}_0\right)\ \underset{A16}{\underbrace{+\frac{\varepsilon {M}^{\prime }{u}_a^2}{\sqrt{{E^{\prime}}^2{w}_s^2+9{\omega}^2}}}}\sin \left(3\omega t+{\theta}_3+{\theta}_0\right)\\ {}\ \underset{A17}{\underbrace{+\frac{2{M}^{\prime }{u}_a{u}_b}{\sqrt{{E^{\prime}}^2{w}_s^2+{\omega}^2}}}}\sin \left(\omega t+{\theta}_1\right)\underset{A18}{\underbrace{+\frac{2{\varepsilon M}^{\prime }{u}_a{u}_b}{\sqrt{{E^{\prime}}^2{w}_s^2+4{\omega}^2}}}}\sin \left(2\omega t+{\theta}_2+{\theta}_0\right)\underset{A19}{\underbrace{-\frac{N_0{u}_b}{E^{\prime }{w}_s}}}\ \\ {}\ \underset{A20}{\underbrace{-\frac{N_1{u}_b}{\sqrt{{E^{\prime}}^2{w}_s^2+{\omega}^2}}}}\sin \left(\omega t+{\theta}_1+{\theta}_{11}\right)\underset{A21}{\underbrace{-\frac{N_2{u}_b}{\sqrt{{E^{\prime}}^2{w}_s^2+4{\omega}^2}}}}\sin \left(2\omega t+{\theta}_2+{\theta}_{12}\right)\\ {}\ \underset{A22}{\underbrace{+\frac{M^{\prime }{u}_b^2}{E^{\prime }{w}_s}}}+D\exp \left(-{E}^{\prime }{w}_st\right)\\ {}\tan {\theta}_1=\frac{E^{\prime }{w}_s}{\omega },\tan {\theta}_2=\frac{E^{\prime }{w}_s}{2\omega },\tan {\theta}_3=\frac{E^{\prime }{w}_s}{3\omega },\tan {\theta}_4=\frac{E^{\prime }{w}_s}{4\omega },{M}^{\prime }=\frac{M}{H},{E}^{\prime }=\frac{E}{H}\end{array}}$$

The first seven terms (A 1 to A 7) in the solutions come from the M1 tide, while the next seven terms (A 8 to A 14) represent the effects of the M2 tide. The last four terms (A 19 to A 22) represent the effects of the residual flow. The rest of solutions (A 15 to A 18) are the result of the asymmetric bed shear stress due to the interactions among the M1, M2 tidal currents and the residual flow. The depth-integrated SSC includes local resuspension due to M1 tidal current (A1 and A4) and the M2 tide (A8 and A9) and the residual flow (A22), and the horizontal advection as a result of the M1 tidal advection of M1 component of ∂C/∂x (A2 and A5) and M2 component of ∂C/∂x (A6 and A7) and the mean part of ∂C/∂x (A3), and the horizontal advection as a result of the M2 tidal advection of M1 component of ∂C/∂x (A11 and A12) and M2 component of ∂C/∂x (A13 and A14) and the mean part of ∂C/∂x (A10), and the horizontal advection as a result of the residual current advection of M1 component of ∂C/∂x (A20) and M2 component of ∂C/∂x (A21) and the mean part of ∂C/∂x (A19).

From the solutions, it can be seen that the mean depth-integrated SSC comes from A4, A5, A9, A14, A19 and A22, which is the bottom resuspension due to the interactions between the residual flow and itself, and between tidal components and themselves, and the horizontal advection of the residual current, tidal components and the respective component of ∂C/∂x. The SSC at the M1 tidal frequency includes A3, A7, A12, A15, A17 and A20, indicating that the SSC can be generated by the bottom resuspension by the joint interaction of the residual flow, the M1 tidal current and the M2 current, and the advection of horizontal SSC gradient at different frequency by the respective current (spatial settling lag), including the M1 tidal advection M2 component of ∂C/∂x and the M2 tidal advection of M1 component of ∂C/∂x. Similarly, the depth-integrated SSC at the M2 tidal frequency is mainly composed of A1, A2, A10, A16, A18 and A21. The M4 SSC is from A8 (resuspension from M2 tidal current), and A13 (advection by M2 tidal current of M2 component of ∂C/∂x).