The erosion—deposition process and associated control mechanisms of the Nanliu River subaqueous delta, Southern China coast

Understanding the erosion–deposition process of sediments and the associated controlling mechanisms in subaqueous deltas is important for coastal environment protection. In this study, field observations and numerical simulations were performed for the Nanliu River subaqueous delta in Guangxi Province (Southern China) to investigate the sediment dynamic processes at the bottom boundary layer. The results show that the sediment resuspension mainly occurs during periods of spring tides and is mainly controlled by the wave action. When the seabed is free from erosion, suspended sediment settling caused by lateral transport is an important source of maintaining near bed suspended sediment concentration. It was also found that increasing the shear parameter could facilitate the formation of flocs, after which the small flocs tend to merge to large flocs. Finally, by performing a consistency analysis between the seabed erosion and deposition processes obtained from numerical simulation, and the changes of seabed level recorded by the equipment during the field observation, we determined that the local erosion coefficient was 5 × 10-5 kg/m2•s. The one-dimensional simulation is also capable of revealing the general trend at the seabed where it is first subjected to erosion and then deposition, as indicated during the field measurements.


Introduction
The subaqueous delta is a key region associated with land-sea interaction. As a river flows towards the sea, the majority of the substances carried by the river are distributed among delta, near-shore, and shelf areas; whereas only a small amount of the substances are transported to the outer shelf and deep-sea regions (Wright et al. 2001;Bianchi and Allison 2009;Gao and Collins 2014). Hence, several deposited systems are formed in different geomorphological environments within the coastal shelf area, and these sedimentary systems are the carriers of sedimentary records, which can be used for interpretation of land and marine environment variations and human activities (Gao and Collins 2014;Romans et al. 2016). The preservation of sedimentary records is mainly determined not only by sediment supply but also by sediment dynamic processes within the bottom boundary layer (BBL) (Gao and Collins 2014;Denommee et al. 2016). Therefore, an improved understanding of sediment dynamic processes becomes important. The erosion, transport, and sedimentation of sediments delivered by rivers are controlled by multiple external forces including surface runoff, tidal currents, and waves. The mutual interaction and associated underlying mechanisms from these external forces can be very complex. The BBL is the interface between the seabed and the overlying water where the interaction between these two regions is most intense. In particular, the erosion, transport, and sedimentation of sediments become very active in this interfacial area and the extent of scouring and sedimentation at the seabed is directly determined by the relative magnitude of the sediment erosion and deposition flux (Carniello et al. 2012). Understanding the mechanism that determines how the hydrodynamics is affected by the seafloor erosion and deposition in the subaqueous delta is important for both dredging and for controlling the transport of pollutants in the estuary and adjacent areas in the short term, as well as for dealing with shoreline erosion caused by changes in sea level over the long-term (Whitehouse et al. 2000;Winterwerp et al. 2012).
The erosion and deposition processes of sediment in the near bed are controlled by hydrodynamic processes, critical shear stress, flocculation and settling velocity, and erosion coefficient (Krone 1962;Partheniades 1965). However, these parameters are closely related to the composition of the sediment (Aberle et al. 2004;Ha and Maa 2009;Jacobs et al. 2011;Forsberg et al. 2018). Because there is a huge difference in the erosion and deposition characteristics of cohesive sediment and non-cohesive sediment (Mitchener and Torfs 1996), the erosion-deposition process of the seabed sediments in an estuary with a wide distribution of mud can be extremely complex (van Ledden 2003). It has been shown experimentally that mixing a small amount of mud with sand can induce a significant change to the anti-erosion characteristic of the sediment (Mitchener and Torfs 1996;Whitehouse et al. 2000;van Ledden 2003;Wu et al. 2018). The flocculation and settling velocity of cohesive sediment is much more complex because the settling velocity is closely related to multiple external factors including the hydrodynamic strength, turbulence characteristics, suspended sediment concentration (SSC), and sediment properties (Manning 2001;Wang et al. 2010;Manning and Schoellhamer 2013;Markussen and Andersen 2013).
In this study, we focus mainly on the wave-current interaction that affects cohesive sediment erosion and deposition processes. We present experimental data of hydrodynamic processes datasets, SSC, floc size and volume concentration, and the change in seabed elevation in the Nanliu River subaqueous delta. The aims of this study are to (i) understand the erosion-deposition processes of cohesive sediments in the delta under the effect of wave-current interaction in the Nanliu River subaqueous delta, (ii) reveal the flocculation and break up of flocs at the BBL, and (iii) explore variation in the erosion coefficient for cohesive sediments.

Study area
The Nanliu River is the largest river in Guangxi Province that flows into the sea. It has a total drainage area of 9700 km 2 and a total length of 287 km. Near Dangjiang Town in Hepu County, the Nanliu River divides into three main inlets called the Nangan River, Nanxi River, and Nandong River. These three inlets flow into the Beibu Gulf with a combined average annual river flow and sand transport of 51.3 × 10 8 m 3 and 118 × 10 4 t, respectively (State Oceanic Administration 1998), and then the subaqueous delta is formed under the interaction among sediment input, tidal current, wave action, and shelf current circulation (Jiang et al. 2008). The river basin is located in the low latitudes of southwestern Guangxi and faces the Beibu Gulf in the south. Its flood season is affected by the marine climate and the local climate is usually hot and rainy. The river basin is also one of the central rainstorm areas in Guangxi (Mo 1988;Huang et al. 2012). The tidal form number (F = (K 1 + O 1 )/(M 2 + S 2 )) is 3.45, which indicates that the tide near the Nanliu River estuary is a mixed tide that is dominated by diurnal tide (Song et al. 2014). The average and maximum tidal ranges are 2.46 and 5.36 m, respectively (State Oceanic Administration 1998). The statistical results also show that the maximum average wave height and the average wave height in the Nanliu River estuary are 1.36 and 0.30 m, respectively. The local waves do not change significantly over the years, and are mainly composed of wind waves followed by pure swells and mixed waves. The chance of occurrence of a main wave (N∼NE) and sub wave (SW∼WSW) are 36% and 19.2%, respectively (Chen 1988;Jiang et al. 2008). The concentration of suspended sediment in the Nanliu River Estuary is relatively low and declines from 16-24 to 2 mg/L with distance away from the estuary to the sea (Jiang et al. 2008).

Field observation
From 15 to 22 November 2015, continuous near bed observation was performed using a square frame in the Nanliu River subaqueous delta in the southwest of Guangxi (21°32.48′N, 108°57.96′E), as shown in Fig. 1. An acoustic Doppler velocimeter (ADV, manufactured by Nortek, Rud, Norway) was installed on the square frame. The sensor of the ADV was facing downwards and extended to a distance of 0.3 m from the seabed. The sampling interval, duration, and frequency were 3600 s, 1024 s, and 4 Hz, respectively. The current velocity and direction, and change in seabed elevation were recorded by ADV (0.15 mab, meter above bed). In addition, an electromagnetic current meter (ECM, manufactured by Valeport, Totnes, UK) was installed on the square frame. This device was equipped with velocity, temperature, salinity, and turbidity sensors for collecting the current velocity and direction, turbidity, temperature, and salinity data at 1.0 mab with a sampling interval, duration, and frequency of 600 s, 60 s, and 1 Hz, respectively. In addition, a LISST-100X (manufactured by Sequoia, Menlo Park, Calif., USA) was also installed on a square frame at 1.0 mab for collecting the volume concentration and particle size distribution of suspended particulate matter in the local region with a sampling interval, duration, and frequency of 1800 s, 300 s, and 1 Hz, respectively (Fig. 2). An additional square instrument frame installed with an acoustic Doppler current profiler (ADCP, 1200 kHz, manufactured by Teledyne RD Instruments, Poway, Calif., USA) was also placed in the water. The ADCP sensor was facing upwards to record the hydrodynamic parameters, such as wave height, wave period, velocity profile, and flow direction with bin size of 0.2 m. The distance between the sensor head of the ADCP and the seabed was 0.5 m. The sampling interval, duration, and frequency for recording the velocity profile were 600 s, 60 s, and 1 Hz, respectively, while the sampling interval and duration for recording waves were 3600 and 1200 s, respectively (Fig. 2). The field observations started from a spring tide and ended with a neap tide. The total duration of the observation was to be 168 h and to contain seven complete tidal cycles. However, only the data in the first 96 h were recorded due to malfunction of the LISST-100X.

Sample collection and analysis
During the observation period, surface sediment samples were collected from the upper 5 cm with a small-scale grab. After the samples were brought back to the laboratory, a 2.5 g sub-sample was taken from the well-mixed sample and mixed with 0.5% of a dispersion agent ((NaPO 3 ) 6 ). The mixture was subsequently soaked for 24 h before analyzing its particle size distribution using the Mastersizer 2000 laser particle-size analyzer (measuring range 0.01-2000 μm, manufactured by Malvern Panalytical Ltd., Malvern, UK). To obtain the SSC data in accordance with the instrument observation, the surface sediment samples were made into a turbid liquid in the laboratory, which provided a certain suspensionconcentration gradient sequence. By comparing the signal-to-noise ratio (SNR) recorded by the ADV and the turbidity recorded by the ECM, we successfully developed correlations between SSC, SNR, and turbidity (Figs. 3a and 3b). These correlations enable us to convert the SNR data recorded by the ADV and the turbidity data recorded by the ECM into time-series SSC data. Such method has been widely used in previous studies with satisfactory results (Salehi and Strom 2012;Wang and Ye 2013;Wei et al. 2013;Xiong et al. 2017).

Floc settling velocity
The effective density of the flocs can be calculated from the volume concentration of the flocs and the SSC (Fennessy et al. 1994)  where Δρ is the effective density of the floc (kg/m 3 ) and VC is the volume concentration of the floc (μL/L). The settling velocity of the flocs can be calculated using Stokes' equation (Sternberg et al. 1999): where ω f is the settling velocity (m/s), g is the gravity acceleration (m/s 2 ) taken as 9.81 m/s 2 , d f,m is the mean particle size (m) of the floc, and υ is the kinematic viscosity of seawater (m 2 /s), which can be calculated based on the observed salinity, temperature, and pressure (Sharqawy et al. 2010;Nayar et al. 2016). In this study, the calculated υ was 0.96 × 10 −6 m 2 /s based on the method recommended by Sharqawy et al. (2010) using the in situ measured data.
In this study, the majority of floc were small (<100 μm) and settling within the Stokes region (i.e., Reynolds numbers <1). However, the Oseen correction was also applied to Stokes' law for the remaining flocs with a size >100 μm (Manning and Schoellhamer 2013). Generally, the larger suspended particles exist in highly porous flocs in an estuary. The porous flocs under higher Reynolds numbers endure less boundary layer separation and a smaller wake than non-porous flocs, due to the flow through the floc's interior (Lee 1996;Xia et al. 2004). In similar estuaries, Stokes' law has been widely used to estimate the floc settling velocity or effective density (Xia et al. 2004;Manning and Schoellhamer 2013;). Giardino et al. (2017) proposed a method for calculating the critical shear stress of sandmud mixture sediment. Such an equation was formulated based on the Shields curve and corrected the cohesive effect caused by mud ( van Rijn 2007)  in which τ cr is the critical shear stress (N/m 2 ); γ 1 and γ 2 are the lateral and longitudinal slope factors of the seabed, respectively (because the seabed was almost level, we have γ 1 = γ 2 = 1 (Giardino et al. 2017)); p m is the content of the mud (grain size <63 μm) in the sand-mud mixtures; d d is the threshold particle size separating sand and mud (taken as 63 × 10 −6 m); and d s,50 is the median particle size (m) of the mixture sediment. Here, τ cr,s is the critical shear stress without considering the cohesive effect. τ cr,s and can be calculated as follows (Soulsby 1997):

Critical shear stress for sediment
where θ cr is the critical Shields number for the initial motion for the sediment, ρ s is the particle density of sediment (taken to be 2650 kg/m 3 ), ρ sw is the density of sea water (taken to be 1020 kg/m 3 ), and D * is the dimensionless grain size.

Bed shear stress
In the turbulent logarithmic layer, the ratio between turbulent kinetic energy (TKE) and the bed shear stress induced by the tidal current τ c should be a constant (Soulsby and Dyer 1981;Stapleton and Huntley 1995) given by where c 1 is the proportionality constant whose value varies slightly in different studies (0.19-0.21) (Soulsby and Dyer 1981;Stapleton and Huntley 1995;Kim et al. 2000). In this study c 1 = 0.19 (Stapleton and Huntley 1995). The fluctuating velocities of horizontal and vertical directions (i.e., u′, v′, and w′) can be derived from the high frequency datasets recorded by the ADV.
Based on the linear wave theory, the shear stress induced by the wave τ w can be expressed as (Soulsby 1997) where f w is the friction coefficient of the wave, which can be calculated using the method recommended by Madsen (1995), and U w is the peak orbital velocity of the wave, which can be calculated through the formula recommended by Soulsby (1997). The bed total shear stress τ cw comprises both the shear stress induced by the tidal current and the shear stress induced by the wave, which can be calculated as (Grant and Madsen 1979) where φ cw represents the angle between the direction of the tidal current and the direction of wave propagation. In addition, we converted τ cw into the shear parameter G (s −1 ) to evaluate the impact of shear stress on the flocculation for flocs. G is defined as the rootmean-square of the gradient in the turbulent velocity fluctuations, which can be expressed as (Soulsby et al. 2013 where u * is the friction flow velocity, κ = 0.4 is the von Karman's constant, and z is the distance from the measuring point to the seabed (0.15 mab).
3.6. Erosion-deposition flux 3.6.1. Erosion flux In general, the bed erosion flux (F e ) associated with cohesive sand-mud mixtures sediment can be calculated using the following formula (Partheniades 1965): where M e is the erosion coefficient (kg/m 2 ·s). Based on the previous research results and ADV observations of change in bed elevation, the erosion coefficient M e is determined when the simulated erosion-deposition flux is in accordance with the change in the actual bed elevation. Then M e is input into eq. (11) to calculate the erosion flux.

Deposition flux
When the SSC is less than the gelling concentration c gel (defined as the concentration at the transition from hindered settling to consolidation, about 30-180 kg/m 2 ), the deposition of sand and mud can be treated as two independent processes (van Ledden 2003). Therefore, the total deposition flux within the BBL F d should be calculated as the sum of mud flux F d,c and sand F d,nc as In this equation, because the ADV measuring point is very close to the seabed, it is reasonable to assume that the composition of the suspended sediments near the seabed is very similar to the composition of the seabed surface sediments, namely, p c ≈ p m . F d,c and F d,nc can be calculated as follows (Krone 1962): where ω s is the settling velocity calculated using Stokes' equation with d s,50 .

The change in the bed elevation
The change in the seabed level is controlled directly by the net flux in the horizontal bedload transport and the vertical erosion-deposition, and at each time step the variation in bed elevation (∂z b / ∂t) is evaluated as (van Ledden 2003) where ε is the porosity of the bed (ε ≈ 0.4), and F net is the net flux of erosion and deposition given by F net = F d + F e . Past studies have demonstrated that there is almost no bed-load transport in cohesive sand-mud mixture sediment (van Ledden 2003). Combining this with the characteristics of the surface sediments below the measuring point, the bed load transport is taken as 0.

Hydrodynamic characteristics
During the observation, the maximum water depth, minimum water depth, spring tidal range, and neap tidal range at the observation site were 6.91, 3.01, 3.77, and 2.60 m, respectively. The significant wave height during the observation period varied from 0.05 to 0.74 m with an average value of 0.32 m. The variations of the significant wave height are related to the water depth (i.e., the wave height increases with increasing water depth during the flood tides, and decreases with the reducing water depth during ebb tides; Fig. 4a). The wave period varied from 1.9 to 7.3 s, with an average value of 4.4 s. The wave is generally directed towards the south, but there was a large fluctuation after 21 November (1200) (Fig. 4b).
The current speed decreased from the surface to the bottom along the water column, and the maximum velocity occurred at upper layer during the middle of the flood and ebb tide stages, which could reach 1.0 m/s, whereas the minimum flow velocity generally Time series of the near bed water salinity and temperature at 1.0 mab, as measured by ECM were shown in Fig. 4e. The tidal variability is clearly exhibited in the salinity signal, but not evidently in the water temperature signal. The near bed water salinity and temperature at 1.0 mab were 24.63-30.34 and 23.73-26.81°C, with average values of 29.01 ± 1.18 and 25.81 ± 0.80°C, respectively.

Bed shear stress and SSC
During observation, τ c varied from 0 to 1.27 N/m 2 with an average value of 0.21 N/m 2 , whereas τ w ranged from 0 to 1.30 N/m 2 with an average value of 0.42 N/m 2 . The τ cw ranged from 0.03 to 1.80 N/m 2 with an average value of 0.59 N/m 2 (Fig. 5a). The corresponding G varied from 0.45 to 27.72 s −1 with an average value of 11.47 s −1 (Fig. 5b). The SSC at 1.0 mab varied from 4.18 to 69.42 mg/L with an average value of 23.24 mg/L, while that measured at 0.15 mab varied from 10.28 to 44.08 mg/L with an average value of 23.08 mg/L (Fig. 5c). The near bed SSC increased with increasing τ cw or G, and vice versa (Figs. 5c and 5d).

Floc characteristics
The floc volume concentration varied from 10.66 to 800.00 μL/L with an average of 133.59 μL/L (Fig. 6a). The mean floc size ranged from 55.33 to 312.90 μm with an average of 105.97 μm. If the small flocs and large flocs are differentiated with a critical boundary value of 160 μm, then the mean floc sizes for small flocs and large flocs were 32.75 and 296.80 μm, respectively (Fig. 6b). The average contribution of small flocs to total volume concentration is around 81%, which suggested that the main floc component at 1.0 mab was dominated by small flocs (Fig. 6c). The calculated settling velocity of the flocs ranged from 0.38 to 6.20 mm/s with an average value of 2.24 mm/s (Fig. 6d).

Critical shear stress for surface sediment
Multi-modality was observed in the grain size distribution of surface sediment at the observation site. The ranges and median grain sizes were 0.3-917 and 77 μm, respectively. The contents of sand and mud were 53% and 47% (35% silt + 12% clay), respectively (Fig. 7). Neglecting the cohesive effect induced by the sand and mud interaction, the critical shear stress was 0.11 N/m 2 . However, the critical shear stress was increased to 0.35 N/m 2 after considering the cohesive effect induced by mud.

Erosion-deposition flux
Based on the calculation results from Partheniades-Krone formula, the maximum and average erosion fluxes at the bottom boundary during the observation were 0.92 and 0.18 kg/m 2 ·h, respectively. The maximum, minimum, and average deposition fluxes were 0.43, 0.10, and 0.23 kg/m 2 ·h, respectively. The erosion flux within a single tide cycle during the spring tides could reach 8.43 kg/m 2 , while the erosion flux in a single tide cycle in the neap tide was only 1.75 kg/m 2 . The deposition flux during spring tides was inherently greater than neap tide period. The cumulative sediment flux in a single tidal cycle during spring tide was 7.05 kg/m 2 , while the neap tide stage was 4.14 kg/m 2 (Fig. 8a).
The change in the seabed scouring and sedimentation process was analyzed based on the time sequence change of seabed elevation as measured by the ADV (Andersen et al. 2007;Wang and Ye 2013). During the observation period, however, the seabed elevation recorded by the ADV did not seem to change in a constant manner. Such a trend in the seabed scouring and sedimentation could be better presented by smoothing the seabed elevation data with a moving average. The observation results showed that the seabed was under a deposition trend between 1200 h 15 and 16 November. The seabed was eroded slightly from 1200 h 16 and 18 November. The sediments continued to deposit on the seabed from 1200 h 18-21 November. Starting from 2400 h on 20 November until the end of observation, the seabed maintained a relatively stable elevation. During the observation, the maximum siltation depth and maximum erosion depth were around 6.8 and 1.8 mm, respectively. In general, the seabed was being subjected to siltation and the net sediment thickness of the seabed was about 3.7 mm during the observation (Fig. 8b).

Response of the erosion-deposition flux to the hydrodynamics
Generally speaking, in shallow water the BBL can fill the whole water depth. In this study, we calculated the BBL depth using the formula recommended by Dyer (1986), and the calculated result showed that the theoretical depth of the BBL near the observation site was varied from 1.35 m to over 100 m during the observation. It is generally considered that the ADV sampling elevation <40 cm distant from the bed is suitable for estimating the bed shear stress by TKE method (Kim et al. 2000;Andersen et al. 2007). In this study, the height of ADV measuring point is 15 cm, which is much larger than the thickness of wave boundary layer or wave-current boundary layer estimated by Fredse (1984) (<1 cm), therefore, wave interference could also be avoided, and the two near bed observation layers are within the BBL in this study, and the related boundary layer parameters computed based on the BBL theory in this study are suitable.
Generally, the seabed is affected by waves and tidal currents through shear stress, which causes erosion or deposition at the seabed. The seabed is eroded if the bed shear stress exceeds the critical shear stress for erosion. The erosion rate determines how much erosion occurs and how much the concentration of suspended sediment increases in the water column within a certain interval (Shi 2013). In contrast, the concentration of suspended sediment in the water column decreases when the bed shear stress is less than the critical shear stress for deposition. This causes the sediment to deposit on the seabed. In this study, the change in the scouring and siltation at the seabed recorded by the ADV matched closely the erosion-deposition flux results obtained by the Partheniades-Krone model (Fig. 8). The variation in the shear stress was also found to agree well with the change in the concentration of suspended sediment (Figs. 5a, 5c, and 5d). The correlation analysis showed that there was a good positive relationship between bottom shear stress induced by waves and SSC at 0.15 mab, that is, the stronger the wave action, the higher SSC in the near bed; there is no obvious relationship between bottom shear stress induced by tidal current and SSC at 0.15 mab (Fig. 9). These findings suggest that the seabed erosion-deposition process at the observation site was mainly controlled by the wave action, and the contribution of tidal current to sediment erosion-deposition is relatively weak during the observation. Waves play a very important role in the re-suspension of surface sediments from the bed in coastal zones (Wright et al. 2001;Webster and Ford 2010;Green 2011). This is particularly important in areas with strong waves where the contribution from waves to the re-suspension and transport of sediments is much more significant than that from the tide (Webster and Ford 2010;Green 2011). In shallow water areas, the SSC in near the bed is directly related to the wave height (Anderson 1972). Studies have shown that the effect of waves must be considered when the water depth is 2-12 m and the waves can act directly on the seabed to cause sediment re-suspension (You 2005). During the observation in this study, the maximum water depth was only 6.91 m. The average bed shear stresses induced by the waves and tidal currents were 0.42 and 0.21 N/m 2 , respectively (Fig. 5a). The waveinduced shear stress was two times current-induced shear stress, which demonstrates that the wave is an important factor affecting the re-suspension of sediment in the Nanliu River subaqueous delta.
For the entire deposition system, the erosion and deposition of the sediments is always balanced. This means that the erosion in a certain region will cause the deposition of sediments in another region (Zhu et al. 2017). The key in maintaining such balance is realized by the sediment transport function of the tidal current. During the observation, τ w kept decreasing from spring to neap tides while τ c was always maintained at a relatively low and stable level. When τ cw was less than τ cr (e.g., from 1200 h 21 to 22 November), the seabed was free from erosion (Fig. 5a). However, the SSC of the bed overlying water still remained at around 15 mg/L due to the suspended sediment transported from other eroded areas (Figs. 5c and 5d).
Current progressive vector diagrams were obtained from ADCP in this study to track the water movement at five different layers. The net displacements of water, gradually increasing from lower layer to upper layer, were 29.3, 25.6, 32.4, 75.1, and 101.8 km during the observation and the direction of net displacement was counterclockwise, from northeast to northwest (Fig. 10). As shown in Fig. 10, the upper water was also affected by the river discharge, particularly during the neap tide. The net displacement of water in different layers shows that the upper layers (>2.7 mab) at the observation site may be more influenced by the fluvial (northeastern), which results in the direction of water net transport being much different from that at the lower layers (<2.2 mab) (Fig. 10). This means that suspended sediment in the BBL may be maintained by sediment deposition in the upper water body, when the bed was free from erosion. The change of salinity could also indicate the influence of rivers. During the observation, the time-series variation of salinity at 1.0 mab was not evident, which indicated that the influence of fluvial was weak in near bed.
By comparing the SSC of 0.15 and 1.0 mab layers, we could quantitatively determine the contribution of lateral transport at different periods. If the SSC at 1.0 mab was greater than that at 0.15 mab, the difference could not be caused by re-suspension, but by deposition or lateral transport (Figs. 5c and 5d). From 1200 h to 2400 h 17 November, the average of SSC at 1.0 mab was 10.75 mg/L greater than that at 0.15 mab, and lateral transport is the most obvious cause. At the same stage, the wave direction changed from 200°to 250°, so we speculated that the changes of wave direction may lead to enhance lateral transport, although this requires more evidence.

Mechanisms of flocculation and break-up of flocs
The cohesive sediments in the BBL will flocculate during deposition, which is very different behavior from the deposition process for non-cohesive sediments (Whitehouse et al. 2000). When individual particles coagulate to form flocs, the floc size increases and the effective density is reduced. However, the settling velocity was increased significantly within the Stokes region (Manning and Dyer 1999). The formation of flocs from individual particles involves two main processes: collision and flocculation. Any factors that may influence these two processes, such as sediment characteristics and environmental dynamic conditions, can potentially affect the formation of flocs (Whitehouse et al. 2000;Manning 2001). In this study, the shear parameter G, SSC, water salinity, temperature, and other factors that may affect the flocculation process were measured in accordance with the Fig. 10. Progressive vectors of the measured instantaneous flow at 1.2, 1.7, 2.2, 2.7, and 3.2 mab by the ADCP during the observation. evolution of flocs observed in situ. The variation in these parameters can be used to analyze the mechanisms of floc formation and break-up. Based on the measurements of shear parameter, SSC, water salinity, temperature, and average floc size, it was found that the shear parameter and water salinity are highly related to the average floc size. The corresponding correlation coefficients were found to be 0.374 and −0.353 (significant at 99% confidence level). On the other hand, no significant correlations were found between the SSC, water temperature, and the average floc size (Table 1).
The water temperature can affect the collision frequency of flocs by influencing the magnitude of Brownian motion. In the estuary environment, the Brownian motion only affects particles with a size between 0.5 and 2 μm (van Leussen 1994). Particles with size smaller than 2 μm were found to account for 6% in the seabed sediments and 3% in the suspended sediment at the observation site. Such difference was found to be quite small. Furthermore, the flocs formed through Brownian motion are very fragile and may easily break up during the deposition process or under the influence of shear stress (Manning 2001). Results from related analysis have also shown a poor correlation between the change in water temperature and the floc size. This indicates that the water temperature has a small impact on the growth of the flocs. Under normal conditions, "salt flocculation" is an important factor affecting the formation of flocs due to the large change in salinity in the estuary area. As the flocs are transported into the estuary with dilute river waters, an increase in the salinity reduces the zeta potential. This causes the flocs to destabilize and condense (Manning 2001;Webster and Ford 2010). However, "salt flocculation" can only make positive contributions within a certain salinity range. For example, Mietta et al. (2009) showed experimentally that increasing salinity would only help formation of flocs when the salinity is <15. Therefore, the "salt flocculation" behavior is not significant for salinity exceeding a certain range, where high salinity may even destroy the flocs formed (Manning and Schoellhamer 2013). In this study, the salinity was always more than 24. Thus, the effect of "salt flocculation" behavior on floc formation was not evident (Figs. 11a and 11c).
When the shear stress is stable, the floc size of the flocs in the water column shows a trend of periodic variation in the time domain. Specifically, the particle size first grows rapidly and then increases slowly until the formation and break-up rate of the flocs reaches a balance. At this stage, the particle size distribution of the flocs in water became stable, which can be considered a quasi-static stage (Spicer and Pratsinis 1996;Colomer et al. 2005). Further investigation revealed the existence of a shear parameter threshold value G opt during the early stage of floc formation. When G < G opt , the collision frequency of the particles increases with increasing turbulence, which promotes the formation of flocs. When G > G opt , however, further increase in the turbulence will eventually lead to the break-up of the flocs (Eisma 1986;Manning and Dyer 1999;Winterwerp 2002). However, different scientists have obtained very different values of G opt ranging from 15 to 30 s −1 . For example, Manning and Dyer (1999) performed experimental measurements where they found G opt = 20 s −1 , Zu et al. (2018) combined experimental measurements and field sampling and found that G opt = 19.94 s −1 . In this study, the average floc size kept increasing with further increase of G, and no significant turning point for G opt was identified in the results (Fig. 11b). By performing correlation analysis between G and volume concentrations of 32 classes measured by LISST-100X, it was found that G is negatively correlated with most size classes of flocs, of which the floc sizes range between 4 and 130 μm, and is positively correlated with the flocs with whole floc sizes >200 μm. For flocs with a particle size smaller than 4 μm or ranging between 130 and 200 μm, no significant correlations were found between the shear parameter and the floc volume concentrations (Figs. 11b and 11e). These results also demonstrated that increase of G provided more chances for collision between small particles (4-130 μm), which aggregate to form larger flocs (>200 μm). Such phenomena reduce the number of microflocs and increase the number of macroflocs in the BBL. The average floc size kept increasing with the shear parameter, which indicates that G in this study may not reach the critical value. When the SSC is relatively low, the collision frequency of the particles can be increased by increasing the SSC. This can lead to a higher settling velocity (Eisma and Li 1993). However, once the concentration of the suspended sediments reaches a certain level, a hindered setting phenomenon will take over in which further increase in the concentration reduces the setting velocity (Whitehouse et al. 2000;Manning 2001;Winterwerp 2002). It is generally considered that such hindered setting phenomena occur when the SSC reaches 2-10 g/L (Puls and Kuehl 1986;Whitehouse et al. 2000). In this study, the SSC near the seabed was much smaller than the concentration required initiating suspension hindrance. Therefore, such hindrance effect can be neglected in this study. The correlation analysis between the concentration of suspended sediments (1.0 mab) and volume concentrations Fig. 11. Relationship between the floc size and water salinity (a), shear parameter (b), SSC (c), the correlation coefficient between each size class of flocs with water salinity (d), shear parameter (e), and SSC (f). of 32 classes measured by LISST-100X revealed a positive correlation between the concentration and floc size ranging between 20 and 60 μm. A negative correlation was found between the concentration and the flocs with particles size ranges 120-240 μm (Figs. 11c and 11f). Because a floc size of 20-60 μm is less than the mean grain size of the surface sediment on the seabed (77 μm), the positive correlation discovered in this study cannot be attributed to the transformation from other flocs with different particle sizes. Instead, the positive correlation is more likely to be caused directly by the re-suspension of sediments. Because there is no significant correlation between the concentration and more than half of the floc sizes, the above relationships are not sufficient to support the claim that the concentration of suspended sediment during the observation affected the conversion of large and small flocs. When the SSC is <300 mg/L, there is no significant relationship between the floc size or setting velocity and the SSC (Krone 1962;Xia et al. 2004;Manning and Schoellhamer 2013;Guo et al. 2017). The floc size or setting velocity can even become smaller with increasing SSC (Burban et al. 1989). During the observation, the SSC was smaller than 70 mg/L (Fig. 5c). Such low concentration resulted in a poor correlation between the SSC and floc size.
Apart from the four factors mentioned above, other parameters, such as the content of organic material in the flocs can also contribute to the formation of these flocs (Manning and Schoellhamer 2013). While the results indicate that increase in the shear parameter can promote the formation of flocs in the boundary layer at the Nanliu River Estuary, whether such a phenomenon can affect the deposition flux is still affected by other factors, including the salt flocculation mechanism and the organic content of materials.

Determination of the erosion coefficient of cohesive sediments
The erosion coefficient M e of cohesive sediment is affected by multiple factors including the density, porosity, consolidation, and biological processes of the seabed. Therefore, the erosion coefficient varies both spatially and temporally (Amos and Mosher 1985;Amos et al. 1992;Winterwerp et al. 2012). The erosion coefficient is often between 5 × 10 −5 and 3 × 10 −3 kg/m 2 ·s and can be categorized in high and low levels depending on the mud content in the sediments. When the sediment content >20%, the erosion coefficient M e will be reduced substantially (by 6-10 times) (Houwing 1999;Andersen et al. 2007). In general, the erosion coefficient M e can be treated as an empirical constant (Winterwerp et al. 2012). If the bed shear stress exceeds the critical shear stress for erosion and can be maintained constant over a period, the approximate range of the erosion coefficient M e can then be determined using the Partheniades equation in combination with the variation in bed elevation measured by the ADV (Andersen et al. 2007). However, in real measurements, the variation in bed elevation measured by the ADV, despite being in close agreement with the calculation results obtained from simulation over a long time scale, can be affected by a number of factors and deviate from the calculation results over a short interval. Therefore, it is difficult to determine the value of M e within a short measurement time using this method. Considering this, this study employs an index of agreement I for assessing the consistency of the datasets obtained from ADV measurement and theoretical calculation. The index of agreement is usually used to evaluate quantitatively the level of consistency of the same variable obtained through two different approaches (Willmott 1981). Such coefficient has been widely used in numerical simulations (Blumberg and Goodrich 1990;Zhu et al. 2017).
where x and y are the two datasets being compared; 0 < I ≤ 1. The larger the value of I is the better the consistency between the x and y datasets. With the other parameters fixed in Partheniades-Krone model, the most trustworthy and reasonable value of M e is obtained when the ADV measurements and simulation results show high consistency in the bed elevation. The index of agreement I between the simulated results and actual ADV measurements are shown in Fig. 12. It can be seen that the index of agreement I first increases and then decreases with increasing M e . The maximum value of the index of agreement I is found to be 0.81, with M e = 5 × 10 −5 kg/m 2 ·s. Andersen et al. (2007) performed measurements using the ADV on a tidal flat with high mud content (>95%) and obtained M e = 8 × 10 −5 and 5 × 10 −5 kg/m 2 ·s in January and November, respectively. Houwing (1999) carried out in situ observation on intertidal mudflat with a mud content of 35% (the mud was defined as grain size smaller than 50 μm in the original thesis) and obtained an erosion coefficient M e = 5.5 × 10 −5 kg/m 2 ·s using an in situ erosion flume. The composition of the sediment in his measurement was very similar to the sediment measured in this study. Therefore, the erosion coefficient determined in this study is considered trustworthy. These calculation results further suggest that it is feasible to obtain the erosion coefficient by performing numerical simulation over a region that shares a similar composition of sediment to the research target (Houwing 1999).
Comparing the simulation result and ADV measurements of the bed elevation (Fig. 8b), it was found that while the Partheniades-Krone model can predict the general trend of erosion and deposition behavior of the seabed during the observation period, the erosion strength calculated from the model is greater than the in situ measurements by the ADV during the erosion stage (from 15 to 18 November). Moreover, the simulation model did not reveal a quasi-steady stage shown in the ADV measurement (from 21 November to the end of the observation). Instead, the seabed was always under a deposition process during the whole period in the simulation. Such phenomena may be attributed to the fluctuation of the erosion coefficient M e or the critical shear stress τ cr at different stages. Neither of these values are constant in a natural environment (Andersen et al. 2007).

Conclusion
In the boundary layer of Nanliu River subaqueous delta, the exchange of materials between the seabed and bottom water is controlled by the bed shear stress, which further affects the erosion-deposition process. Wave action plays a major role in the re-suspension of the sediment, while the current also plays an important role. Variations of salinity indicate that the bottom water was weakly affected by the fluvial directly during the observation, while the water in the upper layer was obviously affected by the river revealed by the net displacement of water in different layers. When the seabed was free from erosion, the lateral transport and deposition from the upper layer may make an important contribution to maintain the SSC in the bottom layer. According to the estimation from the model, the maximum erosion flux, average erosion flux, maximum deposition flux, and average deposition flux during the observation were 0.92, 0.18, 0.43, and 0.23 kg/m 2 ·h, respectively.
A negative correlation was found between the salinity and average floc size, while a positive correlation was found between the shear parameter and average floc size. The effect of "salt flocculation" on floc formation was not evident in this study. Increase of shear parameter can facilitate the formation of flocs and promote the conversion of small flocs into large flocs. During the observation, the SSC in the water was very low (<70 mg/L) and has negligible impact on the formation of the flocs.
A consistency analysis was performed between the simulation results and ADV measurements of the scour and siltation on the seabed, which indicate that the erosion coefficient M e = 5 × 10 −5 kg/m 2 ·s. The change in the seabed elevation calculated from the Partheniades-Krone model can provide a general description of the erosion and deposition process at the seabed, which yields results with the same order of magnitude compared to the field measurements obtained from the ADV. The high local deviations between the simulation results and the ADV measurements (especially the erosion stage during spring tides) may be caused by a non-constant erosion coefficient and critical shear stress, which vary spatially and temporally.