Delft3D-FLOW (version 4.00.01) is a numerical model based on the finite difference method constructed to simulate three-dimensional (3D) unsteady incompressible flow in different water masses. In the Delft3D model, the extended ADI method and a central difference are applied as the horizontal and vertical convective terms, respectively (Dastgheib et al., 2008; Deltares, 2014). This model has been applied to calculate hydrodynamics, sediment erosion, and deposition in coastal areas, estuaries, lagoons, rivers, and lakes (Lesser et al., 2004; Volp et al., 2016). The governing equation includes a continuity equation and momentum equations, and the specific expressions are: ∂ ζ ∂ t + 1 G ξ ξ G η η ∂ d + ζ U G η η ∂ ξ + 1 G ξ ξ G η η ∂ d + ζ V G ξ ξ ∂ η = d + ζ Q (1) ∂ u ∂ t + u G ξ ξ ∂ u ∂ ξ + v G η η ∂ u ∂ η + w d + ζ ∂ u ∂ σ − v 2 G ξ ξ G η η ∂ G η η ∂ ξ + u v G ξ ξ G η η ∂ G ξ ξ ∂ η − f v = − 1 ρ 0 G ξ ξ P ξ + F ξ + 1 d + ζ 2 ∂ ∂ σ υ ν ∂ u ∂ σ + M ξ + F ξ z (2) ∂ v ∂ t + u G ξ ξ ∂ v ∂ ξ + v G η η ∂ v ∂ η + w d + ζ ∂ v ∂ σ − u 2 G ξ ξ G η η ∂ G ξ ξ ∂ η + u v G ξ ξ G η η ∂ G η η ∂ ξ + f u = − 1 ρ 0 G η η P η + F η + 1 d + ζ 2 ∂ ∂ σ υ ν ∂ v ∂ σ + M η + F η z (3)

The vertical velocity in σ coordinates is:

w = ϖ + 1 G ξ ξ G η η u G η η σ ∂ H ∂ ξ + ∂ ζ ∂ ξ + v G ξ ξ σ ∂ H ∂ η + ∂ ζ ∂ η + σ ∂ H ∂ t + ∂ ζ ∂ t (4) where ζ is the water level above the reference surface (z = 0); d is the water depth below the reference surface (z = 0); H is the total water depth; U and V are the average depth velocity; Q represents the source or sink per unit area; u, v, and w are the velocities in three directions; f is the Coriolis force; υ _ν is the vertical eddy viscosity coefficient; ρ ₀ is the water density; G _ξξ , P _ξ , F _ξ , M _ξ , and F _ξ (z) are the coordinate conversion coefficients, the pressure gradient, the unbalance of horizontal Reynolds stresses, source or sink of momentum, and the drag forces produced by the vegetation in the directions of ξ; and G _ƞƞ , P _ƞ , F _ƞ , M _ƞ , and F _ƞ (z) are the coordinate conversion coefficients, the pressure gradient, the unbalance of horizontal Reynolds stresses, source or sink of momentum, and the drag forces produced by the vegetation in the directions of ƞ.

The influence of the vegetation on drag leads to the momentum equations containing an extra term for friction force, F(z) (N/m⁻³), caused by the cylindrical plant stalks. The drag force of vegetation is expressed as: F ξ z = 1 2 ρ 0 C d ϕ z n z u z u z , F η z = 1 2 ρ 0 C d ϕ z n z v z v z (5) where ϕ(z) is the stem width as a function of z; C _d is the drag coefficient of the vegetation; n(z) is the number of plants per unit area; u(z) is the horizontal velocity profile; and v(z) is the vertical flow velocity profile.

Where the influence of the vegetation on turbulence means that the k-ε equations and transport equations must be solved for both turbulent kinetic energy k and for energy dissipation ε.

The sediment transport module computes suspended sediment concentrations and sedimentation rates for each time step and each grid cell and, based on the three dimensional advection-diffusion equation for suspended sediment, can be expressed as (Deltares, 2014): ∂ C ∂ t + ∂ u C ∂ x + ∂ v C ∂ y + ∂ w − w s C ∂ z = ∂ ∂ x ε s , x ∂ C ∂ x + ∂ ∂ y ε s , y ∂ C ∂ y + ∂ ∂ z ε s , z ∂ C ∂ z + C e q − C T s (6) where C is suspended sediment concentration; ε _s,x , ε _s,y , and ε _s,z are sediment eddy diffusivity in the x, y, and z directions, respectively; w _s is the settling velocity of suspended sediment; C _eq is the local equilibrium depth-averaged suspended sediment concentration; and T _s is an adaptation time scale.

In this paper, two examples from the literature (Plew, 2011; Zhao et al., 2017) were selected to verify the model and to further analyze the change in the main stream velocity of water flow through floating vegetation groups. In case A, the length of the flume was 20 m, the width was 0.6 m, and the height was 0.5 m. In case B, the flume was 6 m long, the width was 0.6 m, and the height was 0.5 m. The flume bottom slope was 0.1% in both cases and the vegetation was arranged in the form of floating vegetation. In the model, the grid resolutions in three directions (horizontal, lengthwise, and vertical) were 5 cm, 5 cm, and 0.9 cm, respectively. The number of grids in case A were 400 × 12 × 40, and the total number of grids in case B were 120 × 12 × 40. A discharge was set as the inlet boundary condition, and the water depth was set as the outlet boundary in these case studies. There were four cases (A, B2, B12, and B14), where the parameters in these case studies were as follows (Plew, 2011; Zhao et al., 2017), the flume inlet flow rate Q were 26.5 L/s, 7.1 L/s, 10.5 L/s and 10.1 L/s, respectively, water depth h are 36 cm, 20 cm, 20 cm and 20 cm, respectively, the clearance height between the vegetation and flume bottom hg were 25 cm, 2.5 cm, 10 cm and 10 cm, the ratio of clearance height to water depth hg/h were 0.694, 0.125, 0.5, and 0.5, respectively, the drag coefficient of vegetation C _d were 1.208, 0.780, 1.010, and 0.850, respectively, the projected area per unit volume of floating vegetation a are 3.2 m⁻¹, 1.272 m⁻¹, 1.908 m⁻¹ and 0.850 m⁻¹, respectively.

In order to clearly represent the vertical distribution of horizontal flow velocities in the flume, the calculation results are dimensionless. The horizontal axis represents the dimensionless velocity, and the vertical axis is dimensionless as the ratio of water depths Z and H. The specific results are shown in Figure 1. The simulated results were consistent with the experimental data, demonstrating that this model provides good accuracy in flow velocity through vegetated regions using the appropriate drag coefficient. Due to the resistance of vegetation, the main stream velocity is smaller in the vegetated area, while it is larger under the suspended canopy in the flume, therefore, there is a large velocity gradient in the main stream velocities across the transition from the canopy to the depth under the vegetation. In general, the simulated results indicate that the Delft3D-flow module can precisely reflect the movement of water flow in vegetated regions.

The bathymetry of the LRE is complex and contains a series of coastal shoals, creek channels, mudflats, islands, and large wetland areas (Figure 2). The wetlands of the Liao River Delta are salt marsh wetlands populated by the common salt marsh plants Suaeda heteroptera (an annual halophyte plant) and Phragmites australis in the inter-tidal areas. These areas are regularly flooded by the rise and fall of the tides. It is the largest P. australis marsh in Asia and hundreds of miles of S. heteroptera line the coastal beaches, forming the famous “red beach” landscape.

For this study area, a three-level nested grid simulation was set to encompass all the computational domains (Figure 3). The smallest grid resolutions in the Bohai Sea, Liaodong Bay and Liao River Estuary were 1,500 m, 500 m, and 10 m, respectively. The time step of each models are all 60 s. On the premise of ensuring the orthogonality of grid (φ < 0.02), the grid resolution decreases successively from offshore to the estuary, which effectively improves the computational accuracy and efficiency of the Delft3d model. The three-dimensional model is used for numerical simulations, and the σ coordinate is applied in the vertical direction to make 10 layers. The level-1 ocean-scale domain covers the entire Bohai sea, with Dalian and Yantai taken as the open boundaries of the level-1 grid, where eight dominant constituents (M2, S2, N2, K2, K1, O1, P1, and Q1) are selected for harmonic analysis to obtain tide level time series for the open boundary conditions. The level-2 regional domain covers Liao Dong Bay, and its open boundary condition water levels are provided from level-1 grid model. The level-3 domain covers the area of interest with the highest resolution, i.e., the tidal wetlands of the LRE, it receives boundary conditions from level-2 and considers the fresh water input of the upstream rivers. The runoff from the Liao River and Daliao River were 101 m³/s and 57 m³/s during study period, respectively (Zhang and Xu, 2021). The computation period was from 1 May 2019 to 31 May 2019 (including two spring tides and neap tides). Four tide level stations (Bayuquan, Jinzhou port, Juhuadao, and Tanggu) were used to verify the tide levels. The study area is mainly a muddy estuarine area with a median particle size of less than 30 μm, therefore, the sediment transport model for cohesive suspended sediment was applied in the study region. The parameters related to the cohesive suspended sediment including following contents, the reference density for hindered is 1,600 kg/m³, the specific density is 2,650 kg/m³, the dry bed density is 952 kg/m³, the settling velocity is 4.5 × 10⁻⁴ m/s, the initial thickness at bed is 0.05 m, the critical bed shear stress for sedimentation is 0.75 N/m³, the critical bed shear stress for erosion is 1.75 N/m³, the erosion rate is 1 × 10⁻⁴ kg/m²/s. In addition, the input sediment concentrations at the two river boundaries were taken from the measured data.

Our study region contained six observation stations (S1, S2, S3, S4, S5, and S6) used to validate the performance of the proposed model in terms of water levels, flow currents, and suspended sediment concentrations (SSCs), as shown in Figure 2. Field measurements were carried out at a series of observation stations in the Liao River Estuary area, the survey periods for tidal flow and SSC were divided into neap and spring tides, the spring tide period was from 10:00 on 20 April to 10:00 on 21 April 2019, and the neap tide period was from 7:00 on 26 April to 7:00 on 27 April 2019. Furthermore, several observation points in the tidal flats (E1–E4) were selected to investigate and compare the influence of vegetation on water surface elevations, flow velocities, and SSCs. E1 and E4 were located in areas occupied by S. heteroptera and E2 and E3 were located in areas occupied by P. australis, as shown in Figure 4. In addition, cross sections (C1–C4) in the eastern tidal flat were also configured to study the discharge flux process in the studied areas.

We evaluated the coverage of S. heteroptera and P. australis using RS images from May 2019 in the coastal wetlands of the LRE. The RS images used in this paper had a spatial resolution of 30 m and were downloaded from the USGS website (https://glovis.usgs.gov/next) from orbit number 120/32. The ENVI 5.4 software was used to conduct radiometric calibration and atmospheric correction in the RS images. The images underwent multi-resolution segmentation and were interpreted using the decision tree in eCognition 9.0. Based on the decision tree algorithm using three normalized indices (Wang and Zhang, 2022), we carried out a series of analyses with the help of visual interpretation of satellite images to identify water bodies, tidal flats, and salt-marsh vegetation in the LRE and categorized them according to their different features, as shown in Figure 4. Areas in red represent S. heteroptera cover, areas in green represent P. australis cover, areas in blue represent water bodies, and areas in gray are tidal flats. In these simulation scenarios, we used the digital map and the land cover distributions to assign vegetation type, stem height, and stem density to each grid to be used in the hydrodynamic model. We obtained the physical parameters of the two salt marsh plants by the field survey, they are as follow: the stem diameters of S. heteroptera and P. australis were 0.002 m and 0.005 m, respectively; the densities of S. heteroptera and P. australis were 250 stems/m² and 65 stems/m², respectively; the stem heights of S. heteroptera ranged from 15 to 25 cm and averaged 20 cm ± 3 cm, and those of P. australis ranged from 120 to 180 cm and averaged 150 cm ± 20 cm. The drag force coefficients of the vegetation were kept constant with a value of 1.0 corresponding to this growth period (Zhang and Xu, 2021).

Figure 5 shows the comparison between the simulated and observed results in tidal levels for the four stations. The tides at the four stations presented two high and low tides each day, all were irregular semi-diurnal tides. The tidal ranges of the stations to the north were greater than that near to the south side in this study region, and the maximum tidal range occurred at the Bayuquan tidal station. The correlation coefficient R ² and RMSE for all water level stations were 0.9286 and 0.24 m, respectively. R ² values over 0.9 indicate very good results, therefore, it can be concluded that the model had good accuracy and the coarse mesh model can provide precise boundary conditions for the nested grids. Figure 6 shows comparisons of the simulated and measured results in flow velocities and flow directions, respectively, at the surface and bottom layers; where stations S3 and S6 are in the second nested grid, stations S1, S2, S3, S4, and S5 are in the third nested grid. The simulated results followed the measured values very well. The flow velocities gradually increased from the bottom to the surface at all six gauge stations. The flow velocity at station S1 was influenced by the shoreline and deviated from the values measured to a certain extent. Topography had a great influence on velocity and flow direction, as shown by the lower velocities at stations S1, S2, and S3, which were located near the shoal area. Figure 7 shows comparison of the simulated and observed SSCs in the surface and bottom water layers, the simulated SSCs were in good agreement with the observed data. The SSCs at the bottom were higher than those at the surface in the study areas, and the SSCs at all stations were higher during the spring tide period than the neap tide period. We found that the influences of spring and neap tides on SSC processes were stronger in the near shore waters, and weaker in offshore waters. These results indicated that these modeling systems are capable of reproducing the tidal level, tide movement, and sediment transport processes. Therefore, the model can be used to investigate the hydrodynamic processes and distribution characteristics of SSC in coastal wetland areas.

To understand how vegetation impacts the hydrodynamics and water fluxes in coastal wetlands during flood and ebb processes, we ran the model to analyze the flow of water through salt-marsh plants in the LRE. Figure 8 shows a comparison of simulated tidal levels without and with vegetation at stations E1, E2, E3, and E4, and the results of the two conditions were almost identical. This showed that salt-marsh plants have little influence on the tidal fluctuation in coastal wetlands, whether in spring tide or neap tide periods, and the maximum water level and the time to reach flood peak remain unchanged despite differences in plant distribution and plant type. Figure 9 shows the vertical profiles of the horizontal currents at different times, where the water levels shifted from being within to above the vegetation canopy during an inundation cycle. All horizontal flow velocity profiles showed gradual decreases from surface to bottom, including cases with and without vegetation, but flow velocities were obviously greater in flood tide periods than ebb tide periods. In the absence of vegetation, the peak velocities of the four stations (E1–E4) in the flood period were 52.19%, 85.43%, 80.03%, and 88.04% higher than those of the ebb period. However, with vegetation the peak velocities for four stations during the flooding period were relatively smaller, and were only 51.42%, 80.15%, 59.47%, and 60.39% higher than those of the ebb period. This indicated that flow velocities at all stations were reduced in vegetated areas due to the flow resistance caused by vegetation, therefore, the salt-marsh plants can slow water flows to some extent. The vertical distributions of flow velocities in E1 and E4 stations were relatively gentle in S. heteroptera areas, where the plants attenuated the peak velocities by 10.50% and 22.87%, respectively. However the vertical distributions of flow velocities exhibited dramatic changes in P. australis areas, and the attenuation rates for peak velocities at stations E2 and E3 were 80.78% and 77.20%, respectively. These results indicated that the effects of P. australis on tidal currents are stronger than those of S. heteroptera. Figure 10 gives a comparison of the simulated fluxes in four cross-sections under vegetated and non-vegetated conditions. The water fluxes exhibited similar trends in all four cross sections, with water flux reductions occurring near the vegetation because the vegetation increases the seabed roughness and causes water to seek lower resistance paths through tidal creeks. In particular, the water volume exchanged in a tidal cycle was reduced by 60.92% in the presence of vegetation in the cross section of C1, and similar but smaller reductions in the water exchange rate were seen in other sections. The largest attenuation rates of water exchange occurred mainly in P. australis areas. Thus it could be seen that salt-marsh plant (P. australis and S. heteroptera) covering in coastal wetlands of the LRE may play an important role in reducing flow velocity and altering tidal fluxes during the flood and ebb of the tide.

Figure 11 shows the spatial patterns of flow structure in cases comparing the effects of vegetated and non-vegetated conditions. These numerical experiments showed that the presence of vegetation increased the bed resistance in tidal flats and effectively reduced the flow velocity. This was because, as the water flows through the vegetation, a lot of momentum and energy is consumed by the drag exerted by the plants, which effectively imposes resistance on the flow, resulting in decreased flow velocity compared to non-vegetated areas. Compared with S. heteroptera, P. australis is taller and larger in diameter, and it is a non-submerged emergent tidal wetland plant; due to these attributes, there were obvious slow flow regions in areas of P. australis (Figure 11B). Although the density of S. heteroptera (250 stems/m²) is bigger than that of P. australis (65 stems/m²), however its stem diameter and stem height are less than P. australis. These results showed that differences in flow velocities in vegetated region can be dependent on vegetation type, diameter, and height of salt marsh plants growing on tidal flats.

Suspended sediment in water is driven by tidal currents estuaries, where salt-marsh plants on tidal flats alter the magnitude and direction of flow currents while also changing the patterns of suspended sediment deposition distributaries within coastal wetlands. To better understand the effect of vegetation on the spatial distribution of suspended sediment, we carried out a series of numerical experiments to investigate how SSC varied across different areas, as shown in Figure 12. The comparison period was from 6:00 to 18:00 on 20 April 2019. In the early period of the flood tide and the later period of the ebb tide, the SSC was relatively low, with lower values than those at the transition period from flood to ebb. On average, the flood SSCs at the selected stations were more than double the ebb SSCs. For example, at station E1, the peak SSCs were 0.019, 0.025, and 0.002 kg/m³ at the beginning of the flood tide, highest tide period, and the end of the ebb tide, respectively. The SSCs at station E2 near the creek were clearly higher than those at other observation stations, and the high SSC in this area could be transported into the tidal flats and the coastal wetlands by tidal creeks during the flood tide. We found that the SSCs in all stations gradually decreased from the bottom to surface water layers, but the SSCs in vegetated areas were smaller than areas without vegetation, indicating that vegetation significantly influences suspended sediment transport in water. By comparing values with and without vegetation, we saw that the peak values of SSC at stations E1 and E4 were 18.92% and 45.63% lower in the presence of vegetation, while stations E2 and E3 decreased by 82.36% and 60.85% due to vegetation. Generally speaking, P. australis had stronger effects on the suspended sediment transport in the wetlands of the LRE than S. heteroptera. This was related to the vertical change in the suspended sediment concentration in areas with P. australis, which made sediment more likely to be deposited on the estuary bottom. These differences are related to the different physical forms of P. australis and S. heteroptera, with P. australis having larger stem heights and stem diameters, which give it a higher sediment capturing ratio.

Applying the Delft3D model, we calculated the maximum shear stress at each monitoring location during a spring tide cycle, the bottom shear stresses were computed with and without vegetation (Figure 13). There was no significant difference in bottom shear stress between offshore, bay, and tidal creek areas, but there was a notable difference between wetland regions with the two different salt marsh plant types. In the P. australis area, the shear stress was reduced by more than 50% compared to areas without vegetation, and it was reduced by 10% compared to S. heteroptera areas. Lower bed shear stress reduces the erosion and resuspension of seabed sediments, resulting in low SSCs in the water column of wetland areas. Interestingly, the presence of salt-marsh plants had a strong effect on flow velocity, and the maximum bottom shear stress on the marsh tidal flat of the LRE was significantly reduced when vegetation was present.

Vegetation can trap suspended sediments and facilitate accretion, and therefore promote the elevation of tidal flat landforms. We conducted several numerical experiments to study the degree to which different landscape types capture suspended sediments in the coastal wetlands of the LRE. Three monitoring periods were selected to consider different flow conditions, including spring tide (Apr. 20, 2019), middle tide (Apr. 24, 2019), and neap tide (Apr. 27, 2019). The SSC simulation with changing tidal level during spring tide indicated that the SSCs in the flood and ebb tides are closely related with the water level change (Figure 14A), but there is a time delay between the maximum sediment concentration and the maximum tidal level.

To track the suspended sediment transport in the LRE wetlands, we also computed the total amount of suspended sediment in the defined polygon, which was located in a S. heteroptera vegetation region. The suspended sediment fluxes in the selected area were calculated by establishing cross sections L1–L18, as shown in Figure 14B. It could be seen that the incoming flux of sediment during the flood tide period was larger than that in the ebb tide period, so a portion of suspended sediment is retained in the polygon region upon transition from flood to ebb tide. This showed that the salt-marsh plants in the wetlands of the LRE have a marked effect on sediment transport, trapping it in the study area during the tidal cycle. Figure 15A shows the calculated suspended sediment flux during different time periods. During the spring tide period, the input flux of suspended sediment in the selected area was 177.99 kg during the flood tide, while the output flux was only 45.77 kg during the ebb tide. This indicated that 74.28% of the total sediment input was retained as sediment during spring tide periods. The sediment catch gradually decreased during the transition from spring tide to neap tide. Moreover, we also analyzed the effect of salt-marsh plants on suspended sediment capture by comparing areas with and without vegetation, as shown in Figure 15B showed that there were the higher suspended sediment capturing rates (>60%) in areas occupied by S. heteroptera; furthermore, the sediment capture rate decreased slightly in lower tidal flat areas. These results indicated that sediment trapping can result when suspended sediment is advected over vegetated regions, and large marsh wetlands with relatively healthy plant communities can uptake larger amounts of sediment than baren tidal flats in estuary regions. Where the healthy plant communities can effectively slowed down the tidal current when the flow through the vegetation area, so the sediment easily attached to the plants and settled down the roots of the plants. However, the influence of salt marsh plants on suspended sediment capture may be different during different periods.