Estuaries are flanked by tidal marshes, which are unique ecosystems with a very high biomass that modify the local hydromorphodynamic conditions . Vegetation affects hydromorphodynamics in rivers , and this effect on hydromorphodynamics has also been shown on the scale of individual tidal marshes . The effect of vegetation on hydromorphodynamics in tidal marshes is therefore relatively well known on the individual plant or patch scale , while its effect on estuary-scale morphodynamics has barely been studied. Incorporating vegetation in estuarine morphodynamic models is considered one of the three biggest challenges to overcome in modelling the long-term evolution of tidal networks . A comprehensive but qualitative model suggests that tidal marshes reach their largest extent in the mixed-energy zone of the estuary . Here we investigate whether plant species can collectively have eco-engineering effects that are significant enough to modify entire estuarine landscapes. As we do not differentiate between different types of marshes, we will use a generic marsh species which will be referred to as either tidal marsh or marsh.

In rivers, riparian vegetation stabilises channels by reducing floodplain flow and adding bank strength to the floodplains . These eco-engineering effects can be strong enough to cause the transition from braiding towards meandering or even sinuous rivers . However, the presence of vegetation can also cause the bifurcation of channels by stabilising bar tips, causing flow resistance on point bars and diverging the flow from the channel onto the floodplain . Furthermore this increased flow resistance causes flow to decelerate and water levels to rise, which may induce flooding events . The presence of mud has a partly similar effect to vegetation because it can lead to the stabilisation of systems as well, and mud has shown to preferentially accumulate in vegetated areas . Based on these insights and general similarities between rivers and the tidal–fluvial transition, it is easily conceivable that similar biogeomorphological interactions shape upstream parts of estuaries. While salinity is an important variable determining which species prevail, here we focus on a single and often dominant tidal marsh vegetation species.

Tidal marsh vegetation flanks estuaries from the brackish zone to the mouth. Tidal marsh enhances sedimentation both through reduced flow velocities and through particle capture, somewhat comparable to what happens on river floodplains, but tidal marsh is not considered a particularly effective channel and bank stabiliser . If the hydroperiod, the time that tidal marshes are submerged every day, gets longer the sediment supply to the marsh increases and therefore so does the sediment accretion. Several authors therefore found that tidal marshes are most productive at a certain rate of sea level rise (SLR) because this keeps the hydroperiod more or less constant as accretion rates balance with SLR . However, tidal marshes may drown when the sea level rise rate is too large relative to the sediment supply, which leads to vegetation loss and therefore marsh drowning at an enhanced rate . In general, tidal marshes are thought to approach an equilibrium level relative to the sea level whether rising or not .

For tidal marsh to accrete, the supply of mud is essential as the source of inorganic accumulation. This mud may have a coastal or fluvial source, and the main source might have significant effects on the evolution of the estuary . Although mud is transported in suspension and thus reaches higher, low-energetic elevations and areas more distal from the main channel, it is not unlimited. Suspended sediment rapidly settles in tidal marshes and therefore the concentration in the water quickly decreases with distance into the marsh . Nevertheless, cohesive mud is more difficult to erode than sand when it consolidates, so that on the estuary-scale mud leads to narrower systems with reduced bar dynamics through mudflat accumulation . The logical hypothesis is that the added effect of vegetation leads to even more accretion at the flanks of the estuary .

The availability of mud is partly determined by the changing hydrodynamic energy along the river continuum, especially in shallow, well-mixed estuaries that we focus on (Fig. ) . The tidal–fluvial transition appears to be a zone of sand and mud convergence, both of which are therefore conducive to tidal marsh establishment (Fig. ). Alternatively, it could be the mixed-energy setting that is conducive to tidal marsh establishment, which, in turn, enhances sedimentation. A central zone of lower energy where the average grain size decreases has been observed where bedload converges . Bedload convergence means that both the river and the sea transport more sediment towards this central zone in the estuary than they export, resulting in net accumulation. suggested that this area of bedload convergence often coincides with the relatively largest tidal marsh extent (Fig. ). Furthermore, in many estuaries a turbidity maximum zone (TMZ) occurs in the same mixed-energy zone of the estuary, which are characterised by elevated suspended sediment concentrations e.g.. It is important to realise that the relative contribution of the tides, river and waves to the total hydrodynamic energy is gradually changing along the estuary . We will use a rough classification of the estuary into an outer, central and river part, which is characterised by a dominance of tides, mixed importance of tides and river, and dominance of the river over hydrodynamics respectively.

Our hypothesis derives from a combination of three independent and complementary analyses. First, a reconstruction of the Holocene development of estuaries and tidal basins suggests that vegetation combined with mud tends to infilling of estuaries. Through a reduction in intertidal water storage at the system margins, due to vegetation-enhanced sedimentation, the tidal prism reduces and tends towards flood-dominant transport . Second, a large number of estuaries fill all space wider than that covered by an idealised convergent estuary with tidal bars . This analysis excluded tidal marshes, but clearly a number of estuaries were larger in the past and have at least partly been filled by mudflats, tidal marsh or mangroves. A model study by on the effects of mud on the system-scale development of estuaries over millennia showed that mud decreases the morphodynamics and decreases the total system width depending on mud concentration. All three approaches – geological, remote sensing and numerical – point to system-scale effects of mud and vegetation in estuaries.

Our aims are to determine the combined effects of mud and vegetation on estuarine planform and morphodynamics, specifically in the setting of a sandy estuary with mud input from the river. To this end we will use a numerical model for a century-scale simulation of flow, sediment transport, morphology and vegetation. We ignore the binding of sediment by roots because of the relatively shallow rooting and only explore the cohesive effects of mud, the floodplain-filling effects of mud and the flow resistance effects of vegetation. This allows us to apply an existing model for riparian vegetation to the tidal environment. Two questions of specific interest are how the zonation of vegetation, as found by , can be explained and what the morphological and hypsometric changes are as a result of the presence of vegetation.

Delft3D is a widely tested open-source model that can calculate both sand and mud transport. The 2DH (depth-averaged) version was used with a parameterisation for bend flow effects on the direction of sediment transport. We used a rectangular grid, which affects the form of the equations given below. Here we will state the main equations used in Delft3D, which are either default or activated by choice. The only equations incorporated into our MATLAB model are related to the settling, growth, mortality and bookkeeping of the vegetation.

The model is mainly based on two hydrodynamic equations, the first being the conservation of mass equation: ∂h∂t+∂hu∂x+∂hv∂y=0, where h is the water depth, t is time, u is the flow velocity in the x direction and v is the flow velocity in the y direction. Equation () states that any change in water depth follows from a discharge gradient in the x direction (qx) or a discharge gradient in the y direction (qy) for a 2-D model. Momentum conservation is calculated as ∂u∂t+u∂u∂x+v∂u∂y+g∂zw∂x+guu2+v2C2h-V∂2u∂x2+∂2u∂y2+Fx=0,∂v∂t+u∂v∂x+v∂v∂y+g∂zw∂y+gvu2+v2C2h-V∂2v∂x2+∂2v∂y2+Fy=0, where zw is the water surface height, C is the Chézy roughness, which will be calculated by the vegetation model described below, V is the horizontal eddy viscosity and Fx,y is the streamline curvature-driven acceleration term . These two equations describe the velocity variations in the x–y plane in one grid cell over time under the influence of advection, eddy diffusivity, friction, changing water depth and streamline curvature. Sediment transport is calculated by separate equations for the different sediment constituents. Sand transport in the case of a non-cohesive bed is calculated with the Engelund–Hansen sediment transport predictor: S=0.05u2+v25gC3ρs-ρwρwD50, where ρs the sediment density, ρw the water density and D50 the median grain size. The sediment transport of the mud fraction of the model is calculated by Partheniades–Krone equations for erosion flux Em, Em=Mmτcwτcr,e-1, and for deposition flux Dm: Dm=wscb1-τcwτcr,d for τcw>τcr,e, where τcw is the maximum bed shear stress due to currents, τcr,e is the critical erosion shear stress, Mm is an erosion parameter, ws is the mud settling velocity and cb the average sediment concentration in the near-bottom layer. Above a critical mud content threshold (pm>pm,cr), the sand and mud flux are proportional to their respective fractions in the sediment bed. Mud erosion is the same in the cohesive and non-cohesive regime, but the sand erosion becomes dependent on the mud entrainment in the cohesive regime, when the mud content in the bed exceeds 40 %. The transport of sand becomes fully dependent on the mud flux, as bedload transport is assumed to be zero in the cohesive regime. Once sediment is suspended following the Partheniades–Krone equation, it is transported by the advection–diffusion equations. A constant mud settling velocity of 2.5×10-4 m s-1 was assumed based on .

A parameterisation is needed for helical flow due to streamline curvature in a depth-averaged simulation to create point bars in river bends and estuarine bars and is included as follows. The bedload transport direction ϕτ is given by the following equation: tan⁡(ϕτ)=v-αIuUIsu-αIvUIs, where U is the depth-averaged flow velocity, Is is the spiral flow intensity factor, here taken at unity, and αI is given by the following equation: αI=2κ21-12gκC, where κ is the von Kármán constant, taken as 0.41. Lastly, bed slope effects are included in the model to simulate a deviation in sediment transport direction from the shear stress direction due to grains moving downslope. The sediment transport in the x and y direction under influence of the bed slope effect is given by qx=qscos⁡(ϕτ)-1f(θ)∂zb∂x,qy=qssin⁡(ϕτ)-1f(θ)∂zb∂y, where qs is sediment transport, zb is the bed height, and f(θ) is given by the following equation: f(θ)=αθβ. In this equation θ is the shields parameter and α and β are calibration parameters specified later.

A model programmed in MATLAB was used to simulate the vegetation in the estuary . This model simulates vegetation colonisation, growth and mortality and translates this to hydraulic roughness used in Delft3D as based on the equation: C=11Cb2+Cdnhv2g+gκln⁡hhv, where C is the Chézy roughness value due to the bed and vegetation roughness (m/s), Cb is the Chézy value for the bed without vegetation, Cd is the drag coefficient, n is the number of stems per square metre times the stem diameter, hv the vegetation height and κ=0.41 is the von Kármán constant. Vegetation of different ages and therefore with different characteristics can occur simultaneously in one grid cell up to a total fraction of 1. The Chézy value is calculated for each age class, and afterwards a total Chézy coefficient is calculated based on the fraction coverage of each age class.

The vegetation model divides the morphological year into 24 ecological time steps, which correspond with half a month of morphological development (Table ). Following each ecological time step the hydromorphodynamic calculations are stopped and the bed level changes, water levels and flow velocities are exported from Delft3D to the vegetation model. A 2-week interval, during which vegetation properties are assumed constant, was chosen to capture the dominant vegetation development processes. Over a 2-week growth period, the species have no appreciable changes in size, and this time step balances with the computational cost that increases with a decreasing time step. The vegetation has both general and life-stage-specific characteristics (Tables  and ). General characteristics are the seedling dimensions, i.e. shoot length and diameter and root length, maximum age, growth factors for logarithmic shoot, root and diameter development, and seed dispersal timing . Life-stage-specific characteristics are rules for mortality due to flooding and uprooting, number of stems per area, drag coefficient, and fraction of the grid cell surface covered with vegetation. All the variables in the equation are thus accounted for. The new vegetation characteristics are then used to update the Chézy roughness field in Delft3D.

Colonisation takes place during the month of seed dispersal on every location where water has been present (Table ). This means that all cells in the intertidal zone are colonised with Spartina anglica by the predefined colonisation density. Given that the tides in the model are simplified to M2, the supratidal zone where vegetation settles in nature can be seen as included as high intertidal. There is no seed dispersal module other than that we assume the seeds to spread through the water (hydrochorously), and neither do seeds end up above the water surface. This means that seedlings colonise lower intertidal areas, after which mortality determines which plants survive such that the lower intertidal zone is not occupied by plants during the flow modelling. We do not model rhizomic growth since this is a process occurring at a much smaller spatial scale than the grid cell size.

The vegetation follows a logarithmic growth function dependent on age, which limits their growth once they mature: G=Fvlog⁡(a), in which G is the length or diameter of the shoot or root, Fv is a characteristic growth factor for the root or shoot, and a is the vegetation age in years. The initial dimensions of the seedlings are defined in the general characteristics, after which plant growth is calculated yearly following the equation.

Mortality is calculated yearly as a function of burial, uprooting, maximum flow velocities, flooding and ageing. Burial and uprooting are determined by comparison of the plant dimensions and bed level change. If the erosion in an ecological time step exceeds the length of the root, the plant is uprooted, and if the sedimentation exceeds the shoot length, it is considered buried, both leading to mortality . To calculate mortality due to flooding and flow velocity, the maximum, minimum and average water depth at each cell are determined during the tidal cycle. Because tidal marsh vegetation starts to occur above mean tide and usually quickly accretes to the high tide mark, the subsequent days that the cells are flooded during mean tide are recorded. For flow velocity, the maximum value during the tidal cycle in each cell is stored. Lastly, vegetation dies when its maximum age is reached.

A dose–effect relation is applied to model gradual plant demise as the fraction of plants that do not survive the hydrodynamic pressure. Until a threshold is exceeded no mortality occurs, while above this threshold an increasing portion of the plants start dying with increasing stress. The threshold value and the slope of the stress–mortality relation are user-defined and can vary between the life stages of the plants (Table ). Mortality was applied to each age class in all grid cells .

We set up four model scenarios based on our earlier work and about 30 preliminary test runs, where we balanced time efficiency and the processes that could be realistically represented .

The initial bathymetry is the final outcome of a model run that started from an idealised convergent shape . This avoids long computational time to develop sufficient bars and mudflats where vegetation can settle. The rectangular cell size varies from 50 m by 80 m in the estuary to 125 m by 230 m offshore. This is done to balance computational time and sufficient spatial resolution. A 0.2 min time step was used based on the Courant criterion. We applied a 1.5 m tidal amplitude defined by two harmonic water levels at the north and south coastal boundaries and a constant 100 m-3 s-1 discharge at the upstream river boundary. The bed is initially entirely composed of sand and has a sand supply equal to the transport capacity at the river boundary, which avoids sedimentation or erosion at the upstream boundary. Mud, on the other hand, is supplied as a constant concentration at the upstream boundary of 20 mg L-1, the same as in the run by that led to large-scale equilibrium of the estuary planform. This model was run for 1000 years without vegetation in , and the final bathymetry was used as the initial condition for further simulations including vegetation (Fig. b). Note that this bathymetry was the result of calculations including mud. However, we only use the initial bathymetry and not the bed composition as our initial condition in order to isolate the effect of the addition of vegetation and mud through the upstream supply.

Several parameters for hydromorphodynamic processes, numerical processes and vegetation development were varied (Table ) to study their effect on estuary developments. Model scenarios were run for 100 years, which is about the minimum time required for morphological changes at the system scale to occur due to vegetation and the practical maximum time given computational and input–output costs of about 2 months on a single node in a fast desktop computer (Table ). A small morphological scale factor of 30 was used, since preliminary testing showed that this allowed vegetation settlement, growth and mortality over a number of tidal cycles without significant morphological change. In contrast, for sandy estuaries without vegetation, values up to 1000 have been used . In the vegetation model a balance is required between morphological and hydrological timescales, since these both affect the development of the plants. If the morphology changes significantly faster than the hydrodynamics, plants are subject to large-scale burial and uprooting. A default Chézy value of 50 for bare sediment was chosen as in . Vegetation traits of Spartina anglica were based on and (Tables , ).

For a first quantitative comparison of model results with real estuaries, we mapped along-channel variability of unvegetated channel width and width of the vegetated zone in nine natural estuaries. The real estuaries were selected from the dataset of based on the presence of tidal marsh vegetation and include one system with mangrove species (Table ).

The area of each estuary was visually classified as either unvegetated or vegetated in Google Earth. The unvegetated polygons come from the dataset by , and this analysis adds polygons of the vegetated area (Fig. ). The vegetated area comprises the area that borders the active estuary and is covered with pioneering or fully grown tidal marsh vegetation. The presence of sinuous tidal creeks and vegetation other than, for instance, forest, were used as an indicator of present-day or recent tidal influence and older riparian vegetation was excluded. Tidal vegetation was distinguished by its different colour compared to surrounding forests and grass fields and by its clumpy and patchy structure. The elevation data in Google Earth were used as further evidence for the outer boundary of the tidal vegetation area to avoid steep gradients and cliffs at the transition from a supratidal elevation level to higher elevated areas bordering the estuary.

Subsequently, centre lines of the polygons were constructed along the channel, which allowed width measurements perpendicular to this centre line following the approach of. This resulted in along-channel profiles of the active channel width, summed width of vegetation and estuary width, in which the estuary width is defined as the active channel width including bars plus the summed width of vegetation. The along-channel distance from the mouth was normalised with the length of the estuary. Estuary length is defined as the length from the mouth up to the point where the estuary width is equal within a few percent to the active channel width, in our case the upstream river. By this normalisation a direct comparison is possible between estuaries with different lengths and our modelled simulations. Through this normalisation it becomes possible to compare estuaries with different tidal–fluvial dominance. Estuaries with a small river might have a smaller, more upstream, mixed-energy zone than estuaries with a larger river. As the mixed-energy zone is a somewhat objective designation because it is part of a continuum, we investigate vegetation cover as a function of the normalised position in the estuary and as a function of total energy. By doing this we do not delimit the mixed-energy zone but compare vegetation cover development with the development of the total energy along the estuary.

Estimates of local tidal prism and total energy were made for each of the real estuaries based on . Local tidal prism was estimated by multiplying the along-channel width profile with the tidal range profile and integrating over the distance upstream of a given point. The volume added by the river was characterised by river discharge multiplied by tidal period. We then calculated a characteristic velocity by dividing the local prism TP by the local active width Wa and half the tidal M2 period TM2/2. As a proxy for the total flow energy, this velocity was taken to the power of 3 as this is also a common indicator of sediment movement , so that flow energy is here calculated as 2TP(WaTM2)-3.

The mouth of the modelled estuary has a 3 m tidal range, which decreases gradually in the landward direction to disappear roughly 14 km into the estuary (Fig. ). The flow velocity, on the other hand, increases in the outer part of the estuary because the convergence is stronger than the friction. Further in the estuary the convergence decreases and the increase in friction begins to dominate, which results in a decreasing flood velocity. Therefore, there is a peak in the flood flow velocity at roughly 5 km into the estuary (Fig. ). The changes in tidal range along the estuary are thus similar to those in a hyposynchronous system while the changes in the current are similar to those in a hypersynchronous system (Fig. ).

In the simulation without mud and vegetation, i.e. the reference scenario, channels and shoals are dynamic, but no system-scale changes occur as the initial system seems to be close to dynamic equilibrium. Only a slight change in hypsometry occurs: the intermediate heights are slightly eroded, while the higher parts accrete slightly (Fig. ).

The simulation with vegetation only develops fringing marshes at the edges of the estuary. The marshes start from the estuary mouth up to the tidal limit, roughly 14 km upstream (Fig. ). The relative width of the tidal marshes is fairly constant at ≈10% of the estuary width in the outer zone. Between roughly 6 and 11 km, however, the relative width of the marshes suddenly increases. The relative width of the tidal marshes can go up to 60% of the estuary width. This area coincides with the area where the flood velocity and river velocity start to decrease due to friction and estuary shape respectively (Fig. ). Beyond 14 km there is no vegetation anymore; this is because this is beyond the tidal limit and therefore there is no drying and flooding area where seeds are distributed and seedlings survive. The morphology in the simulation with vegetation only shows little differences compared to the reference simulation. This indicates that the vegetation is unable to enhance sedimentation in the absence of suspended fine sediment and that it predominantly colonises locations that are not prone to erosion because there is no significant reduction in the erosion of the intertidal area (Fig. ).

The simulation with mud only results in a fairly continuous mud cover along the entire estuary (Fig. ). There are small amounts of mud which deposit on tidal bars, in the order of an accumulated 10 cm admixed in sand over 100 years, but the more pronounced accumulations occur on the edges of the system. Similar to the simulation with vegetation the relative mud abundance starts to increase landward of the maximum flood velocity, which occurs at roughly 6 km. The relatively large mud extent in the central zone of the estuary is due to the low flow velocities in this zone (Figs. , ). Unlike the vegetation cover, however, the relative mud abundance does not decrease to zero at the tidal limit, but approaches a roughly constant value of approximately 30% of the system width (Fig. ). This is because the estuary is small in this area, as the river is only several cells wide, and not because there are large extensive mudflats. In terms of hypsometry the largest effect of mud is that the intermediate bed elevations increase slightly (Fig. ). This shows that the higher elevations are nearly filled as much as possible, and that the estuary develops in a feedback of further filling and reduction in tidal prism.

The distribution of vegetation and mud in the combined simulation shows similar patterns to the simulations with either mud or vegetation only. There are some marshes and mud deposits in the outer estuary, but these become more pronounced towards the central zone (Fig. ). There is a positive feedback between mud and vegetation. Not only do mud and vegetation occur in the same area, but their relative abundance also increases compared to simulations where one of them is absent (Figs. , ). This is emphasised by the total mud and vegetation cover in the estuary, which are almost identical after 100 years (Fig. a). There is an especially strong feedback in the beginning of the simulation, when vegetation cover increases strongly, after which mud cover starts to increase faster (Fig. a). On top of that, the addition of vegetation to the simulation with mud further enhances the aggradation of the upper hypsometric heights and thus the intertidal area.

Vegetation presence affects the location and thickness of mud deposits mainly in the central estuary (Fig. b) and to a lesser degree in the outer area (Fig. ). The vegetation cover develops faster than the mud cover but afterwards stimulates the mud sedimentation, which reaches a higher final area (Fig. ). A major difference in hypsometry is, however, that the outer estuary has a concave profile while the central and river reach have a convex profile. This has direct consequences for the available area for vegetation. Because the effect of vegetation is largest in the central part of the estuary, a series of close-up images is provided (Fig. ). The bathymetry of the reference simulation shows limited changes (Fig. a). Vegetation colonises the edges of the area in the simulation without mud but remains distal from the main ebb channel, and the bathymetry develops similar to that of the reference simulation (Fig. c). Larger differences occur in simulations where mud is present. When mud is added to the simulation, it first focusses the main ebb channel, but afterwards the entire area starts to gradually fill and becomes shallower (Fig. b).

The combined effect of vegetation and mud in the central estuary is to raise the intertidal areas and deepen the subtidal areas relative to the run with mud alone, but the overall depth compared to the control run and vegetation run is reduced. This means that the vegetation acts to focus flow into the channels, but the dominant effect is the filling of intertidal area that reduces the overall tidal prism over time. In the simulation with mud and vegetation, the deeper parts of the estuary no longer accrete. Instead the vegetation captures mud in the intertidal area, and the vegetation expands laterally towards the main channel while focusing the flow (Fig. d). Vegetation traps the mud in the higher intertidal areas and through this redistribution decreases the siltation of the deeper parts of the estuary. Simultaneously the accumulation of mud increases the bed level in the central part of the estuary, which enables the vegetation to laterally expand in the direction of the channel. Because mud enables vegetation to expand laterally and because mud accumulation increases within vegetated areas, the total mud and vegetation cover increases when both are present (Fig. ). Also, the vegetation causes the deposition of mud on bars in the middle of the estuary (Fig. d) where mud barely occurs when vegetation is absent (Figs. c, ).

The water elevation and mean flow velocity in the middle of the estuary were plotted over time to test the hypothesis that the system becomes flood dominant when vegetation (and mud) are present (Fig. ). The system is ebb dominant from the start. The peak flow velocities occur roughly 1 h before low and high water, and thus the tidal velocity is slightly out of phase. The rise of the tide occurs somewhat faster than the fall of the tide. Normally this would result in higher flood velocities, but in the mixed-energy zone of the estuary they are compensated for by the river discharge. The tidal asymmetry does not change much over time for the four scenarios, but the tidal range decreases for the scenario with mud and vegetation and both simulations with vegetation cause a decreased average flow velocity (Fig. b). Furthermore, the effect of combined vegetation and mud is disproportionally larger than that of vegetation or mud alone, confirming the idea of interaction. Moreover, the effect of reduction in tidal prism that determines overall flow energy dominates over the effect of reduction in intertidal area that determines the tendency of flood dominance.

The model simulations showed that the relative vegetation abundance increases especially in the mixed-energy zone of the estuary. This is in close agreement with observations in nine real estuaries (Table ). In real estuaries, vegetation increases in abundance from the estuary mouth towards a short distance before the tidal limit, while landward of the tidal limit the vegetation cover decreases quickly towards zero (Fig. ). Similar to the modelled scenarios, the landward vegetation cover increase coincides with the decrease in the flow energy. The upper limit of the vegetation is slightly beyond the tidal limit, but this is probably because we included old marshes, which are rarely flooded.

Modelled marshes reach their largest extent in the central estuary, where the tidal energy is the lowest in agreement with the qualitative model of . The tidal marsh expands mostly landward from the maximum flood current velocity. This is also where the bedload convergence zone begins and in natural estuaries where the turbidity maximum zone may occur (Fig. ). The main reason for the increase in tidal marsh extent is the combination of flow velocities being low enough and the presence of suitable bed elevations. The establishment of tidal marshes requires a window of opportunity with a long enough mild hydrodynamic stress . However, the modelled marshes develop primarily landward and not seaward of the maximum flood velocity, which shows that the hydrodynamics are not the only limiting factor. In reality, however, the hydrodynamic stresses will be larger in the outer part and wave magnitude is also more significant there , and waves are a major limiting factor for seedling establishment in tidal marsh and mangrove landscapes . Waves would result in a further reduction in tidal marsh extent in the outer estuary but will have limited effect on the central part of the estuary and therefore strengthen the trends in our model.

The importance of sediment accumulation in the central part for tidal marsh development is shown in the scenario with mud and vegetation. This simulation shows a further extent of the marshes because mud preferably accumulates in the central part of the estuary, regardless of the fact that no preferential establishment of vegetation on a muddy substrate is included in the model. While it is known that suspended sediment is a requirement for tidal marshes to keep up with sea level rise , the present model results show that suspended sediment is also a requirement for significant lateral marsh progradation into the estuary. We show that the presence of vegetation increases the mud deposition in the upper intertidal area in agreement with observations , but also that this reduces accumulation in the lower intertidal area. Once the vegetation starts to expand and approaches the main channel (Fig. ), it starts to focus and concentrate the flow (Fig. ). After vegetation settlement and stabilisation, vegetation causes flow focusing, similar to the fluvial environment .

Despite the reduction in intertidal flood storage, the central zone barely becomes more flood dominant and the tidal limit shifts seaward. This is in contrast to expected tidal dynamics , probably because the river in this part of the estuary already dominates over the tidal influence. The seaward shift of the tidal limit implies that the inundation time, and therefore stress, of the marshes decreases, explaining why vegetation density increases in the central estuary. Regardless, the river flow, if large enough to move sediment, will keep a channel open even if the floodplains fill up, such that an equilibrium tidal river may develop. This amounts to progradational filling of the estuary as observed in the Holocene .

The general agreement between trends in real estuaries and the numerical model indicates that the overall pattern of tidal marsh and mudflats along the estuary is determined mainly by the tidal hydromorphodynamics and the interaction with mud and vegetation. Figure  shows the mean relative vegetation abundance for nine alluvial systems along the tidal–fluvial transition with pronounced marshes. The relative extent of the vegetation can be higher in real estuaries, which has three main causes. First, the modelled system started as a narrow convergent estuary while many real estuaries start from unfilled basins. This leads to the question of whether the pattern of vegetation abundance and the tendency to accumulate sediment in the central estuary would have occurred for other initial conditions. The model results of show that mud generally settles in similar patterns over most of the modelled period and for most mud concentrations, suggesting that vegetation likewise would have formed similar patterns and central estuary sedimentation. Differences in patterns arise in conditions with very different boundary conditions as discussed below. Second, real estuaries are to a much larger degree infilling than our ebb-dominant system with little sediment import from the sea, and they had a much longer time to fill gradually. Third, many natural estuaries develop pronounced TMZs under influence of density-driven currents, tidal currents and river discharge. Such a TMZ would develop roughly in the mixed-energy zone, and a pronounced TMZ can be hypothesised to enhance accretion and tidal marsh expansion of the central part of the estuary that already occurs without a turbidity maximum zone .

Our model study simplifies real estuaries in several aspects. First, sediment supply coming from the sea could enhance tidal marsh establishment in the outer estuary. On the other hand, the presence of waves would reduce vegetation survival mainly in the outer estuary where waves are most powerful. Third, the absence of multiple tidal components may reduce the ebb dominance and also limit vegetation development further upstream due to the absence of wetting and drying. Ebb dominance may arise due to the interaction of multiple tidal components which interact and result in a skewed velocity and thus ebb or flood dominance. In our model, there is only velocity asymmetry due to friction-induced lags as a function of tidal stage similar to the process described by . The strongest driver of tidal asymmetry in the central zone is, however, the river discharge. River discharge is known to affect velocity skewness and the timing of slack water and appears to be dominant in the central zone of the estuary . Fourth, the salinity gradient is ignored, the vegetation along the entire estuary is the same and there are no changes in how vegetation affects hydromorphodynamics along the estuary. While it is not yet known whether typical marsh species along the salinity gradient have different eco-engineering traits which significantly differently affect the long-term morphodynamics, our model is a new tool that, in further research, may lead to new insights in such patterns emerging along the estuary. Regardless, enhanced sedimentation would not change the conclusions, which is that the fundamental feedback mechanism between mud and vegetation affects the larger-scale estuary development: mud facilitates the expansion and survival of marshes while vegetation facilitates the capture of mud, especially in the mixed fluvial–tidal zone.