Estuarine morphodynamics and development modified by floodplain formation

Rivers and estuaries are flanked by floodplains built by mud and vegetation. Floodplains affect channel dynamics and the overall system's pattern through apparent cohesion in the channel banks and through filling of accommodation space and hydraulic resistance. For rivers, effects of mud, vegetation and the combination are thought to stabilise the banks and narrow the channel. However, the thinness of mudflats and estuarine floodplain, comprised of salt marsh in estuariesand mudflats, compared to channel depth raises questions about the possible effects of floodplain as constraints on estuary dimensions. To test these effects, we created three estuaries in a tidal flume: one with mud, one with recruitment events of two live vegetation species, one with mud and a control with neither. Both mud and vegetation and mud reduced channel migration and bank erosion and stabilised channels and bars. Effects of vegetation include local flow velocity reduction and concentration of flow into the channels, while flow velocities remained higher over mudflats. On the other hand, the lower reach of the muddy estuary showed more reduced channel migration than the vegetated estuary. The main system-wide effect of mudflats and salt marsh is to reduce the tidal prism over time from upstream to downstream. The landward reach of the estuary narrows and fills progressively, particularly for the muddy estuary, which effectively shortens the tidally influenced reach and also reduces the tidal energy in the seaward reach and mouth area. As such, estuaries with sufficient sediment supply are limited in size by tidal prism reduction through floodplain formation. formation in estuaries limit ebb flood flow, reducing channel migration, and shortening the tidally-influenced reach. Vegetation establishment on bars reduces local flow velocity and concentrates flow into channels, while mud flats fill accommodation space and reduce channel migration. These results are based on experimental estuaries in the Metronome facility supported by numerical flow modelling.

raises the question what limits the widening of estuaries, particularly how vegetation and mud sedimentation affect the channel pattern in estuaries as far as such estuaries are not laterally constrained by valley walls. The objective is to understand the different mechanisms by which vegetation or mud affect local channel dynamics and system-scale effects on the channel-bar pattern. Two alternative hypotheses for effects of floodplainsdynamic floodplain on the dimensions of estuaries are proposed here from observations and mechanisms in rivers.
The first hypothesis relates to the conservation of tidal energy in the landward direction. In some systems, floodplain formation along estuaries may have led to relatively deep channels allowing further landward tidal penetration than in shallow estuaries. Estuaries that formed as part of tidallydominated deltas such as the Mekong, Mahakam, Yangtze and Rhine developed narrow, deep channels surrounded by high floodplains \cite[][]{tamura2012,wang2015,dehaas2019}, as did some late-Holocene ingressive estuaries \cite[][]{vanderspek1997}. The channel depth and convergence possibly cause the tides to propagate far landwards with backwater effects up to the delta apex.
The alternative, opposing hypothesis relates to landward tidal energy reduction. The reduction of intertidal area by accreting floodplains with vegetation reduces the tidal energy, especially on the fluvial-tidal transition, and pushes the tidal limit in the seaward direction. Indeed, on longer timescales, floodplain formation along estuaries was concurrent with a reduction in tidal discharge, landward tidal penetration and overall filling that reduced tidal system extent and depth over some portion of the The expansion or filling of estuaries not only depends on mudflat and salt marsh formation but also on the morphodynamic interactions between river discharge and tides and the channels and bars morphology. While significant river discharge causes net seaward sediment transport ,lokhorst2018,boechat2020,bruckner2020}. The direct link of tidal prism and tidal asymmetry with the area occupied by bars and floodplain is potentially another mechanism through which salt marsh and mud flat expansion affect the dimensions of estuarine systems. The underlying cause for the reducing planform estuary dimensions may be the reduction of tidal prism \cite[][]{friedrichsaubrey1988,robins2010,brown2010} by sediment filling of intertidal storage area and vegetation causing hydraulic resistance and amplifying vertical accretion. In other words, hypothetically there is a direct effect of mud and vegetation by filling and an additional, indirect effect on the tidal dynamics that may determine net sediment import or export. . The tidal forcing was kept simple, with one primary tidal component only, and a small river discharge. In all experiments we supplied a minor river discharge and applied monochromatic waves by a paddle in front of the ebb delta to diffuse coastal transport and form beach ridges \cite[as in][]{leuven2018c}.. The first experiment had only sand, while the second and third had mud or live vegetation or mud to compare the two styles of floodplain formation against a control without floodplain. Low-density sediment was supplied as a mud simulant; this experiment is also reported in \cite{braat2019}. The experiment with live vegetation reported here is novel and is based on vegetation experiments in \cite{vandijk2013a} and \cite{lokhorst2019}. Low-density sediment was supplied as a mud simulant; this experiment is also reported in \cite{braat2019}. Furthermore, to avoid practical difficulties withof flow measurements, we apply a numerical flow model to all experiments \cite[][]{weisscher2020}, modifying the roughness where vegetation is present. In this section, the experimental methods, vegetation treatment and numerical modelling methods are described.
\subsection{Experimental methods} Experiments were conducted in the Metronome, which tilts with a sinusoidal motion over the short middle axis with a slope amplitude of 0.0068~m/m at a period of 40~seconds. This drives tidal currents with a depth-averaged velocity amplitude in the channels of about 0.3~m/s. The initial bed was screed flat at millimetre accuracy. The initial convergent channel of 0.2-1.0~m wide and 0.03 ~m deep was carved into a sand bed of 0.07~m thick, while the sea was kept free of sand between 17.8--20~m. The initial water depth above the channel bed, set by the seaward weir, was 0.025~m. We used poorly sorted sand with a $D_{10}$ of 0.33~mm, a $D_{50}$ of 0.57~mm and a $D_{90}$ of 1.2~mm. Flume settings were chosen such that sediment mobility, expressed as the Shields number, was up to 0.5 \cite[][]{kleinhans2014a,kleinhans2017a,braat2019}.
The landward boundary condition is a river discharge of 0.1~L/s supplied for half the tidal cycle when the flume was tilted seaward. The river discharge in isolation did not mobilise the sediment but was essential to maintain a long estuary \cite[see online supplement in][]{braat2019}. The seaward boundary condition is a broad-crested weir with constant water supplied from a basin to have a constant head condition. The weir moves up and down in the opposite phase of the tilting motion such that the sea remains approximately horizontal. This prevents surges into the estuary and drawdown that would cause incision in the ebb delta and ensures that the tidal flow is entirely forced by the periodically varying gradient. The weir amplitude was reduced linearly with the progradation of the delta towards the boundary. Furthermore, monochromatic waves of 0.5~s period and 0.01~m height were generated by a horizontal paddle during the landward tilting half of the tidal cycle. Waves in isolation hardly mobilised the sediment but in combination with tidal currents caused coastal transport diffusion to round the delta during progradation and form beach ridges. Testing and analyses of scaling of waves is described in the supplement to \cite{leuven2018c}. One experiment had a supply of suspended sediment sufficient to simulate the formation of mudflats.One Mud was simulated by a supply of crushed nutshell at the river boundary. This experiment has already been published earlier \cite[][]{braat2019} and is reanalysed here for different aspects. The nutshell had a diameter of 0.2~mm and a dry density of 1350~kg/m$^{3}$. The large grain size prevents mud infiltration in the sand bed. The nutshell was kept in suspension in a mixing tank and was supplied at a dry volume of about 1~ml per tidal cycle, such that a total volume of 0.013~m$^{3}$ (0.009~m$^{3}$ without 30\% pore space) was added to the experiment. Given a 20~s river discharge duration per tidal cycle, the mud concentration in the river influx was about 405~mg/L, or 810~mg/tidal~cycle. The velocity required to suspend the mud is much lower than that to suspend the sand, so that the mud can deposit in much shallower flow Another experiment had regular vegetation recruitment events through periodic supply of vegetation seeds of two species followed by four days of rest to allow sprouting above the still water surface. ThisThe seeding was started after 4,500~cycles to allow time for formation of bars where vegetation could settle, and was done every 2,000~cycles. Vegetation was added by seeding at the river boundary, similarly to the hydrochorous seed distribution in the river experiment of \cite{vandijk2013a} \cite[also see for scaling of vegetation][]{kleinhans2015a}. After growth tests, we selected two species that grow above the water surface to simulate effects of salt marsh species by enhanced flow resistance and capturing of suspended sediment \cite{lokhorst2019}. \emph{Veronica beccabunga} forms 10~mm tall plants that grow at the waterline in dense elongated patches and above the waterline in sparse cover, and \emph{Lotus pedunculatus} grows up to 20~mm tall at somewhat higher elevations above still water, usually with sparse cover and sometimes in tussocks. The combination of species that settle in somewhat different zones is expected to lead to a larger vegetation cover than a single species, but since all species have similar hydraulic roughness parameters \cite[][]{lokhorst2019}, the differences in their effects on the hydrodynamics may be negligible.
Our first, geometric scaling consideration for the selection of these species was thatgeometric: roots in natural estuaries have lengths of a fraction of the main channel depth, and our smallest plants still have relatively large roots. Our second, dynamic scaling consideration was that ofdynamic: bank erosion and channel incision reductionshould reduce. Earlier experiments with vegetation (pilots conducted for \cite{vandijk2013a}, also see \cite{gran2001} showed that more extensive and interlocking root systems can completely fixate systems. In view of this experimental difficulty, we chose the smallest plants, which have measurable bank erosion reduction effects as shown in \cite{[][]{lokhorst2019} in bespoke bank erosion tests at the scale of the experiments. The third dynamic scaling consideration was that ofalso dynamic: vegetation should cause hydraulic resistance. As long as the stems penetrate the water surface and there is sufficient stem density, the vegetation has a strong measurable hydraulic resistance effect \cite{lokhorst2019}. Unlike roots that are small relative to channel depth in large, natural estuaries, the vegetation settles at such high elevations that its effect on shallow flow can be large as shown in numerical modelling of meandering rivers with riparian vegetation All seeds were soaked for 24~hours to prevent floating and speed up germination. We released batches of seeds at the upstream boundary after every dry bed photograph. After 10~tidal cycles for initial wetting, 12.5~g or about 10,000~seeds of \emph{Lotus pedunculatus} were supplied. Another 25~cycles later, 3.75~g or 15,000~seeds of \emph{Veronica beccabunga} were allowed to disperse for 35~more tidal cycles and then left to germinate for four days without tilting but with river discharge. These 70~tidal cycles were subtracted from the 1,000~cycle run before the next dry bed photography session so that spacing between the DEMs was exactly 1,000~cycles. Laboratory conditions were around 300~lux light intensity by daylight-toned luminescent tube at all times \cite[as in the controlled vegetation experiments of][]{lokhorst2019}, a water temperature of 20$^\circ$~C and a room temperature of about 17--20$^\circ$~C. As found in earlier experiments with vegetation, these conditions do not limit sprouting \cite[][]{vandijk2013a}, whereas water depth and unrooting are limiting or terminating growth \cite{lokhorst2019}. The plant species stopped growing after 5-7~days as the sand and tap water were free of nutrients. Chlorine was added to the water as pest control to prevent algae, fungi and bacterial growth, and the bed of the vegetated experiment was further treated with anti-algae spray at 8,000, 10,500 and 12,500 tidal cycles. The duration of the vegetated experiment was about two months. The other experiment with floodplain had a supply of suspended sediment from the start sufficient to simulate the formation of mudflats. Mud was simulated by a supply of crushed nutshell at the river boundary. This experiment has already been published earlier \cite[][]{braat2019} and is reanalysed here for different aspects. The nutshell had a diameter of 0.2~mm and a dry density of 1350~kg/m$^{3}$. The large grain size prevents mud infiltration in the sand bed. The nutshell was kept in suspension in a mixing tank and was supplied at a dry volume of about 1~ml per tidal cycle, such that a total volume of 0.013~m$^{3}$ (0.009~m$^{3}$ without 30\% pore space) was added to the experiment. Given a 20~s river discharge duration per tidal cycle, the mud concentration in the river influx was about 405~mg/L, or 810~mg/tidal~cycle. The velocity required to suspend the mud is much lower than that to suspend the sand, so that the mud can deposit in much shallower flow All three experiments developed a convergent, multi-channel estuary with mid-channel bars and a prograding ebb delta ( Fig.~\ref{fig:dems}, movie in Supplementary Online Materials). All three estuaries widened by bank erosion from the initial, monotonously converging estuary to form channels and bars. As the original 0.03~m high sand bed flanking the estuaries was never flooded, mud or vegetation or mud was confined in the reworked area. The vegetation and the mud first settled on the most upstream mid-channel bars and the shore-connected bars ( Fig.~\ref{fig:dems}b,c). MudSeeds and seedsmud were also observed in suspension in the channels and deposited seaward of the ebb delta (without sprouting).
The distribution of bed elevations generally broadened in the experiments (Fig.~\ref{fig:bedelevationdistribution}). Initially, the carved channel rapidly shallowed by deposition of sediment eroded from the banks. After about 1,000~cycles, the channel-bar morphology had formed and the slower process of estuary widening dominated the trend in bed elevations. Especially in the middle reach ( Fig.~\ref{fig:bedelevationdistribution}b), the muddy shoals increased several millimetres in elevation, while the channels deepened. All three estuaries gained a broader bed elevation distribution with deeper channels and higher shoals in the middle reach, as well as in the upstream reach for the vegetated estuary. In the other reaches, the bed elevation distributions did not broaden much. In the upstream reach ( Fig.~\ref{fig:bedelevationdistribution}a), the channels became shallower for the sandy estuary and stayed constant for the muddy estuary, while the vegetated estuary developed slightly deeper channels. In the downstream reach ( Fig.~\ref{fig:bedelevationdistribution}c), bed elevations increased particularly in the vegetated estuary, while the sandy estuary remained the deepest.
The channel-bar patterns and bed elevation distributions were caused by the morphodynamics of channel erosion and migration, estuarine bank erosion, and bar formation and accretion. In the upstream and middle reaches of the muddy and vegetated and muddy estuaries, these processes reduced considerably compared to the control experiment ( Fig.~\ref{fig:dynamicsmapschange}). As a result, the upstream 7~m of the estuaries with floodplain remained narrower, especially of the muddy estuary. The downstream half of the estuaries (10--16~m) widened similarly but upstream the muddy estuary showed fewer channels (Fig.~\ref{fig:dynamicsmapschange}) and less lateral channel migration (Fig.~\ref{fig:dynamicsmapsage})  The hydrodynamics were characterised by numerical flow modelling for the entire tidal cycle on all measured bathymetries. At the end of the experiments, the path of maximum ebb velocity during the tidal cycle mainly follows a single channel in all three experiments, while the maximum flood velocity is more distributed over the width in the downstream half of the estuaries (Fig.~\ref{fig:velocitymaps}). The velocities in the upper reach are generally lower in the muddy estuary than in the sandy estuary, which is consistent with the lower width and the raised bars due to mud deposition. The vegetated estuary shows a striking difference with the other two: the higher friction of vegetated bars (compare Fig.~\ref{fig:roughnessmaps} and Fig.~\ref{fig:velocitymaps}) not only strongly reduces flow velocity over the bars, but also focuses the flow into the channels, even during the flood phase when the flow enters the system through the relatively wide mouth unconfined by vegetation.
To quantify the velocity patterns in the different experiments, the probability distributions of the flow velocities were calculated for the shallowest and the deepest parts in middle section, halfway and at the end of the experiments (Fig.~\ref{fig:velocitydistr}, consistent with the bed elevation percentiles shown in Fig.~\ref{fig:bedelevationdistribution}b). Comparison between 6,000~cycles and 13,000~cycles shows a reduction of flow velocity over the shoals (peaks of dashed lines shift to the left from Fig.~\ref{fig:velocitydistr}a to c and b to d), especially for the vegetated experiment. Comparison between the experiments at 6,000~cycles shows that the ebb and flood flow in the channels is lower and broader distributed in the muddy estuary ( Fig.~\ref{fig:velocitydistr}a,b), although the differences disappear towards the end of the experiments. The vegetated experiment, on the other hand, has a narrower distribution of high channel velocities around 6,000~cycles, and lower velocities over the shoals around 13,000 cycles when vegetation has settled more generally. Clearly, the vegetation baffles the flow by resistance on the shoals, whereas the mud reduces the flow in the channels.
The tidal prism is here not only calculated at the mouth but at every cross-section along the estuary to resolve more local effects of vegetation and mud \cite[as in][]{braat2019}. The tidal prism increased in the seaward direction and is the smallest for the experiments with mud ( Fig.~\ref{fig:tidalprismprofile}). After 13,000 tidal cycles the tidal prism in the mouth area had reduced most for the muddy experiment compared to 6,000 cycles. In the upstream half, the change was small though the tidal prism of the sandy experiment continued to increase. This is consistent with the rapid initial channel shallowing of the upstream reach ( Fig.~\ref{fig:bedelevationdistribution}) and concurrent infilling (Fig.~\ref{fig:crossections}). The spatial variation in tidal prism shows the expected seaward increase, but has a superimposed secondary pattern of around 6~m and 14~m. A similar pattern in the tidal prism for the initial bathymetry (dashed line in Fig.~\ref{fig:tidalprismprofile}) shows that this is likely due to a deviation of tidal flow generation by tilting from what is generally observed in natural estuaries. Specifically, in somewhat more open and less filled reaches of the estuaries, the tilting was visually observed to drive periodically reversing flow regardless of the connection with the mouth. Nevertheless, the landward penetration of tides reduced over time. The most upstream flood flow velocity was slightly increased in the muddy estuary as the flow was concentrated in a single channel and flanked by high mudflats, but the tidal prism at that point was already smaller than in the other estuaries.
The tidal prism changed through time in different ways along the estuaries (Fig.~\ref{fig:tidalprismtime}). The vegetated estuary shows a pattern of gradual increase of tidal prism until about 8,000~cycles followed by a decrease, unlike the muddy estuary. This can also be seen in the higher channel velocities in the vegetated experiment (Fig~\ref{fig:velocitydistr}a,b). The decrease is due to the gradual increase in vegetation cover as the recruitment events added up, and the particularly rapid expansion of vegetation after about 8,000~cycles (Fig.~\ref{fig:vegcovertime}). The tidal prism reduction in the vegetated estuary is approaching that of the muddy estuary after 13,000~cycles (Fig.~\ref{fig:tidalprismprofile}).
In the upstream reach, the tidal prism of the muddy estuary decreased rapidly in the beginning and then remained about constant, while that of the sandy and vegetated estuaries decreased almost linearly over time. In the middle reach, the tidal prism in the muddy and vegetated estuaries stay about constant after initially increasing, while that of the sandy estuary continues to increase nearly until the end. Close to the mouth, the tidal prism is the collective result of tides along the entire estuary (excluding a secondary effect of locally generated tides due to tilting) and the differences in magnitude are largest. Here, the sandy estuary has the largest tidal prism andin the muddy estuary the smallest byis about two-thirds, and70\% of that in the sandy estuary, and the tidal prism in the vegetated estuary takes an intermediate positionis about 80\% of the sandy control. The muddy and sandy estuaries initially show a rapid increase of tidal prism but then a gradual, though limited, decline. This is consistent with the declining depth in the downstream reach ( Fig.~\ref{fig:bedelevationdistribution}c). The ongoing decline at the end of the experiments shows that complete convergence to some equilibrium has not yet taken place, but the slowing of the change and the opposite trends in the middle and downstream reaches suggest that convergence is nearly reached.
The reduced tidal prism in the muddy estuary is not merely lower than in the other two experiments because a certain volume of mud was supplied that filled space: the total added volume was 0.013~m$^{3}$, which is only a small fraction of the difference in tidal prism between the sandy and the muddy estuary (about 0.5~m$^{3}$ during nearly the entire experiment; see Fig.~\ref{fig:tidalprismtime}). As also shown in Figs~\ref{fig:dynamicsmapschange} and \ref{fig:dynamicsmapsage}, mud had a system-wide morphological effect on the estuary development. Regardless of the limited filling, the mud reduced the overall channel dynamics.
The vegetated estuary shows a pattern of gradual increase of tidal prism until about 8,000~cycles followed by a decrease, unlike the muddy estuary. This can also be seen in the higher channel velocities in the vegetated experiment (Fig~\ref{fig:velocitydistr}a,b). The decrease is due to the gradual increase in vegetation cover as the recruitment events added up, and the particularly rapid expansion of vegetation after about 8,000~cycles (Fig.~\ref{fig:vegcovertime}). As a result, the tidal prism reduction in the vegetated estuary is approaching that of the muddy estuary after 13,000~cycles (Fig.~\ref{fig:tidalprismprofile}). It is unclear whether the muddy estuary would have filled further, given the mud supply, or whether the vegetated estuary would have been covered more extensively by vegetation with the ongoing seed distribution events. While the tidal prism at the end of the experiments was nearly constant, the erosion of the outer estuary banks, composed of pure sand, and the expansion of the ebb delta could slowly continue.

\section{Discussion}
The experimental results suggest that vegetation and mud have similar, but not the same, effects on the landward reduction of tidal energy. While mud fills the accommodation space to reduce lateral channel mobility and overall depth, the vegetation reduces the tidal flow through vegetationenhanced hydraulic resistance on the bars. Surprisingly, the enhanced bar accretion in the muddy estuary reduced the flow over the bars less than the vegetation despite the blockage of flow by mudflats growing up to the water surface. This is all the more surprising as the shallow experimental flow was probably laminar for a greater part of the tidal cycle \cite[][]{kleinhans2014a,kleinhans2015a,kleinhans2017a} which would increase friction more.
Equally surprising is the much lower lateral channel mobility in the muddy estuary than in the vegetated estuary, despite the fact that the mud deposits were much thinner than the channels \cite[][]{braat2019}, which allows for unhindered undercutting into the noncohesive sand underlying the mud. Moreover, the mud simulant, nutshell, was not found to be so cohesive as to reduce bank erosion, even after tens of days \cite[ Fig.~13 in][]{braat2019}. In contrast, the vegetation rooting could be as deep as the channels \cite[][]{lokhorst2019} but this did not reduce the mobility as much as the mud. The growth of vegetation in nature, even at supratidal level, causes high hydraulic resistance during high tides. This leads to reduced and often negligible flow on the bars and strong focusing of the flow in the channels as also found in experiments and models of river systems braudrick2009,vandijk2013a,oorschot2015,kleinhans2018}. This happens particularly in upstream reaches of the estuaries where the tidal dynamics are reduced sufficiently for vegetation to settle and where estuarine bars and mudflats can accrete to the high-intertidal and supratidal levels required for vegetation to settle \cite[][]{vos2000,woodroffe2016,lokhorst2018}. Possibly, the difference between the vegetated and muddy estuary occurred because the cover of vegetation is smaller than that of the mud, and given more time for recruitment, or more inundation-resistant species, the vegetated estuary might have developed more similar to the muddy estuary.
A morphological effect of filling of intertidal space by vegetation and by mud is the reduction of flow shear stress over tidal bars. This, combined with the increased resistance against erosion, diminishes the likelihood of cross-cutting bars by channels that would otherwise lead to channel braiding as in rivers \cite[][]{ASHMORE1991A}. The data suggest a transition from rapid channel avulsion in the control experiment to more gradual migration in the vegetated estuary and even reduced migration in the muddy estuary. This filling effect is paralleled in river morphodynamics, where initiation of braiding through chute cut-offs and unhindered bank erosion is inhibited by the vegetation and the suspended sediment on the floodplain. Both vegetation and suspended sediment reduce excess shear stress, regardless of whether the sediment is cohesive \cite[][]{vandijk2013} or non-cohesive \cite[][]{braudrick2009,vandijk2013a}. ThisNote that this inner-bend effect of floodplain on the channel pattern, unlike the usually assumed outer-bend effect of floodplain on eroding bank stability, works both in rivers and estuaries without rooting depth or cohesive sediment deposit thickness that approach the channel depth \cite[][]{kleinhans2018}.
The reduced channel cutting tendency is important for overall floodplain formation because channel migration is far more effective in eroding bars and removing floodplain by undercutting than direct overflow during flooding. This was also evident from the comparison between the vegetated and muddy estuaries with the control. In field data, the tendency to stabilise channels and reduce bar cross-cutting was also observed \cite[][]{swinkels2009,wang2015,vandijk2021} but the effects of increasing sand bar height, mud sedimentation and salt marsh expansion occurred simultaneously and could not be separated, unlike in the experiments. The only factor reducing the tidal penetration in such estuaries is tidal damping by the bottom friction, which increases with reducing depth and shallow bar area, and tidal damping by large flood storage areas, which were absent in the experiments. Friction increased more rapidly in the muddy estuary due to the upstream depth reduction and in the vegetated estuary due to the large relative surface area with vegetation ( Fig.~\ref{fig:vegcovertime}).
The two local effects outlined above, namely space-filling and flow resistance, could both lead to lateral constraints and tidal channel deepening, which would, according to the first hypothesis, enhance tidal energy in the upstream estuary and cause further landward tidal penetration. However, the long-term development of tidal prism in the experiments demonstrate a positive feedback between floodplain formation, channel morphodynamics and planform dimensions. The filling of intertidal space, on the fluvial-tidal transition and further seaward, causes a reduction in the tidal prism at the mouth as hypothesised in \cite{dehaas2018}. This is especially the case for the muddy estuary where accommodation space is filled with mud, and less so for the vegetated area where flow over vegetated bars is reduced. Regardless of the widening by cohesionless bank erosion, the tidal prism at the mouth reduced due to vegetation and mud and, in the sandy estuary, also due to shallowing. In this sense, the effect of floodplain formation on an estuary is different from that on a river, where the flow discharge is locally unchanged, as it is externally imposed. As a result, narrowing of the channel in rivers leads to deepening at the same time, which is not the case in estuaries where the tidal discharge reduces.
The long-term effects of a reducing tidal prism on the system are considerable. Where a large intertidal area with delayed outflow would have enhanced ebb-dominance and sediment export, its reduction due to floodplain formation may invert this tendency and cause import \cite[][]{friedrichsaubrey1988,dehaas2018}. In other words, mud deposition and vegetation development could cause large-scale filling of estuaries. This direct link between sedimentation and vegetation growth and estuary dimensions dominates over the effect of floodplain observed in rivers because the total flow discharge is modified in estuaries as opposed to rivers. As filling progresses, this zone is expected to shift seawards as well, but testing this requires experiments with initially unfilled estuaries and control on the landward sediment transport from the coastal zone. Experiments conducted in the Metronome after the experiments reported in this paper indeed showed that mud and vegetation tend to fill up unfilled lagoonal estuaries, given sufficient sediment supply from the coastal and fluvial boundaries for the vegetation to settle \cite[][]{weisscher2022metronome}. While those experiments show how coastal plains drowned in the early Holocene could fill, the present findings explain how initial estuary widening, following