Long-term sea level rise modeling of a basin-tidal inlet system reveals sediment sinks

Domain: earth_science
Published: 2023-11-06
Editorial outcome: accept

Abstract
Much of the world’s population lives close to coastlines and this proximity is becoming increasingly impactful because of sea-level rise (SLR). Barrier islands and backbarrier salt marshes, which comprise >10% of these coasts, are particularly susceptible. To better understand this risk, we model backbarrier morphologic and hydrodynamic evolution over a 200-year period of SLR, incorporating an erodible bed and a range of grain sizes. Here, we show that reduction in intertidal area creates negative feedback, shifting transport of coarse sediment (silt and sand) through the inlet from net export to net import. Imposing a modest marsh vertical accretion rate decreases the period of silt and sand import to 40 years (years 90 to 130) before being exported again. Clay is continuously exported thereby decreasing inorganic deposition on marshes and threatening their sustainability. Simulated marsh loss increases tidal prism and the volume of sand contained in ebb deltas, depleting coastal sand resources.

Introduction
Quantifying the physical response of coastal systems to SLR remains one of the most important tasks within the fields of coastal geology and engineering. During the 20th century, global (eustatic) Mean Sea Level (GMSL) rose at a rate of ~2mm/yr, but this rate has steadily increased, and by 2100, projections suggest a cumulative rise of between 0.79 and 1.46 m (RCP8.5)1. SLR increases the risk of coastal flooding and storm impacts, particularly for the ~10% of the global population who live in coastal areas less than 10 m above sea level2. Continued coastal population growth3, accelerating sea-level rise4, and increased storminess5 exacerbate this threat to coastal inhabitants, infrastructure, and economic activities. Ten percent of the world’s shorelines are fronted by barrier chains6 and half of these coasts consist of mixed-energy barriers backed by marsh and tidal channels and separated by numerous tidal inlets (Hayes 1979). The inlets provide a means of the tidal exchange between the coastal ocean and the backbarrier basin. Future coastal impacts to barrier coasts will largely be driven by SLR, but the extent of change will also depend on how barrier-related geomorphic features evolve in response to these forcings7. Although anecdotal examples and conceptual models have been put forward to predict the future of these systems, a rigorous quantification is needed to lower uncertainty and demonstrate theorized feedbacks. To date, research using modeling to predict the effects of SLR on basin geometry and inlet sediment transport trends is divided. Some studies predict that tidal inlets will import sediment 8–13, which is supported by field evidence14. Alternatively, other studies suggest that sediment will be exported as sea level rises15,16, retarding the ability of marshes to build vertically15. Here, we examine how gradual submergence of the backbarrier system by SLR will change the backbarrier morphology and hydrodynamics, which alters sediment transport trends for different grain sizes.

How sediment is re-distributed during the evolution of coastal systems depends greatly on the underlying hydrodynamics of the basin, which in turn are strongly influenced by the distribution of salt marsh and tidal channels. Tidal asymmetry, the difference in magnitude or duration between ebb and flood currents, is produced by distortion of the tidal wave as it propagates through tidal basins17,18. This occurs when the mean water depth is small, such that the geometry of tidal channels and resulting flow patterns are significantly different between high and low tide19. Imbalance in the flood and ebb periods impacts the associated current velocities; a shorter period transporting the same volume of water generates a higher velocity. The nonlinear dependence of the transport of coarse sediments on velocity means that even a slight asymmetry in velocity produces net bedload (sand) transport, facilitating sediment import if tides are flood-dominant or export if tides are ebb-dominant7,19. However, for suspended load (clay/fine silt), slack water duration dictates residual flux rather than maximum current asymmetries, due to the slower rate of settling19–21. Residual flood-directed transport of fine-grained sediment is enhanced when channel depth decreases in a landward direction, or if the velocity variation is slower near the pre-ebb slack than the pre-flood slack. This trend in net sediment transport can be counteracted by wind waves, which, due to the shallower water depths, maintain more sediment in suspension near pre-flood slack than pre-ebb slack, when tidal flats are flooded19,21. Under these conditions, variations in the wetted area impact slack water durations and therefore, the net transport of fine sediment. The direction of the net transport is controlled by the elevation of intertidal regions, with high intertidal regions compared to the channel depth being characterized by longer pre-ebb slack, promoting fine-grained import, while a greater area of lower intertidal regions has the opposite effect, with longer low water slacks and net fine-grained export. A large intertidal area also leads to slower drainage from flats to the channels during the ebb; this water surface gradient leads to a peak in ebb-velocities that can result in residual ebb-directed transport of coarse-grained sediment19,21,22.

If changes in basin morphology are neglected, then rising sea level will gradually increase water depths in the backbarrier throughout the tidal cycle. While the change in depth will be small relative to deep channels, water depths over the marsh platform could increase substantially. The increased depth over intertidal areas at high tide decreases frictional effects and allows faster propagation of the flooding tidal wave crest within the basin22. Relatively small deepening of the channels due to SLR will have little impact on the friction of ebbing flows within the channels. Finally, increasing tidal prism will also enlarge the channel cross-section, thus, with faster propagation of the flooding tide, there will be a smaller discrepancy between flooding and ebbing durations such that ebb-dominance is reduced. Thus, the gradual loss of intertidal storage area due to marsh submergence coupled with marsh edge erosion will serve to re-establish the natural flood-dominance of a progressive wave (due to nonlinear effects) or co-oscillating wave in moderate-length basins (due to frictional effects)19,22. Because sediment transport is related to a power function of velocity22, a slight shift to stronger flood versus ebb velocities will lead to net landward sediment movement through the inlet and within backbarrier channels22. For example, field evidence of landward sand transport in flood-dominated backbarrier by channels has been documented in Willipa Bay, Washington23 and in Essex Bay, Massachusetts24.

The response of tidal inlet and basin systems to SLR has previously been investigated with both semi-empirical or rule-based, and process-based models25. Several researchers have applied a sediment equilibrium model, aggregating morphologic response into volume changes of tidal flats, inlet channel, ebb-delta, and adjacent coast elements9,26. At two inlets along the Dutch Wadden Sea, the model predicts that increasing SLR rates induces a disequilibrium in element volumes that is compensated by expanding the inlet cross-section, as well as erosion of interior flats and the ebb-tidal delta8. Recent studies have also suggested that the demand of sediment in tidal basins is a product of increasing accommodation related to SLR12,13. Additional research has focused on process-based, morphologic models of conceptual tidal basins with varying geometries27,28. Using a schematized model of the Ameland Inlet9, one study found that initially flood-dominant hydrodynamics are enhanced with SLR, resulting in increased import of sand that is partially supplied from the eroding ebb-delta. Despite consistent sediment import, the tidal channel network and tidal flats are only maintained under low rates of SLR (0.2m increase from 1990 water level by 2100). Resulting morphologies show the development of relatively deep, narrow backbarrier tidal channels with multiple ebb-dominant channels dissecting the ebb-tidal delta9,29. This work was expanded to incorporate the development of a laterally unconstrained inlet-basin system with different SLR rates and varying tidal ranges30,31. Results show that, for a SLR rate of 5.6 mm/y, tidal prism increases due to a lateral expansion of inundated area and consistent growth of ebb-delta shoals. However, trends in residual sediment transport direction (import or export) were found to vary with tidal range30,31. Long-term (millennial scale) modeling of a conceptual, large, elongated estuary (80-km long, 2.5-km wide) focused on tidal asymmetries responding to the loss of intertidal areas due to an imposed SLR of up to 6.7 mm/y10. In all SLR scenarios, the basin shifted from exporting to importing sediment, consistent with developing overtides due to tidal asymmetry22,32, although at rates insufficient to prevent the intertidal area loss10. Recent work modeled SLR effects on sediment budgets in Plum Island Sound, Massachusetts, finding that SLR enhanced marsh sedimentation, while at the same time increasing the ebb-dominance of the system and export of sediment15. Another study tested the impacts of imposed marsh loss on six tidal basins along the U.S. East Coast, finding positive feedback whereby marsh loss reduced the sediment trapping efficiency of remaining marshes and enhanced ebb-dominance16. In a later investigation of Jamaica Bay, New York, the same authors33 suggest that sedimentation inside the basin is derived from marsh edge erosion, as well as from marine sources. Finally, studies focusing solely on sedimentation of the marsh surface indicate conflicting projections. For example, a meta-analysis of existing data suggest that most marshes will be stable34 which contrasts with eco-geomorphic modeling35 indicating that marshes are highly vulnerable to SLR. A recent global meta-analysis shows that while marshes appear to be presently resilient, they are increasingly vulnerable with accelerating SLR due to auto-compaction and subsidence36.

To address the very different conclusions of previous studies and investigate longer time scales and more alternative SLR conditions than possible with field studies, we undertake a rigorous, numerical investigation into changing basin morphology and hydrodynamics with SLR (Fig. 1). We improve upon previous research by using an erodible bed with a range of sediment classes (fine sand [200 μm], coarse silt [64 μm], clay [20 μm]) and study the response caused by SLR and a coupled SLR with a stipulated rate of marsh platform accretion. Thus, we allow for the full morphological evolution of the basin without intervention during the entire simulation period. We quantify relationships between SLR and the hydrodynamic and morphologic response of a representative tidal inlet-basin system. We specify a moderately sized basin geometry (12-km long) containing marsh and tidal channels, characteristic of mixed-energy barrier shorelines37 that are common throughout the world (Table 1). Importantly, through numerical modeling, we provide a quantitative relation between predicted morphological evolution (based on empirical, equilibrium relationships) and expected hydrodynamic behavior (developed from numerical studies), with emphasis on the varying responses of both coarse and fine-grained sediment. By imposing SLR on the conceptual inlet/basin system examined here, we test the theory that an expanding inlet reduces friction and alters the propagating tidal wave, increasing accommodation space as well as shifting currents from ebb- to flood-dominance.

Results
Basin Morphologic Response to SLR
Following a 200-year morphologic simulation, cumulative erosion and deposition for all scenarios: control with no SLR (Figs. 2a), 5 mm/y SLR (Fig. 2b), and 8 mm/y SLR with 3 mm/y marsh accretion (Fig. 2c), show a deepening of the inlet and backbarrier channels. Deposition occurs on backbarrier tidal flats and at the margin of the expanding ebb-tidal delta. Channel and tidal inlet deepening in the control simulation is a product of gradual adjustment of the backbarrier to the 1.5 m amplitude tidal range. Greater depths are attained in the simulations with SLR (Fig. 2b, Fig. 2c) due to continuing basinal flooding causing a steady increase in tidal prism. Moreover, the simulation with 5 mm/y SLR shows higher low- and high-tide levels, which decreases the intertidal area by approximately 13%. The morphological trends of the basin/inlet system (Fig. 2, Fig. 3. Supplementary Fig. 1) are consistent with tidal prism equilibrium relationships of inlet cross-sectional area38,39 and ebb-tidal delta volume40.

Broad comparisons of aggregate changes in basin geomorphology are valuable metrics of system response to SLR41,42 and were evaluated for each of the simulations (Fig. 3) to test the functional relationships among tidal prism and inlet area, ebb-delta volume, tidal channel volume, and tidal flat volume, because they are useful predictors of response to large scaled disturbances including SLR26,41,43,44.

With SLR, increasing tidal prism (Fig. 3a) is associated with increasing tidal inlet area (Fig. 3b), increasing volume of sediment sequestered in the ebb-tidal delta (Fig. 3c) and transfer of sediments from incising channels to accreting tidal flats (Fig. 3d). Results conform to established equilibrium relationships39,40,45,46 and the transgression hypothesis7 whereby the increasing tidal prism produces an expanding inlet cross section, ebb-tidal delta, and channel system, as well as a decrease in volume of tidal flats8. Without external sediment input, including sand that would be added from adjacent barrier islands, the inlet and bay channel incision provides sediment for ebb-delta and tidal flat accretion. For the control case, the tidal prism, channel volume, and tidal flat volume remain constant through time, albeit with small increases in inlet area and ebb-delta volume likely due to the initial basin configuration not yet being in full morphodynamic equilibrium since adaptation timescales of tidal basins to external conditions could be on the order of millennia47. Comparisons of predicted morphologic parameters using empirical functions of tidal prism44,45 show that for the simulations with SLR, the inlet throat is larger than expected, while the total volume of tidal channels initially falls within predicted ranges (Supplementary Fig. 1). The larger inlet cross-sectional area is consistent with the over prediction of inlet incision, potentially due to the absence of wave-driven nearshore inlet sediment supply. However, the volume of the backbarrier channels, where nearshore processes have less influence, indicate an overall basin morphology that is consistent with natural mixed-energy systems45.

Hydrodynamic and Sediment Transport Response to SLR
The morphology of a basin-inlet system is continuously shaped by the evolving hydrodynamics, and thus, we compare peak flood and ebb velocities at the inlet for each tidal cycle as a general indication of the net sediment transport patterns. Since the transport of non-cohesive sediment is a higher-order function of velocity48, an evaluation of peak velocities (in Fig. 4a) can be used to determine net direction and magnitude of sediment transport at the inlet (Fig. 4b). Our modeling indicates that peak ebb (channel-averaged) velocity exceeds the peak flood velocity until ~year 90 when they become equal for the 5 mm/y case. For the remaining 110 years of simulation, peak flood currents become dominant, reaching a maximum in year ~135 due to both an increase in peak flood velocities and diminished peak ebb velocities. Sediment transport trends mimic those of velocity, as expected (Fig. 4b), indicating for the first 90 years the inlet exports sediment and after that, it strongly imports sediment. In the control case, peak currents are relatively constant, and as such ebb-directed peak flow and sediment transport remain dominant for the entire simulation. For the 8 mm/y SLR case with manually imposed 3 mm/y marsh accretion (Fig. 4d), the shift to sediment import is modulated by the additional backbarrier sediment supply so that the fine sand and coarse silt fractions are imported for the years between 90 and 130.

For the control case, the constant, positive cumulative transport rate (Fig. 4c) indicates continued sediment export for all sediment fractions and total sediment load. For the 5 mm/y SLR case, the fine sand and coarse silt fractions are exported for the first ~90 years (87 and 93 years, respectively) after which time these coarser fractions are first imported and then strongly imported by year 135 (Fig. 4c). The model also shows that the total sediment flux discharging from the inlet persisted for another ~10 years after the net export of fine sand and coarse silt have ceased. Thereafter, the total sediment flux at the inlet shifts to importing sediment. Interestingly, fine sediment, such as clay, is continuously exported for the duration of the simulation. Due to its grain size, unconsolidated clay is easily suspended into the water column and can potentially be transported onto the marsh surface.

The shift from net sediment export to sediment import through the inlet for the 5 mm/y SLR case is also observed in backbarrier tidal creeks, where residual sediment transport patterns are ebb-dominant at the beginning of the simulation (Fig. 5a) and flood-dominant at the end (year 200; Fig. 5b). Before substantial SLR has occurred, residual transport in the main tidal channels is directed towards the inlet (Fig. 5a), but at the end of the simulation with 1 m of cumulative SLR, residual transport is directed landward in the main tidal channels. This trend indicates that sediment entering the inlet, due to its flood dominance, will be transported farther landward into the basin.

Backbarrier residual transport patterns for the 8 mm/y SLR 3 mm/y accretion case are also consistent with the basin sediment import and export trends seen in the 5 mm/y SLR case; however, channel residual transport is ebb dominant during the full simulation except for during a period between years 90 and 130 when creeks are flood dominant.

The eventual shift in net transport direction for both sand and total sediment is indicative of a shift in the tidal asymmetry from ebb- to flood-dominance, while slack-tide asymmetry (Fig. 6c) continues to favor fine sediment export19.

Hydrodynamic predictions compared with theory
Our conceptual tidal basin is moderate in length, such that the water surface slope within the basin is nearly horizontal throughout the tidal cycle. Horizontal tidal velocity is 90 degrees out of phase with the water level fluctuations so that slack tides occur approximately simultaneously with the high and low tides. This lack of progressive wave enables a simplified framework for examining tidal asymmetry based on classical hydrodynamic studies19 (Supplementary Fig. 5). For all cases, the basin is initially ebb-dominant, with this ebb-dominance persisting in the control case for the full simulation. The basin is characterized by deep channels and relatively high tidal flats. The initial morphology (referred to as Type I by Dronkers, 1986) produces a basin spatial-mean depth that is greater at low tide than at high tide, favoring ebb-dominance with higher ebb-directed tidal currents19,49,50. Likewise, deep channels compared to the tidal amplitude and large high-tide storage also produce ebb dominance22. The initial modeled mean basin water depth (Fig. 3e) is much greater at low tide than at high tide due to the deep channels and high elevation of tidal flats. With continued SLR and without adequate sedimentation on tidal flats (even with a proxy for organic marsh accretion in the 8 mm/yr SLR, 3 mm/yr accretion case), mean depths at high tide increase while mean depths at low tide decrease, reducing the mean depth differential that favors ebb-dominance.

In Type I basins, the tidal wave propagates faster in the deep channels than on the shallow flats, leading to a strong current during the last stage of the ebb-cycle when slower intertidal drainage produces higher water surface gradients19,51. This process is visible in the relationship between stage and velocity in a backbarrier creek (see Fig. 6a). Peak ebb-directed currents occur near the average tidal flat elevation (representative of the marsh edge in many backbarrier systems) of +0.5 m throughout the simulation, when tidal flats are nearly fully drained after high tide. Peak flood currents, however, occur with higher stages when flats are already inundated. While extensive intertidal area remains even in later years of the simulation, increased water depth over the zone due to SLR reduces frictional effects that slow the propagation of high water, thereby reducing ebb-dominance18,22. The continued inlet incision similarly reduces ebb-currents, as the ebb-directed residual current (Stokes return flow) generated by the Type I geometry are applied over an expanding inlet area50.

For moderate-length tidal basins without significant frictional effects, the acceleration around slack tide is proportional to the basin area, and inversely proportional to the rate of change of channel cross-sectional area19. For a Type I basin (deep channels and high, extensive flats), currents accelerate and decelerate more quickly at high tide than at low tide. This condition favors an extended pre-flood slack water and fine sediment export19. While the increasing inundation depth over the extensive tidal flats with SLR shifts the basin away from the idealized Type I (favoring import of fine sediments), a counteracting effect reduces this effect. The tendency of sediment import increases as the period of high slack water increases, which allows more fine sediment to settle out of the water column over tidal flats20. However, as SLR increases, the water over the tidal flats is continually deepening, despite marsh accretion, which increases the required settling time for particles to reach the substrate, thereby decreasing the amount of sediment deposited on the flats.

Changes in flood/ebb asymmetry and resulting net sediment transport
The duration of slack tide before flood for both the control and the SRL case (Fig. 6c) remains longer than the slack tide before ebb throughout the simulation. The longer period of low water slack allows greater deposition of suspended sediment in interior tidal creeks while tidal flats are exposed. Persisting throughout the simulation, this discrepancy in slack tide durations promotes the continued export of fine sediments seen in all cases (Fig. 4c, Fig. 4d). The long-term export of clay in both SLR cases is an important finding, indicating an enhanced vulnerability of backbarrier salt marshes, dependent on the supply of fine suspended sediment for mineral accretion52–57. The presence of wind-generated waves within the basin (a process not included in this model formulation) would naturally serve to further increase fine sediment export by reducing deposition over shallow tidal flats during the slack water period before ebb19, and offshore waves would create a more-realistic ebb-delta morphology characterized by an arc-shaped bar and single main channel.

The impacts of vegetation on the flow across the marsh surface and resulting influence on sediment transport patterns are also neglected in the current model, though results from previous work aid in determining the implications of this simplification. Vegetation would colonize tidal flats once the elevation exceeds mean sea level58 (Fig. 2), which would enhance fine sediment deposition and vertical accretion59,60. Accretion of the marsh platform, as well as building of subtidal flats to elevations conducive to vegetation colonization is highly dependent on the suspended sediment concentrations in the inundating tide53,61–64. The persistence of tidal distortion and the continued export of fine sediment would gradually reduce the supply available for deposition within the basin, including vegetated regions57,65,66. This condition, if combined with acceleration in SLR would lead to an increased rate of inundation, an effect corroborated by a modeling study67 of a tide-dominated, funnel-shaped estuary with eroding salt marshes, despite the presence of vegetation on tidal flats decreasing the export of fine sediments.

Elevated tidal flat regions relative to the rising mean high-water level, however, could maintain the Type I basin behavior due to deepening channels without increased tidal flat inundation. Vegetation within the basin would likely enhance channel erosion with SLR68,69 such that the ebb-tidal delta volume would grow commensurate with increasing tidal prism. The eco-geomorphic processes that determine the rate of marsh and tidal flat accretion relative to SLR rates are generally site specific34,56 and depend on presence of absence of vegetation as well as dominant vegetation species coverage70 but could promote tidal flat submergence or persistence in the modeled conceptual basin, with corresponding impacts to the evolution of tidal asymmetries and ebb-/flood-dominance70.

Overall, our results show a shift from sediment export to a period of import with SLR. This is counter to recent findings16 indicating a positive-feedback whereby marsh loss reduces the sediment trapping efficiency of the remaining marsh and enhances ebb-dominance. This conclusion16 was based solely on a reduction in backbarrier deposition of suspended clay, which was determined by manually (in their model) releasing a fixed quantity of sediment in the backbarrier and evaluating where it was transported and deposited after a period of 30 days without allowing the bed to erode or aggrade. Moreover, the study16 accommodates increasing tidal prism by widening the channel without deepening the inlet, a process shown to reduce ebb-dominance (in our study). Additionally, our study shows that SLR deepens the inlet including the backbarrier channels, which enhances flood dominance causing an influx of coarse sediment. Our model demonstrates the importance of co-evolution of the inlet-basin system forced by SLR and increasing tidal prism. Furthermore, our study is consistent with previous findings showing that with increasing tidal prism: (1) fine-grained sediment is exported15 (2) inlet cross-sectional area increases39,46, (3) ebb-tidal delta expands17, (4) backbarrier tidal creeks enlarge33, and (5) sand is imported9,31.

Methods
System Geometry and Physical Setting
We used an idealized basin so that relationships can be easily quantified and compared with theory. Both hydrodynamics and morphology are evolved over decadal to centennial timescales, complementing spatially- and temporally limited field studies of natural systems. The model is forced at the open-ocean boundary with a tidal signal superimposed by varying SLR scenarios. The evolving inlet and basin hydrodynamics are tracked using time-series outputs of backbarrier water level and inlet throat tidal currents. Sediment volume change for the morphological elements is calculated using bathymetric surface differencing, and sediment exchange between the basin and open coast is tracked using integrated fluxes through the inlet.

The conceptual inlet-basin system we used for the model experiment was evolved dynamically with fully coupled hydrodynamics, sediment transport, and morphology from an initial flat bed bathymetry (Fig. 1b). The model hydrodynamic and morphologic grid consists of an elongated basin of approximately 15 km by 5 km (with 50 m resolution) and a 30 km alongshore by 10 km cross-shore section of the nearshore. We started with a theoretical maximum basin depth of 2 m without predefined channels. We then forced the model with a 1.5 m amplitude semidiurnal, sinusoidal tide at the seaward boundary and ran a 2-year simulation to dynamically evolve the bathymetry using computed sediment fluxes to an near equilibrium condition employing a morphodynamic upscaling factor of 100 (Delft3D MORFAC feature), generally consistent with or less than values used in other similar modeling studies9,45. Using a symmetrical, undistorted tidal signal at the offshore open boundaries ensures that any emerging asymmetries are entirely due to variations in the inlet and basin geometry with water level increases19 (distortion of the tidal wave over the nearshore zone between the offshore boundaries and tidal inlet is negligible). The final bathymetry following the 2-year simulation was used as the initial bathymetry for the experiments we performed here. While a 200-y morphologic timescale simulation is inadequate to achieve full dynamic equilibrium with no further bathymetry changes47 (Fig. 2a), both the volume of backbarrier morphologic features (Fig. 3) and net sediment fluxes (Fig. 4c) have reached steady-state conditions (indicating dynamic equilibrium of aggregate morphology) onto which perturbations could be imposed. Basin dimensions are fixed, mimicking the anthropogenic infrastructure or steep uplands that limits lateral migration of many coastal wetlands77. The simulated tidal channels are generally deeper than those found in prototype tidal basins but are consistent with experimental channels generated using similar methods29 (Supplementary Fig. 2, initial basin hypsometry at start of experiments).

Basin Strategy
We purposely chose basin dimensions (5 km by 15 km) and tidal range (3 m) that are representative of backbarrier systems along mixed-energy barrier island coasts (sensu: Davis and Hayes 1984)78, for example Plum Island Sound in northern Massachusetts (in Fig. 1a). As seen in Table 1, mixed-energy coasts with a range of physical settings (like our basin model) exist throughout the world; barrier island coasts comprise 10% of the world’s shoreline. Essential characteristics of these backbarriers include their moderate basin lengths and relatively deep channels that in combination produce a Dronkers Type 1 standing-wave tidal signature. In addition, like our modeled system, their backbarriers consist of a marsh (or upper intertidal flat, e.g., East Frisian Islands, Copper River Delta barriers) incised by tidal channels and an accompanying tidal inlet fronted by well-formed sandy ebb-tidal deltas. Moreover, as demonstrated by examples in the Table 1, the vertical accretion rate chosen in the model is well within range of mixed-energy barrier systems. Finally, it should be noted that modeling results do not change by using a more symmetric drainage geometry because the hydrodynamics (yielding standing wave conditions) are dependent on basin length from the inlet mouth and channel morphology.

Experimental Design
Multiple hydrodynamic and morphologic simulations were run for comparison: a SLR case where a 5 mm/yr linear SLR is superimposed on the 1.5 m amplitude semi-diurnal, sinusoidal tide, a control case with the same tidal boundary conditions without SLR, representing still-stand, early Holocene conditions79 and a higher SLR case (8 mm/y) with marsh platform accretion of 3 mm/y manually imposed every 5 years of simulation. With the same rate of SLR relative to marsh accretion (i.e., 5 mm/y), the 8 mm/y SLR run investigates the influence of basin elevations and hypsometry interacting with higher SLR rates expected after 20501 and the influence of any organic accretion that is not included in other simulations. A 5-yr marsh platform accretion update interval was chosen to maximize the simulation time between manual bathymetry updates while limiting the cumulative accretion between updates to a reasonably small value that would not impact model stability when instantaneously imposed (sensitivity testing also showed minimal differences in cumulative flux results among update intervals of 2, 5, and 10 years). Additional simulations with varying rates of SLR and marsh accretion were conducted, with the three cases presented here being representative, and respective elevations of the Mean Low Water (MLW), Mean Sea Level (MSL), and Mean High Water (MHW) tidal datums during the three simulations shown (Fig. 1c, Fig. 1d, Fig. 1e). While previous modeling studies of inlet and basin response to SLR used a single, representative sand fraction9,10,30, we employ three sediment classes: 200 μm (fine sand), 64 μm (non-cohesive coarse silt), and cohesive clay with a fall velocity of 0.25 mm/s (corresponding to an approximate median grain diameter of 20 μm assuming Stokes’ settling;48). The use of multiple sediment classes provides the potential to capture differences in net behavior of fine and coarse sediment under dynamically evolving basin geometry and changing tidal asymmetry. We employed a homogeneous and uniform stratigraphy throughout the basin and modeled area based on equal volumes of the three grain sizes. The sediment transport module used a critical shear stress for the erosion of cohesive sediments of 0.25 Pa, vertically uniform mixed stratigraphy initially composed of approximately 43% fine sand, 43% coarse silt, and 14% clay, and horizontally uniform sediment properties. The erosion and deposition of cohesive sediment are calculated using the Partheniades‐Krone method (critical shear stress of 0.25 Pa, and erosion rate parameter of 0.0001 Kg/m2/s), and transport of non cohesive sediment is calculated using the Van Rijn formula48,80. We specified a sediment thickness of approximately 7 m to avoid limiting erosion, beyond which we used a non-erosional depth of 7 m to represent reasonably consolidated material or bedrock that would not easily erode for the timescales simulated. The dry cell erosion factor was set to one to allow tidal channel lateral migration (Supplementary Table 2).

Inclusion of wind-waves in the model show their impact on sediment transport is limited and localized, particularly in the backbarrier due to the narrow basin geometry. The ebb-tidal delta and adjacent shoreline are areas where waves augment sediment transport processes. Our modeling results of variable conditions show that waves produce limited net sedimentological change in the basin. For example, using a scenario that simulates 100 years and imposing a 5 mm/yr SLR, identical to a previous run, and using a schematized wave with an oblique wave approach (75-degree), a 6-second period, and 0.25-m wave height, we see that the seaward portion of the ebb-tidal delta undergoes uniform erosion while the region inside the inlet experiences areas of slight erosion and deposition (see SI for more detailed results and discussion). It is noted that events triggering wave-induced sediment transport inside the basin are highly infrequent and exceedingly diminutive when compared to tidal transport. We acknowledge the importance of waves in modifying the ebb-tidal deltas and resuspending fine-grained sediment in certain nearshore settings81, which affect basinal sediment exchange with the coastal ocean. However, this study focuses primarily on the backbarrier basin and sediment transport is dominated by tidal currents, particularly at the inlet entrance, main channel, and inside the basin.

Implementing an accretion rate
Representative accretion rates were chosen based on measured values in both vegetated and unvegetated regions, according to elevation. Applying an elevation-related accretion rate, using empirical data, has previously been shown to provide very similar results to the implementation of a vegetation-based morphological model, such as the Marsh Elevation Model (MEM) that computes accretion rates based on biomass production and inorganic sedimentation, but with lower computational expense. For example, previous analysis82, using an accretion rate based on average values from the literature, estimated the conversion of a New England marsh from high to low marsh by 2055 (Authors Fig. 5, panel 1)82. Using a high rate of sea level rise condition, similar to the RCP 4.5 scenario previously used82 (both reaching +1 m in 2100), in the same marsh system, but using a fully parameterized MEM marsh accretion model83 found the conversion to occur between 2045 and 2070, and most likely around 2058.

Vegetation roughness sensitivity analysis
The impacts of vegetation on the flow across the marsh surface and resulting influence on sediment transport patterns are neglected in the model experiments presented herein. Additional sensitivity analyses were performed that utilize the Delft3D trachytope roughness schematization (as a function of vegetation stem height and density according to the Baptist 2 model84) that increases bed roughness over the marsh platform84, defined as the basin areas with elevations between the time-varying MSL and MHW elevations. For the 5 mm/y SLR case, inlet sediment fluxes were negligibly impacted despite minor increases in marsh deposition (Supplementary Fig. 3). For the 8 mm/y SLR, 3 mm/y marsh accretion case, enhanced bottom roughness slightly increases ebb currents during the middle portion of the simulation (approximately years 80 through 140) which increases export of coarse sediments relative to the simulation with no trachytope roughness, though flux trends outside of this period are minimally impacted (Supplementary Fig. 4).

Evaluation of water and sediment fluxes and analysis
The analysis of net sediment transport trends was made possible by use of a cross-section across the inlet of the system, to correctly account for all sediment fluxes for each of the sediment classes used. Sediment fluxes at this location were integrated to determine cumulative transport. Similarly, inlet geometry information such as inlet area, tidal prism volume, instantaneous and cumulative water flux, water velocity, and water level information were also evaluated at this location to establish correlations and facilitate analysis used in the paper, including comparison to theory.

Data availability
The data generated by the simulations in this study can be reproduced using the modeling setup files provided in a public repository (https://doi.org/10.5281/zenodo.7672511). All other data generated are provided in Supplementary Information/Source Data Files.

Code availability
The numerical model used in the analysis is the Delft3D-4 modeling suite and is available in the public domain. The software and computer source code are available at https://oss.deltares.nl/web/delft3d/downloads.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "I thank the authors and the editor for the opportunity to review this manuscript. I thoroughly enjoyed reading the results and discussion and recommend the paper for publicafion pending minor edits.\nKey results\nThe authors use idealized modeling based on realisfic estuarine geometry to explore the effects of sea-level rise (and background interfidal accrefion) on backbarrier and inlet sedimentafion and hydrodynamics. The key important finding is that, as predicted in the runaway transgression conceptual model, the ebb fidal delta and flood fidal delta eventually sequester more sand, which along a real barrier coast would starve the adjacent barrier islands of sand (in addifion to the sand scoured from the inlet thalweg). Addifionally, the authors find that estuaries have the potenfial to import sediment in the long run, an idea that runs counter to other recent work. As such, the work contributes meaningfully to the debate around the fate of salt marshes (and the general response of mixed-energy backbarrier estuaries) in the face of sea-level rise.\nValidity\nThe model-derived data and interpretafions are robust. While exact detail and assumpfions can be debated and discussed, the approach and conclusions are scienfifically valid. The authors’ conclusions are supported by the results of the modeling.\nSignificance\nThese results are broadly relevant and significant. The authors provide new insights on estuarine response to sea-level rise and add to ongoing conversafions about the morphodynamic response of mixed-energy backbarrier marshes to sea-level rise. The results are relevant not only to acfive discourse about the fate of salt-marshes, but the big-picture takeaways and conclusions will aid coastal managers in understanding potenfial pathways along which estuaries (and their associated sediment budgets) may evolve with sea-level rise.\nData and methodology\nI am familiar with the hydrodynamic and morphologic data the authors generated and am comfortable evaluafing its validity. The authors rely on idealized physics-based numerical modeling to address a fimescale that cannot be reached based solely on field data. The model used (Delft3D) is one of a few commonly used for this type of scenario modeling and has been around for nearly two decades. The authors clearly state their assumpfions and the limitafions of the approach.\nAnalyfical approach\nThe authors primarily rely on straight-forward fimeseries data and surface-change maps. These are more than sufficient at communicafing the relevant results.\nSuggested improvements\nThe authors intenfionally focus on three key scenarios in their modeling and jusfify their reasons for that. Addifional data from the three modeling scenarios or other scenarios run does NOT need to be presented here.\nClarity and context\nI found all parts of the text clear and easy to follow. The authors rely on numerical methods and a physics-based model, which can be challenging to describe to all readers. However, the authors do an excellent job of clearly explaining their methods and assumpfions. For the rare occasions where clarity could be improved (select figures, occasional lines of text), I direct the authors to my line item comments.\nReferences\nThe authors cite a broad literature base, including numerically-focused papers, field-informed papers, and those that are a mix of the two approaches. The authors are clearly familiar with both the foundafional literature on estuarine dynamics, as well as more recent literature relafing those dynamics to the fate of salt marsh ecogeomorphic systems. I do not see any noficeable gaps in the literature cited. Furthermore, the authors center this work in the relevant literature and engage with that literature in the discussion.\nLine Item Comments and Suggesfions:\nMain Text\nLine 219 to 221 – This text reads like discussion. I suggest moving it there.\nFigure 3 Panel E – The capfion is doing a lot of the work here. It certainly helps clarify what is going on. I suggest a minor tweak to the y-axis label so that it reads “Mean Basin Water Depth (m)” to match what is described in the capfion.\nFigure 4 Panel B – Y-axis label is hard to read and confusing. I think it is referencing total and individual fluxes but the capfion could address that (similar to how the authors' treat panel C). I suggest remaking the axis label.\nFigure 4 Panel D – There is no capfion and it needs to be clearer that the reason for having C and D is simply to show the 5 mm/yr versus 8 mm/yr cases. The change in y-axis scale also needs to be clearer. I found myself staring at this figure trying to make sense of it for much longer than necessary. A capfion as good as the others in this paper would go a long way.\nSupplementary Materials\n“SRL” (2 places) should be SLR. Suggest defining sea-level rise (SLR) on first instance in supplementary materials since it is separate from the main text.", "reviewer_2": "The manuscript describes a study dealing with a very important problem: the impact of sea level rise on fidal inlet systems. The findings would potenfially be very relevant for the sustainable management of coastal system. The study is based on process-based morphodynamic modelling of an idealized fidal basin. Compared to a similar previous study (Dissanayake et al., 2012) the model is extended by including mulfi-fracfion sediment transport, viz. three fracfions (sand, silt & clay) instead of a single sand fracfion. However, instead of focusing on a single real-world fidal inlet system (Ameland Inlet in the Dutch Wadden Sea) by the former study the present manuscript claims that the findings are relevant for mixed-energy fidal inlet systems that occur throughout the world. I think that this is a too far-reaching claim, as the model simulafions concern only one idealized fidal inlet. Thus, no variafion in basin geometry, inifial bathymetry, inifial boftom composifion, and forcing condifions is considered. It is well known that the response of a fidal basin to (changing) sea level rise, e.g. whether (accelerafing) sea level rise causes extra import or extra export, very much depends on its morphology (Friedrichs et al., 1990). The modelling study as presented by the manuscript can at most be relevant for a certain group/category of fidal inlets in the world. However, it is not clear which fidal inlets the modelled case would represent, as some essenfial characterisfics of the idealized basin are not presented. It would help if the hypsometry of the basin was presented. Moreover, the modelled case does not represent mixed-energy fidal inlets as waves are ignored in the model.\nAnother concern of mine is that no validafion of the used model has been presented. Not any comparison of the model results after the spin-up simulafion, which are used as inifial condifions (bathymetry, and boftom composifion?) for the simulafions with sea level rise, with any real-world case is presented. Even though the idealized case cannot be compared with any specific case, at least some essenfial morphological and sedimentological characterisfics should be qualitafively compared with real-world cases. One of the findings that the fine sediment fracfions, especially the clay fracfion sediment, are exported due to sea level rise is against the finding from a recent study for the Wadden Sea based on field observafions (Colina Alonso et al., 2021). I am afraid that the finding in this modelling study is due to some specific sefting concerning e.g. the boftom composifion.\nThe conclusion that “Sediment sinks on the ebb-delta and within the backbarrier system will be at the expense of proximal sediment reservoirs“ is not based on the presented modelling results. As waves are not included in the model the model results do not show sediment transport from the adjacent coasts to the ebb-fidal delta.\nThe manuscript does not include all essenfial informafion concerning the model set up. Which transport (/erosion) formulafions are used for the three sediment fracfions? How do you disfinguish interfidal flat and marsh plat form (or are they the same)? Unless the model files are made available the presented informafion does not allow someone else to reproduce the presented modelling results.\nDetails\nLine 71-73. Also for fine sediment maximum current asymmetry has influence on the net residual flux in addifion to the asymmetry in slack water durafion. Which of the asymmetries is more important differs from case to case.\nLine 79-82. The statement on the relafion between slack water durafion asymmetry and direcfion of net transport is wrong. The correct relafion is: longer pre-ebb / HW slack promotes import of fine sediment, and vice versa.\nLine 92-93: what is meant by “the flood fidal wave”? Highwater? Or rising fide?\nLine 108-109. The predicted decreases of the fidal flat volume and ebb-fidal delta volume are not due to erosion but due to the rising sea level. The volume of interfidal flat in the basin is defined as the sediment volume between MOVING LW and HW. More recent results on impact of sea level rise on the Dutch Wadden Sea are reported by Lodder et al. (2022) and Huismans et al. (2022).\nLine 210. What is “cumulafive transport rate”? Cumulafive transport often (e.g. in the output of Delft3D) refers to the fime integral of sediment transport rate, but in Fig.4c it has the unit of sediment transport rate.\nLine 292-293. The fidal flat above MSL vegetated? To my knowledge, the transifion between bare mud flat and vegetated marsh is around MHW. I do understand that the used model only includes a single fidal consfituent, so MHW cannot be used.\nLine 327. 911?\nLine 396. The open boundary? There are three boundaries in the sea.\nLine 397. The fidal wave also deforms as it propagates in the shallow sea outside the inlet.\nLine 456-458. Waves also influence residual sediment transport as they can cause sediment concentrafion difference between inside and outside the inlet.", "reviewer_3": "General:\nThe manuscript is generally well wriften, and of high quality.\nI really like to detail and thought put into the beginning of the discussion.\nUnfortunately is the chosen main message not always clear which is reflected in inconsistencies in the manuscripts structure.\nMore specifically:\n1. it is unclear whether to focus lies on the morphological backbarrier basin response to SLR or the interacfion between vegetated and unvegetated plafform in response to SLR\n2. it is unclear whether the main quesfion focuses on the impact of mulfiple grainsizes on the basin response and how applicable this would be to other systems?\n3. how important is the expansion of the ebb-fidal data, how is this incorporated in the model?\nI am not saying these sub-quesfions could not be linked, however in the current form this link remains unclear to the reader --> addifionally what is the main message the reader can take home from this paper, the current manuscript structure more closely reflects a submission to a specialized journal like JGR than nature communicafions?\n4. Broader impact,the manuscript protrays the results to be generally applicable to backbarrier salt marshes, however it remains uncertain how representafive the phyiscal- and boundary condifions of the chosen test case (i.e. Plum Island sound) is for barriers world wide. For instance even along the US east coast we encounter a wide variety of back barrier basin sizes and forcing condifions(mixed, mixed-fide, wave-dominated) at the seaward side. For instance mixed energy systems as indicated in table.1 have vastly different dynamics in barrier inlet and thus sediment fluxes, for instance waddensea inlets act as sinks for liftoral sediment transport except sediment transported by sediment bypassing around the ebb-fidal delta.\n5. Focusing on the specific model case study, how well is the model capable reproducing the hydrodynamic characterisfics of the model system, e.g. fidal asymmetry, slack water durafion. How well is the model, on average able to reproduce the distriubfion of different sediment types as shown in Fig.1, finer(clay silt) and coarse(sand) sediment types?\n6. Vegetafion: I appreciate the sensifivity study carried out by the authors, tesfing the impact of vegetafion presence on the plafform. It is not fully clear which vegetafion parameters have been tested, where on the plafform they where implemented?\nabstract:\nThe abstract is not easy to understand and fails to summarize the main points.\nMore specifically:\nLine 21: from the abstract the effect of imposed salt marsh accrefion is unclear,\nwhich trend gets diminshed, the shift from export to import?\nLine 22: What do the authors mean by the trend for sand is more subdued? How is does clay\nimport or export change with or without saltmarshes?\nLine 23: \"This loss of sand will threaten barrier resources and infrastructure\" remains unclear\nmain text:\ngenerally difficult to follow\nline 33: rephrase \"the ~37% of coastal populafion that live there\"\nline 37: what are the authors referring to, what type of coastal systems do they focus on?\nis this true for all systems,.. rocky and sedimentary coasts? cliff erosion and dune\noverwash migth appear at a specific type of coastal systems, however are they the main\ndriver of coastal hazards ?\nLine 40: are the barriers themselves heavily developed, which systems do the authors have in mind?\nor are the authors referring to the back-barrier basin?\nBefore this line, for the reader to appreciate the subject ot this study a short introducfion\nin barrier-systems needs to be given, what kind of morphological units can we disfinguish, how can they\nstructure barrier dynamics?\nLine 45: What do field observafions reveal ? Is this proposed gap a problem with our ability to model\nbarrier systems or a trend also observed across real systems ?\nThe proposed summary is very difficult to follow:\n\"Some studies predict that fidal inlets will import sediment 8–10 or that fidal range will control net inlet\ntransport pafterns 11, and more recent studies suggest that sediment will be exported as sea level rises\n12,13, retarding the ability of marshes to build verfically\".\n--> how is this sentence linked to the underlying processing increasing vs. decreasing fidal prism,\nincreasing vs. decreasing load of suspended or bed load sediment,.. are there also rivers discharging\nsediment into the backbarrier lagoon? what is the impact of waves, vs. fides, which process is dominant,\nwhen and where?\nLine 49: the research quesfion is unclear ?? in general backbarrier lagoons are characterized by finer\nsediment types, such as fine sand, silt and clay. Is fine sediment considered ? What do the authors mean\nby sequestrafion of sand?\nLine 52: Especially flood fidal delta evolufion is governed by waves by litoral drift (longshore transport)\nand sediment bypassing caused by oblique coastal waves ! --> please revise , .e.g. De Swart, H. E., and J.\nT. F. Zimmerman. \"Morphodynamics of fidal inlet systems.\" Annual review of fluid mechanics 41.1\n(2009): 203-229. what kind of barriers are the authors referring to, fide-, mixed- or wave-dominated\nbarriers since the realfive contribufion of processes\nwill very as will ebb and flood-fidal delta volumes, shapes and dynamics? e.g. using the classificafion of\nHayes 1979\nLine 58/supplement: I recommend for the authors go over the supplementary text and remove present\ntypos:\nMoreover, the discussion on the marsh plafform keeping pace with sea level rise, seems\nto jump between an oversimplified 0d approach(1st paragraph) and a more detailed/realisfic marsh\nplatorm, levees and channel approach (2nd paragraph).\n--> i suggest for the authors to:\n1st merge this to points-of-view in a cohesive text\n2nd since salt marshes seem to exert important control on the backbarrier system\nin respect to the posed research quesfions I propose to move at least part of it\nto the main text !\nLine62-85: is an excellent paragraph and in my opinion should be moved into the main focus of the\ncurrent study\nLine 98: Will the net import of sand into the inlet lead to different cross-secfional areas in fidal channels\nand shallower backbarrier basin depths ? Will sand be also transported onto the marsh plaffrom?\nIs an increase in transport capacity to be expected leading to coarser parficles being deposited\non interfidal plaffroms. If so has this been observed in previous field studies? the provided references\nmainly point to a model study (friedrichs and aubry '88), and a review\nfrom Fitzgerald '08) ?\nLine 122- 138: different impressions on marsh survival and ebb-flood dominance originate from field and\nmodel exercises with varying complexfiy? I think here the authors miss a chance to jusfify the current\nappraoch, i.e. what do we know from field studies what are their boundaries, what do we need models\nfor (and what are there boundaries)\nLine 138: current research quesfion\nLine 139: i think using a nummerical model does not represent a theorefical invesfigafion, or are the\nauthors referring to something else?\nLine 140-143: here the research gap and quesfion remains unclear and the reader is provided with\ndetails, which are appreciated but unforunately without sufficient context.\nLine 143: \"Thus we allow for full .\" unclear compared to what kind of model?\nLine 147: Table.1 incomplete how does sediment fluxes and fidal ranges compare?\nLine 178ff: reference missing\nLine 223-224: which figure shows slack-fide asymmetry ?\nLine 229: rephrase\nLine 239-288: is an execellent discussion which should be put more in the focus of this study\nLine 253: it think the autor mean infilling of the channels which could be stated more explictly\nLine 298: I am not sure the reference to Aubry friedrichs is applicable here\nDiscussion:\nLine 313 if the a Main aim was to disproving results by Donatelli 2020, and thereby indicafing a posifive\nfeedback between marsh loss and sediment trapping efficiency this should have been indicated earlier?\nLine 398: was the bathymetry in some dynamic equilibrium? unclear using Fig.3 and Fig.4c?\nLine 410: how comparable are the forcing compared to your system as in sediment supply and fidal\nrange,... which might alter their dynamics as shown in line 244ff. Ebb-fidal dela volume is dependent on\nwave and fide dominance, which raises the quesfion to how many system Plum Island is comparable\ntoo?\nLine 419: see point Line 410\nLine 446: specifics of the model setup is missing, sediment transport equafions, treatment of mixed\nbeds, if not in the main arficle this should be present in the appendix so the study stays reproducible.\nLine 463: It is unclear how the MEM implemented, I understand that not the whole model can be\ndescribed, however sufficient informafion should be present to interpret the results, how does\naccrefion rate change over space?\nLine 471: insufficient details describing vegetafion roughness tests."}, "author_response": "Response: These lines have been moved to the Discussion\nResponse: We have changed the y-axis title to read: Mean Basin Water Depth.\nResponse: The Y-axis has been changed.\nResponse: We fixed the caption for Panel D\nResponse: This has been done.\nResponse: While the system we study is a single inlet system, the system geometry, and physical characteristis represent mixed energy systems, and as outlined in Table 1, there are many similarities of the system studied to many other systems worldwide. As shown in Table 1, this type of barrier island coast occurs throughout the world. Moreover, this type of backbarrier morphology and geometry tends to produce ebb-dominated inlet channels. Exceptions to this characterization occur where there have been significant human alterations (e.g., dredging at Saint Mary’s Inlet, GA; tidal basin shortening by dam constructions along The Netherland coast).\nResponse: We have included the basin hypsometry in the SI. However, it is beyond the goals of this paper to investigate all the possible backbarrier variability as listed by Reviewer 2. These are admirable goals and hopefully will be pursued by us and other investigators in future studies. We chose to limit our study to standing wave systems that produce ebb-dominant inlet channels so we could investigate how different grain sizes will respond to backbarrier evolution forced by SLR. We added a statement in the paper acknowledging that variability in backbarrier geometry and hypsometry could and likely would vary results from this conceptualized model. (see: Figure S2)\nResponse: We are investigating the evolution of the backbarrier systems as a consequence of SLR. Because these basins are characterized by marsh and tidal creeks with limited open-water area, we do not consider waves an important forcing agent. Wave energy is important in affecting the morphology of the ebb-tidal delta and the inlet shoreline but plays a very minor role in hydrodynamics and sediment transport in the backbarrier. Also, the sand volume of the ebb-tidal delta is primarily a function of the tidal prism as noted by Walton and Adams, 1976.\nResponse: We have added comparisons of model results to the Plum Island system and added this to the SI. Basically, we show that Plum Island Sound has a geometry consistent with that of modeled basin and experiences standing tidal wave signature. We also demonstrate that like the modeled basin sand is imported through the inlet and deposited on a large backbarrier sand shoal known as Middle Ground Shoals (flood-tidal delta).\nResponse: We must take exception to this comment. We had considered the Alonso et al (2021) study, but it was noted in the paper that the import of clay was not attributed to SLR, but rather to closure of a major part of the basin. The following quote is taken directly from the Alonso et al 2021 paper: “Elias et al. (2012) show that the sedimentation of the basins has been primarily a response to the closure of the South Sea and not an adaptation to SLR.”\nResponse: The modeling results show that ebb-tidal delta grows in volume. Movement of sand into tidal inlets from adjacent barrier shore is a very well know concept dating to the 1970s along barrier coasts throughout the world (Dean and Walton, 1977; Oertel 1977; Findlay; 1978; Hayes, 1979; Nummedal and Penland, 1981; FitzGerald 1984, Smith and FitzGerald, 1994; FitzGerald et all 2000; Elias van der Spek, 2017; Herrling and Winter 2018; Elias et al 2022). These publications show diagrams with arrows indicating longshore sediment transport into the inlet. Thus, we did not believe it was necessary to impose waves into the model to affirm what is established in the literature.\nResponse: This is now stipulated.\nResponse: We added elevation range (MSL to MHW) where vegetation was imposed.\nResponse: The simulation and set-up files have been uploaded.\nResponse: Agreed, this has been corrected in the text\nResponse: We apologize for this error and have changed the text. Thanks for catching this!\nResponse: Changed to “flooding tide”\nResponse: In addition to the Van Goor, M. A., Zitman, T. J., Wang, Z. B. & Stive, M. J. F. Impact of sea-level rise on the morphological equilibrium state of tidal inlets. Mar Geol 202, 211–227 (2003) reference has been added: Wang, Z.B., Elias, E.P.L., Van der Spek, A.J.F., Lodder, Q.J., 2018. Sediment budget and morphological development of the Dutch Wadden Sea - impact of accelerated sea-level rise and subsidence until 2100. Neth. J. Geoscience. 97–3, 183–214, which discusses import of sand to tidal basins through contribution from ebb-tidal deltas. In addition, we will cite Lodder et al 2022 and Huismans et al 2022 as studies that show that demand of sediment by tidal basins is a response to SLR.\nResponse: The plotted quantities represent the time derivative (slope) of the cumulative transport (Delft3D output that is the time integral of sediment transport rate, units of volume, after it has been filtered to remove tidal fluctuations) so properly have the units of volume/time. A better description is “Residual Transport Rate”, and figure labels and captions are updated accordingly.\nResponse: We have added the McKee and Patrick, 1988 citation (see Figure 2) that shows that most marshes begin colonizing tidal elevation at mean sea level and above.\nResponse: Should be 9 and 11\nResponse: This has been updated to read “offshore open boundaries”\nResponse: We added the clause “distortion of the tidal wave over the nearshore zone between the offshore boundaries and tidal inlet is negligible”\nResponse: We acknowledged the importance of waves in modifying the ebb-tidal delta and resuspending fine-grained sediment in some nearshore settings (e.g., Castagano et al 2018), which might affect basinal sediment exchange with the coastal ocean, but this paper is focused primarily on the backbarrier basin.\nResponse: We have made substantive changes to the Abstract, Introduction, and Conclusions to ensure that our main message is focused and clear.\nResponse: The focus of the paper is the morphological evolution of the backbarrier as forced by SLR, which causes an overall deepening of the basin and increase in tidal prism. This evolutionary path led to the ensuing goal of determining how the changing hydrodynamics of the basin affected the import versus export of different grain sizes. Sediment being transported in the model was derived from sediment being eroded in the backbarrier as well as sediment outside of the basin. Tracking was accomplished by stipulating a bed composed of clay, silt, and sand.\nResponse: Yes, a major goal is to show how net sediment transport trends of individual grain sizes (clay, silt, sand) will evolve as SLR changes the hydrodynamics of the backbarrier. A unifying characteristic of Mixed-energy barrier coasts throughout the world is that backbarriers are dominated by sandy substrates near the inlet mouth and grain size tends to fine up tidal creeks and up basin. Thus, the trends illustrated here are transferable and relevant to other Mixed-energy tidal inlet systems. For example, the sand moving into the basin is similar to what is documented in field studies by Wang et al 2018: “A characteristic feature of the Wadden Sea region is its continuous sedimentation of the tidal flats in order to keep pace with relative SLR, and its siltation along the Wadden shores. These processes are responsible for an important influx of sand, which is basically delivered by the adjacent coastal system. This is the cause of a structural retreat of the Wadden island shores.”\nResponse: One of the important responses to SLR is a deepening of the basin and an attendant increase in tidal prism. This explains why the volume of the ebb-tidal delta increases (Walton and Adams, 1976). Our modeling captures this dynamic process very well effectively differentiating between the control case and the remaining scenarios with sea level rise.\nResponse: Understood and thus the major question and sub-questions are more intimately linked in Abstract, Introduction and the cascading and connected responses are better defined in the Discussion, & Conclusions.\nResponse: This study provides a major advancement in our understanding of how Mixed Energy backbarriers will respond to SLR. Our findings show that basins will import sand and increasing tidal prism enlarges the ebb-tidal deltas. Also, fine-grained sediment is exported which diminishes inorganic sediment that can help maintain the marsh platform. These is a very important findings because they address backbarrier evolution and the future resiliency of the marsh .\nResponse: We acknowledge that the coasts listed in Table 1 have different hydraulic regimes and that is now better stated in the paper. However, we are modeling a conceptual basin that is fashioned after Mixed-Energy barrier island coasts (sensu: Hayes 1979) in which the backbarrier contains a relatively short basin length that produces a standing tidal wave. All the coasts listed in Table 1 have a tidal basin of similar length to that of the model and support standing tidal waves. Likewise, all these coasts (Table 1) have semidiurnal tides and their inlets experience inlet sediment bypassing and variable sediment fluxes through the inlet mouth. Present sediment dynamics of the Wadden Sea Inlets are largely a response to basin infilling and artificial closures (Elias et al., 2021) so are less comparable.\nResponse: We have chosen to add Plum Island Sound in the SI as a comparison to the conceptual model in terms of basinal geometry, standing wave character (as demonstrated with velocity times series) and importation of sand.\nResponse: section updated to include descriptions of vegetation model, parameters, and marsh platform definition: “The impacts of vegetation on the flow across the marsh surface and resulting influence on sediment transport patterns are neglected in the model experiments presented herein. Additional sensitivity analyses were performed that utilize the Delft3D trachytope roughness schematization (as a function of vegetation stem height and density according to the Baptist 2 model 78 ) that increases bed roughness over the marsh platform 78 , defined as the basin areas with elevations between the time-varying MSL and MHW elevations.”\nResponse: The Abstract has been completely rewritten to simplify and emphasize the major points and findings of this study.\nResponse: We have made this clear in the Abstract that when we impose marsh accretion, the trend of coarse silt and sand influx decreases to a single 40-year period. After this period, coarse silt and sand are exported.\nResponse: We meant that the curve for sand was flatter and the trend less dramatic than that for coarse silt. We have changed the wording to make this point clearer.\nResponse: The modeling Results show that marsh will be converted to open water deepening the backbarrier and increasing tidal prism and corresponding increase in volume of the ebb-tidal delta. It has been established that change in volume of the ebb-tidal delta will influence inlet sediment bypassing and thus sand reservoirs of adjacent barriers (Pearson et al 2020; added to references). We revised the paper for clarification.\nResponse: The Introduction has been rewritten to correct these issues.\nResponse: We have changed this to read: … particularly for the ~10% of the global population who in coastal areas less than 10 m above sea level 2\nResponse: This text has been rewritten.\nResponse: This section has been completely rewritten, including the addition of a primer for what a “Mixed Energy” Barrier system is.\nResponse: This section has been completely rewritten to sharpen the difference of opinions in predicted SLR forcings of future sediment transport trends and the focus of our paper. Additional citations have been added, including field examples.\nResponse: We have removed this from the Introduction and put a fuller treatment of future increases in tidal prism and its effects in the Discussion. We did not include backbarrier systems that contain important sediment contribution.\nResponse: Again, this section has been rewritten and effects of tidal prism increases and sequestration of sand on ebb tidal deltas have been removed and in put in the Discussion.\nResponse: We are intimately familiar with Hayes’ classification (one of us was his PhD student and helped with his1979 paper, particularly Figure 15 of that paper). Barriers only exist in Wave-dominated and Mixed Energy settings. Ebb-tidal delta morphology can be related to waves and tides and Hubbard et al 1979 came up with a classification: Tide- Dominated, Wave-Dominated and Transitional to describe ebb-tidal delta shape. One of us has also published numerous papers concerning sediment transport in the vicinity of tidal inlets. Most importantly, this section of the introduction has been removed and the important points have been added to the Discussion.\nResponse: We apologize for the typos, which have been corrected. The structure of this section was intentional, as marsh platform elevation dynamics are a “0d” process governed by factors such as sediment supply, inundation duration, and organic production that vary spatially.\nResponse: We agree and have made this an important point (see below).\nResponse: We agree and have moved this paragraph up into the Main focus of goals.\nResponse: We have removed the sentence discussing sand imported into the basin from the barrier shoreline but have added references to demonstrate field evidence of sand import to the backbarrier by flood- dominated channels (Nowacki and Ogston 2013; FitzGerald et al 2022).\nResponse: We have added the clause “and investigate longer timescales and more alternative SLR conditions than possible with field studies”\nResponse: We have replaced “theoretical” with “numerical”\nResponse: Ioannis will rewrite these sentences\nResponse: Information about sediment fluxes for the different sites listed in Table 1 largely does not exist. Also, this study is not concerned with how sediment fluxes are influenced by tidal range. That is beyond the goals of the paper.\nResponse: Citations have been added\nResponse: This has been changed Please see Figure 6C.\nResponse: I am unsure what sentence he wants us to change? Ioannis and Kevin help!\nKH: maybe the “after 200 years and approximately 1 m of SLR”? Could rephrase to “but at the end of the simulation with 1 m of cumulative SLR, residual transport …)”\nResponse: This section is actually well-positioned in the paper because it lays the foundation (see second sentence) for the immediate next section of the paper: “Changes in flood/ebb asymmetry and resulting net sediment transport”\nResponse: mean depth at low tide can decrease due to both channel infilling and the increased inundation extents at low tide (even with a static channel bed). If the elevation of low tide continues to increase, channel banks can begin to be inundated even during low tide, introducing a larger area low-depth values that decrease the mean depth.\nResponse: We did not cite an Aubrey reference in this section of the paper. The Friedrichs & Aubrey reference is cited on Line 248, as this paper discusses ebb dominance as a function of tidal amplitude and channel depth.\nResponse: The Introduction has been rewritten and the goals of the paper have been narrowed and more clearly stated. The Donatelli et al 2020 paper and Zhang et al 2020 suggest that SLR will result is the export of sediment which is contrary to other studies, and thus one aspect of our paper serves to investigate this divergence of ideas. This is now better defined in the Introduction.\nResponse: Additional information has been provided in this sentence for clarity: “While a 200-yr morphologic timescale simulation is inadequate to achieve full dynamic equilibrium with no further bathymetry changes 41 (see Figure 2a), both the volume of backbarrier morphologic features (see Figure 3) and net sediment fluxes (see Figure 4c) have reached steady-state conditions (indicating dynamic equilibrium of aggregate morphology) onto which perturbations could be imposed.”\nResponse: They are comparable to Mixed-Energy systems listed in Table 1. The lack of significant sediment input from rivers or other upland sources is similarly consistent with many (though not all) of the prototype basins.\nResponse: Ebb-tidal delta volume is primarily dependent on tidal prism and as Walton and Adams (1976) showed, wave energy has a secondary influence on volume. The morphology of the ebb delta indeed is a product of wave versus tidal dominance, but not the volume. The Plum Island Sound ebb delta exhibits a moderately ebb-dominant morphology.\nResponse: see response to Line 410 comment above.\nResponse: This section is updated to note sediment transport equations and more detail on initial bed composition\nResponse: More information is given on the mechanisms of the MEM: “...such as the Marsh Elevation Model (MEM) that computes accretion rates based on biomass production and inorganic sedimentation”. For more information on the specific model formulations and settings in the referenced study, see Farron et al., 2020.\nResponse: This section is updated to include descriptions of vegetation model, parameters, and marsh platform definition: “The impacts of vegetation on the flow across the marsh surface and resulting influence on sediment transport patterns are neglected in the model experiments presented herein. Additional sensitivity analyses were performed that utilize the Delft3D trachytope roughness schematization (as a function of vegetation stem height and density according to the Baptist 2 model 78 ) that increases bed roughness over the marsh platform 78 , defined as the basin areas with elevations between the time-varying MSL and MHW elevations.”\nResponse: There have been several recent studies reporting sediment import to backbarrier basins including inlets along the Virginia coast (Castagno et al 2018) and at New Inlet in Central Massachusetts (Baranes et al 2022). The import of sediment through Rockaway Inlet into Jamaica Bay along the Long Island coast in New York was published by Renfro et al (2010) and later confirmed by Donatelli et al (2020). The response of the model to the initial bed sediment composition is also referenced in another comment by the reviewer. To address both comments/questions, we have performed additional experiments where we varied the initial bed composition by increasing and decreasing the mud content and repeated the control simulations as a sensitivity analysis. We found that varying the clay content (4%, 14, 24%) did not change in sediment transport trends (export and import) or magnitude of the sand and silt fractions. Likewise, clay is continuously exported and as expected the larger the percentage of clay sized sediment, the greater amount clay is cumulatively transported (exported).\nResponse: Thank you for pointing this out, indeed our conclusion is an outgrowth of the modeling results, but also based on inlet processes published in the literature. We have made this clear in the text:\nChanged to:\n9\n“Contrary to recent studies of mixed-energy tidal systems, particularly in the Netherlands , results from this study infer that the ebb-tidal delta will expand with SLR due to increasing tidal prism17, which may reflect the use of a moderate-sized tidal inlet-basin system for the modeling. Sediment losses to the backbarrier system and sand trapped on the ebb-delta and will lessen inlet sediment bypassing18 and reduce the proximal sediment reservoirs, most likely from the adjacent barriers. This will make some barriers more susceptible to breaching and transgression.”\nResponse: We appreciate the comment; it seems we omitted revising the text. We edited the manuscript for clarity and to reflect the following message: current asymmetry dominates bedload transport, and duration asymmetry for slack water dominates suspended load transport.\nResponse: Thank you\nResponse: The focus of the paper is indeed on the morphodynamics of the backbarrier as it changes with rising sea level. One of the important outputs of the modeling is that the tidal prism increases, which, as the published literature would predict, results in an increase in dimensions of the inlet and enlargement of the ebb-tidal delta. These relationships are shown in our Figure 2. Both inlet size and volume of the ebb-tidal delta are related primarily to tidal prism. Waves impart a much lesser influence as many studies have demonstrated, although the reviewer is correct in saying that wave versus tidal energy will affect the shape of the ebb delta. Moreover, most of the sediment exchanged between the backbarrier basin and the coastal ocean occurs through the main channel, which due to its depth, is primarily affected by tidal currents and not waves. The computed volume of the ebb-tidal delta adheres well with the Walton and Adams (1976) relationship and is similar in planform to many mixed-energy ebb-tidal deltas.\nResponse: We chose to use a relatively low clay content for our sediment regime because most tidal inlets tend to be coarser-grained systems (sand and coarse silt) but may contain clay at the heads of smaller tidal creeks and up estuary (at the drainage divides in East Frisians). However, close to the inlet and main tidal channels, where most of the sediment is exchanged, are floored by sand, as are the flood deltas and point bars. As channels deepen in the backbarrier, they may erode into sedimentary layers containing more clay, but usually in mixed energy systems that contain backbarrier marshes and tidal creeks or tidal flats (East Frisian Islands, North Frisian Islands, Copper River Delta barrier, Alaska), the channels erode into deposits that consist of sandy sediment that was transported into the backbarrier as the barriers and inlets were stabilizing and the basin was filling. Again, in these cases, clay will be minimal. However, to look at the importance of clay, we have run the model using a content of 10% less clay and 10% more clay content. We have performed a sensitivity analysis using different clay content and found minimal effects on our results. Please see our response above (Response to Reviewer’s #2) and articulated in the SI (text and figures).\nResponse: As stated in the methods, we assume a homogenous mixed bed, with the said compositions (sand, silt, and clay). Clay is transported as cohesive and coarse silt, and sand as non-cohesive. All sediment types are available for erosion, with an initial sediment thickness of 7 m.\nResponse: Both cohesive and non-cohesive sediments are actively (or available) transported within the active layer.\nResponse: During the first revision of the manuscript, we included the model setup files in a repository as requested by the reviewer. We do not fully understand what the reviewer is asking. However, from the methods, we re-iterate here that clay, which has an equivalent diameter of 20 microns in our model is delineated (14%) and transported as cohesive sediment. Any sediment with a diameter of more than 63 microns is delineated and transported as non-cohesive sediment. Since we are using a mixed bed. The fractions of 14% (clay, 20 microns), 43% (silt, 64 microns), and 43% (sand, 200 microns). The methods currently consist of all the above information.\nWe added a table with more information in the supplemental documents. We do not think the selection of these parameters or properties influences the robustness of the model. Moreover, the importance of the study lies in the differences in the results among the different simulations, thus, since all initial coefficients/conditions are the same between the simulations, the experiments remain robust.\nResponse: We understand and agree that the examples listed in Table 1 will not necessarily behave exactly like our conceptualized basin, because of differences in hypsometry, grain size distributions, tidal ranges, etc. and this acknowledgement is now clearly stated in the text. However, there is relevance to the systems listed in Table 1, because they similar basin lengths, tidal ranges and deep channels would tend to produce standing tidal wave regimes leading to similar hydrodynamics and ebb-dominated inlets. Moreover, these backbarrier systems have comparable ebb-tidal deltas and backbarriers consisting of marsh or well-developed tidal flats incised by tidal channels.\nResponse: Lenstra et al’s first figure and nomenclature in that publication are that from one of the present authors. Lenstra’s paper focuses on time scales and processes of how sand bypasses an inlet through changes in the morphology and sediment transport patterns of the ebb-tidal delta. Indeed, Lenstra’s paper expanded our understanding of the ebb-tidal delta breaching process and showed the importance of waves and tides. In our paper we are focusing on sea level induced volume changes and not detailed cyclic morphological changes, which is an important subject but beyond the scope of this paper.\nResponse: Thank you.\nResponse: Yes, additional experiments are beyond the scope of this study, but please see above Response 3.b. which related our results to many other mixed-energy coastal systems due to similarities on the hydrodynamic regimes.\nResponse: We are concentrating on hydrodynamics and sediment transport into and out of a backbarrier basin where wave energy is typically low due to limited fetch, particularly at mid to low tide. We agree that waves affect the morphology of the ebb-delta and processes of inlet sediment bypassing (cyclic behavior, see Lenstra et al); waves have a minor influence on ebb-tidal delta volume over centennial timescales.\nResponse: We feel that we have adequately addressed several comments related to this issue. Also, this study is about backbarrier basins and their evolution due to sea level rise.\nResponse: Sediment transport within the basin and at the inlet is driven by tidal currents, dictating net transport directions and volumes. Waves influence the distribution of sand shoals, how they migrate, pattern of sand transport along the periphery of the ebb-delta, and to some extent “ebb-tidal delta breaching,” but we are focusing on change to the basin with SLR. One of the results is an increase in tidal prism, which also causes an increase in tidal inlet cross sectional area and volume of the ebb delta, and both trends as predicted by the literature, and in our modeling.\nResponse: Thank you for bringing this topic forward. There are three examples from the published literature that corroborate our findings. 1. Ocean City Inlet, Maryland. Hurricane breaching in 1933. As the inlet accessed the backbarrier lagoon and thus a greater tidal prism, the inlet deepened from 5 m in 1937 to > 14 m by 1995. Over the same period, the ebb delta volume enlarged to 10 million cubic meters. 2. Barataria Basin in Louisiana. Wetland loss increased over an 80 year period in Barataria Basin converted more than 1100 km2 of wetlands to open water (14 km2/year; Couvillion et al 2011). Consequently, the combined cross-sectional areas of four inlets draining this basin increased by almost 70% and the ebb-tidal delta volumes increased by ~ 35% causing a seaward migration of the terminal lobe by 2 km (FitzGerald et al, 2018). 3. East Frisian Islands. Here, poldering decreased the area of the backbarrier > 60% vastly diminishing the tidal prism, which in turn resulted in a decrease in the cumulative widths of the inlets by >40% and cumulative lengthening of the barrier islands by 20%. The sand that contributed to the growth of barriers came from the ebb-tidal delta that decreased in size because of the decreasing tidal prism.\nResponse: We have included the Table below in the Supplemental Information. We note that stem diameter is not a parameter in the Baptist equation.\nSI Table 1. Vegetation parameters used in Baptist Equation\nParameter Value\nStem Height [m] 0.5\nVegetation Density [stems/m] 0.05\nStem Density [stems/m2] 185\nDrag Coefficient 1\nAlluvial Bed Roughness [m^(1/2)/s] 60\nResponse: We have revised the text in the methods for clarity and provide a response here as well. To simulate marsh vertical accretion, we modified the bathymetry of the model for areas that were occupied by vegetation. Mineral sediment was added (every 5 years) in the top (active) layer of the model, and the added sediment reflected the same composition as the underlying sediment (all sediment fractions). The added sediment is implicitly incorporated into the next sediment computations following sediment continuity and thus doesn’t influence sediment imbalance. When a model cell containing marsh is eroded, the sediment in the cell enters the domain in the adjacent cells and transported per sediment transport module depended on the sediment type as previously described, and as stated in the methods.\nResponse: We apologize for this oversight.\nResponse: We created a table containing the chosen parameters, shown below and added to the Supplemental Information. Also per request by the reviewer in our first revision, we included simulation setup files in an online repository which has been active and available since the previous revision.\nSI Table 2. Sediment Characteristics and other sediment and morphology relevant parameters\nCategory Parameter Values\nSand median grain size (D50) 200 µm\n64 µm\nCoarse silt median grain size (D50)\nSediment characteristics\n0.25 mm/s (velocities correspond\nSettling velocity (clay fraction) to D50s of 20 µm, respectively)\nCritical shear stress for erosion of\n0.5 Pa\nconsolidated mud (i.e., clay)\nDry bed (or bulk) density of\n500 kg/m3\nconsolidated mud (i.e., silt and clay)\nDry bed (or bulk) density of sand 1600 kg/m3\nErosion parameter 0.0001 Kg/m2/s\nSediment transport Current related reference\nconcentration factor/transport 1 / 1\nmagnitude factor\n43% sand / 43% silt / 14% clay\nSensitivity with\nMobile bed composition\n53% sand / 43% silt / 4% clay\n33% sand / 43% silt / 24% clay\nMorphology\nMorphological scale factor (MorFac)\n100\nfor cold-front simulations\nDry cell erosion factor 1\nResponse: We did not use the MEM and as such we removed mention of MEM that from the method section. Please also see response to how accretion was implemented in a previous comment.\nResponse: The requested table is shown above and was also included in the paper supplement.\nResponse: Thank you\nResponse: Thank you"}]

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