High Platform Elevations Highlight the Role of Storms and Spring Tides in Salt Marsh Evolution

We combine sea level records and repeat lidar surveys at 8 sites in the United Kingdom and the United States to explore controls on marsh accretion. We compare marsh elevations relative to sea level as well as lidar-derived marsh accretion rates to simple 0-dimensional settling simulations in order to explore constraints on suspended sediment concentration and particle size. We find that the marsh platforms examined occupy a narrow range of elevations in the upper tidal frame, situated between Mean High Tide $MHT$ and the Observed Highest High Tide $OHHT$. Under sinusoidal tidal forcing, common in marsh accretion models, marshes at these elevations are never inundated, highlighting the inadequacy of sinusoidal forcing in numerical models of salt marshes. Forcing the model with year-long tidal records, deposition rates follow hyperbolic contour lines when expressed as a function of sediment concentration and median grain size. We also observe that when using a median sediment grain size $D_{50} = 50 \ \mu m$ and sediment concentrations derived from satellite data, modeled deposition rates are much lower than when using field data. We find that the deposition of coarse, concentrated sediment is necessary for platforms in the upper tidal frame to withstand sea level rise, suggesting a strong dependance on infrequent high-deposition events. This is particularly true for marshes that are very high in the tidal frame, making accretion increasingly storm-driven as marsh platforms gain elevation. Finally, we reflect on the capacity of marshes to regenerate after erosion events within a context of changing sediment supply conditions.


INTRODUCTION
The issue of salt marsh elevation change is one that preoccupies coastal geomorphologists and land managers alike. Often measured relative to mean sea level, elevation determines the frequency and depth of flooding of the marsh surface, both from astronomic tides and storms (Cahoon and Reed, 1995). Flooding frequency in turn determines salinity, which influences the type and productivity of the plant communities on the marsh (Pennings et al., 2003;Silvestri et al., 2005;Belliard et al., 2017), and therefore underpins the functioning of the entire ecosystem. Coastal marshes around the world face accelerating rates of sea level rise (IPCC, 2014). Decreased sediment supply due to anthropogenic activities is set to accentuate the pressure of sea level rise on coastal wetlands, particularly in deltaic systems (Syvitski et al., 2009). Furthermore, subsidence caused by water, gas and oil extraction add to the existing stress on wetland ecosystems (Kennish, 2001). Factors that influence marsh growth are less favorable now than in the past (Kirwan et al., 2011), and so determining if salt marshes will maintain their elevation within the tidal frame is an intensively studied research question (Crosby et al., 2016;Kirwan et al., 2016;Lerberg, 2016).
One approach to explore the future evolution of salt marsh elevation is numerical modeling, and several models of salt marshes have been created over the past decades to address the question (Fagherazzi et al., 2012). Models of salt marsh elevation change may be divided into point-based models (0-D), profile models (1-D) or spatially distributed models (2-D). Whereas 2-D models are effective at predicting the evolution of topographic or ecological patterns on the marsh surface Temmerman et al., 2007;Belliard et al., 2016), their high computational cost often precludes their use for long-term simulations or large regions. 1-D models are often used to represent the marsh scarp and simulate salt marsh and mudflat interactions  and lateral erosion processes (Tonelli et al., 2010).
Contrary to these approaches, 0-D models do not take into account the propagation of hydrodynamic forcing, nor do they account for the spatial heterogeneity of marsh topography. These models often use synthetic elevations, simplified tidal forcings and assume constant suspended sediment concentration and median grain size. With these assumptions, they have been used to explore the response of marshes to various sea level rise scenarios (D'Alpaos et al., 2011) or the variations in vegetation productivity (Morris et al., 2002;Mudd et al., 2010;Marani et al., 2013). More recently, Schuerch et al. (2018) used a 0-D model to assess the potential of salt marshes to adapt to projected sea level rise over the twentyfirst century, assuming that all coastal wetlands occupy the same continuous vertical space between Mean Sea Level (MSL) and Mean High Water Spring (MHWS). However, due to the scarcity of local sediment size and concentration data, few studies using 0-D models consider variability in sediment supply.
Simulations of salt marsh behavior may be compared with observations of salt marsh elevation change, measured in the field or via remote sensing. Sediment Elevation Tables (SET) allow for highly accurate measurements (Cahoon, 2015;Anisfeld et al., 2016), but lack the spatial coverage provided by less accurate lidar surveys (Nolte et al., 2013;Webb et al., 2013). While they are affected by false ground returns due to vegetation (Schmid et al., 2011;Hladik and Alber, 2012;Rogers et al., 2016Rogers et al., , 2018, their large footprint enables lidar surveys to account for the variability of salt marsh elevation in a way that would be too costly to implement on the field.
In this contribution, we use lidar-derived marsh platform elevations and local tidal records to simulate yearly settling fluxes for 8 salt marshes in the United Kingdom and the United States of America. We then compare the calculated settling rates under various sediment size and concentration conditions to various rates of sea level rise. Finally, we investigate the potential of pioneer platforms for rapid accretion. Our aim is not to perfectly simulate sediment settling on these marshes, but rather to use observed marsh elevations and tide records to constrain some of the conditions of sedimentation.

Numerical Framework for Settling Fluxes
Following Exner's equation, 0-dimensional numerical models describe the change in elevation of a point on the marsh surface as the sum of deposition and erosion fluxes Kirwan and Temmerman, 2009;D'Alpaos et al., 2011). Over a given period of time t, the average variation of elevation relative to sea level z is the sum of positive deposition fluxes Q dep, t and belowground organic production Q org, t , and negative erosion fluxes Q eros, t on the platform surface, minus the relative sea level rise R t , which includes eustatic sea level variations and local subsidence. If dt is an infinitesimal time period, the change in elevation dz over dt is therefore expressed by Equation (1): where it is assumed that Q eros,dt = 0 m yr −1 , as the dampened currents and waves on elevated platforms are unlikely to erode a vegetated surface (Carniello et al., 2005;Möller et al., 2014). Deposition fluxes on vegetated surfaces are expressed as the sum of particle settling and capture by stems and leaves. Here, capture fluxes are considered significantly smaller than settling fluxes (Marani et al., 2010;Mudd et al., 2010). Over a tidal cycle of period T, we therefore express Q dep,T according to equation (2) (D'Alpaos et al., 2011): where w s is the terminal settling velocity calculated using Stoke's law for a spherical particle of diameter D 50 and volumetric mass ρ s = 2650 kg m −3 in unagitated water of volumetric mass ρ s = 1000 kg m −3 and dynamic viscosity µ = 0.0010518 kg s m −1 . The assumption of low turbulence on the marsh surface implicitly assumes low velocities, as vegetation increases turbulence on the surface (Nepf, 1999). We therefore anticipate settling fluxes obtained through this model to overestimate real settling. ρ b = ρ s (1 − λ) is the bulk density where λ = 0.5 is a parameter accounting for compaction (Marani et al., 2010;D'Alpaos et al., 2011). The depth-averaged instantaneous suspended sediment concentration C(z, t) is the solution of the first order differential Equation (4): R is the rate of sea level rise, C 0 is the suspended sediment concentration, D 50 is the median sediment grain size, H is the maximum tidal elevation for a given tidal cycle, B is the biomass of a given species, and F is the fitness function for that species.
where the instantaneous water depth D(z, t) is the difference between the water level h(t) and the elevation z(t). In Equation (5), C(z, t) is dependent on flooding conditions during ebb ( dh dt < 0), but is forced by the boundary sediment concentration C 0 during flood ( dh dt > 0). Equation (4) is solved for positive values of D(z, t) under the assumption that at any given time t, either dz dt is negligible in front of dh dt or both are null. The solution of Equation (4) under these conditions is then: where D max is the maximum flooded depth for a given tidal cycle.
Since dry areas cannot accrete through deposition, we consider = 0 for negative values of D(z, t).

Modified Forcing and Representation of Elevations
Due to their exploratory nature, 0-D models seldom represent any particular marsh platform elevation or vegetation association. Likewise, maritime forcing parameters are often synthetic, using a sine wave of amplitude H = MHT − MSL as a tidal signal, and considering the forcing sediment concentration C 0 or the median grain size D 50 as time-invariant (D'Alpaos et al., 2011) ( Figure 1A). Figure 1B illustrates the parameters required to force a more realistic model. Such models are usually implemented for a particular marsh platform (e.g., D'Alpaos et al., 2007;Temmerman et al., 2007) and successfully simulate observed accretion values.
We examine the effects of using observed rather than sinusoidal or predicted tidal forcing to simulate the vertical accretion on marsh platforms extracted from lidar topographic data. This approach is implemented in the model by describing the mineral accretion flux over a period t, Q dep, t , as the sum of settling fluxes over each of the N t tidal cycles in t (7).
We initially consider fixed values for C 0 and D 50 , as detailed in section 2.3. Our aim is to determine whether these parameters can be used to explain observed marsh elevations and accretion rates, as well as the conditions necessary for platform elevations to match rising sea levels. Later in this contribution, we relax our assumptions about C 0 and D 50 and allow them to vary as free parameters.

Site Description and Sediment Supply Conditions
In this study, we examine 8 marsh sites where two lidar topographic surveys acquired at least 4 years apart are located in close proximity to a tidal gauge with a long-term record of hourly data. For each site, we obtain total suspended matter (TSM) using the GlobColour MERIS product (Barrot et al., 2007), which contains monthly values TSM in the Earth's oceans and lakes between 2002 and 2012. Monthly coverage of MERIS, however, is incomplete. Consequently, we use the averaged TSM between 2002 and 2012 in order to cover our sites. The angular resolution of MERIS products is 1/24 • at the equator. While this is insufficient to observe the exact TSM value at our sites, MERIS data has already been used to calculate local sediment availability in global estimates of wetland response to sea level rise (Schuerch et al., 2018). In this study, we therefore use MERIS data in combination with field data on sediment supply conditions sourced from the literature, as described below. The location of each site is given in Figure 2 and the Supplementary Material.

Boston Harbor
The marsh studied in Boston Harbor is located in Squantum, MA, and borders Quincy Bay, approximately 6 km from Boston Harbor tide gauge. Flume experiments conducted by Ravens and Gschwend (1999) show tidal flat sediments to range between 30 and 60µm in D 50 , and to contain 3 − 4.5% of organic matter. Under stresses of 0.05 Pa, TSM oscillates around 25 g m −3 , peaking around 160 g m −3 under stresses of 0.5 Pa. These values are slightly greater to those found by Hopkinson et al. (2018) in the nearby Plum Island Sound (median SSC around 15.6 g m −3 and peaks around 40 g m −3 ), however organic content is much lower than the 30% assumed in Plum Island.

Morro Bay
The marsh studied in Morro bay is located North of Morro Bay State Marine Reserve, CA, on the Chorro Creek estuary, approximately 20 km from Port San Luis tide gauge. Few data on sediment size, concentration and organic content was found for Morro Bay. Instead, we use data for San Francisco Bay, CA. There, acoustic backscatter was used to estimate sediment grain size between 50 and 90 µm and suspended solids to 20 − 300 g m −3 (Gartner, 2004).

Morecambe Bay
The marsh studied in Morecambe Bay is located South of Jenny's point, Lancashire, approximately 15 km from Heysham tide gauge. Few data were found for sediment concentrations. Instead we use data for the Mersey estuary. Aldridge (1997) finds sandy sediments around 150 µm and Pringle (1995) finds silts of around 31 µm. Gray and Scott (1977) mention loss on ignition of 8%.

Mersey Estuary
The marsh studied in the Mersey Estuary is located in Ellesmere Port, Cheshire, approximately 15 km from Gladstone tide gauge. Acoustic Doppler Current Profiler (ADCP) measurements in the Mersey river near Liverpool found D 50 in the channel to be approximately 9 µm, and were found up to approximately 50 µm. Suspended solids concentrations vary between 10 and 650 g m −3 (Holdaway et al., 1999).

Poole Harbour
The three marshes studied in the Poole Harbour, Dorset, are all under 7 km from the Bournemouth tide gauge. Gao and Collins (1994) show in the neighboring Christchurch Harbour that sediment grain sizes vary between 65 and 250 µm in the proximity of marshes, with concentrations measured around 120 g m −3 but known to reach 600 g m −3 during storm events (Green, 1940).

Sheerness
The marsh studied in the Swale Estuary, Kent, is approximately 16 km from the Sheerness tide gauge. Wharfe (1977) reports D 50 values ranging from 50 to 90 µm, while Zhou and Broodbank (2013) report concentrations ranging from 100 to 2, 000 g m −3 .

Collection and Processing of Topographic Data
Topographic survey are sourced from either the NOAA Digital Coast archive or the United Kingdom Environment Agency. All datasets are referenced to their respective national topographic datum: the North American Vertical Datum 1988 in the USA and Ordnance Datum at Newlyn in the UK. Errors in elevation measurements may stem from the georeferencing of the lidar point clouds. Vertical error margins are determined by comparing lidar elevations to the elevation of multiple ground control points. The root mean square error (RMSE) of this comparison is given by both data providers (Tables 1-3). Vegetation is another factor of error when measuring salt marsh ground elevation (Schmid et al., 2011;Parrish et al., 2014;Rogers et al., 2018). On Sapelo Island, GA, Hladik and Alber (2012) found that low plants such as short  (Table 1).
From the downloaded point clouds, we use CloudCompare (https://www.cloudcompare.org/) to generate rasters of  minimum and maximum elevations within a grid cell, respectively, Z min and Z max . Grid cell size is determined to fit a minimum of 6 points per cell, up to a maximum of 3 m. The marsh platform elevation is then extracted from Z min using the Topographic Identification of Platforms (TIP), which accurately delineates marsh platforms for grids of up to 3 m in horizontal resolution (Goodwin et al., 2018). For each survey, we select a low-relief, non-vegetated structure (road, car park, etc.) for which we calculate the 1st, 2nd and 3rd quartile of the difference Z max − Z min . Two subsampling methods are then applied to the marsh platform. First, pixels classified as marsh platforms for which Z max − Z min is less than the median of Z max − Z min of the reference structure are preserved, as shown for the Mersey Estuary in Figures 3A-C (red pixels). Similar figures for other sites are available in the Supplementary Material. This subsampling ensures that high elevation gradients do not exist within the pixel, whether they are due to topographic features (hummocks or pools) or locally high vegetation. Pixels classified as marsh platforms that are also levee points are selected by the second method (green pixels). Due to the larger spread of elevation and the potentially large errors in elevation associated with levee pixels, we do not use them further in this study ( Figure 3D). Vertical offset between the two selected surveys is accounted for as the average difference of Z min for the reference structure, the first survey being taken as reference by default. The values of vertical offset are given in Table 2.

Collection and Processing of Sea Level Data
Each selected marsh site is associated with a tidal station in its close vicinity. For these stations, we download sea level observations from the GESLA-2 dataset, a global collection of hourly sea level data up to the year 2015 (Woodworth et al., 2016), or the British Oceanographic Data Centre (BODC) data repository. From these records we extract the monthly mean high and low tides MHT m and MLT m . We fit a linear trend to each of these times series, the difference of which constitutes the mean tidal range MTR. The same process is applied to determine the trend of monthly observed highest high tide OHHT. Time series of monthly mean sea levels (MSL m ) were collected from the NOAA sea level trend dataset. For stations in the United Kingdom that do not have a long-term record of MSL m , we choose the closest long-term tide gauge as a substitute. From this record we extract the linear trend of MSL m , named MSL, the slope of which constitutes the rate of relative sea level rise RSLR. Figure 4a shows the tidal records with their associated metrics, as well as the 1-year subset of data used to calculate yearly deposition fluxes (see section 3). Figure 4b shows the cumulative distribution function of flooding time at each station, for both the whole record and the selected subset.

High Platform Elevations Cannot Be Explained by Sinusoidal Tidal Forcing
For each of the 8 selected marshes, Figure 5 shows the probability distribution function of elevation f z of the marsh platform at the dates S1 (left of bar) and S2 (right of bar). Gray filled areas f z represent the subsampled marsh platform (see Figure 3C). Gray lines represent the same pixel sets plus or minus half the RMSE reported by ground truthing reports. For each survey, marsh elevation is relative to its contemporary sea level. In all of the sites, irrespective of measurement error, the major part of the marsh platform lies within the upper tidal frame, defined as the range of elevations between MHT and OHHT. While megatidal marshes show a wider distribution, no platform occupies more than half FIGURE 3 | Marsh platform subsampling results for the Mersey Estuary Marsh. (A,B) Show the marsh hillshade (respectively for S1 and S2) overlayed with subsampled pixels (red) and levee pixels (green). (C) Boxplot of differences Z max − Z min for the reference infrastructure and the marsh platform. (D) Probability distribution functions for the entire marsh platform (gray), levee pixels (green), and subsample pixels (red).
of the upper tidal frame. This observation is supported by surveys of vegetation populations relative to tidal levels (Belliard et al., 2017) and refines the approach of Schuerch et al. (2018), where marshes are assumed to occupy the entire range of elevations between MSL and MHT.
In models using a sinusoidal tidal forcing of amplitude H = MHT − MSL, the equilibrium elevation z eq relative to MSL is given by Equation (8) where k = Q dep,y + Q org,y [mm yr −1 ] is the sum of yearly deposition and below-ground production rates. While z eq is seldom truly reached, it gives an indication of the elevation toward which marsh platforms converge. Equation (8) suggests that, under sinusoidal forcing, no part of any marsh platform may reach elevations higher than MHT. This constraint is relaxed by the fact that platform elevation tends to lag behind sea level variations (Kirwan and Temmerman, 2009): salt marshes that have experienced higher sea levels may then be found at higher elevations. All of the marshes examined in this study are higher than both their equilibrium elevations and their maximum elevation H + MSL. However, no stations other than Gladstone and Heysham have experienced late quaternary uplift (Shennan and Horton, 2002;Donnelly, 2006;Bromirski et al., 2011;Shennan et al., 2012) and no stations show significant negative modern variations in monthly MSL (see Figure 4). Hence, the high elevation of the examined marsh platforms cannot be explained by a sinusoidal forcing of amplitude H, notwithstanding the use of this forcing by several studies on marsh elevation change for lower marshes (e.g., Morris et al., 2002;Marani et al., 2007;D'Alpaos et al., 2011;Tambroni and Seminara, 2012;Da Lio et al., 2013).
Furthermore, platforms that are higher than z eq are predicted by Equation (8) to lose elevation, as they are not flooded frequently enough to allow accretion rates that match sea level rise. However, Figure 5 shows that in all but two sites, platforms are gaining elevation on MSL. This affirmation stands for all but when extreme positive error in S1 and extreme negative error in S2 are considered. All the examined platforms therefore experience deposition, and may be considered active, rather than relics of higher sea levels. This result strongly suggests that the marsh platforms in our study depend on deposition of concentrated coarse sediment to maintain their position in the tidal frame, typically provided by spring tides and storms. The latter are shown by Castagno et al. (2018) to positively influence sediment import into back-barrier bays. This effect, however, is less important for fine sands (D 50 ≥ 125 µm), which hints at a potential depletion in this size fraction, which may in turn lead to marshes failing to keep pace with RSLR. Dependance on infrequent deposition events is also consistent with the findings of  in micro-tidal backbarrier marshes, who showed that storm surges contribute to the erosion of scarps as well as to the recycling of eroded marsh sediment onto the platform.

Modeling Accretion Rates With Real Tidal Forcing Highlights the Influence of Elevation, Grain Size and Concentration
Following the observations of section 3.1, we examine the effect of using a realistic tidal forcing by simulating deposition fluxes over a year for each marsh site. The sea level record used to force accretion is a subset of the full tidal record for each station, shown as the green highlighted data in Figure 4. In this experiment, we use three sets of values for C 0 and D 50 . Lower values for C 0 and D 50 referenced in Section 2.3 are the first set. The second set is D 50 = 50 µm, which is within the higher range of values used in long-term modeling studies D'Alpaos et al., 2011). C 0 is determined by the values obtained from the MERIS Total Suspended Sediment (TSM) dataset at the location of the tidal station. In the third set, higher values for C 0 and D 50 referenced in section 2.3 are selected. Table 3 summarizes sediment supply conditions used in the simulations. Figure 6 compares the observed and modeled elevation change of the dominant platform elevation z max(f Z ) relative to the terrestrial datum, with relative sea level rise as a reference. Despite the precautions taken to reduce error in the elevation samples, observed accretion rates (red bars) are visibly unreliable. For instance, Arne Bay exhibits negative accretion rates while Wych Lake and Shell Bay, located less than 5 km away, exhibit accretion rates close to those recorded at Wax Lake Delta, one of the fastest accreting marshes in the world. Morro Bay and Boston Harbor also exhibit unrealistic accretion rates, particularly in regard to the low rates of associated sea level rise. While such rapid elevation variations have been observed using SETs (Kirwan et al., 2016), they may also be the product of uncertainty in elevation values. Indeed, errors in the measurement of elevation for both S1 and S2 lead to considerable error in rates of accretion, as shown by the error bars in Figure 6. However, the elevation error in S1 typically leads to errors of 5% or less on the modeled accretion rate (brown bars). Although variations in sediment supply and flooding patterns prevent a direct comparison between sites, we observe an overall decrease in modeled deposition rates with increasing tidal range and platform elevation. Conversely, we note a significant positive response of accretion rates to the combined increase in sediment size and concentration, as shown by the differences in accretion rates between low C 0 and D 50 and high C 0 and D 50 . This response leads us to postulate that the low values of C 0 are the cause for the low modeled accretion rates when using MERIS data. Indeed, the MERIS dataset has a spatial resolution of 300 m and is primarily an oceanic dataset. It does not account for complex coastal inlets, estuaries and bays where salt marshes are found, and where higher concentrations are likely to be found (Amos and Alfoldi, 1979). Furthermore, Fagherazzi et al. (2014) find strong spatial variations in sediment size within the tidal creeks of a single site at Plum Island Sound. In this respect, the site-specific data collected in section 2.3 is likely representative of the spatial variability of sediment supply found in the sites examined. The relative influence of C 0 and D 50 , however, is not discernable at this point.

Constraints on Sediment Supply and Consequences for Platform Equilibrium
Whether a marsh keeps pace with sea levels has been suggested to depend on forcing sediment concentration (Kirwan et al., 2010;D'Alpaos et al., 2011;Kirwan and Megonigal, 2013). We establish in Section 3.2 that deposition is also conditioned by the initial platform elevation, as suggested by Cahoon and Reed (1995), and the grain size of the deposited sediment. We calculate Q dep for a range of C 0 and D 50 , assuming a contribution of 6% from below-ground production Q org . This value is the lower bound of a range estimated from loss on ignition organic matter contents for several marshes around the world (Crooks et al., 2002;Neubauer, 2008;Roner et al., 2016), and approximates to local data in Boston Harbor and Morro Bay (see section 2.3). For each site, Figure 7 shows the contour lines of C 0 and D 50 values that yield given values of k = Q dep +Q org . The dashed blue line corresponds to conditions on C 0 and D 50 for marsh accretion to match the current RSLR. Dashed red lines indicate the observed accretion rates, but do not represent the associated error. Sediment supply conditions corresponding to low and high C 0 and D 50 bound the gray box, and the black star represents the concentration determined using the MERIS data and D 50 = 50 µm. We remind the reader that due to the assumption of negligible turbulence on the marsh surface, Q dep is likely overestimated and therefore the required sediment supply to match a given RSLR is likely under estimated.
In all cases, the contours follow a hyperbolic curve. This behavior implies that at high sediment concentrations, variations in C 0 have less impact on Q dep than variations in D 50 , and vice versa. Conversely, the point of the contour line that is closest to graph origin represents the conditions where variations in each parameters exert an equal influence on accretion rates. This behavior is preserved along the 1:1 diagonal. High sediment concentrations require high shear stress at the bed to mobilize sediment (Fagherazzi et al., 2006) if generated in situ. If the sediment is sourced from either offshore or rivers, high turbulence is needed to keep sediment in suspension. High suspended sediment concentrations are associated with strong currents or high waves, increasingly so for large particle sizes (Yang et al., 2008). Consequently, we may expect higher sediment concentrations to be associated with larger particle sizes. Such conditions are typical of storm events, spring tides or fluvial flood discharges. They may be observed on the field, for instance when gravel is backed-up against marsh scarps after storm events, or when strong tides leave sandy trail bars on the lee side of pioneer plants.
Figures 7A-C represent three neighboring marshes in Poole Harbour, Dorset, UK, for which tidal and sediment conditions are considered identical. Wych Lake ( Figure 7C) is higher in the tidal frame than the other sites, and as a consequence, the contour lines are both further from the origin and further apart. Hence, for equal sediment supplies and tidal forcing, increasing elevation reduces deposition rates and increases the demand in sediment to maintain elevation within the tidal frame. For example, platforms in Morecambe Bay and the Mersey Estuary (Figures 7G-H) are close to OHHT, and are seldom flooded. As a consequence, not only do these sites require more sediment to match current rates of sea level rise, but they would also require a greater increase in C 0 or D 50 if RSLR increased. This situation is hinted at by Pringle (1995), who finds medium to coarse silts (31 µm) and very fine sands of up to 100 µm in Morecambe Bay marshes. Conversely, ranges of 20 − 40 µm were observed by Roner et al. (2016) in the Venice Lagoon, where salt marshes are notoriously low in the tidal frame .
We show the conditions necessary to match observed positive accretion rates (dashed red lines), but recommend caution when considering these data (see section 3.2). Indeed, though it seems that most sediment supply condition boxes (gray boxes) contain the dashed red lines, the existence of negative accretion when conditions predict more than 10 mm y −1 of accretion demands a critical view of the observed accretion values. Regardless, all field-measured sediment supply conditions generate enough accretion in all sites, except the Mersey Estuary and Morecambe Bay (Figures 7G-H), for the platform to keep up with current RSLR (dashed blue lines). Aside from Boston Harbour (Figure 7E), even the lower bounds of measured sediment supply are sufficient to match more than 10 mm y −1 of sea level rise. Our application of Stokes' law with negligible current and turbulence may explain this overestimation of k. However, we must also consider that field measurements provide only a snapshot of sediment supply conditions at any given location. Leroux (2013) highlighted the high temporal variability of sediment supply; he measured peak concentrations of up to 5, 000 g m −3 during a spring tide, while base concentrations were 500 g m −3 in tidal creeks of the Mont-Saint-Michel Bay, France. The high shear stresses caused by storms also generate peaks in sediment concentrations (Fagherazzi and Priestas, 2010). In this respect, averaged MERIS data (black stars) may better represent the temporal variability of sediment supply. To further improve our understanding of sediment supply, we suggest that k contour lines may be combined with accretion monitoring through marker horizons and grain size distribution (GSD) analyses to determine average sediment concentrations during deposition events. While our 0-D model does not account for distance to creeks, the results of Zhang et al. (2019) show that it is an important factor of marsh deposition, and we suggest that these results should orient future methods of deposition measures.

Insight on the Roles of Elevation and Tidal Range
In this section, we compare the 8 marsh sites to better understand the interaction between platform elevation and tidal records. In Figure 8, we calculate k for the same range of sediment supply conditions as in section 3.3 and represent the conditions leading to k = 2.5 mm y −1 . Each subplot shows the accretion contour lines for each site for various initial elevations z 0 . Indeed, elevation within the tidal frame determines the (1) proportion of N t tidal cycles for which the platform floods (Equation 6), and (2) the maximum depth D max of each flooding event, thus influencing deposition within each cycle (Equation 7). Although below-ground production is known to vary with elevation, these variations are not well quantified above elevations of MHT (Morris et al., 2002), and we therefore maintain Q org = 0.06·Q dep .
In Figure 8A, the initial elevation is the observed main platform elevation z max(f Z ) . Regardless of mean tidal range, the normalized elevation in the upper tidal frame, defined as z * in Equation (9), exerts a positive influence on the sediment supply necessary to meet k = 2.5 mm y −1 .
We note that for z 0 = OHHT (Figure 8B), sediment requirements are so high that for Boston Harbor and the Swale Estuary, sediment larger than fine sand would be needed for marshes to be at equilibrium of moderate sea level rise rates. Such conditions are typical of beaches and sand dunes rather than marshes (Hayden et al., 1995), suggesting that flooding patterns at these sites do not allow marshes to reach these elevations.
Conversely, if z 0 = MHT, very little variation between sites of different tidal ranges is observed, suggesting that the effect of tidal range on accretion rates increases with platform elevation. Hence, similar sediment supply conditions shown ( Figure 8C) may allow low marsh platforms around the world to withstand moderate sea level rise rates of RSLR = 2.5 mm y −1 , whereas local tidal regimes would affect high platforms more strongly. This low sediment demand is similar to that observed in Figure 8D, where initial elevations are z 0 = MSL. For these low elevations, mean tidal range also exerts a weak influence on accretion rates. More importantly, the little difference in accretion rates between z 0 = MSL and z 0 = MHT imply that pioneer platforms are likely to reach MHT, thus ensuring the regeneration of marsh surface area after lateral erosion events. We note that our model does not account for variable sediment concentrations on the platform, and is likely to overestimate deposition on parts of the platform that are far from creeks or scarps. Indeed, Temmerman et al. (2005) show that deposition rates decrease with distance from creeks and marsh edges. Pioneer platforms with different creek network properties, due for example to vegetation development (Kearney and Fagherazzi, 2016), may grow at different rates.

CONCLUSIONS
In this contribution, we test a 0-dimensional settling model to estimate elevation change on real salt marsh platforms, and compare these results with accretion fluxes derived from DEM surveys taken at least four years apart. While elevation changes observed through lidar have too high errors to yield accurate results, initial elevation measurements are sufficiently accurate to examine model results and their sensitivity to sediment supply conditions. We find that using a sinusoidal tidal forcing to simulate elevation evolution cannot explain the current elevation of the marshes we examined, which were located between MHT and OHHT. While we did not examine enough sites to draw general conclusions on the distribution of salt marsh platforms within the tidal frame, our results suggest that simplified sinusoidal tides cannot account for the full evolution of salt marshes.
Using a representative subset of real tidal forcing, we calculate settling fluxes that better explain current platform elevations. When accounting for a 6% contribution of belowground organic production to accretion fluxes, modeled accretion rates for marshes that are low in the upper tidal frame (but still above MHT) are mostly sufficient to keep pace with current rates of relative sea level rise under most observed sediment supply conditions determined by MERIS. Conversely, sites that are closer to OHHT require coarser or more concentrated sediment. The low hydroperiod associated with such high platforms suggests that small or light flocs do not have time to settle in sufficient quantity for the platform to maintain its elevation. Under storm surge conditions, however, advection of highly concentrated fine material and prolonged hydroperiod may counteract the effect of elevation. It follows that marshes that reach a high position in tidal frame should contain coarser sediment than platforms that do not attain this elevation, unless they are subject to frequent storms. The existence of such high platforms is therefore conditioned by the availability of coarse sediment or finer material in high volumes (or very high organic matter contents), typically mobilized during storms, floods and spring tides. Conversely, we find that low platforms require a weaker sediment supply conditions to keep pace with RSLR. Further investigation into accretion rates with low starting elevations (MHT and MSL) suggests that established low platforms are likely to contribute to longterm marsh regeneration regardless of tidal regimes, but also that plant establishment is likely the bottleneck of marsh progradation processes.
To add weight to the conclusions drawn above, further research may investigate the relationship between marsh elevation and tidal records over a larger dataset. Furthermore, measuring sedimentation and back-calculating sediment concentration from field samples in different sites would allow to confirm the behavior suggested by the model. Future work may also investigate the size of deposited particles at various distances from scarps and tidal creeks to determine the detailed mechanisms of settling on wide vegetated platforms.

AUTHOR CONTRIBUTIONS
GG designed the study, collected and analyzed the data and wrote the article with input in all aspects from SM.