Landscape evolution in tidal embayments: Modeling the interplay of erosion, sedimentation, and vegetation dynamics

Authors

  • Andrea D'Alpaos,

    1. Dipartimento di Ingegneria Idraulica, Marittima Ambientale e Geotecnica and International Centre for Hydrology “Dino Tonini,”, Università di Padova, Padua, Italy
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  • Stefano Lanzoni,

    1. Dipartimento di Ingegneria Idraulica, Marittima Ambientale e Geotecnica and International Centre for Hydrology “Dino Tonini,”, Università di Padova, Padua, Italy
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  • Marco Marani,

    1. Dipartimento di Ingegneria Idraulica, Marittima Ambientale e Geotecnica and International Centre for Hydrology “Dino Tonini,”, Università di Padova, Padua, Italy
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  • Andrea Rinaldo

    1. Dipartimento di Ingegneria Idraulica, Marittima Ambientale e Geotecnica and International Centre for Hydrology “Dino Tonini,”, Università di Padova, Padua, Italy
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Abstract

[1] We propose an ecomorphodynamic model which conceptualizes the chief land-forming processes operating on the intertwined, long-term evolution of marsh platforms and embedded tidal networks. The rapid network incision (previously addressed by the authors) is decoupled from the geomorphological dynamics of intertidal areas, governed by sediment erosion and deposition and crucially affected by the presence of vegetation. This allows us to investigate the response of tidal morphologies to different scenarios of sediment supply, colonization by halophytes, and changing sea level. Different morphological evolutionary regimes are shown to depend on marsh ecology. Marsh accretion rates, enhanced by vegetation growth, and the related platform elevations tend to decrease with distance from the creek, measured along suitably defined flow paths. The negative feedback between surface elevation and its inorganic accretion rate is reinforced by the relation between plant productivity and soil elevation in Spartina-dominated marshes and counteracted by positive feedbacks in multispecies-vegetated marshes. When evolving under constant sea level, unvegetated and Spartina-dominated marshes asymptotically tend to mean high water level (MHWL), different from multiple vegetation species marshes, which can make the evolutionary transition to upland. Equilibrium configurations below MHWL can be reached under constant rates of sea level rise, depending on sediment supply and vegetation productivity. Our analyses on marine regressions and transgressions show that when the system is in a supply-limited regime, network retreat and expansion (associated with regressions and transgressions, respectively) tend to be cyclic. Conversely, in a transport-limited regime, network reexpansion following a regression tends to take on a new configuration, showing a hysteretic behavior.

1. Introduction

[2] Tidal environments and landforms, both channeled and unchanneled, host dynamic ecosystems of vital biological importance that are exposed to the effects of climatic changes (e.g., relative mean sea level (RMSL)) and may be negatively impacted by human pressures. To address related issues of conservation, it is of critical importance to improve our understanding of the key land-forming processes which drive their morphogeneis and evolution. The variety and complexity of landforms and morphological patterns displayed by tidal environments, together with their relevance as ecosystems characterized by high primary productivity and as buffer zones between land and sea, make these environments a subject of great theoretical and practical interest. Modeling of tidal environments requires characterizing the strong interaction among dynamical processes of physical and biological nature. Marsh platforms and channel networks cutting through them represent a clear example of the interplay between hydrodynamics, morphological and ecological dynamics. We aim at the construction of a robust theoretical framework capable of providing elements for the prediction of the long-term morphological fate of tidal embayments in general. Such a target can be pursued only through a model describing the intertwined ecomorphodynamic processes governing the evolution of marsh platforms and of the tidal channels cutting and meandering through them.

[3] As a first step toward a complete tidal ecomorphodynamic model, D'Alpaos et al. [2005] recently addressed the problem of channel network initiation over an existing tidal flat, deemed of central importance because of the strong control exerted by channel networks on hydrodynamics, sediment transport dynamics and nutrient exchanges within tidal environments [Fagherazzi et al., 1999; Rinaldo et al., 1999a, 1999b; Christiansen et al., 2000; Marani et al., 2003, 2006b; Feola et al., 2005; Temmerman et al., 2005]. They assumed that the process of tidal network early development acted on timescales considerably shorter than those involved in other relevant ecomorphodynamical processes shaping the system, e.g., tidal meandering, organic and inorganic sediment deposition, vegetation dynamics, soil compaction, subsidence and sea level rise (SLR), an approach taken by Rinaldo et al. [1993, 1995] and Rigon et al. [1994]. In fact, in agreement with a number of conceptual models of salt-marsh growth (see, e.g., the review by Allen [2000] and references therein), the hypothesis is supported that a time in the life of a tidal network exists during which it quickly cuts down the intertidal areas giving them a permanent imprinting. Such a process is later possibly followed by a slower network elaboration (e.g., by meandering [Gabet, 1998]) and by vertical accretion of intertidal areas. In turn, these areas usually become vegetated, thus radically changing their morphodynamic behavior, when a critical elevation is reached or exceeded. The complex network structures generated through the model proposed by D'Alpaos et al. [2005] met distinctive real-network statistics, reproducing several observed characteristics of geomorphic relevance, such as, e.g., the probability distribution of unchanneled lengths [Marani et al., 2003].

[4] However, although tidal channels control hydrodynamics as well as sediment and nutrient fluxes, sedimentation and accretion patterns in salt marshes and the related ecological dynamics prove of vital importance. The latter processes influence tidal fluxes within the channel network thus leading to their erosion, infilling or maintenance. Moreover, accretion of mud flats and salt marshes provides a valuable natural coastal defence in a regime of rising sea level, serving to dissipate energy from high tides and wind waves. In essence, it is this slow morphodynamic component that dictates the long-term fate of tidal landforms, ultimately determining whether or not the ecosystems can self-adjust to changing environmental conditions like (RMSL). In order to embody the key mechanisms responsible for the delicate balance and strong feedbacks between hydrodynamics, morphological and ecological dynamics of tidal environments, in this paper we address the problem of the coevolution of the topography of the intertidal areas and of a network of tidal channels in its early and mature development stages.

[5] Several models have been proposed to investigate the vertical growth of salt marshes, where the sedimentation on the marsh platform is a function of sediment supply and marsh elevation [e.g., Krone, 1987; French, 1993; Allen, 1990, 1995; Temmerman et al., 2005] or biomass [Randerson, 1979; Morris et al., 2002]. Suspended sediments are transported across the shallow areas adjacent to channel networks mainly by advection [Pritchard and Hogg, 2003] even though dispersion processes driven by concentration gradients become important as flow velocities decrease (e.g., around high or low water slacks or in proximity of watershed divides).

[6] Biotic factors also play a fundamental role in influencing salt-marsh morphodynamics. When vegetation extensively encroaches the marsh surface, it influences tidal velocity profiles [e.g., Leonard and Luther, 1995; Nepf, 1999]. The rate at which water floods onto and drains from the platform adjacent to a channel is in fact influenced by the drag caused by the stems of macrophytes living upon it [Nepf, 1999], which increases linearly with plant density [Lopez and Garcia, 2001]. Furthermore, the presence of vegetation increases the deposition of inorganic particles by trapping the suspended sediment [Leonard and Luther, 1995; Christiansen et al., 2000], and enhances the accretion of the marsh surface through the production of organic matter [e.g., Gleason et al., 1979; Randerson, 1979; Leonard et al., 2002; Morris et al., 2002]. Temmermann et al. [2005] recently analyzed short-term morphodynamic changes associated with the effects of vegetation on flow and sediment patterns. Vegetation dynamics influence also the planimetric evolution of tidal channels [e.g., Garofalo, 1980; Marani et al., 2002]. The influence of benthic fauna on erosion/deposition processes, and on sediment characteristics through bioturbation and biodeposition has been observed as well [Yallop et al., 1994; Wood and Widdows, 2002]. For example, microphytobenthos can physically shield sediment and alter substantially its cohesion, and overall bioturbation due to, e.g., clam harvesting can play a role in altering the morphology of a lagoon [e.g., Wood and Widdows, 2002].

[7] Other studies have analyzed the influence of vegetation on the long-term morphodynamic evolution of tidal environments. For example, Mudd et al. [2004] modeled the vertical growth of a marsh transect encroached by vegetation, while D'Alpaos et al. [2006] focused on the evolution of channel cross sections, starting from the initial channel formation within a tidal flat, taking into account the role played by vegetation on the observed cross-sectional geometry. However, a comprehensive approach taking into account the fully 3-D morphogenesis and long-term intertwined morphodynamic evolution of salt marshes and of the channel networks cutting through them is still missing, although attempts of modeling ecological and morphological dynamics have been proposed [Kirwan and Murray, 2005]. We therefore address the driving factors which lead to the observed sedimentation patterns displayed by tidal environments, tracking the growth of the intertidal platform, the evolving channel morphology and vegetation dynamics. The model is set up to be directly coupled with the model of channel network ontogeny previously proposed by D'Alpaos et al. [2005].

[8] The outline of this paper is as follows. In section 2 we briefly describe the model structure and the main physical and mathematical assumptions. Section 3 then presents and discusses the main results obtained by applying the model under different scenarios of varying suspended sediment concentration (SSC), absence or presence of halophytic vegetation, RMSL rise. In section 3 we also compare the modeled sedimentation patterns and marsh topographies to observed tidal morphologies. Finally, section 4 draws a set of conclusions and some remarks on forthcoming developments.

2. Morphodynamic Model

[9] We have developed a shallow water, depth-integrated morphodynamic model able to describe the long-term evolution of the intertidal areas and their channel network, accounting for the strong feedback mechanisms between channel and marsh surface morphology. The use of a simplified process-oriented model is motivated by the necessity of gaining fundamental knowledge about the key physical and biological processes involved while simulating geologic time spans. Indeed, modeling of biological processes is essential [Marani et al., 2006a, 2006b]. Moreover, our parsimonious approach is justified by the fact that complex models could not be used to describe the evolution of a tidal environment over morphologically meaningful periods of time, without a prohibitive numerical effort. We therefore model the hydrodynamic field on the marsh platform using a simplified version of the 2-D shallow water equations, suitably modified in order to account for wetting and drying processes on the marsh surface. The flow field within the channel network is obtained by assuming a quasi-static 1-D propagation of the tide. The overall hydrodynamic field, obtained by coupling tidal propagation within the channels and on the marsh area, is then used in the sediment transport model under the assumption that sediment transport is in local equilibrium with hydrodynamics. A suspended load parametrization for fine cohesive sediment, containing advective and dispersive contributions and accounting for erosion and deposition effects, is developed to model the topographic evolution of the marsh surface.

2.1. Depth-Averaged Hydrodynamic Field

[10] In the case of frictionally dominated tidal embayments, the 2-D shallow water equations can be simplified by assuming that a balance holds in the momentum equations between water surface slope and friction [Rinaldo et al., 1999a]

equation image

where η1(x, t) is the local deviation of the water surface from its instantaneous average value, η0(t), referenced to the mean sea level (MSL); U(x, t) is the local depth-averaged velocity with components (Ux, Uy) in the x, y directions, respectively; D(= η0 + η1zb) is the local flow depth on the marsh surface, with zb the local bottom elevation of unchanneled areas, referenced to the MSL; ∇ = (∂/∂x, ∂/∂y) is the gradient operator; t is time; λ is a bottom friction coefficient which derives from Lorentz' linearization of bed shear stress formulation. Such a coefficient, which depends on Chèzy's friction parameter, χ, and on a characteristic value of the maximum tidal current, equation imagemax, is taken to be constant within the considered intertidal regions. In the present model we have assumed χ = 10 m1/2/s and equation imagemax = 0.2 m/s in agreement with Rinaldo et al. [1999b] and Marani et al. [2003].

[11] By substituting equation (1) in the continuity equation Rinaldo et al. [1999a] showed that, for a given instant t, the field of free surface elevations over unchanneled marsh areas, characterized by an average water depth D0(= η0zmean, where zmean is the mean marsh bottom elevation), can be determined by solving a Poisson boundary value problem

equation image

with the requirement of zero flux on impermeable boundaries, and by assuming spatially independent local elevations, i.e., η1 = 0, within the channel network, which embodies the hypothesis of instantaneous propagation of the tide within the channels. Equation (2) can be solved at any instant through the tidal cycle once a forcing tide is assigned. On the basis of the resulting water surface topography, flow directions can be obtained at any location on the intertidal areas by determining its steepest descent direction, and watersheds related to any channel cross section may be identified. The above simplified Poisson model, applies, in principle, to relatively short tidal basins (i.e., the length of the basin is much smaller than the frictionless tidal wavelength [e.g., Lanzoni and Seminara, 1998]), in which the tidal propagation across the intertidal areas flanking the channels is dominated by friction (circumstance enhanced, e.g., by the presence of dense vegetation [Marani et al., 2003]) and the spatial variations of the instantaneous water surface within the intertidal areas are significantly smaller than the instantaneous average water depth. Nevertheless, as thoroughly discussed by Marani et al. [2003], the Poisson model leads to quite robust estimates of watersheds and land-forming discharges (which have been shown to be related to watershed and cross-sectional areas), even when the hypothesis of a small tidal basin is not strictly met.

[12] On the basis of the water surface elevation field on the unchanneled portion of the basin, the distribution of bottom shear stresses due to tidal currents, can be determined as follows

equation image

where τ(x, t) is the local value of bottom shear stress with components (τx, τy) in the x, y directions respectively, and γ is the specific weight of water.

2.2. Sediment Erosion and Deposition

[13] We model the time evolution of marsh sedimentation patterns by considering cohesive and nearly uniform bottom sediment, consistently with field observations. Furthermore, we assume that this fine sediment, characterized by a mean given diameter, d, is transported mainly in suspension. The morphological evolution of the bed topography of the marsh surface is governed by the sediment continuity equation which reads

equation image

where zb is the local bottom elevation, p is void fraction in the bed, Qd and Qe are the local deposition and the erosion fluxes, respectively, with the dimensions of [L/T], representing sediment volume exchange rates, per unit area, between the water column and the bed. The deposition flux, Qd, is given by

equation image

where Qds is the settling rate, Qdt is the trapping rate due to the effect of the plant canopy, Qdb is the net organic production due to the presence of vegetation, and equation image is a coefficient accounting for the frequency with which a given concentration value, equation image0, occurs, as will be described in detail in section 2.4. If the marsh is not vegetated, both Qdt and Qdb are identically zero, whereas Qds acts even when the marsh surface is not vegetated and, in this case, is the chief process responsible for marsh accretion. The settling and trapping rates can be determined only once the equation for SSC has been solved. In fact, a feedback mechanism exists according to which sediment transport processes, influenced by the hydrodynamic field, produce changes in the elevation of the marsh platform, which in turn modify both the hydrodynamics and sediment dynamics [e.g., French, 1993; Lanzoni and Seminara, 2002; Mudd et al., 2004]. However, the bottom topography usually evolves on a much longer timescale than the water motion does. This makes it possible to decouple the solution of the hydrodynamic field from the morphological evolution.

[14] Using the velocity field and water depth calculated through the simplified hydrodynamic model, the equation for the conservation of sediment transported as a dilute suspension is first solved, in order to determine concentration values on the unchanneled portion of the basin. Under the assumption that the flow is fully turbulent such an equation takes the form of a 2-D advection-diffusion equation for depth-averaged volumetric sediment concentration, equation image(x, t), which reads

equation image

where D is the local water depth, U is the local depth-averaged velocity field, km is a horizontal mixing coefficient which is assumed to be constant in space and time and which accounts for dispersive effects associated with vertical variations in both flow velocity and sediment concentration. On the basis of the Elder relationship [Elder, 1959], km has been assumed equal to 0.3 m2/s, in the present model, neglecting, for the sake of simplicity, as a first approximation, its spatial variability and dependence on plant density [Nepf, 1999]. The evolution in time of the amount of sediment in the water column is therefore determined by the advective and dispersive transport of sediment and erosion and deposition processes at the bottom.

[15] Laboratory and field investigations have been extensively carried out with the aim of bringing insight into the processes of erosion and deposition of cohesive sediments [e.g., Einstein and Krone, 1962; Mehta, 1984]. Even though many models have been proposed to determine Qe and Qds, a significant contention concerning the most appropriate mathematical formulations which should be adopted exists. This is a consequence of the complexity of the involved processes.

[16] In the present study we evaluate the erosion flux, Qe, by way of a relationship which can be applied when the bed properties are relatively uniform over the depth and the bed is consolidated [e.g., Mehta, 1984], i.e.,

equation image

where τ0 = ∣τ∣ is the absolute value of the local bottom shear stress evaluated through (3), τe is a critical shear stress which must be exceeded in order to break up the bed and entrain particles, and Qe0 is an empirical coefficient, with the dimensions of [L/T], which depends on sediment properties, on the salinity of water, biological disturbance or binding. In accordance with field observations showing that tidal currents are too weak to produce excess shear stress causing erosion over a vegetated marsh platform [e.g., Christiansen et al., 2000], we further assume that the erosion flux vanishes as vegetation grows on the marsh surface. Furthermore, sediment resuspension on salt marshes and tidal flats is mainly caused by wind-wave-induced shear stress, a process requiring a proper description [e.g., Carniello et al., 2005] which has not been yet included in our modeling approach.

[17] As far as the deposition rate is concerned, various sedimentation mechanisms have to be considered. We estimate the deposition due to settling, Qds, which is mainly due to the formation and breakup of flocs, by way of the formulation proposed by Einstein and Krone [1962] who assumed that most of the particles settled in flocs as long as near bed shear stresses are small enough to prevent their breaking up, namely,

equation image

where ws is the settling velocity which depends on the size of sediment flocs, τd is a critical shear stress above which flocs break up and no longer settle, being reentrained in the water column, and equation image the local depth-averaged volumetric SSC. Such an empirical description which takes into account the probability that a floc will survive the near-bed turbulence, is usually employed to describe cohesive sediment deposition in coastal environments [e.g., Krone, 1987; Pritchard and Hogg, 2003; Temmerman et al., 2005].

[18] Vegetation encroachment at the surface, for emergent marsh platforms, increases sediment deposition rates as a consequence of trapping effects and of organic soil production. It is generally agreed that turbulence has a primary influence on sediment transport in intertidal areas [e.g., French et al., 1993]. A number of previous analyses and studies indicate that the amount of trapped sediment is proportional to the SSC and to the number of plant stems that can both reduce the turbulent energy and capture sediment particles [e.g., Leonard and Luther, 1995; Nepf, 1999; Leonard et al., 2002]. Similar to D'Alpaos et al. [2006], we have expressed the trapping rate using the approach proposed by Palmer et al. [2004], which reads

equation image

where U = ∣U∣ is the absolute value of the local flow speed, ε is a capture efficiency which gives the rate at which transported sediment particles are captured by plant stems, ds is the stem diameter, ns is the stem density, hs is the average height of the stems, and D is the local flow depth. Such vegetation characteristics are linked to plant biomass, as it will be specified later on. Note that when vegetation protrudes above the water surface, hs is replaced with D, i.e., the minimum between hs and D is chosen in order to determine the effective height which contributes to the trapping of sediment particles. The capture efficiency, ε, can be written as

equation image

where d is particle diameter, ν is the kinematic viscosity of water, αε = 0.224, βε = 0.718, and γε = 2.08 are empirical coefficients [Palmer et al., 2004].

[19] Finally, the production of organic matter, Qdb, can be directly linked to annually averaged aboveground plant dry biomass, equation image, following the pioneering work of Randerson [1979]. According to the formulation proposed by Mudd et al. [2004] and employed by D'Alpaos et al. [2006], Qdb can be expressed as follows

equation image

where equation imagemax is the maximum value of the biomass, and Qdb0 is a typical deposition rate, with the dimensions of [L/T], which is derived empirically from field measurements. Blum and Christian [2004] report a maximum organic sediment accretion of about 9 mm/yr for a Spartina alterniflora marsh in Virginia. However, as will be discussed later in the paper, salt marshes populated by a single species plant may experience different organic accretion rates and sedimentation patterns than marshes on which various vegetation species compete with one another. Moreover, it should be noted that the aboveground storage of organic material in salt marshes is an extremely complex process that involves root production, microbial decomposition, as well as edaphic factors such as nutrient availability and salinity [Blum and Christian, 2004; Silvestri and Marani, 2004] which are not considered in our simplified approach. Vegetation characteristics such as stem dimensions and density, and plant productivity will be discussed in detail in section 2.3.

2.3. Parametrization of Vegetation

[20] In order to determine the deposition rate due to trapping, Qdt, and the production of organic matter, Qdb, the dependence of these quantities on vegetation characteristics, and in particular on plant biomass needs to be specified. While several biotic and abiotic factors may be relevant in determining plant productivity [see Silvestri and Marani, 2004, and references therein], locally, biomass production can be related mainly to the elevation of the marsh platform encroached by plants. We furthermore consider two different vegetated scenarios.

[21] In the first scenario we consider a salt marsh populated by a monospecific vegetation species. This is, for example, the case of the salt marshes developed at North Inlet estuary, South Carolina, which are characterized by a prevailing presence of Spartina alterniflora, a species of halophytic vegetation quite common in tidal environments. On the basis of a long record of plant productivity, collected by Morris and Haskin [1990] and Morris et al. [2002] at North Inlet estuary, plant biomass may be expressed as a linearly decreasing function of salt marsh elevation [D'Alpaos et al., 2006]. This agrees with the observation put forth by a number of researchers, who have shown that the increased pore water salinity caused by evapotranspiration, enhanced by the progressive reduction of the duration and frequency of inundation, as the platform elevation increases, can limit the growth of, or be fatal to, salt marsh macrophytes [e.g., Phleger, 1971]. We therefore assume that Spartina alterniflora biomass decreases as the elevation of the marsh platform increases, namely,

equation image

where equation imageIps is the local peak season biomass according to the first scenario, equation imagemax is the maximum annual biomass value, zb is the local marsh elevation, zmax is the maximum elevation withstood by Spartina, zmin is the minimum value at which Spartina grows on the marsh surface. We assume that zmin is equal to the MSL, in agreement with observations reported by a number of researchers [e.g., Frey and Basan, 1985]. The progressive increase in zb toward zmax leads to a decrease in plant productivity, eventually preventing Spartina survival.

[22] In order to take into account the seasonal variability in biomass, which usually peaks during the summer months [Morris and Haskin, 1990], we rely on the relationship proposed by Mudd et al. [2004] and consider equation image as an annually averaged biomass value.

[23] Relationship (12) does not seem to hold, however, when the salt marsh surface is covered by a variety of halophytic species as in the case of the marshes located in the Venice Lagoon, where a mosaic of vegetation patches is observed [Marani et al., 2004; Silvestri et al., 2005]. Field and remote sensing analyses provide evidence for an increase in vegetation biomass (and also in species richness) with soil elevation, thus clearly indicating that more favorable conditions for plant development are found on higher soils. These results suggest that less frequently flooded, and thus better aerated, soils are colonized by a greater number of species, whereas lower marsh areas, which are flooded frequently and for longer periods, usually host only few selected, more resistant species usually developing in monospecific populations. Therefore, in order to investigate sedimentation patterns arising from this second scenario and compare the results to those obtained by applying the model to the single-species scenario, we have modified equation (12) as follows:

equation image

where zmin is the elevation at which halophytes start to encroach the marsh surface; and zmax is the elevation in correspondence to which halophytes have their maximum biomass productivity. Equation (13) states that the local peak season biomass in the second scenario, equation imageIIps, is a linearly increasing function of marsh platform elevation as long as zb is in the range between zmin and zmax, while, as soon as zb becomes greater than zmax, equation imageIIps keeps constant and equal to the maximum annual biomass value.

[24] Finally, on the basis of the data collected by Morris and Haskin [1990], vegetation characteristics like stem density per unit area, ns, average height of the stems, hs, projected plant area per unit volume, as, and stem diameter, ds, can be expressed as a function of plant biomass as follows:

equation image

where αn = 250, βn = 0.3032, αh = 0.0609, βh = 0.1876, αa = 0.25, βa = 0.5, αd = 0.0006, and βd = 0.3, are empirical coefficients whose values have been assigned according to Mudd et al. [2004] and D'Alpaos et al. [2006]. In order to carry out a fair comparison we have assumed that analogous relationships linking plant characteristics to their biomass, hold in both vegetated scenarios.

2.4. Numerical Approach

[25] We assume that the marsh bottom evolves over a much longer timescale than the flow field. A morphodynamic iteration, whose definition requires the numerical solution of the equations presented above, proceeds as follows. For a given configuration of the bottom topography, which is taken to be fixed in the short timescale represented by a tidal cycle, equation (2) is solved at any instant of the tidal cycle, and the characteristics of the 2-D flow field within the considered tidal domain are therefore determined.

[26] It is worthwhile to observe that, as a consequence of the morphodynamic evolution of the bottom, some portions of the marsh surface are subject to repetitive flooding and drying processes. In order to deal with partially wet domains, we follow the procedure proposed by Defina [2000], which allows for the application of classical numerical schemes without any ad hoc modification. We refer the reader to Defina [2000] and Lanzoni and Seminara [2002], for the detailed derivation, through a phase-averaging procedure, of the set of shallow water equations governing the flow over a partially dry surface. Here we only report the momentum and Poisson equations obtained by applying the phase-averaging procedure which read

equation image
equation image

where

equation image
equation image
equation image
equation image

[27] In particular, subscript 0 denotes the average value of a given variable; e is a characteristic scale of the spatial variations of bottom elevation; erfc is the complementary error function; equation image is the local value of the effective flow depth; Ψ = Ψ(x, η0) accounts for the fraction of the domain which is wetted when the free surface elevation η0 exceeds zmean, and strictly depends on the statistical distribution of bottom elevation within each representative elementary area used to discretize the flow domain. Under the assumption that, as a first approximation, the probability density function of bed elevations distributed around the mean bed elevation is Gaussian, the function Ψ can be expressed analytically through equation (18). It is easily recognized that when equation imagee, Ψ = 1 and Φ = equation image3/2, and therefore equations (1) and (2) are recovered.

[28] The 2-D flow field resulting from the solution of equation (16) is then used to calculate the erosion and deposition fluxes given by equations (7), (8), and (9). It is also used to solve the advection-diffusion equation (6) for the SSC, with the constraint that a constant concentration, equation image0, is available throughout the semidiurnal tidal cycle along the channel network or, as will be specified later, at the inlet of the considered tidal embayment. Moreover, in order to take into account that in real settings a given concentration is likely to occur with a frequency equation image (and therefore not at every tidal cycle), the deposition rates, which depend on the local value of the concentration, must be multiplied by equation image (e.g, equation (5)). Concentration measurements carried out at our field sites within the Venice Lagoon (Consorzio Venezia Nuova, http://www.salve.it), show that equation image = 0.15 when ρsequation image0 = 55 mg/L. In order to define morphologically significant bed elevation changes (i.e., affecting the flow field) we proceed as follows. We compute the maximum local bottom variation relative to one tidal cycle, Δzmax, and multiply it by a number of tidal cycles, ncycles, such that ∣Δzmaxncycles = 0.01(MHWL − zmean). Such a procedure makes it possible to determine a varying morphodynamic time step throughout the simulation (depending on the magnitude of sedimentation and erosion processes and the mean marsh elevation), which is equal to ncycles times the tidal period. The resulting computational steps make it possible to compute the morphologic time characterizing the evolution process. Once a new topographic configuration of the marsh platform is determined, a new morphodynamic iteration is carried out.

[29] The assumption of a constant SSC along the channel network can be relaxed (of course with additional computational effort), and the effects related to variations in SSC, in space and time, along the channel network can be accounted for. To this end we have imposed a constant value of sediment concentration at the inlet of the considered watershed, and, taking advantage of the fact that tidal channel curvature ratio (i.e., the ratio of channel width to the minimum radius of curvature of channel axis) is a typically small parameter from field observations [Marani et al., 2002], we have solved numerically the 1-D advection equation for depth-averaged sediment concentration

equation image

where s is the curvilinear landward oriented longitudinal coordinate of the channel axis; Q is the local discharge flowing within the channel; Ω is the local cross-sectional area; B is the local channel width, Uc and Dc are the local depth-averaged velocity and the local water depth within the channel, respectively. Qe and Qds are the erosion and deposition fluxes which are computed once the along-channel bottom shear stress has been determined. Values of the SSC within the network, equation image0(s, t), determined through the solution of equation (21), are then used for the numerical solution of the 2-D advection-diffusion equation (6). The discharge flowing through a given channel cross section, Q(s, t), can be computed, at every t, on the basis of a quasi-static propagation [e.g., Boon, 1975] within the channel network

equation image

where V(s, t) is the volume of water flowing through the considered cross section.

[30] The model can also describe the evolution of the channel network in response to changes in the tidal prism, P, which is the total volume of water exchanged through the outlet of a tidal network between low water slack and the following high water slack, i.e. during flood or ebb phases. Such changes are possibly due to variations in the elevation of the marsh platform or in RMSL. On the basis of Jarrett's “law” [O'Brien, 1969; Jarrett, 1976], we consider the cross-sectional area, Ω, to be related to the flowing tidal prism, P, through the relationship Ω = βpPαp, with βp = 10−4 and αp = 1.2. Observational evidence [e.g., Rinaldo et al., 1999b; Allen, 2000; Marani et al., 2002] and previous conceptual models of salt marsh growth [Allen, 2000], suggest that a reduction in P, due to the vertical accretion of the marsh platform flanking the channels, leads to a possible regression of the network for knickpoint retreat, and to a shrinking of channel cross sections as a consequence of the reduction of tidal fluxes within the network. On the contrary, an increase in the tidal prism, should lead to further incision of the channels through headward growth [D'Alpaos et al., 2005] and to an expansion of channel cross sections as a consequence of the swelling discharges. We further assume, following our earlier results, an instantaneous adaptation of channel cross-sectional geometry to the land-forming tidal fluxes shaping the network, and that channel width is related to the average channel depth through a constant width-to-depth ratio [Marani et al., 2002].

3. Results and Discussion

3.1. Simulation Settings

[31] We performed a number of numerical experiments in order to analyze the influence of (1) the initial configuration of marsh surface elevations, (2) the magnitude of SSC available within the channel network, (3) the parametrization of vegetation growth on the marsh surface, and (4) RMSL variations, on the long-term morphological evolution of the marsh platform.

[32] In all runs we considered fine cohesive and uniform sediments characterized by density ρs = 2600 kg/m3; particle diameter d = 50 μm; settling velocity ws = 2.0 × 10−4 m/s; porosity p = 0.4; and erosion rate parameter Qe0 = 1/ρs × 3.0 × 10−4 m/s [D'Alpaos et al., 2006]. Furthermore, because we are interested in the long-term morphological evolution of the marsh surface, the critical bottom shear stresses for erosion, τe, and deposition, τd, are those characterizing fully consolidated mud, i.e., τe = 0.4 N/m2, τd = 0.1 N/m2 [D'Alpaos et al., 2006]. A forcing semidiurnal sinusoidal tide, typical of spring conditions with a semiamplitude equal to 0.74 m around MSL, was assumed as appropriate for the Lagoon of Venice, where our primary observational data were collected [e.g., Day et al., 1999; Rinaldo et al., 1999b; Amos et al., 2004]. The simulations presented here were carried out in the computational domain represented by the actual tidal watershed of a channel network within the San Felice salt marsh, in the Venice Lagoon, which is shown in Figure 1 (see Marani et al. [2003] for details on the study area). This makes it possible to compare our results to observed morphologies. We assumed zmin = MSL; zmax = MHWL; the maximum value of the biomass equation imagemax = 2000 g/m2; and the deposition rate parameter Qdb0 = 0.01 m/yr [Blum and Christian, 2004].

Figure 1.

Channel network and topography in a portion of the San Felice salt marsh (Venice Lagoon, Italy) as determined from a lidar survey. Here color-coding shows higher elevations in red, and lower elevations are coded in shades of blue.

3.2. Unvegetated and Vegetated Scenarios With No RMSL Rise

[33] A first series of simulations was carried out by tracking the emergence of a marsh platform starting from a deep tidal flat with a spatially constant elevation below MSL (i.e., zb0 = −0.80 m below MSL, everywhere on the marsh surface). At the beginning of the simulation the bottom was submerged during the whole tidal cycle. As a first approximation, we assumed the volumetric SSC within the channel network to be constant in space and time. We furthermore neglected variations of the channel network structure and of the related watershed divides, as the marsh surface evolved in the vertical direction, and we did not consider RMSL rise effects.

[34] We analyzed the long-term evolution of marsh surface topographies in the absence of vegetation (e.g., Figures 2 and 3) and compared the results to those obtained by considering the two different vegetated scenarios (e.g., Figures 4, 5, and 6) .

Figure 2.

(a) Time evolution of bottom elevations and (b) total accretion rates as a function of bottom elevation at three salt marsh points (P1, P2, amd P3) along the overmarsh flow path shown in the inset of Figure 2a, in the absence of vegetation. P1 is located near the channel bank; P2 is located in the middle of the flow path; P3 is located near a watershed divide. MLWL, MSL, and MHWL are also shown. The inset in Figure 2b shows time evolution of deposition rates made dimensionless with the deposition rate computed at the channel bank plotted against the dimensionless distance from the channel ℓ/ℓmax (ℓ is the distance measured along a flow path, and ℓmax is the distance from the channel to the watershed divide). We note that the peak migrates toward the inner marsh as the platform grows in the vertical direction. This is due to the counteraction between the reduction in the advective transport with distance from the channel and the negative feedback between accretion rates and local elevation.

Figure 3.

Time evolution of mean marsh elevation (thick solid line) and of the variance of marsh elevations (dashed line) in the absence of vegetation. Maximum and minimum values of salt marsh elevations during the process of morphologic evolution are also shown (thin solid lines).

Figure 4.

Comparison of the temporal evolution of marsh surface topographies within the actual San Felice salt marsh, according to different scenarios portraying (top) the case of absence of vegetation, (middle) the case of Spartina dominance, and (bottom) the presence of a wide variety of vegetation species. The initial uniform bottom elevation was zb = −0.80 m above MSL.

Figure 5.

(a) Comparison of the time evolution of marsh surface elevations and (b) comparison of total accretion rates as a function of bottom elevation at point P1 of the flow path shown in Figure 2a, according to different scenarios: (1) the case of absence of vegetation, (2) the case of Spartina dominance, and (3) the presence of a variety of vegetation species. MLWL, MSL, and MHWL are also shown. The strong nonlinear behavior for the tidal system appears clearly.

Figure 6.

Comparison of (a) the time evolution of mean marsh elevation and (b) of the variance of marsh elevations, according to different scenarios portraying the case of absence of vegetation, the case of Spartina dominance, and the presence of a variety of vegetation species.

3.2.1. Unvegetated Scenario With No RMSL Rise

[35] In the unvegetated scenario the accretion rate is entirely due to settling of inorganic sediment. Figure 2 shows the temporal evolution of bottom elevation (Figure 2a) and the relationship between total accretion rate and local bottom elevation (Figure 2b), for three marsh points (P1, P2, and P3) located along the flow path shown in the inset of Figure 2a. Such a flow path was defined by considering a point located near a watershed divide (i.e., P3) and tracking the hydrodynamic path connecting such a point to the nearest channel through the time-invariant procedure proposed by Rinaldo et al. [1999a]. It is clearly seen that both the vertical growth and deposition rates tend to decrease with distance from the channel. This is due to the reduction in sediment concentration with distance from the channel, owing to deposition due to settling and to a progressive decrease of advective transport as prescribed by the advection-diffusion equation (6). In fact, advective transport attains a maximum near the channel and tends to vanish near the watershed divide, where, by definition, flow velocity is equal to zero. As a consequence, soil elevation at P1, which is located near the channel bank, quickly approaches MHWL, which is the maximum elevation that a given marsh point can attain, according to this scenario. It is interesting to note that, as long as the local elevation of the marsh surface lies below the mean low water level (MLWL), the hydroperiod, i.e., the ratio between the time interval during which a given marsh area is submerged to the total duration of the period of reference, remains nearly constant (e.g., Figure 2b). Therefore the deposition rates of allochthonous sediments exhibit their maximum, constant value. On the contrary, when the marsh platform emerges for a part of the tidal cycle, a qualitatively similar evolutionary behavior is observed (e.g., compare soil elevations at P1, P2, and P3). A negative feedback thus exists between local surface elevation and accretion rates (Figure 2b). Sedimentation rates progressively decrease, vanishing as soon as the local elevation tends to MHWL. In fact the reduction in hydroperiod progressively reduces sediment deposition, so that the long-term equilibrium elevation (equal to MHWL), at a given location, is attained asymptotically. This is in accordance with observational evidence by Pethick [1981] and with a number of numerical models describing salt-marsh vertical accretion within the tidal frame [e.g., Allen, 1990, 1995].

[36] The description of the evolutionary trend experienced by the three marsh points analyzed in Figure 2, although referring to site-specific conditions, are representative of the general morphological evolution of the marsh platform. Indeed, the evolution in time of bottom elevations along different flow paths (see e.g., Figure 4) displays, qualitatively, a general trend, showing that the magnitude of deposition processes decreases as the distance from the channel increases. Nevertheless, local hydrodynamics and morphology of the marsh surface greatly affect the magnitude of the deposition rates, so that deposition processes cannot merely be considered as function of the distance from the creek. A progressive migration of a deposition front from the channel banks to the inner portion of the marsh is also observed, emphasizing that the marsh platform evolves both in the vertical and in the horizontal planes. Such a migration is due to the counteraction between the reduction in the advective transport with distance from the channel and the negative feedback between accretion rates and local elevation (e.g., Figure 2b).

[37] An overall view of the evolution of the marsh platform is provided by Figure 3, which portrays the evolution in time of the mean and of the variance of marsh elevations, in the absence of vegetation. During the first stages of the evolution, the vertical accretion of the marsh platform is remarkably nonuniform, owing to the site-specific magnitude of the deposition rates, thus leading to an increase in both zmean and σz2. The variance of marsh surface elevations increases to a maximum value, which is approximately attained when the upper limit for the local elevation of the marsh surface (MHWL) is firstly reached by some marsh points, mainly located near the channel banks. The elevation at these sites, however, cannot grow any further within the tidal frame, and, in the following stages of marsh accretion, the gap in elevation between these points and lower sites progressively decreases. Therefore zmean asymptotically increases toward MHWL and σz2 asymptotically decreases to zero.

[38] The evolutionary scenario described above, is summarized in Figure 4 (top), which portrays some snapshots of the time evolution of marsh surface elevations in the absence of vegetation. The spatial representation of the bottom topography makes it possible to distinguish the different sedimentation patterns which characterize the marsh platform evolution. Because the drainage density of tidal networks is properly described by the mean unchanneled flow length, i.e., the mean overmarsh distance from a channel (measured along suitably defined hydrodynamic flow paths) [Marani et al., 2003], the rapid decrease in SSC and deposition rates with distance from the network, shows that the drainage density of a tidal network largely controls patterns of inorganic accretion. The evolving morphology is characterized by the formation of marsh levees, paralleling channel banks, which later broaden toward the inner portion of the marsh platform, that exhibits a typical concave-up profile (see, e.g., Silvestri et al. [2005] and Figure 1 for a qualitative comparison).

3.2.2. Vegetated Scenarios With No RMSL Rise

[39] We then turned to the analysis of the effects of vegetation growth on the evolution of the marsh surface by considering two different scenarios: (1) the case of a Spartina-dominated environment (e.g., North Inlet estuary) in which biomass decreases as soil elevation increases, due to the fact that Spartina is well-adapted to waterlogged soil conditions and (2) the case of an environment in which a large species diversity is present (e.g., the case of the Venice Lagoon). In the latter case the biomass-elevation relationship is reversed, because, as elevation increases, species adapted to hypoxic soil conditions are substituted by other species which are more competitive in a less stressful environment.

[40] Figure 5 portrays the temporal evolution of bottom elevations and the relative accretion rates for point P1 (see, e.g., Figure 2a), in the unvegetated scenario and in the two vegetated scenarios. Clearly, the temporal trends are the same in all of the cases when the marsh platform is not encroached by vegetation (zb(P1) < zmin, i.e., t < 72 years). However, as soon as vegetation starts populating the marsh surface, significant differences emerge.

[41] In the Spartina-dominated case, vegetation encroachment significantly accelerates the vertical growth of the marsh platform (Figure 5a). In fact, the enhanced inorganic sediment deposition due to the trapping effects of the canopy, together with the deposition of organic matter, produce an abrupt increase in the total accretion rate (Figure 5b) when the local elevation of the marsh platform reaches the elevation at which Spartina exhibits its maximum productivity (zmin ≅ MSL). In subsequent times, two negative feedback mechanisms progressively decrease the total accretion rate, which vanishes as the local bottom elevation asymptotically tends to MHWL(≅ zmax). The first is due to the reduction in the deposition rate of inorganic sediment, associated with the progressive reduction in the hydroperiod, as the local elevation of the marsh increases. The second is due to the decrease in Spartina biomass production with bottom elevation.

[42] A more gradual acceleration in the vertical growth of the marsh surface (Figure 5a), together with a smoother increase in the total accretion rate (Figure 5b), characterizes the multiple vegetation-species scenario. In this case, a positive feedback mechanism holds between bottom elevation and the production of plant biomass, which is minimum for zb = zmin and linearly increases to a maximum as zb approaches zmax. Such a positive feedback mechanism counteracts the reduction in the deposition rate of allochthonous sediment with soil elevation. As a consequence, marsh soil elevation increases faster than in the previous scenarios, and eventually exceeds MHWL and the tidal range. The total accretion rate increases up to a local maximum and then decreases to a constant value, dictated by the organic sediment production rate, when zb becomes larger than MHWL ≅ zmax.

[43] The evolution in time of the averages of marsh elevations in the three scenarios (Figure 6a), presents remarkably different features, their evolutionary trends being analogous to the site-specific ones shown in Figure 5a. Also, the variance of marsh elevations exhibits different behaviors in the three scenarios. In the Spartina-dominated case, σz2 displays a very rapid increase as soon as vegetation starts to encroach the marsh surface, reaching a maximum when MHWL is attained by a portion of the marsh platform (similarly to the unvegetated case). In the subsequent stages, σz2 decreases asymptotically to zero, and such a reduction is faster than in the unvegetated case because the presence of vegetation allows lower sites to grow faster toward MHWL. On the contrary, in the multiple vegetation-species scenario, σz2 exhibits a more gradual increase when vegetation starts developing, but it then continues to increase indefinitely, according to the positive feedback between marsh elevation and plant productivity above described.

[44] The space-time dynamics of marsh surface topographies in the three modeled scenarios (Figure 4) indicate that vegetation largely contributes to drive sediment patterns on the marsh surface, and that the coupled evolution of vegetation and morphology gives rise to different system properties. Although channel network structure strongly controls sediment transport dynamics on the marsh surface, the evolution of soil topography shows notably different features in the nonvegetated case (Figure 4, top), with respect to the two vegetated cases (Figure 4, middle and bottom). In particular, the enhanced deposition of inorganic sediment, due to the trapping effect of the marsh canopy and the production of organic soil, leads to more pronounced spatial gradients of bottom topography, particularly in the first stages of the evolution. However, important differences characterize also the two vegetated scenarios. As soon as the marsh platform reaches MSL (the threshold elevation at which halophyte encroachment is initiated; compare all series at t = t1), the Spartina-dominated marsh exhibits a more rapid vertical growth, because of the higher biomass productivity at these stages of the evolution. The following stages are instead characterized by a progressive decrease in plant productivity, which decreases with soil elevation. The accretion patterns which arise in the Spartina-dominated scenario are therefore qualitatively similar to the ones developed in the absence of vegetation, although with much larger total deposition rates, and the elevation of the marsh platform asymptotically tends to MHWL, which represents an equilibrium condition for the considered scenario. On the contrary, the evolution of the marsh platform in the multiple vegetation-species scenario (e.g., a Venice-like scenario) is characterized by a smoother initial increase in bottom elevation as soon as halophytes start to colonize the marsh surface. In the subsequent stages the vertical growth of the marsh platform progressively accelerates because biomass increases with soil elevation (compare Figure 4, middle and bottom at t = t3). In this case the accretion patterns established on the marsh present quite different features when compared to the ones developed in the other scenarios. In fact, the positive feedback between soil elevation and organic production counteracts the progressively decreasing deposition of allochthonous sediment, and the marsh platform can make the evolutionary transition to upland. Furthermore, the topography is characterized by higher levees near the channel banks, and by a sharper transition to the lower inner portions of the marsh (compare Figure 4, middle and bottom at t = t4).

[45] It is worthwhile to note that the development of vegetation patterns presents quite different features in the two vegetated scenarios. In the monospecific vegetated scenario, Spartina initially colonizes areas near channel banks, where soil elevations firstly reach zmin and then propagates toward the inner portion of the marsh as soon as these areas reach the minimum elevation at which Spartina grows on the platform, zmin. The vertical growth of the marsh, enhanced in areas next to the creeks, makes Spartina productivity progressively decrease to zero, as soon as the marsh elevation reaches MHWL (i.e., the maximum elevation withstood by Spartina), so that such a vegetation species cannot survive. In the multiple-species scenario vegetation also first is established in the proximity of channel banks and then encroaches the inner portions of the marsh platform. However, the positive feedback between soil elevation and (multiple-species) plant productivity, allows vegetation survival and transition to upland. The model results thus suggest that different ecogeomorphic patterns are to be expected as a result of the coupled evolution of morphology and different vegetation physiologies.

3.3. Vegetated Scenarios With RMSL Rise

[46] We carried out a second series of simulations in order to analyze the effects of RMSL variations on the morphological evolution of marsh topographies. To this end, we imposed a constant rate of RMSL rise equal to 5 mm/yr, in accordance with observations in the Venice Lagoon [Day et al., 1999], starting from the same configuration considered in the first series of simulations (i.e., zb0 = −0.80 m below MSL, everywhere on the marsh surface). We assumed a constant SSC within the channel network and neglected variations of the channel network structure as the marsh surface evolved in the vertical direction.

[47] Figure 7 shows a comparison of the temporal evolution of bottom elevations and of the relative total accretion rates for the marsh points P1, P2, and P3 (see e.g., Figure 2a), in the Spartina-dominated scenario. The response of the marsh platform to RMSL rise is found to be strongly site specific. The relative total accretion rate of point P1 is greater than the accretion rates at points P2 and P3 and thus the critical elevation for plant colonization is first reached here. As soon as Spartina colonizes the site, it further increases the total accretion rate, by promoting sediment trapping and contributing organic sediment. Points P2 and P3 follow a qualitatively similar behavior, though with some delay, which is strongly site specific. At all marsh points a dynamic equilibrium is reached (though at different times), such that the local accretion rate equals the rate of RMSL rise. It is interesting to note that the inclusion of RMSL rise effects allows the system to reach a configuration in which the relative elevation of the platform within the tidal frame allows vegetation survival, quite differently from the Spartina-dominated scenario described in section 3.2.1. The depth below MHWL of the equilibrium configuration is a function of the rate of RMSL rise whenever the other forcing processes related, e.g., to sediment supply and vegetation characteristics, remain unchanged.

Figure 7.

(a) Time evolution of bottom elevations and (b) total accretion rates as a function of bottom elevation at three salt marsh points (P1, P2, and P3) along the flow path shown in Figure 2a in the Spartina-dominated scenario and with a rate of sea level rise equal to 5 mm/yr.

[48] The multiple vegetation species scenario under a constant rate of RMSL rise (Figure 8) shows different features, as soon as vegetation starts populating the marsh surface. Although the vertical growth of the marsh surface is determined by a more gradual increase in local accretion rates, also in this case, all of the three points considered in Figure 8 become vegetated after exceeding the critical elevation for plant colonization. The time required to exceed such a threshold depends on the local morphodynamic conditions, and is thereby strongly site specific.

Figure 8.

(a) Time evolution of bottom elevations and (b) total accretion rates as a function of bottom elevation at three salt marsh points (P1, P2, and P3) along the flow path shown in Figure 2a in the multiple vegetation species scenario and with a rate of sea level rise equal to 5 mm/yr.

[49] The numerical experiments performed overall show that marshes populated by a variety of vegetation species may make a transition to upland, differently from Spartina-dominated ones, whereas an equilibrium configuration can be reached only under relatively larger RMSL rise rates.

[50] A comparison of the overall evolutionary trends associated with a constant rate of RMSL rise for the two vegetated cases is shown in Figure 9. It emerges that in the Spartina-dominated scenario the mean marsh elevation tends to the MHWL, whereas it tends to exceed the tidal range in the multiple vegetation species scenario. The variance of marsh elevations displays trends qualitatively similar to the ones characterizing the constant MSL scenarios, tending to increase indefinitely in the multiple vegetation species scenario, and to asymptotically decrease to zero after having reached a maximum (not shown in Figure 9) in the Spartina-dominated scenario.

Figure 9.

Time evolution of mean marsh elevations and of the variance of marsh elevations in the Spartina-dominated scenario (solid and dashed thin lines) and in the multiple vegetation species scenario (solid and dashed thick lines) with a rate of sea level rise equal to 5 mm/yr.

3.4. Spatially Varying SSC Within the Channel Network

[51] In order to analyze how the hypothesis of a constant concentration forcing within the channel network influences the morphological evolution of the marsh surface, we relaxed this assumption and imposed a constant value of SSC at the inlet of the watershed. Figure 10 shows a comparison between marsh bottom topographies characterized by the same constant average value of zmean = 0.3 m above MSL, in the case of constant (Figure 10a) and space-dependent (Figure 10b) SSC within the network. Figure 10b, emphasizes that different sedimentation patterns arise if the effects related to the spatial and temporal variations of the SSC within the channel network are taken into account. In particular, the intensity of sedimentation processes on the marsh surface diminishes not only with distance from the channel banks, but also landward with distance from the inlet of the tidal basin. A landward gradient of the topography is therefore observed. Moreover, Figure 11 shows that the mean elevation of the marsh surface grows slower toward MHWL than in the case of constant sediment concentration, as a consequence of the reduced availability of suspended sediment. Interesting differences also emerge when analyzing the evolution in time of the variance of marsh bottom elevations. The site-specific deposition rates, and the consequent nonuniform vertical accretion of the marsh platform, yield a relatively rapid increase in σz2 up to a maximum, which is later followed by a much slower decrease if compared to the case of constant sediment concentration within the channels. A progressive reduction of the tidal prism, due to the increase in the mean marsh platform elevation, produces a reduction in the values attained by the discharge and flow velocity within the channel network. As a consequence, the intensity of advective transport is progressively reduced, together with the SSC along the channel network, and the deposition rates decrease accordingly.

Figure 10.

Comparison between marsh bottom topographies characterized by the same constant average value of zmean = 0.3 m above MSL in the case of (a) constant and (b) space-dependent sediment concentration within the network of the San Felice salt marsh in the absence of vegetation. The initial uniform bottom elevation was zb = −0.80 m above MSL.

Figure 11.

Time evolution of the mean and of the variance of marsh elevations in the case of absence of vegetation and sediment concentration values varying within the channel network.

3.5. Marine Regressions and Transgressions

[52] We finally studied the effects of marine regressions/transgressions on the evolution of the tidal landscape. The aim of this last set of simulations is to address the morphological coevolution of both the marsh platform and the tidal channel network as a consequence of a decrease (marine regression) or an increase (marine transgression) in the tidal prism. It should be emphasized that such an experiment is not aimed at addressing in detail the effects of marine regression/transgression at the site at hand, which will be the topic of forthcoming research, but rather to test its purview of complex, possibly hysteretic morphological responses to a variety of scenarios related, say, to climate change and changing RMSL. For the sake of simplicity we considered the case of constant SSC within the network in the absence of vegetation.

[53] Figure 12a shows the initial topographic configurations adopted. We start from an idealized flat marsh surface characterized by a spatially constant value of bottom elevation equal to −0.30 m above MSL. The marsh is incised by a channel network reminiscent of the real geometry of our field site within the San Felice salt marsh (e.g., Figure 1), i.e., the initial network structure is obtained by artificially adapting the actual network cross sections to the tidal prism computed on the basis of the initial topography, in analogy to the procedure proposed by D'Alpaos et al. [2005], under the assumption that channel cross sections are in dynamic equilibrium with the flowing tidal prism [e.g., Jarrett, 1976]. We start by simulating a marine regression (Figure 12b) and considering an important deposition of inorganic sediment on the marsh platform in the absence of sea level rise. Actually, this corresponds to a case where the timescale for RMSL change is comparable with that inducing sizable deposition within the platform, i.e., local accretion rates are assumed larger than the rate of RMSL rise. Figure 12b shows the planimetric configuration of the network after a 220-year depositional period during which the marsh platform rises with respect to the RMSL. The progressive vertical growth of the marsh surface leads to a decrease in the tidal prism flowing within the channel network. A headward retreat of the channel network is observed as a consequence of the progressive reduction in channel cross-sectional areas (the channels progressively reduce their average width and depth maintaining, by assumption, the same constant width-to-depth ratio) and silting up of some of the channels.

Figure 12.

Comparison between planar configurations of the network cutting through the San Felice salt marsh as a consequence of marine regressions and transgressions. Bottom topographies are color-coded, with higher bottom elevations coded by lighter shades of gray. (a) Planar configuration of the network obtained on the basis of the actual San Felice network, adjusted to the tidal prism corresponding the initial condition (zb = −0.30 m above MSL assigned to the salt marsh platform). (b) Marine regression: retraction of the network as a consequence of the decrease in the tidal prism due to a nonuniform vertical accretion of the marsh platform up to a mean bottom elevation zb = 0.40 m above MSL. Marine transgressions through the reexpansion of the San Felice network (c) in transport-limited landscapes, through the carving of the nonuniform topography (notice the deposition bumps near the channels, indeed a typical morphological trait of the marsh features in transport-limited frameworks), and (d) in the case of uniform marsh bottom elevations (somewhat loosely referred to the case of supply-limited transport), through the carving of a smoothed topography.

[54] Marine transgression was then analyzed (Figure 12c) by applying the tidal network growth model proposed by D'Alpaos et al. [2005]. To this end we imposed a 50 cm increase in RMSL to the configuration shown in Figure 12b, and used its hydrodynamics and morphology as the initial condition for the model of network development. The increase in the mean hydraulic duty is seen to produce two different effects which both contribute to modify the channel network: an increase in the flowing tidal prism, on the one side, and an enhancement of the hydrodynamic shear stresses exerted by tidal fluxes on the marsh platform, on the other. As a consequence, the channels increase in width and depth because of a general expansion of their cross-sectional areas, and furthermore the channel network structure changes because of headward growth and tributary initiation driven by the spatial distribution of local bottom shear stresses. This leads to increasing channel density and complexity. Marine transgression was modeled in the heterogeneous case where channel growth is determined following the statistical tracking of shear stresses in excess of a critical threshold [D'Alpaos et al., 2005]. It clearly emerges that marsh topographies strongly influence network expansion. For example, the regrowth of the left tributary closest to the outlet is inhibited by the relatively higher values of the local marsh elevation, which lower the local value of the bottom shear stress preventing channel reincision. As soon as a breach is opened on the newly formed levees paralleling the channels, the network restarts to develop cutting through the portion of the marsh characterized by lower elevations. On this basis alone we deem that a marked hysteretic behavior in expansion or retraction ought to characterize the localization of the channeled portion of tidal landscape whenever significant sedimentary structures have occurred. Note also that we have not tuned the particular expansion mechanism suitable to reproduce the original pattern (Figure 12a). In order to emphasize the effects of local accretion processes on channel network expansion following a marine transgression, we have artificially smoothed the bottom topography of the configuration shown in Figure 12b by assigning a constant value to bottom elevations, equal to the mean bottom elevation of the above cited configuration (i.e., zb = 0.40 above MSL). Figure 12d shows channel network expansion according to this scenario. It appears that, in the absence of strong gradients of bottom topography, one may indeed recover the original network structure whenever the dynamic conditions reoccur. In fact, the lack of depositional mounds surrounding the tips of the channels allows the network to rechannelize the old courses and incisions that had disappeared. This creates a substantially reversible pattern of expansion and retraction that can result in the disappearance of the signatures of past climates. Also in this case, owing to the nature of the exercise, we have not tuned the specifics of the tidal expansion to the case at hand, on which forthcoming research is focused.

[55] In summary, the processes of tidal network incision and channel retraction (due, for instance, to decreasing RMSL) are rather different. The marked difference in the spatial location of channelized sites under cyclic RMSL, produces hysteresis where geomorphic signatures of past RMSLs remain imprinted on the landscape. Interestingly, we identify two different behaviors, namely, supply- and transport-limited. In the former, the lack of inorganic sediment transported prevents major modifications of the platform, and therefore channel regressions and transgressions are somewhat cyclic. Consequently, signatures of past RMSLs disappear. Thus once you stand on a marsh platform and look across the tidal landscape, you see forms essentially in equilibrium with current RMSL and no climatic signatures. Alternatively, large supply of inorganic sediment results in a substantially altered landscape once the network is ready to reexpand, and thus transgressions and regressions of the tidal network are largely hysteretic. Records of the past, however difficult to decode, are thus present.

[56] Although we have not explicitly accounted yet for possibly important processes, like, e.g., wind-wave resuspensions [Carniello et al., 2005] or bioturbation processes (chiefly, systematic ruptures of microbial biofilms [e.g., Yallop et al., 1994; Amos et al., 2004] due to unsustainable clam harvesting typical of our field sites), we argue that these could be incorporated into the proposed framework. It seemed reasonable, in fact, to limit our analysis to two classes of problems operating at different timescales (channel network processes, on one side; marsh platform processes on the other), to avoid clouding the main issues with unnecessary details.

4. Conclusions

[57] The main conclusions of this paper can be summarized as follows.

[58] 1. Landscape evolution of tidal environments has been proposed to be seen as the byproduct of chief land-forming processes with quite different timescales: channel incision/retraction; tidal channel cross-sectional adjustment to landscape-forming flow rates related to the evolving tidal prism; the vagaries of RMSL; and marsh erosion/deposition processes strongly affected by the possible colonization by halophytic vegetation. We have proposed a mathematical framework for general tidal landscape evolution where suitable decoupling of network and marsh platform dynamics occurs.

[59] 2. Marsh platforms evolving under unvegetated and vegetated scenarios are characterized by very different accretion patterns, and distinct evolutionary regimes are obtained depending on the types of colonization by halophytes. The negative morphodynamic feedback existing between inorganic deposition rates and marsh elevation, prevents marshes dominated by allochthonous inorganic sediment from making the evolutionary transition to upland (their mean elevation, in fact, approaches asymptotically MHWL) when evolving under constant RMSL. Such a negative feedback is reinforced by the relation between plant productivity and soil elevation in Spartina-dominated marshes. If a mosaic of vegetation patches is observed, however, as in our field site within the Venice Lagoon, a positive feedback between plant productivity and soil elevation counteracts the negative one between accretion rates and elevation. As a consequence, under constant RMSL scenarios, Spartina-dominated marshes can only asymptotically approach MHWL, while marshes populated by a variety of halophytic species may make the transition to upland.

[60] 3. Spartina-dominated marshes evolving under a constant rate of SLR, may attain an equilibrium elevation at a certain depth below MHWL, depending on SLR rates. Marshes populated by a variety of vegetation species may make a transition to upland, differently from Spartina-dominated ones, whereas an equilibrium configuration can be reached only under relatively larger SLR rates.

[61] 4. Inorganic accretion rates and related vertical growth of the marsh surface tend to decrease with distance from the creek, measured along suitably defined flow paths. Although the tidal network structure controls sediment transport dynamics on the marsh surface, the magnitude of deposition rates is suggested to be greatly affected also by local hydrodynamics and morphology. The intensity of sedimentation processes is found to decrease not only with distance from the channel but also landward with distance form the inlet of the basin, if sediment concentration is assumed to vary along the channel network.

[62] 5. Marine regressions, and the related reduction in the tidal prism, lead to shrinking channel cross sections and to a contraction of the network through knickpoint retreat. A marine transgression following regression leads to further incision of the channels and to an expansion of channel cross-sectional areas. The processes of incision and contraction are suggested to be rather different. We identify two different behaviors, namely, supply- and transport-limited. In the former, the lack of inorganic sediment transported prevents major modifications of the platform, and therefore channel regressions and transgressions tend to be cyclic and geomorphic signatures of past RMSLs pertain only the extent of the channelized portion of the tidal landscape, as contractions and expansions tend to occur within the same planar blueprint. Alternatively, large supply of inorganic sediment results in a substantially altered landscape once the network is ready to reexpand, and thus transgressions and regressions of the tidal network are largely hysteretic. We thus support the view that modeling relative sea level changes needs to be considered when addressing long-term tidal morphodynamics.

Acknowledgments

[63] Funding from TIDE EU RTD Project (EVK3-2001-00064) (all authors); Progetto di Ricerca di Ateneo Telerilevamento della Zonazione e della Biodiversità della Vegetazione sulle Barene della Laguna di Venezia (M.M.); CORILA (Consorzio per la Gestione del Centro di Coordinamento delle Attivita' di Ricerca inerenti il Sistema Lagunare di Venezia) (Research Program 2000–2004, Linea 3.2 Idrodinamica e Morfodinamica Linea 3.7 Modelli Previsionali) (A.D. and S.L.); and Fondazione Ing. A. Gini (A.D.) is gratefully acknowledged.

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