Flow, Sedimentation, and Biomass Production on a … · A 1-D model for exploring the interaction between ... at North Inlet estuary, ... depends on a large number of biotic and abiotic

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Flow, Sedimentation, and Biomass Productionon a Vegetated Salt Marsh in South Carolina:Toward a Predictive Model of Marsh Morphologicand Ecologic Evolution

Simon Marius Mudd, Sergio Fagherazzi, James T. Morrisand David Jon Furbish

Abstract

A 1-D model for exploring the interaction between hydrodynamics, sedimentation, andplant community evolution on a salt marsh populated by Spartina alterniflora is deve-loped. In general macrophyte characteristics are determined by a wide range of processes;here, based on field studies at North Inlet estuary, South Carolina, the biomass of theS. alterniflora on the marsh platform is simply related to the time of submergence undertidally induced flows. Additionally, field data collected at North Inlet are used to relatebiomass to plant area per unit volume, stem diameter, and an empirical drag coefficient.Sedimentation is also related to biomass, through either organogenic deposition or trap-ping of suspended sediment particles, whereas tidally induced flows over marsh platformsare affected by S. alterniflora through drag forces. The morphologic evolution of simu-lated marshes is explored by varying the sedimentation process and the rate of sea levelrise. Different sedimentation processes result in marshes with different morphologies.An organogenic marsh is predicted to evolve under a regime of steady sea level rise intoa platform with a relatively flat surface, whereas a marsh developed primarily through atrapping mechanism is predicted to have a surface that slopes gently away from the saltmarsh creek. Marshes that accrete through sediment trapping adjust to changes in sea levelmore rapidly than marshes that accrete through organogenic deposition. Further researchneeds are discussed.

1. Introduction

Vegetated salt marshes are a common feature along tectonically quiescent coastal mar-gins. At elevations below mean high tide, the vegetation of southeastern and Gulf Coastsalt marshes is typically dominated by a monoculture of the macrophyte Spartina alterni-flora, and at higher elevations or in brackish tidal marshes Juncus roemerianis is common.

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Book titleCoastal and Estuarine Studies ##Copyright 2004 by the American Geophysical Union10.1029/##CE##

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During times of tidal submergence these species affect the flow of water through theircanopies by the drag created by their stems [Kadlec, 1990; Nepf, 1999] and affect theaccretion rate of the marsh through subsurface biomass growth, the deposition of leaf litter,and by trapping of sediment by the plant canopy [Gleason et al., 1979; Morris et al., 2002;Ranwell, 1964]. These salt marshes are an ideal location for interdisciplinary studieswhich combine ecology, hydrology, and geomorphology due to the predictable forcing ofthe hydrodynamic system (the tides) and the relatively low number of dominant plantspecies present on the marsh [Randerson,1979]. In addition to affecting the physical mor-phology and hydrodynamic properties of the marshes they live on, salt marsh macrophytesare a key component of and also have influence on the local ecological community healthand structure [Bruno and Bertness, 2001].

Because of the importance of salt marshes in relation to ecology, pollutant and nutrientbuffering and storage, and storm protection, the prediction of the long term health and sta-bility of these environments is a fundamental research goal. Vegetated salt mashes are sen-sitive to both sediment supply [Baumann et al., 1984] and sea level change [Reed, 1995].

A number of authors have constructed numerical models that predict the response of saltmarshes to sea level change. One class of models for this purpose are zero-dimensionalmodels, where one point is considered representative of an entire marsh [e.g., Allen, 1995;Chumra et al., 1992; French, 1993; Krone, 1987; Morris et al., 2002; Randerson, 1979;Temmerman et al., 2003]. The sedimentation rate in these models is a function of sedimentsupply and either marsh elevation [Allen, 1995; French, 1993; Krone, 1987; Temmermanet al., 2003] or biomass [Morris et al., 2002; Randerson, 1979]. The models of Morriset al. [2002] and Randerson [1979] also predict biomass production and standing biomasson the marsh, whereas the others use either a steady organogenic sedimentation rate or anorganogenic sedimentation rate that is a function of the marsh elevation. The studies thatmodel the sedimentation rate as a function of marsh elevation assume that sedimentationrate is a steeply decreasing function of marsh elevation, based on the empirical findings ofPethick [1980; 1981]. The empirical findings of Pethick [1980; 1981] are similar to theobservation by Krone [1987] that sedimentation decreases with shorter times of marshinundation due to the decreased likelihood that suspended sediment is advected onto themarsh platform. If the sedimentation rate on the marsh platform is a steeply decreasingfunction of marsh elevation, then the marsh platform will always be able to keep pace withrelative sea level rise because an accelerated sea level rise will be met with an associatedrise in the sedimentation rate. Morris et al. [2002], however, argue that the salt marsh sys-tem may be unstable and may drown at a rate of sea level rise faster than some critical rateof sea level rise, mirroring the observations of [Allen, 1995].

Although zero-dimensional models have yielded insights into the long term growth andstability of salt marsh platforms, they do not address the spatial variations of marsh pro-perties found in natural marshes. Field studies have shown that there are strong spatialgradients in flow velocity, turbulence [Leonard and Luther, 1995], suspended sedimentconcentrations [Christiansen et al., 2000], and sedimentation rates [Stumpf, 1983] withinvegetated salt marshes. Standing biomass also varies spatially, typically being highest nearsalt marsh creeks where flushing of the salt water occurs regularly and declining in loca-tions which are either constantly inundated or where tidal flooding occurs irregularly suchthat evapotranspiration leads to high saline levels that inhibit macrophyte growth[Mendelssohn and Morris, 2000; Morris et al., 2002; Phleger, 1971; Valiela et al., 1978;Webb, 1983].

Both Allen [1994] and Woolnough et al. [1995] have presented spatially distributedmodels of salt marsh evolution, but neither of these models include dynamic change in themacrophyte community. In this contribution we develop a model that combines the flow

2 PREDICTIVE MODEL OF MARSH EVOLUTION


hydrodynamics, sediment transport and deposition, and biomass dynamics on simulatedsalt marsh platforms.

The biomass of salt marsh macrophytes depends on a large number of biotic and abioticfactors, including but not limited to soil salinity, soil redox potential, water table depth[Sanchez et al., 1998], nutrient and sediment loading, oxygen availability, and competitionbetween plant species [Pennings and Callaway, 1992]. For reviews of the factors influenc-ing plant zonation and productivity in salt marshes see Mendelssohn and Morris [2000],Silvestri and Marani [this volume] and references therein. Here we take a simplifiedapproach and suppose that aboveground biomass production is only linked to duration ofinundation [Boorman et al., 2001; Olff et al., 1988; Pethick, 1984]. The duration of inun-dation is a surrogate for a number of variables that have a more direct influence on pro-duction such as soil salinity and oxygen. Furthermore, we consider only one plant species,Spartina alterniflora, which is ubiquitous in salt marshes of the gulf and east coasts of theUnited States. In reality, as shown in the studies of Bockelmann et al. [2002], Sanchezet al. [1996], and Silvestri et al. [2002], biological zonation is a fundamental characteristicof marsh vegetation, with specific plant communities living at different marsh elevationsor for different inundation frequencies and durations. Expansion of invasive species fromthe upland area (e.g., Phragmites) can also modify sediment accretion and flow dynamics,thus influencing the long term morphological evolution of the marsh [Leonard et al., 2002;Rooth et al., 2003]. Furthermore, other factors can influence the spatial distribution of biomass in a salt marsh, as, for example, spatial variation in nutrient availability or in theamount of oxygen available for roots aerobic respiration [see Mendelssohn and Morris,2000; Sanderson et al., 2001; Sanderson et al., 2000]. These processes are not incorporatedin the present model. This notwithstanding, our model is able to mimic the vegetationencroachment on emerging tidal flats, separating vegetated from non-vegetated areas. Thisis the fundamental aspect of the coevolution of landscape and vegetation, and has impor-tant consequences for both sedimentation and tidal hydrodynamics.

In the future our approach can be generalized to account for the presence of differentplants in competition, provided that precise relationships between biomass and duration ofinundation are available for each species, together with a quantitative estimate of the effectof competition on biomass distribution. We begin by summarizing the model formulationin the section 2. The model is divided in three components that account for the tidal hydro-dynamics, the aboveground biomass production, and sediment transport and deposition ina salt marsh. Next we run a selected number of simulations to predict the evolution of themarsh surface under a variety of assumptions. In particular, we carry out two series ofsimulations, first for marshes that accrete through organogenic deposition, and then formarshes that accrete through trapping of suspended sediment by the macrophytes, eitherwith or without sea level rise.

2. Model Formulation

The model simulates the evolution of the marsh surface on a transect perpendicular to atidal creek. The hydrodynamic component of the model calculates water velocities andwater levels as a function of the tidal signal (here supposed sinusoidal for simplicity) anddrag forces produced by the vegetation canopy. Inorganic sediment is assumed to be car-ried on the marsh surface from the creek whereas organic material is locally produced bymacrophytes. Sediment deposition on the marsh surface is thus divided into three compo-nents: sedimentation due to particle settling, trapping by salt marsh macrophytes, andorganic deposition. Furthermore, given the low velocity of water on typical marsh surfaces

MUDD ET AL. 3


[e.g., Christiansen et al., 2000; Davidson-Arnott et al., 2002; Leonard and Luther, 1995,Shi et al., 2000], we neglect erosion in the model.

Vegetation influences both hydrodynamics (through the drag coefficient) and sedimentdeposition (sediment trapping and organic deposition). We directly link drag, organicdeposition, and trapping to the aboveground vegetation biomass. To determine the vegeta-tion biomass we derive, from the hydrodynamic model, the duration of inundation at eachmarsh location, and calculate, through appropriate relationships, the aboveground biomassproduction.

Since we utilize a sinusoidal tide, we do not consider neap-spring tide cycles.Furthermore vegetation is assumed uniform and dominated by one species (Spartinaalterniflora), so that the model applies only to undisturbed marshes with native vegetation.The model considers neither deposition of wrack onto the marsh surface, nor the explicitaccretion of the products of belowground production, though we assume that accretion ofsediment organic matter is proportional to aboveground production. Finally, throughoutthe manuscript, we always refer to aboveground biomass.

2.1. Hydrodynamic component

Tidally induced flow on vegetated salt marsh platforms are governed by a balance of theforce due to the drag generated by plant stems and the gravitational force due to the slopeof the water surface on the marsh [Nepf, 1999]. Inertial terms in tidally induced flows maybe neglected [Rinaldo et al., 1999]. Field data show that the water surface slope can besignificant, for example Christiansen et al. [2000] recorded an ~8 cm difference in watersurface elevation at high tide between the bank of a tidal creek and a station 7.5 m fromthe bank. The balance of gravity and drag forces in one dimension is:

(1)

where g is gravitational acceleration (L T−2), ζ is the elevation of the water surface (L), x is horizontal distance from the tidal creek (L), h is the flow depth (L), U is the fluid velocity (L T−1), is the bulk drag coefficient of the vegetation (dimensionless), a is theprojected plant area per unit volume (L−1), d is the stem diameter (L), and Cb is the beddrag coefficient (dimensionless). The calculation of a and will be discussed in section2.2. The first term on the right is the force due to drag generated by plant stems, and thesecond term on the right is the force due to the bed drag. The bed drag term is negligiblewith respect to the plant generated drag except for very shallow flows. The flow depth, h,may be written as

(2)

where η is the elevation of the marsh surface (L). Both ζ and η are measured relative tosome arbitrary baseline.

Equation (1) may be solved for velocity:

(3)Ux

gh

ahC ad C xd b

= − ∂∂

+ −

∂∂

sgn

ζ ζ2

2 1

1

2

( ),

h = −ζ η,

Cd

Cd

gx

C aUad

hC Ud b

∂∂

= + −ζ 1

2

12 2( ),



where is a function that takes the value 1 if the water surface slope is positiveand −1 if the water surface slope is negative. If one assumes the time rate of change ofmarsh surface elevation is negligible compared to the change in the elevation of the watersurface for flow calculations, the one-dimensional continuity equation is:

(4)

Equation (4) does not account for the change in elevation due to infiltration of water intothe salt marsh. A scaling analysis determined that for the sediment at North Inlet, SouthCarolina (hydraulic conductivity = ~4 × 10−6 m s−1, Morris [1995]), infiltration may beneglected. For marshes with greater hydraulic conductivities, wetting and drying processes(including infiltration) may become important. Wetting and drying processes are neglectedin this study in the interest of simplicity. Equation (3) may be inserted into the continuityequation to give the governing equation for flow hydrodynamics on a one-dimensionalvegetated salt marsh:

(5)

Equation (5) was solved using an explicit predictor-corrector (PC) finite volumemethod. This method introduces slight errors in the location of the wetting and dryingfront, which may affect the time of flood propagation on the marsh. A more accurate esti-mate of the location of the wetting or drying front could be obtained using a shock cap-turing numerical scheme [e.g., Bradford and Sanders, 2002], or statistically describing thebottom irregularities and then modifying accordingly the continuity equation [Defina,2000]. However, uncertainties introduced by using the explicit predictor-corrector methodare limited, since both the propagation of the wetting front and the vegetation drag do notconsiderably change the flooding periods in a flat marsh of limited extension [Mudd andFurbish, 2002]. Boundary conditions are discussed in section 3.

2.2. Biomass component

Morris et al. [2002] carried out field measurements that quantified a relationshipbetween the depth of S. alterniflora below mean high tide (MHT) and their biomass pro-duction. The depth below mean high tide dictates the duration of inundation on an inter-tidal marsh surface, and the duration of inundation will affect soil salinity [Morris, 1995],as evapotranspiration can increase the salinity of pore waters if the pore waters are not regu-larly flooded. A number of researchers have shown that heightened pore water salinitycaused by evapotranspiration can limit growth or be fatal to salt marsh macrophytes whenflooding occurs infrequently [e.g., Morris, 2000; Phleger, 1971; Webb, 1983].

The field data of Morris et al. [2002] showing a relationship between the depth belowMHT and biomass were collected at discrete points on a salt marsh and over time. At asingle point on a salt marsh, the depth below MHT will be closely related to the time inter-val that point is inundated in a tidal cycle, and the duration of inundation and biomass willchange with variability in mean sea level [Morris, 2000]. Bockelmann et al. [2002] foundthat inundation frequency (which may relate to the duration of inundation on a given point

∂∂

− ∂∂

∂∂

+ −

∂∂

ζ ζ ζt x

hx

gh

ahC ad C xd b

sgn2

2 1

1

2

( )

= 0.

∂∂

+ ∂∂

=ζt

hU

x0.

sgn( / )∂ ∂ζ x

MUDD ET AL. 5


on a marsh) was a better predictor of macrophyte zonation than marsh elevation and thatMHT on the marsh was not merely a function of marsh elevation but also of the locationof the study site. This difference in MHT between sites is presumably due to damping ofthe tidal wave due to vegetation and the marsh creek structure. Because the duration ofinundation may be a better predictor of biomass than marsh elevation, the model uses ameasure of the time of inundation to determine biomass. An inundation ratio (τi, dimen-sionless) can be defined that compares the time the platform is inundated during one tidalcycle (ti, T) to the period of the tidal cycle (P, T):

(6)

The relationship between the depth below mean high tide and the inundation ratio for agiven location on a salt marsh will depend on the tidal amplitude. The tidal range at NorthInlet estuary in South Carolina, the site of the experiments of Morris et al. [2002], is~1.4 m. For depths below mean high tide in the range of 0.1-0.60m (the range of depthreported in Morris et al. [2002] over which biomass is present), the relationship betweeninundation time (and consequently inundation ratio) and depth below mean high tide canbe approximated as linear (see Figure 1), although as shown in Figure 1 the linear appro-ximation will diverge from the idealized inundation time for locations on the marsh wherethe marsh surface elevation is near the mean high tide or mean low tide.

Morris et al. [2002] report that the vertical range of S. alterniflora does not appearto extend to depths greater than the depth assumed to be the optimum for biomass pro-duction. They argue that at depths greater than the optimum, anomalies in mean sea level

τiit

P= .


Figure 1. Solid line is the inundation time as a function of depth below mean high tide for alocation in the tidal creek (i.e. unaffected by flow effects present on a marsh platform). Apartfrom depths near the upper and lower bounds of the tidal range, the inundation time as a func-tion of depth below mean high tide can be reasonably approximated by a linear function.


periodically ‘prune’ back the vegetation due to hypoxia resulting in a truncated biomassdistribution. In this paper we assume that there exists a threshold phenomenon in which atany depth greater than the depth below MHT of maximum biomass production the macro-phyte community drowns. The data of Morris et al. [2002] are thus adequately fit using alinear function with a threshold depth below MHT below which the salt marsh macro-phytes drown (see Figure 2).

The linear biomass function can be formulated as

(7)

where Bps is the peak season biomass (M L−2), Bmax is the biomass at the maximum inun-dation time (M L−2), τimax is the maximum inundation ratio for which the salt marshmacrophytes can survive (dimensionless), and τimin is the minimum inundation ratiorequired for the survival of the salt marsh macrophytes (dimensionless).

The biomass will vary through the seasons, peaking in the summer months [Morris andHaskin, 1990]. This effect can be approximated by

(8)

where B is the biomass (M L−2), m is the month, with m = 1 corresponding to January, andω is a dimensionless factor.

BB m

Bpsps=

−−

+

+

( )sin

1

2

2

12 21

ωω

π π

B

BB

B

ps i

psi

i i i

p

= <

=−

− ≤ ≤

0 τ τ

τ ττ τ τ τ τ

imin

max

max iminmin imin imax( )

ss i i= >0 τ τ max

MUDD ET AL. 7

Figure 2. Biomass as a function of depth below mean high tide. The open circles represent datacollected at a field site in North Inlet estuary, South Carolina. The solid line is a linear fit thathas a critical depth below MHT (dotted line). Below the critical depth we assume that hypoxialimits further range expansion, while biomass trends toward zero near MHT due to dessicationand salt stress.


(9)

where Bdec is the biomass in December (M L−2). The factor ω is assumed to be the samefor all Spartina on the marsh and is not a function of the peak season biomass. It is equalto one if there is no seasonal variation in biomass, and will be zero if the Spartina com-munity dies in the winter.

Eighteen years of data on stem density and biomass were collected at North Inlet estu-ary in South Carolina as part of a long term study on primary production of salt marshmacrophytes [Morris and Haskin, 1990]. Empirical relationships between biomass andprojected stem area per unit volume (a) and biomass and stem diameter (d) have been cal-culated for Spartina using data from North Inlet for the years 1984 to 2002 (Figure 3).These empirical functions are power laws of the form:

(10)

(11)

where α1, α2, δ1, and δ2 are all empirical coefficients. Both α2 and δ2 are dimensionlessand the units of α1 and δ1 will depend on the exponent coefficients.

Nepf [1999] proposed that the bulk plant drag coefficient, is a function of the pro-duct of the projected plant area per unit volume and the stem diameter (ad). Because botha and d are functions of biomass, is also a function of biomass. Relating the biomassto the product of the projected plant area per unit volume and the stem diameter using datafrom North Inlet estuary, and then relating this to the drag coefficient of Nepf [1999] givesan empirical function for the drag coefficient as a function of biomass, which may beapproximated as linear (Figure 4):

(12)

where Scd is the slope of the linear fit between drag and biomass (L2−1), and is the bulkdrag coefficient as the product ad approaches zero (dimensionless).

2.3. Sediment transport component

2.3.1. Conservation of suspended sediment

It is assumed in the model that sediment transport in one dimension is dominated byadvection. The governing equation of sediment transport used in the model is

(13)

where C is the sediment concentration (M L−3), Ss is the sedimentation rate per unitarea due to particle settling (M T−1 L−2), St is the sedimentation rate per unit area due totrapping by salt marsh macrophytes (M T−1 L−2), and Sorg is the sedimentation rate perunit area due to organic deposition (M T−1 L−2). Previous studies have used a number ofequations to solve for Ss, St, and Sorg, but there is a relative lack of experimental or field

∂∂

∂∂t

hCx

UhC S S Ss t org( ) ( ) ,+ = + +

C0

C S B Cd cd= + 0,

Cd

Cd

d B= δ δ1

2 ,

a B=α α1

2 ,

ω = B

Bdec

ps

,



data to support these equations. As demonstrated by Morris et al. [2002], Gleason et al.[1979], and Randerson [1979], salt marsh macrophytes play a critical role in determiningthe sedimentation rate. These experiments found that the sedimentation rate within emer-gent vegetation is an increasing function of aboveground biomass [Morris et al., 2002;Randerson, 1979] or stem density [Gleason et al., 1979]. These two observations mayseem contradictory, because the time of peak biomass and the time of peak stem density(stems per area) in a salt marsh macrophyte community are out of phase by several months[Morris and Haskin, 1990]. This effect is due to self thinning, where mature plants withgreater stem diameters crowd out smaller plants, thus reducing the number of stems per

MUDD ET AL. 9

Figure 3. The projected plant area per unit volume (a.) and stem diameter (b.) vs. biomasscalculated from data collected at North Inlet estuary, S.C. The empirical data may be fit withpower law functions.


area at the time of peak biomass. The reason for this apparent discrepancy in measure-ments of sedimentation rate as a function of the macrophyte community is that the Gleasonet al. [1979] experimental study used planted sprigs, in which the average diameter of thesprigs was the same for varying stem densities. Therefore in the case of the Gleason et al.[1979] study the stem density was an increasing function of biomass.

Sedimentation through settling, trapping, and organogenic deposition will change theelevation of the marsh surface. This change is

(14)

where Cη is the concentration of sediments on the marsh surface (M L−3), and Rc is a surfacelowering rate due to the autocompaction of the sediments that make up the marsh (L T−1).

2.3.2. Sedimentation due to settling

The sedimentation due to settling will be

(15)

where wse is the effective settling velocity that is a function of the dissipation of kineticenergy caused by plant stems [Christiansen et al., 2000; Leonard and Luther, 1995; Lopezand Garcia, 1998], and is therefore a function of biomass.

S w Cs se= ,

∂∂ η

ηt

S S S

CRs t org

c=+ +

−( )

,


Figure 4. Drag coefficient as a function of biomass, calculated using the data relating projectedplant area per unit volume (a) and stem diameter (d) to biomass (B) collected at North Inletestuary, S. C., and the relationship between drag coefficient and the product of the pro-jected plant area per unit volume and the stem diameter (ad) presented by Nepf[1999]. The datais fit with a linear function.

( )Cd


2.3.3. Organogenic sedimentation

In the model of salt marsh platform development presented by Randerson [1979], a lin-ear relationship between sedimentation and biomass is used, based on field measurements.This linear relationship may be appropriate for settings in which organic deposition is dom-inant, as the data of Randerson [1979] show that this linear relationship between biomassand accretion rate breaks down at sites with higher inorganic sediment content. The sedi-mentation due to organic deposition used in the model follows Randerson [1979], and is

(16)

where kB is a rate coefficient (T−1).

2.3.4. Sedimentation due to trapping

Morris et al. [2002] assume a priori that sediment trapping is linearly related to biomass,and add a sediment loading term which is assumed to be constant in time, although theydo point out that sediment loading will depend on sediment supply and distance from thetidal creek. Here we hypothesize that the trapping of sediment should be proportional tothe amount of sediment suspended in the flow. The trapping efficiency should also berelated to the probability that a particle in suspension will encounter a plant stem. Thisprobability will be directly related to the projected area of the plant stems per unit volumeof fluid. The projected area of plant stems per unit volume of fluid is an increasing func-tion of biomass (see equation 10). The sedimentation rate due to trapping for the model isformulated as:

(17)

where Tmax is the maximum trapping rate (T−1) and amax is the maximum projected plantarea per unit volume (L−1).

3. Simulations

In the simulations the initial marsh surface is a 125 meter wide flat surface bordered bya gently sloping surface (slope = 0.01) on the landward side (Figure 5a). The values for theparameters used in the model are shown in Table 1. For simplicity, the tidal forcing ismodeled as a sinusoid with a period of 12 hours. The tidal amplitude was set to be 1 meter.Parameters have been selected to roughly approximate physical conditions at North Inlet,South Carolina. The water surface elevation predicted by the tidal sinusoid constitutes theboundary condition at the tidal creek. In each of the simulations, one tidal cycle is assumedto be representative of a month of flooding and sedimentation, because the computationalexpense of modeling continuous flows is prohibitive. The amount of deposition during onetidal cycle is then multiplied by the number of cycles in the month, and the elevation ofthe marsh surface (η) is updated.

Two series of simulations were performed, the first series being performed on marshesthat accrete through organogenic deposition, and the second series being performed onmarshes that accrete through trapping of suspended sediment by the salt marsh macrophytes.

S Ta

aCht =

max

max

,

S k Borg b= ,

MUDD ET AL. 11


Because of the large uncertainties in calculating the effective settling velocity (see section5.4) we have not performed simulations involving the term Ss. This is equivalent to assum-ing that either organic deposition or suspended sediment trapping is the dominant accretionprocess. We recognize that other sedimentation processes exist and multiplesedimentation processes can operate over a salt marsh concurrently, but in the interest ofsimplicity only one sedimentation mechanism is chosen for each of the two series ofnumerical simulations. In practice, Ss and St are both set equal to zero for the organogenicmarsh simulations, and Ss and Sorg are set equal to zero for the trapping simulations. Duringa given simulation, the relative rate of sea level rise (RRSLR) is constant, but RRLSR isvaried for different simulations. The relative rate of sea level rise is sum of the rate ofcompaction and the actual rate of sea level rise (RRSLR = RSLR + Rc where RSLR is therate of sea level rise measured by a stationary datum). Both the rate of sea level rise meas-ured by a stationary datum and compaction rate may be complex functions of time, but forsimplicity both Rc and RSLR were assumed to be constant in space and time for each of


Figure 5. a. Geometry of the initial surface of the marsh platform. b. Surface elevation of simu-lated marshes accreting through organogenic deposition. The solid line has a RRSLR of0.25 cm yr−1, the dashed line has a RRSLR of 0.5 cm yr−1, the dotted line has a RRSLR0.75 cm yr−1, and the dash-dot line has a RRSLR of 1 cm yr−1. c. Surface elevation in time atlocation x = 5 m. Note the change in scale of the vertical axes.


the simulations. Model results for deposition rate and biomass were averaged annuallyin the analysis of the 75 year marsh simulations. Two dimensionless variables are usedthroughout the following three sections. The first is the dimensionless deposition rate:

, (18)

where D is the deposition rate as a function of time and space (L T−1) and is a scalingrate (L T−1). For the simulations with a rising sea level, is chosen to be the rate of rela-tive sea level rise, so if the deposition rate exactly matches RRSLR then D* is equal to one.In model simulations with a RRSLR = 0, the scaling rate is chosen to be the deposition rateat t = 75 yrs. The second dimensionless parameter is the dimensionless biomass:

(19)

3.1. Long term adjustments to sea level rise of a marsh that accretes through organogenic deposition

Long term simulations of 75 years were performed to investigate the effect of the rela-tive rate of sea level rise (RRSLR) on the evolution of the marsh surface. The evolution ofthe surface of marshes that accrete through organogenic deposition is shown in Figure5b,c. The flat initial surface of the marsh evolves into a gentle incline that slopes awayfrom the tidal creek (Figure 5b). The marshes that are experiencing lower rates of sea level

BB

B* .=max

D̂D̂

* ˆD

DD

=

MUDD ET AL. 13

TABLE 1. Parameters used for marsh simulations.

Parameter Value

kb 1.4 × 10−5 months−1

Tmax 3 × 10−5 s−1

amax 10−1

Cη 1000 kg−3

Bmax 2000 g−2

P 43200sτimin 0.02τimax 0.6τio 0.35rir 0.5 ω 0.1α1 0.25α2 0.5δ1 0.0006δ2 0.3Scd −0.0003

1.1C0


rise tend to slope away from the salt marsh creek at the end of 75 years more than marshesthat experience higher rates or relative sea level rise.

The spatial and temporal pattern of deposition and biomass on marshes that accretethrough organogenic deposition is shown in Figure 6. Since the inundation ratio varies onlyweakly, the biomass is almost constant across the initially flat marsh surface (Figure 6d,e;the steep drop in biomass at distances greater than 125 m from the tidal creek is due to thesloping surface of the initial topography). As shown in Figures 6f, the average biomass ata given point on the marsh approaches a steady value that is a function of the rate of rela-tive sea level rise. Whether the simulated marshes approach this steady average biomassvalue by slowly increasing or decreasing through time will depend on the parameterizationof equation (7) and the initial tidal conditions that determine the inundation ratio.

For organogenic marshes, where deposition is linearly related to biomass (equation (17)),the consequence of the weak spatial variation in biomass is a correspondingly weak spa-tial variation in the deposition rate (Figure 6a,b). Here we are assuming that organic matteraccretion, whether from above or belowground production, is proportional to abovegroundbiomass. Adjustments of the deposition rate to sea level rise do not appear to be strong


Figure 6. a. Average annual dimensionless deposition rate of simulated marshes accretingthrough organogenic deposition after 20 years of simulation. The solid line has a relative rateof sea level rise (RRSLR) of 0.25cm yr−1, the dashed line has a RRSLR of 0.5 cm yr−1, the dot-ted line has a RRSLR 0.75 cm yr−1, and the dash-dot line has a RRSLR of 1 cm yr−1. b. After75 yrs, c. Deposition rate in time at the location x = 5 m, d. Average annual biomass of simu-lated marshes accreting through organogenic deposition after 20 yrs, e. After 75 yrs, f. Biomassas a function of time at the location x = 5 m. Note the change in scale of the vertical axes.


functions of the discrepancy between the instantaneous deposition rate and the RRSLR.Most of the temporal trajectories of the deposition rate for organogenic marshes can beapproximated with linear functions (Figure 6c). The dimensionless deposition rate variesin this approximately linear way towards unity, unless the drowning process begins. Bydrowning processes we mean the processes by which the sedimentation rate cannot keeppace with the relative rate of sea level rise and the marsh eventually becomes submerged.None of the simulations had a RRSLR high enough to induce drowning of the marshmacrophytes.

3.2. Long term adjustments to sea level rise of a marsh that accretes through sediment trapping

Figure 7 shows the evolution of the marsh surface for marshes that accrete through trap-ping of suspended sediment. At the initial stages of marsh evolution, sediment depositionis greatest near the salt marsh creek (Figure 7a and 8a), but as a stable configuration of a

MUDD ET AL. 15

Figure 7. a. Surface elevation of simulated marshes accreting through sediment trapping after30 yrs of simulation. The solid line has a RRSLR of 0.25 cm yr−1, the dashed line has a RRSLRof 0.5 cm yr−1, the dotted line has a RRSLR 0.75 cm yr−1, and the dash-dot line has a RRSLRof 1 cm yr−1. b. After 75 yrs c. Surface elevation in time at the location x = 5 m.


surface that gently slopes away from the salt marsh creek develops, the deposition rateadjusts to be homogeneous across this steady portion of the marsh (that portion of themarsh which is not advancing landward up the sloped surface), and the sloping surfacesimply accretes at the rate of sea level rise. The stable configuration is qualitatively simi-lar to marsh profiles surveyed by Christiansen et al. [2000], but this steady morphologydoes not include the sharp levee surveyed in other studies [e.g., Temmerman et al., 2003].

The initial deposition patterns of marshes that accrete through a trapping mechanism aremore spatially heterogenous than the deposition patterns of the organogenic marshes. Inthe first several years of marsh evolution there is a strong spatial gradient in deposition ratefrom the tidal creek moving landward (Figure 8a), with the highest deposition rates beingnear the salt marsh creek. After 75 years, however, the marshes have achieved steady stateacross much of their surface (Figure 8b). Figure 8c shows the nonlinear approach to steadystate taken by the deposition rate at a point 5m from the marsh creek. At the beginning ofthe simulation sediment is deposited at a rate greater than the rate of relative sea level rise.As a consequence, the marsh elevation increases thus reducing the submergence period


Figure 8. a. Average annual dimensionless deposition rate of simulated marshes accretingthrough sediment trapping after 20 yrs. The solid line has a RRSLR of 0.25 cm yr−1, the dashedline has a RRSLR of 0.5 cm yr−1, the dotted line has a RRSLR 0.75 cm yr−1, and the dash-dotline has a RRSLR of 1 cm yr−1.−1. b. after 75 yrs., c. Deposition rate in time at the locationx = 5 m; d. Average annual biomass of simulated marshes accreting through sediment trappingafter 20 yrs., e. After 75 yrs., f. Biomass as function of time at the location x = 5 m. Note thechange in scale of the vertical axes.


and sedimentation rate. This is equivalent to the field findings of Pethick [1980; 1981] inwhich the sedimentation rate is an exponentially decreasing function of marsh elevation.

The spatial distribution of average biomass (Figure 8d,e,f) is weakly decreasing as onemoves away from the tidal channel (until the sloping surface initially at 125 m is encoun-tered). Greater rates of relative sea level rise lead to greater average annual dimensionlessbiomass, up to a critical rate of relative sea level rise, in which the average biomass willdecrease abruptly to zero over time.

Figure 9 shows the depth below mean high tide of the marsh surface for a point on themarsh at x = 5 m after the point has achieved a steady state. The exact depth will varybased on the parameterization of the biomass and sedimentation equations (equations (7),(8), and (17)) and the distance from the tidal creek, but the emergent trend is that the depthbelow mean high tide of the steady state surface of the marsh is an increasing function ofthe relative rate of sea level rise (Figure 9).

3.3. Long term evolution of marshes with no relative sea level rise

Simulations were also performed for marshes undergoing no relative sea level rise. Thespatial patterns of deposition, biomass, and marsh morphology are compared for differentsedimentation processes in Figure 10. As in the simulated marshes experiencing sea levelrise, the initial deposition rate for marshes accreting through sediment trapping are veryhigh, in contrast to the initially slower deposition rates on marshes accreting throughorganogenic deposition (Figure 10b). The difference in the marsh morphology at this earlystage of marsh evolution can be seen in Figure 10a. As the marsh surface accretes andapproaches the elevation of the mean high tide, a filling process occurs away from the saltmarsh creek in the marshes accreting through sediment trapping, and the sloping surfacethat develops in the early stages of marsh evolution evolves into a flatter surface that issimilar to the surface that develops on the organogenic marsh (Figure 10d). The implica-tion of this is that if the marsh develops under a regime of steady sea level rise, the marshmorphology will be different for marshes favoring one deposition process, whereas if sealevel rise occurs as a series of punctuated periods with intervening periods of no change

MUDD ET AL. 17

Figure 9. Depth below mean high tide of a point on marsh that accretes through sediment trap-ping 5 m from the salt marsh creek at steady state (D* = 1).


in sea level, then marsh morphology will be similar except in the period immediatelyfollowing sea level rise.

The difference of marsh adjustment and evolution in time for the two sedimentationprocesses can be seen in Figure 10g,h,i. The deposition and marsh elevation as a functionof time have a much weaker nonlinear trend than marshes accreting through sediment trap-ping. For these marshes, as the marsh surface adjusts and the average flow depth decreases,the average biomass begins to fluctuate, due to the increased influence of nonlinear termsin the flow equations for shallow flows. As flows become shallower drag forces becomelarger, and therefore inundation time is more sensitive to biomass feedbacks.

4. Conclusions

The exploratory simulations presented in this contribution demonstrate the feasibility ofcombining ecological and hydrodynamic components in spatially distributed predictivemodels of salt marsh platform evolution. The morphology of salt marshes depends ondepositional processes, which have been shown to be sensitive to the distribution of saltmarsh macrophytes, which in turn are affected by tidal hydrodynamics. Understanding theinteractions between these physical and biological components is a key to predicting thelong term evolution and health of salt marshes.


Figure 10. Marsh elevation, deposition rate, and biomass for simulated marshes with norelative sea level rise. The solid lines represent data for marshes that accrete through organicdeposition, the dashed lines represent data for marshes that accrete through sediment trapping.The dimensionless deposition for these plots is scaled by the deposition of the point 5 m fromthe marsh creek at the last time step of the simulation. a. Elevation after 5 yrs. b. Elevation after75 yrs., c. Elevation in time at x = 5 m, d. Deposition rate after 5 yrs., e. Deposition rate after75 yrs., f. Deposition rate in time at x = 5 m, g. Biomass after 5 yrs., h. Biomass after 75 yrs.,i. Biomass in time at x = 5 m.


Simulations show that the temporal and spatial pattern of salt marsh evolution varystrongly depending on the sedimentation process acting upon the marsh surface. Thesespatial patterns can account for the observation that no consistent range of elevation forthe realized limits of growth of S. alterniflora have been demonstrated [Mckee andPatrick, 1988]. Marshes accreting through organogenic deposition tend to develop a rela-tively flat surface as the deposition rate approaches steady state (deposition rate equals therate of sea level rise), whereas marshes that experience sediment trapping develop a sur-face that slopes away from the tidal creek. This is due to the decreased availability of sediment in the water column as one moves away from the tidal creek, because of the sediment trapping closer to the creek.

In the first phase of marsh formation the deposition rate is stronger for marshes thataccrete through sediment trapping than for organogenic marshes. The empirical observa-tions of Pethick [1980; 1981], where the accretion rate is a strongly decreasing function ofmarsh elevation, is mirrored only in the temporal pattern of deposition for the marshes thataccrete through trapping. Finally, biomass varies weakly with space in all simulations,with a noteworthy variation in time only for marshes accreting by sediment trapping. Inthis contribution we have demonstrated that ecological processes may be coupled to flowprocesses and sedimentation through empirical constitutive equations based on ecologicalfield data and laboratory results. More research is needed to verify these equations as wellas to determine the range of variability of the parameters involved.

5. Future Research Needs

5.1. General Remarks

The exploratory simulations performed by the model demonstrate the feasability ofmodeling the spatial and temporal variation of sedimentation and standing biomass onvegetated salt marsh platforms. The model is a step toward a fully predictive model of saltmarsh platform evolution in both a geomorphic and ecologic sense, but is limited tomarshes vegetated with Spartina alterniflora and specific sedimentation processes. A fullypredictive model (one that could be constrained by parameters measured in the field andconfirmed by field and laboratory studies) could ultimately be used to investigate the longterm effects of important variables that impact salt marsh evolution such as sediment sup-ply and sea level rise. The exercise of constructing the model for this contribution hasbrought to our attention a number of deficiencies in the current understanding of salt marshprocesses which need to be addressed before the goal of a fully predictive model may beachieved.

5.2. Research needs for flow hydrodynamics

The work of Nepf [1999] represents the most recent understanding of flow processesthrough emergent vegetation. The Reynolds number based on stem diameter (Red = (Ud)/νwhere ν is the kinematic viscosity (L2 T−1)) performed in the experiments of Nepf [1999]were between 4000 and 10000. In flows over vegetated salt marshes values of Red that areless than 200 are common [Christiansen et al., 2000; Davidson-Arnott et al., 2002;Leonard and Luther, 1995; Leonard et al., 2002; Nepf, 1999; Shi et al., 2000; Yang, 1999].In flows around a single cylinder a transition in the relationship between Red and Cd occursat Red ~200 [Furbish, 1997]. At Red >~200, Cd does not change in relation to

MUDD ET AL. 19


Red whereas for Red < ~200 Cd increases nonlinearly as a function of Red. Although dataon drag coefficients for arrays of cylinders for Red < 200 do not exist, the authors suspectthat the nonlinear inverse relationship between Red and Cd seen in flows around a singlecylinder are also manifested in flows through arrays of cylinders. At Red < 200 viscousdrag becomes increasingly important, which dissipates flow energy without generatingturbulence and therefore reducing the modification of Cd in an array of cylinders due toturbulent interference. These hypotheses should be tested experimentally to accuratelyquantify the relationship between Cd and Red in an array of cylinders (as an analog foremergent vegetation) for Red similar to those found in the field.

Correctly predicting flow velocity is important in predicting inundation time of the saltmarsh platform, as well as the advection of sediments and nutrients onto the platform. Ifthe hypothesis that the drag coefficient as a function of Red in arrays of cylinders behavessimilarly to the behavior of the drag coefficient of a single cylinder is correct, then therewill be more resistance due to drag than predicted by equation (12). Greater flow distancewill lead to slower flow velocities and greater spatial variation of both sedimentation andstanding biomass than predicted by the exploratory model presented here.

5.3. Research needs for salt marsh macrophyte dynamics

We have assumed a simple linear relationship between inundation ratio and biomassbased on the field data of Morris et al. [2002] collected at North Inlet estuary, SouthCarolina. This relationship may not be appropriate for marshes populated with differentspecies in different geographic locations [e.g., Silvestri and Marani, this volume]. Wechose the data of Morris et al. [2002] because it demonstrated a clear relationship betweenan abiotic variable (depth below MHT) and biomass, and because the 18-year data set ofmarsh stand characteristics at North Inlet allowed us to quantify the relationship betweenbiomass and stem diameter and stem density. Similar data sets that relate biomass to stemdiameter and stem density to biomass will need to be collected at other locations and forother plant species if the model is to be generalized. Although a significant body of workon biotic and abiotic factors that affect salt marsh macrophyte growth exists [e.g., Silvestriand Marani, this volume, and references therein], more experimental and field researchcould be conducted in a spatially distributed framework.

5.4. Research needs for sedimentation

As discussed in sections 1., 2., and 3., there have been a number of hypotheses on themechanics of sedimentation of vegetated salt marsh platforms. The experimental data ofMorris et al. [2002] demonstrate that standing biomass is positively correlated with thesedimentation rate and that there is little sedimentation during the winter months whenthere is little standing biomass. Neubauer et al. [2002] also found minimal deposition inthe winter months, although the standing biomass was not measured in that study. Theequations for settling deposition that do not include a dependance on biomass miss a cri-tical aspect of salt marsh accretionary processes, and the models using these equations areinadequate for predicting the drowning of vegetated salt marshes that is a result of theinability of marsh accretion to keep pace with relative sea level rise.

Settling of suspended sediments onto the salt marsh platform occurs when the down-ward settling of particles exceeds their upward diffusion due to turbulence. The turbulentdissipation caused by plant stems will reduce the upward turbulent diffusion, and increase



accretion rates. Lopez and Garcia [1998] model this upward diffusion based on a gradient-flux model. Calculating the effective settling rate using this model would give

(20)

where ws is particle settling velocity (L T−1), Cµ is and empirical constant, σc is thePrandtl-Schmidt number for sediment particles (dimensionless), κ is the turbulent kineticenergy per unit mass, and ε is the turbulent dissipation rate. Solving equation (20) wouldrequire knowledge of the vertical concentration field. To solve for the vertical concentra-tion field, the vertical velocity field would also have to be calculated, adding considerablecomplexity and computational expense. Nepf [1999] has demonstrated that the turbulentkinetic energy in emergent vegetation can be described by

(21)

with

(22)

where β1 is an O(1) scale coefficient. The use of equation (21) becomes limited forRed < 200, however. Experimentation is necessary to gain a better understanding of boththe turbulent energy and dissipation as a function of biomass (a, d, and C̄d are all functionsof biomass, so k and ε are also functions of biomass) at Red < 200, as well as the effectivesettling velocity as a function of biomass at these low Reynolds numbers. Understandingthe turbulence and how it is affected by salt marsh macrophytes is critical because it hasbeen suggested by a number of researchers [e.g., Leonard and Luther 1995] that the reduc-tion in turbulent energy from the tidal creek to the marsh is a dominant factor in control-ling marsh platform sedimentation. This drop in turbulent energy is the likely cause of thedistinct levees near the marsh creek that are not predicted by the model presented in thiscontribution.

Another important feature of vegetated salt marsh platforms is subsidence due to theautocompaction of sediment. Cahoon et al. [1995] found that vertical distance of autocom-paction was of the same magnitude as the vertical accretion at four field sites. Pizzuto andSchwendt [1997] calculated autocompaction rates for a coastal wetland on the order of 1 mm yr−1 using a finite-strain numerical model with stain coefficients determined by fieldmeasurements. Knott et al. [1987] found that compressibility is directly related to organiccontent. This may require the next generation of models to track the relative amounts oforganic and inorganic deposition in order to correctly predict autocompaction as a func-tion of marsh characteristics, rather than using a uniform relative rate of sea level rise aswas done in this study.

Acknowledgments. This research was supported by the National Science Foundation(EAR-0120582 and DEB-9816157) and the Florida State University Cornerstone Program.We would like to thank Marco Marani and two anonymous reviewers for their insightfulcomments and suggestions.

∈ −~ ,κ3

2 1d

κβ

UC add= 1

1

3( ) ,

w w CC C

se sc

= +∈

∂∂

µ κ

σ

2

z,

MUDD ET AL. 21


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