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Estuarine, Coastal and Shelf Science 172 (2016) 128e137

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Estuarine, Coastal and Shelf Science

journal homepage: www.elsevier .com/locate/ecss

The hydrodynamics of surface tidal flow exchange in saltmarshes

David L. Young*, Brittany L. Bruder 1, Kevin A. Haas, Donald R. WebsterSchool of Civil and Environmental Engineering, Georgia Institute of Technology, 790 Atlantic Dr., Atlanta, GA, 30332-0355, USA

a r t i c l e i n f o

Article history:Received 16 July 2015Received in revised form2 February 2016Accepted 5 February 2016Available online 8 February 2016

Keywords:Tidal marshEstuarine dynamicsShallow water tidesIntertidal environmentFlow through vegetationUSAGeorgiaSavannahRose Dhu Island

* Corresponding author.E-mail addresses: dyoung8@gatech.edu (D.L.

(B.L. Bruder), khaas@gatech.edu (K.A. Haas(D.R. Webster).

1 Current address: Center for Applied Coastal Rese209 Academy Street, Newark, DE, 19706, USA.

http://dx.doi.org/10.1016/j.ecss.2016.02.0060272-7714/© 2016 Elsevier Ltd. All rights reserved.

a b s t r a c t

Modeling studies of estuary circulation show great sensitivity to the water exchange into and out ofadjacent marshes, yet there is significant uncertainty in resolving the processes governing marsh surfaceflow. The objective of this study is to measure the estuary channel-to-saltmarsh pressure gradient and toguide parameterization for how it affects the surface flow in the high marsh. Current meters and high-resolution pressure transducers were deployed along a transect perpendicular to the nearby LittleOgeechee River in a saltmarsh adjacent to Rose Dhu Island near Savannah, Georgia, USA. The verticalelevations of the transducers were surveyed with static GPS to yield high accuracy water surfaceelevation data. It is found that water level differences between the Little Ogeechee River and neighboringsaltmarsh are up to 15 cm and pressure gradients are up to 0.0017 m of water surface elevation changeper m of linear distance during rising and falling tides. The resulting Little-Ogeechee-River-to-saltmarshpressure gradient substantially affects tidal velocities at all current meter locations. At the velocitymeasurement station located closest to the Little Ogeechee River bank, the tidal velocity is nearlyperpendicular to the bank. At this location, surface flow is effectively modeled as a balance between thepressure gradient force and the drag force due to marsh vegetation and bottom stress using the DarcyeWeisbach/Lindner's equations developed for flow-through-vegetation analysis in open channel flow.The study thus provides a direct connection between the pressure gradient and surface flow velocity inthe high marsh, thereby overcoming a long-standing barrier in directly relating flow-through-saltmarshstudies to flow-through-vegetation studies in the open channel flow literature.

© 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Saltmarshes are valuable and productive ecosystems that serveas storm buffers, fish nurseries, and nutrient sources, and they playa significant role in the dynamics of estuary circulation. The limitedamount of precise field data on the spatial variation of water sur-face elevation in estuarine creeks, channels, and in particular highmarshes, is a critical gap in the understanding of saltmarsh hy-drodynamics. The lack of data negatively impacts our ability toassess the effect of vegetation on surface water flow and accuratelyestimate the bottom stress in these settings. For instance, modelingresults show that a channel-to-saltmarsh pressure gradient (i.e.,differential water levels between the estuary main channel and the

Young), bbruder@udel.edu), dwebster@ce.gatech.edu

arch, University of Delaware,

adjacent saltmarsh) is responsible for surface transport of waterbetween the saltmarsh and the channel at high spring tide (Bruderet al., 2014). However, the modeling results are based on non-validated assumptions and the resulting pressure-gradient-drivensurface flows show great sensitivity to the parameterization ofthe bottom stress, in agreement with earlier modeling results(Kjerfve et al., 1991). Therefore, detailed measurements of thepressure gradient and corresponding surface flows, together withapplication of appropriate hydrodynamic models, are needed toimprove our understanding of the flow into and out of the highmarsh.

In an effort to determine the effect of vegetation on the transi-tion from channelized flow to sheet flow on the marsh platform,Vandenbruwaene et al. (2015) directly measured the velocity of thesurface flow and estimated the water surface elevation in a highmarsh. Their study is the only published fieldmeasurements we areaware of that show the presence of differential water levels be-tween the high marsh and the adjacent main channel in a salt-marsh. No study to our knowledge has attempted to quantitativelyrelate the corresponding pressure gradient to the sheet flow

D.L. Young et al. / Estuarine, Coastal and Shelf Science 172 (2016) 128e137 129

through the high marsh vegetation.Analyses of the effects of variable marsh friction (i.e., variable

marsh vegetation) on the mean flow in tidal creeks and deeperestuary channels are predominantly restricted to modeling studies(Kjerfve et al., 1991; Rinaldo et al., 1999a,1999b; Bruder et al., 2014).Attempts to quantify water surface elevations on high marshplatforms (and thus quantify the pressure gradient between thehigh marsh and the creeks and channels) are also chiefly limited tomodeling studies (Kjerfve et al., 1991; Rinaldo et al., 1999a, 1999b).Unfortunately, due to the paucity of available field data, thesemodels were unable to validate their results in the high marsh. Theprincipal gaps in current knowledge are the lack of available watersurface elevation measurements, the lack of directly observed flowpatterns (although see Temmerman et al., 2012; Vandenbruwaeneet al., 2015), and an inability to verify the model's parameterizationof the bed/vegetation friction (e.g., through Manning's n or drag-coefficient formulations; Kjerfve et al., 1991; Huang et al., 2008;Bruder et al., 2014). We note that several recent studies havefocused on the dissipation of wave energy by the marsh vegetationrather than addressing the relationship between the mean surfaceflow and bed/vegetation friction (Lowe et al., 2005; Augustin et al.,2009; Riffe et al., 2011; Wu, 2014). Thus, the objective of this studyis to determine the estuary channel-to-saltmarsh pressure gradientand to evaluate how it affects the surface flow in the high marsh.

1.1. Background

Studies on water movement in saltmarshes generally havefocused on one of three areas: the surface flow in the network ofbranching tidal creeks (e.g., Bayliss-Smith et al., 1979; French andStoddart, 1992; Allen, 1994), the surface flow high in the marshplatform (Eiser and Kjerfve, 1986; Leonard and Luther, 1995), andthe groundwater flow (Howes and Goehringer, 1994; Gardner et al.,2002; Gardner, 2005; Wilson and Gardner, 2006). The flow in tidalcreeks depends on the water surface elevation relative to themarshbathymetry. For low relative water surface elevation, the creeksremain below bankfull and the flow velocity is small,� 0:1� 0:2m=s (Bayliss-Smith et al., 1979; Pethick, 1980; Healeyet al., 1981; Dankers et al., 1984; French and Stoddart, 1992;Leopold et al., 1993; Allen, 1994; Pringle, 1995). The water surfaceelevation (i.e., pressure gradient) slopes into the tidal creek duringflood and towards the ocean during ebb (Leopold et al., 1993). Forhigh relative water surface elevation, the flow velocity in the creeksremains small while the creek is below bankfull and peaks at muchlarger values ð� 1m=sÞ once the marsh is flooded (Bayliss-Smithet al., 1979; Pethick, 1980; Healey et al., 1981; Dankers et al.,1984; French and Stoddart, 1992; Allen, 1994; Pringle, 1995;Rinaldo et al., 1999a, 1999b). Some studies observed “pulses” inthe tidal creek velocity, which correspond to sudden changes invelocity as the marsh is flooded (e.g., Temmerman et al., 2005b;Torres and Styles, 2007). Similar pulses also have been observedas the creek itself initially flooded or became dry (Hazelden andBoorman, 1999). Consistent with low relative water surface eleva-tion conditions, the pressure gradient in high relative water surfaceelevation conditions slopes into the tidal creek during flood andtowards the ocean during ebb (Healey et al., 1981; French andStoddart, 1992).

Regarding the hydrodynamics on the highmarsh platform, Allen(2000) writes, “the local hydraulics of channels has undoubtedlybeen over-emphasized at the expense of what are in effect tidalfloodplains.” Allen (2000) acknowledges that studies consideringflow on the high marsh platform face formidable challenges due tothe difficulty in accurately measuring small gradients in the watersurface elevation (Horstman et al., 2013) and the difficulty inmaking direct flow measurements in dense vegetation (Mazda

et al., 2007). Flow velocities across the high marsh surface aremuch smaller than in the creeks � 0:01� 0:1m=ð sÞ and decrease inproximity of bathymetric obstacles (Eiser and Kjerfve, 1986; Wanget al., 1993; Allen, 1994). The flow is generally governed by thebathymetry of the high marsh (Eiser and Kjerfve, 1986; Davidson-Arnott et al., 2002; Temmerman et al., 2005a), the pressuregradient from the slope in thewater surface elevation (Kjerfve et al.,1991; Bruder et al., 2014), and the vegetation characteristics(Leonard and Luther,1995; Temmerman et al., 2012). At low relativewater surface elevation, the flow essentially follows the highmarshbathymetry (Eiser and Kjerfve, 1986; Davidson-Arnott et al., 2002).As the relative water surface elevation becomes higher, currents inthe high marsh begin to behave more analogously to sheet flow(Temmerman et al., 2005b; Vandenbruwaene et al., 2015) and areeffectively forced by the water surface elevation slope betweenneighboring positions (Kjerfve et al., 1991; Bruder et al., 2014;Vandenbruwaene et al., 2015). This interplay betweenbathymetry-driven flow and sheet flow is also observed in estuariesdominated by mangrove swamps (e.g., Aucan and Ridd, 2000;Mazda et al., 2005; Horstman et al., 2013). In all cases, the flow ismediated by the characteristics of the vegetation and the relativewater surface elevation (Leonard and Luther, 1995; Temmermanet al., 2012; Vandenbruwaene et al., 2015). When vegetation ispartially submerged, the mean velocity depends on the plantmorphology and density (Leonard and Luther, 1995). For deeplysubmerged vegetation, the flow is characterized by a two-layervelocity profile (Leonard and Luther, 1995). The bottom layer ex-tends from the bed to the approximate height of the vegetationstems, and the flow characteristics are similar to the partially-submerged case. The upper layer is a logarithmic-law turbulentboundary layer that extends from essentially the top of the vege-tation to the free surface (Leonard and Luther, 1995).

Groundwater flow rates in marshes are typically substantiallysmaller than flow rates on the surface (Wolanski and Elliott, 2015).However, the authors noted that groundwater flow is a critical areaof study because it influences the soil properties and fluid salinity.Salinity is governed by a combination of marsh soil porosity, uplandgroundwater level, and tidal inundation (Wolanski and Elliott,2015). The water table and salinity respond rapidly to precipita-tion and tidal inundation, as groundwater moves rapidly throughsaltmarshes (Gardner et al., 2002; Gardner, 2005; Wolanski andElliott, 2015). It is important to note that rapid changes occur inresponse to the tide in areas that are not inundated due to tidaleffects on subsurface pore pressure gradients (Gardner et al., 2002;Gardner, 2005; Wilson and Gardner, 2006). Model results suggestthat the majority of the direct groundwater interaction withseawater occurs during the recharge and drainage of groundwateralong the banks of tidal creeks that branch into themarsh (Gardner,2005; Wilson and Gardner, 2006).

2. Materials and methods

A field experiment was conducted in the tidal marsh adjacent toRose Dhu Island near Savannah, Georgia, USA (Fig. 1) fromNovember 2nd to November 6th, 2014, coinciding with the largestspring tide in November 2014. The project site was selected due tothe availability of numerical model data of water levels(Bomminayuni et al., 2012; Bruder et al., 2014) and previously-collected bathymetric/topographic and vegetation data.

Three Onset HOBO pressure transducers (PTs), two AcousticDoppler Velocimeters (ADVs, Nortek Vector e Nortek AS, Rud,Norway) and a current profiler (Nortek Aquadopp HR-profiler)were deployed along a transect perpendicular to the Little Ogee-chee River in the tidal marsh. The ADVs measure the fluid velocityat essentially a point in the flow, whereas the Aquadopp measures

Fig. 1. Map showing the locations of the six stations (courtesy of Google Earth). The instrument transect is shown as a dashed black line. Rose Dhu Island is outlined in red in theupper left image and shown as a yellow triangle on a map of the southeastern United States in the bottom right image. The lower left panel is the bathymetry (or topography, ifexposed) along the transect in NAVD88. Green squares denote data points and the dashed gray line is the approximate bathymetry in the data gap. For reference, GPS coordinates forstation D are Lat: 31�55011.6200N Long: 81� 8020.9900W. The highest and lowest high tides observed at station A during the experimental period are 1.40 m and 1.24 m (in NAVD88),respectively. Imagery data from November 20th, 2014.

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the flow velocity in a series of evenly-spaced vertical bins. Instru-ment locations are shown in Fig. 1. The PTs were housed in custom-made PVC stands (Fig. 2). The stand's aluminum plate preventedinstrument settling during the deployment cycle and the bolt/dive-

Fig. 2. (a) Diagram of a pressure transducer stand, (b) in situ photograph of a pressuretransducer stand during the GPS survey, and (c) in situ photograph of an ADV duringdeployment.

weight assembly fixed the vertical elevation of the PTs within thestand. The three PTs were surveyed daily with static GPS for at leasttwo hours. Additionally, a GPS base station, located on the nearbyfixed dock, was surveyed daily for at least eight hours to improveGPS vertical elevation accuracy during post-processing. The GPSantennae were Ashtech Duel Frequency Marine Antenna (AshtechS.A.S., Carquefou, France) that were connected to either AshtechProFlex 500 GS or Z-Surveyor receivers and were programmed torecord internally at 10 s intervals. Further, the ADV and Aquadopplocations were surveyed daily using a total station. The watersalinity wasmeasured near the surface from the dock (Fig.1) at 4:15PM on November 3rd, 2014 and 11:35 AM on November 6th, 2014and was 25.7 and 26.3, respectively.

Field data collected at this site also included Spartina alternifloravegetation surveys at 25 locations (1 m � 1 m quadrats) across themarsh (within 0.6 km of the transect) conducted in December 2010.The data consisted of the number of stalks in each quadrat and thediameter of at least ten randomly-selected stalks. Visual compari-son of the 2014 experiment and 2010 survey periods at ground leveland via Google Earth images (20 November 2014 vs. 28 January2011) indicate little change in the gross vegetation patterns.

2.1. Pressure to water surface elevation

The PTs measured absolute pressure and temperature every30 s. To convert the absolute pressure to gauge pressure, atmo-spheric pressure readings from the nearby (~13 km away) weatherstation at Skidaway Institute of Oceanography were employed.

Fig. 3. Scatter plot of the north and east velocity components at station E. Symbolsindicate the measured data, and the ellipse is the best fit to the data. There are 24,100velocity samples included in the plot.

D.L. Young et al. / Estuarine, Coastal and Shelf Science 172 (2016) 128e137 131

Gauge pressure was converted to water depth above the PT byassuming the pressure variation in the vertical direction was solelydue to hydrostatic effects. The water density was determined fromthe PT temperature measurement and the salinity measured at thedock, which was assumed to be equal to the salinity in the vicinityof the PTs. Temperature and salinity were assumed to be verticallyhomogeneous.

To improve the accuracy of the absolute pressure readings (andthus the estimated water surface elevation), the three PTs werecalibrated in a 1 m deep tank at seven temperatures, ranging from12 to 26 �C. Linear calibration curves were developed to calculatethe pressure difference between two of the PTs (stations A and D)and the third reference PT (station F) as a function of temperature.These curves were used during data processing to adjust thepressure data to a common reference pressure. The standard de-viations of the mean pressure difference between the PTs at sta-tions A and D and the reference PT at station F were calculated foreach calibration temperature. The difference was found to be lessthan 10 Pa in all cases, which corresponded to less than 1 mm ofwater surface elevation difference. Note that the ADVs and theAquadopp are equipped with built-in PTs. Unfortunately, the ac-curacy of the built-in PTs is one order-of-magnitude worse than theaccuracy of the Onset HOBO PTs and is not sufficient to resolve sub-cm water level differences.

The water surface elevation was calculated relative to theNAVD88 vertical datum by adding the water depth data to the PTelevation using the dimensions of the stand (shown in Fig. 2) andthe GPS measurement of the antenna position. To arrive at suffi-ciently accurate water surface elevation measurements, the GPSmeasurements were post-processed using GrafNet (NovAtel, Cal-gary, Alberta, Canada), treating the GPS system as a stationaryclosed loop network. The system included four GPS antenna/re-ceivers (one at each PT and one on the dock) and several Contin-uously Operating Reference Stations (CORS) operated by the U.S.National Geodetic Survey (NGS). The estimated vertical accuracyfromGrafNet was approximately 0.5 cm for all stations. This level ofaccuracy was obtained using simultaneous GPS measurements. Thevertical positions of the PT stands did not vary during the experi-mental periods.

2.2. ADV data processing

The ADV measurements have a resolution of 1 mm/s and werecollected continuously at 1 Hz. Data collected during low tide(determined by instances of the PT at station D being dry) werediscarded. Following the recommendations of Chanson et al. (2008)and Wilson et al. (2013), data for which the average correlationcoefficient of the three beams was less than 70% for 45 consecutivesamples, or for which the average over 300 samples of the meancorrelation coefficient of the three beams dropped below 70%, werediscarded. This filtering predominately removed data collectedwhile the instrument was not submerged, and less than 2% of thesubmerged instrument data were removed due to filtering. Thedominant flow direction (if one was present) was determined foreach ADV. An ellipse was fit to a scatter plot of the measured eastand north velocity components for each ADV, and the major axis ofthe resulting ellipse is defined as the “along-stream” flow direction.Correspondingly, the minor axis is defined as the “cross-stream”

direction. Fig. 3 illustrates this process for the ADV at station E.

2.3. Aquadopp data processing

Aquadopp measurements were collected at 1 Hz. The Aquadoppreturned the velocity within 10 cm vertical bins, equally spacedfrom 0.3 to 2.2 m above the instrument. Dry bins were identified

using the built-in PT and temperature gauges to estimate the waterdepth above the instrument. All bins in which the water depth hadnot reached at least the midpoint of the next highest bin werediscarded. The velocity measurements in each bin were averagedover 30 s intervals to smooth out turbulent velocity fluctuations.The flux-per-unit-width (q) was estimated by summing the velocityin each bin multiplied by the bin height. Flux-per-unit-widththerefore corresponded to the fluid flow through a vertical lineextending from the Aquadopp to the surface. The ellipse fittingtechnique (Section 2.2) combined with polar histograms of the fluxvectors were used to determine the along-stream flow direction inthe Crooked Creek tributary. The horizontal flux vector was rotatedto correspond to the defined along-stream and cross-streamdirections.

3. Results and discussion

Tidal flow in and out of the saltmarsh is more complex than thetypical behavior of estuarine channels due to the highly variablebathymetry and vegetation across the marsh. Further, thecomparatively strong Little-Ogeechee-River-to-saltmarsh pressuregradient significantly affects the marsh flow characteristics, aspresented below. A typical tidal cycle in this saltmarsh proceeds asfollows (illustrated in Fig. 4, which shows the relative water surfaceelevation at five instances in the tidal cycle):

(1) Early Flood: Starting from low tide, thewater begins to rise asthe tide comes in. At the earliest stages of rising tide, thewater in the Crooked Creek tributary and the nearby LittleOgeechee River rise at roughly the same rate. The waterprogresses into the marsh along the Crooked Creek tributaryand the flux-per-unit-width (at station B e see Fig. 1) beginsto increase towards a maximum value as the water rises (seeFig. 5). The ADV at station C becomes inundated after theAquadopp (at station B) due to the station's higher elevation.Water at station C initially flows into the marsh towards thenorthwest along a small non-vegetated depression (seeFig. 1).

(2) Mid Flood: The water level begins to rise more rapidly inLittle Ogeechee River than in the Crooked Creek tributary. Asthe water level in Little Ogeechee River rises above its banks,

Fig. 4. Illustration of the tidal flow sequence. The blue shade indicates the relativewater surface elevation at the position along the transect for each stage. The ba-thymetry (or topography) along the transect is shown as a dashed gray line. Thecompass roses with velocity arrows indicate the velocity direction and magnitude atthe respective instruments (lack of an arrow indicates the instrument was not sub-merged during that stage).

Fig. 5. Tidal stage (NAVD88) e along-stream-flux-per-unit-width (q) diagram at sta-tion B for a November 5th, 2014 tidal cycle. Positive values of flux-per-unit-widthdenote flood (inundation) and negative values represent ebb (draining). The colortransition indicates time progression from the beginning (green) to end (blue) of thetidal cycle. The dashed gray line marks the elevation of the bank of the Little OgeecheeRiver (1.1 m).

D.L. Young et al. / Estuarine, Coastal and Shelf Science 172 (2016) 128e137132

the highmarsh floods from Little Ogeechee River towards theCrooked Creek tributary. The flow of water from LittleOgeechee River briefly (i.e., 20e30 min) forces the flow atstation C out of alignment with the small northwesterly-oriented depression and shifts the flow direction towardsthe northeast along the instrument transect (i.e., towards theCrooked Creek tributary). Station E becomes inundated andthe initial velocity at the instrument is similarly towards thenortheast along the instrument transect. The flux-per-unit-width at station B, which has been increasing with the ris-ing tide, begins to slow towards a local minimum value(Fig. 5) as the water flooding into the marsh from LittleOgeechee River briefly restricts the water flooding along theCrooked Creek tributary.

(3) Late Flood: Before high tide is reached, the water level in theCrooked Creek tributary (station A) catches up to and ex-ceeds the water level in Little Ogeechee River (station F).Simultaneously, the flux-per-unit-width in the CrookedCreek tributary increases towards a local maximum value(smaller than the previous maximum described in (1) Early

Flood, Fig. 5), and the velocity at station E switches direction,flowing to the southwest (towards Little Ogeechee River)along the instrument transect. The velocity at station Creturns to the direction aligned with the depression towardsthe northwest.

(4) Early Ebb: The water level in Little Ogeechee River begins todrop slightly before the water level in the Crooked Creektributary. The water level in Little Ogeechee River dropssubstantially faster, such that the water level in the CrookedCreek tributary remains higher for the remainder of the tidalcycle. The water level in the marsh becomes sufficientlyhigher than that in Little Ogeechee River to once againtemporarily force the flow at station C out of alignment withthe small depression. The flow at station C shifts towards thesouthwest along the instrument transect (towards LittleOgeechee River). The flow at station E remains stronglysouthwestern towards Little Ogeechee River until the ADVbecomes dry. Concurrently, the flow in the Crooked Creektributary slows and switches to ebbe uponwhich it follows amore standard tidal stage-flux pattern (Fig. 5).

(5) Mid-Late Ebb: As the water level in Little Ogeechee Riverdrops below its banks, the flow at station C returns toalignment along the small depression, flowing towards thesoutheast.

3.1. Water levels and pressure gradients

As the narrative of the tidal cycle sequence made clear (illus-trated in Fig. 4), the differential water level between the highmarshand Little Ogeechee River strongly affects the flow characteristics atall instrument locations. To quantify the differential water levels(and corresponding pressure gradients), the water surface eleva-tions at each PT are shown in Fig. 6 for a representative tidal cycle.

The water levels at the two PTs in the marsh (stations A and D)are nearly identical over much of the tidal cycle, but the data alsoreveal some differences. The water level in Crooked Creek tributary(station A) rises slightly faster and falls more quickly than the water

Fig. 6. Water surface elevation (NAVD88) for the tidal cycle shown in Fig. 5 for eachpressure transducer (PT). Flat segments indicate dry periods for the instrument. If thepressure gradient is the dominant forcing term, then water flows from the locationwith higher water surface elevation to the location with lower water surface elevation,as indicated by the black arrows.

D.L. Young et al. / Estuarine, Coastal and Shelf Science 172 (2016) 128e137 133

level in the highmarsh (station D), which is to be expected from thereduced tidal wave propagation speed in the high marsh (Parker,1991).

In contrast, the water level in Little Ogeechee River (station F) issubstantially different than the water level at either of the twomarsh PT stations. The water level difference between LittleOgeechee River and themarsh is approximately 7e8 cm at high tideand becomes as large as 15 cm during rising and falling tide. Thewater level difference is similar to that observed inVandenbruwaene et al. (2015) during flood tide. Given that thedistance between stations D and F is less than 90 m, the observedwater surface elevations translate to a substantial Little-Ogeechee-River-to-saltmarsh pressure gradient.

Another interesting feature in Fig. 6 is that the water level in theCrooked Creek tributary and Little Ogeechee River (stations A andF) are very similar at the beginning of flood tide prior to theinundation of the high marsh. Once the water level in the CrookedCreek tributary (station A) exceeds the level of the bank, approxi-mately 0.4 m (Fig. 1), its rate of rise decreases as the marsh isflooded until it matches the water level in the high marsh (stationD). During ebb tide, the water surface elevation in the CrookedCreek tributary (Station A) and the high marsh (Station D) initiallydecrease at the same rate, then thewater level in the Crooked Creektributary (Station A) starts to decrease more rapidly. The watersurface elevation in the Crooked Creek tributary (station A) isgreater than that in the Little Ogeechee River (station F) throughoutthe ebb tide, which indicates the tributary drains at a slower rate.

Fig. 7. Along-stream velocity at station E (red stars) and depth-based Reynolds number(Reh e green pluses) plotted as a function of the corresponding pressure gradient (m ofwater surface elevation drop per m of linear distance). The blue line represents themodel for dstalk ¼ 1 cm and Nstalk ¼ 93. 96% of the variance in the velocity parameter isexplained by the model.

3.2. Effects of the Little-Ogeechee-River-to-saltmarsh pressuregradient on flow

The effect of the Little-Ogeechee-River-to-saltmarsh pressuregradient on the flow is more subtle at stations B and C than atstation E (see Fig. 1), largely due to the bathymetry. The effect of theLittle-Ogeechee-River-to-saltmarsh pressure gradient at station B isapparent in the stage versus along-stream flux-per-unit-width (q)diagram shown in Fig. 5. Typical estuary channel stage-flux (orvelocity) diagrams appear as a tilted ellipse (with the angledepending on the standing versus progressive nature of the tidal

wave). Therefore, a typical flow is characterized by a singlemaximumvalue of flux during flood and a single maximumvalue offlux during ebb. Fig. 5 shows an obvious “pulse” in the flood stage,where the flux-per-unit-width reaches a maximum value, thentemporarily decreases and subsequently increases to a localmaximum value before returning to a more standard diagramshape. As described in the tidal sequence, this brief slowing andlocal minimum value of flux-per-unit-width coincides with flow ofwater from Little Ogeechee River towards the Crooked Creek trib-utary due to the higher water level (in Little Ogeechee River)overtopping the Little Ogeechee River bank. This flow of wateressentially retards the flux of water up the Crooked Creek tributaryuntil the water level in the tributary rises above the water level inLittle Ogeechee River and the tributary flux begins to increaseagain. Torres and Styles (2007) observed similar stage diagrams fora tidal creek near Winyah Bay (Georgetown, South Carolina, USA),in which marsh inundation was strong enough to temporarilyreverse the tidal creek flow, thus producing a tidal stage diagram inthe shape of a figure eight.

The flow at station C appears to be predominately confined to anatural mud-flat depression (see Fig. 1) roughly parallel to LittleOgeechee River. However, during both rising and falling tide, theLittle-Ogeechee-River-to-saltmarsh pressure gradient becomessufficiently large to redirect the velocity at station C to beperpendicular to the alignment of the natural depression. The flowdirection in these instances is aligned with the instrument transecttowards either the Crooked Creek tributary (if the Little OgeecheeRiver water level is higher) or Little Ogeechee River (if the marshwater level is higher).

The flow at station E is obviously affected by the pressuregradient between stations D and F. The angle between the along-stream flow direction (i.e., major axis of the best fit ellipse inFig. 3) and the instrument transect is less than 9�, which indicatesthe adjacent PTs were well-placed to capture the pressure gradientdriving the flow at this location. Fig. 7 plots the along-stream ve-locity, averaged over 30 s intervals, at station E against the corre-sponding pressure gradient (i.e., the water surface elevationdifferential between the PT at station D and the PT at station Fdivided by the distance between stations) for all measured tidalcycles. Along-stream velocity is defined as positive to the

D.L. Young et al. / Estuarine, Coastal and Shelf Science 172 (2016) 128e137134

northwest, roughly along the PT transect, and positive pressuregradient is defined as higher water level in the high marsh (PT atstation D) than in the Little Ogeechee River (PTat station F). Becauseof the direct correlation of the sign and magnitude of the surfaceflow and pressure gradient, Fig. 7 strongly indicates the pressuregradient between stations D and F governs the flow characteristicsat this location, regardless of tidal cycle or water level.

3.3. Predicting velocity given the pressure gradient

It is desirable to accurately predict the surface flow velocitygiven the slope of the water surface elevation by defining anequation (or set of equations) that relate these quantities. The datashown in Fig. 7 afford an excellent opportunity to explore thisrelationship since the flow at station E appears unconfined by ba-thymetry and thus is driven by the pressure gradient betweenstations D and F. A simple control volume analysis yields thefollowing force balance (J€arvel€a, 2004):

rgAbhvz

vx¼ 1

2rCdApV2 (1)

The primary forcing is due to the pressure gradient (from theslope in the water surface elevation, vz

vx, which accounts for thecomponent of the fluid weight in the flow direction due to the bedslope and the net force on the control volume due to the variablewater depth, i.e., the unequal hydrostatic pressure distributions). Inthe formulation on the left-hand-side of Eqn. (1), x is the coordinatedirection along the instrument transect, z is the water surfaceelevation, h is the total water depth (i.e., h ¼ h0 þ z), h0 is the stillwater depth, Ab is the bed area, and g is the acceleration due togravity. The primary retarding force is the drag force due to the bedand vegetation (i.e., the right hand side of Eqn. (1)). The drag force ismodeled with a drag coefficient, Cd, formulationwhere r is the fluiddensity, V is the fluid velocity, and Ap is the projected (frontal) areaof the vegetation (Munson et al., 2013). The assumptions leading tothe force balance in Eqn. (1) include neglecting the local (temporal)acceleration (because the tidal variation occurs over comparativelylarge time scales, e.g., hours), neglecting the convective accelera-tion (because the velocity magnitude in Fig. 7 is small in compar-ison to the marsh spatial scales, i.e., V ~10 cm/s versus spatial scalesof ~100m), and neglecting the cross-stream flow (because the flowat station E is nearly aligned with the transect).

Much discussion in the flow-through-vegetation literature isdevoted to the optimum parameterization of the drag coefficientand effective areas (Ab and Ap in Eqn. (1)) under a variety of cir-cumstances (e.g., Lindner, 1982; Koch and Ladd, 1997; Wu et al.,1999; Nepf, 1999; Tsihrintzis, 2001; J€arvel€a, 2002; Stone andShen, 2002; Lee et al., 2004; Tanino and Nepf, 2008; Cheng andNguyen, 2011). The literature is generally in agreement that theeffective areas must depend on marsh plant morphology anddensity (e.g., the stalk diameter and the spacing between thestalks), but the authors have not come to a consensus on the form ofthe dependence. Additionally, the drag coefficient's dependence onReynolds number is unresolved. Some studies exclude the Reynoldsnumber dependence entirely (e.g., Lindner, 1982; J€arvel€a, 2002),whereas others include the drag coefficient as a function of thedepth-based Reynolds number (Reh ¼ Vh

n, e.g., Wu et al., 1999;

Tsihrintzis, 2001; Stone and Shen, 2002; Lee et al., 2004) or thestalk-diameter-based Reynolds number (Red ¼ Vdstalk

n, e.g., Koch and

Ladd, 1997; Nepf, 1999). The most recent studies incorporate thepore velocity between the cylinders/stalks as the relevant velocityscale (Tanino and Nepf, 2008) or the pore velocity as the velocityscale and the vegetation-related-hydraulic-radius (rv ¼ p

41�ll

dstalk,where l is the stem density) as the relevant length scale (e.g., Cheng

and Nguyen, 2011) in the formulation of the Reynolds number. It isalso important to note that the two-layer velocity profile describedfor deeply submerged saltmarsh vegetation in Leonard and Luther(1995) has previously been shown to exist in atmospheric turbulentboundary layers above crops or forests (Raupack et al., 1991; Kaimaland Finnigan, 1994), in flume studies of flow through submergedplants (e.g., Murota et al., 1984; Gambi et al., 1990), and in flumestudies of flow through roughened cylinders (Stone and Shen,2002). The vegetation in our study remained emergent in the vi-cinity of the ADV stations during spring tide; therefore we restrictour discussion to the partially submerged case.

The data in this study are best modeled by a DarcyeWeisbachfriction factor (f) approach, making use of Lindner's equation(Lindner, 1982) to estimate f based on local vegetation-related pa-rameters. This modeling approach has been successfully applied innumerical studies of river floodplains (Stoesser et al., 2003), as wellas flume studies with natural vegetation (J€arvel€a, 2002). Originallyintended for pipe flow, the DarcyeWeisbach equation (Eqn. (2))

adopts a shear velocity, u* ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffigh

�vz=vx

q �, to account for the

pressure gradient and parameterizes the velocity as follows:

Vu*

¼ffiffiffi8f

s(2)

By comparing Eqns. (1) and (2), f can be written in terms of Cd asf ¼ 4Cd

Ap

Ab(Lindner, 1982). Lindner (1982) employs the plant stalk

diameter (dstalk) multiplied by the water depth (h) as a surrogate forprojected vegetal area (Ap) and the longitudinal and lateral plantspacing (ax and ay, respectively) as a surrogate for bottom area (Ab):

f ¼ 4Cddstalkhaxay

(3)

Flume experiments by J€arvel€a (2002) indicate that the dragcoefficient falls in the range 1.43 � Cd � 1.55 for Lindner's equation(Eqn. (3)).

To apply the model, the pressure gradient in Eqns. (1) and (2)�vz=vx

�is taken as the absolute value of the measured quantity,

and the direction of the velocity is assumed to be opposite the signof the measured pressure gradient. The water depth (h) is assumedto be equivalent to that at the nearby station D. The vegetationparameters (dstalk, ax, ay) are determined from the vegetation sur-vey of the grass within the quadrat located closest to station E (seeFig. 1): the average stalk diameter is dstalk ¼ 1.0 ± 0.07 cm[mean ± standard error of the mean] and the number of stalks inthe quadrat is Nstalk ¼ 93. The parameters ax and ay are bothassumed to be equal to the mean spacing (s) between individual

stalks given by s ¼ffiffiffiffiAs

p�

ffiffiffiffiffiffiffiffiNstalk

pdstalkffiffiffiffiffiffiffiffi

Nstalk

p�1

for a square vegetation survey

area (As). The value of Cd that results in the best fit is 2.0, which isslightly larger than the value range reported by J€arvel€a (2002). Thisdiscrepancy is discussed in greater detail below.

3.4. Discussion of the DarcyeWeisbach/Lindner equation fit

The model results, employing Eqns. (2) and (3), are shown inFig. 7. The model effectively predicts the along-stream velocity atstation E for the majority of the dataset. The model performsparticularlywell near the change in flow direction (i.e., velocity¼ 0)as well as in the range of large negative velocity values (whichforms the majority of the data). The model does not predict as wellthe apparent transition in slope at velocity values around �6 cm/s(and pressure gradients near 2 � 10�4 m of water surface elevation

D.L. Young et al. / Estuarine, Coastal and Shelf Science 172 (2016) 128e137 135

drop per m of linear distance).When applying the DarcyeWeisbach equation to pipe flow as

originally intended, the dependence of Cd (or more properly, f) onReynolds number is given by the Moody diagram (Moody, 1944).Lindner's formulation effectively assumes f is independent ofdepth-based Reynolds number, analogous to the “fully rough”regime in pipe flow or the flow at stalk-based Reynolds numbersgreater than 200 described in Nepf (1999), and thusmay be entirelydetermined fromvegetative properties. In contrast, some studies inthe flow-through-vegetation literature (e.g., Wu et al., 1999;Tsihrintzis, 2001; Lee et al., 2004) parameterize Cd as a functionof the depth-based Reynolds number (Reh ¼ rVh

m ). Tsihrintzis (2001)in particular raises the possibility that the dependence on Reh maychange with Reh regime, analogous to the regime dependence ofthe drag coefficient for flow past cylinders.

The apparent transition in slope at pressure gradients near2 � 10�4 m/m in Fig. 7 raises the possibility of a Reynolds numbertransition. Thus, the corresponding depth-based Reynolds numberis also plotted in Fig. 7, revealing a transition in the slope of the Rehcurve also near pressure gradient values of 2 � 10�4 m/m (a similartransition is observed for the stalk-diameter-based Reynoldsnumber, although not shown in Fig. 7). The transition occurs at amuch higher Reynolds number than that observed for the transi-tion to unsteady flow described in Koch and Ladd (1997) or Nepf(1999) and could be associated with the velocity becoming suffi-ciently large such that the stem flexibility is no longer negligible(note that dissipation of wave energy by saltmarsh vegetation isaffected by stem flexibility, Riffe et al., 2011). As a result, a two-equation approach was considered to model these data using theTsihrintizis (2001) formulation for Cd (Cd ¼ gRe�k

h , where g and kare parameters determined via the procedures in Lee et al., 2004)for the low Reh regime and the DarcyeWeisbach/Lindner approachfor the high Reh regime. This approach was ultimately discarded infavor of applying the DarcyeWeisbach/Lindner formulation to alldata because g and k must be determined from a multi-variableleast-squares fit to an existing dataset and the resulting modelperformed only marginally better in the low Reh regime than theDarcyeWeisbach/Lindner model. Formulations incorporating thestalk-diameter-based Reynolds number (Tanino and Nepf, 2008) orthe hydraulic radius-based Reynolds number (Cheng and Nguyen,2011) were similarly discarded.

3.5. Parameter sensitivity

It is beneficial to evaluate the sensitivity of the Dar-cyeWeisbach/Lindner formulation to the various input parameters(i.e., Nstalk, dstalk, h, and the pressure gradient). The effect of theexpected level of variability or uncertainty in each of the four inputvariables on the DarcyeWeisbach/Lindner model is shown in Fig. 8.The variability observed inNstalk and dstalk among the 25 locations ofthe vegetation survey quadrats provides insight to the expectedrange of values of these parameters. Among the data from thesequadrats, Nstalk ¼ 80.4 ± 18.1 and dstalk ¼ 0.77 ± 0.13 cm[mean ± standard deviation], hence one standard deviation corre-sponds to approximately 20% for each parameter. Therefore, thepotential variability in Nstalk and dstalk is taken to be up to 20%higher or lower than the representative values used in the originalformulation (which are specific for the quadrat location nearest tostation E). The potential uncertainty in the water depth and pres-sure gradient estimates is based on the constraints of the mea-surements. The uncertainty in the water depth is assumed to be±0.54 cm by combining the uncertainty in the PT water levelmeasurements and the accuracy of the GPS survey elevation esti-mates. Similarly, combining the resolution of the physical mea-surements yields an uncertainty in the pressure gradient values of

±8.9 � 10�5 m of water surface elevation difference per m of lineardistance.

Fig. 8 (a) and (b) indicate that variability in Nstalk and dstalk in-fluences the estimated velocity magnitude for a given pressuregradient, which highlights the need to accurately estimate theseparameters via vegetation surveys or other means. Fig. 8 (c) revealsthat the net effect of water depth variation is negligible, as expectedbased on Eqns. (2) and (3). Lastly, despite the comparatively smallexpected uncertainty in the pressure gradient (relative to thevegetation-related quantities), the effect on the estimated velocitymagnitude can be quite significant, particularly near the predictedchange in flow direction. At large values of the pressure gradient(regardless of sign), the impact on the predicted velocitymagnitudeis smaller because the velocity is proportional to the square root of

the water surface elevation slope (ffiffiffiffiffiffiffiffiffiffiffivz=vx

q).

The results shown in Fig. 8 help explain the need to increase thevalue of Cd relative to the range recommended by J€arvel€a (2002)when modeling the flow velocity at station E. In addition to theuncertainties in the vegetation parameters already discussed, onemust consider that the vegetation varies substantially along thetransect between stations D and F (i.e., the PTs that bracket stationE � see Fig. 1). It is possible that the use of representative values ofNstalk and dstalk near the site of the flow measurements is insuffi-cient to adequately capture the effects of the variation in Nstalk anddstalk along the transect. Similarly, the reported values of the pres-sure gradient at station E are the best estimate of the slope of thewater surface elevation based on the information available (i.e., theslope of the line connecting two neighboring water surface eleva-tion locations at stations D and F). As shown in Fig. 8, even smallerrors in the pressure gradient estimates can have strong effects onthe estimated velocity magnitude. Great care was taken in thecurrent measurements to minimize the uncertainty in pressuregradient, and the results show that the change in sign of thecalculated pressure gradient coincides very well with the change invelocity direction (see Fig. 7). However, it is possible that the waterlevel measurements at stations D and F are capturing the macro-scale pressure gradient switch properly, but overestimating themagnitude at station E due to localized variation in water levelbetween the two PTs from effects induced by the variable ba-thymetry (Fig. 1). Additionally, although the saltmarsh ground-water flow rate is typically much smaller than the surface flow rate(Wolanski and Elliott, 2015), this could be another contributingfactor in the increase in the drag coefficient, e.g., if the pressuregradient is driving groundwater flow unaccounted for in our forcebalance. Further, groundwater intrusion can affect the surface wa-ter salinity and temperature (Wolanski and Elliott, 2015), intro-ducing an error in our calculated water density and thus the watersurface elevation measurements. As a result, one can reasonablysuggest that the need to increase Cd is an artifact of the uncertaintyin quantifying the vegetation and/or pressure gradient parametersor potentially due to unaccounted groundwater flow.

4. Conclusions

The results of this study offer strong support for the existence ofa Little-Ogeechee-River-to-saltmarsh pressure gradient, corrobo-rating similar observations in the numerical study of Bruder et al.(2014) and field study of Vandenbruwaene et al. (2015). Fig. 6clearly shows the existence of large differential water levels be-tween Little Ogeechee River and the adjacent tidal marsh for themajority of the tidal cycle. Further, data from the current metersindicate that the resulting Little-Ogeechee-River-to-saltmarshpressure gradient has a significant effect on the flow throughoutthe marsh.

Fig. 8. Sensitivity of the DarcyeWeisbach/Lindner model to variation in (a) Nstalk, (b) dstalk, (c) h, and (d) pressure gradient. The upper and lower bounds for each parameter are 20%higher/lower for Nstalk and dstalk, ±0.54 cm for h, and ±8.9 � 10�5 m of water surface elevation drop per m of linear distance for pressure gradient. Note that the curves are obscuredby near perfect overlap in (c).

D.L. Young et al. / Estuarine, Coastal and Shelf Science 172 (2016) 128e137136

At station E (on the high marsh near the bank of Little OgeecheeRiver) the flow characteristics are governed by the pressuregradient between the neighboring stations (Fig. 7). At this site, theflow velocity is quantitatively related to the pressure gradient be-tween stations D and F via modeling techniques adapted from theopen-channel-flow-through-vegetation literature. The model isbased on a balance between the force of the pressure gradient andthe drag force due to the vegetation and bottom stress. Specifically,the DarcyeWeisbach/Lindner equations effectively model the ve-locity based on specific vegetation-related parameters and thepressure gradient between stations D and F.

This study demonstrates the ability to quantify thewater surfaceelevation measurements to sufficient accuracy to directly relate theresulting pressure gradient to the flow velocity in the high marsh.The study, therefore, overcomes a long-standing barrier in directlyrelating flow-through-saltmarsh studies to quantitative relation-ships developed in flumes for flow through vegetation. Many ofthese formulations, such as the DarcyeWeisbach/Lindner model,may prove superior for estimating the drag coefficient in the highmarsh (i.e., re-arranging Eqn. (3)) than the current Finite VolumeCoastal Ocean Model (FVCOM) technique of taking the greater of auser-entered drag coefficient or a logarithmic-boundary-layer-fit-estimated drag coefficient (Bruder et al., 2014). The Dar-cyeWeisbach/Lindner model may likewise prove superior tosingle-coefficient equations that assume a logarithmic-law velocityprofile, such as Manning's equation (e.g., Wolanski and Elliott,2015), which is known to be ineffective in modeling flow throughemergent vegetation (Kadlec, 1990; Jadhav and Buchberger, 1995;Nepf, 1999). Estimating the drag coefficient via Eqn. (3) withspatial variability in the vegetation characteristics (and thus thedrag coefficient) across the highmarsh based on vegetation surveysand/or satellite image estimates of grass distributions will signifi-cantly enhance models of surface flows in the marsh.

Acknowledgments

Funds were provided by the Georgia Water Resources Institutethrough the Fiscal Year 2014 104b program of the National In-stitutes for Water Resources and United States Geological Survey(Project #2014GA344B) and the U.S. National Science Foundation(Grant #OCE- 1234449). Additionally, the authors gratefullyacknowledge Dr. Terry Sturm (Georgia Institute of Technology) forhelpful discussions.

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