Dynamic response of surface water-groundwater exchangeto currents, tides, and waves in a shallow estuary

Audrey H. Sawyer,1,2 Fengyan Shi,3 James T. Kirby,3 and Holly A. Michael1

Received 8 October 2012; revised 23 February 2013; accepted 4 March 2013; published 3 April 2013.

[1] In shallow, fetch-limited estuaries, variations in current and wave energy promoteheterogeneous surface water-groundwater mixing (benthic exchange), which influencesbiogeochemical activity. Here, we characterize heterogeneity in benthic exchange within thesubtidal zone of the Delaware Inland Bays by linking hydrodynamic circulation models withmathematical solutions for benthic exchange forced by current-bedform interactions, tides, andwaves. Benthic fluxes oscillate over tidal cycles as fluctuating water depths alter fluidinteractions with the bed.Maximum current-driven fluxes (~1–10 cm/d) occur in channels withstrong tidal currents. Maximum wave-driven fluxes (~1–10 cm/d) occur in downwind shoals.During high-energy storms, simulated wave pumping rates increase by orders of magnitude,demonstrating the importance of storms in solute transfer through the benthic layer. Undermoderate wind conditions (~5m/s), integrated benthic exchange rates due to wave, current, andtidal pumping are each ~1–10m3/s, on the order of fluid contributions from runoff and freshgroundwater discharge to the estuary. Benthic exchange is thus a significant and dynamiccomponent of an estuary’s fluid budget that may influence estuarine geochemistry and ecology.

Citation: Sawyer, A. H., F. Shi, J. T. Kirby, and H. A. Michael (2013), Dynamic response of surface water-groundwaterexchange to currents, tides, and waves in a shallow estuary, J. Geophys. Res. Oceans, 118, 1749–1758, doi:10.1002/jgrc.20154.

1. Introduction

[2] Estuaries are ecologically diverse, productive marinehabitats that also serve as reactive storage zones for solutesand sediments discharging to the oceans. Net productivityof estuarine ecosystems surpasses productivity of coastalshelves by a factor of 5 [Whittaker and Likens, 1973].Estuaries play a critical role in moderating nutrient deliveryto the world’s oceans. In spite of increasing anthropogenicnutrient loads, estuarine denitrification removes approximatelyhalf of total dissolved inorganic nitrogen inputs [Seitzingerand Kroeze, 1998]. Fluid exchange across the estuary floor(benthic exchange) is an ecologically important process thatinfluences both nitrogen and carbon cycles by transportingsolutes between the water column and microbially activesediment. In some cases, benthic nitrification is the primarysource of nitrate for estuarine denitrification [Boynton andKemp, 1985]. Benthic exchange also influences cycles ofphosphorous, silica, iron, and manganese [Bhadha et al.,

2007; Pakhornova et al., 2007; Pratihary et al., 2009;Roy et al., 2011]. Quantification of benthic fluid and solutefluxes is essential for understanding chemical cycling andfor managing nutrients in eutrophic estuaries.[3] Many processes drive benthic exchange, leading to

a wide range of exchange length and timescales [Santoset al., 2012]. Temperature, salinity, and onshore hydraulicgradients drive exchange over large (kilometer) scales[Wilson, 2005]. At smaller (centimeter to meter) scales,tides, waves, and currents interact with the sediment-waterinterface to drive shallow circulation [King, 2012; Prechtand Huettel, 2003; Riedl et al., 1972]. Benthic organismsactively pump water across the sediment-water interface toflush metabolites from burrows [Rhoads, 1974]. Manysmall-scale processes involve no net exchange: seawatercycles through shallow sediment and returns to the watercolumn. Gross fluxes can be large, however. Net (typicallyfresh) fluxes of terrestrially derived groundwater and grossfluxes of saline water may play equally critical roles insolute transport and biogeochemical cycles.[4] Benthic fluxes are difficult to estimate, and the subset

of small-scale, net-zero fluxes particularly eludes measurement.Natural radioactive tracers such as Rn and Ra are commonlyused to estimate submarine groundwater discharge [Moore,2010]. Tracer concentrations in discharging porewater dependin part on fluid residence times within the sediment. Sinceresidence times are relatively short for small-scale, net-zerofluid exchange, tracers may only resolve a portion of thisbenthic flux component [Michael et al., 2011]. Seepagemeters are an alternative, local approach for measuringbenthic flux, but manual Lee-style seepage meters[Lee, 1977] do not resolve flux components that contributezero net exchange over the timescale of deployment.

Additional supporting Information may be found in the online version ofthis article.

1Department of Geological Sciences, University of Delaware, Newark,Delaware, USA.

2Now at Department of Earth and Environmental Sciences, Universityof Kentucky, Lexington, Kentucky, USA.

3Center for Applied Coastal Research, University of Delaware, Newark,Delaware, USA.

Corresponding author: A. H. Sawyer, Department of Earth andEnvironmental Sciences, University of Kentucky, 111 Slone Bldg.,Lexington, KY 40506, USA. (audrey.sawyer@uky.edu)

©2013. American Geophysical Union. All Rights Reserved.2169-9275/13/10.1002/jgrc.20154

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JOURNAL OF GEOPHYSICAL RESEARCH: OCEANS, VOL. 118, 1749–1758, doi:10.1002/jgrc.20154, 2013

High-frequency seepage meters that utilize heat-pulse andultrasonic measurement techniques have successfullyquantified net-zero exchange associated with tidal pumping[Paulsen et al., 2001; Taniguchi and Fukuo, 1993].However, current and wave pumping rates remain difficultto measure for two reasons: meters disturb the exchangepatterns [Smith et al., 2009], and the exchange rates canfluctuate over milliseconds. Pore water chemistry ortemperature profiles can be used to estimate the verticalcomponent of benthic fluxes, given a known dispersivity.However, effective dispersion depends in part on thesmall-scale benthic flux components of interest, which mixsolutes and heat in pores [Rapaglia and Bokuniewicz, 2009].[5] Mathematical models are among the best available

tools for estimating rates of small-scale benthic exchange.Solutions depend on factors such as sediment permeability,water depth, and the intensity of hydrodynamic forcing(for example, wave height, current velocity, or tidal range).Analytical solutions have been used to evaluate benthic fluxcomponents along coasts due to multiple mechanisms understeady conditions [King, 2012] and to characterize wave-drivenbenthic fluxes across the continental shelf [Riedl et al., 1972].From shoreline to shelf edge, exchange rates typicallydecrease as water depth increases [Precht and Huettel, 2003].[6] Unlike continental shelves, shallow estuaries have

mild bathymetric slopes, and water depth varies moderatelyin space but strongly over tidal timescales. Wave energyvaries in space and time with fetch and wind conditions.These surface water hydrodynamics should drive responsesin benthic flux over tidal and storm timescales. We exploredthe magnitudes of spatial and temporal variation by linkinga model for hydrodynamic circulation in a shallow estuarywith analytical solutions for benthic fluxes due to currents,tides, and waves. Rather than modeling a hypothetical estuary,we adopted the Delaware Inland Bays (Delaware, USA) asa representative system (Figure 1), though our goal is notto estimate total saline benthic fluxes for this particularestuary. Instead, our goal is to assess the sensitivity ofseveral individual benthic exchange mechanisms to surfacewater hydrodynamics. We first simulate benthic fluxesusing uniform sediment properties, a semidiurnal tide, andsteady wind. These relatively simple cases isolate the roleof surface water hydrodynamics in driving unsteady andheterogeneous benthic fluxes. We then present simulations

with heterogeneous sediment properties to illustrate theimpact on spatial heterogeneity in benthic fluxes. Last, wepresent year-long simulations with variable wind speedand direction based on records from 2010 to test benthicflux responses to a wider range of surface water conditions.In this shallow, fetch-limited, microtidal estuary, we show thatbenthic fluxes associated with current, tide, and wave forcingvary strongly in time and space. Saline benthic exchange rep-resents an important component of the estuarine water budget:exchange rates due to each mechanism are comparable torates of runoff and fresh submarine groundwater discharge.

2. Methods

[7] The Delaware Inland Bays are located on the easternside of the Delmarva Peninsula and include Rehoboth Bayto the north and Indian River Bay to the south (Figure 1).A narrow inlet connects Indian River Bay to the AtlanticOcean, and a channel separates the two bays. Our modelingapproach links hydrodynamic simulations of bay circulationwith analytical solutions for benthic fluxes across thesediment-water interface. Surface water circulation is firstsimulated using NearCom, which solves the depth-averagedshallow water equations using a non-orthogonal curvilineargrid [Shi et al., 2003]. Water depths and currents from thesurface water simulation are used to determine wind-drivenwave dynamics using empirical equations [Young andVerhagen, 1996]. Together, water depths, currents, and wavemetrics are final inputs to analytical solutions for benthic flux.[8] We limit our study to three benthic flux mechanisms

that operate in the subtidal zone: pumping due to current-bedform interactions, tidal pumping, and wave pumpingabove a flat bed (Figure 2). These are only a subset of activemechanisms in the Delaware Inland Bays. We neglected saltfingering and other density-dependent effects, which are diffi-cult to quantify in the absence of distributed pore water salinitydata. Though potentially large, density-driven benthic fluxesare spatially restricted to a narrow near-shore region wherefresh groundwater discharges to the bay [Bokuniewicz,1992]. We also neglected bioirrigation, which may contributesubstantial benthic fluxes [i.e.,Martin et al., 2004]. As a result,benthic flux estimates in this study are likely an underestimateof total benthic fluxes in the Delaware Inland Bays.[9] In our initial base case simulations and 1 year-long

simulation, we simplified bay floor sediment properties toelucidate variations in benthic flux due to surface waterhydrodynamics. These simulations assume a homogeneous,infinitely thick sediment column with hydraulic conductivity(K) of 10�5m/s, representative of the underlying aquifer. Thinaccumulations of reworked and fresh sediment locally drapethe aquifer, but the chosen K is within the expected range forthese deposits, which vary from silty clay (~5% of themapped bay floor) to sand (~37%) [Chrzastowski, 1986].One simulation tests the impact of heterogeneous sedimenton benthic fluxes. In this simulation, regions mapped assand, silty sand, sandy silt, clayey silt, and silty clay wereassigned K values of 10�4, 10�5, 10�6, 10�7, and 10�8m/s,respectively [Freeze and Cherry, 1979].[10] We do not calibrate simulations because our primary

goal is to explore the response of several benthic fluxmechanisms to surface water hydrodynamics in a shallowestuary rather than assess total saline benthic exchange

76°W 75°W

39°N

38°N

N

z [m]0 -2 -4 -6

inlet

Indian River Bay

Atlantic Ocean

Rehoboth Bay

2 km

Figure 1. Location and bathymetric map of the DelawareInland Bays (Delaware, USA).

SAWYER ET AL.: BENTHIC EXCHANGE IN SHALLOW ESTUARY

1750

rates for the Delaware Inland Bays. Furthermore, seepagemeasurements from Indian River Bay and other availabledatasets [Russoniello, 2012] are not appropriate for calibratingthe small-scale, net-zero benthic fluxes in this study. However,tidal amplitudes and currents in NearCom simulations are infair agreement with measurements at a field station on thesouthern shore of Indian River Bay.

2.1. Surface Water Hydrodynamics

[11] Surface water elevations and currents were simulatedfor eight cases with constant, uniform wind and one casewith a year of wind data recorded at NOAA buoy LWSD1.All simulations were allowed at least 2 days of “spin up” fortidal circulation to attain dynamic equilibrium. Shore edgesadjacent to dry cells were specified as zero perpendicularflux boundaries. Water level at inlet cells was specified witha constant M2 semidiurnal tide. Discharge from IndianRiver was set to 2.8 m3/s at the westernmost active cell inIndian River Bay, based on annual discharge statistics atUSGS gauging station 01484525. Discharge rates fromother streams and creeks are significantly smaller and areneglected in the model. Bathymetry data are from the U.S.Coastal Relief Model available through NOAA (Figure 1).The total number of grid cells was 9600.[12] Wave response to a uniform wind was evaluated using

empirical equations for depth- and fetch-limited wave growthdeveloped in a lake with similar size and depth as the DelawareInland Bays [Young and Verhagen, 1996]. Dimensionlesswave height (Hwg/W

2) is calculated as follows:

Hwg

W 2¼ 0:241 tanh 0:493d0:75

� �tanh

0:00313w0:57

tanh 0:493d0:75� �

" # !0:87

;

(1)

where Hw is the wave height, g is the gravity, and W is thewind speed (measured at a reference height of 10m in Youngand Verhagen [1996]). w is the dimensionless fetch (Xg/W2),and d is the dimensionless water depth (dg/W2), where X is

the fetch, and d is the water depth. We used local depthrather than fetch-averaged depth since depth varies littleacross the Delaware Inland Bays (Figure 1). Dimensionlesswave period (Twg/W) is calculated as follows:

Twg

W¼ 7:52 tanh 0:331d1:01

� �tanh

0:0005215w0:73

tanh 0:331d1:01� �

" # !0:37

; (2)

where Tw is the wave period. The wave dispersion equationrelates wave period and height to wavelength (Lw) as follows:

2pTw

� �2

� g2pLw

tanh2pLw

d

� �: (3)

[13] We evaluated wave heights, periods, and lengths acrossthe estuary at each time step based on simulated water depthsfrom NearCom, specified uniform wind speed, and fetch(determined as the distance to shore in the windward direction).

2.2. Current-Bedform Pumping Model

[14] The flow of currents over bedforms (Figure 2a)creates a pressure high on the stoss face of the bedformand a pressure low on the lee face. Elliott and Brooks[1997] developed the solution for average pumping ratesover one bedform wavelength (qb), assuming a sinusoidalpressure distribution along the immobile bedform surface:

qb ¼ 2KabLb

; (4)

where Lb is the bedformwavelength,K is the hydraulic conduc-tivity, and ab is the amplitude of the head distribution along thebed. Fehlman [1985] produced an empirical solution for ab:

ab ¼ 0:28U2

2g

Hb

0:34d

� �3=8

Hb=d≤0:34

Hb

0:34d

� �3=2

Hb=d≥0:34;

8>>><>>>:

(5)

where U is the current velocity, Hb is the bedform height,and d is the water depth. Equation (5) was developed from

(a) (b) (c)

Figure 2. (top) Conceptual sketches and (bottom) analytical solutions for benthic exchange due to (a) current-bedform interactions, (b) vertical one-dimensional tidal pumping, and (c) wave pumping. Dashed linein Figure 2c indicates depth-wavelength ratios that are not realizable under depth-limited conditions inequations (1) – (3).

SAWYER ET AL.: BENTHIC EXCHANGE IN SHALLOW ESTUARY

1751

flume pressure measurements along a solid triangular bedformand has been used to predict pumping rates over a range ofbedform lengths and current velocities [e.g.,Precht andHuettel,2003; Worman et al., 2006; Stonedahl et al., 2010]. Current-bedform pumping increases with relative bedform height(Hb/d), current velocity, and hydraulic conductivity anddecreases with bedform wavelength (Figure 2a).[15] Current-bedform pumping rates were evaluated

using water depths and currents from NearCom simulationsand uniform bedform wavelength and height of 0.5 and0.02m, respectively. We based bedform size on qualitativeobservations from the southern shore of Indian RiverBay following a summer storm, but actual wavelengthsand heights likely vary in space and time.

2.3. Tidal Pumping Model

[16] Tides can drive large benthic fluxes near the intertidalzone due to the response of the water table and pore fluiddensity patterns within the beach face sediment [King et al.,2010; Robinson et al., 2007; Sun, 1997]; this intertidal processis often referred to as “tidal pumping” [e.g., Santos et al., 2012].In the Delaware Inland Bays, concrete and steel reinforce muchof the shore and may limit intertidal circulation. However, tidalwater level fluctuations also drive vertical, one-dimensionalbenthic exchange throughout the subtidal zone (Figure 2b). Thisone-dimensional, vertical tidal pumping is often neglected inmathematical analyses of submarine groundwater discharge,but we consider it here.[17] When water level fluctuates with tides, the poroelastic

sediment supports a fraction of the change in stress on thebed. In undrained conditions (impermeable sediment), thechange in stress drives a uniform, instantaneous, nonhydrostaticpore pressure response throughout the sediment column. Indrained conditions (permeable sediment), vertical pressuregradients near the sediment-water interface drive fluid flow.Surface water flows into the bed on the rising tide and outof the bed on the falling tide. Wang and Davis [1996]presented the solution for unsteady, one-dimensional pressurewith depth due to tidal loading:

p ¼ rgat

"1� gð Þ exp �p

zffiffiffiffiffiffiffiffiffipcTt

p� �

cos2pTt

t � pzffiffiffiffiffiffiffiffiffipcTt

p� �

þg cos2pTt

t

� �#;

(6)

where p is the incremental change in nonhydrostatic pressure,z is the depth in the sediment, t is the time, r is the fluiddensity, at is the tidal amplitude, c is the hydraulic diffusivity,Tt is the tidal period, and g is the loading efficiency. 1� g isthe fraction of the tidal load supported by the sedimentframework. The first term represents the diffusive pressureresponse, and the second term represents the instantaneousporoelastic pressure response.[18] By Darcy’s Law, benthic flux is proportional to the

partial derivative of nonhydrostatic pressure with respect todepth at the sediment-water interface:

� K

rg@p

@z z¼0 ¼ Kat 1� gð Þ �pffiffiffiffiffiffiffiffiffipcTt

p� �

cos2pTt

t

� �� sin

2pTt

t

� �� �:

(7)

[19] By integration, the average benthic flux over one tidalperiod (qt) is as follows:

qt ¼ 2 sinp4

� atK 1� gð ÞffiffiffiffiffiffiffiffiffipcTt

p : (8)

[20] Tidal pumping increases with hydraulic conductivityand tidal amplitude and decreases with hydraulic diffusivity,tidal period, and loading efficiency (Figure 2b).[21] Tidal pumping rates were evaluated with amplitudes

from simulated water surface elevations. We assumed aloading efficiency of 0.9, typical for sediments [Wang,2000], and a hydraulic diffusivity of 0.01m2/s.

2.4. Wave Pumping Model

[22] King et al. [2009] provided the solution for the averagewave pumping rate over one wavelength and wave period(qw):

qw ¼ KHw

Lw cosh 2pLwd

� ; (9)

where Hw is the wave height, and Lw is the wavelength. Wavepumping increases with hydraulic conductivity and relativewave height (Hw/d). For a given relative wave height, maximumwave pumping occurs at intermediate relative wavelengths(Lw/d): short waves do not interact with the bed, and longwaves produce negligible pressure gradients (Figure 2c).[23] In estuaries, depth and fetch limit possible combinations

of water depth, wavelength, and wave height. As fetch, depth,and wind speed increase, wavelength and wave height bothincrease nonlinearly (Figures 3a and 3b). Because wavelengthincreases relatively slowly with increasing depth (Figure 3b),large relative wavelengths (dashed line in Figure 2c) are not pre-dicted under depth- and fetch-limited conditions. Combinationof empirical wave equations (equations (1–3)) with equation(9) demonstrates that benthic flux increases with fetch anddecreases rapidly with water depth, in spite of the potential forgreater wave heights over deeper water. For a given fetch andwater depth, benthic flux increases with wind speed (Figure 3c).[24] Wave pumping rates were evaluated using water

depths from NearCom simulations and wave heights andwavelengths from equations (1–3). Notably, equation (9)assumes a flat bed, while equation (4) assumes a rippledbed. Ripple topography can significantly enhance wavepumping [Shum, 1992, Figure 6], but in the absence of apurely analytical solution, we retain the flat bed solution asa conservative estimate.

3. Results

3.1. Base Case Simulations

[25] Under simple scenarios with semidiurnal tide andsteady, uniform wind, surface water hydrodynamics drivelarge spatial variations in benthic flux. Fluxes associatedwith current-bedform interaction (qc) are greatest in shoalsnear the inlet to Indian River Bay and the channel betweenIndian River Bay and Rehoboth Bay, where currents aregreatest (Figures 4a and 4b). Time-averaged fluxes exceed5 cm/d in these well-circulated regions. Currents stagnateand reverse during tidal maxima and minima, drivingfluctuations in benthic exchange. The greatest fluxes occuron rising and falling tides (Movie S1 in the supportinginformation). Tidal pumping rates (qt) are greatest at the

SAWYER ET AL.: BENTHIC EXCHANGE IN SHALLOW ESTUARY

1752

inlet where tides are magnified and least in Rehoboth Baywhere tides are attenuated (Figures 4c and 4e). Maximumtidal pumping rates approach 0.4 cm/d. Note that high andlow tides are asynchronous across the estuary (Figure 4d),which implies that benthic recharge and discharge due totidal pumping are also asynchronous. Wave pumping rates(qw) are generally greatest in shoals on the downwind sidesof the bays where wave height and wavelength are signifi-cant (Figures 4f, 4g, and 4h). With a northerly wind at 5m/s(the 70th percentile wind speed in 2010), time-averaged wave

height and wavelength increase sharply from north to southacross the bay as fetch increases (Figures 4f and 4g). Maxi-mum wave pumping exceeds 1.5 cm/d. Because wavepumping depends strongly on water depth, qw varies overthe tidal cycle (Movie S1).[26] At this wind speed (5m/s), spatially integrated rates of

current, tidal, and wave pumping averaged over one tidal cycleare roughly balanced at 1.3, 0.92, and 1.4m3/s, respectively.Locally, however, the relative importance of each mechanismvaries (Figure 5b). Near the inlet and channel between

W

-3

1

-1

0

1.6

0.8

0

0.1

0.2

-4

-2

0

0

5

2.5

2 km

0

0.5

1

0

0.1

0.3

0.2

-5

0

-2.5

(a) (b)

(f) (g) (h)

(c) (d) (e)

Figure 4. Simulated surface water hydrodynamics and benthic fluxes with constant M2 tide andsteady uniform wind of 5m/s from the north. Averages are taken over one tidal cycle. (a) Current speed.(b) Benthic flux due to current-bedform interactions, where bedform wavelength is 50 cm and height is2 cm throughout the estuary. (c) Tidal amplitude. (d) Phase of tide relative to open ocean (negative valuesindicate a phase lag). (e) Benthic flux due to tidal pumping. (f) Significant wave height. (g) Wavelength.(h) Benthic flux due to wave pumping.

0.02 0.04

0.06

0.080.1

0.12 0.5 1

2 3 4

-100 -50

-20

-10

-5

-2

(a) (b) (c)-200

Figure 3. (a) Dimensionless wave height (Hwg/W2) increases with dimensionless fetch (Xg/W2) and

dimensionless depth (dg/W2) (equation (1)). (b) Dimensionless wavelength (Lwg/W2) increases with

dimensionless fetch and dimensionless depth (equations (1–3)). (c) Benthic wave flux recast in termsof sediment hydraulic conductivity, wind speed, fetch, and water depth using equations (1–3) andequation (9). Wave pumping increases with hydraulic conductivity, wind speed, and fetch and decreasesstrongly with water depth.

SAWYER ET AL.: BENTHIC EXCHANGE IN SHALLOW ESTUARY

1753

Rehoboth and Indian River Bay, fluxes due to current-bedform interactions are greater than fluxes due to tidesand waves. On the southern shores of Rehoboth and IndianRiver Bay where fetch is greatest, wave pumping domi-nates. Wind direction does not significantly impact the mag-nitude of benthic fluxes but influences the location ofmaximum wave pumping (Figures 5a, 5b, 5c, and 5d). Aswind rotates, maximum wave energy shifts downwind,causing a migration in maximum wave pumping regions.[27] At a greater wind speed of 10m/s (95th percentile

wind speed in 2010), integrated wave pumping far exceedsbedform-current and tidal pumping. The wave pumping rate

increases from 1.4 to 5.1m3/s (254%). Wave pumping dom-inates over much of the bay, regardless of wind direction(Figures 5e, 5f, 5g, and 5h). Tidal pumping only dominatesalong the upwind shoreline, while current-bedform pumpingdominates in narrow regions with strong currents such as theinlet. Simulated current-bedform pumping rates respondnegligibly to wind speed because we assume uniform,stable bedforms. In natural systems, strong winds createwaves that can alter bedform topography, driving largechanges in current-bedform pumping rates. As an example,the current-bedform pumping rate increases from 1.3 to5.0m3/s (285%) if bedform wavelength decreases from

2 km

wavescurrents tides

(a)

(e)

(b)

(f)

(c)

(g)

(d)

(h)

Figure 5. Spatial distribution of dominant flux mechanisms for eight cases with constant wind speed,W.Benthic flux due to current-bedform interaction (blue) dominates near the inlet and channels where tidalcurrents are greatest. Wave pumping (red) dominates downwind. (a–d) Wave, current, and tidal pumpingare approximately balanced at a wind speed of 5m/s, but (e–h) wave pumping dominates over most of thebay at a wind speed of 10m/s.

W

2 km

(a)

Sediment Cover

-6

2

-2

-6

-3

0

0

1

0.5

(b)

(d)(c)

Figure 6. (a) Composition of bay floor sediment [Chrzastowski, 1986] used in simulation withheterogeneous permeability, constant M2 tide, and steady uniform wind of 5m/s from the north. Assignedhydraulic conductivities are in parentheses. (b) Benthic flux due to current-bedform interactions, wherebedform wavelength is 50 cm and height is 2 cm throughout the estuary. (c) Benthic flux due to tidalpumping. (d) Benthic flux due to wave pumping. Fluxes are averaged over one tidal cycle.

SAWYER ET AL.: BENTHIC EXCHANGE IN SHALLOW ESTUARY

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50 to 10 cm and height-wavelength ratio increases from0.04 to 0.10.

3.2. Effect of Permeability Heterogeneity

[28] Like surface water hydrodynamics, permeabilitystrongly influences benthic exchange rates. The range ofbenthic exchange rates is greater with heterogeneousbay floor sediments (compare Figures 4 and 6), but spatialpatterns remain similar. Fluxes associated with current-bedforminteraction (qc) remain greatest in shoals near the inlet toIndian River Bay and the channel between Indian River Bayand Rehoboth Bay (Figure 6b). These regions of the estuaryhave moderate to fast currents (Figure 4a) and sandy substrate(Figure 6a). Tidal pumping rates (qt) remain greatest at theinlet where tides are magnified. Tidal pumping rates are greatlyreduced in silty regions of the estuary where tides aretypically attenuated (Figure 6c). Wave pumping rates (qw)remain greatest in shoals on the downwind sides of the bayswhere wave height and wavelength are significant andsubstrate is sandy (Figure 6d). The general agreementbetween flux distributions in homogeneous and heterogeneous

sediment reflects the relationship between surface waterhydrodynamics and sediment transport. More energeticenvironments tend to have coarser, more permeable sediment.Together, large currents, tides, waves, and sediment permeabilitypromote the greatest benthic fluxes.[29] Spatially integrated rates of current, tidal, and wave

pumping averaged over one tidal cycle are greater inthe simulation with heterogeneous sediment by a factor of8.7, 1.3, and 7.1, respectively. One explanation is that thespatially averaged hydraulic conductivity is slightly greaterfor the heterogeneous than homogeneous simulation(3.5� 10�5 m/s versus 1.0� 10�5 m/s, the value for theaquifer beneath the estuary). More importantly, the spatialpermeability distribution effectively weights benthic fluxestoward greater values because sandier (more permeable)sediments are collocated with more energetic regions of theestuary that contribute most of the total benthic exchange.Siltier (less permeable) regions correspond with calmregions that contribute negligible benthic exchange regardlessof permeability.

3.3. Year-Long Simulation

[30] Simulated benthic fluxes over a full year vary inresponse to wind and wave energy. Storms with strongwinds significantly enhance wave pumping, as in earlyFebruary 2010, when wind speeds in excess of 20m/saccompanied a nor’easter storm (Figure 7). Simulatedbenthic fluxes associated with wave pumping increased fromnegligible rates on the calm day preceding the storm to over12m3/s during the storm’s peak. Wind did not significantlyimpact simulated current-bedform or tidal pumping. We didnot specify storm surge at the inlet boundary, which wouldtemporarily increase simulated current and tidal pumping.[31] Over the year, the strongest winds were from the east,

but moderate winds were also common from the northwestto southwest (Figure 8a). The top 10% of winds generatedmore than 36% of simulated wave-driven benthic fluxes.Wave pumping rates ranged from 0 to 12m3/s (Figure 8b),while fluxes due to tidal pumping did not vary becausesimulated tides only included the M2 frequency component.True variations in tidal pumping over spring-neap cycles arelikely small because tidal amplitude only varies approximatelytwofold. During about 30% of the simulated year, winds

0 2 4 6 8 100

50

100

% L

ess

Tha

n

waves

currents

tides

000

180

090270

W [m/s]

0

24

12

6

18

3%

6%

(a) (b)

Figure 8. (a) Wind rose for 2010 data from National Data Buoy Center Station LWSD1. (b) Cumulativedistribution function of simulated volumetric benthic exchange for 2010. Dashed lines separate threeregimes: calm conditions with tidally dominated benthic fluxes, moderate conditions with balancedbenthic fluxes, and storm conditions with large wave-dominated benthic fluxes.

0

5

10

15

30 32 34 36 38 40

0

10

20

t [d]

2/5/2010 nor’easter

(a)

(b)wavescurrentstidesriver

Figure 7. (a) Measured wind speed,W, during a nor’easterstorm (data from NOAA buoy LWSD1). (b) Simulatedvolumetric benthic flux, Q. Discharge from Indian Riverto the estuary (USGS gauging station 01484525) is shownfor comparison.

SAWYER ET AL.: BENTHIC EXCHANGE IN SHALLOW ESTUARY

1755

were calm, currents were slack, and tidal pumping was theprimary mechanism driving exchange over the estuary.About 40% of the year, all three mechanisms were roughlyin balance. Another 30% of the year, winds were gusty, andwave pumping was the dominant exchange mechanism(Figure 8b). Transitions between these regimes occurredover a range of timescales. Currents waxed and waned overtidal periods, whereas wind-driven wave pumping waxed andwaned over timescales ranging from hours to days (Figure 7).

4. Discussion

[32] In shallow, fetch-limited estuaries such as the DelawareInland Bays, spatial and temporal gradients in currents,water depths, and wave energy promote patchy and dynamicbenthic fluxes. Implications are twofold. First, local fieldmeasurements of benthic fluid or solute fluxes in estuariesare unlikely to represent conditions throughout the estuaryand throughout time. Attempts to scale local measurementsacross an estuary may produce order-of-magnitude errors inbenthic fluid or solute flux estimates, even in estuaries withrelatively uniform water depths and tidal ranges. Second,spatial and temporal variations in benthic flux may promote“hot spots” or “hot moments” of enhanced biogeochemicalcycling [McClain et al., 2003]. Maximum biogeochemicalcycling occurs when the residence time of surface water inthe benthic zone is long relative to the reaction timescale,and the supply of reactants across the sediment-water interfaceis rapid [e.g.,Harvey and Fuller, 1998; Zarnetske et al., 2011;Gu et al., 2012]. In some cases, rates of benthic uptakeor production also depend on the supply of reactants fromsediments or upwelling fresh or saline groundwater withlonger flow paths, but we focus here on supply from thesurface water. During a storm, benthic exchange ratesincrease, but benthic residence times may decrease. Responsein uptake or production depends on the initial condition.If pore water residence times are long relative to reactionrates but reactant supply is sluggish, an increase in benthicexchange rate will relieve the supply limitation and increaseuptake or production. However, if reactant supply is initiallyample but pore water residence times are short relative to thereaction timescale, the further reduction in pore waterresidence times will decrease uptake or production. In general,faster exchange rates may not directly correlate with greateruptake or production rates. Indeed, uptake or production ratesmay be greater in regions of slow exchange, as long as reactantconcentrations in surface water are sufficient to maintainadequate chemical mass flux to the benthic zone.[33] On a moderately windy day, simulated benthic fluxes

due to currents, tides, and waves are each ~1–10m3/s in ourmodel estuary. These estimates depend not only on windand tidal conditions but also on the distribution of sedimentpermeability, which can be difficult to constrain. Each of thethree simulated benthic exchange mechanisms generatesfluxes on the order of freshwater inputs to the DelawareInland Bays from runoff and submarine groundwaterdischarge (~3.3 and 4.6m3/s, respectively) [Russoniello,2012]. Total saline benthic fluxes in the Delaware InlandBays are likely much greater, due to contributions fromadditional mechanisms such as bioirrigation, density-drivenconvection, bedform migration, and sediment resuspension.For example, the upper 5mm of estuary sediment contains

100,000m3 of pore fluid, assuming 30% porosity. If a stormmobilized this sediment over a timescale of 1 h, exchange rateswould be on the order of 30m3/s. Our results therefore suggestthat saline benthic exchange rates are similar to, if not muchgreater than, fresh submarine groundwater discharge to theDelaware Inland Bays, particularly during storms. Theseresults agree broadly with numerous field and modelingstudies that suggest saline benthic exchange rates are oftenseveral times greater than fresh submarine groundwaterdischarge [Li et al., 1999; Martin et al., 2007; Michaelet al., 2005; Santos et al., 2009].[34] Though saline benthic exchange may represent a

large portion of total submarine groundwater discharge tothe Delaware Inland Bays, ocean-estuary exchange throughthe inlet dominates the fluid budget. Average surface waterexchange through the inlet over one tidal cycle is ~1000m3/s.Fresh inputs from runoff and submarine groundwaterdischarge are comparatively small yet influence nutrientbudgets because of their high nutrient concentrations [Andres,1995; Ritter, 1986]. Saline benthic exchange may similarlyinfluence nutrient and solute budgets if biogeochemicaltransformations along flow paths are rapid.[35] We have employed a novel modeling approach that

links hydrodynamic circulation in an estuary with analyticalsolutions for benthic exchange due to several mechanisms.A primary advantage of this approach is the ability to upscalebenthic exchange processes with characteristic length scalesof centimeters over an entire estuary at high computationalefficiency. The modeling approach can also be appliedto other estuarine systems. Additional benthic exchangemechanisms could be incorporated as appropriate, such astidal pumping in the intertidal zone [King et al., 2010].[36] Our model approach has several limitations. First, we

do not consider the effects of a mobile bed on either benthicexchange or surface water circulation. Bedform sizes andorientations vary over tidal and storm timescales. An idealmodeling scheme would use surface water hydrodynamicsto predict bedform morphologies and update the coefficientof friction at the bed to reflect morphodynamics. Additionally,evolving bedform morphologies would influence computa-tions of current pumping, wave pumping, and pore water“turnover” (alternating entrapment and release of pore wateras bedforms migrate) [Elliott and Brooks, 1997]. Theseoperational steps would require empirical relationships thatrelate hydrodynamics with morphodynamics and the useof numerical rather than analytical solutions for benthicexchange across a moving sediment-water interface. Thelatter modification would greatly reduce computationalefficiency. Another limitation of our model is the assumptionof uniform pore water salinity and density. We retain thisassumption because we lack both distributed data on porewater salinity in the Delaware Inland Bays and analyticalsolutions for buoyancy-driven benthic exchange. Becausemost fresh groundwater discharges near shore, variabledensity effects on benthic exchange are likely negligibleover much of the estuary.[37] One of the greatest limitations is that our approach

cannot address interactions between benthic exchangemechanisms. We intentionally did not sum rates of wave,current, and tidal pumping because these processes likelyinteract nonlinearly [King, 2012]. For instance, infiltrationand exfiltration due to tidal pumping may periodically

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restrict shallow wave pumping. Similarly, net groundwaterupwelling may limit shallow benthic exchange mechanisms[Cardenas and Wilson, 2006], but upwelling rates typicallydecay rapidly with distance from shore [Bokuniewicz,1992]. In the absence of these interactions, exchange depthsrange from centimeters to meters for the three exchangemechanisms we considered. Exchange depths due to currentpumping are on the order of one bedform wavelength[Cardenas and Wilson, 2007; Elliott and Brooks, 1997;Thibodeaux and Boyle, 1987]. Exchange depths due to tidalpumping are on the order of millimeters to centimeters,depending on hydraulic diffusivity and tidal period, whichinfluence penetration of the tidal pressure wave, and permeabilityand tidal amplitude, which influence seepage rates.Exchange depths due to wave pumping are on the order ofthe surface water wavelength [King et al., 2009] (~1m). Anactive area for future research is to evaluate constructive anddestructive interactions between benthic flux mechanisms thatoperate over various spatial and temporal scales.

5. Conclusions

[38] Estuaries are unique environments where shallowbathymetry and complex coastal geography promote stronggradients in tidal and wave energy, which propagate across thesediment-water interface into the benthic layer. Estuaries maytherefore exhibit more heterogeneity in benthic fluxes thanopen marine environments such as continental shelves. Insimulations based on the Delaware Inland Bays, benthicfluxes are patchy and dynamic, varying over spatial scalesof hundreds of meters and temporal scales of hours. Undermoderate winds of 5m/s, simulated pumping rates due tocurrents, tides, and waves are individually ~1–10m3/s, onthe order of fresh input rates from runoff and submarinegroundwater discharge. Under strong winds of 10m/s,saline benthic exchange rates can exceed all fresh water inputrates many times over, particularly if sediment resuspensionoccurs. Heterogeneity in benthic fluxes within estuaries maycontrol hot spots and hot moments in biogeochemical activityand contribute to habitat complexity in these highly productiveand diverse ecosystems. A clear need exists for improvedtechnology to measure spatially distributed, unsteady fluidand geochemical fluxes across sediment-water interfaces.

[39] Acknowledgments. This research was funded by the NationalScience Foundation through the Christina River Basin Critical Zone Observatory(EAR-0724971) and EAR-0910756. J.T.K. and F.S. acknowledge support fromthe Delaware Sea Grant College, R/HRCC-2, award NA10OAR4170084. Wethank Haibo Zong for processing the bathymetric grid for NearCom. We thankan anonymous reviewer whose suggestions strengthened the manuscript.

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