Journal of Geophysical Research: Oceans

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

Authors


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

Abstract

[1] In shallow, fetch-limited estuaries, variations in current and wave energy promote heterogeneous surface water-groundwater mixing (benthic exchange), which influences biogeochemical activity. Here, we characterize heterogeneity in benthic exchange within the subtidal zone of the Delaware Inland Bays by linking hydrodynamic circulation models with mathematical solutions for benthic exchange forced by current-bedform interactions, tides, and waves. Benthic fluxes oscillate over tidal cycles as fluctuating water depths alter fluid interactions with the bed. Maximum current-driven fluxes (~1–10 cm/d) occur in channels with strong 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. Under moderate wind conditions (~5 m/s), integrated benthic exchange rates due to wave, current, and tidal pumping are each ~1–10 m3/s, on the order of fluid contributions from runoff and fresh groundwater discharge to the estuary. Benthic exchange is thus a significant and dynamic component of an estuary's fluid budget that may influence estuarine geochemistry and ecology.

1 Introduction

[2] Estuaries are ecologically diverse, productive marine habitats that also serve as reactive storage zones for solutes and sediments discharging to the oceans. Net productivity of estuarine ecosystems surpasses productivity of coastal shelves by a factor of 5 [Whittaker and Likens, 1973]. Estuaries play a critical role in moderating nutrient delivery to the world's oceans. In spite of increasing anthropogenic nutrient loads, estuarine denitrification removes approximately half of total dissolved inorganic nitrogen inputs [Seitzinger and Kroeze, 1998]. Fluid exchange across the estuary floor (benthic exchange) is an ecologically important process that influences both nitrogen and carbon cycles by transporting solutes between the water column and microbially active sediment. In some cases, benthic nitrification is the primary source of nitrate for estuarine denitrification [Boynton and Kemp, 1985]. Benthic exchange also influences cycles of phosphorous, 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 solute fluxes is essential for understanding chemical cycling and for managing nutrients in eutrophic estuaries.

[3] Many processes drive benthic exchange, leading to a wide range of exchange length and timescales [Santos et al., 2012]. Temperature, salinity, and onshore hydraulic gradients drive exchange over large (kilometer) scales [Wilson, 2005]. At smaller (centimeter to meter) scales, tides, waves, and currents interact with the sediment-water interface to drive shallow circulation [King, 2012; Precht and Huettel, 2003; Riedl et al., 1972]. Benthic organisms actively pump water across the sediment-water interface to flush metabolites from burrows [Rhoads, 1974]. Many small-scale processes involve no net exchange: seawater cycles through shallow sediment and returns to the water column. Gross fluxes can be large, however. Net (typically fresh) fluxes of terrestrially derived groundwater and gross fluxes of saline water may play equally critical roles in solute 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 commonly used to estimate submarine groundwater discharge [Moore, 2010]. Tracer concentrations in discharging pore water depend in part on fluid residence times within the sediment. Since residence times are relatively short for small-scale, net-zero fluid exchange, tracers may only resolve a portion of this benthic flux component [Michael et al., 2011]. Seepage meters are an alternative, local approach for measuring benthic flux, but manual Lee-style seepage meters [Lee, 1977] do not resolve flux components that contribute zero net exchange over the timescale of deployment. High-frequency seepage meters that utilize heat-pulse and ultrasonic measurement techniques have successfully quantified net-zero exchange associated with tidal pumping [Paulsen et al., 2001; Taniguchi and Fukuo, 1993]. However, current and wave pumping rates remain difficult to measure for two reasons: meters disturb the exchange patterns [Smith et al., 2009], and the exchange rates can fluctuate over milliseconds. Pore water chemistry or temperature profiles can be used to estimate the vertical component of benthic fluxes, given a known dispersivity. However, effective dispersion depends in part on the small-scale benthic flux components of interest, which mix solutes 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 flux components along coasts due to multiple mechanisms under steady conditions [King, 2012] and to characterize wave-driven benthic fluxes across the continental shelf [Riedl et al., 1972]. From shoreline to shelf edge, exchange rates typically decrease as water depth increases [Precht and Huettel, 2003].

[6] Unlike continental shelves, shallow estuaries have mild bathymetric slopes, and water depth varies moderately in space but strongly over tidal timescales. Wave energy varies in space and time with fetch and wind conditions. These surface water hydrodynamics should drive responses in benthic flux over tidal and storm timescales. We explored the magnitudes of spatial and temporal variation by linking a model for hydrodynamic circulation in a shallow estuary with 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) as a representative system (Figure 1), though our goal is not to estimate total saline benthic fluxes for this particular estuary. Instead, our goal is to assess the sensitivity of several individual benthic exchange mechanisms to surface water hydrodynamics. We first simulate benthic fluxes using uniform sediment properties, a semidiurnal tide, and steady wind. These relatively simple cases isolate the role of surface water hydrodynamics in driving unsteady and heterogeneous benthic fluxes. We then present simulations with heterogeneous sediment properties to illustrate the impact on spatial heterogeneity in benthic fluxes. Last, we present year-long simulations with variable wind speed and direction based on records from 2010 to test benthic flux responses to a wider range of surface water conditions. In this shallow, fetch-limited, microtidal estuary, we show that benthic fluxes associated with current, tide, and wave forcing vary strongly in time and space. Saline benthic exchange represents an important component of the estuarine water budget: exchange rates due to each mechanism are comparable to rates of runoff and fresh submarine groundwater discharge.

Figure 1.

Location and bathymetric map of the Delaware Inland Bays (Delaware, USA).

2 Methods

[7] The Delaware Inland Bays are located on the eastern side of the Delmarva Peninsula and include Rehoboth Bay to the north and Indian River Bay to the south (Figure 1). A narrow inlet connects Indian River Bay to the Atlantic Ocean, and a channel separates the two bays. Our modeling approach links hydrodynamic simulations of bay circulation with analytical solutions for benthic fluxes across the sediment-water interface. Surface water circulation is first simulated using NearCom, which solves the depth-averaged shallow water equations using a non-orthogonal curvilinear grid [Shi et al., 2003]. Water depths and currents from the surface water simulation are used to determine wind-driven wave dynamics using empirical equations [Young and Verhagen, 1996]. Together, water depths, currents, and wave metrics 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 pumping above a flat bed (Figure 2). These are only a subset of active mechanisms in the Delaware Inland Bays. We neglected salt fingering and other density-dependent effects, which are difficult to quantify in the absence of distributed pore water salinity data. Though potentially large, density-driven benthic fluxes are spatially restricted to a narrow near-shore region where fresh groundwater discharges to the bay [Bokuniewicz, 1992]. We also neglected bioirrigation, which may contribute substantial benthic fluxes [i.e., Martin et al., 2004]. As a result, benthic flux estimates in this study are likely an underestimate of total benthic fluxes in the Delaware Inland Bays.

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 line in Figure 2c indicates depth-wavelength ratios that are not realizable under depth-limited conditions in equations ((1)) – ((3)).

[9] In our initial base case simulations and 1 year-long simulation, we simplified bay floor sediment properties to elucidate variations in benthic flux due to surface water hydrodynamics. These simulations assume a homogeneous, infinitely thick sediment column with hydraulic conductivity (K) of 10−5 m/s, representative of the underlying aquifer. Thin accumulations of reworked and fresh sediment locally drape the aquifer, but the chosen K is within the expected range for these deposits, which vary from silty clay (~5% of the mapped bay floor) to sand (~37%) [Chrzastowski, 1986]. One simulation tests the impact of heterogeneous sediment on benthic fluxes. In this simulation, regions mapped as sand, silty sand, sandy silt, clayey silt, and silty clay were assigned K values of 10−4, 10−5, 10−6, 10−7, and 10−8 m/s, respectively [Freeze and Cherry, 1979].

[10] We do not calibrate simulations because our primary goal is to explore the response of several benthic flux mechanisms to surface water hydrodynamics in a shallow estuary rather than assess total saline benthic exchange rates for the Delaware Inland Bays. Furthermore, seepage measurements from Indian River Bay and other available datasets [Russoniello, 2012] are not appropriate for calibrating the small-scale, net-zero benthic fluxes in this study. However, tidal amplitudes and currents in NearCom simulations are in fair agreement with measurements at a field station on the southern shore of Indian River Bay.

2.1 Surface Water Hydrodynamics

[11] Surface water elevations and currents were simulated for eight cases with constant, uniform wind and one case with a year of wind data recorded at NOAA buoy LWSD1. All simulations were allowed at least 2 days of “spin up” for tidal circulation to attain dynamic equilibrium. Shore edges adjacent to dry cells were specified as zero perpendicular flux boundaries. Water level at inlet cells was specified with a constant M2 semidiurnal tide. Discharge from Indian River was set to 2.8 m3/s at the westernmost active cell in Indian River Bay, based on annual discharge statistics at USGS gauging station 01484525. Discharge rates from other streams and creeks are significantly smaller and are neglected 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 growth developed in a lake with similar size and depth as the Delaware Inland Bays [Young and Verhagen, 1996]. Dimensionless wave height (Hwg/W2) is calculated as follows:

display math(1)

where Hw is the wave height, g is the gravity, and W is the wind speed (measured at a reference height of 10 m in Young and Verhagen [1996]). χ is the dimensionless fetch (Xg/W2), and δ is the dimensionless water depth (dg/W2), where X is the fetch, and d is the water depth. We used local depth rather than fetch-averaged depth since depth varies little across the Delaware Inland Bays (Figure 1). Dimensionless wave period (Twg/W) is calculated as follows:

display math(2)

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

display math(3)

[13] We evaluated wave heights, periods, and lengths across the estuary at each time step based on simulated water depths from 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 bedform and a pressure low on the lee face. Elliott and Brooks [1997] developed the solution for average pumping rates over one bedform wavelength (qb), assuming a sinusoidal pressure distribution along the immobile bedform surface:

display math(4)

where Lb is the bedform wavelength, K is the hydraulic conductivity, and ab is the amplitude of the head distribution along the bed. Fehlman [1985] produced an empirical solution for ab:

display math(5)

where U is the current velocity, Hb is the bedform height, and d is the water depth. Equation (5) was developed from flume pressure measurements along a solid triangular bedform and has been used to predict pumping rates over a range of bedform lengths and current velocities [e.g., Precht and Huettel, 2003; Worman et al., 2006; Stonedahl et al., 2010]. Current-bedform pumping increases with relative bedform height (Hb/d), current velocity, and hydraulic conductivity and decreases with bedform wavelength (Figure 2a).

[15] Current-bedform pumping rates were evaluated using water depths and currents from NearCom simulations and uniform bedform wavelength and height of 0.5 and 0.02 m, respectively. We based bedform size on qualitative observations from the southern shore of Indian River Bay following a summer storm, but actual wavelengths and heights likely vary in space and time.

2.3 Tidal Pumping Model

[16] Tides can drive large benthic fluxes near the intertidal zone due to the response of the water table and pore fluid density patterns within the beach face sediment [King et al., 2010; Robinson et al., 2007; Sun, 1997]; this intertidal process is often referred to as “tidal pumping” [e.g., Santos et al., 2012]. In the Delaware Inland Bays, concrete and steel reinforce much of the shore and may limit intertidal circulation. However, tidal water level fluctuations also drive vertical, one-dimensional benthic exchange throughout the subtidal zone (Figure 2b). This one-dimensional, vertical tidal pumping is often neglected in mathematical 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 the bed. In undrained conditions (impermeable sediment), the change in stress drives a uniform, instantaneous, nonhydrostatic pore pressure response throughout the sediment column. In drained conditions (permeable sediment), vertical pressure gradients near the sediment-water interface drive fluid flow. Surface water flows into the bed on the rising tide and out of the bed on the falling tide. Wang and Davis [1996] presented the solution for unsteady, one-dimensional pressure with depth due to tidal loading:

display math(6)

where p is the incremental change in nonhydrostatic pressure, z is the depth in the sediment, t is the time, ρ is the fluid density, at is the tidal amplitude, c is the hydraulic diffusivity, Tt is the tidal period, and γ is the loading efficiency. 1 − γ is the fraction of the tidal load supported by the sediment framework. The first term represents the diffusive pressure response, and the second term represents the instantaneous poroelastic pressure response.

[18] By Darcy's Law, benthic flux is proportional to the partial derivative of nonhydrostatic pressure with respect to depth at the sediment-water interface:

display math(7)

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

display math(8)

[20] Tidal pumping increases with hydraulic conductivity and 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 a loading efficiency of 0.9, typical for sediments [Wang, 2000], and a hydraulic diffusivity of 0.01 m2/s.

2.4 Wave Pumping Model

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

display math(9)

where Hw is the wave height, and Lw is the wavelength. Wave pumping increases with hydraulic conductivity and relative wave height (Hw/d). For a given relative wave height, maximum wave pumping occurs at intermediate relative wavelengths (Lw/d): short waves do not interact with the bed, and long waves 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 both increase nonlinearly (Figures 3a and 3b). Because wavelength increases relatively slowly with increasing depth (Figure 3b), large relative wavelengths (dashed line in Figure 2c) are not predicted under depth- and fetch-limited conditions. Combination of empirical wave equations (equations ((1)-(3))) with equation (9) demonstrates that benthic flux increases with fetch and decreases rapidly with water depth, in spite of the potential for greater wave heights over deeper water. For a given fetch and water depth, benthic flux increases with wind speed (Figure 3c).

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 terms of sediment hydraulic conductivity, wind speed, fetch, and water depth using equations ((1)-(3)) and equation (9). Wave pumping increases with hydraulic conductivity, wind speed, and fetch and decreases strongly with water depth.

[24] Wave pumping rates were evaluated using water depths from NearCom simulations and wave heights and wavelengths from equations ((1)-(3)). Notably, equation (9) assumes a flat bed, while equation (4) assumes a rippled bed. Ripple topography can significantly enhance wave pumping [Shum, 1992, Figure 6], but in the absence of a purely analytical solution, we retain the flat bed solution as a conservative estimate.

3 Results

3.1 Base Case Simulations

[25] Under simple scenarios with semidiurnal tide and steady, uniform wind, surface water hydrodynamics drive large spatial variations in benthic flux. Fluxes associated with current-bedform interaction (qc) are greatest in shoals near the inlet to Indian River Bay and the channel between Indian River Bay and Rehoboth Bay, where currents are greatest (Figures 4a and 4b). Time-averaged fluxes exceed 5 cm/d in these well-circulated regions. Currents stagnate and reverse during tidal maxima and minima, driving fluctuations in benthic exchange. The greatest fluxes occur on rising and falling tides (Movie S1 in the supporting information). Tidal pumping rates (qt) are greatest at the inlet where tides are magnified and least in Rehoboth Bay where tides are attenuated (Figures 4c and 4e). Maximum tidal pumping rates approach 0.4 cm/d. Note that high and low tides are asynchronous across the estuary (Figure 4d), which implies that benthic recharge and discharge due to tidal pumping are also asynchronous. Wave pumping rates (qw) are generally greatest in shoals on the downwind sides of the bays where wave height and wavelength are significant (Figures 4f, 4g, and 4h). With a northerly wind at 5 m/s (the 70th percentile wind speed in 2010), time-averaged wave height and wavelength increase sharply from north to south across the bay as fetch increases (Figures 4f and 4g). Maximum wave pumping exceeds 1.5 cm/d. Because wave pumping depends strongly on water depth, qw varies over the tidal cycle (Movie S1).

Figure 4.

Simulated surface water hydrodynamics and benthic fluxes with constant M2 tide and steady uniform wind of 5 m/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 is 2 cm throughout the estuary. (c) Tidal amplitude. (d) Phase of tide relative to open ocean (negative values indicate a phase lag). (e) Benthic flux due to tidal pumping. (f) Significant wave height. (g) Wavelength. (h) Benthic flux due to wave pumping.

[26] At this wind speed (5 m/s), spatially integrated rates of current, tidal, and wave pumping averaged over one tidal cycle are roughly balanced at 1.3, 0.92, and 1.4 m3/s, respectively. Locally, however, the relative importance of each mechanism varies (Figure 5b). Near the inlet and channel between Rehoboth and Indian River Bay, fluxes due to current-bedform interactions are greater than fluxes due to tides and waves. On the southern shores of Rehoboth and Indian River Bay where fetch is greatest, wave pumping dominates. Wind direction does not significantly impact the magnitude of benthic fluxes but influences the location of maximum wave pumping (Figures 5a, 5b, 5c, and 5d). As wind rotates, maximum wave energy shifts downwind, causing a migration in maximum wave pumping regions.

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 tidal currents are greatest. Wave pumping (red) dominates downwind. (a–d) Wave, current, and tidal pumping are approximately balanced at a wind speed of 5 m/s, but (e–h) wave pumping dominates over most of the bay at a wind speed of 10 m/s.

[27] At a greater wind speed of 10 m/s (95th percentile wind speed in 2010), integrated wave pumping far exceeds bedform-current and tidal pumping. The wave pumping rate increases from 1.4 to 5.1 m3/s (254%). Wave pumping dominates over much of the bay, regardless of wind direction (Figures 5e, 5f, 5g, and 5h). Tidal pumping only dominates along the upwind shoreline, while current-bedform pumping dominates in narrow regions with strong currents such as the inlet. Simulated current-bedform pumping rates respond negligibly to wind speed because we assume uniform, stable bedforms. In natural systems, strong winds create waves that can alter bedform topography, driving large changes in current-bedform pumping rates. As an example, the current-bedform pumping rate increases from 1.3 to 5.0 m3/s (285%) if bedform wavelength decreases from 50 to 10 cm and height-wavelength ratio increases from 0.04 to 0.10.

3.2 Effect of Permeability Heterogeneity

[28] Like surface water hydrodynamics, permeability strongly influences benthic exchange rates. The range of benthic exchange rates is greater with heterogeneous bay floor sediments (compare Figures 4 and 6), but spatial patterns remain similar. Fluxes associated with current-bedform interaction (qc) remain greatest in shoals near the inlet to Indian River Bay and the channel between Indian River Bay and Rehoboth Bay (Figure 6b). These regions of the estuary have moderate to fast currents (Figure 4a) and sandy substrate (Figure 6a). Tidal pumping rates (qt) remain greatest at the inlet where tides are magnified. Tidal pumping rates are greatly reduced in silty regions of the estuary where tides are typically attenuated (Figure 6c). Wave pumping rates (qw) remain greatest in shoals on the downwind sides of the bays where wave height and wavelength are significant and substrate is sandy (Figure 6d). The general agreement between flux distributions in homogeneous and heterogeneous sediment reflects the relationship between surface water hydrodynamics and sediment transport. More energetic environments tend to have coarser, more permeable sediment. Together, large currents, tides, waves, and sediment permeability promote the greatest benthic fluxes.

Figure 6.

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

[29] Spatially integrated rates of current, tidal, and wave pumping averaged over one tidal cycle are greater in the simulation with heterogeneous sediment by a factor of 8.7, 1.3, and 7.1, respectively. One explanation is that the spatially averaged hydraulic conductivity is slightly greater for the heterogeneous than homogeneous simulation (3.5 × 10−5 m/s versus 1.0 × 10−5 m/s, the value for the aquifer beneath the estuary). More importantly, the spatial permeability distribution effectively weights benthic fluxes toward greater values because sandier (more permeable) sediments are collocated with more energetic regions of the estuary that contribute most of the total benthic exchange. Siltier (less permeable) regions correspond with calm regions that contribute negligible benthic exchange regardless of permeability.

3.3 Year-Long Simulation

[30] Simulated benthic fluxes over a full year vary in response to wind and wave energy. Storms with strong winds significantly enhance wave pumping, as in early February 2010, when wind speeds in excess of 20 m/s accompanied a nor'easter storm (Figure 7). Simulated benthic fluxes associated with wave pumping increased from negligible rates on the calm day preceding the storm to over 12 m3/s during the storm's peak. Wind did not significantly impact simulated current-bedform or tidal pumping. We did not specify storm surge at the inlet boundary, which would temporarily increase simulated current and tidal pumping.

Figure 7.

(a) Measured wind speed, W, during a nor'easter storm (data from NOAA buoy LWSD1). (b) Simulated volumetric benthic flux, Q. Discharge from Indian River to the estuary (USGS gauging station 01484525) is shown for comparison.

[31] Over the year, the strongest winds were from the east, but moderate winds were also common from the northwest to southwest (Figure 8a). The top 10% of winds generated more than 36% of simulated wave-driven benthic fluxes. Wave pumping rates ranged from 0 to 12 m3/s (Figure 8b), while fluxes due to tidal pumping did not vary because simulated tides only included the M2 frequency component. True variations in tidal pumping over spring-neap cycles are likely small because tidal amplitude only varies approximately twofold. During about 30% of the simulated year, winds were calm, currents were slack, and tidal pumping was the primary mechanism driving exchange over the estuary. About 40% of the year, all three mechanisms were roughly in balance. Another 30% of the year, winds were gusty, and wave pumping was the dominant exchange mechanism (Figure 8b). Transitions between these regimes occurred over a range of timescales. Currents waxed and waned over tidal periods, whereas wind-driven wave pumping waxed and waned over timescales ranging from hours to days (Figure 7).

Figure 8.

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

4 Discussion

[32] In shallow, fetch-limited estuaries such as the Delaware Inland Bays, spatial and temporal gradients in currents, water depths, and wave energy promote patchy and dynamic benthic fluxes. Implications are twofold. First, local field measurements of benthic fluid or solute fluxes in estuaries are unlikely to represent conditions throughout the estuary and throughout time. Attempts to scale local measurements across an estuary may produce order-of-magnitude errors in benthic fluid or solute flux estimates, even in estuaries with relatively uniform water depths and tidal ranges. Second, spatial and temporal variations in benthic flux may promote “hot spots” or “hot moments” of enhanced biogeochemical cycling [McClain et al., 2003]. Maximum biogeochemical cycling occurs when the residence time of surface water in the benthic zone is long relative to the reaction timescale, and the supply of reactants across the sediment-water interface is rapid [e.g., Harvey and Fuller, 1998; Zarnetske et al., 2011; Gu et al., 2012]. In some cases, rates of benthic uptake or production also depend on the supply of reactants from sediments or upwelling fresh or saline groundwater with longer flow paths, but we focus here on supply from the surface water. During a storm, benthic exchange rates increase, but benthic residence times may decrease. Response in uptake or production depends on the initial condition. If pore water residence times are long relative to reaction rates but reactant supply is sluggish, an increase in benthic exchange rate will relieve the supply limitation and increase uptake or production. However, if reactant supply is initially ample but pore water residence times are short relative to the reaction timescale, the further reduction in pore water residence times will decrease uptake or production. In general, faster exchange rates may not directly correlate with greater uptake or production rates. Indeed, uptake or production rates may be greater in regions of slow exchange, as long as reactant concentrations in surface water are sufficient to maintain adequate chemical mass flux to the benthic zone.

[33] On a moderately windy day, simulated benthic fluxes due to currents, tides, and waves are each ~1–10 m3/s in our model estuary. These estimates depend not only on wind and tidal conditions but also on the distribution of sediment permeability, which can be difficult to constrain. Each of the three simulated benthic exchange mechanisms generates fluxes on the order of freshwater inputs to the Delaware Inland Bays from runoff and submarine groundwater discharge (~3.3 and 4.6 m3/s, respectively) [Russoniello, 2012]. Total saline benthic fluxes in the Delaware Inland Bays are likely much greater, due to contributions from additional mechanisms such as bioirrigation, density-driven convection, bedform migration, and sediment resuspension. For example, the upper 5 mm of estuary sediment contains 100,000 m3 of pore fluid, assuming 30% porosity. If a storm mobilized this sediment over a timescale of 1 h, exchange rates would be on the order of 30 m3/s. Our results therefore suggest that saline benthic exchange rates are similar to, if not much greater than, fresh submarine groundwater discharge to the Delaware Inland Bays, particularly during storms. These results agree broadly with numerous field and modeling studies that suggest saline benthic exchange rates are often several times greater than fresh submarine groundwater discharge [Li et al., 1999; Martin et al., 2007; Michael et al., 2005; Santos et al., 2009].

[34] Though saline benthic exchange may represent a large portion of total submarine groundwater discharge to the Delaware Inland Bays, ocean-estuary exchange through the inlet dominates the fluid budget. Average surface water exchange through the inlet over one tidal cycle is ~1000 m3/s. Fresh inputs from runoff and submarine groundwater discharge are comparatively small yet influence nutrient budgets because of their high nutrient concentrations [Andres, 1995; Ritter, 1986]. Saline benthic exchange may similarly influence nutrient and solute budgets if biogeochemical transformations along flow paths are rapid.

[35] We have employed a novel modeling approach that links hydrodynamic circulation in an estuary with analytical solutions for benthic exchange due to several mechanisms. A primary advantage of this approach is the ability to upscale benthic exchange processes with characteristic length scales of centimeters over an entire estuary at high computational efficiency. The modeling approach can also be applied to other estuarine systems. Additional benthic exchange mechanisms could be incorporated as appropriate, such as tidal 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 benthic exchange or surface water circulation. Bedform sizes and orientations vary over tidal and storm timescales. An ideal modeling scheme would use surface water hydrodynamics to predict bedform morphologies and update the coefficient of friction at the bed to reflect morphodynamics. Additionally, evolving bedform morphologies would influence computations of current pumping, wave pumping, and pore water “turnover” (alternating entrapment and release of pore water as bedforms migrate) [Elliott and Brooks, 1997]. These operational steps would require empirical relationships that relate hydrodynamics with morphodynamics and the use of numerical rather than analytical solutions for benthic exchange across a moving sediment-water interface. The latter modification would greatly reduce computational efficiency. Another limitation of our model is the assumption of uniform pore water salinity and density. We retain this assumption because we lack both distributed data on pore water salinity in the Delaware Inland Bays and analytical solutions for buoyancy-driven benthic exchange. Because most fresh groundwater discharges near shore, variable density effects on benthic exchange are likely negligible over much of the estuary.

[37] One of the greatest limitations is that our approach cannot address interactions between benthic exchange mechanisms. We intentionally did not sum rates of wave, current, and tidal pumping because these processes likely interact nonlinearly [King, 2012]. For instance, infiltration and exfiltration due to tidal pumping may periodically restrict shallow wave pumping. Similarly, net groundwater upwelling may limit shallow benthic exchange mechanisms [Cardenas and Wilson, 2006], but upwelling rates typically decay rapidly with distance from shore [Bokuniewicz, 1992]. In the absence of these interactions, exchange depths range from centimeters to meters for the three exchange mechanisms we considered. Exchange depths due to current pumping are on the order of one bedform wavelength [Cardenas and Wilson, 2007; Elliott and Brooks, 1997; Thibodeaux and Boyle, 1987]. Exchange depths due to tidal pumping are on the order of millimeters to centimeters, depending on hydraulic diffusivity and tidal period, which influence penetration of the tidal pressure wave, and permeability and tidal amplitude, which influence seepage rates. Exchange depths due to wave pumping are on the order of the surface water wavelength [King et al., 2009] (~1 m). An active area for future research is to evaluate constructive and destructive interactions between benthic flux mechanisms that operate over various spatial and temporal scales.

5 Conclusions

[38] Estuaries are unique environments where shallow bathymetry and complex coastal geography promote strong gradients in tidal and wave energy, which propagate across the sediment-water interface into the benthic layer. Estuaries may therefore exhibit more heterogeneity in benthic fluxes than open marine environments such as continental shelves. In simulations based on the Delaware Inland Bays, benthic fluxes are patchy and dynamic, varying over spatial scales of hundreds of meters and temporal scales of hours. Under moderate winds of 5 m/s, simulated pumping rates due to currents, tides, and waves are individually ~1–10 m3/s, on the order of fresh input rates from runoff and submarine groundwater discharge. Under strong winds of 10 m/s, saline benthic exchange rates can exceed all fresh water input rates many times over, particularly if sediment resuspension occurs. Heterogeneity in benthic fluxes within estuaries may control hot spots and hot moments in biogeochemical activity and contribute to habitat complexity in these highly productive and diverse ecosystems. A clear need exists for improved technology to measure spatially distributed, unsteady fluid and geochemical fluxes across sediment-water interfaces.

Acknowledgments

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

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