Modeling sediment-related enterococci loading, transport, and inactivation at an embayed nonpoint source beach

Authors

  • Zhixuan Feng,

    Corresponding author
    1. NSF NIEHS Oceans and Human Health Center, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, USA
    • Division of Applied Marine Physics, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, USA
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  • Ad Reniers,

    1. Division of Applied Marine Physics, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, USA
    2. NSF NIEHS Oceans and Human Health Center, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, USA
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  • Brian K. Haus,

    1. Division of Applied Marine Physics, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, USA
    2. NSF NIEHS Oceans and Human Health Center, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, USA
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  • Helena M. Solo-Gabriele

    1. NSF NIEHS Oceans and Human Health Center, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, USA
    2. Department of Civil, Architectural, and Environmental Engineering, College of Engineering, University of Miami, Coral Gables, Florida, USA
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Corresponding author: Z. Feng, Division of Applied Marine Physics, Rosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149, USA. (zfeng@rsmas.miami.edu)

Abstract

[1] Enterococci are the U.S. Environmental Protection Agency recommended fecal indicator bacteria for assessing recreational marine water quality. Traditional methods of enterococci analyses are time consuming, resulting in delays in issuing beach closures. Models can potentially circumvent these delays by forecasting times when beaches should be closed. The objective of this study is to develop an innovative coupled microbe-hydrodynamic-morphological model. The unique feature of this model is its capability of simulating the release of microbes attached to coastal beach sands as a result of combined wave and tidal forcing. A nearshore process model (XBeach) was coupled with a microbe transport-decay equation. This equation included source functions that accounted for microbial release from mobilized sand, groundwater flow, entrainment through pore water diffusion, rainfall-runoff loading, and a fate function that accounted for solar inactivation effects. The model successfully simulated observed spatial and temporal patterns of enterococci in the beach water, including the reproduction of diel and tidal fluctuations and the rapid decrease of enterococci levels from the waterline to offshore. Primary processes for enterococci loading to the water column included wave-induced sediment resuspension and tidal washing for the entrainment of enterococci from the pore water in the intertidal zone. Diffusion was the major mechanism to transport enterococci from the intertidal zone to offshore. Sunlight inactivation was a key process to reduce enterococci levels during the day and to produce the diurnal cycles. Rainfall runoff was found to be an intermittent source of enterococci to beach water, whereas groundwater exchange was of secondary importance. Sensitivity analyses suggested that the processes and coefficients related to enterococci loading have quasi-linear characteristics, whereas model results of enterococci levels were sensitive to both diffusion and sunlight inactivation coefficients, showing high nonlinearity and spatial and temporal dependence.

1. Introduction

[2] The utilization of coastal waters and shorelines at beach sites as recreation and tourism resources requires regular monitoring of water quality to protect human health. When levels of fecal indicator bacteria (FIB) exceed regulatory thresholds, set at 104 colony-forming units (CFU) per 100 mL for enterococci in a single water sample, beach advisories or even closures may be issued by local beach managers [U.S. Environmental Protection Agency, 1986]. Traditional culture-based methods need at least 18–24 h for laboratory analysis, so that exceedance of FIB cannot be identified until the second day, resulting in delays in issuing beach advisories. Model approaches, on the other hand, can be timely, effective, and powerful tools in beach management to supplement existing beach monitoring programs.

[3] Traditionally, regression models have been used to predict FIB levels based on the local hydrodynamic and hydrometeorological conditions [e.g., Olyphant, 2005; Nevers and Whitman, 2005; Frick et al., 2008]. Another type of model is the conceptual/analytical model, which largely simplifies physical and biological processes to achieve analytical solutions for particular beach systems. Two good examples are the conceptual surf zone model [Boehm et al., 2005; Grant et al., 2005] and the enclosed beach boundary layer model [Grant and Sanders, 2010]. More recently, process-based models have been applied to hindcast microbial concentrations in aquatic environments, to evaluate influences of various pollutant sources and environmental conditions on beach water quality, and to determine the subsequent transport and fate of bacteria of interest [e.g., Sanders et al., 2005; Hipsey et al., 2008; Zhu et al., 2011; Ge et al., 2012]. Those models resolve detailed hydrodynamics, coupled with a microbial balance and appropriate biotic and nonbiotic processes representing source loading, transport, and fate, and can include sediment resuspension effects [Sanders et al., 2005; Hipsey et al., 2008; Ge et al., 2012].

[4] Beach sediment has been recognized as an important nonpoint microbial source [e.g., Whitman and Nevers, 2003; Shibata et al., 2004; Yamahara et al., 2007; Halliday and Gast, 2011; Shah et al., 2011]. Bacteria can live and persist within the sand and even replicate under favorable conditions [Yamahara et al., 2009]. Previous environmental studies suggested that tidal washing of intertidal sand may be responsible for the observed high microbial levels after high tide [Shibata et al., 2004; Wright et al., 2011; Abdelzaher et al., 2011]. However, the mechanisms responsible for the bacterial release from bed sediment to the water column are unclear, impeding quantification of the bacterial fluxes across the sediment-water interface.

[5] Past process-model studies accounted heuristically for the release of microorganisms during sediment resuspension through a critical bed shear stress [Sanders et al., 2005; Ge et al., 2012] or an organism concentration balance in the sediment [Hipsey et al., 2008], but all ignored the sediment transport processes. At beach sites, ignoring wave-related bacterial source contributions from the mobilized sediment may lead to model underestimation of microbial levels. This study aims to develop a uniquely coupled microbe-hydrodynamic-morphological model with source and fate functions capable of simulating the transport of microbes from coastal beach sands. The source functions include the transfer of microbes: attached to mobilized sand grains, between the water column and sand pore water (i.e., entrainment), from groundwater exchange, and from rainfall-runoff overland flow. The fate term accounted for the die-off of microbes due to solar radiation. Model performance was evaluated using temporally intense measurements of enterococci levels at a recreational beach. The significance of various transport, forcing, and source/fate functions was evaluated through scenarios that individually removed processes from the model. Model outputs were further examined through local sensitivity analysis by individually varying key parameters by ±50% of optimized or literature values.

2. Materials and Methods

2.1. Site Description

[6] The study site, Hobie Beach, is a subtropical marine beach on Virginia Key to the southeast of the city of Miami, Fl. (Figure 1). The beach is about 1600 m long, straight, and oriented in a northwest–southeast direction. It is located within a coastal embayment, Biscayne Bay, and sheltered from waves from the Atlantic Ocean due to the layout of two barrier islands, Virginia Key and Key Biscayne. Locally generated wind waves within the bay may have impacts on the beach but are moderate to small because of the limited fetch and shallow water depth (most areas are less than 4.0 m). In addition, nearby waters are heavily used for recreational boating, especially during weekends and holidays, and, thus, the beach may also be influenced by boat-generated waves. The tide is dominated by the principal lunar semidiurnal (M2) constituent with an approximate tidal range of 0.6 m. Although tidal currents in the adjacent Bear Cut inlet channel are fairly strong (up to 1.0 m s−1) [Fiechter et al., 2006], their magnitudes decrease significantly near the beach [Zhu et al., 2011]. No known point source is found to have a direct impact on the beach [Shibata et al., 2004]. Local water circulation, demonstrated by Lagrangian coherent structures, may favor the retention of pollutants originating from the shoreline [Fiorentino et al., 2012]. The beach sediments are mainly composed of medium sand with an average medium grain diameter of 0.39 ± 0.05 mm [Phillips et al., 2011a].

Figure 1.

Geographical location and aerial photo of Hobie Beach (Google Earth). Surveyed topography is illustrated by a color contour, and color bar shows depth from −1.0 to 1.0 m with respect to MSL. The position of tide and wave recorder (TWR) is indicated by the white triangle. Water and sand were sampled along a transect oriented normally to the beach offshore of the pole location (red dot). The hydrometeorological measurements are obtained from the Weatherpak station (green square).

2.2. Field Measurements

2.2.1. Topographic Survey

[7] The beach topography (Figure 1) was obtained from a walking survey in June 2010, using a Global Positioning System (GPS) backpack unit (Trimble TSC1, Sunnyvale, Calif.).

2.2.2. Water and Sediment Sampling and Analysis

[8] From 1 to 11 June 2010, water and sediment samples were collected hourly at knee-depth (approximately 0.3 m deep) locations. Every 6 h, the seawater was also sampled at waist-depth (approximately 1.0 m deep) locations, and subtidal, intertidal, and supratidal sand samples were also collected at that time. Concentrations of culturable enterococci in the water and sediment were measured by a membrane filtration method, expressed for water as CFU 100 mL−1 and for sand as CFU g−1 of the dry sand. Turbidity of water samples was also measured in the laboratory using a nephelometer (TD-40, Turner Designs, Sunnyvale, Calif.) with units expressed as nephelometric turbidity units (NTU). For details of field sampling and laboratory analysis, refer to Enns et al. [2012].

2.2.3. Environmental Conditions

[9] A tide and wave recorder (RBR TWR-2050, Ottawa, ON, Canada) was bottom-mounted to measure waves and tides at a mean depth of 2.35 m, approximately 190 m offshore of the sampling site (Figure 1). Water elevations were sampled every 32 s to obtain the tidal conditions. Wave conditions were also measured every 20 min with a burst mode that recorded 4 Hz surface elevations for a total of 512 samples. The elevations were processed with the Wave Analysis for Fatigue and Oceanography Matlab toolbox [Brodtkorb et al., 2000] to obtain significant wave heights and peak wave periods from the variance density spectra. Hydrometeorological parameters, such as wind speed and direction, solar insolation and rainfall rate, were measured every 2 min at a research weather station (Weatherpak, Seattle, Wash.) on the roof of a building at the University of Miami Rosenstiel School campus (Figure 1), which is about 1 km southeast of the beach site (http://yyy.rsmas.miami.edu/etc/download-weatherpak.cgi). Note that solar insolation was measured using an Eppley Precision Spectral Pyranometer that directly senses whole sunlight spectrum.

2.3. Coupled Microbe-Hydrodynamic-Morphological Model

2.3.1. Model Concept

[10] In simulating nearshore beach water quality, the variations of microbial levels are controlled by the processes that relate to loading, transport, and fate of microbes (Figure 2). Note that, in terms of a certain beach, not all loads and processes are important; in other words, controlling mechanisms are site specific. As for Hobie Beach, beach sand in the intertidal zone is known to be a major reservoir of bacteria [Wright et al., 2011; Shah et al., 2011]; thus, the priority of the model is to include bacterial loading from the sand, which further requires resolving current and wave dynamics and related sediment transport. Additional processes considered include groundwater flow since a portion of microbes is found to reside in the pore water [Phillips et al., 2011a], rainfall runoff since very high levels of microbes have been observed in the runoff [Wright et al., 2011], and solar radiation as local observations have shown a strong influence on FIB levels [Abdelzaher et al., 2010; Enns et al., 2012].

Figure 2.

Cross-shore section of a beach and a control volume corresponding to one model cell (box of dark dashed line), which is exaggerated to illustrate detailed model components. Within the box, surface water column is shown with light blue, affected by both waves and tides. Contaminated and clean sands are shown with red and yellow colors, the fractions (p1 and p2) of which can vary with depth. Yellow arrows indicate processes related to the sediment transport, whereas red arrows indicate processes related to the microbe transport. The microbial processes and loads not taken into account in the model are crossed out.

[11] Processes and sources not considered include (1) exchange of microbes across the air-sea interface, although airborne transport may be occasionally influential (e.g., in the case of airborne transport of harmful algal toxins [Pierce et al., 2003]); (2) animal fecal events, although studies have shown that dog fecal events may intermittently affect water quality [Wright et al., 2009; Zhu et al., 2011]; and (3) human shedding [Elmir et al., 2007; Enns et al., 2012], which has been demonstrated to impact the bacterial quality of water especially for bacteria of skin origin [Plano et al., 2011].

2.3.2. Coupling Microbe Module Into XBeach

[12] XBeach is an open source modeling tool in the nearshore community, which has been widely used to simulate a variety of small-scale hydrodynamic and morphological phenomenon, such as barrier island and dune erosion due to tropical storms [Roelvink et al., 2009; McCall et al., 2010], megacusp formation in a rip-channeled beach [Orzech et al., 2011], wave-driven circulations on coral reefs [Symonds et al., 2011], evolution of a gravel beach profile [Williams et al., 2012], and sediment transport in the swash zone [van Rooijen, 2011; Reniers et al., 2013]. XBeach solves coupled two-dimensional (2-D) depth-averaged equations for wave propagation (i.e., wave action balance equation for evolution and roller energy balance equation for breaking), water circulation (i.e., shallow water equations), groundwater, sediment transport, and bottom changes on the time scale of wave groups [Roelvink et al., 2009].

[13] In this study, we coupled a microbe transport-decay equation with XBeach to link microbial water quality with hydrodynamic and sediment transport processes. The interrelationships between primary model components are shown in Figure 3. The microbe module solves the depth-averaged microbial balance within the water column, which accounts for nonpoint source loads, i.e., sediment attached, pore water trapped, and rainwater-runoff microbe loading. The pore water component includes inputs through groundwater advection and diffusion-like entrainment. Solar inactivation was the only fate term incorporated into the model.

Figure 3.

Flow diagram for wave, flow, sediment, groundwater, and microbe computations and linkages between primary model components.

2.3.3. Microbe Transport-Decay Equation

[14] The transport, source loading, and die-off of microbes (i.e., enterococci in this paper) in Figures 2 and 3 can be expressed by a depth-averaged microbe transport-decay equation:

display math(1)

where h is the water depth (m), ENT is a depth-averaged concentration of culturable enterococci (CFU m−3), uL and vL are the Lagrangian velocities (m s−1; see Roelvink et al. [2009] for details), and Dm is the microbe diffusion coefficient (m2 s−1). In XBeach, the low-frequency and mean flows (i.e., uL and vL) are directly solved from shallow water equation using a depth-averaged generalized Lagrangian mean formulation [Roelvink et al., 2009]. Assuming isotropic and homogeneous diffusion, the diffusion coefficient is set a constant 0.03 m2 s−1. The waist-depth samples are used to find the physically appropriate value of Dm showing that, by including diffusive transport, the predictions are of the same order as the observations. The lumped coefficient Dm represents the combined effects of turbulent diffusion and tidal dispersion. The terms on the right-hand side (RHS) of equation (1) represent source loading or die-off rates, which are explained one by one in the following subsections. Note that all β coefficients are fixed and are, therefore, independent of space and time.

2.3.3.1. Model Treatment of Sand Contaminated With Microbes

[15] We utilize the multiple sediment class formulation in XBeach to assign contamination and distribution of microbes in the sand by artificially dividing sediment into two classes, which allows for the tracking of each sediment class during computations. Two distinct classes are assigned, contaminated sand (class 1) and clean sand (class 2), and their corresponding fractions were denoted by p1 and p2 (= 1 − p1; Figure 2). Two classes are then calculated separately with sediment transport formulations (see Appendix A for details). If there is no contaminated sand, p1 equals zero and, consequently, there are no microbes within the sand. In effect, the distribution of p1 describes the availability of microbes in the sand ready for mobilization by the bed shear stress, groundwater flow, and entrainment. The model input values of p1 are fitted to field data, which are described in section 2.3.4.1.

2.3.3.2. Enterococci Released From Mobilized Sand

[16] The model assumes that once the sand is mobilized, a portion of enterococci attached to the grains is directly desorbed and enters the water column. The mobilized suspended and bed-load sediment are in a dynamic equilibrium, i.e., there is continuous exchange of sediment between the bed and the fluid layer while maintaining the sediment concentration, bringing up new sediment with enterococci from the bed reservoir, and thus acting as a conveyer belt for the enterococci uptake. Through a dimensional calibration factor β1 (CFU m−3 s−1), the release flux of enterococci from sand is linked to the total instantaneous concentration of mobilized contaminated sand, a combination of suspended load (Cs,1 is volumetric concentration of contaminated suspended sediment in L L−1) and bed load (Cb,1 is volumetric concentration of contaminated bed-load sediment). However, there is no existing research/literature that provides guidance in choosing the value of β1 to date. Thus, the model calculations used a calibrated β1 value of 8.0 × 107 CFU m−3 s−1, obtained by fitting and optimizing simulated and observed enterococci levels. Developing robust β1 values in the laboratory based on controlled wave conditions and microbial sources in the sand is a subject of future research.

2.3.3.3. Groundwater Transport

[17] Groundwater exfiltration (from the ground into the open water column) or infiltration (from the open water column into the ground) is the bidirectional advective exchange of materials across sediment-water interface, similar to the hyporheic exchange between stream and streambed [Grant et al., 2011]. β2 is a dimensional calibration coefficient (CFU m−3) representing a maximum enterococci concentration of bed pore water for the transport across the bottom boundary. The vertical groundwater flow rate, wbed, is defined positive downward and negative upward (see Appendix B). The Kronecker delta function is used to determine the direction of wbed. If wbed < 0 (i.e., exfiltration), an enterococci flux associated with pore water joins surface water; otherwise, if wbed > 0 (i.e., infiltration), an enterococci flux of surface water goes into the bed.

[18] To relate the standard unit, CFU g−1 of the dry sand, to CFU m−3 of the bulk sediment volume (including sand grains and pore spaces), we used the following relation [Grant et al., 2011]:

display math(2)

where the sand grain density ρs is set to a standard value of 2.65 × 103 kg m−3 [Soulsby, 1997], and porosity np (= 0.4) is locally measured [Phillips et al., 2011a]. This yields a level of ENTmax = 1.6 × 108 CFU m−3 at the shoreline. Previous sand core experiments using local sand determined an average of 10% of total enterococci residing in the pore water, from which we may estimate β2 of 1.6 × 107 CFU m−3 ( math formula) [Phillips et al., 2011a]. Notice that β2p1 represents spatial dependent enterococci concentration in the pore water. If p1 equals 1, then the water that flushes from the bed into the surface water has a maximum concentration of β2. This also implies that the release rate of enterococci does not increase with increasing groundwater flow velocity, consistent with the microbe release from the laboratory experiments [Phillips et al., 2011a].

[19] The groundwater flow velocity is calculated according to Darcy's law (see Appendix B), and this module has been tested by another study [Williams et al., 2012]. Measured hydraulic conductivity may vary by 2 orders of magnitude, from 4.0 × 10−5 to 4.0 × 10−3 m s−1 [Phillips et al., 2011a]. For model calculations, we applied a value of 2.9 × 10−4 m s−1, least squares fitted from 16 sets of measured head difference and volumetric rate relationships in Phillips et al. [2011a].

2.3.3.4. Entrainment Exchange Across Sediment-Water Interface

[20] The entrainment exchange is diffusional transfer between water column and underlying pore water across the bottom boundary layer, most likely due to coherent turbulence in this case [Grant and Marusic, 2011]. Molecular microbial diffusion is unimportant based on the small diffusion coefficient for fecal bacteria, in the order of 10−13 m2 s−1 [van de Mei et al., 1994]. The flux of entrainment exchange is assumed proportional to the difference in concentrations across the interface according to Grant and Marusic [2011]. The entrainment coefficient ( math formula) was given according to the mass transfer coefficient for the sand bed from experiments and also derived from a diffusive sublayer model [Reidenbach et al., 2010].

2.3.3.5. Rainfall-Runoff Loading

[21] To quantify the rainfall-runoff loading rate, the measured rainfall intensity Ir (m s−1) was utilized and filtered with an hourly moving average window. β4 is a lumped coefficient (CFU m−3) for the enterococci flux associated with rainfall runoff and determined from the rational formula, which relates the runoff flux to rainfall rate and land usage, population density, and degree of imperviousness [Lindeburg, 1986]. Therefore, total enterococci flux (Qr) flushed into the beach water via overland flow is as follows:

display math(3)

where Di, Ad,i, Wd,i, and Ld,i are the drainage coefficients, areas, widths, and lengths of various ground types i = 1, 2,…, respectively. At Hobie Beach, there are two distinct drainage types: paved asphalt road and sandy beach (see Figure 1), the drainage coefficients of which are 0.9 and 0.6, respectively [Elmir, 2006]. The width of paved road is 6 m, whereas beach width depends on tidal elevations with an average of 20 m. ENTr is the enterococci concentration in the runoff that varies by 2 to 3 orders of magnitude based on the prior field experiments, and we gave an average of 1.5 × 108 CFU m−3 in this study [Wright et al., 2011].

[22] In reality, runoff drains through spaced runnels on the beach, which eventually results in nonuniform runoff influx alongshore the beach. Therefore, instead of assigning an unrealistic point source to the one-dimensional (1-D) model, we created a line source for runoff loading by assuming that when runoff water joins beach water, associated microbes immediately distribute along an Xr (= 10 m, width of intertidal zone) wide wedge of water extended from shoreline. Hence,

display math(4)

where Ar, Xr, and Lr are the surface area, cross-shore, and alongshore lengths of the receiving water body (Ar = Xr × Lr), assuming two land types have the same alongshore length as receiving water body. Finally, the lumped coefficient is as follows:

display math(5)
2.3.3.6. Solar Inactivation

[23] The solar inactivation follows the widely used first-order exponential decay [e.g., Sinton et al., 2002; Sanders et al., 2005; Zhu et al., 2011]. The sunlight inactivation coefficient (β5 = 3.68 × 10−7 m2 J−1) was determined from an in situ experiment at this beach and was used in a previous study [Zhu et al., 2011]. Recorded solar radiation intensity Is (W m−2) was filtered with a 1 h moving average window before input to the model.

2.3.4. Model Implementation

[24] In this study, calculations were performed in a mode that neglected bathymetric evolution based on the fact that profile change is very little for this low-energy beach in a relatively short 10 day period. We also assumed steady-state concentrations of microbes within the bed. This implies that any microbe lost from the sand and interstitial water is (continuously) compensated by concomitant regrowth in the bed. It is a reasonable approximation if the released amount of microbes is relatively small, with respect to the whole bed reservoir. The other reason for this assumption is that regrowth, competition, and predation of microbes in the sand are very complex microbiological processes, dependent on a number of environmental conditions (e.g., moisture content, salinity, temperature, and nutrients) and sand characteristics (e.g., minerals, grain size, and biofilms) as well as microbial communities [Yamahara et al., 2007, 2009; Piggot et al., 2012]. Therefore, the formulations of those processes need further study and are not investigated in this paper. We will only briefly discuss the steady-state bed reservoir assumption in section 4.2.

2.3.4.1. Cross-Shore Distribution of Sand Enterococci Source

[25] The enterococci levels within the sand during the experiment exhibited significant spatial and temporal variability. At the upper beach face (permanently dry), the observed levels of enterococci in the sand vary between 0.4 and 718 CFU g−1 with an observed mean of approximately 100 CFU g−1. This also holds for the sand sampled at knee-depth locations, varying by 3 orders of magnitude, (Figure 4a). This variation can arise from the fact that the microbes attached to the sand are patchy and spatially and temporally inhomogeneous. As a consequence, the (initial) fractional distribution of contaminated sand that corresponds to enterococci levels within the sand, a prerequisite for model initialization, was unknown. Using the arithmetic mean enterococci concentrations (i.e., averaged over time and space), a simple exponential fit was used to describe the initial cross-shore distribution, referred to as an exponential distribution (Figure 4a):

display math(6)

Also, corresponding distribution of fraction of contaminated sand is (Figure 4b) as follows:

display math(7)

where x = 195 m corresponds to the higher high tide line where dry beach sand was sampled and CFUmax = 100 CFU g−1 is the maximum enterococci level of the sand prescribed in the model. The resultant fraction of contaminated sand decreases rapidly offshore (Figure 4b), which also agrees with a prior field experiment [Wright et al., 2011]. It reduces to below 15% beyond the low tide line and becomes almost negligible in the areas between 0 and 140 m. This also implies there are no distant sand enterococci sources for the purposes of this model.

Figure 4.

Model setup. (a) Observed cross-shore distributions of enterococci concentrations within the sand (dots), spatially averaged (at 5 m intervals) arithmetic mean values (squares) and corresponding standard deviations (dashed vertical lines). Observed dry beach samples are marked by crosses. Exponential fit curve as initial cross-shore distribution of enterococci is shown by the solid line. (b) Fractional distribution of sand contaminated with enterococci for three cases: exponential (corresponding to above exponential fit), uniform, and linear (used later in the scenario tests of section 3.3.7). The shadows indicate intertidal zone in the model domain between 185 and 195 m. (c) Bottom profile (solid line) and a tidal elevation envelope of ±0.3 m (light dotted lines) around MSL (cross markers shown at grid points).

2.3.4.2. Model Setup

[26] Model simulations were performed for a single cross-shore transect (i.e., 1-D computations); in other words, we neglected all alongshore variations in the y direction. The bottom profile was alongshore averaged using the surveyed bathymetric data at the microbe sampling site (Figure 1). This shows the presence of a small sand bar, around x = 145 m (Figure 4c). Offshore of the sand bar, the subtidal terrace illustrates a mild slope of 1:120, whereas a flat terrace of about 40 m width is located onshore of the bar. The upper beach face is much steeper (a slope of 1:20), leading up to a dry berm of approximately 0.8 m above mean sea level (MSL). The model grid spacing is variable with a 2 m coarser resolution offshore (x < 90 m), gradually decreasing to 0.25 m near the low tide line and a 0.25 m resolution in the intertidal and supratidal areas (x>175 m; Figure 4c). The time step for the model calculation is determined by the Courant stability criterion and is calculated automatically based on a Courant number of 0.9. In this study, the model applies the same time step for all modules that involve updating in time. The model uses a cold start as initial conditions of water depth, current velocity, and enterococci level of the water. Given the fact that the model domain is small (i.e., 200 m) and response time scales are short, the spin-up time is only minutes for hydrodynamics and in the order of 1 h for enterococci levels.

[27] The offshore boundary was located along a shore-parallel line at a distance where the tide and wave recorder was deployed. At this boundary, an absorbing-generating or weakly reflective boundary condition was used to prevent re-reflection of long waves generated in the surf and swash zones, in combination with prescribed tidal elevations recorded by the sensor (Figure 5a). Normally incident waves were specified with a parametric JONSWAP (Joint North Sea Wave Project) spectrum entering into the computational domain, defined by the measured significant wave heights (Hm0) and peak frequencies (Tp; Figures 5b and 5c). The wave propagation and breaking were then calculated based on wave and roller energy balance equations (see Roelvink et al. [2009] for details on the model description).

Figure 5.

Time-series measurements of environmental conditions during the 10 day intensive study at Hobie Beach: (a) surface elevations measured by the tide and wave recorder (see Figure 1 for equipment location), (b) corresponding significant wave heights measured by the recorder, (c) peak wave periods, (d) hourly moving-averaged cross-shore (dark line) and alongshore (light-colored line) wind speeds, (e) hourly moving-averaged solar insolation, and (f) hourly moving-averaged rainfall intensities.

[28] For the groundwater calculation, since a barrier island beach with tidal influence tends to have an elevated water table above MSL, the initial groundwater head 0.1 m was given according to the water table overheight approximation deduced from the Boussinesq equation [Nielsen, 1990, 1999]. All relevant model parameters and corresponding values are summarized in Table 1.

Table 1. List of Model Parameter Settings
ModuleParameterDescriptionValue
FlownuhBackground horizontal eddy viscosity0.03 m2 s−1
CChezy bottom roughness coefficient65.0 m1/2 s−1
CFLCourant number0.9
WavegammaBreaker parameter in dissipation model0.45
alphaDissipation parameter1.0
betaSlope of breaking wave front in roller model0.1
nPower in breaking probability function10
gammajspPeak enhancement factor in JONSWAP spectrum3.3
sDirectional spreading coefficient in JONSWAP spectrum1000
fnyqHighest frequency to create JONSWAP spectrum1.0 Hz
dfjStep size frequency to create JONSWAP spectrum0.01 Hz
SedimentDhSediment diffusion coefficient0.03 m2 s−1
fmorMorphological speed-up factor0
αbBed-slope factor0
ngdNumber of sediment classes2
ndNumber of sediment layers2
dzgThickness of sediment layers0.25 m
d50Uniform D50 sediment diameter0.0004 m
d90Uniform D90 sediment diameter0.0005 m
Groundwaterkx,kyHorizontal hydraulic conductivity2.9 × 10−4 m·s−1
kzVertical hydraulic conductivity2.9 × 10−4 m·s−1
npPorosity0.4
dwetlayerThickness of wet layer0.1 m
zb,aquiferBed level of the aquifer−5.0 m
Microbeβ1Sediment-related enterococci release coefficient8.0 × 107 CFU·m−3 s−1
β2Pore water enterococci concentration coefficient1.6 × 107 CFU·m−3
β3Entrainment mass transfer coefficient1.0 × 10−5 m·s−1
β4Rainfall-runoff loading coefficient2.6 × 108 CFU·m−3
β5Sunlight inactivation coefficient3.68 × 10−7 m2 J−1
DmMicrobe diffusion coefficient0.03 m2 s−1
CFUmaxMaximum reference enterococci concentration in the sand100 CFU·g−1
2.3.4.3. Model Skill

[29] The skill of the model was evaluated by comparing log10-transformed model results with observations at both the knee-depth and waist-depth sampling locations in terms of the correlation coefficient and refined Willmott index of agreement.

[30] Correlation coefficient:

display math(8)

[31] Refined Willmott index of agreement [Willmott et al., 2011]:

display math(9)

where COV and σ refer to covariance and standard deviation, respectively. P and O represent model-predicted and field-observed log10-transformed enterococci levels, respectively. Willmott index provides dimensionless measure of model-observation agreement, which is bounded between −1.0 (i.e., poor agreement) and 1.0 (i.e., perfect agreement).

3. Results

3.1. Environmental Observations

[32] Tidal elevations were predominantly semidiurnal with a range of about 0.6 m (Figure 5a). Significant wave heights were less than 0.3 m with a dominant peak period of around 2.5 s (Figures 5b and 5c). The onshore direction roughly aligned with the longest wind wave fetch, and wave heights correlated well with onshore wind speeds (R = 0.71; Figure 5d) This indicates that waves affecting Hobie Beach are locally wind-generated inside Biscayne Bay, but wave height is limited by relatively short fetch and shallow depth of the bay environment [Young, 1997]. Solar radiation intensity illustrated predominant diel cycles but could be occasionally suppressed in the daytime when the weather was overcast or rainy (Figure 5e). During the 10 day period, rainfall events were short-lived and episodic, most of which were local convective thunderstorms (Figure 5f).

3.2. Model Simulations

3.2.1. Hydrodynamic and Morphological Simulations

[33] We modeled a period of 10 days, starting from 12:30 pm, 1 June 2010, when the first wave measurement was recorded. The hydrodynamic model was driven by observed tides and waves at the offshore boundary. The root-mean-square (RMS) wave orbital velocities at knee depth were quasi-linear to wave heights, with magnitudes ranging from 0 to 0.25 m s−1 (Figure 6a). Meanwhile, both the Lagrangian and Eulerian (cross-shore) velocities were 1 order of magnitude lower than wave orbital velocities, less than 0.05 m s−1. The presence of waves increased Eulerian velocities, showing small peaks of return (offshore) flows. Such results agreed with other studies at this beach, suggesting that cross-shore velocities in the nearshore shallow region were minimal [Zhu et al., 2011; Fiorentino et al., 2012]. One important feature of the velocities was that the wave orbital velocity dominated the Eulerian velocity in terms of initiating incipient bed sediment motion and, therefore, sediment-bounded microbe release. This notion was also supported by modeled suspended sediment concentrations at knee depth, which correlated well with RMS orbital velocities (R = 0.87). Bed-load sediment concentrations followed the same trend as suspended load, but their magnitudes were always lower (Figure 6b). Suspended and bed-load sediment concentrations at waist depth also corresponded to incoming waves but were at least 1 order of magnitude lower than those of the knee depth location (Figure 6d). This indicated that the majority of sediment resuspension occurred in the nearshore shallow region. Correlations were found between simulated suspended sediment concentrations of both knee-depth (R = 0.30) and waist-depth (R = 0.35) water with respect to corresponding turbidity measurements (Figures 6b–6e). Although turbidity, an indication of occurrence of sediment resuspension, corresponded to incident waves, we did not observe perfect correlations to suspended sediment concentrations, mainly because the turbidity measurement is more sensitive to smaller particles [Hannouche et al., 2011]. Suspended solids at the site were a combination of fine silt and medium sand, which confounded the correlation between turbidity and modeled sand sediment concentrations. Overall, the model was satisfactory in hindcasting hydrodynamics and sediment transport.

Figure 6.

Model results of current and sediment concentrations and turbidity measurements: (a) modeled Lagrangian, Eulerian, and RMS wave orbital velocities (m s−1) at knee depth, (b) hourly moving-averaged suspended and bed-load sediment concentrations (mg L−1) at knee depth, (c) measured turbidity (NTU) of hourly knee-depth water samples, (d) hourly moving-averaged suspended and bed-load sediment concentrations at waist depth (only shown in the time spots corresponding to six hourly sampled waist-depth water), and (e) measured turbidity of six-hourly waist-depth water samples.

3.2.2. Microbial Simulations

[34] The model reproduced the spatial and temporal trends and patterns of enterococci variation in beach water for the 10 day period (Figure 7a). Spatially, enterococci levels were always highest next to the waterline and then decreased rapidly in the offshore direction, by 1 to 2 orders of magnitude in a 100 m distance away from the shore. This pattern was coincident with two earlier field studies [Shibata et al., 2004; Wright et al., 2011]. This could be explained by the facts that (1) the most important microbe reservoir, beach sand, has a maximum microbial concentration above the shoreline in the dry sand, followed by gradually decreasing concentrations from the high to low tide line within the intertidal sand, whereas, in the subtidal region, their concentrations become even lower to minimal; (2) two loading mechanisms, wave-induced resuspension and bottom boundary layer entrainment, occur predominantly in the narrow water wedge just below the high tide line, explained in more detail in section 3.3; (3) during rainfall events, runoff that contains large amounts of microbes washed off from the upper beach face initially flows into the nearshore water through local ditches and afterward dilutes further offshore; and (4) the cross-shore beach profile is gently sloping so that microbes are concentrated in the shallow shoreline region since the model is in 2-D depth-averaged mode.

Figure 7.

Model results of enterococci levels during the 10 day study. (a) Contour of log10-transformed enterococci levels (CFU 100 mL−1), showing the cross-shore transect from beach shoreline to offshore boundary. Solid white line indicates corresponding knee-depth sampling locations in the model domain. Dashed white line indicates the 1 m isobath, approximating to waist depth, and white circles indicate exact waist-depth sampling locations in the model domain. (b) Comparisons of simulated and measured enterococci levels at knee-depth locations. The red triangles and black crosses illustrate time periods of rainfall events (rainfall rates larger than 1.0 mm h−1) and wave events (offshore significant wave heights larger than 0.1 m), respectively. (c) Comparisons of simulated and measured enterococci levels at waist-depth locations. Note that magenta squares illustrate simulated enterococci levels at corresponding waist-depth water sampling times.

[35] Temporally, log10-transformed enterococci levels demonstrated strong diel and tidal cycle signals (Figure 7a). High levels predominantly occurred and persisted longer in the nighttime when solar radiation became minimal, allowing bacteria to remain viable and culturable. During the daytime, on the contrary, sunlight can effectively inactivate released enterococci. For the constant deactivation coefficient (β5) given in Table 1, the time duration for a certain percent die-off is inversely proportional to the solar radiation intensity. It takes 2.2 h to deactivate 90% of the total enterococci at noon time with a near maximum solar insolation of 800 W m−2. Within one tidal cycle, the highest predicted enterococci concentration was typically found tens of minutes to several hours after high tide, which was consistent with the analysis using hourly measurements of enterococci levels at knee-depth locations [Enns et al., 2012]. The highly elevated enterococci levels that occurred for five consecutive nights from 3 to 7 June also coincided with high tides, locally medium to high waves (Hm0 > 0.1 m), and occasionally rainfall events (Ir > 1 mm h−1). Those patterns apparently indicate that the concurrence of high tides particularly on the ebb phase, local wind waves, and/or rains at night can greatly elevate microbial levels, which may result in exceedances of indicator bacteria levels for several hours or even throughout the night.

[36] Simulated enterococci levels were compared with the field measurements at both knee-depth and waist-depth locations (Figures 7b and 7c). The arithmetic mean (and standard deviation) of log10-transformed hourly measurements at knee depth, log10(ENT_knee) = 1.87 (±0.74), compared well with that of the model, 1.96 (±0.41). The standard deviation calculated from the model results was lower than that from the measurements. As a result, model predictions were smoother and unable to capture most transient spikes or extremely high levels (those of enterococci levels around or above 1000 CFU 100 mL−1). To reduce the bias of those extreme values on statistical scores, we used the 3 h moving averaged time series to calculate statistics for this case and later test cases (Table 2). The correlation (R = 0.612) and index of agreement (dr = 0.595) at the knee depth were fairly good, considering the fact that observations were so highly variable. The model also yielded the correct pattern that enterococci concentrations of the waist-depth samples were significantly lower than those of the knee-depth samples, since waist depths are farther away from the enterococci sources. At the waist depth, however, both correlation (R = 0.267) and index of agreement (dr = 0.467) were not as good as those at the knee depth, and no significant correlation was found (pN=37 = 0.111).

Table 2. Summary of Error Statistics for Each Scenario Test
ScenarioRdr
KneeWaistKneeWaist
Baseline0.6120.2670.5950.467
No diffusion0.5840.2880.4720.432
No waves0.5240.2970.4450.485
No groundwater0.6100.2700.5780.468
No entrainment0.4940.2090.4560.404
No rainfall0.6100.2540.5710.466
No sunlight0.3970.1220.5200.230
Uniform distribution0.5070.2660.5390.438
Linear distribution0.5470.2440.5670.422

3.3. Scenario Tests

[37] To assess the contributions of the various processes described in section 2.3 on the loading, transport, and fate of enterococci, we performed a series of calculations in which different processes were either turned off or modified. This was done to evaluate and compare the relative importance of each of the processes in affecting beach water quality from a mechanistic point of view. The result of Figure 7a was used as the baseline scenario, and differences were calculated by subtracting enterococci levels of scenario experiments from those of the baseline (Figure 8). The scenarios focused on evaluating the importance of cross-shore diffusion, waves, source functions (groundwater, entrainment, rainfall), and the solar radiation fate. Waves were considered to represent a surrogate to evaluate the influence of mobilized sediment (the first term on the RHS of equation (1)). Moreover, the impact of different spatial distributions of enterococci within the intertidal sand was also evaluated.

Figure 8.

Model simulations for different scenario experiments compared with baseline, showing only the model domain from beach shoreline to about 120 m offshore. (a) Contour of differences in enterococci levels between no diffusion and baseline. Note that color bar is in the conventional linear unit scale of CFU 100 mL−1. Contour of differences in enterococci levels (b) between no wave and baseline, (c) between no groundwater and baseline, (d) between no entrainment and baseline, (e) between no rainfall and baseline, (f) between no sunlight and baseline, (g) between uniform distribution and baseline, and (h) between linear distribution and baseline.

3.3.1. No Cross-Shore Diffusion

[38] To deactivate cross-shore diffusion, we set both sediment and microbe diffusivity to be zero. In this scenario, most enterococci are constrained to a narrow strip next to the waterline, which causes the persistence of high levels in the intertidal zone and overestimation at knee depth while underestimation at waist depth (Figure 8a). This suggests that turbulent diffusion is a crucial process in far-field mixing. It should be noted that diffusion mixes not only free-living microbes that exist in the water but also bacteria-contaminated sand in the form of suspended load and concomitant release.

3.3.2. No Waves

[39] Without any wave forcing, the Eulerian current alone is too weak to suspend sediment. In this case, the release from the bed sediment is almost negligible, which causes a remarkable underestimation of microbe influxes and levels, especially in the middle part of the 10 day period (Figure 8b). Model skill is clearly better when waves are present, resulting in a smoother observed microbe response which is well matched by the model (Figure 7b). By comparing the model results between baseline and no-wave experiments, we could identify a threshold significant wave height of approximately 0.05–0.1 m before apparent wave-induced release of bacteria at this beach site occurs.

3.3.3. No Groundwater

[40] The difference between the cases with and without groundwater is small and indiscernible most of the time (Figure 8c), which suggests that the role of groundwater in microbial balance is insignificant. Slight differences occur around low tide when the highest groundwater head gradient is achieved, which generates the largest groundwater flow. This result is consistent with sand core experiments, which showed that pore water flow releases a relatively small amount of enterococci from the sands at this site [Phillips et al., 2011a].

3.3.4. No Entrainment

[41] The entrainment coefficient was set to zero so that diffusive exchange across the bottom boundary layer is prevented. The role of entrainment is to slowly redistribute the enterococci between the open water column and the pore water within the sediment bed, and the rate of the entrainment is dependent on the concentration difference between the two reservoirs. Within the intertidal zone, the open water column has generally lower concentrations except when other influxes dominate and subsequently increase enterococci levels in it (e.g., during thunderstorms with a large quantity of runoff influx or during wave events that release enterococci from the bed). Therefore, entrainment mostly acts as a one-way microbial influx process to the beach water within the intertidal zone, previously termed “tidal washing” [Abdelzaher et al., 2011; Wright et al., 2011; Enns et al., 2012]. However, when enterococci levels are sometimes highly elevated, the direction of entrainment will reverse with enterococci transfer into the bed, which provides another potential mechanism to mitigate extremely high levels of bacteria in the water column in addition to sunlight deactivation, advection, and diffusion. Note that there is no empirical evidence showing microbial flux from surface water into the bed, which could be an area of future research in both the laboratory and field. Without entrainment, these high levels would last several hours longer (see red and yellow areas in Figure 8d), whereas, at other times, when rain is absent and waves are minimal, neglecting entrainment would result in slight underprediction of enterococci levels especially during the ebb tide (see blue areas in Figure 8d).

3.3.5. No Rainfall

[42] Runoff associated with rainfall is a direct but episodic microbial source to the beach water in the 10 day period. Without the rainfall-runoff loading, several events of elevated enterococci concentrations were clearly missed with the most significant difference observed for the night of 4 June (Figure 8e). Another potential effect of rainfall on beach water quality is to raise groundwater level and increase the exfiltration rate, but that process cannot be examined at present without further groundwater monitoring.

3.3.6. No Sunlight

[43] By turning off sunlight deactivation, the overpredictions of enterococci levels spread across almost the entire 10 day period and expand from the waterline to nearly 100 m offshore, especially in the daytime (Figure 8f). In this case, the model certainly overestimates both knee-depth and waist-depth enterococci levels. Again, solar inactivation is a key process to reduce enterococci levels during the day and responsible for both observed and modeled diurnal fluctuations of enterococci levels.

3.3.7. Uniform and Linear Distributions of Sand Enterococci Levels

[44] To understand the model sensitivity to different distributions of the sand enterococci source, we tested two scenarios: (1) a constant level (9.0 CFU g−1) within 145–200 m and zero everywhere else, referred to as uniform distribution; (2) a linear increase from 0 CFU g−1 at 145 m to the maximum 18.0 CFU g−1 at 195 m, referred to as linear distribution (Figure 4b). Those two distributions ensure the total enterococci reservoir of the area from the subtidal point (x = 145 m) to higher high water line (x = 195 m) equals that of the exponential distribution used before. It is not surprising that major differences are found in the intertidal zone where the latter two distributions provide fewer available enterococci, resulting in underestimations of enterococci levels in that area, especially when tide is ebbing (Figures 8g and 8h). Nevertheless, the general spatial and temporal patterns do not change much, compared with the baseline case. Overall, the linear distribution slightly better fits the baseline result than the uniform one because of its relatively higher concentrations of contaminated sand in the intertidal zone. In summary, sand enterococci source distribution influences the levels of enterococci observed in the water column, and the best fit to the data occurs when the sediments higher upon the shore are characterized by higher enterococci levels.

3.4. Sensitivity Analysis

[45] Sensitivity analysis was conducted as a further evaluation of model performance and to better understand its behavior in response to parameter changes. As illustrated in scenario tests, six parameters in equation (1) may have substantial influences on model output of enterococci level of beach water, by controlling physical transport (Dm), source loading (β1, β2, β3, β4), or biological decay (β5). Due to the complexity and large sets of parameters in this model, we only applied simple local sensitivity analysis method by perturbing one factor at a time to two proportions (50% and 150%) of corresponding calibrated or literature value, ±50% variations [Saltelli et al., 2000]. Again, we used the result of Figure 7a as the baseline or control, and percentages of variation with respect to the control were calculated (Figure 9).

Figure 9.

Sensitivity analyses on six key parameters. Percentage variations of enterococci levels when microbe diffusion coefficient Dm (a) decreases by 50% or (b) increases by 50%, when sediment-related enterococci release coefficient β1 (c) decreases by 50% or (d) increases by 50%, when pore water enterococci concentration coefficient β2 (e) decreases by 50% or (f) increases by 50%, when entrainment mass transfer concentration coefficient β3 (g) decreases by 50% or (h) increases by 50%, when rainfall-runoff loading coefficient β4 (i) decreases by 50% or (j) increases by 50%, and when sunlight inactivation coefficient β5 (k) decreases by 50% or (l) increases by 50%.

3.4.1. Microbe Diffusion Coefficient Dm

[46] The model responses to the changes of diffusion coefficient showed opposite variational patterns between nearshore and offshore regions. The decrease of Dm weakens diffusive transport of enterococci from high concentration intertidal zone to further offshore. Therefore, the smaller Dm is, the more enterococci stay near the waterline, whereas the less are transported away. In general, 50% decrease of Dm causes enterococci levels to increase by less than 40% in the nearshore while to increase more than 50% in the offshore (Figure 9a). Changing Dm to 1.5 times of calibrated value results in less than 20% decrease of enterococci levels in the nearshore and greatly above 50% increase in the offshore (Figure 9b). Such results demonstrate the nonlinearity of diffusion process in the model, which can also be deduced from equation (1) that diffusion terms are second-order derivatives.

3.4.2. Enterococci Sediment Release Coefficient β1

[47] Increasing (decreasing) β1 means larger (smaller) enterococci loading rate from sediment when sediment suspension and transport occur, resulting in rise (fall) of enterococci levels throughout the spatial domain in the beach water when waves are present (Figures 9c and 9d). The simulated enterococci levels respond quasi-linearly to the variation of coefficient β1when wave heights are noteworthy.

3.4.3. Pore Water Concentration Coefficient β2

[48] Since β2 represents the abundance of enterococci in the pore water, it can indicate the proportions of enterococci living in the interstitial as oppose to attaching to the sand grain. This will affect both advective exchange by groundwater infiltration/exfiltration and diffusive exchange due to entrainment, with the latter being more important. Reducing (enlarging) β2 means lower (higher) enterococci concentrations in the pore water, which will decrease (increase) pore water enterococci loading flux. When sediment or runoff loading is insignificant in the beginning and ending of the 10 day period, lowering β2 to half will cause around 40%–50% decrease in enterococci levels; otherwise, the reductions of enterococci levels are generally less than 20% (Figure 9e). Increasing β2 leads to exactly opposite patterns (Figure 9f).

3.4.4. Entrainment Coefficient β3

[49] The model responses to entrainment coefficient are fairly complicated. The increase (decrease) of β3 will facilitate (suppress) the diffusive exchange across the bottom boundary. As previously discussed, pore water generally has higher enterococci levels than surface water, so the decrease of β3 will reduce enterococci transfer rate from higher pore water to lower overlaying water column and, therefore, lower enterococci levels of surface water. However, when enterococci levels are highly elevated in the surface water, becoming higher than those in the pore water at nights during the middle of the 10 day period, enterococci levels contrarily increase by 10%–40% in the case of reducing β3 by 50% (Figure 9g). We observed just opposite patterns with the case of 150% β3 (Figure 9h).

3.4.5. Rainfall-Runoff Loading Coefficient β4

[50] The changes in the runoff loading coefficient have little impact on enterococci levels except during rainfall periods, showing quasi-linear responses to coefficient change (Figures 9i and 9j). The magnitudes of enterococci level variations seem smaller than coefficient changes and never exceed 40%.

3.4.6. Sunlight Inactivation Coefficient β5

[51] The influence of the inactivation coefficient varies significantly with time and is highly nonlinear. The change of enterococci levels due to coefficient change is generally very small in the nighttime when sunlight is nonexistent. However in the daytime, modeled enterococci levels are quite sensitive to the changes of β5. Reducing it to half leads to more than 100% to up to 10 times increase in enterococci levels, which are beyond the uniform color scale (±50%) used for all figure panels (Figure 9k). If β5 becomes 1.5-fold of literature value, the enterococci levels decrease by 10%–80% of baseline values, with offshore areas having larger variations than the nearshore (Figure 9l). This suggests that β5 is an important coefficient to correctly predict enterococci levels in the daytime due to the exponential decay feature of the sunlight inactivation process.

4. Discussion

4.1. Model-Observation Comparisons

[52] The comparisons between model results and field measurements raise the question why the diurnal maxima of enterococci concentrations were underpredicted by the model. This may be attributed to both inherent inhomogeneity of natural sediment and other potential microbial loads not represented in our model, such as dog feces, human activities, and seaweed debris. For example, one fecal event from a small dog may contributes 1.5 × 108 CFU enterococci [Wright et al., 2009]. If we assume this microbial load is well mixed and distributed in the water volume with depths from 0 (i.e., waterline) to 0.3 m (i.e., knee depth), a mean slope 1/25 in the intertidal zone, and a 10 m long shoreline, it would yield a mean concentration of 1.3 × 103 CFU 100 mL−1, which is in the same order as typically observed spikes. Previous model studies also suggested that dog fecal events may have transient impacts (hundreds of CFU 100 mL−1) in a limited area for several hours [Zhu et al., 2011]. Other possibilities can be bathers, dogs, and/or samplers walking in the water and stirring up bottom sediment and attached microbes, and the signals may be captured by the water samples. Such artificial disturbances are more influential during high tide than low tide because of the geographical location and relative abundance of microbial sources. This partly explains the fact that extreme elevations are more frequently observed around high tides [Enns et al., 2012]. In addition, an abnormally wide and thick wrack line was formed in this beach site during the last 4 days of the field experiments and covered the entire shoreline from the dry berm to nearly 10 m offshore. Seaweed is not only potential microbial sources themselves [Grant et al., 2001; Badgley et al., 2011] but may also provide favorable environments for bacteria survival and growth in the sand underneath [Shibata et al., 2004].

[53] The model has a better skill in hindcasting enterococci levels in the water closer to the shore (knee depth) than farther offshore (waist depth). The lack of observations and the low levels of enterococci at offshore locations may contribute to the lower skill offshore. Moreover, in present model setup, the cross-shore exchange is primarily controlled by diffusion rather than advection. This is due to extremely weak cross-shore currents in the order of 10−2 m s−1 or lower for the whole period (Figure 6a). Other processes not resolved due to the 1-D model setting, specifically alongshore advection, may be as important as cross-shore diffusion. Alongshore uniform assumption should be valid at the central portion of the beach. The bathymetry at the experiment site is mostly alongshore uniform (see Figure 1). The alongshore current velocity at the site, observed with GPS-equipped drifters, is also quite uniform with velocities in the order of 10−1 m s−1 [Fiorentino et al., 2012]. Although there is significant spatial variability in the enterococci levels within the sand, these spatial scales are much smaller than the scales associated with the alongshore bathymetry, O (100 m), and hydrodynamics; therefore, that can be considered alongshore uniform after local averaging. We examine the relative importance of alongshore advection and cross-shore diffusion by estimating Reynolds number for two different zones: nearshore and offshore. The Reynolds number is the ratio of two terms in the left-hand side of equation (1):

display math(10)

where V is a mean alongshore velocity (m s−1), Dm is the diffusion coefficient (m2 s−1), and Lx and Ly are the characteristic cross-shore and alongshore length scales, respectively (m).

[54] If we consider a mean alongshore velocity of 0.1 m s−1 offshore the beach, a diffusivity of 0.03 m2 s−1, and cross-shore and alongshore characteristic lengths of 10 m and 100 m respectively, a Reynolds number of 3.3 is obtained for the offshore region, which suggests alongshore advection and cross-shore diffusion are of the same order of magnitude in transporting microbes. However, since concentration gradient is so high in the narrow and shallow nearshore region, the cross-shore length scale (Lx = 1 m) is much smaller. In addition, due to the increased friction in such shallow water, the mean alongshore velocity is reduced to 0.05 m s−1. Then, we obtain a Reynolds number of 0.016 for the nearshore region, which indicates that nearshore is dominated by cross-shore diffusion. The Reynolds number analysis also explains why model performance is not as good in the offshore as in the nearshore because of the missing of alongshore transport. To achieve better predictions in the offshore, a 2-D model configuration that can include alongshore transport mechanism is required, which will be our following work.

4.2. Constant Bed Reservoir Assumption

[55] There is another interesting question from this modeling effort: is the growth of enterococci in the sand able to replenish the loss of enterococci due to the release? To answer this question, we have to investigate what occurred in the bed reservoir during the 10 day period, although the model assumes constant enterococci reservoir within the bed. Due to depletion and regrowth, the total amount of enterococci in the bed reservoir is time dependent in reality. The observations show that the enterococci levels in hourly sampled knee-depth sands are highly variable, spatially and temporally inhomogeneous (Figure 10a). Sand closer to the high tide line (x = 195 m) generally have higher enterococci levels, whereas those in the subtidal zone have much lower levels. Such spatial distribution is one of the most important characteristics of this type of enterococci source, which we have extensively explained in section 2.3.4.1. To achieve a good estimation of the reservoir using this sparse data set, we calculate daily mean enterococci levels and compare them with model-based constant enterococci level of the sand (Figure 10b). Note that the daily mean calculation excludes the samples taken beyond a subtidal line (x = 170 m), which is outside intertidal zone, the prevailing source region. The model-based constant enterococci level of the sand is spatially averaged between 195 and 170 m using equation (6), corresponding to where most knee-depth sand samples locate. The daily mean enterococci levels of the reservoir are fairly stable in those 10 days, slightly oscillating around the model-based constant level. This suggests that the removal of enterococci by the tides and waves has little impact on the total availability of enterococci within the bed, which is consistent with the model assumption of steady-state reservoir. The replenishing of removed enterococci is hypothesized to be due to regrowth within the sand, which should be fully explored in the future. In that way, instead of assuming a stable source, a time-varying source function, dependent on environmental parameters and constraints (e.g., temperature, nutrient, and salinity) and sand characteristics (e.g., grain size, mineral, and biofilm), can be applied to the model.

Figure 10.

(a) Measured knee-depth enterococci levels of the sand (colors of dots demonstrate enterococci levels in log10-transformed CFU g−1 dry sand) and (b) mean enterococci levels in the bed reservoir (CFU g−1). The histograms show daily mean measured enterococci levels of the sand, an indicator of the mean enterococci levels in the bed reservior. These values correspond to the average of the knee-depth samples at a distance, x, between 170 and 195 m. The dashed line is the model-based constant spatially averaged enterococci levels of the sand in the area from 170 to 195 m.

4.3. Importance and Role of the Tide

[56] One of the most unique features making marine beaches differ from freshwater and inland counterparts, like those around the Great Lakes, is tide. Tidal oscillations create a dynamic intertidal zone, superimposed with wave-induced motions. Tides may also elevate the water table above MSL and drive water table variations [Nielsen, 1990]. The interactions of tides with other coastal processes are fairly complex. This effort elucidates the roles of the tide in beach microbial dynamics in the following aspects, from high to low importance. First of all, the tide periodically changes the location of waterline and surf zone and, therefore, the abundance and availability of bacterial sources. In general, high tide initiates the elevation of microbial levels that is more evident in the ebb tidal phase. Second, high tide typically facilitates diffusive exchange from bed pore water to the open water column. Third, tides are also the major generating force of water table fluctuations and groundwater flows and, thereby, interfacial advective exchange.

[57] Note that there are also some other tide-related processes that may affect beach water quality but are not investigated in this paper. At first, the 1-D beach-scale model developed in present study is not capable of simulating currents associated with bay-scale circulation, generated by tidal wave propagation in the outer ocean and continental shelf and modulated by the bathymetry and geomorphology in the coastal zone. Circulation pattern and features (e.g., alongshore currents, eddies, and coherent structures) are different among tidal phases, which affect transport and dilution of fecal bacteria in the water [Zhu et al., 2011; Fiorentino et al., 2012]. Second, tidal stages will determine the inundated duration of the wrack line and can control the additional contributions of bacteria from seaweed debris washed off to beach water [Shibata et al., 2004]. Moreover, tides may also influence the activities of birds, dogs, and bathers, all of which are potential fecal bacterial sources [Wright et al., 2009; Wang et al., 2010].

4.4. Beach Management Implications

[58] From beach management perspective, our model results address the question concerning when an elevated level of enterococci would be expected during regular open beach hours. The model simulations suggest that locally energetic waves, generated by strong and persistent onshore or southwest winds, occurring at high tide (especially in the ebb phase), will very likely yield exceedances of enterococci levels at this beach. The other environmental factor that should be considered is rainfall, particularly heavy and/or long rains. The persistence of high fecal bacterial levels usually depends on the severity of the exceedance and the intensity of solar inactivation. It should also be noted that exceedances more often occurred in the nighttime are of less concern to human health, given the fact that Hobie Beach is routinely closed from sunset to sunrise by Miami-Dade County. However, if an extraordinary elevation is reached by a combination of several favorable conditions, like the one that occurred in the night of 4 June, the very high levels cannot be reduced fast enough so that the exceedance persists until the next morning, thereby triggering beach advisories and a potential of negative human health impact.

[59] In addition, the model results suggest that the microbial quality of sand, in terms of the abundance of microbes within the sediment, is a fundamental factor in determining overall beach water quality. This is also confirmed by the surveys of multiple south Florida beaches, which found that beaches with high levels of enterococci in the sand had more reported exceedances of U.S. Environmental Protection Agency standards [Phillips et al., 2011b].

4.5. Applications and Limitations of the Model

[60] Although we have showed a case study in an embayed subtropical beach with relatively low wave energy and small tidal range, the coupled microbe-hydrodynamic-morphological model can be adapted to model bacterial release at other beaches. The approach illustrated herein may be useful for beaches where the pervasive fecal bacteria source comes from the shoreline sand. It may also be useful in different environmental settings such as rip-channeled beaches, where XBeach can be used to reproduce the circulation cells on the top of rip channels and shoals [Orzech et al., 2011]. In that case, the pollutants originated from the beach may have long retention times in the surf zone [Reniers et al., 2009].

[61] The limitations of the model are associated with the need: for additional parameter calibration and to carefully evaluate the model initial conditions and assumptions. The parameterization issues may be resolved in the future with more field studies and extensive model validations against new data sets, as well as well-designed laboratory experiments in wave flumes to determine appropriate sediment-related enterococci release coefficient β1. Furthermore, one must pay attention to the initial conditions and basic assumptions made in this study when applying the model to other time periods or beach sites. For instance, Hobie Beach was completely renourished months after the 10 day study. In that case, the initial distribution of microbes in the sand used in this study does not represent the microbial beach environment after the nourishment, and, consequently, a modified initial condition based on the new field experiments must be established before model simulations. Also, the cross-shore distribution of microbes in the sand is assumed to be stable over the simulation time, which is unlikely to be the case during times of significant beach changes under the impact of storms [Gast et al., 2011].

Appendix A: Sediment Transport

[62] Suspended sediment transport is calculated from a depth-averaged advection-diffusion equation [Galappatti and Vreugdenhil, 1985]:

display math(A1)

where Cs,i represents the depth-averaged suspended sediment concentration of sediment class i, with classes 1 and 2 representing contaminated and clean sand, respectively; Dh is the sediment diffusion coefficient, h is the local water depth, and uE and vE are the shortwave-averaged Eulerian velocities (see Roelvink et al. [2009] for details). The uptake of sediment is represented by an adaptation time Ts,i, given by a simple approximation based on the local water depth h and sediment fall velocity ws:

display math(A2)

where a small value of Ts,i corresponds to nearly instantaneous sediment response [Reniers et al., 2004]. Uptake of sediment, U, occurs if there is a positive difference between the equilibrium concentration, Ceq,s,i, and the actual sediment concentration, Cs,i, thus representing the source term in the sediment transport equation (see Figure 2). Deposition, D, occurs when there is a negative difference and thus represents a sink term for the suspended sediment.

[63] The equilibrium suspended sediment concentration is calculated with the sediment transport formulation of Soulsby-van Rijn [Soulsby, 1997], considering the stirring due to both Eulerian mean velocity uE and near-bed shortwave orbital velocity urms:

display math(A3)

where pi represents the fraction of sediment class i within the active layer at the bed (top sediment layer in Figure 2). Suspended load coefficient Ass,i is a function of sediment grain size, relative density of the sediment, and the local water depth (see Soulsby [1997] for details). Cd,i is the drag coefficient due to flow velocity only. A threshold velocity ucr must be exceeded before sediment is set to motion. Bed slope (m) and a calibration factor (αb) are introduced to account for bed-slope effects.

[64] The near-bed shortwave orbital velocity, urms, is obtained using linear wave theory:

display math(A4)

where Hrms is the RMS wave height calculated from a wave action balance equation (see Roelvink et al. [2009] for details), and Trep is the representative intrinsic wave period.

[65] The critical velocity is given by [Soulsby, 1997]

display math(A5)

where d50 is medium grain diameter, and d90 is the grain diameter where 90% of the sediment is finer.

[66] Cross-shore suspended sediment transport due to advection and diffusion is given by

display math(A6)

[67] Also, similarly, for the alongshore transport,

display math(A7)

[68] The bed-load sediment transport is assumed to react instantaneously to the near-bed velocity and is given by

display math(A8)
display math(A9)

where the equilibrium bed-load concentration (Ceq,b,i) is also given by the Soulsby-van Rijn formulation [Soulsby, 1997]:

display math(A10)

where Asb,i is bed-load coefficient.

[69] By summing the calculated sediment transport rates for all sediment classes, the change in bed elevation is computed from the sediment balance:

display math(A11)

where zb is the bed level, np is the porosity, and fmor represents a morphological factor to speed up the bed evolution [e.g., Reniers et al., 2004] (fmor = 0 means constant bed level).

Appendix B: Groundwater Flow

[70] Groundwater system is an ongoing developing module in XBeach (R. McCall, personal communication). Darcy's law is utilized to calculate horizontal flow velocities from the groundwater head (pgw) gradient, assuming laminar flow conditions for sandy beaches:

display math(B1)
display math(B2)

where ugw and vgw are the groundwater flow velocities (m s−1), and kx and ky are the hydraulic conductivities (also in m s−1).

[71] The groundwater head is determined as follows. If there is no surface water (i.e., a dry grid), the groundwater head is equal to the groundwater surface level (ηgw) of the same grid at previous time step:

display math(B3)

where wetz is a wet-dry grid identifier, which is equal to one when a grid is wet and zero when it is dry.

[72] For a wet cell with surface water, if groundwater surface level is higher or equal to the bed level zb, the groundwater head is equal to the surface water head zs. When groundwater level is more than a depth value (dwetlayer) below the bed, the groundwater head is no longer affected by the surface water head but equal to groundwater level. Within the intermediate depth or the interaction layer, linear interpolation is conducted using a relative groundwater level (fac), defined as

display math(B4)

where dwetlayer is the thickness of surface-subsurface water interaction layer.

[73] The groundwater head is thereby determined as

display math(B5)

[74] The vertical flow across the sediment-water interface, referred to as exfiltration or infiltration, is also simulated in XBeach. This flow is defined positive downward from surface to groundwater and is given in terms of surface water for the continuity equation (i.e., 100% porosity). Such flow may have important implications to the microbial balance that involves the convective microbial exchange between surface water and groundwater.

[75] Exfiltration takes place when groundwater level exceeds the bed level. That exceeding amount of groundwater determines the flow rate and also joins in the surface water in the same numerical time step:

display math(B6)

where np is the porosity.

[76] Infiltration can occur where surface water is on the top of bed and groundwater level is below bed. XBeach models infiltration uses a quasi-three-dimensional model and Darcy's flow:

display math(B7)
display math(B8)

where dinfiltration is the thickness of infiltration layer, which increases at the end of each time step by the infiltration water.

display math(B9)

[77] The infiltration velocity is limited by the amount of water available or surface water depth in the cell:

display math(B10)

[78] For numerical stability, dinfiltration is restricted to a minimum of one third of dwetlayer (i.e., corresponding to the centroid of the instantaneous infiltration part), and the maximum is equal to the depth of groundwater level below the bed level. Once a cell is dry, the corresponding dinfiltration is reset to the minimum value.

display math(B11)
display math(B12)

[79] The continuity equation for groundwater system can be written as

display math(B13)

where the effective depths (hugw and hvgw) are calculated by taking the mean differences between the groundwater level and bed of the aquifer (zb,aquifer) in the surrounding η points:

display math(B14)
display math(B15)

[80] The new groundwater level can then be solved from continuity equation:

display math(B16)

Acknowledgments

[81] This study is funded by the NSF NIEHS Oceans and Human Health Program (NIEHS P50 ES12736 and NSF OCE0432368/0911373/1127813) and partly supported by the NSF REU program in Oceans and Human Health. We thank students from the University of Miami and volunteers from the Miami-Dade County Department of Health who participated in the field and laboratory work. We are grateful to John Wang and Lora Fleming for their valuable discussions and suggestions. We acknowledge insightful comments from three anonymous reviewers, which help us to improve the readability and quality of this paper. Additional thanks are given to the XBeach team for providing source codes and Robert McCall for his help on the groundwater module setup.

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