Modeling the Transport andInactivation of E. coli andEnterococci in the Near-ShoreRegion of Lake MichiganL U B O L I U , † M A N T H A S . P H A N I K U M A R , * , †

S T E P H A N I E L . M O L L O Y , ‡

R I C H A R D L . W H I T M A N , §

D A W N A . S H I V E L Y , §

M E R E D I T H B . N E V E R S , §

D A V I D J . S C H W A B , | A N D J O A N B . R O S E ‡

Department of Civil & Environmental Engineering andDepartment of Fisheries and Wildlife, Michigan StateUniversity, East Lansing, Michigan 48824, Lake MichiganEcological Research Station, U.S. Geological Survey, Porter,Indiana, and NOAA Great Lakes Environmental ResearchLaboratory (GLERL), Ann Arbor, Michigan

To investigate the transport and fate of fecal pollution atGreat Lakes beaches and the health risks associated withswimming, the near-shore waters of Lake Michigan andtwo tributaries discharging into it were examined for bacterialindicators of human fecal pollution. The enterococcushuman fecal pollution marker, which targets a putativevirulence factorsthe enterococcal surface protein (esp)in Enterococcus faecium, was detected in 2/28 samples (7%)in the tributaries draining into Lake Michigan and in 6/30samples (20%) in Lake Michigan beaches. This was indicativeof human fecal pollution being transported in the tributariesand occurrence at Lake Michigan beaches. To understandthe relative importance of different processes influencingpollution transport and inactivation, a finite-elementmodel of surf-zone hydrodynamics (coupled with modelsfor temperature, E. coli and enterococci) was used.Enterococci appear to survive longer than E. coli, whichwas described using an overall first-order inactivationcoefficient in the range 0.5-2.0 per day. Our analysis suggeststhat the majority of fecal indicator bacteria variation canbe explained based on loadings from the tributaries. Sunlightis a major contributor to inactivation in the surf-zoneand the formulation based on sunlight, temperature andsedimentation is preferred over the first-order inactivationformulation.

IntroductionMillions of people visit the 500 plus recreational beaches inthe Great Lakes every year. Recently, water quality degrada-tion due to fecal bacteria at the shoreline has been increasing,

and thus, the potential risk to human health is of interest tobeach managers and the public. There were more than 1800(combined) days of closings and advisories caused bypollution at Great Lakes beaches in 2003 (32% more than inthe previous year), and in 2004 the number went up to 3081(1). The closings and advisories at Michigan Great Lakesbeaches were due to elevated fecal bacteria levels fromunknown sources of contamination (1). Fecal pollution ofsuch recreational waters has been associated with gastro-intestinal diseases and infections (e.g., eye or respiratory) inbeachgoers (2). Water quality at these beaches is impactedby a variety of fecal pollution sources (e.g., agriculture,human, wildlife), and the indicators, such as Escherichia coli(EC) and enterococci (ENT), that are used to evaluaterecreational water quality are found in a variety of mam-malian hosts. Thus, they give no indication as to the sourceof fecal pollution. Identification of fecal pollution sources isimportant in assessing the risk to human health associatedwith water use and for the management and remediation ofbeaches and contamination sources. Microbial source-tracking, coupled with process-based modeling, has thepotential to test hypotheses about sources of contaminants.One tool for identifying human-sourced fecal pollution isthe presence of a putative virulence factor, the enterococcalsurface protein (esp) in Enterococci faecium. This marker hasbeen found only in Enterococcus faecium isolated from fecalsamples of human origin, and the presence of this markeris thus indicative of human fecal pollution (3).

Understanding factors that influence transport of fecalpollution along the shoreline will enable us to quantify risksto human health from recreational use of these beaches.Besides human health risks, beach closures have significantnegative impact on local economies. Traditional techniquesused for recreational beach monitoring require an incubationperiod of 24 h for the assays; however, EC concentrations areknown to vary significantly even in a short period. Therefore,predictive modeling has been suggested as an alternative tothe current practice based on measurements. Past efforts todevelop mechanistic models for pathogenic organisms insurface waters focused mainly on marine coastal waters (4-6), and relatively few studies examined large freshwatersystems such as the Great Lakes. Due to the complexity ofthe processes and the large number of variables involved,statistical approaches have been used to predict beachclosures (7). Modeling near-shore, wind-driven circulationand the transport of chemical and biological agents ischallenging due to interactions with complex lake-widecirculation (8). The goals of this study were to (a) identifywhether human fecal pollution may be impacting the GreatLakes beaches, (b) develop a near-shore transport model forfecal pollution in Lake Michigan and to identify key processesinfluencing inactivation, and (c) see if the observed variabilityin the concentrations can be explained based on loadingsfrom Trail Creek and Kintzele Ditch.

Description of SitesThe region of our primary interest included approximately72 km of shoreline within the state of Indiana (Figure 1). Thewatershed that contributes to the shoreline encompassesthe Porter, Lake, and LaPorte counties. The cities of Gary,Hammond, East Chicago, and Michigan City along theshoreline are the major population centers in the watershed.The monitoring data were focused on the locations close toMichigan City. There are three main tributaries and a smallditch flowing into Lake Michigan in the domain of interest:Indiana Harbor Canal at East Chicago (USGS 04092750),

* Corresponding author phone: (517)432-0851; fax: (517)355-0250;e-mail: phani@egr.msu.edu. Corresponding author address: A130Engineering Research Complex, Michigan State University, EastLansing, MI 48824.

† Department of Civil & Environmental Engineering, MichiganState University.

‡ Department of Fisheries and Wildlife, Michigan State University.§ U.S. Geological Survey.| NOAA Great Lakes Environmental Research Laboratory (GLERL).

Environ. Sci. Technol. 2006, 40, 5022-5028

5022 9 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 40, NO. 16, 2006 10.1021/es060438k CCC: $33.50 2006 American Chemical SocietyPublished on Web 07/14/2006

Portage-Burns Waterway (Burns Ditch, USGS 04095090), TrailCreek at Michigan City Harbor (USGS 04095380), and KintzeleDitch. Other creeks flowing into Lake Michigan contributelittle discharge and were not considered in our modeling.For transport simulations, it was important to quantify thestrengths of various loadings, which are “beachshed de-pendent”. Potential sources in the near-shore environmentinclude point sources (e.g., wastewater treatment plants),combined sewer overflows (CSOs), nonpoint sources (e.g.,faulty septic systems, manure storage, wildlife), and tributar-ies themselves. Most of the CSOs discharge into the riverswhich eventually drain into the lake but few CSOs dischargedirectly to the shoreline; therefore, CSOs were not consideredas sources in this study. Tributaries that enter Lake Michiganwithin Indiana are considered the most significant source ofEC and ENT to the shoreline. Septic systems were notconsidered in our modeling due to lack of information onthe areas with high septic vulnerability along the shoreline.Previous research shows that contamination at beach sitesin Lake Michigan is mainly associated with localized sourcesof pollution. Based on historical water-quality monitoringdata, Kintzele Ditch and Trail Creek were considered as thepathogen sources out of the four main tributaries. For thehydrodynamic model, however, all four tributaries discharg-ing into Lake Michigan were considered.

Materials and MethodsSampling took place in the summer of 2004 (July-August).Samples were collected and analyzed for fecal pollutionindicator bacteria (EC and ENT) and for the presence of theputative human fecal pollution source marker (the markerthat targets the esp gene in Enterococcus faecium) (3). Watersamples were collected from knee-deep water (∼45-cmdepth) from two sites at Central Avenue Beach, three sitesat Mt. Baldy Beach, and one site each at the mouths of KintzeleDitch and Trail Creek. Solar insolation was measured usinga Campbell pyranometer near Trail Creek (+ Figure 1). ECwere evaluated in water samples using membrane filtrationaccording to section 9222G (9). Membrane filters wereincubated on mFC agar at 44.5 °C for 24 h, transferred toEC-MUG agar (Difco, 222200), and incubated for 24 h at44.5 °C. Individual colonies that produced fluorescence undera long-wavelength (366-nm) ultraviolet light were consideredEC. Colony-forming units (CFU) per 100 mL were recorded.

ENT were isolated on mEI agar according to U.S. EPA Method1600, incubated at 41 °C, and CFU enumerated after 24 h.Membrane filters that contained approximately 50 or moreCFU were assayed for the presence of the esp gene inEnterococcus faecium using primers specific to bacteria ofhuman origin (3). Bacterial colonies were removed from themembrane filters by suspending the filters in 10 mL of trypticsoy broth and incubating for 2 h at 41 °C. DNA was extractedfrom 1 mL of this suspension using the Qiagen QIAamp DNAMini Kit according to the manufacturer’s directions (cell lysisthrough DNA purification). The forward primer, which isspecific for the E. faecium esp gene used, was (5′-TAT GAAAGC AAC AGC ACA AGT T-3′) (3). A conserved reverse primer(5′-ACG TCG AAA GTT CGA TTT CC-3′) was used for allreactions (10). PCR reactions contained 1X PCR buffer,1.5 mM MgCl2, 200 µM of each dNTP, 0.3 µM of each primer,0.5 U of HotStarTaq DNA polymerase (Qiagen), and 1 µLtemplate DNA per 20 µL of reaction. Amplification wasperformed with an initial step at 95 °C for 15 min followedby 35 cycles at 94 °C for 1 min, 58 °C for 1 min, 72 °C for 1min, and a final extension at 72 °C for 7 min. PCR productswere separated on a 1.5% agarose gel stained with GelStarnucleic acid stain (BioWhittaker) and viewed under UV light.

Modeling

Interactions between the near-shore and lake-wide circula-tion are important; hence, our computational domainincluded the entire Lake Michigan (Figure 2). To resolve theshoreline accurately, a finite-element model was used. Thefinite-element mesh was gradually refined from a resolutionof approximately 1-2 km for the whole lake to about 100 mnear-shore. Major considerations in the model developmentincluded the representation of shoreline and bathymetry,meteorological data including wind direction and speed, solarinsolation, hydrological flows, water temperature, and load-ings of EC and ENT. Bathymetry data with a resolution of3 arc-seconds were obtained from the NOAA National Geo-physical Data Center. Figure 2 shows the details of the finite-element mesh and the near-shore bathymetry. Hourlymeteorological data (air and dew point temperatures, baro-metric pressure, wind speed and direction) were obtainedfrom the NOAA National Climatic Data Center. Water-leveldata were obtained from the Center for Operational Oceano-graphic Products and Services (CO-OPS), NOAA, and theNational Data Buoy Center. The finite-element mesh con-sisted of 8-noded-quadrilateral and 6-noded-triangular ele-ments with a total number of 11,716 elements (30,829 nodes).Wind fields and initial conditions for temperature wereobtained by interpolating data from several stations inMichigan (Harbor Beach, Rock Cut, Ludington, Muskegon),Indiana (Michigan City), and Illinois (Calumet Harbor,Chicago) as well as from two NDBC buoys in Lake Michigan(45002 and 45007). Wind data measured at different heightswere reduced to a common 10 m height using a methodproposed by Smith (11).

Since our primary interest was in the near-shore regionwhere depths are shallow, we employed a vertically integratedhydrodynamic model based on the finite-element modelRMA10 (12) to describe the wind-driven circulation in LakeMichigan. Water quality models for temperature, EC, andENT were coupled to the hydrodynamic model. A 1-monthperiod (July 12-August 13, 2004, Julian days 194-226) thatcorresponded to our sampling period was selected for themodeling. The vertically integrated hydrodynamic equationsin x and y directions are shown below (12)

FIGURE 1. Map of southern Lake Michigan showing the Indianashoreline.

∂h∂t

+ U∂h∂x

+ V∂h∂y

+ h(∂U∂x

+ ∂V∂y) ) 0 (1)

VOL. 40, NO. 16, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY 9 5023

where U,V are the depth-averaged velocities in the x,ydirections, h is the water depth, a denotes the bottom surfaceelevation, g is the acceleration due to gravity, W is the windvelocity, ψ is the wind direction, ú is an empirical windcoefficient, and f is the Coriolis parameter. n denotes theManning’s roughness coefficient, and εj is the depth-averagededdy viscosity. A constant value of 2.0 m2/s was used for theeddy viscosity in the near-shore region. Viscosity values inthe offshore region were variable and depended on theelement size and the velocity gradients as described by theSmagorinsky formulation. Equations for the transport of EC,ENT, and temperature have the following general form

where C denotes the depth-averaged temperature or theconcentrations of EC or ENT (CFU/100 mL), and Dxx, Dxy,Dyy, and Dyx are the depth-averaged dispersion and turbulentdiffusion coefficients. In (4), G is a general term that denotessources and sinks. Equation 4 is coupled to the hydrodynamicmodel and was solved using RMA11 (12). For the temperatureequation, G included contributions due to the net shortwaveradiation, the longwave back radiation, evaporation, con-

densation, the heat flux due to sensible heat transfer, andheat inputs from tributaries. Details of these different fluxesand the ranges of parameters have been described by Martinand McCutcheon (13). Initial conditions for the modelassumed that the lake was at rest at time t ) 0. A backgroundvalue of 3 CFU/100 mL was used as the initial condition forboth EC and ENT based on our observations. Observed watertemperatures at different stations were interpolated to thefinite-element mesh to create an initial condition for thethermal model. Boundary conditions for the hydrodynamicmodel included the no leakage condition across the surfaceand the bottom, zero pressure and wind stress at the freesurface, and drag at the bottom surface.

Numerous factors influence the fate, transport, andpersistence of EC and ENT. These include sunlight, nutrientcontent, suspended solids concentration, removal by sedi-mentation, water temperature, pH, and predation. EC andENT could potentially replenish at night time (14) either dueto the recovery of nonculturable cells or due to unidentifiedsources. The presence of suspended solids in the watercolumn has been shown to increase EC survival rates bylimiting the effects of sunlight (15). EC survive longer in turbidconditions (16), and both EC and ENT survive longer in coldtemperatures than in warm temperatures (17). Increaseddeath rates at the higher temperatures may be due to damageto the bacterial cell components or due to increased predation(18). For the enteric bacteria, the effects of temperature havebeen reported to be less important in the presence of light(16). Many studies have also reported that the inactivationof EC is more rapid in saline waters than in freshwater (19).An important question often addressed in the literature isrelated to the differences in disappearance rates for differentbacterial strains. For example, Menon et al. (20) did not finda significant difference in the rates of disappearance of thestrains tested (E. coli, S. faecium, and S. typhimurium). Sintonet al. (18), on the other hand, reported a disappearance ratefor EC that is four times higher compared to ENT. Afterexamining the important inactivation mechanisms reportedin the literature and their mathematical formulations, weused two different formulations for inactivation: (a) an overall

FIGURE 2. (a) Finite-element mesh of Lake Michigan showing (b) the Indiana Shoreline and (c) the near-shore bathymetry.

h∂U∂t

+ hU∂U∂x

+ hV∂U∂y

- fVh ) 1F[ ∂

∂x(εjxxh∂U∂x ) +

∂

∂y(εjxyh∂U∂y )] - gh(∂a

∂x+ ∂h

∂x) -Ugn2x(U2 + V2)

h1/3+

úW2cosψ (2)

h∂V∂t

+ hU∂V∂x

+ hV∂V∂y

+ fUh ) 1F[ ∂

∂x(εjyxh∂V∂x) +

∂

∂y(εjyyh∂V∂y)] - gh(∂a

∂y+ ∂h

∂y) -Vgn2x(U2 + V2)

h1/3+ úW2sin ψ

(3)

∂(hC)∂t

+ U∂(hC)

∂x+ V

∂(hC)∂y

) ∂

∂x(Dxxh∂C∂x

+ Dxyh∂C∂y) +

∂

∂y(Dyxh∂C∂x

+ Dyyh∂C∂y) - khC ( G (4)

5024 9 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 40, NO. 16, 2006

first-order inactivation rate that did not depend on tem-perature, light, or settling and (b) a time-dependent inac-tivation rate based on temperature, sedimentation, andobserved solar insolation as shown below (5)

where k(I,T,vs) is the overall inactivation rate, kI is theinactivation rate for light (W-1m2 d-1), I(t) is the measuredsolar insolation (Wm-2) as a function of time, θ is atemperature correction factor (usually 1.07 (21)), fP is the

fraction of pathogens attached to the suspended sediment,vs is the settling velocity, and H is the water column depth.The above formulations provided quantitative estimates ofthe overall inactivation in addition to allowing us to explorefurther the relative importance of the effects of light,temperature, and sedimentation during summer conditionsin Lake Michigan.

Results and DiscussionDischarge, temperature, and concentrations of EC and ENTfrom tributaries flowing into the study region are shown inFigure 3. The hydrodynamic model was calibrated using data

FIGURE 3. Discharges and inflowing concentrations from Kintzele Ditch and Trail Creek during the summer of 2004.

FIGURE 4. Comparison between observed (symbols) and simulated (lines) hydrodynamic variables. (a) Depth-averaged currents at BurnsDitch, IN. Symbols show the ADCP data. (b) Water surface elevation at Calumet Harbor, IL and (c) water surface elevation at Green Bay, WI.

k(I,T,vs) ) (fP

vs

H+ kII(t))θ(T-20) (5)

VOL. 40, NO. 16, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY 9 5025

obtained from a 1200 kHz Acoustic Doppler Current Profiler(ADCP) deployed at Burns Ditch during summer 2004 aswell as water-surface elevations for several stations through-out the lake. These comparisons are shown in Figure 4.Results from the hydrodynamic model were generally foundto be consistent with known circulation patterns in southernLake Michigan (8). While the water surface elevations aresimulated fairly accurately, simulating near-shore currentswas relatively challenging due to the lack of high resolutioncoastline and bathymetric data required to describe currentsaccurately. Our simulated currents were of the same orderof magnitude as the observed currents, and some errors arelikely involved in averaging the ADCP data as well. Overall,the hydrodynamic model provided a reasonable descriptionof currents and water surface elevations. Comparisonsbetween the observed and simulated temperatures (Figure5) showed that the vertically integrated model was able todescribe the transport mechanisms of advection and disper-sion reasonably well.

Comparison of observed and simulated EC and ENTcounts at Mt. Baldy Beach are shown in Figures 6 and 7 fordifferent first-order inactivation rates as well as the formula-tion shown in eq 5. Mt. Baldy is approximately mid-waybetween Trail Creek and Kintzele Ditch. Pollution is generallycarried along-shore in an eastward direction, but simulations

indicated that currents often reversed their direction, result-ing in pollutant plumes that traveled in the opposite directionas well. As a result, observed EC and ENT counts at Mt. Baldywere influenced by loadings originating from both Trail Creekand Kintzele Ditch. Results for k ) 0 (no inactivation) indicatethat the observed data cannot be described based onadvection and dispersion alone. Both EC and ENT can bedescribed using an overall first-order rate. k values between0.5 and 0.8 d-1 described the observed EC concentrations atMt. Baldy. However, values around 0.5 or less better describedthe inactivation of ENT. This can be seen clearly from thecumulative probability plots in Figure 7. Published k valuesfor EC in freshwater typically range from 0.72 to 1.44 d-1 (20,21). Our results suggest that, in Lake Michigan, the lowerrange of the decay rates should be employed for describingthe peak values which are important from the point of beachclosures. Figure 7 shows that two different first-orderinactivation rates were required to describe the higher andlower (or background) concentrations. For example, itappears that k ) 1.5 d-1 was required to describe ENT valuesless than 50 CFU/100 mL, while values less than 0.5 d-1

described the higher concentrations better. This is attributedto the inability of the first-order formulation to describe theentire range of variability in inactivation. Our results indicatethat ENT survive longer in Lake Michigan compared to E.coli. This implies that if enterococci was used as an indicatororganism as opposed to E. coli, then more unsafe-waternotifications would result.

Comparisons based on the light-dependent rates showeda similar pattern as obtained from an overall first-order rate(Figures 6 and 7). For EC, the light-dependent rate produceda slightly better description (RMSE ) 0.808) compared to thefirst-order rate with k ) 0.5 (RMSE ) 0.835), but k ) 0.8 andk ) 2.0 produced better overall agreement with data (RMSE:0.770 and 0.705, respectively). The RMSE values are somewhatbiased by the relatively large number of low concentrationsin the observed data. The light-dependent inactivation resultsshown in Figure 7 used a kI of 0.0026 W-1 m2 d-1, a fractionfP of 0.1 (4), and a vS value of 5 m d-1 (22). These numbersrepresent one of several possible scenarios that describe thepeak concentrations reasonably well. Although we did notattempt to find the best parameters in the light-basedformulation that minimize the RMSE, this formulation is moregeneral. Comparison of the relative magnitides of various

FIGURE 5. Observed and simulated water temperatures at twobeaches in the near-shore region of Lake Michigan.

FIGURE 6. Comparison of observed and simulated counts of (a) E. coli and (b) enterococci for a 1-month period during summer 2004 atthe Mt. Baldy Beach.

5026 9 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 40, NO. 16, 2006

terms in eq 5 showed that inactivation was primarily light-controlled, and temperature and settling effects were rela-tively weak for this 1-month period. Figure 8 shows thecomparisons for EC and ENT at the Central Avenue Beachbased on the light-based inactivation formulation and thesame set of parameters used earlier for the Mt. Baldy Beach.The model was able to describe the observed data well(RMSE: 0.83 for EC and 0.55 for ENT) which indicates thatthe parameters are probably reasonable.

Fecal contamination from sewage is a significant publichealth concern due to the known presence of human virusesand parasites in these discharges. The esp human pollutionmarker was found (Figure 6) on three occasions (Julian days205, 217, 218), suggesting that a human fecal pollution sourcewas partially contributing to the fecal contamination at Mt.Baldy Beach on these dates. On Julian day 218, there was alarge variation between the observed and simulated ENTpeak concentrations at Mt. Baldy (Figure 6b). This suggeststhat, at one location on the beach, there was a significantinput of fecal contamination that was not likely to be sourcedfrom Trail Creek or Kintzele Ditch. Detailed informationrelated to EC sources and loadings is required to improvemodel predictions, particularly the variability in the back-ground concentrations. The Indiana recreational water qual-ity standards require that the geometric mean of 5 samplesover a 30-day period is less than 125 CFU/100 mL, with nosample testing higher than 235 CFU/100 mL. The model wasable to predict (and the observed data showed) that Mt. BaldyBeach was above the Indiana standard for full-body contactfor recreational waters approximately 10% of the time (Fig-

ure 7a). Recently, a rapid method for detection of ENT hasbeen used (2). Our results suggest that ENT is a viableindicator for freshwater beaches in Lake Michigan, based ontransport and fate. Measurements of in situ die-off rates willprovide additional support to this observation. The use ofthe sewage marker demonstrates the risk associated withhuman sewage, and the enhanced persistence of ENTcompared to EC suggests this to be a surperior indicator ofpollution. While other factors need to be investigated andincorporated into the model to improve these predictions,the findings shown here indicate the usefulness of modelingthe near-shore environment using this approach and in beingable to predict, and thus potentially reduce, threats to humanhealth from use of these recreational waters.

AcknowledgmentsThis research is funded by the NOAA Center of Excellencefor Great Lakes and Human Health and a contract from theNational Park Service. This article is Contribution 1378 ofthe USGS Great Lakes Science Center and GLERL contributionnumber 1393.

Supporting Information AvailableAdditional data and analysis including text, tables, and figures.This material is available free of charge via the Internet athttp://pubs.acs.org.

Literature Cited(1) National Resources Defense Council (NRDC). Testing the

Waters: A Guide to Water Quality at Vacation Beaches; 2004.(2) Wade, T. J.; Calderon, R. L.; Sams, E.; Beach, M.; Brenner, K. P.;

Williams, A. H.; Dufour, A. P. Rapidly measured indicators ofrecreational water quality are predictive of swimming-associatedgastrointestinal illness. Environ. Health Perspect. 2006, 114 (1),24-28.

(3) Scott, T. M.; Jenkins, T. M.; Lukasik, J.; Rose, J. B. Potential useof a host associated molecular marker in Enterococcus faeciumas an index of human fecal pollution. Environ. Sci. Technol.2005, 39 (1), 283-287.

(4) McCorquodale, J. A.; Georgiou, I.; Carnelos, S.; Englande, A. J.Modeling coliforms in storm water plumes. J. Environ. Eng. Sci.2004, 3 (5), 419-431.

(5) Grant, S. B.; Kim, J. H.; Jones, B. H.; Jenkins, S. A.; Wasyl, J.;Cudaback, C. Surf zone entrainment, along-shore transport,and human health implications of pollution from tidal outlets.J. Geophys. Res., [Oceans] 2005, 110 (C10025), 1-20.

(6) Boehm, A. B.; Keymer, D. P.; Shellenbarger, G. G. An analyticalmodel of enterococci inactivation, grazing, and transport in thesurf zone of a marine beach.Water Res. 2005, 39 (15), 3565-3578.

FIGURE 7. Cumulative probability plots showing observed and simulated concentrations for (a) E. coli and (b) enterococci.

FIGURE 8. Comparison of observed and simulated counts of (a) E. coliand (b) enterococci at the Central Avenue Beach.

VOL. 40, NO. 16, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY 9 5027

(7) Nevers, M. B.; Whitman, R. L. Nowcast modeling of Eschericiacoli concentrations at multiple urban beaches of southern LakeMichigan. Water Res. 2005, 39 (20), 5250-5260.

(8) Beletsky, D.; Saylor, J. H.; Schwab, D. J. Mean circulation in theGreat Lakes, international association of Great Lakes research.J. Great Lakes Res. 1999, 25 (1), 78-93.

(9) APHA. Standard Methods for the Examination of Water andWastewater, 20th ed.; 1998.

(10) Hammerum, A. M.; Jensen, L. B. Prevalence of esp, encodingthe enterococcal surface protein, in Enterococcus faecalis andEnterococcus faecium isolates from hospital patients, poultry,and pigs in Denmark. J. Clin. Microbiol. 2002, 40 (11), 4396-4396.

(11) Smith, S. D. Coefficients for sea surface wind stress, heat fluxand wind profiles as a function of wind speed and temperature.J. Geophys. Res. 1988, 93, 15467-15472.

(12) King, I. P. RMA-10 User guide - - A Finite Element Model forThree-Dimensional Density Stratified Flow; 1993. Also, User guideof RMA-11 - - A Three-Dimensional Finite Element Model forWater Quality in Estuaries and Stream; 2004.

(13) Martin, J. P.; McCutcheon, S. C. Hydrodynamics and Transportfor Water Quality Modeling; Lewis Publishers: Boca Raton, FL,1999.

(14) Whitman, R. L.; Nevers, M. B.; Korinek, G. C.; Byappanahalli,M. N. Solar and temporal effects on escherichia coli concentra-tion at a lake Michigan swimming beach. Appl. Environ. Microb.2004, 70 (7), 4276-4285.

(15) Milne, D. P.; Curran, J. C.; Wilson, L. Effects of sedimentationon removal of fecal coliform bacteria from effluents in estuarinewater. Water Res. 1986, 20 (12), 1493-1496.

(16) Alkan, U.; Elliott, D. J.; Evison, L. M. Survival of enteric bacteriain relation to simulated solar radiation and other environmentalfactors in marine waters. Water Res. 1995, 29 (9), 2071-2080.

(17) Medema, G. J.; Bahar, M.; Schets, F. M. Survival of Cryptospo-ridium parvum, Escherichia coli, faecal enterococci and Clostrid-ium perfringens in river water: influence of temperature andautochthonous microorganisms. Water. Sci. Technol. 1997, 35(11-12), 249-252.

(18) Sinton, L. W.; Hall, C. H.; Lynch, P. A.; Davies-Colley, R. J. Sunlightinactivation of fecal indicator bacteria and bacteriophages fromwaste stabilization pond effluent in fresh and saline waters.Appl. Environ. Microbiol. 2002, 68 (3), 1122-1131.

(19) Davies, C. M.; Evison, L. M. Sunlight and the Survival of EntericBacteria in Natural Waters. J. Appl. Bacteriol. 1991, 70 (3), 265-274.

(20) Menon, P.; Billen, G.; Servaisa, P. Mortality rates of autoch-thonous and fecal bacteria in natural aquatic ecosystems. WaterRes. 2003, 37 (17), 4151-4158.

(21) Thomann, R. V.; Mueller, J. A. Principles of Surface Water Qualityand Control; Harper Collins: New York, 1987.

(22) Eadie, B. J. Probing particle processes in Lake Michigan usingsediment traps. Water., Air., Soil Pollut. 1997, 99 (1-4), 133-139.

Received for review February 23, 2006. Revised manuscriptreceived May 26, 2006. Accepted May 30, 2006.

ES060438K

5028 9 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 40, NO. 16, 2006

Environmental Science & Technology, es060438k (2006)

Modeling the Transport and Inactivation of E. coli and

Enterococci in the Near-Shore Region of Lake Michigan

Lubo Liu1, Mantha S. Phanikumar1∗, Stephanie L. Molloy2, Richard L. Whitman3,Dawn A. Shively3, Meredith B. Nevers3, David J. Schwab4, and Joan B. Rose2

1Department of Civil & Environmental Engineering2Department of Fisheries and Wildlife

Michigan State University, East Lansing, MI 48824.3Lake Michigan Ecological Research Station, U.S. Geological Survey, Porter, IN

4NOAA Great Lakes Environmental Research Laboratory (GLERL), Ann Arbor, MI∗ Corresponding Author Phone: (517) 432-0851; e-mail: phani@egr.msu.edu

Supporting Information

1 Horizontal Mixing

In the momentum equations (2) and (3), horizontalmixing was described using the Smagorinsky eddy pa-rameterization, as shown below.

εS = αA

[(∂u

∂x

)2

+

(∂v

∂y

)2

+12

(∂u

∂y+

∂v

∂x

)2] 12

(S1)

where εS is the viscosity computed by the Smagorin-sky formulation (Smagorinsky, 1963), α is a constantin the range 0.01-0.5 and A denotes the area of thecurrent element. A value of α = 0.1 was used keep-ing in mind the fine resolution of the mesh. Similarto the eddy viscosity, turbulent diffusion in the trans-port equations (equation 4 in the paper) represents allthose processes that can not be explicitly resolved bythe computational grid. Turbulent diffusion values areusually estimated using either scale arguments and em-pirial relations (e.g., Richardson’s 4/3 power law) orfrom dye diffusion studies conducted in the near-shoreregion. Based on dye studies, Inman et al. (1971) re-ported turbulent diffusion values in the range 2.0 to 5.9m2/s for Scripps Beach in California. We used a con-stant diffusion coefficeint of 2 m2/s in the near-shoreregion but values in the range 2 to 10 m2/s producedsimilar results. Since our hydrodynamic and transportmodels used the same computational grid, we used the

same values for both eddy viscosity and turbulent diffu-sion in the near-shore region (Holland et al., 2003). Inthe offshore region, eddy diffusion values in our modelchanged with grid size and velocity as shown below.

D = αD|V|LS (S2)

where αD is a constant, V is the velocity vector andLS is a characteristic length scale (element size). E.coli distributions in the Mt. Baldy area using a turbu-lent diffusion value of 2.0 m2/s are shown in Figure 1.The flow reversals predicted by the model were also ev-ident from our ADCP data. The hydrodynamic modelwas calibrated by adjusting the Manning’s roughnesscoefficient n after examining the sensitivity of modelcurrents to the horizontal viscosity. A constant Man-ning’s coefficient of 0.1 was used in the model.

2 Near-Shore Processes

The effects of buoyancy, waves, and sediment resuspen-sion events could potentially influence the transport ofenteric bacteria. The long-shore current componentis an important part of the circulation pattern in thenear-shore region (Grant et al., 2005). During the timeperiod we modeled (July 12 - August 13), the waveheight recorded at the Burns Ditch ADCP in 10 m wa-ter depth only exceeded 1 m on two occasions. OnJuly 23-24, the wave height was over 1 m for about 26hours with a maximum of 1.5 m. On August 5-6, waveheights were over 1m for about 36 hours with a peak of1.9 m. Waves only create long-shore currents inside of

1

Liu et al.: Transport and Inactivation of E. coli and Enterococci in Lake Michigan

the wave breaking line which occurs at a depth approx-imately 1.3 times the offshore wave height. There areonly two occasions during the simulation period whenwaves might generate significant long-shore currents,and these currents would only affect the computationalelement nearest to the shore (assuming the size of theelements is about 100 m), and even then would proba-bly only serve to slightly augment the wind-generatedlong-shore current. Sediment resuspension events areimportant in Lake Michigan. Satellite images show anannually occurring major sediment resuspension eventin late winter and early spring (Lou et al., 2000). Theimages show a sediment plume approximately 10 kmwide and extending over 200 km along the southernshore of the lake (Eadie et al., 1996). In Lake Michi-gan, the fine sands are mainly located at water depthsgreater than 30 m. The most energetic currents andwaves occur during winter and spring storms, whentemperature gradients in the lake are lowest and windsare strongest. During the one month simulation periodno major sediment events were recorded and thereforenot incorporated into our modeling. Buoyancy effectscould potentially play an important role in near-shoremixing and transport. Warm runoff flowing into a coldlake can form a surface lens and produce a plume thathugs the shoreline (especially for winds blowing fromthe north) since it is relatively easy to mix waters in thesurface layers. An examination of the buoyancy flux(Fischer et al., 1979) into the near-shore region for thesummer conditions showed that, for a mean dischargeof 2.19 m3/s from Trail Creek and a 2 ◦C temperaturedifference between the lake and outfall waters, buoy-ancy is unlikely to be important compared to the effectsof wind-driven circulation. These effects are thereforenot included in our modeling.

3 Settling Velocities

Based on Stokes’ formula (Chapra, 1997), the settlingvelocity of a particle is directly proportional to thesquare of the particle diameter and the density differ-ence between water and the bacterium.

vs = αfg

18

(ρs − ρw

µ

)d2 (S3)

Here µ (g/cm.s) is the dynamic viscosity of water, ρs

and ρw are the densities of the bacterium and water(g/cm3) and αf is a dimensionless form factor thataccounts for the shape of bacteria (αf = 1 for sphericalshapes). Thomann and Mueller (1987) re-expressed theStoke’s law in a more convenient form using a value of0.014 g/cm.s for the viscosity of water:

vs = 0.033634α(ρs − ρw)d2 (S4)

Figure 1: E. coli distribution around Trail Creek andKintzele Ditch on Julian Days 197 and 217. The direc-tion of the currents is marked with an arrow.

where vs is in m/d, d is in µm and the densities arein g/cm3. The effective diameter and density rangesfor E. coli and enterococci bacteria were obtained fromthe literature (Characklis et al., 2005; Nazaroff andAlvarez-Cohen, 2001; Linsley et al., 1992; Bratbak andDundas, 1984 ) and the average settling velocities aresummarized in Table 1.The table shows that settling velocities are low if weconsider the bacteria to be planktonic or free-living.Bacteria are either planktonic (in the 1 µm size range)or associated with sediments (in the 10 µm range orabove). There is evidence in the literature to sug-gest that bacteria are associated with suspended solids(Characklis et al., 2005; Jamieson et al., 2005; Cham-berlin and Mitchell, 1978: Gannon et al., 1983). Ifwe assume that this is the case, then we obtain signifi-cantly higher settling velocities. We considered silt par-ticles and two different particle diameters in the aboveexample. For simulations reported in the paper, weassumed that bacteria are associated with suspendedmaterial and used vs = 5 m/d, which corresponds tosilt particles in the 10 µm range. The 5 m/day veloc-ity estimate is also supported by earlier observationsmade in Lake Michigan using sediment traps (Eadie,1997). Even for this relatively high velocity, we foundthat settling losses makeup an insignificant part of theoverall inactivation rate. To arrive at this conclusion,we plotted different terms of the overall inactivation

2

Liu et al.: Transport and Inactivation of E. coli and Enterococci in Lake Michigan

190 195 200 205 210 215 220 225 2300

0.2

0.4

0.6

0.8

1

1.2

1.4

Julian Day, 2004

Inac

tivat

ion

Rat

e (d

ay−1

)

Overall Rate (term 1)Settling Losses (term 2)Sunlight−modulated (term 3)

}Eq. (S5)

Figure 2: Relative contributions of settling and solarinsolation to the overall inactivation of E. coli at theMt. Baldy Beach. All parameters are the same asin Figure 6 in the paper (θ = 1.07, vs = 5m/d, kI =0.0026W−1m2d−1, fp = 0.1)

rate as a function of time as shown in Figure 2.

k(I, T, vs)︸ ︷︷ ︸(1)

=(fp

vs

H+ kII(t)

)θ(T−20)

=fpvs

Hθ(T−20)

︸ ︷︷ ︸(2)

+ kII(t)θ(T−20)

︸ ︷︷ ︸(3)

(S5)

Figure 2 shows the terms (1), (2) and (3) plotted as afunction of time. It is clear that sunlight is the mostdominant component of the overall inactivation. Sinceterms (2) and (3) in equation (S5) have been temper-ature corrected and plotted in Figure 2, we ran ad-ditional simulations for different values of θ to under-stand the effect of temperature (Figure 3). Since therange of θ and vs values used in our simulations is rep-resentative of field conditions, we conclude that theeffects of temperature and settling are relatively weakand that sunlight plays the most dominant role in in-activation. However, additional numerical simulations,sensitivity analyses and field observations are neededto test this conclusion. The relative importance of set-tling losses and temperature depends on the values ofthe parameters vs, T and θ. The slight variation interm (2) in Figure 2 (the blue line) is due to changesin the water depth, H over the one month simulationperiod.

4 RMSE

The root mean squared error for the comparisons re-ported in the paper was computed based on the log-

concentrations as follows:

RMSE =

√√√√ 1N

N∑

i=1

[log10(Csim)− log10(Cobs)]2 (S6)

where Csim and Cobs are the simulated and observedconcentrations respectively and N is the number of ob-servations. Table 2 summarizes the RMSE values forall the comparisons shown in the paper. We note thatthe RMSE values for the light-based inactivation rateare higher compared to the values for the first-orderrates in some cases. This is due to the fact that wedid not optimize the parameters in equation (S5). Thelight-based formulation is more general as it allows therelative importance of terms 2 and 3 in (S5) to changewith time (unlike the first-order inactivation formula-tion).

190 195 200 205 210 215 220 225 2300

200

400

600

800

1000

1200

1400

Julian Day, 2004

E. c

oli

(C

FU

/100

mL

)

DataNo temperature effect: θ = 1.0θ = 1.07θ = 1.10

Figure 3: Effect of temperature correction factor θ onthe E. coli simulations for the Mt. Baldy Beach

5 References

1. Bratback, G.; Dundas, I. Bacterial dry matter con-tent and biomass estimations. Appl. Environ. Mi-crobiol. 1984, 48(4), 755-757.

2. Chamberlin, C. E.; Mitchell, R. A Decay Model forEnteric Bacteria in Natural Waters, In R. Mitchell(ed) Water Pollution Microbiology. 1978, 2, 325-348. John Wiley & Sons: New York.

3. Chapra, S.C. Surface Water Quality Modeling,McGraw-Hill: New York, 1997.

4. Characklis, G. W.; Diltsb, M. J.; Simmons III, O.D.; Likirdopulosc, C. A.; Krometisc, L. H.; Sobsey,M. D. Microbial partitioning to settleable particlesin stormwater. Water Res. 2005, 39, 1773-1782.

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Liu et al.: Transport and Inactivation of E. coli and Enterococci in Lake Michigan

Table 1: Average Settling Velocities for E. coli and EnterococciDiameter (d) Density (ρ) Average Settling Velocity (vs)

E. coli 1 - 2.5 µm 1.09 - 1.13 g/cm3 0.011 m/dEnterococci 1 - 4.0 µm 1.09 - 1.13 g/cm3 0.023 m/d

Silt 10 µm, 20 µm 2.65 g/cm3 5.55, 22.2 m/d

Table 2: Summary of RMSE values for the different comparisons shown in the paper.k RMSE Remarks

k = 0.5 (first-order) 0.835 Mt. Baldy E. colik = 0.8 (first-order) 0.770 Mt. Baldy E. colik = 2.0 (first-order) 0.705 Mt. Baldy E. coli

k = k(I, T, vs) 0.808 Mt. Baldy E. colik = 0.5 (first-order) 0.991 Mt. Baldy enterococcik = 0.8 (first-order) 0.936 Mt. Baldy enterococcik = 1.5 (first-order) 0.866 Mt. Baldy enterococci

k = k(I, T, vs) 0.932 Mt. Baldy enterococcik = k(I, T, vs) 0.829 Central Avenue E. colik = k(I, T, vs) 0.553 Central Avenue enterococci

5. Eadie, B. J.; Schwab, D. J.; Leshkevich, G. A.; Jo-hengen, T. H.; Assel, R. A.; Hawley, N.; Holland,R. E.; Lansing, M. B.; Lavrentyev, P.; Miller, G.S.; Morehead, N. R.; Robbins, J. A.; Van Hoof,P. L. Recurrent coastal plume in southern LakeMichigan. EOS Trans. AGU. 1996, 77, 337-338.

6. Eadie, B. J. Probing particle processes in LakeMichigan using sediment traps. Water. Air. Soil.Poll. 1997, 99, 133-139.

7. Fischer, H. B.; List, E. J.; Koh, R. C. Y.; Im-berger, J. Brooks, N. H. Mixing in Inland andCoastal Waters; Academic: New York, 1979.

8. Grant, S. B.; Kim, J. H.; Jones, B. H.; Jenkins, S.A.; Wasyl, J.; Cudaback, C. Surf zone entrain-ment, along-shore transport, and human healthimplications of pollution from tidal outlets. J.Geophys. Res. 2005, 110 (C10025), 1-20.

9. Gannon, J. J.; Busse, M. K.; Schillinger, J. J. Fecalcoliform disappearance in a river impoundment.Water Res. 1983, 17, 1595-19601.

10. Holland, P. R.; Kay, A.; Botte, V. Numerical mod-elling of the thermal bar and its ecologicalconse-quences in a river-dominated lake. J. Marine Syst.2003, 43, 61-81.

11. Inman, D. L.; Tait, R. J.; Nordstrom, C. E. Mixingin the Surf Zone. J. Geophys. Res. 1971, 76 (15),3493-3514.

12. Jamieson, R.; Joy, D. M.; Lee, H.; Kostaschuk, R.;Gordon, R. Transport and deposition of sediment-

associated Escherichia coli in natural streams.Water Res. 2005, 39, 2665-2675.

13. Linsley, R. K.; Franzini, J. B.; Freyberg, D. L.,Tchobanoglous, G. Water Resources Engineering,McGraw-Hill: New York, 1992.

14. Lou, J.; Schwab, D. J.; Beletsky, D.; Hawley, N.A model of sediment resuspension and transportdynamics in southern Lake Michigan. J. GeophysRes., 2000, 105 (C3), 6591-6610.

15. Mortimer, C. H. Lake Michigan in Motion; Uni-versity of Wisconsin Press: Milwaukee, 2004.

16. Nazaroff, W. W.; Alvarez-cohen, L. Environmen-tal Engineering Science; Wiley: New York, 2001.

17. Smagorinsky, J. General circulation experimentswith the primitive equations I. The Basic Experi-ment, Mon. Weather Rev. 1963, 91, 99–164.

18. Thomann, R. V.; Mueller, J. A. Principles of Sur-face Water Quality Modeling and Control; Harperand Row: New York, 1987.

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