Modeling the Photoinactivation and Transport of Somatic and F+ Coliphages at a Great Lakes Beach

Abstract

Fecal indicator organisms (FIO), such as E. coli and enterococci, are often used as surrogates of contamination in the context of beach management; however, bacteriophages may be more reliable indicators than FIO due to their similarity to viral pathogens in terms of size and persistence in the environment. In the past, mechanistic modeling of environmental contamination has focused on FIO, with virus and bacteriophage modeling efforts remaining limited. In this paper, we describe the development and application of a fate and transport model of somatic and F+ coliphages for the Washington Park beach in Lake Michigan which is impacted by riverine outputs from the nearby Trail Creek. A three-dimensional model of coliphage transport and photoinactivation is tested and compared with a previously reported E. coli fate and transport model. The light-based inactivation of the phages was modeled using organism-specific action spectra. Results indicate that the coliphage models outperformed the E. coli model, in terms of reliably predicting E. coli/coliphage concentrations at the beach. This is possibly due to the presence of additional E. coli sources that were not accounted for in the modeling. The coliphage models can be used to test hypotheses about potential sources and their behavior and for predictive modeling.

INTRODUCTION

Fecal indicator organisms (FIOs) such as Escherichia coli and enterococci are routinely monitored at recreational beaches to protect the public from exposure to contaminated waterways. Although the use of FIO-based recreational water quality criteria associated with epidemiological studies continues to offer public health protection, illnesses resulting from exposure to contaminated water are primarily caused by viral pathogens (Fong, Phanikumar, Xagoraraki, & Rose, 2010; Shen et al., 2008; Wong et al., 2009). Therefore, viral indicators may be more suitable for beach management, especially because survival of bacterial indicators in natural waters and their response to water treatment are known to be different from those of viral pathogens (Jofre, Lucena, Blanch, & Muniesa, 2016). Bacteriophages are viruses that infect and replicate in a bacterial host, and coliphages are a subset of bacteriophages that selectively infect E. coli (Grabow, 2001; Jofre et al., 2016). Bacteriophages have received attention as being suitable candidates as indicators of viral contamination (Arredondo-Hernandez, Diaz-Avalos, Lopez-Vidal, Castillo-Rojas, & Mazari-Hiriart, 2017; Donnison & Ross, 1995; Muniesa et al., 2018; Palmateer, Dutka, Janzen, Meissner, & Sakellaris, 1991; Shen et al., 2008; Vergara et al., 2015). Two major subgroups of coliphages include somatic and F-specific (F+) coliphages. Although both subgroups infect E. coli, they differ in their routes of infection, and F+ coliphages are not expected to replicate in the environment outside the intestinal tract of warm-blooded animals (Jofre et al., 2016). Both groups of coliphages were found to be abundant in environments that are likely to be contaminated by animal feces, including lakes, rivers and streams, groundwater, and beach sand, as well as in manure and wastewater (Davies-Colley et al., 2005; USEPA, 2015). These coliphages are comparable to viruses in terms of morphology, including size, shape, surface properties, and persistence in the environment, making them suitable as indicators (Jofre et al., 2016). Because of this suitability, there is continuing interest in using coliphages as alternative indicators for managing recreational beaches (USEPA, 2015; Wanjugi et al., 2018). Other advantages include association of coliphages with human viruses (Ballester, Fontaine, & Margolin, 2005; Jiang, Noble, & Chu, 2001), support from epidemiological studies (Colford et al., 2007; Wade et al., 2010; Wiedenmann et al., 2006), and cost-effective and reliable detection methods (Jofre et al., 2016).

Previous research has shown that sunlight inactivation, defined by loss of culturability, is an important loss mechanism in nearshore waters for microorganisms, including indicator bacteria such as E. coli as well as viruses and bacteriophages (Davies-Colley et al., 2005; Hipsey, Antenucci, & Brookes, 2008; Mattle, Vione, & Kohn, 2015; Nguyen, Silverman, & Nelson, 2014; Silverman, Nguyen, Schilling, Wenk, & Nelson, 2015; Sinton, Finlay, & Lynch, 1999, 2002; USEPA, 2015; Zepp et al., 2018). Viruses are generally believed to be more resistant to solar radiation than bacteria (Davies-Colley et al., 2005; Sinton, Hall, Lynch, & Davies-Colley, 2002). A major portion of the energy received from the sun is in the form of shortwave radiation in the wavelength range 100–780 nm. The shorter wavelengths cause more damage to organisms in water, with ultraviolet (UV)-C bandwidths (250–280 nm) being the most potent and lethal. However, UV-C radiation is completely absorbed by the ozone layer, making UV-B wavelengths (280–320 nm) the most important from the point of virus inactivation in natural waters (Sinton et al., 2002). The direct inactivation potential (or the endogenous mechanism in which photons are absorbed by virus particles causing inactivation) declines as wavelengths approach the UV-A region (320–400 nm) (Hipsey et al., 2008). On the other hand, the exogenous mechanism involves external sensitizer compounds, such as dissolved organic carbon or reactive oxygen species, that absorb light (Silverman et al., 2015). These photosensitizers can directly react with viruses after light absorption and cause inactivation. Different organisms respond differently to these wavelengths, and information linking photoinactivation to specific wavelengths for a particular organism is referred to as the “photoaction spectrum” (or simply “action spectrum”). The action spectra, also called biological weighting functions (BWFs), are mathematical relations based on laboratory and field data (Nelson et al., 2018; Nguyen, Silverman, & Nelson, 2014; Silverman et al., 2015).

Environmental factors such as temperature, pH, salinity, and organic and inorganic matter within the water column are known to modulate the effects of sunlight (Feng, Ong, Hu, Tan, & Ng, 2003; Jończyk, Kłak, Międzybrodzki, & Górski, 2011; Langlet, Gaboriaud, & Gantzer, 2007; Schaper, Durán, & Jofre, 2002; USEPA, 2015; Zepp et al., 2018). Somatic and F+ coliphages are among the most persistent viruses at ambient temperatures, and virus inactivation is significantly faster at temperatures above 50 °C than below 50 °C (Bertrand, Schijven, Sánchez, Wyn-Jones, & Ottoson, 2012; Romero, Straub, Kohn, & Nguyen, 2011; Seo, Lee, Lim, & Ko, 2012). Allwood, Malik, Hedberg, and Goyal (2003) found that the F+ coliphage MS2 survived three times longer than E. coli at 25 °C, although the two survival rates were comparable at higher temperatures. Somatic coliphages were found to be highly persistent for all temperatures and media reported in the literature (Bertrand et al., 2012; Hipsey et al., 2008).

Although a large number of studies have evaluated coliphages as potential indicators of fecal contamination (Jofre et al., 2016; Ravva & Sarreal, 2016; USEPA, 2015; Wong et al., 2009; Wu, Long, Das, & Dorner, 2011; Zepp et al., 2018), a number of confounding factors make it difficult to generalize conclusions from individual studies. These include differences in the relative contributions of different sources at field sites as well as differences in detection methods used and the relative importance of transport processes across sites. Mechanistic modeling of coliphages and traditional indicator bacteria such as E. coli for the same site and study period may offer additional insights into the generalizable similarities and differences between viral and bacterial indicators as surrogates of human pathogenic viruses in natural waters. However, previous mechanistic modeling efforts for coliphages were limited either to detailed hydrodynamic and transport models coupled with relatively simple descriptions of the complex photoinactivation processes (Abu-Bakar, Ahmadian, & Falconer, 2017) or detailed modeling of photoinactivation processes of essentially laboratory systems that do not have the complexities of field sites (Silverman & Nelson, 2016). To the best of our knowledge, the present work represents the first comprehensive application of a coliphage model that combines hydrodynamic and transport modeling with mathematical descriptions of photoinactivation to assess the predictability of coliphages at field sites; this is the major contribution of this work. After testing the coliphage models using field observations, we evaluate a model of E. coli using a new E. coli dataset collected at the same time the coliphage data were collected and compare the relative performance of both (coliphage and E. coli) models; this is the second major contribution of this work. Predictive modeling of FIO for beach management is an attractive alternative to the current practice based on testing water samples, which is slow due to the 24–48 h required to run the assays. Once tested, mechanistic models, such as the ones described in this paper, can be used to make real-time or near–real-time predictions to issue beach closures and advisories. In this context, if coliphages are to be considered as alternative indicators, it is important to know if coliphage models can be developed that provide comparable or superior performance relative to models of current indicators such as E. coli. Therefore, the objectives of the current research are to (a) describe the development and application of mechanistic models of fate and transport for somatic and F+ coliphages, (b) test the models using field data collected at a Great Lakes beach, (c) evaluate models for coliphages relative to a previously developed model of E. coli fate and transport for the same beach site, and (d) understand similarities and differences between coliphages and E. coli as indicators of microbiological contamination at a beach.

MATERIALS AND METHODS

Site Description

Washington Park Beach is a historic public beach located on Lake Michigan. It is located at 115 Lakeshore Drive, Michigan City, LaPorte County, IN, and covers a distance of approximately 1,070 m. Figure 1 shows the sample location (marked “WP Beach”) with coordinates (86.904057 W, 41.729335 N). Bathymetry in the nearshore region around the sample location is shown in Supplemental Figure S1. Discharge from nearby Trail Creek, which is recorded at USGS gauging station 04095380 (Figure 1) and used as input to the hydrodynamic model, affects the shoreline on either side of the outfall, depending on prevailing local circulation patterns and wind speed and direction. Notable nearshore features that play an important role in the transport of material originating from the river mouth include orientation of the beach relative to the horizontal as well as the presence of an offshore breakwater that deflects river plumes away from the beach site on most days. The attached breakwater extending from the river outlet guides plumes offshore and to the northwest, and the detached breakwater offshore redirects the plumes in the northeast and southwest directions, away from Washington Park beach (Supplemental Figure S1). The outfall of a wastewater treatment plant (Michigan City Sanitation Department - Gifford Wastewater Treatment Plant) is located on Trail Creek at the location marked “WWTP” in Figure 1. Time series data in the form of coliphage and E. coli concentrations were obtained from water quality sampling on the river, and the data were used as input to the model. The sampling location (marked as “River” in Figure 1) is downstream of the WWTP outfall; therefore, the WWTP represents a source of both coliphages and E. coli to the river (and eventually the beach site), and this contribution is represented in the model via the river input.

Fig. 1.

(a) Map of the study area showing the Washington Park beach and surroundings. Microbial sampling took place at the location marked WP Beach and a USGS gauging station (#04095380) on Trail Creek is also marked. Three acoustic Doppler current profilers (ADCPs) were deployed at LM1, LM2 and LM3. River water quality sampling took place at location marked River which is downstream of a wastewater treatment plant (WWTP).

Coliphage and E. coli Measurements and Photoinactivation Experiments

Details of coliphage and E. coli enumeration methods and observed data from Washington Park used for mechanistic modeling in this work are presented in Wanjugi et al. (2018), and the data are shown in Supplemental Figure S2 in the form of box plots. Briefly, sampling was done 5 d wk−1 (Sunday–Thursday) from June to September 2015. A D-HFUF-SAL method was used for F+ and somatic coliphage enumeration (plaque forming units [PFU] L−1) as described in McMinn, Huff, Rhodes, and Korajkic (2017). The single agar layer procedure was then used (method 1602; USEPA, 2015). Escherichia coli counts (most probable number [MPN] 100 ml−1 of water sample) were obtained using Colilert Quanti-Tray (Idexx). Observed concentrations of coliphages and E. coli at the beach site represent a composite sample of six individual samples collected from two depths (0.3 and 1.0 m). Photoinactivation data were represented by first-order inactivation rate constants computed for each indicator organism following Zepp et al. (2018). The BWFs were computed using the irradiance data and first-order rate constants observed with five different cutoff filters in place (Griffin, Donaldson, Paul, & Rose, 2003). The data were then expressed using best-fit exponential equations of the general form shown below, where A, a, and b are constants, and λ represents wavelength of light. Different sets of constants were used for somatic and F+ coliphages:

$$BWF(\lambda )=B{e}^{a\lambda +b}$$ [1]

where B is a scaling factor with units of m2 J−1 (J denotes energy measured in Joules). The coefficients of the BWFs in Equation 1 for somatic and F+ coliphages as well as their confidence intervals are summarized in Zepp et al. (2018).

Hydrodynamic and Meteorological Data and Modeling

To test the ability of the hydrodynamic model to describe observed currents, three acoustic Doppler current profilers were deployed on 2 June 2015 (day of year [DOY] 153) at depths of 7.7, 15.2, and 7.7 m, respectively. The acoustic Doppler current profiler locations (marked LM1, LM2, and LM3) are shown in Figure 1. Both currents and their directions were recorded through 2 Sept. 2015 (DOY 245) at these locations. The time series of discharge (Supplemental Figure S3a) measured at the USGS Station 04095380 on Trail Creek (Figure 1) was used as input to the hydrodynamic model. Positive values (Supplemental Figure S3a) indicate water flowing from Trail Creek to Lake Michigan with a maximum value of 75.3 m3 s−1, and negative values indicate flow reversals (maximum value, −68.6 m3 s−1). The average daily discharge during the study period was 0.28 m3 s−1.

An unsteady, three-dimensional hydrodynamic model of Lake Michigan based on the unstructured-grid Finite-Volume Community Ocean Model (Chen, Liu, & Beardsley, 2003, 2006) was used in the present work. This model has been tested and used extensively in previous modeling efforts involving lakes and rivers in the Great Lakes region (Anderson & Phanikumar, 2011; Nguyen, Thupaki, Anderson, & Phanikumar, 2014, 2017; Safaie et al., 2016; Safie, Dang, et al., 2017; Safie, Litchman, & Phanikumar, 2017). Heat flux and momentum fields over the lake surface were calculated from wind speed, wind direction, air temperature, cloud cover, and relative humidity and evaluated at the element centroids and nodes of the model grid domain. In this study, we used hourly meteorological data obtained from the National Oceanic and Atmospheric Administration (NOAA) National Data Buoy Center (NDBC) and National Centers for Environmental Information (NCEI). We used 29 NDBC stations and 30 NCEI stations around Lake Michigan. Additional details, including surface heat flux formulations, are described in Nguyen, Thupaki, et al. (2014). Incoming shortwave radiation calculations are described by Bunker (1976), with the clear-sky shortwave radiation calculated using the methods described by Annear and Wells (2007). The incoming long-wave radiation was calculated following Parkinson and Washington (1979), and the sensible and latent heat transfers were calculated at each grid point based on the COARE 2.6 bulk aerodynamic formulation (Fairall, Bradley, Rogers, Edson, & Young, 1996).

Coliphage and E. coli Fate and Transport Models

The fate and transport model for the coliphages and E. coli is based on the following advection dispersion reaction equation:

$$\frac{\partial C}{\partial t}+u\frac{\partial C}{\partial x}+v\frac{\partial C}{\partial y}+w\frac{\partial C}{\partial z}=\frac{\partial }{\partial x}\left(K_H\frac{\partial C}{\partial x}\right)+\frac{\partial }{\partial y}\left(K_H\frac{\partial C}{\partial y}\right)+\frac{\partial }{\partial z}\left(K_V\frac{\partial C}{\partial z}\right)+S$$ [2]

where C denotes the concentration of either coliphages (PFU L−1) or E. coli (MPN L−1), and S denotes a loss term described below. The variables u, v, and w are unsteady velocities in the x, y, and z directions, respectively; KH and KV represent horizontal and vertical mixing coefficients, respectively; and t denotes time. In Equation 2, the horizontal eddy diffusivity coefficient KH is related to the horizontal eddy viscosity coefficient in the momentum equations via the turbulent Prandtl number, and horizontal mixing in the model is based on the Smagorinsky formulation (Pope, 2000; Smagorinsky, 1963). The vertical mixing coefficient KV is computed using the Mellor–Yamada turbulence closure scheme (Mellor & Yamada, 1982). Details of these mixing schemes can be found in Chen et al. (2003, 2006). The loss term S takes different forms depending on whether E. coli or coliphages are being modeled. A tracer transport module, based on Equation 2 but with S = 0, is used to simulate tracer plumes originating from the river mouth.

Coliphage loss in the water column was modeled using an inactivation rate computed as the cross product of spectral irradiance at a given depth and the BWF for the specific organism (Equation 1) integrated over wavelengths, λ, of the action spectrum (Equation 3):

$$S=-(k_{I,C}C){\theta }_1^{T-20}$$ [3a]

$$k_{I,C}=\int E_{e,\lambda }(z,\lambda )\times BWF(\lambda )d\lambda$$ [3b]

$$E_{e,\lambda }(z,\lambda )=E_{e,\lambda }(0,\lambda )e^{-k_d(\lambda )z}$$ [3c]

where Ee, λ(0,λ) denotes the wavelength-dependent surface irradiance, kI,C denotes the photoinactivation rate of coliphages (h−1), and BWF(λ) (m2 W−1 h−1) denotes the biological weighting function for the coliphage being modeled (Silverman & Nelson, 2016). If Φe denotes the radiant energy (units: W) received at a surface whose area is A (m2), then irradiance Ee (W m−2) and spectral irradiance Ee,λ (W m−2 nm−1) can be expressed as:

$${E_e=\frac{\partial {\mathrm{\Phi }}_e}{\partial A},E}_{e,\lambda }=\frac{\partial E_e}{\partial \lambda }$$ [4]

The Tropospheric Ultraviolet and Visible (TUV) model, a surface solar irradiance model developed by researchers at the National Center for Atmospheric Research (Madronich, 1993; Madronich & Flocke, 1999), was used to compute Ee, λ(0,λ). Spectral absorption coefficients (molar absorptivity as a function of wavelength λ) were measured for water samples collected at the beach and river sites, and the data were used to compute the diffuse attenuation coefficients kd(λ) for Equation 3 following Zepp et al. (2018), which allowed the computation of irradiance at any depth z using Equation 3c. Additional details can be found in Miller, Moran, Sheldon, Zepp, and Opsahl (2002) and Zepp and Cline (1977). The TUV model accounts for the geographical location and time of day (NCAR, 2019) as well as the total column ozone amount on a given day. Ozone data were obtained from the NOAA-EPA Brewer Spectrophotometer UV and Ozone Network service (NOAA Earth System Research Laboratory, Global Monitoring Division, data available at https://www.esrl.noaa.gov/gmd/grad/neubrew/). The ozone data were used as input to the TUV model. The wavelength-dependent (290–329 nm) irradiance data were then multiplied by the BWF (Equation 1) and integrated over wavelengths to compute the photoinactivation rates kI,C. In the above calculation, θ1 is a temperature correction factor for coliphages. Previous research has shown that the mortality rates of somatic coliphages change little with temperature, with θ1 ≈ 1.01 (Hipsey et al., 2008), and that F+RNA coliphages are generally stable below 25 °C (Allwood et al., 2003); therefore, considering the observed temperature variation during our study period (Supplemental Figure S4), the temperature effect is assumed to be negligible for coliphages (θ1 = 1.0). The penetration of surface irradiance into water at the beaches and tributaries was determined using the absorption coefficients of water samples from these sites assuming Beer–Lambert propagation of the downwelling light, as shown in Equation 3c. The most essential part of the inactivation rate calculation was the use of BWF derived from indoor phage kinetics experiments (Griffin et al., 2003). The weighting functions provide the spectral characteristics of the phage photoinactivation that are required to compute inactivation rates. These inactivation rates for the F+ and somatic coliphages were then normalized to surface inactivation rates that were measured in the summer of 2015 to better express their variability with depth.

The E. coli model is not based on BWFs for E. coli (Silverman & Nelson, 2016) but includes base mortality, losses due to settling, and solar inactivation (Equation 5) as described in Safaie et al. (2016). The loss term S for E. coli is represented as:

$$S=-\left(\frac{\partial (f_P{v}_{S}C)}{\partial z}+k_{I,EC}{I}_0{e}^{-k_{e}z}C+k_{b}C\right){\theta }_2^{T-20}$$ [5]

where I0 denotes shortwave radiation at the water surface (W m−2); ke is the sunlight extinction coefficient for shortwave radiation (m−1); kI,EC is the solar inactivation rate relative to shortwave radiation, including both photosynthetically active radiation and UV wavelengths (m2 W−1 h−1); kb represents an empirically derived base mortality rate for E. coli; fP and vS denote the fraction of bacteria attached to suspended matter within the water column and the settling velocity of bacteria attached to suspended material, respectively; and θ2 is a temperature correction factor for E. coli. The E. coli model has been tested (Liu et al., 2006; Thupaki, Phanikumar, Beletsky, Schwab, & Nevers, 2010, 2013), and the parameters used to simulate a new set of E. coli observations in the present work are the same as those reported in Safaie et al. (2016).

To quantitatively evaluate models of F+ and somatic coliphages as well as E. coli and to avoid biases in judgment that may result from the use of a single metric, we have used multiple model performance metrics (described in Supplemental Material) because no single metric captures all aspects of the comparisons (Legates & McCabe, 1999). The metrics used include the RMSE, R2, percent bias, the Nash–Sutcliffe efficiency, RSR (RMSE to the SD of measured data, a standardized version of RMSE) (Fry, Hunter, Phanikumar, Fortin, & Gronewold, 2013; Safaie, Litchman, & Phanikumar, 2017), and the normalized Fourier norm (Thupaki, Phanikumar, Schwab, Nevers, & Whitman, 2013). A Taylor diagram (Taylor, 2001) was also used to compare the three models. Additional details of these metrics and their meanings and the Taylor diagram are included in the Supplemental Material.

The coupled hydrodynamic and transport models were run with a simulation period starting on 10 May 2015 (DOY 130) and ending on 30 Sept. 2015 (DOY 273) to allow sufficient model spin-up time. Initial conditions for the model were based on a lake at rest at a constant average temperature measured at the NDBC buoy 45007 in Lake Michigan on 10 May 2015. After testing the stability of numerical models based on the Courant–Friedrichs–Lewy criterion, the external time step used was 1 s, and the ratio of internal to external time step was 5. Because the model uses small time steps, it is important to accurately represent riverine fluxes of water and bacteria/viruses entering the nearshore lake environment (Supplemental Figure S3). Absolute values of the daily-average discharge in Supplemental Figure S3a (solid blue line) are significantly smaller compared with the absolute values of instantaneous discharge (red line) recorded at the USGS station. Although there was bidirectional flow into and out of the river throughout the study period, after DOY 218, the average daily discharge remained negative. To better represent these dynamics, hourly inflow concentrations of bacteria and viruses at unsampled times at Trail Creek were estimated using probability distributions as reported previously (Bravo, Mclellan, Klump, Hamidi, & Talarczyk, 2017; Madani, Seth, Leon, Valipour, & McCrimmon, 2020). This method was described and examined in Safaie et al. (2016), and additional details are included in the Supplemental Material.

RESULTS AND DISCUSSION

Observed E. coli and coliphage concentrations at the river mouth and the beach site are shown in the form of box plots in Supplemental Figure S2. At both sites the concentrations of F+ coliphages were the lowest, followed by somatic coliphages, and E. coli concentrations were the highest (Wanjugi et al., 2018). Levels of E. coli and coliphages decreased at the beach site compared with the river site (Supplemental Figure S2) due in large part to mixing/dilution.

Comparisons between observed and simulated currents and temperature are included in Supplemental Figures S7 and S8. To facilitate direct comparisons between model results and observations and to closely mimic the sampling protocol used at the beach site, simulated coliphage and E. coli concentrations were generated at the same locations and depths (0.3 and 1.0 m) where samples for the composite sample were collected. Comparisons between observed and simulated concentrations are shown in Figure 2, in which the solid black line in each panel corresponds to the average of the concentrations at the six different locations and represents the “composite sample” based on simulations. To show the variability within the sample, simulated concentrations at the six individual stations were plotted using light gray lines and superimposed on the solid black line, which represents the average. Overall, a majority of the observed data fall within the range of variability simulated by the model (Figure 2). Visual inspection of the time series comparisons in Figure 2 shows that comparisons for all three organisms look similar; therefore, multiple quantitative metrics of model performance (summarized in Table 1) were used to identify superior models. Several important conclusions can be drawn from the comparisons in Figure 2 and the metrics in Table 1. First, models for the two coliphages outperformed the E. coli model because several peaks in observed E. coli after DOY 218 were not adequately captured. This observation is supported by the model performance metrics against observed data, as summarized in Table 1, including R2 and RMSE. Based on the metrics in Table 1, the best agreement with data was obtained for the F+ coliphage model, followed by the models for somatic coliphage and then E. coli. Additional details, including the definitions and meanings of the metrics, are in the Supplemental Material. The three models are compared using a Taylor diagram in Supplemental Figure S13, which shows that the performance of the two coliphage models was similar, although the best model was that of F+ coliphage, which had the lowest normalized standard deviation (relative to data) and bias of all three models. We also notice from the comparisons in Figure 2 that a number of peaks associated with E. coli and, to a lesser extent, somatic coliphage, were not captured by the models. On the other hand, F+ coliphage peaks were captured by the model for the most part, which is an indication that the riverine source was able to reproduce the observed data for the three indicators with varying degrees of success (F+ and somatic coliphages followed by E. coli).

Fig. 2.

Comparison of observed and simulated concentrations of (a) E. coli (b) Somatic, and (c) F+ coliphages. The black solid line represents the simulation result corresponding to the composite sample from observations. The light gray color lines are the simulation results from all six individual samples of the composite sample. Symbols denote observed data based on the composite sample.

Table 1.

Performance of E. coli and coliphage models evaluated against observed data using different model performance metrics (for definitions of the performance metrics and their meaning, see Supplemental Material).

	NSE	PBAIS	RSR	R2	RMSE	Fn
	[-]	[%]	[-]	[-]	[log(MPN/L)] or [log(PFU/L)]	[-]
E. coli [log10(MPN/L)]	0.42	−5.17	0.76	0.62	0.44	0.16
F+ [log10(PFU/L)]	0.67	4.02	0.57	0.76	0.23	0.47
Somatic [log10 (PFU/L)]	0.67	0.25	0.57	0.75	0.35	0.20

All three models tested in the present work used a single source of contamination originating at the river mouth (although the levels were different for each organism at any instant of time). Model performance was assessed by the ability of each model to reproduce the observed data for the organism of interest. Because hydrodynamic/transport pathways are the same for all three organisms and loss mechanisms are similar, an underlying assumption was that a model that performs relatively poorly requires, in all probability, additional sources or processes beyond those already included in the modeling. Our results indicate that the F+ coliphage model did a better job of predicting the observed F+ coliphage data than did the E. coli model in predicting the observed E. coli data. We note, however, that the prediction accuracy of the different models and the suitability of an indicator for water quality monitoring are two different aspects. Therefore, the superior performance of the coliphage models does not automatically imply that the F+ model is better than the E. coli model for predicting fecal contamination more generally or for predicting public health outcomes. Because coliphages represent fecal contamination associated with the WWTP, and thus human sources, which are of more concern than the sources of E. coli (which likely include birds, resuspension, and perhaps environmental regrowth), predictive modeling of coliphages may be an attractive avenue if the primary interest is human viral contamination. In what follows, we examine ancillary data measured at the beach site in an attempt to infer the importance of additional processes and sources not included in our modeling.

The daily average discharge from the river (red line in Supplemental Figure S3a) shows that, after DOY 218, the contribution from the river to the lake was negligible, on average, because the daily-average discharge remained negative. This implies that, because flow was bidirectional in the freshwater estuary, after DOY 218 the flow entering the river from the lake (negative Q) was slightly larger in magnitude than the flow leaving the river (positive Q) each day. To understand this aspect further, we plotted simulated versus observed concentrations as a 1:1 plot in Supplemental Figure S12. A majority of the mismatches between observations and models for all organisms were associated with negative discharge values. All models (and, in particular, the E. coli model) performed better when daily-average discharge from the river to the lake was positive, and model performance deteriorated when discharge became negative, indicating that additional sources such as beach sand (Boehm, Yamahara, Love, Peterson, & McNeill, 2009; Weiskerger et al., 2019) may have become important during flow reversals. Several E. coli peaks were not captured by the model after DOY 218 because these additional sources were not included in the modeling. Potential impacts of additional sources on nearshore water quality are discussed in the Supplemental Material. The number of birds, humans, and boats in water at the beach site as a function of time during the study period is shown in Supplemental Figure S14.

Our E. coli model is not based on BWFs similar to those reported in Silverman and Nelson (2016); there are pros and cons associated with this choice as it relates to model evaluations because the two coliphage models are based on BWFs. The E. coli model used here has been tested extensively using multiple datasets within the same geographical area (southern Lake Michigan, Indiana shoreline). A new E. coli model based on BWFs can be developed, but it will not be possible to test the model as extensively as the model used here. Safaie et al. (2016) reported high R2 values (∼0.8) for three Ogden Dunes beaches in Lake Michigan, and it is not clear if the use of BWFs will further improve model performance. We acknowledge that, although our primary objective was to report the application of our coliphage models, the use of an E. coli model based on BWFs could further strengthen the model evaluation.

In conclusion, the coliphage models developed by combining detailed photoinactivation process descriptions with unsteady, three-dimensional hydrodynamic and transport models successfully described observed data collected at a freshwater beach. Coliphage concentrations were predicted well by riverine sources alone, and our analysis shows that it may be more difficult to model E. coli accurately compared with coliphages. Overall, in the context of predictive modeling of nearshore water quality, our analysis shows that coliphages may serve as alternative indicators of fecal contamination in recreational waters affected by anthropogenic sources. This is especially true if other sources, including avian fecal matter, contribute E. coli to the beach because coliphages seem to be less ubiquitous than existing FIO species. The modeling approach described in our work can be used at other sites if site-specific data, such as bathymetry, meteorological (winds, solar radiation), and other forcings (tides, riverine discharge), are considered. Once developed and tested, models such as the ones reported in this paper can be used to make near real time predictions of coastal water quality to issue beach closures and advisories whenever concentrations of the indicator organism exceed the local beach action value. Real-time data from weather stations, sensors, and sensor networks can be used as model inputs, as described in Shively et al. (2016). Additional results and discussion are available in the Supplemental Material.

Core Ideas.

• Somatic and F+ coliphages modeled using organism-specific action spectra

• Performance of coliphage models compared with a previously-tested E. coli model

• It may be more difficult to accurately model E. coli due to additional sources/processes involved

• Coliphages may serve as conservative indicators of microbiological contamination