A practical model for sunlight disinfection of a subtropical maturation pond

Accepted Manuscript A practical model for sunlight disinfection of a subtropical maturation pond N.W. Dahl, P.L. Woodfield, C.J. Lemckert, H. Stratton, A. Roiko PII:

S0043-1354(16)30831-4

DOI:

10.1016/j.watres.2016.10.072

Reference:

WR 12470

To appear in:

Water Research

Received Date: 18 August 2016 Revised Date:

26 October 2016

Accepted Date: 27 October 2016

Please cite this article as: Dahl, N.W., Woodfield, P.L., Lemckert, C.J., Stratton, H., Roiko, A., A practical model for sunlight disinfection of a subtropical maturation pond, Water Research (2016), doi: 10.1016/ j.watres.2016.10.072. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Progessive die−off of depth distributed E. coli

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Surface die−off from daytime stratification

0.2 0.3 0.4 0.5

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Progressive vertical mixing via top down natural convection

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A practical model for sunlight disinfection of a subtropical maturation pond

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a

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b

Griffith School of Engineering, Griffith University, Gold Coast, QLD, Australia

Smartwater Research Centre, Griffith University, Gold Coast Campus, Edmund Rice

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Drive, Southport, Queensland 4215, Australia

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N.W. Dahla,∗, P.L. Woodfielda, C.J. Lemckerta,b, H. Strattonb,c, A. Roikob,d

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c

School of Natural Sciences, Griffith University, Nathan Campus, 170 Kessels Road, Nathan, Queensland 4111, Australia

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School of Medicine, Griffith University, Gold Coast Campus, Parklands Drive, Southport,

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Queensland 4222, Australia

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Abstract

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Maturation ponds are a type of waste stabilisation pond (WSP) designed to reduce carbon, nutrients and pathogens in

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the final stages of a WSP wastewater treatment system. In this study, a one-dimensional plug-flow pond model is

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proposed to predict temperature and E. coli concentration distributions and overall pond disinfection performance.

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The model accounts for the effects of vertical mixing and ultraviolet light-dependent die-off rate kinetics.

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Measurements of radiation, wind-speed, humidity and air temperature are recorded for model inputs and good

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agreement with measured vertical temperature distributions and outlet E. coli concentrations is found in an

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operational, subtropical maturation pond. Measurements and the model both show a diurnal pattern of stratification

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during daylight hours and natural convective mixing at night on days corresponding to low wind speeds, strong heat

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input from solar radiation and clear night skies. In the evenings, the thermal stratification is shown to collapse due to

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surface energy loss via longwave radiation which triggers top-down natural convective mixing. The disinfection

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model is found to be sensitive to the choice of die-off kinetics. The diurnal mixing pattern is found to play a vital

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role in the disinfection process by ensuring that pathogens are regularly transported to the near-surface layer where

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ultraviolent light penetration is effective. The model proposed in this paper offers clear advantages to pond designers

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by including geographical specific, time-varying boundary conditions and accounting for the important physical

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aspects of vertical mixing and sunlight inactivation processes, yet is computationally straightforward.

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Keywords:

E. coli, eddy diffusivity, inactivation, ultraviolet, wastewater

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∗Corresponding

author. Address: Building G09, Room 1.02, Griffith School of Engineering, Gold Coast Campus, Griffith University, QLD

4222, Australia. Tel.: +61 (0)7 5552 7608; fax: +61 (0)7 5552 8065

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Email addresses: [email protected] (N.W. Dahl), [email protected] (P.L. Woodfield), [email protected]

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(C.J. Lemckert), [email protected] (H. Stratton), [email protected] (A. Roiko)

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1. Introduction

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Maturation ponds make use of sunlight and other naturally occurring phenomena for disinfection of pathogens and

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reduction of carbon and nutrients in waste stabilisation pond (WSP) wastewater treatment systems (Nelson, 2000;

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Jemli et al., 2002; Kohn and Nelson, 2007). In such systems, the maturation pond is usually the final WSP in a series

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of shallow earthen basins with a typically depth of 1-1.5 m, and is exposed to the atmosphere and has a significant

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effect on the final effluent quality. Predicting and managing the quality of the effluent from these ponds is important

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due to the widespread use of WSP systems, particularly where recycling of treated wastewater is employed as a

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strategy for enhancing water use management (Scheierling et al., 2011; Bichai and Smeets, 2013).

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Inactivation of pathogens and indicator microorganisms present in wastewater has been shown to be affected

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significantly by sunlight under both laboratory and field conditions (Curtis et al., 1992a,b; Davies-Colley et al., 2000;

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Bolton et al., 2010; Kadir and Nelson, 2014; Nguyen et al., 2015; Maraccini et al., 2016a,b). Photoinactivation, or

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inactivation involving sunlight, of pathogens and indicator microorganisms in pond systems can occur via three

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primary mechanisms: endogenous direct, endogenous indirect, and exogenous indirect (Davies-Colley et al., 1999;

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2000). Endogenous direct photoinactivation occurs when photons are absorbed by cellular molecules, causing

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damage to genetic material, such as microbial DNA from ultraviolet-B (UVB) wavelengths (280-320 nm) (Schuch

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and Menck, 2010).Indirect photoinactivation occurs either within (endogenous) or external (exogenous) to the cell

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and involves energy or electron transfer to form reactive species that can then cause cell death (Maraccini et al.,

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2016b). Endogenous indirect photoinactivation is caused mostly by UVB (Maraccini et al., 2016a), while exogenous

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indirect photoinactivation can involve both the ultraviolet spectra and wavelengths extending to 550 nm (Kadir and

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Nelson, 2014).

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The efficacy of UV disinfection in the water column depends strongly on a microorganism’s vertical position and

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proximity to the water surface as sunlight is strongly attenuated in turbid water (Curtis et al., 1994; Davies-Colley et

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al., 2005). The resulting vertical distribution of inactivation means that die-off in the lower water column is reduced,

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reducing overall treatment efficiency. Empirical evidence has been reported by Maïga (2009b) identifying higher

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die-off in shallow microcosms while die-off in microcosms at increasing depth showed little change. Other studies

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have also reported lower concentrations of coliforms present in the near surface region (Brissaud et al., 2003).

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Thermal stratification supresses the vertical transport of heat and mass, further complicating the understanding of

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vertical die-off distributions (Pernica et al., 2013; Yang et al., 2015). Observations from many WSPs, and studies on

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other shallow water bodies, have shown that heat generation from sunlight attenuation warms the upper water

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column producing a stable stratification during sunlit hours (Losordo and Piedrahita, 1991; Gu and Stefan, 1995;

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Brissaud et al., 2003; Badrot-Nico et al., 2009). The physical consequence is to effectively confine microorganisms

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to stratified layers and limit inactivation to those contained within the surface layer only, where sunlight is present.

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While stratification may exist during daylight, the onset of natural convection occurs with surface cooling in the late

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afternoon. In shallow water bodies, like maturation ponds, vertical thermal distributions have been reported to mix

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completely via this mechanism (Losordo and Piedrahita, 1991). In this context, shallow water bodies refer to depths

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where stratification and complete mixing occur diurnally, typically begin less than 3 m.

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Predictions of log unit reduction of target pathogens for the design of new maturation ponds currently use empirical

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ideal flow models which are very convenient but neglect many of the complex interactions between fluid mixing,

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stratification and sunlight disinfection (Ashworth and Skinner, 2011). Furthermore, the effect of transient

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atmospheric boundary conditions is often not included. At the other extreme, computational fluid dynamics (CFD)

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has been applied to existing ponds to account for spatial and temporal effects giving valuable insight into pond

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behaviour (Shilton and Harrison, 2003; Badrot-Nico et al. 2009; Alvarado et al., 2012; Passos et al., 2014) but

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computations can take days, weeks or longer to run. Thus, while CFD models can capture the physics more

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accurately, the computational expense and expertise required reduces the appeal for design purposes.

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A solution to overcome the practical shortcomings of utilizing CFD and weaknesses of perfectly-stirred or simple

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plug-flow reactor models is to develop one-dimensional models to account for the effects of sunlight inactivation and

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vertical mixing. Further, inclusion of transient boundary conditions for site-specific applications is necessary to

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improve on the current models. One-dimensional models have been developed successfully for other water bodies

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(Dake and Harlem, 1969; Herb and Stefan, 2005; Jacobs et al., 2008). This paper makes a unique contribution by

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coupling vertical mixing and sunlight inactivation of E. coli in a one-dimensional model of a maturation pond,

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representing the simplest possible method to account for the spatial and temporal effects. Furthermore, we provide a

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practical set of field data showing the diurnal mixing pattern, E. coli die-off, and boundary conditions for testing of

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this type of model.

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86 2. Methods

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Experimental data were collected from a maturation pond to act as input and validation data for the numerical model.

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Data included two continuous vertical profiles of temperature, E. coli concentrations and atmospheric conditions.

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The one-dimensional numerical model was developed by combining published work on UV disinfection kinetics

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with available fluid mixing and dispersion models for ponds and lakes.

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2.1 Experimental methods

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Field data were collected from an operational maturation pond located South East Queensland (SEQ), approximately

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90 km west of Brisbane. The sewage treatment plant (STP) services a population of approximately 1000 and is

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located within the Lockyer Valley region of SEQ. Typical climate conditions in this region have average daytime air

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temperatures of 31 °C in summer and 20 °C in winter, peak solar radiation of 1200 W m-2 (summer) and 600 W m-2

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(winter) and monthly rainfall averages of 100 mm (summer) and 35 mm (winter).Treatment consists of a screening

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rack to remove large solid items before entering a primary facultative pond, secondary maturation pond (the focus of

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this study), two wetland cells, a series of reed beds and is chlorinated before final discharge to an adjacent, privately

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owned reservoir.

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The maturation pond layout is presented in Fig. 1a, showing five baffles traversing the width at 30 m in length,

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inlet/outlet locations and dimensions. Vertical temperature distributions were sampled within the pond at two

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locations (points 1, 2 in Fig. 1a). Five discrete temperature sensors were used for each vertical distribution along the

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depth sampling at 5 minute intervals. The locations of the two thermistor chains are shown on this schematic. A

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thermistor chain is simply a series of temperature sensors spaced along a line, in this case traversing the vertical

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are the temperature sensors located at a depth of 0, 0.1, 0.3, 0.5 and 0.9 metres below the water surface, respectively.

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Measurements of temperature were recorded over the period of 22 February - 09 March 2015. Meteorological data

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were recorded on site, taking 15 minute averages of air temperature, wind speed, solar radiation, relative humidity

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and absolute pressure; wind direction was recorded as the current direction every 15 minutes.

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Irradiance () profiles were measured on site using a cosine collector (Trios Ramses UV/VIS spectrometer) lowered

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through the water column, measuring at discrete depths for the purpose of determining radiation attenuation

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coefficients. The spectral range measured is 280-700 nm.

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Water samples of 100-500 mL were taken from the maturation pond inlet and outlet, in duplicate, over the period of

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22 February, 2015 – March 9, 2015 at 8 hour intervals (6 am, 2 pm and 10 pm Australia Eastern Standard Time).

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Samples were stored in a refrigerated compartment for no longer than 24 hours before being analysed. E. coli was

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enumerated using the membrane filtration technique (APHA, 1992) with some modifications. Wastewater samples

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were mixed thoroughly, serially diluted in PBS or sterile distilled water and filtered through 0.45 um sterile mixed

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cellulose ester membrane filters (Advantec, Tokyo, Japan) using a CombiSart® manifold filtration unit (Sartorius,

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Gottingen, Germany). The filter was placed on modified mTEC agar plates (BD, Sparks, AR, USA) incubated at

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35 °C for 2 h followed by an additional incubation at 44.5 °C for 24 h. Single magenta colonies were quantified and

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reported as E. coli numbers.

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Duplicate samples were averaged for E. coli counts and Log10 colony-forming units (CFU) per 100 ml-1 are reported

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below from the inlet and outlet.

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2.2 Model Development

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Conservation equations for energy and concentration of living E. coli are given by:

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   =   +     + 

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=











 

(1)

! − " #

(2)

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where is the density (kg m−3),  is the specific heat capacity (J kg−1 K−1), $ is the temperature (°C), t is time (s), %

is the vertical distance measured positive from the water surface downwards (m),  and  are the molecular

 is the volumetric heat thermal conductivity and eddy thermal conductivity, respectively (W m−1 K−1), and 

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generation from shortwave penetration (W m−3). C is the concentration (-),

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concentration (m2 s-1) and kc is the decay rate coefficient (s-1).

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The effect of turbulent convective heat transport from wind shear and internal currents is modelled by the concept of

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eddy diffusion:

d d d

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 = & (01'()*+,) ,

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('()*+,) ,

is the eddy diffusion coefficient of the

(3)

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where keddy(unstable) accounts for buoyancy driven turbulent diffusion (unstable stratification) and keddy(stable) for wind

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driven mixing:

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('()*+,) = 

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where Ri is the Richardson number in the form proposed by Sundaram and Rehm (1973):

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Ri =

3,445

(1,0(6)+)

78.8Ri

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:; <' = > d d

(4)

(5)

@A is the coefficient of thermal expansion (K−1), B is the gravitational constant (m s−2) and (1,0(6)+) in Eq. 4 is

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the neutrally buoyant eddy diffusivity (m2 s−1) (Smith, 1979) given by:

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(1,0(6)+) =

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E ?<'CD  >

F83 ∗

G H3

∗

(6)

where  ∗ is the vertical decay in current velocity (m−1) calculated by  ∗ = 6JH.KL .

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Turbulent mixing as described by Eqs 4 to 6 is a function of depth, wind speed and density gradient (Henderson-

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Sellers, 1984). This kind of one-dimensional diffusion model (Eqs, 1, 4-6) has been applied to large lakes and

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shallow ponds (e.g. Dake and Harlem, 1969; Sundaram and Rehm, 1973; Henderson-Sellers, 1985; Losordo and

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Piedrahita, 1991), the shallowest being 20 cm in depth (Jacobs et al., 2008).

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In the late afternoon, surface cooling creates unstable buoyancy and natural convection is initiated. Thus there is a

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need to include keddy(unstable) in Eq. 3. The unstable layer is effectively mixed from the surface down (Sundaram and

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Rehm, 1973; Bednarz et al., 2009b). This is illustrated in Fig. 2b by an unstable temperature gradient where the

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hatched areas show the depth to which the column will mix (Dake and Harlem, 1969). The temperature gradient is

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approximated by the average temperature (conserving energy and mass) shown by the vertical line separating the

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two hatched areas. Lumley and Panofsky (1964) noted that free convection is far more efficient as a transport agent

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than wind-driven mechanical mixing and as such, it is sufficient to simply set (01'()*+,) (see Eq. 6) to a large

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numerical value to achieve the effect shown in Fig. 2b; here we use (01'()*+,) =  ⋅ 1 W m-1 K-1 (c.f. Losordo

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and Piedrahita (1991)).

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Concentration transport of Eq. 2 (D) is analogous to the transport of heat. Therefore, the vertical transport of

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concentration is determined through a turbulent or effective Lewis number (OG ) , which relates the thermal

diffusivity  +   to mass (concentration) diffusivity ( ). For modelling of turbulent transport of passive

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scalars, turbulent Prandtl, Schmidt and Lewis numbers (OG =   /QR ) are typically assigned (or observed to have)

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similar values in the range from about 0.6 to 1.0 depending on the flow situation (e.g. Reynolds, 1975; Weigand et

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al., 1997; Chang and Cowen, 2002; Tominaga and Stathopoulos, 2007). The near unity values arise in situations

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where the passive scalars are transported predominantly via the same turbulent convective mechanism (Tennekes

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and Lumley, 1972). For Eulerian modelling of dispersion of microorganisms, Elyasi and Taghipour (2006) assumed

a turbulent Schmidt number of 0.7. For the present purpose, OG is assumed to be a constant with a value of unity. In

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the absence of more precise data for dispersion of E. coli, in Eq. 7 we have assumed the same Lewis number applies

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to laminar and turbulent diffusion. Thus:

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where

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diffusivity (m2 s−1).

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Concerning boundary conditions for Eq. 2, the concentration flux at the free surface and at the soil-water interface is

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zero, assuming that in field conditions no losses occur. Adiabatic conditions for Eq. 1 are imposed at the base of the

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soil domain. Soil properties have been assumed to be VWXY = 1500 kg m-3, VWXY = 1 W m-1 K-1 and  = 1000 J kg-1 K-

<"U T(

(7)

is the effective diffusion coefficient for the representative pathogen (m2 s−1) and @ is the effective thermal

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1

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the energy flux comprising of short and longwave radiation and convective heat and mass transfer (Eq. 8):

(Kimball, 1983; Lamoureux et al., 2006; Paaijmans et al., 2008). The water–atmospheric boundary is modelled by

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− +  



Z

 [8

= (1 − R)\V] + Y] + A + "W^A

(8)

where r is the albedo of the shortwave radiation (-), \ is the fraction of shortwave radiation absorbed at the water surface (-), V] is the measured atmospheric shortwave radiation (W m−2), Y] is the net longwave radiation (W m−2),

A and "W^A are the heat fluxes from mass and heat transfer, respectively (W m−2). The energy flow vectors are

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defined as positive when providing energy to the water.

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Incident short-wave radiation (V] ) in Eq. 8 was measured on site, of which a portion is reflected from the water

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surface (albedo, r), another portion is absorbed at the surface (\), and the remainder penetrates the column and is

attenuated through absorption. Albedo is calculated using Fresnel’s equation (Eq. 3) where the zenith angle (_ ) is

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calculated in the simulation as a function of time based on the geographical coordinates and time of day (equations

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are presented in Kirk (2010, Ch 2) and are based on the work of Spencer (1971)). The refracted angle (_] ) is

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assumed to follow Snell’s law for pure water (refractive index of 1.33).

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R=

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` abc> (d) 7de )

+

 fgc> (d) Hde ) ` fgc> (d) 7de )

(9)

A constant value of \ = 0.4 has been assumed for each of the wavelength bands (Dake and Harlem, 1969); although

our measurements show that \ + R is not constant between UVB, ultraviolet-A (UVA, 320-400 nm) and the

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photosynthetically active radiation (PAR) portion of sunlight (400-700 nm). Larger values of 0.55 for \ have been

used by Yang et al. (2015), taking shortwave radiation as extending to 2800 nm; our measurements of V] extend only to 1000 nm and hence have a lower value of \.

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Net longwave radiation is determined by the Stefan-Boltzmann law applied to a small surface in a large enclosure

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(i.e. a ‘small pond’ under a ‘large sky’) (Eq. 10) using the emissivity of water (i] ) as 0.96 (e.g. Incropera and

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DeWitt, 1996; Lamoureux et al., 2006).

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L Y] = i] j($V3 − $VL )

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(10)

where σ (5.67 × 10HK W m−2 K−4) is the Stefan-Boltzmann constant, $V is the simulated water surface temperature (K)

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and $V3 is the effective sky temperature (K). In this study we assume a constant value for $V3 of 0 °C noting the

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limitation that this will not take into account cloud cover. However, it has been shown to be a reasonable value for

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clear skies, particularly at night (Pandey, 1995; Pérez-Garcı́a, 2004; Gliah et al., 2011).

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Convective transfer from the surface removes heat through two mechanisms; sensible and latent heat transfer (qconv

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and qevap respectively in Eq. (8)). Sensible heat transfer is driven by the temperature gradient while the rate of latent

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heat is driven by the water vapour concentration gradient, both occurring at the free surface. The Chilton-

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Colburn/Reynolds analogy is used to model these two heat fluxes. This method is applicable to heat transfer from a

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flat plate in turbulent flow conditions (Incropera and DeWitt, 1996).

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 ) Heat generation ( in Eq. 1 is modelled by the penetration of radiation into the water column. Irradiance

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penetration is calculated by the Lambert-Beer law (Eq. 11), first removing the surface reflection and absorption; η is

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 is then equal to −n/n%. a function of wavelength and assumed to be spatially and temporally constant. 

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 = (1 − R)(1 − \)V] G Hop

(11)

where q is the path length correction factor (-) and r is the attenuation coefficient (m−1). Eq. 11 is evaluated

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assuming a proportion of V] is comprised of UVB, UVA and PAR and evaluating the attenuation separately. r was

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measured on site and these values (as listed in Table 1) have been used in the model.

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It is assumed that 6.4 % of V] is in the UV band (Maïga et al., 2009a), our measurements further show that UVB is

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5.6 % of the UV spectrum. q is necessary to account for the refraction angle of the radiation and is calculated by CD

q = (1 − (1.33H sin _ )`) >

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Three equations from the literature are used to model sunlight inactivation (kc in Eq. 2) of E. coli. Eq. 13 models the

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endogenous decay of wastewater E. coli as a function of photon fluence (wWW^ , units of m2 Ei−1) (Nguyen et al.,

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2015). In this simulation, irradiance is converted to einsteins (Ei) in two discrete bands, one centred on UVB (300

(12)

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nm) and the other on UVA (360 nm). wWW^ has a value of 3.8 m2 Ei-1. Maïga et al. (2009a) regressed both the UV

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and sunlight intensity influence against E. coli concentrations to determine Eq. 14 and 15 where either could explain

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the die-off observed. The two coefficients to I in Eq. 14 and 15 have units of m2 J-1.

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" = wWW^ ⋅ 0.836 × 10HK y{[`K8 (z, %)z nz

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{[L88

(13)

" = 12.54 × 10H} ⋅ ~

(14)

" = 0.8 × 10H} ⋅ €

(15)

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where λ is the wavelength (nm), ~ is the irradiance of UVB and UVA, and € is the irradiance of wavelengths

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greater than 400 nm.

230 2.3 Numerical Implementation

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The model has been implemented numerically using the method set out by Patankar (1980). A uniform grid is

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employed (Fig. 2a) and the discretized algebraic equations are solved using a tridiagonal matrix solution.

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Linear interpolation between atmospheric data recorded on site is used to calculate the boundary conditions and the

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water column and soil heights were taken as 0.9 and 0.5 m, respectively. The chosen time step was modelled at 1

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minute intervals. Grid and time-step size independence was confirmed by comparing the water surface temperature,

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area-averaged temperature and water surface heat flux at the end of a 12 hr simulation.

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3. Results

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Observations of stratification and meteorological data show the diurnal nature of stratification and natural convection.

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Inlet and outlet E. coli concentrations were measured and log reductions were calculated and compared with

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simulations.

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3.1 Diurnal mixing pattern

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The diurnal mixing pattern recorded by the two vertical thermistor chains is shown clearly in Fig. 3c and d for a

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seven-day period (Fig. 3c,d), with selected atmospheric variables also graphed; (a) air temperature and wind speed,

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(b) solar radiation and atmospheric pressure. The wind speeds observed show that during night-time there are

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generally small velocities, close to zero in magnitude, and greater velocities in the order of 3-4 m s-1 during the day.

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Observations of solar radiation indicate relatively clear days with intermittent cloud cover. The same pattern of

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stratification was observed at different locations as illustrated by comparing Fig. 3c and d. Greater stratification and

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temperatures can be seen in the data recorded by thermistor chain 2 (Fig. 3d) which was located on the west side,

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opposite thermistor chain 1 (Fig. 3c). The large daytime wind speeds were observed to move from east to west. The

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cyclic nature of diurnal stratification has also been observed in the same pond during winter (data not shown).

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Fig. 4 shows a close-up of the measured and simulated temperatures from February 28 to March 1. As can be seen,

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thermal transport is remarkably different at different times of the day. For example, before 8 am on March 1, the

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pond is well mixed with all sensors showing almost the same temperature. As the day progresses, from about 9 am to

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2 pm the thermal field becomes stably stratified with the highest temperatures near the surface. After 2 pm the water

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surface starts to cool and unstable temperature gradients cause mixing to gradually progress from top to bottom until,

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by about 10 pm, the fluid is well mixed vertically with all sensors showing the same temperatures again. These

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features are clearly evident in both the simulation and the experimental results. Comparison of the interfacial

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temperature between the experimental and observed data (blue line in Fig. 4a and b) shows that field conditions are

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much more gradual.

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In relation to the model, the approximation used for night-time convection (keddy(unstable) in Eq. 3) reproduces the

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effect shown in the experimental data. The buoyantly unstable temperature gradient decays from the surface in layers

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(Fig. 4b 4pm-10pm on Feb 28) following the assumption of Fig. 2b. The turbulent nature of this phenomenon has

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been shown experimentally in Bednarz et al. (2009a,b) and indicates that there is significant mixing during this

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process.

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3.2 Disinfection of E. coli

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E. coli enumeration from the inlet and outlet are presented in Fig. 5a and are graphed on their measured date. Inlet

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and outlet measurements exhibit diurnal variation and the mean inlet E. coli concentration from samples was

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1.48 × 10 CFU 100 ml-1. To calculate log reductions, outlet concentrations of E. coli were for t + 16 d, where t is

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the time the sample was taken from the inlet. These data are presented in Fig. 5b on the sampled outlet date. The

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reduction is fairly consistent and centred on a mean of 2.1 log units. The daytime samples (square symbols) can

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clearly be seen to have a higher reduction (lower concentration) to the night and early morning samples, indicating

273

the importance of resolving the vertical distribution.

274

The period of 22 February 2015 – 10 March 2015 has been modelled and the surface concentration for a ‘plug’ of

275

water progressing through the pond is shown in Fig. 6. Results using the three different decay equations (Eqs 13-15)

276

are presented. In addition, two further simulations are presented, both utilizing die-off equation Eq. 13. The two

277

additional simulations show the effect of (1) complete day and night-time vertical mixing by artificially increasing

278

k eddy and (2) daytime transport by molecular diffusion only and night-time natural convection. Experimental E. coli

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log reductions that were introduced in Fig. 5b have been represented by the symbol in Fig. 6 which corresponds to

280

the case of E. coli entering the pond on 22nd February and the plug of fluid reaching the outlet on the 10th March. For

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this case, a reduction in concentration of 2 orders of magnitude is observed. The error bars correspond to the

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uncertainty in the pond residence time and scatter in the measured concentrations (see Fig. 5b).

283

Comparing the results from the different die-off kinetics shows that the UV dependent equations of Nguyen et al.

284

(2015) and Maïga et al. (2009a) are very similar in magnitude (Eq. 13 and 14). However, the sunlight dependence

285

proposed by Maïga et al. (2009a) shows a far higher reduction (Eq. 15). Eq. 15 should produce similar results to Eq.

286

14 due to the equations being regressed against the same experimental data, and indeed they do produce similar

287

results as the depth tends to zero. However, as the depth increases, the combination of wavelength dependent

288

attenuation and vertical concentration distribution becomes significant and the longer wavelengths produce a greater

289

die-off effect. Considering that there are likely other disinfection mechanisms and influences occurring (i.e. dark

290

inactivation, temperature, pH, DO) which have not been simulated here, the UV dependent results appear quite

291

reasonable.

292

The daytime peaks in surface concentration observed in Fig. 6 can be explained by the vertical distributions of

293

normalized E. coli concentrations which are shown in Fig. 4d. The applied decay rate for Fig. 4d is given by Eq. 13.

294

The distribution is very similar in nature to the thermal distributions. During daytime and for a stable density

295

gradient, it can be seen that the surface concentration is inactivated more quickly than the concentration beneath it.

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Mixing from wind shear causes the near surface concentrations to mix together, and although inactivation is

297

vertically distributed within this region, die-off appears to be uniform as a result (see red/black line in Fig. 4d). For

298

the case of complete vertical mixing, this effect occurs over the entire water column and as a result, the modelled

299

surface concentration seen in Fig. 6 has increased die-off compared to a stratified water column. At the opposite

300

extreme, vertical transport due to molecular diffusion and natural convection only is observed to produce large

301

surface reductions. However, due to the shallow surface layer daytime inactivation occurs in, the majority of the

302

concentration beneath is not inactivated and mixes to the surface so that the overall die-off is significantly reduced

303

compared to complete mixing. Thus, the daily fluctuations in concentration at the surface sampling point in both the

304

model and experimental results are strong evidence that stratification and sunlight are contributing significantly to

305

the die-off of pathogens.

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4. Discussion

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The analysis presented in this study is based upon the empirically derived eddy diffusivity concept, for which the

309

turbulent heat and species transport are dependent upon. Therefore it is valuable to discuss briefly the limitations and

310

assumptions made in the model formulation and their impact on the interpretation of simulation results.

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4.1. Physical considerations and model effects

312

There are several model assumptions which have been made in the model formulation which, while they greatly

313

simplify the solution, may prove significant to the transport of heat and E. coli. The first is the neglect of stream-wise

314

(i.e. horizontal) mixing. The mixing problem is multi-dimensional while our one-dimensional plug-flow model

315

considers vertical mixing only. The merit of the one-dimensional formulation is that it is the simplest way possible to

316

account for both the effect of sunlight penetration and vertical mixing leading to a practical method of calculation for

317

pond design. However, it makes it impossible to directly account for large scale recirculation (c.f. Badrot-Nico et al.

318

(2009)) and the subsequent dispersion that is occurring. In our simulation we indirectly accounted for stream-wise

319

dispersion by shortening the residence time from that of simple plug flow.

320

Concerning the Eulerian model for E. coli transport and the choice of Lewis number, the actual dispersion behaviour

321

for self-propelled or swimming particles is likely to be significantly more complex than can be captured by Eq. (2)

322

(Wensink et al., 2012). Nevertheless, consistency with the level of complexity in the thermal diffusion model makes

323

Eq. 2 an appropriate choice for the present study in the absence of precise data for E. coli dispersion.

324

Model applicability is primarily limited to ponds which operate close to plug-flow conditions, such as baffled ponds,

325

as stream-wise dispersion is neglected. Although this study is applied in subtropical conditions, the limit of model

326

application to different climatic regions is only limited by freezing conditions which alter dispersion and sunlight

327

penetration.

328

4.2 E. coli reduction effects

329

Here the main assumption in the model is that sunlight-mediated mechanisms (Eq. 13-15) were the primary

330

mechanisms for inactivation with effects of other environmental conditions being of secondary influence (i.e.

331

temperature, pH, predation, sedimentation). Moreover, even amongst the three light-mediated inactivation

332

mechanisms, Eq. 13 is strictly valid only for the endogenous UV inactivation mechanism, while Eqs. 14 and 15 were

333

regressed against field data which should explain the entire sunlight driven die-off observed. E. coli has been

334

reported as being insensitive to the mechanism of direct damage by UVB irradiation and the exogenous inactivation

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mechanism non-applicable (Kadir and Nelson, 2014; Nguyen et al., 2015), therefore leaving the majority of die-off

336

to occur through a UV driven endogenous mechanism. Clearly, the results of Eqs. 14 and 15 are very similar (see Fig.

337

6), indicating that the effect of Eq. 14 is interpreted appropriately as an endogenous mechanism. The difference in

338

magnitude between the simulated UV decay results and the measured E. coli concentrations shown in Fig. 6 could

339

potentially be explained by the synergistic effect of elevated pH and DO which would occur throughout the day from

340

algae photosynthesis (Davies-Colley et al., 1999; Kadir and Nelson, 2014).

341

Applying an Eulerian transport model to represent microorganisms imposes the limitation of not being able to

342

account for time dependent inactivation. This is due to the inability to track specific microorganisms and may

343

become important when interpreting the simulation results of Fig. 6 which suggest that constant vertical mixing will

344

produce greater die-off. However, this physically involves microorganisms cycling vertically in the water column

345

and receiving an intermittent sunlight dose. The effect of this cyclic nature has not yet been elucidated in the

346

literature and thus the model results are based on the current knowledge.

347

In addition to the consideration of E. coli cycling in and out of the radiation, the decay equations (Eq. 14) are linear

348

(log reductions) with increasing energy dose. However, it has recently been reported that increasing the energy dose

349

to E. coli does not produce a linear trend in log reductions against UV exposure time, but instead the die-off plateaus,

350

causing no additional inactivation (Kollu and Örmeci, 2012). The experimental evidence for this conclusion was

351

collected under laboratory conditions with UVC irradiation (at 253 nm) so further confirmation may be required for

352

the longer wavelengths occurring in the wastewater environment.

353

Dark inactivation is generally present during field observations and may cause additional reductions overnight and

354

beneath the thermocline during the day (Craggs et al., 2004; Nguyen et al., 2015). This may be countered by repair

355

mechanisms which are believed to occur within WSPs (Sinton et al., 2002). From laboratory results, Bohrerova et al.

356

(2015) did not identify an irradiation threshold at which repair mechanisms would not occur, although the total repair

357

was relatively low. Regrowth, as opposed to repair, showed a 3 log unit increase in concentration over a 48 hr

358

period in which the E. coli was subject to no further inactivation. Kollu and Örmeci (2015) further showed that

359

regrowth was more significant and could prevail for longer periods after being subject to higher UV intensities. They

360

suggested the reason was due to the damaged cells providing nutrients to those surviving and that in nutrient rich

361

wastewater the effect would be even more pronounced.

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Sheludchenko et al. (2016) measured E. coli through a baffled maturation pond and reported that the most significant

363

reduction occurred within the first half of the pond. Nguyen et al. (2015) also noted this, showing that the most

364

significant reduction was immediately after the inlet, however monthly variation showed that in certain months

365

further reduction could be gained through the remaining length of pond, and in other months no further reduction

366

was found. The effect of this observation was also noted by Blaustein et al. (2013) who identified that a piece-wise

367

linear trend with respect to time was most common amongst temperature dependence studies in dark conditions in

368

laboratory experiments. Temperature, however, is not a primary cause of inactivation when lower than 45 °C

369

(McGuigan et al., 1998; Craggs et al., 2004). Therefore, to explain the results of these studies, there may be another

370

mechanism occurring within WSPs immediately after entering that causes a large die-off that is not seen through the

371

remainder of the pond, such as predation or simply dilution by horizontal mixing.

372

Considering that the sunlight decay equations (e.g. Eq. 14) and many temperature-dependent relationships (e.g. de

373

Brauwere et al., 2011; Blaustein et al., 2013) are first order and if applied to the distribution model (Eq. 2), they will

374

produce log-linear die-off patterns similar to the calculated results shown in Fig. 6 for our plug flow model.

375

Therefore a more complete kinetic model should be based on a detailed understanding of the individual mechanisms

376

rather than regression of field data against one parameter, such as temperature or UV light exposure. Based on

377

laboratory and field data by Maïga et al. (2009a) and Nguyen et al. (2015), the present model has demonstrated that

378

the interaction of sunlight damage and stratification plays a significant role. The diurnal pattern with lower near-

379

surface E. coli concentrations measured during daylight hours supports this. Extending the present model to include

380

other mechanisms, once the details and appropriate rate-kinetics have been established, is straight forward.

381

5. Conclusion

382

A one-dimensional model for temperature distribution, coupled with a concentration distribution is proposed. It has

383

been shown to perform well against measured data and provides further elucidation of the physics behind

384

observations made of pathogen concentrations in a maturation pond. It is evident that daytime stratification causes

385

higher reductions within the surface region of the pond from sunlight disinfection. Vertical mixing from natural

386

convection at night-time brings the non-disinfected, daytime concentration, to the surface and the subsequent

387

outflow concentration is much higher at night. The measured outflow E. coli concentration from the maturation pond

388

had far higher fluctuations indicating that other disinfection mechanisms are most likely occurring, or a higher

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importance to sunlight disinfection is required to reproduce this effect. Incorporation of altered equations for

390

turbulent diffusive transport and kinetic models is easily achieved, making the models’ application versatile. The

391

proposed model offers the simplest solution to solving pathogen die-off by including transient boundary conditions

392

and accounting for vertical mixing and inactivation, thus offering clear advantages to current depth-integrated

393

models.

394

Acknowledgements

395

We would like to acknowledge the funding provided from the Australian Water Recycling Centre of Excellence, the

396

Queensland Government Science Fund Support and Queensland Urban Utilities.

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Figure Captions:

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Fig. 1 - Maturation pond layout showing: (a) the location of two thermistor chains, baffles, north direction and inlet

546

(thermistor chain 1 is located at the outlet) and (b) a thermistor chain schematic showing dimensions and sensor

547

numbers.

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Fig. 2 - Model concept emphasising (a) example control volumes (one control volume for each calculation location),

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calculation locations (filled circles) and material location limits (bounded by solid lines) with example eddies in the

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water column. (b) An unstable temperature gradient is approximated in the simulation as an equivalent temperature

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where the two hatched areas equate to the same energy.

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Fig. 3 - Experimental observations of (a) air temperature and wind speed, (b) solar radiation and atmospheric

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pressure, and water column temperatures recorded by thermistor chains 1 and 2 for (c) and (d), respectively.

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Fig. 4 – Comparison of (a-b) experimental temperatures to modelled results of (c) temperature and (d) E. coli. The

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period starts from 28 February 2015 6 am for two days. Simulation results illustrate periods of stratification and

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mixing. Legend labels align with thermistor positions given by Fig. 1b.

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Fig. 5 – Experimental data showing the (a) average E. coli concentrations of duplicate samples measured from the

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inlet and outlet and (b) E. coli log reductions highlighting that daytime (10 am – 2 pm) sampled concentrations are

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mostly lower than night-time concentrations.

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561

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Fig. 6 - Simulated log reductions from the surface element and experimental points located between a theoretical

566

residence time of 12 to 20 days. The effect of complete mixing and night-time convection are shown as additional

567

simulations.

568

23

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Tables:

570

Table 1 – Observed averages of radiation parameters with 1 standard deviation shown in parenthesis. Number of

571

samples was 7 throughout a single day. Spectra

R+\

UV Fraction

r

-

m-1

UVB

5.61 (0.2)

0.54 (0.1)

39.2 (3.24)

UVA

94.4 (0.2)

0.48 (0.1)

44.6 (5.3)

PAR

-

0.39 (0.09)

18.5 (3.2)

M AN U

SC

%

RI PT

569

AC C

EP

TE D

572

24

ACCEPTED MANUSCRIPT

35 m

Buoy S1

5m

Outlet

M AN U

60 m

S2

S4

AC C

EP

TE D

N

S3 0.9 m

1

RI PT

5m

SC

2 3m

Inlet S5

a)

Weight b)

RI PT

T

SC

z(+ve)

M AN U

WL

Control Volumes

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SL

AC C

EP

TE D

Water

Soil

a) Model Concept

b) Unsteady Thermal Gradient

a)

7.5

20

5

10

2.5

SC

30

0 1500

−2

b)

104

1000

103 102

500

101

0

0.6

0

30

TE D

0.4

35

0.8 d) Chain 2 0.6

EP

0.4

25

0.2

AC C

0 22

23

24 25 26 27 Time (day of February 2015)

28

01

20

Temperature (°C)

100

0.2

Radiation (W m )

0 105

0.8 c) Chain 1

Water Column Height (m)

RI PT −1

10

Wind Speed (m s )

40

M AN U

Atmospheric Pres. (kPa)

Air Temperature (°C)

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ACCEPTED MANUSCRIPT

30

b) Experimental Chain 2

35

SC

25

30 25 40

c) Modelled temperature 35 30 25

surface mixed stratified bottom

TE D

Temperature (°C)

RI PT

S1 S2 S3 S4 S5

35

40 Temperature (°C)

a) Experimental Chain 1

M AN U

Temperature (°C)

40

stratified

0.4

completely mixed

d) Modelled E. coli

natural convection progessive mixing

C/C 0

EP

0.3

night time

AC C

0.2

0.1 06

surface die−off continuously mixed layer

12

18 00 06 12 18 00 Time (day hour of 28 Feb / 01 March 2015)

06

6

a) Experimental raw data

10

5

10

4

M AN U

Enumeration (CFU 100 mL−1)

7

10

10

3

10

Inlet Outlet

2

10

1

10

0

b) Calculated E. coli log

10

−2 −3 −4

reduction

TE D

log10 C/C 0

−1

SC

RI PT

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Night−time

Daytime

AC C

EP

−5 05 F 08 F 11 F 14 F 17 F 20 F 23 F 26 F 01 M 04 M 07 M 10 M Time (day of February/March 2015)

SC

RI PT

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M AN U

0

log 10 C/C 0

−1

−2

−3

TE D

−4

daytime peak Eq. 13 Eq. 14 Eq. 15 Experiment Eq. 13 Complete vertical mixing Eq. 13 Natural convection only

AC C

EP

−5 22 F 24 F 26 F 28 F 02 M 04 M 06 M 08 M 10 M 12 M 14 M Time (day of February/March 2015)

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A practical model for sunlight disinfection of a subtropical maturation pond Highlights:

EP

TE D

M AN U

SC

RI PT

A practical model for the prediction of E. coli die-off is proposed Vertical sunlight inactivation and mixing is accounted for Stratification isolates bottom pathogens from sunlight Night-time mixing redistributes pathogens for following day Transient boundary conditions reproduce effects of observed weather conditions

AC C

• • • • •