Modelling Escherichia coli removal during domestic wastewater treatment in outdoor pilot scale High Rate Algal Ponds

While there is growing evidence that High Rate Algal Ponds (HRAPS) can support disinfection during wastewater treatment, the mechanisms of pathogen removal involved remain unclear. Based on previous findings, the present study aimed at verifying the occurrence and significance of dark decay, alkaline-pH toxicity, and sunlight direct damage in conditions representative of ‘real’ HRAP operation. For this purpose, Escherichia coli cell count was monitored hourly during 24 h periods in outdoor pilot HRAPs fed domestic wastewater. The data generated was used to create 2 distinct data sets that were then used to calibrate and validate a model of E. coli removal in HRAP. By modelling the contribution of the three mechanisms considered, E. coli removal in HRAPs could be predicted with a mean relative absolute error of 5.34% (N = 46). The model was then inputted yearly environmental data obtained from the continuous operations of the pilot scale HRAPs to evaluate the yearlong contributions from each mechanism to overall E. coli removal. Dark decay was thus predicted to support the highest yearlong mean contribution (78.6 – 91.0% of total E. coli decay, at the 95% confidence level) followed by sunlight mediated disinfection (6.01 – 17.8%) and pH toxicity (0.22 – 6.2%). Significant seasonal and daily fluctuations of decay mechanism contributions were evidenced in this study.


Introduction
Ponds are simple wastewater treatment systems widely used to remove organic pollutants and pathogens in rural areas (Maynard et al. 1999;Von Sperling 2005;Gruchlik et al. 2018). As an alternative to also remove nutrients and provide capabilities for biomass valorisation, high rate algae ponds (HRAPs) are shallow mixed ponds designed to enhance algae photosynthesis (Golueke et al. 1957;Craggs et al. 2012). While HRAPs also support pathogen removal (Bahlaoui et al. 1998;Craggs et al. 2004;Ruas et al. 2017;Buchanan et al. 2018;Chambonniere et al. 2020Chambonniere et al. , 2021, insufficient knowledge of the mechanisms actually driving pathogen removal limits our ability to better design and operate these processes (Young et al. 2016;Chambonniere et al. 2020). Using laboratory (approx. 100 mL) and bench scale (approx. 5L) experiments, Chambonniere et al. (2022a) recently determined from laboratory-scale (approx. 100 mL) and bench scale experiments (approx. 5L) that Escherichia coli removal in HRAP broth was significantly influenced by alkaline pH toxicity (the toxic effect of elevated pH increased with temperature), sunlight direct damage (including deoxyribonucleic acid damage and endogenous photo-oxidation), and dark mechanisms. While these authors could not identify the dark mechanism(s) involved, predation and toxicity from algal metabolites were postulated to cause most of E. coli removal under the conditions studied. Chambonniere et al. (2022a) also mathematically predicted that alkaline-pH toxicity, sunlight mediated disinfection, and dark decay, respectively accounted for 8.6 -46.5%, 0 -23.9%, and 45.0 -89.0% of the total E. coli decay recorded in the HRAP broth when exposed to natural sunlight followed by a dark period. These contributions were predicted under conditions relevant to the conditions experienced in full-scale HRAPs but the model used was 1 3 calibrated using data generated from small-scale controlled experiments, with all tests being performed in late spring. Independent validation under conditions fully representative of full-scale operation (e.g. full scale operated for a whole year) is therefore still required.
The present study was therefore conducted to refine the model developed by Chambonniere et al. (2022a) using experimental data from two pilot HRAPs continuously treating domestic wastewater outdoors. For this purpose, the accuracy of the model developed by Chambonniere et al. (2022a) was first assessed against data collected over 3 seasons. The model was then re-calibrated using a subset of the same data set and model fitness was assessed against the remaining dataset. Following this validation, the contributions of the main mechanisms of E. coli decay listed above were mathematically estimated based on environmental data collected from the monitoring of the two pilot scale HRAPs over a full year. These results were used to discuss how disinfection could be improved in HRAPs.
While wastewater treatment in HRAP is generally followed by biomass settling (Craggs et al. 2012, the present study focused on the fate of pathogens inside the HRAP. Evaluating disinfection performance during post-HRAP settling was therefore outside our scope.

Pilot scale HRAPs
Two identical pilot scale HRAPs, henceforth referred to as HRAP A and HRAP B, were operated in parallel at the wastewater treatment plant of Palmerston North, New Zealand (Latitude: 40° 23´ 7″ S; Longitude: 175° 34´ 47″ E). These HRAPs had a working volume of 0.86 m 3 , an illuminated surface area of 3.42 m 2 , and a working depth of 0.25 m. The HRAPs were fed with primary settled domestic wastewater from Palmerston North treatment plant. They were operated at a median Hydraulic Retention Time (HRT) of 7.9 day (influent flow around 0.108 m 3 day −1 ). The experimental data used in the present study was generated as part of a longer and broader research with treatment performance data already published in the literature (Plouviez et al. 2019;Chambonniere et al. 2020). More details about the ponds design, operation and monitoring can be found in these past studies, which also demonstrated that these HRAPs supported a performance representative to full scale secondary domestic wastewater treatment in HRAPs (median COD and N-NH 4 + removal values of 74.8% and 97.9%, respectively; Chambonniere et al. 2020). On 30 Sept 2015, 12 Oct 2015, 28 Oct 2015, 16 Nov 2015, 03 Feb 2016, 10 Feb 2016 Mar 2016, a refrigerated autosampler (ISCO 6712FR, Teledyne ISCO, USA) was used to withdraw 200 mL HRAP A samples every hour from 9 A.M. on the first day until 9 A.M. on the next day. These samples were withdrawn approximately 20 cm downstream from the pond paddlewheel and approximately 5 cm below the water surface. These samples were stored at 4 °C in the refrigerated chamber of the autosampler until collection at 9 A.M. the next day, when another 250 mL HRAP broth sample was saved for total suspended solids (TSS) measurement and the influent flow rate was controlled. Temperature and pH were logged every 15 min (data logger Multimeter Thermo Scientific Orion Star A326) and hourly sunlight data was downloaded (New Zealand National Institute of Water and Atmospheric Research 2018, Palmerston North station agent number 21963). On the 30/09 and 12/10, data for pH, temperature, and E. coli cell counts were only available from 11 A.M. and 3 P.M. respectively. The high-sampling frequency dataset thus generated is presented in S1 and was divided in two independent subsets: the first subset was used to recalibrate the model of Chambonniere et al. (2022a) and the second subset was used to validate the newly calibrated model.

Year-long monitoring
The pilot HRAPs were frequently monitored for temperature, pH, and TSS concentration from 02 Jun 2016 to 01 Jun 2017 for HRAP A and from 19 Jul 2016 to 01 Jun 2017 for HRAP B. For this purpose, pH and temperature were quantified directly from the pilot HRAPs broth using a data logger (Multimeter Thermo Scientific Orion Star A326) recording data every 15 min over the periods listed in S2. TSS measurements were performed in the laboratory from grab samples collected from both HRAP at approx. 9 A.M. twice a week. Hourly sunlight data was downloaded over the period of interest as indicated above.

Laboratory analysis
E. coli cell density was quantified as most probable cell count (MPN) using the IDEXX Quantitray Colilert-18 method and according to the manufacturer procedure (following 100 -1,000 times dilutions of the HRAP samples). TSS was quantified via dry weight measurements according to the standard method 2540.D (Eaton et al. 1998) using GF/C grade filters (General Electric, USA).
1 3 E. coli decay prediction from daily profiles E. coli decay was mathematically modelled assuming that 1) the pilot HRAPs were well mixed (Chambonniere et al. 2020), 2) the influent flow rate was constant between monitoring events; 3) the influent and effluent flow rates were similar (i.e. constant working volume and no significant impact of evaporation and rainfall); and 4) the influent E. coli concentration was constant during each sampling period. Under these assumptions, E. coli cell count was predicted as: where C(t) is E. coli cell count (MPN per 100 mL) in the HRAP at time t , k HRAP (t) the first order decay rate (day where k dark 20 is E. coli dark decay rate at 20 °C (day −1 ), dark is the temperature compensation coefficient for dark decay, T(t) is the broth temperature at time t (°C),k pH 20 is E. coli decay rate at 20˚C and pH 14 (day −1 ), pH is the temperature-compensation coefficient for alkaline-pH toxicity, pH(t) is the broth pH at time t , is the sunlight-mediated decay coefficient due to direct sunlight damage (m 2 .W −1 .day −1 ), d is the water column depth (m), (t) is the light extinction coefficient of the algal broth (m −1 ) at time t , and Hs(t) is the incident sunlight intensity at the water surface (W m −2 ) at time t . The parameters Hs(t) and (t) are henceforth referred to as input variables because they are determined experimentally (or estimated from experimental data). Because the time-steps used for the measurements of pH (15 min), temperature (15 min) and sunlight intensity (60 min) created divergences in E. coli cell counts at the highest predicted decay rates, the values of these parameters at smaller time steps were computed by linear interpolation between 2 adjacent experimental data points until disappearance of the model divergence. The value of (t) was likewise computed using TSS data linearly interpolated from two consecutive TSS measurements and the experimental correlation shown in S3. The parameters k dark 20 , dark , k pH 20 , pH , and are henceforth referred to as fitted parameters because their values is determined by fitting Eqs. (1) and (2) against experimental E. coli MPN data and experimental (or interpolated) input data. The initial values of k dark 20 , dark , k pH 20 , pH , and used for the fitting algorithm were the values determined by Chambonniere et al. (2022a) as listed in Table 2.

Initial model validation
For each daily profile, E. coli cell counts were mathematically predicted using the Euler method according to time (Butcher 2016) applied to Eqs. (1) and (2), and using the first E. coli cell count measured in the pilot HRAP as the initial value (i.e. C(t = 0) ). Model fitness was estimated by computing the coefficient of determination (R 2 ) and mean relative absolute error ( MRAE , %) between measured and predicted log-transformed E. coli cell counts. The initial values of E. coli cell count were inputs and were therefore excluded from the calculation of model fitness.

Model re-calibration
The model developed was recalibrated using pilot data by minimizing the sum of squared residuals of the log-transformed cell counts when varying the values of the fitted parameters using interior-point algorithm limited to a maximum of 200 iterations (Matlab R2019a, MathWorks, USA). This re-calibration was only conducted using the data subset from 30/09-01/10 (spring), 28-29/10 (spring), and 03-04/02 (summer) and the remaining data subset was used to assess the fitness of the newly calibrated model as described above. The sensitivity of the calibration to measurement uncertainty on input variables was evaluated by repeating model calibration after changing the value of each input variable to its extreme values of uncertainty as listed in Table 1.

Model fitness and sensitivity analysis
The fitness of the re-calibrated model was assessed against the validation data subset (4 daily profiles for 12-13/10, 16-17/11, 10-11/02, and 16-17/03 covering spring, summer, and fall) by computing the MRAE from the E. coli cell count predicted over these 4 days. The model fitness sensitivity to input variable uncertainty was then tested by successively changing the values of each input variable to one of its extreme values of uncertainty (Table 1) and computing the MRAE again.

Contribution analysis
Using the re-calibrated model, the value of E. coli decay rate was mathematically predicted for each data point of the year-long dataset collected for pH, temperature, sunlight irradiance, and total suspended solids. The relative contributions of the 3 decay mechanisms to the overall decay were then calculated as the ratio between the decay rate due to a given mechanism over the total decay rate for each data point. Because uncertainty on the fitted parameters values also caused uncertainty on mechanism contributions to overall decay, uncertainty on relative contributions was determined using Monte-Carlo simulations (USEPA 2001). Briefly, input variables were varied within their uncertainty range (Table 1) using normal laws centred on measured values with standard deviation being half of the uncertainty range. A total of 2,000 new modified calibration datasets were thus obtained and used to generate 2,000 sets of values for the 5 fitted parameters. The yearly contributions of each mechanism to the overall E. coli decay were then evaluated using each of these 2,000 sets of fitted parameters values.

Validation against previously calibrated model
The model calibrated by Chambonniere et al. (2022a) poorly predicted E. coli cell counts (R 2 = -1.35, MRAE = 12.6%, S5). The uncertainty associated with the fitted parameters described by Chambonniere et al. (2022a) generated a large uncertainty on the predicted E. coli cell counts that could explain the poor model fitness (Fig. S5.2). The differences in conditions experienced in prior bench scale assays (Chambonniere et al. 2022a) and the present study (pilot HRAP) could also explain the poor fitness as E. coli decay was generally overestimated outside of the most extreme summer days (Fig. S5.2), suggesting the rate of 'dark decay' in the pilot HRAPs was lower than initially predicted from benchscale assays. In contrast, E. coli decay was underestimated at its peak experimental values in the late afternoons of summer days (Fig. S5.2) but often overestimated at the beginning of those days, suggesting a more complex and intense action of alkaline pH toxicity, temperature, and/or sunlight irradiation than initially predicted. It was therefore necessary to recalibrate the model using a sub-set of the pilot hourly data and then quantify the model fitness against the remaining hourly data sub-set.  (Chambonniere et al. 2022a) and new (present study) values of the fitted parameters generated using the pilot data calibration subset (S6). The recalibrated model was able to describe the experimental trends seen in spring and summer conditions. This new calibration confirmed the original calibration overestimated the rate of dark decay (see decrease in k dark 20 value, Table 2) and evidenced an impact of temperature on this mechanism ( dark > 1 ) previously not seen at bench scale. Chambonniere et al. (2022a) carried out their experiments under a relatively narrow range of temperature while pilot HRAP experienced large and rapid changes in temperature over short periods of time. Hence, the impact of  temperature on dark decay was more likely to be perceived at pilot scale in the present study. The initial calibration underestimated the impacts of alkaline pH toxicity and light damage (see increases in k pH 20 and values). This may explain why the initial model underestimated decay during daytime in summer, when pH and light irradiation are both high. As with temperature, pH and sunlight intensity varied significantly diurnally and seasonally. The recalibration therefore likely captured the sensitivity of E. coli decay to temperature, sunlight intensity, and pH, which were the only environmental parameters found to significantly impact E. coli decay during the study of Chambonniere et al. (2022a).

Re-calibration using pilot data subset
The sensitivity of the model calibration to experimental uncertainty is shown in Fig. 1.
The model calibration showed limited sensitivity to input parameters. Uncertainty on broth pH causes uncertainty on the temperature compensation coefficients for alkaline pH induced toxicity and dark decay, likely due to the existing covariance between pH and temperature. As could be expected, the light damage decay coefficient ( ) was mostly impacted by input variables linked to light penetration in the algae broth. Due to significant uncertainty on the light absorption coefficient (S3), the value of the light damage decay coefficient could therefore also hold significant uncertainty. Critically, the sensitivity analysis showed that uncertainty on the model assumptions related to the influent flow (constant), effluent flow (equal to influent flow), and reactor volume (constant) should have little impact on the accuracy of the model predictions. Unless large variations in influent E. coli cell counts are actually experienced (which is unexpected, S5), the assumption that this value remains constant on a given day should also have little impact on the model predictions.

Model validation using pilot data
The re-calibrated model could predict the validation data subset with a coefficient of determination of 0.48 and MRAE of 5.34% (N = 46, Fig. 2 and Fig. S7.1). The model fitness was also relatively unsensitive to measurement uncertainty, the MRAE remaining within 4.5 -6.5% (see Fig. S8.1) when input data was varied within uncertainty range. The dynamics of removal during summer were predicted accurately although the model consistently underestimated E. coli removal on the spring day of 12-13/10. Sensitivity analysis indicated that uncertainty on E. coli cell count in the influent or light attenuation coefficient are the most likely explanations for this systematic error.

Long term contribution analysis
The pH, sunlight intensity, and temperature experienced by the pathogens in pilot HRAPs vary significantly daily and seasonally (Fig. S9.1). To assess the impact of these variations on E. coli removal, the relative contributions of the decay mechanisms modelled were predicted using the re-calibrated model ( Table 2). Using year-round input data (Fig. S9.1), dark decay was thus predicted to be the main contributor to E. coli decay over the entire year at the 95% confidence level (41.8 -100% for HRAP A and 24.1 -100% for HRAP B, Fig. S9.2) and sunlight direct damage was the second most significant mechanism (0 -54.7% for HRAP A; 0 -51.4% for HRAP B). Alkaline pH toxicity had a lower impact and was the only mechanism having different impacts in the 2 HRAPs (0.00 -25.8% in HRAP-A against 0.00 -71.9% in HRAP-B) as a consequence of the different environmental conditions recorded in these ponds (Fig. S9.2).
Looking more specifically into the contributions averaged over each season (Fig. 3), alkaline pH toxicity was predicted to be insignificant in winter and remained generally low in spring and fall. During summer, the contribution of pH toxicity increased to a level similar to the impact of sunlight direct damage in HRAP B, while remaining low in HRAP A. The relative contributions of sunlight direct damage and dark decay did not vary significantly across seasons. Monte Carlo analysis to estimate error on mechanisms contribution linked to the uncertainty generated during model calibration showed these conclusions were obtained with high confidence.

Daily variations from the decay rate of E. coli decay mechanisms
Large diurnal variations in pH, temperature, and sunlight intensity can be experienced in pilot HRAPs (Fig. S1.1), meaning the magnitude and relative contribution of E. coli decay mechanisms may also vary greatly throughout the day.

Sunlight direct damage
The absolute magnitude of sunlightinduced E. coli decay was predicted to be stable throughout the year as lower light attenuation in winter (due to lower biomass productivity and, therefore, lower TSS concentration) compensates for lower sunlight intensity. Noteworthy, sunlight direct damage regularly becomes significant (often being the most significant) mechanism of E. coli decay during the day but this effect is brief, explaining the low overall contribution of this mechanism (Fig. 3).
Alkaline pH induced toxicity Alkaline pH toxicity was never predicted to be significant in winter and fall (Fig. 4). In contrast, this mechanism was predicted to occasionally become significant in spring and summer. Alkaline pH toxicity was even predicted to regularly become the most significant mechanism of E. coli decay in the late afternoon in summer, when both pH and temperature are also at their highest. However, alkaline pH toxicity is generally only felt during daytime because the broth pH only increases above 10 when photosynthetic CO 2 uptake is intense, but then decreases back to around neutrality at night-time due to atmospheric transfer and microbial respiration (Chambonniere et al. 2021).
Uncharacterized dark decay Dark decay was the only mechanism predicted to cause significant pathogen removal at night in all seasons. Dark decay was also significant during daytime, but its contribution decreases in winter as temperatures are lower. The absolute impact of dark decay was predicted to peak in summer due to the higher temperatures recorded.

Implications for design
Dark decay The present study confirms the prevalence of dark decay as the main E. coli removal mechanism in the pilot HRAPs monitored, in agreement with Chambonniere et al. (2022a). While the actual mechanisms involved are unknown, it has been hypothesized that predation and algal metabolites toxicity are the likely underlying mechanisms (Flint 1987;Falaise et al. 2016;Dias et al. 2017). Consequently, identifying conditions that favour the establishment of efficient predators and/or the production and release of toxic algal metabolites could significantly enhance disinfection during algae-based wastewater treatment. Temperature was the only parameter predicted to influence E. coli dark decay and increasing temperature could be practically achieved via recovery of low-value heat (if available) or locating the ponds inside greenhouses.

Sunlight direct damage
Increasing the effect of sunlight direct damage could enhance HRAP disinfection, especially in winter when dark decay is slower due to lower temperature and alkaline pH toxicity is insignificant due to weak photosynthetic activity. Sutherland et al. (2015) reported that cell exposure to light increased with decreasing depth and HRT, meaning that attempts to increase pathogen exposure to light may also boost algal productivity, and consequently light attenuation. While boosting algal productivity may also enhance dark decay from algal toxicity, manipulation of depth and/or HRT also impacts temperature: for instance, decreasing depth at constant HRT decreases heat inertia of the HRAPs meaning more intense peaks of both high and low temperature (Béchet et al. 2016). The overall impact of changing depth or HRT on E. coli removal is therefore unclear and requires further investigation. Finally, because microalgae significantly contribute to light attenuation in the HRAP water column (Curtis et al. 1994), wastewater pre-treatment to decrease turbidity may have a negligible impact when the microalgae are established.
Alkaline pH toxicity In HRAPs, an imbalance between photosynthetic CO 2 uptake and CO 2 inputs from atmospheric diffusion, influent alkalinity, and heterotrophic respiration causes pH to increase during daytime (Chambonniere et al. 2021). Any intervention to increase CO 2 uptake and/or reduce CO 2 inputs can therefore theoretically increase the frequency and magnitude of high pH (> 10) events in HRAPs. Lowering HRAP depth could enable to increase pH as Sutherland et al. (2014) measured a significant increase in pH in summer in a HRAP operated at 0.2 m depth compared with two HRAPs operated at 0.3 m and 0.4 m (despite continuous CO 2 bubbling in all ponds). The impact of depth is however complex as it can also impact temperature, HRT (at constant HRAP area), light penetration and algae productivity (as discussed above), but also the area/volume ratio for atmospheric CO 2 transfer (a lower depth means a higher transfer rate (Weber et al. 2019)). Alternatively, it may be possible to host the HRAP inside a greenhouse to reduce atmospheric CO 2 supply, but this will increase capital costs. The relatively low contribution of pH induced toxicity to overall E. coli removal also indicates that CO 2 bubbling to optimize biomass growth (de Godos et al. 2010;Mehrabadi et al. 2017) should not critically impact the disinfection performance. If toxic compounds secreted by algae cause E. coli removal, the trade-off between decreased pH versus increased photosynthetic activity may improve disinfection performance of the system. Recent studies have however shown that CO 2 supply did not affect E. coli removal despite an increase in algal biomass productivity (Ruas et al. 2017(Ruas et al. , 2020. Fig. 4 Predicted daily contribution of removal mechanisms to E. coli removal in HRAP B over a week across 4 seasons. It must be noted that the summer Y-axis scale is different from the other season due to episodes of significantly higher decay during this season Impact of design The model henceforth validated supports that E. coli removal follows a first order rate. If the HRAP can be considered as a well-mixed system, the use of several ponds in series instead of a single pond may significantly increase the overall disinfection performance of the system (Marais 1974). However, Jupsin et al. (2003) suggested culture broth flow could be described as a plug-flow with high recirculation rate in large HRAP due to the long time needed for water to circulate through the raceway. Since a plug-flow is the most effective mixing condition for first order kinetics processes (Shilton and Walmsley 2005), HRAP disinfection performance may practically increase with pond scale.

Conclusions
The model of E. coli removal calibrated and validated in the present study predicted with high confidence that E. coli removal during domestic wastewater treatment in pilot HRAPs was largely supported, over the long term, by dark mechanism(s) followed by sunlight direct damage. Despite high seasonal and diurnal variations in its impact, pH toxicity accounted for a negligible part of E. coli removal throughout the year.
Because design parameters of HRAPs (e.g. depth, HRT) often have antagonistic impacts on the parameters influencing E. coli removal (e.g. temperature, sunlight intensity in the water column, algal activity, or pH), coupling the model herein presented with a model predicting HRAP environmental conditions based on design, operation, and location (Solimeno et al. 2017;Casagli et al. 2021) could inform on how to best design and operate HRAPs for wastewater disinfection. It must be noted that the model herein presented is only valid for E. coli (a common yet non-universal indicator of wastewater treatment efficiency, Ashbolt et al. 2001). Similar efforts should therefore also focus on other indicators shown to have different response to environmental stress than E. coli (e.g. Gram-positive bacteria, spore-forming bacteria, helminths). Finally, the fate of pathogens should also be studied during post-HRAP treatment to remove the microalgal-bacterial biomass generated during secondary treatment.

Author contribution
The article was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Dr. Paul Chambonniere is the lead author on the manuscript. He designed and conducted the experimental work, analysed the results, developed the mathematical model, and wrote the core of the manuscript. Prof. Benoit Guieysse (Principal Investigator of the research) helped with the conceptualization of the study, analysing and interpreting the data, as well as drafting the manuscript. He also reviewed and edited the manuscript before final submission. Dr. Maxence Plouviez helped analysing and interpreting the data, and reviewed and edited the manuscript before final submission.
Funding Open Access funding enabled and organized by CAUL and its Member Institutions This study was financially supported by internal funds from Massey University, New Zealand.

Competing interests
The authors have no relevant financial or nonfinancial interests to disclose.
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