Filter operation effects on plant‐scale microbial risk: Opportunities for enhanced treatment performance

Granular media filtration remains a critical treatment process and regulatory requirement for managing pathogenic protozoa in drinking water. It is a dynamic process in which performance inherently varies. While research has focused on characterizing or maximizing (oo)cyst removal in individual filters, the risk implications of combinations of filters moving through different phases of the filter cycle (leading to temporal variation in plant‐scale performance) have not been described. Increasing threats from climate‐change‐exacerbated landscape disturbances leading to more variable source water quality emphasize the need for such evaluations. Here, a modeling framework was developed to investigate the impacts of individual filter performance variation on plant‐scale performance. It is shown that improving maximal removal during stable operation does not necessarily improve average performance. The effect of other design and operational strategies like increasing the number of filters or implementing proactive operations (e.g., avoiding breakthrough) are analyzed, thereby providing guidance for increasing treatment resilience.

particular concern.In North America, regulatory policies focus on reducing infection risk by requiring drinking water system owners to implement treatment by granular media filtration (or equivalent technology) and disinfection of surface water and groundwater classified as under the direct influence of surface water (AEP, 2012; U.S. EPA, 1998EPA, , 2002EPA, , 2006;;O. Reg. 170/03, 2003).While Giardia is the most reported enteric protozoan globally (Adam et al., 2016), Cryptosporidium is also ubiquitous in the environment and often a focus for surface water supplies.This is because it is more difficult to remove by filtration and insufficiently treated by traditional oxidantbased disinfection processes such as chlorination (Korich et al., 1990;H. Li et al., 2001).Virus removal during filtration is also of recent interest because some viruses are resistant to inactivation by disinfection and some removal by filtration is also expected (Nilsen et al., 2019).
Granular media filtration (i.e., physico-chemical filtration with sand and other materials in rapid filters) remains essential in the treatment of Cryptosporidium and Giardia.All drinking water systems are vulnerable to increasingly extreme source water quality fluctuations resulting from climate-change-exacerbated landscape disturbances such as heavy precipitation events, wildfires, and hurricanes (IPCC, 2022).While UV irradiation provides effective treatment against the passage of infectious protozoa to treated water supplies, increasingly variable source water quality that can be expected because of climate-change-exacerbated landscape disturbances (Stone et al., 2011) can lead to conditions that potentially challenge coagulation and subsequent (bio)particle removal by filtration or disrupt residuals management (Emelko et al., 2011;Kundert et al., 2014).This, in turn, can reduce the efficacy of downstream UV disinfection (Mamane, 2008).
US and Canadian regulations for treated water quality rely on indirect measures of treatment system performance and provide pathogen removal credits based on indicators of "well-operated" treatment (AEP, 2012; U.S. EPA, 2006;O. Reg. 170/03, 2003).This is due to the impracticality of monitoring pathogen concentrations in treated drinking water (Regli et al., 1991), which requires the analysis of large volumes (on the order of 10 5 -10 6 L) to confirm drinking water safety and is subject to considerable uncertainty in the case of non-detects and low counts (Chik et al., 2018;Emelko et al., 2008).For example, both the U.S. Environmental Protection Agency (U.S. EPA, 1998EPA, , 2002EPA, , 2006) ) and Health Canada (2012Canada ( , 2019) ) indicate a 3-log (i.e., thousand-fold or 99.9%) Giardia cyst and Cryptosporidium oocyst removal credit for conventional filtration systems that meet certain performance criteria.These criteria are mostly related to turbidity: a 95th percentile of combined filter effluent turbidity below 0.3 NTU is required by the suite of the enhanced US surface water treatment rules (U.S. EPA, 1998EPA, , 2002EPA, , 2006)), though a limit of 0.1 NTU for the 95th percentile of filter effluent turbidity is recommended by the Partnership for Safe Water (AWWA, n.d.).
A wide range of oocyst removal by filtration has been reported and used globally in risk assessment (Hijnen & Medema, 2010).Whether derived from bench-, pilot-, or full-scale testing, these values reflect the treatment performance of individual filters.In regulatory policy and quantitative microbial risk assessment, the associated log-removal values for pathogen treatment are generally regarded as a constant within and between similar systems (U.S. EPA, 2006;Health Canada, 2012, 2019;WHO, 2016).Nonetheless, it is recognized that treatment performance can vary depending on the source water quality, treatment technology, and operational conditions, which may include inherent phases of the filter cycle that are characterized by changes in performance (Emelko et al., 2005).Plant-scale treatment performance reflects the collective, concurrent performance of all individual unit treatment processes and can differ from individual treatmentunit-scale performance.Although it has not previously been discussed, is important to characterize because this plant-scale treatment performance-not individual treatment unit performance-determines ultimate health risk.
Pathogen (and particle) removal by filtration involves physico-chemical attachment of microorganisms to the filter media; this occurs when the pathogens-bioparticlesare sufficiently destabilized through coagulation so that they attach to media grain surfaces or previously deposited particles because of short-range electrostatic attraction forces (Amirtharajah, 1988;Emelko, 2001;Emelko et al., 2005;O'Melia, 1985).Thus, coagulation is essential for maximizing pathogen removal by filtration (Barkay-Arbel et al., 2012;Emelko, 2003;Huck et al., 2002).Similar levels of protozoa removal by filtration can be achieved when sufficient coagulant is added, regardless of coagulant type (Brown & Emelko, 2009).However, sufficient coagulation does not ensure consistent removal of pathogens while filters are in operation.This is because filtration is a dynamic process with characteristically cyclical operational phases.
A filter cycle comprises at least three distinct phases (ripening, stable operation, and breakthrough), though

Article Impact Statement
Knowledge about performance variations during a filter cycle can improve filter design and operation, increase plant-scale treatment performance, and reduce microbial risks in drinking water.not all filters are in service or operated through all phases.Ripening is the initial period of effluent quality degradation and subsequent improvement during which backwash remnant particles pass through filters and the removal of pathogens (and particles) from influent streams is dynamic and not maximal (Amirtharajah, 1988;Emelko & Huck, 2004;Huck et al., 2002;Patania et al., 1995).It has been suggested that more than 90% of particles passing through well-operated filters do so during the ripening phase (Amirtharajah, 1988), though operational strategies for minimizing the effects of this phase are also available, like filter-to-waste operation during ripening and modifications in backwashing such as extended terminal subfluidization wash (Amburgey et al., 2003).Stable operation is usually a prolonged period of low and stable effluent turbidity that occurs after ripening; however, the removal efficiency for particles including microorganisms can be more dynamic than for turbidity removal (Clark et al., 1992;Darby & Lawler, 1990;Nilsen et al., 2019).Breakthrough is the final phase of the filter cycle during which filters become overloaded and particles are increasingly likely to detach from or not attach to filter media (Moran et al., 1993).During breakthrough, filter effluent water quality increasingly deteriorates, often rapidly, and it has been associated with order-of-magnitude increases in pathogen passage (Emelko et al., 2003).Because of that, backwashing is necessary to remove deposited materials from the filters and restore performance.Consistently increasing effluent turbidity or particle counts indicate breakthrough and usually trigger backwashing.It can also be initiated due to increasing head loss or scheduled either for convenience or as a precautionary measure.Thus, characterizing performance variations is important for optimizing filter operation to minimize pathogen passage (Huck et al., 2001).
The passage of microorganisms through individual filters has been shown to vary during both the regular, expected phases of the filter cycle as well as periods of suboptimal operation such as hydraulic surges or sub-optimal coagulation (Emelko et al., 2005;Huck et al., 2002;Nilsen et al., 2019;Patania et al., 1995).Although performance changes throughout the filter cycle are widely reported and recognized, they are usually not reflected in microbial risk assessment or management in drinking water; rather, a constant log-removal credit is commonly used, as discussed above.In this context, Brown (2004) developed a model to assess the risk of Cryptosporidium passage through filtration systems in different operational conditions.Nilsen (2020) suggested that pathogen concentration variations caused by variable filtration performance are unlikely to affect risk estimates relative to a model that uses an equivalent mean concentration.Focusing on viruses and bacteria, that analysis described individual filter performance, like most filtration performance studies.However, full-scale water treatment almost always includes multiple filters operated in parallel with staggered backwashes.The dynamic treatment performance that filtration studies reflect has generally not been integrated to describe the risk implications of combinations of filters passing through different phases of the filter cycle and resulting variation in plant-scale performance.Controlling microbial risks through drinking water in public water systems depends on the resulting treatment performance of several filters being operated at the same time and cannot be limited to the analysis of a single filter.Therefore, an understanding of plant-scale filtration performance and how operational conditions contribute to it is needed to better support microbial risk management.
The goal of this study is to provide a modeling framework to evaluate the effects of filtration design and operational conditions on plant-scale filtration performance.Specifically, a simple mathematical model is used to (1) illustrate how temporal variability in oocyst removal performance of a granular media filter throughout a filter cycle affects the combined plant-scale performance of filters operated in parallel, both instantaneously and on average, and (2) evaluate the predicted effects on plant-scale performance of alternative design and/or operational strategies (e.g., changes in number of filters, backwashing schedules, durations and log reductions during individual filter phases).Previously reported, detailed data that describe oocyst removal by filtration during various phases of the filter cycle are used to demonstrate how pathogen removal performance of plant-scale filtration processes-as opposed to individual filters-can be assessed.While the quantitative results are system-specific, they nonetheless underscore that focusing exclusively on individual unit operation (e.g., filter) performance may preclude the identification of performance optimization and risk management opportunities and/or barriers.

| Filter cycle variability of pathogen removal in granular media filtration
The variability of pathogen removal during a filter cycle was represented by a step function reflecting ripening, stable operation, early breakthrough, late breakthrough, and backwashing.Breakthrough is divided into two phases to reflect the progressive deterioration of performance.Although a step function omits variations in performance within phases and features abrupt transitions in performance between phases, it is more representative of the cyclical pattern of filter performance than the use of a single log-reduction value and enables simple evaluation of the effects of various performance changes known to regularly (e.g., ripening) or occasionally (e.g., suboptimal coagulation) occur during the filter cycle.Table 1 presents the assumed duration and log reduction for each phase of the filter cycle.These values were drawn from pilot experiments assessing Cryptosporidium parvum oocyst removal by filtration at the Britannia Water Treatment Plant in Ottawa, Canada (Huck et al., 2001).That study was illustratively used herein due to the availability of extensive performance data during ripening, stable operation, breakthrough, and other operational conditions, which are not available elsewhere.As the goal of this work is to investigate the effect of filter cycle variability on plant-scale filtration performance, the relative difference among log reductions and durations during the various phases of a filter cycle is more important than the values themselves.Data for other pathogens and treatment performance values based on site-specific information, or hypothetical scenarios, may be used to support planning and risk management.
The raw data from all ripening and stable operation experiments conducted at the Ottawa pilot plant were used to calculate the average performance (expressed as an effective log reduction) corresponding to each of these two phases.It should be noted that such high stable operation log reductions can only be attained in certain water types with optimized coagulation and operation of the filters.Breakthrough conditions were defined by increasing filter effluent turbidity beyond 0.2 NTU, with early breakthrough remaining below 0.3 NTU (Emelko et al., 2003;Huck et al., 2001).To represent the wide range of performance that could be achieved as stable operation gives way to breakthrough, one experiment was selected from each set of tests at early and late breakthrough; specifically, the ones leading to the greatest change in breakthrough performance were selected (i.e., the highest removal during early breakthrough and the lowest removal during late breakthrough).The phase durations for ripening and stable operation were similar to values reported in Huck et al. (2001).Here, the relatively short durations of the breakthrough and backwashing periods are hypothetical.It is important to note that the effects of ripening and breakthrough are often limited or avoided in practice with filter-to-waste operation and timely backwashing, respectively; however, they are included here to illustrate their effects on system performance if such practices are not followed.Because turbidity is monitored to assist these operational practices, deteriorated effluent turbidity may be avoided; however, Nilsen et al. (2019) showed diminished removal of viruses and bacteria persisting beyond the ripening phase with respect to turbidity as well as deteriorating removal commencing prior to turbidity breakthrough.Although the study did not assess (oo)cyst removal, it suggests that excellent control of filtration with respect to effluent turbidity may not be sufficient to ensure high and stable pathogen removal throughout the period that the filter is in service.Emelko et al. (2003) showed that oocyst removal can deteriorate before turbidity breakthrough.Accordingly, the analyses performed here may be emblematic of the effects of reduced pathogen removal at the bounds of stable operation for systems that employ filter-to-waste operation during ripening and that commence backwashing promptly following the arrival of turbidity breakthrough.

| Model for analysis of several filters operated in parallel
The pathogen removal performance of a system of parallel filters was evaluated using the effective log-reduction metric, which expresses average treatment performance as a log reduction and emphasizes that log-reduction values themselves should not be averaged because doing so overstates average treatment performance (Schmidt et al., 2020).The model considers n similar filters running in parallel, receiving settled water with a constant influent pathogen concentration and with a combined flow that is evenly divided among the operating filters.The presumption of evenly divided flow simplifies the model by averting the need for a volume-weighted approach.However, it presumes an increase in flow through operating filters during backwashing of one or more filters to maintain a constant total filtered water production and does not reflect accumulating head loss through a filter cycle.Supplemental Information 1 provides a comparison between this model and one considering no redistribution of flow during backwashing (i.e., with constant filter flow and reduced total volume of produced water during a backwash).The indices i and t represent individual filters and time, respectively, and the variable Op i,t indicates if a filter is in service (Op i,t ¼ 1) or is being backwashed (Op i,t ¼ 0).The filters LR combined,t ¼ Àlog 10 To assess the overall filtration performance, the combined performance of all filters over a full filter cycle is averaged.This metric is presented in Equation ( 2), which considers time discretized in T one-second intervals.
Given n filters, a defined pattern of filter performance throughout a filter cycle (phase durations and log reductions), and the initial condition of each filter (e.g., time since completion of backwashing) as inputs, the analysis presented here yields the combined log-reduction pattern over time and the overall log reduction to evaluate system performance in a particular scenario.Figure 1 illustrates a system with n filters being operated in parallel over time and the representation of combined and overall log reduction in this system.
To evaluate and compare the proportion of pathogens passing through the filter among the different phases of an individual filter cycle, the percent passage (PP) is calculated, as expressed in Equation (3).LR p and D p represent, respectively, the log reduction and the duration associated with phase p of the filter cycle (of m phases in service).The influent concentration of the pathogen is assumed to be constant over time so that only the effect of treatment performance is considered.The percent passage metric, by integrating both the log reduction and the duration of the phases of a filter cycle, is useful to evaluate how the different phases contribute to total microbial risk.Ultimately, it can indicate which phase contributes most to pathogens reaching the filter effluent (thus posing a potential risk) and, conversely, which phases have negligible contribution to risk.

| Application of parameter sweep method to evaluate impacts of changing model inputs
A simple parameter sweep approach defines the set of scenarios presented in this study.In it, only one parameter is changed at a time relative to a base case, to explore the effect of each design or operational practice individually.Although the alternative scenarios are not comprehensive, they illustrate the sensitivity of the model to each one of these parameters.In this work, the "base case" uses the filter cycle information as described in Table 1 with four parallel filters and evenly staggered backwashes.From this base case, eight sets of scenarios were explored to evaluate the effect of varying operational contexts or specific model inputs.Although some of these parameters are fixed with plant design and cannot be operationally varied, these analyses underscore the importance of detailed knowledge of system characteristics to improve treatment.Instead of representing a common or a proper way of operating a plant, the base case includes all phases of a filter cycle and a wide range of log reductions values among them to better investigate the model sensitivity to each individual change.The values of the parameters in each scenario are summarized in  (Lin et al., 2013).This analysis explored the impact of different values of log reduction during stable operation (4.7, 5.0, 5.3, 6.0, and 7.0 log) upon system performance.The lowest value is equal to that of ripening in the base case to avoid a removal during stable operation lower than the one during ripening, and 5.3 log represents the base case.4. Duration of minimum pathogen removal performance (early and late breakthrough).An operational strategy to limit pathogen passage is reducing the occurrence of breakthrough with earlier backwashing, as soon as stable operation ends and the limit for head loss, effluent turbidity, or operating time is reached (Kline, 2007).The effect of this strategy was investigated considering five pairs of early and late breakthrough duration (1 h, 0.5 h; 1 h, 0.25 h; 1 h, 0 h; 0.5 h, 0 h; 0 h, 0 h) that successively trim operation in late breakthrough and then early breakthrough conditions. 5. Magnitude of minimum pathogen removal performance (late breakthrough).Breakthrough is the phase of the filter cycle most vulnerable to pathogen passage; thus, it is important to know how much treatment can deteriorate during this critical period and how sensitive overall system performance can be to breakthrough.
Although in practice early and late breakthrough performance would be linked, this analysis considered only the effect of late breakthrough because this is the phase with minimum pathogen log reduction during the filter cycle.Five scenarios (0, 0.6, 1.2, 2.0, and 2.8 log) were considered.A log-removal of zero presumes equality of attachment and detachment while 2.8 log is the log-reduction value assigned to early breakthrough in the base case.6. Backwash staggering.Most of the available discussion related to filtration performance focuses on methods to ensure effective backwashing (Amburgey & Amirtharajah, 2005;Slavik et al., 2013).In contrast, the issue of how different backwashing schedules affect the whole system's performance is evaluated herein.Five alternative schedules are used to analyze the impact of overlapping periods of backwashing and breakthrough in different filters: case a (evenly staggered backwashes), case b (a random schedule with no backwash overlapping), case c (backwashes separated by 10 h), case d (backwashes separated by 0.5 h), and case e (backwashes separated by 0.25 h). 7. Chemical pre-treatment/coagulation.The degree of sensitivity of pathogen removal performance in filtration to coagulation varies substantially among systems.It depends on factors such as the coagulation mechanism, type of coagulant used, water quality, and plant design.Sub-optimal coagulation can also have different meanings (under-or overdosing of coagulant) and effects on filtration depending on how long the condition persists.Here, three scenarios were tested: optimal coagulation (i.e., the degree of coagulation leading to the 5.3 log reduction, in which filter effluent turbidities were below 0.1 NTU) in the base case, and two other sub-optimal coagulation scenarios.Two experiments were selected to represent the sub-optimal coagulation scenarios according to data reported by Huck et al. (2001).In sub-optimal coagulation cases I and II, the coagulant doses were reduced by 52% and 47% from the optimum doses, leading to 1.4 and 3.1 log reduction during stable operation, respectively.Concerning the effect of coagulation on performance, only data during stable operation are available.In the absence of data to evaluate the impact of sub-optimal coagulation on the other phases of the filter cycle, ripening, and early breakthrough log reductions were changed as needed so that they were no higher than the sub-optimal coagulation performance during stable operation.8. Filter-to-waste operation.Filter-to-waste operation during ripening is a common practice for avoiding subsequent treatment and distribution of water with deteriorated post-filtration quality (Soucie & Sheen, 2007).In this analysis, the total volume of water filtered during ripening would be discharged to waste.This was compared against four other scenarios without filter-to-waste operation including the base case and lower values of log reduction during ripening (4.7, 3.3, 2.0, and 1.2 log) to show the relative benefit of filter-to-waste operation in each case.These values varied from the removal during ripening (4.7 log) to the removal during late breakthrough (1.2 log) in the base case.
Notably, the performance of a filtration system can also be impacted by other factors like filter design (Papineau et al., 2013;Swertfeger et al., 1999) and hydraulics (Edzwald, 2011;Han et al., 2009).These effects were not considered in the present study because changes in performance vary on a case-by-case basis.log reduction averaging the combined performance over a full filter cycle (dark green line) for the base case of four parallel filters with evenly staggered backwashes.As a result of the step function assumed for each filter's logreduction pattern throughout the filter cycle, the combined log reduction also follows a step function with each step corresponding to a transition in the number of filters in each of the various phases of the filter cycle.In this figure, the combined log reduction starts at 5.1 when Filter 1 starts the ripening phase and Filters 2, 3, and 4 are in stable operation (Point A).After 0.5 h (Point B), ripening ends and Filter 1 joins the other three filters in stable operation, making the combined log reduction 5.3.All filters remain in stable operation for another 13.125 h until stable operation ends for Filter 4 and the combined log reduction decreases to 3.4 (Point C) with three filters in stable operation and Filter 4 in the early breakthrough phase.One hour later, Filter 4 moves to the late breakthrough phase while the other filters are still in stable operation, resulting in a combined log reduction of 1.8 (Point D).After 0.5 h at this level, when Filter 4 gets backwashed, all the other filters are in stable operation, and the combined log reduction returns to 5.3 again (Point E).When the backwash ends, the described process repeats with Filters 1, 2, and 3 in stable operation and Filter 4 at the beginning of ripening.

| RESULTS AND DISCUSSION
The overall log-reduction value represents the pathogen removal performance of the entire system of filters (i.e., plant-scale treatment performance) over the period spanning one full cycle of each filter, in the absence of any performance disruptions.Notably, overall log reduction is substantially impacted by operational phases other than stable operation.In this case, these phases represent only 3.2% (2 of 62 h) of the filter cycle and are still responsible for reducing performance from the 5.3 log achieved when all filters are in periods of stable operation (and presumed maximum performance) to a combined average performance of 3.27 log at plant-scale.This simple case study underscores that low values often drive average performance when it is evaluated on a logarithmic scale, as is commonly done in describing the treatment of waterborne pathogens.

| Number of filters operated in parallel
The treatment performance impact of splitting influent flow between more or fewer filters operated in parallel is illustrated in Figure 3.The maximum and minimum values differ depending on the number of filters at each phase of the filter cycle.For example, with 50 filters it is not possible to have them all in stable operation with evenly staggered backwashes, thus 5.3 log pathogen removal is never achieved at plant-scale, even though individual filters can achieve this level of treatment performance.Although operating fewer filters enables higher levels of plant-scale pathogen removal during some points of the filter cycle when filters are concurrently in stable operation, it also notably enables lower levels of performance at other periods of the filter cycle, as can be seen by the minimum values of the blue lines in each panel of Figure 3.The minimum level of pathogen removal achieved at plant-scale increases with increased numbers of filters because having more filters in concurrent operation with better performance dilutes (or averages out) the effect of one or more poorly performing filters.Hence, changing the number of filters does not impact overall plant-scale filtration performance (3.27 in all panels); however, increasing the number of filters reduces performance variability (variability decreases from left to right among the panels in Figure 3).This type of analysis may be useful for operations planning to increase treatment resilience because it enables the evaluation of trade-offs between maximum and minimum performance during brief periods of the filter cycle.Further work is needed to evaluate the implications of brief plant-scale performance variations on health risk.

| Duration of maximum pathogen removal performance (stable operation)
Figure 4 illustrates how the length of the stable operation period affects plant-scale performance, presuming the level of removal during stable operation is maintained.As expected, a longer duration of stable operation improves overall plant-scale pathogen removal (represented by the increasing green values from left to right among the panels in Figure 4).This is because longer periods of stable operation result in larger proportions of the filter cycle during which higher pathogen removals are achieved.In this example, the proportion of time in which combined log reduction is greater than three, which is a common minimum threshold for protozoan removal established by guidelines (U.S. EPA, 2006;Health Canada, 2019), was 88.6%, 93.8%, 96.8%, 97.8% and 98.4% for 15, 30, 60, 90, and 120 h of stable operation, respectively.Hence, filter design and operation leading to a longer stable operation phase result in increased overall plant-scale treatment performance, therefore reducing the probability of microbial contaminant passage to treated water.The length of a typical filter run should be predominantly composed of stable operation and is reflected in many performance assessment metrics such as unit filter run volume (AWWA, 2011).Periods of deteriorated source water quality tend to reduce the length of stable operation and can reduce filtration performance because of increased solids loading to filters (Polyakov, 2009), especially when chemical pre-treatment (e.g., residuals management in clarifiers) is strained (Kundert et al., 2014).
Extending the length of stable operation while avoiding breakthrough, which is not represented in this analysis, will lead to the same positive impact on plant-scale performance because stable operation would have a greater contribution to the overall log reduction.This result is particularly relevant for systems treating high-quality source water because filters are often backwashed more frequently than necessary under the belief that more frequent backwashing is better for ensuring treated water quality and managing microbial risks.

| Magnitude of maximum pathogen removal performance (stable operation)
The analysis presented in Figure 5 demonstrates the impact of increased maximum pathogen removal during stable operation on combined performance.Higher maximum pathogen removals lead to better-combined performance when all operating filters are in stable operation but do not change the periods of time at which combined performance is lowest, as indicated by the increasing maximum values and consistent minimum values, respectively, of the blue lines from left to right among the Figure 5 panels.For example, the percentage of time with pathogen removal lower than 3 log was equal to 3.2% in all cases tested.As discussed above, the lowest pathogen removal values can substantially impact overall filtration performance; thus, overall performance does not change substantially even when maximum pathogen removal is increased by orders of magnitude.Comparing the second and the last scenario in Figure 5, overall pathogen removal improved only trivially (from 3.27 to 3.28) when maximum pathogen removal increased by more than 2 log.This is because the maximum pathogen removal becomes trivially different from 100% (e.g., 99.99% at 4 log and 99.999% at 5 log) relative to the minimum log reduction (e.g., 98.42% at 1.8 log).In the base case, approximately 0.9% of the pathogens passing through a filter during a full cycle do so during stable operation, so reducing this passage by improving performance during stable operation necessarily has limited effect on the overall performance.Focusing only on stable operation, efforts to filtration performance can focus on either improving the level of pathogen removal achieved or increasing the duration of the stable operation period.However, increasing the pathogen removal performance of individual filters during stable operation has a negligible effect on overall plant-scale performance if the percentage of pathogens passing during stable operation is minimal compared to the other phases of a filter cycle.This result can be counterintuitive because of the natural tendency to consider performance data on linear rather than logarithmic scales, especially if the focus is put on the long durations of stable operation compared to the other phases of the filter cycle.Comparing the results in Figure 5 to the previous analysis (Figure 4) suggests that efforts to improve plantscale pathogen removal performance may sometimes be more impactful when directed toward increasing the duration of stable operation rather than striving to achieve inconsequential improvements in maximum pathogen removal by individual filters.Therefore, if water providers seek to increase overall treatment performance, pathogen removal performance during stable operation may not be the most important parameter to focus on, especially if performance is substantially lower during other operational periodsend-of-run breakthrough is of particular concern (Emelko et al., 2003(Emelko et al., , 2005)).

| Duration of minimum pathogen removal performance (early and late breakthrough)
The phases of the filter cycle during which performance is the poorest can substantially impact overall plant-scale filtration performance, as discussed above.Figure 6 demonstrates how decreasing the duration of the breakthrough phase improves the average performance of the system (as illustrated by the increasing green values from left to right among the panels).Whereas substantial increases in the duration of stable operation were needed to get better overall filtration performance (Figure 4), relatively small reductions in the duration of periods with minimum performance (i.e., breakthrough, here) have a substantial effect.This is because truncating the periods of low removal allows them to have less influence on the temporal average performance.Here, eliminating 0.5 h of the worst performance from each filter cycle (third scenario) improved overall pathogen removal performance more than an additional 60 h of stable operation would improve The difference in overall removal between the base case and the case with breakthrough eliminated is 2 logs, as indicated by the green values in the first and last panels of Figure 6.In the base case, 94% of the pathogen passage would occur during late breakthrough, so eliminating that phase by backwashing sooner is highly impactful.Thus, minimization or elimination of the phases of the filter cycle during which performance is the poorest can be a significant operational strategy for increasing overall plant-scale pathogen removal by filtration and increasing public health protection.The importance of these operational strategies is indicated by the continued development of tools such as online monitoring equipment that detects bacteria breakthrough to signal microbiological risk (Fujioka et al., 2019).
This analysis emphasizes the value of monitoring individual filter performance to avoid breakthrough (Huck et al., 2002).Limiting maximum individual filter effluent turbidity can improve overall plant-scale treatment performance by reacting to individual filter breakthrough while filter effluent blending still leads to acceptable combined filter effluent turbidity.The magnitude of this impact would require system-specific data for quantification.Nonetheless, given that the onset of turbidity and pathogen breakthrough can occur quickly at the end of a filter cycle (Emelko et al., 2003), it is important to eliminate or decrease the duration of breakthrough, thereby limiting individual filter effluent turbidities at the end of the filter cycle.Operational strategies like proactive backwashing can substantially enhance overall plant-scale filtration performance.Optimizing the timing of backwashing to eliminate periods of pathogen breakthrough while realizing the full benefits of stable operation by not backwashing too soon is an operational challenge.

| Magnitude of minimum pathogen removal performance (late breakthrough)
Higher minimum pathogen removal during the filter cycle (i.e., during late breakthrough) led to substantial increases in overall plant-scale filtration performance, as shown by the increasing green values from left to right among the panels in Figure 7.In contrast to the negligible effects of increasing pathogen removal during stable operation (Figure 5), this effect was similar to that of decreasing the duration of phases in the filter cycle with minimum pathogen removal (Figure 6); overall pathogen removal performance increased as the minimum pathogen removal during individual filter cycles increased.This emphasizes the importance of resilience in water treatment: performance is not only governed by how well a system can perform and how long it can perform well-it is also important to understand how much treatment deterioration occurs and can be tolerated during sub-optimal conditions.For example, it has been shown that short periods of failure and/or interruption in treatment can have a substantial impact on health risks and may not be counterbalanced by periods of good performance (Hunter et al., 2009).

| Backwash staggering
The effect of backwash staggering is illustrated in Figure 8. Case a represents the base case where the backwashes of the four filters are evenly spaced.In all other cases, the backwashes are not evenly spaced.In case b, backwash staggering was randomized.In the remaining cases, backwashes are spaced by 10, 0.5, and 0.25 h (cases c, d, and e, respectively).By reducing the time between backwashes, the phases of the filter cycle with the poorest pathogen removal performance increasingly overlap.In case c no backwashes or breakthrough periods overlap, in case d, backwashes do not overlap but up to three filters may be in breakthrough at one time (two in early breakthrough, one in late breakthrough), and in case e up to two filters can be offline for backwashing at a time and it is possible for all four filters to be in breakthrough at the same time (two in early breakthrough, two in late breakthrough).
Generally, the results show that the effect of backwash staggering on overall filtration performance (green values) is minimal; however, the minimum pathogen removal values (minimum values of blue lines) will differ depending on whether the phases of the filter cycle with the poorest pathogen removal performance coincide.It can be concluded that uneven backwash staggering presents similar performance to the base case if at least three of the filters are always in stable operations (cases b and c).Because cases d and e allow several filters to be in the breakthrough phase at the same time, a substantial reduction in combined performance is expected around the time filters are backwashed.A slight reduction in overall performance occurs in these cases because the flow is redistributed to filters exhibiting breakthrough while others are being backwashed.For example, case includes a brief period of time during which two filters are undergoing backwashing and the two filters in service are in late breakthrough.The increased flow through filters in service while other(s) are being backwashed can further reduce filter performance, but this effect was not considered in this analysis.
Because redistribution of the influent flow to other filters while a filter is being backwashed was presumed, the number of filters that can be backwashed at the same time without impacting operation depends only on how much flow the other filters can handle while maintaining equivalent performance.In this case, a good operational strategy for maintaining overall pathogen removal would be to avoid overlapping filter cycle phases with deteriorated pathogen removal when staggering filter backwashes.Ideally, backwashes should be conducted while other filters are in stable operation.This analysis was repeated without flow redistribution during backwashing, and the results are presented and discussed in Supplemental Information 1.In summary, without flow redistribution, the overall performance is not impacted by backwash scheduling because each filter processes the same amount of water regardless of other filters being backwashed; thus, various periods of treatment performance are not differently weighted by different flows.

| Chemical pre-treatment/ coagulation
As discussed in Section 2.3, the effect of coagulation conditions is variable among systems.In the present investigation depicted in Figure 9, a 1.9-and a 0.4-log decline in the overall log reduction of pathogens (green values) were observed when coagulation was not optimized in sub-optimal coagulation cases I and II, respectively.This analysis has an important contrast with Section 3.3.The analysis presented in Figure 5 showed that increasing the removal achieved during stable operation had negligible effect on overall filtration performance.Reducing the already small number of pathogens passing through the filter during this phase would be ineffective when breakthrough is the principal problem.Here, on the other hand, decreasing the removal achieved during stable operation due to sub-optimal coagulation affects overall filtration performance.The difference is that the filtration performance during stable operation in the unoptimized scenarios (1.4 and 3.1 log) is not much better than the poorest pathogen removal achieved during the filter cycle (1.2log).As a result, stable operation also contributes significantly to pathogen passage throughout a filter cycle, which explains the differences between the overall log reduction results in Figure 9.If breakthrough is prevented, stable operation affect overall filtration performance even more.Thus, the impact of coagulation on overall filtration performance is often critical.In a study conducted by Westrell et al. (2003), many microbial risks in the drinking water system studied were due to sub-optimal particle removal.

| Filter-to-waste operation
Figure 10 presents the effect of filter-to-waste practice on treatment performance.By comparing the filter-to-waste scenario to another scenario with the filter in service during ripening, it is possible to evaluate how much overall plant-scale performance (green values) may be improved by filter-to-waste operation.In this example, even when pathogen log reduction during ripening is poor (e.g., 2.0 log), there is relatively little improvement in overall log reduction if filter-to-waste operation is implemented.The fifth panel with a log reduction of 1.2 during ripening, on the other hand, shows a more marked deterioration in overall performance if filter-to-waste operation is not implemented.When filter-to-waste is not conducted, the period of deteriorated performance during ripening is averaged out by other filters in stable operation and over the course of the filter cycle by a prolonged period of stable operation.When ripening is not the worst phase of the filter cycle, the effect of filter-to-waste operation during ripening will generally be limited and the worst phase is the greater concern.Here, late breakthrough is the period of worst performance (accounting for 94%, 94%, 82%, and 49% of the pathogen passage with log reductions of 4.7, 3.3, 2.0, and 1.2 during ripening, respectively); thus, it is more impactful to avoid operation during breakthrough conditions than during ripening.Decreasing the performance during ripening increases the proportion of pathogens passing through the filters during this phase (0.03%, 0.7%, 13%, and 49%, respectively), increasing the value of filter-to-waste operation.
From a performance perspective, this practice is beneficial if pathogen removal during the ripening phase is substantially lower (e.g., 1.2 log in this example) than overall plant-scale pathogen removal considering filter-to-waste (e. g., 3.27 log in this example).However, other factors should also be considered when analyzing the benefit of filterto-waste operation.From a risk management perspective, filter-to-waste contributes to the provision of safe water by providing a means to divert effluent at any time if one or more events (e.g., sudden changes in water quality or insufficient coagulation) could lead to pathogen passage filters and, eventually, to waterborne outbreaks.

| Implications for practice research
Moving from single filter analysis to a deeper understanding of filtration operation at plant scale is critical to improve filtration performance.Due to the linearity of dose-response models at low doses (Haas et al., 1999), effects in treatment performance are carried over 1:1 to risk (e.g., a 1-log change in treatment leads to an approximately 1-log change in risk).Therefore, the results presented here are important to the management of microbial risks in drinking water and to support progress toward Sustainable Development Goal 6 to "Ensure availability and sustainable management of water and sanitation for all" (United Nations, 2023).The analyses conducted herein demonstrate how changes in several model inputs (removal and duration of various phases) can impact system performance in removing waterborne pathogens.These inputs are in turn influenced by design and operations in water treatment plants.Table 3 links elements of design and/or operational considerations to each of the eight sets of scenarios investigated.For example, if water treatment design changes the number of operating filters during an expansion project, or if filters are taken out of operation due to failures or maintenance, there will be changes in filtration performance as illustrated in the number of filters analysis.Stable operation can be impacted by design, which usually targets maximizing performance during this phase, or other operational conditions like water quality, coagulation, and hydraulic changes.While backwash staggering is mostly an operational concern (possibly within flow constraints based on design), filterto-waste operation requires modifications in the infrastructure to waste or recirculate water to the beginning of treatment.Pathogen removal during breakthrough is not practically specified as a part of design or operation but it is a function of the filter design.The duration of breakthrough, on the other hand, depends on the monitoring technologies available to support its detection and the operational strategy of timely backwashing.Given the substantial impact of this phase on overall filtration performance, it is valuable to know how sensitive the system is to breakthrough, especially if pathogen removal deteriorates before effluent turbidity.Characterizing the efficacy of pathogen removal and duration of each phase of the filter cycle could help practitioners know how system performance can be improved.The results of this research can be leveraged to support decision-making as it pertains to reducing the impact of filter operation and design decisions/practices to control potential pathogen passage.
T A B L E 3 Elements of design and operation with potential to lead to changes in plant-scale pathogen removal performance.

Analysis Design Operation
(1) Number of filters Water treatment plant design Filters taken out of operation (e.g., maintenance, low demand) (2) Duration of stable operation Filter design (configuration, media type(s) and depth, etc.) Water quality after pre-treatment (e.g., turbidity) (3) Removal during stable operation Filter design (configuration, media type(s) and depth, etc.) Coagulation optimization, Hydraulic loading (4) Duration of breakthrough Monitoring infrastructure to inform backwash initiation (e.g., turbidimeters, particle counters, software for data analysis) Although no element of operation is identified that would affect the removal during breakthrough, knowledge about the sensitivity of overall plant-scale performance to the degree of pathogen removal deterioration during breakthrough can enhance operational decisions.
Plant-scale filtration is a process comprised of smaller individual systems with inherent variations in performance, therefore is critical to understand how periods of vulnerability affect overall system (i.e., plant-scale) performance.Accordingly, the impact of individual filter design or operation on plant-scale pathogen removal performance of filtration was investigated here and the effects that changes in duration or performance during the various phases of the filter cycle have on the combined performance of several filters, either temporally or averaged over time, were demonstrated using a modeling approach.The developed framework allows assessment of whether various changes improve, degrade, or have a trivial effect on overall plant-scale performance.Hence, this framework can be used as a tool in water utilities to investigate opportunities to enhance filtration performance in the removal of microbial contaminants.The main conclusions that can be drawn from this work are as follows.
• Increasing the number of filters in asynchronous operation makes combined performance less variable without changing the overall plant-scale pathogen removal performance (Section 3.1).• Increasing the pathogen removal performance of individual filters (i.e., "higher log reduction") is not necessarily better with respect to the protection of public health.Specifically, improving filter performance during stable operation (with adequate coagulation) has a limited effect on overall plant-scale pathogen removal if the lowest pathogen removals during the filter cycle are substantially lower than those during stable operation.If portions of the filter cycle with lower pathogen removal performance are unavoidable, a longer duration of stable operation may lead to better overall plant-scale performance than higher pathogen removal performance during stable operation.In systems treating high-quality source water, avoiding unnecessary backwashing that decreases the length of the stable operation period is also beneficial to overall filtration performance (Sections 3.2 and 3.3).• Avoiding end-of-run breakthrough can markedly impact combined and overall filtration performance.Operationally, prompt backwashing following or just before the onset of breakthrough may be the most practical and beneficial change that is possible (Sections 3.4 and 3.5).• Different backwash staggering schedules change the combined pathogen removal pattern, although minimal or no changes are observed in the overall plantscale performance, depending on the adopted flow distribution regime during backwashing (Supplemental Information 1).When flow is redistributed to other filters during backwashing, overlapping of phases with poor pathogen removal should be avoided to prevent increased production from filters with low removal performance.In general, this practice also limits the severity of brief periods of deteriorated performance.Ideally, filters should be backwashed when other filters are in stable operation (Section 3.6).• Considerable deterioration of the log reduction during stable operation caused by unoptimized coagulation will often compromise the system performance, underscoring the critical importance of sufficient chemical pre-treatment by coagulation for ensuring filtration performance (Section 3.7).• From a performance perspective, filter-to-waste operation is beneficial if the pathogen removal during ripening is substantially lower than the overall plant-scale removal during the remainder of the filter cycle (Section 3.8).
differing phases of their respective filter cycles at a certain point in time; therefore they achieve different instantaneous log reductions of pathogens (LR i,t ) when they are not being backwashed.The instantaneous combined performance of the filters in operation is represented by the combined log-reduction LR combined,t , according to Equation (1).

Figure 2
Figure 2 presents the combined log reduction of pathogens at plant scale (blue step function) and the overall

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I G U R E 3 Temporal variation of combined log reduction of pathogens over one full filter cycle with varying numbers of filters and evenly staggered backwashes (analysis 1).The blue lines represent temporal variation in the combined log reduction and the dark green lines (and corresponding values) indicate overall plant-scale log reduction of pathogens.F I G U R E 4 Temporal variation of combined log reduction of pathogens over one full filter cycle with four filters, evenly staggered backwashes, and varying durations of the stable operation phase (analysis 2).The blue lines represent temporal variation in the combined log reduction and the dark green lines (and corresponding values) indicate overall plant-scale log reduction of pathogens.

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I G U R E 5 Temporal variation of combined log reduction of pathogens over one full filter cycle with four filters, evenly staggered backwashes, and varying removals during stable operation (analysis 3).The blue lines represent temporal variation in the combined log reduction and the dark green lines (and corresponding values) indicate overall plant-scale log reduction of pathogens.

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I G U R E 6 Temporal variation of combined log reduction of pathogens over one full filter cycle with four filters, evenly staggered backwashes, and varying durations of early and late breakthrough (analysis 4).The blue lines represent temporal variation in the combined log reduction and the dark green lines (and corresponding values) indicate overall plant-scale log reduction of pathogens.

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I G U R E 7 Temporal variation of combined log reduction of pathogens over one full filter cycle with four filters, evenly staggered backwashes, and varying removals during late breakthrough (analysis 5).The blue lines represent temporal variation in the combined log reduction and the dark green lines (and corresponding values) indicate overall plant-scale log reduction of pathogens.

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I G U R E 8 Temporal variation of combined log reduction of pathogens over one full filter cycle with four filters and varying backwash staggering patterns (analysis 6).The blue lines represent temporal variation in the combined log reduction and the dark green lines (and corresponding values) indicate overall plant-scale log reduction of pathogens.Case a: base case, case b: random backwash staggering, case c: backwashes spaced by 10 h, case d: backwashes spaced by 0.5 h and case e: backwashes spaced by 0.25 h.

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I G U R E 9 Temporal variation of combined log reduction of pathogens over one full filter cycle with four filters, evenly staggered backwashes, and varying coagulation conditions during stable operation (analysis 7).The blue lines represent temporal variation in the combined log reduction and the dark green lines (and corresponding values) indicate overall plant-scale log reduction of pathogens.

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I G U R E 1 0 Temporal variation of combined log reduction of pathogens over one full filter cycle with four filters, evenly staggered backwashes, and varying removals during ripening (analysis 8).The first case illustrates the filter-to-waste procedure under the base case condition.The blue lines represent temporal variation in the combined log reduction and the dark green lines (and corresponding values) indicate overall plant-scale log reduction of pathogens.
Table 2 and the code used in this paper is presented in Supplemental Information 2. The eight analyses are: 1. Number of filters operated in parallel.To represent a wide range of the number of filters that could be operated in water treatment plants of different capacities, five scenarios were analyzed with 2, 4, 8, 20, and 50 filters operated in parallel.The minimum number of fil- mance (stable operation).From a treatment perspective, filter performance is frequently associated with a high pathogen removal capacity.Accordingly, research has focused on developing technologies or applying aids to increase pathogen removal by filtration during stable operation Summary of parameter values used in each analysis.
T A B L E 2 a Alternative values tested in analyses (1-8) are shown (e.g., only the number of filters varies relative to the base case in analysis 1).