Introduction

Outbreaks of infectious intestinal diseases caused by Giardia spp. cysts and Cryptosporidium spp. oocysts are evidenced worldwide, in both developed and developing countries (Conners et al., 2021; Costa et al., 2022; Fantinatti et al., 2020; Mac Kenzie et al., 1995). Giardiasis, the disease caused by Giardia cysts, has a high incidence, and is considered the main intestinal parasite that affects human beings. These cysts and oocysts are excreted in human and animal feces and, as they are resistant to conventional methods of sewage and water treatment, the main form of transmission is through contact with contaminated water (Efstratiou et al., 2017). Despite this, a considerable part of the protozoa present in raw water can be removed during the water treatment steps, such as coagulation, filtration and disinfection (Betancourt and Rose, 2004). Some studies report that under optimized conditions of coagulation, the conventional treatment can achieve removal of cysts and oocysts of 1 to 2 logs by decantation and up to 4 logs by filtration (LeChevallier et al., 2004). However, the United States Environmental Protection Agency (USEPA, 2005, 2006) assumes a maximum of only 0.5 logs removal for the decantation step and 2.5 logs for the filtration step. Additionally, some researchers have carried out full-scale experiments and developed equations that relate the removal of protozoa to the efficiency of turbidity removal, such as the Neminski and Ongerth model (Nieminski and Ongerth, 1995). In the disinfection step of the water treatment, a strongly oxidizing chemical agent is used to inactivate (eliminate) the microorganisms. The efficiency of the inactivation of protozoa is determined by the concentration of the disinfectant agent and its contact time with the protozoa. In the water treatment, the contact time refers to the period during which the water remains in the reservoir in contact with the disinfectant agent. Giardia cysts can be efficiently inactivated in a relatively short contact time using free chlorine as a disinfectant agent, while Cryptosporidium oocysts are more resistant and require the use of stronger oxidizing agents, such as chlorine dioxide and ozone disinfection (Betancourt and Rose, 2004).

In Brazil, the current legislation (Brasil, 2017, 2021) imposes the following requirements for water treatment plants: Samples of filtered water must be collected from each filtration unit every 2 h while the plant is in operation. In at least 95% of the samples, the values of turbidity must be ≤ 0.5 NTU (nephelometric turbidity unit). On the other hand, when the arithmetic mean of Cryptosporidium concentration present in the raw water is greater than or equal to 1.0 oocyst/L, the filtration units must produce water with a turbidity value ≤ 0.3 NTU in 95% of the samples.

The Brazilian legislation also requires that, during the chlorination step, water treatment plants adhere to the necessary contact time to promote the inactivation of 1.0 log of Giardia cysts. When the treatment plant operates with free chlorine residual, the required contact time is reasonably short, making the inactivation of 1 log of Giardia cysts (or more) viable. However, when the unit is operating with residual of chloramines (combined chlorine), the necessary contact time to achieve at least 1 log of cyst inactivation is extremely long and impractical. For this reason, it is advisable for treatment plants to always operate with residual of free chlorine. Regrettably, achieving this objective is not always possible. The presence of organic matter and ammonia nitrogen causes the natural formation of chloramines during the disinfection stage of water treatment (Yang et al., 2021; Blume et al., 2010). Elevating the dosage of chlorine can eliminate a significant portion of chloramines and maintain the minimum required concentration of free chlorine residual (Tao Hui et al., 2013). Nevertheless, under certain circumstances, the concentration of organic matter may reach levels so elevated that the chlorine dosage needed to operate with free chlorine residual becomes unfeasible. Consequently, the treatment plant is compelled to use residuals of chloramines as agent disinfectant. This unwanted situation is very common in most Brazilian water treatment plants and occurs due to the excessive presence of organic matter, promoted by the improper disposal of industrial effluents and domestic sewage into water bodies (Blume et al., 2010).

Even after undergoing rigorous processes to remove impurities and pathogenic organisms, it is still possible to find small quantities of living microorganisms in the treated water. This is a result of the practical complexity of achieving complete sterilization during the water treatment. Additionally, due to technical limitations of the available methodologies (Jain et al., 2019), there are no reliable indicators that can attest the absence of pathogenic organisms in treated water samples. Therefore, it becomes pertinent to estimate and monitor the risks of microbiological infection that a population may be exposed, which can be carried out through the Quantitative Microbiological Risk Assessment (QMRA) methodology (Owens et al., 2020). This approach has been integrated into standards and criteria for the microbiological quality of water intended for human consumption across various regions worldwide. Notable instances of its adoption include Canada’ (Health Canada, 2022), New Zealand (Ministry of Health, 2005), and the USA (USEPA, 2005, 2006). The Environmental Protection Agency of Ground Water and Drinking Water Standard defines a tolerable risk value of 1.0E-4 per person per year (pppa) for several pathogenic organisms transmissible via water supply for human consumption. That means an annual risk of one infected person per 10,000 people. The World Health Organization (WHO) assumes a tolerable burden of disease of 1.0E-6 DALY (disability adjusted life years), which corresponds to a tolerable annual risk of 2.2E-3 pppa or two infected people for every 1,000 people (WHO, 2016).

The magnitude of the risk of protozoa infection relies on specific variables, including the virulence and susceptibility of the host population, the amount of water consumed during the exposure period, the concentration of (oo)cysts in the collected raw water and the removal of protozoa in the water treatment. (Owens et al., 2020; Health Canada, 2022; Kui et al., 2021; Bataiero et al., 2019). While it presents evident advantages, the QMRA methodology also comes with a notable disadvantage, as its application tends to be more intricate and, possibly, less accessible to the general public. The mathematical model incorporates probabilistic elements, where the input variables are represented by probability distributions (stochastic modeling) (Morgan & Heroin, 2007). Additionally, the data is processed through successive and numerous random samplings (iterations) using specific simulation programs.

As the estimation of infection risk directly relies on the probability distributions of the input variables, the parameters defining the shapes of the distribution curves, namely kurtosis and skewness, also become important factors. Kurtosis characterizes the flatness of the probability distribution curve. The more negative the kurtosis value, the flatter the curve compared with a normal distribution curve, meaning that the data will be more dispersed and distant from the mean. Skewness can also be negative or positive. Negative skewness indicates that the data is more concentrated to the right of the mean, i.e., in the zone of values higher than the mean. The opposite occurs when skewness is positive (Demir, 2022).

Within this context, this study proposed the application of the QMRA methodology to estimate and assess the annual risk of Giardia and Cryptosporidium infection associated with a water treatment plant located in southern Brazil. The efficiency of the treatment plant was evaluated concerning the removal of protozoa. Additionally, the study analyzed the effectiveness of Brazilian legislation concerning microbiological protection, aiming to assess the relevance of implementing the QMRA methodology. Furthermore, two distinct approaches were employed to estimate the mechanical removal of protozoa and evaluate the impact of each on the estimated values of infection risk.

Materials and methods

The study was carried out using the monitoring data from a Drinking Water Treatment Plant (DWTP) of the Municipal Department of Water and Sewage of the city of Porto Alegre (DMAE), in the state of Rio Grande do Sul, Brazil. The plant operates in conventional treatment with rapid sand filters and a mean flow rate of approximately 77 m3/min. It produces water for approximately 167,415 inhabitants, 11.26% of the total population of the municipality.

In the water treatment facilities of Porto Alegre, the presence of protozoa is not common at the points where raw water is collected. However, quantifiable concentrations of Giardia and Cryptosporidium were observed in one of the city’s five water treatment plants during the years 2015, 2016, and 2017. Consequently, the data collected in these specific years were incorporated into the current study. Additionally, the data spanning from 2018 to 2021, obtained from the same treatment plant, were included to offer a more recent and accurate representation of the standard conditions of water treatment in Porto Alegre.

From a general and summarized perspective, the study adhered to the following sequence of execution:

  1. (1)

    Estimation of the mechanical removal of protozoa (Giardia and Cryptosporidium) based on the turbidity data from raw and filtered water provided by the monitoring history of the treatment plant.

  2. (2)

    Estimation of inactivation of Giardia cyst based on the reservoir water data, such as contact time, residual of free chlorine, pH, and temperature, obtained from the monitoring history of the treatment plant.

  3. (3)

    Estimation of the total removal of Giardia cysts by combining mechanical removal and inactivation data. The total removal of Cryptosporidium oocysts was equivalent to the mechanical removal, given that this protozoan is not inactivated by chlorine.

  4. (4)

    Identification of the distribution functions that most accurately represents the behavior of the removal data of protozoa and the (oo)cyst concentration data in raw water.

  5. (5)

    Estimation of the risk values of protozoa infection based on the data and results obtained in the previous steps.

  6. (6)

    Evaluation of the obtained results.

Mechanical removal of protozoa

The water treatment plant has 12 filtration units. The analysts of the treatment plant collected and analyzed samples of raw water and filtered water from each filter every 2 h. In total, approximately 360 samples of raw water and 4320 samples of filtered water were analyzed per month. All the collected samples were considered in the present study. The method of analysis used was the nephelometric method according to the Standard Methods for the Examination of Water and Wastewater 23rd Edition.

Two different approaches were used to estimate the mechanical removal of protozoa (via filtration): the USEPA definitions, referred to as Approach A, and the mathematical model of Neminski and Ongerth, referred to as Approach B. Considering the USEPA definitions, a 3 logs removal of protozoa was defined for the months in which at least 95% of the samples of filtered water presented turbidity ≤ 0.3 NTU. As to the months in which the limit of 0.5 NTU was respected in at least 95% of the samples, a removal of 2.5 logs was considered for Giardia cysts and 2.0 logs for Cryptosporidium cysts. In Table 1, this classification can be observed more clearly. To apply the Neminski and Ongerth model (Eqs. 1 and 2), the percentage of turbidity removal was determined by utilizing the monthly median values from the turbidity data of raw water (approximately 360 samples per month) and the turbidity data of filtered water (approximately 4320 samples per month).

Table 1 Values of protozoa removal in accordance with the turbidity limits of filtered water and the classification defined by the USEPA (Approach A)​​
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$$\mathrm{Log}\;\mathrm{Giardia}\;\mathrm{removal}\;=\;1,0093\;\mathrm{logs}\;\left(\%\mathrm{turbidity}\;\mathrm{removal}\right)\;+\;1,6697$$
(1)
$$\mathrm{Log}\;\mathrm{Cryptosporidium}\;\mathrm{removal}\;=\;0,931\;\mathrm{logs}\;\left(\%\;\mathrm{turbidity}\;\mathrm{removal}\right)\;+\;1,009$$
(2)

Inactivation of Giardia

In the disinfection stage, the water treatment plant employs chlorine gas as disinfectant agent. The residuals of free chlorine at the outlet of the reservoirs were monitored every two hours by the treatment plant analysts. The analytical method used was the colorimetric method according to the methodology described in the Standard Methods for the Examination of Water and Wastewater 23rd Edition (4500-Cl-G—SMEWW). The managers of the treatment plant calculated the daily contact time based on the average water flow in the reservoirs and the dimensions of the pipes and reservoirs, following the guidelines of the LT1ESWTR Disinfection Profiling and Benchmarking Technical Guidance Manual (USEPA, 2003).

After collecting all the necessary data, the Eq. 3 was used to estimate the daily inactivation (measured in logs) of Giardia cysts, where, “t” is the daily contact time, “C” is the daily mean of residual free chlorine at the reservoir monitoring point, and “pH” and “T” is the pH and the temperature of the water stored in the reservoir. (USEPA, 1991).

$$\mathrm{Log}\;\mathrm{inactivation}\;\mathrm{of}\;\mathrm{Gardiacyst}=\frac{C\times t}{0.2828\times pH^{2.69}\times{0.933}^{T-5}}$$
(3)

The treatment plant has two reservoirs for storing treated water. The reservoirs have different dimensions, and therefore, different contact times and inactivation efficiencies. The longer the contact time, the higher the logs value of inactivation. To organize the evaluation of the results, the author chose to classify the smaller reservoir as “Reservoir 1” and the larger reservoir as “Reservoir 2.”

Total removal of protozoa

The total daily removal of Giardia cysts (logs) was calculated by adding the daily mechanical removal (filtration) to the daily chemical inactivation (chlorination). For the total daily removal of Cryptosporidium oocysts, only the daily mechanical removal was considered, since the oocysts are resistant to chlorine. The monthly means of the daily results were subsequently used in the assignment step of the distribution function of the annual data. It is important to highlight that the removal of protozoa was measured in logs.

Concentration of protozoa in raw water

The samples for determining the concentration of cysts and oocysts in raw water were collected monthly from 2015 to 2017 and annually throughout the years 2018 to 2021. The sampling frequency obeyed the Brazilian standard, which requires the protozoa monitoring only when is identified a moving geometric mean ≥ 1000 Escherichia coli/100 mL. The concentration of protozoa in raw water was determined by the EPA Method 1623.1:2012, which has a limit of quantification (LQ) of 0.1 cyst or oocyst per liter. This means that this analytical technique is not capable of providing a reliable result for concentrations of (oo)cysts below this value. These analyses were conducted by an external laboratory certified in accordance with the Standard ISO/IEC 17025 (General requirements for the competence of testing and calibration laboratories).

Estimation of the probability of infection

The probability of pathogen exposure is characterized by the Poisson distribution, while the probability of infection is described by a binomial process, meaning there are two possible outcomes: infection or non-infection. The literature has established the exponential dose–response model to express the probability of protozoa infection (Haas et al., 2014). This model assumes that all organisms have the same probability of survival and causing infection in the host. Thus, the probability of infection associated with any organism is equal to 1/k, where k is the dose–response parameter that characterizes the agent-host interaction. The daily dose ingested of protozoa is estimated based on the data of protozoa concentration in the raw water, the removal of protozoa during the water treatment, and the amount of water ingested daily. Therefore, the probability of infection associated with the ingestion of a daily dose is given by Eq. 4 (Haas et al., 2014; VOSE, 2008).

$${\text{P}}_{\text{i}}\text{ = 1- }{\text{e}}^{\text{(}-{\text{k}}\text{ . }{\text{C}}\text{ . }{\text{I}}\text{ . }{10}^{-{\text{R}}}\text{)}}$$
(4)

where the input variables are “I” is the daily water ingestion per person, “C” is the pathogen concentration in the raw water, “R” is the removal of the pathogen in the water treatment, and “k” is the dose–response model parameter.

The probability of infection for a daily exposure is given by “Pi,” so the probability of not being infected is “1-Pi.” Therefore, for 365 days of exposure, the probability of infection is given by the Eq. 5 (Haas et al., 2014).

$${\text{P}}_{\text{j}}\text{ = 1-}\prod\nolimits_{{\text{j}}= \text{1} }^{365}\text{[1} \, - \, {\text{P}}_{\text{i}}^{\left({\text{j}}\right)}\text{]}$$
(5)

Before estimating the infection risk values, it was necessary to define the distribution functions of the input variables. For the parameter “k,” referring to the Giardia-host interaction, a triangular distribution function was considered with the minimum value of 0.009798, the most likely value of 0.01982 and the maximum value of 0.03582 (Rose et al., 1991). While for the “k” referring to the Cryptosporidium-host interaction, a triangular distribution was considered with the minimum value of 0.0022, the most likely value of 0.00419 and the maximum value of 0.0085 (Dupont et al., 1995). For the daily water ingestion per person, a triangular distribution was also considered, with the following values: 0.5 L (minimum value), 1.5 L (most likely value) and 2.0 L (maximum value).

As previously mentioned, Cryptosporidium oocysts exhibit high resistance to chlorine. Consequently, in this study, their removal was solely mechanical. The turbidity data of filtered water is characterized by values of low amplitude. Consequently, the estimated data for the removal of Cryptosporidium presents an insignificant variation. Due to this, fitting a distribution function to this data is neither necessary nor feasible. Therefore, for each year, the authors opted to use the annual average removal of Cryptosporidium as a constant value in the input variable “R” of the Eq. 4.

The estimated values for removal of Giardia, as well as the concentration data of protozoa in raw water, were analyzed using Minitab® Statistical Software (Minitab LLC, State College, PA, 2022) to identify the distribution function that best represented (highest p-value) the behavior of these data in each year. Each dataset evaluated had a size of 12 samples, that is, a value representing each month of the year. For the extended periods where there was no detection or quantification of protozoa in raw water, i.e., for periods where the protozoa concentration could be any value below 0.1 (oo)cysts/L (limit of quantification of the analytical technique), the authors defined a uniform distribution function with a mean of 0.05 (oo)cysts/L, a minimum limit of 0.01 (oo)cysts/L, and a maximum limit of 0.09 (oo)cysts/L.

After defining the distribution functions of the input variables, the daily risk of infection was estimated through successive and random sampling (iterations) using the Latin Hypercube simulation technique in the @RISK® 8.0 software (Vose, 2008; Palisade Corporation, 2022). In summary, 1,825,000 values of daily risk of infection were obtained (Eq. 4) through 365 iterations repeated 5000 times. That is, for every 365 daily risk values, an annual risk value was calculated, totaling 5000 values of annual risk of infection (Eq. 5). This operation was performed for each condition investigated, specifically, for each year, each Approach (A or B) and for each type of water reservoir (Reservoirs 1 and 2).

Nomenclature for results presentation

To facilitate the presentation of the results, a nomenclature was established for each condition studied:

  • Res1A-Considering the water stored in the Reservoir 1 and the USEPA definitions to estimate the mechanical removal of protozoa (Approach A).

  • Res2A-Considering the water stored in the Reservoir 2 and the USEPA definitions to estimate the mechanical removal of protozoa (Approach A).

  • Res1B-Considering the water stored in the Reservoir 1 and the Neminski and Ongerth Model to estimate the mechanical removal of protozoa (Approach B).

  • Res2B-Considering the water stored in the Reservoir 2 and the Neminski and Ongerth Model to estimate the mechanical removal of protozoa (Approach B).

Summarizing the study in flowcharts

For a clearer understanding of how the study was implemented, Fig. 1 provides flowcharts summarizing the necessary steps to estimate the total removal of Giardia (a), the total removal of Cryptosporidium (b), and the annual risk of protozoa infection (c).

Fig. 1
figure 1

Flowchart summarizing the necessary steps to estimate the total removal of Giardia (a), the total removal of Cryptosporidium (b), and the annual risk of protozoa infection (c)

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Statistical tests

The data related to the inactivation of Giardia, the total removal of protozoa and the annual infection risk were subjected to statistical analysis using the Student’s t-test. The normality of the data was checked using the Shapiro–Wilk and d’Agostino-Pearson tests. The homogeneity of the variances among the datasets was examined using the Levine test with the purpose of adapting the t-test for each type of condition (homoscedastic or heteroscedastic).

The datasets of annual infection risk were also tested concerning the tolerance limits established by the WHO and the USEPA. All calculations were conducted with a significance level set at 0.05. Therefore, for results with p-values greater than 0.05, the “null hypothesis” was not rejected, and the means of the datasets were considered statistically equal.

Additionally, the Student’s t-test was used to estimate the margins of error (considering 95% confidence) of the inactivation data of Giardia and the total removal data of protozoa.

Results and discussion

Concentration of protozoa in raw water

The graph in Fig. 2 shows the concentrations of cysts and oocysts present in the samples of raw water collected throughout the years 2015 to 2017. In most months, it was not possible to detect or quantify Cryptosporidium oocysts. In these cases, the concentration was plotted as zero on the graph.

Fig. 2
figure 2

Concentration of protozoa in raw water throughout the years 2015 to 2017

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The peak concentrations of Giardia cysts were observed in 2016, reaching maximum values of 21.5 and 17.4 cysts/L during the months of September and October, respectively. As for Cryptosporidium oocysts, the highest concentration recorded was 1.3 oocysts/L in July 2016.

Table 2 shows the annual medians values of the Giardia and Cryptosporidium concentration and the distribution function that best represented these data. The highest values of protozoa concentration occurred in 2016, when medians of 8.0 cyst/L and 0.6 oocyst/L were obtained.

Table 2 The median values and the type of function distribution of protozoa concentration data throughout the years 2015 to 2021
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From January 2018 to December 2021, no cysts and oocysts were detected or quantified in raw water (methodology quantification limit of 0.1 (oo)cyst/L). During this period, the data distribution was considered a uniform distribution with a lower limit of 0.01 and upper limit of 0.09 (oo)cyst/L, in addition to a median value of 0.05 (oo)cyst/L.

Turbidity and mechanical removal of protozoa

Table 3 presents the number of months per year in which at least 95% of the samples collected of filtered water did not exceed the limits of 0.3 and 0.5 NTU (nephelometric turbidity unit). In total, during the period between 2015 and 2021, in 75% of the months the value of 0.3 NTU was not exceeded in at least 95% of the data of turbidity. In the remaining 25%, the amount of data with a turbidity value ≤ 0.3 NTU ranged from 78.5 to 94.6%, with the maximum limit of 0.5 NTU being respected in at least 95% of these data.

Table 3 The number of months per year in which at least 95% of the turbidity data from filtered water did not exceed the 0.3 and 0.5 NTU limits, and the percentage of turbidity removed per year
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The removal values of turbidity (%) obtained for each year are also exposed in Table 3. From these values, a mean and a standard deviation of 99.18% ± 0.31% were obtained, with a minimum value of 98.00% (in April/2021) and a maximum value of 99.62% (in August /2016).

An excellent performance of filtration was observed during the years 2019 and 2020, where 92% of the months had at least 95% of the values of turbidity less than or equal to 0.3 NTU. However, in 2020, it was noticed the lowest percentage of removal of turbidity compared with other years (98.94%). This occurred because the percentage of removal of turbidity also depends on the value of the initial turbidity, i.e., the turbidity of the raw water. In other words, the removal of turbidity was lower because the “amount” of turbidity to be removed in 2020 was also lower.

In terms of legislation, it can be stated that the filtration units of the treatment plant showed a good performance. In accordance with Brazilian regulations, it is obligatory to maintain turbidity ≤ 0.3 NTU only when the arithmetic mean of Cryptosporidium concentration is greater than or equal to 1.0 oocyst/L. According to the results presented in the previous section, this threshold was not exceeded at any time. This suggests that maintaining turbidity below 0.5 NTU would be sufficient to meet regulatory requirements.

Through the Approach A, the mechanical removal values of protozoa were determined based on the classification presented in Table 1. To exemplify, throughout the year of 2015, the mechanical removal was set at 2.5 logs for Giardia and 2.0 logs for Cryptosporidium for five months, while for the remaining 7 months, the mechanical removal of protozoa was defined as 3.0 logs.

Therefore, we can state that in the years 2015, 2017, and 2021 the performance in mechanical removal of protozoa was lower than the performance in the years 2016, 2018, 2019, and 2020.

When employing the Approach B (Eqs. 1 and 2), the same removal values of 3.69 logs for Giardia and 3.02 logs for Cryptosporidium were obtained to all years. In other words, the annual variation among the percentage values of turbidity removal (presented in Table 3) was not significant enough to yield a difference among the values of annual mechanical removal of protozoa obtained through the Approach B.

The maximum value of mechanical removal of Giardia achievable under the Approach A is 3.0 logs. Then, in summary, we can attest that the Approach B may produce mechanical removal values of giardia greater (3.69 logs) than the maximum possible value obtained via the Approach A (3.0 logs).

Statistical tests (p-values)

Statistics of the inactivation data of Giardia

Table 4 displays the p-values from t-tests conducted to compare the inactivation data of Giardia from different reservoirs for each year. Meanwhile, Table 5 presents the p-values obtained to compare the inactivation data from different years in each reservoir.

Table 4 Results of Student’s t-test statistics between the datasets from different reservoirs, per year
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Table 5 Results of Student's t-test statistics between the datasets from different years, per reservoir
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The p-values (t-test) below 0.05 and approaching zero confirmed the statistical distinctions between the data from the Reservoir 1 and the Reservoir 2. The same was evidenced when comparing the data across the years, with a few exceptions: Considering the data from the same reservoir, the mean of the 2015 dataset can be considered statistically equivalent to the means of the 2017 and 2018 datasets, as p-values ranged from 0.16 to 0.23. Similarly, the means of the 2016 and 2021 datasets from Reservoir 2 exhibited a p-value of 0.18, supporting the conclusion that they can be deemed statistically equivalent.

Statistics of the removal data of Giardia

Table 6 presents the results of the Student’s t-test statistic (p-value) determined for the removal data of Giardia from all possible year combinations within each studied condition (reservoir and approach). Some datasets presented p-values > 0.05, which means that there is no statistical difference among them. These results will be further discussed in the “Total removal of Giardia” section.

Table 6 Results of Student’s t-test statistics between the datasets from different years and same condition (reservoir and approach)
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To validate the discussions developed in “The impacts of skewness and kurtosis” section, Student’s t-test were applied to confirm whether the mean of the removal of Giardia in the 2021 Res2A condition was statistically different from the means of the 2020 Res2A, 2018 Res1A, and 2019 Res1A conditions. As observed in Table 7, the obtained p-values were < 0.05, indicating that these datasets are statistically distinct.

Table 7 Results of t-test statistics between data from the 2021 Res2A condition and data from the 2020 Res2A, 2018 Res1A and 2019 Res1A conditions
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Statistics of infection risk datasets

In all t-tests performed with the data of annual infection risk, every obtained p-value was found to be below 0.05 and the vast majority of them were equal to absolute zero, confirming the statistical difference among these datasets.

Inactivation of Giardia

The inactivation values (in logs) of Giardia were calculated (Eq. 3) for each day of each year, meaning that 365 inactivation values of Giardia were obtained per year (per dataset). Table 8 provides a summary of these values through the annual mean and a margin of error considering 95% confidence, along with the standard deviation (SD) of the samples.

Table 8 The annual mean (± margin of error considering 95% confidence) and the standard deviation (SD) values of the inactivation data of Giardia (in logs)
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The inactivation values of Giardia associated with the Reservoir 2 exceed those of the Reservoir 1 by more than twice. This was expected, since the Reservoir 2 is significantly larger than Reservoir 1 and, therefore, provides a longer contact time between the pathogens and the oxidizing agent.

In general, the years 2015, 2017, and 2018 showed the best performances, with annual means of inactivation of Giardia close to 2.2 logs in the Reservoir 1 and 4.8 logs in the Reservoir 2.

The least favorable inactivation results occurred in 2020, with means of 1.10 logs ± 0.08 logs in the Reservoir 1 and 2.58 logs ± 0.20 in the Reservoir 2. In comparison with 2020, the years 2016 and 2021 showed improved inactivation performances. In the Reservoir 1, the means were 1.68 ± 0.07 logs and 1.54 ± 0.09 logs for the years 2016 and 2021, respectively. As for the Reservoir 2, the removal mean ranged between 3.57 and 4.05 logs in the years 2016 and 2021.

In the monitoring history of the treatment plant, it was observed that the plant was unable to operate with residuals of free chlorine on approximately 13% of the days in 2016, 40% of the days in 2020, and 25% of the days in 2021. In other words, during these periods, the microbiological disinfection was conducted with chloramine residuals, consequently impairing the performance of inactivation of Giardia cysts. As previously mentioned in the “Introduction” section of this study, the formation of chloramines can naturally occur in the presence of organic matter. In addition to the volume and frequency of improper discharge of pollutants, the concentration of organic matter in the raw water can also vary with weather variations, such as temperature, rainfall volume, and sunlight exposure. These variations can directly impact the self-purification capacity of the water body used to supply the water treatment plant. In summary, it is presumed that during the periods when the plant operated with chloramine residuals, the concentration of organic matter and ammonia nitrogen at the collection points of raw water was higher than usual.

Total removal of Giardia

The chemical inactivation values of Giardia were added to the values of mechanical removal to obtain the total removal values of Giardia (in logs). Table 9 presents the values of arithmetic mean and a margin of error considering 95% confidence, the standard deviation (SD), the median, and the type of distribution function of each total removal dataset of Giardia, including their shape measurements (skewness and kurtosis).

Table 9 The values of arithmetic mean (± margin of error considering 95% confidence), standard deviation (SD), median, skewness, kurtosis, and the type of distribution function of the data of total removal of Giardia
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In summary, the following ascending order of the median values of total removal of Giardia was observed: Res1A < Res1B < Res2A < Res2B. This behavior was already expected, since the inactivation values of Giardia were higher in the Reservoir 2 (Table 8).

In general, the distributions showed skewness values between − 1 and + 1, indicating a low degree of skewness. In addition, most of the dataset showed a negative skewness, which indicates that the data is concentrated above its mean. This is possible to confirm by observing the mean and median data in Table 9: The conditions with negative skewness presented median values greater than the mean values. As for kurtosis, the negative values indicated a platykurtic distribution, that is, most of the data shown in Table 9 are distributed in a more dispersed way (flatter curve) than in a normal distribution.

The graph in Fig. 3 displays the values of the mean total removal of Giardia on the y-axis and the studied years on the x-axis, with each line representing a studied condition.

Fig. 3
figure 3

The mean of the total removal of Giardia (logs) by year and condition

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Analyzing Fig. 3 together with Table 6 (p-values) allowed for the following observations: In all studied conditions, the means of the data of 2020 are indeed lower than the means of the data from other years (p-value < 0.05), except for the means of the 2021 data from Reservoir 1, which can be considered equal to those of 2020 (p-value > 0.05). Therefore, it is appropriate to assert that the poorest performance in removal of Giardia occurred in the years 2020 and 2021, in the Reservoir 1, using the Approach A (mean between 4.00 and 4.40 logs).

The mean values for the years 2015, 2017, 2018, and 2019 are statistically equal within each condition studied (p-value > 0.05). Consequently, it is possible to affirm that, considering the same reservoir and approach, the removal performances of Giardia of these years can be considered similar to each other and superior to the performances presented in the other years (2016, 2020, and 2021).

The less satisfactory performances of the years 2016, 2020, and 2021 can be explained by their low efficiencies in chemical inactivation, as highlighted in Table 8 and discussed earlier in the corresponding section.

Comparing the obtained values among the different conditions, it was concluded that the best performance occurred in the Reservoir 2 using the Approach B (Res 2B). In Fig. 3, it is possible to observe that the highest means reached values around 8.5 logs of total removal of Giardia. (in the years 2015, 2017, 2018, and 2019).

Annual risk of Giardia and Cryptosporidium infection

During the period in which protozoa were detected in the raw water (2015 to 2017), the concentration of Giardia cysts was significantly higher than the concentration of Cryptosporidium oocysts (Fig. 2). Despite this, the annual risk values for Cryptosporidium infection were considerably higher than the annual risk values for Giardia infection, as observed in Table 10. Table 10 presents the 95th percentile values derived from the data of annual infection risk obtained through the simulations carried out in this study.

Table 10 The annual risk values of Giardia and Cryptosporidium infection calculated for the Reservoirs 1 and 2 using the Approach A and the Approach B
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These results can be attributed to the fact that Cryptosporidium oocysts does not undergo inactivation during the chlorination stage. In some years, the differences between the risk values of Cryptosporidium and Giardia infection were even more pronounced. In the year 2018, the annual risk values of Cryptosporidium infection were approximately 7000 and 59,000 times higher than the annual risk values of Giardia infection using the Approach A and the Approach B, respectively. In the year 2019, the annual risk values of Cryptosporidium infection were approximately 5000 and 16,000 times higher than those of Giardia infection, using the Approach A and the Approach B, respectively. These notable differences can be explained by the high levels of inactivation of Giardia in the years 2018 and 2019 (as evidenced in Table 8) combined with Giardia concentrations below 0.1 cysts/L (LQ of the method), which contributed to a significant reduction in the estimated values of infection risk.

Table 11 presents the reduction values (in percentage) in the annual risk of protozoa infection when the Approach A was replaced by the Approach B to estimate the removal values of protozoa. In this case, the annual risk of Giardia infection reduced by approximately 86% ± 6.4%. For the annual risk of Cryptosporidium infection, the reduction was more pronounced in the years 2015 (− 64%), 2017 (− 70%), and 2021 (− 55%). This is plausible, considering that in these years, the mechanical removal estimated by the Approach A presented the lowest values, according to the observations presented in the “Turbidity and mechanical removal of protozoa” section.

Table 11 The percentage reduction in the infection risk due to the replacement of the Approach A by the Approach B
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The impacts of skewness and kurtosis

For a better evaluation of the datasets, the annual risk results of Giardia infection (obtained by the Approach A) were ranked in descending order in Table 12. This table also presents the values of median concentration of cysts, total removal mean of cysts, and the parameters that define the shape of the distribution curves of total removal data of Giardia cysts (skewness and kurtosis). The highest risk values of Giardia infection occurred in the year 2016 (5.04E-03), which is probably related to the highest median concentration of cysts in raw water (8 cysts/L).

Table 12 Classification (in descending order of risk) of the conditions studied in the Approach A and the input variables (total removal of cysts, skewness, kurtosis, and Giardia concentration)
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The influence of the values of skewness and kurtosis on the magnitude of the annual risk values can be evidenced through the conditions classified in the positions 7 to 10 of Table 12.

Although the conditions classified at the positions 8, 9, and 10 presented considerably lower mean values of total removal than the condition 2021 Res2A (position 7), these conditions presented lower risk values of infection. To facilitate the comparison among these results, the data were plotted in a graph in the Fig. 4. The distribution curve of the total removal data of cysts for the condition 2020 Res2A (position 8) showed a positive skewness (0.12) and a negative kurtosis (− 1.13), while the distribution curve for the condition 2021 Res2A (position 7) showed a negative skewness (− 0.74) and a positive kurtosis (0.48). This suggests that the negative kurtosis of − 1.13 was the factor responsible for the value of infection risk of the condition 2020 Res2A (position 8) not being higher than the value obtained for the condition 2021 Res2A (position 7), even the latter presenting a higher mean value of total removal of cysts. Furthermore, the results presented for the conditions 2018 Res1A and 2019 Res1A (positions 9 and 10) indicated that the reduction in the risk of infection was even more pronounced when both skewness and kurtosis values were negatives.

Fig. 4
figure 4

Comparison among the results of annual risk of infection, total removal mean of cysts, skewness, and kurtosis of the distribution curves of the cysts removal data; for the conditions 2021 Res2A, 2020 Res2A, 2018 Res1A, and 2019 Res1A

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As anticipated, the distribution characteristics of the removal data of Giardia (skewness and kurtosis) were as crucial for reducing the infection risk values as the magnitude of the mean values of total removal of cysts.

It is well established that a negative kurtosis indicates a flatter distribution curve, meaning the data points are more dispersed than on a normal curve. When a negative kurtosis is combined with a negative skewness, it may indicate that a significant portion of the dataset values is considerably higher than the mean. Consequently, in simulations of such distributions, a majority of iterations will involve values significantly exceeding the mean. This, in turn, can results in a notably lower annual risk value of infection (95th percentile) at the conclusion of the simulations.

The annual infection risks and the tolerable limits

The annual risks of infection were compared with the tolerable annual risks defined by the US Environmental Protection Agency—USEPA (1.0E-4 pppa) and by the World Health Organization -WHO (2.2E-3 pppa), in Table 13.

Table 13 Comparison of the annual risks of infection obtained in this study with the tolerable annual risks defined by the USEPA (1.0E-4 pppa) and WHO (2.2E-3 pppa)
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Conditions in which the annual risk did not exceed the tolerable annual risk were flagged with an “OK.” The others were evaluated based on the magnitude of the risk according to the tolerable values (1.0E-4 and 2.2E-3 pppa), for example: the 2016 Res1A condition presented an annual risk of Giardia infection 50 times greater than the tolerable risk stipulated by the EPA and 2.5 times greater than the tolerable risk stipulated by the WHO.

Except for Res1B in 2016, all conditions demonstrated an annual risk of Giardia infection within the tolerable limits when utilizing the Approach B. From 2017 to 2021, none of the annual risk values for Giardia infection exceeded the WHO tolerable limit, regardless of the Approach applied.

For the annual risk of Cryptosporidium infection, none of the conditions studied respected the limit imposed by the USEPA, not even the conditions with concentrations below 0.1 oocysts/L (2018 to 2021). However, considering the WHO limit, only the year 2016 (in both the Approaches) and the years 2015 and 2017 (only in the Approach A) presented risk values considered intolerable.

Table 14 presents the values of annual infection risk obtained under conditions that represent the requirements of the Brazilian legislation (17, 18). In the condition of 3.0 logs of removal of Cryptosporidium and 1.0 oocyst/L of concentration of Cryptosporidium, the annual infection risk obtained was higher than the values considered tolerable.

Table 14 The estimated annual infection risks based on the requirements of the Brazilian legislation
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In the other conditions, the values of annual infection risk remained below the tolerable value recommended by the WHO (2.2E-3 pppa), but above the tolerable value recommended by the USEPA (1.0E-4 pppa). Therefore, it is evident that when the concentration of protozoa is greater than 1.0 (oo)cysts/L, the value of annual infection risk must significantly exceed the recommended tolerable value. Due to this observation, it was concluded that the conventional requirements present in the Brazilian legislation are not sufficient to guarantee the microbiological safety of drinking water.

Conclusion

The water treatment plant examined in this study successfully reached the biological control requirements mandated by the Brazilian legislation. Due to the greater chlorine resistance exhibited by Cryptosporidium oocysts, the estimated values for the annual risk of Cryptosporidium infection were higher compared with the calculated values for annual risk of Giardia infection. This occurred even when the concentration of Giardia cysts in the raw water intake was significantly higher than the concentration of Cryptosporidium oocysts. Given that a high level of pollution in water bodies is predominant in the Brazilian context, it is possible to state that the risk values of protozoa infection estimated were satisfactory, closely approaching or falling below the tolerable risk defined by the World Health Organization.

The values of infection risk derived from the Neminski and Ongerth model (Approach B) were notably lower than those obtained using the USEPA definitions (Approach A). This highlights the impact that the approach used to estimate the removal of protozoa can have on the estimation of infection risk. Despite the mathematical complexity associated with the Quantitative Microbial Risk Assessment (QMRA) method, it is imperative for the Brazilian authorities to consider and evaluate its implementation. This is essential given that the requirements and guidance provided by the local legislation have proven to be ineffective, and the QMRA application can effectively contribute to the prevention and investigation of outbreaks of waterborne diseases.

In conclusion, it is important to emphasize that efforts to ensure a low risk of microbiological infection should not solely focus on water treatment. Instead, it is crucial to direct greater attention to resolving the problems related to inappropriate disposal of industrial effluents and domestic sewage into water bodies.