Seasonal variations of potentially toxic elements (PTEs) in drinking water and health risk assessment via Monte Carlo simulation and Sobol sensitivity analysis in southern Iran's largest city

The escalating concern over the presence and health implications of potentially toxic elements (PTEs) in drinking water has underscored the need for rigorous risk assessments. Our study aimed to quantify both the non-carcinogenic and carcinogenic health risks associated with exposure to selected PTEs—namely arsenic (As), chromium (Cr), and cadmium (Cd). Also, we evaluated ingestion and skin contact exposures to risks during summer and winter using metrics such as the hazard quotient (HQ), hazard index (HI), and cancer risk (CR) for children, adult males, and adult females. For all demographic groups and exposure pathways, the HQ values remain below the established safety threshold (HQ < 1). Notably, As consistently had the highest average HI value across children, male adults, and female adults. Seasonal variations were statistically significant (p < 0.05) for As and Cr, but not Cd. During the summer, the average total carcinogenic risks (TCR) from drinking water exposure were 7.61 × 10–6, 8.94 × 10–6, and 1.12 × 10–5 for children, male adults, and female adults, respectively. In the winter, these values were 1.18 × 10–5, 1.40 × 10–5, and 1.75 × 10–5, respectively. The fuzzy C-means clustering analysis provided insights into our dataset's Cr, Cd, and As distribution patterns. Results indicate that As, Cr, and Cd mean concentrations were below the World Health Organization health-based guidelines. The CR values for children and adults from drinking water exposure were slightly above or below the US Environmental Protection Agency’s standards. These findings can inform research and policy-making regarding the risk of PTEs in drinking water and highlight the need to monitor Shiraz water regularly.


Introduction
The world is undergoing unprecedented, rapid urbanization, which has profound impacts on water resources across the globe (Ajloon et al. 2022;Ayejoto et al. 2023b;Alao et al. 2023).In many regions, the establishment and growth of cities are directly influenced by accessibility to water.The growth of the human population in both urban and rural settings has been accompanied by a consequential increase in waste produced from residential, commercial, and industrial activities (Ezugwu et al. 2019;Ayejoto et al. 2022Ayejoto et al. , 2023a)).Further, industrialization, mining, widespread application of potentially harmful agricultural chemicals, poor land management, unsanitary practices, and excessive water consumption contribute significantly to the deterioration of groundwater quality.This compromised water quality substantially threatens human health (Egbueri et al. 2023b, a).Potentially toxic elements (PTEs) are one of the most significant categories of contaminants that enter the water supply regularly from both natural and anthropogenic sources (Egbueri and Enyigwe 2020;Luo et al. 2022;Talema 2023;Nie et al. 2023).Heavy metal (loid) levels in natural water are influenced by the aquifer's geology, water quality, and geochemistry (e.g., decomposition and weathering of bedrock and mineral deposits) (Aşkan et al. 2021;Chauhan et al. 2022;Hui et al. 2023).Anthropogenic activities that pollute water sources include electroplating, metal processing, quarrying, industrialization, and farming wastewater discharges (Hu et al. 2019).PTEs do not degrade; they can bioaccumulate and directly or indirectly threaten human health and ecosystems (Gao et al. 2022a;Zoghi et al. 2022;Onyeaka et al. 2022).Many PTE ions are toxic or carcinogenic (Bera et al. 2022).The accumulation of PTEs in the body has serious health repercussions, including growth and developmental problems, cancer, neuromuscular defects, mental disease, and metabolic issues (Mishra et al. 2019;Ameri et al. 2021;Cai et al. 2023).The World Health Organization (WHO) has established maximum contaminant levels (MCLs) for many PTEs to protect public health (Abdullah et al. 2019).
Arsenic (As) is a metalloid that may be present in both inorganic and organic types and is a human carcinogen (Hu et al. 2022;Genchi et al. 2022).As is a naturally occurring element in the air, stones, minerals, earth, waters, and the ecosystem.The WHO health-based guideline for As in drinking water is a maximum concentration of 10 µg/L (Mondal et al. 2021).The availability of As (up to > 1000 µg/L) in many water supplies is due to natural contamination caused by As migration from geogenic origins.Human activities like mining and associated operations can accelerate the release of As.Due to increasing world population, farming practices, and unsustainable groundwater consumption, As can dissolve in aquifers (Sarkar et al. 2012;Mahlknecht et al. 2023).As also has anthropogenic sources, such as livestock feed supplements, electrical products, weedicides, pesticide residues (monosodium methyl arsenate (NaMeHAsO 3 ), disodium salt (Na 2 MeAsO 2 ), wood care agents (chromate copper arsenate), nutritional supplements, health supplements, pharmaceutical drugs, coal burning, tobacco products, dyes, and cosmetic products (Basu et al. 2014).As exposure has been related to many carcinogenic and non-carcinogenic outcomes in acute and non-acute health responses.It has been classified as a group 1 element in the carcinogenic classification (Awual et al. 2019;Genchi et al. 2022).Excessive arsenic consumption is linked to cancer, cardiovascular disease, diabetes, respiratory issues, and neurodevelopmental/reproductive abnormalities (Zheng et al. 2014;Hu et al. 2022;Barbhuiya et al. 2023).
Chromium, a common industrial element and one of the most toxic heavy metals, exists in two primary forms: trivalent chromium [Cr (III)] and hexavalent chromium [Cr (VI)].
Cr (III) is an essential nutrient for life, impacting metabolic activities, while Cr (VI) is a highly soluble, transportable, and significantly more toxic form (Lian et al. 2019).Industrial activities, such as mineral processing, metal plating, and manufacturing, contribute to chromium environmental contamination.WHO suggests a maximum Cr concentration in drinking water of 50 µg/L (Prasad et al. 2021).Although Cr (III) is necessary for metabolic processes, Cr (VI) poses significant health risks, including respiratory issues and detrimental impacts on reproduction, oxidative DNA damage, and lifespan impacts in aquatic life.Chromium also hampers plant growth by inhibiting seed germination, photosynthesis, enzyme activity, and nutrient absorption (Sharma et al. 2022).
Cadmium (Cd) is a toxic element that is detrimental to both humans and the environment.The International Agency for Research on Cancer (IARC) categorized Cd as a carcinogenic substance (group 1) based on evidence from human and animal carcinogenic research (Nordberg et al. 2021).According to WHO guidelines, the concentration of Cd in drinking water should be less than 3 µg/L (Kubier et al. 2019).Common routes of Cd exposure include oral intake, cutaneous absorption, inhalation of polluted air, and ingesting contaminated food and beverages.From certain occupational activities or tobacco consumption, ingestion is the principal source of ambient Cd (Schaefer et al. 2020).The primary source of dietary Cd is the frequent ingestion of crops such as potatoes, rice, green salad vegetables, wheat, and other cereals products (Jean et al. 2018).Because of Cd's extended half-life, it has a broad spectrum of adverse health consequences in humans and animals, particularly in the liver and kidneys.Research indicates that Cd levels in a large industrial zone's water, soil, air, and plants exceeded safe levels (Genchi et al. 2020).Using health risk assessment models, researchers estimated that Cd in these mediums presents a mild carcinogenic and non-carcinogenic risk (Mohammadi et al. 2019).
Human health risk assessment can be used to determine the type and probability of adverse health consequences in individuals exposed to environmental chemicals (Jiménez-Oyola et al. 2021).Sobol sensitivity analysis and Monte Carlo simulation play pivotal roles in health risk assessment, offering rigorous tools to evaluate complex models and their inherent uncertainties (Rajabi et al. 2022).Sobol sensitivity analysis allows researchers to decompose the variance in model outputs, distinguishing among the contributions of individual parameters and their interactions.This is particularly valuable in identifying critical factors influencing health risks (Rajabi et al. 2022).Monte Carlo simulation facilitates the probabilistic assessment of risks by repeatedly sampling from the distribution of input parameters, thereby generating a distribution of possible outcomes (Zarei et al. 2022).This probabilistic approach informs understanding of the range and likelihood of potential health outcomes, essential for informed decision-making in public health policies and interventions.Together, these methodologies provide a robust framework for quantifying and navigating the uncertainties inherent in health risk modeling.
The current investigation presents a detailed assessment of the concentration levels of potentially toxic elements (PTEs)-namely arsenic, chromium, and cadmium-in the groundwater sources of Shiraz, Iran.The analysis examines non-carcinogenic and carcinogenic risks these PTEs present to different subpopulations-children, adult males, and adult females.This approach can greatly inform understanding of the potential public health ramifications, significantly adding to the existing literature.The employment of Sobol sensitivity analysis, a methodology that has yet to be widely applied in this sphere, provides further robust insights into the factors contributing to these risks.Fuzzy C-Means clustering and spatial risk distribution offer a more nuanced understanding of the landscape of risks and are potent tools for guiding specific remediation efforts.

Study area
Shiraz is the capital of the Fars province in Iran's south, with coordinates of longitude 52°32′0″ E and latitude 29°37′0″ N. Shiraz has two geological structures: Asmari and Razak.The Razak structure is mainly in the residential and urban sections.The Drak, Bamu, Baba Koohi, and Poshte Mole mountains are on the north and northwest border of the Shiraz Plain.The research regions are depicted in Fig. 1.The average yearly temperature is 18℃.The area's annual average rainfall is around 337 mm, with an average elevation of 1480 m above sea level.The weather in Shiraz typically aligns with the characteristics of a hot semi-arid zone as defined by the Köppen climate system.The Dry River, which flows through Shiraz, is seasonal.After passing through the city, it continues southeastward into its catchment area, eventually emptying into Maharloo Lake (Azhdari et al. 2018;Kashki et al. 2021).

Sample collection
The studied PTEs in this research, As, Cr, and Cd, were selected due to their toxicity and possible environmental During the summer and winter of 2021, 90 samples were collected and analyzed from the 45 sites (drinking Water Samples Collected from Kitchens Tap Water).Samples were collected in 60-mL Falcon tubes from the water of a kitchen faucet at each sampling site and pretreated with filtration using a glass fiber filter (GF/F, Whatman, 450 °C for 4 h).Before analysis, the samples were transferred to the laboratory in compliance with the cold chain and stored at 4 °C for less than a week.The PTEs amount in the water samples was identified using an inductively coupled plasma mass spectrometry (ICP-MS) apparatus of Model Agilent 7500, USA.Water samples were injected directly into plasma with no additional dilution.They were frequently acidified with nitric acid (HNO 3 , 65%) to retain their elemental and metallic constituents in the solution.A centered nebulizer and a cyclonic spray container are common sample entrance techniques for this type of analysis.A nebulizer can normally handle particles in a solution close to one-third of the capillary size without being blocked (Kumar et al. 2019).

Quality assurance and quality control
Quality assurance (QA) and quality control (QC) principles significantly enhanced the reliability of our analytical results.Following QA protocols, each sample was consistently assayed three times, with the average value reported.This approach ensured precision and minimized potential variations from the instrument or sample.Our QC measures focused on assessing the method's accuracy; blank samples were used to establish a reference point, enabling us to detect systematic biases or contaminants.By analyzing samples of known concentrations, we could directly benchmark our method's outputs, reaffirming its credibility and robustness.

Method validation
Aqueous solutions and standard injection calibrated the ICP/ MS system.The limit of detection (LOD) and regression coefficient (R 2 ) were calculated under optimum conditions to assess the method's performance.The R 2 value ranges from 0.990 to 0.970, indicating a significant association.LOD values for As (0.050 ppb), Cr (0.050 ppb), and Cd (0.005 ppb) were found.

Health risk assessment
Health risk assessments are needed to assess water quality evaluations and inform the management of water resources (Heshmati et al. 2021;Jafari et al. 2021).People can be exposed to contaminated water through different paths, the most prevalent of which are drinking water intake and skin contact (Luo et al. 2020).Since As, Cr, and Cd are typical water pollutants in this region, they are used as risk assessment parameters in this investigation.Calculations for health risk assessment are based on the factors listed in Table 1.Equations 1 and 2 represent the non-carcinogenic risk of drinking water ingestion (Li et al. 2016): Intake oral is the average daily exposure dose per unit weight (mg/(kg.d))by drinking water intake (oral route).C refers to the PTE concentration in water (mg/L) as measured by laboratory analysis.For non-carcinogenic effects based on exposure through the oral pathway (mg/(kg.d)),HQ oral and RfD oral represent the hazard quotient and reference dose, respectively.The RfD oral values for As, Cr, and Cd in this investigation are Intake oral RfD oral .The exposure dose of each PTE (mg/cm 2 ) is derived utilizing empirical calculations in these Eq.s.For non-carcinogenic effects by the dermal contact exposure route (mg/(kg.d)),HQ dermal and RfD dermal denote the hazard quotient and the reference dosage, respectively.Applying Eq. ( 7), RfD dermal is calculated from RfD oral , whereby ABS gi is the gastrointestinal absorption factor.All the PTEs investigated had an ABS gi of (3)  The non-carcinogenic hazards are computed using Eqs.8 and 9 after computing the hazard quotients for the dermal contact and drinking water exposure routes.HI represents for hazard index.Under the assumption that thresholds are correct and no health impact occurs below these levels, human health is considered safe when the HQ and HI values are less than one.However, we recognize that for many environmental hazards, no safe level exists.People are vulnerable to non-carcinogenic risk when levels surpass one (Marufi et al. 2022).

Sobol sensitivity analysis
This study integrated Sobol sensitivity analysis with a Monte Carlo technique to determine the input variables and analyze their influence on the exposure results' variance.Sobol sensitivity analysis uses the rule of the total variance (Eq.15), which can be normalized to Eq. 16.It separates a model function f (Eq.14) into the following growing multiplicity conditions (Sobol 2001  Y is the scalar forecasting model, and X = (x 1 , x 2 , x 3 , ……x p ) is the model input data set.
It is possible to compare single-factor variance (partial variable) to total output variance (interactions across variables).Every constituent of Eq. ( 16) displays a variable up to pth order, and the Sobol sensitivity indices (SIs) is the ratio of the partial variable to the total variable.The first-order sensitivity index (FOSI) is the first component in Eq. ( 16) and describes the influence of a single variable, x j X, on the model outputs variances (Eq.17).The second-order sensitivity index (SOSI) is the second component.It demonstrates the influence of the interaction among variables x i and x j (x i , x j X, and i ≠ j) (Eq.18).
The total effect of the variable on the highest variance is computed using the total order sensitivity index (TOSI).It is calculated utilizing the variance Vi achieves by changing all parameters but xi ∈ X. (Eq.19).

Fuzzy C-Means of drinking water data
The research was conducted with the primary objective of discerning inherent groupings within a multivariate dataset, particularly on the dispersion and concentration of elements like Cr, Cd, and As.We adopted the FCM clustering methodology, a statistical instrument proficient in detecting intricate patterns and classifications within multifaceted multivariate data.The unique strength of FCM lies in its capacity to attribute a 'membership grade' to each data point for every cluster rather than assigning it rigidly to a single cluster.This flexibility ensures that a data point can concurrently belong to multiple clusters, each with a different degree of membership (Zhang et al. 2009).This approach affords a more comprehensive understanding of the data structure, accommodating overlaps and commonalities among clusters (Pérez-Ortega et al. 2022;Tzanes et al. 2023).

Statistical analysis
The concentrations of PTEs (As, Cr, and Cd) in the samples were evaluated using descriptive statistical analysis.The ANOVA test was used to analyze the differences in average values across seasons and locations.SPSS software version 26 was used for statistical analysis, and a p-value of less than 0.05 was considered significant.The spatial distributions of PTEs and the HI and CR of PTEs were assessed using the geostatistical analysis GIS program ArcGIS 10.1 (ESRI Inc, Redlands, California, USA).The FCM clustering was employed, utilizing the fanny function and 'cluster,' 'ggplot2', and 'scatter pie' packages from the cluster package in R.  samples was 0.23 µg/L, 1.05 µg/L, and 0.01 µg/L in the summer and 0.22 µg/L, 1.93 µg/L, and 0.08 µg/L in the winter, respectively.Cr > As > Cd was the order of PTE content in the studied region.The average concentrations of As, Cr and Cd elements were lower than WHO guidelines (WHO 2017).The highest mean metal concentrations in drinking water were found for Cr, whereas the lowest levels were found for Cd.In drinking water, the concentration of As was higher than that of Cd.As shown in Table 2, the concentrations of these metals were higher in the winter than in the summer.According to ANOVA analysis, the average variations for As and Cr in the two analyzed seasons were significant (p < 0.05) but not for Cd.In addition, there was no significant correlation between the sample points.The viscosity of water decreases during warm periods, such as summer, and the water tends to penetrate the pores of the bedrock, resulting in bedrock cracking and weathering, releasing salts in rocks and PTEs into water sources during the cold seasons, such as winter.The difference in bedrock accessibility, industrial operations, soil type, regional human activities, and the solubility of PTEs in water will result in distinct rises in PTE concentrations in water (Bahita et al. 2021;Kazemi et al. 2022).Physicochemical parameters of water, such as pH, acidity, alkalinity, and electroconductivity, affect the dissolving rate of PTEs, which might be another cause for the variation in PTE concentrations (Khan et al. 2021).

PTEs concentrations
The existence of industrial wastewater containing Cr PTE, such as battery processing, vehicular emissions, and the chemical industry in this region, is potential contributors to the greater concentration of Cr relative to As and Cd.
As and Cd are less concentrated than Cr but are generally of natural origin and less likely to infiltrate the environment and water supplies through the industry (Fattahzadeh et al., 2021;Jahandari et al. 2020).Previous research of heavy metals across 27 potable water locations in Shiraz documented elevated concentrations; As averaged 3.84 μg/L, Cr 8.1 μg/L, and Cd 1.7 μg/L (Abolfazli et al. 2023).In a parallel study focusing on the water quality of wells proximate to the Shiraz landfill, the reported concentrations were 3.02 ± 0.26 μg/L for As, 2.15 ± 0.083 μg/L for Cr, and 0.48 ± 0.005 μg/L for Cd (Abolfazli et al. 2023).A study on Maharlu Lake water in Shiraz highlighted considerably higher metal concentrations, with Cr registering at 370.24 μg/L, Cd at 46.43 μg/L, and Cu at 40 μg/L (Zare et al. 2020).The disparity in results between our study and those of Abolfazli et al., Fattahzadeh et al., and Zare et al. can relate to a confluence of factors, including divergences in sampling periods and sites, the analytical instruments utilized, and specific sampling protocols adopted.

Non-carcinogenic risk
Table 3 shows the results of PTEs' non-carcinogenic risk assessment.The data revealed that all samples had HQ < 1, indicating that drinking water met regulatory safety and human health standards.The data indicated that every sample had an HQ of less than 1, signifying that the well water complied with human health safety regulatory standards.The mean HI values for children, adult females, and adult males during the summer were all < 1 at 0.0553374, 0.0257663, and 0.0149398, respectively.Similarly, in the winter, the mean HI values were 0.07930527 for children, 0.03736518 for adult females, and 0.02274501 for adult males, again all less than one.However, their HI value rose because the concentration of PTEs was higher in the winter than summer.The non-carcinogenic risk in children was slightly greater than for male or female adults, reflecting the higher exposure for children (Zhao et al. 2020).A study of drinking water sources in Sistan and Baluchistan, southeastern Iran, observed levels below thresholds for non-carcinogenic impacts for Pb, Cd, and Cr (Mirzabeygi et al. 2017).The levels of HQ suggested a considerable risk related to the PTEs level in water supplies throughout the cities located in Yazd Province in the central region of Iran (Fallahzadeh et al. 2017).Other work found that water quality in rural regions of Kurdistan, Iran, did not exceed established safety levels (except As) (Maleki and Jari 2021).Furthermore, an additional study observed no levels exceeding such thresholds for PTEs As, Pb, Zn, Cr, and Cd in the groundwater of Aliabad Katol Plain in Gorgan, Iran (Rajaei et al. 2012).

Carcinogenic risk
The risk to human health from metals in drinking water depends on many factors, including the concentration, the water intake, other forms of exposure (e.g., dermal contact), and the individual's characteristics, such as baseline health status.Individuals may use more or less water daily depending on their occupation, climate zone, and financial resources (Abeer et al. 2020).Using the approach established by USEPA, the carcinogenic risks of As, Cr, and Cd through gastrointestinal and dermal exposure pathways were determined for children and male and female adults, as shown in Table 4.All sampling sites' CR values for As, Cr, and Cd in drinking water were lower than the USEPA risk assessment recommendation levels (1 × 10 -4 -1 × 10 -6 ).The CR levels for adults and children for the oral route were highest for Cr and lowest for Cd.Across all age groups, the CR indices during the summer season surpassed those observed in winter.
Page 11 of 17 237 The levels of 13 elements (Al, As, Cr, Cd, Pb, Mn, Fe, Co, Ni, Cu, Zn, Hg, U) in seven streams in northeastern Turkey (Giresun) region were evaluated in an earlier study (Ustaoğlu and Aydın 2020).As levels in the Aksu Stream were over the limit values for both children (1.46 × 10 -4 ) and adults (1.32 × 10 -4 ), The streams' water quality was assessed to be satisfactory, and there were no hazards identified (Ustaoğlu and Aydın 2020).In another study, shallow groundwater samples presented carcinogenic health risks based on Cr and As pollution.Deep groundwater samples presented carcinogenic health concerns due to Cr pollution, which exceeded the established threshold values (Qiao et al. 2020).

Spatial distribution
The assessment of PTEs revealed a contamination region ranging from mild to severe.Nevertheless, the regional distribution patterns of environmental risk indicated by the HI of the three groups (children, males, and females) were similar (Figs. 2, 3).Since the concentration of these PTEs is higher in the southeast of Shiraz than in other regions, the hazard in this area is significantly higher than in other areas.Within these zones, there are clear environmental risks warranting increased monitoring.In the eastern and southeastern districts, groundwater sources serve as the primary water supply.Meanwhile, surface reservoirs are the predominant water source in the northwestern, northern, and western regions.The results indicate that groundwater PTE concentrations are higher than surface water concentrations (Saleh et al. 2019).The increased concentration of PTEs can be attributed to geological composition, land use in the region of groundwater sources, pollution leakage from various sources, and penetration of PTE-containing industrial effluent (Badeenezhad et al. 2020).
Additionally, PTE concentrations vary with precipitation and yearly rainfall, and groundwater storage levels change from season to season.The height of the watershed and the depth of the unsaturated zone are frequently low in areas with a high concentration of PTEs.Another factor to consider is the Shiraz Plain's overall east-to-southeast slope.As a result, some scholars have suggested that farming operations be developed cautiously (Amin et al. 2011).Overutilizing groundwater resources to meet residential, industrial, and farming demands can alter water's characteristics and natural components.Due to its shallow aquifer, research has indicated that the Shiraz Plain is also vulnerable to surface pollution releases (Fattahzadeh et al. 1430).Other variables impacting water contaminants' concentration include the construction and upgrading of the wastewater collection system and the industrial effluents (e.g., PTEs).Due to the effect of the natural and anthropogenic influences on the concentration of PTEs in groundwater, monitoring wells, reservoirs, and adjacent areas is critical to monitoring potentially harmful levels (Shiraz et al. 2009;Hughes et al. 2021).

Sobol sensitive analysis
The Sobol sensitivity analysis was used to investigate the most significant input factors associated with non-carcinogenic and carcinogenic health concerns associated with PTE pollution in the region's population drinking water.The components of this analysis are stated in Table 1.PTE concentrations in groundwater (As, Cr, and Cd), body weight (BW), exposure frequency (EF), and consumption rate are inputs to the oral model (IR).
Given the uncertainty of the parameters considered for carcinogenic and non-carcinogenic risk assessment, the Monte Carlo simulation was performed for a population of one million; the results are reported in the supplementary file (Figure S1 and Figure S2).The supplementary file contains multi-scatter plots of the parameters' interaction (Figure S3 and Figure S4).The interaction may be readily seen in plots S3 and S4.
According to the plots in Figure S1, the estimated noncarcinogenic risk values for children's 5%, 50% (median), and 95% percentiles were 0.025, 0.049, and 0.093, respectively.For males, the values were 0.012, 0.023, and 0.043, while for females, they were 0.016, 0.029, and 0.051, respectively.According to a Monte Carlo simulation, the rate of non-carcinogenic risk rate was higher in children than adults in earlier research, which found similar results to this study (Badeenezhad et al. 2021).
As shown in Figure S2, the estimated carcinogenic risk for the 5%, 50% (average), and 95% percentiles for children is 3.136 × 10 -6 , 6.747 × 10 -6 , and 1.426 × 10 -5 , for males, 3.599 × 10 -6 , 7.745 × 10 -6 and 1.637 × 10 -5 , and females 4.940 × 10 -6 , 9.915 × 10 -6 and 1.978 × 10 -5 , respectively.Since this risk assessment has no endpoint for measuring carcinogenic risk, the analysis cannot provide conclusive evidence that there is no carcinogenic risk; instead, we can only estimate the proportion of the population at reduced and greater risk of developing cancer.Other research also found that children had a higher chance of developing cancer than adults, as determined by the Monte Carlo simulation (Gao et al. 2022b).
The parameter for concentrations of As, Cr, and Cd, based on Sobol's sensitivity analysis (Fig. 4), is the most efficient and significant parameter for HQ in all three groups: children (0.087, 0.177, 0.006), adult males Fig. 4 Sensitivity analysis As in drinking water from Shiraz city based on non-carcinogenic risk for the three age groups considering first-order effect (S i ) and total effect (T i ) and pair-wise interactions ◂ Page 13 of 17 237 (0.087, 0.177, 0.006), and adult females (0.113, 0.229, 0.008).After concentration, the parameters in the groups of children and adult males had the same values and were ordered as BW (0.325) > IR (0.235) > EF (0.115), whereas the parameters for female adults were ordered as BW (0.323) > EF (0.149) > IR (0.136).The Cd value is less than 0.01 in all groups, showing that it is insensitive regarding significance, but the BW value is susceptible in the three groups.Furthermore, because the concentration parameter is larger in women than in men, this parameter has a larger impact on women.In contrast, the IR and BW parameters have a larger impact on men.Because total sensitivity is greater than the first-order sensitivity, it is reasonable to assume that these factors interact.For total Sobol sensitivity in HQ, the effective parameters for children and men were As = 0.097, Cr = 0.197, Cd = 0.007, IR = 0.265, EF = 0.132, and BW = 0.360, and for adult females, As = 0.122, Cr = 0.247, Cd = 0.008, IR = 0.151, BW = 0.351, and EF = 0.165.In children and men, the interaction diagram (Fig. 4) reveals that the concentration parameter interacts with three factors, with the impact being substantially larger between BW-IR > Cr-BW > C r-IR > BW-EF > IR-EF > As-IR, which changes for various IR values.For women, there are interactions between Cr-BW > BW-IR > BW-EF.According to the results, adult females are more exposed to non-carcinogenic risks from water pollutants than children and men.The Cr concentration parameter was among the most influential on the HQ of all groups.
According to Sobol's sensitivity analysis (Fig. 5), the concentrations of As and Cr parameter seems to be the more influential and significant parameter for CR in all three groups: children (0.019, 0.424), adult males (0.019, 0.424), and adult females (0.023, 0.529).The parameters in the groups of children and men had the same values after concentration and were ordered BW (0.235) > IR (0.170) > EF (0.083), but the parameters in the group of female adults were ordered BW (0.218) > EF (0.101) > IR (0.092).The Cd value was less than 0.01 in all groups, indicating that it was non-sensitive.However, the BW value in the three groups was extremely sensitive.Moreover, because the concentration parameter has a higher value in women than men, this parameter may be considered more influential in women.In contrast, the IR and BW parameters are more influential in men.These factors may interact since total sensitivity is larger than first-order sensitivity.The effective parameters for total Sobol sensitivity in CR were As = 0.021, Cr = 0.473, Cd = 0.000, IR = 0.202, EF = 0.101, and BW = 0.274 for children and adult men, and As = 0.025, Cr = 0.555, Cd = 0.000, IR = 0.107, BW = 0.250, and EF = 0.118 for adult females.The interaction diagram (Fig. 5) shows that the Cr concentration parameter interacts with three factors in children, with the influence being significantly greater between Cr-BW > Cr-IR > BW-IR > Cr-EF and Cr-BW > Cr-IR > BW-IR > Cr-EF > BW-EF in men.The interactions between Cr-BW > Cr-EF > CR-IR > BW-IR have been shown in women.According to the findings, females are more vulnerable to carcinogenic risk from water contaminants than children and men.The Cr concentration parameter was among the most impactful on the CR of all groups.Karunanidhi et al. found that children are more susceptible to changes in factors determining health risk than men and women in research on chromium concentrations omen (Karunanidhi et al. 2021).

Fuzzy C-Means of drinking water data
By employing the FCM clustering methodology, we mapped the distribution and interconnections of Cr, Cd, and As within our dataset of interest.To achieve this, we stratified the data into three distinct groups, a strategy grounded in prior research.Figure 6 serves as a visually compelling representation, highlighting the presence of well-defined cluster formations and areas where elements overlap.
These delineations serve a dual purpose: they contribute to our understanding of elemental distributions and emphasize promising avenues for future research endeavors.The clear groupings and the identification of overlapping regions strongly suggest intricate interactions and associations among the elements considered, underscoring the need for further research.

Conclusion and future directions
This research investigated the health risks associated with PTEs, including As, Cr, and Cd.We focused on assessing these risks through daily consumption and exposure, considering both skin absorption and ingestion of drinking water among three subpopulations: male adults, female adults, and children in Shiraz.Our findings indicate that the primary mode of metal exposure for the people of Shiraz is ingestion through drinking water, followed by cutaneous exposure.Importantly, we observed that the daily intake of PTEs from drinking water exceeded that from cutaneous contact by a substantial margin, ranging from 10 to 100 times higher across all demographic groups.Furthermore, we evaluated the non-carcinogenic and carcinogenic risk levels associated with dermal exposure to PTEs.In all cases, these risk levels were below the risk Fig. 5 Sensitivity analysis of Cr, Cd, and As in drinking water from Shiraz city based on carcinogenic risk for the three age groups considering first-order effect (S i ) and total effect (T i ) and pair-wise interactions ◂ 237 Page 14 of 17 management guidelines established by the US EPA.This suggests that PTEs do not pose a significant health risk to male adults, female adults, or children through dermal exposure.We found that carcinogenic risks related to PTEs from drinking water ingestion were either marginal or lower than the permissible levels set by the US EPA.This indicates the lack of substantial increase in health risks associated with PTE ingestion through drinking water.However, children were identified as more susceptible to exposure to carcinogenic and non-carcinogenic PTEs through ingestion and dermal contact.Our study underscores the urgent need for measures to reduce PTE levels in Shiraz's drinking water.Implementing effective purification systems and managing PTE discharge is critical to safeguard the local population and prevent potential health concerns.Additionally, we conducted a Sobol sensitivity analysis, which revealed the sensitivity ratings of various parameters.For non-carcinogenic risk, the most sensitive parameters were BW (body weight), followed by IR (ingestion rate), Cr (chromium), EF (exposure frequency), As (arsenic), and Cd (cadmium).Cr was found to be the most sensitive for carcinogenic risk, followed by BW, IR, EF, As, and Cd.BW consistently emerged as the most influential parameter across all three demographic groups.Our FCM clustering analysis provided valuable insights into the distribution patterns of Cr, Cd, and As within Shiraz City.This detailed examination serves as a significant foundation for future regional research and initiatives and can inform water quality management with respect to public health.However, many critical research questions remain, and as more scientific evidence on the health impacts of established thresholds becomes available, our results may need to be revisited and refined accordingly.

Fig. 1
Fig. 1 Map of the study area and water sampling points

Fig. 2
Fig. 2 Spatial distribution of hazard index in drinking water from Shiraz city for children (a), male adults (b), and female adults (c)

Fig. 3
Fig. 3 Spatial distribution of cancer risk in drinking water from Shiraz city for children (a), male adults (b), and female adults (c)

Table 2
Statistical analysis of Potentially Toxic Elements (PTEs) concentrations (ppb)

Table 4
Carcinogenic health risks for children, adult males,

Table 2
shows a descriptive survey of PTEs properties.The mean concentration of As, Cr, and Cd found in water