Introduction

Heavy metal (HM) contamination, especially in the aquatic environment, is one of the most serious health issues worldwide, mainly because of their anthropogenic inputs (De Silva et al. 2015; Deepa and Jitendra 2019; Islam et al. 2020b). HMs frequently accumulate in sediments, and they cannot easily be removed by biodegradation or chemical degradation (Bartoli et al. 2012; Haris et al. 2017; Hossain et al. 2019; Haghshenas et al. 2019; Hosseini et al. 2020). The sources of HMs in the aquatic environment are natural and anthropogenic activities, such as agriculture runoff, unfettered industrialization, rapid urbanization, and massive use of fossil fuels (Zafra et al. 2017). It should be specifically mentioned that HMs, like mercury (Hg), arsenic (As), copper (Cu), chromium (Cr), lead (Pb), zinc (Zn), and cadmium (Cd), are of a high concern since they have direct impacts on human health through affecting the food chains (Martinez-Cortijo and Ruiz-Canales 2018; Paschoalini et al. 2019). Exposure to these HMs, dermal absorption, inhalation, and direct intake could result in serious diseases, such as hypertension, renal dysfunction, and cancer (Saha et al. 2017; Devi and Yadav 2018; Tepanosyan et al. 2018). Hence, analyzing the sources, spatial distribution patterns, and health risks of HMs in the aquatic environment is an important undertaking (Swain and Sahoo 2017).

Currently, the level of HM contamination in the aquatic environment and the related risks have received considerable attention, and multiple approaches have been applied for their assessment (Nath et al. 2018; Pal and Maiti 2018; Withanachchi et al. 2018; Zivkovic et al. 2019;). Excess abundances of As in shellfish was detected in the Pearl River Delta in South China (Yu et al. 2021). Copper, zinc, and iron were widely detected in the Dawen River basin of Shandong Province in China, followed by nickel, arsenic, selenium, lead, and mercury (Liu et al. 2021). Among these researches, the widely used analysis techniques for metal contamination based on existing water quality standards are the heavy metal pollution index (HPI) and pollution index (PI). These simple approaches facilitate the analysis of pollution sources and the verification of protection measures based on generated solutions (Zhang et al. 2017). According to the U.S. Environmental Protection Agency (USEPA), the evaluation of potential health risks and the spatial distribution of HMs should be conducted to identify carcinogenic and non-carcinogenic risks. For example, Singh and Kumar (2017) focused on HM contamination in the Ajay River with consideration of seasonal and spatial variations by analyzing 76 samples for 2 years. Results showed that the mean values of HPI and PI were found above the critical index owing to a higher concentration of Cd, Pb, and Fe. Solutions of health risk assessment disclosed that high loads of Cd, Pb, and Fe in the surface water could harm the population. Islam et al. (2020a) analyzed concentrations of eight trace elements in surface water in Bangladesh. Six assessment methods were used to evaluate the water quality and health risks, including hazard index and Monte Carlo simulation. Results showed that the values of the hazard index surpassed the acceptable level. Carcinogenic risks of Cr also exceeded the acceptable level for adults and children. Habib et al. (2020) appraised 10 trace metals in groundwater samples using multivariate statistical approaches, health risk model, and Monte Carlo simulation. Results of hazard index evaluation showed the values exceeded the safe levels for adults and children. The carcinogenic risk values of Cd and Cr exceeded acceptable levels as well, with oral intake as the key exposure pathway.

Although existing efforts have helped identify the associated health risks of HM contamination in the aquatic environment, much needs to be done with regard to the uncertainties arising from modeling parameters, such as pollutant concentration, carcinogenic slope factors, and daily ingestion (Keller et al. 2002; Albuquerque et al. 2017; Troldborg et al. 2017; Eze et al. 2019; Shabanda et al. 2019). The lack of consideration for uncertain information could cause the obtained solutions to deviate from the “true” solutions of identified problems (Harris et al. 2017; Sharafi et al. 2019). Uncertainties expressed as probability distributions have been widely investigated, and the results could provide decision-makers with multiple optimal strategies under different probability levels. However, in the general decision-making process, difficulties arise when tackling cumbersome water quality datasets. Multiple statistical analyses, e.g., principal component analysis (PCA) and cluster analysis (CA), provide a powerful approach for classifying, modeling, and interpreting complex water quality datasets (Astel et al. 2007; Peiris et al. 2010; Maere et al. 2012; Viswanath et al. 2015; Javadi et al. 2017). In water quality evaluation, identifying the interrelations in huge datasets, and the key factors greatly affecting the aquatic environment is critical. Accordingly, PCA should be applied to process water quality datasets so as to identify the hypothetical sources of HMs, minimizing the number of variables with high loadings on each component. CA can classify these samples with similar HM contents. Specifically, R-mode CA could evaluate the association between various parameters and sources of water quality while Q-mode CA is used to determine similar site clusters (Bayo and López-Castellanos 2016; Delpal et al. 2018).

The purpose of this study is to establish evaluation methods for identifying the degree of contamination and health risk of HMs in the aquatic environment. Seven HMs (Pb, As, Cr, Cd, Cu, Hg, and Zn) will be considered to compute the exposure rates of HMs for human health through ingestion owing to their toxic properties. Spatial distribution of these HMs will be presented to exhibit the impact of contaminants on the aquatic environment. Additionally, multiple statistical analysis is used to determinate the connection between different HM contamination.

Materials and methods

Overview of the study region

This study focuses on the North Canal of Fengtai District (from 39 45′ to 39 55′ N in latitude, and from 116 03′ to 116 30′ E in longitude), which is located along the western border of Beijing, China (Fig. 1). This district has an area of 205.87 km2 and 2.26 million of the population (Chen et al. 2016). In terms of the geological and geomorphology, there are different geological conditions in the western and eastern parts of Fengtai District, where stratigraphic lithology in different geologic time is distributed. The western and eastern parts are respectively composed of mountains and plains. The soil types in Fengtai District are mainly brown and tidal soils, which account for 67% and 29% of the soil in the whole region, respectively, while the rest are mostly composed of wind sand and paddy soils. Among them, the brown soil is mainly distributed in the western, northern, southeastern parts of the region, and the tidal soil is principally located in the middle and southern parts. When it comes to the meteorological and hydrological conditions, this district is a typical continental and semi-arid climate of a warm temperate zone. The annual average temperature is 11.7 °C, and the annual average precipitation is 580.6 mm. The average annual surface evaporation is 934.7 mm, and the land evaporation is about 472.2 mm.

Fig. 1
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Schematic of the aquatic environment in Fengtai district, Beijing, China

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In addition, there are three major rivers in this district, namely the Yongding River, North Canal, and Daqing River. Because of insufficient water in the Yongding River and Daqing River for many years, this study centers mostly on the North Canal, which has a length of 68 km (8.8 km in Fengtai District) and a basin area of 630 km2. With rapid development of economy and continued acceleration of the population, the increasingly severe water contamination has become one of the trickiest problems. For example, rivers with grade V accounted for more than 95% of all rivers in 2013, and according to Fengtai District environmental quality report in 2012, the super standard rate of chemical oxygen demand (COD), potassium permanganate index (PPI), biological oxygen demand (BOD), ammonia nitrogen (NH3-N), and total phosphorus (TP) were examined up to 67.4%, 37.5%, 87.5%, 85.9%, and 100%, respectively (Fig. 2) (Chen et al. 2017). The study area belongs to a warm temperate semi-arid and semi-humid continental monsoon climate. The annual average temperature is 11~12 °C, the annual average precipitation is 551.9 mm, and more than 85% of the annual rainfall is concentrated in June to September. The study area is located in the alluvial proluvial plain of Chaobai River, with a Quaternary sedimentary thickness of more than 300 m. the lithology is mainly composed of interbedding of silty clay, silty sand, and fine sand. In this study, eight sampling sites have been used to determine its water contaminations (Fig. 1). All of the eight sampling sites are on the North Canal. The monitoring sites are established by the government of Fengtai District, and the water quality is regularly monitored by the Beijing Municipal Ecology and Environment Bureau.

Fig. 2
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Variations in pollutant concentrations in different sampling sites

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Multivariate statistical analysis

Principal component analysis aims to turn multiple index problems into a few comprehensive variables with less information loss, which could significantly improve the efficiency of analysis. According to the sample attributes, a hierarchical clustering method set is introduced to cluster the network nodes. In this study, R software and SPSS software are applied to reduce the dimension of seven HMs based on PCA and to analyze the correction and primary sources of pollutants. Moreover, these seven HMs are classified by cluster analysis, the HMs with similar attributes or sources are then obtained, and such results could be further verified by a PCA approach.

Human health risk assessment

It is increasingly desired to identify the probability of carcinogenic and non-carcinogenic risks to a human body owing to HMs in the aquatic environment (USEPA 2000; Lu et al. 2018). There are two major exposure pathways, i.e., dermal contact absorption and direct ingestion. In this study, only direct ingestion is considered due to its higher environmental risks. The chronic daily intake (CDI), hazard quotient (HQ), and hazard index are calculated according to USEPA standards, which could determinate the ingestion rate of contamination.

$$ {CDI}_i=\frac{EC_i\cdot DI}{BW} $$
(1)

where EC denotes pollutant concentration (mg/L); DI denotes daily ingestion, which is suggested by 2.0 L/day for adult, and 0.7 L/day for children; BW denotes body weight, which is assumed as 60 kg for adult, and 14.2 kg for children.

$$ {HQ}_i=\frac{CDI_i}{RfD_i} $$
(2)

where RfD denotes the oral toxicity reference dose values, which are determined as 0.0003, 0.0004, 0.04, 0.3, 0.0005, 0.0014, and 0.0015 mg/kg-day for As, Hg, Cu, Zn, Cd, Pb, and Cr, respectively. There are four scales of HQ: HQ≤1 (no risk), 1<HQ≤5 (low risk), 5<HQ≤10 (medium risk), and HQ>10 (high risk).

Then, the carcinogenic risk (CR) can be calculated as follows (Ren et al. 2016; Dehghani et al. 2017):

$$ \left\{\begin{array}{l}{CR}_i={CDI}_i\cdot {SF}_i\\ {} CR=\sum {CR}_i\end{array}\right. $$
(3)

where SF denotes the carcinogenic slope factors, which are suggested by 0.5, 15, and 1.5 mg/kg-day for Cd, Cr, and As, respectively. A CR value between 1 × 10−6 and 1 × 10−4 implies acceptable/tolerable carcinogenic risk; the risk changes to be unacceptable with a CR value higher than 1 × 10−4, while it has no significant health hazards when the value is lower than 1 × 10−6 (Men et al. 2018).

Heavy metal pollution index

To evaluate the critical level of water quality, the heavy metal pollution index (HPI) is determined based on the weighted arithmetic mean calculation of selected parameters, which can be calculated as follows:

$$ \left\{\begin{array}{l}{W}_i=\frac{k}{S_i}\\ {}{Q}_i=100\cdot \left(\frac{C_i}{S_i}\right)\\ {} HPI=\sum \limits_{i=1}^n\frac{Q_i\cdot {W}_i}{\sum \limits_{i=1}^n{W}_i}\end{array}\right. $$
(4)

where Wi denotes the weighting factors of each heavy metal; k is the proportionality constant and is set as 1 in this study; Si denotes the desirable limit of each heavy metal given by regulatory standard; Ci denotes the average concentration of each heavy metal; Qi denotes the sub-index of each heavy metal. When HPI ≤ 100, it means that the contamination of HMs in the aquatic environment could be acceptable.

Monte Carlo–based uncertainty analysis

Uncertainties associated with carcinogenetic risk could be conducted into a matrix and vectors based on Monte Carlo simulation, during which each execution generates a sample output. The output can then be stochastically analyzed for identifying the corresponding cumulative probability distributions. Generally, the detailed Monte Carlo process can be summarized as follows: (a) producing lots of random numbers for each stochastic input; (b) according to a special statistical distribution, these random numbers could be transformed into the related random variates; (c) storing the obtained stochastic variates in an array for each parameter; (d) each parameter would generate a value, which is used as a deterministic input in the computation formula of the allowable carcinogenetic risk; (e) computing the acceptable carcinogenetic risk based on a numerical model for each Monte Carlo run; (f) the outputs of the acceptable carcinogenetic risk would be stored; (g) repeating Steps (a)–(f) for specified Monte Carlo runs; and (h) analyzing the calculation results and achieving a cumulative probability distribution. Carcinogenic risk describes the probability when human beings are exposed to cancer-causing contaminants like heavy metals. It is one of the most concerning health problems in human beings. Therefore, it is significant to accurately evaluate the level of carcinogenic risk. However, quantitative calculation of carcinogenic risk involves parameters with a mount of uncertainties. The value of these parameters (e.g. slope factors and daily ingestion) are recommended by USEPA, based on numerous animal toxicity experiments. It is hard to accurately predict the value for humans in this special case (a case study of China). The uncertainty of parameters can directly influence the accuracy of carcinogenic health risk assessments. Monte Carlo simulation is one of the most effective methods to solve the randomness and uncertainty within model operations. Moreover, sensitivity analysis could be given to determine the impacts of modeling components or modeling inputs on the final results of carcinogenetic risk. Sensitivity analysis could reflect the impacts of parameters uncertainties on carcinogenic risk calculation and make the values of carcinogenic risk of heavy metals close to the “real” ones.

Results and discussion

Compositional analysis and identification of pollution sources

The statistical descriptions of HMs and the physicochemical parameters with minimum, maximum, and mean values are presented in Table 1. The HM variations in the aquatic environment are illustrated in Fig. 3. The monitoring data of all the seven heavy metals were measured by the official government considering Environmental Quality Standards for Surface Water of National Standard of China (GB3838-2002). In this work, the pH values varied between 7.17 and 8.63, and the mean value is 7.58 for the aquatic environment. All water samples showed neutral to slightly alkaline pH level, and no contamination by acidic pollutants was noted. S8 had high concentrations of As, Hg, and Cr; S4 had high concentrations of Cu; S1 and S2 had high values of Pb; and S5 and S7 had high concentrations of Zn and Cd, respectively. According to the mean concentrations in the water samples, the metals followed this decreasing order of concentration: Cu > Zn > Pb > Cr > Cd > As > Hg. All of them met the water quality standard of GB3838–2002 grade III. The mean concentration of HMs and their spatial distribution patterns along the sample sites are displayed in Figs. 4 and 5, respectively. As can be seen in Fig. 4, the concentration of Cd in the studied samples was less than 0.0095 mg/L, with the mean value being 0.0011 mg/L. The common sources of Cd in the aquatic environment are the burning of fossil fuels, wastewater from industrial and urban effluence, and agriculture activities. The Cr level mainly ranged from 0.0028 to 0.0050 mg/L, with a mean of 0.0033 mg/L; hence, it did not exceed the permissible limit of grade III water quality of 0.0050 mg/L. In terms of As concentration, it ranged from 0.0001 to 0.0018 mg/L, with a mean of 0.0007 mg/L. Located downstream of the river, S7 and S8 showed relatively high values of Cd, Cr, and As. As illustrated in Fig. 5, the concentration of Cu was within the permissible limit of l.0 mg/L. A high Cu concentration was observed at S2 and S4, possibly because of the presence of copper bucket industries in these two areas. Meanwhile, Zn is an important micronutrient for ensuring proper metabolic processes in living organisms. However, high Zn levels could exert a negative impact on such processes, especially from a long-term perspective. In the study area, the average concentration of Zn was 0.284 mg/L, which was within the safe limit. S5 showed higher Zn levels than the other sites. As for Pb contamination, its concentration ranged from 0.007 to 0.011 mg/L, with a mean of 0.0094 mg/L. The major source of Pb contamination was identified to be anthropogenic activities. For example, the extensive application of fossil fuels in thermal power plants might lead to high Pb contaminations in S1 and S2. The concentrations of heavy metals are directly influenced by the nearby industrial activities.

Table 1 Statistical description of heavy metal and physicochemical parameters
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Fig. 3
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Heavy metal variations in the aquatic environment of different sampling sites

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Fig. 4
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Distribution patterns of carcinogenic HMs along the sample sites

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Fig. 5
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Distribution patterns of non-carcinogenic HMs along the sample sites

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Table 2 presents the correlation matrix for heavy metals. Pearson’s correlation analysis indicated that the correlations between different HMs were weak and not significant (p > 0.05), except for As and Cr. The poor correlations might be due to the geochemical behaviors of the parameters and the differences in the sources of HMs, implying that non-point sources exhibited strong contamination characteristics, such as contamination distributing disperses, component complexities, and contamination approach diversity. Additionally, CA was conducted to classify the HMs in the surface water dataset. Multiple tools, including the complete method, average method, ward method, and centroid method, were applied to visualize this process. The corresponding results are displayed in Fig. 6. The results showed that regardless of the model used, the two major clusters were (1) Pb Cr Cd As Hg and (2) Cu Zn. Moreover, PCA was used to conduct composition analysis, as it could help reduce the dimension of multivariate data and provide useful information associated with the significant parameters present in the whole dataset. Hence, its application greatly reduces the complexities of the evaluation framework. Four principal components explained 91.381% of the total variance (Table 3 and Fig. 7), with 44.126%, 20.263%, 16.449%, and 10.543% of the variance explained by Comp. 1, Comp. 2, Comp. 3, and Comp. 4, respectively. Comp. 1 loaded strongly on As, Hg, Cr, and Zn, and these metals were mostly from natural sources and industry activities. Comp. 2 was mainly composed of Cu, Pb, and Cd possibly because of the extensive utilization of fossil fuels and wastewater emissions. Comp. 3 exhibited high loadings of Cu because of the copper bucket industries around this river. Comp. 4 showed high loadings of Hg and Cr, from natural sources. The above results indicate the sources of the seven heavy metals and their interrelations.

Table 2 Correlation matrix for heavy metals
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Fig. 6
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Clustering tree of the HMs based on different methods

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Table 3 Loading scores of heavy metals to each component
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Fig. 7
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Principal component analysis of HMs concentrations in aquatic environment

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HPI analysis

PIs, such as the HPI, were evaluated for different sampling sites in the aquatic environment. The results are displayed in Fig. 8. All of these HPI values were significantly higher than the critical level (i.e., 100), thus implying that this aquatic environment was contaminated by multiple HMs. High HPI values were observed in S5, S6, and S8 while low HPI values were noted in S1 and S2. Hence, the upper and middle parts of this river had high contaminations while the downstream of this river had slight loadings. This result might be attributed to a large number of production and living activities upstream and dilution and flushing effect by the natural discharge of the river.

Fig. 8
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Solutions of HPI along the sampling sites

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Potential risk assessment for human health

HMs are potentially harmful to human health, and HQ could be used to assess the risks of chronic health through the ingestion of water. CDI represents the daily exposure of the population to HM contaminations in mg/kg-day. The descriptions of the mean CDI and HQ for adults and children through ingestion are presented in Table 4. The CDI values in both groups showed that water was Cu > Zn > Pb > Cr > Cd > As> Hg type, with Cu in the highest CDI value (1.63E–0.3 for adults and 2.29E−0.3 for children) among all metals. Figure 9 illustrates the distribution of HQ values of HMs with consideration of the two receptors (i.e., adults and children). The HQ values of all sampling sites were below 1 and ranged from 0.48 to 0.74, which indicated a low non-carcinogenic hazard. The results showed that the sampling sites in this study area followed the decreasing order of HQ values: S7 > S8 > S1 > S6 > S4 > S2 > S5 > S3. Such a tendency revealed that the HQ value in the northern section of the aquatic environment was significantly higher than that in the southern and central sections. Additionally, HMs followed the decreasing order of HQ values: Pb >As > Cr > Cd > Cu > Hg >Zn. The total HQ value for children reached 5.69, which was 1.65 times higher than that for the adults. In terms of different HMs, Pb (0.224 mg/kg-day for adult and 0.316 mg/kg-day for children) had the greatest health risk with a total HQ value of 2.53, especially in S1, followed by As (0.079 mg/kg-day for adults and 0.111 mg/kg-day for children) with a total HQ value of 0.89, especially in S8. Thus, these two pollutants should be controlled for the purpose of public safety.

Table 4 Description of the mean CDI and HQ for adult and children through ingestion
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Fig. 9
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Distribution of hazard quotient (HQ) indices of HMs in the aquatic environment

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Among these HMs, As, Cd, and Cr pose significant carcinogenic risks to the public. As shown in Fig. 10 and Table 5, the carcinogenic risk of Cd was the highest, especially in S1, S3, and S7, with some values exceeding 1 × 10−4 for adults and children. These values indicated unacceptable carcinogenic risks. The CR values of other metals (i.e., As and Cr) for all populations were between 1 × 10−6 and 1 × 10−4, implying acceptable or tolerable carcinogenic risks. Although the insignificant carcinogenic risks posed to the public are insignificant, decision-makers should pay attention particularly to children because most values exceeded 1 × 10−5. Additionally, the sampling sites followed the decreasing order of CR values: S7 > S1 > S2 > S3 > S6 > S4 > S8 >S5. This result is due to S7 comprising many industries, which generate wastewater that could increase HM concentrations. For example, Cd emitted from industrial activities might enter the aquatic environment through atmospheric sedimentation and surface runoff, eventually enriching the sedimentation environment. Generally, variations in hazard quotient and carcinogenic risk along the sampling sites are illustrated in Fig. 11.

Fig. 10
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Distribution of carcinogenic risk (CR) indices of As, Cd, and Cr in the aquatic environment

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Table 5 Carcinogenic risks As, Cd, and Cr for adult and children through ingestion
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Fig. 11
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Variations in hazard quotient and carcinogenic risk along the sampling sites

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Uncertainty analysis

Uncertainty, especially as stochastic property, extensively exist in the water quality evaluation framework. In this study, the Monte Carlo simulation method as a widely used tool is applied for better understanding the variations in carcinogenic risk, during which the majority of parameters were assumed as triangular distributions (Table 6). For example, the concentrations of As, Cd, and Cr are presented as a triangular distribution with determining their maximum, minimum, and mean values as shown in Table 1.

Table 6 Parameters of the model for probabilistic risk assessment
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Figures 12, 13 and 14 show the probability distributions of the carcinogenic risks of As, Cd, and Cr for adults and children. With regard to these two populations, the CR values followed the order Cd > As > Cr. The Monte Carlo results revealed that regardless of the quantile considered, the CR value of Cd was significantly higher than 1 × 10−4, even reaching 7.3 × 10−4 for children under the 90th quantile (Table 7). In terms of As, its mean carcinogenic risks were 0.8 × 10−4 and 1.2 × 10−4 for adults and children, respectively. Their resulting 90th quantile values respectively reached 1.1 × 10−4 and 1.7 × 10−4 (Table 7), thus exceeding 1 × 10−4 and indicating obvious carcinogenic risks for both populations. Relative to those of Cd and As, all CR values of Cr were below the risk threshold, with the mean carcinogenic risks being 0.16 × 10−4 and 0.58 × 10−4 for adults and children, respectively. In addition, the total carcinogenic risks respectively reached 4.4 × 10−4 and 6.3 × 10−4 for adults and children on average (Fig. 15). Their corresponding 90th quantile values changed to 6.2 × 10−4 and 9.3 × 10−4. Cd contributed over 70% to the total carcinogenic risk, followed by As (above 19%). Moreover, sensitivity analysis indicated that daily ingestion and slope factors exerted significant impacts on the total carcinogenic risk as they accounted for 40.8% and − 35.5% of the total, respectively (Fig. 16). The results also indicated that the concentration of Cd in S7 had a moderate impact (i.e., 13.1%) on the total carcinogenic risk; the other was mostly contributed by body weight (i.e., − 7.9%). In general, uncertainties relative to modeling parameters exerted significant effects on the final CR solutions. A high quantile corresponded to a high CR value and a low standard-reaching rate; conversely, a low quantile led to a low CR value and then to a high probability of acceptable risks. These results could help decision-makers coordinate the conflict interaction between carcinogenic risks and system reliability.

Fig. 12
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Probability distributions of As carcinogenic risk for adult and children

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Fig. 13
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Probability distributions of Cd carcinogenic risk for adult and children

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Fig. 14
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Probability distributions of Cr carcinogenic risk for adult and children

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Table 7 Quantile statistics of carcinogenic risks for adult and children
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Fig. 15
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Probability distributions of the total carcinogenic risk for adult and children

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Fig. 16
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Sensitivity analysis of the total carcinogenic risk

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Actually, each step of health risk assessment is full of uncertainty. In this study, majority of parameters for carcinogenic risk are taken into consideration. Surely, the overall effects of other coefficients and risk assessment kinds may hardly be ignored. Moreover, the steps and evaluation criterion of health risk assessment are recommended by the U.S. EPA. Although parameter values are scientifically based on statistics of a large amount of toxicological experiments, they are not absolutely suitable for all case studies from different countries. It is thus desired that a new system for health risk assessment of our own country should be developed as soon as possible, which is applicable to local conditions.

Conclusions and recommendations

This study proposes an evaluation framework for characterizing and quantifying the sources and contamination degrees of heavy metal contamination in the North Canal of Fengtai District, China. The framework could exhibit the impacts of heavy metals on human health and their relationships with uncertainties by integrating multidisciplinary approaches, involving multivariate statistical method, health risk assessment, and uncertainty analysis. Results indicated that (1) the downstream of the river had higher concentrations of Cd, Cr, and As; sources of Cd were identified as domestic and industrial wastewater, consumption of fossil fuels, as well as agriculture activities; (2) Pearson’s correlation analysis revealed that the correlations between different HMs were weak and not significant (p > 0.05), except for As and Cr, which was mostly owing to geochemical behaviors of parameters and differences in sources of heavy metals. There were two major clusters: Pb Cr Cd As Hg and Cu Zn; (3) principal component analysis showed that four principal components were given to explain 91.381% of the total variance. Solutions from HPI values presented that they were significantly higher than the critical level, especially in S5, S6, and S8, implying that this aquatic environment has been contaminated by multiple HMs; (4) health risk assessment demonstrated that all HQ values in each sampling sites ranged from 0.48 to 0.74, representing a low non-carcinogenic hazard; and HQ value in the northern section of the aquatic environment was significantly greater than that in the southern and central sections. The highest carcinogenic risk was from Cd in S1, S3, and S7with unacceptable carcinogenic risks. The CR values of As and Cr were lower than acceptable carcinogenic risks; (5) uncertainty analysis disclosed that a low quantile led to a low CR value, and then to a high probability of the acceptable risk. Conversely, a higher quantile corresponded to a higher CR value and a lower standard-reaching rate. These results could help decision-makers coordinate the conflict interaction between carcinogenic risk and system reliability. Sensitivity analysis indicated that both daily ingestion and slope factors had significant impacts on the total carcinogenic risk, accounting for 40.8% and − 35.5%, respectively.

As multiple complicated characteristics were merged into the evaluation framework, difficulties emerged with regard to addressing the evaluation issues exclusively on the basis of mathematical approaches, particularly when uncertainties were considered in the decision-making process. Although all the concentrations of HMs met the standard of GB3838-2002 grade III, their carcinogenic risks and other pollutants should attract the attention of decision-makers. Some effective management measures should also be taken to ensure water safety. For example, regulation of pollutant sources (Wang et al. 2015), and development of advanced technologies for treating wastewater in municipal wastewater treatment plants. Any human activities within the areas with higher environmental risks (i.e., S7 and S8) should be also prohibited to the most extent.

The specific recommendations of this work could be summarized as follows. Firstly, thorough investigations are obviously needed. With respect to the upstream performances being significantly better than the downstream performance, the junction of S1, S5, and S2 should be studied with a focus on the key pollutant discharging enterprises along the river. The objective is to identify explicitly the channels and patterns of pollutant discharge, which could lay the foundation for the diversion of rain and wastewater. Secondly, remediation requires unification. Local governments should construct infrastructure and protection facilities to protect water resources. To ensure water quality and water supply to the river, they should conduct sewage interception that will prevent secondary pollution. Thirdly, supervision should also be strengthened through the enforcement of environmental laws and regulations, particularly those pertaining to illegal activities. It is also required to strengthen identification of risk sources, assessment of environmental risks, and disposal of emergency. Finally, publicity and education for local people should be improved by emphasizing the significance of the health and biodiversity of the ecosystem (Zhang et al. 2017).

Two concerns should be addressed in future studies. On the one hand, this study only assesses seven heavy metals, probably leading to an unrealistic state of heavy metal contamination in the aquatic environment. Therefore, more heavy metal types should be integrated into the improved evaluation framework to comprehensively reflect the real status of heavy metal contamination. On the other hand, in most cases, there might be more uncertain information (e.g., interval and fuzzy parameters) associated with the modeling inputs. Future studies will be required to deal with the impacts of multiple uncertainties on the health risks of heavy metals.