*4.2. Risk Characterization Based on MCS*

MCS allows to iteratively generate time series by setting up a stochastic process, calculating parameter estimates and statistics, and studying the characteristics of their distribution. Because As and Cr6+ concentrations vary under local hydrogeological conditions and population properties, this study used a Crystal Ball model based on MCS to produce an assessment of the possible carcinogenic health risks to children.

As shown in Figure 4, The forecast for the 2017 dry season ranged from 0–1.80 <sup>×</sup> <sup>10</sup>−0.5 , with a mean of 3.26 <sup>×</sup> <sup>10</sup>−0.6 and a standard deviation of 5.75 <sup>×</sup> <sup>10</sup>−0.6, while the forecast for the rainy season of the same year ranged from 0–1.00 <sup>×</sup> <sup>10</sup>−0.3, with a mean of 1.39 <sup>×</sup> <sup>10</sup>−0.4 and a standard deviation of 2.92 <sup>×</sup> <sup>10</sup>−0.4. The forecast for the 2018 dry season ranged from 0–6.00 <sup>×</sup> <sup>10</sup>−0.4, with a mean of 2.06 <sup>×</sup> <sup>10</sup>−0.4 and a standard deviation of 3.47 <sup>×</sup> <sup>10</sup>−0.4 , while the forecast for the rainy season of the same year ranged from 0–5.00 <sup>×</sup> <sup>10</sup>−0.4, with a mean of 1.79 <sup>×</sup> <sup>10</sup>−0.4 and a standard deviation of 2.65 c. The simulations yielded a CR for children between 0 and 1 <sup>×</sup> <sup>10</sup>−0.6 with probabilities in 2017 of 16.59% and 0%, and

in 2018 of 0% and 0% for the dry and rainy season, respectively, indicating that children are at a higher health risk and prompt action on this respect should be considered. MCS can also be used to determine the sensitivity of the chosen parameters depending on their uncertainty [44–46]. In fact, different parameters have different sensitivities to carcinogenic risk values. Accordingly, in this study, the analysis of the effect of As and Cr on carcinogenic risk was performed. *Water* **2022**, *14*, x FOR PEER REVIEW 18 of 23 *Water* **2022**, *14*, x FOR PEER REVIEW 18 of 23

**Figure 4.** Assessment of the possible carcinogenic health risks to children. **Figure 4.** Assessment of the possible carcinogenic health risks to children. **Figure 4.** Assessment of the possible carcinogenic health risks to children.

As shown in Figure 5, the association values for As in the dry and rainy seasons for 2017 were 0.9958 and 1, respectively, and Cr was 0, while the association values for As in the 2018 dry and rainy seasons were 0.7424 and 0.5759, respectively, and Cr was 0.6237 and 0.8182, respectively. As you can see, during the 2018 rainy season, the association value of As was lower than the association value of Cr. In the 2017 dry rainy season and the 2018 dry season, the association value of As was higher than the correlation value of Cr. As shown in Figure 5, the association values for As in the dry and rainy seasons for 2017 were 0.9958 and 1, respectively, and Cr was 0, while the association values for As in the 2018 dry and rainy seasons were 0.7424 and 0.5759, respectively, and Cr was 0.6237 and 0.8182, respectively. As you can see, during the 2018 rainy season, the association value of As was lower than the association value of Cr. In the 2017 dry rainy season and the 2018 dry season, the association value of As was higher than the correlation value of Cr. As shown in Figure 5, the association values for As in the dry and rainy seasons for 2017 were 0.9958 and 1, respectively, and Cr was 0, while the association values for As in the 2018 dry and rainy seasons were 0.7424 and 0.5759, respectively, and Cr was 0.6237 and 0.8182, respectively. As you can see, during the 2018 rainy season, the association value of As was lower than the association value of Cr. In the 2017 dry rainy season and the 2018 dry season, the association value of As was higher than the correlation value of Cr.

Moreover, as can be seen in Figure 6, in 2017 the sensitivity of As was 100%, while that of Cr was 3% and 0% in the dry and rainy seasons, respectively. In 2018, the sensitivity of As

respectively. This indicates that As was the most sensitive to total carcinogenic risk [47].

**Figure 5.** Association values for As and Cr. **Figure 5.** Association values for As and Cr.

**Figure 5.** Association values for As and Cr.

was 54.1% and 57.8% and that of Cr was 45.9% and 42.2% in the dry and rainy seasons, respectively. This indicates that As was the most sensitive to total carcinogenic risk [47].

Moreover, as can be seen in Figure 6, in 2017 the sensitivity of As was 100%, while that of Cr was 3% and 0% in the dry and rainy seasons, respectively. In 2018, the sensitivity of As was 54.1% and 57.8% and that of Cr was 45.9% and 42.2% in the dry and rainy seasons, respectively. This indicates that As was the most sensitive to total carcinogenic risk [47]. *Water* **2022**, *14*, x FOR PEER REVIEW 19 of 23

**Figure 6.** Sensitivity of As and Cr. **Figure 6.** Sensitivity of As and Cr.

Based on these results, the analysis of the possible patterns of As present in the water environment of the study area was conducted. Based on these results, the analysis of the possible patterns of As present in the water environment of the study area was conducted.

In summary, in this study, limited data were employed through the use of MCS to determine probability density functions and confidence intervals for carcinogenic risks, and an uncertainty analysis was performed to reveal the possible influence of various parameters on human health risks [48]. In summary, in this study, limited data were employed through the use of MCS to determine probability density functions and confidence intervals for carcinogenic risks, and an uncertainty analysis was performed to reveal the possible influence of various parameters on human health risks [48].
