## 2 Materials and Methods
### Validation and Model Test  
[PERSON] (2000) presented 12 tests to measure the SD model's robustness [68]. As some model tests are employed for pre-modeling, this study used three robustness tests: calibration, sensitivity analysis, and extreme condition test.  
The model calibration was conducted in two steps: checking the correspondence of the model parameters with relevant descriptive and numerical knowledge of the real system and testing the accuracy of historical fit [23]. We collected six years of DO and BOD field data during the 2010-2020 period. We then simulated the model retrospectively from 2010 to 2020 using these data. We then compared the models using simulated and historical data and observed a similar pattern (Figure 6a,b). Thus, our model reflected reality and correlated with historical data. Moreover, we collected the projected population data of the study area from the United Nations from 2020 to 2030 [69]. We then compared the models using projected and simulated data and observed similar trends (Figure 6c). Thus, the model forecasted population trends perfectly.  
In addition to the calibration tests, we carried out extreme condition and sensitivity tests. The extreme condition test was conducted considering the values of three policy variables: streamflow, waste control, and migration control [68]. We set two extreme values of waste control (streamflow, migration control) from 0% to 100% (0-160 m\({}^{3}\)/s, 0-6%). We then simulated the model and obtained no shocks. Each equation was found to be applicable despite the extreme input values, and model behavior was appropriate (Figure 6d).  
Subsequently, we performed the univariate sensitivity test [68]. We selected waste (BOD) control and set the optimum reduction value in influuents to 87.778%, as [PERSON] et al. (2021) indicated that a reduction by 87.778% is the optimum value for maintaining sustainable water quality in an urban river system [45]. Afterward, we applied 10% standard deviation to optimum BOD reduction value (87.778%) of influents, which resulted in three BOD reduction values: 79.009% (10% low), 87.78% (optimum value), and 96.56% (10% high). After the simulation, the three values generated three different IW values, which varied significantly (Figure 7a). Similarly, we selected three values of migration control such as 0%, 3% and 6% and run the sensitivity analysis. The results indicated that 0% and 3% migration control produced negative IW after 26 years and 70 years respectively as population density exceeded the carrying capacity in this area. On the other hand, 6% migration control produced non-declining IW over the time. Therefore, we set it as the optimum value for migration control (Figure 7b). Overall, the validation, calibration and extreme condition tests, and sensitivity analysis confirmed that the model was valid and appropriate for application in impact assessment.  
Figure 6: Model test results of calibration (**a**) dissolved oxygen (DOI), (**b**) biological oxygen demand (BOD), (**c**) population and (**d**) Extreme condition test: Inclusive, Wealth (**W**).  
Figure 7: Model test results, sensitivity analysis: Inclusive Wouth (IW), (a) Based on waste control and (b) Based on migration control.