*2.4. Kinematic Wave*

For most simple river systems, the kinematic wave formulation is applicable. The kinematic wave calculates flow wave dissemination and flow velocity variations over a network of streams. The roughness of the slope and river bottom affect kinematic flow waves. By changing the Manning equation (Equation (1)) in the continuity equation and differentiating cross-sectional area with respect to time, the kinematic wave differential equation may be produced (Equation (2)).

$$Q = \frac{1}{n} \frac{A^{5/3}}{B^{2/3}} S\_0^{1/2} \tag{1}$$

$$\frac{\partial Q}{\partial \mathbf{x}} + \alpha \beta Q^{\beta - 1} \frac{\partial Q}{\partial t} = 0 \tag{2}$$

where *Q* is the flow rate, *x* is longitudinal distance in channel, *t* is time, *α* and *β* are functions of hydraulic coefficients, *S*<sup>0</sup> is the slope of the channel, *n* is the Manning friction factor, *A* is the cross-sectional area, and *B* is the channel width. The depth exponent is used along with segment geometries to estimate hydraulic coefficients, which are later used to calculate segment flow depths under specific flow rates. [38] gave a complete description of WASP's stream transport. To quantify variations in velocities, widths, and depths across the network, the kinematic wave based on solutions of one-dimensional continuity equations, and a condensed version of the momentum equation that takes the effects of friction and gravity into account, was utilized.

#### *2.5. Discretization*

The river network was discretized using a 500 m interval. This led to 319 horizontal, one-dimensional water segments in WASP. Segment widths, average depths, and depth exponents were among the hydrodynamic metrics produced by HEC-RAS. The depth exponent controls channel shape in WASP. For these segments, a depth exponent value of 0.3 was used to simulate an uneven cross-section. Along with segment widths, slopes, and roughness factors, these depths are used in simulations to determine segment depths. The model's input variables include channel geometry, flow routing, boundary conditions, environmental time functions, loads, and initial segment conditions. Hydraulic parameters were obtained using a calibrated and validated HEC-RAS model and utilized as inputs for the flow functions in WASP [38]. From the 319 HEC-RAS cross-sections separated by 500 m, geometry for the WASP segments (average depths, widths, and slopes) was derived. Based on the station's water quality data closest to the study region, spatial linear interpolation was used to identify the boundary and initial conditions for the current investigation.

The study's duration was from 2020 to 2021. Initial heavy metal concentrations for each model component were derived by interpolating between two nearby long-term monitoring stations: the upstream boundary conditions were defined using the nearest long-term heavy metal data, which was Outlook. The boundary data for downstream was used based on the data from Weldon Ferry.

A segment length of 500 m was used for modelling. This length is deemed appropriate based on processing times, a reasonable uniform volume for segments, and an acceptable mixing. Benthic segments were inserted underneath each section of surface water to quantify erosion and sedimentation. The measured concentration at the upstream and downstream boundaries was used to calibrate the deposition rate of metals. In the HEC-RAS model, the spaces between each pair of cross-sections were split into individual WASP segments. Output files of the hydrodynamic model (HEC-RAS) were specific for each crosssection. These results then needed to be averaged between two consecutive cross-sections to obtain the exact values for each WASP segment. This procedure is shown in Figure 2 and was implemented in Microsoft Excel (Version 2211) for all input values. *Water* **2023**, *15*, x FOR PEER REVIEW 7 of 16

**Figure 2.** Model segmentation. **Figure 2.** Model segmentation.

session.

#### *2.6. Visualization, Calibration, and Validation 2.6. Visualization, Calibration, and Validation*

The modelled heavy metal concentrations and hydrodynamics were calibrated and validated. The calibration of heavy metal concentrations involved several iterations in the parameter space within reasonable parameters of the observed values. The best curve fitting with the observed data was achieved by choosing the optimum parameter values. To validate the model, a run with these values was compared against an independent set of field data. The modelled heavy metal concentrations and hydrodynamics were calibrated and validated. The calibration of heavy metal concentrations involved several iterations in the parameter space within reasonable parameters of the observed values. The best curve fitting with the observed data was achieved by choosing the optimum parameter values. To validate the model, a run with these values was compared against an independent set of field data.

how many geographical grids, x/y plots, or even model result files a user can employ in a

An effective way to review model simulations and calibrate them using collected data is to utilize the post-processor (MOVEM). Results from every WASP run, as well as others, can be visualized using MOVEM. MOVEM allows the modeller the choice of two graph-

An effective way to review model simulations and calibrate them using collected data is to utilize the post-processor (MOVEM). Results from every WASP run, as well as others, can be visualized using MOVEM. MOVEM allows the modeller the choice of two graphical representations of the results: geometric grid and x/y plots. There is no restriction on how many geographical grids, x/y plots, or even model result files a user can employ in a session. *Water* **2023**, *15*, x FOR PEER REVIEW 8 of 16

#### **3. Results 3. Results**

#### *3.1. Deposition Rates and Overall Concentration Trends 3.1. Deposition Rates and Overall Concentration Trends*

First, it was assumed that the deposition rate for copper and nickel should be the same as sediment. Deposition rates for copper and nickel were calibrated using the sampled concentration at the upstream and downstream model boundaries (Figure 3). A previously developed model for sediment transport was used, and the model was calibrated with an acceptable range of deposition [38]. Concentration plots (Figure 4) show the trend for both trace metals at selected sampling sites (Downtown, Clarkboro Ferry, and Highway 312) for both water and sediment samples. Concentration values for all sites can be found in the Supplementary Information. First, it was assumed that the deposition rate for copper and nickel should be the same as sediment. Deposition rates for copper and nickel were calibrated using the sampled concentration at the upstream and downstream model boundaries (Figure 3). A previously developed model for sediment transport was used, and the model was calibrated with an acceptable range of deposition **[**38**]**. Concentration plots (Figure 4) show the trend for both trace metals at selected sampling sites (Downtown, Clarkboro Ferry, and Highway 312) for both water and sediment samples. Concentration values for all sites can be found in the Supplementary Information.

**Figure 3.** Calibrated deposition curve for both trace metals Cu and Ni. **Figure 3.** Calibrated deposition curve for both trace metals Cu and Ni.

Both trace metals were modelled for the same time periods for water and sediment in the years 2020 and 2021 and matched to the field sampling of water and sediment samples to maintain uniformity.

#### *3.2. Copper*

In 2020, copper concentrations were observed in the range of 1–5 µg/L except for two sites (Highway 3 and Weldon Ferry), with values at 42.2 µg/L and 20.2 µg/L, respectively (refer to Supplementary Information). Cu concentrations in river water in 2021 were in the range of 0.8 µg/L to 5 µg/L. That the observed concentrations remained uniform, for the most part, is indicative of the complex mixing of copper across the sampling sites, whereas elevated concentrations of copper at Highway 3 and Weldon Ferry could be attributed to various constructions around the location (bridges and roadway) in this area (S. Prajapati, pers. obs.). Many of the measured concentrations were over the long-term CCME water quality guideline for Cu of 4 µg/L at the given water hardness > 180 mg/L CaCO3, which indicates that risks to aquatic life could not be excluded. Sediment Cu concentrations ranged from <LOQ to 19 mg/kg in 2020 and <LOQ to 15 mg/kg in 2021 [27]. Since the

resulting concentrations are below the CCME ISQG of 35.7 mg/kg, the authors do not expect adverse effects. In sediments, Cu ranged from 1–15 mg/kg, with Clarkboro Ferry being on the higher end for both sampling years, with values in the range of 12–15 mg/kg. *Water* **2023**, *15*, x FOR PEER REVIEW 9 of 16

**Figure 4.** Concentrations of Cu and Ni in water and sediment for selected sites during the 2020 and 2021 field seasons. **Figure 4.** Concentrations of Cu and Ni in water and sediment for selected sites during the 2020 and 2021 field seasons.

Both trace metals were modelled for the same time periods for water and sediment in the years 2020 and 2021 and matched to the field sampling of water and sediment samples to maintain uniformity. *3.2. Copper* In 2020, copper concentrations were observed in the range of 1–5 µg/L except for two Figures 5 and 6 show a longitudinal comparison of measured and modelled copper concentrations in water and sediment for 2020 and 2021. The concentrations modelled through the sampling time points almost uniformly increased between the upstream and downstream boundaries of the study area. Copper concentrations for water samples remained mostly consistent for June 2020, August 2020, and October 2020, but increased gradually and became more consistent in June 2021 and August 2021. Within the study

sites (Highway 3 and Weldon Ferry), with values at 42.2 µg/L and 20.2 µg/L, respectively (refer to Supplementary Information). Cu concentrations in river water in 2021 were in

period, discharge and flow velocity of the South Saskatchewan River were highest in June 2020, which can explain this observed pattern of copper concentrations, as increased discharge would cause significant erosion of riverbanks and stream beds. Thereafter, longitudinal profiles for August 2020, October 2020, and June 2021 remained relatively consistent throughout the segments. *Water* **2023**, *15*, x FOR PEER REVIEW 11 of 16

**Figure 5.** Longitudinal profiles of water concentrations with observed values for both trace metals in the 2020 and 2021 field seasons. **Figure 5.** Longitudinal profiles of water concentrations with observed values for both trace metals in the 2020 and 2021 field seasons.

**Figure 6.** Longitudinal profiles of sediment concentrations for both trace metals in the 2020 and 2021 field seasons. **Figure 6.** Longitudinal profiles of sediment concentrations for both trace metals in the 2020 and 2021 field seasons.

#### *3.3. Nickel*

*3.3. Nickel* In 2020, nickel concentrations ranged consistently from 2–6 µg/L for water samples and ranged from 0.3–1.4 µg/L in 2021. The high-flow season in 2020 (due to elevated discharge and precipitation mentioned above) helps explain the almost three- to fourfold greater nickel concentrations in that year. Levels of nickel in sediments for 2020 ranged from 10.5–25 mg/kg and mostly remained consistent throughout the year. However, in contrast to concentration values for water samples, the concentration of nickel in 2021 remained around the same range, with a very slight decrease, ranging from 10–20 mg/kg. No measured values were observed to be over the long-term CCME water quality guide-In 2020, nickel concentrations ranged consistently from 2–6 µg/L for water samples and ranged from 0.3–1.4 µg/L in 2021. The high-flow season in 2020 (due to elevated discharge and precipitation mentioned above) helps explain the almost three- to fourfold greater nickel concentrations in that year. Levels of nickel in sediments for 2020 ranged from 10.5–25 mg/kg and mostly remained consistent throughout the year. However, in contrast to concentration values for water samples, the concentration of nickel in 2021 remained around the same range, with a very slight decrease, ranging from 10–20 mg/kg. No measured values were observed to be over the long-term CCME water quality guidelines for Ni of 150 µg/L at the given water hardness > 180 mg/L CaCO3.

lines for Ni of 150 µg/L at the given water hardness > 180 mg/L CaCO3. Longitudinal profiles for nickel (Figures 5 and 6) followed almost the same trend as those for copper, with very little variability in concentration values during the different Longitudinal profiles for nickel (Figures 5 and 6) followed almost the same trend as those for copper, with very little variability in concentration values during the different sampling time points. Nickel concentrations remained consistent for August 2020, October 2020, June 2021, and August 2021, with a slight gradual increment with every major segment (i.e., sampling station). The concentration values followed a similar trend of gradual increase. For sediment samples, the modelled progressions again followed similar patterns in August 2020, October 2020, and June 2021, with a consistent and slight decline throughout the study area. Again, high flow in 2020 could explain the three- to fourfold greater nickel concentrations in 2020 compared to 2021 water samples. Similarly, for sediment samples, settling and transverse mixing can contribute to consistent and slight declines in the concentration values.
