The lower Athabasca River was used as a test case using total suspended sediment, chloride and vanadium as the model variables. Upstream model boundary conditions included water from the tributary Clearwater River (right stream tube) and the upper Athabasca River extending upstream of the tributary mouth (left stream tube). This model will be extended to include the Peace-Athabasca Delta (PAD), to determine the implications of mining outfall discharges on a large region of the Athabasca – PAD region. A novel, quasi-two-dimensional surface water-quality modelling approach is presented in which the model domain can be discretised in two dimensions, but a one-dimension solver can still be applied to capture water flow between the discretisation units (segments). The approach requires a river reach to be divided into two stream tubes, along the left and right river sides, with flows exchanging through the segments longitudinally and also laterally between adjacent segments along the two streams. The new method allows the transverse mixing of tributary and outfall water of different constituent concentrations to be simulated along the course of the river. Additional diffuse loading of dissolved vanadium could be determined from the model’s substance balance. A scenario was then simulated in which the transport and fate of vanadium in a floodplain lake and a secondary channel was determined. • Quasi-2D modelling approach proves to be viable for transverse mixing. • Quasi-2D approach allows secondary channels and side lakes to be modelled. • Quasi-2D approach is appropriate to scale up to entire lower Athabasca River reach. • The approach allowed a diffuse loading of dissolved vanadium to be quantified.

A quasi-two-dimensional (quasi-2D) modelling approach is introduced to mimic transverse mixing of an inflow into a river from one of its banks, either an industrial outfall or a tributary. The concentrations of determinands in the inflow vary greatly from those in the river, leading to very long mixing lengths in the river downstream of the inflow location. Ideally, a two-dimensional (2D) model would be used on a small scale to capture the mixing of the two flow streams. However, for large-scale applications of several hundreds of kilometres of river length, such an approach demands too many computational resources and too much computational time, especially if the application will at some point require ensemble input from climate-change scenario data. However, a one-dimensional (1D) model with variables varying in the longitudinal flow direction but averaged across the cross-sections is too simple of an approach to capture the lateral mixing between different flow streams within the river. Hence, a quasi-2D method is proposed in which a simplified 1D solver is still applied but the discretisation of the model setup can be carried out in such a way as to enable a 2D representation of the model domain. The quasi-2D model setup also allows secondary channels and side lakes in floodplains to be incorporated into the discretisation. To show proof-of-concept, the approach has been tested on a stretch of the lower Athabasca River in Canada flowing through the oil sands region between Fort McMurray and Fort MacKay. A dye tracer and suspended sediments are the constituents modelled in this test case.

A quasi-two-dimensional (quasi-2D) modelling approach is introduced to mimic transverse mixing of an inflow into a river from one of its banks, either an industrial outfall or a tributary. The concentrations of determinands in the inflow vary greatly from those in the river, leading to very long mixing lengths in the river downstream of the inflow location. Ideally, a two-dimensional (2D) model would be used on a small scale to capture the mixing of the two flow streams. However, for large-scale applications of several hundreds of kilometres of river length, such an approach demands too many computational resources and too much computational time, especially if the application will at some point require ensemble input from climate-change scenario data. However, a one-dimensional (1D) model with variables varying in the longitudinal flow direction but averaged across the cross-sections is too simple of an approach to capture the lateral mixing between different flow streams within the river. Hence, a quasi-2D method is proposed in which a simplified 1D solver is still applied but the discretisation of the model setup can be carried out in such a way as to enable a 2D representation of the model domain. The quasi-2D model setup also allows secondary channels and side lakes in floodplains to be incorporated into the discretisation. To show proof-of-concept, the approach has been tested on a stretch of the lower Athabasca River in Canada flowing through the oil sands region between Fort McMurray and Fort MacKay. A dye tracer and suspended sediments are the constituents modelled in this test case.