*1.1. Background*

Much of the process water from oil sands surface mining operations is recycled and managed in tailing ponds. However, the capacity for storage is approaching unmanageable and unsustainable levels; hence, some release of treated process water into the Athabasca River is anticipated as early as 2025 [1]. The release of treated process water may pose a risk to aquatic species and to humans who harvest and consume these species, in particular fish. Therefore, effective models to describe the transport and fate of oil sands related substances are required [2]. These substances can be transported downstream and deposited in Lake Athabasca and the Peace-Athabasca-Delta (PAD); in addition, secondary channels and lakes within the floodplain along the lower river reach may also trap released sediment and associated constituents. An important objective of this research is to determine the fate of such effluent within these features using computer modelling.

**Citation:** Sabokruhie, P.; Akomeah, E.; Rosner, T.; Lindenschmidt, K.-E. Proof-of-Concept of a Quasi-2D Water-Quality Modelling Approach to Simulate Transverse Mixing in Rivers. *Water* **2021**, *13*, 3071. https:// doi.org/10.3390/w13213071

Academic Editors: Leon Boegman and Tammo Steenhuis

Received: 16 September 2021 Accepted: 30 October 2021 Published: 2 November 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

#### *1.2. Water-Quality Modelling*

The development of complex three-dimensional integrated hydrodynamic, sediment transport, and water quality models has been proposed to characterize the transport and fate of sediment and associated constituents in the lower Athabasca River, advocated by several researchers and government agencies [2]. However, the implementation of complex modelling frameworks may not be advantageous for many reasons, including cost, the time required to develop the framework, and lengthy model simulation times. Additionally, model complexity can obfuscate rather than elucidate key processes, and both overly complex and overly simple models can have reduced reliability.

We propose using the Water Quality Analysis Simulation Program (WASP) [3] to develop a model to characterize the fate and transport of sediment and associated constituents within the lower Athabasca River. WASP is a dynamic compartment-modelling program for aquatic systems, including both the water column and the underlying benthos. Its representation of sediment and material kinetics is more sophisticated than other commonly used models [4]. WASP is a widely used framework for developing site-specific models for simulating toxicant concentrations in surface waters and sediments over a range of complexities and temporal and spatial scales. WASP has an advanced toxicant module that includes representation of a range of solids classes, with individual physical and chemical characteristics. Solids classes can be organic materials (e.g., plankton, algae, detritus) or inorganic (e.g., sand, silt, clay).

#### *1.3. Quasi-Two-Dimensional Modelling*

This paper describes a unique quasi-two-dimensional representation of river hydraulics that is particularly suited to the application of the WASP model to accurately represent the configuration of the lower Athabasca River with a high level of computational efficiency. In the current study, we introduce a novel approach to modelling transverse mixing in a river with secondary channels and side lakes to study the water quality along the area of the Athabasca River with extensive oil sands development.

In order to maintain short computational times, a one-dimensional (1D) modelling approach is necessary. However, the transverse mixing along the river requires modelling with at least a two-dimensional (2D) representation, especially since the lengths of complete mixing along this river are relatively long (>100 km). Hence, the use of a quasi-twodimensional (quasi-2D) approach is proposed, in which flow is simulated in 1D, but in such a way to allow a 2D discretisation of the domain.

Quasi-2D water-quality modelling has been carried out in the past for other applications. For off-channel storage facilities (polders) along the Elbe River in Germany, Lindenschmidt et al. [5] modelled dissolved oxygen and nutrient dynamics for various flow regimes (low, medium, high (flood) flows). Deposition of sediments and heavy metals in the off-channel storage basins was captured using the quasi-2D method [6–8]. The quasi-2D approach has also been used to capture flows between main river channels and their floodplains, in particular through dike breaches [9] and capping flood peaks using side-channel storage [10,11]. Flow between the Mekong River and its delta [12] and between the Po River and a portion of its floodplain [13] were simulated using quasi-2D models. Sediment transport was included in a quasi-2D model of the Rhine River's main channel and floodplain [14]. In this study, we extend the quasi-2D approach to model transverse mixing in rivers.
