A shallow water numerical method for assessing impacts of hydrodynamics and nutrient transport processes on water quality values of Lake Victoria

Lake Victoria is the world's largest tropical lake and the third-largest water body, providing significant water resources for surrounding environments including the cultural, societal, and livelihood needs of people in its basin and along the White Nile. The aim of this study was to use decade-long time series of measured lake flow in the lake system and phosphorus deposition to develop a suitable numerical model based on shallow water equations (SWE) for assessing water quality in Lake Victoria, an increasingly important tool under climate variation. Different techniques were combined to identify a numerical model that included: i) a high-resolution SWE model to establish raindrop diffusion to trace pollutants; ii) a two-dimensional (2D) vertically integrated SWE model to establish lake surface flow and vertically transported wind speed flow acting on lake surface water by wind stress; and iii) a site-specific phosphorus deposition submodel to calculate atmospheric deposition in the lake. A smooth (non-oscillatory) solution was obtained by applying a high-resolution scheme for a raindrop diffusion model. Analysis with the vertically integrated SWE model generated depth averages for flow velocity and associated changes in water level profile in the lake system and showed unidirectional whole lake wind blowing from the southwest to northeast. The atmospheric phosphorous deposition model enabled water value assessment for mass balances with different magnitudes of both inflows and outflows demonstrating annual total phosphorus at 13, 500 tons concentrating at mid-lake western and eastern parts. The model developed here is simple and suitable for use in assessing flow changes and lake level changes and can serve as a tool in studies of lake bathymetry and nutrient and pollution transport processes. Our study opens towards refining models of complex shallow-water systems.