A mathematical model provides the ability to predict the contaminant concentration levels of a river. The advection-diffusion equation is used as a first approximation for such a model. The validity of the model's results are compared with data gathered and compiled by the Minnesota Pollution Control Agency. A portion of the Mississippi River beginning at a site in the Southeast portion of Saint Paul, Minnesota and ending at a bridge near La Crosse, Wisconsin was used. The focus was to create the mathematical model and to compare its estimations against the available data on this portion of the river. Proceeding downstream, a river's contaminant concentrations can both increase and decrease due to factors such as tributaries, weather, and agricultural runoff. To fit the assumptions of a steady state advection-diffusion model, the contaminant concentration values that were utilized for the model were monotone increasing or decreasing above and below the tributary.
"River Quality Modeling Using Differential Equations,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 2
, Article 1.
Available at: https://scholar.rose-hulman.edu/rhumj/vol2/iss1/1