Modeling of Nitrogen, Phosphorus, and Potassium Concentrations in Lakes Affected by Soil Fertilization

The excessive use of fertilizer on agricultural land has led to a significant build-up of chemical nutrient stocks in the soil, which increases the risk of diffuse pollution of surface waters. The reservoirs to which these waters drain are also polluted by the chemical components of the fertilizer. This is a major environmental problem. Indeed, the fishery products contained in these water reservoirs are directly contaminated, and this remains a major public health problem. Thus, using ordinary partial derivatives, we established budget equations for the mass concentrations of the major components of fertilizer chemicals such as nitrogen (N), phosphorus (P) and potassium (K) found in each natural water reservoir. Using the Euler discretization method, we linearized these budget equations in order to formulate them numerically with AMPL and solve them. The numerical solutions obtained thus make it possible to predict the mass concentrations of the chemical elements (N, P, K) at the level of each water reservoir in time by taking the measures for a substantial reduction of the chemical content of fresh water.