Mathematical model development for non-point source in-stream pollutant transport

Non-point source pollution is a primary cause for concern globally. Various models have been developed to tackle this situation with much emphasis placed on best management practices. This practice has, however, proven to be insufficient to solve the NPS pollution situation. Existing non-point source models are watershed- -based and complicated both in operation, parameter estimation and data requirements. A non-point source model is proposed using the concept of the Hybrid Cells in Series model. The model is a three-parameter model made up of three zones, which describes pure advection through time delay in a plug zone, with combined advection and dispersion occurring when the other two zones are considered as thoroughly mixed. The proposed model is tested using synthetic data and field data from the Snake River, Colorado, USA, obtained from literature. Simulations were performed at four sample points; two from the tracer injection point along the Snake River before a confluence and two further downstream after the confluence. A regression analysis was carried out to determine the model’s capability to simulate pollutant transport for the four sampling points. The coefficients of determination are 0.98, 0.94, 0.84 and 0.97 while the standard error for each reach is 2.28E-2, 2.70E-2, 2.32E-2 and 9.35E-3 respectively. The results show good agreement between the measured and the simulated data. The response of the C-t profiles produced by the proposed model for both synthetic and field data demonstrates its ability to effectively simulate pollutant transport in natural rivers subject to non-point source pollution.