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Numerical modeling has become an indispensable tool for solving various physical problems. In this context, we present a model of pollutant dispersion in natural streams for the far field case where dispersion is considered longitudinal and  one-dimensional in the flow direction. The Transmission Line Matrix (TLM), which has earned a reputation as powerful and efficient numerical method, is used. The presented  one-dimensional TLM model requires a minimum input data and provides a significant gain in computing time. To validate our model, the results are compared with observations and experimental data from the river Severn (UK). The results show a good agreement with experimental data. The model can be used to predict the spatiotemporal evolution of a pollutant in natural streams for effective and rapid decision-making in a case of emergency, such as accidental discharges in a stream with a dynamic similar to that of the river Severn (UK)

Pollutant Dispersion Modeling in Natural Streams Using the Transmission Line Matrix Method