[en] Whenever there is an accidental spill of hazardous chemicals or radioactive materials into any river, it is vitally important to be able to issue an immediate forecast of the arrival time and peak concentration of a pollutant at each downstream city, to enable water users downstream to take effective precaution measures. Adequate forecast of this type was not possible in the past because of the lack of a proper model to predict one-dimensional dispersion in natural streams. This study resulted in the development of an improved model. The new model is a modified Fickian model which uses a time-dependent dispersion coefficient, a time-scale much greater than the Fischer time-scale, and a Pearson-Type-III distribution of concentration