Stochastic Model for BOD and DO in Streams

A stochastic model for pollution and dissolved oxygen in streams is obtained. Given the stream parameters and the initial conditions, the model predicts not only the mean amounts of pollution and dissolved oxygen at any point downstream, but also their variability in time. One can determine the proportion of the time that pollution is above any given concentration or that dissolved oxygen is below any given concentration. The theoretical results are tested by comparing them with controlled laboratory experiments and with data from the Sacramento River. It is observed that the means of both pollution and dissolved oxygen follow the equations already obtained by Dobbins (BOD and Oxygen Relationships in Streams, Journal of the Sanitary Engineering Division, ASCE, Vol. 90, No. SA3, Proc. Paper 3949, June, 1964, p. 53). A new and unexpected observation is that the greatest variability in dissolved oxygen occurs at the sag, where it is most critical.