This research will focus on the feasibility of devising a relatively simple predictability model for a variety of dispersion problems in air or water. If successful, valid representations of the concentration distribution in both physical space and ensemble space may be achieved with sufficiently few parameters to permit an attractive engineering model. Prediction of the probability distribution function as well as the expected mean distribution should permit such a model to be rigorously verified and applied to the solution of problems involving pollution of air and water.